UNIVERSITY OF NAIROBI FACULTY OF ENGINEERING DEPARTMENT OF ELECTRICAL AND INFORMATION ENGINERRING PROJECT TITLE: POWER STABILITY WITH RENEWABLE ENERGY

Transcription

1 UNIVERSITY OF NAIROBI FACULTY OF ENGINEERING DEPARTMENT OF ELECTRICAL AND INFORMATION ENGINERRING PROJECT TITLE: POWER STABILITY WITH RENEWABLE ENERGY PROJECT INDEX: PRJ (051) SUBMITTED BY MC LIGEYO DIANA ADHIAMBO F17/37449/2011 SUPERVISOR: PROFESSOR O.N ABUNGU EXAMINER: MR. PETER MOSES MUSAU PROJECT REPORT SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE AWARD OF THE DEGREE OF: BACHELOR OF SCIENCE IN ELECTRICAL AND INFORMATION ENGINEERING OF THE UNIVERSITY OF NAIROBI DATE OF SUBMISSION: 16 TH May, 2016 i

2 DECLARATION OF ORIGINALITY NAME OF STUDENT: REGISTRATION NUMBER: COLLEGE: FACULTY: DEPARTMENT: COURSE NAME: TITLE OF WORK: MC LIGEYO DIANA ADHIAMBO F17/37449/2011 ARCHITERCTURE AND ENGINEERING ENGINEERING ELECTRICAL AND INFORMATION ENGINEERING BACHELOR IN SCIENCE IN ELECRICAL AND ELECTRONIC ENGINEERING POWER STABILITY 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: ii

3 CERTIFICATION This report has been submitted to the Department of Electrical and Information Engineering in The University of Nairobi with my approval as supervisor... Prof. Nicodemus Abungu Odero Date: iii

4 DEDICATION To my family, for their zealous motivation and encouragement throughout my academic journey. iv

5 ACKNOWLEDGEMENTS First I would like to thank God, for His uning grace throughout my academic life. Without it I would not have made it this far. I ext my utmost appreciation to my advisor Mr. Peter Moses Musau for his valuable insights into my project, criticism and encouragement. I would also like to thank my supervisor, Prof. Nicodemus Abungu for his priceless motivation and support. I would also like to acknowledge Mr. Oscar Ondeng for his help in the technical aspects of my project. I appreciate all my lectures and all non-teaching staff at the Department of Electrical and Electronic Engineering, University of Nairobi for their contribution towards my degree. I am indebted to my fris Noreen Moraa, Edwin Oloo, Dennis Njau and Samuel Simiyu Khaemba for their help in understanding the project. I am also thankful to my classmates for their moral support as I did the project. Finally, I would like to thank my family and especially my parents for their support and unmatched encouragement throughout my academic life. v

6 ABSTRACT Renewable Energy such as Photovoltaic (PV) and wind energy power generation play an important role in energy production. However the output power of PV and wind power generation are fluctuant due to the uncertainty and intermittence of solar and wind energy. This affects the power stability of a power system. Hence there is a need to improve power stability when a distributed generation is incorporated into a power system. This is achieved by carrying out a load flow study of the power system where a distributed slack bus and STATCOM are implemented. Renewable Energy is introduced by using the distributed slack bus which is based on participation factors. The STATCOM is a FACT device used to improve power stability of a power system. In this project real participation factors are used to distribute system losses among generators while STATCOM is used provide reactive power compensation. One of the causes of power instability is lack of sufficient reactive power which leads to voltage instability hence STATCOM provides reactive power compensation which in turn improves the voltage stability. An algorithm is developed and implemented using a Newton-Raphson Solver on a MATLAB platform. The IEEE 30 Bus is used as a case study. When the STATCOM was implemented during the normal operating conditions, it resulted in overall increase in voltage magnitude in comparison to when it is not included. Real and reactive power line losses are also reduced in the buses. A disturbance in terms of load change was implemented leading to decrease in voltage but when a STATCOM was inserted in the system the voltage magnitudes improved. vi

7 Table of Contents DECLARATION OF ORIGINALITY... ii CERTIFICATION... iii DEDICATION... iv ACKNOWLEDGEMENTS... v ABSTRACT... vi LIST OF FIGURES... x LIST OF TABLES... xi LIST OF ABBREVIATIONS... xii CHAPTER POWER SYSTEM STABILITY WITH RENEWABLE ENERY Introduction Power System Stability Power System Stability Renewable Energy What is Power Stability with Renewable Energy? Problem Statement Project Objectives Project Scope Project Questions Organization of the Report... 4 CHAPTER LITERATURE REVIEW INTRODUCTION ON POWER STABILITY Rotor-Angle stability... 7 vii

8 2.1.2 Frequency Stability Voltage Stability INTRODUCTION TO FACTS Types of FACTS [9] Series Controller Shunt Controllers Combined Series-Series Controller Combined Series-Shunt Controller Effects of Renewable Energy on Power Stability CHAPTER THREE SOLUTION TO POWER STABILITY WITH RENEWABLE ENERGY Methods of Solving Power Stability with Renewable Energy Problem Load Flow Bus Classifications The Load Flow Problem Newton Raphson Method Gauss Seidel Method The Fast De-coupled Method Power Stability with Renewable Energy Problem Formulation Solution of Power Stability with RE using Newton-Raphson Method Formulation of The Real Participation factors Solution Algorithm for Solving Stability with Renewable Energy Flow Chart CHAPTER FOUR RESULTS AND ANALYSIS Case study: IEEE 30-Bus System Results and Validation Analysis and Discussion CHAPTER FIVE CONCLUSION AND RECOMMENDATON FOR FURTHER WORK Conclusion viii

