Technical and Economic Assessment of a 500W Autonomous Photovoltaic System with Lifepo4 Battery Storage Electrical and Computer

Technical and Economic Assessment of a 500W

Autonomous Photovoltaic System with LiFePO4 Battery Storage

João Filipe Esteves Carriço

Thesis to obtain the Master of Science Degree in Electrical and Computer Engineering Supervisor: Prof. José Paulo da Costa Branco

Examination Committee Chairperson: Prof. Rui Manuel Gameiro de Castro Supervisor: Prof. José Paulo da Costa Branco Member of Committee: Prof. João José Esteves Santana Prof. Carlos Alberto Ferreira Fernandes

November 2015

Acknowledgments

I would like to express my gratitude and appreciation to the supervisor of this work, Professor Paulo Branco for giving me this opportunity, his guidance, persistency and encouragement. It would not be possible without his contribute. I would like to thank all my family, specially my mother, father and sister for all the patience and support and a very special thanks to my girlfriend Inês Freire who gave me strength. Finally, to all my colleagues and friends who listened, advised and made their questions mine contributing to a better research.

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Abstract

The access to electricity in some African countries is still very poor. For isolated villages where the distance to the major cities is higher than hundreds of kilometres and the number of populations is very low, it is not economically viable to build a connection to the electrical grid. Autonomous photovoltaic (PV) installations are the key for future full autonomy of the household at a low infrastructure cost. More particularly, this thesis studies and tests the behaviour and efficiency of a low-cost isolated (autonomous, off-grid or stand-alone) photovoltaic (PV) system with the novel Lithium Iron Phosphate

(LiFePO4) battery storage, for the rural area near Luena in Angola. The system (solar panel, batteries, controller and inverter) is designed having in mind the required household load and energy available from the sun. These determined the sizing of the PV panels’ nominal power, LiFePO4 battery pack storage capacity, the energy monitoring system as well as the power of the inverter.

In this context, the autonomous solar energy production system was developed for a nominal power of 500W. It was configured considering the load diagram of a typical rural house in order to achieve a high lifespan of LiFePO4 batteries with less maintenance as possible. The experimental tests were made under real conditions with the relevant electrical parameters being measured and logged along the day. These tests have shown that, although the system ensures the energy supply effectively between the months of February to November, during the rainy season the system should be complemented with a second source of alternative energy.

Keywords

Autonomous/Off-grid PV system, Angola, system efficiency, LiFePO4

Resumo

O acesso à eletricidade em alguns países africanos é ainda muito precário. Em vilas isoladas onde a distância às grandes metrópoles é superior a algumas centenas de quilómetros e o número de habitantes é pequeno, não é economicamente viável construir uma interligação à rede elétrica. Os sistemas fotovoltaicos autónomos são a chave para pequenas habitações autossuficientes em termos energéticos a um preço de infraestruturas reduzido. Em particular esta tese estuda e testa o comportamento e eficiência de um sistema isolado de custo reduzido com as recentes baterias de Lítio-

Ferro-Fosfato (LiFePO4) para a zona rural de Luena em Angola. O sistema (painéis solares, baterias, controlador e inversor) é dimensionado tendo em vista a energia necessária ao abastecimento dos consumidores e a energia solar disponível. Estes irão determinar os valores de potência nominal dos painéis, a capacidade do “pack” de baterias de lítio, do sistema de gestão de energia assim como a potência nominal do inversor.

Neste contexto, o sistema de produção elétrica autónomo foi desenvolvido para uma potência nominal de cerca de 500W. O sistema foi configurado tendo em consideração o diagrama de carga típico destas pequenas habitações rurais, de forma alcançar o maior tempo de vida útil das baterias de LiFePO4 com a mínima manutenção possível. Os ensaios experimentais foram realizados em condições reais com todos os sinais elétricos relevantes medidos e gravados ao longo do dia. Estes mostraram que, apesar de o sistema assegurar o abastecimento energético de forma eficaz entre os meses de Fevereiro a Novembro, durante a época das chuvas o sistema deverá ser complementado com uma segunda fonte de energia alternativa.

Palavras-chave: Sistema fotovoltaico autónomo, Angola, rendimento, LiFePO4

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Contents

Acknowledgments ...... III Abstract ...... V Resumo ...... VII Contents ...... IX List of Figures ...... XIII List of Tables ...... XV List of Symbols ...... XVII List of abbreviations ...... XIX 1 Introduction ...... 1 1.1 Motivation and problem definition ...... 1 1.2 Objectives ...... 2 1.3 Thesis structure ...... 3 2 Autonomous PV Systems – Actual Panorama ...... 5 2.1 Photovoltaic Systems Types ...... 6 2.1.1 Grid-tied Systems ...... 7 2.1.2 Off-Grid Systems ...... 8 2.1.3 Hybrid Systems ...... 9 2.2 Solar Radiation ...... 10 2.2.1 Direct and diffuse radiation on a tilted plane ...... 10 2.2.2 GHI, DNI ...... 11 2.2.3 Angle definition ...... 11 2.2.4 Solar radiation measuring instruments ...... 15 2.3 Angola Case-Study ...... 16 2.3.1 Introduction ...... 16 2.3.2 General Overview ...... 16 2.3.3 Solar Resource ...... 18 2.3.4 Temperature and sunshine hours ...... 19 2.3.5 Energy sector scenario ...... 20 2.3.6 Energy consumption costs ...... 22 2.4 Conclusions ...... 23 3 Photovoltaic Energy Systems Constitution ...... 25 3.1 Electrical Loads ...... 25 3.1.1 Refrigerator ...... 26 3.1.2 Lighting ...... 27 3.1.3 CRT TV ...... 28 3.2 PV Panels ...... 28 3.2.1 Working Principle ...... 29 3.2.2 Electrical parameters ...... 30

3.3 Energy Storage - LiFePO4 Batteries ...... 31 3.3.1 Cell Operation ...... 33 3.3.2 State of Charge (SOC) and Depth of Discharge (DOD) ...... 34 3.3.3 Battery pack initial balancing ...... 35 3.4 Batteries Management System ...... 37 3.4.1 Safety Functions ...... 38 3.4.2 Cell Balancing ...... 38 3.4.3 SOC estimation ...... 44 3.5 Autonomous or Off-Grid Inverters ...... 44 Pure sine wave inverters ...... 45 3.6 Cables ...... 48 3.7 PV System Efficiency ...... 49 3.8 Conclusions ...... 50 4 Autonomous PV System – Project ...... 51 4.1 Loads ...... 51 4.1.2 Experimental loads power ...... 53 4.1.3 Daily consumed energy ...... 53 4.2 PV Panels Production Capacity ...... 54 4.3 PV array sizing ...... 55 4.4 Batteries ...... 55 4.5 Autonomous or Off-Grid Inverter ...... 56 4.6 Regulator ...... 58 4.7 DC Cables ...... 58 4.8 Protection – DC Switch and DC Fuses ...... 58 4.9 Prototype costs ...... 59 4.10 Economic analysis of the off-grid PV system ...... 61 4.11 Conclusions ...... 62 5 Experimental Results ...... 63 5.1 Electrical parameters measurement ...... 63 5.2 The Autonomous PV Experimental Set-up ...... 63 5.3 Initial Charging of the Cells ...... 65 5.4 Bottom vs Top Balancing ...... 67 5.5 The Autonomous PV Run – Lisbon, Portugal ...... 69 5.6 Reserve Days ...... 74 5.7 Comparison Methods ...... 74 5.8 Operation in the remaining months of the year ...... 77 5.9 Autonomous PV Run – Luena, Angola ...... 79 5.10 Conclusions ...... 84 6 Conclusions and Future Prospects ...... 87 6.1 Conclusions ...... 87 6.2 Future Work ...... 89 7 Bibliography ...... 91

8 Appendix ...... 95 8.1 National Instruments NI-USB6008/9 Data Acquisition Device ...... 95 8.2 Current Transducer LA-25-NP Datasheet ...... 97 8.3 Power Logger Fluke 1735 ...... 99 8.4 Tektronix TDS 2001/2012C Oscilloscope ...... 99 8.5 Data logging ...... 100 8.5.1 Voltage log ...... 100 8.5.2 Current log ...... 101 8.6 CALB SE130AHA Battery Cell Datasheet ...... 104 8.7 Suntech polycrystalline STP225 – 20/Wd PV panels Specifications ...... 105 Solar Cell Electrical Model ...... 106 8.8 TUV Solar Cable ...... 109 8.9 BMS Off-Grid 123 Electric ...... 109 8.10 Livre Pure Sine wave Inverter 1500W ...... 111 8.11 KENTT 201E Refrigerator Datasheet ...... 112 8.12 Sony KV-14LT1E 13’’ Color TV Datasheet ...... 114 8.13 IST Meteorological station ...... 115 8.14 Temperature Logger Tiny Tag Talk 2 – TK-4014 ...... 115 8.15 Economic Evaluation Indicators ...... 115 8.15.1 Net Present Value (NPV) ...... 115 8.15.2 Internal Rate of Return (IRR) ...... 116 8.15.3 Payback Period ...... 116

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List of Figures

Figure 2.1 - Global cumulative growth of PV Capacity (Source IEA) ...... 5 Figure 2.2 - Grid-tied PV system block diagram ...... 7 Figure 2.3 - Block diagram of an isolated PV system – Inverter connected to the regulator ...... 9 Figure 2.4 - Block diagram of an isolated PV system – Inverter connected to the battery ...... 9 Figure 2.5 - Block diagram of a hybrid isolated PV-Wind system with energy storage ...... 10 Figure 2.6 - Incident radiation on a tilted surface (source: adapted from The Irradiation Data, Andres Cuevas) ...... 10 Figure 2.7 - Angles of a tilted surface (source: adapted from ITACA website) ...... 12 Figure 2.8 - Solar rays on a) geographical and b) panels referential ...... 13 Figure 2.9 - Solar irradiance measuring instruments – a) pyranometer and b) pyrheliometer (source: NREL and IBPSA-USA website) ...... 15 Figure 2.10 - Campbell-Stokes sunshine recorder (source: WeatherBug blog) ...... 16 Figure 2.11 - Africa and Middle East Global Horizontal Irradiation average annual sum between 04/2004 and 03/2010 [10] ...... 17 Figure 2.12 - Angola Global Horizontal Irradiation (GHI) map [10] ...... 18 Figure 2.13 - Daily mean solar radiation averages in Luena, Angola (source: PVGIS Climate-SAF database 2001-2012) ...... 19 Figure 2.14 - Average temperatures in Luena, Angola [30] ...... 20 Figure 2.15 - Angola electrical sector intervenients [33] ...... 20

Figure 3.1 - Autonomous PV System electric block diagram ...... 25 Figure 3.2 - EU energy efficiency labels (source: which.co.uk website) ...... 27 Figure 3.3 - Fluorescent Lamp Lighting block diagram (source: next electronics website) ...... 27 Figure 3.4 - Sony TV operating current ...... 28 Figure 3.5 - Multi-junction cell (source: solar cell central) ...... 29 Figure 3.6 - Exothermic reaction evolution with temperature [45] ...... 32 Figure 3.7 - LiFePO4 simplified cross section cell [46] ...... 33 Figure 3.8 - LiFePO4 typical cell charging curve [49] ...... 34 Figure 3.9 - Parallel cell charging with power supply ...... 35 Figure 3.10 - LiFePO4 balancing time [48] ...... 37 Figure 3.11 - BMS block diagram (adapted from “The Electropaedia” website) ...... 37 Figure 3.12 - Types of balancing [51] ...... 39 Figure 3.13 - Passive vs active Cell Balancing (Source: Texas Instruments) ...... 39 Figure 3.14 - Passive switched shunting resistor balancing (based on [51]) ...... 41 Figure 3.15 - Example of a passive cell balancing circuit TI BQ77PL900 [52] ...... 41 Figure 3.16 - a) Bottom balancing and respective b) after charging ...... 42 Figure 3.17 - a) Top balancing and b) after discharging ...... 42 Figure 3.18 - Passive cell balancing based on voltage [52] ...... 43 Figure 3.19 - Block diagram of a sine wave inverter (adapted from Texas Instruments) ...... 45 Figure 3.20 - Inverter output waveform and corresponding harmonics ...... 45 Figure 3.21 - Inverter efficiency characteristic a) Xantrex Prosine off-grid inverter efficiency curve for 1000 and 1800W 24V system (source: Xantrex) and b) 1500W Livre Inverter ...... 47 Figure 3.22 - Cable losses ...... 48 Figure 3.23 - Off-grid PV system connection diagram ...... 49

Figure 4.1 - KENT 201E refrigerator load diagram (1h) ...... 52 Figure 4.2 - Total daily load diagram ...... 53 Figure 4.3 - Refrigerator a) starting and b) operating current ...... 57

Figure 5.1 - a) Autonomous PV system testing bench and b) system components ...... 64 Figure 5.2 - Battery pack and BMS monitoring boards ...... 64 Figure 5.3 - Battery pack voltage during discharge on a constant resistive load of 6Ω a) without and b) with initial balancing ...... 65

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Figure 5.4 - Cell’s voltage during discharge on a resistive load of 6Ω a) without and b) with initial individual charging ...... 66 Figure 5.5 - Discharge at approximate 0.06C current rate or 8A (3.3Ω resistor) ...... 67 Figure 5.6 - Discharge on a resistive load of 6Ω a) bottom and b) top balancing ...... 67 Figure 5.7 - Charge at constant current I=6A with a) bottom and b) top balancing ...... 68 Figure 5.8 - PV installation site and sun trajectory in March 2015 ...... 69 Figure 5.9 - Total solar irradiance incident on a horizontal (red) and 35º tilted plane (black) on 14th March 2015 with clouds ...... 70 Figure 5.10 - PV (blue) and battery pack voltage (black) on 14th March 2015 ...... 71 Figure 5.11 - Battery pack voltage on 14th March 2015 ...... 71 Figure 5.12 - PV panel output power on 14th March 2015 ...... 73 Figure 5.13 - PV module temperature and efficiency on 14th March 2015 ...... 74 Figure 5.14 - Global horizontal irradiance measured at IST meteorological station (red) and PVGIS global clear-sky irradiance (black) ...... 75 Figure 5.15 - Global irradiance incident on the PV panel plane calculated from experimental GHI (red) and PVGIS database (black) ...... 76 Figure 5.16 - Monthly global irradiation average and temperature on a 35º tilted plane [26] ...... 77 Figure 5.17 - Global horizontal irradiation in a) Angola and b) Portugal [10] ...... 80 Figure 5.18 - Monthly average global irradiation on a β=35º plane in Lisbon, Portugal (blue) and β=19º in Luena, Angola (black) [26] ...... 81 Figure 5.19 - Monthly average temperatures in Lisbon, Portugal (blue) and Luena, Angola (black) [26, 30] ...... 81

Figure 8.1 - LA 25-NP current transducer characteristic ...... 99 Figure 8.2 - Connecting a Differential Voltage Signal [NI USB-6008/6009 User Guide] ...... 100 Figure 8.3 - LabVIEW Signal Express Monitor / Record interface ...... 100 Figure 8.4 - LabVIEW Signal Express Playback interface ...... 101 Figure 8.5 - LEM LA25-NP equivalent circuit according to datasheet parameters [58] ...... 102 Figure 8.6 - Experimental setup to obtain LA-25 NP characteristic ...... 103 Figure 8.7 - Experimental characteristic test of the LEM LA25-NP ...... 103 Figure 8.8 - Equivalent electrical model of a solar cell a) three parameters and b) five parameters [59] ...... 106 Figure 8.9 - Stationary characteristic I(V,G) of a photo-diode exposed to solar light [59] ...... 107 Figure 8.10 – BMS 123 a) dashboard and b) system settings ...... 110 Figure 8.11 - Inverter characteristic with a resistive load ...... 111 Figure 8.12 - Capacitor-start motor a) connections and b) phasor diagram at starting [60] ...... 112 Figure 8.13 - Single-phase equivalent circuit with core losses [61] ...... 113

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List of Tables

Table 2.1 - PV module prices in 2012 in European countries [5] ...... 6 Table 2.2 - PV systems combinations ...... 7 Table 2.3 - Average annual GHI, GTIopt and D/G in some Angola cities [10, 26] ...... 19 Table 2.4 - Annual sunshine hours and climate conditions for different Angola regions [30, 31] ...... 20 Table 2.5 - Normal low voltage electricity tariff in Angola (single phase) [33] ...... 22

Table 3.1 - Battery technologies comparison [42, 43, 44] ...... 32 Table 3.2 - Balancing topologies comparison [51] ...... 40 Table 3.3 - Comparison of Balancing Algorithms [48] ...... 43 Table 3.4 - Typical actuation voltage levels of off-grid pure sine wave inverters and PWM regulators 47

Table 4.1 - Loads electrical experimental parameters ...... 53 Table 4.2 - Experimental dairy loads energy ...... 53 Table 4.3 - Irradiation on Luena, Angola [26] ...... 54 Table 4.4 - Pure sine wave inverter price and specifications ...... 60 Table 4.5 - Total system cost ...... 60

Table 5.1 - Energy of the discharge tests in Figure 5.3(a) - unbalanced and Figure 5.3(b) - balanced cells ...... 65 Table 5.2 - Energy and mean daily efficiency of the different components ...... 72 Table 5.3 - Statistical test results ...... 76 Table 5.4 - Autonomous PV system average technical data ...... 77 Table 5.5 - Monthly average vs 14th March irradiation ...... 78 Table 5.6 - Estimated energy available to the loads ...... 78 Table 5.7 - Percentage of days of full and empty battery [26] ...... 79 Table 5.8 - Radiation comparison between Angola and Portugal (source: PVGIS climate-SAF Europe and Africa maps database 2001-2010) [10, 57, 26] ...... 80 Table 5.9 - Global irradiation in Luena, Angola and Lisbon, Portugal on the horizontal and optimal inclined plane [10, 26, 30]...... 81 Table 5.10 - Estimated energy available to the loads in Luena, Angola ...... 82 Table 5.11 - Percentage of days of full and empty battery [26] ...... 83

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List of Symbols

A – Amp 퐴 – PV surface azimuth angle

퐴푆 – Solar azimuth angle 퐶 – Cell Capacity D – Daylight saving time EOT – Equation of Time (min)

퐸푑 ≡ 푊퐷 – Daily energy required by the loads

퐸퐼푁 – Energy received (in)

퐸퐿표푎푑푠 – Energy of the loads

퐸푂푈푇 – Energy delivered (out)

퐸푃푉 – Energy produced by the PV panels

푓푠 – Sampling rate 퐺 – Solar Irradiance (W/m²)

퐺푏 – Beam radiation

퐺푏_ℎ표푟푖푧 – Incident (beam) radiation component perpendicular to the ground horizontal plane

퐺푏_푖푛푐푖푑푒푛푡 – Maximum incident (beam) radiation

퐺푏_푚표푑푢푙푒 – Module (beam) radiation or radiation incident on the tilted plane

퐺푑 – Diffuse radiation

퐺𝑔푙표푏푎푙 – Global radiation

퐺푟 – Reflected radiation

퐻ℎ – Irradiation on horizontal plane (Wh/m²/day)

퐻푖 – Solar Irradiation (kWh/m²)

퐻표푝푡 – Irradiation on optimally inclined plane (Wh/m²/day)

퐼푛 퐷퐶 푆푤푖푡푐ℎ – Nominal current of the DC switch

퐼푅푀푆 – Root mean square current

퐼푏푝1, 퐼푏푝2, . . , 퐼푏푝푁 – Cell’s by-pass current

퐼푝푎푐푘 – Current circulating in the battery pack

퐼푟푒𝑔_푚푎푥 – Maximum regulator current

퐼푧 – Admissible current on the cables LCT – Local Clock Time (h)

LiCoO2 – Lithium Cobalt Oxide

LiCoPO4 – Lithium Cobalt Phosphate

LiFePO4 - Lithium Iron Phosphate LL – Local Longitude (°) LSTZ – .Longitude of Local Standard Time Meridian (°) 푚 – the diode ideality factor

XVII mmf – Magnetomotive force 푁 – Day of the year NiCd – Nickel-Cadmium NiMH – Nickel-metal hydride

푃퐽표푢푙푒 – Joule losses on the cables

푃푃푉 - Power produced by the panel(s)

푃푅 – Power dissipated in a resistor (Joule Power)

푃푖푛푗푒푐푡푒푑 - Power at the end of the cables terminals, injected in the batteries

푃푖푛푣_푚푖푛 – Minimum inverter power

푃푙표푎푑푠,푝푒푎푘 – Peak power of the loads 푅 – Resistance

푅퐷푆푂푁 – Transistor resistance

푅퐵푎푙 – On-Board resistor in parallel with the cell at passive balancing 푆 – Incident radiation or sun ray vector 푡푎푟푖푓푓 – Electrical tariff (€/kWh)

푡푠 – solar hour (h)

푈퐵퐴푇,푇표푡 ≡ 푈퐷퐶 – Total battery DC voltage (V)

푈푅푀푆 – Root mean square voltage (V) V – Volt W – Watt Wh – Watt-hour

푊퐵푎푡,푇표푡 – Total energy of the batteries

푊퐷 ≡ 퐸푑 – Daily energy required by the loads (Wh) 훼 – Solar altitude or solar elevation angle (º) 훽 – Surface inclination angle (°)

훽표푝푡 – Optimal inclination angle (°)

휃푖 – Incidence angle (°) 훿 – Declination angle (°)

∆푇푠 – Sampling time ∆푈 – Cables Voltage drop

휂퐵퐴푇 – Battery efficiency (%)

휂퐵푀푆 – BMS efficiency (%)

휂퐵푀푆+퐵퐴푇+퐼푛푣 – BMS, batteries and inverter efficiency

휂푃푉 – PV panels efficiency

휂푖푛푣 – Inverter efficiency

휂푙표푠푠푒푠 – Cable losses factor

휂푠푦푠푡,푎푢푡 – Autonomous/Off-grid system efficiency 휙 – latitude (°) 휔 – hour angle (°)

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List of abbreviations

AC – Alternating Current AM1.5 –Spectral Distribution of Solar Radiation BMS – Battery Management System CC – Constant Current CFL – Compact Fluorescent Lamps CPV – Concentrated Photovoltaics CRT – Cathode Ray Tube CSP – Concentrated Solar Power CV – Constant Voltage DAQ – Data Acquisition DC – Direct Current DEEC – Department of Electrical Energy and Computers D/G – Beam vs Diffuse Radiation Ratio DIF – Diffuse Horizontal Irradiance/Irradiation DOD – Depth of Discharge DNI – Direct Normal Irradiance/Irradiation EDEL – Empresa de Distribuição de Electricidade de Luanda ENDE – Empresa Nacional de Distribuiçao de Electricidade ENE – Empresa Nacional de Eletricidade EOT – Equation of Time EU – European Union GAMEK – Gabinete de Aproveitamento do Medio Kwanza GER – Gabinete de Energias Renováveis GHI – Global Horizontal Irradiance/Irradiation IEA PVPS – International Energy Agency Photovoltaic Power Systems IRR – Internal Rate of Return IRSE - Instituto Regulador do Sector Energético (Energy Sector Institute Regulator) IST – Instituto Superior Técnico LCT – Local Clock Time

LFP - Lithium Iron Phosphate (LiFePO4) LL – Local Longitude LSTZ – .Longitude of Local Standard Time Meridian MBE – Mean Bias Error MINEA – Ministério da Energia e Águas MPPT – Maximum Power Point Tracking (or Tracker) NOCT - Normal Operating Cell Temperature NPV – Net Present Value OCV – Open Circuit Voltage

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Op Amp – Operational Amplifier OV – Overvoltage PFC – Power Factor Correction PV – Photovoltaic PVGIS – Photovoltaic Geographical Information System PRODEL – Empresa Nacional de Produção de Electricidade RELOP – Associação de Reguladores de Energia dos Países de Língua Oficial Portuguesa (Portuguese Official Language Energy Regulators Association) RMSE – Root Mean Square Error RNT – Rede Nacional de Transporte (National Transport Grid) SOC – State of Charge SR – Switched Shunt Resistor STC – Standard Test Conditions THD – Total Harmonic Distortion UPS – Uninterruptible Power Supply USD – Unites States Dollar Wp – Watt-peak

1 Introduction

In the rural areas of developing countries, the access to electricity is still very deficient. This happens once the distances involved are very large and do not justify the investment for supplying small populations. The focus on rural electrification aims to give people better living conditions at low cost, with the certainty that there will be no short or medium term return, but those conditions will make all the difference on the development of that country.

This work aims to create a final solution that is actually possible to use immediately, add value and solve these issues improving the living standard of people. The fully autonomy depends on the energy storage, its efficient management and control is the key to ensure a long operation period.

Photovoltaic (PV) systems are a convenient solution for having a clean and reliable source of energy and also provide electricity in locations where it is not possible to connect to the conventional electricity grid or the connection has a high cost. The decrease of photovoltaic panels manufacturing cost make autonomous photovoltaic systems more beneficial over the years. Consequently, PV installations have been growing significantly in many countries over the past years. The use of PV installations meets then economic, environmental and social causes. It is imperative to provide access to energy to ensure socioeconomic development in the world’s poorest and developing countries. Although its relatively high cost, autonomous/isolated or off-grid PV systems gradually expands with government economic support and private investments.

