Voltage stability Analysis using GridCal
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Power system voltage stability is characterized as being capable of maintaining load voltage magnitudes within specified operating limits under steady state conditions. This presentation deals with the modeling of two standard power systems test cases i.e the Nordic-32 and the Nordic-68, comparing the power flows results obtained from GridCal against PSS/E, finding the respective P-V curves for the two test cases using the continuation power flow under contingencies, and finally proposing a graph-based test statistic which can be used for an imminent voltage instability. The simulations are carried out using an open-source power system software called GridCal and the scripts for this project are written in python.
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Voltage stability Analysis using GridCal
- 1. Voltage Stability Analysis using GridCal by Anmol Dwivedi April 2020 by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 1 / 29
- 2. Content Background: Voltage Stability GridCal: a research oriented power systems software Goals of this project Modeling in GridCal Results for Nordic-32 test case Results for Nordic-64 test case Technologies Used References by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 2 / 29
- 3. Background Classification of Voltage Stability Large Disturbance Voltage Stability Concerned with the system’s ability to control voltages under faults, loss of generation etc. Similar to transient stability analysis, however, voltage stability analysis require additional detailed models of devices. Is analyzed by using non-linear time-domain simulations. Small Disturbance Voltage Stability Concerned with the system’s ability to control voltages following small disturbances such as gradual changes in load. by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 3 / 29
- 4. Important Questions to consider How close is the system to voltage instability? How and why does voltage stability occur? What are the factors that contribute to voltage instability? What effective measures can be taken to avoid voltage instability? by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 4 / 29
- 5. Factors Affecting Voltage Stability Generators and their excitation controls In generators, AVRs are the most important means of voltage control in a power system. Under low system voltages, the reactive power demand on generators may exceed their field/armature current limits and hence, not maintaining the terminal voltage to be constant. Load Characteristics The system voltage attains values governed by the characteristics of the transmission system and load. Common reasons for voltage instability Heavily loaded system Loss of a heavily loaded line Generator reaching field current limits by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 5 / 29
