Load Frequency Control in Multi Machine Systems Using PID Controller

بسم هللا الرحمن الرحيم

Sudan University of Science and Technology College of Graduate Studies

التحكم في تردد الحمل في األنظمة متعددة الماكينات باستخدام الحاكمة التناسبية- التكاممية- التفاضمية

A Thesis Submitted in Partial Fulfillment of the Requirements of M.Sc. Degree in Electrical Engineering (Microprocessor and Control)

Prepared by: Yahia Amir Yahia Gamal

Supervised by: Ust. Abdullah Salih Ali

اآلية

بسم اهلل الرمحن الرحيم

 َ َ َ َ َ َ َ  ق ََال ََو َاَ َس َب ََحَا َن ََكَال ََ َع َم ََمَل َ َنَاََإ َالَ ََمَاَ ََعَم ََمت َ َنَاََإ َن ََكَأ ََن ََتََا َل ََعَمَي ََمََا َل ََحَكَي َمَ َ

صدقَاهللَالعظيم َ

سورةَالبقرةَاآلية)23( َ

Dedication

For my father Dad, thanks for knowing exactly when to stop holding my hand and begin watching my back. You carried me in your arms when I was little and you held my hand while I was growing up. Dad, I am going to be your pillar when you are old and I will carry you in my heart until I die. Thanks for everything Sweet Bucket for my Mother Mother! A vast, revered, honored word; full of love, feelings, emotions and care that cannot be expressed in words. Mother is not only a parent for her children but a friend, helper, guider and a well-wisher. She is the one who brings us up, gives courage to face the world, confidence to achieve, teaches perseverance, moral ethics and to stand along. Mother is the name from where you begin; she remains with you in her life and even after her life, her prayers surround you everywhere. I love you for ever A brother and sister shares my childhood memories and grown-up dreams Brothers and sister don't necessarily have to say anything to each other- they can sit in a room and be together and just be completely comfortable with each other.

Acknowledgement

I would like to thank Prof. my supervisor, Ust. Abdullah Salih for his highly appreciable and valuable supervision and advice throughout the study. I am deeply indebted to the teaching staff of School of Pharmacy, for their guidance, advices and efforts throughout the course of our graduation. Finally, my deep appreciation goes to anyone who supported us in this research until it reached its final steps.

III

Abstract

Modern power systems networks consist of a number of utilities interconnected together. Power is exchanged between utilities over tie- lines by which they are connected. Automatic generation control (AGC) plays a very important role in power system. Its main role is to maintain the system frequency and tie-line flow at their scheduled values during normal period and also when the system is subjected to small step load perturbations.

The most commonly used controller is the PID controller, which requires a mathematical model of the system. It is a good tool for the control of systems that are difficult to model.

In this study, a power system with two areas connected through tie-line is considered. The objective of AGC, based on PID controller, is to damp the transient deviations (frequency and power) and to provide zero steady-state error of these variables in a very short time. The simulation is implemented by using MATLAB Simulink program.

مستخلص

ذحرىي َظى انقذسج انكهشتائٍح انحذٌثح عهى عذد يٍ انشثكاخ انكهشتائٍح ذشذثػ يع تععها انثعط و ذ ر ث ا د ل ا ن ط ا ق ح ا ن ك ه ش ت ا ئ ٍ ح ع ٍ غ ش ٌ ق خ ط ى غ ا ن ش ت ػ ا ن ك ه ش ت ا ئ ً . ٌ ه ع ة ا ن ر ح ك ى اال ن ً ن ه ر ى ن ٍ ذ د و س ا سئٍسٍا فً ذثثٍد انرشدد نهُظاو انكهشتائً وكزنهك اَسٍاب انقذسج خالل خػ انشتػ انكهشتائً تانقٍى انًثشيدح أثُاء دوسج انرشغٍم انعادٌح وأٌعا خالل اهرضاصاخ انحًم انكهشتائً انخفٍفح. أصثر انًرحكى انرُاسثً- انرفاظهً- انركايهً ٌطثق تُداذ فً عذد كثٍش يٍ ذطثٍقاخ أَظًح انرحكى. وٌعرثش أداج خٍذج نهرحكى فً األَظًح انرً ٌصعة وظع ًَىرج سٌاظً نها. ف ً ه ز ِ ا ن ذ س ا س ح ، أ خ ز ف ً ا ال ع ر ث ا س َ ظ ا و ق ذ س ج ك ه ش ت ا ئ ٍ ح ٌ ر ك ى َ ا ٌ يٍ يُطقرٍٍ ذشذثطاٌ عٍ غشٌق خ ػ س ت ػ ك ه ش ت ا ئ ً . ا ن غ ش ض ي ٍ ا س ر خ ذ ا و ا ن ر ح ك ى اال ن ً ن ه ر ى ن ٍ ذ- انزي ٌعرًذ عهى)انًرحكى انرُاسثً- انركايهً-انرفاظهً( - هىاخًاد االَحشافاخ انعاتشج نهرشدد وانقذسج وكزنك أٌ ٌعطً هزا انًرحكى خطأ صفشي نهحانح انًسرقشج نهزِ انًرغٍشاخ فً صيٍ وخٍض. ذى عًم انًحاكاج وانرحهٍم تاسرخذاو نغح يعًم انًصفىفاخ )ياذالب( عٍ غشٌق تشَايح ساتػ انًحاكاج.

