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Developing Verification Models for Corona Discharge Suppression in High Voltage Capacitor Banks

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Degree Project Developing Verification Models for Corona Discharge Suppression in High Voltage Capacitor Banks Author: Mohammadjavad Javadi Supervisors: Henrik Andersson, Sven Nordebo Examiner: Sven-Erik Sandström Term: Spring 2020 Subject: Electrical engineering Level: Master 30 hp Course code: 5ED36E Department of Physics and Electrical Engineering Abstract Due to the universal considerable population and economic growth rate, demands for energy have risen significantly over the past decade. Integration of renewable energies in the power grid has increased as well as requests for reactive power compensation, voltage stability, and mitigation of harmonic filters. Capacitor banks are widely used in the modern electrical transmission system in order to improve power quality and efficiency. In other words, this device aims to contribute in harmonic disturbance elimination, improve the power factor (PF), and provide voltage control and stability which leads into more sustainable energy systems. Utilizing high voltage components, such as shunt capacitors in the power grid can introduce new challenges. One of these challenges is known as corona discharge. The aim of the presented master thesis is to study and develop corona discharge suppression models on high voltage capacitor banks. The main concerns are, effective factors on corona emergence, corona inception voltage levels, and corona suppression methods. Also, this study evaluates the verification of existing suppression. Two various approaches were applied and compared. The aim of the first approach is to evaluate corona discharge by electric field calculations on three various capacitor banks with different voltage levels. The simulation was implemented based on Maxwell’s equations and finite element method (FEM) by utilizing COMSOL Multiphysics software. The second approach is based on streamer inception and propagation. The calculation on this method is fulfilled with the help of MATLAB software. The results of both approaches were found reasonably compatible. It is discovered that corona discharge can appear at different voltage levels on capacitor banks based on various factors, such as the geometry of the bank. Consequently, the suppression method may vary case by case and different proposals were suggested in order to optimize the corona suppression rings. Keywords: Corona discharge, electric field, stream inception, negative corona, positive corona, capacitor banks, corona ring, stream propagation. Sammanfattning På grund av den allmänna betydande befolknings- och ekonomiska tillväxttakten har kraven på energi ökat markant under det senaste decenniet. Detta innebär att integrationen av förnybara energier i elnätet har eskalerat samt begäran om reaktiv effektkompensering, spänningsstabilitet och mildring av harmoniska filter. kondensatorbatterier används ofta i det moderna elektriska transmissionssystemet för att förbättra strömkvaliteten och effektiviteten. Med andra ord syftar denna enhet till att vara involverad i eliminering av harmonisk störning, förbättra effektfaktorn (PF), tillhandahålla spänningskontroll och stabilitet som leder till mer hållbara energisystem. Att använda högspänningskomponenter, som shuntkondensatorer i elnätet, kan skapa nya utmaningar. En av dessa utmaningar kallas korona-urladdning. Syftet med den presenterade masteruppsatsen är att studera och utveckla korona- urladdningsmodeller på högspännings-kondensatorbatterier. De viktigaste problemen är effektiva faktorer för korona uppkomst, spänningsnivåer korona och metoder för att underlätta korona. Dessutom utvärderar denna studie verifieringen av befintliga undertryckningsmetoder. Två olika tillvägagångssätt tillämpades och jämfördes. Syftet med det första tillvägagångssättet är att utvärdera korona-urladdning genom elektriska fältberäkningar på tre olika kondensatorbatterier med olika spänningsnivåer. Simuleringen implementerades baserat på Maxwells ekvationer och finita elementmetoden (FEM) genom att använda COMSOL Multiphysics programvara. Det andra tillvägagångssättet är baserat på strömningslinjernas början och utbredning. Beräkningen av denna metod genomförs med hjälp av MATLAB-programvaran. Resultaten från båda metoderna tycktes vara rimligt kompatibla. Det upptäcks att korona-urladdning kan förekomma i olika spänningsnivåer på kondensatorbatterier baserat på olika faktorer, till exempel batteriets geometri. Följaktligen kan undertryckningsmetoden variera från fall till fall och olika förslag föreslogs för att optimera koronaundertryckningsringarna. Acknowledgments Special thanks to: Henrik Andersson, Erik Nylund, Håkan Rörvall, Fredrik Jansson, Göran Eriksson, Peter Holmberg, Emma Petersson, Nils Lavesson, Sven Nordebo, Liliana Arevalo. Contents 1 Introduction 1 1.1 Overview and background 1 1.2 Aim and objectives 3 1.3 Methodology 3 1.4 Thesis outlines 4 2 Theory 5 2.1 Physics of corona discharge 5 2.2 Electric field theory 9 2.2.1 Electric field calculation 9 2.2.2 Stream inception and propagation 14 2.2.3 Corona