- 6. To summarize the problem Voltage Stability Analysis Dynamic Analysis While it is accurate/useful, it is very time consuming as it require large number of time domain simulations. It answers whether the system is stable for any given operating condition, however, provides no quantitative information like how much the system is stable. Static Analysis Tells us how much the system is stable i.e provides us information about the stability margin for a given operating point. Continuation Power Flow (CPF) analysis is one such tool which remains well conditioned even when the jacobian is singular, making it a useful tool to determine the shortest path to instability. This project deals with the CPF analysis for two test cases (i.e Nordic 32 and 64) using an open-source python tool called GridCal. by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 6 / 29
- 7. GridCal: a research oriented power systems software An open source power system software for steady state power system analysis. Can be used both as a library and GUI (drag and drop). This project uses GridCal as a library and the scripts are written in Pycharm. Offers steady state analysis tools like: Power Flow computation Optimal Power Flow computation. Time series analysis Continuation Power Flow analysis GridCal uses an object-oriented approach for all the data and simulation management, which means that in a given power system, the generators, buses, branches, shunts etc. are modeled as objects such that various instances of these objects can be created to construct a desired power system. by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 7 / 29
- 8. Goals of this project To model two specific power system test cases i.e to specifically model the Nordic-32 system and the Nordic-64 test system by using GridCal as a library. Perform voltage stability analysis using the CPF tool offered by GridCal to find out the stability margin of the two test systems. To compare the power flows results obtained from GridCal and that obtained by PSS/E. Use python tools like networkx and matplotlib to facilitate topological analysis and visualization of power system test cases. by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 8 / 29
- 9. Modeling in GridCal MultiCircuit: Once the circuit is built, the results of the circuit are passed on to the specific drivers (like the power flow driver, CPF driver, Voltage Collapse Driver etc.) in order to perform specifc simulations. by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 9 / 29
- 10. Modeling in GridCal Universal Branch Model: Transmission lines, Transformers, DC-Line, Switch π model of a branch is considered with variables as R, X, G, B, tap by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 10 / 29
- 11. Modeling in GridCal Loads Can be connected to a specific bus with required P(MW) and Q(MVar) GridCal can model both constant PQ loads and constant current loads. I have used constant PQ loads for my simulation. Generators Can be connected to a specific bus with required Power and Voltage set point. Modeled as constant voltages source behind a reactance. Shunts Can be connected to a specific bus with required B (MVar) by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 11 / 29
- 12. Single Line Diagram of the Nordic-32 test case Diagram form the IEEE PES voltage stability analysis report [3] by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 12 / 29