Table of Contents

Content Page NO I اٌَح Dedication II Acknowledgement III Abstract IV V يسرخهص Table of Contents VI List of Figures IX List of Tables XI Chapter One Introduction 1.1 General 1 1.2 Problem Statement 2 1.3 Objectives 2 1.4 Methodology 2 1.5 Layout 2 Chapter Two Literature and Theoretical Background 2.1 Power Plants 3 2.2 Types of Steam Turbine 4 2.2.1 Non-reheat steam turbine 4 2.2.2 Reheat steam turbine 4 2.2.3 Tandem Compound 5 2.2.4 Cross Compound 6 2.2.5 Hydro-turbine 6 2.3 Generation 7

Content Page NO 2.4 Electromagnetic Generators 7 2.4.1 Dynamo 8 2.4.2 Alternator 9 2.4.3 Induction generator 10 2.4.4 Magneto-hydro-dynamic generator 10 2.5 Control Theory 10 2.6 Automatic Generation Control 11 2.7 Proportional Integral Derivative Controller 12 2.7.1 Droop 15 2.7.2 Loop tuning 17 2.7.3 Stability 18 2.7.4 Optimum behavior 18 Chapter Three Mathematical Model of the System 3.1 Introduction 20 3.2 Generator Model: 20 3.3 Load Model 21 3.4 Prime Mover Model: 22 3.5 Governor Model: 23 3.6 Isochronous Governors 24 3.7 Governors with Speed-Droop Characteristic 25 3.8 Percent Speed Regulation or Droop 26 3.9 Load Sharing by Parallel Units 27 3.10 Control of Generating Unit Power Output 28 3.11 AGC in A Single Area System 29 3.12 AGC in the Multi Area Power System 30

VII

Content Page NO 3.13 Tie-Line Bias Control 32 Chapter Four System Design and Simulation 4.1 Introduction 34 4.2 Two Area Power System 35 4.2.1 System response without AGC 35 4.2.2 AGC using Conventional PID Controller 37 4.3 Comparative Results 39 Chapter Five Conclusion and Recommendations 5.1 Conclusion 40 5.2 Recommendations 41 References 42

VIII

List of Figures

Figure Title Page No 2.1 A simple non-reheat steam turbine 4 2.2 A simple reheats steam turbine 5 2.3 Tandem compound, single reheat 6 2.4 Cross compound, single reheat 6 2.5 A simple hydro-turbine 7 2.6 PID controller 14 2.7 PV versus time, for three values of Kp 15 2.8 PV versus time, for three values of Ki 16 2.9 PV vs time, for three values of Kd 16 3.1 Generator block diagram 21 3.2 Generator and load block diagram 22 3.3 Block diagram for a simple non reheat steam turbine 22 3.4 Speed governing system. 23 3.5 Schematic of an isochronous governor 24 3.6 Governor with steady state feedback 25 3.7 Block diagram of a speed governor with droop 26 3.8 Ideal steady state characteristics of governor with 26 speed droop 3.9 Load sharing by parallel units with drooping governor 27 characteristic 3.10 Governor with load reference control for adjusting 29 speed load Relationship 3.11 Effect of speed changer setting on governor characteristic 29

Figure Title Page No 3.12 AGC for an isolated power system 30 3.13 Equivalent network for a two-area power system 32 3.14 AGC block diagram of two-area power system 33 4.1 Simulation block diagram for two area systems 35 without AGC 4.2 Frequency deviation step response without AGC 36 4.3 Power deviation step response without AGC 36 4.4 Simulation block diagram for two-area using 37 conventional PID 4.5 Frequency deviation step response using conventional 38 PID 4.6 Power deviation step response using conventional PID 38

List of Tables

Table Title Page No 2.1 Effects of increasing a parameter independently 19 4.1 Power system parameters 34 4.2 Time response specifications for two area power 39 system 4.3 Power deviation values in the steady state for two 39

area power system

Chapter One Introduction

Chapter One Introduction 1.1 General Automatic Generation Control (AGC) has been an important issue in power system operation and control since last several decades. The objective of the AGC is to enable each generator to control its generation independently to achieve zero state value of area control error and economic loadings of its generators against unpredictable changes in the load demand which occur continuously in a power system. If the load on the system increased, the turbine speed drops before the governor can adjust the input of the steam to the new load. As the change in the value of speed diminishes, the error signal become smaller and the positions of the governor fly-balls gets closer to the point required to maintain constant speed. However, the constant speed will not be the set point, and there will be an offset. One way to restore the speed or frequency to its nominal value is to add an integrator. The integral unit monitors the average error over a period of time and will overcome the offset. Because of its ability to return a system to it’s a system set point, integral action is also known as the rest action. Thus, as the system load changes continuously, the generation is adjusted automatically to restore the frequency to the nominal value. This scheme is known as the AGC.In an interconnected system consisting of several pools, the role of theAGC is to divide the loads among system, stations and generators so as to achieve maximum economy and correctly control the scheduled interchanges of tie-line power while maintaining a reasonably uniform frequency [1].

1.2 Problem Statement An industrial process, such as power system, contains different kinds of uncertainties due to change in system parameters, characteristics and load variations. On the other hand, the operating points of a power system may change very much during a daily cycle. The load is always changing, this needs to maintain power balance, and generators need to produce more or less power to keep up with the load. When generation is less than load the generator speed and frequency will drop and vice versa. So AGC is used to maintain frequency to the nominal value. 1.3 Objectives The main objectives of this research:  To develop automatic generation control of two area power system using PID controller.  To keep the type at the rated value.

 To response due to the load increase and also when load is

decreases. 1.4 Methodology MATLAB /Simulink is used, and the results are to serve verifying the usefulness of application of PID controller in AGC. 1.5 Layout This thesis consists of five chapters. Chapter two gives a general view of various generators types; PID control is described as well as automatic generation control overview. In chapter three a mathematical modeling of the power system and block diagram of AGC are obtained. Chapter four gives the computer simulation of PID, and simulation results using MATLAB/Simulink. Finally, chapter five contains conclusion andrecommendations.

Chapter Two Theoretical and Literature Background

2.1 Power Plants The power plant is a facility that transforms various types of energy into electricity or heat for some useful purpose. The energy input to the power plant can vary significantly, and the plant design to accommodate this energy is drastically different for each energy source. The forms of this input energy can be as follows:  The potential energy of an elevated body of water, which, when used, becomes a hydroloic power plant.  The chemical energy that is released from the hydrocarbons contained in fossil fuels such as coal, oil, or natural gas, which becomes a fossil fuel fired power plant  Solar energy from the sun, which becomes a solar power plant.  The fission or fusion energy that separates or attracts atomic particles, which becomes a nuclear power plant. In those power plants, the conversion of water to steam is the predominant technology.  A thermal power station is a power plant in which the prime mover is steam or gas driven. The greatest variation in the design of thermal power stations is due to the different fuel sources. Some prefer to use the term energy center because such facilities convert forms of heat energy into electrical energy. Almost all coal, nuclear, geothermal, solar thermal electricity, and waste incineration plants, as well as many natural gas power plants are

thermal [2].

