# An Assessment Of Distribution System Reliability Of PHCN (A Case Study Of Aba District)

## Abstract

In the recent past various attempts have been made to improve the adequacy of power supply and reliability of the supply network. This project work focuses on the reliability of the distribution system of PHCN with Aba distribution network as case study, using daily fault report data for three years viz: 2006, 2007, and 2008.

The Poisson distribution and the chi-square were used to determine the appropriateness of the observed data collected. In other words, the chi-square was used to asses the goodness of fit of the Poisson distribution hypothesis at 0.05 level of significance.

Lastly, the project work estimates the reliability indices of failure rate R(t), system reliability R(t), failure density function F(t) and system interruption frequency index.

## Table Of Contents

- Title page
- Approval page
- Dedication
- Acknowledgement
- Abstract

### Chapter One

- 1.1: Introduction
- 1.2: Definition of terms

### Chapter Two

- 2.1: Literature review

### Chapter Three

- 3.1: Research methodology
- 3.2: Sampling of techniques
- 3.3: Source of data
- 3.4: Validation of instruments
- 3.5: Techniques of data analysis

### Chapter Four

- 4.1: Case study Aba distribution Network
- Table 1: Monthly peak load and number of consumers on Aba network.
- Table 4.2: Summary of fault data for Aba network (2006)
- Table 4.3: Summary of fault data for Aba network (2007)
- Table 4.4: Summary of fault data for Aba network (2008)

- 4.1.1: Computation of fault intervals/mean
- 4.1.2: Computation of variance
- Table 4.5: table of values for F(x-x)2

- 4.1.3: computation of Expected frequency
- 4.1.4: Computation of chi-square
- Table 4.6: Fault intervals, observed frequencies calculated or expected frequencies, mean, variances and calculated chi-square for Aba network

- 4.2: Computations of reliability indices operating in hour:
- 4.2.1: Failure rate for months in hours
- 4.2.2: System reliability for months
- 4.2.3: failure distribution functions for the system:
- 4.2.4: Life time cumulative distribution function (CDF) operating in hours
- 4.2.5: Life probability distribution function (PDF)
- Reliability R(t) operation time in hours.
- Table 4.7: Reliability indices for Aba

### Chapter Five

- 5.1: Discussion
- 5.2: Summary

### Chapter Six

- Conclusion And Recommendation
- 6.1: Conclusion
- 6.2: Recommendation
- References

## Chapter One

### 1.1 Introduction

Distribution networks differ from transmission networks in quite a number of ways, ranging from voltage magnitude to the number of branches and sources. The number of branches and source is mush higher in distribution networks and the voltage magnitude lower. Its general structure of make up is quite different from that of the transmission networks.

A typical distribution system consist of a step- down transformer e.g. 132/11kv, at a bulk supply point feeding a number of cables. In a series of step-down three-phase transformers e.g. 11kv/415v, are spaced in route and from these, the consumers are supplied three-phase, four wire networks which gives 240V single phase to houses and other similar loads.

The objective of power system is to maintain a continuous and adequate power supply to its consumers at a reasonable rate of return. In Nigeria, this objective is far fetched. Hence, there is the need to focus our attention on reliability as a way of assessing and improving the “wire business” as well as optimizing our investment in the distribution network.

It has been observed that a major part of service interruptions experienced by consumers has its origin in failure from the distribution system (mostly 33kv and below in Nigeria, with radial arrangement and the distribution system reliability studies have been hindered due to the unavailability of component outage on the distribution system.

Thus, the need to maintain a reliable and effective electrical service to consumers using the available apparatus on the system is very important and necessary.

In this project, the assessment of distribution system reliability can be facilitated using Poisson model, with PHCN Aba as case study.

### 1.2 Definition Of Terms:

#### 1.2.1: Reliability:

Can be define as the ability of an item/equipment/system to perform a required function under a stated condition for sated period of time.

#### 1.2.2 Failure Rate:

This is the number of faults or failure per unit time and symbolized by λ.

#### 1.2.3: Mean Time Before Failure (MTBF):

This is the mean value of the length of time that elapses between failures.

### 1.3: Causes Of Faults:

Faults could be caused by the following;

- Lightning strokes
- Strong swind
- Tree falling across
- Vehicles collision with tower/poles of consumers
- Erosion of tower/poles foundation
- Vandalization
- Illegal operation of consumers

## Chapter Five

### Discussion

The failure rate for Aba ranges between 0.583 to 0.622 from table 4.7. This is evenly or there about distributed through the months and it can be adduced to availability of good maintenance action to the system.

From table 4.7 also it could be seen that the reliability of the distribution system decreases with in the number of working hours which was from 0 to 9 hours. In other words, the system reliability was inversely proportional to the operating time in hours.

Like wise the CDF-F(t) of the system increases as the working hours increase PDF-F(t) decreases with an increase in operating hours and vice versa

### 5.2 Summary

From the analysis of the results obtained, it could be summarized that;

- The distribution system reliability is inversely proportional to the operating time in hours. That is R(t) x (
^{1}/_{Tgh}) In other words, the system reliability increase, as the operating time in hour tend to zero - The life time CDF F(t) of the system is directly proportional to the working hours. That is; F(t) x T(h); in other words, CDF increases as operating hours increase
- The lifetime PDF F(t) is inversely proportional to the operating hours. That is; F(t) x
^{1}/_{T}(h)

### 5.3 Conclusion

** **The use of chi-square test confirmer that the data on the system failure rates in Aba district is quite reliable. The reliability index for the three years under review should be a remarkable stability. This implies the net work is adequately maintained within these years.

This implies good economic activities and in social comfort

Good reliability index could be as a result of combination of two or more of these:

- Good equipment
- Good maintenance team
- Moderate loading of the system
- Protection against vandals
- Good location for the system network and others.

### 5.5 Recommendation

From the study carried out, it would be okey to make the following recommendation

- Aba district network is stable within the years of study.
- Reliability is high range for 0.583 to 0.625
- Retraining of PHCN staff to increase efficiency particularly with respect to equipment maintenance
- Always improve on capacity before adding more network
- Government should provide more generation, transmition and distribution networks to enhance their operation.

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