- 13. Power Flow results for Nordic-32 using GridCal Voltage Magnitude Variation in Per Unit (PSS/E results for Nordic - 32) by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 13 / 29
- 14. Power Flow results for Nordic-32 using GridCal Voltage Angle Variation in Degrees (PSS/E results for Nordic - 32) by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 14 / 29
- 15. Networkx Equivalent of Nordic-32 Type: MultiGraph Number of nodes: 74 Number of edges: 102 Average degree: 2.7568 by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 15 / 29
- 16. Graphical Visualization for Nordic-32 using networkx and matplotlib Graph representation without any contingency 130kV 1011_1 013_1 130kV 1011_1 013_2 130 kV line 101 2_10 14_1 130 kV line 101 2_10 14_2 130kV line 1013_1014_1130kV line 1013_1014_2 130kVline1021_1022_1 130kVline1021_1022_2 130kV line 1041_104 3_1 130kV line 1041_104 3_2 130kV line1041_104 5_1 130kV line1041_104 5_2 130kV line 1042_ 1044_ 1 130kV line 1042_ 1044_ 2 130kV line 1042_ 1045_ 1 130kV line1043_1 044_1 130kV line1043_1 044_2 220kV line 2031_ 2032_ 1 220kV line 2031_ 2032_ 2 400kVline4011_4012_ 1 400kV line 4011_4 021_1 400kV line 4011_4 022_1 400kV line 4011_ 4071_ 1 400k V line 4012 _402 2_1 400kV line 4012_ 4071_ 1 400kV line 4021_40 32_1 400kV line 4021_ 4042_ 1 400kV line 4022_4 031_1 400kV line 4022_4 031_2 400kVline4031_4032_1 400 kV line 403 1_40 41_1 400 kV line 403 1_40 41_2 400kVline4032_4042_1 400 kV line 403 2_40 44_1 400kVline4041_4044_1 400k V line 4041 _406 1_1 400kV line4042_40 43_1 400kV line 4042_4044_1 400k Vline 4043 _404 4_1 400k Vline 4043 _404 6_1 400kVline4043_4047_1 400kV line 4043_4045_1 400kV line 4044_4045_2 400kV line 4045_4051_1400kV line 4045_4051_2 400kV line 4045_ 4062_ 1 400k V line 4046 _404 7_1 400k V line 4061 _406 2_1 400 kV line 406 2_40 63_1 400 kV line 406 2_40 63_2 400 kV line 407 1_40 72_1 400 kV line 407 1_40 72_2 Tran sfor mer line 1041 _1_1 Transfo rmer line1042_2_ 1 Transfor merline1043_3_1 Transform erline1044_4_1 Transformer line 1045_5_1 Tran sform er line 1011 _11_1 Transformer line 1012_12_1 Transform erline1013_13_1 Tran sfor mer line 102 2_22 _1 Transformerline2031_31_1 Transformerline2032_32_1 Transforme rline4041_41_1 Trans form erline 4042 _42_1 Transformer line4043_43_1 Trans forme rline 4046 _46_1 Transf ormer line 4047_ 47_1 Transfo rmer line 4051_5 1_1 Transfo rmer line4061_61 _1 Transf ormer line 4062_6 2_1 Transformer line 4063_63_1 Transform er line 4071_71_ 1 Transform er line 4072_72_1 Tran sfor mer line 4011 _101 1 Transf ormer line 4012_1 012 Trans forme r line 1012 _5000 1 Tran sform er line 1013 _500 02 Transforme r line 1014_5000 3 Transformer line1021_50004 Transformer line4022_1022 Transfo rmer line1022_5 0005 Transfo rmer line 1042_50 006 Transformer line1043_50007 Trans form erline 1044 _4044 B Tran sform erline 1045 _404 5B Transfo rmer line4031_2 031 Tran sform er line 2032 _500 08 Transfo rmer line4011_5 0009 Transforme rline4011_50010 Trans forme rline 4021_ 50011 Transformerline4031_50012 Tran sfor mer line 404 1_50 013 Tran sfor mer line 404 2_50 014 Transformer line4047_50015 Transfo rmer line 4051_50 016 Transformer line 4062_50017 Trans forme rline 4063 _5001 8 Transform erline4071_5001 