Energy production is the basis for the working time capacity of an autonomous system which additionally requires energy storing, in other words, batteries. Within the range of available chemical types, lithium type has high electrochemical potential which makes it one of the most reactive of metals. These properties give lithium the potential to achieve very high energy and power densities in many applications such as automotive and photovoltaic. Lithium Iron Phosphate (LiFePO4) have some advantages compared with other lithium battery types, having a very stable thermal behaviour. For this reason they are object of study and also the best ways of using this type of cells.

This is the context of this study, more particularly PV isolated systems with LiFePO4 storage to supply residential buildings in Angola and all the related elements necessary for its operation.

1.1 Motivation and problem definition

Electrical energy is a fundamental good for the development and well-being of a society. Africa is a continent with a low rate of access to electricity, so it is important to develop solutions to improve life conditions of the populations without harming the environment. Despite its huge natural resources (mostly hydric potential), Angola is a country inserted in this context, with a per-capita consumption

1 below the average in Africa [1]. It is estimated that in Angola less than 20% of the population has access to energy [2]. The power grid is still very limited supplying only the big cities. There are groups of diesel generators that run on local networks to supply industries located in remote places, with problems of continuous electricity supply. The prolonged drought affects river flows which in turn require electricity production to stop. Also the dependence of the price of diesel fuel and its transportation costs, which despite being relatively low compared with European countries, are continually growing due to the decrease of natural resource reserves.

LiFePO4 have some advantages compared with other lithium battery types but some working constrains. Lithium cells tend to have different state of charge (SOC) when used in groups (connected in series or parallel) and submitted to several charge/discharge cycles. Enumerating some of the reasons, this could happen due to external temperature differences, cell’s impedance differences or capacity manufacturing differences. The SOC of each cell individually is not detected by any SOC measuring instruments. The strategy to have the SOCs as close as possible is to do what is called balancing which should always depend on system application and is generally done by a Battery Management System (BMS). Protecting a single cell has a certain complexity, protecting a battery (a series string) is harder: cell voltages do not divide equally, temperatures vary, etc. The higher the protection the higher the system cost, for this reason the project is a balance between costs and capabilities as usual.

The electrical needs in developing countries is constantly growing which sets new horizons for energy isolated systems.

1.2 Objectives

This thesis aims on the use of autonomous photovoltaic systems with LiFePO4 batteries to supply individual or collective residential buildings in rural areas, more particularly at Luena zone in Angola. The main objectives are the following:

1. Definition of the energy pathways in an autonomous photovoltaic home system (recognition the involved elements); 2. Identification of the typical consumers profile on a small residential building in Angola. Based on this, project the nominal values of each element that constitutes the system regarding the typical consumers profile; 3. Cost–benefit analysis of the system in study by verification and analysis of total experimental system efficiency results.

4. Study and test the behaviour of the novel LiFePO4 batteries under load when used in group as

a battery pack; Identify the best balancing typology for LiFePO4 batteries using the available measuring equipment;

1.3 Thesis structure

This thesis is constituted by six chapters organized in the following sequence:  In Chapter 1 is done a general overview of the work;  In Chapter 2 the different types of autonomous photovoltaic systems are introduced, basic solar radiation concepts and the contextualization of Angola and the introduction of economic indicators;  In Chapter 3 is introduced the photovoltaic system and the various features of the components necessary for its implementation;  In Chapter 4 is made the project of the components is done accordingly to the objectives;  In Chapter 5 is done the experimental study system elements behavior and its efficiency;  In Chapter 6 is made a summary of the conclusions drawn from work and some proposals for future developments;

2 Autonomous PV Systems – Actual Panorama

The thermic conversion of the solar radiation can be used in several applications from water heating (concentrated solar thermal, also known as concentrated solar power - CSP) to electricity production (electrical) since the discovery in 1954 by Bell Labs who found that silicon doped with certain impurities was very sensitive to light. As a result emerged the first solar modules that allowed a practical application and with an energy conversion efficiency around 6% in laboratory. Photovoltaic (PV) technology is an active solar system type based on the photoelectric effect, converting light into electrical energy through photovoltaic cells that in turn form a photovoltaic panel. Nowadays, the most established solar PV technologies are crystalline silicon-based systems. Silicon terrestrial module efficiencies cells reach 22.9% at Standard Test Conditions1 (STC) in laboratory [3]. Each cell generates a Direct Current (DC) power of about 1.5W (0.5V and a 3A current) and the number of cells depends on the panel technology [4]. A PV System consists of several PV panels connected in series and parallel forming what is called a string. Photovoltaic modules power is usually between 50W and 315W. This systems may be connected to the grid (grid-tied) or be isolated (off-grid) and are basically constituted by controllers, batteries and inverters so they may feed the consumers. With the correct maintenance the durability is higher than 20 years, making this a very reliable source of energy.

The global PV capacity grew 49% a year on average since 2003 as illustrate in Figure 2.1. Decentralised systems represent approximately 60% of the global market, while centralised systems are close to 40%. The share of off-grid installations is very small compared to grid-tied, once grid-tied systems expanded in large scale from 2000 to 2013. However, like PV technologies in general off-grid systems are expanding, especially in developing countries with high solar exposure. [5] [6]

Figure 2.1 - Global cumulative growth of PV Capacity (Source IEA)

1 Cell temperature, 휃푟 = 25°퐶 ≡ 푇푟 = 298.16 K; Incident radiation, 퐺푟 = 1000 푊/푚2; Spectral Distribution of Solar Radiation AM1.5 - Total solar spectral irradiance distribution (direct and diffuse) at sea level, clear sky day, at an inclined plane at 37° tilt toward equator facing the sun, an absolute air mass (AM) of 1.5 (solar zenith angle 48.19°S)

As with other investments, prices tend to be smaller as the investments in photovoltaic systems expand. In autonomous systems, batteries represent the largest share of investment usually greater than 40% and can raise the cost of Watt-peak (Wp) to twice of a grid-tied system. The photovoltaic panels constitute about 15-20% of the investment and the inverter another 20%. The remaining stands for the control system and other costs. Additionally, the price is difficult to define as it depends on location, size, and component specifications regarding the consumer’s needs. With data from 2013, a survey of system prices in International Energy Agency Photovoltaic Power Systems (IEA PVPS) European reporting countries2 showed the system prices in the off-grid sector (<1 kW), irrespective of the type of application, typically ranged from about 2.7 to 20 USD/W. This means that a 500W system may cost between 1250 and 10.000 USD [5].

Data from selected IEA PVPS reporting countries showed that the price evolution of PV modules and small-scale systems (<1 kW) has been decreasing specially since 2007. Table 2.1 specifies that different PV technologies module prices varies from 0.5 to 1.54 USD/W in European countries. This represents a price between 112.5 to 346.5 USD for a 225W PV panel. In 2012 some manufacturers have reported losses which resulted in a price increase. The future trend is a price stabilisation of about 1 USD/W for PV modules and 2.5 USD/W3 for residential systems [5].

Table 2.1 - PV module prices in 2012 in European countries [5] Country USD/W Austria 0.5 – 0.72 Denmark 0.72 – 1 France 0.96 Germany 0.92 Italy 0.67 – 0.87 Netherlands 1.39 Spain 0.73 Sweden 1.54 Switzerland 0.86 – 1.08

2.1 Photovoltaic Systems Types

In terms of PV systems network connectivity, there are currently two types: grid-tied systems and isolated or autonomous systems with and without battery energy storage. In some literature [4] [7] [8] [9], the hybrid systems with several energy sources (PV, diesel generators, wind, etc.) are considered a third type; however due to the hybrid definition is more correct to portray it as a category. Table 2.2 shows different possible combinations of PV systems that are further explained in more detail. The electrical loads may be Direct Current (DC) or Alternating Current (AC) power depending on application, however only AC loads go in line with the context of this work. There may also be found grid-tied systems with energy storage, the batteries work as a backup of energy in case the grid fails, Uninterruptible

2 Austria, Denmark, France, Italy, Spain, Sweden and Switzerland 3 Battery costs are not included

Power Supply (UPS), however this solution makes the installation more expensive and therefore used only in very specific cases.

Table 2.2 - PV systems combinations Types of PV systems Energy storage No energy storage Hybrid Grid-tied X X X Autonomous/Off-grid X X X

2.1.1 Grid-tied Systems

In grid-tied systems, the connection to the electric grid allows the sale of electricity to the power distribution companies and the feeding of the loads. The generated energy is injected directly in the grid. Therefore, batteries and regulators are not necessary, what makes the system simpler and less maintenance.

Figure 2.2 represents the main equipment of a grid-tied system with AC loads (the protection elements are not represented). Purchase and sell back energy meters may be, in some cases, substituted by bidirectional meters. A power inverter makes possible the connection to the grid and the connection of the consumers is done at the grid side node.

Medium power grid-tied inverters use a Maximum Power Point Tracker (MPPT) to optimize PV panels performance. This device constantly adjusts the input of a DC/DC converter (accordingly to the actual irradiance and temperature) which selects the voltage output based on a simulated model. Selecting an output voltage the current automatically adjusts and its value depends on the IV curve of the panel (Figure 8.9). In many countries there are several incentive policies for small home systems sell your energy to the grid with advantageous rates.

MPPT PDC Energy meter: Sell back PV Grid

Energy meter: DC/DC Converter Inverter Isolation PAC Transformer Purchase

Consumers

Figure 2.2 - Grid-tied PV system block diagram

Another recent solution that is being implemented is the connection of the inverter directly to consumers’ houses circuit for immediate consumption. This is done using an inverter for each panel – Microinverter4. A photovoltaic system typically includes several panels wired together in series/parallel, with their total

4 Inverter used for a single panel that automatically synchronizes with the grid

DC output going to a central “string” inverter. This design has a few significant weaknesses. First, if the inverter goes down, the whole system is down. Second, at any given moment, each solar panel may be producing different amounts of power depending on shading, age, wear, and other factors. In the central configuration, the overall system performance is dragged down by the weakest link. A string inverters has to go with the average of the array rather than optimizing the outputs of each panel.

Microinverters are dedicated to a single PV panel and use the MPPT algorithm for each panel individually, optimizing the overall system output regardless of minor shading issues and other variations among individual panels. The connection of this type of inverters to consumers’ houses circuit allows power reduction required from the network and consequent energy cost reduction for consumers without the need of a producer contract, thus being autonomous (off-grid system).

2.1.2 Off-Grid Systems

The term isolated, autonomous or off-grid system owes its name due to the lack of any connection to the electrical grid. In an isolated system without energy storage and DC or AC loads, consumers utilize immediately the electric energy produced by the photovoltaic module. The investment in this type of system is lower compared to systems with energy storage elements incorporated. However, the supply to consumers is only possible during energy production hours. For example, a very common application is water pumping systems.

Autonomous PV systems with energy storage are constituted by a string of PV panels, a solar regulator/controller to monitor the batteries’ voltage levels and a battery pack. The energy produced by the PV panels is delivered to the loads, and the surplus energy is stored in the batteries. The stored energy may be used during the night when there is no solar radiation. Consequently, the batteries must have enough capacity to feed the load during the night and/or in low solar radiation days. The regulator has the ability to cut-off the PV and also cut-off the consumers supply accordingly to the battery voltage levels. The use of DC loads only may avoid the use of an inverter. Inverter efficiency and consumption in stand-by reduces the amount of available power to the loads. However, the use of DC loads is not very usual and this equipment is always more expensive than AC equipment. Using only AC loads is a cheaper solution and has more interest in terms of project.

Two configurations are possible – connect the inverter to the solar regulator (Figure 2.3) or directly to the batteries (Figure 2.4). The use of an off-grid inverter is required when using AC loads. Solar regulators are usually projected for currents up to 50A. In case of loads without high current peaks, the inverter may be connected to the regulator as shown in Figure 2.3.

DC Loads

PV Solar Reg. PDC

PDC AC Loads Battery Pack Inverter PAC

Figure 2.3 - Block diagram of an isolated PV system – Inverter connected to the regulator

PV Solar Reg. DC Loads

PDC PDC PAC Battery AC Loads Pack

Inverter

Figure 2.4 - Block diagram of an isolated PV system – Inverter connected to the battery

AC loads are usually constituted by electrical motors, lights, TVs and other equipment with high starting currents that produce prohibitive currents on the DC side. These peaks may reach 100A in the battery pack and going through the regulator. To avoid such currents in the solar regulator, a direct connection of the inverter to the batteries is a possible solution, as shown in Figure 2.4. With this configuration, the regulator may connect/disconnect the PV panels and the DC loads. The inverter acts like a regulator being the under-voltage protection for the batteries thus disconnecting the AC Loads. In this case, the efficiency of the inverter has to be taken into account once it might be working at 20% of its nominal power once an oversizing is necessary due to power peaks. The two different typologies choice depend on the cut off parameters of the inverter and regulator nominal current.

2.1.3 Hybrid Systems

Hybrid systems consist of a combination of several energy sources in photovoltaic applications. Diesel/gas generators, wind power and other sources may be used besides PV panels. This systems need more complex control and protection circuits and are generally used for medium to high power applications. For example in PV/Diesel medium power systems, the generator should work only when the batteries reach the low voltage level and shuts down when the batteries are charged.

Figure 2.5 shows a hybrid isolated system with PV and wind energy sources. Different from configuration in Figure 2.4, this configuration allows the charge of the batteries during the day and night. Wind generators are always AC power, so the wind regulator makes possible the connection to the batteries in DC current.

PV Solar Reg. PDC Battery Consumers PDC Pack

Inverter Wind PAC Wind Reg. Generator

AC P

Figure 2.5 - Block diagram of a hybrid isolated PV-Wind system with energy storage

For autonomous PV systems, there are no regulations in many countries, giving some freedom to their implementation. Autonomous PV systems with electric energy storage based on LiFePO4 battery pack is the focus of this work, being studied in more detail. Particular care is the requirement to ensure the batteries and the power plant to have the longest possible useful lifetime.

2.2 Solar Radiation

Before analysing some data is important to make a brief introduction to the concepts of solar radiation. Sunlight is part of the electromagnetic radiation given off by the Sun. The visible spectrum is constituted by infrared, visible and ultraviolet light. The incident solar power per unit area, 퐺, is the solar irradiance 2 and is measured in 푊⁄푚 . The solar energy incident per unit area, 퐻푖, is designated irradiation and is measured in 푘 푊ℎ⁄푚2. Only a part of the solar radiation hits the earth surface and this radiation is classified in two different types regarding its way of incidence: direct and diffuse [4].

2.2.1 Direct and diffuse radiation on a tilted plane

When the surface under study is tilted with respect to the horizontal, the total irradiance on the tilted surface is the direct (beam) normal radiation projected onto the tilted surface, plus the diffuse plus the reflected radiation on the tilted surface. Figure 2.6 illustrates the types of radiation for a tilted surface being the reflected radiation a particular case of diffuse radiation. Note that if the surface is not tilted the reflected radiation component does not exist as explained below. [4, 10, 11]

Figure 2.6 - Incident radiation on a tilted surface (source: adapted from The Irradiation Data, Andres Cuevas)

Direct or Beam radiation 퐺푏, is the quantity of solar radiation received directly from the sun. Diffuse radiation 퐺푑, is the sunlight received indirectly being scattered by atmosphere particles (clouds, fog, dust, etc.). There is also a particular case of the diffuse radiation if the focusing surface is tilted relatively to the horizontal plane: Albedo or reflected radiation 퐺푟, is the radiation reflected in any non-atmospheric element and is calculated as the ratio between the amount of reflected radiation and received radiation. If the radiation is referred as “horizontal” or “tilted”, it means that the receiver plane is a horizontal plane or a tilted plane relatively to the horizontal plane, respectively. Global Insolation, Total Irradiance or Global Irradiance/Irradiation on a tilted surface is the sum of direct and diffuse radiation that focus on a surface [12, 13]:

퐺𝑔푙표푏푎푙 = 퐺푏 + 퐺푑 + 퐺푟 (2.1)

The global radiation is the most important parameter for evaluation of solar energy potential of a particular region and the most basic value for PV simulations.

2.2.2 GHI, DNI

Global Horizontal Irradiation (GHI) is the sum of the solar radiation energy (direct and diffuse) that hits one square meter in a horizontal plane in one day. Global Tilted Irradiation at the optimal inclination

GTIopt, is the same as GHI but for a tilted surface facing north (south hemisphere) at the optimum inclination angle 훽표푝푡. Another radiation sometimes seen in the literature and project software is the Direct Normal Irradiance/Irradiation (DNI) which is the quantity of solar radiation received by a surface that is perpendicular (normal) to the direction of the sun rays. Typically, the amount of irradiance annually received by a surface may be maximized by keeping it normal to incoming radiation. This type of radiation is usually important for CSP and concentrated photovoltaic installations (CPV)5.

2.2.3 Angle definition

The angle of the sun rays on the PV surface influences the amount of solar energy produced. This angle is called angle of incidence, 휃푖, and is the angle between the sun rays and the normal to the PV panel surface. The optimal angle 훽표푝푡, refers to the fixed module inclination angle at which PV modules should be oriented in order to maximize power (annual mean value). This angle depends mainly on the installation geographical position (latitude) due to the variation of the sun altitude angle (훼) in the sky across the year. The greater the location latitude (furthest from the equator) the lower the solar altitude and more oblique the incident sun rays. The normal to the centre of the Earth is also referred as local zénite. The solar azimuth angle 퐴푆 is the angle between the horizontal projection of the sun vector 푆 and the north direction. The panel azimuth angle 퐴, is the angle between the horizontal projection of the normal to the panel 푁 and the north direction (convention adopted in this work). The convention N=±180º, S=0º, E=-90º, W=90º is also usually used in the northern hemisphere once at solar noon the

5 CPV use lenses and curved mirrors to focus the sunlight onto highly efficient multi-junction solar cells

11 sun is directly south in the northern hemisphere. Figure 2.7 shows the referred angles of PV panel’s orientation [4, 7, 10].

The solar irradiance is usually measured at meteorological/radiometric stations on a horizontal plane as global and diffuse irradiance, however the panels are often tilted and the data on inclined surfaces is not available [13]. Due to their very different dependences on the tilted irradiance, the direct and the diffuse components of the global irradiance must be considered separately [14]. The direct and reflected radiation can be computed with good accuracy using simple algorithms but the diffuse component is more complex and has to be estimated with different models requiring the information of global and direct radiation incident on a horizontal surface [12, 13, 15].

Figure 2.7 - Angles of a tilted surface (source: adapted from ITACA website)6

푆 – Incident radiation or sun ray vector;

휃푖 – Angle of incidence between the DNI and the normal to PV surface; 훽 – Angle of inclination of the surface from the horizontal; 훼 – Solar altitude or solar elevation angle; 퐴 – PV surface azimuth angle.

The monthly average daily radiation calculation method was first developed by Liu and Jordan [16] and refined by Klein [17] where the diffuse radiation is considered isotropic (distributed uniformly all over the sky). However, for the daily efficiency calculation purposes of this work, the diffuse irradiance is not considered, once it usually corresponds to less than 10% of the total irradiance in clear sky days.7 Besides, the diffuse component decreases with the tilt angle. At the same time, the ground diffuse part of irradiance increases, but is a small portion of the total irradiance [14]. Regarding this, the beam

6 http://www.itacanet.org/the-sun-as-a-source-of-energy/part-3-calculating-solar-angles/ 7 calculated using the Liu and Jordan model [16]

12 radiation incident (normal) to a fixed tilted surface 퐺푏_푚표푑푢푙푒, may be calculated accordingly to the following expressions [4, 18, 19]:

a) b) Figure 2.8 - Solar rays on a) geographical and b) panels referential

퐺 퐺 = 푏_ℎ표푟푖푧 (2.2) 푏_푖푛푐푖푑푒푛푡 sin 훼

퐺푏_푖푛푐푖푑푒푛푡 represents the maximum beam radiation from the sun and is illustrated in Figure 2.8 a). It changes during the day and year and gather information about the position of the sun in the sky (its zenith and azimuth angles). 퐺푏_ℎ표푟푖푧 is the usually measured radiation component perpendicular to the ground horizontal plane as Figure 2.8 a) vectors relationship examples. The solar angle 훼 [º], may be defined by:

훼 = sin−1(sin 훿 sin 휙 + cos 훿 cos 휔 cos 휙) (2.3) where 휙 is the latitude [º], ω is the hour angle [º].

The declination angle 훿, is the angle between a line joining the centers of the sun and the earth to the equatorial plane. It is zero at the vernal an autumnal equinoxes and has the value of approximately 23.5º at the summer solstice and -23.5º at the winter solstice. The declination angle is usually considered constant for 24h [20]. The expression for 훿 in degrees is given by [21]:

2휋 훿 = 23.45° × sin ( (284 + 푁)) (2.4) 365 where 푁 is the day of the year. The hour angle in degrees:

휔 = 15(푡푠 − 12) (2.5)

where 푡푠 is the solar hour [h]. It may be calculated from civil time using the following equation [11]:

퐸푂푇 퐿퐿 − 퐿푆푇푍 푡 = 퐿퐶푇 + − − 퐷 (2.6) 푠 60 15 where LCT is the local clock time in hours, LL is the local longitude, LSTZ is the longitude of the meridian of the reference hour both in degrees8, D is the daylight saving time parameter (equal to 1 (hour) if the location is in a region where daylight savings time is currently in effect, or zero otherwise). EOT is the equation of time in minutes. It represents the difference between the medium solar hour and the real solar hour and may be approximated by:

퐸푂푇 = 0.258 cos 푥 − 7.416 sin 푥 − 3.648 cos 2푥 − 9.228 sin 2푥 (2.7) where 푥 in degrees is given by:

360°(푁 − 1) 푥 = (2.8) 365.242 where N is the number of days since the begging of the year.

The irradiance on a tilted planes varies significantly with its orientation (azimuth and inclination angle) and the vector N is defined to gather this information. The incidence angle 휃푖, between the sun vector and the normal to any tilted surface, is exposed on Figure 2.8 b) and is given by the relation:

퐺푏 퐺푏_푚표푑푢푙푒 cos 휃푖 = = (2.9) 퐺푏_푖푛푐푖푑푒푛푡 퐺푏_푖푛푐푖푑푒푛푡

Defining the incidence angle in terms of the date, hour and localisation:

cos 휃푖 = (sin 훿 sin 휙 + cos 훿 cos 휙 cos 휔) − cos 훿 sin 휔 sin 훽 sin 퐴 (2.10) + sin 훽 cos 퐴 (sin 훿 cos 휙 − cos 훿 sin 휙 cos 휔) reminding that A is the PV surface azimuth angle as defined in Figure 2.7 Substituting (2.2) in (2.9), the radiation incident on a tilted surface finally results as:

퐺 퐺 = 푏_ℎ표푟푖푧 cos 휃 (훽) (2.11) 푏_푚표푑푢푙푒 sin 훼 푖

Note that this method has a mathematical limitation for low solar angles once that result in a division by close to zero values.

2.2.3.1 Optimal Angle The optimal angle varies throughout the year and an energy gain up to 12% is possible when the panels are tilted this angle [22]. The most accurate way to determine it is to make measurements on site once

8 Note that west longitudes are negative, and time zones west of GMT are negative as well

14 it depends on the local weather and climate conditions [14]. Previous studies show that, if local and weather and climatic conditions are not considered, the optimal fixed angle of PV modules depends only on geographical latitude, 휙. Considering only the direct radiation the optimal tilt angle is calculated by 휙 − 훿, knowing that the declination angle is zero at the equinox (22 March and 23 September) and ±23.45° at the solstices (21 June 22 December). There are other proposed paths to calculate the optimal angle in the literature [23, 24, 25]. The weather and climate effect is considered in PVGIS9 data [26] in the next chapters. PVGIS tool is explained in more detail in 2.3.3.

2.2.4 Solar radiation measuring instruments

Hourly or daily global, beam and diffuse radiation measurements are very important to get reliable data. This data is used to estimate the energy available at the PV panels plane at a given place. For this measurements two types of measuring equipment exist: pyranometers and pyrheliometers.

a) b) Figure 2.9 - Solar irradiance measuring instruments – a) pyranometer and b) pyrheliometer (source: NREL and IBPSA-USA website)

A pyrheliometer or actionometer (Figure 2.9 b) measures the direct beam solar radiation (small portion of the sky around the sun) at normal incidence in W/m². The instrument is mounted on a tracking mechanism with the thermopile detector at the end of the tube which converts heat to an electrical signal. The aperture angle of the instrument is 5.7° so the detector receives radiation from the sun and from an area of the circumsolar sky two orders of magnitude larger than that.

A pyranometer or solarimeter (Figure 2.9 a) measures the total irradiance (beam and diffuse) from all the hemisphere (180º field of view) on a planar surface by a thermopile sensor in W/m². The sensor may be coupled to a shade disk, ring or sphere that follows the position of the sun in the sky “blocking” the beam radiation. With this accessory only the diffuse radiation is measured. Depending on the instrument accuracy and reliability, the International Standard ISO9060 defines three different categories for pyranometers: second and first class instruments (1-2% accuracy), and secondary standard instruments (maximum uncertainty of 3%) [27, 28].

