Institute of Electrical Power Systems Power Electrical Institute of September September Dipl. Univ. Supervisor Arranz iLópez Irene A self system for of agrid Design and simulation M aster - - Ing. Mike Alexander Mike Ing. Prof. DDipl. ’s -
T 2020 consumption hesis
- by Ing. Ing.
- Dr.techn. Robert Schürhuber Robert Dr.techn. connected PV
Lagler
© fotopro - Design and simulation of a grid-connected PV system for self-consumption
Graz University of Technology Institute of Electric Power Systems Inffeldgasse 18/I 8010 Graz Austria
Head of Institute Univ.-Prof. DDipl.-Ing. Dr.techn. Robert Schürhuber
Supervisor Univ.-Prof. DDipl.-Ing. Dr.techn. Robert Schürhuber Dipl.-Ing. Mike Alexander Lagler
A Master’s Thesis by Irene Arranz i López
September 2020
II Design and simulation of a grid-connected PV system for self-consumption
Statutory Declaration
I declare that I have authored this thesis independently, that I have not used other than the declared sources / resources, and that I have explicitly marked all material which has been quoted either literally or by content from the used sources.
Graz, 15-08-2020
Irene Arranz i López
III Design and simulation of a grid-connected PV system for self-consumption
Acknowledgements
This thesis is the end to a Master’s Degree, and it is as well a representation of a whole experience abroad. Foremost, I would like to pay my special regards to my thesis tutor at TU Graz, Mike Lagler. I would like to express my sincere gratitude to him for his feedback, help and support during the development of the project in the extraordinary circumstances of a global health emergency.
I would like to thank everybody who participated in either a direct or indirect way in my work, making it easier and more enjoyable with their encouragement. I am truly grateful to all the people I have met in Graz and with whom I have created the most marvellous memories. I must give special thanks to Javi, for his unconditional care and for always having my back. To Ada, for motivating me to leave Barcelona and embarking on such a journey. To Silvia, for showing me the right way to do things, and to Kimchi, for his inspiration.
At last, but not least, I would like to thank my family for their commitment to my education, and their continuous assistance and guidance, even from the distance, as this would not have been possible without them.
IV Design and simulation of a grid-connected PV system for self-consumption
Abstract
Although Spain is one of the countries with the highest incidence of solar irradiance in Europe, in many areas of the country PV technology is not fully deployed. This thesis is focused on designing and assessing through a simulation software the performance of a grid-connected PV system for self- consumption installed on a building’s rooftop in a location with a high solar potential unused.
An in-depth search on photovoltaic literature was made in order to gain information on the field, as well as on the grid code requirements in both Europe and Spain. Then, a prospection to find the proper location for the installation was done. Afterwards, a load profile was created to know the building’s energy demand, and finally the technology to implement was chosen and sized. With these premises, a CAD 3D model of the building and surrounding elements was implemented into a simulation software (PVsyst). This allowed to create the PV layout, to find the most accurate values for the parameters to optimize the performance of the system (tilt angle, azimuth, and row spacing), and to develop a shading and loss analysis. The first scenarios were further refined with an additional simulation which took into account a storage system, providing a final scenario. Finally, an economic study was performed.
The system renders an annual energy production of 20,38 MWh/year, an annual specific yield of 1.742 kWh/kWp with a performance ratio of 79,3%, which cover the household’s demand with an estimate saving of 2.635,8 €/a and 3409 tCO2/a emitted to the atmosphere. The study showed the system to be effective and economically viable and profitable, and also provides a design guide for grid-connected PV systems for self-consumption.
V Design and simulation of a grid-connected PV system for self-consumption
List of Symbols
α Elevation angle
β Tilt angle
δ Declination angle
η Efficiency
θ Azimuth angle
λ Temperature coefficient for open-circuit voltage
µ Imbalance degree
σ Temperature coefficient for short-circuit current
ϕ Zenith angle
Azc Azimuth correction angle
c표푠휑 Power factor
List of Abbreviations
AM Air Mass
Bn Direct normal radiation
CAD Computer-aided design
CAPEX Capital Expenditure
CdTe Cadmium Telluride
CO2 Carbon Dioxide
CSV Comma-separated values
DOD Depth of Discharge
EVA Ethyl vinyl acetate
VI Design and simulation of a grid-connected PV system for self-consumption
FF Fill Factor
G Global solar radiation
Gb Direct radiation
GCR Ground Coverage Ratio
Gd / Dh Diffuse radiation
Gh Global horizontal radiation
Gr Reflected radiation
GSC Solar constant
IAM Incidence angle modifier
IEC International Electrotechnical Commission
ISC Short-circuit current
LCOE Levelized Cost Of Energy
MPP Maximum Power Point
MPTT Maximum Power Point Tracker
NOCT Nominal Operating Cell Temperature
O&M Operations and Maintenance
OPEX Operational Expenditure
PR Performance Ratio
PV Photovoltaic
PVGIS Photovoltaic Geographic Information System
RD Royal Decree
REE Red Eléctrica de España
SE/SW South East/South West
SOC State of Charge
STC Standard Test Conditions
VII Design and simulation of a grid-connected PV system for self-consumption
TSO Transmission System Operator
UV Ultraviolet
VOC Open-circuit voltage
Wp Watt Peak
VIII Design and simulation of a grid-connected PV system for self-consumption
Table of Contents
Introduction ...... 1
Objectives ...... 3
Methodology and project scope ...... 4
Theoretical background ...... 5
4.1 Solar radiation ...... 5
4.2 Atmospheric phenomena ...... 5
4.3 Air Mass (AM) ...... 5
4.4 Position of the sun ...... 6
Photovoltaics fundamentals ...... 8
5.1 Solar PV modules ...... 9
5.1.1 Orientation of the PV modules ...... 9
5.1.2 Electrical configuration of modules ...... 10
5.1.3 Parameters and electric properties ...... 11
5.1.3.1 Open-circuit voltage ...... 11
5.1.3.2 Short-circuit current ...... 12
5.1.3.3 Characteristic IV curve...... 12
5.1.3.4 Fill factor ...... 13
5.1.3.5 Cell’s efficiency ...... 13
5.1.4 Effects of temperature and irradiance ...... 13
5.1.5 Mismatch effects ...... 14
5.1.5.1 Hotspots ...... 14
5.1.5.2 Shading ...... 14
5.1.6 Technology on PV panels ...... 15
5.1.6.1 Silicon-based solar cells ...... 16
5.1.6.2 Thin-film technology...... 17
5.1.6.3 Multijunction technology ...... 21
5.2 Inverters ...... 21
IX Design and simulation of a grid-connected PV system for self-consumption
European Grid Code ...... 24
6.1 Frequency and stability requirements...... 24
6.2 Limited Frequency Sensitive Mode - Overfrequency (LFSM-O) ...... 25
6.3 Admissible active power reduction ...... 26
6.4 Active power cessation ...... 27
6.5 Reactive power output and voltage control ...... 27
6.6 Automatic connection to the network ...... 27
6.7 Fault-ride-through capability ...... 28
6.8 System restoration capability ...... 29
6.9 Electrical protection schemes and settings ...... 30
Spanish Grid Code ...... 31
7.1 Exchange conditions...... 32
7.1.1 Product quality ...... 32
7.1.2 Exchanged power ...... 32
7.1.3 Electromagnetic disturbance limits ...... 32
7.1.4 Planification levels ...... 33
7.2 Imbalance situations ...... 34
7.3 Frequency variations ...... 34
7.4 Protection system for devices ...... 34
7.5 Power equipment for connections with the grid ...... 35
Design and sizing of the PV system ...... 36
8.1 Site identification ...... 36
8.2 Building studied ...... 41
8.3 Load profiles of the building analysed ...... 43
8.4 Technology selection ...... 48
8.4.1 PV modules ...... 48
8.4.2 Solar Inverter ...... 50
8.5 Voltage dimensions ...... 51
8.5.1 Maximum open-circuit voltage ...... 52
8.5.2 Minimum MPP voltage ...... 53
8.5.3 Maximum PV module current ...... 53
X Design and simulation of a grid-connected PV system for self-consumption
8.6 String limit sizing ...... 54
8.6.1 Maximum number of PV modules per string ...... 54
8.6.2 Minimum number of PV modules per string ...... 54
8.6.3 Maximum and minimum string voltage ...... 55
8.7 Energy output estimation ...... 56
Modelling and simulation of the PV system ...... 58
9.1 Software ...... 58
9.2 Design process ...... 58
9.2.1 Location and climate data ...... 58
9.2.2 System components ...... 59
9.2.3 Module tilt and orientation ...... 60
9.2.4 Row spacing ...... 63
9.2.5 3D Modelling ...... 65
9.2.6 Module layout and near shadings ...... 67
9.2.7 Detailed losses ...... 70
9.2.8 Self-consumption ...... 71
9.2.9 Horizon ...... 72
9.3 Simulation scenarios...... 72
Results ...... 75
Implementation of a storage system ...... 81
Economic analysis ...... 90
Conclusions ...... 94
Bibliography ...... 97
15 Appendix ...... 102
15.1 Datasheets ...... 102
15.1.1 FS-6450 ...... 103
15.1.2 Sofar 12KTL-X ...... 105
15.1.3 LG Chem RESU13 ...... 106
XI Design and simulation of a grid-connected PV system for self-consumption
15.2 Simulation reports ...... 107
15.2.1 Scenario A ...... 107
15.2.2 Scenario B ...... 113
15.2.3 Scenario C ...... 119
15.2.4 Scenario D ...... 125
15.2.5 Scenario E ...... 131
15.2.6 Scenario F ...... 137
15.2.7 Scenario G ...... 143
15.2.8 Scenario H ...... 149
15.2.9 Scenario SS ...... 155
15.3 Economic analysis ...... 161
XII Design and simulation of a grid-connected PV system for self-consumption
List of figures
Figure 1. Representation of air mass spectrum in the Earth’s atmosphere [9] ...... 6
Figure 2. Angles considered for solar orientation [84] ...... 7
Figure 3. P-N junction of a semiconductor [13] ...... 8
Figure 4. Electrical configurations of solar cells [18] ...... 10
Figure 5. Comparison of the I-V curves depending on the electrical configuration of the modules [19]11
Figure 6. Representation of the ideal PV cell as an equivalent circuit [20] ...... 11
Figure 7. Current-voltage curve and Power-voltage curve of a solar cell [14] ...... 12
Figure 8. Scheme of a shaded cell on a series, cause of a hotspot [21] ...... 14
Figure 9. Diodes configuration in panels connected in series and parallel [22] ...... 15
Figure 10. Global market share by PV technologies (1999-2009) [23] ...... 16
Figure 11. Percentage of global PV production regarding thin-film technologies (2016) [23] ...... 18
Figure 12. Microstructure of a CIGS solar cell: Coloured image of cleaved CIGS sample (left), Schematic of the standard structure of a CIGS solar cell (right) [35] ...... 20
Figure 13. Inverter typologies: a) Central inverter, b) String inverter, c) Microinverter, d) Multistring inverter [85] ...... 23
Figure 14. Active power frequency response capability of power-generating modules in LFSM-O [41]
...... 26
Figure 15. Maximum power capability reduction with falling frequency [41] ...... 27
Figure 16. Fault ride-through profile of a power-generating module [41] ...... 29
Figure 17. Typologies of connections to the grid [43] ...... 35
Figure 18. Map of current photovoltaic plants in Spain [46] ...... 36
Figure 19. CTE map of Spain with classified zones regarding the incident irradiance [47] ...... 37
Figure 20. Irradiance map of Spain [48] ...... 38
Figure 21. Location of Linyola in the territory of Catalonia [51] ...... 38
Figure 22. Maximum and minimum daily temperatures for Linyola [49]...... 39
Figure 23. Global solar radiation for Linyola [49]...... 39
Figure 24. Monthly solar irradiation estimates for Linyola (2016) [50] ...... 40
Figure 25. Area of the terrain where building studied is located [51] ...... 42
Figure 26. Available and unavailable areas on the building for the placement of PV modules [51] ..... 42
XIII Design and simulation of a grid-connected PV system for self-consumption
Figure 27. Load profiles of the cars for weekdays and weekends [52] ...... 44
Figure 28. Time distribution for daily activities for each member [52] ...... 45
Figure 29. Device profile on 14.02.2020 [52] ...... 46
Figure 30. Duration curves for the devices on the household [52] ...... 46
Figure 31. Load profile of the household for weekdays and weekends [52] ...... 47
Figure 32. Sum profile of the household during the simulated year [52] ...... 47
Figure 33. Effect of temperature on ISC, VOC and PMAX [56] ...... 52
Figure 34. Relation between GCR and tilt angle of the PV modules [59] ...... 57
Figure 35. Meteorological data introduced on PVsyst [60] ...... 59
Figure 36. Technology and devices data introduced on PVsyst [60] ...... 60
Figure 37. Tilt angle and module orientation introduced on PVsyst for a fixed tilted plane [60] ...... 61
Figure 38. Production graph of different modes of tilting modules [61] ...... 62
Figure 39. Tilt angle and module orientation introduced on PVsyst for a seasonally tilt-adjusted plane
[60] ...... 63
Figure 40. Row spacing between modules on a PV system [63] ...... 63
Figure 41. Sun path chart for Linyola [64] ...... 64
Figure 42. Axonometric projection of the CAD model of the building and surrounding elements [60] .. 66
Figure 43. Overhead projection of the CAD model of the building and surrounding elements [60] ...... 66
Figure 44. Available zones on the building’s rooftop for the installation of the PV system [60] ...... 67
Figure 45. Electrical configuration of a PV module in landscape (left) and portrait (right) position [69] 68
Figure 46. Side projection of the module layout on the rooftop [60]...... 69
Figure 47. Axonometric projection of the module layout on the rooftop [60] ...... 69
Figure 48. Loss graph of the PV modules selected [60] ...... 70
Figure 49. Consumption data of the household introduced on PVsyst [60] ...... 71
Figure 50. Specified monthly energy need of the household [60] ...... 72
Figure 51. Simplified scheme of the grid-connected PV system [60] ...... 73
Figure 52. Iso-shadings diagram for scenario A [60]...... 76
Figure 53. Iso-shadings diagram for scenario B [60]...... 77
Figure 54. Iso-shadings diagram for scenario C [60] ...... 77
Figure 55. Module layout on scenarios G (left) and H (right) [60] ...... 79
Figure 56. Iso-shadings diagram for scenario D [60] ...... 80
XIV Design and simulation of a grid-connected PV system for self-consumption
Figure 57. Graph of monthly production and losses for scenario D [60] ...... 80
Figure 58. Loss diagram for scenario SS [60] ...... 82
Figure 59. Simplified scheme for charging mode [60] ...... 83
Figure 60. Simplified scheme for discharging mode [60] ...... 83
Figure 61. Simplified scheme for direct mode with sufficient irradiance and full charge [60] ...... 84
Figure 62. Simplified scheme for direct mode with insufficient irradiance and no charge [60] ...... 84
Figure 63. Simplified scheme for night mode [60] ...... 84
Figure 64. Graph of battery’s charging and discharging energy for the month of June [60] ...... 86
Figure 65. Graph of battery’s charging and discharging energy for the month of December [60] ...... 86
Figure 66. Comparison graph between battery discharging energy, energy injected or purchased from the grid, and energy supplied to the user for the month of June [60] ...... 87
Figure 67. Comparison graph between battery discharging energy, energy injected or purchased from the grid, and energy supplied to the user for the month of December [60] ...... 88
Figure 68. Loss diagram for scenario SS [60] ...... 89
Figure 69. Saved carbon dioxide emissions of the PV system on scenario SS [60] ...... 93
XV Design and simulation of a grid-connected PV system for self-consumption
List of tables
Table 1. Limits for thresholds for type B,C and D power-generating modules ...... 24
Table 2. Minimum time periods for which a power-generating module has to be capable of operating on different frequencies, deviating from a nominal value, without disconnecting from the network...... 25
Table 3. Parameters for fault ride-through capability of synchronous power-generating modules ...... 28
Table 4. Limits on harmonic voltage for each node of the network ...... 33
Table 5. Planification levels for harmonic voltage on the network ...... 34
Table 6. Meteorological data for Linyola ...... 40
Table 7. Data of the PV modules selected ...... 49
Table 8. Data of the solar inverter selected ...... 50
Table 9. Energy output estimation for the PV installation ...... 58
Table 10. Definition parameters for simulation scenarios A to H ...... 74
Table 11. Definition parameters and simulation results for scenarios A, B and C ...... 75
Table 12. Definition parameters for scenarios D, E and F ...... 78
Table 13. Definition parameters and simulation results for scenarios D, E and F ...... 78
Table 14. Definition parameters and simulation results for scenarios G and H ...... 79
Table 15. Definition parameters and simulation results for scenario SS...... 85
Table 16. CAPEX and OPEX amounts for the PV system ...... 90
Table 17. Energy savings and retributions ...... 91
Table 18. Prices of charging the electric cars in a public charging station ...... 92
Table 19. Main economic results of the 25-year analisys ...... 92
XVI Design and simulation of a grid-connected PV system for self-consumption
Introduction
Energy is a fundamental pillar of human progress. For over two centuries, fossil fuels (coal, and more recently natural gas and oil derivatives) have been the main sources of energy, but as societies and industries develop, the need for energy resources increases. The world’s population is expected to increase to more than 11,2 billion by the end of the century and recently, a mathematical model that combined world population, wealth and oil consumption, estimated that to support the natural global growth of gross domestic product, world energy consumption should increase by approximately 1,7 billion tons of oil equivalent per year by 2025. This means that maintaining an oil energy share of around 33% (2015 levels) would require increasing current oil production by more than 11 million barrels per day [1].
However, fossil resources are not only exhaustible, but also generate emissions of greenhouse gases responsible for climate change that can have devastating and irreversible consequences on the environment. Therefore, the foreseeable increase in energy demand and the depletion of fossil fuels forces humanity to accelerate the transition to a low carbon economy, which requires the search for clean and renewable alternative energies. These include hydropower, wind, biomass, geothermal, and solar energy. All of them are renewable energies, which means that they are naturally replenished and, therefore, inexhaustible. Nonetheless, the amount of energy they produce is limited per unit of time and, on the other hand, not all of these sources are sustainable.
Solar energy is the cleanest and most abundant source of energy of our planet and is also inexhaustible. According to NASA calculations, the Sun still has 6500 million years of life left and, every hour, it throws onto Earth more of the energy necessary to supply the global demand of a whole year. The Earth’s surface receives 120,000 terawatts of solar irradiation, which is 20000 times more power than the entire planet needs [2] and it is calculated that in just 18 days of solar irradiation, the Earth receives an amount of energy equivalent to that accumulated for all the world’s reserves of coal, oil and natural gas [3].