9 Transf ormer line 4072_ 50020 1_LOAD 1041 2_LOAD 1042 3_LOAD 1043 4_LOAD 1044 5_LOAD 1045 11_LOAD 1011 12_LOAD 1012 13_LOAD 1013 22_LOAD 1022 31_LOAD 2031 32_LOAD 2032 41_LOAD 4041 42_LOAD 4042 43_LOAD 4043 46_LOAD 4046 47_LOAD 4047 51_LOAD 4051 61_LOAD 4061 62_LOAD 4062 63_LOAD 4063 71_LOAD 4071 72_LOAD 4072 1011 1012 1013 1014 1021 1022 1041 1042 1043 1044 1045 2031 2032 4011 4012 4021 4022 4031 4032 4041 4042 4043 4044 4045 4046 4047 4051 4061 4062 4063 4071 4072 50001_G1 50002_G2 50003_G3 50004_G4 50005_G5 50006_G6 50007_G7 50008_G8 50009_G9 50010_G10 50011_G11 50012_G12 50013_G13 50014_G14 50015_G15 50016_G16 50017_G17 50018_G18 50019_G19 50020_G20 by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 16 / 29
- 17. Graphical Visualization for Nordic-32 using networkx and matplotlib Graph representation with contingency (400kV line 4031–4032) 130k V 1011 _101 3_1 130k V 1011 _101 3_2 130kV line 1012_10 14_1 130kV line 1012_10 14_2 130kVline1013_1014_1130kVline1013_1014_2 130kVline1021_1022_1 130kVline1021_1022_2 130kV line 1041_104 3_1 130kV line 1041_104 3_2 130kV line1041_104 5_1 130kV line1041_104 5_2 130kV line 1042_ 1044_ 1 130kV line 1042_ 1044_ 2 130kV line 1042_ 1045_ 1 130kV line1043_1 044_1 130kV line1043_1 044_2 220k Vline 2031 _2032 _1 220k Vline 2031 _2032 _2 400kVline4011_4012_1 400k V line 4011 _402 1_1 400k V line 4011 _402 2_1 400k V line 4011 _407 1_1 400k V line 4012 _402 2_1 400k Vline 4012 _407 1_1 400kV line 4021_4032_1 400kV line 4021_ 4042_ 1 400kV line 4022_40 31_1 400kV line 4022_40 31_2 400k Vline 4031 _404 1_1 400k Vline 4031 _404 1_2 400kVline4032_4042_1 400kV line 4032_4 044_1 400kVline4041_4044_1 400kV line 4041_ 4061_ 1 400k Vline 4042 _4043 _1 400kV line 4042_4044 _1 400k Vline 4043 _404 4_1 400k Vline 4043 _404 6_1 400kVline4043_4047_1 400kV line 4043_4045_1 400kV line 4044_4045_2 400kV line 4045_4051_1400kV line 4045_4051_2 400kV line 4045_ 4062_ 1 400k V line 4046 _404 7_1 400k V line 4061 _406 2_1 400k V line 4062 _406 3_1 400k V line 4062 _406 3_2 400 kV line 407 1_4 072 _1 400 kV line 407 1_4 072 _2 Tran sfor mer line 1041 _1_1 Transfo rmer line1042_2 _1 Transfor merline1043_3_ 1 Transform erline1044_4_1 Transformer line 1045_5_1 Transf ormer line 1011_1 1_1 Transforme rline1012_12_1 Transformer line 1013_13_1 Transf ormer line 1022_2 2_1 Transformerline2031_31_1 Tran sfor mer line 203 2_32 _1 Transformerline4041_41_1 Trans forme rline 4042 _42_1 Transform erline4043_43_1 Tran sform erline 4046 _46_1 Trans forme rline 4047_ 47_1 Transfo rmer line 4051_5 1_1 Transf ormer line 4061_6 1_1 Trans forme rline 4062_ 62_1 Transformer line 4063_63_1 Tran sfor mer line 407 1_71 _1 Transfor mer line 4072_72_ 1 Transfo rmer line 4011_1 011 Tran sfor mer line 4012 _101 2 Tran sfor mer line 101 2_50 001 Tran sform er line 1013 _500 02 Tran sfor mer line 101 4_50 003 Transformer line1021_50004 Transformer line4022_1022 Tran sfor mer line 102 2_50 005 Transfo rmer line 1042_50 006 Transformer line1043_50007 Tran sform erline 1044 _404 4B Tran sfor mer line 1045 _404 5B Trans forme rline 4031_ 2031 Transformerline2032_50008 Transf ormer line 4011_ 50009 Transforme rline4011_50010 Trans form erline 4021 _5001 