2.2 Types of Steam Turbines 2.2.1 Non-reheat steam turbine Figure 2.1 shows the non-reheat steam turbine. After passing through the control valve, the high pressure steam enters the turbine through the steam-chest. The chest introduces a time delay of TCH in the steam flow resulting in transfer function:

(2.1) Where:

PT: Turbine power

PCV: Power control valve before entering the turbine

TCH: Chest introduces a time delay, between 0.2 – 0.5 sec

Valve steam Control signal ∆P CV Steam Chest Valve

∆P T

Turbine

Steam (to condenser)

Figure 2.1: A simple non-reheat steam turbine 2.2.2 Reheat steam turbine Figure 2.2 shows the reheat steam turbine. Have several turbine stages between which steam is led via reheaters. This design increases power plant efficiency and is usually accepted in large power plants. Assume that two stages in Figure 2.1are rated at half total power each and the reheater can be represented by a time delay TRH, then total turbine power then given by:

4 (2.2) The overall transfer function is

(2.3) Where:

PT: Turbine Power

PCV: Power control valve before entering the turbine

TRH: Reheater time delay, between 3-10 sec

Control ∆P signal CV Steam steam Chest

Control ∆P Negligible T delay

HP Section LP section section Steam (to condenser) condenser)

Figure 2.2: A simple reheats steam turbine

2.2.3 Tandem Compound Has only one shaft on which all the turbines, High Pressure (HP), Intermediate Pressure (IP) and Low Pressure (LP) turbines are mounted. Sometimes there is a Very High Pressure (VHP) turbine also. Tandom compound is shown in Figure 2-3.

Figure 2.3: Tandem compound, single reheat 2.2.4 Cross Compound Systems have two shafts driving two independent generators. The configurations corresponding to: Tandem compound, single reheat cross compound, Single Reheat as shown in Figure 2.4. Figure 2.3 tandom compounds, single reheat

Figure 2.4: Cross compound, single reheat 2.2.5 Hydro-turbine Depending upon the magnitude of water head (i.e. low head, medium head, high head); hydro-turbines have varying designs. However, the transfer function, in general, can be expressed as

(2.4) Where: Tps is the time of water taking to pass through the penstock Figure 2.5 shows a simple hydro – turbine [2].

6 Dam

Head Penstock ∆P T

∆P CV

turbine Figure 2.5: A simple hydro-turbine 2.3 Generation Before the connection between magnetism and electricity was discovered, electrostatic generators were used. They operated on electrostatic principles. Such generators generated very high voltage and low current. They operated by using moving electrically charged belts, plates, and disks that carried charge to a high potential electrode. Because of their inefficiency and the difficulty of insulating machines that produced very high voltages, electrostatic generators had low power ratings, and were never used for generation of commercially significant quantities of electric power. The Wimshurst machine and Van de Graaff generator are examples of these machines that have survived. Large power generation dynamos are now rarely seen due to the now nearly universal use of alternating current for power distribution. Before the adoption of alternative current (AC), very large direct-current dynamos were the only means of power generation and distribution. AC has come to dominate due to the ability of AC to be easily transformed to and from very high voltages to permit low losses over large distances [3]. 2.4 Electromagnetic Generators An electromagnetic generator is a device that transforms mechanical energy into electrical energy, using the interconnected principles of

7 magnetism and electricity. The process by which an electromagnetic generator produces electricity is called electromagnetic induction, which basically means that an electric current is induced within a conductor through use of a magnet. Most electric generators work on electromagnetic induction, and some of these use renewable energy sources such as water power and wind power to create the initial mechanical energy. Mechanical energy can basically be thought of as kinetic energy, or movement energy. Induction in an electromagnetic generator is the process which creates the electricity inside the conductor. This process works because the forces of electricity and magnetism are basically the same thing. Both work on the principle that some particles have a charge, and objects with opposing charges are attracted to each other. Negatively charged electrons are attracted to positively charged protons, through the process of basic magnetism. The flow of electrons to a positive charge is referred to as electricity. 2.4.1 Dynamo A dynamo is an electrical generator that produces direct current with the use of a commutator. Dynamos were the first electrical generators capable of delivering power for industry, and the foundation upon which many other later electric-power conversion devices were based, including the electric motor, the alternating-current alternator, and the rotary converter. Today, the simpler alternator dominates large scale power generation, for efficiency, reliability and cost reasons. A dynamo has the disadvantages of a mechanical commutator. Also, converting alternating to direct current using power rectification devices (vacuum tube or more recently solid state) is effective and usually economic [3].

8 2.4.2 Alternator Without a commutator, a dynamo becomes an alternator, which is a synchronous singly fed generator. Alternators produce alternating current with a frequency that is based on the rotational speed of the rotor and the number of magnetic poles. Automotive alternators produce a varying frequency that changes with engine speed, which is then converted by a rectifier to Direct Current (DC). By comparison, alternators used to feed an electric power grid are generally operated at a speed very close to a specific frequency, for the benefit of AC devices that regulate their speed and performance based on grid frequency. Some devices such as incandescent lamps and ballast-operated fluorescent lamps do not require a constant frequency, but synchronous motors such as in electric wall clocks do require a constant grid frequency. When attached to a larger electric grid with other alternators, an alternator will dynamically interact with the frequency already present on the grid, and operate at a speed that matches the grid frequency. If no driving power is applied, the alternator will continue to spin at a constant speed anyway, driven as a synchronous motor by the grid frequency. It is usually necessary for an alternator to be accelerated up to the correct speed and phase alignment before connecting to the grid, as any mismatch in frequency will cause the alternator to act as a synchronous motor, and suddenly leap to the correct phase alignment as it absorbs large inrush current from the grid, which may damage the rotor and other equipment. Typical alternators use a rotating field winding excited with direct current, and a stationary (stator) winding that produces alternating current. Since the rotor field only requires a tiny fraction of the power generated by the machine, the brushes for the field contact can be relatively small [4].