9 5.2 Recommation REFERENCES APPENDIX 1: STATCOM Data APPENDIX 2: Program for formation of Bus Admittance Matrix APPENDIX 3: Newton Raphson Solver APPENDIX 4: Newton Raphson Solver with STATCOM APPENDIX 5: Program for Calculating Power Outputs, Line Flows and Losses ix

10 LIST OF FIGURES Figure 1: Classification of Power Stability... 6 Figure 2: Power Transfer Characteristic... 8 Figure 3: STATCOM Representation Figure 4: Flowchart for Power Stability with Renewable Energy Figure 5: IEEE 30 Bus Test Network Figure 6: Voltage Profile in Normal Operating Conditions Figure 7: Comparison of Losses under Normal Operating Conditions Figure 8: Voltage Profile after Disturbance Figure 9: Comparison of Total Losses after Disturbance x

11 LIST OF TABLES Table 3.1: Comparison of load Flow Methods Table 4.2: Line Data Table 4.3: Comparison between voltages with and without Renewable Energy Table 4.4: Comparison of Voltages with renewable with and without STATCOM in normal operating Conditions Table 4.5: Comparison of voltages with renewable energy without STATCOM and with renewable energy and STATCOM after disturbance (50% load change) Table 4.6: Comparison of Total Real and Reactive Power Injected and Generated Without Renewable Energy, with Renewable Energy and with Renewable Energy and STATCOM Table 4.7: Comparison of Total Real and Reactive Losses without Renewable Energy, with Renewable Energy and with Renewable Energy and STATCOM xi

12 LIST OF ABBREVIATIONS IEEE - Institute of Electrical and Electronic Engineers RE - Renewable Energy NR - Newton Raphson DG - Distributed Generator FACT - Flexible Alternating Current Transmission System STATCOM - Static Synchronous Compensator SVC - Static VAR Compensator PV - Photovoltaic xii

13 CHAPTER 1 POWER SYSTEM STABILITY WITH RENEWABLE ENERY 1.1 Introduction Power System A network of components used to generate, transmit and distribute electric power is called a power system. This is a network consisting of more than one electrical generation units, power transmission lines and loads including the associated equipment s connected electrically and mechanically to the network Stability This is the resistance to change whereby there is equilibrium between opposing forces and a state of instability will occur when a disturbance leads to a sustained imbalance between opposing forces [1] Power System Stability Power System Stability is defined as that ability of an electric power system to remain in a state of operating equilibrium under normal operating conditions and after being subjected to a disturbance to regain an acceptable state of equilibrium [1, 12] Renewable Energy Renewable Energy is energy that is obtained from natural resources and thus can be constantly replenished such as sunlight, wind, rain, tides and geothermal heat. The renewable energy sources exist over a wide geographical area in contrast to other energy sources which are limited. Renewable Energy includes bio-mass energy, wind energy, solar energy, hydro-power, geothermal energy just to mention a few. This study is interested in two types of renewable energy which include solar energy and wind energy. Solar Energy Solar energy makes the production of solar electricity possible due to the energy in the form of solar radiation. Thus solar energy is simply provide by the sun. Electricity can be produced from photovoltaic cells directly. These cells exhibit photovoltaic due to the materials they are made up 2

14 of. Light excite the electrons in the cell and cause them to flow when sunshine hits the Photovoltaic cell and hence generating electricity. Wind Energy Wind energy is a form of solar energy. The wind energy is harvested by modern wind turbines. The wind-turbine is used to convert the Kinetic energy in the wind to mechanical power. A generator is used to convert the mechanical power into electrical power What is Power Stability with Renewable Energy? Stability is a condition of equilibrium between opposing forces. Power stability is generally divided into three parts [1]. They include: Voltage Stability Frequency Stability Rotor-angle Stability Frequency stability is the ability of a power system to restore balance between power system generation and load after a disturbance has occurred. Voltage stability is the ability of the power system to maintain steady accepted voltages at all buses of the system under normal operation and after being subjected to a disturbance. While rotor-angle stability is the ability of interconnected machines of a power system to remain at synchronism after a disturbance [12, 15]. When renewable energy is introduced to a power system it brings a lot of advantages such as, it is in vast amount and it reduces pollution but it also brings about its own set of challenges in terms of power stability. The challenges of wind energy and solar energy are brought about due to their unpredictable nature as well the characteristics of the wind generators and photovoltaic cells. 1.2 Problem Statement We are owed with an enormous wind energy source and solar energy resources across the globe. However the integration of the renewable energy is bound to impact the generation, transmission and distribution of the power system. Due to the limited predictability of the weather conditions and the resources of the renewable energy and the characteristics of the wind generators and photovoltaic cell, the outputs cannot be controlled. Hence there is a need to counter-effect this consequence when wind energy and solar energy are implemented in a power system. 3