As said, due to its extraordinary potential, solar energy has been the subject of intense research and has undergone spectacular development, especially in recent years, mainly applied to the conversion of solar energy into electrical energy or heat or to production of fuels through an artificial photosynthesis process. Among renewable energies, photovoltaic energy offers some unique advantages that other technologies do not provide:
It is 100% renewable: solar energy will radiate the earth for millions of years. It is sustainable: it does not emit greenhouse gases or any type of pollutant. It has a global availability: it can be used anywhere in the world, reaching places where the power line does not reach. It is sizeable from large plants to domestic installations. Since the photovoltaic panels have no moving parts their maintenance is cheap and simple and does not produce noise pollution.
1 Design and simulation of a grid-connected PV system for self-consumption
Although it has some drawbacks as well:
Requires a high initial investment. The energy produced is variable, since it depends on the geographical location of the installation and the weather conditions. Solar batteries for energy storage are not yet sufficiently developed. Installation requires sufficient space. The efficiency of the panels is limited.
Despite these drawbacks, the photovoltaic solar energy has not stopped evolving, managing to reduce panel prices until they are competitive with conventional sources of electricity generation in some countries, and this way it is foreseeable that in a few years it will become a substantial part of a globally sustainable energy system.
2 Design and simulation of a grid-connected PV system for self-consumption
Objectives
The main aim of this project is to design and simulate a grid-connected PV system installed on a rooftop in Spain that can cover the energy demand of a house through self-consumption, and that can additionally cover the charging of two electric cars. Moreover, other specific goals are set for this study, such as:
Reduce significantly the amount of energy purchased from the grid. Design a PV system that uses cutting-edge technologies for PV modules that are more efficient and have a less pollutant manufacture. Study and design a storage system that can fit the load profiles of the household, and that can help exploit the full potential of the installation, helping to purchase the minimum amount of energy from the grid. Create a self-consuming household that can cut the dependence on big electricity providers that produce energy from non-renewable sources. Implement a sustainable system that can use renewable energy sources and that can contribute to reduce pollution and emissions to the environment. Implement an economically viable and financially profitable PV system. Establish a design and simulation guide for future study lines.
With an average of almost 3,000 hours of sunshine per year, Spain is one of the countries in Europe with the highest number of insolation hours, and is positioned as one of the leading countries in the production of solar energy. The Royal Decree of April 2019, which favours self-consumption abolishing the “Sun tax”, demonstrates the current solid commitment to the use of photovoltaic energy. In fact, the National Integrated Energy and Climate Plan (PNIEC) foresees a total installed capacity of 37 GW of photovoltaic solar energy in 2030 and sets the goal of a 100% renewable electricity sector in 2050.
3 Design and simulation of a grid-connected PV system for self-consumption
Methodology and project scope
The design of the domestic PV plant is divided into different steps. The first one must be taken before starting any design or calculations: it is necessary create a solid theoretical basis of concepts and literature, among which the design can be done. The review of legislation, regulations and grid codes is also an essential point whenever any grid-connected electrical system wants to be brought into reality.
Secondly, the development phase takes place. Details and data are analysed in order to find the best location for the building that can make the most out of the solar potential of the region. The rooftop area of the chosen building is measured, and a usual load profile for the household is drawn out taking into account all the activities carried out by the users and the house devices consuming energy during each hour of the day.
Afterwards, the technology used needs to be chosen, considering new types of modules, prices and quality. By means of the calculation of different parameters, the electrical configuration of the PV modules is defined: voltage sizing, minimum and maximum number of panels per string, number of modules and inverters and a gross estimation of the energy yield produced.
Once an estimated pre-design is done, it can be modelled into the specialized software that will help to simulate the electrical behaviour and performance of the PV system installed at the house. Different scenarios need to be created, with diverse orientations and tilts, as the final design is eventually defined after an iterative process of comparing, discarding and changing parameters on the simulations. Losses due to shadings and electrical connections are also contemplated on this step, which leads finally to the analysis of the best layout, and to the application of a storage system to it, that can optimize the use of the produced energy. This final scenario is then simulated, and from the drawn results, an economic study and a discussion can be made.
However, this project encounters certain limitations that cannot be solved without making simplifications and assumptions. The PV system has been only implemented on a rooftop, without considering facades or other zones that could have a great solar potential. Moreover, aesthetic and architectural details have not been reviewed. Therefore, this study is totally based on efficiency and performance.
It has to be considered as well that the software used is a simplified tool to simulate PV systems, and so there is a minimum error that must be assumed, as losses and other multiple factors are approximations and average values extracted from papers and literature. A PV system by itself is a complex element to study, as it is subject to many open variables (such as cloud movement) which are impossible to define in an absolute realistic way. Additionally, updated meteorological data for 2020 were not available, so older values have been used for the simulations.
4 Design and simulation of a grid-connected PV system for self-consumption
Theoretical background
4.1 Solar radiation
As described elsewhere [4] , the Sun is an element behaving as a blackbody at a temperature of 5778 K. It is an ideal absorber and emitter of a reasonably constant amount of radiation from its surface by means of fusion reactions.
The solar constant, understood as the intensity of sun radiation flux interacting with a unity of surface, whilst being measured outside the terrestrial atmosphere in a perpendicular plane to the sun beams, is
2 considered to have a value of GSC =1367 W/m [5]. It includes all wavelengths of the solar radiation, not only the visible light range. However, this value varies widely when it reaches the atmosphere due to phenomena and interactions that will be further explained in the following sections.
4.2 Atmospheric phenomena
Upon reaching the atmosphere, solar radiation is affected by different major factors that reduce its power and split it. These are radiation absorption (by dust and air molecules), scattering and reflection [6].
As a consequence, solar radiation is divided into three components: direct, diffuse and reflected radiation [7]. Direct radiation (Gb), the most important one in terms of photovoltaic applications, reaches the Earth’s surface without having changed its direction through the atmosphere, so it does not scatter.
Second, diffuse (or scattered) radiation (Gd) undergoes some previous directional changes on its way to the Earth’s surface. The sum of these two types constitutes the global solar radiation (G). Lastly, the reflected radiation (Gr) onto the soil or other elements can also be reabsorbed by other objects.
4.3 Air Mass (AM)
Air mass (Fig. 1) is defined as the ratio of the distance solar radiation travels through Earth’s atmosphere (pathlength) and the distance it would travel if the sun’s beams were directly overhead (shortest pathlength) [5]. This is usually understood as the mass of air solar radiation must travel through to encounter the Earth’s surface. It can be calculated using the formula below (Eq. 1) [8], being ϕ the Sun’s vertical angle or zenith angle:
1 1 퐴𝑖푟 푀푎푠푠 = ≃ (1) cos(휙) + 0.50572 · (96.07995 − 휙)−1,6364 cos(휙)
Therefore, air mass reflects the reduction in the power of light because of its absorption by dust and air as it passes through the atmosphere.
5 Design and simulation of a grid-connected PV system for self-consumption
Figure 1. Representation of air mass spectrum in the Earth’s atmosphere [9]
The spectral distribution of the sun outside the atmosphere is considered to be air mass zero, or AM0, and its power density is the solar constant explained above. Inside the atmosphere, however, when the vertical angle (zenith angle) of the sun is θ = 0, this spectrum coming directly overhead is called AM1. Therefore, the standard value for photovoltaic work has been fixed at AM1.5, which refers to a zenith angle of 48,2 º from overhead, and which gives a power density approximate to 1000 W/m2 including direct and diffuse radiation [10].
4.4 Position of the sun
The Sun’s position varies constantly depending on the season of the year and the hour of the day, and therefore so does its radiation. The declination angle is the angle measured between a straight line linking the centre of the Earth with the centre of the Sun, and the Earth’s axis. Hence, due to the Earth’s rotation and orbit, the declination angle changes depending on those factors mentioned above ranging from +23,45º on the summer solstice to -23,45º on the winter solstice, whilst this value reaches 0º on the equinoxes [11]. This variation must be taken into account when sizing PV installations.
6 Design and simulation of a grid-connected PV system for self-consumption
Figure 2. Angles considered for solar orientation [84]
Additionally, two more angles (Fig. 2) are essential for PV applications: the elevation angle and the azimuth angle. The elevation angle (α) can be measured between the Sun and the horizontal, so being 0º at sunsets and sunrises. The azimuth angle (θ) is the compass direction from where the beams are coming relating to the exact south.
7 Design and simulation of a grid-connected PV system for self-consumption
Photovoltaics fundamentals
The aim of photovoltaic energy is to achieve the conversion of light into direct current electricity, through the photoelectric effect shown by some materials show. These kind of materials (usually silicon), used in solar cells, are classified as semiconductors. Hence, a solar cell is a wafer of a semiconductor material composed of an upper layer of n-type silicon, whose crystal lattice has a higher number of free electrons than a layer of pure silicon, and a lower layer of p-type doped silicon that has less amount of free electrons than a pure silicon layer as well, and therefore, positively charged holes in it. This is known as a p-n junction [12].
When a p-n junction is produced, a diffusion flow is then pushed between the n-type layer, which contains a high concentration of free electrons, and the p-type layer, the one with a high amount of holes. Thus, free electrons migrate from one part to fill the holes to the other, and this results in a positive charge along the junction in the n-region (where electrons are missing) and a negative charge along the junction in the p region (where the holes have been filled). As a consequence, a depletion layer is created in the middle of them. This layer does not contain any electrons or holes, meaning that at its sides a driving force appears, that is, an electric field (Fig. 3).
Figure 3. P-N junction of a semiconductor [13]
8 Design and simulation of a grid-connected PV system for self-consumption
So, when solar radiation in the adequate wavelength strikes the n-layer of the cell, the absorbed photons pass through the material breaking silicon bonds and tearing off free electrons, thereby creating holes in the excited atoms. Both free electrons and holes pair up in the depletion region. However, the driving force of this layer ousts electrons and holes out of it. Hence, free electrons and holes under the effect of the electric field take opposite directions. This develops into a high concentration of electrons in the n-region and holes in the p-region, and thus creating a clear potential difference between the layers.
Whenever a load is connected between these two sides, an electric flow will pass through it, travelling from the n-part to the p-part and eventually recombining with the holes in this one. In this way, solar cells continuously give direct current. Normally, solar cells use a thin and highly electron-doped n-layer, and a thick and lightly doped p-layer, so that the depletion region is wider and the cell’s performance increases [12].
5.1 Solar PV modules
A PV module is formed when multiple solar cells are organized and encapsulated by means of bus bar connectors in order to maximize their output power. Similarly, if modules are put together in series they create PV panels, which likewise are put into solar strings or arrays when interconnected.
Most PV modules are stable units with a front surface of a non-reflective material, so that they can absorb the greatest amount of radiation. This material, usually a tempered, low-iron content glass, prevents the cells from coming into contact with water, dust, gases and other elements, so they are not corroded or damaged [14]. Furthermore, as the cells are thin and delicate, the front cover also provides mechanical resistance and rigidity, as well as a safety barrier that prevents the user from suffering an electrical shock. Therefore, they must have low thermal resistivity, high resistance to impact and water good impact and water resistance and a high stability under prolonged exposure to UV rays.
The second component of the modules would be the encapsulation layers. The encapsulant is responsible for providing adhesion between the strings of solar cells and the front and rear surfaces of the module. Ethyl vinyl acetate (EVA) is the most commonly used material [15]. When heated up to 150 ºC, it polymerizes and bonds together with the cells and the coatings. It should be transparent, with low thermal resistance and stable.
Then, a rear surface is needed in order to protect the back part of the module and to provide support to the aforementioned elements and the wiring. Typically, it is made out of a polymer material [14]. Finally, an aluminium frame is added to the edge of this series of elements, to attach them and to avoid lateral lodgement of dirt or water, thus increasing the lifetime of the module.
5.1.1 Orientation of the PV modules
The power that reaches a PV module depends not only on the power of the sunbeams, but also on the tilt angle between the panel and the Sun. Power density will reach a maximum peak whenever the panel is totally perpendicular to the sunlight. Theoretically, if there were no losses, the power density of the
9 Design and simulation of a grid-connected PV system for self-consumption absorbing surface would equal the one from the sunlight. Nonetheless, due to the Sun’s constantly changing position, and to various types of losses, this power density is always less than the incident one.
Finding the optimal tilt angle for panels is essential to obtain the maximum output power from it [16]. There are basically two main kinds of mounting structures for solar systems: fixed systems and tracking systems. When a panel is fixed, the best tilt angle is equal to the location’s latitude. When increasing the tilt angle, energy production is optimized during the winter season. Otherwise, decreasing it is advisable for energy production during the summer. Nevertheless, they are not capable of modifying neither their orientation nor their tilt angle.
Given these conditions, it is possible to maximize the PV system output power by installing solar tracking panels [17]. These structures follow the Sun during the day, capturing its direct perpendicular component of light during the maximum amount of time possible. The most common types of tracking systems have one or two rotation axis, and thus they differ in the degrees of freedom they have.
One-axis tracking systems are usually aligned with the north-south meridian so they can pursue the Sun’s path from east to west. On the other hand, two-axis tracking systems have a first axis on the north- south meridian (tilt, β), and a second axis on the east-west line (azimuth, θ), so they are able to track the Sun in whichever position in the sky, as well as changing the tilt angle with seasonal height variations of the Sun. These kind of systems is, of course, much more expensive than fixed ones, and require more installing and maintenance processes, but energy harnessing is notoriously enhanced.
5.1.2 Electrical configuration of modules
A single normal solar cell is meant to give an amount of power of about 1 Wp in Standard Test Conditions (STC; AM1.5, T=25 ºC, 1000 W/m2). When arranged in series on a module, normally 60 to 72 cells are used [14].
If modules are connected in series, a solar panel or string is created. Otherwise, when several strings are connected in parallel they form a solar array (Fig.4).
Figure 4. Electrical configurations of solar cells [18]
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Under uniform operating conditions, that is, with identical cells and subject to the same irradiance and temperature values so that there are no mismatch effects, differences between these two types of arrangement can be spotted [14]. When stringing in series each individual module works with the same current as the others, but adds to the total voltage of the string. However, the main drawback would be that when a module is shadowed, the entire string’s current is reduced to that of the module with the lowest current.
Nonetheless, when creating arrays by connecting panels in parallel, the voltage for each panel remains the same, while the amperage increases with each additional panel. When a panel is shadowed, the rest of the array continues with the normal operation without reductions (Fig. 5). This will be further explained in the following sections.
Figure 5. Comparison of the I-V curves depending on the electrical configuration of the modules [19]
5.1.3 Parameters and electric properties
5.1.3.1 Open-circuit voltage
The open-circuit voltage, VOC, is the maximum amount of voltage that can be obtained from a solar cell when the net current is null [14]. In an ideal photovoltaic cell model, it can be simplified on a theoretical equivalent circuit as the one shown below (Fig. 6):
Figure 6. Representation of the ideal PV cell as an equivalent circuit [20]
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퐼f 퐾·푇cell 푉OC = 휂 · 푉T · ln ( + 1) ; 푉T = 퐼0 푞 (2)
The VOC depends mainly on the saturation current of the solar cell and the light-generated current. The saturation current, I0, is a function of the recombination effect on the p-n junction (Eq. 2). Thus, VOC is the measure of the recombination on the solar cell.
5.1.3.2 Short-circuit current
This is the current (ISC) flowing through the device when the voltage is zero. It is the one that would flow through the equivalent circuit when short-circuited [14]. It is the largest current that could be drawn from the PV cell. It depends on a number of factors such as the area of the cell, the number of photons or the light intensity arriving to it, the light spectrum (usually standardized as AM1.5), the optical properties of absorption and reflection that it may have, as well as on other properties (Eq. 3).
푞·푉 퐾 · 푇cell 퐼(푉) = 퐼 − 퐼 = 퐼 − 퐼 · (푒푛·퐾·푇푐푒푙푙 − 1) ; 𝑖푓 푉 = 0 → 퐼 = 퐼 = (3) f D f 0 SC f 푞
5.1.3.3 Characteristic IV curve
The characteristic IV curve of a solar cell represents the different working points of it [14]. It is the fourth- quadrant curve of a diode inverted as the cell delivers light-generated power. It presents a single Maximum Power Point (MPP) that gives the peak power value of the cell. In addition, parameters such as VOC or ISC can be quantified on it (Fig. 7).
Figure 7. Current-voltage curve and Power-voltage curve of a solar cell [14]
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5.1.3.4 Fill factor
The fill factor, commonly abbreviated as FF, is a measure of the quality of the PV cell. . It is defined as the ratio of the maximum power from the PV cell to the product of VOC by ISC, as seen below (Eq. 4). Open-circuit voltage and short-circuit current are maximum parameters of a solar cell. Nevertheless, when working at these operating points, the output power equals zero. Therefore, the FF, along with
VOC and ISC determines the performance, i.e. the maximum available power, from a solar cell [14].
푉mp · 퐼mp 퐹퐹 = < 1 (4) 푉OC · 퐼SC
Graphically, when looking at the IV curve, the FF is an indication of its “squareness” that is, of the area of the largest rectangle that could fit inside the curve, so the closer to 1 is its value the better.
5.1.3.5 Cell’s efficiency
The efficiency of the cell often gives a reliable idea of their performance, and allows the user to compare it to another type of cell. The efficiency depends on the spectrum and intensity of the light that arrives to the cell, and is usually measured under STC [14]. Generally, standard solar cells have an efficiency under 20%. This is determined as the ratio of the electric output energy to the incident solar energy, which is calculated as the product of irradiance and surface (Eq. 5):
푉mp · 퐼mp 휂 = (5) 푃solar incident
5.1.4 Effects of temperature and irradiance
Characteristic curves are measured under STC, but the truth is that under different conditions and depending on environmental changes, the curves may vary notoriously [14].
As solar irradiance impacting a PV cell increases, so does proportionally its short-circuit current, whilst the open-circuit voltage rises as well following a logarithmic function, as seen in its formula. Thus, total power and the maximum power point obviously increase.
On the other side, a detrimental effect to the performance of a solar cell has been shown when it is heated. With the rise of temperature the band gap energy of the p-n junction is reduced, so bonding is weaker and more photons are able to create pairs. While it is true that short circuit current may remain approximately the same, or even increase its value, the open circuit voltage decreases dramatically, and therefore so does the total power.
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5.1.5 Mismatch effects
Sometimes in a structure of interconnected modules it happens to appear losses and malfunctions due to cells or modules behaving differently from one another under different conditions. For example, the cells or modules can be shadowed by trees, clouds, dust, etc… Whenever the electrical parameters of a cell or module are altered in relation to those of other cells or modules, mismatch losses appear. These mismatch effects cause, in the majority of cases, the module or panel to work with the lowest output in the series, as explained before. Additionally, this can lead to highly localized energy dissipation, resulting in local heating that may cause irreversible damage to the devices [14].