9 2.4.3 Induction generator An induction generator or asynchronous generator is a type of AC electrical generator that uses the principles of induction motors to produce power. Induction generators operate by mechanically turning their rotor faster than the synchronous speed, giving negative slip. A regular AC asynchronous motor usually can be used as a generator, without any internal modifications. Induction generators are useful in applications such as mini-hydro power plants, wind turbines, or in reducing high-pressure gas streams to lower pressure, because they can recover energy with relatively simple controls. To operate an induction generator must be excited with a leading voltage; this is usually done by connection to an electrical grid, or sometimes they are self-excited by using phase correcting capacitors. 2.4.4 Magneto-hydro-dynamic generator A Magneto-Hydro-Dynamic (MHD) generator directly extracts electric power from moving hot gases through a magnetic field, without the use of rotating electromagnetic machinery. MHD generators were originally developed because the output of a plasma MHD generator is a flame, well able to heat the boilers of a steam power plant [4]. 2.5 Control Theory Is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems with inputs. The external input of a system is called the reference. When one or more output variables of a system need to follow a certain reference over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system. The usual objective of a control theory is to calculate the proper corrective action from the controller that result in system stability, that is,

11 the system will hold the set point and not oscillate around it. The inputs and outputs of a continuous control system are generally related by differential equations. If these are linear with constant coefficients, a transfer function relating the input and output can be obtained by taking their Laplace transform. If the differential equations are nonlinear and have a known solution, it may be possible to linearize the nonlinear differential equations at that solution. If the resulting linear differential equations have constant coefficients one can take their Laplace transform to obtain a transfer function [5]. The transfer function is also known as the system function or network function. The transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant solution of the nonlinear differential equations describing the system. 2.6 Automatic Generation Control In an electric power system, automatic generation control is a system for adjusting the power output of multiple generators at different power plants, in response to changes in the load. Since a power grid requires that generation and load closely balance moment by moment, frequent adjustments to the output of generators are necessary. The balance can be judged by measuring the system frequency; if it is increasing, more power is being generated than used, and all the machines in the system are accelerating. If the system frequency is decreasing, more loads are on the system than the instantaneous generation can provide, and all generators are slowing down. In electricity generation, droop speed control is the primary instantaneous system using net frequency deviations to distribute with stability load changes over generating plants. For stable operation of the electrical grid

11 of North America, power plants operate with a five percent speed droop. This means the full-load speed is 100% and the no-load speed is 105%. This is required for the stable operation of the net without hunting and dropouts of power plants. Normally the changes in speed are minor due to inertia of the total rotating mass of all generators and motors running in the net. Adjustments in power output are made by slowly raising the droop curve by increasing the spring pressure on a centrifugal governor or by an engine control unit adjustment. Generally, this is a basic system requirement for all power plants because the older and newer plants have to be compatible in response to the instantaneous changes in frequency without depending on outside communication. Voltage control of several power sources is not practical because there would not be any independent feedback, resulting in the total load being put on one power plant. The inertia is given by the parallel operation of synchronous generators; the frequency speed droop is the primary instantaneous parameter in control of an individual power plant's power output (MW). In equation (2.5) S is the ratio of frequency deviation when comparing the load versus the nominal frequency. S = (2.5)

Where: S is the ratio of frequency deviation is deviation in the load frequency is the nominal frequency. 2.7 Proportional Integral Derivative Controller Is a generic control loop feedback mechanism (controller) widely used in industrial control systems – a PID is the most commonly used feedback controller. A PID controller calculates an error value as the difference

12 between a measured process variable and a desired set point. The controller attempts to minimize the error by adjusting the process control inputs. The PID controller calculation (algorithm) involves three separate constant parameters, and is accordingly sometimes called three-term control: the proportional, the integral and derivative values, denoted P, I, and D. Heuristically, these values can be interpreted in terms of time: P depends on the present error, I on the accumulation of past errors, and D is a prediction of future errors, based on current rate of change[5].The weighted sum of these three actions is used to adjust the process via a control element such as the position of a control valve, or the power supplied to a heating element. In the absence of knowledge of the underlying process, a PID controller has historically been considered to be the best controller [6]. By tuning the three parameters in the PID controller algorithm, the controller can provide control action designed for specific process requirements. The response of the controller can be described in terms of the responsiveness of the controller to an error, the degree to which the controller overshoots the set-point and the degree of system oscillation. Note that the use of the PID algorithm for control does not guarantee optimal control of the system or system stability. Some applications may require using only one or two actions to provide the appropriate system control. This is achieved by setting the other parameters to zero. A PID controller shown in Figure 2.5 will be called a PI, PD, P or I controller in the absence of the respective control actions. PI controllers are fairly common, since derivative action is sensitive to measurement noise, whereas the absence of an integral term may prevent the system from reaching its target value due to the control action. Figure 2.6 shows block diagram of PID controller.

Figure 2.6: PID controller The PID control scheme is named after its three correcting terms, whose sum constitutes the Manipulated Variable (MV). The proportional, integral, and derivative terms are summed to calculate the output of the PID controller. Defining y(t) as the controller output, the final form of the PID algorithm is: y(t) = MV(t) = e(t) + + (2.6)

Where: : Proportional gain, a tuning parameter.

: Integral gain, a tuning parameter. : Derivative gain, a tuning parameter. e: Error =SP –PV. t: Time or instantaneous time (the present). The proportional term produces an output value that is proportional to the current error value. The proportional response can be adjusted by multiplying the error by a constant Kp, called the proportional gain constant.

Figure 2.7 shows PV versus time, for three values of Kp (Kp = 0.5, 1, 2),

Ki and Kd are constant.

