Answer to Question #223756 in Electrical Engineering for Zoleka

Question

Multiple choice questions
Question 5
Because of the nature of the power flow bus data, nodal equations do not directly fit
the linear-equation format, and power flow equations are actually nonlinear. However,
the Gauss-Siedel method can be used for the power flow solution.
(1) True.
(2) Only true for systems with less than 14 buses.
(3) False.
(4) Only true for systems with fully transposed transmission lines.

Answer 1

The given statement is True (Option 1)

Consider the following for a bus k

P_k = real component of power

Q_k = reactive component of power

V_k = Voltage magnitude

Since power-flow bus data consists of P_k and Q_k for load buses or P_k and V_k for voltage-controlled buses, nodal equations do not directly fit the linear equation format and due to this reason, the current source vector I is unknown and the equations are actually nonlinear. The Gauss-Siedel method can be applied for the power-flow equation in the following way: 

$v_k (i+1)= \frac{1}{Y_{kk}}[\frac{P_k-jQ_k}{V^*_k(i)}-\sum_{n=1}^{k-1}Y_{kn}V_n(i+1)-\sum_{n=k+1}^{N}Y_{kn}V_n(i)]$

Where, Y_kn is the element in the k^th row and n^th column of matrix Y. Hence, the given statement is 

True.