Comparison of controllers design for two area interconnected Hydro- Thermal power generation system

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1 Comparison of controllers design for two area interconnected Hydro- Thermal power generation system A.HIMA BINDU 1, V. LAKHMA NAIK 2 1 Assistant Professor, Dept of EEE, BIT Institute of Technology, Hindupur, Anantapur (Dt), AP, India, 2 Assistant Professor, Dept of EEE, BIT Institute of Technology, Hindupur, Anantapur (Dt), AP, India, ABSTRACT: In this paper is an optimal load frequency controller for two area interconnected hydro & thermal power system is presented to quench the deviations in frequency and tie line power due to different load disturbances. Here, a PID type controller is considered for LFC problem. The parameters of the proposed PID controller are tuned using Particle Swarm Optimization (PSO) method. A two-area electric power system with a wide range of parametric uncertainties is given to illustrate proposed method. To show effectiveness of the proposed method, a PI type controller optimized by Genetic Algorithms (GA) is designed in order to comparison with the proposed PID controller. The simulation results visibly show the validity of PSO-PID controller in comparison with the GA-PI controller and conventional PI controller. Index Terms PID, PSO, GA, PSO-PID & GA-PI controllers. 1). INTRODUCTION The Generation system is basically the heart of any power system. The collapse of generation system leads to the biggest failure of the utility system, the recovery is not only time consuming but tougher than any other system such as Transmission and Distribution system. Increased industrialization and better standard of living become possible with increased availability and consumption of electrical energy. To satisfy the increased demand for electric power, it becomes necessary to use all the sources of power generation in the country for the development of maximum electric power. The main objectives behind the design of AGC are: The steady state frequency error following a step load perturbation should be zero. The energy efficiency of a conventional thermal power station, considered salable energy produced as a percent of the heating value of the fuel consumed, is typically 33% to 48%.[citation needed] as with all heat engines, their efficiency is limited, and governed by the laws of thermodynamics. 1.2). HYDRO POWER PLANT: The main objctive of this project is to study the Load Frequency Control problem for multi area power system and design of control strategies for the Load frequency control in two area Hydro-thermal power system working in parallel. In order to obtain better steady state values this work represents various controller techniques.various control strategies like, conventional PI controller, PSO employed PID controller, GA based PID controller and BA based MPC controller are implemented to obtain better time domain performance specifications. 2). MODELLING OF POWER SYSTEM The modeling of a two area hydrothermal power plant is introduced. Basically design of a control system is frequently divided into two steps: determination of a mathematical model and design of a control strategy. 2.1). Two area load frequency Control: An extended power system can be divided into a number of load frequency control areas interconnected by means of tie lines. Without loss of generality we shall consider a two area case connected by a single tie line as illustrated in Fig. In an isolated control area case the incremental power( P G P D ) was accounted for by the rate of increase of strode kinetic energy and increase in area load caused by increase in frequency. Since a tie line transports power in or out of an area, this fact must be accounted for the incremental power balance equation of each area. The steady state change in the tie flow following a step load change in an area must be zero. An automatic generation controller providing a slow monotonic type of generation Responses should be preferred in order to reduce wear and tear of the equipment. 1.1). THERMAL POWER PLANT A thermal power station is a power plant in which the prime mover is steam driven. Water is heated, turns into steam and spins 0a steam turbine which drives an electrical generator. After it passes through the turbine, the steam is condensed in a condenser and recycled to where it was heated; this is known as a Rankin cycle. Fig.1: composite block diagram of two-area load frequency control 1

2 3). PID CONTROLLERS The PID controller consists of three parameters those are proportional, Integral and derivatives. The proportional value determines the reaction to the current error, the integral determines the reaction based on the sum of recent errors and the derivative determines the reaction to the rate at which the error has been changing. PID controller is most widely used in industrial applications. Fig.2: state space model of two area system Thus, under steady condition change in the tie line power and frequency of each area is zero. This has been achieved by integration of ACEs in the feedback loops of each area. Dynamic response is difficult to obtain by the transfer function approach ( as used in the single area case) because of the complexity of block and multi input( P D1, P D2 ) and multi output ( P tie,1, P tie,2, f 1, f 2 ) situation. A more organized and more conveniently carried out analysis is through the state space approach (a time domain approach). 2.2). Optimal (two area) load frequency control Modern control theory is applied in this section to design and optimal load frequency controller for a two area system. In accordance with modern control terminology and will be referred to as control inputs and in the conventional approach and were provided by the integral of ACEs. In modern control theory approach and will be created by linear combination of all the system state (full state feedback). For formulating the state variable model for this purpose the conventional feedback loops are opened and each time constant is represented by a separate block as shown in Fig. 2. State variables are defined as the outputs of all blocks having either an integrator or a time constant. We immediately notice that the system has nine state variables. Table.1: Effect of coefficients by varying controller parameters 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, some of them: Manual tuning method, Ziegler Nichols tuning method, PID tuning software methods. 3.1).Manual Tuning Method: In manual tuning method, parameters are adjusted by watching system responses. K p, K i, K d are changed until desired or required system response is obtained. Although this method is simple, it should be used by experienced personal. Table 2: Effects of changing control parameters. 3.2).Ziegler Nichols tuning method: The tuning procedure is as follows: I. Bring the process to (or as close to as possible) the specified operating point of the control system to ensure that the controller during the tuning is feeling representative process dynamic and to minimize the chance that variables during the tuning reach limits. Process is brought to the operating point by manually adjusting the control variable, with the controller in manual mode, until the process variable is approximately equal to the set-point. II. Turn the PID controller into a P controller by setting set Ti = and Td = 0. Initially, gain K p is set to 0. Close the control loop by setting the controller in automatic mode. III. Increase K p until there are sustained oscillations in the signals in the control system, e.g. in the process measurement, after an excitation of the system. (The 2