Figure 2.7: PV versus time, for three values of Kp The proportional term is given by: e(t) (2.7)

A high proportional gain results in a large change in the output for a given change in the error. If the proportional gain is too high, the system can become unstable (see the section on loop tuning). In contrast, a small gain results in a small output response to a large input error, and a less responsive or less sensitive controller. If the proportional gain is too low, the control action may be too small when responding to system disturbances. Tuning theory and industrial practice indicate that the proportional term should contribute the bulk of the output change. 2.7.1 Droop Because a non-zero error is required to drive the controller, a pure proportional controller generally operates with a steady-state error, referred to as droop. Droop is proportional to the process gain and inversely proportional to proportional gain. Droop may be mitigated by adding a compensating bias term to the set point or output, or corrected by adding an integral term [5]. The integral term accelerates the movement of the process towards set- point and eliminates the residual steady-state error that occurs with a pure proportional controller. However, since the integral term responds to

15 accumulated errors from the past, it can cause the present value to overshoot the set-point value. Figure 2.8 shows PV versus time, Ki (Ki =

0.5, 1, 2), Kp and Kd are constant.

Figure 2.8: PV versus time, for three values of Ki

The contribution from the integral term is proportional to both the magnitude of the error and the duration of the error. The integral in a PID controller is the sum of the instantaneous error over time and gives the accumulated offset that should have been corrected previously. The accumulated error is then multiplied by the integral gain ( ) and added to the controller output. The integral term is given by:

(2.8)

Figure 2.9 shows PV versus time, for three values of Kd, (Kd = 0.5, 1, and

2), Kp and Ki are constant [6]

Figure 2.9: PV vs time, for three values of Kd

16 The derivative of the process error is calculated by determining the slope of the error over time and multiplying this rate of change by the derivative gain . The magnitude of the contribution of the derivative term to the overall control action is termed the derivative gain, . The derivative term is given by:

= (2.9)

The derivative term slows the rate of change of the controller output. Derivative control is used to reduce the magnitude of the overshoot produced by the integral component and improve the combined controller-process stability. However, the derivative term slows the transient response of the controller. Also, differentiation of a signal amplifies noise and thus this term in the controller is highly sensitive to noise in the error term, and can cause a process to become unstable if the noise and the derivative gain are sufficiently large. Hence an approximation to a differentiator with a limited bandwidth is more commonly used. Such a circuit is known as a phase-lead compensator. 2.7.2 Loop tuning Tuning a control loop is the adjustment of its control parameters (proportional band/gain, integral gain/reset, derivative gain/rate) to the optimum values for the desired control response. Stability (bounded oscillation) is a basic requirement, but beyond that, different systems have different behavior, different applications have different requirements, and requirements may conflict with one another. PID tuning is a difficult problem, even though there are only three parameters and in principle is simple to describe, because it must satisfy complex criteria within the limitations of PID control. There are accordingly various methods for loop tuning, and more sophisticated techniques are

17 the subject of patents; this section describes some traditional manual methods for loop tuning. Designing and tuning a PID controller appears to be conceptually intuitive, but can be hard in practice, if multiple (and often conflicting) objectives such as short transient and high stability are to be achieved. Usually, initial designs need to be adjusted repeatedly through computer simulations until the closed-loop system performs or compromises as desired. Some processes have a degree of non-linearity and so parameters that work well at full-load conditions don't work when the process is starting up from no-load; this can be corrected by gain scheduling (using different parameters in different operating regions). PID controllers often provide acceptable control using default tunings, but performance can generally be improved by careful tuning, and performance may be unacceptable with poor tuning. 2.7.3 Stability If the PID controller parameters (the gains of the proportional, integral and derivative terms) are chosen incorrectly, the controlled process input can be unstable, i.e., its output diverges, with or without oscillation, and is limited only by saturation or mechanical breakage. Instability is caused by excess gain, particularly in the presence of significant lag. Generally, stabilization of response is required and the process must not oscillate for any combination of process conditions and set points, though sometimes marginal stability (bounded oscillation) is acceptable or desired [5]. 2.7.4 Optimum behavior The optimum behavior on a process change or set-point change varies depending on the application. Two basic requirements are regulation (disturbance rejection – staying at a given set-point) and command tracking (implementing set-point changes) – these refer to how well the

18 controlled variable tracks the desired value. Specific criteria for command tracking include rise time and settling time. Some processes must not allow an overshoot of the process variable beyond the set-point if, for example, this would be unsafe. Other processes must minimize the energy expended in reaching a new set-point. If the system must remain online, one tuning method is to first set and values to zero. Increase until the output of the loop oscillates, then the should be set to approximately half of that value for a "quarter amplitude decay" type response. Then increase until any offset is corrected in sufficient time for the process. However, too much will cause instability. Finally, increase , if required, until the loop is acceptably quick to reach its reference after a load disturbance. However, too much will cause excessive response and overshoot. A fast PID loop tuning usually overshoots slightly to reach the set-point more quickly; however, some systems cannot accept overshoot, in which case an over-damped closed-loop system is required, which will require a setting significantly less than half that of the setting that was causing oscillation [6]. Table 2.1: Effects of increasing a parameter independently Parameter Rise time Over Settling Steady state Stability shoot time error

Decrease Small Small Decrease Degrade change change

Decrease Increase Increase Eliminate Degrade

Miner Decrease No change in Improve change Decrease theory if small

Chapter Three Mathematical Model of the System

3.1 Introduction The objective of the control strategy is to generate and deliver power in an interconnected system as economically and reliably as possible while maintaining the voltage and the frequency within permissible limits. Changes in real power affect mainly the system frequency, while reactive power is less sensitive to changes in frequency and is mainly dependent on changes in voltage magnitude. Load Frequency Control (LFC) loop controls the real power and frequency and automatic voltage regulator (AVR) loop regulates the reactive power and voltage magnitude. LFC has gained in importance with the growth of interconnected systems and has made the operation of interconnected systems possible. Today, it is still the basis of many advanced concepts for the control of large systems [8]. The methods developed for control of individual generators, and eventually control of large interconnections, play a vital role in modern energy control centers. Modern Energy Control Centers (ECC) are equipped with on line performing all signals processing through the remote acquisition systems known as Supervisory Control and Data Acquisition (SCADA) systems. 3.2 Generator Model: Applying the swing equation of a synchronous machine given by (3.1) to small perturbation it can be:

Where: H is per unit inertia constant.