The impact the effects may have depend on the type of device (hence their parameters), the electrical configuration and their operating point. Short-circuit current or open-circuit voltage, commonly causes the most usual mismatches, although others can happen.
5.1.5.1 Hotspots
Hotspot heating appears as a result of the generation of low current by a single solar cell (maybe due to shading) in a series connection (Fig. 8). When this occurs, the operating current of the entire string starts lowering down to the short-circuit current of the shaded cell, and then the overall current suffers a limitation [14]. Despite that, the extra current produced by the normal operating cells follows a forward bias through them, but when the string is short circuited, this forward bias can cause a reverse bias due to a higher voltage production of the properly working cells on the shaded one. Therefore, the whole capacity of power generation the string has dissipates on that bad cell. This huge dissipation in a local spot heats the cell, leading to great and destructive damage, such as glass cracking, circuit paths soldering, cell degradation or melting, and reduction of the cell’s lifetime.
Figure 8. Scheme of a shaded cell on a series, cause of a hotspot [21]
5.1.5.2 Shading
The output power production of a cell is proportional to the irradiance they receive. When shading of a cell occurs, this output declines proportionally to the amount of shading. As explained before, hotspots and other defects can appear due to shading [14], when a cell starts acting as a resistive load.
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Thus, it is important to protect the system from these kind of destructive effects by placing diodes in the circuit that block the current flowing through the shaded devices. When modules are connected in series, by-pass diodes are installed in parallel, so in case one of the modules is shaded and working as a resistive load, the current can pass through the diode and not through the module.
If the modules are put in a parallel configuration, like arrays, and one of them is shaded, the Kirchhoff Laws are contradicted, as all the modules should have the same voltage. In this case, the shaded module works as a resistive load at a voltage imposed by the other units in an unstable configuration. In this situation, blocking diodes installed in series with the devices are needed, so they can isolate the shaded branches (Fig. 9).
Figure 9. Diodes configuration in panels connected in series and parallel [22]
5.1.6 Technology on PV panels
Photovoltaic technology has been improving exceptionally in the last decades. Nowadays, scientists and institutes are putting their minds to the research of new systems, materials, devices and designs that can enhance the performance of the current technology, whilst reducing its economic impact.
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Figure 10. Global market share by PV technologies (1999-2009) [23]
The different technologies used nowadays are reviewed in the section below, but it is worthy of attention the fact that still in 2020, Silicon-based solar cells have the largest market share [24] among semiconductor materials. Nonetheless, other designs are starting to rise up in the market.
5.1.6.1 Silicon-based solar cells
It is the first generation of PV technology, yet the most used type in solar panels. Although not obsolete yet, further refinements have been made on it and the range of technology types existing is nowadays really wide.
However, Silicon is the most abundant solid element on Earth [25], and about 28% of the Earth’s composition corresponds to this material. This, added to the fact that its processing and manufacturing technology is now very mature and widely developed after more than 30 years of use, and considering its relatively high efficiency and low risk of failure, less than 1%, makes Silicon-based solar cells still the most attractive, with a market share, of about 87% of PV technologies in 2019.
The main kinds of Silicon-based cells are monocrystalline, polycrystalline and back-contact cells:
● Monocrystalline Silicon: This technology was first used in the earliest generation of photovoltaics, both in on-grid applications and in stand-alone systems, being the most commonly used one.
Monocrystalline panels are based on Silicon crystal with a high purity. The Silicon material presents an ordered and periodic arrangement of the atoms, so that it has a single crystalline orientation. Thus, all the atoms are placed symmetrically. Through the Czochralski process [26], single crystals are grown by melting the semiconductor-grade material under a strictly controlled
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temperature gradient, and adding dopants such as phosphorus or boron for converting the silicon into p-type or n-type as desired, depending on the electronic properties needed.
A Silicon ingot has a cylindrical shape with a diameter of 13 to 21 cm, and can reach up to 200 cm in length. It has a deep blue colour and a distinctive metallic luster. Although some experiments have shown higher values, their efficiency is considered to be of approximately 17% [27].
● Polycrystalline silicon: In the search of ways to reduce the manufacturing cost of monocrystalline cells, new techniques were found, among them polycrystalline cells, a new kind of cell, which is nowadays the most used one.
The crystalline structure that constitutes these solar cells has different shapes and directions. Polycrystalline silicon ingots are obtained by melting and casting the material, then allowing it to solidify in a parallelepiped-shaped cast. Therefore, the thin wafers obtained have a square section. These types of cells can be easily recognized by their superficial appearance, as their glass grains and metal flakes are highly visible, due to its heterogeneous structure.
Although laboratory experiments with these cells have shown a maximum efficiency of 22%, their actual efficiency is in between 12% and 14%, a slightly lower value than that of monocrystalline cells, yet their cost is as well lower [28].
It is worth mentioning that both mono and polycrystalline cells lately have been converted into Passive Emitter Rear Contact cells, which means that they have a back surface that reflects photons back into the cell for a second absorption attempt, enhancing their performance.
● Back contact solar cells: Rear contact solar cells provide a new cell design concept in which all the front contact grids are moved to the back of the cell, eliminating shading losses this way, and reducing their contact resistance [29]. Therefore, the cells can be interconnected easily and placed with no space between them in the panels. This design increases efficiency and it its mainly used in solar concentrators and industrial processes. There are three main types of back-contact cells: metal wrap-through (MWT), emitter wrap-through (EWT), and back-junction (BJ).
5.1.6.2 Thin-film technology
This is known as the second generation of PV technology. Thin-film technology came about by trying to make devices lighter and cheaper in order to cut costs, along with greener and more ecological processes. By reducing the thickness of a solar cell, its open-circuit voltage rises up as a consequence of a decrease in the saturation current [30].
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These cells are created by adding one or more thin layers of light-absorbing material to a metal, plastic or glass backing support. The thickness of the cell is much less than that of conventional cells (conventional cells can use wafers of 200 µm, while thin-film cells can be of only 1 µm [31]), thus thin- film cells become flexible and lighter. On the other hand, the manufacturing process and materials used are cheaper, and the lifetime of the cells is practically identical to the standard Silicon ones.
However, they show less efficiency. Indeed, the smaller thickness results in a decrease in capacity, which although generally compensated by the use of different materials, does not equal the efficiency of the common Silicon cells. Despite the fact that laboratory tests have shown quite good maximum efficiencies, the market share of this technology has followed a slight downward trend in recent years after a big growth. Additionally, tests and physical evidence have shown that the degradation of these modules is greater and faster, so additional barriers and protectors are needed to prevent damage caused by heating, oxidation and moisture.
Figure 11. Percentage of global PV production regarding thin-film technologies (2016) [23]
● Amorphous silicon: It is one of the first thin-film technologies created. It consists of a hydrogenated silicon compound that lacks an ordered structure, so that its atoms form a continuous random network without forming a crystalline matrix. This is precisely what differentiates amorphous from crystalline silicon, apart from containing 1/300th part of the active material present in a crystalline cell.
For its making, the silicon is laid on a transparent support forming a fine layer that work as a cell presenting a brown and dark ash colour. When exposed to the sunlight, the cells suffer a degradation caused by the Staebler-Wronski effect [32], lowering their efficiency. In order to optimize this efficiency, other elements can be added to create variations, such as carbon or germanium.
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Amorphous silicon cells seem to have a promising future prospect, as this technology enables cells of such small thickness to be created, combined with easy and cheap manufacturing. Nonetheless, they have a reduced efficiency, between 6 and 8% in commercially available cells, although the maximum achieved in a laboratory is around 10% [33].
● Cadmium Telluride (CdTe): These cells are one of the solar technologies with the highest potential. Since its band gap is almost the ideal (1,5 eV), it has a soaring absorption coefficient, catching about 90% of the incident photons [34].
CdTe's main advantage lies in its manufacturing process, which is lower in costs than silicon- based cells, and it is suitable for large-scale applications. Its conductivity can be changed to p- type or n-type, as it can be doped with impurities. An excess of Cd results in n-type, and an excess of Te in p-type.
Nevertheless, Cadmium is a toxic element with long-term effects on the environment, and the dearth of telluride might have a repercussion on the selling cost of the technology. Hence, measures must be adopted in order to make an appropriate use of it. In terms of efficiency, laboratory testing has shown values of around 21%, but the maximum efficiency in commercially available cells is in between 9 and 11% [33].
● Copper Indium Selenide/diSelenide (CIS/CuInSe2): These cells are part of the newest technology being developed and implemented in the most recent PV panels. In these, the silicon in standard solar cells is replaced by special alloys, such as copper, indium and selenide. There also exist CIGS (Copper, Indium, Gallium and Selenide) and CIGSS (Copper, Indium, Gallium, Selenide and Sulfur) cells [34].
The structure of these cells (Fig. 12) is reminiscent of that of silicon cells, since they are essentially junctions of two semiconductors. Just as the emitter and the receiver in silicon cells are made out of this material, the emitter in CIS and CIGS is made out of the union of other semiconductors. In these cells, that possess outstanding electrical properties due to is ideal band gap energy, which can be increased by adding Gallium, semiconductor elements with a high optical absorption coefficient are used. Furthermore, the cells can have very small thicknesses, of around 2-3 µm, in contrast to the 200 µm of common silicon ones, which results in a cheaper manufacturing process.
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Figure 12. Microstructure of a CIGS solar cell: Coloured image of cleaved CIGS sample (left), Schematic of the standard structure of a CIGS solar cell (right) [35]
The constituent chemical elements of them are extremely rare, in particular Se and In. In addition, some have very high toxicities, which compromises the recycling processes of panels at the end of their useful life. Moreover, Indium presents a shortage problem that rises up the price of the cells. CIS and CIGS cells can achieve an efficiency of 15% in their commercial form, with a maximum laboratory efficiency value of almost 20% [33].
● Dye-sensitized solar cell: This is one of the so-called third generation photovoltaics. Also called Grätzel solar cells [36], their behaviour is based on a non-galvanic chemical process in which the chemicals are constantly regenerated. The cells are thin, flexible and transparent. They are formed by a photosensitive anode, a semiconductor and an electrolyte that regenerates the dye. This electrolyte can freeze at low temperatures and stop the current generation; That is why alternative solutions are being researched. By means of using a sensitizer dye composed by Titanium dioxide nanoparticles, the cells generate electrical current, as this layer of dye absorbs a wide range of wavelengths. When a photon is absorbed, an electron is injected into the conduction band of the semiconductor, and there appears a diffusion effect of the particles creating a forward bias current.
Although the technology is still under development, it has shown efficiencies from 11 to 16%, while having an easy and inexpensive manufacturing process that makes the Grätzel cells a strong competitor in mass-production.
● Organic cells: Despite the advances in the field of the solar industry, the cost of PV cell manufacturing continues to be very high for many applications, especially large-scale ones. The complicated cell manufacturing process, which requires a hot vacuum environment limits the production to batches that cut their economic profitability. Organic Photovoltaic cells (OPV) are a rapidly emerging third generation technology that can be produced in large surfaces at a
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relatively low temperature, both by vacuum or sublimation methods, and also by film-forming polymers [37]. Plenty of organic materials (molecular or polymeric) can be synthesized for the absorber and the electron acceptor.
In addition, solar panels composed of OPVs are cheaper, lighter and easier to install. In order to compete with existing silicon technology and to find new applications, organic solar cells have had to meet a number of requirements in terms of stability, efficiency and cost Although their lifespan is generally less than that of the inorganic cells, OPVs improve efficiency, being it currently around 13% but still have long-term reliability as a significant barrier.
5.1.6.3 Multijunction technology
The so-called multijunction cells, or usually tandem cells, are those that combine two different types of semiconductor materials. This superposition of p-n junctions increases the sensitivity of different wavelengths and improves performance, since each type of material uses only a part of the electromagnetic spectrum of solar radiation. Multijunction devices use a high-bandgap top cell that absorbs the photons with the highest energy, while letting the lower-energy ones make their way to the next material with a slightly lower bandgap to be absorbed there. By combining two or three types of materials it is possible to profit of a greater part of the sunlight. With this type of cells, efficiencies of 35% have been achieved. According to some studies, theoretically, unions of three materials could reach efficiencies of almost 50% [38].
● Gallium Arsenide (GaAs): The GaAs technology [39] has its production limited by the high budget of its manufacture and the shortage of material. These kind of cells are mainly used for space applications, taking profit out of their small thickness and unvarying thermal properties. Additionally, from the point of view of efficiency, it is the most interesting technology, since it is among values of 25 to 30%.
5.2 Inverters
Inverters are essential to change the type of output current according to its end use. In the case of photovoltaic plants or installations, these produce a direct current. Within the installations, distribution is carried out using DC as well, but when delivered to the grid, it must be in the AC form, so that to transform it into the alternating current compatible and synchronized with the electrical grid, it is necessary to use an inverter. In addition, they are equipped with a Maximum Power Point Tracker (MPPT), which searches for the point at which the output power is maximum, selecting the best pair of voltage and current (MPP) that is constantly varying due to irradiance and cell temperature. There exist multiple types of solar inverters [40]:
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Central inverters: Working within a range of 100-1200 kW, they are inverters that merge several strings together connecting them in parallel and boosting their current and voltage. These are classified as single-stage inverters, as only a single converter is in charge of the maximum power point tracking (MPPT), the grid current control and the voltage amplification. They are used in the system when all the modules perform under the same conditions, and generally in large PV plants.
String inverters: This is the most used and common type of inverter. As a string is a group of modules connected in series, each of these strings in a PV installation is assigned a single solar inverter. As explained, if a module is shadowed, the output of the string is reduced to that generated by that module, so string inverters are not a good solution whenever the modules are oriented in different directions, as for instance, on the two sides of a rooftop. They can bear a power range of 0,4-2 kW and they are the most affordable type of inverter. Their maintenance tasks are simple, as there is only one section of the circuit to watch over. Batteries can be charged if connected before the inverter, so they can feed from the direct current supply before it converts to alternating current.
Microinverters: This kind of inverters is used in the opposite way as string ones. In this case, a whole string is connected to an inverter, but each of the of the array's PV modules is also connected to a microinverter, and all these microinverters are connected in parallel creating an alternating current circuit. In this way, each single PV panel works independently, and thus, if one of them fails, the rest of the array can proceed with normal operation conditions without being affected. Shading or different orientations, therefore, won’t be a problem in these installations. They work within a range of 50 to 400 kW in small PV installations.
Additionally, each microinverter can perform monitoring functions for each individual panel, detecting problems and solving them. Although grounding is fairly easy as it can be integrated in the general circuit, this kind of system is much more expensive than the others, and its maintenance is as well complex, because each inverter is under the panels. Whenever panels are installed in a way that their racking is not easily accessible, maintenance becomes a complicated task. Moreover, as the direct current output of the panels is directly converted into alternating current, there is no option for charging a battery tank.
Multistring inverters: This system is similar to the string inverter configuration. However, each string is first connected to a DC/DC converter for the MPP tracking and the voltage amplification. Then, several strings are connected to a usual DC/AC converter or inverter that controls the grid current. This dual-phase inverter topology is used in small ground PV plants or in medium- large rooftop panels with strings from 1,5 to 6 kW.
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Figure 13. Inverter typologies: a) Central inverter, b) String inverter, c) Microinverter, d) Multistring inverter [85]
As long as the voltage of an array exceeds the maximum limit of the inverter, the production will be interrupted by the inverter’s output and, in addition, as the inverter is working outside its nominal range, its lifetime can be substantially reduced. On the other hand, if the array voltage is under the chosen inverter’s minimum limit, the inverter will not work until the starting voltage has been reached. Therefore, the entire PV system will be underproducing.
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European Grid Code
The European Union established some standard requirements for the member countries in regard to electrical grid in the document Commission Regulation (EU) 2016/631: Establishing a network code on requirements for grid connection of generators [41]. As stated in the Article 1 of the document, it is “a network code which lays down the requirements for grid connection of power-generating facilities, namely synchronous power-generating modules, power park modules and offshore power park modules, to the interconnected system. It, therefore, helps to ensure fair conditions of competition in the internal electricity market, to ensure system security and the integration of renewable electricity sources, and to facilitate Union-wide trade in electricity” [41, p. 4].
According to that same document, a generating installation with a capacity within a range of 1 MW and 50 MW is considered a type B installation in Continental Europe (Tab. 1).
Table 1. Limits for thresholds for type B,C and D power-generating modules [41]
For this project, as it will be seen in the next sections, the installation capacity will be in between these values. In articles 13 and 14 [41, pp. 14-18] there appear stated the general requirements for type B installations.
6.1 Frequency and stability requirements
The installation has to work within the frequency range specified in the document, and ensure a stability in its operation.
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Table 2. Minimum time periods for which a power-generating module has to be capable of operating on different frequencies, deviating from a nominal value, without disconnecting from the network [41]
6.2 Limited Frequency Sensitive Mode - Overfrequency (LFSM-O)
To avoid complications on inhabited areas, in the aforementioned document some regulations can be found [41, pp. 15-16]:
The installation shall activate the provision of active power frequency response at a specified frequency threshold and droop settings, decided by the TSO
A frequency threshold within 50,2 Hz and 50,5 Hz is stablished
Droop settings are comprised within 2 % and 12 %
The delay at the beginning of the power frequency response must be as short as possible. If the delay lasts longer than two seconds, technical evidence must be provided
If minimum regulating level is ever reached, the installation module should either: o Keep operating at that level o Diminish the active power output
The installation should operate with stability during LFSM-O operation. Whenever LFSM-O is active, its setpoint will prevail over any other active one.
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Figure 14. Active power frequency response capability of power-generating modules in LFSM-O [41]
In the figure above (Fig. 14), extracted from the same document [41, p. 16], ΔΡ is the representation of the change in the active power produced by the installation. On the other hand, fn equals the network’s nominal frequency (50 Hz), and Δf its deviation. Whenever in an overfrequency Δf is above Δf1, the power-generating module needs to create a negative active power output variation, defined by S2.
6.3 Admissible active power reduction
Active power output shall remain constant despite of variations in frequency. However, there is a value range within for this output, specified by the TSO, regarding an admissible active power reduction from maximum output with falling frequency:
Below 49 Hz falling by a reduction rate of 2 % of the maximum capacity at 50 Hz per 1 Hz frequency drop
Below 49,5 Hz falling by a reduction rate of 10 % of the maximum capacity at 50 Hz per 1 Hz frequency drop.
The reduction must specify the ambient conditions applicable, as well as take account of the technical capabilities of power-generating modules.