15 1.2.1 Project Objectives The objective of the project is to investigate the integration of renewable energy to a power system and find the effects it has on power stability and explore measures that will deal with the challenges it brings about Project Scope The project will be limited to the impact of wind energy and solar energy on voltage stability in normal operating conditions and after a disturbance which was implemented by a 50% load increase and the method used to mitigate the negative effects Project Questions The project will attempt to answer the following questions: 1) Does renewable energy bring about voltage stability or instability to a power system? 2) If power system instabilities are brought about how can we reduce their effects? 3) If it brings about voltage stability how can we improve the power system further? 1.3 Organization of the Report The report has been organized into five chapters: In Chapter 1. An introduction to Power Stability. The problem statement and project objectives have also been discussed. In Chapter 2. A literature review on power stability, renewable energy and FACTS Devices have been discussed indepently. In Chapter 3. Load flow studies. Data to be utilized in the formulation of power stability with renewable energy is introduced. The Data is obtained from the IEEE 30 bus test network. The design of power stability with renewable is discussed in detail and a flow chart as well as an algorithm to be used in the project is developed. In Chapter 4. The simulated results obtained from the MATLAB simulation in chapter 3 are analyzed and discussed. 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. 4

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17 CHAPTER 2 LITERATURE REVIEW 2.1 INTRODUCTION ON POWER STABILITY Power System Stability is the ability of an electric power system to remain in a state of operating equilibrium under normal operating conditions and after being subjected to a disturbance to regain an acceptable state of equilibrium [1, 12]. Power stability is sub-divided into three: Rotor-Angle Stability Frequency Stability Voltage Stability As power systems are non-linear, their stability deps on both the initial conditions and the size of a disturbance. Thus rotor-angle and voltage stability can be divided into small and large disturbance stability. Figure 1: Classification of Power Stability Physical quantities such as phase angle and magnitude of the voltage at each bus, the active and reactive power describe a power- system operating conditions. The system is in steady state if they are constant in time. When the steady state condition is subjected to a change in the system quantities, a power system undergoes a disturbance. The disturbance can be a small disturbance or a large disturbance deping on the origin and the magnitude. A power system is said to be steady-state stable if after being subjected to a small disturbance, it is able to return to essentially the same steady state condition. While if a system reaches a new acceptable state different from 6

18 the original steady-state condition especially under a large disturbance, the system is said to transiently stable [1, 12, 16] Rotor-Angle stability This is the ability of inter-connected synchronous machines of a power system to remain in synchronism. Instability in the form of increasing angular swings of some generators may result in loss in synchronism. Rotor angle stability is depent on the ability to maintain or restore equilibrium between electromagnetic torque and mechanical torque in each of the machines in the system [1]. The relationship between interchange power and angular position of the rotors of synchronous machines is an important characteristic having a bearing on power system stability. It is highly non-linear. Let us assume machine 1 represents a generator feeding power to a synchronous motor represented by machine 2. The power transferred from the generator to the motor is given by: [1] Where EG = emf of the generator EM = emf of the motor XT = the total reactance P = E GE M sin(δ) X T δ = the angular separation between the rotors of the two machines As the angle is increased, the power transfer increases up to a certain limit but upon further increase in the angle, usually 90 0, it results in a power decrease in the power transferred [16]. The power angle curve is as shown below [15]. 7

19 Figure 2: Power Transfer Characteristic The equilibrium of between opposing forces is called stability. The restoring forces is the mechanism by which interconnected synchronous machines maintain synchronism. The restoring forces act whenever there are forces acting on one or more machines with respect to other machines ting to accelerate to decelerate them [1, 16]. Electromechanical oscillations inherent in power systems is the study of the rotor angle stability problem. Under steady-state, the speed remains constant due to equilibrium between the input mechanical torque and output electromagnetic torque of each generator. If the equilibrium is upset, it results in acceleration or deceleration of the rotors of the machines. The angular position relative to the slower machine, if one machine temporarily runs faster than another, will advance. The resulting angular difference transfers part of the load from the slow machine to the fast machine deping on the power-angle relationship. This ts to reduce the speed difference and hence angular separation [1]. An increase in angular separation beyond a certain limit is accompanied by a decrease in power transfer. This continued increase in angular separation leads to instability. Hence the stability of a system deps on whether there is sufficient restoring torques due to deviations in angular positions of the rotors. The change in electromagnetic torque can be resolved in two components following a perturbation in synchronous machines. They include: [1, 16, 18] a) Synchronizing torque component in phase with rotor angle deviation 8

20 b) Damping torque component in phase with the speed deviation System stability deps on the existence on both components. Lack of sufficient damping torque results in oscillatory instability whereas lack of sufficient synchronizing torque results in aperiodic or non-oscillatory instability. Rotor-angle stability can be sub-divided into: Transient stability Small Signal (or small disturbance) Stability Transient stability It is concerned with the effect of large disturbances. It is the ability to maintain synchronism of a power system when subjected to a sever disturbance such as three phase short circuit, single-line to earth faults, short circuit in transmission lines etc. [18, 19]. Transient stability deps on both the severity of the disturbance and the initial state of the operating system. The instability in most cases manifests itself as the first swing instability in the form of aperiodic angular separation due to insufficient synchronizing torque. Methods of analysis include [15]: Swing equation Equal Area Criterion Numerical Integration methods such as Euler method, Runge-Kutta etc. Lypanov Analysis Small signal (or small disturbance) Stability This is the ability of a power system to maintain synchronism under small disturbances. This disturbances occur continually on the system because of small variations in loads and generation [18]. The rotor-angle small signal instability may occur in two forms: Rotor oscillations of increasing amplitude due to lack of sufficient damping torque Steady increase in rotor angle due to lack of sufficient synchronizing torque Small signal stability is largely a problem of insufficient damping oscillations. The following types are of concern [1, 16]: I. Control modes. They are associated with generating units and other controls 9