discharge threshold 17 2.3 Effective factors on emergence of corona 17 2.3.1 Polarity 18 2.3.2 Pressure 18 2.3.3 Humidity 20 2.3.4 Pollution 21 2.4 Corona discharge suppression methods 22 3 Methods and modeling 26 3.1 Introduction to COMSOL Multiphysics 26 3.1.1 Finite element method (FEM) 27 3.1.2 Boundary conditions 30 3.2 Simulation of capacitor banks 31 3.2.1 DC capacitor bank 31 3.2.2 AC capacitor bank 32 3.3 MATLAB model based on streamer inception and propagation 33 4 Results 35 4.1 Simulation results 35 4.1.1 DC capacitor bank 35 4.1.2 AC capacitor bank 37 4.2 Results of MATLAB model based on streamer inception and propagation 39 5 Discussion and conclusion 40 5.1 Corona supression verification and design analysis 40 5.2 Future work 40 References 41 List of Figures 1.1 Reactive power flow between AC capacitors and load 1 2.1 Avalanche, (a) Individual cloud chamber of an avalanche (b) streamer formation 6 2.2 Discharge transition process 6 2.3 Positive corona discharges under the various impulse voltages 7 2.4 Different discharge modes for positive corona regarding rod-plane model 8 2.5 Type of negative corona discharges 8 2.6 Different discharge modes for negative corona regarding rod-plane model 9 2.7 Rod-plane model 11 2.8 Two cylindrical conductors in parallel (±휌푙) 12 2.9 Two cylindrical conductors in parallel with symmetrical charge lines 13 2.10 Geometry of domain Ω 14 2.11 Streamlines from an electrode towards a grounded plane and equipotential lines 16 2.12 Propagation pattern of the streamers starting from Г0 16 2.13 Paschen’s law 19 2.14 Paschen’s curve 20 2.15 Electric field under three various humidity conditions 21 2.16 Cross section equipotential lines. (a) Block with ring. (b) Block without ring 23 2.17 Corona ring effective parameters 23 2.18 Cross section equipotential lines with tube radius of 0.1m and with tube radius of 0.2m 24 2.19 Cross section equipotential lines with ring diameter of 4m and with ring diameter of 2m 24 2.20 Cross section equipotential lines. (a) Block and ring. (b) Cone and ring 24 3.1 FEM (a) Two-dimensional model. (b) Subdivided two-dimensional region A 28 3.2 Four-element system with 4 known potentials and 1 unknown 30 3.3 Geometry of DC bank 32 3.4 Meshing of DC bank 32 3.5 Geometry of AC bank 33 3.6 Meshing of AC bank 33 3.8 Streamline 34 3.9 Excel table for streamline data 34 3.10 MATLAB model based on streamer inception and propagation 34 4.1 Electric field simulation result for DC capacitor bank (kV/mm) 36 4.2 Electric field simulation result for DC capacitor bank (kV/mm) 35 4.6 Equipotential lines around the top level (kV) 37 4.12 Electric field with (left) and without (right) suppression rings on bank 37 4.13 Equipotential lines with (left) and without (right) suppression rings on bank 38 4.14 Electric field variation along the bank (kV/mm-m) with and without suppression rings 38 4.23 MATLAB model based on streamer inception and propagation 39 4.24 Streamline plot 39 List of Tables 2.1 Gauss’s law and Faraday’s law summary 11 Acronyms AC Alternating current AP Atmospheric pressure CIV Corona inception voltage DC Direct current EF Electric field eqn Equation Es Electrostatic FEM Finite element method GAT Glow to arc transition HV High voltage HVDC High voltage direct current kV Kilovolt LV Low voltage PF Power factor Q Reactive power rms Root mean square SI Stream inception SP Stream propagation Chapter 1 Introduction 1.1 Overview and background Capacitors are widely used in AC and DC power systems specifically due to the rising trend of renewable energies utilization. Since loads and transmission devices (transformers and transmission lines) are inductive, additional reactive power (Q) is required to flow in the system due to the lagging power factor. As a result, the capacity of the system decreases, system voltage drops, and losses increase. IEEE standard 1036 [24], has introduced shunt capacitors as an optimal solution for reactive power compensation. Shunt capacitors reduce the power losses and increase the system capacity by preventing the reactive power flow in the system as it is produced locally i.e. near the loads at transmission and distribution substations (Figure 1.1). As it is featured by the blue arrow in the figure, reactive power surges to the load from AC capacitor bank such that Q does not flow through the entire system. Suppose an induction motor which consumes considerable amount of reactive power as the load. The required Q for this motor can be produced locally by shunt capacitors. The moment that induction motor is switched on, reactive power flows instantly from the capacitors. This solution has significant advantages such as improvement in voltage control and PF, system stability increase, and reactive power reduction at generation point. Applying shunt capacitors will result in the voltage rise from the installation point, up to the generation location along with capacity increase of the system. This can be fully utilized during the rapid increase of the load in the system. In addition, studies have shown that the current which flows between the installation point of shunt capacitors and generators, reduces considerably.
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