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Figure 15. Maximum power capability reduction with falling frequency [41]
6.4 Active power cessation
Cessation of the active power output shall be done within five seconds after receiving instruction at the input port, which the module shall be equipped with. The TSO has the right to put requirements for the equipment in order to make a remote operation possible.
6.5 Reactive power output and voltage control
The operator of the system is able to define the potential of an installation to produce reactive power, whenever it has a synchronous operation [41, p. 32].
The installation must have an excitation control system that creates a stable voltage for the alternator terminal [41, p. 32].
6.6 Automatic connection to the network
The European Comission [41, p. 17] notes that “automatic connection is allowed unless it is specified by the system operator”. The requirements set by the TSO for an installation to be able to connect on its own to the grid contemplate:
The frequency range limits amongst which the system can automatically connect
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The maximum variation in the active power rise
6.7 Fault-ride-through capability
In concern of the fault-ride-through capability of the installation, according to Article 14 in the European Comission document [41, p. 18]:
The TSO should define a profile of voltage and time for fault situations, in which it can be shown how the installation can stay connected and operating with stability after there has been a power fault in the transmission system.
This profile expresses a minimum limit that shall not be underpassed by the phase-to-phase voltages, whenever a symmetrical fault occurs. It is plotted related to time, and it is defined by the TSO according to the parameters and ranges specified in the table below (Tab. 3).
Table 3. Parameters for fault ride-through capability of synchronous power-generating modules [41]
It is a duty of the TSO to define pre and post-fault requirements for ride-through capability regarding: o Minimum short-circuit capacity calculations o Operating points for active and reactive power before faults
28 Design and simulation of a grid-connected PV system for self-consumption
Figure 16. Fault ride-through profile of a power-generating module [41]
In the document [41, p. 19] it can be noted that in the diagram (Fig. 16) shown:
“the minimum value of voltage is plotted against time as a percentage of its actual value 1 p.u. value
before, during and after a fault. Being Uret the retained voltage at the connection point during a fault,
and tclear the instant when the fault has been cleared. Urec1, Urec2, trec1, trec2 and trec3 specify certain points of lower limits of voltage recovery after fault clearance”.
The installation must be able to keep connected and continuously and stably operating when the actual course of the phase-to-phase voltages during a symmetrical fault remains over the lower limit specified before, except if disconnection from the network is needed by the protection scheme. Protection schemes and settings for internal electrical faults must not jeopardise fault- ridethrough performance.
Protection against undervoltage situations must be installed by the facility, taking into account the technical capability of the installation. It the system operator needs other settings, they should be proven and justified by the owner.
Synchronous power-generating modules considered of type B must be able of providing a robust post-fault active power recovery, with a magnitude and time specified by the TSO.
6.8 System restoration capability
The installations must comply with the following according to the restoration capability of the system:
29 Design and simulation of a grid-connected PV system for self-consumption
The TSO has to specify the conditions under which the installation can connect again to the network after an incidental disconnection.
Installation of automatic systems for the reconnection must be authorised by the relevant system operator.
6.9 Electrical protection schemes and settings
In terms of protection, the European Comission declares [41, p. 20]:
Any setting or operation essential for the protection of the grid must be defined by the system operator. These measures taken to fix internal electrical faults must not threaten the generating performance of the installation.
System security, mitigating damages on the installation, as well as the health and safety of staff and public must be considered, so electrical protection takes precedence over operational controls.
Changes made on the schemes and protections must always be discussed and acknowledged by the system operator and the facility owner before they are implemented.
30 Design and simulation of a grid-connected PV system for self-consumption
Spanish Grid Code
In Spain, the only Transmission System Operator (TSO) is Red Eléctrica de España (REE), and its publications specify the requirements for the operation of electrical systems in relation to power generating installations. The Spanish legislature on photovoltaic installations is extensive, detailed and complex. Naturally, depending on the type of installation, the existing regulations in force impose some different rights and obligations for each type. As this thesis is solely considering a self-consumption PV system, the grid code and other regulations shown do not apply to off-grid PV system. Generally, the main goal of on-grid PV systems is to inject into the grid the maximum surplus of electrical energy they can produce from sunlight, so they are dimensioned with respect to economic profitability.
Although the so-called “Sun tax” has been recently abolished in the country, numerous rules apply to on-grid photovoltaic systems, in terms of design, production, distribution, supply and other technical aspects. The main decrees and laws concerning administrative and economic requirements are the following (for further details, the reader is referred to Boletín Oficial del Estado [42]):
● RD 1955/2000: Regulates transportation, distribution, commercialization, supply and authorisations for electrical installations.
● RD 842/2002: Approves the low-voltage electrotechnical regulations for Spain (REBT)
● RD 1699/2011: Regulates grid connection of low-power electrical installations.
● RD 1047/2013: Provides calculation methodology for the economic retribution for the transportation of electric energy.
● RD 413/2014: Regulates the production activity of electrical power by means on renewable energy, cogeneration or biomass.
● RD 15/2018: Provides urgent measures for energetic transition to more sustainable systems and for consumer safety.
● Law 24/2013: The Electrical System Law (LSE) ensures a supply guarantee, self-consumption, electrical planification, energy exchange, tariffs and others.
However, the technical details on the design, installation, parameter limits and integration of all the new installations wanting to access and to connect to the main grid, as well as modifying the existing power systems are collected in the new version of the document Procedimientos de Operación [43] (operating procedures) in the articles 12.1 (“Solicitudes de acceso para la conexión de nuevas instalaciones a la red de transporte”), 12.2 (“Instalaciones conectadas a la red de transporte peninsular: requisitos mínimos de diseño y equipamiento”) and 1.4 (“Condiciones de entrega de la energía en los puntos frontera de la red gestionada por el operador del sistema”).
31 Design and simulation of a grid-connected PV system for self-consumption
7.1 Exchange conditions
7.1.1 Product quality
This concept refers to the characteristic parameters of the voltage wave. The most significant ones that may influence the product quality are [43, pp. 5-9]:
Faults and ride-throughs: It sets the sudden voltage drop the system may experience, at a value in between 90% and 1% of the nominal voltage value. This fault by definition might last 10 ms to 1 minute, followed by a ride-through and restoration and recovery of voltage. Its depth is equal to the difference between the effective voltage during the fault and the nominal value. Power installations must be able to withstand these failures without being damaged or disconnected.
Voltage imbalance: It corresponds to a state in which the effective voltage values of each phase or the phase angles between consecutive phases in a three-phase system are not the same.
Harmonics: Defined as the sinusoidal voltage whose oscillating frequency is an integral multiple of the supply voltage (fundamental).
Flicker: Voltage fluctuations cause variations in the luminance of the lights. This results in a visual effect called flicker, which is a natural effect associated to a visual sensation of instability due to a luminous stimulus whose luminosity changes through time.
7.1.2 Exchanged power
The power exchanged between the transportation grid and the installations shall never exceed the nominal power indicated by the TSO in the established access documentation [43, p. 9]. The power value will be limited by means of physical devices or special procedures so as not to surpass the contract values. In the event that these devices may potentially interfere with the safety of the system, the TSO has the ability to notify of the programmed disconnection of the installation.
7.1.3 Electromagnetic disturbance limits
Limits for electromagnetic disturbances emitted by all the devices, systems and components of an installation connected to the same node of the transmission network have been collected in the design requirements [43, pp. 7-8]. Emission limits are established for points with a voltage higher than 220 kV and all generation installations connected to the grid.
Voltage imbalance: Emitters of these kind of perturbations shall never exceed the following total limits for voltage imbalance on each node of the transmission network:
o µ ≤ 0,7% for low-duration deviations (more than 10 minutes) o µ ≤ 1% for very low-duration deviations (less than 10 minutes)
32 Design and simulation of a grid-connected PV system for self-consumption
Harmonics: In order not to surpass the planification levels of the TSO, the harmonic voltage shall comply with the following limits on each node of the transmission network (Tab. 4):
Table 4. Limits on harmonic voltage for each node of the network [43]
Odd harmonics Even harmonics Non-multiple of 3 Multiple of 3 Harmonic Harmonic Harmonic Harmonic Harmonic Harmonic order (n) tension (%) order (n) tension (%) order (n) tension (%) 5 1,8 3 1,8 2 1 7 1,8 9 0,9 4 0,7 11 1,3 15 0,3 6 0,3 13 1,3 21 0,2 8 0,3
17 10 17 ≤ n ≤ 49 1,1 · 21 ≤ n ≤ 45 0,2 10 ≤ n ≤ 50 0,17 · + 0,14 푛 푛 TOTAL HARMONIC DISTORTION RATE (THD) 3,00%
Flicker: The following flicker emission limits for each node of the transmission network, taking into account the transfer coefficient from HV to LV, so they ought to be compared with the HV flicker:
o Short term flicker (PST) ≤ 0,8 o Long term flicker (PLT) ≤ 0,6
7.1.4 Planification levels
They correspond to the maximum level of the electromagnetic disturbances for which the grid has been designed. The planification levels are a measure of quality that ensures the electromagnetic compatibility of the system [43, pp. 5-6].
o Faults and ride-throughs: As mentioned, power installations must be capable of supporting these faults without being damaged or disconnected.
o Voltage imbalance: The imbalance degree (μ) has some planification levels in form of percentage ratio. Dividing the reverse sequence component (vector magnitude) by the direct sequence component (vector magnitude) of the voltage, values are obtained. These are a function of the duration of the voltage imbalance.
µ ≤ 1% for low-duration deviations (more than 10 minutes) µ ≤ 2% for very low-duration deviations (less than 10 minutes)
Harmonics: According to the International Electrotechnical Commission (IEC) in the “Assessment of emission limits for the connection of distorting installations in MV, HV and EHV power systems” in order to ensure a good quality on the wave, the harmonic voltage shall comply with the following planification levels on the transmission network (Tab. 5):
33 Design and simulation of a grid-connected PV system for self-consumption
Table 5. Planification levels for harmonic voltage on the network [43]
Odd harmonics Even harmonics Non-multiple of 3 Multiple of 3 Harmonic Harmonic Harmonic Harmonic Harmonic Harmonic order (n) tension (%) order (n) tension (%) order (n) tension (%) 5 2 3 2 2 1 7 2 9 1 4 0,8 11 1,5 15 0,3 6 0,4 13 1,5 21 0,2 8 0,4
17 10 17 ≤ n ≤ 49 1,2 · 21 ≤ n ≤ 45 0,2 10 ≤ n ≤ 50 0,19 · + 0,16 푛 푛 TOTAL HARMONIC DISTORTION RATE (THD) 3,00%
o Flicker: According to the IEC in “Assessment of emission limits for the connection of fluctuating installations to MV, HV and EHV power systems” the following levels have been defined for the transmission grid, taking into account the transfer coefficient from HV to LV, so they ought to be compared with the HV flicker:
Short term flicker (PST) ≤ 1,0 Long term flicker (PLS) ≤ 0,8
7.2 Imbalance situations
All generation units must support in permanent operation a 5% reverse bias component of the nominal current.
7.3 Frequency variations
The nominal frequency of the Spanish electric system at which the electricity is exchanged is 50 Hz. Any variations between 49,85 Hz and 50,15 Hz are considered as normal.
7.4 Protection system for devices
There should always exist a double safety system on every device and component of the installation, regardless of its type (L, T1, T2, or combinations). The protection system must follow the requirements specified in the REE document “Criterios Generales de Protección de los Sistemas Eléctricos Insulares y Extrapeninsulares” [44].
34 Design and simulation of a grid-connected PV system for self-consumption
7.5 Power equipment for connections with the grid
According to the REE documents [45, pp. 12-15], the connection between a power system and the grid can be done in different ways:
● Type L: By means of a no-transport line without transformation (generation or consumption connection)
● Type T: Using a no-transport transformer:
○ Type T1: Connection of generation or consumption.
○ Type T2: Connection of distribution.
The following figures represent these basic configurations with their parts, borders and components.
Figure 17. Typologies of connections to the grid [43]
35 Design and simulation of a grid-connected PV system for self-consumption
Design and sizing of the PV system
8.1 Site identification
As stated in the objectives of this study, the designed PV system would be located in Spain, as it is one of the countries in Europe with the greatest solar potential, due to its geographical situation. However, in order to define the exact location of the power installation, it would be interesting to know the number of PV power plants that are currently active in the country and their location (Fig. 18), to see if there is a region with a high solar potential being currently unused.
Figure 18. Map of current photovoltaic plants in Spain [46]
Additionally, taking into account the average solar irradiance map shown in the Código Técnico de Edificación (CTE) [47], a regulating document that is an equivalent to a technical building code, the different zones in Spain would be classified in the following way (Fig. 19):
36 Design and simulation of a grid-connected PV system for self-consumption
Figure 19. CTE map of Spain with classified zones regarding the incident irradiance [47]
When comparing and studying both maps simultaneously, it can be seen that southern Spain, and mainly the autonomous community of Andalucía, is fully equipped with photovoltaic power plants, due to its high levels of irradiation. There is also a huge amount of active PV plants in Murcia and Extremadura, such as the power plant of Mula, with an installed power capacity of 493,74 MW. However, the situation in Catalonia is striking, since its southwest region is classified as type IV, yet there is only one PV plant in Flix, Tarragona, with an installed capacity of 11 MW approximately. Therefore, Catalonia would be a compelling place for the new PV power installation designed in this thesis, despite it will be a self-consumption one.
The next step in finding the geographical location of the plant is considering a more detailed map of the solar irradiation (Fig. 20), where it is possible to analyse Catalonia in further detailed. Hence, it can be observed that the territory around the province of Lleida receives a daily global irradiance of 4,9 kWh/m2 [48].
37 Design and simulation of a grid-connected PV system for self-consumption
Figure 20. Irradiance map of Spain [48]
In this specific province region, it is seen that the town of Linyola has no photovoltaic power plant in the nearest surroundings that could supply its energy demand, only a thermosolar plant, although the surrounding terrain is wide, flat and without populated areas that could interfere with the construction of a power plant, as Lleida is one of the less populated provinces in Catalonia. Nonetheless, the aim of the project is to install PV modules on a building, preferably on its rooftop, located on the suburban area. Linyola is placed at latitude 41°42′44″N and longitude 0°54′20″E (Fig. 21) and at 248 metres above sea level. These details make the location a substantial candidate for the project.
Figure 21. Location of Linyola in the territory of Catalonia [51]
38 Design and simulation of a grid-connected PV system for self-consumption
Still, it is necessary to know the monthly evolution of the irradiance data, as well as the hours of sunlight in the region. Irradiance and other meteorological data are obtained for Linyola, as it may be representative for all the terrain of the nearby surroundings. The data shown below is the most recent found in Meteonorm 7.3, a meteorological database containing worldwide weather data (1991-2010), and from the Photovoltaic Geographical Information System, a tool developed by the European Comission (2016).
Figure 22. Maximum and minimum daily temperatures for Linyola [49]
Figure 23. Global solar radiation for Linyola [49]
39 Design and simulation of a grid-connected PV system for self-consumption
Figure 24. Monthly solar irradiation estimates for Linyola (2016) [50]
Table 6. Meteorological data for Linyola [49]
Gh Dh Bn Air temperature Wind speed Month [kWh/m2] [kWh/m2] [kWh/m2] [ºC] [m/s]
January 54 28 72 9,2 3 February 87 30 132 10,4 3,4 March 139 44 181 13 3,5 April 172 62 182 15,2 3,5 May 207 76 202 18,8 3,1
June 227 74 228 23,4 2,9 July 234 68 253 25,4 3,1 August 200 61 216 25,4 3 September 152 50 183 22,1 2,9 October 105 43 128 18,3 2,7 November 68 26 111 12,8 3 December 48 28 64 9,4 3
ANNUAL 1691 589 1950 17 3,1
Where:
2 Gh: Global Horizontal Irradiation (GHI) [kWh/m ]
2 Dh: Diffuse Radiation [kWh/m ]
Bn: Direct Normal Radiation [kWh/m2]
In summary, Linyola is a great placement for the implementation of a PV installation, as it is a region in Spain with a high solar radiation, but with only one PV plant active at the moment, quite remote from the town. If it was necessary to install the PV system in a surface other than a building rooftop, the topography of the location would be essential for the future energy production, and it would be also
40 Design and simulation of a grid-connected PV system for self-consumption
related to the installation cost. As said, the ideal terrain in the study location should be flat or with a slight south-facing slope, with no urbanistic constructions or with the presence of big mountains around that could create undesired shading. The selected area is considered to meet these requirements.
The soil in Linyola is assumed suitable for the study, regarding its dryness, resistivity, ability to bear big loads, chemical properties and presence of obstructions, as generally the ground layer in the region is really thick and steady. Information about other aspects such as wind speed, average temperature, snow risk, rainfalls, flooding risk, etc… need to be collected too so it can be analysed whether they are influential to the performance of the plant or not. Extreme temperatures can drastically decrease the efficiency of the cells. High wind speeds could damage the technology and the components used. Rainwater, snow and dust could lower seasonally the energy production of the installation, and also cause damages to the structures, increasing the maintenance cost. However, the chosen location is not under extreme weather conditions, so every parameter is assumed to not affect the performance of the plant.
8.2 Building studied
The building of study for this project is a residential household placed in Linyola. The exact location of the house is.
Table 7: Location of the studied house
Latitude 41º42’ 33’’ N
Longitude 0º 53’ 49’’ E
Metres above sea level 244 m
The terrain, as seen in the picture below (Fig. 25), is placed in a corner formed by the crossing of streets. The measured area of the whole parcel, including the garden space, consists of 488,5 m2. The front facade of the building is oriented almost towards the northern direction, with an angle of 2,2º with respect to it (87,8º from the eastern direction).
41 Design and simulation of a grid-connected PV system for self-consumption
Figure 25. Area of the terrain where building studied is located [51]
The house has two floors and two balconies, which represent a useless space in terms of installing a PV system for the energetic supply of the building. Nonetheless, the rooftop of the building is a flat and wide space that is totally suitable for the installation of PV modules. This open-air surface is shown, marked in green, in the image below (Fig. 26). It provides 161,66 m2 of available space for the PV infrastructure.
Figure 26. Available and unavailable areas on the building for the placement of PV modules [51]
42 Design and simulation of a grid-connected PV system for self-consumption
Therefore, this area will be studied, and some module layouts displayed and simulated in order to find the optimal that can cover the demand of the household.
8.3 Load profiles of the building analysed
Load profiles represent the measurement of the electrical demand throughout time. When designing a self-consumption system, it is important to know the load profiles of the user in order to size it and calculate some parameters, such as the efficiency or the degree of autonomy of the installation. Additionally, these profiles give information about the peaks and valleys of the load.