The hours of bright sunshine is the time in which the solar disc is visible and is usually used for long- term averages of solar radiation. For this measurements the Campbell-Stokes sunshine recorders use

9 Photovoltaic Geographical Information System

15 a solid polished glass sphere as a lens, concentrating the incident light to two photoelectric cells represented on Figure 2.10. One is shaded from beam radiation and one exposed to it. With no beam radiation the two sensors read a close radiation level. When beam radiation is present the output levels are widely apart.

Figure 2.10 - Campbell-Stokes sunshine recorder (source: WeatherBug blog)

2.3 Angola Case-Study

2.3.1 Introduction

The case study presented in this chapter is Angola – a country on the west coast of Africa in a tropical zone in the latitude range of 6 to 17ºS and 12 to 23ºE longitude range. More particularly, the rural interior zone of Luena at 11º47’31.3’’S and 19º54’30.1’’E is studied in more detail. In order to contextualize this work as well as possible in the Angolan energy sector reality, it is important to assess the energy scenario and the solar availability in this country.

2.3.2 General Overview

Most communities in Africa don’t have access to electricity, thus the use of individual generators, mostly diesel is very common. These generators are used due to the low cost of oil, but high emissions and noise are down factors. Africa is a continent with high solar potential due to high sun exposure between latitudes of 14 to 30º N (all of the Sahara zone) and 14 to 30° S latitude band (Namibia zone), as represented in Figure 2.11. Only the areas of this latitude in the Americas, Middle East and Australia have the same solar potential on the planet. For this reason and due to the continued fall in prices of PV panels, photovoltaic technology is becoming a viable alternative in this continent.

Angola is a country with a large energy gap, 250 kWh/per capita, which places it behind the average per-capita consumption in Africa [1]. It is estimated that in Angola less than 20% of the population has access to energy, and within these consumers 75% live in the capital [2]. According to the Angolan ministry of energy and waters, there is a need for implementation of solar photovoltaic systems in rural zones, for electrification of social infrastructure, including schools, medical centres and administrative buildings [29]. The need for approval of legislation to encourage the use of renewable energy technologies is another of the plans for the development of "green" energy in Angola. In this context, PV autonomous systems are a more clean and environmental friendly solution.

Figure 2.11 - Africa and Middle East Global Horizontal Irradiation average annual sum between 04/2004 and 03/2010 [10]

Angola has a lower price of electricity due to its high hydric potential and hydroelectric plants. Since the end of the civil war in 2002, generating capacity expanded to 1,160 MW in 2007, of which 67% was hydroelectric and 33% was diesel-generated. There are three main transport zones, north, center and south and some small isolated systems. Capanda dam on the Kwanza River near the northern town of Malange in 2004, with two turbines produces 260 MW following a 112 million USD investment, which doubled its capacity to 520 MW. Northern Angola has the 180 MW Cambambe dam on the Kwanza River, which supplies Luanda, and the 18 MW Mabubas dam on the Dande River. The Biópio hydro plant on the Catumbela River and several small thermal plants serve the central provinces. The 51 MW Matala dam on the Cunene River, which started rehabilitation in 2007, is the main source of electricity in the southwest. Angola's internal electricity grid is weak and poorly integrated, with much power lost in transmission, common power outages, worsened by poor maintenance and below-cost tariff structures. [2]

Although the climate of Angola is tropical, it is not characterised as such due to the influence of three factors:  The cold Benguela current along the southern coast;  The relief in the interior zones;  The influence of the Namibe desert on the southwest.

With two very clear seasons: the dry season (cacimbo), with less amount of cloudiness and lower temperatures from May to September, and the rainy season with up to 70% cloudiness especially along the ocean coast and higher temperatures from September to May. The shortest day is on June 21rst solstice and the longest on December 21rst solstice10.

10 http://www.timeanddate.com/

Angola has a tremendous potential of both wind and solar resources. Being a developing country with a population of 21.47 million people in 201311, Angola offers great promise and opportunity for launching renewable energy products.

2.3.3 Solar Resource

There are some databases and web tools to assess the solar resource and PV systems performance. SolarGIS and PVGIS are two of those tools and will be used as a reference in this work. SolarGIS is a high resolution solar radiation database developed from Meteosat MSG data available for Europe, North Africa, and Southwest Asia [10]. PVGIS is a free solar radiation web application that uses satellite images (Meteosat) and ground measurements to calculate the solar radiation at the surface of the earth. CM-SAF is the most recent PVGIS database representing a total of 12 years of data from the first generation of Meteosat satellites (Meteosat 5-7, known as MFG), there are data from 1998 to 2005 and from the second-generation Meteosat satellites (known as MSG) there are data from June 2006 to December 2011. The algorithms differ between MSG and MFG. The spatial resolution is 1.5 arc-minutes (about 3km right below the satellite at 0° N, 0° W). The coverage extends from 35° S to 58° N and from 18° W to 55° E. It is available for Europe, Africa, Mediterranean Basin and more recently expanded to cover south-west Asia [26].

In Angola the global solar irradiation is above 2000kWh/m²/year especially in the interior and south areas accordingly to SolarGIS maps in Figure 2.12.

Figure 2.12 - Angola Global Horizontal Irradiation (GHI) map [10]

11 The world bank (http://data.worldbank.org)

Table 2.3 - Average annual GHI, GTIopt and D/G in some Angola cities [10, 26] ퟐ ퟐ ퟐ 푳풐풄풂풕풊풐풏 푮푯푰 [풌 푾풉⁄풎 ⁄풚풆풂풓] 푮푯푰 [푾풉⁄풎 ⁄풅풂풚] 푮푻푰풐풑풕[푾풉⁄풎 ⁄풅풂풚] 푫/푮 Luanda 1900 5430 5490 0.42 Luena 2100 5870 6100 0.33 Huambo 2200 5890 6140 0.33 Lubango 2300 6090 6380 0.29 Namibe 2200 6370 6540 0.28

Table 2.3 represents the averages irradiances at the horizontal (GHI) and Tilted (GTI) plane. D/G is the annual ratio of the total radiation arriving at the ground which is due to diffuse radiation. GTI and GHI are the most important radiations to projects using PV panels and when tilted to the optimum angle some annual mean gains may be observed relatively to the horizontal position. For this reason GTIopt is the radiation to consider.

Regarding Angola climate characteristics, Figure 2.13 represents the daily average GHI and GTI (irradiation) for each month in Luena city. According to this database the optimal inclination for Luena area is 19 degrees (annual mean). [26]

/day] 2 5

2 Irradiation [kWh/m Irradiation

1 GHI GTIopt 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure 2.13 - Daily mean solar radiation averages in Luena, Angola (source: PVGIS Climate-SAF database 2001- 2012)

Luena registered the lowest values in the rainy season from November to March and the highest in the dry season from April to October. This result goes in line with the rest of the country. The annual GHI average is 5870 Wh/m²/day and the GTIopt is 6100 Wh/m²/day resulting in a gain of 3.92% at the optimally inclined plane.

2.3.4 Temperature and sunshine hours

The geographical position of Angola provides a radiation of 10 to 12 hours per day during the entire year. Table 2.4 shows some annual mean climate conditions for Angola regions. The annual mean sunshine hours ranges from 2200 to about 2400 hours and the mean temperatures from 19 to 25ºC.

Table 2.4 - Annual sunshine hours and climate conditions for different Angola regions [30, 31] Location Alt. (m) Climate Min / Av. / Max Temp. (ºC) Sunshine hours Luanda 74 Subtropical thorn woodland 22 / 25 / 28 2340 Luena 1357 Subtropical moist forest 14 / 21 / 28 2464 Huambo 1700 Subtropical moist forest 12 / 19 / 26 2401 Namibe 44 Subtropical desert 17 / 21 / 33 2230

The dry season has more than 260 hours of sunshine per month and the rainy season reduces to 150- 160 hours [32]. In Figure 2.14 is represented the monthly average temperatures in Luena, Angola. The lower temperatures are registered in the dry season between May and September (Tmin=9ºC, Tmed=18, Tmax=26ºC). The higher temperatures between September and March occur at the cloudy season when the days are longer.

30 /day]

2 25

Irradiation [kWh/m Irradiation 10 Tmax Tmed Tmin 5 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure 2.14 - Average temperatures in Luena, Angola [30]

2.3.5 Energy sector scenario

In Angola, the government institution responsible for the energy sector is the Ministry of Energy and Water (MINEA – Ministério da Energia e Águas) with the public investments plans being made by the Ministry of Planning and the coordination of the Energy National Commission by the Ministry of Finance (Figure 2.15).

Figure 2.15 - Angola electrical sector intervenients [33]

MINEA Ministry of Planning Ministry of Finance Responsible

IRSE Regulator

Generation Transport Distribution

ENE, SOCEL and ENE and GAMEK ENE and EDEL GAMEK

To accelerate the energetic situation in Angola, on 20th November 2014, an executive decree was signed by José Eduardo dos Santos to extinguish two national companies of the energy sector and create three new ones. The objective is to create companies dedicated exclusively to each of the sectors of production, transport and distribution. Empresa Nacional de Electricidade (ENE) and Empresa de Distribuição de Electricidade de Luanda (EDEL) were replaced by two new power companies – Empresa Nacional de Produção de Electricidade (PRODEL) responsible for the exploration of the production power plants and Empresa Nacional de Distribuição de Electricidade (ENDE) which operates exclusively on the commercialization and distribution of electrical energy. Besides this, Rede Nacional de Transporte de Electricidade (RNT) was also created which operates on the transport sector. [34]

This sector is regulated by the Electrical Sector Regulator Institute (IRSE – Instituto Regulador do Sector Energético operating four national companies: Socel, GAMEK – Gabinete de Aproveitamento do Medio Kwanza and Luanda Electricity Distribution Company (EDEL). ENE is the biggest generation player, operates most of the National Transport Grid (RNT) and also distribution outside Luanda. In Luanda the distribution is taken by EDEL. In the production sector GAMEK is responsible for the implementation and management of the biggest hydroelectric dam in the country – Capanda Central – in the north of the country with 520MW of installed capacity [33, 35].

The legislation for the energy sector in Angola is governed accordingly to the General Law of Electricity, Law nº 14A/96 of 31st May 1996, which establishes the legal regime for energy production, transport, distribution and utilisation. The population’s electricity needs is ensured by the Public Electric System constituted by the National Transport Grid (RNT) and the set of installations of production and distribution associated to it. IRSE is the public regulator entity with the duty of monitoring and implementing the General Law of Electricity, preparing studies and projects principles of the relationship between the different sector agents. The approval of concessions, as well as their assignment is the responsibility the Council of Ministers. The National Department of Renewable Energy (Direcção Nacional de Energia Renováveis) is the MINEA department with the objective of promoting and developing renewable energy projects in the country. The realisation, promotion, evaluation, implementation and monitoring actions of the renewable energy sector are executed by the Renewable Energy Cabinet (GER - Gabinete de Energias Renováveis) accordingly to the Executive Order Nº 134/09 Republic Diary Nº 226 Series I of 30th November 2009.

The 1st phase of the implementation of the new policies started after 2009 and ended in June 2011 with the installation of 63 grid-tied solar systems with 3-5 kWp. The 2nd phase began with the launch of the competition for the installation of 244 systems in 47 locations in 12 provinces: Bengo, Bié, Huíla, Huambo, Kuando Kubango, Luanda, Lunda Norte, Lunda Sul, Malange, Moxico, Uíge and Zaire [29]. A Programme of Activities named “ENERCAP SunLighting™ Africa – Programme to replace kerosene lamps with micro PV LED systems in the sub-Sahara” region is currently in the process of validation covering a number of African countries, including Angola. In a 2012 Bloomberg article, Angola revealed its plans to invest in about 130 solar projects, although there was no information regarding the size or

21 technology. There is also a CDM project in the feasibility stage, providing a total of 0.730 MW from 70 solar PV villages (grid connected). Furthermore, a capacity building programme conducted by Econ Pöyry emphasizes a large potential for solar PV in the south of the country, where hydropower resources are more limited. The study includes a 3 MW solar plant in Tombua, with potentially further solar plants being installed in Namibe and Benguela. [2]

In Angola there is no regulation for microgeneration once the politics related to renewable sources and decentralised production were taken only after 2009 in order to take the signed international commitments on the reduction of CO₂. Having this in consideration in this work, it is considered the price of the electricity tariff and the price of the fuel to produce the equivalent power to access the economic viability of an autonomous systems and its payback period.

2.3.6 Energy consumption costs

The electric tariff in Angola is regulated and established accordingly to the Executive Decree nº 118/06 of 14th August 2006 represented in the next table:

Table 2.5 - Normal low voltage electricity tariff in Angola (single phase) [33] Electricity tariff in 2015 Electricity tariff in 201512 3.35 kwanza/kWh 0.0265 €/kWh

The tariff for the active energy does not express the real cost of energy, which should be many times higher. Besides, this tariff ensures only 20% of the costs of the system and should increase in the next years due to the foreseen electrical grid expansion programme [36].

12 Based on a rate of 1€=123.677 AOA on 9th Jun 2015 (www.xe.com)

2.4 Conclusions

This chapter presented the different types of photovoltaic systems with special focus on isolated autonomous systems. An introduction to different types of radiation and context of the work on the African continent was made. As to radiation concerns, it was specified the proposed measurement method that will be used to calculate on the experimental chapters. In order to reduce the complexity, diffuse radiation is neglected once this is less than 10% of the total radiation incident on the panels on a clear day. Also the reflected radiation on the ground is neglected for simplification.

Angola has a high solar potential with high average irradiance and sunshine hours rates, near 2000 kWh/m²/year and 2300h respectively. The energy sector is expanding and the government is encouraging renewable energies and grid interconnection, living room for this systems in that country and in many others in Africa. The cost of energy is very low nowadays, however in the next years the tariff is expected to be updated and the price should increase to support infrastructure expansion costs which will make this systems economically more interesting.

3 Photovoltaic Energy Systems Constitution

Isolated PV systems main objective is to feed electrical loads. They are basically constituted by five elements: a set of PV modules (production), batteries (storing), a regulator to manage the state of charge of the batteries (control), an inverter to convert DC to AC current (conversion) and loads (consume). Each of this elements is going to be seen in detail next.

The off-grid PV system has the following architecture:

BMS

Battery AC PV Pack Consumers DC PDC Inverter PAC P

Figure 3.1 - Autonomous PV System electric block diagram

The straight lines represent a direct connection and the dashed lines the control unit. The panels and the inverter work at the nominal voltage of the batteries and the BMS monitors each cell or the whole battery pack electrical parameters. It actuates on the relays opening and closing the circuit, if the batteries go over or undercharging respectively. The inverter has also its own protection, like short- circuit, under and over voltage; however, it should be ensured that the inverter and BMS actuation voltages do not conflict.

A feasibility analysis of the system is made by customer’s need of power by studying the capacity required for storage and power generation.

3.1 Electrical Loads

The purpose of an autonomous PV system is to cover the demand of remote consumers. The characterization of load depends on several factors, being power and working time the main factors for a long-term working. In order to perform a correct project of the system, it is important to know the consumption of the loads as precisely as possible. Regarding this, whenever possible, an experimental measurement of daily loads consumption at the installation site should be made.

In this work, the electrical load for a rudimentary house in the countryside of Angola consists of: 1) 100W nominal power refrigerator; 2) 13’’ CRT TV; 3) 60W Incandescent Lamps or equivalent.

The refrigerator is the most critical of the loads, as it stores the essential goods. The system should be projected to ensure its correct operation for the longest time possible. In order to meet the basic needs of a house, the refrigerator should have both refrigerator and freezer compartments. The power of this device is the key element for the dimensioning and should be as low as possible, and at the same time meet the needs of a small family.

The lighting is the second most important of the three loads referred above. In remote locations, the most frequently used light is the incandescent lamp, once it is cheaper than the other types. These lamps are no longer produced in EU since 2012, due to the large energy spent and in 2016 it will be extinct almost all over the world. Incandescent bulbs convert less than 3% of the energy they use into visible light.13 In Angola, as referred before in chapter 2.3.5, they are still widely used but there are more and more initiatives such as the "Green Wave" in 2014. to make the replacement for fluorescent lights [37] [38].

The TV is the less priority load once it is for entertainment purposes but its use may be substituted by other important loads as an iron or other devices.

3.1.1 Refrigerator

The refrigerator is constituted by an induction motor which requires a high starting torque to overcome mechanical friction having a high starting current that may be more than 5 times the rated current.

Manufacturers consume estimation procedures Refrigerators testing procedures are diversified globally. There are standards to regulate this market to ensure that the devices comply with certain quality standards. In order to complement the information from manufacturers, energy efficiency labels describe product’s energy efficiency, energy consumption, fridge and refrigerator capacity and noise level (for refrigeration products). The energy rating calculation differs across different products (washing machines, fridges, dishwashers, light bulbs, etc).

Since 1 July 2012 all new models must have a rating of A+, A++ or A+++. In Europe the tests are regulated by the ISO 15502 standard. It specifies an environmental temperature of 25°C and a relative humidity between 45% and 75%. The test lasts at least 24 hours, and the freezer and refrigerator space has to be filled partially. During the course of testing, the doors are kept closed [39].

13 Keefe, T.J (2007). “The Nature of Light”. Archived from the original on 2012-07-24. Retrieved 2007-11-05

Figure 3.2 - EU energy efficiency labels (source: which.co.uk website)

This test conditions are obviously far from real conditions particularly with respect to the opening of the door. The room temperature may be considered a good average for a house in Europe and in Angola the average temperature does not differ too much from that as seen in 2.3.4.

The market offers various solutions at various prices, but the most common and cheaper refrigerator power goes up to 100W.

3.1.2 Lighting

The most used lights in Angola are incandescent light bulbs, which are purely resistive loads and electrically represented by a resistance. It is constituted by a filament that becomes incandescent when crossed by electric current.

Figure 3.3 - Fluorescent Lamp Lighting block diagram (source: next electronics website)

The second more common lamps are compact fluorescent lamps (CFL) or compact fluorescent lights using three to five times less energy and lasting eight to fifteen times more than incandescent light bulbs (Figure 3.3). They also produce harmonics, if possible CFLs with low THD (below 30 percent) and power factors greater than 0.9 should be selected.

Traditional (iron-core ballast and starter) fluorescent lamps also draw a higher current during the switch- on cycle. During the start-up process, there are filaments at each end of the tube that are heated, and this draws more current than normal operation. This surge current is typically between 1.25 and 1.5 times the normal current. Power Factor Correction (PFC) capacitors are used in parallel with many fluorescent lamp ballasts, especially those designed for industrial use. These are necessary to minimise the excess current drawn by a relatively linear but reactive load. When power is turned on, the surge current may be very high - typically up to 30 Amps or more depending on the exact point in the main cycle when power is applied. This is many times the rated current of the PFC capacitor (as determined by the capacitance, voltage and frequency). The ballast is basically an inductor that is in series with the gas tube to limit the current through it, which would otherwise rise to destructive levels, due to the tube's negative resistance characteristic.

3.1.3 CRT TV

Comparing with Plasma, LCD (Liquid-Crystal Display), LED LCD and other recent TV technologies, CRT TV’s are the least energy-efficient but also the cheaper and most common in Angola.

CRT TVs have also a high surge current when heating the metal plate at the back of the electron gun. They are non-linear loads – a switchmode power supply. Next Figure 3.4 shows the typical operating current waveform (blue curve) of a CRT TV experimentally obtained for the Sony TV (appendix 8.12) with high harmonic content. The orange curve is the voltage at the terminals of the TV.

Figure 3.4 - Sony TV operating current

Most of the electronic equipment has a single-phase rectifier with a capacitive filter producing currents with impulsive character and high THD, approximately centered in the voltage wave peak (orange). The power factor does not apply in this case, once the current wave is not sinusoidal; however, we might say that non-linear circuits have a poor power factor because the current waveform is distorted.

3.2 PV Panels

There are several types of active (conversion of sunlight into other forms of thermic or electric energy) and passive (heating buildings through constructive strategies) solar systems. PV panels are active

28 solar systems constituted by solar cells associated in series and parallel to create a PV module with appreciate power. The first generation technology is the crystalline silicon with a market share of 87% in three mainly types: monocrystalline, polycrystalline and silicon tapes. The polycrystalline cells are less efficiency but represent 49% of the market against 35% of monocrystalline cells. They have also a lower manufacturing cost (about 20%) being the right choice to project the cheapest system possible [4].

3.2.1 Working Principle

The working principle of solar cells is the photovoltaic effect discovered by Alexandre Edmond Becquerel in 1839. In photovoltaic effect the electrons-hole pairs generated are transferred between different bands (valence bands to conduction bands) within the material itself, resulting in the development of electrical voltage between two electrodes. Solar cells are made of the same kinds of semiconductor materials, such as silicon, used in the microelectronics industry. For solar cells, a thin semiconductor wafer is specially treated to form an electric field, positive on one side and negative on the other. When photons strike the solar cell, electrons are knocked loose from the atoms in the semiconductor material. If electrical loads are attached to the positive and negative sides, forming an electrical circuit, the electrons can be captured in the form of an electric current.

Figure 3.5 - Multi-junction cell (source: solar cell central)

The use of several layers revealed higher efficiencies in the conversion process with less thermal energy lost. Since sunlight will only react strongly with band gaps roughly the same width as their wavelength, the top layers are made very thin so they are almost transparent to longer wavelengths. This allows the junctions to be stacked, with the layers capturing the shortest wavelengths on top, and the longer wavelength photons passing through them to the lower layers. The example of a multi-junction cell in Figure 3.5 has a top cell of gallium indium phosphide, then a "tunnel diode junction", and a bottom cell of gallium arsenide. The tunnel junction allows the electrons to flow between the cells and keeps the electric fields of the two cells separate.

A number of solar cells electrically connected to each other and mounted in a support structure or frame is called a photovoltaic module. Modules are designed to supply electricity at a certain voltage, such as

29 a common 12 volts system. The current produced is directly dependent on how much light strikes the module.

3.2.2 Electrical parameters

To uniform the measurements of the characteristic parameters the manufactures accepted to use the Standard Test Conditions (STC) represent by the index r [4]:  Cell temperature, 휃푟 = 25°퐶 ≡ 푇푟 = 298.16 퐾;  Incident radiation, 퐺푟 = 1000 푊/푚2;  Spectral Distribution of Solar Radiation AM1.514.

The thermal potential at the reference conditions: 퐾 푇푟 푉푟 = 퐵 = 0.0257 V (3.1) 푇 푞

The maximum output power at STC is the peak-power:

푟 푟 푟 푃푃 = 푃퐷퐶 = 푉푀푃퐼푀푃 (3.2)

The efficiency at STC:

푃 푟 푃 휂푟 = 퐷퐶 = 푝 (3.3) 퐴퐺푟 퐴퐺푟 where 퐴 is the area of the cell/panels. With other working conditions:

푃 휂 = 퐷퐶 (3.4) 퐴퐺 where 퐺 is the total (beam and diffuse) radiance incident on the PV surface. The fill factor (FF) is: 푃 푟 퐷퐶 (3.5) 퐹퐹 = 푟 푟 푉푐푎 ∙ 퐼푐푐 It should as high has possible to take the most of the panel power.

A simplified model to estimate the temperature of the module uses a relation proportional to the incident irradiance. Manufacturers provide the Normal Operation Cell temperature (NOCT15)

퐺(푁푂퐶푇 − 20) 푇 = 푇 + (3.6) 푐 푎 800

The efficiency of the panel may be estimated knowing the temperature of the cells, decreasing with increasing temperature due to the higher dark current [40]. It will produce better results with experimental data using the following expression [14]:

14 Total solar spectral irradiance distribution (direct and diffuse) at sea level, clear sky day, at an inclined plane at 37° tilt toward equator facing the sun, an absolute air mass (AM) of 1.5 (solar zenith angle 48.19°S) 15 NOCT conditions: ambient temperature of 20°C, G=800W/m². The typical value is 45°C

휂(푇) = 휂푆푇퐶[1 + 훾(푇푐 − 푇푆푇퐶)] (3.7)

where 푇푐 is the temperature of the cells, 푇푆푇퐶 = 25°C is the temperature of the cells at STC conditions, 휂푆푇퐶 is the efficiency of the module at STC conditions and γ is the empirically estimated relative efficiency temperature coefficient, approximately equal to -0.004/K for polycrystalline silicon cells [41].

The voltage level is also very important as it determines the currents flowing in the circuit given a certain power load. The higher the voltage, the lower the currents, and therefore less losses, which leads to a cheaper system (lower regulator, fuses, cables cross section).

PV nominal voltage is used to make sure the module is compatible with a given system and refers to the voltage of the battery that the module is expected to charge. The real PV output voltage changes with environmental conditions, so there is never one specific voltage at which the module operates, but a voltage rang, instead.

