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Optimal Power Flow for an HVDC Feeder Solution for AC Railways

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Optimal Power Flow for an HVDC Feeder Solution for AC Railways Optimal Power Flow for an HVDC Feeder Solution for AC Railways Applied on a Low Frequency AC Railway Power System JOHN LAURY Masters' Degree Project Stockholm, Sweden 2012 TRITA: XR-EE-E2C 2012:012 Optimal Power Flow for an HVDC Feeder Solution for AC Railways Applied on a Low Frequency AC Railway Power System JOHN LAURY Master’s Thesis at Electrical Machines and Power Electronics Supervisor: Lars Abrahamsson Examiner: Stefan Östlund TRITA: XR-EE-E2C 2012:012 Abstract With today’s increasing railway traffic, the demand for electrical power has increased. However, several railway systems are weak and are not being controlled optimally. Thus, transmission losses are high and the voltage can be significantly lower than the nominal level. One proposal, instead of using an extra HVAC power supply system, is to implement a HVDC sup- ply system. A HVDC supply line would be installed in parallel to the current railway catenary system and power can be exchanged between the HVDC grid and the catenary through converters. This thesis investigates different properties and behaviours of a proposed HVDC feeder solution. An AC/DC unified Optimal Power Flow (OPF) model is developed and presented. Decision variables are utilized to obtain proper control of the converters. The used power flow equations and converter loss function, which are non linear, and the use of bi- nary variables for the unit commitment leads to an optimization problem, that requires Mixed Integer Non-Linear Programing (MINLP) for solving. The optimization problem is formulated in the software GAMS, and is solved by BONMIN. In each case in- vestigated, the objective is to minimize the total ac- tive power losses. The results of the investigated cases presented in this thesis, show that the proposed OPF-controlled HVDC solution reduces the losses and provides better voltage profile at the catenary, compared with today’s supply systems. Referat Med dagens ökande järnvägstrafik har efterfr˙aganp˙a elkraft ökat. Dock är flera järnvägssystem svaga och kontrolleras inte optimalt. S˙aledes,är överföringsför- luster höga och spänningen kan vara betydligt lägre än den nominella niv˙an. Ett förslag, istället för att använda en extra HVAC system, är att installera ett HVDC försörjningssy- stem. En HVDC ledning skulle installeras parallellt med den nuvarande kontaktlednings system och ef- fekt kan utväxlas mellan HVDC nätet och kontakt- ledningen via omriktare. Detta examensarbete undersöker olika egenska- per och beteenden hos ett föreslaget HVDC försörj- ningssystem. En AC/DC enad Optimal Power Flow (OPF) modell är framtagen och presenteras. Beslut variabler används för att kontrollera omriktarna. De använda kraftflödes ekvationer och omriktar- nas förlustfunktion, som inte är linjära, och använd- ningen av binära variabler för att kontrollera omrik- tarenheternas leder till ett optimeringsproblem som kräver Mixed Integer Non-Linear Programmering (MIN- LP) för att lösas. Optimeringsproblemet formuleras i programvaran GAMS, och löses med BONMIN. I varje undersökt fall är m˙alet att minimera de totala aktiva förlusterna. Resultaten av de undersökta fallen som presente- ras i denna avhandling visar att den föreslagna OPF- kontrollerade HVDC-lösning minskar förlusterna och ger bättre spänningsprofil p˙akontaktledningen, jäm- fört med dagens försörjningssystem. Acknowledgements First of all I would like to express my gratitude to Professor Stefan Östlund for allowing me to expand my knowledge in this field. Thanks, Lars Abrahamsson for your support, guidance, patience and under- standing during this time. I also want to thanks my master thesis colleagues for their aid with LaTeX and the fun moments we spent in the master thesis room. I wish to thank my friend Patrik Janus, for his support, aid and the interesting discussions we had during our time inside and outside school. I also would like to thank my friend Reinhard Kaisinger for his help and sup- port with the English language, during my work with this thesis. Finally, I want to thanks my family for their endless love and support. John Laury, September 2012 Contents 1 Introduction 1 1.1 Outline . 2 2 Background 5 2.1 Rail Power Supply Systems . 5 2.1.1 Rotary Converters . 6 2.1.2 Static Converters . 6 2.2 Catenary systems . 7 2.3 HVDC Transmission . 9 2.3.1 General Introduction . 9 2.3.2 General Advantages and Disadvantages . 9 2.3.3 HVDC converter for the RPSS . 10 2.4 Optimization theory . 11 2.4.1 Types of Optimization Programming . 11 3 Models 15 3.1 Power Flows . 15 3.1.1 AC Power Flows . 15 3.1.2 DC Power Flows . 17 3.2 Rotary Converter . 18 3.3 HVDC Converter . 19 3.4 The Network model . 