Distributed Slack Bus for the Economic Dispatch with Renewable Energy

UNIVERSITY OF NAIROBI

FACULTY OF ENGINEERING

DEPERTMENT OF ELECTRICAL AND INFORMATION ENGINEERING

DISTRIBUTED SLACK BUS FOR THE ECONOMIC DISPATCH WITH RENEWABLE ENERGY

PROJECT INDEX:PRJ (044)

SUBMITTED BY

OCHIENG O BILLY

F17/1397/2010

SUPERVISOR: MR PETER MOSES MUSAU

EXAMINER: MR OGABA

PROJECT REPORT SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE AWARD OF THE DEGREE OF

BACHELOR OF SCIENCE IN ELECTRICAL AND ELECTRONIC ENGINEERING

OF THE UNIVERSITY OF NAIROBI 2014

SUBMITTED ON:

24th April, 2015

DECLARATION OF ORIGINALITY

NAME OF STUDENT: / OCHIENG O BILLY
REGISTRATION NUMBER: / F17/1397/2010
COLLEGE: / Architecture And Engineering
FACULTY/ SCHOOL/ INSTITUTE: / Engineering
DEPARTMENT: / Electrical and Information Engineering
COURSE NAME: / Bachelor of Science in Electrical and Electronic Engineering
TITLE OF WORK: / DISTRIBUTED SLACK BUS FOR ECONOMIC DISPATCH WITH RENEWABLE ENERGY

1)I understand what plagiarism is and I am aware of the university policy in this regard.

2)I declare that this final year project report is my original work and has not been submitted elsewhere for examination, award of a degree or publication. Where other people’s work or my own work has been used, this has properly been acknowledged and referenced in accordance with the University of Nairobi’s requirements.

3)I have not sought or used the services of any professional agencies to produce this work.

4)I have not allowed, and shall not allow anyone to copy my work with the intention of passing it off as his/her own work.

5)I understand that any false claim in respect of this work shall result in disciplinary action, in accordance with University anti-plagiarism policy.

Signature:

…………………………………………………………………………………

Date:

…………………………………………………………………………………

CERTIFICATION

This report has been submitted to the Department of Electrical and Information Engineering, University of Nairobi with my approval as supervisor:

…………..………………………………

Dr. Nicodemus AbunguOdero

Date :…………………………….

DEDICATION

I dedicate this project to my dear mother for her love, support and encouragement throughout my academic journey.

ACKNOWLEDGEMENT

First, my deepest appreciation and thanks are expressed towards my supervisor and advisor, Mr. Peter Musau Moses, for his support, criticism , direction and belief in this work. Without his consistent guidance and encouragement, the accomplishment of this study would not be possible. My appreciation also goes to Prof. Nicodemus AbunguOdero, thank you for the advice and encouragement during the life of this project.

Second, I wish to thank my colleagues and friends. I would like to acknowledge Kimani Elijah Mugo for his help in both technical and personal aspects. I would also like to appreciate AtanasioMutiriaMugambi, Kelvin J Obade and Joseph Munene for their contribution towards the accomplishment of this project. Finally, my special thanks go to my dearest mother andsiblings, without their love, support and encouragement, I could not finish my undergraduate study.

ABSTRACT

Power Systems are established in order to facilitate transfer of power to the respective load centers with reliability, security and economy using sound technical and commercial principles. The nature of electrical energy is such that it is produced and consumed on a real-time basis whereby production and consumption should have an ideally instantaneous balance. In order to arrive at this balance, all network parameters need to be determined so as to achieve effective power transfer. This is achieved through carrying out load flow studies in the power system. With the increased penetration of distributed generation into the power distribution system due to deregulation and liberalization of the energy market, the traditional load flow analysis that assumes a single slack us has become impractical. A Distributed Slack Bus (DSB) remedies the shortfalls of the single slack bus model. The DSBs are based on participation factors which may be constant values or network based whereby they reflect network parameters, load distribution, generator locations and capacities. In this project, a DSB usingcombined participation factors based on scheduled generation capacities of the system is designed in order to distribute the system losses among the generators. A DSB algorithm is developed and implemented using a Newton Raphson Solver on a MATLAB platform. The IEEE 14 Bus is used as a case study. Renewable energy sources were introduced into the system and the generation cost compared between systems with Renewable Energy sources and those with only thermal generators in both the single slack bus model and the distributed slack bus model.