δ is electrical power angle. fo is frequency

is mechanical power

is electrical power

=∆ ∆

Or in terms of small deviation in speed: d 1 s = (∆p ∆p ….. (3 .3) dt 2 e With speed expressed in per unit, without explicit per unit notation, we have:

= ∆p ∆p ……………………………………………. (3.4) e Taking Laplace transform of Eq. (3.4), it becomes:

∆Ω(s) = [∆p (s)-∆ (s)] ………………………………………. (3.5)

The above equation (3.5) is shown in block diagram of Figure 3.1.

Figure 3.1: Generator block diagram 3.3 Load Model The load on a power system consists of a variety of electrical devices. For resistive loads, such as lighting and heating loads, the electrical power is independent of frequency. Motor loads are sensitive to changes in frequency. How sensitive it is to frequency depends on the composite of the speed load characteristics of all the driven devices. The speed load characteristic of a composite load is approximated by: ∆p p (3.6) e

Where ∆p is the non-frequency sensitive load change and D is the frequency sensitive load change. D is expressed as percent change in load divided by percent change in frequency. Figure 3.2 illustrates load model in the generator model.

Figure 3.2: Generator and load block diagram 3.4 Prime Mover Model: The source of mechanical power is commonly known as the prime mover, may be hydraulic turbines at waterfalls, steam turbines whose energy comes from the burning of coal, gas nuclear fuel, and gas turbines. The model for the turbine relates changes in mechanical power output ∆p to changes in stea valve position ∆p . Different types of turbines vary widely in characteristics. The simplest prime mover model for the non- reheat steam turbine can be approximated with a single time constant , resulting in the following transfer function [8].

p 1 (s) = = p 1 s The block diagram for a simple turbine is shown in Figure 3.3

∆Pv(s) ∆Pm(s) 1/1+ Ts

Figure 3.3: Block diagram for a simple none reheat steam turbine 22

3.5 Governor Model: When the generator electrical load is suddenly increased, the electrical power exceeds the mechanical power input. This power deficiency is supplied by the kinetic energy stored in the rotating system. The reduction in kinetic energy causes the turbine speed and, consequently, the generator frequency to fall. The change in speed is sensed by the turbine governor which acts to adjust the turbine input valve to change the mechanical power output to bring the speed to a new speed steady state. The earliest governors were the watt governors which sense the speed by means of rotating fly-balls and provide mechanical motion in response to speed changes. However, most modern governors use electronic means to sense speed changes. Figure 3.4 shows schematically the essential elements of conventional watt governor, which consists of the following major parts:

Figure 3.4: Speed governing system i. Speed governor: The essential parts are centrifugal fly-balls driven directly through gearing by turbine shaft. The mechanism provides upward and downward vertical movements proportional to the change in speed. ii. Linkage mechanism: These are links for transforming the fly-balls movement to the turbine valve through a hydraulic amplifier and providing a feedback from the turbine valve movement.

iii. Hydraulic amplifier: Very large mechanical forces are needed to operate the steam valve. Therefore, the governor movements are transformed into high power forces via several stages of hydraulic amplifiers. iv. Speed changer: The speed changer consists of a servomotor which can be operated manually or automatically for scheduling load at nominal frequency. By adjusting this set point, a desired load dispatch can be scheduled at nominal frequency. 3.6 Isochronous Governors The adjective isochronous means constant speed. An isochronous governor adjusts the turbine valve/gate to bring the frequency back to the nominal or scheduled value. Figure 3.5 shows the schematic of such speed governing system. The measured rotor speed r is compared with reference speed o. The error signal (equal to speed deviation) is a plified and integrated to produce a control signal ∆y which actuates the main steam supply valves in the case of a steam turbine, or gate in the case of a hydraulic turbine. Because of the reset action of the integral controller. ∆y will reach a new steady state only when the speed error ∆ r is zero.

Valve/gate Steam Pm Turbine G Pe or water

ωr ∆Y _ _ Integrator -K ∑ Speed ref. ωo ωr :rotor speed ∆ωr Y: valve/ gate position Pm: mechanical power

Figure 3.5: Schematic of an isochronous governor

3.7 Governors with Speed-Droop Characteristic The isochronous governors cannot be used when there are two or more units connected to the same system since each generator would have to have precisely the same speed setting. Otherwise, they would fight each other, each trying to control system frequency to its own setting. For stable load division between two or more units operating in parallel, the governors are provided with a characteristic so that the speed drops as the load is increased. The speed droop or regulation characteristic may be adding a steady state feedback loop around the integrator as shown in Figure 3.6

Valve/gate

Steam Shaft Turbine To or water generator

ωr ∆Y _ _ Integrator K ∑ ∑ Speed ref. ωo ∆ωr R

Figure 3.6: Governor with steady state feedback The transfer function of the governor of Figure 3.6 reduced to the form shown in Figure 3.7. This type of governor is characterized as a proportional controller with a gain of 1/R.

∆Y ∆ωr ∑ K 1/S _

(a) Block diagram with steady state feedback

∆ωr -1/R 1/1+sTG ∆Y

TG = 1/KR

(b) Reduced block diagram Figure 3.7: Block diagram of a speed governor with droop 3.8 Percent Speed Regulation or Droop The value of R determines the steady state speed versus load characteristic of the generating unit. he ratio of speed deviation (∆ r) or frequency deviation (∆f) to change in valve/gate position (∆y) or power output (∆p) is equal to R. the para eter R is referred to as speed regulation or droop. It can be expressed in percent as: percent speed or frequency change Percent R = *100= [ ……… (3.8) percent power output change Where: : Steady state speed at no load.

: Steady state speed at full load.

Nominal or rated speed. For example, a 5% droop regulation means that a 5% frequency deviation causes 100% change in valve position or power output

Figure 3.8: Ideal steady state characteristics of governor with speed droop

3.9 Load Sharing by Parallel Units If two or more generators with drooping governor characteristics are connected to a power system, there will be a unique frequency at which they will share a load change. Consider two units with droop characteristics as shown in Figure 3.9. They are initially at nominal frequency fo with outputs and . When a load increase ∆ causes the units to slow down, the governors increase output until they reach a new common operating frequency f ' [7]. The amount of load picked up by each unit depends on the droop characteristic:

∆ = (3.9)

∆ = (3.10)

Hence,

(3.11)

If the percentages of regulation of the units are nearly equal, the changes in the outputs of each unit will be nearly in proportion to its rating.