21 II. III. IV. Torsional modes. They are associated with the turbine governor shaft system rotation Inter-area modes. They are associated with the swinging of many machine in one part of the system against machines in other parts. Local modes. They are associated with the swinging units at a generating station with respect of the power system Frequency Stability Frequency stability is the ability of a power system to balance generation and load following a severe system upset hence maintaining a steady frequency. It indicates whether there is equilibrium or no equilibrium between power generation and consumption [17]. With regard to frequency stability considerations, there must be sufficient power available to cover transient power fluctuation to maintain the system frequency within required ranges. Instability that may occur results in the form of sustained frequency swings leading to tripping of generator units or loads [21]. Frequency stability issues may occur in different time frames ranging from a few seconds (inertia problems) to several minutes or even hours (load following reserve). If a load is suddenly connected to the system or if a generator is suddenly disconnected there will be a long term distortion in power balance between that delivered by the turbines and that consumed by the loads. The imbalance is initially covered from kinetic energy of rotating turbines, generators and motors and as a result the frequency in the system will change [16, 17]. The stored kinetic energy of all generators (and spinning loads) on the system is given by [13]: K. E = 1Iw2 2 Where I = moment of inertia of all generators (kgm 2 ) W= rotational speed of all generators (rad/s) Any imbalance between the produced and consumed power may lead to frequency change. When the generated power is less than the load power, the electrical torque of generator is less than the mechanical input torque. The speed of the generator will slow down decreasing the frequency. Otherwise when the generated power is greater than the load power, the speed of the generator will increase, increasing the frequency [17, 20]. 10

22 The torque balance of any spinning masses determines the rotational speed [13]; T m T e = I dw dt In power system it is conventional to express the inertia in per unit as H constant H = 1 2 Iw s 2 S rated [Ws VA] Where Srated is the MVA rating of either and individual generator or the whole system Ws is the angular velocity (rads/sec) at synchronous speed A generator s rotating mass provides kinetic energy to the grid or absorbs it due to the electromechanical coupling in case of a frequency deviation. The grid frequency is directly coupled to the rotational speed of a synchronous generator and this to the active power balance. The inertia constant H that is the rotational inertia minimizes the rate change of frequency in case of frequency deviations. This rers frequency dynamics slower and thus increases the available response time to react to faults. For stable operations of power system it is a necessary requirement to maintain grid frequency within an acceptable range. Low levels of rotational inertia in power system caused in particular by shares of inverters connected renewable energy sources that is wind-turbine and PV units have implications on frequency dynamics because they do not normally provide any rotational inertia. Hence leading to frequency control scheme being to slow in respect with to the disturbance dynamic for preventing large frequency deviations. Hence leading to the frequency instability phenomena [17] Voltage Stability Voltage stability is the ability of a power system to maintain steady acceptable voltages at all buses in the system under normal operating condition and after being subjected to a disturbance. When there is a progressive and uncontrollable drop of voltage due to a disturbance, increase in load or change in system condition, a system enters s state of voltage instability [1, 16, 22]. The inability of the power system to meet demand for reactive power is the main factor causing voltage stability 11

23 [5]. Instability that may result occurs in the form of a progressive fall or rise of voltages of some buses. Due to voltage instability the following may occur [16]: Tripping of transmission lines and other elements by their protective systems leading to cascading outages Loss of load in an area If voltages after disturbance are close to voltages at normal operating condition we say a power system is voltage stable. At a given operating condition for every bus in the system, the bus voltage magnitude increases as the reactive power injection at the same bus is increased, this is the criteria for voltage stability. A system is voltage unstable, if the bus voltage magnitude (V) decreases as the reactive power injection (Q) at the same bus is increased, for at least one bus in the system [1]. The term voltage collapse is the process by which the sequence of events accompanying voltage instability leads to a blackout or abnormally low voltages in a significant part of a power system leading to a low voltage profile [5]. We can classify voltage stability into; a. Large-disturbance voltage stability It is concerned with a system s ability to maintain steady voltages following large disturbances such as faults, loss of generators. This ability is determined by the system load characteristics and interactions of both discrete and continuous controls and protections. The study period may last from a few seconds to tens of minutes. b. Small-disturbance voltage stability It is concerned with a system s ability to maintain steady voltages following small disturbances such as changes in load demands. 2.2 INTRODUCTION TO FACTS Flexible Alternating Current Transmission System (FACTS) is a system incorporating power electronic based and other static controllers for the AC transmission of the electrical energy. They are used to enhance controllability and increase power transfer capability [25, 26]. The advantages of FACTS include [25]: 12

24 a. Control power flow and voltage as desired. b. It decreases overall generation reserve requirements. c. Increased system security and reliability. d. Overall enhancement of the quality of electric energy delivered to customers. Types of FACTS [9] 1. Series Controllers 2. Shunt Controllers 3. Combined series-series Controllers 4. Combined Series-Shunt Controllers Series Controller The series compensator could be a variable impedance such as a capacitor or variable source. All series controllers inject voltage in series with the line [25]. The series compensators include: Static Synchronous Series Compensator Thyristor Controlled Series Capacitor Thyristor Switched Series Capacitor Thyristor Controlled Series Reactor Thyristor Switched Series Reactor Static Synchronous Series Compensator (SSSC) It is implemented using GTO based voltage source inverter that can provide controllable compensating voltage over an identical capacitive or inductive range indepent of the line current. In principle, the inserted series voltage can be regulated to change the impedance (more precisely reactance) of the transmission line. It is capable of handling power flow control, improvement of transient stability margin and improve damping of transient [11, 2, 28]. Thyristor Controlled Series Compensator (TCSC) It is a capacitive reactive compensator consisting of a series capacitor bank shunted by a thyristor controlled reactor in order to provide a smoothly variable series capacitance, the bi-direction thyristor valve is fired with an angle ranging between 90 0 and with respect to capacitor voltage [25, 29]. It can operate in 13