The distributed slack bus employed resulted in a reduction in overall real power generation from 272.593 MW to 272.409 MW in the 14 bus model and cost of generation also decreased in both buses. Real power line losses also reduced in the buses. The change in the generation levels of the voltage controlled buses resulted in a proper economic dispatch scheme which gave an accurate representation of the network parameters. The cost of generation was considerably reduced upon introduction of wind and solar generators into the system as compared to systems without these sources. An even more accurate network model was obtained by using combined participation factors.

TABLE OF CONTENTS

DECLARATION OF ORIGINALITY

CERTIFICATION

DEDICATION

ACKNOWLEDGEMENT

ABSTRACT

LIST OF FIGURES

LIST OF TABLES

LIST OF ABBREVIATIONS

CHAPTER 1

INTRODUCTION

1.1 Distributed Slack Bus for Economic Dispatch of Renewable Energy

1.1.1 Economic Dispatch

1.1.2 Slack Bus

1.1.3 Distributed Slack bus

1.1.4 Renewable Energy

1.2 Methods of Solving ELD Problems

1.2.1 Categories of Optimization methods.

1.3 Problem Statement

1.3.1 Project Objectives

1.3.2 Project Questions

1.4 Organization of the Report

CHAPTER 2

LITERATURE REVIEW

2.1 Literature Review on Distributed Slack Bus for Economic Dispatch for Renewable Energy

2.1.1 Bus Classification

2.1.2 Bus Admittance Matrix

2.1.4.3 Fast Decoupled Method [2]

2.1.2 What is a Distributed Slack Bus?

2.1.3 Participation Factor Studies

2.1.4 Classical Economic Dispatch

CHAPTER 3

THE DESIGN METHODOLOGY

Solution of the Distributed Slack Bus for the Economic Load Dispatch of Renewable Energy.

3.1 Formation of the Improved Newton Raphson Matrix [10]

3.2Formulation of Fuel Cost Functions

3.2 Algorithm

Solution Algorithm for Real and Reactive Power Participation Factors

3.2.1 Distributed Slack bus algorithm based on Real power participation factors

3.2.2 Distributed Slack bus algorithm based on Reactive Power Participation factors

3.3Flow Charts

CHAPTER 4

RESULTS AND ANALYSIS

4.1 Case Study:

4.2 Results and Validation

4.2.1.2 IEEE 14 Bus Distributed Slack Bus Model

4.3 Analysis and Discussion

CHAPTER 5

CONCLUSION AND RECOMMENDATION FOR FUTURE WORK

5.1 Conclusion

5.2 Recommendations

REFFERENCES

APPENDICES

APPENDIX 1: Definition of Terms used in the Distributed Slack Bus Algorithm

APPENDIX 2: Program for formation of Bus Admittance Matrix

APPENDIX 3: Newton Raphson Solver

APPENDIX 4: Program for Calculating Power Outputs, Line Flows and Losses

APPENDIX 5: Program for Calculating Generating Costs

APPENDIX 6: Results Display Code

LIST OF FIGURES

Figure 2. 1 Four Bus system

Figure 2. 2 Fuel Cost Curve

Figure 4.1 : IEEE 14 Bus Test Network

Figure 4. 2 Voltage Profile Comparison

Figure 4. 3: Voltage Angle Comparison

Figure 4. 4: Comparison of Real Power Generation

Figure 4. 5: Comparison of Generation Costs

LIST OF TABLES

Table 2. 1 Bus Types

Table 2. 2: Comparison of power flow methods

Table 4. 1: Bus Data for IEEE 14 Bus Test Network

Table 4. 2 :Line Data for IEEE 14 Bus Test Network

Table 4. 3: Cost Coefficients for IEEE 14 Bus

Table 4. 4: IEEE 14 Bus Output Data with Single Slack Bus

Table 4. 5 IEEE 14 Bus Line Flows and Losses with Single Slack Bus

Table 4. 6: IEEE 14 Bus Output Data with Distributed Slack Bus using Real Power PF

Table 4. 7 :IEEE 14 Bus Line Flows and Losses with Distributed Slack Bus using Real Power PF

Table 4. 8 :IEEE 14 Bus Line Flows and Losses with Distributed Slack Bus using Reactive Power PF

Table 4. 9 :IEEE 14 Bus Line Flows and Losses with Distributed Slack Bus for Real Power

