ECE 411 Project

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California State University, Northridge *

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411

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Electrical Engineering

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Jan 9, 2024

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docx

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Fall 2021 California State University, Northridge Department of Electrical & Computer Engineering December 4, 2021 Fall Semester ECE 411 Project

Introduction: In this project, we are studying the load flow analysis in which steady-state voltages are computed from a given two-generator power system. We do this by recreating this system in a program used to simulate power flow (Matlab) and analyzing the effects that are seen on elements of the power system when implemented with one another. This given model was built using an arrangement of 2 generators, 2 transformers, and 7 buses with slightly different values at the beginning and end of our system. In order to know which elements of the system needed particular pieces of information that were not given to us, we broke down the load flow of the entire system, and performed hand computations for certain values of the system that were needed to make this model operate as intended. Procedure: Software Needed for This Project:

Matlab (Simulink) was used to recreate the entire 7-bus power system pictured above, also using the system parameters given initially before starting. We used the value of z1 as the rating for the transmission lines, in addition to the given variable lengths of each individual line. The given values of X’’ and X0 were assumed to be presentations of the generator's impedances, and the transformer impedances. We then needed to make our Ybus calculations by hand, and used Matlab as well, to help us do the computations necessary for the unknown values. Once the unknowns were found, and we could see the oversaturation of the system as a whole, we added a shunt capacitor onto bus 4 in order to balance out the system. We gave this capacitor a rating of 100 Mvars. After adding in this additional element to our system, we are able to conclude that our MVA ratings are well within the desired criteria of the system. Results: Bus voltages before AND after capacitive load was added YBus Matrix: Calculations:

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------------------------------------------------------------------------------------------------------------ Ibase = Sbase / Vbase = 100MVA / 13.8kV = 7.2 kA Zbase = (Vbase)^2 / Sbase = (230kV)^2 / 100MVA = 529 Ω G1: 100MVA / 100MVA = 1pu ----> 13.8kV / 13.8 kV = 1pu G2: 200MVA / 100MVA = 2pu ----> 15kV / 13.8 kV = 1.087pu T1: 100MVA / 100MVA = 1pu ----> 1pu = 16.67pu T2: 200MVA / 100MVA = 2pu ----> 1.087pu = 16.67pu Bus 1: Y11 = (1 / j(.12) ) + (1 / j(0.1)) = -j18.33 Y11 = Y21 = j10 Y22 = (1 / j(0.1)) + (L1pu) = 11 - j(78.76) Y23 = Y32 = - (1 / Lin) = -11 + j(68.76) ------------------------------------------------------------------------------------------------------------ Zin = (0.08 + 0.5i) / 529Ω = (1.512 * 10^-4 + j(9.451 * 10^-4)1/km L1pu = (2.268 + 14.17i) / 1000 = 0.002268 + j(0.014175) L2pu = (1.0586 * 10^1 + 6.616i * 10^1) / 1000 = 0.01058 + j(0.06616i) L3pu = (6.04 + 37.807i) / 1000 = 0.00605 + j(0.0378) L4pu = (2.268 + 14.17i) / 1000 = (1/L2) + (1/L5) + (1/L3) L5pu = (2.561 + 47.25i) / 1000 = 0.00756 + j(0.04725) ------------------------------------------------------------------------------------------------------------ (1 / L2) = 2.3579 - j(4.73i) Y32 = (11 - j(68.76)) + (1 / (0.01058 + 0.06616i)) = 8.6421 - 54.03i Y34 = Y43 = - (1 / (0.01058 + 0.06616i)) = - 2.3579 + 14.73i *L4pu = (2.3579 - 14.73i) + (3.3 - j20.632) + (4.126 - j25.7898) ------> Y44 = 9.7839 - j61.1518 Y45 = Y54 = - (L3) = - 4.126 + j25.17898 Y46 = Y64 = - (L5) = - 3.3 + j20.632 ------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------ Y55 = (1 / L3) + (1 / L4) = (4.1284 - 25.7898i) + (11 - j68.78)

------> Y65 = 15.126 - j94.5698 Y56 = Y65 = -Y65 = (-11 + j68.78) = - L4 X12 (New) = (0.1) * (100MVA / 200 MVA) * (230kV / 230kV)^2 = 0.5pu ------> Y66 = (1 / j(0.05)) + (1 / L5) + (1 / L4) Y66 = -20j + (3.3 - j20.632) + (11 - j68.78) = 14.3 - j109.412 ------> Y77 = (1 / j(0.12)) + (1 / j(0.05)) = - j8.33 - j20 = -j28.33 ------------------------------------------------------------------------------------------------------------ Simulink Power System (Before Capacitor is Added) Simulink Power System (After Capacitor is Added) Conclusion: The value of the capacitive bank was tested by implementing various values of Mvar, and seeing which of them gave us a reasonable balance to our system as a whole. We needed to find a value that would not only satisfy a Q rating between the minimum and maximum values given at the PV bus, but would also result in a PQ bus voltage of over 0.96pu. The value we found to work for our criteria was 100 Mvar. Here, we have the case where the capacitor bank was set to 50 Mvar, where the PQ voltages didn’t unanimously go greater than 0.96 And here, we have the capacitor bank that we set to 150 Mvar, where some of the PQ voltages go above 1pu, showing over-voltage in the system. In conclusion, it is easy to see how adding in a capacitive bank clearly balanced our entire system, where it was previously overloaded without the addition of the new element, and could not run to the appropriate efficiency that our project criteria desired. By extensively testing our system, and imputing numerous values into the bank until we found the perfect balance, we were

successfully able to design the power system to the most appropriate standard that achieves a perfectly balanced load flow through all elements of the schematic.

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