25 I. Bypass-thyristor mode II. Blocked-thyristor mode III. Vernier mode In bypass thyristor mode, thyristors are made to conduct with conduction angle of There is a continuous flow through the thyristor valves because gate pulses are applied as soon as the voltage across the thyristor reaches zero and becomes positive. It behaves like a parallel capacitorinductor combination. In blocked thyristor mode firing pulses of TCSC are blocked. The net TCSC reactance is capacitive. The vernier mode allows TCSC to behave as a continuously controllable capacitive reactance or continuously controllable inductive reactance [28]. Thyristor Switched Series Capacitor It consists of a capacitor shunted by a pair of reversely parallel connected thyristor. The operation of a TSSC is to make use of a thyristor to act as a valve or switch for the capacitor connected in parallel to it such that when thyristor is triggered the capacitor will be activated to start compensator [29]. Thyristor Controlled Series Reactor (TCSR) It is an inductive reactance compensator consisting of a series reactor shunted by a thyristor controlled reactor in order to provide a smoothly variable series inductive reactance. When the firing angle of the thyristor controlled reactor is 180 0, it stops conducting and the controlled reactor acts as a current limiter. As the angle decreases below 180 0, the net inductance decreases until firing angle of 90 0, when net inductance in the parallel combination of the two reactors. Thyristor Switched Series Reactor TSSR is an inductive reactance compensator which consists of a series reactor shunted by a thyristor-controlled switched reactor in order to provide a stepwise control of series inductive reactance [28] Shunt Controllers They maybe variable source, variable impedance or a combination. At the point of connection, all shunt controllers inject current in the system [25]. They are 14

26 Static Var Compensators (SVCs) Static Synchronous Compensator (STATCOM) Thyristor Controlled reactor Thyristor Switch Capacitor Static Var Compensator This is a shunt connected static Var absorber or generator whose output is adjusted to exchange capacitive or inductive current so as to maintain or control specific parameters of the electrical system [25]. It consists of fixed capacitors or reactance, Thyristor Switched Capacitors (TSC) for lagging VAR and Thyristor Controlled Reactors (TCR) for leading VAR are connected in parallel with electrical system [8]. The basic idea of the TSC is to split up capacitor bank into sufficiently small capacitor steps and switch the steps on and off, using anti-parallel connected Thyristors as switching elements. It is based on thyristors with GTO capability. In a power system the load varies from time to time. This may change reactive power balance. The SVC may be installed at various points in the system to maintain the voltage at accepted levels by providing sufficient reactive power to the system thus maintain reactive power balance and further reducing losses [25, 28]. Static Synchronous Compensator (STATCOM) STATCOM is a self-commutated switching power converter supplied from an appropriate electric energy source and operated to produce a set of adjustable multiphase voltage which maybe coupled to an AC power system for the purpose for exchanging indepently controllable real and reactive power. It consist of thyristors with gate turn-off capability (GTO) or many IGBT s. It is a solidstate based power converter of the SVC. They do not require large inductive and capacitive components to provide inductive or capacitive power to high voltage transmission networks as required by SVC [11, 28]. A STATCOM comprises of three main parts; Voltage Source Converter Step-up Coupling transformer A controller 15

27 From a DC input Voltage source, provided by the charged capacitor, the converter produces a set of controllable 3 phase output voltages with frequency of the AC system. Via a relatively small tie reactance, each output voltage of the converter is in phase with the corresponding AC system voltage. By varying the output voltage produced, the reactive power exchange between the convertor and the AC system can be controlled. For the voltage source converter, its AC output voltage is controlled so that it is just right for the required reactive current flow for any AC bus voltage. The DC capacitor voltage is automatically adjusted as required to serve as a voltage source for the converter [25]. If the amplitude of the output voltage is increased above the AC system voltage, then the current flows through the reactance from the converter to the AC system and the converter generates reactive power. If the amplitude of the output voltage is decreased to that of the AC system voltage, then the reactive flows from the AC system to the converter and the convertor absorbs reactive power. If the amplitude of the output voltage is equal to that of the AC system voltage, the reactive power exchange is zero. Thyristor Controlled Reactor (TCR) This is a shunt connected thyristor controlled inductor whose effective reactance is varied in a continuous manner by partial control of the thyristor valve. TCR is a subset of SVC in which conduction time and hence shunt in a reactor is controlled by a thyristor based ac switch with firing angle control. It consists of a fixed reactor of inductance and a bidirectional thyristor valve [8, 28]. Thyristor Switch Capacitor It is a shunt connected capacitor whose effective reactance is varied in a stepwise manner by full or zero conduction operation of the thyristor valve [28] Combined Series-Series Controller This may be a combination of separate series controllers, which are controlled in a coordinated manner, in a multi-line transmission system. The IPFC (Interline Power Flow Controller) is the combination of two or more Static Synchronous Series Compensators which are coupled via a common dc link to facilitate bi-directional flow of real power between the ac terminals of the SSSCs [28]. 16