Table 4. 10: Comparison of Generated Real Power

Table 4. 11: Comparison of Generation Costs

LIST OF ABBREVIATIONS

DSB-Distributed Slack Bus

SSB-Single Slack Bus

ELD-Economic Load Dispatch

GS-Gauss - Seidel

NR-Newton Raphson

DLF-Decoupled Load Flow

FDLF-Fast Decoupled Load Flow

PF-Participation Factor

SLFE-Static Load Flow Equations

IEEE -Institute of Electrical and Electronic Engineers

RE-Renewable Energy

1

CHAPTER 1

INTRODUCTION

1.1 Distributed Slack Bus for Economic Dispatch of Renewable Energy

1.1.1 Economic Dispatch

Economic dispatch is the process of ensuring that the total load is appropriately shared the generating units operating in parallel in a power system [6]. It uses two notions as its basis:

• The generating units must provide for the load requirements of the power systemwithin the minimum cost bracket by optimally using the units.[1]
• The generating units must be able to provide back up if other units fail. However, this is constrained within a margin

1.1.2 Slack Bus

The slack bus is the bus that provides additional real and reactive power to supply the transmission losses in a power system. It is also take as the reference where the magnitude and phase angle are taken. It is the reference bus for voltage measurements.

1.1.3 Distributed Slack bus

The use of a distributed slack bus is a technique of removing the concentrated burden of the slack bus by distributing losses to each generator bus in the power system.This results in the system generators adjusting their outputs appropriately subject to their operational limits in order to achieve economic operation. The model was designed to remedy the inadequacies of the single slack bus model which does not exist in actual power systems. This has been motivated by the increase in distributed generation, deregulation and liberalization of the power generation sector.

1.1.4 Renewable Energy

Renewable energy is energy that utilizes sources that are continually replenished by nature to produce usable forms of energy. Examples of these sources include, the sun,wind,water,the earth’s heat and plants[4]. This study is interested in two types of renewable energy: wind and solar.

1.1.4.1 Wind Energy

Wind energy is really just another form of solar energy. Sunlight falling on oceans and continents causes air to warm and rise, which in turn generates surface winds. The wind has been used by humans for thousands of years, first to carry ships across oceans and, later, to pump water and grind grain. More recently, wind has been harnessed as a clean, safe source ofelectricity.

1.1.4.2 Solar Energy

Solar energy being in abundance almost all over the country is justifiably seen as the ultimate resource to tap. Although mainly supplemental in nature, it is also a that addresses the problems of atmospheric pollution and climate change.

1.2 Methods of Solving ELD Problems

The Economic Load Dispatch (ELD) problem is solved by the optimization of power systems. Optimization is the art of achieving the best possible solution to a problem with a variety of competing and conflicting parameters. Optimization is the tendency to search for the best solution under defined circumstances. In mathematical terms, optimization is seeking the best solution with imposed constraints [5].

1.2.1 Categories of Optimization methods.

There are various optimization techniques that have been developed to solve power system operation problems. The methods have been broadly classified into traditional and modern optimization methods. The methods have been classified into three groups namely:[2]

1. Conventional Optimization methods
2. Intelligence search methods
3. Non quantity approaches to address uncertainties in objectives and constraints

1.2.1.1 Conventional optimization methods

The conventional optimization methods include:

Newton Raphson

Gradient method

Line search

Lagrange multiplier method

Trust region optimization

Quasi Newton method

Nonlinear Programming

Quadratic Programming

Generalized Reduced Gradient Method

Newton Method

Network Flow Programming(NFP)

Mixed Integer Programming (MIP)

Interior Point

1.2.1.2 Intelligent Search Methods

These include:

Neural Network (NN)

Evolutionary Algorithms

Tabu Search

Particle Swam Optimization (PSO)

Ant Colony

Simulated Annealing

1.2.1.2 Non-Quantity approaches to address uncertainties in objectives and constraints

Probabilistic Optimization

Fuzzy Set Application

Analytic Hierarchical Process (AHP)

The power flow problem in power system is solved by a number of power flow algorithms including Newton Raphson, Gauss-Siedeland Fast Decoupled which will be discussed in the next chapter. Other decoupled methods like BX and XB methods and decoupled power flow without major approximation can also be used.

1.3 Problem Statement

1.3.1 Project Objectives

The main aim objective of this project is to introduce the distributed slack incorporating renewable energy sources in the system for the economic dispatch problem, investigate the economies of these losses, and the compare the results to those with a single slack bus and those with distributed slack bus without renewable energy sources.

This paper attempts a basic concept for a modified power flow analysis with a sense of the economic load dispatch to remove the concentrated burden of the slack bus. The power flow calculation in the proposed method is incorporated into the economic load dispatch (ELD) with renewable energy. Furthermore, the proposed method eliminates not only the burden of a slack bus for real power losses, but also applies the technique of the distributed slack bus to reactive power losses. The IEEE 14- system is used to verify the usefulness of the proposed technique.