1 Transformerline4031_50012 Tran sform erline 4041 _500 13 Tran sfor mer line 404 2_50 014 Transformerline4047_50015 Transfor mer line 4051_50 016 Transformer line 4062_50017 Tran sform erline 4063 _500 18 Transformer line 4071_50019 Trans form erline 4072 _5002 0 1_LOAD 1041 2_LOAD 1042 3_LOAD 1043 4_LOAD 1044 5_LOAD 1045 11_LOAD 1011 12_LOAD 1012 13_LOAD 1013 22_LOAD 1022 31_LOAD 2031 32_LOAD 2032 41_LOAD 4041 42_LOAD 4042 43_LOAD 4043 46_LOAD 4046 47_LOAD 4047 51_LOAD 4051 61_LOAD 4061 62_LOAD 4062 63_LOAD 4063 71_LOAD 4071 72_LOAD 4072 1011 1012 1013 1014 1021 1022 1041 1042 1043 1044 1045 2031 2032 4011 4012 4021 4022 4031 4032 4041 4042 4043 4044 4045 4046 4047 4051 4061 4062 4063 4071 4072 50001_G1 50002_G2 50003_G3 50004_G4 50005_G5 50006_G6 50007_G7 50008_G8 50009_G9 50010_G10 50011_G11 50012_G12 50013_G13 50014_G14 50015_G15 50016_G16 50017_G17 50018_G18 50019_G19 50020_G20 by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 17 / 29
- 18. P-V curves for Nordic-32 Loss of the most heavily loaded transmission line (N-1 contingency) by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 18 / 29
- 19. P-V curves for Nordic-32 Loss of a lightly loaded transmission line (N-1 contingency) by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 19 / 29
- 20. Power Flow results for Nordic-64 using GridCal Voltage Magnitude Variation in Per Unit (PSS/E results for Nordic - 64) by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 20 / 29
- 21. Power Flow results for Nordic-64 using GridCal Voltage Angle Variation in Degrees (PSS/E results for Nordic - 64) by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 21 / 29
- 22. Networkx Equivalent of Nordic-64 Type: MultiGraph Number of nodes: 66 Number of edges: 111 Average degree: 3.3636 by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 22 / 29
- 23. Graphical Visualization for Nordic-64 using networkx and matplotlib Graph representation without any contingency 130k V 1011 _1013 _1 130k V 1011 _1013 _2 130k V 1012 _101 4_1 130k V 1012 _101 4_2 130kV1013_1014_1130kV1013_1014_2 130kV 1021_10 22_1 130kV 1021_10 22_2 130 kV 104 1_10 43_1 130 kV 104 1_10 43_2 130kV 1041_1045 _1 130kV 1041_1045 _2 130kV1042_1044_1130kV1042_1044_2 130kV 1042_1045 _1 130kV1043_1044_1130kV1043_1044_2 220kV2031_2032_1220kV2031_2032_2 400kV 4011_ 4012_ 1 400kV 4011_4 021_1 400 kV 401 1_40 22_1 400 kV 401 1_71 00_1 400kV 4012_4022_1 400k V 4012 _710 1_1 400kV 4021_403 2_1 400kV 4021_4042 _1 400kV 4022_403 1_1 400kV 4031_402 2_1 400k V4031 _403 2_1 400 kV 403 1_40 41_1 400 kV 403 1_40 41_2 400kV4032_4042_1 400kV 4032_4044_1 400 kV 404 1_40 44_1 400k V 4041 _4061 _1 400k V4041 _510 1_1 400k V4041 _510 1_2 400kV4042_4043_1 400kV 4042_4 044_1 400k V4043 _404 4_1 400k V 4043 _404 6_1 400kV 4043_4 047_1 400 kV 404 4_40 45_3 400 kV 404 4_40 45_2 400kV 4045_4 051_1 400kV 4045_4 051_2 400kV 4045_4062_1 400kV 4046_4 047_1 400kV 4061_ 4062_ 1 400kV4062_4063_1400kV4062_4063_2 400kV4063_8500_1 300kV 5100_530 0_1 300kV5100_5500_1 400kV5101_5501_1 400k V 5102 _5301 _1 400kV5102_6001_1 400 kV 510 2_60 01_1 300 kV 540 0_55 00_1 300kV 5400_600 0_1 300k V 5400 _610 0_1 400k V5401 _550 1_1 400k V5401 _560 2_1 400kV 5401_6001_1 