The load profile will always depend on the type of user, the season, the local holidays, etc… Thus, defining the load profile data is crucial for calculating and making an evaluation of equipment needs, maintenance and upgrades, as well as knowing when the system can supply the user or when it is unable to do so.
For the chosen building, a first load profile is going to be created. The household is considered to shelter a family with two children in school age, and in which both of the adult parents have a normal day job. This means that this house will most likely present peaks in the morning and afternoon, whilst during the working hours nobody will be at home, and only standby consumption is going to be reflected on the profile.
The vacation period is considered to be of 27 days between the 1st and the 28th of August for all the family members, being this period one with the family being absent from the house and with all the electrical devices turned off. Nonetheless, an assumption is made: some devices are still turned on and in standby mode because the family does not unplug them all. Hence, some energy use is still present on the load profile.
The rest of holidays, like Christmas or Easter (plus taking into account all the holidays of the Spanish calendar), are spent at home with the energy consumption peaks this fact represents.
Moreover, a usual route has been added to define a way between the house and the workplace. Two means of transport have been decided for the transportation of the adults: one car usually running at an average speed of 50 km/h (which travels a 5 km route to the workplace in an urban area) and a fast car running at an average speed of 70 km/h (making a 30 km route to the second workplace). Both of them, assumed electric cars, can be charged at a maximum power of 22 kW. However, the charging station installed at the household is only able to give an output charging power of 3,7 kW. This domestic charging station is considered to have a dynamic control of the power load, this meaning that if the household’s consumption rises, the power demanded by the electric car charging at that moment diminishes in order not to surpass the contracted power.
Given that the cars are used during the day, the charge is going to be made either after the working time or at night. The load profile for the charging cars performing as loads can be seen in Figure 27:
43
Design and simulation of a grid-connected PV system for self-consumption
2000
[W]
1000 Weekday 0
2000 [W] 1000
Saturday Saturday 0
2000
[W]
1000
Sunday 0 00:00 06:00 12:00 18:00 00:00
Figure 27. Load profiles of the cars for weekdays and weekends [52]
On the other hand, a list of activities, devices used, personal needs and illness periods is defined for each family member, so individual and collective consumption can be calculated separately, although the total data values are the ones to be used for an accurate recording of the load profile for the household. The amount of time spent for each action by the members is also specified, as in Figure 28:
44 Design and simulation of a grid-connected PV system for self-consumption
100
%) 87747 min min 87747
80
(16,6
Media use Media %)
60
(22,0%)
(21,1
Media use Media
Media use Media
115701 min min 115701
Sleep
111021 min min 111021
(38,4%) 202600 min min 202600
40 ,4%)
244796 min min 244796
(46
min min
%)
%)
Time in percent [%] percent in Time
2,9
Sleep
Sleep
Sleep
(3
(32,6 173636 20 min 171570
0
Figure 28. Time distribution for daily activities for each member [52]
The activities reviewed include basic domestic chores, like washing, cooking, drying, cooling or using the lights or the bathroom, as well as other spare time actions, such as watching TV, playing instruments or using a computer. An example of device profiles used for each chore is shown in Figure 29 for a normal weekday.
Then, specific device models are introduced in the load profile so a power value can be registered and the duration curves can be drawn, so an overview of power consumption can be given, as seen in Figure 30.
The computation of the load profile is made in time steps of 15 minutes throughout a whole year, from January 1st to December 31st. The load profile data created is then going to be introduced into the simulation software in CSV format to calculate the PV supply to the home. The key graph is shown in Figure 31, where an average daily curve is shown for different seasons and split by weekdays, Saturdays and Sundays.
45 Design and simulation of a grid-connected PV system for self-consumption
7
6
5
4
3 Electricity [kW] Electricity
2
1
0 00:00 06:00 12:00 18:00 00:00
Figure 29. Device profile on 14.02.2020 [52]
12
10
8
6 Electricity [kW] Electricity 4
2
0 0 50 100 150 200 250 300 350 400 450 500
Time step (·103)
Figure 30. Duration curves for the devices on the household [52]
46 Design and simulation of a grid-connected PV system for self-consumption
2000
[W]
1000 Weekday 0
2000 [W]
1000 turday turday
Sa 0
2000
[W]
1000 Sunday 0 00:00 06:00 12:00 18:00 00:00
Figure 31. Load profile of the household for weekdays and weekends [52]
It can be noticed that the biggest peak for all four seasons graphed is located in the range time between 18 p.m. and 1 a.m. A summed up profile of the energy consumption during the whole year can also be observed in Figure 32:
12
10
8
6 Electricity [kW] Electricity 4
2
0 0 50 100 150 200 250 300 350 400 450 500 Time step (·103)
Figure 32. Sum profile of the household during the simulated year [52]
47 Design and simulation of a grid-connected PV system for self-consumption
After running the simulations for the PV system, this load profile will be analysed using the optimal technology configuration and module layout previously found. The study of the suitability of the PV system for supplying the installation of the electric car charger in the household will be carried out too.
8.4 Technology selection
Before starting any calculations for the sizing of the PV system it is essential to choose which kind of devices are going to be implemented on it. Making a wise choice in terms of technology is going to be an essential factor in order to reduce costs and ensure the lifetime of the building plant.
8.4.1 PV modules
When choosing solar modules, it is important to take into account some guidelines and criteria in order to make the most out of their performance. The most important parameters for the choice are [53]:
Solar module type: As explained in former sections, the materials used for the cells have an essential role in the behaviour of the module’s performance. Each way of production and working principle change completely the output of each kind of panel.
Efficiency of the module: It is representative of the amount of solar energy that a module can transform into usable electricity. Therefore, it is one of the most important parameters to bear in mind.
Wiring and busing: Heat losses may happen excessively depending on how the mounting of wires and buses is done.
Power rating: This is the amount of direct current the module can produce under Standard Test Conditions.
Temperature coefficient: Measures how the power output, the open-circuit voltage and the short-circuit current values change with any variations in the temperature of the solar cell. The temperature coefficient is a percentage of that change expressed in (%/ºC). All three variables of a module are inversely proportional to the temperature. The less sensitive the temperature coefficient, the longer the module will last.
Power tolerance: Measures a range (with an upper limit as positive tolerance and a lower limit as negative tolerance) within the electrical power output can have a value, higher or lower than its nominal rating.
48 Design and simulation of a grid-connected PV system for self-consumption
Module warranty: It gives an idea of the quality of the module. If a sudden drawback takes place after the installation of the module the manufacturing company shall take care of it and provide the necessary service.
Durability: A module’s durability is a measure of the resistance of the module to the damage that time may cause. It is important to check the encapsulating material, the seals, and the connectors and back sheets. The International Electrotechnical Commission sets the standard in the IEC 61215, testing the modules under stress conditions that simulate the outdoor circumstances that they will face during their lifetime.
Quality: The quality check is done when the standard ISO 9000 is met, meaning that a certified manufacturer has developed the product.
One model of PV module has been chosen for this study. It is a CdTe panel (FS-6450) made by FirstSolar, one of the biggest module manufacturers in the US. It is built with up to 264 thin-film cells, with a rated power of approximately 400 Wp at Normal Module Operating Temperature (NMOT), and 450 Wp at STC, and it presents an efficiency of 18,2%. The product has a lifetime warranty of 25 years with a power output of 86%. More information can be found in the table below (Tab. 7) and in the attached datasheets in the Appendix 15.1.1.
Table 8. Data of the PV modules selected [54]
Ratings at STC (1000 W/m2, AM 1.5, 25ºC)
Nominal values FS-6450
Nominal power (-0/+5%) PMAX (W) 450 Efficiency η (%) 18,2
Voltage at PMAX VMAX (V) 186,8
Current at PMAX IMAX (A) 2,41
Open Circuit Voltage VOC (V) 221,1
Short Circuit Current ISC (A) 2,57
Maximum System Voltage VSYS (V) 1500
Limiting Reverse Current IR (A) 5
Ratings at NOCT (Cell temp of 45ºC, 800 W/m2, 20ºC air temp, AM1.5, 1 m/s wind speed)
Nominal power PMAX (W) 339,9
Voltage at PMAX VMAX (V) 175,2
Current at PMAX IMAX (A) 1,94
Open Circuit Voltage VOC (V) 208,8
Short Circuit Current ISC (A) 2,07
49 Design and simulation of a grid-connected PV system for self-consumption
8.4.2 Solar Inverter
The inverter selected for the project is one manufactured by the Chinese company SofarSolar. The model, a central inverter compliant with the Spanish grid regulations, is the SOFAR 12KTL-X, which has two independent MPPT. With an efficiency of 98,3% and a total harmonic distortion of less than 3%, it can provide a rated power output of 12 kW. More data than the shown below (Tab. 8) can be checked in the Appendix 15.1.2.
Table 9. Data of the solar inverter selected [55]
Input (DC) SOFAR 12KTL-X Typical PV Power 14400 W Max. DC power per MPPT 8800 W (800 V-850 V)
Max. input voltage 1000 V Start-up input voltage 180 V Rated input voltage 600 V MPPT voltage range 160 V-960 V
Full load DC voltage range 575 V-850 V
Max. input current per MPPT 11 A Input short-circuit current per MPPT 14 A
Output (AC)
Rated power 12000 W Max. AC power 13200 VA
Max. output current 19,1 A Nominal grid voltage 3/N/PE, 240/415 Grid voltage range 184 V/276 V (According to local standard) Nominal frequency 50/60 Hz Grid frequency range 50 Hz, ± 5 Hz (According to local standard)
Active power adjustable range 0 ~ 100%
THDi < 3% Power factor 1 (Adjustable ± 0,8)
50 Design and simulation of a grid-connected PV system for self-consumption
Depending on the environment conditions, being the air temperature a crucial factor on it, the nominal AC active power generated, in this case 12 kVA, may vary. Regarding the standard conditions, as well as the power factor (푐표푠휑) and the apparent nominal output power of this model of inverter, the active power produced can be easily calculated with the formula below (Eq. 6):
푃 = 푆 · cos 휑 (6)
In which: P = AC active power S = Apparent power of the inverter 푐표푠휑 = Power factor
푃 = 12 푘푉퐴 · 1 = 12 푘푊
On the other hand, the DC power injected into the inverter in order to provide the expected AC output is depending on the efficiency of the device (Eq. 7). Therefore:
푃AC 푃 = (7) DC 휂 In which:
PDC: DC input power of inverter
PAC: AC active power 휂: Inverter efficiency
As the maximum efficiency, according to the inverter’s datasheet, has a value of 98,3%:
푃AC = 12 푘푊 · 0,983 = 11,78 푘푊
8.5 Voltage dimensions
PV cell temperature knowledge is required to evaluate its performance. Temperature is an important parameter to consider in the location of the plant, as it interacts directly with many others, such as the voltage and the current of the modules, affecting in consequence their electrical function (Fig. 33). Therefore, the data given with the module model is just orientative, as it is necessary to make the appropriate calculations with the local temperature.
51 Design and simulation of a grid-connected PV system for self-consumption
Figure 33. Effect of temperature on ISC, VOC and PMAX [56]
8.5.1 Maximum open-circuit voltage
As the open-circuit voltage diminishes with the increase of the solar cell temperature, it is interesting to consider the lowest temperature in the selected location, in order to calculate the maximum open circuit voltage that can be reached by the module at that temperature value (Eq. 8).
푉OC = 푉OC,STC · [1 − 휆 · (푇Cell − 25)] (8)
Where:
VOC: Maximum open-circuit voltage
VOC, STC: Open-circuit voltage under STC
λ: Temperature coefficient for VOC
TCell: Cell temperature, corresponding to the minimum temperature in the location
The coldest temperature registered in the place of study is -1,98 ºC in the last 20 years of record [57]. Hence, for the selected PV modules:
CdTe (FS-6450):
−1 푉OC = 211,1 푉 · [1 − 0,0028 º퐶 · (−1,98 º퐶 − 25)] = 237,8 푉
52 Design and simulation of a grid-connected PV system for self-consumption
8.5.2 Minimum MPP voltage
On the opposite, the minimum voltage on the PV module is calculated taking into account the highest temperature value on the location. Analogously, the calculations should be made with 34,6ºC, being that the temperature peak in the last 20 years [57]. However, the datasheet considers the module operating range to be between -40 ºC and 85 ºC for the model. Therefore, the formulas (Eq. 9) will apply the 85 ºC value:
푉MPP = 푉MPP,STC · [1 − 휆 · (푇Cell − 25 °퐶)] (9)
Where:
VMPP: Minimum MPP module voltage
VMPP, STC: Module’s voltage at the maximum power point
λ: Temperature coefficient for VSC
TCell: Cell temperature, corresponding to the maximum operating temperature of the module
CdTe (FS-6450):
−1 푉OC = 186,8 푉 · [1 − 0,0028 º퐶 · (85 º퐶 − 25)] = 155,41 푉
8.5.3 Maximum PV module current
The current in a PV module is also dependant on temperature, although not as much as voltage. It slightly rises when the temperature of the module does so. In consequence, in order to know the maximum current, it should be considered the maximum temperature value of the site. Nonetheless, following the prior methodology, the maximum operating temperature will be used (Eq. 10).
퐼SC = 퐼SC,STC · [1 + 휎 · (푇Cell − 25 °퐶)] (10)
Where:
ISC: Maximum short-circuit current
ISC, STC: Short-circuit current under STC σ: Temperature coefficient for Isc
TCell: Cell temperature, corresponding to the maximum temperature in the location
53 Design and simulation of a grid-connected PV system for self-consumption
CdTe (FS-6450):
−1 퐼SC = 2,57 퐴 · [1 + 0,0004 º퐶 · (85 º퐶 − 25)] = 2,63 퐴
8.6 String limit sizing
8.6.1 Maximum number of PV modules per string
In this case, the inverter maximum input voltage limits the amount of modules that can be connected in series on a string. The formula below (Eq. 11) shows the calculation of the number of panels:
푉푖푛푝푢푡 푛MAX ≤ (11) 푉max 푚표푑
Where: nMAX: Maximum number of modules on a string.
Vinput: Maximum input voltage of the inverter
Vmax mod: Maximum module voltage
CdTe (FS-6450): 960 푉 푛 ≤ ≤ 4,04 ~ 4 푚표푑푢푙푒푠 MAX 237,8 푉
8.6.2 Minimum number of PV modules per string
The other way around, it is important to know the lower limit of modules that can be connected to the string (Eq. 12), in order to achieve the minimum input voltage of the inverter and minimize the losses.
푉min 푀푃푃 푖푛푝푢푡 푛MIN ≤ (12) 푉min 푚표푑
Where: nMIN: Minimum number of modules on a string.
Vmin MPP input: Minimum mpp voltage of the inverter
Vmin mod: Minimum module voltage
54 Design and simulation of a grid-connected PV system for self-consumption
CdTe (FS-6450): 160 푉 푛 ≤ ≤ 1,03 ~1 푚표푑푢푙푒 MIN 155, 41 푉
8.6.3 Maximum and minimum string voltage
The chosen number of modules per string is the maximum allowed at first instance in order to calculate the maximum and minimum string voltages. Later on, the exact number of modules needed will be decided, but for now the use of the maximum amount of PV modules per string is considered in order to have an idea of the voltage threshold. However, the maximum and minimum voltage values must be in between the inverter’s voltage range. They are calculated by the following method (Eq. 13, Eq. 14):
푉푚푎푥 푠푡푟 = 푛 · 푉푚푎푥 푚표푑 (13)
푉푚푖푛 푠푡푟 = 푛 · 푉푚푖푛 푚표푑 (14)
Where:
Vmax: Maximum voltage per string
Vmin: Minimum voltage per string n: Number of modules per string
Vmax mod: Maximum PV module Voltage
Vmin mod: Minimum PV module Voltage
CdTe (FS-6450):
푉푚푎푥 푠푡푟 = 4 · 237,8 푉 = 951,2 푉
푉푚푖푛 푠푡푟 = 4 · 155,41 = 621,64 푉
These values are comprised in between the MPP voltage range of the inverter, from 160 V to 960 V (Appendix 15.1.2). This would allow in reality a minimum of two modules per string, which would result in a maximum voltage of 475,6 V and a minimum voltage of 310,82 V for each one.
The exact number of PV modules will be decided during the modelling process regarding the area available on the rooftop, as the maximum amount of panels will be installed. Other factors such as row spacing and shading will be taken into account.
55 Design and simulation of a grid-connected PV system for self-consumption
8.7 Energy output estimation
It is possible to make a rough estimation of the energy output that could be obtained out of the PV system installed on the building rooftop [58]. Later on, however, this value is going to be compared and substituted with the highly accurate one from the simulation software, but at first instance it allows to foresee an idea of the performance of the setup. The calculation is done using the formula below (Eq. 15):
퐸OUT = ∑ 퐺i · 퐴i · 퐺퐶푅 · 휂SYST (15) 푖
In which:
EOUT: Estimation of the energy output from the PV system [kWh/year].
ηSYST: Efficiency of the PV system
Gi: Irradiation value for the area i € [1,12].
2 Ai: Available rooftop area for the installation of the PV modules [m ], i € [1,12] GCR: Ground Coverage Ratio
The Ground Coverage Ratio (Eq. 16), or GCR, is the ratio between the area covered by the PV modules and the total ground area where the modules are placed [59].
푃푉 푚표푑푢푙푒푠 푎푟푒푎 퐺퐶푅 = (16) 퐺푟표푢푛푑 푎푟푒푎 표푓 푡ℎ푒 푎푟푟푎푦
In a fixed structure module system (as the one usually installed on a rooftop), if the tilt angle is increased, less area is covering the ground in an overhead projected view, so the GCR decreases (Fig. 34). Additionally, inter-row shading rises proportionally to the tilt angle, so if the modules are more tilted, more space between rows needs to be implemented to avoid it.
56 Design and simulation of a grid-connected PV system for self-consumption
Figure 34. Relation between GCR and tilt angle of the PV modules [59]
This ratio is always below 1, and it usually takes values around 30 and 70%. In this approximate calculation case, a 0.3 coefficient is going to be used, along with an efficiency of 20% for the whole system. The estimation of the energy is then made with the yearly irradiation mean value to the area. The sun radiation on the modules shown is also an estimation calculated from the GCR, and considering these panels are ideal (Tab. 10).