1.3.2 Project Questions

This project will attempt to answer the following questions:

• What is the economic effect of distributing the losses of a system to other generating units?
• What is the effect on generating costs of introducing renewable energy sources into a power system?

1.4 Organization of the Report

The report has been organized into five chapters:

In Chapter 2, a literature review of load flow studies, economic load dispatch, the distributed slack bus model and renewable energy have been discussed independently. They are separately addressed and a link between the three aspects of power system optimization is shown.

In Chapter 3, data to be utilized in the formulation of the distributed slack bus is introduced. The Data is obtained from the IEEE 14 bus test network. The design of the distributed slack bus is discussed in detail and a flow chart as well as an algorithm to be used in the project is developed. Wind and Solar renewable energy is introduced to the system, and economic dispatch performed.

In Chapter 4, the simulated results obtained from the MATLAB simulation in chapter 3 are analyzed and discussed. The results are compared with the distributed slack bus model without renewable energy using Newton Raphson method.

Chapter 5 concludes this report by giving a review of the study in the preceding chapters and examining the extent of the achievement of the objectives of the project.

CHAPTER 2

LITERATURE REVIEW

2.1 Literature Review on Distributed Slack Bus for Economic Dispatch for Renewable Energy

2.1.1 Bus Classification

Buses are classified into three categories depending on which two variables are specified [7]

There are four potentially unknown quantities associated with each bus: [1]

• P- Real Power
• Q-Reactive Power
• |V|- Voltage magnitude
• δ - Voltage angle

1. P-Q Bus (Load Bus)

In these buses, P and Q are known:Pg and Qg are specified and Pd and Qd are known from load forecasting, historical method or measurement [1, 7]. Pg and Qg are taken to be zero.In practice, often the real power is known and hence the reactive power based on an assumed power factor. The load bus is referred to as the P-Q bus since the scheduled values are known and mismatches ΔP and ΔQ can be defined. The mismatch equations can be explicitly applied to the statement of the power flow problemto determine the two unknown quantities which in this type of buses are:

• Voltage magnitude, |V|
• Voltage angle, δ

1. PV Bus (Voltage Controlled buses) [3,1]

PV buses are also called generator buses or regulated buses. At these buses, the real power and voltage magnitude are specified. Any bus in the system at which the voltage magnitude id kept constant is said to be voltage controlled. At each bus connected to the generator, the real power (Megawatt) generation can be controlled by adjusting the prime mover and the voltage magnitude can be controlled by adjusting the exciting. Therefore, at each generator bus, it is possible to Pgiand |Vi|. With Pdi also known from load forecasting, the mismatch can be controlled by adjustingthe excitation, therefore, at each generator bus it is possible to specify Pgiand |Vi|. With Pdi also known from load forecasting, the mismatch can be defined from the equation:

ΔPi = Picalc–(Pgi - Pdi)where Pisch = Pgi - Pdi

The generator reactive power, Qgi required to support the scheduled voltage cannot be known in advance hence mismatch, ΔQi is not defined. At the generator bus,the voltage angle, δ is the unknown quantity to be determined and the equation

g'i = Picalc – (Pgi - Pdi) = 0

is the equation available to obtain δi.

After the load flow problem is solved,Qi can be calculated from:

Qi = Σ |YinVinVn| Sin (θin + δn + δi)

Buses that are not connected to a generator but have voltage control capabilities are also called voltage-controlled buses for which real power generation is zero [1]

1. Slack Bus

The slack bus is also called the swing bus or reference bus. The slack bus mainly serves two purposes [2]

1. Supply the transmission losses by providing additional real and reactive power. [3]The power loss of the network is not known during the power flow calculation and can only be known when the power flow study is complete. It is therefore important to have one bus (i.e. the slack bus) at which the complex power is unspecified so that it can supply the difference in total system loss puss losses and the sum of the complex power specified at the remaining buses[7] the slack u therefore balances the system in this respect.[2]
2. Taken as the reference where magnitude and phase angle of the voltage are specified.It is necessary to have a bus with a zero voltage angle as reference for the calculation of the other voltage angles [2]. The voltage magnitude for this bus is also set to zero. The slack bus is distinguished from the other two types of busses by the fact that the real and reactive powers at this bus are not specified [7], traditionally therefore, there is only one slack bus in the power flow calculations.

Since the complex power of the slack is not initiallyspecified, the power allocated to it is determined as part of the solution to the power flow problem. The bus connected to the largest generation station is normally selected as the slack bus so that the variations in real and reactive powers in the slack bus during the iterative process while solving the power flow problem is only a small percentage of the generating capacity of this bus.