3 sustained oscillations correspond to the system being on the stability limit.) This K p value is denoted the ultimate (or critical) gain, K pu. The excitation can be a step in the setpoint. This step must be small, for example 5% of the maximum set-point range, so that the process is not driven too far away from the operating point where the dynamic properties of the process may be different. On the other hand, the step must not be too small, or it may be difficult to observe the oscillations due to the inevitable measurement noise. It is important that K pu is found without the control signal being driven to any saturation limit (maximum or minimum value) during the oscillations. If such limits are reached, there will be sustained oscillations for any (large) value of K p, e.g , and the resulting K p -value is useless (the control system will probably be unstable). One way to say this is that K pu must be the smallest K pu value that drives the control loop into sustained oscillations. IV. Measure the ultimate (or critical) period Pu of the sustained oscillations. V. Calculate the controller parameter values according to table 3, and these parameter values are used in the controller. If the stability of the control loop is poor, stability is improved by decreasing K p, for example a 20% decrease. generations or when the string fitness value exceeds a certain threshold. 4.2). GENERAL ALGORITHM OF GENETIC ALGORITHM The algorithm consists of the following steps: Begin Initialize Chromosomes in the population Evaluate fitness of all chromosomes do until Number of generation is large enough do until The new populationif formed Select parents from the old population Produce offspring s via reproduction,crossover or mutation process Evaluate fitness of offspring s end do end do Table 3: Ziegler Nichols tuning method, gain parameter s calculation. In this thesis, Ziegler Nichols tuning method is used for tuning P, PI, PID Controllers. The controller parameters are calculated by using the above formulas mentioned in table 3. end 4.3). FLOW CHART OF GENETIC ALGORITHM The flowchart of genetic algorithm is presented in Fig 4.1). ALGORITHM 4). GA BASED CONTROLLERS The steps involved in creating and implementing a genetic algorithm Generate an initial, random population of individuals for a fixed size. 1. Initialize population 2. Evaluate their fitness 3. Select the fittest members of the population 4. Reproduce using a probabilistic method (e.g.,roulette wheel) 5. Implement crossover operation on the reproduced chromosomes (choosing probabilistically both the crossover site and the mates). 6. Execute mutation operation with low probability. 7. Repeat step 2 until a predefined convergence criterion is met The convergence critereion of a genetic algorithm is a userspecified conditions for example the maximum number of Fig. 3 Genetic algorithm process flowchart The following are some GA applications in use control engineering Multi Objective Control PID Control Optimal Control 3