Table 10. Energy output estimation for the PV installation
Irradiation Available roof area PV area Sun radiation on modules Energy output Month [kWh/m2] [m2] [m2] [MWh] [MWh]
January 54 2,22912 0,445824
February 87 3,59136 0,718272
March 139 5,73792 1,147584
April 172 7,10016 1,420032
May 207 8,54496 1,708992
June 227 9,37056 1,874112 137,6 41,28 July 234 9,65952 1,931904
August 200 8,256 1,6512
September 152 6,27456 1,254912
October 105 4,3344 0,86688
November 68 2,80704 0,561408
December 48 1,98144 0,396288
ANNUAL 1691 69,81 13,98
57 Design and simulation of a grid-connected PV system for self-consumption
Modelling and simulation of the PV system
9.1 Software
In order to model, simulate and analyse the system and its performance, the software PVsyst [60] is going to be used in this project. This software allows to define and size a PV installation (regardless of it being a stand-alone system, an on-grid one or a DC-grid system), whilst calculating and analysing its behavioural data. It enables tools such as 3D shading simulation, meteorological and irradiation models, a wide database of the technology available with their parameters, ageing simulation or, for instance, design and optimization of storage systems. For a detailed study, it is necessary to know some data for the design:
Geographical information Irradiation and meteorological data Technology selection of PV modules and inverters Available roof area or output power of the system User’s needs or load profiles 3D model of the building and surrounding elements Orientation and tilt angle of the PV modules System’s losses
Various simulations will be run so they can be compared, hence the system design can sequentially be optimized. Results on the total energy output and losses will be provided by the software, as well as an economic assessment with prices, energy costs and profitability.
9.2 Design process
The design process and implementation of the system into PVsyst requires entering data and defining plenty of parameters in order to create a precise, valid and detailed grid-connected system. The idea of installing solar panels on a household is to be able to cover its demand whenever it is possible, but without the use of storage systems, so the excess of energy can be directly injected and sold into the grid, or otherwise, the lack of it can be extracted from it. Hereunder are stated and explained the various steps followed for the whole definition of the installation, right before the simulations can be run.
9.2.1 Location and climate data
As stated before, meteorological data is key to an accurate simulation of the PV system. As the location of the building is not on the software’s database, a Meteo file for Linyola (Fig. 35) is created using the
58 Design and simulation of a grid-connected PV system for self-consumption
latitude and longitude of the place, and irradiance and temperature data are imported from Meteonorm 7.2.
Figure 35. Meteorological data introduced on PVsyst [60]
9.2.2 System components
As explained in sections above (Ch. 8.4), the used modules are the First Solar FS-6450 with a peak power of 450 Wp, and an inverter made by the manufacturer SofarSolar, the SOFAR 12000TL-X. This inverter has an operating voltage of 160-960 V and a global power of 12kW, which allows the system to connect in series up to 4 modules. At first instance, 8 strings are going to be implemented, as the maximum space on the rooftop grants the installation of 31 panels, which represent an active area of 78,7 m2.
Later on, should be modified this layout on other scenarios, it will be noted. However, the technology used is going to be implemented in all the simulation scenarios, as the aim this project is not based on comparing technology, but to compare layouts, whilst trying a new module technology apart from the usual Silicon-based panels.
59 Design and simulation of a grid-connected PV system for self-consumption
Figure 36. Technology and devices data introduced on PVsyst [60]
9.2.3 Module tilt and orientation
The orientation and tilt angle of the PV modules must be set in order to get the maximum energy output. In the study case, fixed modules are used due to economic reasons and an ease on maintenance duties. Moreover, as it is a domestic rooftop PV system, the installation of tracking systems would not be amortized in a short period of time.
Therefore, given a fixed structure for the panels, their tilt angle and azimuth orientation shall be defined. For that aim, and according to the PVGIS tools of the European Commission, the optimal angles for the chosen location should be 37º for a fixed tilt angle β throughout the whole year, and 1º for the azimuth angle.
Other approaches [61] propose different means of calculation, as for example the formula shown below (Eq. 17):
(퐿푎푡𝑖푡푢푑푒 · 0,76) + 3,1 = (41,71º · 0,76) + 3,1 = 34,79 º (17)
60 Design and simulation of a grid-connected PV system for self-consumption
Figure 37. Tilt angle and module orientation introduced on PVsyst for a fixed tilted plane [60]
Despite this value, adjusting the tilt angle twice a year is also considered as a possibility that is going to be evaluated on the performed simulations. Seasonal adjustment usually provides a better performance (Fig. 38). To calculate the values for the summer and winter angles, a rough method [62] is considered at first instance, consisting on adding and subtracting 10º from the site’s latitude (Eq. 18). Then:
퐿푎푡𝑖푡푢푑푒 ± 10º = 41,71º ± 10º = 31,71º (푆푢푚푚푒푟) ; 51,71º (푊𝑖푛푡푒푟) (18)
Despite this, another calculation model [61] suggests the following procedure (Eq. 19, Eq. 20) when adjusting the tilt angle twice a year:
(퐿푎푡𝑖푡푢푑푒 · 0,93) − 21 = (41,71º · 0,93) − 21 = 17,79º (푆푢푚푚푒푟) (19)
(퐿푎푡𝑖푡푢푑푒 · 0,875) + 19,2 = (41,71º · 0,875) + 19,2 = 55,69º (푊𝑖푛푡푒푟) (20)
61 Design and simulation of a grid-connected PV system for self-consumption
Full year Adjusted Winter Tracking
Figure 38. Production graph of different modes of tilting modules [61]
However, many models are used in several studies and scientific papers that differ so much from each other. Hence, in this situation, a 35º tilt angle is going to be used as a first simulation value for a fixed tilt throughout the year, and 18º and 55º values will be implemented for the adjusting tilt simulation. In regard to the azimuth orientation, the modules will be facing South direction, this meaning an azimuth angle of 0º to create the first layout.
62 Design and simulation of a grid-connected PV system for self-consumption
Figure 39. Tilt angle and module orientation introduced on PVsyst for a seasonally tilt-adjusted plane [60]
These angles will be optimized by means of running simulations on PVsyst for an iterative design process that will eventually lead to the optimal position of the modules.
9.2.4 Row spacing
For an optimal layout of the PV modules, the right minimum inter-row distance has to be implemented so there are no undesired shadows between them (Fig. 40).
Figure 40. Row spacing between modules on a PV system [63]
63 Design and simulation of a grid-connected PV system for self-consumption
To have a first approach to this distance value, the Sun path chart [64] below is going to be used for the location of study:
Figure 41. Sun path chart for Linyola [64]
This chart (Fig. 41) plots data between solstices, from December through June, so the worst case scenario can be studied. Considering solar hours from 9am to 3pm for the winter solstice, a solar elevation of 13º and an Azimuth correction of 41º are obtained.
Using the optimal tilt angle of 35º, a rough estimation of the row spacing distance between panels can be calculated. There are different methodologies to get this distance value. One of the most common, yet basic methods [65] is to use an inter-row distance of three times the height of the panel (Eq. 21):
퐷 = 3 · 퐻 = 3 · 퐿 · sin(훽) = 3 · 1,232 푚 · sin(35º) = 2,12 푚 (21)
However, this calculation can be more exact when using other and most complex formulas [66] (Eq. 22). Therefore:
sin(훽) · 퐿 sin(35º) · 1,232 푚 퐷 = = = 3,06 푚 (22) tan 훼 tan(13º)
Where:
64 Design and simulation of a grid-connected PV system for self-consumption
L: Module length β: Desired Tilt Angle α: Elevation Angle on December 21st at 9:00am
Adding a final product to this formula (Eq. 23), using the azimuth angle, the minimum row-spacing distance can be obtained:
sin(훽) · 퐿 sin(35º) · 1,232 푚 퐷 = · cos(퐴푧푐) = · cos(41º) = 2,31푚 (23) tan 훼 tan(13º)
Where:
Azc: Azimuth correction angle, or difference between the azimuth angle on December 21st at 9:00am and the southern direction.
In conclusion, from this approximate value, the first module layout is going to be done, and the different scenarios for the performed simulations are going to be decided.
9.2.5 3D Modelling
The 3D scene can be created by use of the PVsyst design tools, or otherwise importing a building or scene CAD model from other design software compatible with PVsyst, such as Autocad. In this case, the building is modelled, placed and oriented towards the appropriate direction, following the coordinates on the map. On this scene no surrounding buildings are created, as it is assumed that they have no influence on shadowing the panels. However, four trees are integrated on the scene, introducing their diameter and height, so the near shadings can be analyzed. The model can be seen in the figures below (Fig. 42, Fig. 43).
65 Design and simulation of a grid-connected PV system for self-consumption
Figure 42. Axonometric projection of the CAD model of the building and surrounding elements [60]
Figure 43. Overhead projection of the CAD model of the building and surrounding elements [60]
66 Design and simulation of a grid-connected PV system for self-consumption
With the 3D model of the scene, the available rooftop area to lay the modules shall be selected using a polygonal shape. Afterwards, the layout of the modules will be created, depending on parameters such as pitch distance, tilt angle, the model of the panels and the inverter used, or the lateral spacing. In the picture below (Fig. 44), three zones are created, although Zone #2 and Zone #3 are very likely to be unused.
Figure 44. Available zones on the building’s rooftop for the installation of the PV system [60]
9.2.6 Module layout and near shadings
After having implemented into the software the 3D model of the building, the surrounding elements must be analysed in terms of shading to see if they interfere with the full performance of the PV system. Although the building has an inclination of 2,2º with respect to the vertical line that defines the northern direction, to create the layout this fact has been disregarded, as it does not make any difference to the layout of the modules (which will be oriented at azimuth 0º), and it becomes easier to design it on the program.
67 Design and simulation of a grid-connected PV system for self-consumption
In this project, the shadings taken into account for the simulations are considered linear shadings, which measure the lack of irradiance without considering the electrical effect, which will be assumed as a loss percentage on other sections of the modelling, as in practice the linear shading factor is not so far from the real effect with electrical losses.
For the layout, it is precise to define the position of the modules, as in landscape or portrait form [67]. In a horizontal or landscape position, the shading losses are minimized, due to the electrical interconnection of the cells. The bypass diodes (usually three in each panel) are placed in such way that when a row of cells is shaded, the rest of the cells can continue working at their fullest output power value. However, when in portrait position, or vertically placed, the bypass diodes induce the whole module to stop its energy production whenever the lower row of cells is shaded, or covered by snow or dust [68].
Figure 45. Electrical configuration of a PV module in landscape (left) and portrait (right) position [69]
On the figure above (Fig. 45), it is shown how for the landscape position on the left, if row S1 is shaded, the other ⅔ of the module can still produce energy by bypassing S1, while on the other hand for the portrait position on the right, if the lower row of cells is shaded, S1, S2 and S3 would be bypassed with a null energy output resulting from it. For this reason, in order to optimize the losses, the landscape position is the one to be used for this study.
On the 161,65 m2 of free rooftop area, the layout of modules must be drawn, using the pitch distance, tilt angle and azimuth corresponding to each simulation scenario. The lateral spacing between panels is fixed to be 0,2 m as it does not affect the system’s behaviour (Fig. 46, Fig. 47).
68 Design and simulation of a grid-connected PV system for self-consumption
Figure 46. Side projection of the module layout on the rooftop [60]
The near shadings simulation will be run defining the winter solstice as the day of study, in steps of 15 minutes, and the main objective is to detect the shadows caused by the near trees also modelled in the 3D scene, by the building shapes and by the panels themselves, as there are no higher surrounding buildings that could induce shadings on the PV system.
Figure 47. Axonometric projection of the module layout on the rooftop [60]
69 Design and simulation of a grid-connected PV system for self-consumption
9.2.7 Detailed losses
Regarding the losses, the thermal ones are set to be the ones corresponding to free outdoor mounted modules with air circulation, and not modified respecting to the default value the software suggests. The wind loss factor in this study is considered not relevant.
Ohmic losses on the DC circuit are set to a loss fraction at STC of 1,5%, while the voltage drop across the diodes and the losses on the AC circuit after the inverter are not considered. Light induced degradation (LID) is not taken into account given that crystalline silicon modules are not being used, so the loss factor for LID is 0%. The mismatch losses are fixed at the default value of a power loss at MPP of 0,8%.
In terms of unavailability of the system, a constant loss of 2% is assumed, this corresponding to 7,3 unavailable days a year, while the soiling loss factor (losses caused by dust, dirt or debris on the module surface) is set to 3%. Spectral correction, ageing of the technology and Incidence Angle Modifier (IAM) are neither considered in the simulations, although an initial degradation for the modules is said to be of 5% due to the Staebler-Wronski effect [32], as this causes the module to work at a higher voltage during the first two or three operating months. The losses can be seen graphed in Figure 48:
Figure 48. Loss graph of the PV modules selected [60]
70 Design and simulation of a grid-connected PV system for self-consumption
9.2.8 Self-consumption
The energy demand files have to be introduced into the software as well in order to calculate the amount of energy produced that is dedicated to self-consumption, and to know consequently which part of it is injected into the grid. In the worst case scenario, it is to be calculated too if the energy produced by the PV system is not enough to supply the household’s demand.
To do so, a table with the energy consumption data of the household is imported into the program (Fig. 49). This document contains sub hourly data of the demand in time steps of 15 minutes during the 365 days of the year, despite PVsyst simulates in time steps of 1h, by making an average of the consumption every 15 minutes.
Figure 49. Consumption data of the household introduced on PVsyst [60]
The software will analyse the CSV file and calculate the average and maximum load needs for the household, which will be later shown on graphs in an hourly, daily or monthly scale. According to these values, the simulations will be run to see if the demand can be covered. The load profile defined in section 8.3 draws an annual need of 7.211 kWh/year (Fig. 50), which represents a daily average demand of 19,76 kWh/day.
71
Design and simulation of a grid-connected PV system for self-consumption
ly energy [kWh] lyenergy Month
Figure 50. Specified monthly energy need of the household [60]
9.2.9 Horizon
The horizon is by definition a broken line superimposed on the sun path diagram, which can hold any number of height or azimuth points. It is used for the setting and analysis of far shadings on the PV field. However, after having defined the near shadings parameters, the horizon study is only useful for shadings caused by objects placed sufficiently far, as at a distance typically higher than ten times the PV field size.
In the case of study, it has been assumed that there are no objects or buildings in the surroundings of the PV system that could act directly on it by shading the modules. The objects around, besides from the trees planted on the selected terrain, are not higher than the studied building, so the sunlight shouldn’t encounter any obstacles on its way to the rooftop.
Hence, as explained, the default values of the horizon profile for Linyola are not going to be modified in any simulation as the effect of far shadings is not considered to affect the scene in a direct way. Given this, only diffuse and albedo factors are taken into account.
9.3 Simulation scenarios
Once the steps stated in the sections above are completed, and all the details established and fixed, the grid-connected system that has been created looks in a simplified schema like in Figure 51:
72 Design and simulation of a grid-connected PV system for self-consumption
Figure 51. Simplified scheme of the grid-connected PV system [60]
In the PV installation, whenever there is an excess of energy production not used for the self- consumption needs of the household, that energy surplus will be injected into the grid. Otherwise, when there is not enough energy to cover the demand of the user, such as during night time, the energy consumed by the load will be extracted from the grid as back-up energy. For now, no storage system is going to be implemented in the first simulations.
Thus, with all this explained, several simulation scenarios can be defined. To start, the inter-row spacing or pitch distance is going to be compared in different layouts to minimize the shadings. From the minimum distance calculated in section 9.2.4, with a value of 2,31 m (rounded to 2,3 m), a first scenario (Scenario A) will be built with the 35º tilt and a 0º azimuth orientation. That layout will allow the installation of 30 panels in the building rooftop (in a configuration of up to 4 panels per string and 8 strings).
Then, the pitch distance will be increased to 3 m and to 3,3 m (Scenarios B and C), without modifying the tilt nor azimuth angles. The loss percentage is going to be evaluated at this point. Nonetheless, the number of PV modules is subsequently going to decrease as the pitch distance rises, so a whole assessment is required to find a balance point between losses and energy production.
Once the best pitch distance is chosen, regarding as well the number of PV modules that fit into the rooftop, a change in tilt will be performed in the next simulation (Scenario D), in order to gauge the beneficial or detrimental effect of seasonal tilt adjustment. The PV modules in this scenario will remain oriented to the southern direction.
Afterwards, having already determined the optimal pitch distance, the number of panels, and whether the tilt should be fixed of adjustable, different tilt angles will be studied, by means of trying the initial tilt and adding and subtracting 10º from that value (Scenarios E and F).
73 Design and simulation of a grid-connected PV system for self-consumption
Moreover, two simulation scenarios (Scenarios G and H) with a different azimuth orientation for the modules are going to be compared as well. The modules in these scenes will be oriented south west and south east and aligned with the building orientation, maintaining the best tilt found in the previous scenarios.
Trying other layouts apart from these explained above might be interesting if the results issued by the software show any tendencies or if any findings are made. Afterwards, the best scenario found is going to be optimized with the installation of a storage system that will be defined later on.
In summary, all the simulation scenarios are collected in the Table below (Tab. 10):
Table 11. Definition parameters for simulation scenarios A to H
Scenario Tilt [º] Azimuth [º] Pitch [m] Number of PV modules
A 35 2,3 31 B 35 3 26 C 35 3,3 26 Chosen Corresponding to chosen D 18/55 from A/B/C pitch distance 0 Chosen from A/D Chosen Corresponding to chosen E +10º from A/B/C pitch distance
Chosen from A/D Chosen Corresponding to chosen F -10º from A/B/C pitch distance
Chosen Corresponding to chosen G Chosen from A-F 2,2 SW from A/B/C pitch distance
Chosen Corresponding to chosen H Chosen from A-F 87,7 SE from A/B/C pitch distance
74 Design and simulation of a grid-connected PV system for self-consumption
Results
The results obtained from the simulations are going to be shown in this section, along with the process used to find the best solution for the PV system. Details can be further seen in the Appendix 15.2.
Initially, scenarios A, B and C were implemented on the 3D scene and in the software data, and each simulation was run according to the parameters stated in Table 11. For these first three cases, an azimuth angle of 0º was used with a tilt angle of 35º. The inter-row distances vary from 2,3 to 3 to 3,3 m in each corresponding scenario. As said in sections above, other parameters such as losses or technology configuration are kept the same for every situation. Scenario A presents an active module area of 79,2 m2, whilst both scenarios B and C have an active module area of 64,4 m2.
The main results for scenarios A, B and C are shown below in Table 11:
Table 12. Definition parameters and simulation results for scenarios A, B and C
Installed Energy Specific Shading System Pitch Azimuth Tilt PR Scenario power production production losses efficiency [m] [º] [º] [%] [kWp] [MWh/year] [kWh/kWp·year] [%] [%] A 2,3 14,4 23,89 1659 81,98 4,38 17,74 B 3 0 35 11,7 19,71 1685 83,28 2,93 18 C 3,3 11,7 19,73 1686 83,36 2,85 18,02
In this table (Tab. 11), the energy production represents the effective energy value at the inverter output, without considering the unavailability of the system, which will be counted in later on for the calculations of the grid-injected energy.