3.3 Energy Storage - LiFePO4 Batteries

An electric battery is a device that converts stored chemical energy into electrical energy in accordance to the chemical reactions – redox equations. Rechargeable batteries have largely replaced primary cells, as they save resource and reduce pollution. The most commonly used batteries for storing applications are lead-acid batteries [7] type, but they are being substituted by Lithium-ion batteries over time due to several advantages. Li-ion batteries have high capacity, high electrochemical potential, superior energy density, durability, as well as the flexibility in design. All the above outstanding properties accelerate the substitution of conventional secondary batteries.

The batteries used in autonomous PV systems must have the following characteristics:  Reduced maintenance requirements;  Long service time;  Reduced self-discharge and high energy efficiency;  High storage capacity and power density;  Good performance/price relation;  Protection against the occurrence of hazards to the environment and health.

The four most promising cell chemistries considered for energy storage applications are

LiMn2O4/graphite cell chemistry, which uses low-cost materials that are naturally abundant; LiNi1-X-

Y2CoXAlYO2/graphite cell has high specific energy and long life; Li4Ti5O12 is used as the negative electrode material in Li-ion batteries with long life and good safety features and LiFePO4/graphite (or carbon) cell chemistry is a type of Lithium that has a very good thermal and chemical stability, leading to safety characteristics and very low risk of fire.

Table 3.1 represents a lithium ion cathode chemistry comparison (using carbon anodes). Lithium-ion batteries advantages are evident. Less weight, more life cycles and less cycle discharge.

Table 3.1 - Battery technologies comparison [42, 43, 44] Lithium-Ion Batteries Specifications Lead-Acid NiCd NiMH Cobalt Manganese Phosphate Specific energy 30-50 45-80 60-120 150-225 100-135 90-120 density (Wh/kg) Specific power density 180 150 250-1000 1000 1500 - 2400 (W/kg) Cycle Life (80% 500- 200-300 1000 300-500 500-1000 2000-3000 discharge) 1000 Self-discharge/month 5-15% 20% 30% <5% <5% <5% (room temp.) Cell Voltage 2.0 1.2 1.7 3.7 4 3.3 Thermal Stability Poor Good Very Good Price (€/kWh) ~1500 - 250 - 390

Nowadays, the largely manufactured cathode is LiCoO₂ which offers high specific energy, but safety risks especially when exposed to high temperatures. LiFePO4 cells have the best number of cycles performance and thermal stability, which may be seen by the differential scanning calorimetry (DSC) comparison in Figure 3.6. Charged cells were disassembled in an argon box. The positive electrodes were washed in a liquid electrolyte (DMC), dried overnight, and sealed in punctured aluminium cans, for simultaneous thermal analysis. The thermal scans were performed with a heating rate of 10 K/min up to a temperature of 400°C in an argon stream.

Figure 3.6 - Exothermic reaction evolution with temperature [45]

The delithiated lithium nickel oxide (blue) shows the most vehement exothermic reaction at a temperature beneath 250°C, followed by a large weight loss, due to oxygen evolution. The charged

32 lithium cobalt oxide electrode (red) also reacts at such low temperatures, but with less reaction enthalpy and oxygen evolution. The exothermic reaction of the delithiated lithium manganese (green) spinel starts at a much higher temperature and there is no weight loss up to 400°C. The delithiated lithium iron phosphate (purple) however, shows no exothermic reaction and no weight loss up to 400°C, at all.

Next figure shows a simplified representation of a LifePO4 cell’s cross section:

Figure 3.7 - LiFePO4 simplified cross section cell [46]

On the top of the cell, two external electric terminals are accessible to connect to an external circuit and a safety valve provides air circulation. The cathode (+) material is LiFePO4, a polyanion oxide, possessing olivine-type crystal structure making its structure stability very good.

On one hand, LFP batteries present a lower capacity than other lithium-ion batteries (LiCoO2, etc), which leads to more weight for the same amount of energy. On the other hand, LFP batteries have a much better thermal stability, a longer cycle life. LFP batteries are extremely stable working for a wide range of temperatures being so a safer technology. For this reasons they are ideal for off-grid PV systems [47].

3.3.1 Cell Operation

LiFePO4 batteries have a very constant discharge voltage. Voltage stays close to 3.3V during discharge until the battery is exhausted. This allows the battery to deliver virtually full power until it is discharged. The characteristic of the cell defines the important relation between the cell’s voltage and correspondent SOC. The typical cell charging curve versus its state of charge (SOC) at an 80% DOD (2.6V – 3.6V) is represented in Figure 3.8. Note that the discharging curve has a slightly negative offset relatively to the charging curve. This happens due to the internal resistance voltage drop of the batteries. Regarding the charging/discharging characteristic the following conditions should be verified [48]:  The voltage of the cell must not exceed 3.65V when charging;  The voltage of the cell must not go under 2.5V when discharging;  The lifetime of the cells will be drastically reduced if charged outside the range 0°C ~ 40°C;  The lifetime of the cells will be drastically reduced if discharged outside the range -20°C ~ 60°C;  Cell’s lifetime will be reduced if charge/discharged at current rate higher than 30% of the capacity (0.3C);

 Cells may be damaged if operated at high pulse currents for more than a few seconds.

16 Figure 3.8 - LiFePO4 typical cell charging curve [49]

These limits vary to a certain extend with the manufacturer and for that reasons the datasheet of the battery should be always considered. Besides, working on the “flat” part of the characteristic is more beneficial in terms of control once the voltage variation is lower requiring a less complex control. The less deep the discharge more cycles the battery does but less energy is extracted. It is preferable to make deeper discharges once the battery components suffer less stress over time.

It is important to take into account the effect of temperature on the batteries. The capacity increases as the temperature rises and vice versa. On the one hand, if the installation local has temperatures near 0ºC a higher capacity battery should be used in comparison to the capacity calculated to 25ºC.

3.3.2 State of Charge (SOC) and Depth of Discharge (DOD)

The SOC of a battery is a measure of the amount of its stored electrical energy. The DOD is exactly the complement of SOC: when one increases, the other decreases. The prediction of the state of charge can be performed by invasive methods and non-invasive methods. Invasive methods are based on the chemical oxidation state of the active materials and are performed in laboratories. This method requires the batteries to be offline. Nowadays, the existence of mobile systems with batteries such as electric vehicles, battery operated power tools, or temporary storage systems for renewable energy sources requires the prediction/estimation of the state of charge with non-invasive methods. Thus, the research for non- invasive and instantaneous methods for SOC determination is becoming dominant. That will be [47]:  coulomb counting (current based);  voltage or current pulse response;  voltage based;  battery internal impedance measure.

16 OCV - Open Circuit Voltage

The coulomb counting technique simply indicates the remaining capacity of the battery by using electric current integration according to the coulomb counting equation [50]:

푡 휂 ∙ 푖(푡) 푆푂퐶푡 = 푆푂퐶0 − ∫ 푑푡 (3.8) 0 퐶푛 where 푆푂퐶0 is the initial SOC, 휂 the coulomb efficiency, 퐶푛 the battery estimated capacity and 푖(푡) the current. This method have some disadvantages like lack of precision due to the low accuracy of the coulomb counting technique itself, the noise from the sensors for the acquisition of the respective magnitudes and the increase over time of the error in the SOC estimation.

For this reason coulomb counting is usually additionally combined with others sensors such as voltmeters to measure the battery voltage to calibrate the SOC when the actual charge approaches either ends. After all, it is simple and has been used in many BMS’s products on the market, 123BMS™ corrects the value of the state of charge in each iteration [48].

In general, the cells voltage increases with SOC level. At 100% SOC voltage, it is not yet possible to know what capacity really is. A 100 AH cell maybe as little as 100 AH or as much as 120 AH. However in a battery bank, the weakest cell dictates the capacity of the whole battery system.

3.3.3 Battery pack initial balancing

New LFP batteries are usually partly charged from factory. However, due to transport, climate and environment conditions cells’ SOC is different at the pack assembly moment. Before assembly the cells in series to make a battery pack it is absolutely necessary to balance the cells so that they have a similar voltage and consequent SOC when charging/discharging.

The power supply should be connected to both ends of the parallel row as in the following diagram considering ideal batteries and the real power supply representation:

Power Supply Thévenin Equivalent Circuit Is

VS Cell 1 Cell 2 Cell 3 Cell 4

Figure 3.9 - Parallel cell charging with power supply

The starting point is to have all the cells at the same reference voltage point. It is easier to build a battery pack with balanced cells, than to balance it after it is built. BMS balance can take weeks as it might have a low balancing by-pass current for example, and even damage the cells if the voltage levels are not correctly set. This balancing is done charging the cells individually or in parallel with a CC/CV power supply (Constant current/Constant voltage). The charging/discharging current should be done at maximum current of 1C, however to optimize durability the recommended current should be lower than 0.3C. Regarding this, before the parallel assembly it is important to ensure that all cell’s SOC is nearly 80% and consequent voltages are similar.

In order to reach 100% SOC, the power supply current should be set to 0.2C maximum and the voltage equal to cell’s highest operating voltage specified by the manufacturer – 3.6V. The charging has two stages: 1) The power supply starts working as a constant current source (CC), reducing the current when the voltage gets close to 3.6V; 2) At a voltage close to 3.6V, the power supply switches to constant voltage source mode (CV) while the current reduces approximately to zero.

The charging time taken from [48] is given by:

푖푛푖푡푖푎푙 푆푂퐶 [%] (1 − ) ∙ 푁º 퐶푒푙푙푠 ∙ 퐶 [퐴ℎ] 100 % (3.9) 퐶ℎ푎푟푔푖푛푔 푡푖푚푒 [ℎ] = 퐼푆 [퐴]

The balancing time depends on:  SOC level;  Cell’s internal series resistance;  Slope of the voltage vs. SOC curve at that SOC;  Initial SOC unbalance;  Desired final match of SOC.

The cells' unbalance, the balancing current, and the cells' OCV all decrease with a time constant that is [48]:

휏[ℎ] = 푅푐푒푙푙⁄훥푉푆푂퐶 (3.10) where 푅푐푒푙푙 is the relative resistance of the cell [Ω – Ah] and ∆푉푆푂퐶 is the voltage drop in the SOC curve [V]. The balance time is then [48]:

퐼푛푖푡푖푎푙 푢푛푏푎푙푎푛푐푒 [%] 퐵푎푙푎푛푐푒 푡푖푚푒 [ℎ] = 휏 ∙ 푒 퐹푖푛푎푙 푢푛푏푎푙푎푛푐푒 [%] (3.11)

Figure 3.10 shows an example of LiFePO4 cells (A123 M1 type) balancing time at about 50% SOC, balanced from 10% SOC unbalance (difference between SOCs) to 0.1% match. Its time constant τ, is about 7.5 minutes and the balance time is about 34 minutes.

Figure 3.10 - LiFePO4 balancing time [48]

3.4 Batteries Management System

A Battery Management System (BMS) is an electronic monitor device which controls the status of individual rechargeable cells batteries and battery pack. In order protect and maximize battery pack's life, cell's temperature, voltage and current are monitored at a certain rate via several integrated control modules and actuators. To provide a better performance, the SOC and eventually the SOH are estimated and different balancing strategies can be used depending on the system application. The general functionalities block diagram of a BMS is represented in Figure 3.11.

Charge Load Battery Pack Relay Relay

On Board PV Load By-Pass Sensors Current BMS Power In Circuit (Voltmeter & Sensor Thermistor)

CAN BUS (Communications)

CAN Battery Comparator / BUS Software Monitor Battery Decision Logic Interface Unit SOC Model

Battery Control Signal Control Unit Control Signal

Figure 3.11 - BMS block diagram (adapted from “The Electropaedia” website)

The mains power circuit is represented outside the green box all at the voltage of the batteries (no MPPT and no inverter for simplification). The Charge and Load relays may connect/disconnect the load and production between electrical parameters given in the software interface. The BMS block inside the green box is powered by the battery itself and is constituted by:  On Board Sensors – measure the electrical parameters to monitor the batteries state (cell voltage and temperature);  Current sensor (current shunt, hall effect transducers, GMR magneto resistive sensors) – to measure the current flowing in and out the battery pack for SOC estimation;  By-pass Circuit – constituted by a resistor in series with a controllable transistor in parallel with each cell;  Software interface – human-machine interface to define the system desires behaviour;  CAN BUS (communication)– communication connection BUS between the BMS components;  CAN BUS – CAN BUS of the battery monitor unit;  Battery SOC Model – Estimated SOC based on expression (3.8) using the sensors’ inputs on the boards ;  Comparator/Decision Logic – electronic circuit that compares the sensors values with the values defined by the user in the software (this values are loaded to the microcontroller after input);  Battery monitor unit - microprocessor based unit incorporating the functions inside the grey box;  Battery control Unit – sends the control signals to the charge/load relays and to the by-pass circuit transistor’s gate.

3.4.1 Safety Functions

The most important feature in any application is to ensure no damaging. The BMS protects each cell from overcharge, over-discharge and external fault situations acting like an AC breaker, reading and comparing the cell's voltage and temperature with specified data and controlling the switch of the source and load circuits.

Monitoring cell temperature is essential for the proper working of the system. In case of overheat under operation, protection measures like current limiting (usually loads), current interruption or cooling system regulation can be adopted. A cooling system can be used in more complex systems, however this traduces in a more expensive and complex solution. The monitoring is done using a thermistor on the cell electronic board. This is a type of resistor with a characteristic that changes the resistance almost linearly with temperature, over a limited range. In an overheating situation, its electrical signal may be used to end the charge, stop the charge when the cell’s maximum operational temperature is reached, or it could be used to turn on cooling fans.

3.4.2 Cell Balancing

Battery balancing is an energy transfer process where individual cells’ capacity is managed so all the cells that constitute the battery pack have a similar SOC, ensuring a longer lifetime in service and

38 maximizing cells’ capacity. Without balancing, the battery with the lowest capacity in the pack is likely to be a weak point during discharging, decreasing the ability of the pack to store energy over time as the process need to be stopped. The cells must therefore be balanced. The balancing is usually categorized in two types - active or passive. Figure 3.12 shows the some topologies which differ in the type of passive elements connected in parallel with the cells, being used to adjust cell’s voltage and SOC levels during charge, discharge or idle. Note that not all the existing topologies are discriminated.

Balancing

Passive Active

Fixed Switched Inductor & Capacitor Converter Shunting Shunting Transformer Based Based Resistor Resistor Based

Single Single Single / Multi Buck / Boost Switched Windings Inductor Converter Capacitor Transformer

Figure 3.12 - Types of balancing [51]

Figure 3.13 illustrates the simplified behaviour of the two types. Active type uses inductors or capacitors to charge or discharge single cells transferring energy between them. There is almost no energy lost during the balancing, so it is more efficient but it requires components of higher cost comparatively to passive type. Passive type is a dissipative method - it balances the cell with the higher voltage (by- passing it) in the battery pack discharging its energy to produce heat in a resistor. It is the simplest and most commonly used due to its performance vs simplicity and cost benefit. [52]

Figure 3.13 - Passive vs active Cell Balancing (Source: Texas Instruments)

Table 3.2 shows a comparison between the two topologies of passive balancing and the some active balancing topologies in a scale of satisfactory (±), good (+), very good (++) and excellent (+++). It is then obvious that the passive type topologies are the best size, complexity and consequently price due to its smaller and cheaper electronic elements.

Table 3.2 - Balancing topologies comparison [51] Equalization Control Implementation Charge Topology Size Cost Application speed Complexity simplicity discharge Fixed Resistor ± Very Simple +++ +++ +++ Fixed Low Power Switched + Simple +++ +++ +++ Charge Low Power Resistor Single Medium / Switched + Complex ++ ++ ++ Bidirectional High Capacitor Medium / Single Inductor ++ Complex ++ + + Bidirectional High Single Windings + Complex + + ± Charge Medium Transformer Buck-Boost Medium / +++ Complex +++ + + Bidirectional Converter High

This facts goes in line with the objectives of this work, the choice of the passive type is justified by the need of an economic system with the ability to control the parameters accordingly with system behaviour over time. Therefore BMS123™ by 123electri.nl meets the requirements and is studied in more detail.

Passive or Active balancing is sub-categorized in three types – top, middle and bottom balancing. Middle balancing is a type of balancing used in power packs [48], designed to deliver energy in a short period of time which is not the purpose of this work. The balancing can be done during or at the end of charging or discharging. Bottom balancing can be done making controlled discharge (connecting a known fixed dummy load), however this is a waste of battery capacity for balancing activity (increasing wear) and has no advantage vs top balancing where mains power is used as the energy source instead of the battery power. Although balancing during entire charging and discharging is more accurate top balancing is simpler and consequently less expensive.

3.4.2.1 Passive balance The primary balance process algorithms are based on cell voltage equalizing. As explained before, the excess energy is removed from highest voltage cells, by-passing it, until the lower voltage cell is in the same level. The SOC is managed indirectly as it is associated to a specific voltage accordingly to cells' characteristics. Voltage differences between cells is minimized through by-passing cells with higher voltage. This algorithms may lead to cells overbalancing or under-balancing due to different impedance between cells. This means that the voltage deviation can be caused by a different cell capacity or impedance - a variation of its internal resistance due to higher temperature for example. Consequently, this type of balancing does not guarantee a 100% SOC at the end of charge. [52]

In order to minimize the effect of impedance differences between cells some balancing techniques act near the end of charge – top balancing, where the current starts decreasing at a higher SOC. This type of balancing is used in 123electric BMS® used in this work as it is explained further on.

Control

R1 R2 RN

Ibp1 Ibp2 IbpN Ipack

Cell 1 Cell 2 Cell N V V V

Figure 3.14 - Passive switched shunting resistor balancing (based on [51])

The switched shunt resistor (SR), performs the voltage equalization controlling switches/transistors. It could work in two modes. First, the continuous mode, where all switches are controlled by the same on/off signal. Second, the detecting mode shown in Figure 3.14, where the cells voltages are monitored and when cell’s imbalance is detected, it decides which resistor should be shunted. The current 퐼푝푎푐푘 that circulates through the battery pack is the same in every cell, however dissimilar impedance, temperature and capacity make cell’s voltage evolve differently. The by-pass currents 퐼푏푝1, 퐼푏푝2, . . , 퐼푏푝푁 are 10 to 100 times smaller than 퐼푝푎푐푘 so the balancing is smooth. The voltmeter has to be in parallel with the cell once the switch has a drop voltage associated. The main drawback in these methods is the excess energy from the higher cell(s) is dissipated as heat, there is a need for thermal management and has to be applied during charging, otherwise it will shorten the battery’s run time. [51]

Figure 3.15 - Example of a passive cell balancing circuit TI BQ77PL900 [52]

Figure 3.15 shows the circuit that performs the passive balancing. In parallel with the cell, a MOSFET transistor is controlled by the main microcontroller. When in conduction the microcontroller transistor creates a differential voltage at the external transistor (on-board) gate, activating it, which on the other hand closes the path that connects a resistor in parallel with the cell - 푅퐵푎푙 The external transistor resistance 푅퐷푆푂푁 is negligible in comparison with 푅퐵푎푙. The balancing current 퐼퐵푎푙 is low, typically under 1A and therefore may require multiple cycles to correct a typical imbalance.

3.4.2.2 Bottom Balancing Batteries have a slightly different capacity at the exit of the manufacturing line which requires special care when using a battery pack for long periods of time so the cells don’t get damaged. In bottom balancing process, all the cells have the same reference point at the low end voltage, about 2.5V. If the pack goes under the minimum critical voltage, all the cells get there together and there is not just one cell going above the critical voltage what does not happen with top balancing.

y y

t t

i i

c c

a a

p p

a a C C Vmin Vmin

Cell 1 Cell 2 Cell 3 Cell 4 Cell 1 Cell 2 Cell 3 Cell 4 a) b) Figure 3.16 - a) Bottom balancing and respective b) after charging

To perform bottom balancing, the batteries should be discharged one by one to the 2.5V voltage, left resting for 24 hours and discharged again to 2.5V (Figure 3.16 a). The resting voltage after discharging is about 2.7V. After this they should be connected in series and be charged as a pack until one cell reaches 3.6V (Figure 3.16 b). Bottom balancing makes the monitoring less exigent and simpler so it may be used in applications that do not have a BMS to protect cells from undercharging, but it requires protection from overcharging. [48]

3.4.2.3 Top balancing In top balancing, the reference point is the maximum cell voltage of 3.65 V or other near that. When one cell goes under the minimum critical voltage the remaining cells may have a higher voltage.

a C Vmin C Vmin

Cell 1 Cell 2 Cell 3 Cell 4 Cell 1 Cell 2 Cell 3 Cell 4 a) b) Figure 3.17 - a) Top balancing and b) after discharging

Top balancing process starts by charging all the cells individually to 3.65 V to reach the 100% SOC through a CC/CV power supply (Figure 3.17). After the individual charge they may be connected in series and when discharging as a battery pack, the “weakest cell” will be the first to reach the minimum voltage of 2.5V. This is the cell with less energy storage in the battery pack. As the cells are top balanced, all the others will be above 2.5V and consequently higher SOC. This method is particularly less risky, once if one cell is over discharged all the other may be in good conditions.

Table 3.3 - Comparison of Balancing Algorithms [48] Voltage Based Final Voltage Based SOC History Based Balances whenever Principle Balances all the time. charging, Balances at high SOC. Strives to match cell DOD, of regardless of SOC. Strives to match cell voltages based on previous history of Strives to match operation cells cell voltages. At high SOC the cell voltage changes rapidly, it gives The BMS balancing current can better data on the true SOC. be lower, and balancing can be Pros Very simple method Charging current can be done in fewer cycles, as reduced so errors due to balancing can occur all the time. internal resistance variations Cell resistance has little effect. are minimized Cell voltage as an indications of SOC is not effective. Balancing only at the top Requires more computing OCV vs SOC curve Cons means there is less time to power and more memory to is quite flat at mid balance with high currents store the history of each cell SOC levels. Strongly affected by cell’s resistance.

Table 3.3 resumes the balancing typologies most frequent. Once each method has its pros and cons, the choice depends on the application. Voltage based method produces poor results so the best choice is to combine the final voltage based method with computing and memory capabilities. Although 123 electric BMS™ (appendix 8.9) uses the final voltage based method only, this results in the best performance vs. price. Figure 3.18 is an example of voltage evolution in two different cells when charging.

Figure 3.18 - Passive cell balancing based on voltage [52]

The charging process ends properly by reaching the by-pass voltage. In each cycle, the BMS shortens the balancing time once the voltages get closer each cycle. The bigger the cells the higher the needed time to balance.

3.4.3 SOC estimation

As seen before in 3.3.2, the usual method for estimating the SOC is the coulomb counting method done with a “fuel gauge” that consists of a DC current meter. The basic calibration in this type of BMS consists in the following steps: 1. At the beginning the algorithm considers the SOC given by the user. 2. If the first cycle is a discharging cycle, then Amperes are deducted until 2.5/V per cell is reached. At the moment when 2.5V (or different number in Vmin value) is reached, 0% is shown at SOC gauge. 3. After charging starts and once the voltage reaches 3.6V (or different Vmax value), the gauge is set to 100%. Anytime when Vmin or Vmax value is reached by any cell

4. The 푆푂퐶0 is recalibrated for the newer calculated value.

3.5 Autonomous or Off-Grid Inverters

For any photovoltaic (PV) system, the off-grid inverter is the essential electronic device that converts low voltage DC electricity from a battery or other power source to 100V-120V or 220V-240V AC signal. Off-grid Inverters produce a voltage wave, with an independent frequency from the grid. This is the point where the off-grid inverters differ from grid-tied once the last need the grid voltage wave to “couple” and inject power. Not only does the inverter convert DC to AC power but it may also regulates the PV system if correctly dimensioned according to the battery voltage levels.

Some requirements are indispensable for an off-grid inverter [7]:  Auto starting and adequate protection warning signs;  Peak power capacity – it should support more than two times its nominal power;  Low THD;  Low stand-by power;  High efficiency;  Voltage stability – between the range of 230V±10%;  Possibility to connect other inverters in parallel.

The waveform should be selected accordingly to the type of application. They are classified in three classes: 1. Square wave – The simplest and cheapest DC-AC converter. Usually constituted by thyristors controlled by the grid clock, not appropriated if the loads are not purely resistive (not suitable for off grid systems) and high THD (≈45%); 2. Modified Sine or semi-sine wave – Provide rectangular pulses with an approximate 42% THD; 3. Sine Wave – The inverter with the lowest THD (<3%). Appropriate for motor loads such as medical equipment, refrigerators, laser printers, etc. It is also used in grid-tied applications. It is the most expensive inverter of the three types.