22 3.4.1 Line Model . 22 3.4.2 Unified AC/DC Load Flow . 22 3.5 Simplifications . 24 3.5.1 Power Lines . 24 3.5.2 Trains . 24 3.5.3 Public Grid to DC Grid Converter . 24 4 The Optimization Problem 25 4.1 Minimizing Losses . 25 4.1.1 Boundaries . 26 4.1.2 The Objective Function . 27 5 Software and Implementation 29 5.1 Platform for Solution . 29 5.1.1 GAMS . 29 5.1.2 BONMIN . 29 5.1.3 Optimization with Rotary Converters . 30 5.2 Implementation . 30 6 Studied Cases 31 6.1 Investigated Cases . 31 6.1.1 Train Traffic . 32 6.1.2 Investigation of the Cases . 35 7 Results of Simulations 39 7.1 Dense Traffic Case . 39 7.1.1 AT Catenary . 39 7.1.2 BT Catenary . 44 7.2 Light Traffic Case . 50 7.2.1 AT Catenary . 50 7.2.2 BT Catenary . 56 8 Analysis and Discussion 63 8.1 Analysis . 63 8.1.1 Different PF at Train Locomotives: Dense Traffic Case 63 8.1.2 Different PF at Train Locomotives: Light Traffic Case . 64 8.1.3 OPF sensitivity to Converter Losses: Dense Traffic Case 64 8.1.4 OPF sensitivity to Converter Losses: Light Traffic Case 65 8.1.5 Smaller Type of Converters: Dense Traffic Case . 66 8.1.6 Smaller Type of Converters: Light Traffic Case . 66 8.1.7 Converter Loss Function . 67 8.2 Discussion . 69 8.2.1 Impact of Catenary System . 69 8.2.2 Centralized Solution . 70 8.2.3 Improved Voltage Levels . 71 9 Conclusions and Future Work 73 9.1 Conclusions . 73 9.2 Future Work . 74 9.2.1 Moving Trains . 74 9.2.2 Economical Aspects . 74 Bibliography 75 A Numerical data 79 B Catenary Transformers 81 B.1 Booster Transformer . 81 B.2 Auto Transformer . 82 Chapter 1 Introduction The history of Swedish railway started around 1856 when the first railways were built. They were operated by steam locomotives for approximately 55 years. Around 1910, the first electrified railway was introduced. The lines were electrified with single phase alternating current at a voltage of 15 kV and frequency of 15 Hz1. The power was directly generated from hydro power plants with a frequency of 15 Hz. Later on, when the railway system sig- nificantly expanded, it was decided to not use direct generation from hydro power plants. Instead, the public grid with rotary converters were used, thus converting 50 Hz to 16.7 Hz, which became the standard and still is used [12]. Today, the railway is supplied with power from the Swedish public grid via either rotary converters or static converters, placed at certain distances from each other. The distance between converter stations usually lies between 40 to 200 km. Most catenary systems in service have comparatively high impedances, and the transmission losses are relatively high (between 30-40%). With increasing railway traffic and expansion of the railway system, more power is required. Thus, there is an identified need for a technical solution to fulfil the increasing power demand and to reduce the losses. With the price of semiconductors decreasing, controllable power converters are available at lower cost. Power converters can be used to convert three phase AC to single phase AC and vice versa. They can also be used to convert AC to DC or DC to AC. The converters provide control of both active and reactive power. Therefore, such power converters are suitable for the Rail Power Supply System (RPSS). This is further discussed in [6]. The concept of RPSS using High Voltage Direct Current (HVDC) is pre- sented in [4]. The used converter technology is based on medium frequency transformer, in order to reduce the size of the converter [24]. 1 Porjus and Malmbanan 1 CHAPTER 1. INTRODUCTION This thesis follows the ideas of [4], were the HVDC feeder solution was in- vestigated for an RPSS, where the Overhead Contact Line (OCL) is equipped with Booster Transformers (BT). However, this thesis compares transmission losses and voltage levels for: • OCL with BT and Auto Transformers (AT) systems. • Trains operating at power factor 0.8, 0.9 and 1. • Varied converter size and spatial distribution. • OPF sensitivity to converter losses The OPF HVDC feeder solution is formulated as an optimization problem where the objective is to minimize the overall active power losses. However, the solutions in the studied cases are only valid for a specific time instance, since in real-life the consumptions and locations of the trains will vary over time. Thus, the solutions presented sets a theoretical upper bound on how small the losses can be given a specific time instance, if smart control is applied on the converters. In the calculations, all equations are expressed in the p.u. system, unless the opposite is explicitly stated. 1.1 Outline • Chapter 1 is the Introduction. • Chapter 2 describes the different existing feeding systems for the railway. A general introduction of HVDC technology is given and a description of the converter for the HVDC feeder solution.
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