Specific production is the yield or energy produced for installed kWp of module capacity over a year [70]. It can also be understood as the amount of hours that the PV system would need to work at its nominal power to produce the same energy value as the actual system under the current conditions:
퐸total 푌𝑖푒푙푑specific = (24) 푃plant,nom
Where:
Etotal: Total energy output
Pplant,nom: Installed capacity of the plant
The performance ratio (PR) is an indicator calculated by the ratio of the effectively produced energy that is injected into the grid with respect to the energy that would be produced by an ideal system working continuously under STC conditions [70]. The PR, although it is not directly dependant on meteorological
75 Design and simulation of a grid-connected PV system for self-consumption conditions nor module orientation, includes optical (IAM, soiling, shadings) and array losses. It is a useful indicator for comparison of the system quality between different locations and layouts. It is calculated as:
퐸total 푃푅(%) = −6 · 100 (25) 푃plant,nom · 퐺푡 · 10
Where:
Gt: Incident irradiance on the installation
Shading losses show the percentage of linear losses caused by the shadows of surrounding objects and the own installation elements.
Finally, the system efficiency is the ratio of the produced energy with respect to the incident solar energy.
Then, according to the values on the Table 11, it is seen that Scenario A, although having a higher installed capacity (due to a different module disposition that allows more panels on the rooftop) and consequently a higher energy production, it shows lower specific yield, performance ratio and global system efficiency values. Moreover, the shading losses are much higher than the ones in Scenarios B and C. This comparison can be observed in Figures 51, 52 and 53, in the iso-shadings diagrams for each situation:
Figure 52. Iso-shadings diagram for scenario A [60]
76 Design and simulation of a grid-connected PV system for self-consumption
Figure 53. Iso-shadings diagram for scenario B [60]
Figure 54. Iso-shadings diagram for scenario C [60]
77 Design and simulation of a grid-connected PV system for self-consumption
Regarding these last detrimental results, scenario A is discarded, and the pitch distance chosen between 3 m and 3,3 m has to be decided from studying scenarios B and C. Nonetheless, parameters in scenarios B and C are almost identical, despite the simulations are showing a tendency to better values on scenario C. Because of this slightly higher yield and performance results, pitch distance on scenario C is the one used for the next simulation scenarios (D, E and F).
The next step of the simulation process is performed on scenarios D, E and F. The aim of this part of the simulations is to assess the implementation of a seasonal tilt adjustment on the PV modules. The parameters used in these three simulations are the ones stated in Table 12:
Table 12. Definition parameters for scenarios D, E and F
Azimuth Pitch Number of PV Scenario Tilt [º] [º] [m] modules D 18/55 E 28/65 0 3,3 26 F 8/45
The results obtained for scenarios D, E and F are shown in the table below (Tab. 13):
Table 13. Definition parameters and simulation results for scenarios D, E and F
Installed Energy Specific Shading System Tilt Azimuth Pitch PR Scenario power production production losses efficiency [º] [º] [m] [%] [kWp] [MWh/year] [kWh/kWp·year] [%] [%]
D 18/55 20,38 1742 82,95 3,71 18,62 E 28/65 0 3,3 11,7 20,04 1713 82,11 4,69 18,3 F 8/45 20,16 1723 83,57 2,94 18,41
In regard of these results, it can be seen that scenario D is the one that shows the best performance in terms of specific yield. Its efficiency is fairly higher than the one from scenarios E and F as well. Although the performance ratio and the shading losses in this studied situation are not the optimal ones, the values are considered acceptable and scenario D is the one chosen in between these three.
The numbers for scenarios C and D are subsequently compared to obtain the best tilt configuration for the panels choosing in between a fixed tilt angle of 35º or a seasonal adjustment of 18º for the summer and 55º for the winter. When doing so, it is seen that the specific production is significantly higher for scenario D, despite it has a lower performance ratio due to a larger percentage of shading losses. Nonetheless, it is a meaningless difference, so it is assumed that the best tilt to continue the study is the seasonally adjusted one, as the production seems to be the optimal.
For scenarios G and H, the layout configuration of the modules can be observed in Figure 55:
78 Design and simulation of a grid-connected PV system for self-consumption
Figure 55. Module layout on scenarios G (left) and H (right) [60]
As explained before, these two configurations are tried, aligning the panels to the building orientation to create the most logical layouts, (and facing the southern direction in both scenes), and in order to try new azimuths that could help improve the performance. An azimuth of 2,2º SW is implemented for scenario G, and 87,7º SE is the orientation for scenario H. The results for the simulations are shown in Table 14:
Table 14. Definition parameters and simulation results for scenarios G and H
Installed Energy Specific Shading System Tilt Azimuth Pitch PR Scenario power production production losses efficiency [º] [º] [m] [%] [kWp] [MWh/year] [kWh/kWp·year] [%] [%]
G 18/55 2,2 SW 20,37 1741 82,94 3,72 18,61 3,3 11,7 H 18/55 87,7 SE 15,53 1327 80,18 5,56 14,19
As it was to be expected, scenario H draws results below the average values that have been appearing on the other scenarios, because of an orientation that is almost facing east. Plus, its global efficiency is around a 23% less than the one in scenario D. For these reasons, this scene is discarded against the others. Otherwise, divergences between scenarios D and G are absolutely insignificant, as 2,2º of azimuth angle is almost a southern orientation. Hence, as the values don’t change significantly, scenario D is going to be maintained, because the southern direction is usually considered the optimal one.
In this situation, scenario D is considered the one with the most optimized parameters for its integration on the rooftop. To sum up, this configuration delivers an energy flow at the inverter’s output of 20,38 MWh/year. The near shadings losses represent a 3,71% of the available irradiance (Fig. 56), and thus the performance ratio of the system is of 82,95%.
79 Design and simulation of a grid-connected PV system for self-consumption
Figure 56. Iso-shadings diagram for scenario D [60]
This scenario has an specific production of 1.742 kWh/kWp/year, with an installed capacity of 11,7 kWp out of 26 PV modules oriented south and with a seasonal tilt adjustment of 18º for summer and 55º for winter season. However, the array itself presents losses of 0,81 kWh/kWp/day, whilst the system formed by the inverter and wiring loses 0,16 kWh/kWp/day (Fig. 57).
Figure 57. Graph of monthly production and losses for scenario D [60]
80 Design and simulation of a grid-connected PV system for self-consumption
Implementation of a storage system
In view of the results obtained after the simulations, the best layout has been defined: 26 PV modules south oriented with a tilt angle that varies in between the summer and winter season, with 18º and 55º respectively. Overall, the installation shows a good performance: it produces around 20,4 MWh/year, with pretty low electrical and shading losses.
However, this apparently good operation leaves behind the objective of covering the household’s electrical demand. If the installation was to inject all the energy output into the grid, it would be suitable. But when coming to analyse the load profiles of the household, as observed in Section 8.3, the users have a need for energy in the morning hours before leaving the house for other tasks. During midday and early afternoon hours, the demand of the place stabilises in only the stand-by consumption of the electrical devices that are plugged in, such as the fridge. When the users come back home, they start demanding energy again. Therefore, the consumption peak of the building takes place in the afternoon and evening, when the charge of the two electric cars needs to be done, as well as cooking and other chores.
In the way the installation is intended to operate, it is necessary either to inject the produced energy from the PV modules directly to the grid, or to consume it instantly. During the sun hours, when the demand is at its lowest level, and the irradiance of the panels is the highest, the necessity is fully covered and a great surplus is sold to the grid. Nonetheless, the users encounter the opposite situation in the evening, having no other choice than consuming energy from the grid, as they are unable to use the PV system when there is any sunlight.
Prior to having any PV system, the house consumed 7.211 kWh/year from the grid. On the other hand, in scenario D, and as it can be observed in Figure 58, now the demand from the network is 4.017 kWh/year. Despite having a solar system that produces 20,4 MWh/year, only 3194 kWh/year are used by the family, and the rest of it, 16912 kWh/year, are directly sold to the grid as they are being produced during the hours the family are not at home.
In this situation, one could think that as long as the energy surplus is sold, there is no need to do a self- consumption strategy to cover the demand. Although this excess of output energy is indeed sold, the selling retributions in Spain for self-consumption installations are considerably lower than the price of electricity purchased from the grid. In fact, they are in average about 3 times lower, and as the purchase tariffs are usually time-dependant, consuming at night would require paying the highest tariff. This being stated, there is no point in not using as much energy as it is produced by the household’s own system, and to avoid as long as it is possible to purchase energy.
81 Design and simulation of a grid-connected PV system for self-consumption
Figure 58. Loss diagram for scenario SS [60]
In order to solve these problems and to serve accurately the demand, a storage system is going to be implemented along with the PV modules. This self-consumption strategy with storage allows as said to consume the energy produced by the rooftop installation and to optimize the cost of electricity.
The energy produced by the PV system is stored in the battery pack when the PV production surpasses the needs of the individuals at the house, and from that point, when the demand cannot be covered by the solar irradiation, it is satisfied from the battery until it discharges. The rest of the moments when the battery is empty and the PV production is null, back-up energy is purchased from the grid. However, the
82 Design and simulation of a grid-connected PV system for self-consumption
battery may never inject energy to the grid, as the household’s consumption and the grid share the same circuit, and so the battery’s inverter and control devices shall modulate the power and feed properly the user.
There are five main operating modes for the storage system:
Charging mode
The PV system feeds the battery when it is empty to charge it, as well as feeding the user’s needs as a priority. If the battery pack charges completely and the user’s demand is covered, the surplus energy is injected into the grid (direct mode).
Figure 59. Simplified scheme for charging mode [60]
Discharging mode during the day
Once the battery is fully charged, the PV system covers the user’s demand until it is unable to do so (e.g. lack of sunlight), and so the storage system discharges energy to the household. However, if the battery reaches the full discharge level, energy is purchased from the grid.
Figure 60. Simplified scheme for discharging mode [60]
Direct mode during the day with sufficient irradiance and full charge
Whenever there is enough solar irradiance to cover the user’s demand and the battery is fully charged, direct mode supplies electricity to the user and injects the surplus to the grid.
83 Design and simulation of a grid-connected PV system for self-consumption
Figure 61. Simplified scheme for direct mode with sufficient irradiance and full charge [60]
Direct mode during the day with insufficient irradiance and empty battery
As user’s needs are a priority, if the storage system is fully discharged and there is not enough irradiance to cover the demand, direct mode will only supply the user, who will also have a need to extract back-up energy from the grid, while the battery will remain discharged until surplus energy is available.
Figure 62. Simplified scheme for direct mode with insufficient irradiance and no charge [60]
Night mode
In the night hours, when no sunlight is available, the battery pack and the grid are the responsible sources to feed the user’s consumption, as long as the battery is still charged.
Figure 63. Simplified scheme for night mode [60]
84 Design and simulation of a grid-connected PV system for self-consumption
According to this functioning system, a Lithium-ion battery pack from the manufacturer LG Chem is chosen. The model is RESU13, which has a usable energy of 12,4 kWh and a capacity of 252 Ah.It has a nominal voltage of 51,8 V, and two modules of this battery are connected in parallel, so it can store 21,3 kWh at 80% DOD. The thresholds set to the SOC of the pack are 95% for maximum charging and 20% for maximum discharging, so it can operate with efficiencies in between 95% and 97%.
The maximum charging power the storage system can handle is 11,5 kW, as the installed capacity of the panels is 11,7 kW and with a clear sky the maximum output power obtained from them is 11,29 kW AC. Regarding the maximum discharging power, it is of 9 kW, as the maximum user’s power is 8,91 kW, and the average power is 0,82 kW. The capacity and charge and discharge power values of the battery pack allow a charging time during full sun conditions on 1,8h. Its discharge under an average load can take up to 25,9h and under maximum load conditions about 2,4h (for more details, see Appendix 15.1.3).
Once this battery is implemented along with the parameters defined on Scenario D, a new simulation scenario is completed: Scenario SS. The results drawn from it are the following (Tab. 15):
Table 15. Definition parameters and simulation results for scenario SS
Installed Energy Specific Shading Baterry System Tilt Azimuth Pitch PR Scenario power production production losses losses efficiency [º] [º] [m] [%] [kWp] [MWh/year] [kWh/kWp/year] [%] [%] [%] SS 18/55 0 3,3 11,7 20,38 1742 79,3 3,71 3,09 18,61
Obviously, these results are almost identical to the ones in Scenario D, assuming the internal variations of the simulation software. However, a new variant of losses is added, the losses from the battery pack, which reach a value of around 3%. The performance ratio in this case is slightly diminished from the previous one, down to 79,3%. Taking two representative months of each summer and winter seasons, such as June and December respectively, some graphs can be plotted to easily see the magnitude and management of the energy handled by the system, as in the figures below (Fig. 64, Fig. 65, Fig. 66, Fig. 67):
85
Design and simulation of a grid-connected PV system for self-consumption
Power [kWh/day] Power
Figure 64. Graph of battery’s charging and discharging energy for the month of June [60]
Power [kWh/day] Power
Figure 65. Graph of battery’s charging and discharging energy for the month of December [60]
86 Design and simulation of a grid-connected PV system for self-consumption
Figures 63 and 64 show the battery’s charging and discharging energy through a whole month according to average daily values extracted from the hourly ones. The left axis represents power in kWh/day. There are no significant differences between June and December, as both average values resemble and the charts tendency seems logical, although these variables need to be compared with other ones that consider consumption.
In the following charts (Fig. 66, Fig. 67), there are therefore compared the values of the battery’s discharge (only to the user, as it does not re-inject to the grid), the energy purchased from the grid, the energy injected into the grid (the surplus), and an amount of energy supplied to the user in general, either from solar energy in a direct mode, as from the storage system or the grid.
In this case, there is a huge difference between the two representative months, as the amount of irradiance in winter is much under the one in summer. That turns into a higher consumption of grid energy in December, along with quite less grid injection, as in general terms all the available solar energy goes to the battery pack or to the user directly.
Power [kWh/day] Power
Figure 66. Comparison graph between battery discharging energy, energy injected or purchased from the grid, and energy supplied to the user for the month of June [60]
87
Design and simulation of a grid-connected PV system for self-consumption
Power [kWh/day] Power
Figure 67. Comparison graph between battery discharging energy, energy injected or purchased from the grid, and energy supplied to the user for the month of December [60]
Considering it all in general, from the 20,38 MWh generated at the inverter’s output, a 22,7% is stored, which mean 4,626 MWh/year that are specifically used to supply the family’s demand. The remaining 77,3% of it is used in direct mode. Eventually, the PV system provides the user with 6,84 MWh every year, whilst 12,38 MWh are injected into the grid. Knowing that 4,626 MWh/year come from the battery pack, it is deduced that 2,214 MWh/year come from direct mode (Fig. 68).
Only a 7,6% of the time the user needs to purchase back-up energy from the grid, which represents a value of 370 kWh/year, barely a 5% of the initial consumption value. This brings up the notorious optimization of the energy use, having now little dependence on the grid itself, as the majority of the household’s demand is satisfied by the own system.
88 Design and simulation of a grid-connected PV system for self-consumption
Figure 68. Loss diagram for scenario SS [60]
89 Design and simulation of a grid-connected PV system for self-consumption
Economic analysis
Once the design is simulated and considered viable, it is necessary to study the economic feasibility of the installation of the PV rooftop system. Usually, the technology used in these kind of installations is available on the market at high prices, but when installed in a region with a high solar potential, and given their long-lasting life expectancy, the purchase can be amortized quite easily.
For this economic analysis, the calculation model used includes OPEX, CAPEX, taxes and energy production, along with its PPA (Power Purchase Agreement).
CAPEX is defined as Capital Expenditures [71], which represent all installation and material goods costs in €/Wp, or in other words, all the elements purchased by the user. In the table below (Tab. 16), the devices used in the PV system are summarized, to show the elements that are going to be taken into account when calculating the CAPEX budget of the project. Moreover, the rest of components, such as wires and the installation of the technology have been valued in 1000 €.
On the other hand, OPEX is understood as Operational Expenditures [71], which comprises the permanent cost of maintaining and improving the assets. OPEX may include operations and maintenance (O&M), security, monitoring, insurances or land rentals. In this case, no bank charges, land rents or insurances are going to be taken into account, only a permanent cost due to maintenance, which will be considered as a 2% of the initial investment represented by the CAPEX (Tab. 16). However, this is a simplification, as maintenance would be null the first years of operation, and would increase non-proportionally towards the end of the life cycle of the system. The amortization of the technology is calculated along 25 years of life expectancy with a linear degradation of the item. Therefore, the project lifetime is set to be of 25 years and the calculations are related to annual values.
Table 16. CAPEX and OPEX amounts for the PV system
Unitary price Total price CAPEX item Units [€/unit] [€]
PV Modules [72] 26 243 6318 Inverter [55] 1 2578 2578 Battery [73] 2 4749 9498 Charger [74] 1 530 530 Installation and others - 1000 1000 TOTAL 19924
OPEX item Maintenance - - 300
90 Design and simulation of a grid-connected PV system for self-consumption
However, a vast investment of money would be useless in financial terms without earnings associated to it that could make the investment profitable in a relatively short time scope. For the PV system analysed, income in terms of selling the energy surplus that is not being used or stored produces a certain amount of money each year. The selling price is given by the Power Purchase Agreement (PPA) of Red Eléctrica de España, and valued in 53,28 €/MWh (Precio de la energía excedentaria del autoconsumo para el mecanismo de compensación simplificada [75]). Otherwise, the electricity that had been usually purchased from the grid at the normal Spanish price for kWh (an average of 0,116 €/kWh [76]) is now transformed into saved money as well. This can be observed in Table 17:
Table 17. Energy savings and retributions
Amount Unitary price Total price [kWh] [€/kWh] [€]
Energy purchased before 7211 0,12 865,32 Energy purchased now 370 0,12 44,4 Savings 820,92 Surplus injected into grid 12377 0,05328 659,61 TOTAL 1480,53
Additionally, a notorious amount of money is saved when charging two electric cars at home using solar energy only (Tab. 18). As said in section 8.3 of the project, the household owners use two electric cars to make a usual route to work. One of them makes a 30 km path to the workplace, which sums 60 km of travel a day. The second one, sums 10 km of travel a day, considering the 5 km path to the workplace.
Regardless of the average speed they travel at, to make an estimation of their consumption, two models of electric car for a working class household have been chosen to make the calculations: Opel Corsa-e for the long path and Peugeot e-208 for the short one. The first one of them has an average consumption of 17 kWh/100 km [77], and the second one of 15,1 kWh/100 km [78] in an urban driving environment. In view of this data, the Opel Corsa-e shows a daily consumption of 10,2 kWh. The Peugeot e-208, for its part, presents an energy consumption of 1,51 kWh.