Pure sine wave inverters are the best choice to the correct working of motor or compressor loads once it is the inverter with less harmonics which is seen in more detail. Pure sine wave inverters

These inverters are controlled by a Pulse Width Modulation which allows a wide amplitude of the output sine wave and reduce the amplitude of the low order harmonics. The general block diagram of a sine wave inverter is represented in Figure 3.19. Bridge V+

L1 Filter Switch

Isolation N Transformer V -

DSP Control

Figure 3.19 - Block diagram of a sine wave inverter (adapted from Texas Instruments)

The battery bank DC voltage (12, 24 or 28V) is the input of the bridge which may be full bridge or half bridge depending on the requirement. The power transformer is generally used to isolate the battery from the load and to step up the input voltage in grid-tied inverters or just isolate the output in grid-tied inverters. The IGBT or MOSFET transistors are modulated by a square wave switching frequency in the range of 20 kHz (PWM – class D circuit) to create an AC voltage. A sine wave is compared with a triangular wave to generate a PWM output which drives the transistors bridge – triangulation scheme. This square wave is controlled by the digital signal processor (DSP Control) which also controls the output switch accordingly to certain alarms (low input voltage, overload, short circuit, over temperature protection, etc). The output of the insulation transformer is filtered (low pass filter) to obtain a correct sine wave. The typical waveform of this type of transformers it shown in advance (the inverter was chosen and test in chapter 4) in Figure 3.20:

400 200 300

200 150 100

0 100

Voltage [V] -100 Voltage [V] -200 50

-300 0 -400 0 20 40 60 80 100 0 100 200 300 400 500 Time [ms] Frequency [Hz] a) b)

Figure 3.20 - Inverter output waveform and corresponding harmonics

The experimental output voltage of the Livre Inverter (Appendix 8.10) with a RMS=200,9V confirmed a good quality waveform due to its low harmonic content in Figure 3.20 a). The mainly harmonic is the 1st at 50Hz with 195.68V (45.83 dB). The 3rd, 5th, 7th and 9th harmonics (odd) have a much lower amplitude than the 1st. The THD is 1.19% (2nd to 9th harmonics) THD lower than 3% for this inverters (Figure 3.20 b).

The use of an insulation transformer means protection against indirect contacts (no need of TN-C differential protection) and also reduces the electromagnetic interferences. However, these inverter may not have it and transformerless inverters are gaining popularity in solar systems. The idea behind transformer-less switching has existed long before the PV market was even developed. A pair of field- effect transistors operates most efficiently in a complete ON or OFF state, when no current flows through them, and they dissipate no power. Thus, amplifying an ideal square wave would theoretically be 100% efficient. For this this reason, transformer-less inverters have a lower stand-by consume.

Efficiency The efficiency rating indicates what percentage of DC power is converted to usable AC power. This will never be 100% once the inverter uses some of the input DC power itself, generally around 10-30 W. In general, off-grid inverters have an extremely flat efficiency curve for higher than 30% of the nominal power so less battery power is wasted. This means that the drive must be sized to operate as near as possible of inverter’s rated power.

The efficiency of the inverter is given by [4]:

푃푂푈푇 푃퐴퐶 휂푖푛푣 = = (3.12) 푃퐼푁 푃퐷퐶

An inverter's efficiency is shown in Figure 3.21 efficiency curve. The inverter's efficiency increase sharply until it reaches its peak efficiency point. It will then remain close to level, decreasing slightly as it approaches its rated power output. Ideally, the power used should be at or above inverter's peak efficiency point.

The manufacturer efficiency curve of the Xantrex Prosine inverter may be seen in Figure 3.21 a) for the model of 1000W and 1800W showing the peak after 30% of the nominal power. Figure 3.21 b) shows in advance17 the experimental characteristic of the 1500W Livre Inverter chosen to the off-grid system. The procedure of the test is described in more detail in Appendix 8.10 plotted with 10 points until the maximum power supply was reached (the dashed part of the curve should does not have enough points) . The efficiency ranged from 84-90% between 200-300W with the highest value at 800W (50% of the nominal power like in Xantrex Inverter).

17 the inverter was selected and tested after the project in chapter 4

100

40 Efficiency [%]

0 0 200 400 600 800 Power [W] a) b)

Figure 3.21 - Inverter efficiency characteristic a) Xantrex Prosine off-grid inverter efficiency curve for 1000 and 1800W 24V system (source: Xantrex18) and b) 1500W Livre Inverter

The actual inverters available on the market (mostly PWM regulators) are designed for lead-acid, NiCd or NiMH batteries typically ranging in the following voltage levels:

Table 3.4 - Typical actuation voltage levels of off-grid pure sine wave inverters and PWM regulators Nominal Voltage Minimum voltage cut-off Maximum voltage cut-off 12 V 10.5V±5% 15V±5% 24 V 20 V±5% 31±5% 48 V 41V±5% 60±5%

For example, to have a 24V nominal voltage, 8 LiFePO4 cells are necessary. The minimum voltage of this cells is 2.5V. The inverter minimum voltage of 20V divided by 8 cells will make each cell have 2.5V which is too close to the limit and will damage the cells. For this reason the minimum and maximum voltage levels are not in the correct range for LiFePO4 batteries requiring the use of a BMS or an inverter with controllable voltage levels.

18 Xantrex prosine 1000/1800 Owner’s Manual

3.6 Cables

Figure 3.22 represents the losses on the DC cables, the voltage drops and power losses associated to it. The losses on the cables connecting the batteries to the loads are not represented for simplification19. The length of these cables is small when compared with the length of the PV cables and might be neglected.

R I

P P PV PV injected Battery

R ΔV

Figure 3.22 - Cable losses

where 푅 is the resistance on the cable PV-battery in Ohms, 푃푃푉 is the power at the panel’s terminals,

푃푖푛푗푒푐푡푒푑 is the power at the battery's terminals and ∆푉 is the voltage drop on the cables. R is generally calculated according to the manufacturer resistance and length of the cable. As an example, the specifications of the TUV cable may be consulted in Appendix 8.8.

Joule losses on the cables:

푙 푃 = 휌 ∙ 퐼2 = 푅 ∙ 퐼2 (3.13) 퐽표푢푙푒 푆

The power produced by the panel 푃푃푉, knowing the power at the end of the cables terminals 푃푖푛푗푒푐푡푒푑, is given by:

푃푃푉 = 푃푖푛푗푒푐푡푒푑 + 2푃퐽표푢푙푒 (3.14)

Voltage drop, for both DC and AC cases, is given by the following formula:

휌 ∆푈 = 퐾푐 ( 1 cos 휑 + 휆 sin 휑) × 퐿 × 퐼 푆 퐵 (3.15)

where 퐾푐 is a coefficient equal to 1 for three phase and equal to 2 for single-phase circuits; 휌1 is the resistivity of the conductors at the usual working temperature (1.25 times the resistivity at 20ºC – 0.0225 Ω.mm²/m for copper and 0.036 Ω.mm²/m for aluminium); S is the section of the conductors in square millimetres; cos 휑 is the power factor (cos 휑 = 1 for pure resistive loads making sin 휑 = 0); λ is the linear reactance per length unit of the conductors (default value 0.08 mΩ/m); L is the length of the cable (m) and 퐼퐵 is the current (A).

19 accordingly to the experiment made in chapter 5

The voltage drop in percentage is given by: ∆푈 ∆푈 [%] = × 100 (3.16) 푈0 where 푈0 is the voltage between the phase and the neutral.

3.7 PV System Efficiency

ƞ BMS ƞ BMS ƞ PV inv

Battery AC PV Pack Consumers ƞ PDC Inverter PAC DC, injected BAT P

Figure 3.23 - Off-grid PV system connection diagram

The total efficiency of the module interface system with the loads accordingly to the diagram of Figure 3.23 may be obtained by:

휂푠푦푠푡,푎푢푡 = 휂퐵푀푆 ∙ 휂퐵퐴푇 ∙ 휂푖푛푣 ∙ 휂푙표푠푠푒푠 (3.17)

where 휂푙표푠푠푒푠 = 1 − 푃푙표푠푠푒푠푐푎푏푙푒푠[%] is a factor that considers the losses on the cables.

In case the energy “injected” in the battery pack and the energy consumed by the loads is known, the respective efficiency may be calculated by:

퐸푂푈푇 퐸퐿표푎푑푠 휂퐵푀푆+퐵퐴푇+퐼푛푣 = = (3.18) 퐸퐼푁 퐸푃푉

However, as the batteries store energy, this efficiency needs to be estimated during a time period where the batteries start at a certain SOC return to that same SOC point. This may be more accurately done by a battery voltage reference point. In other words, the battery should start the test charged with a voltage 푈표, discharge during a certain time and charge again until 푈표. Knowing the energy in and out during this period, the efficiency may be calculated.

3.8 Conclusions

The purpose of this chapter is to introduce the basic principles of operation of all the system components – consume, photovoltaic production, storage, control and energy conversion.

To supply the loads of the system, polycrystalline panels were chosen, once the price is more competitive consequence of the highest presence in market. Besides, this was the highest power panel gently provided by Resul – Energy Equipments, S.A on 2014.

Comparing weight versus available energy storage, LFP batteries are about one-third the weight and about half the volume of a lead-acid (LA) battery with equivalent energy storage. Additionally, the storage capacity of LAs drops by 50% at -20°C, compared to 8% with LFP. Keeping lead-acid batteries warm so that they maintain reasonable capacity in cold climates can be challenging, giving advantage to LFPs. LiFePO4 have the best thermal stability of all seen lithium ion types being then appropriate to photovoltaic applications.

The characteristic curve of these batteries requires special care and project of the controllers. A battery management system (BMS) to manage the “health” of the batteries is the best option to ensure reduced maintenance and long service time. Some solar regulators, like PWM regulators, are not yet design for this type of batteries. This process is done better with top balancing, once the batteries are expected to be at full status as much as possible. This way the balancing will be done more often. At high SOC, the cell voltage changes rapidly, which also gives better data on the true SOC.

To convert DC to AC power, pure sine wave inverters are the best inverters type to feed motor loads and have less than 40% THD voltage compared with modified sine and square wave. Inverters should have no screen, as this always increases stand-by power. Besides, its standby consume may be reduced with no insulation transformer on the AC side (requires differential circuit breaker).

4 Autonomous PV System – Project

This chapter aims to project the photovoltaic system for Luena zone in Angola. The project is carried out in accordance with the equipment kindly provided by Resul – Energy Equipments, S.A.20, constituted by two 190W STP190S monocrystalline and two 225W STP225 Suntech PV Panels. The LiFePO4 batteries were also previously obtained by Electrical Department (DEEC) with the objective of studying its performance in this type of systems.

There are several possible processes to project an autonomous PV system. Processes differ in the initial condition that will affect the design of the remaining components [7]:  Maximum daily energy calculation;  Maximum power consumption calculation;  Number of PV modules calculation;  Battery capacity calculation.

To scale a PV system is necessary to know the average radiation values at the installation site. To determine these values radiation PVGIS software was used [26]. This software allows to estimate online the photovoltaic solar energy for isolated or grid-tied systems within the European and African continent and uses Google maps ® to choose the location. This is a reliable and free software that justified the choice for the project.

The maximum daily energy calculation process considers the following steps which will be seen in detail [7]: 1) Determine the dairy energy consumed by the loads; 2) Calculate the energy production of the PV modules at a given tilt, β, and azimuth angle, γ; 3) Project the peak power of the PV modules; 4) Calculation of the batteries parameters; 5) Project of the solar regulator; 6) Project of the autonomous or off-grid inverter.

4.1 Loads

The more accurate the consumption data the better the project, for this reason the loads consumptions and peak currents were analyzed and are presented next. In this chapter some assumptions were made to match the loads profile with the average consumption of a small family house in Angola.

20 Resul website may be consulted at http://www.resul.pt/

4.1.1.1 Refrigerator Load Diagram The refrigerator is the load with the load diagram more complex. The refrigerator used in the experiments is the Kentt 201E which technical data can be seen in Appendix 8.11. This refrigerator has 7 refrigeration levels consuming more energy for higher levels. The load diagram was obtain experimentally for a more precise project. For a reasonable temperature vs energy use, level 3 is the appropriate one. However, once it was not possible to simulate a diary use of the refrigerator, the level 4 was the chosen one to compensate the extra consume caused by the opening of the door on level 3. Figure 4.1 represents the refrigerator active power diagram for one hour at level 4 with no opening of the door measured using Fluke 1735 power logger (Appendix 8.3). The refrigerator compressor is on for periods of approximately 4 min at an average power of 127W four times per hour.

350

300

250

200

150 Power [W] 100

0 00:10 00:20 00:30 00:40 00:50 01:00 Time [h:min]

Figure 4.1 - KENT 201E refrigerator load diagram (1h)

4.1.1.2 Lights and TV Load Diagram For lighting purposes is estimated a power of 60W during 5 hours per day, from 18:30 to 22:30 and from 6:00 to 7:00 according to the working hours in Angola. This power may be achieved with a single lamp or several with less power. This is the second more important load of a family’s house.

For a regular house entertaining purposes is estimated a 40W TV which is on for 2 hours per day from 20:00 to 22:00 or it can be substituted by a more important electronic device if consuming the same equivalent energy.

4.1.1.3 Total Load Diagram The total load diagram is the sum of the three previous loads’ consume profile represented in Figure 4.2 logged with Fluke 1735 (Appendix 8.3).

300

250

200

150

Power [W] Power 100

0 0 2 4 6 8 10 12 14 16 18 20 22 24 Time [h]

Figure 4.2 - Total daily load diagram

The refrigerator switches on and off in regular periods along the day and the lights and TV working periods are those in 4.1.1.2. Unlike the peaks of the inductive loads (refrigerator and TV) are not visible once the integration period of the logging is higher. The maximum power of the system is 250W between 19:00 and 22:00.

4.1.2 Experimental loads power

Table 4.1 shows the experimental electrical parameters of Kentt 201E refrigerator (Appendix 8.11), Philips 60W incandescent light and Sony KV-14LT1E 13’’ TV (appendix 8.12) measured with Fluke 1735 power logger (Appendix 8.3). The energy values represent the refrigerator daily consumption at level 4.

Table 4.1 - Loads electrical experimental parameters Power Energy Reactive Apparent Active Reactive Device Active [W] Factor [Var] [VA] [Wh/day] [Var/day] Refrigerator 127 169 211 0,6 879,407 1148,471 Lights 69,6 0 0 1 TV 41 45,16 61 0.674

4.1.3 Daily consumed energy

The time of usage of each load defines the diary energy needed for the autonomous system. Table 4.2 shows the hours of use considered for this work based on the daily needs.

Table 4.2 - Experimental dairy loads energy Equipment Power [W] Utilization [h/day] Daily Energy [Wh/day] Refrigerator (level 4) 127 6.93 880 TV 41 2 84 Lamps 69.6 5 348 Total 237.6 5.52 1312

The total daily consume is approximately 1300Wh which should be taken in consideration for the project. The use of individual loads independently is equivalent to a power of 238W for 5.5 hours.

4.2 PV Panels Production Capacity

The PV panels are the only source of energy once in this project it is not considered a hybrid system.

Thus, it is necessary to estimate the necessary power to feeds the loads, 푊푑 = 1300 Wh/day, having in mind the losses that may occur on the cables, regulator and inverter as seen before in expression (3.17). The respective efficiencies are calculated below:

휂푙표푠푠푒푠 = 휂푐푎푏푙푒푠 = 1 − 푃푐푎푏푙푒 푙표푠푠푒푠 ≈ 1 − 0.03 = 0.97 (4.1)

The losses on the cables may reach 3% of the total power in isolated systems [7].

휂퐵푀푆 = 0.98 (4.2)

The losses on the regulator or BMS system are considered be less than 2%.

휂푖푛푣 = 0.85 (4.3)

The losses of the inverter are equal to the inverter efficiency which is usually 85% for an operating power of 20% of the nominal inverter power according to Figure 3.21.

The efficiency factor, considering the battery efficiency equal to 1 (currents lower than 10% of the total capacity) and all the applicable losses:

휂푠푦푠푡,푎푢푡 = 휂퐵푀푆 ∙ 휂퐵퐴푇 ∙ 휂푖푛푣 ∙ 휂푙표푠푠푒푠 = 0.98 ∙ 1 ∙ 0.85 ∙ 0.97 = 0.81 (4.4)

The radiation varies along the year and to project the system is necessary to choose which irradiance to consider. Assessing the available energy in Luena area from PVGIS, the following values are obtained for an optimal inclination of 19º with annual irradiation deficit due to shadowing (horizontal) equal to 0%:

Table 4.3 - Irradiation on Luena, Angola [26]

Irradiation Month [Wh/m²/day] Jan 4890 Fev 5070 Mar 5540 Apr 6290 May 6980 Jun 7040 Jul 7170 Aug 7330 Sept 6850 Oct 6150 Nov 5070 Dec 4730 Annual 6093

The best procedure is to project the system by the worst case scenario for permanent use houses, for sporadic use houses the months of September or October should be used [7]. The worst month occurs in the months of less radiation, this way the feed of the loads all the year is guarantee being the system oversized. This is the most commonly used method. The 휏푑(훽, 훾) factor makes the equivalent hours of the irradiance at 1000 W/m² (mean irradiance value for calculation purposes). The worst month irradiance occurs on December with 4730 Wh/m²/day:

푀표푛푡ℎ푙푦 퐴푣푒푟푎푔푒 퐼푟푟푎푑푖푎푛푐푒 [푊ℎ/푚2/푑푎푦] 4730 휏푑(훽, 훾) = = 1000 [푊/푚2] 1000 (4.5) = 4.73 h/day

4.3 PV array sizing

To better predict and deal with eventual non-ideal/standard working conditions, the efficiency of the autonomous system must be taken in consideration. The amount of Peak Solar Hours per day, 휏푑(훽, 훾), already considers the mean energy produced by the PV panels, consequently it is not necessary to consider the total efficiency of the PV, 휂푃푉 in the calculation as used in [53]. The required PV array power is then given by:

푊푑 1300 푃푃푉 = = = 339.31 Wp (4.6) 휂푠푦푠푡,푎푢푡 × 휏푑(훽, 훾) 0.81 × 4.73

However, the off-grid system is not expected to have MPPT’s to make the system cheaper and with less stand by consumption. Thus, to choose the power of the panels it is more realistic to use the maximum power on NOCT conditions. The polycrystalline Suntech STP225 - 20/Wd (Appendix 8.7) provided by Resul was the chosen PV one because its power is higher than the STP190. This panels produce 165W on NOCT conditions. The number of PV modules needed to produce the required power is given by equation (4.7):

푃푃푉 339.31 푁푃푉_푚표푑푢푙푒푠 = = ≈ 2 (4.7) 푃푃푉_푁푂퐶푇 165

Two panels produce 330W to be connected in series or parallel regarding the chosen working voltage of the batteries. In this case, the nominal voltage of the batteries is 24V so the panels must be connected in parallel once is 푉푀푃 = 29.6 푉.

4.4 Batteries

The batteries should be project the more accurate way possible once to many batteries easily make the system much more expensive. Usually, the nominal operational voltage of the PV system can choose between 12V, 24V or 48V. When knowing the voltage, the next step is to express the daily energy requirements of loads in terms of current and average operational time expressed in Ampere-hours. The working voltage chosen was 24V instead of 12V to decrease the current on the cable and consequently the losses. This way the panels have to be connected in parallel to perform a nominal voltage of 24V.

The daily consume in Ah is given by:

푊퐷 1300 푊퐴ℎ = = = 54.17 Ah (4.8) 푈퐷퐶 24

The battery sizing comes as [53]:

푊퐴ℎ × 푁퐷 54.17 × 2.5 퐶퐵퐴푇,푇표푡 = = = 169.28 Ah (4.9) 퐷푂퐷푚푎푥 0.8

where 푁퐷 is the number of reserve days (working days with energy from the sun). 퐷푂퐷푚푎푥 is the maximum deep of discharge of the battery which should be less than 80% allowing the batteries to perform more than 2000 cycles (Appendix 8.6). The battery capacity is added when the batteries are installed in parallel keeping the voltage and remains the same when they are installed in series, adding to the voltage. It may be found batteries with different capacities ranging from 1 to 200 Ah. The number of batteries to perform the capacity needed is calculated as:

퐶퐵퐴푇,푇표푡 169.28 푁퐵퐴푇 = = = 0.94 ≈ 1 (4.10) 퐶퐵퐴푇 180

where 퐶퐵퐴푇 is the capacity of a single battery. It is far cheaper to choose a single battery with a high capacity than to associate several batteries in parallel with a smaller capacity. Besides, parallel association makes the battery bank more unstable once the cell with the smallest internal resistance will be overstressed over the time.

Additionally, the voltage has to be also taken in consideration. Each LiFePO4 battery has a nominal voltage of 3.3V being the real number of batteries:

푈퐵퐴푇,푇표푡 24 푁퐵퐴푇 = = = 7.27 ≈ 8 (4.11) 푈퐵퐴푇 3.3

To build a battery bank with 24V and 169 Ah, eight batteries with 180Ah and 3.3V are needed.

4.5 Autonomous or Off-Grid Inverter

Off-grid inverters having two inductive loads and the fridge an induction machine, special attention is required when dimensioning the inverter. It shall be capable to support not only the normal operating power of the system but also the electronic devices starting peak power. Furthermore, the inverter must not be overloaded to operate without overheating while allowing the possible connection of extra loads in the future. Also, the nominal power of the inverter should be chosen accordingly to its efficiency curve. It was found in 3.5 that this efficiency is usually higher for powers higher than 40% of the rated power of the inverter. Choosing a slightly larger inverter could allow it to operate in a more efficient power range. In the long term, this could offer better value - the loads will take less energy out of your system

56 and the inverter will run cooler, subsequently lasting longer. These inverters support usually twice its rated power, the best inverters support three times its rated power during periods up to 10 seconds.

The power of the inverter is usually calculated as the sum of the nominal powers of the loads plus a 25- 30% reserve power. In case of appliances with motors or compressors, the inverter size should be done accordingly to the surge starting current/power. Generally the inverter nominal power should be 3 times the capacity of those appliances plus the power of the purely resistive which is our study case and seen in more detail next.

To understand what is the peak power of the loads involved it was measured the transitory current of the inductive loads. In Figure 4.3 is represented the starting and the operating current of the Kent refrigerator. In Figure 4.3 a) the amplitude of the sinusoidal wave is not correctly represented due to the high time step used, this is the reason why the current signal is not symmetric to the xx axes. However this was the only way to observe for how long lasts the peak current.

10 1.5

1 5 0.5

0 0

Current [A] Current Current [A] Current -0.5 -5 -1

-10 -1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -100 -80 -60 -40 -20 0 20 40 60 80 100 Time [s] Time [ms] a) b) Figure 4.3 - Refrigerator a) starting and b) operating current

Figure 4.3 b) is the sinusoidal operating current of the refrigerator with an amplitude of approximately 0.9A. The peak amplitude current in Figure 4.3 a) is Ip=9.2A which means an AC power of:

퐼푝 9.2 푆푙표푎푑푠,푝푒푎푘 = 퐼푅푀푆푈푅푀푆 = 푈푅푀푆 = × 230 = 1496.24 푉퐴 (4.12) √2 √2

This power peak is the first requirement of the inverter. This type of inverter usually support only one third of its nominal power:

3 푃 = 푆 ≈ 1122 W (4.13) 푙표푎푑푠,푝푒푎푘 4 푖푛푣

It was also observed that the compressor may request this power for periods up to 10 seconds which is the second requirement of the inverter. The inverter should be projected by the worst case scenario which is the starting of all the loads at the same time. However, starting of all the loads at the same time

57 revealed21 no higher peak current and power than calculated in (4.12) due to the same inductive character of the loads. Considering the general fact the inverter may support twice its nominal power and a 20% heat security factor should be considered, the minimum inverter power is then:

푃 1122 푃 = 푙표푎푑푠,푝푒푎푘 = + 0.2 ∙ 푃 = 785.4 푊 (4.14) 푖푛푣_푚푖푛 2 2 푙표푎푑푠,푝푒푎푘

4.6 Regulator

For the dimensioning of the regulator or BMS the maximum operating current in the circuit should be taken into account. The currents to consider are the currents produced by the PV panels and from the battery to the loads. The panels are connected in parallel once each panel maximum current is summed:

2 × 퐼푀푃 = 2 × 7.61 = 15.22 A. However the current to feed the AC loads is higher than the PV total current. This load current depends on the peak power. Accordingly to the previous analysis in section 4.5 and knowing the voltage of the battery, on the loads side the regulator nominal current should the higher than the DC peak current (simultaneity factor of 100% - all the loads connected at the same time) which is given by:

푃푙표푎푑푠,푝푒푎푘 1500 퐼푟푒𝑔_푚푎푥 = = = 62.5 A (4.15) 푈퐷퐶 24

4.7 DC Cables

The main DC cable connected to the PV panels should be projected to support 1.25 times more than the maximum short circuit current of the PV panels at STC conditions accordingly to IEC 60364-7-712:

퐼푧 ≥ 1.25 × 퐼푃푉 = 1.25 × (8.15 + 8.15) = 1.25 × 16.3 ≥ 20.4 A (4.16) 퐶퐶푡표푡푎푙

This means that admissible current, 퐼푧 ≥ 25 A, which is the current supported by the cable without the risk of melting/fire. Considering the 52-C1 Table of the permissible currents for PVC isolated conductors and the method B of the RTIEBT for the installation22, a permissible current of 25A means a minimum cross section of 2.5mm² for copper conductors and 4mm² for aluminium conductors. In this work the aluminium conductor was the chosen conductor due to its lower price.

