# Laod Flow Analysis Of A Four Bus Network Using Newton Raphson’s Method With NEPLAN Power System Analysis Software

## Abstract

Load flow is the steady state solution of a power system. The necessary information obtained from load flow is active and reactive power flow along the transmission lines as well as Voltage magnitude and phase angle at different buses of the network.

In this project, we have carried out load flow studies on a four bus grid network using Newton Raphson’s method of load flow studies.

The aim of this project was to ensure that no system overload occur in the power system when both generation and loads are varied.

The simulation software used is NEPLAN power system analysis software.

## Table Of Contents

### Preliminary Page(s)

- Contents Pages
- Title pages
- Approval page
- Dedication
- Acknowledgement
- Abstract
- Table of contents

### Chapter One

- 1.0.0 Introduction
- 1.0.1 Neplan power system analysis software
- 1.2.0 Literature review

### Chapter Two

- 2.0.0 Modeling of Transmission line
- 2.0.1 Short transmission line
- 2 .0.2 Medium transmission line
- 2.0.3 Representation of transmission line
- 2.0.4 Long transmission line
- 2.1.0 Transformer modeling
- 2.1.3 Tap Changing Transformer
- 2.1.3 Phase Shifting Transformer
- 2.1.3 Synchronous Motor Modeling

### Chapter Three

- 3.0.0 Newton Raphson load flow technique
- 3.0.1 Bus classification
- 3.0.2 Bus admittance matrix
- 3.0.3 Jacobian matrix
- 3.0.5 Power system simulation data
- 3.1.5 Transmission line data
- 3.2.5 Types of tower design
- 3.3.5 Single circuit tower design
- 3.4.5 Double circuit tower design
- 3.1.0 Types of conductor
- 3.1.2 Standard transmission system impedance
- 3.1.3 Load data
- 3.1.4 Generator data

### Chapter Four

- 4.0.0 Simulation and Result
- 4.1.0 Load Flow simulation result
- 4.2.0 Load Flow analysis

### Chapter Five

- Conclusion
- Recommendation
- References

## Chapter One

### 1.0.0. Introduction

In a 3-phase Ac power system, active and reactive power flow from the generating station to the load through different network buses and branches. The flow of active and reactive power is called the power or load flow.

The bus voltages are affected by the reactive power flow due to the coupling between the two of them. Power flow studies provide a systematic mathematical approach for determination of various bus voltages, their phase angle, active and reactive power flows through different branches, generators and load under steady and unsteady state conditions for adjustments where necessary.

In the last chapter, we shall see how NEPLAN software is used to simulate the reactive and active power in the 330KV on a four bus network.

### 1.0.1 NEPLAN Power System Analysis Software

NEPLAN is educational software that can be used for any kind of power system analysis, such as solving load flow problems.

This can be achieved through the following techniques:

- Gauss – Seidel techniques
- Newton – Raphson’s Techniques
- Fast decouple techniques

### 1.2.0 Literature Review And Historical Development

Load flow study in power system parlance is the steady state solution of the system network.

The power system is usually modeled as an electric network and solution for steady state power and voltage at various buses. The load are given in terms of complex power rather than impedances, the generators behave more like power source than voltage source and as a result of this factors, direct analysis of the circuit is not possible.

The main information obtained from load flow steadies comprises the magnitude and phase angle of load bus voltage, real and reactive power flows on transmission lines and the power at reference bus, other variable being specified. Load flow calculation is the most frequently performed in power system planning, operational planning and operation control and are increasingly being used to solve very large system for purposes such as outage security assessment, transmission line loss minimizing, continuous monitoring of the system, economic dispatch problem and others.

A review of load flow calculation has been presented by B.stott (1929, in his book titled” effective starting process for Newton Raphson”). Prior to 1930, all power flow calculations were made by hand. Between 1930 and 1956, network calculations. These devices are miniature models of the network be studied. The behavior of the system is determined by measuring the electrical quantities in the model.