28 2.2.4 Combined Series-Shunt Controller UPFC is combination of shunt connected device (STATCOM) and a series branch (SSSC) in the transmission line via its DC link [8]. 2.3 Effects of Renewable Energy on Power Stability Due to the unpredictable nature of the renewable energy that is solar energy and wind energy there may be a mismatch between the generation of power and the demand of power. This causes deviations in the system frequency. In the case of a power deficit, the generation is less than the power demand leading to a reduction of speed and hence the system frequency goes down. While if the generation of power is more than the demand, it will cause an increase in speed and hence an increase in the system frequency thus leading to frequency instability. The inertia dictates how large the frequency deviations would be due to a sudden change in the generation and load power balance which plays a significant role in maintaining the stability of a power system during a transient scenario. The larger the inertia of a system, the smaller the rate of change in rotor speed in the generator during a power imbalance. In wind energy power generation, when fixed speed induction generators are used it contributes to the inertia of a power system because the stator is directly connected to the grid and thus changes in frequency manifests as a change in speed. These speeds are resisted by the rotating masses leading to rotating energy transfer. While in variable speed wind turbines, its rotational speed is decoupled from the grid frequency by electronic converter. Thus variation in grid frequency does not alter the turbine output power. With high wind penetration there is a risk that the power system inertial effect decreases thus aggravating the frequency of the grid. In solar power generation, the solar power plant consists of the solar cell and DC to AC converter. Hence they do not possess inertia hence won t release energy to grid when frequency. This can thus can cause frequency instability. In traditional power systems, the rotor angles of synchronous generators are impacted by the changes in active power flow in the system. When there is a change in active power, the synchronizing generators will respond with an electromagnetic torque that will dampen and minimize the rotor angle deviations thus they have synchronizing power. Renewable Energy technology such as wind turbines generator and photovoltaic (PV) are asynchronous machines. They are integrated to the grid via inverters which makes them lose the ability to maintain 17

29 synchronism hence they lack synchronizing power and hence this may bring about rotor angle instability. Voltage instability is brought about by the inability of the power system to meet the demand of reactive power. In the case of wind energy, if the wind turbine technology utilizes the induction machines it may lead to a power system s inability to meet the demand of reactive power this is because induction machine consume reactive power thus leading to voltage instability. While in solar energy, photovoltaic use inverters which are designed to operate at unity power factor hence reactive power is neither produced nor absorbed. Hence there is a need to implement a way of voltage control otherwise it may lead to issues with voltage stability. 18

30 CHAPTER THREE SOLUTION TO POWER STABILITY WITH RENEWABLE ENERGY 3.1 Methods of Solving Power Stability with Renewable Energy Problem Optimization is the art of achieving the best possible solution to an optimization problem where there are a number of competing or conflicting parameters. Categories of Optimization Methods Due to the optimization problems there a number of techniques that are available to solve the problems of power system operation. The techniques have been classified into three groups [14]; 1. Conventional Methods 2. Intelligence Search Methods 3. Non-quality approaches to address uncertainties in objective constraints Conventional Methods The conventional optimization methods include: Gradient Method Linear Search Lagrange Multiplier Method Newton Raphson Method Optimization Quasi-Newton Method Trust-Region Optimization Linear Programming Non-linear Programming Quadratic Programming Newton s Methods Interior Point Method Mixed Integer Programming Network Flow Programming Intelligent Search Methods 19

31 The Intelligent Search Programming Methods include: Optimization Neural Network Evolutionary Algorithms Tabu Search Particle Swarm Optimization Non-quality approaches to address uncertainties in objective constraints The Non-quality approaches to address uncertainties in objective constraints methods include: Probabilistic Optimization Fuzzy Set Application Analytical Hierarchal Process (AHP) 3.2 Load Flow Bus Classifications A bus is a node at which one or many lines, one or many loads and generators are connected. In the power system there are four potentially unknown quantities, they include [23]: P- Real Power Q-Reactive Power V - Voltage magnitude δ - Voltage angle Buses are classified according to which two out of the four variables are specified. They are 1. Load bus(p-q bus) No generator is connected to the bus. At this bus the real and reactive power are specified. It is desired to find out the voltage magnitude and phase angle through load flow solutions. It is required to specify only Pd (real power demand) and Qd (reactive power demand) at such a bus as at a load bus, voltage can be allowed to vary within the permissible values. Pg (real power generated) and Qg (reactive power generated) are taken to be zero. The load bus is referred to as the P-Q bus since the scheduled values are known and the real and reactive power mismatches, ΔP and ΔQ respectively can be defined [1, 5]. 20

32 2. Generator bus or voltage controlled bus (P-V bus) The voltage magnitude and real power are specified. It is required to find out the reactive power generation Q and phase angle of the bus voltage. A generator bus is usually called a voltage controlled or PV bus. This is because a generator connected to a bus, the megawatt generation can be controlled by adjusting prime mover, and voltage magnitude can be controlled by adjusting generator excitation [1, 5]. 3. Slack (swing) bus: This is used as a reference bus in order to meet the power balance condition. Slack bus is usually a generating unit that can be adjusted to take up whatever is needed to ensure power balanced. For the Slack Bus, it is assumed that the voltage magnitude V and voltage phase Θ are known, whereas real and reactive powers P and Q are obtained through the load flow solution [23] The Load Flow Problem The first step in performing load flow analysis is by using the transmission line and transformer input data to form the Y-bus admittance. The nodal equation for a power system network using Y bus can be written as follows [4, 5, 6]: I = Y bus V 1) The nodal equation can be written in a generalized form for an n bus system n I i = Y ij V j for i = 1,2,3 n 2) j=1 The real and reactive power injected to bus i P i + jq i = V i I i.3) Substituting for Ii yields I i = P i jq i V i..4) n P i jq i = V V i Y ij Y ij V j 5) i j=1 n j=1 21