4.8 Protection – DC Switch and DC Fuses

Accordingly to the European standard IEC 60364-7-712 it should be installed a DC circuit breaker between the PV panels and the inverter. Its nominal current is given by [7]:

퐼푛 ≥ 1.25 × 퐼푃푉 = 1.25 × 16.13 ≥ 20.4 (4.17) 퐷퐶 푆푤푖푡푐ℎ 퐶퐶푡표푡푎푙

21 observed with experimental measurements 22 plumbing with insulated conductors mounted in circular pipes installed at sight

It was chose the Hager SB432PV DC Switch with 퐼푛 = 32 A.

The cabling, DC switch, BMS, batteries and the inverter should be protected by a DC Fuse. In DC current the fuses used are gL-gG slow fusion type. A single fuse on the positive pole is enough to ensure the protection. The nominal current, 퐼푛 퐷퐶 푓푢푠푒, on the PV panels side should verify the condition:

퐼푛 퐷퐶 푓푢푠푒 ≤ 퐼푍 = 25 A (4.18)

Thus, to protect the cable and the DC Switch the chosen nominal current was 퐼푛 퐷퐶 푓푢푠푒 = 25 A.

When the distance between the loads and the inverter is higher than 4m it should be installed a differential circuit breaker with In=25A and 30 mA of sensibility. Siemens type B 5SU1356-0KK25 or Hager LFPV meet this requirements.

4.9 Prototype costs

The solutions to this system have been chosen based on equipment assigned for research purposes by the power company Resul S.A. (solar panels and DC cables), other acquired by the Department of

Energy, based on a search in the Portuguese market and some suppliers abroad (LiFePO4 batteries and Inverter).

The chosen BMS was the 123BMS designed by 123electric which features software that allows the user to change the controller parameters. Usually this type of controllers are configured for pre-set values or have some kind of built-in display LCD that allows to change some parameters. There are currently very few solutions on the market that do the programmable control cell by cell at such a competitive price as the chosen 123BMS. The BMS also allows the control of the critical zone where the loads should be turned off, solving this way the fact that the 24V inverters have a cut-off voltage of 20V (20/8= 2.5V/cell) which is a very low voltage that will damage the cells.

According to the foreseen and in line with the objectives of this work, the chosen battery was a 3.3V LiFePO4 battery. Although the design capacity of the battery is approximately 180Ah according to expression (4.9), at the time of purchase, the highest capacity battery available at the supplier’s store was 130Ah. Thus the 130Ah batteries were used for testing, reducing also the system costs that way.

The 25A DC fuse was kindly offered by Hager, S.A. ® since these fuses are sold only in large quantities.

To perform better with engine loads, the inverter must support the peak power easily. Also it should be given margin power for future expansion of the system. As such an inverter was chosen with the capacity to double the peak power required by the loads, i.e., an inverter with nominal power of 1500W (peak power 3000W).

Within these requirements a survey of autonomous inverters was made in the market in January 2015. These inverters have a DC working voltage of 24V, output voltage of 230V and 50Hz frequency. In general, they have always polarity inversion, overheating, short circuit protection and efficiency higher than 85%. Some competitive prices were found in foreign stores, however one of the factors taken into consideration to the choice was the availability and the flexibility to exchange. The most important factor to the decision was the stand-by consume, staying on 24/day, the stand-by power reduces the energy of the batteries available to deliver to the loads. The inverter with the lowest stand-by consume and lowest price was the Victron ® equivalent at a lower price: Livre Inverter (Appendix 8.10).

Table 4.4 - Pure sine wave inverter price and specifications Photo Equipment Characteristics Price [€] Pmax=2xPn=3000W; Inverter Livre 1500W η > 90%; THD <3%; 528.9€ Pstand-by=7W

Next, the costs of all the equipment of the system under study are presented:

Table 4.5 - Total system cost23 Percentage Item Quantity Price with VAT Total of Budget 225W polycrystalline PV Panels 2 303 € 606 € 20.0 % DC Aluminium Cable 4mm2 50x2 m 0.86 €/m 86 € 2.8 % LiFePO4 Batteries 3.3V 130Ah 8 127.48 € 995.84 € 32.9 % BMS + DC Controllable Relay 1 490.58 € 490.58€ 16.2 % BMS Board Cell Module 8 11.06 € 88.48 € 2.9 % DC Current Sensor 100A 1 55.62€ 55.62 € 1.8 % 1500W Off-grid Inverter 1 528.9 € 528.9 17.5 % DC Switch 1 101 € 101 € 3.3% Dead Front Fuse Holders 1 6.22€ 6.22 € 0.2 % Differential circuit breaker 1 68.2 € 68.2 € 2.3 % breaker In=25A, 푰∆풏 = ퟑ 퐦퐀 Total 3026.8 € 100 %

The price of the PV modules is the price in Portugal corresponding to 1.35 USD/W which is in the usual range values in Europe as described in section 2. The total 450 Wp system cost corresponds to a price of 6.3 USD/W24. The most expensive items are the batteries (storing) and then the PV panels (production) making more than 50% of the total cost of the system, then is the inverter (conversion) and the BMS (control). In the future, the final cost may be eventually reduced more than 15% with a hardware based BMS and an inverter with less margin power - Pn=750 to 1000W - (but consequently more losses). It is somehow an expensive system for such a poor country, however the costs of constructing the grid infrastructure in remote places will be thousand times higher and with high installation time.

23 Based on GWL website prices http://www.ev-power.eu/ and energy manufactures and suppliers in Portugal: Hager, Siemens and Resul S.A. 24 Using a conversion ratio of 1€=1USD

4.10 Economic analysis of the off-grid PV system

In economic terms it makes no sense to use the usual economic indicators (NPV, IRR and payback period) for isolated systems, as they are very simplistic. This is due to the fact that there is no direct sale of electricity to consumers and consequently an annual gross revenue. This is the reason why this systems should not be considered investments. However, they may be economically viable, if during its lifetime it is possible to save in an investment as the creation of a power transmission line to a remote location.

It may be analysed the cost of buying the energy consumed by the loads during the useful life of the autonomous system. For that it is necessary to estimate the lifetime in years and the annually energy consumed. Considering that the battery makes a cycle of charging and discharging daily, a total of 2500 cycles during its lifetime and according to Table 5.10, the energy consumed by the load during this period is:

2500 kWh kWh 퐸 = × 1.3 × 365 ≈ 7years × 474.5 ≈ 3 321.5 kWh (4.19) 푡표푡푎푙 365 day year

The equivalent cost of the energy (considering for the real cost of energy, a factor of 5) during the lifetime of the system may be calculated as:

€ 퐸푛푒푟푔푦 푐표푠푡푡표푡푎푙 = 퐸푡표푡푎푙[kWh] × 5 × 푡푎푟푖푓푓 [ ] kWh (4.20) = 3 321.5 × 5 × 0.0265 = 440.10 €

The price of energy in Angola is very low and therefore to spend on energy the corresponding amount of the total cost of the system (3000€) it would take many years. However Angola electrical tariff covers only 20% of system costs and will increase in the future [36]. It is worth noticing that there are additional costs associated with the construction of the non-existent power grid in rural zones. The cost of energy is much higher than € 440 over 7 years in service. Informally, the price by kilometre for a high voltage line is approximately one million euros, cost avoided with an autonomous systems.

To conclude, we should keep in mind that systems of this type are indicated to meet critical local needs and their costs should be subsidized by local governments to offer the people better living conditions.

4.11 Conclusions

This chapter exposes the several possible calculation procedures to project the photovoltaic system for Luena zone in Angola. In this case the maximum daily energy calculation is used to project correctly the needed PV production power, batteries and inverter. The best way to correctly project this type of systems is to measure the average load consume once the nominal power of the equipment is typically under the real power. Then, the estimation of the average daily radiation is very important. Some tools may be used to this, like PVGIS web application, which is based on several years of data. Making measurements on site is a more accurate and reliable estimation method, which should be done whenever as possible, to improve the project process. The project should always be done by the worst case scenario using the lowest monthly irradiance.

All the equipment was chosen according to the project and, at the same time, the available equipment gently provided by Resul – Energy Equipments, S.A. (solar panels and DC cables), Hager, S.A (DC fuse) and acquired by the Department of Energy.

In economic terms, it makes no sense to use the usual economic indicators (NPV, IRR and payback period) for isolated systems, due to the fact that there is no direct sale of electricity to consumers and consequently an annual gross revenue. This type of systems may not be considered investments with a return period, but rather providers of better living conditions of the populations in rural areas. The cost of energy is very low, due to the hydric generation. It is therefore much cheaper to buy the same amount of energy to the energy supplier. It would be necessary to study more deeply the grid network/infrastructures costs to effectively evaluate the economic potential of such a system.

5 Experimental Results

This chapter shows a comparison of experimental results in balanced and unbalanced conditions, various irradiance values, and also the power transit and battery bank energy measured during the operation of the autonomous photovoltaic system connected to the loads.

To analyse the viability of the autonomous system, it is necessary to check some system details as: 1) Determine the amount of energy needs in a daily basis to feed the loads; 2) Verify the effective energy available in the battery pack; 3) Check the energy supplied daily by the solar energy conversion system (PV panels).

5.1 Electrical parameters measurement

To study the PV system behaviour over time, it was necessary to store its main electrical variables. These consisted of voltage, current, and power that was generated and also consumed.

Voltage data logging was performed by a low cost NI USB-6008/6009 DAQ® and is described in more detail in Appendix 8.5.1. The sampling rate 푓푠, used in this study was 1푠푎푚푝푙푒⁄푚푖푛 ≈ 16.7 mHz. The NI USB-6008 has 14 bits to perform the analog to digital conversion in differential mode and the USB-6009 has 16 bits corresponding to a system noise of 1.47mV and 0.37mV respectively (Appendix 8.1). In this test the numbering of the cells, from 1 to 8 is in concordance with the convention of the BMS manual. Thus, the cell 1 refers to the cell that connects the negative pole of the battery pack to the inverter and cell 8 the positive pole.

The electric current logging was done using a LEM LA-25-NP transducer (Appendix 8.2) to reduce the losses of the measurement. The procedure is described in detail in Appendix 8.5.2. The logging of the temperature of the cells was performed using a ©Tiny Tag bound to the PV surface (Appendix 8.14).

The logging data consists of:  Voltage of the panels after the 50m cables (the parallel of the panels is done after the 50m to reduce the current in each circuit);  Output current of the panels;  Individual cell’s voltage (8 cells);  Battery pack voltage;  AC voltage at the load terminals;  AC current at the load terminal.

5.2 The Autonomous PV Experimental Set-up

Figure 5.1 shows the major components of the PV experimental arrangement installed according to the diagram of Figure 2.3 with AC loads only. The battery pack is installed at the bottom of the experimental

63 bench (bottom in Figure 5.1 a) and is connected to a relay (number 5 on Figure 5.1 b) which is controlled by the BMS controller (number 6). The relay is connected to the PV panels and the inverter (number 4). The BMS uses a current sensor (7) to measure the current going in and out of the battery pack. The PV panel’s circuit is protected by a 25A DC fuse (2) and may be manually switched on/off by a DC switch (3). Also visible in Figure 5.1(b) are the DAQ's that perform data logging of the voltages of the system (1).

a) b) Figure 5.1 - a) Autonomous PV system testing bench and b) system components

Figure 5.2 shows a closer look at the 8 cells forming the battery pack and its BMS boards on the top of each one. The mains are the black (- pole) and green (+ pole) cables on the bottom of the image. Each cell is connected to a DAQ differential channel and the BMS boards are connected to each other in a separate circuit from the battery pack.

Figure 5.2 - Battery pack and BMS monitoring boards

5.3 Initial Charging of the Cells

Without the initial individual charging, as described in section 3.3.3, an unbalanced situation may occur between the batteries cells. Figure 5.3 illustrates a partial discharge test comparison between the battery pack voltage without (Figure 5.3 a) and with initial charge balancing (Figure 5.3 b) on a constant resistive load of 6Ω (25.5 V⁄6 Ω = 4.25 A = 0.06C average current). The battery voltage in both figures starts at 26.15V, the cell’s temperature was 15ºC and the test was done until the BMS detected a voltage of 2.7V in one cell, opening the load relay and protecting the “weakest” cell. The initial individual charging or top balancing was done using the procedure described in section 3.3.3.

26.5 26.5

26 26

25.5 25.5

25 25

24.5 24.5

24 24 Voltage [Volts]

Voltage [Volts] 23.5 23.5

23 23

22.5 22.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time [hours] Time [hours] a) b) Figure 5.3 - Battery pack voltage during discharge on a constant resistive load of 6Ω a) without and b) with initial balancing

The dissipated energy should be calculated from the dissipated power in a resistor multiplied by the time interval between samples (one minute), ∆푇푠, in which the power is considered constant:

2 푉 (5.1) 퐸 = 푃푅 × ∆푇푠 = 푉 × 퐼 × ∆푇푠 = ⁄푅 × ∆푇푠

Figure 5.3 b) shows that with the initial balancing the battery pack voltage is more "flat" being more constant compared with figure a), for the same resistance value and a higher voltage the power is higher. There is also a clear gain in the discharge time which allows more energy to be delivered as it can be seen in the following table:

Table 5.1 - Energy of the discharge tests in Figure 5.3(a) - unbalanced and Figure 5.3(b) - balanced cells

Unbalanced cells energy [Wh] Balanced cells energy [Wh]

1351 1539

Figure 5.4 shows a close up of the cell’s voltage for the same previous test in Figure 5.3. After the twelve discharging hours until till the end of the test - fast decay period - the maximum gap voltage was 0.213V

(푉1푠푡 푐푒푙푙 = 2.9184, 푉2푛푑 푐푒푙푙 = 2.7054) with a duration of 14h20m.

3.3 3.3 Cell 1 Cell 1 Cell 8 Cell 2 3.2 3.2

3.1 3.1

3 3

Voltage [Volts] 2.9 Voltage [Volts] 2.9

2.8 2.8

2.7 2.7 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time [hours] Time [hours] a) b) Figure 5.4 - Cell’s voltage during discharge on a resistive load of 6Ω a) without and b) with initial individual charging

It is clear that the cells’ voltages are much closer to each other after the initial individual charging in Figure 5.4(b). Such a high deviation between cell’s voltages in Figure 5.4(a) is a consequence of different cells’ SOC. The previous tests evidence the importance of the initial balancing for the proper work of the cells as a battery pack. As it seen in section 3.3.1, LiFePO4 batteries have a very constant discharge voltage staying close to its nominal value. A balanced pack has a maximum voltage drift of 7mV what is a good indicator for accurate monitoring systems and this influences the available energy and duration of the discharge as seen in Table 5.1. Another key fact is that the fast voltage changing edges of the charge and discharge curve don't have much energy. In this particular example, in Figure 5.3(b) the pack goes from 25.3 to 22.45V (when the 2nd cell almost reached the minimum voltage) in 2.5h, which corresponds to an approximate energy of 235Wh. This is less than 1/15 of the total energy of the battery pack which is calculated below. Additionally, with high charging/discharging currents the batteries’ voltage variation happens very fast at which makes more secure and accurate to actuate the control circuits on the flat part of the charge/discharge curve as seen in section 3.3.1.

To check the real available energy of the battery pack 푊퐵푎푡,푇표푡 ,with its cells top balanced, a discharge on a 3.3 Ω resistor was performed in order to obtain an approximately average current of 8A (26.4 V⁄3.3 Ω = 8 A = 0.06퐶) that is a value near to the current that will enter and exit the battery bank while running as a standalone system. Figure 5.5 shows the battery’s voltage for the test that proceeded continuously for 17h until one of the cells reached a critical voltage of 2.57V (2nd cell) with a cell temperature of 12ºC. The total energy stored in the battery pack was calculated in approximately 3600Wh accordingly to expression (5.1) at 80% DOD (Appendix 8.6), which is higher than the nominal theoretical value of 3328 Wh. The minimum pack voltage with top balancing was 21.5V. Note that the Figure 5.5 axes start at 21V.

24 Voltage [Volts] Voltage 23

21 0 2 4 6 8 10 12 14 16 18 Time [hours]

Figure 5.5 - Discharge at approximate 0.06C current rate or 8A (3.3Ω resistor)

5.4 Bottom vs Top Balancing

The bottom balancing was performed accordingly to the procedure described in 3.4.2.2. The first discharge was done using a resistor connected to each cell and the second using the cell boards (Vbypass=2.56V). The top balancing as seen before, is a complete individual charge of the cells detailed in 3.4.2.3.

3.3 3.3 Cell 8 Cell 1 Cell 2 Cell 2 3.2 3.2

3.1 3.1

3 3

Voltage [Volts] 2.9 Voltage [Volts] 2.9

2.8 2.8

2.7 2.7 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time [hours] Time [hours] a) b) Figure 5.6 - Discharge on a resistive load of 6Ω a) bottom and b) top balancing

As seen in section 3.4.2 which describes both balancing processes, bottom balancing exhibits more close cell’s voltages at the final stage of the discharging. Figure 5.6 shows this differences schematized in Figure 3.16(a) and Figure 3.17(b). Both tests took the same time to discharge the batteries emphasizing the fact that both balancing procedures ensure a good balance of the cells.

To complete the comparison between both methods it is important to access the behaviour of both balancing types during charging. The battery pack was then charged with the same current source after bottom and top balancing. Figure 5.7 a) and b) represents the lowest and highest cell voltage of the battery pack during charging. The use of the same current is important to compare the time of charging and consequently conclude about the energy storage.

3.6

3.5

3.4

3.3

3.2

3.1 Voltage [Volts] 3

2.9

2.8 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time [hours] a) 3.6

3.5

3.4

3.3

3.2

3.1 Voltage [Volts] 3

2.9

2.8 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time [hours] b) Figure 5.7 - Charge at constant current I=6A with a) bottom and b) top balancing

Once again and contrary to what some authors’ reference [48], the charging time is the same (23h) resulting in no energy gains obtained between the two balancing methods. The gap voltage between the cells is higher in top balancing however is very small and reduced by the BMS across the charging cycles, also the curves’ shape is the same what proves that both are accurate methods. The most critical difference is the cells’ voltage at the beginning and end of charge as seen before in the discharging test of Figure 5.6. In the bottom balancing (a), the voltage of the cells is closer and at the end of the charging cycle the gap is higher than on top balancing (b). This makes the choice of the balancing algorithm depend on the application for what the battery pack is destined and the type of control. It is important to notice that in bottom balancing in Figure 5.6(a) and Figure 5.7(a) when one cell reaches the minimum voltage all the cells follow and in top balancing in Figure 5.6(b) and Figure 5.7(b) just the cell with the lowest capacity is damaged. With monitoring boards the system may not operate until the minimum voltage since the monitoring boards power consume will undercharge the batteries in short time damaging the cells to a point of no return.

5.5 The Autonomous PV Run – Lisbon, Portugal

The autonomous PV system essays were performed in March 2015 with two 225W panels (Appendix 8.7) installed on top of the third floor of North tower building at IST (38º44’15.9’’N and 9º08’17.6’’W). The approximate sun's trajectory is shown in Figure 5.8. The solar maximum angle is 48°at 13:00.25 The panels are oriented to the geographical south (7° deviation from south to the west) with an inclination angle of 훽 = 35° (optimal angle generally used in Portugal)26 [7]. For the calculations, it was used the convention of Figure 2.7 (퐴푧푠 = −173°). Due to its location, the PV panels are shaded between 7:00 and 8:30 caused by the building height and after 14:30 caused by the north tower building (located right on the image) which reduces the solar radiation at least 3 hours/day resulting in a test constraint.

Figure 5.8 - PV installation site and sun trajectory in March 2015

This test was done for a load constituted by the refrigerator, TV and lights projected in 4.1 having a daily consume of 1300 Wh and aims to prove the viability of the system.

Figure 5.9 shows in red, the measured solar radiation on a horizontal surface for an almost clear sky working day on 14th March 2015 at the IST meteorological station which is installed on the top of the South Tower where the shading effect after 14:30 does not happen (Appendix 8.13). It also shows in black, the radiation incident on the PV tilted plane (35°) calculated accordingly to the expression (2.11) in section 2.2.3. To simplify the calculations the direct irradiance on the horizontal plane 퐺푏_ℎ표푟푖푧 was substituted by the total horizontal irradiance measured at the IST meteorological station once the diffuse radiation represents less than 10% of the total radiation as seen in 2.2.3. The irradiance is available from 7:00 until 18:30 at the meteorological station. At the PV location the irradiance is similar but is not available from 7:00 to 8:30 and after 14:30 due to the location limitation described before - represented by a grey shadow area on the graph in Figure 5.9. This day particularly had some clouds in the morning which is visible the irradiance from 9:00 to 12:00 and clear sky from 12:00 until the end of the day. The

25 According to the webtool: http://www.sunearthtools.com/dp/tools/pos_sun.php 26 Accordingly to a report by Morse & Czarnecki (1958) the optimally fixed tilt angle is a value 0.9 times the latitude. In Lisbon that is 38º*0.9=34.2º [25]

69 maximum irradiance on the module was 1056 W/m2 at 13:00, an average wind speed of 3.33 m/s, an average ambient temperature of 12ºC and a cells’ temperature of 15ºC [54].

1200 Horiz. Irradiance Module Irradiance 1000

] 2 800

600

400

Irradiance [W/m Irradiance

200

0 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 Time

Figure 5.9 - Total solar irradiance incident on a horizontal (red) and 35º tilted plane (black) on 14th March 2015 with clouds

The solar power is only injected in the batteries when the irradiance is available and voltage of the panels is higher than the voltage of the batteries. The figure below shows the evolution of both voltages during the day. The voltage of the panels depends on the total irradiance incident on the module on 14th March plotted in Figure 5.9. The PV voltage (blue curve) is approximately one volt higher than the battery pack voltage from 8:30 until 14:00 when the sun is hitting the panels. Between 9:00 and 11:00 is visible a decay of the voltage caused by the clouds in this period which consequently reduces the power injected as seen further in Figure 5.12. The peaks seen on the graph after 14:00 o’clock represent the opening of the charging relay when the charging is done and one of the cells voltage is above 3.5 V, remaining open for approximately 10 minutes. Then, the relay closes again connecting the panels when the voltage of the cells goes under 3.35 V. Therefore, the voltage observed is the PV open circuit voltage

(푉푂퐶) of 34V for an approximate 1000W/m² irradiance. After 14:30 the PV voltage is lower than the

70 battery’s voltage once the panels are shaded producing no power. The diode of the panels ensure there is no power flowing from the batteries to the PV.

35 Battery pack 34 PV 33

32 31

Voltage [V] Voltage 29 28

26 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 Time

Figure 5.10 - PV (blue) and battery pack voltage (black) on 14th March 2015

The profile of the loads influences the voltage of the batteries represented in Figure 5.11 which is a closer look to the battery pack voltage curve of Figure 5.10. The variations in the battery’s voltage are caused by the refrigerator. The refrigerator turns on approximately every 15 minutes causing the batteries voltage to drop in order to provide the higher current to start the refrigerator. Meanwhile, the power injected from the panels starts charging the batteries at 8:30 elevating the voltage gradually until one cell reach the maximum voltage and the controller open the circuit at 14:00 for a maximum pack voltage of 27.71V. In this period the panels feed the loads and the exceeding power is used to charge the batteries. After 14:30 the panels inject power no more being the loads feed only by the batteries.

27.5

Voltage [V] Voltage

26.5

26 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 Time

Figure 5.11 - Battery pack voltage on 14th March 2015

The output power and consequently the efficiency of a PV module depends mainly on the total incident irradiance, incidence angle, PV cell temperature (which is a function of the ambient temperature and the

71 wind) and cell’s age. For this reasons the output power was measured to calculate the efficiency and see how it is affected during the day. Beside these factors the output power also depends on the Joule losses in wirings of PV modules that is intrinsic in the injected power in Figure 5.12. The autonomous system efficiency depends additionally on the inverter DC-AC conversion losses (BMS losses are very low and may be neglected) relating the power consumed by the loads over the injected power in the batteries.

In Figure 5.12 is represented the output power of one PV panel on 14th March 2015. This power was calculated using the measured injected power at the battery terminals and the cable losses estimated by expression (3.14). The total power going into the battery is twice this value once there are two PV panels connected in parallel at the testing bench. The sun rises at 7:00 but only after 8:00 the sun’s radiation hits the panels directly. The power decreases with decreasing of the irradiance caused by the shadows of clouds from 9:00 to 10:30. It stabilizes around 10:30 and remains approximately constant until the shadow effect at 14:30 with a maximum of 171 W per panel. Although the irradiance is increasing after 10:30 the power reaches its maximum with a slight decrease over time which happens due to the increase of the temperature of the cells. The same happens with the efficiency as shown below. At 14:00 is the time when the relay actuates after the charging is achieved.

