hw5_solution - Chapter 9(Summary questions for insights Q1...

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Chapter 9: (Summary questions for insights) Q1: a) What is an admittance matrix? Please give definition to all variables. b) For a given system, how to construct its admittance matrix? Answer: Please refer to the note of March 9, P9 and P13. (Please note we use the same definition in the circuit analysis except buses are called nodes in more general circuits. Please note that bus design is an important issue in power systems.) Q2: a) What is a power flow analysis problem? B) Where is the nonlinearity from? Answer: a) Please refer to the note of March 9, pages 19-21. Given generations and loads, we would like to know the power flows on the transmission lines. b) Please refer to the note of March 9, pages 1 and 8. Nonlinearity comes from the constant power loads/generations assumption. Chapter9: (Calculations for insights) 9.1 a)Repeat problem 4.27 by using admittance matrix and its associated power flow equations assuming the given values are in p.u system. Discuss how is modeled in the problem. 2 G Q Answer: a) Here Q G 2 is modeled as constant power, and then the admittance matrix is as: = line line line line y y y y Y , 90099 . 9 990099 . 0 0.1) + 1/(0.01 j j y line = = We can see that Y is a singular matrix. The associated power flow equations are: = = 2 * 2 2 2 1 1 2 1 * 2 2 1 1 1 0 1 1 0 1 δ δ Y S jQ S S V V Y V S V S D G D G =
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