33 The above equation uses iterative techniques to solve load flow problems. The complex conjugate of the power injected at bus i formulated in polar form are Which thus becomes [14] n P i jq i = V i Y ij V j.6) j=1 n P i jq i = Y ij V i V j < θ ij + δ i δ j.7) Expanding this equation and equating real and reactive parts we obtain n j=1 P i = Y ij V i V j cos (θ ij + δ i δ j ) 8) j=1 n Q i = Y ij V i V j sin(θ ij + δ i δ j ).9) j=1 Solving Load flow problems [5, 14] The load flow problems are non-linear in nature hence cannot be explicitly solved by linear methods thus application of Iterative methods are used. The most common methods of solving the load flow problem include: I. Newton Raphson Method II. III. Gauss Seidel Method Fast Decoupled Load Flow method Newton Raphson Method The Newton Raphson Method is an iterative method which approximates a set of non-linear simultaneous equations into a set of linear equations using the Taylor series expansion. The Newton Raphson (NR) method is applied in load flow studied due to its practicality in large power systems and its efficiency. It has the advantage of the number of iterations required to obtain a 22

34 solution is indepent of the size of the problem in load flow studies. Computationally, it is also very fast [4, 5, 14, 23]. A non-linear equation with single variable can be expressed as f(x) = 0 An initial value x is selected for solving this equation. The difference between the initial value and the final solution will be X 0. Then X 0 + X 0 is the solution of non-linear equation above i.e. f(x 0 + x 0 ) = 0.. ii) Expanding the above equation with Taylor series, we obtain f(x 0 + x 0 ) = f(x 0 ) + f (x 0 ) x 0 + f (x 0 ) ( x0 ) f n (x 0 ) ( x0 ) n 2! n! = 0 iii) Where f (x 0 ) f n (x 0 ) are the derivatives of the function f(x). If the difference x 0 is very small, the second and higher derivatives terms can be neglected. Thus equation becomes linear as shown below: Hence Then new solution will then become f(x 0 + x 0 ) = f(x 0 ) + f (x 0 ) x 0 = 0 f(x ) = f (x ) x x 0 = f(x0 ) f (x 0 ) x = x 0 + x 0 f(x0 ) f (x0 ) Since the above equation is an approximate equation hence the solution x is not a real solution. Further iterations are required. The iteration equation is: x k+1 = x k + x k+1 = x k f(xk ) f (x k ) 23

35 If the conditions below are met the iterations will be stopped x k < ε 1 Where ε 1 is the prescribed convergence precision. This newton method may be expanded to a non-linear equation with n variables f 1 (x 1, x 2 x n ) = 0 f 2 (x 1, x 2 x n ) = 0 f n (x 1, x 2 x n ) = 0 For a given set of initial values x1 0, x2 0 xn 0, then the corrected values x1 0, x2 0. xn 0. Hence our equation becomes, f 1 (x x 0 1, x x 0 2 x 0 n + x 0 n ) = 0 f 2 (x x 0 1, x x 0 2 x 0 n + x 0 n ) = 0 f n (x x 0 1, x x 0 2 x 0 n + x 0 n ) = 0 Expanding this we obtain f 1 (x 0 1, x 0 2 x 0 n ) + f 1 x x 1 0 x f 2 x x x f n x x 2 n x 0 n += 0 0 n f 2 (x 0 1, x 0 2 x 0 n ) + f 1 x x 1 x f 2 x 0 x 1 2 x f n x 0 x 2 n x 0 n += 0 0 n f n (x 0 1, x 0 2 x 0 n ) + f 1 x x 1 x f 2 x 0 x 1 2 x f n x 0 x 2 n x 0 n += 0 0 n The above equation can be written in matrix from as 24

36 f 1 (x 0 1, x 0 2 x 0 n ) f 2 (x 0 1, x 0 2 x 0 n ) = [ f n (x 0 1, x 0 2 x 0 n )] [ f 1 x 1 x 1 0 f 2 x 1 x 1 0 f n x 1 x 1 0 f 1 x 2 x 2 0 f 2 x 2 x 2 0 f n x 1 x 2 0 f 1 x n x0 n f 0 x x x 2 n x0 n f [ x 0 n ] n x 1 x0 n ] From above equation, we can get Δx 0 1, Δx 0 2 Δx 0 n.then the new solution can be obtained. The iteration equation can be written as follows: f 1 (x k 1, x k 2 x k n ) f 2 (x k 1, x k 2 x k n ) = [ f n (x k 1, x k 2 x k n )] [ f 1 x 1 x 1 k f 2 x 1 x 1 k f n x 1 x 1 k f 1 x 2 x 2 k f 2 x 2 x 2 k f n x 1 x 2 k f 1 x n xk n f k x 1 2 k x x n xk 2 n f [ x k n ] n x 1 xk n ] x k+1 = x k + x k+1 The equations can be written as F(X k ) = J k X k X k+1 = X k+1 + X k Where J is an n*n matrix called a Jacobian matrix. The NR method is better formulated using polar coordinates and is very accurate. In power flow studies, the elements in the Jacobean matrix are calculated by differentiating the power & reactive power expression and substituting values of voltage magnitude and phase angle. The next stage of Newton Raphson Solution, the Jacobean is inverted. Matrix inversion is a computationally complex task with the resources of time and storage increasing rapidly with order of (J). Assuming all buses are PQ and using estimated values, we obtain the difference between them and the calculated values and represent them as: 25