Figure 3.9: Load sharing by parallel units with drooping governor characteristic

3.10 Control of Generating Unit Power Output The relationship between speed and load can be adjusted by changing an input “load reference set point" as shown in Figure 3.10. In practice, the adjustment of load reference set point is accomplished by operating the "speed changer motor". The effect of this adjustment is depicted in Figure 3.11, which shows a family of parallel characteristics for different speed changer motor settings. The characteristics are for a governor associated with 50Hz system. Three characteristics are shown representing three load reference settings. At 50Hz characteristic A results in zero output, characteristic B results in 50% output, and characteristic C results in 100% output. Thus, the power output of the generating unit at a given speed may be adjusted to any desired value by adjusting the load reference setting through actuation of the speed changer motor. For each setting, the speed load characteristic has 5% droop; that is, a speed change of 5% (2.5Hz) causes a 100% change in power output. When two or more generators are operating in parallel, the speed droop characteristic (corresponding to a load reference setting) of each generating unit merely establishes the proportion of the load picked up by the unit when a sudden change in system load occurs. The output of each unit at any given system frequency can be varied only by changing its load reference, which in effect moves the speed droop characteristic up and down [7].

Valve/gate

Steam Shaft Turbine To or water generator

ωr ∆Y _ _ _ Integrator K ∑ ∑ Speed ref. ωo _ ∆ωr _ _ Load reference R Set-point

(a) Schematic diagram of governor and turbine

∑ 1/1+sTG ∆ωr 1/R ∆Y _

(b) Reduced block diagram of governor Figure 3.10: Governor with load reference control for adjusting speed load Relationship

Figure 3.11: Effect of speed changer setting on governor characteristic When a generating unit is feeding an isolated load, the adjustment of the speed changer changes the unit speed. However, when the unit is synchronized to a power system, the speed changer adjustment changes the unit power output: it has only a minor effect on system frequency, depending on the size of the unit relative to that of the total system generation [7]. 3.11 AGC in A Single Area System With the primary load frequency control loop, in the system load will result in a steady-state frequency deviation, depending on the governor speed regulation. In order to reduce the frequency deviation to zero, a

29 reset action must be provided. The reset action can be achieved by introducing an integral controller to act on the load reference setting to change the speed set-point. The integral controller will force the final frequency deviation to zero. The LFC system, with the addition of the secondary loop, is shown in Figure 3.12. The integral controller gain I must be adjusted for a satisfactory transient response.

∆PL(s)

∆Pv ∆Pm _ ∆Pref. (s) ∆ω(s) _ 1/1+ gS 1/1+ Ts 1/2Hs+D _ Governor Turbine Rotating mass and load 1/R

KI/s

Figure 3.12: AGC for an isolated power system 3.12 AGC in the Multi Area Power System In many cases, a group of generators are closely coupled internally and swing in unison. Furthermore, the generator turbines tend to have the same response characteristics. Such a group generators are said to be coherent. Then it is possible to let the LFC loop represent the whole system, which is referred to as a control area. The AGC of a multi area system can be realized by studying first the AGC for a two-area system consider two areas represented by an equivalent generating unit interconnected by a lossless tie-line with reactance tie. Each area is represented by a voltage source behind an equivalent reactance as shown in Figure 3.13. During normal operation, the power transferred over the tie-line is given by:

= sin

Where = And

Equation (3.13) can be linearized for a small deviation in the tie-line flow

∆ from the nominal value, i.e.,

∆ | ∆

= ∆

The quantity is the slope of the power angle curve at the initial operating angle = – . It is known as the synchronizing power coefficient. This coefficient plays an important part in determining system stability. Thus it becomes:

| = cos

The tie-line power deviation then takes on the form:

∆ = (∆ - ∆ ) The tie-line power flow appears as a load increase in one area and a load decrease in the other area, depending on the direction of the flow. The direction of flow is dictated by the phase angle difference; if ▪ ∆ ∆ , the power flows from area1 to area2.Consider a load change

in area1. In the steady-state, both areas will have the same steady- state frequency deviation, i.e.,

∆ = ∆ = ∆

And∆ - ∆ - ∆ = ∆

∆ + ∆ = ∆ 21) The change in mechanical power is determined by the governor speed characteristics, given by:

∆ =

Substituting equation (3.21) and (3.22) into equation (3.19) and (3.20) respectively and solving for ∆ it can be:

∆ = ( ) ( )

Where:

= +

and are known as the frequency bias factor. The change in the tie- line power is

( )

∆ =- ( ) ( )

X1 Xtie X2

E1 δ1 E 2 δ2

Figure 3.13: Equivalent network for a two-area power system 3.13 Tie-Line Bias Control In the normal operating state, the power system is operated so that the demands of areas are satisfied at the nominal frequency. A simple control strategy for the normal mode is:

1. Keep frequency at the nominal value (50/Hz). 2. Maintain the tit-line flow about schedule. 32

3. Each area should absorb its own load change. Conventional LFC is based upon tie-line bias control, where each area tends to reduce the Area Control Error (ACE) to zero. The control error for each area consists of a linear combination of frequency and tie-line error.

= ∑ +

The area bias i determines the amount of interaction during a disturbance in the neighboring areas. An overall satisfactory performance is achieved when i is selected equal to the frequency bias 1 factor of that area, i.e., i i . Thus, the ACEs for a two-area Ri system are:

= ∆ + ∆

Where: ∆ 12 and ∆ 21 are departures from scheduled interchanges. ACEs are used as actuating signals to activate changes in the reference power set-points, and steady-state is reached, ∆ 12and ∆ will be zero. The integrator gain constant must be chosen small enough so as not to cause the area to go into a chase mode. Figure 3.14 shows the block diagram of a simple AGC for a two-area system.

