Modeling and Simulation of Steady State Load Flow Analysis Techniques and Implementation of Broyden’s Method

Abstract

This thesis presents a study of power flow analysis in electrical power networks. In the case of steady-state or under no external influence, the power flow is mathematically represented in terms of active and reactive components. These equations are in the form of nonlinear algebraic equations that can be used to represent each of the sub-networks or power buses in the complete power network. The unknown parameters of the network can be identified by solving the complete network model/set of equations. Line Losses

and system losses are calculated by computing the difference between total power gen- erated and total power demand. The solution of the network model is possible using

iterative techniques such as Gauss seidel, Fast decoupled, and Newton-Raphson method (NR). Among these methods, the NR method is well used in the literature, however, it involves the inverse of the Jacobian matrix in each iteration which is computationally expensive in large-scale settings. To address this issue Broyden’s method has been used to ensure a rank-1 update of the Jacobian matrix at each iteration and Sherman

Morrison’s formula is implemented to compute the Jacobian inverse using rank-1 up- dates. This saves a large portion of the computational cost associated with the direct

inverse of Jacobian in each iteration. The performance of Broyden’s method is compared with the NR method on various benchmark power networks, including the IEEE 3-Bus, 4-Bus, 5-Bus, 6-Bus, 9-Bus, and 39-Bus systems. Implementing these methods on some benchmark examples of power networks and it is observed that the computational cost is 6% better than the Iterative NR method for the IEEE 3 bus system. In terms of computation time IEEE 3-Bus,4-Bus,5-Bus,6-Bus,9-Bus, and 39-Bus NR method takes about 0.066s,0.063s,0.082s,0.089s, and 0.098s respectively. Similarly, Broyden’s method on IEEE 3-Bus,4-Bus 5-Buss,6-Bus,9-Bus, and 39-Bus improves computational time

0.033s(6%),0.039s(5%),0.042s(%4),0.048s(4%),0.066(2%),0.066s(2%), respectively. Fur- ther applying rank1 update for Jacobin matrix for IEEE 3-Bus,4-Bus 5-Buss,6-Bus, 9-Bus

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and 39-Bus calculation time improves as 0.039s(5%),0.057s(4%),0.061s(2%),0.070s(3%), 0.073s(2%),and0.066s(2%) respectively. The calculation time for power flow analysis increase as the system size increase still less than the Newton-Raphson method. Due to the sparsity of the Jacobin matrix calculation time doesn’t increase notably as the

size goes to IEEE-39 Bus system. The problem of singularity that arises in the Newton- Raphson method is solved. It is observed that the method is robust to the choice of initial

approximation and takes lesser time to simulate as compared to the Newton-Raphson method.