Table 5.2 - Energy and mean daily efficiency of the different components Energy [Wh/day] Efficiency [%] Bat. + BMS + Bat. + System PV Injected in Cable Load Inverter Inverter + (Cables + Bat. production battery losses consume losses BMS + BMS + Inv.) 1693 1600 93 1270 331 79 75

With the batteries full charged at 14:15 the day before (13th March), the system functioned all day and night for the load projected having a daily consume of approximately 1300 Wh as seen in section 0. The charging of the battery pack was achieved in about 6 hours at 14:00. This SOC state was used as the reference point for the estimation of the efficiency. Table 5.2 resumes the energy and mean daily efficiency of the main components of the system. The two panels produced 1693 Wh of 1800 Wh possible in this period (area below the graph of twice the power of the Figure 5.12 until 14:00 plus the energy of the day before from 14:15 to 18:30). The energy produced by the panels was 1693 Wh with 95Wh of losses on the 50 meters cables (5.3%) thus “injecting” 1600 Wh in the batteries. Also 331 Wh were lost on the DC/AC inverter conversion process and stand-by, battery and BMS controller with a mean efficiency of 79.3% (1270 Wh delivered to the load). The mean system efficiency (DC Cables + BMS + Batteries + Inverter) is 75% calculated in terms of energy accordingly to the expression (3.18) considering the energy produced by the panels and the energy consumed by the loads. The typical performance factor used to calculate the output energy for solar systems from the PV module output is usually 85% [14]. This factor does not consider the losses on the cables, batteries, BMS and the stand by consumption of the off-grid inverter once it is used for grid-tied systems not off-grid. This is the reason for the 75% system efficiency obtained. The efficiency may be improved by installing the PV panels closer to the batteries, avoiding the 5% of losses, which was not possible in this experiment. It is

72 estimated that if there were no shading effect the panels could produce more 1000 Wh/day totalizing 2700 Wh available per day.

200

175

150

125

100

Power [W] Power 75

0 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 Time

Figure 5.12 - PV panel output power on 14th March 2015

It is visible that the current starts to be considerably high just after 8:20 when the sun hits the panels on a favourable angle. The PV panel efficiency further represented in Figure 5.13, is calculated accordingly to expression (3.4) using the power injected plotted in Figure 5.12. The area of incidence is constant and the irradiance parameter 퐺 of the equation is the black curve in Figure 5.9 which changes during the day.27 The system has no MPPT so the panels may work in a point where the power is lower than

푃푝.

Before analysing the module efficiency it is important to notice that the manufacturer efficiency of 13.6% is calculated at STC28 accordingly to equation (3.3). The objective of the next figure is to show the influence of the ambient and the photovoltaic cell‘s temperature in the efficiency of the PV panels during the 14th March 2015 day. At the beginning of the day the panels work mainly with diffuse and reflected radiation once the sun rays hit the panels close to 8:30 as seen in Figure 5.12. For this reason the efficiency is not under the assumed conditions of direct radiation making the calculation not valid and is represented by a grey zone on the graph. At this time of the day the cell’s temperature is lower than the ambient temperature increasing gradually when the ambient temperature increases and the panels start producing electrical energy. At the time that the radiation focuses the panels with a considerable power (600 W/m²) its temperature increases considerably to 25ºC being the efficiency 14.7% at 9:00. Between 9:00 and 10:00 the clouds block a considerable part of the direct irradiance making the temperature of the panels decrease (note that the decrease of the temperature of the cells may not result in a higher efficiency once with diffuse radiation the panels have a low efficiency – the radiation is not concentrated). The increase of the efficiency verified at this time of the day is slightly higher than the efficiency of the manufacturer once the clouds make the diffuse radiation component increase

27 Accordingly to PV Panels specifications in 8.7 : 0.991 × 1.665 = 1.65 푚2 28 G=1000 W/m2, module temperature 25ºC, AM=1.5.

73 considerably. This confirms that the calculation process used and described in section 2.2.3 does not work properly for more than 10% diffuse radiation conditions. The diffuse component is summed to the direct component increasing the total incident radiation for a cloudy test conditions study. After 11:00 the system works with clear sky, the temperature of the cells increases to 40ºC, consequence of the increase of the radiation and ambient temperature. This was the maximum temperature of the cell on this day for a 17ºC maximum ambient temperature. It is visible the influence of the wind on the temperature of the cells. After 12:00 de radiation changes gradually being maximum at 13:00 (Figure 5.9), however the temperature of the cells has big fluctuations reflecting the wind cooling effect. This cooling leads to contrary oscillations in the injected power (Figure 5.12) and also efficiency. The average efficiency of the PV panels is 10.8%.

15 50 Ambient Temperature PV Cell Temperature 45 Efficiency 40 35 10 30 25 20

Efficiency [%] Efficiency 5

15 [ºC]Temperature 10 5

0 0 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 Time

Figure 5.13 - PV module temperature and efficiency on 14th March 2015

5.6 Reserve Days

With the load profile projected in section 4.1 (1300 푊ℎ/푑푎푦), the batteries charged, and no energy from the sun the number of reserve days at a 80% DOD may be calculated according to the battery pack energy 푊퐵푎푡,푇표푡, obtained in section 5.3 as:

푊퐵푎푡,푇표푡 3600 푁퐷 = = = 2.77 푑푎푦푠 = 2푑 18ℎ 28 푚푖푛 (5.2) 푊퐷 1300

5.7 Comparison Methods

Although it was not possible to test the system in Lisbon over one year due to the temporal limitation of this work, a mean term analyses may be done. For that it is necessary to call upon the diary and monthly irradiance in the remaining months of the year. The PVGIS provides an estimate of radiation for a clear sky day, for each month of the year at a given slope of the panels. To validate those values, a statistical comparison is made using two statistical tests: the mean bias error (MBE) and the root mean bias error (RMSE). The mean bias error is defined as [13]:

푛 1 푀퐵퐸 = ∑ 퐶 − 푀 (5.3) 푛 푖 푖 푖=1 where n is the number of data pairs in a specific time period, 퐶푖 and 푀푖 are the ith calculated/predicted and measured values. This test provides information on the long-term performance. The lower the MBE the better. A positive MBE indicates an overestimation of the predicted values while a negative MBE indicates an underestimation. A drawback of this test is that over-irradiance of an individual observation will cancel under-irradiance in a separate observation.

The root mean square error is defined as [13]:

푛 1/2 1 푅푀푆퐸 = [ ∑(퐶 − 푀 )2] (5.4) 푛 푖 푖 푖=1

This test provides information on the short-term performance of the correlations by allowing a term-by- term comparison of the actual deviation between the predicted and the measured value; the lower the RMSE the better the accuracy of the predicted values. However, a few large errors in the sum can produce a significant increase in RMSE.

The comparison in Figure 5.14 and Figure 5.15 demonstrates the correlation between the experimental (red) and PVGIS (black) horizontal and tilted irradiance on a clear sky day. The experimental data is the measured GHI on 7th March 2015 at the IST meteorological station (Appendix 8.13). PVGIS irradiance is the average daily global clear-sky irradiance in March, on a horizontal (Figure 5.14) and 35º inclination plane (Figure 5.15) also at IST meteorological station site [26]. The data from PVGIS had to be shifted approximately 50 minutes once it is a monthly mean and the experimental data is particular for 7th March.

1000 Experimental GHI PVGIS GHI 800

]

600

400

Irradiance [W/m 200

0 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 Time

Figure 5.14 - Global horizontal irradiance measured at IST meteorological station (red) and PVGIS global clear- sky irradiance (black)

1200 Calculated from GHI PVGIS 1000

]

2 800

600

400

Irradiance [W/m 200

0 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 Time

Figure 5.15 - Global irradiance incident on the PV panel plane calculated from experimental GHI (red) and PVGIS database (black)

Table 5.3 summarizes the errors obtained for the GHI data in Figure 5.14 and Figure 5.15 respectively.

Table 5.3 - Statistical test results MBE [W/m²] MBE [%] RMSE [W/m²] RMSE [%] Horizontal Irradiance 24.76 5.22 26.71 5.63 Tilted Irradiance -28.62 -4.35 30.61 4.65

The errors values are within an acceptable range. Positive MBE for the horizontal radiation shows that the values predicted by the PVGIS are higher than the experimentally obtained which is confirmed by the position of the two curves in Figure 5.14. Notes that the PVGIS estimative is an average values for a data base over several years opposite to the daily radiation of the experimental data (red). For this reason the radiance values may vary fairly, however the maximum differential between the irradiances of Figure 5.14 is 35 W/m² excluding the "jump" in the data at 17:00h. The MBE negative value for the tilted plane shows that the average differential irradiance is 28 W/m² and the PVGIS value is lower than the value calculated from the horizontal radiation contrary to Figure 5.14. This is due to the fact that PVGIS calculation method considers the diffuse radiation which lowers the estimation, not being however a significant difference as seen in Figure 5.15. The horizontal radiation has a slightly lower MBE and RMSE compared to the inclined plane since the calculation of the radiation in the inclined plane has more variables introducing a progressive error in the data. Although the PVGIS estimate is more accurate for horizontal radiation the irradiance differential on the tilted plane is not significant so this radiation may be consider as a source for further analysis.

5.8 Operation in the remaining months of the year

To ensure the supplying of the loads it is necessary to ensure that the daily photovoltaic production exceeds the consumption throughout the year. This estimation is made considering the area and the average efficiency in the following table according to the values previously obtained in 5.5Error! eference source not found. and the monthly average PVGIS irradiation. The efficiency of the panels takes into account the real effective temperature of the panels, and the system efficiency the inverter+BMS daily standby consumption.

Table 5.4 - Autonomous PV system average technical data

Panel area [m²] Panels total area [m²] PV panels efficiency System efficiency 1,65 3,30 10,80% 80%

According to these values, the minimum daily PV production to ensure the loads consumption is given by: 퐸 1300 푊ℎ 퐸 = 푙표푎푑푠 = = 1625 푊ℎ/푑푎푦 (5.5) 푚푖푛 휂 0.8

7.5 30 Irradiation 7 Temperature 6.5 25

/day] 2 6 20 5.5 5 15 4.5

Temperature [ºC] 4 10

Irradiation [kWh/m 3.5

3 5 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure 5.16 - Monthly global irradiation average and temperature on a 35º tilted plane [26]

The average irradiation on the panel’s plane in March is 5760 Wh/m²/day. It is noticeable in Figure 5.16 that between April and late September the irradiation is greater than this value. In March, once the system reached full charge for several days in a row almost in the limit of the available radiation, at the test site in the months with less radiation and length of day than March the daily charging of the batteries is compromised. However, with the installation in a place without shading, even in the winter sunny days the charging is achieved, once almost more 1000 Wh/day is available. The monthly average temperature follows the tendency of the radiation except between October and January when the operation is more critical. The annual average temperature is 16.3º.

The PV production may be calculated knowing the efficiency of the PV panels multiplied by the irradiation available at the total area of the panels. Examining Table 5.5 it is obvious that for a clear sky day like 14th March 2013 the PV production of 2700wh/day is higher than the PVGIS monthly average

77 of 2053 Wh/day which is 31.5% more. This happens due to the 30 days PVGIS irradiation average that considers the sunny and the cloudy days in the respective month, not just one shinny day. It is also visible that the PV production estimation using the irradiation data is close to the energy experimental value of approximately 2700 Wh/day, which corresponds to a deviation of 2.7%.

Table 5.5 - Monthly average vs 14th March irradiation Estimated from IST meteo PVGIS Autonomous PV (14th March) (14th March) PV Irradiation Irradiation PV production With shadow No shadow production [Wh/m²/day] [Wh/m²/day] [Wh/day] effect [Wh/day] effect [Wh/day] [Wh/day] 5760 2052,88 7372,60 2627,617926 1700 2700

Accordingly to the PVGIS monthly irradiation available per square meter [26], Table 5.6 shows the estimation of the energy delivered to the loads regarding the experimental efficiencies in Table 5.4. The photovoltaic production and the energy available to the loads is calculated using expression (3.4) and, (3.18) respectively.

Table 5.6 - Estimated energy available to the loads Energy on PV Irradiation PV production Energy delivered to Month panels area [Wh/m²/day] [Wh/day] the loads [Wh/day] [Wh/day] Jan 3550 11715 1265 1012 Fev 4700 15510 1675 1340 Mar 5760 19008 2053 1642 Apr 6030 19899 2149 1719 May 6430 21219 2292 1833 Jun 6760 22308 2409 1927 Jul 7060 23298 2516 2013 Aug 7100 23430 2530 2024 Sept 6470 21351 2306 1845 Oct 5260 17358 1875 1500 Nov 4020 13266 1433 1146 Dec 3370 11121 1201 961 Annual 5543 18290 1975 1580

The most critical months in average terms are the lowest irradiation months identified in bold in Table 5.5 once the values are lower than the 1300 Wh/day consume. Note that in this table it is not visible in detail how many days the batteries are at a low load percentage since to do so would it would be necessary a daily analysis or the number of clear sky days. However, this may be estimated in PVGIS for a stand-alone system using the following parameters: PV power 450Wp; battery voltage 24V; capacity 130Ah; discharge cut-off limit 35%; daily consumption 1300 Wh; module inclination 35º and orientation south (0º). The results are shown in Table 5.7.

The result goes in line with the previous conclusions taken to Table 5.6 which showed that the most critical months go from November until February with 50% of the days with the batteries in a lower than 35% SOC state.

Table 5.7 - Percentage of days of full and empty battery [26] Average energy Days with Days with battery Month production per day battery empty full [%] [Wh/day] [%] Jan 1046 29 48 Fev 1255 54 15 Mar 1292 79 5 Apr 1296 84 0 May 1303 90 0 Jun 1301 97 0 Jul 1298 99 0 Aug 1300 96 0 Sept 1296 95 0 Oct 1276 79 3 Nov 1193 31 25 Dec 1039 17 51 Annual 1241

In these months the load profile should be adjusted to the minimum possible (the use of the lights and TV may be reduced) being the refrigerator operation guaranteed during the whole year (Table 4.2). Another possible measure is to manually adjust the angle of the solar panels between November and February to a higher value. In the middle of December the maximum solar angle is 28º29. Thus, the module inclination angle should be perpendicular to the sun rays and adjusted to:

훽표푝푡_푤푖푛푡푒푟 = 90 − 28 ≈ 60° (5.6) reducing to 40, the days of empty battery according to PVGIS.

The temperature of the panels varies approximately in proportion to the ambient temperature in a day with low wind as seen in Figure 5.15. Thus, a 10ºC ambient temperature variation produces about the same variation in temperature of the panels, which results in a change of 0.5% efficiency according to expression (3.7). In Portugal, the temperature range can go beyond 30°C (10º C higher than the temperature on March 14th) what constitutes a minor variation in the experimental efficiency shown in Table 5.4.

5.9 Autonomous PV Run – Luena, Angola

Since it is not possible to make experimental tests in Angola, it is important to compare its radiation with the radiation in Portugal where the system was tested to assess its viability and efficiency. This way, is possible to make an extrapolation of the energy produced in Angola by correcting the real efficiency of the panels to the average ambient temperature in Angola. This adjust method is further used accordingly to expression (3.7). It is necessary to evaluate the photovoltaic solar resource and the ambient temperature conditions of the installation site. Table 5.8 evidences the radiation and mean annual

29 According to the webtool: http://www.sunearthtools.com/dp/tools/pos_sun.php

79 sunshine hours between the two countries. The minimum radiation values correspond to the north and the maximum to the south in both countries. The annual values are based on the map of Figure 5.17 and the daily values on PVGIS database. [26] [55] [56]

Table 5.8 - Radiation comparison between Angola and Portugal (source: PVGIS climate-SAF Europe and Africa maps database 2001-2010) [10, 57, 26] 2 2 2 Countries 퐺퐻퐼 [푘 푊ℎ⁄푚 ⁄푦푒푎푟] 퐺퐻퐼 [푘 푊ℎ⁄푚 ⁄푑푎푦] 퐺푇퐼표푝푡[푘 푊ℎ⁄푚 ⁄푑푎푦] Sunshine hours Angola 1800-2400 4.7 - 6.4 4.7 - 6.8 2000 - 2500 Portugal 1700-2000 4 - 5.3 3.3 - 7 2200 - 300030

The available annual energy on the horizontal plane is higher in Angola besides the lower number of sunshine hours having a slightly higher solar potential. Accordingly to solarGIS maps, the annual energy in Lisbon area is higher than 1700 kWh/m² per year. On the other way, Angola has an annual energy higher than 1800 kWh/m² per year almost in all the country except in the zone north to Luanda (note that the scales in the figures is different). Thus, on average, a system that works all the year in Portugal is expected to work in Angola once the available solar energy per square meter is higher.

c) d) Figure 5.17 - Global horizontal irradiation in a) Angola and b) Portugal [10]

More particularly in Luena city, the values of the irradiation are shown in Table 5.9. Although the higher number of sunshine hours in Lisbon the irradiation in Luena is higher balancing this effect.

30 Collares Pereira, Manuel, Energias renováveis, a opção inadiável, Sociedade Portuguesa de Energia Solar , SPES, 1998

Table 5.9 - Global irradiation in Luena, Angola and Lisbon, Portugal on the horizontal and optimal inclined plane [10, 26, 30] 2 2 2 Location 퐺퐻퐼 [푘 푊ℎ⁄푚 ⁄푦푒푎푟] 퐺푇퐼표푝푡[푘 푊ℎ⁄푚 ⁄푑푎푦] 퐺푇퐼표푝푡[푘 푊ℎ⁄푚 ⁄푦푒푎푟] Sunshine hours Luena 2150 4.7 – 7.3 (β=19°) 2226 (β=19°) 2400 Lisbon 1800 3.3 – 7.1 (β=35°) 2024 (β=35°) 3000

Figure 5.18 represents the monthly average irradiation on both sites evidencing the fact that Luena has a higher solar potential which goes in accordance with the solarGIS map and information on the previous table. The irradiation gap plays a more relevant role between October and January which is favorable to the energy production. The irradiation values are obtained for an optimal inclination angle of 19º in Luena [26].

7.5 Lisbon 7 Luena 6.5

/day] 2 6 5.5 5 4.5 4

Irradiation [kWh/m 3.5

3 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure 5.18 - Monthly average global irradiation on a β=35º plane in Lisbon, Portugal (blue) and β=19º in Luena, Angola (black) [26]

The ambient temperature is higher in Luena almost during all the year accordingly which constitutes a downside to the energy production. Figure 5.19 shows the average temperatures in both locations. The maximum difference between the lowest and highest temperature is 12ºC and as seen in section 3.2.2, a 10ºC temperature gap makes the efficiency decrease by 0.5%. The annual average temperature in Luena is 21.2º opposed to 16.3º in Lisbon (ΔT=5ºC). [26, 30]

30 Lisbon Luena 25

15 Temperature [ºC] 10

5 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure 5.19 - Monthly average temperatures in Lisbon, Portugal (blue) and Luena, Angola (black) [26, 30]

The efficiency variation with ΔT=5ºC is approximately 0.3% accordingly to expression (3.7). Consequently, for the energy production estimation in Table 5.10 the same method and values of Table 5.4 are used except for the efficiency, where 10.5% is considered. Once again, the monthly irradiation values were taken from PVGIS database for Luena location at the optimal angle of 19 degrees. The PV production is calculated multiplying the energy available on the PV panel’s area (3.3 m²) by the panel’s efficiency (10.5%), and the energy delivered to the loads multiplying the PV production by the system efficiency (80%).

Table 5.10 - Estimated energy available to the loads in Luena, Angola

Irradiation Energy on PV panels PV production Energy delivered to Month [Wh/m²/day] area [Wh/day] [Wh/day] the loads [Wh/day] Jan 4890 16137 1694 1356 Fev 5070 16731 1757 1405 Mar 5540 18282 1920 1536 Apr 6290 20757 2180 1744 May 6980 23034 2419 1935 Jun 7040 23232 2439 1952 Jul 7170 23661 2484 1988 Aug 7330 24189 2540 2032 Sept 6850 22605 2374 1899 Oct 6150 20295 2131 1705 Nov 5070 16731 1757 1405 Dec 4730 15609 1639 1311 Annual 6093 20105 2111 1689

On an average basis, even with higher temperatures and a consequent lower efficiency the higher solar potential in Angola leads to better energy production results. Analysing Table 5.10 we might conclude that only January and December are critical with an energy delivered to the loads close to the 1300Wh daily consume, in opposition to the period between November and February in Portugal which leads to a better behaviour. The next table shows the results obtained from PVGIS for a stand-alone system in Luena using the following parameters: PV power 450Wp; battery voltage 24V; capacity 130Ah; discharge cut-off limit 35%; daily consumption 1300 Wh; module inclination 19º and orientation north (180º).

The percentage of days with fully discharged batteries is less than 5% validating (Table 5.11). The highest percentage occurs in December but is far from the 50% Portugal percentage which will produce better results.

Table 5.11 - Percentage of days of full and empty battery [26] Average energy Days with battery Days with empty Month production per day full [%] battery [%] [Wh/day] Jan 1290 68 2 Fev 1301 68 1 Mar 1299 63 3 Apr 1298 91 1 May 1299 97 0 Jun 1300 100 0 Jul 1300 100 0 Aug 1301 99 0 Sept 1294 96 1 Oct 1300 90 1 Nov 1297 65 0 Dec 1291 49 4 Annual 1298

5.10 Conclusions

In this chapter the projected system was tested to study the real behavior, efficiency and parameters of each component. Additionally two types of balancing were analyzed – bottom and top – to understand which is more advantageous to LiFePO4 batteries. The simplification beam radiation method revealed good results for clear sky conditions. Less accuracy is found when the weather conditions are far from clear sky which was already expected. Additionally, the reflected radiation component may be significant at some hours of the day due to the installation constraints, in this case reflected on the building.

The type of balancing should be chose accordingly to the application once both showed the same discharging time. If the system may have periodical maintenance and the user may check the monitor state of the batteries by any means (Ex.: EV’s), bottom balancing is the best option. Bottom balancing requires cheaper electronic systems that only monitor the batteries state instead of balancing (BMS) as the balancing may be yearly performed by a maintenance intervention. On the other hand, if the system is expected to work without maintenance and technical intervention for long periods, a top balancing BMS is the best option. When the battery get fully charged very often which is the case of off-grid systems, top balancing works better once the cells are balanced nearly the high SOC. The disadvantage of BMS systems is the higher probability of reducing batteries’ lifetime due to the regular stand-by energy consumption. The consequences of this effect go beyond the ambit of this work. An autonomous PV system in Angola should have the less maintenance possible and may not be accessible to the user. This requirements make the BMS the only viable option. It provides the balance in every charging cycle with less expended energy in the process over time.

With monitoring boards the system may not operate until the minimum voltage since the monitoring boards power consume will undercharge the batteries in short time damaging the cells to a point of no return. For this reason, a bottom balancing BMS must be projected with a considerable safety voltage margin. The cells should operate in the flat zone of the charging/discharging curve to a minimum voltage of 3.1V (Figure 5.6), this ensures that even with a low battery SOC the control system may be connected enough time until the next solar charging is made.

The experimental tests performed revealed good results for the projected system, the correct charging of the batteries and feed of the loads every day making the PV system works for the consumer daily needs, even with the shadow constrain at the installation site. The consumer’s energy consume requires a minimum PV production of 1625 Wh/day, the excess produced energy charges the batteries. The panels showed an efficiency of 10.8% and the system battery+BMS+inverter an efficiency of 75%. The cable losses seen in section 4.2 revealed to be 5.5% of the energy produced by the panels. This losses obviously depend on the length of the cables and represent a little more than the 3% usually considered for the project in [7]. The number of reserve days of the system is up to two days what gives a good chance to the batteries charge again in a place with good sunshine index. The batteries should be installed in a place as cold as possible to achieve the best batteries’ capacity performance. Portugal has more constrains in the winter than Angola during the rainy season due to Angola’s higher solar potencial.

Both sites require the panels inclination angle adjust during the less favourable months reducing the risk of the system shutdown.

6 Conclusions and Future Prospects

6.1 Conclusions

This paper approached the autonomous energy supply to a typical rural house in Angola. The projected and tested system during the month of March proved to be able to feed the previous specified load with an average consumption of 1300Wh/day. Although March is not the month of the year with the lowest monthly average irradiation in Portugal the measured system efficiency is considered the same all the year. The efficiency of the PV panels obtained experimentally in Portugal was adjusted to the average temperature in Angola, this way, it was made an extrapolation to the monthly irradiation values in Angola. The results showed a good production energy during almost all the year, except in January and December which revealed critical production values of 1356Wh and 1311Wh, respectively. This values are too close to the daily consumed energy and suggests the addition to the system of a 2nd alternative source of energy (wind generator, diesel generator, etc.). Another possible solution to improve performance in the critical months is a manual change of the tilt angle of the panels in order to align them with the sun. Using a β=0º tilt angle the irradiation may be 10% higher according to PVGIS data.

The estimation method of solar direct radiation incident on the plane of the panels (Gb_module) calculated from experimental measurements of radiation in the horizontal plane on site (Gb_horiz), revealed a deviation of about 2.7% from the experimental value. This value shows that the procedure used for the calculation (section 2.2) is suitable for clear sky days. However, this method has the limitation of not working properly when the solar angle is close to zero.