Considering that the battery of the cars is charged at home, the saving in money comes from not having an expenditure in public charging stations. The price per kWh considered in this study is the one offered in the charging stations of Endesa X, the biggest company in Spain for electric charging, and the owner enterprise of the majority of charging stations. The price for the fast-charge is of 0,54 €/kWh [79]. The total consumption of the cars during 260 working days in a year constitutes 3044,6 kWh, and a total amount of money saved in charging stations of 1644,08 €.
91 Design and simulation of a grid-connected PV system for self-consumption
Table 18. Prices of charging the electric cars in a public charging station
Average Daily Charging price Total price consumption consumption [€/kWh] [€] [kWh/100 km] [kWh]
Opel Corsa-e 17 10,2 1432,08 0,54 Peugeot e-208 15,1 1,51 212 TOTAL 1644,08
It must be said too that there are governmental grants conferred to users who decide to install a self- consumption system in Spain, in order to propitiate the use of renewable energy in the country. This financial help is intended to defray the technology used, in order to reduce the initial investment made out of own funds. Specifically, in Catalonia these subventions provide around 5000 € (ICAEN: Sistemes d’emmagatzematge d’energia elèctrica amb bateries associats a instal·lacions fotovoltaiques d’autoconsum [80]) to the citizens that implement PV systems for self-consumption at their own homes.
With these data, a financial study is developed with a 25 year horizon and a discount rate of 10%, which draws the results summed up in Table 19. The details can be further seen in the Appendix 15.3.
Table 19. Main economic results of the 25-year analysis
NPV 1668,02 € IRR 9 % Payback period 6,4 years
According to the results of the simulation of Scenario SS, the amount of CO2 saved with the use of the
PV system is of 85231 tons in a 25 year period (Fig. 69), which means 3409 tCO2/year considering an annual degradation of 1%. This is also a value of 0,291 tCO2/kWp/year, and shows that each tCO2 is worth 5,85€ of inversion, which seems very reasonable in ecological terms.
92 Design and simulation of a grid-connected PV system for self-consumption
Figure 69. Saved carbon dioxide emissions of the PV system on scenario SS [60]
When wanting to know at what cost the energy is generated at the plant during its lifetime, the Levelized Cost Of Energy (LCOE) is used. The LCOE is also very useful to compare different power-generating technologies [81]. Its formula (Eq. 26) is the following:
∑푛 퐼푡+푀푡+퐹푡 푆푢푚 표푓 푐표푠푡푠 표푣푒푟 푙𝑖푓푒푡𝑖푚푒 푡=1 (1+푟)푡 퐿퐶푂퐸 = = (26) 푆푢푚 표푓 푒푙푒푐푡푟𝑖푐푎푙 푒푛푒푟푔푦 푝푟표푑푢푐푒푑 표푣푒푟 푙𝑖푓푒푡𝑖푚푒 ∑푛 퐸푡 푡=1 (1+푟)푡
Where:
It: Investment expenditures in year t
Mt: O&M expenditures in year t
Ft: Fuel expenditures in year t, null in this case
Et: Electrical energy generated in year t r: Discount rate n: Expected lifetime of the system
The system produces 20376 kWh/year, and the initial investment made on it plus the maintenance cost for the 25 year lifetime sums an amount of 27424 €. The LCOE then is 0,1224 €/kWh , that compared to the average LCOE for PV systems with batteries in Spain [82] (between 0,118 and 0,205 €/kWh) is pretty accurate to the range.
93 Design and simulation of a grid-connected PV system for self-consumption
Conclusions
Being Spain one of the countries with the highest incidence of solar irradiance in Europe, it could seem logical to think that photovoltaic energy is quite exploited around the territory. However, this is not the case, among other factors, because of the “Sun tax” that was abolished only a year ago. This means that it is far from common that individual users possess a PV installation to supply the energy demand of their own homes. Hence, this thesis had as a main goal to design and assess through a simulation software the performance of a grid-connected PV system for self-consumption installed on a building’s rooftop in a location with a high solar potential unused. With this purpose, the choice of a suitable site for the installation and of the technology to be used, sizing calculations, the creation of a load profile, the modelling of the building and its simulation were made. The following are the major findings that can be drawn from the study:
The study shows that an iterative design leads to an optimization of the first approach made for the system. For instance, it can be seen that an adjustable tilt angle for summer and winter seasons boosts the annual energy production, discarding the fixed tilt angle calculated at first. Conversely, the azimuth orientation was already the optimal one, as the rear facade of the house is facing the southern direction, so the sunlight reaches the surface of the PV modules most of the daytime.
The shading analysis shows that the surrounding elements of the building do not interfere with the performance of the plant, although the main shading loss is caused by the own modules, as when they are put in winter position (55º), during some hours of the day the inter-row distance is scarce. Broadening the inter-row distance could have avoided the shading losses, but then the limited area of the rooftop would have required to remove some panels. This detrimental action to the energy production would not have been justified by a shading loss of less than 4%.
Once the simulations were completed, a proper functioning scenario was found presenting an annual energy production of 20,38 MWh/year and a specific yield of 1742 kWh/kWp·year. The performance ratio of the plant was of almost 83% and its global efficiency of 18,7%. Although the production was acceptable, it was seen that the PV system mainly injected energy into the grid instead of supplying the user. This would be satisfactory if the retribution obtained from the injected electricity was higher than the price of the energy purchased from the network. Unfortunately, the current situation in Spain stands the opposite way, meaning that systems operating in those circumstances would leave the household’s demand to be supplied by the grid, as the way it was before any PV installations were made. Therefore, such a design was considered not suitable, and a PV system with a storage system was considered more appropriate instead.
The load profiles generated for the house presented a peak in the evening hours, which forced to implement a storage system that could save the energy generated during the sun hours, and that could release it during the consumption peak to fit the curve. Thus, new results were obtained, maximizing in this way the energy used by the people in the house that came from their own PV
94 Design and simulation of a grid-connected PV system for self-consumption
system. In the new scenario with storage system, the user receives 6,84 MWh/year, more than doubling the value of 3,19 MWh/year that they received without the battery pack. The energy purchased from the grid is reduced almost a 95% from the initial demand value, and constitutes the 7,6% of the consumption time, proving that a storage system implies a great improvement to the prior scenario without modifying its global efficiency.
In terms of economic profitability, the system designed can supply the demand of a whole family, including the charge of electric vehicles. The total cost of the PV system for the end user, once discounted the governmental subvention, is of 14924 €, which represents an annual saving of 2635,8 €. The system also produces environmental benefits, saving approximately the emission of
3409 tCO2/year, with a reasonable cost of 5,85€/saved tCO2.
These findings illustrate how new photovoltaic technologies for solar cells, such as thin-film technologies, can meet the standards set by the normal Silicon crystalline (which was a secondary aim of study) with less cost and less pollutant manufacturing processes. Nevertheless, the study has some limitations:
As they were not accessible, meteorological data used to implement in the simulations were not fully updated. Nevertheless, most likely this fact would not have affected the results, as the values used were quite recent.
Calculations were made taking into account current costs of electricity without considering future variations. Also, eventual future changes in user’s needs were not considered, as they are unpredictable.
Small costs attributable to different concepts exist, such as reparations, grid connection costs or transport. As these are almost impossible to calculate, they were included in wider concepts that were imputed an approximate value. Low amounts were assumed for them, so it was considered that this would not have influenced the study significantly.
Also, in regard to the losses of the PV installation, very difficult to calculate accurately, default values were assigned.
Finally, the study could be further completed by means of providing calculations for properly sizing AC and DC wires and other components, studying other possible load profiles to check the versatility of the PV system and even considering installing sun-tracking systems or other technologies for PV panels that for this thesis have been discarded due to their high economic investment.
To summarize, it can be said that the objectives of the project have been fulfilled, as a PV system design has been implemented, evaluated and found effective and economically viable and profitable, while it feeds the energetic demand of a household and it is able to supply the charge of two electric cars. Additionally, this thesis provides a design guide for grid-connected PV systems for self-consumption that can be further optimized in more complex scenarios. Nonetheless, as technical and economic
95 Design and simulation of a grid-connected PV system for self-consumption barriers are breaking down, the use of photovoltaic energy is becoming an unavoidable step to reduce the use of fossil fuels towards the future. Thus, more research needs to be implemented in the field, especially in the regions of Spain with a high solar potential, where these kind of systems can be installed in houses and buildings reducing the need to consume energy that come from non-renewable sources.
96 Design and simulation of a grid-connected PV system for self-consumption
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101 Design and simulation of a grid-connected PV system for self-consumption
15 Appendix
15.1 Datasheets
102 Design and simulation of a grid-connected PV system for self-consumption
15.1.1 FS-6450
103 Design and simulation of a grid-connected PV system for self-consumption
104 Design and simulation of a grid-connected PV system for self-consumption
15.1.2 Sofar 12KTL-X
105 Design and simulation of a grid-connected PV system for self-consumption
15.1.3 LG Chem RESU13
106 Design and simulation of a grid-connected PV system for self-consumption
15.2 Simulation reports
15.2.1 Scenario A
107 Design and simulation of a grid-connected PV system for self-consumption
108 Design and simulation of a grid-connected PV system for self-consumption
109 Design and simulation of a grid-connected PV system for self-consumption
110 Design and simulation of a grid-connected PV system for self-consumption
111 Design and simulation of a grid-connected PV system for self-consumption
112 Design and simulation of a grid-connected PV system for self-consumption
15.2.2 Scenario B
113 Design and simulation of a grid-connected PV system for self-consumption
114 Design and simulation of a grid-connected PV system for self-consumption
115 Design and simulation of a grid-connected PV system for self-consumption
116 Design and simulation of a grid-connected PV system for self-consumption
117 Design and simulation of a grid-connected PV system for self-consumption
118 Design and simulation of a grid-connected PV system for self-consumption
15.2.3 Scenario C
119 Design and simulation of a grid-connected PV system for self-consumption
120 Design and simulation of a grid-connected PV system for self-consumption
121 Design and simulation of a grid-connected PV system for self-consumption
122 Design and simulation of a grid-connected PV system for self-consumption
123 Design and simulation of a grid-connected PV system for self-consumption
124 Design and simulation of a grid-connected PV system for self-consumption
15.2.4 Scenario D
125 Design and simulation of a grid-connected PV system for self-consumption
126 Design and simulation of a grid-connected PV system for self-consumption
127 Design and simulation of a grid-connected PV system for self-consumption
128 Design and simulation of a grid-connected PV system for self-consumption
129 Design and simulation of a grid-connected PV system for self-consumption
130 Design and simulation of a grid-connected PV system for self-consumption
15.2.5 Scenario E
131 Design and simulation of a grid-connected PV system for self-consumption
132 Design and simulation of a grid-connected PV system for self-consumption
133 Design and simulation of a grid-connected PV system for self-consumption
134 Design and simulation of a grid-connected PV system for self-consumption
135 Design and simulation of a grid-connected PV system for self-consumption
136 Design and simulation of a grid-connected PV system for self-consumption
15.2.6 Scenario F
137 Design and simulation of a grid-connected PV system for self-consumption
138 Design and simulation of a grid-connected PV system for self-consumption
139 Design and simulation of a grid-connected PV system for self-consumption
140 Design and simulation of a grid-connected PV system for self-consumption
141 Design and simulation of a grid-connected PV system for self-consumption
142 Design and simulation of a grid-connected PV system for self-consumption
15.2.7 Scenario G
143 Design and simulation of a grid-connected PV system for self-consumption
144 Design and simulation of a grid-connected PV system for self-consumption
145 Design and simulation of a grid-connected PV system for self-consumption
146 Design and simulation of a grid-connected PV system for self-consumption
147 Design and simulation of a grid-connected PV system for self-consumption
148 Design and simulation of a grid-connected PV system for self-consumption
15.2.8 Scenario H
149 Design and simulation of a grid-connected PV system for self-consumption
150 Design and simulation of a grid-connected PV system for self-consumption
151 Design and simulation of a grid-connected PV system for self-consumption
152 Design and simulation of a grid-connected PV system for self-consumption
153 Design and simulation of a grid-connected PV system for self-consumption
154 Design and simulation of a grid-connected PV system for self-consumption
15.2.9 Scenario SS
155 Design and simulation of a grid-connected PV system for self-consumption
156 Design and simulation of a grid-connected PV system for self-consumption
157 Design and simulation of a grid-connected PV system for self-consumption
158 Design and simulation of a grid-connected PV system for self-consumption
159 Design and simulation of a grid-connected PV system for self-consumption
160 Design and simulation of a grid-connected PV system for self-consumption
Economic analysis
12
25
300
300
796,96
796,96
820,92
1644,08
744,26 € 744,26
488,81 € 488,81
659,6064
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
13.105,61 € 13.105,61
-12.800,54 € -12.800,54
95,58924531
300
300
796,96
796,96
820,92
1644,08
215,59 € 215,59
488,81 € 488,81
659,6064
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
11
43.471,02 € 43.471,02
-12.800,54 € -12.800,54
27,68879945
24
300
300
796,96
796,96
820,92
1644,08
818,68 € 818,68
488,81 € 488,81
659,6064
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
10.769,81 € 10.769,81
-12.800,54 € -12.800,54
105,1481698
300
300
796,96
796,96
820,92
1644,08
237,14 € 237,14
488,81 € 488,81
659,6064
10
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
30,4576794
41.135,22 € 41.135,22
-12.800,54 € -12.800,54
23
300
300
796,96
796,96
820,92
1644,08
900,55 € 900,55
488,81 € 488,81
659,6064
8.434,01 € 8.434,01
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
-12.800,54 € -12.800,54
115,6629868
300
300
9
796,96
796,96
820,92
1644,08
260,86 € 260,86
488,81 € 488,81
659,6064
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
38.799,42 € 38.799,42
-12.800,54 € -12.800,54
33,50344734
300
300
22
796,96
796,96
820,92
1644,08
990,61 € 990,61
488,81 € 488,81
659,6064
6.098,21 € 6.098,21
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
-12.800,54 € -12.800,54
127,2292855
300
300
8
796,96
796,96
820,92
1644,08
286,94 € 286,94
488,81 € 488,81
659,6064
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
36.463,61 € 36.463,61
-12.800,54 € -12.800,54
36,85379207
300
300
21
796,96
796,96
820,92
1644,08
488,81 € 488,81
659,6064
1.089,67 € 1.089,67
3.762,41 € 3.762,41
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
-12.800,54 € -12.800,54
139,9522141
7
300
300
796,96
796,96
820,92
1644,08
488,81 € 488,81
659,6064
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
34.127,81 € 34.127,81
-12.800,54 € -12.800,54
40,53917128
40,53917128
300
300
796,96
796,96
820,92
1644,08
20
488,81 € 488,81
659,6064
1.198,64 € 1.198,64
1.426,60 € 1.426,60
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
-12.800,54 € -12.800,54
153,9474355
6
300
300
796,96
796,96
820,92
1644,08
347,20 € 347,20
488,81 € 488,81
659,6064
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
31.792,01 € 31.792,01
-12.800,54 € -12.800,54
44,59308841
300
300
796,96
796,96
820,92
1644,08
488,81 € 488,81
659,6064
-909,20 € -909,20
19
1.318,50 € 1.318,50
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
169,342179
-12.800,54 € -12.800,54
5
300
300
796,96
796,96
820,92
1644,08
381,92 € 381,92
488,81 € 488,81
659,6064
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
29.456,21 € 29.456,21
-12.800,54 € -12.800,54
49,05239725
300
300
796,96
796,96
820,92
1644,08
186,28 € 186,28
488,81 € 488,81
659,6064
1.450,35 € 1.450,35
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
-3.245,00 € -3.245,00
18
-12.800,54 € -12.800,54
4
300
300
796,96
796,96
820,92
1644,08
420,11 € 420,11
488,81 € 488,81
659,6064
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
27.120,41 € 27.120,41
-12.800,54 € -12.800,54
53,95763697
300
300
796,96
796,96
820,92
1644,08
204,90 € 204,90
488,81 € 488,81
659,6064
1.595,38 € 1.595,38
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
-5.580,80 € -5.580,80
-12.800,54 € -12.800,54
17
3
300
300
796,96
796,96
820,92
1644,08
462,13 € 462,13
488,81 € 488,81
659,6064
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
300
300
24.784,61 € 24.784,61
-12.800,54 € -12.800,54
59,35340067
796,96
796,96
820,92
1644,08
225,39 € 225,39
488,81 € 488,81
659,6064
1.754,92 € 1.754,92
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
-7.916,60 € -7.916,60
-12.800,54 € -12.800,54
16
2
300
300
796,96
796,96
820,92
1644,08
508,34 € 508,34
488,81 € 488,81
659,6064
300
300
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
22.448,81 € 22.448,81
-12.800,54 € -12.800,54
796,96
796,96
820,92
65,28874074
1644,08
247,93 € 247,93
488,81 € 488,81
659,6064
1.930,41 € 1.930,41
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
-12.800,54 € -12.800,54
-10.252,40 € -10.252,40
15
1
300
300
796,96
796,96
820,92
1644,08
300
300
559,17 € 559,17
488,81 € 488,81
659,6064
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
796,96
796,96
820,92
20.113,01 € 20.113,01
1644,08
-12.800,54 € -12.800,54
272,73 € 272,73
488,81 € 488,81
71,81761481
659,6064
2.123,46 € 2.123,46
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
-12.800,54 € -12.800,54
-12.588,20 € -12.588,20
14
0
300
300
0
0
0,1
6,4
9%
796,96
796,96
820,92
1644,08
-5000
615,09 € 615,09
488,81 € 488,81
19924
14924
659,6064
-14924
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
17.777,21 € 17.777,21
-12.800,54 € -12.800,54
1.668,02 € 1.668,02
78,99937629
-14.924,00 € -14.924,00
-14.924,00 € -14.924,00
13
300
300
796,96
796,96
820,92
1644,08
676,60 € 676,60
488,81 € 488,81
659,6064
2.335,80 € 2.335,80
1.838,84 € 1.838,84
2.327,65 € 2.327,65
2.635,80 € 2.635,80
15.441,41 € 15.441,41
-12.800,54 € -12.800,54
86,89931392
Discount rate (10%)rate Discount
PAYBACK
PAYBACK
IRR
NPV
Annual NPV Annual
Updated cashflow Updated
Cumulative cashflow Cumulative
Cashflow
Amortization
BAT
TAX (21%) TAX
BBT
Amortization
Car electricity saved electricity Car
Electricity saved Electricity
Electricity injection Electricity
Benefit
OPEX
Subvention
CAPEX
Expenses YEAR
161