400kV 5402_6001_1 300kV5500_5603_1 300k V5600 _560 3_1 300 kV 560 0_6 000 _1 400kV5601_6001_1 300kV 6000_6100_1 400k V7100 _710 1_1 400 kV 710 0_72 00_1 400 kV 710 0_72 00_2 400k V7101 _710 2_1 400k V7102 _720 1_1 400k V 7200 _720 1_1 400kV 7200_7205 _1 400kV 7201_ 7203_ 1 400 kV 720 3_7 204 _1 400kV 7204_ 7205_ 1 DC Termina l 1 DC Term inal 3 Transformerline1041_41_1 Tran sform erline 1042 _42_1 Transfo rmer line1043_4 3_1 Transformer line1046_46_1 Transformerline1047_47_1 Tran sform er line 1051 _51_ 1 Transformer line 1061_61_1 Transforme r line 1062_62_1 Tran sfor mer line 106 3_63 _1 Tran sfor mer line 1011 _401 1_1 Tran sform erline 1011 _401 2_1 Transformer line1022_4022_1 Transformerline1044_4044_2 Transformerline1045_4045_2 Transformerline2031_4031_2 Trans forme r line 5100_ 5101 Tran sform er line 5102 _510 0 Trans form er line 5102 _5100 Transfo rmer line 5300_5 301 Transfo rmer line 5400_54 01 Transformer line 5400_5402 Tran sform er line 5500 _550 1 Transfo rmer line 5600_5 601 Transformer line 5603_5602 Transformerline6000_6001 1_BUS 41 L 1_BUS 42 L 1_BUS 43 L 1_BUS 46 L 1_BUS 47 L BUS 51 L 1_BUS 61 L 1_BUS 62 L 1_BUS 63 L 1_BUS 1011 L 1_BUS 1012 G 1_BUS 1013 G 1_BUS 1014 G 1_BUS 1021 G 1_BUS 1022 G 1_BUS 1041 L 1_BUS 1042 G 1_BUS 1043 G 1_BUS 1044 L 1_BUS 1045 L 2_BUS 2031 L 2_BUS 2032 G 4_BUS 4011 G 4_BUS 4012 G 4_BUS 4021 G 4_BUS 4022 4_BUS 4031 G 4_BUS 4032 4_BUS 4041 G 4_BUS 4042 G 4_BUS 4043 4_BUS 4044 4_BUS 4045 L 4_BUS 4046 L 4_BUS 4047 G 4_BUS 4051 G 4_BUS 4061 4_BUS 4062 G 4_BUS 4063 G 3_BUS 5100 G 4_BUS 5101_NOR 4_BUS 5102 4_BUS 5103 3_BUS 5300 G 4_BUS 5301 3_BUS 5400 G 4_BUS 5401 4_BUS 5402 BUS 5500 G 4_BUS 5501 3_BUS 5600 G 4_BUS 5601 4_BUS 5602 3_BUS 5603 3_BUS 6000 G 4_BUS 6001 3_BUS 6100 G 4_BUS 7100 G 4_BUS 7101 G 4_BUS 7102 4_BUS 7200 4_BUS 7201 G 4_BUS 7203 G 4_BUS 7204 G 4_BUS 7205 G 4_BUS 8500 G by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 23 / 29
- 24. Graphical Visualization for Nordic-64 using networkx and matplotlib Graph representation with contingency (400kV 4031–4032) 130kV 1011_ 1013_ 1 130kV 1011_ 1013_ 2 130kV 1012_ 1014_ 1 130kV 1012_ 1014_ 2 130kV 1013_10 14_1 130kV 1013_10 14_2 130kV 1021_1 022_1 130kV 1021_1 022_2 130 kV 104 1_10 43_1 130 kV 104 1_10 43_2 130kV 1041_104 5_1 130kV 1041_104 5_2 130kV1042_1044_1130kV1042_1044_2 130kV 1042_1045_1 130kV1043_1044_1130kV1043_1044_2 220kV2031_2032_1220kV2031_2032_2 400kV4011_4012_1 400k V 4011 _4022 _1 400k V4011 _710 0_1 400kV 4012_4022_1 400 kV 401 2_71 01_1 400kV 4021_40 32_1 400kV4021_4042 _1 400kV 4022_4031_1400kV 4031_4022_1 400k V4031 _403 2_1 400kV 4031_40 41_1 400kV 4031_40 41_2 400kV4032_4042_1 400kV 4032_ 4044_ 1 400kV4041_4044_1 400k V 4041 _4061 _1 400k V4041 _510 1_1 400k V4041 _510 1_2 400kV4042_4043_1 400kV 4042_4044_1 400 kV 404 3_40 44_1 400k V4043 _404 6_1 400kV 4043_ 4047_ 1 400 kV 404 4_4 045 _3 400 kV 404 4_4 045 _2 400kV 4045_405 1_1 400kV 4045_405 1_2 400kV 4045_ 4062_ 1 400kV4046_4047_1 400k V4061 _406 2_1 400kV4062_4063_1400kV4062_4063_2 400kV4063_8500 _1 300kV 5100_5300_1 300kV5100_5500_1 400kV5101_5501_1 400kV 5102_ 5301_ 1 400kV5102_6001_1 400 kV 510 2_6 001 _1 300 kV 540 0_55 00_1 300kV5400_6000_ 1 300k V 5400 _610 0_1 400kV 5401_ 5501_ 1 400k V5401 _560 2_1 400kV 5401_6001_1 400kV 5402_6001_1 300kV 5500_560 3_1 300kV 5600_ 5603_ 1 300 kV 560 0_60 00_1 400kV5601_6001_1 300kV 6000_6100_1 400kV 7100_ 7101_ 1 400kV 7100_7 200_1 400kV 7100_7 200_2 400kV 7101_7 102_1 400k V 7102 _720 1_1 400kV 7200_7201_1 400kV7200_7205_1 400kV 7201_7203_1 400k V7203 _7204 _1 400kV 7204_7205_1 DC Term inal 1 DC Term inal 3 Transformerline1041_41_1 Tran sform erline 1042 _42_1 Transform erline1043_43_ 1 Transformerline1046_46_1 Transformer line 1047_47_1 Trans forme r line 1051_ 51_1 Transformer line 1061_61_1 Transformer line 1062_62_1 Tran sfor mer line 1063 _63_ 1 Trans forme r line 1011_ 4011_ 1 Tran sfor mer line 101 1_40 12_1 Transfo rmer line1022_40 22_1 Transformerline1044_4044_2 Transformerline1045_4045_2 Transfo rmer line2031_4 031_2 Tran sform er line 5100 _510 1 Tran sfor mer line 510 2_51 00 Trans forme r line 5102_ 5100 Transf ormer line 5300_ 5301 Transf ormer line 5400_5 401 Transformer line 5400_5402 Tran sfor mer line 5500 _550 1 Transform er line 5600_560 1 Transformer line 5603_5602 Transformerline6000_6001 1_BUS 41 L 1_BUS 42 L 1_BUS 43 L 1_BUS 46 L 1_BUS 47 L BUS 51 L 1_BUS 61 L 1_BUS 62 L 1_BUS 63 L 1_BUS 1011 L 1_BUS 1012 G 1_BUS 1013 G 1_BUS 1014 G 1_BUS 1021 G 1_BUS 1022 G 1_BUS 1041 L 1_BUS 1042 G 1_BUS 1043 G 1_BUS 1044 L 1_BUS 1045 L 2_BUS 2031 L 2_BUS 2032 G 4_BUS 4011 G 4_BUS 4012 G 4_BUS 4021 G 4_BUS 4022 4_BUS 4031 G 4_BUS 4032 4_BUS 4041 G 4_BUS 4042 G 4_BUS 4043 4_BUS 4044 4_BUS 4045 L 4_BUS 4046 L 4_BUS 4047 G 4_BUS 4051 G 4_BUS 4061 4_BUS 4062 G 4_BUS 4063 G 3_BUS 5100 G 4_BUS 5101_NOR 4_BUS 5102 4_BUS 5103 3_BUS 5300 G 4_BUS 5301 3_BUS 5400 G 4_BUS 5401 4_BUS 5402 BUS 5500 G 4_BUS 5501 3_BUS 5600 G 4_BUS 5601 4_BUS 5602 3_BUS 5603 3_BUS 6000 G 4_BUS 6001 3_BUS 6100 G 4_BUS 7100 G 4_BUS 7101 G 4_BUS 7102 4_BUS 7200 4_BUS 7201 G 4_BUS 7203 G 4_BUS 7204 G 4_BUS 7205 G 4_BUS 8500 G by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 24 / 29
- 25. P-V curves for Nordic-64 Loss of the most heavily loaded transmission line (N-1 contingency) by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 25 / 29
- 26. P-V curves for Nordic-64 Loss of a lightly loaded transmission line (N-1 contingency) by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 26 / 29
- 27. Technologies Used GridCal (as a library) Python (scripting) networkx (Topological analysis and Visualization) matplotlib (Visualization) numpy (Calculations) Pycharm (IDE) PSS/E (for power flow comparison) by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 27 / 29
- 28. References GridCal: a research oriented power systems software. Lecture series on Power System Dynamics by Prof.M.L.Kothari, Department of Electrical Engineering, IIT Delhi. IEEE Power and Energy Society technical report PES-TR19 voltage stability analysis and security assessment Joe H. Chow; Juan J. Sanchez-Gasca, ”Steady-State Voltage Stability Analysis,” in Power System Modeling, Computation, and Control , IEEE, 2020, pp.47-85 by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 28 / 29
- 29. Codes for this project Thank You by Anmol Dwivedi Voltage Stability Analysis using GridCal April 2020 29 / 29