With respect to the batteries, the initial charging revealed to be essential to ensure a long life of the batteries and with a balanced pack (close SOC) it is possible to achieve more energy. In order to keep the balance at levels of millivolts without maintenance over the life of the battery, it is necessary to use a Battery management System (BMS) which should balance the cells near the end of the charging curve. Thus, the balancing is done close to the high charge states in which the batteries should remain as long as possible. Also the control systems are closely related to the performance of the batteries. These systems should consume the lowest power possible, as their use "drains" battery power continuously to supply the installed sensors. This fact will unbalance the batteries faster compared with a system without a battery management system. The Deep of Discharge (DOD) must not exceed 80%

(Vmin> 3.0 V), since if the system is discharged for an extended period, BMS stand-by consumption, although very small, can cause the cells to be exceed the minimum voltage. However, the implications of this idle power have not been verified experimentally once it would be necessary to measure the cells capacity after some years of operation. The stand-by power of ©BMS123 is less than 0.3W (idle current <10mA). The control system had some limitations in reading the output currents of the batteries. Since the inverter voltage input signal is a square wave the current is not a constant DC value. This introduces small errors on the real SOC Coulomb counting estimation method which may lead the controller to open the circuit before the batteries are actually discharged. This may be fixed by calibrating the current sensor offset or ignoring the estimation of SOC that could make the system simpler and cheaper to

87 implement. Nevertheless, the cells’ protection is ensured once the relays open the circuit based on voltage signals which work properly.

On site, the polycrystalline solar panels used showed a daily average efficiency of 10.8% and the total system a 75% efficiency which may be improved about 5%, if the panels are installed at a distance lower than 10m of the battery pack.

Actually, PV modules present a relatively high cost, however its cost have been reducing across the years. In the future, it is expected to observe a growing investment in these systems by developing countries such as Angola. This work was an approach to autonomous PV isolated systems with the objective of clarify and deepen some aspects in the management and control of LiFePO4 battery storage. It is expected to open new opportunities for further investigations which may improve with more detail methods of operation of these systems.

6.2 Future Work

Due to the need for access to energy, environmental concerns and the growing demand for renewable energy, isolated photovoltaic systems should also feel an increase in demand. It is expected that "plug and play" (easy installation) solutions emerge. The controller used in this system has very favorable characteristics to its comprehension and modification that may in the future be improved and compacted in order to integrate and manufacture a system ready easy to install.

For end users, this BMS has features that are not of the most importance to isolated systems. This happens since this BMS was firstly designed to electric vehicles and then integrated in isolated systems. Among this features is the SOC estimation. For isolated systems in rural places, the consumer will not have a computer access the sensors’ readings, so he will not have information on the batteries’ SOC. Thus, a controller of this type may be based only on voltage levels, both switch on/off as well as reconnection voltage. This way, it may be set that the relays are to be reconnected when the predetermined voltage is reach, not the predetermined SOC as it happens actually. The system will be more economical if the electronic boards are pre-programmed to the voltage levels, in LiFePO4 this levels are between 3 to 3.6V.

It would be also interesting to study the batteries’ manufacturing energy cost versus the energy delivered during its lifetime in a more environmental approach. The temperature management is also an important aspect to improve, however this is more relevant with high current applications.

As concluded before, to improve significantly its autonomous capacity, these systems should be integrated with alternative energy sources that allow the supply of the loads not only during the hours of sun but during all day. Wind sources are the ideal solution, this will increase the cost of the installation but decrease the effort of batteries as the loads can be supplied almost exclusively by generation. It would be interesting to analyse the cost benefit of implementing a wind generator, in opposition to increase the solar power production and storage capacity.

The development and continuous improvement of energy sources shows a promising future for these systems making possible to provide electric energy for all.

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8 Appendix

8.1 National Instruments NI-USB6008/9 Data Acquisition Device

8.2 Current Transducer LA-25-NP Datasheet

9 8 7 6

5 y = 5,6026x - 0,0833 4 3

Primary current [A] current Primary 2 1 0 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 Secondary voltage [V]

Figure 8.1 - LA 25-NP current transducer characteristic

8.3 Power Logger Fluke 1735

Model Fluke 1735 Three-Phase Power Logger Memory 3.5MB for measuring data Sample Rate 10.24 kHz V-RMS wye resolution 0.1V Operating Error ±0.5% of measured value +10 digit A-RMS resolution 0.01A

Operating Error ±1% of measured value +10 digit

8.4 Tektronix TDS 2001/2012C Oscilloscope

Brand Tektronix Model TDS 2001/2012C Analog Bandwidth 100MHz Sample Rate 2GS/s Record Length 2.5k Point Analog Channels 2

8.5 Data logging

Data logging is the process of using a computer to collect data through sensors, analyse, save and output the results. Data logging also implies the control of how the computer collects and analyses the data. Data logging is commonly used in scientific experiments and in monitoring systems where there is the need to collect information faster than a human can and in cases where accuracy is essential.

8.5.1 Voltage log

The voltage logging in this work was done using the four National Instruments NI USB-6009 DAQ® input channels and LabVIEW Signal Express software for data acquisition.

The maximum input voltage of the DAQ is 20V (Appendix 8.1). All the signals lower than 20V like the cell’s voltage may be directly connected to the DAQ. The voltage higher than 20V as the PV voltage or the battery bank voltage are read through a voltage divider to decrease the voltage by a 2 times factor.

Figure 8.2 - Connecting a Differential Voltage Signal [NI USB-6008/6009 User Guide]

After the DAQ have been connected the LabVIEW Signal Express or LabVIEW software may be used to log the data. LabView software offers the capabilities of LabView Signal Express but in at a lower and more complex level of interface. For logging purposes Signal Express is more intuitive and has an easy to use interface.

Figure 8.3 - LabVIEW Signal Express Monitor / Record interface

100

The range of the input, type of acquisition, number of samples and frequency of acquisition is defined here. It was used a continuous sample acquisition mode, with a frequency of 1sample/min and a 1440 number of samples. Every time the number of samples is reached after starting the log is saved to a file and it may be used a routine to start a new saving after the previous has finished to save loggings every day for several days in a row.

Figure 8.4 - LabVIEW Signal Express Playback interface

The playback window is where the signals are analysed and exported to Excel or to a text file to be the plotted.

8.5.2 Current log

In order to log the current in high power circuits directly with NI® DAQ an extra resistance is necessary and therefore its voltage can be read. However, with this assembly a considerable energy will be dissipated in the resistor. A better solution is to use a transducer as LEM LA25-NP® to measure the current.

This transducer consists of a u-shaped magnetic core with a primary winding (power circuit) and secondary winding (measure circuit). The magnetic field created by the power circuit circulating in the core changes the position of a moving part and consequently the output of an Op Amp powered by +15/- 15V. This way the sensor provide isolated measurements from the power stage. According to the law of Conservation of Energy, the relationship between the voltage on the primary and secondary in an ideal transformer is given by:

푈1퐼1 = 푈2퐼2 (8.1)

101

For a primary nominal current, 퐼푃푁 = 25 퐴 and primary maximum current, 퐼푃 = 36 퐴, the turns ratio is (according to datasheet 8.2):

푈1 퐾푁 = 푚 = ⁄ = 1/1000 (8.2) 푈2

Substituting (8.2) in (8.1):

퐼2 = 푚 × 퐼1 (8.3)

With a peak current no higher than 36퐴, the sensor works in the linear zone which means that the current and the voltage have a linear relation.

This secondary voltage 푈2 = 푈푆, is the voltage at the terminals of the resistor 푅푀 and can be theoretically calculated using expression (8.4) knowing the secondary current.

푈푆 = 푅푀 × 퐼2 (8.4)

The secondary voltage 푈푆 is logged using the NI-6009 and the primary current may be obtained by the following voltage/current relation substituting (8.3) in (8.4) :

푈푆 퐼1 = (8.5) 푅푀 × 푚

Figure 8.5 - LEM LA25-NP equivalent circuit according to datasheet parameters [58]

To achieve the best relation, the sensor’s experimental characteristic may was obtained measuring several points with a current source connected to the primary of LA-25 NP starting from 0A and reading the secondary’s voltage using the following circuit:

102

M DC 1 A Up Us V

0 V OUT Figure 8.6 - Experimental setup to obtain LA-25 NP characteristic

This leads to the relation between voltage and current:

푉 퐼 [퐴] = 푠 − 0.0833 (8.6) 0.1785

Figure 8.7 - Experimental characteristic test of the LEM LA25-NP

The voltage measured is 0.927 푉 which corresponds to a current of 5.224 A according to the expression (8.1). The current read by the current probe is 5.157 A, giving a 47 mA or a 0.9% current error.

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8.6 CALB SE130AHA Battery Cell Datasheet

Model name SE130AHA Alternative product marking CSE130AH Nominal voltage 3,3 V Operating voltage under load is 3,0 V Capacity 130 Ah +/- 5% Internal impenetrableness <1 mOhm 1kHz AC Operating voltage min 2.6V - max 3,6 V At 80% DOD Discharging cut-off voltage 2.5 V The cells is damaged if voltage drops Charging cut-off voltage 3,65 V The cells is dbaemloawg edthi sif lveovlelta ge exceeds Recommended charging - this level discharging Current 39 A 0,3C Maximum short-time discharging current 1000 A 10C period = 10s Life cycles 2000 0,3C 80% DDC Operating thermal ambient - charging 0°C ~ 45°C High risk of damaged cells if out of these Operating thermal ambient - ranges discharging -20°C ~ 55°C Storage thermal Ambient -20°C ~ 45°C Shell Material Plastic Flame retardants Dimensions 182 x 56 x 278 mm Millimetres (tolerance +/- 1 mm) Weight 4,4 kg Kilograms (tolerance +/- 100 g)

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8.7 Suntech polycrystalline STP225 – 20/Wd PV panels Specifications

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Solar Cell Electrical Model

The simplified electrical model of a solar cell (Figure 8.8 a) is the 3 parameters model (1M3P), which are: 퐼푃푉 the illumination current associated to the photoelectric effect, 퐼0 the reverse bias saturation current for the diode and 푚 the diode ideality factor. The p-n junction is represented by a diode in parallel with the current source which depends on the voltage at the terminals of the cell. A more accurate and realistic model would take into account the influence of contacts - a series resistor Rs - and leakage currents -shunt resistor Rsh (Figure 8.8 b) [4, 59].

I I Rs

ID ID

R V D V sh D

Ipv Ipv

a) b)

Figure 8.8 - Equivalent electrical model of a solar cell a) three parameters and b) five parameters [59]

This is known as the single mechani Regarding the three parameter (ideal) model:

퐼 = 퐼푃푉 − 퐼퐷 (8.7)

푞푉 푚퐾 푇 퐼퐷 = 퐼0 (푒 퐵 − 1) (8.8)

퐼푃푉 ∝ 퐴퐺 (8.9)

−19 where 퐼0 is the reverse bias saturation current for the diode, 푞 = 1.6 × 10 C is the modulus of the −23 electron charge, 푚 is the diode ideality factor, 퐾퐵 = 1.38 × 10 J/K is the Boltzmann constant, 푇 is the absolute temperature of the cell and 푉 the voltage at the terminals of the cell, 퐴 is the area of the cell and 퐺 the solar irradiance. This model tells that the power is proportional to the area of the panels and to the irradiance on the cells.

The I(V) characteristic (Figure 8.9) of a photovoltaic cell exposed to solar light varies accordingly to different solar irradiances, the shaded area is the PV working region.

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G

G G Ipv

Figure 8.9 - Stationary characteristic I(V,G) of a photo-diode exposed to solar light [59]

To better understand the real behaviour of the panels (voltage gaps and shading effects), the five parameters model (1M5P) should be used cell (Figure 8.8 b). This is a more accurate and realistic model which take into account two more parameters: the influence of contacts, using a series resistor Rs, and leakage currents, using a shunt resistor Rsh. For that model:

푞(푉+푅푠퐼) 푉 + 푅 퐼 푚퐾 푇 푠 퐼 = 퐼푃푉 − 퐼퐷 − 퐼푠ℎ = 퐼푃푉 − 퐼0 (푒 퐵 − 1) − (8.10) 푅푠ℎ

Using the short circuit and open circuit (푉 = 0) and after some manipulation of the expressions the relation between the current and the voltage is given by:

푞푅푠퐼푐푐 푅 퐼 푞푅푠퐼푐푐 푚퐾 푇 푠 푐푐 푚퐾 푇 퐼푐푐 = 퐼푃푉 − 퐼0 (푒 퐵 − 1) − ≈ 퐼푃푉 − 퐼0 (푒 퐵 − 1) (8.11) 푅푠ℎ where 퐼푐푐 is the current value when the cell is short circuited (푉 = 0) and the simplification is made knowing that in general 푅푠ℎ ≫ 푅푠.

The open circuit voltage 푉표푐 is the voltage across the diode with 퐼 = 0. For simplicity, the cell open circuit voltage Voc is calculated assuming the ideal characteristics of the solar cell; the accuracy is not much affected by this assumption. Thus using (8.7) and (8.8):

푚퐾퐵푇 퐼푃푉 푉표푐 = ln (1 + ) (8.12) 푞 퐼0

According to the power convention, the power related with the diode is P= - V I. In the PV quadrant of the stationary current-voltage characteristic this value is negative, meaning that in this zone the device is active or, equivalently, the power is delivered by the solar cell and given by:

푞푅푠퐼푐푐 푉 + 푅 퐼 푚퐾 푇 푠 푃 = 푉퐼 = 푉 (퐼푃푉 − 퐼0 (푒 퐵 − 1) − ) (8.13) 푅푠ℎ

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The temperature influence and the solar irradiance may be included in the single model assuming that

푚 is constant, the temperature variation is included in 퐼0 and the variation of the incident irradiance in the parameter 퐼푐푐:

퐺 퐼 (퐺) = 퐼푟 (8.14) 푐푐 푐푐 퐺푟

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8.8 TUV Solar Cable

Section 6mm2 Insulation Thickness 0.90 / 1.10 Overall Diameter 6.8 mm Max Electric resistance 3.39 Ω/km at 20ºC Reactance (at 50 Hz) 0.135 Ω/km

8.9 BMS Off-Grid 123 Electric31

123electric Battery Management System is primarily intended for prismatic LiFePO4-cells, but can also be adapted by the end-user for other cells like Li-Ion and LiPo in the range of 2V to 5V. It measures each cell voltage and temperature (thermal management) and computes this parameters to calculate the SOC of the battery pack. Balancing is done during charging only.

123electric BMS is designed for battery-packs that have many cells in series, to form a high voltage battery-pack. Each cell is equipped with a small BMS-board that monitors cell parameters like current, voltage and bypass-current and communicates over a one-wire interface with the BMS-controller. Once the software values are loaded to the microcontroller it is not required a permanent connection to the computer to operate the system. This BMS-controller collects this data, and displays that via a USB- interface on a Windows Computer.

Supply-voltage of BMS-controller 8-60 Volt Idle current of the BMS-controller (including the < 10 mA current sensor) Number of cells 2 - 255 Balancing current 1 Amp. Idle-current BMS-board < 100 uA Current-sensor 100 Amp. A/D-resolution 1024 steps ( 10 bit ) Cell-voltage in steps of 0,01 Volt ( 2,00 – 5,00 V ) Cell-temperature in steps of 1 degree ( -40 to 99 Celsius ) Scan-time per cell 0,015 Seconds

System structure  Consumer relay (Max. 60 Ampere DC)  Current Sensor used (100A)  Charge relay (Max. 60 Ampere DC)  Cell Capacity (10 - 999 Ah)  Voltmeter  Real Time Clock (24 h)

31 http://www.123electric.nl/uploads/file/BMS_EV_Manual_v1_3.pdf

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 Consumers start time  Minimum Cell Temperature (error-level)  Consumers stop time  Maximum Cell Temperature (error-level)  Minimum Cell Voltage (error-level)  Gauge linearization (for current- and  Maximum Cell Voltage (error-level) capacity- gauge)  Bypass Voltage (balancing voltage)  Current-scale selection  Recharge Voltage

Control Conditions  Charge Relay - The incoming charge current will be blocked through the relay when the battery pack capacity is 100% SOC, and switches on again if the capacity is below the programmable “Charge restart”.  Consumers Relay - The consumers will be switch off if the battery pack capacity is 0% or one of the cells goes below the programmable minimum cell voltage, and switches on again if the capacity is above the programmable “Discharge restart”.

SOC estimation The system sets the coulomb counter to 100% when either all cells get to V-bypass or one cell reaches V-max (values may be changed on the software) using the couloumb counting method which updates the capacity of the cell in each iteration.

BMS software – parameters settings

a) b) Figure 8.10 – BMS 123 a) dashboard and b) system settings

On the BMS software, the readings of the sensors may be observed (battery pack current of 0A, SOC of 91%, battery pack voltage of 26.7V, minimum and maximum cell voltage, 3.33V and 3.34V respectively and temperature, both 21ºC. In this case both relays are connected (green symbols in Figure a). The voltage and temperature levels, the charge/discharge capacity and stop and start time that actuate the controllable relays may be set in the software window of system settings (Figure 8.10 b). The voltage levels will define what will be the DOD of the discharge which should not be higher than 80% (approximately 3.1 to 3.55V).

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8.10 Livre Pure Sine wave Inverter 1500W

Nominal Power Pn=1500W Peak Power 2xPn=3000 W Pstand-by 7W (tested) DC input voltage 12V, 24V or 48V Vmin (cut-off) 10.5V± 0.5V, 21V±1V, 42V±2V Vmax (cut-off) 15V± 0.5V, 30V±1V, 60V±2V

Output voltage 220V Output frequency 50Hz THD <3% USB Output DC 5V +/-5% 500mA Notes External fuse

Protection Overheat, Low-High voltage, Short-Circuit, Polarity Certificates CE, ISO9001, RoHS

Experimental Efficiency Characteristic Procedure To measure the real characteristic of the inverter it was set an experiment with a 1000W DC power supply (Figure 8.11 a) and a resistive load (Figure 8.11 b). This power supply was used to test the high and low voltage alarms and switch off voltage which were in accordance to the datasheet. The resistance was changed from 517 Ohm to 62.2 Ohms and the DC and AC powered were measured to plot the real efficiency curve.

a) b)

Figure 8.11 - Inverter characteristic with a resistive load

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8.11 KENTT 201E Refrigerator Datasheet

Type 200 Model 201 E Gross Capacity 200 l Available Capacity 179 l Freezer Capacity 14 l Voltage (frequency) 230V (50Hz) Suction/Pressure 10/30 bar Power 90 W

Kentt 201E uses a SOKO HEKOM AE 1336A compressor made in Yugoslavia.

The refrigerator is constituted by a start-up winding to create a flux 90º in space relatively to the main winding and supplied by a current with a 90º offset in time, Îaux (Figure 8.12 b). This phase offset difference is obtain through a resistor, an inductance or a condenser in series with the starting winding which is disconnected after the motor has started (Figure 8.12 a).

a) b)

Figure 8.12 - Capacitor-start motor a) connections and b) phasor diagram at starting [60]

The single phase induction motor may be seen as one stator winding and two imaginary rotor windings. One rotor is rotating in forward direction (direction of rotating magnetic field) with slip s, while other is rotating in backward direction (direction of oppositely rotating magnetic field), with slip 2 - s. The oppositely rotating mmfs have the same magnitude. The equivalent circuit of a single-phase induction motor is the circuit in next figure:

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Figure 8.13 - Single-phase equivalent circuit with core losses [61]

The upper part of the circuit represents the forward-moving and the lower part the backward mmf.

퐸퐹 – voltage associated with the forward mmf

퐸퐵 – voltage associated with the forward mmf

퐸 = 퐸퐹 + 퐸퐵 – voltage applied to the stator

푟1 푎푛푑 푗푥1 – stator resistance and stator leakage reactance

푟2 푎푛푑 푗푥2 – rotor resistance and rotor leakage reactance referred to the stator

2푅푚 – total resistance of the winding, friction and iron losses

2푗푋푚 – total magnetizing reactance 푠 – slip

푍̅̅1̅ = 2푟1 + 2푗푥1 – total stator impedance

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8.12 Sony KV-14LT1E 13’’ Color TV Datasheet

TV System B/G/H PAL; SECAM, NTSC 3.58, 4.43 Colour System (only video in) VHF E2-E12 UHF E21-E69 Channels CATV S1-S20 HYPER S21-S41 1 x 6W (musical) Sound 1 x 3W (RMS mono) Weight 11.5 Kg

Energy consumption 42 W Standby consumption ≤0.55 W Dimensions 393 x 358 x 415 mm

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8.13 IST Meteorological station

The IST meteorological station is located at Latitude 38.736º, Longitude -9.138º, Altitude 90m (+49m) on the top of south tower and is equipped with a CR10X data logger from Campbell Scientific, Inc. The station records in 5 min time period the data is constituted by32: 1. Air temperature [ºC]; 2. Real fell temperature [ºC]; 3. Relative humidity [%]; 4. Wind velocity [km/h]; 5. Wind direction; 6. Precipitation [mm]; 7. Air pressure [hPa]; 8. Total solar irradiance on a horizontal plane [W/m²].

8.14 Temperature Logger Tiny Tag Talk 2 – TK-4014

©Tinytag Talk 2s is a compact, lightweight, economical logger housed in a 35mm film canister. With ©Tinytag Explorer Software all the data may be analysed, stored and exported. Reading range -40ºC to +85ºC Sensor type 10K NTC Thermistor (internally mounted) Total Reading 16 000 readings Capacity Reading resolution 0.05ºC or better Logging interval 1sec to 10 days Stop options When full After n readings Never (overwrite oldest data)

8.15 Economic Evaluation Indicators

To understand if an investment is worth it is important to study its economic viability. Some of the indicators regularly used are presented below. It is more correct to refer this indicators as previsions once the future is always unknown. The solar panels and batteries are expensive compared to diesel generators however PV panels require less maintenance and have a long lifetime. A system initially more expensive may prove to be more economical at the end of its lifetime requiring a study more detailed.

8.15.1 Net Present Value (NPV)

Net present value is a calculation used to determine the present value of an investment by the discounted sum of all cash flows (monetary flux) received from the project. In other words, the amount

32 IST Institutional meteorological station website: http://meteo.ist.utl.pt/odata-now

115 invested is compared to the future cash amounts after they are discounted by a specified rate of return where the period of time corresponds to the life time of the system in study. In the simplified model assumptions: all the investment at t=0, the annual utilization of the installed capacity is constant and equal to ℎ푎, the operation and maintenance expenses during the lifetime are constant and equal to 푂&푀, there are no expenses with fuel and others or they are included in 푂&푀 expenses [4].

푛 푅퐿 푁푃푉 = −퐼 + ∑ 푗 (8.15) 표 (1 + 푎)푡 푡=1

where 퐼표 is the initial investment, 푛 is the lifetime of the project, 푅퐿푗 is the total income for each year which is given by the income subtracted to the 푂&푀 expenses and 푎 is the rate of return.

The decision based on the NPV is done according to the following conditions:  NPV<0 – the investment is not returned, once the project should be rejected;  NPV=0 – the investment is returned exactly at a rate of return 푎 that allows the investor to pay its initial investment, however there is no profits;  NPV>0 – the investment is returned at a given rate of return 푎 and generates profits equal to the NPV making the project attractive.

8.15.2 Internal Rate of Return (IRR)

The internal rate of return is the rate of return that makes the NPV equal to zero, in other words the project allows to return the investment [4].

푛 푛−1 퐸푥푝푙표푟푎푡푖표푛 푐푎푠ℎ푓푙표푤 퐼푛푣푒푠푡푚푒푛푡 푐푎푠ℎ푓푙표푤 ∑ − ∑ = 0 ⇔ (1 + 퐼퐼푅)푗 (1 + 퐼퐼푅)푗 푗=1 푗=0 (8.16) 푛 푛−1 푅퐿 퐼 ∑ 푗 − ∑ 푗 = 0 (1 + 퐼퐼푅)푗 (1 + 퐼퐼푅)푗 푗=1 푗=0

The IRR measures the interest of the project on the financial market evaluation scale what does not happen with the previous indicators. If the IRR is higher than the rate of return considered in the NPV calculation means that the project generates a profitability higher than the opportunity capital cost. In this situation the project should be economically viable.

8.15.3 Payback Period

The payback period is the time (years) necessary to return the investment during the exploration of the project. It more elaborated than the payback calculation. An approximate way to calculate the payback period is to consider the annual mean income during the lifetime of the project. In this case the formula is given by [4]:

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퐼 ∑푛−1 푗 퐼푛푣푒푠푡푚푒푛푡 푐푎푠ℎ푓푙표푤 푗=0 (1 + 푎)푗 푃푎푦푏푎푐푘 푃푒푟푖표푑 = = 퐸푥푝푙표푟푎푡푖표푛 푐푎푠ℎ푓푙표푤 푅 ∑푛 푛 퐿푗 푗=1 (1 + 푎)푗 ∑푗=1 푗 (1 + 푎) 푛 푛 ( ) (8.17) 퐼 ≅ 푡 푅 푛 퐿푗 ∑푗=1 푗 (1 + 푎) 푛 ( ) The project is accepted when the payback period is shorter than its lifetime. In a photovoltaic project connected to the grid, the payback period is usually between the 6 to 8 years of exploration.

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