1/R1 ∆PL1(s) 1 ∆Pm1 _ _ ∆Pv _ ∆ω1 KI1/s 1/1+ g1s 1/1+ T1s 1/2H1s+D1 ACE1 _ _ Governor1 Turbine1

+ ∆P12 ∆P12 Ps/s _

∆Pv2 ∆Pm2 + + ∆ω2 KI2/s 1/1+ g2s 1/1+ T2s 1/2H2s+D2 _ _ _ ACE2 Governo r 2 Turbine2 ∆PL2(s) 1/R2

Figure 3.14: AGC block diagram of two-area power system

Chapter Four System Design and Simulation

4.1 Introduction The power system with two areas having two units (steam turbines) is considered in simulation study. In this study, the simulation is executed by using MATLAB program. In the simulation, first area of power system a step load is increased. The controllers which used to control power system is conventional PID. Two area system connected by a tie line has the parameters which are used in simulation shown in Table 4.1. Table 4.1: Power system parameters Area 1 2

Governor speed regulation (R) = 0.05 = 0.0625

Frequency sensitivity load coefficient (D) p.u. p.u.

Inertia constant (H) = 5sec. = 4sec. Base power 1000 MVA 1000 MVA

Governor time constant ( = 0.2 sec = 0.3 sec.

Turbine time constant = 0.6 sec. = 0.8 sec.

oad change (∆ ) ∆ =0.1 p.u. ∆ Synchronizing power coefficient (T) p.u.

The work in this chapter is divided into two sections; firstly, two areas power systems (without controllers), then two area power system using conventional PID controllers. The simulation of the system is done to improve the controller's performance. With primary speed control action, a change in the load of the system will appear in a steady-state frequency deviation, depending on the governor droop characteristic and frequency sensitivity of the load. 34

4.2 Two area power system A two area power system with parameters of area1, area2 and tie line is studied and simulated without AGC and with AGC. 4.2.1 System response without AGC The simulation block diagram for two area power systems in MATLAB/SIMULIMK is shown in Figure 4.1. The simulation result of frequency deviation step response is shown in Figure 4.2. The change of power in area1 is met by increase in generation in both areas associated with a change in the tie-line power and a reduction in frequency. The simulation result for power deviation response is shown in Figure 4.3.

Figure 4.1: Simulation block diagram for two area systems without AGC

Figure 4.2: Frequency deviation step response without AGC

Figure 4.3: Power deviation step response without AGC From the results of two area power systems in Figure 4.2, we can realize that; the steady-state error in two area power system is low, because of kinetic energy in the two areas, but the tie-line power flow is deviated from the agreed value, as shown in Figure 4.3. To keep the frequency at the nominal value and to maintain the tie-line power flow, AGC is used.

4.2.2 AGC using conventional PID controller In each area, AGC controller tends to reduce the area control error to zero. The control error for each area consists of a linear combination of frequency and tie line error. MATLAB simulation block diagram for the two area power systems with AGC control using conventional PID controller is shown in Figure 4.4. The PID controller gains (parameters) are tuned using trial and error tuning method. The simulation result for PID controller1 parameters

( =2, i 1.3 and d=0.8) in area-1 and PID parameters ( =1.6,

i =1.2 and d=0.7) in area-2 is shown in Figure 4.5 which represents the frequency deviation response. The simulation result for power deviation response in area-1, area-2 and tie-line power flow is shown in Figure 4.6.

Figure 4.4: Simulation block diagram for two-area using conventional PID

Figure 4.5: Frequency deviation step response using conventional PID

Figure 4.6: Power deviation step response using conventional PID

4.3 Comparative Results Table 4.2Time response specifications for two area power system Cases of Area Steady state Settling time Peak over shoot simulation error (p.u.) (Sec.) (absolute value) Two area 1 -0.003 27.4 -0.007 without AGC 2 -0.003 28 -0.002 Two area with 1 0 16.3 -0.004 AGC using PID 2 0 17.25 -0.001 Table 4.3Power deviation values in the steady state for two area power system Cases of simulation Area1(p.u.) Area2(p.u.) Tie- line(p.u.) Two area without AGC 0.054 0.042 -0.045 Two area with AGC using 1 0 0 PID

Chapter Five Conclusion and

Recommendations

Chapter Five Conclusion and Recommendations 5.1 Conclusion This study is an application of PID controller to automatic generation control in power system with two areas connected through a tie line. In practice, power systems generally have more than one area and each area has different properties from others. Because of this, in this research, the power system of two areas with two thermal units with different parameter is considered. The study has investigated the performance of conventional PID controller on a two area systems comparing with two area systems without AGC. The frequency deviation and power deviation are observed and analyzed. Then the comparison is made to see the performance of two area systems by considering the settling time, peak time, steady state error and how much oscillation occurs. The MATLAB simulation results illustrates that, in power system without AGC controller, the frequency deviation and power deviation steady state errors in two area power systems are increasing with increase in load changes. By using AGC controller in power system, steady state errors are forced to zero. The settling time and peak time are less with the conventional PID controllers. For the load change in area1 only, AGC controller in area2 is approximately not important and vice versa. The power change in area1 is absorbed by generation in area1. Generation in area2 and tie line flow changed a little bit in the transient period and then returned to zero in steady-state.

5.2 Recommendations 1) Tuning using Fuzzy controller can be used. 2) The controller can also be built using various types of membership functions and can be compared for sensitivities in order to decide which type of member function is the best. 3) In further researches an interconnected power system with different types of units (i.e. hydro-thermal or wind power) can be investigated.

References

[1] Sonipat, Haryana, "International Journal of Science and Research (IJSR) ", Murthal University, Department of Electronic Engineering, YMCA UST, Faridabad, India [2] S. Sivanagaraju and . ereenivasan, “ ower yste Operation and Control”, orling indersley vt. td, India, 2010 [3] Langdon Crane, "Magneto-Hydrology-Dynamic (MHD) Power Generators", Library of Congressional Research service, 1981. [4] Lostly H.H.W and Lewis D. L, "Homo Polar Machines", Philosophical Transactions for the Royal society of London, 1973. [5] King Myke, "Process control: A practical Approach", Wiley, 2010.

[6] Graham Ron, "FAQ on PID Controller Tuning", Mike Mc Hugh,2005. [7] P.Kundur, "Power System Stability and Control", McGraw-Hill, U.S.A, 1994. [8] Hadi Saadat, "Power System Analysis", McGraw-Hill, U.S.A, Second Edition, 2004.