1.0 Introduction
The load flow study in a power system constitutes a study of paramount importance. This is the study that reveals the electrical performance and power flows (real and reactive) for specified conditions when the system is operating under steady state. The load flow study also provides information about the line and transformer loads (as well as losses) throughout the system and voltages at different points in the system for evaluation and regulation of the performance of the system under conditions known as prior (problem in order of importance).
The term contingency in the power system network is the loss of major transmission element or a large generating unit. The necessary information obtained from load flow are the active and reactive power flow along the transmission lines, voltage magnitude and phase angles of different buses up the network.
In a 3 — phase A-C power system active and reactive power flows from the generating stations to the load through different network bases and branches/transmission line. The flow of active and reactive power is known as power or load flow. The bus voltages are affected by the reactive power flow due to the compiling between the two of them.
Load flow provides a systematic mathematical approach for determination of various bias voltages, their — phase angles, active, and reactive power flow through different branches, generators and loads under steady state conditions.
We shall see in chapter four how NEPLAN software is used to simulate the reactive and the active power in 330KV network on the Eastern part of Nigeria.
1.1 Literature Review
Load flow study in power system, a parlance (a particular way) is the steady state solution of the power system network. The power system is usually modeled as an electric network and solved for the steady — state powers and voltages at various buses.
The loads are given in terms of complex power rather than impedance. The generators behave more like power sources than voltages and as a result of these failures directs analysis of the circuit is not possible. The main information obtained from load flow studies comprises the magnitude and phase angles of load bus voltages, real and reactive power flows on transmission lines and the power at the reference bus.
Load flow calculation is most frequently performed in power system planning, operating planning and operation control and is increasingly being used. To solve very large system for purposes such as outage, security, assessment, transmission line loss.
A review of load flow calculation has been presented below:
Form ward and Hale I in 1956, describe the first real computed program for solving load problems .Gauss — seidel algorithm for the solution of linear equations was the first method developed for solution of the equation that describes an electrical method. Since the network equations are quadratic, an iterative procedure is required.
Because of the nature f parameters in power system work, a solution is usually obtained.
The Gauss-seidel method encountered greater difficulty in arriving at a solution of the larger networks. Since the effect of an adjustment in the bus voltage during an iteration is reflected only to the buses that are the immediate neighboring buses, several iterations are required for the adjustments to propagate across the system.
Conflicting adjustments may be made and number of iteration increased dramatically for large systems. In some cases no solution was obtained for an actual workable system.
According to B. Stott (2) prior to 1930, all power flow calculations were made by hand. Between 1930 and 1956, network calculator or network analyzers were used to perform load flow calculation. There devices are miniature models of the network being studies. The behaviour of the system is determined by measuring the electrical quantities in the model.
In 1967, W. F. Tinney and C. E. Hart describe load flow using Newton-Raphson Method Solution as the important and most sophisticated method of power flow studies, which users polar coordinate preferably, because rectangular coordinates needs more memory. The number of iteration is more on less independent of the system vary between 3 and 5 iterations.
The Newton-Raphson method solution of power flow problem was described by Van Ness the technique produced a solution in very few iterations. It is faster than Gauss method but it requires large computer memory for the strage of the Jacobian matrix.
Due to the ability of the N — R method to store difficult problems and speed advantage, the Beneville power replaced their power program with the N. R. method. One characteristic of the system is that the real power is mostly dependents on the voltage magnitude. Due to these factors, the fast decompiled load flow 5 solution was developed by B. Stalt in 1974, the decompiled technique took the advantages of the weak compiling between the real and voltage magnitude and also between the reactive power and the voltage magnitude and also between the reactive power and the voltage angle.
Bonneville Power administration was the first to develop a very successful method of calculating load flow. This method uses Newton-Raphson algorithm to solve the simultaneous quadratic equations that describe the power system. In this method the number of iteration required to obtain a solution is practically independent of the size of the system is practically independent of the size of the system.
Other assumptions which are valid in power system operations were also made in order to simplify the power flow problem. The time The N — R method and the memory requirement is about sixty, percent of the normal Newton's method. Several requirements have been made such as reactive model and the hybrid model by Behnam-Gudani for improved convergence characteristic.
Also research have been going on in developing load flow fast convergence algorithm, the Qausi — Newton power flow was developed by Adam Semlyen. This method exploits the combination of Newton —Raphson steps where the whole jacobian is computed and consequently factorized, the recent Jacobian is reused with forward and backward substitution were only a small portion of the Jacobian Matrix is updated.
The partial Jacobian updates are introduced in the power flow program into two ways. Partially refactorization of the Jacobian and a simple step solution is corrected using the Metrix Modification Lemma (MML).
The strategy to reduce the computational burden of the Newton power solution is to keep the Jacobian constant for a number of iterations. An idea introduces to reduce the computing time is partial updates of the Jacobian matrix. It was noticed that not all equations converge at the sometimes, there is not need for updating the whole Jacobian Matrix at every step as it is done in the conventional Newton method.
It was also noticed that at a certain step in the iteration process some residuals have already converged and most residuals are decaying within a few iterations and also few identifiable residuals will converge fast only if the corresponding part (rows) of the Jacobian is updated.
A saving in the order of 50% was achieved compared to the Newton method. The rectangular formulation of the N — R method has cover the years received great attention, such improvement in N R load flow is reported in this paper, an attempt was made to use as linear a model as possible, both the model and the bus constraints are retained.
The N — R method was then applied to the enlarge set of equations written in terms of bus voltages and currents. The scheme combined with a procedure for handling P I buses loads to a computationally efficient algorithm particularly efficient and advantageous in the presence of zero — injection buses.
The idea is to solve an augmented system in which both bus voltages and current injections appear as state variable and both power and current mismatches are zerned. When rectangular coordinates are employed, this yields a set of linearly — coupled quadratic equations rather than the usual set of fully coupled non-linear equations.
This material contains electrical diagrams, circuits, illustrations and more (Very detailed)
…