J.B ward and H.W. Hale, (in 1956, in book titled “Digital computer solution of power flow problems”), described the first real computer program for solving power flow problem Gauss Seidel algorithm for the solution of linear equations that descried an electrical network. Since the network equations are quadratic, an interactive procedure is required. Because of the nature of parameters in power system networks, a solution is usually obtained.

The Gauss Seidel method encountered greater difficultly in arriving at a solution for large networks, since the effect in adjusting the bus voltage during iterations is reflected only to the buses that are the immediate neighboring buses, several iterations are required for adjustment may be made and the number of iterations increased dramatically for an actually workable system. Other methods includes Bonneville power administration (1963, which used “Newton method of load flow problems”) was the first to develop a very successful method of load flow calculations.

This method uses the Newton Raphson’s algorithm to solve the simultaneous quadratic equations that describe the power system. In this method, the number iterations required to obtain a solution is practically independent of the size of the system. Many problems that could not be solved with Gauss Seidel method, for instance, systems with negative impendence were successfully solved by the Newton Raphson’s method.

The Newton Rephson’s methods, if the starting values of voltage profit are not judiciously chosen, early power flow programs used one iteration of the Gauss Seidel method before beginning the Newton Raphson procedure. This process was found to the ill-advised because the Gauss Seidel algorithm usually distorts the voltage profile on the first few iterations and causes some buses of the system to be far away from the solution them is the original estimate. The addition, the restriction of non negative impedances imposed on the gauss method unnecessarily limits the Newton method.

The Newton Raphson method of solution of power flow problem was described by van ness, the technique produced a solution in very little iteration. It is a computer memory for the storage of the Jacobian matrix. Due to the ability of the Newton Raphson method to solve difficult problems and speed advantage, the Bonneville power administration group replaced their power program with the Newton Raphson method in production work, they noticed that the Newton method is slower than Gauss method and requiring a great deal of memory.

They concluded that the difficult was not with the Newton algorithm but the ordering of the equation in the elimination procedure. The solution to this problem was not solved, it still exceeded that of the Gauss Seidel method but the speed and stability of solution justified the conversion of the method.

One important characteristics of the power system is that the real power is mostly dependent on the voltage angles at different buses while the reactive power is highly dependent on the voltage magnitude. Due to these factors, the fast decoupled technique took the advantages of the weak coupling between the reactive power and the voltage magnitude, and also between the real power and the voltage angle.

Other assumptions which are also valid in power system operation were also made in order to simplify the power flow problem.

## Chapter Five

### Conclusion, Recommendation And Reference.

#### Conclusion:

The field of power is so complex that theoretical and practical knowledge should complement. In view of the complexity of project involving load flow simulation on a 330kV grid network on northern part of Nigeria using NEPLAN, good knowledge and supervision are required for the successful execution of this project.

This project helps us to determine the voltage at the buses and equally to understand the flow of reactive and active voltage in the transmission line. It equally solves the load flow problem retaining the robust convergence characteristics of Newton’s method.

Finally this project on load flow simulation on a 330kV network was carried out in a way it should be easy for references.

#### Recommendation

We hereby recommend to the Federal Government of Nigeria and to the appropriate authorities to see the load flow” studies on the grid network as a guide to alleviate the country from the present epileptic power supply. With this, Region or area that is deficient of power supply, maybe, due to increase in load can be easily be compensated by the introduction of SVC (static valve compensators) or by introducing more transmission lines or new generating stations into the network system.

Also, Federal Government and appropriate authorities should liaise with the sole producer of this package (NEPLAN) to make it affordable to individuals and schools so that it use can be understood and applied in studying the network, with all these put in place we hope that, persistent power failure in Nigeria will come to minimal.

**Laod Flow Analysis Of A Four Bus Network Using Newton Raphson’s Method With NEPLAN Power System Analysis Software **

**Laod Flow Analysis Of A Four Bus Network Using Newton Raphson’s Method With NEPLAN Power System Analysis Software**

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