37 P i = P isch P icalc Q i = Q isch Q icalc Note, the Jacobean matrix gives the linearized relationship between small changes in Pi and voltage magnitude (Vi k ) with the small changes in real and reactive power Pi and Qi. Formulating the load follow problem in polar form, P 2 P n Q 2 [ Q n ] = P 2 P 2 δ 2 δ n P n P 2 P 2 V 2 V n P 2 P n P 2 [ δ n δ n ] [ V 2 V n ] Q 2 Q 2 δ 2 δ 2 Q n The matrix can be simplified to [ [ Q n [ δ 2 δ n ] Gauss Seidel Method Q 2 [ P Q ] = [J 1 J 2 ] [ δ J 4 V ] J 3 δ 2 δ n V 2 Q 2 V 2 V n [ V n ] Q n Q n [ V 2 V n ]] ] This method is developed based on the Gauss method. It is an iterative method of solving simultaneous non-linear equations. The type of data specified for different kinds of buses makes it complex to obtain formal solutions for power flow in a power system. The method makes use of an estimated value of voltage, to obtain a new calculated value for each bus voltage. The estimated value is replaced by a calculated value and both real power and reactive power are specified.. A new set of bus voltages is hence available, these voltages are used to calculate yet another set of voltages at the buses. The process is then repeated until the iteration solution converges. The convergence is quite sensitive to the starting values assumed. But this method suffers from poor convergence characteristics [4, 24]. 26

38 This is an iterative method used to solve the load flow problem for the value of Vi, and the iterative sequence hence becomes P sch sch i jq i + Y (k+1) V ij V j V i = i j 1 Y ij Where Pi sch = Pgi-Pdi and Qi sch = Qgi-Qdi Pi sch and Qi sch is the net scheduled real and reactive power being injected into bus i Pgi and Qgi denotes the real and reactive power being generated Pdi and Qdi denotes the real and reactive power demand at that load bus It is assumed that the current injected into bus i is positive, then the real and the reactive powers supply into the buses, such as generator buses, Pi sch and Qi sch have a positive value. The real and the reactive powers flowing away from the buses, such as load buses Pi sch and Qi sch have a negative values. Pi and Qi are solved from Equation (5) which gives n P (k+1) i = Real [V i { Y ij V i }] j 1 i 0 n (k+1) Q i = Imaginary [Vi { Y ij V i }] j 1 i 1 The power flow equation is usually expressed in terms of the bus admittance matrix, using the diagonal elements of the bus admittance and the non-diagonal elements of the matrix, then the Equation 10) becomes, And P sch sch i jq i Y (k+1) V ij V j V i = i Y ij n P (k+1) i = Real [V i {V i Y ii Y ij V i }] j 1 n ji i=1,j=1 n ji 27

39 n (k+1) Q i = Imaginary [Vi {V i Y ii Y ij V i The Fast De-coupled Method i=1,j=1 }] j 1 In the Newton Raphson power flow method, for every iteration the jacobian matrix has been recalculated. The Fast Decoupled Power Flow Method is based on a simplification of the Newton- Raphson method. This method, offers calculation simplifications, fast convergence and reliable results and became a widely used method in load flow analysis. However in some cases, where there is a high resistance-to-reactance (R/X) ratios or heavy loading (low voltage) at some buses, it does not converge well because many assumptions are made to simplify the Jacobian matrix and it is an approximation method. In a practical power system, the resistance of the branch is much lower than the reactance of the branch, therefore, there exists strong coupling between the real power and voltage angles whereas the coupling between the voltage magnitude and the real power is weak hence changes in the voltage magnitude have little effect in the real power. On the other hand, the reactive power has a strong coupling relationship with the voltage magnitude while it has a weak coupling relationship with the voltage angle [5, 33]. The Jacobian matrix is reduced by half by ignoring the element of J2 and J3 and it simplifies to: [ P Q ] = [J J 4 ] [ δ V ] Expanding the equation above gives two separate equation P = J 1 δ = [ P δ ] δ Q = J 4 V = [ P V ] V P V i Q V i = B δ = B V 28

40 B' and B'' are the imaginary parts of the bus admittance. It is better to ignore all shunt connected elements, as to make the formation of J1 and J4 simple. This will allow for only one single matrix than performing repeated inversion. The successive voltage magnitude and phase angle changes are δ = [B P ] 1 V V = [B Q ] 1 V A summary of comparison of the methods of power flow solution is given in the table below: PROPERTIES NEWTON -RAPHSON GAUSS SEIDEL DECOUPLED METHODS Storage Requirements Requires the most Memory Space as the Jacobian matrix are more. It has the minimum memory space requirement. It has a less memory requirement as compared to NR as it stores less Jacobian elements. Accuracy It is the most accurate. It is moderately accurate. Due to the general assumptions made it is the least accurate. Speed It is relatively fast as It is the slowest. It is the fastest. compared to Gauss- Seidel System Size It is Indepent of The number of It is indepent of system system size. iterations increase size. with increase of system size. Complexity It is the most complex It is the least complex It is relatively complex as compared to GS. Table 3.1: Comparison of load Flow Methods 29