4 Robust Control Intelligent Control 5). PARTICLE SWARM OPTIMIZATION (PSO) It is an algorithm, very simple and easy to implement. The algorithm keeps track of 3 global variables: Target value or condition Global best value indicating which that which particle s data is currently closest to the target. Stopping value indicating, when the algorithm should stop if the target is not found. Each particle consists of: A velocity value indicating how much the data can be changed. A personal best (p best ) value indicating the closest the particle s data has ever come to the target. PSO learned from the scenario and it used to solve the optimization problem in PSO, each single solution is a bird in the search space. It is known as particle. All particles have fitness values which are evaluated by the fitness function to be optimized. And have the velocities which direct the flying of the particles. The particles fly thorough the problem space by following the current optimum particles. PSO initialized with a group of random particles and then searches for optima by updating generations. In every iteration, each particle is updated by following two best values. 1. The best solution it has achieved so far, this value is called p best. 2. Another best value that is tracked by the particle swarm optimizer is the best value, obtained so far by any particle in the population. This best value is known as g best.. When a particle takes part of the population as its topological neighbors, the best value is a local best and is called p-best. After finding the two best values, the particle updates its velocity and positions with following equations. The parameter V max determines the resolution, or fitness, with which regions are to be searched between the present position and the target position If V max is too high, particles may fly past good solutions. If V min is too small, particles may not explore sufficiently beyond local solutions. In many experiences with PSO, V max was often set at 10-20% of the dynamic range on each dimension. The constants C 1 and C 2 pull each particle towards p best and g best positions. Low values allow particles to roam far from the target regions before being tugged back. On the other hand, high values result in abrupt movement towards, or past, target regions. The acceleration constants C 1 and C 2 are often set to be 2.0 according to past experiences. Suitable selection of inertia weight ω provides a balance between global and local explorations, thus requiring less iteration on average to find a sufficiently optimal solution. In general, the inertia weight w is set according to the following equation, W =W max [(W max -W min )/(ITER max )]*ITER. V.I. SHORT COMES OF PSO Slow convergence in refined search stage (weak local search ability) V.II. APPLICATIONS OF PSO Training of neural networks Identification of Parkinson s disease Extraction of rules from fuzzy networks Image recognition Optimization of electric power distribution networks Structural Optimization Optimal shape and sizing design Topology optimization Process biochemistry System identification in biomechanics V.III. FORMALIZATION OF PSO Initialize the each particle. Calculate fitness value for each particle. If the fitness va lue is better than the best fitness value in history, then set the current value as the new P best. Choose the particle with the best fitness value of all the particles as the g best. V.IV. ALGORITHM STEPS FOR PSO: Steps of PSO as implemented for optimization: Step 1: Initialize an array of particles with random positions and their associated velocities to satisfy the inequality constraints. Step 2: Check for the satisfaction of the equality constraints and modify the solution if required. Step 3: Evaluate the fitness function of each particle. Step 4: Compare the current value of the fitness function with the particles previous best value (P best ). If the current fitness value is less, then assign the current fitness value to P best and assign the current coordinates (positions) to P best. Step 5: Determine the current global minimum fitness value among the current positions. Step 6: Compare the current global minimum with the previous global minimum (g best ). If the current global minimum is better than g best, then assign the current global minimum to gbest and assign the current coordinates (positions) to g best. Step 7: Change the velocities. Step 8: Move each particle to the new position and return to step 2. Step 9: Repeat step 2-8 until a stop criterion is satisfied or the maximum number of iterations is reached. V.V. FLOW CHART OF PSO 4

5 Fig.4 : Flow chart of PSO 6). BAT BASED MPC 6.1). BAT ALGORITHMS If we idealize some of the echolocation characteristics of microbats, we can develop various batinspired or bat algorithms. For simplicity, we now use the following approximate or idealized rules: 1. All bats use echolocation to sense distance, and they also know the difference between food/prey and background barriers. 2. Bats fly randomly with velocity v i at position x i. They can automatically adjust the frequency (or wavelength) of their emitted pulses and adjust the rate of pulse emission r [0, 1], depending on the proximity of their target. 3. Although the loudness can vary in many ways, we assume that the loudness varies from a large (positive) A 0 to a minimum value A min. Another obvious simplification is that no ray tracing is used in estimating the time delay and three-dimensional topography. Though this might be a good feature for the application in computational geometry, we will not use this simplification here, since it is more computationally extensive in multidimensional cases. In addition to these simplified assumptions, we also use the following approximations for simplicity. In general, the frequency f in a range [ f min, f max ] corresponds to a range of wavelengths [λ min, λ max ]. For example, a frequency range of [20 khz,500 khz] corresponds to a range of wavelengths from 0.7 mm to 17 mm. For a given problem, we can also use any wavelength for the ease of implementation. In the actual implementation, we can adjust the range by adjusting the frequencies (or wavelengths). The detectable range (or the largest wavelength) should be chosen such that it is comparable to the size of the domain of interest, then toned down to smaller ranges. Furthermore, we do not necessarily have to use the wavelengths themselves at all. Instead, we can also vary the frequency while fixing the wavelength λ. This is because λ and f are related, since λ f is constant. We use this latter approach in our implementation. For simplicity, we can assume f [0, f max ].We know that higher frequencies have short wavelengths and travel a shorter distance. For bats, the typical ranges are a few meters. The rate of pulse can simply be in the range of [0,1], where 0 means no pulses at all and 1 means the maximum rate of pulse emission. Based on these approximations and idealized rules, the basic steps of BA can be summarized as the schematic pseudo code shown in figure. Bat Algorithm Initialize the bat population x i and v i (i = 1, 2,..., n) Initialize frequencies f i, pulse rates r i and the loudness A i while (t <Max number of iterations) Generate new solutions by adjusting frequency, Update velocities and locations/solutions [(6.1) to (6.3)] if (rand > r i ) Select a solution among the best solutions Generate a local solution around the selected best solution end if Generate a new solution by flying randomly if (rand < A i & f(x i ) < f(x * )) Accept the new solutions Increase r i and reduce A end if Rank the bats and find the current best x * end while Fig.5.Flow Chart For Bat Search Algorithm 5

6 6.2). PREVIEW OF PREDICTIVE CONTROL A conventional controller observes only the current (and remembers the past) process variables. A predictive controller observes the current and also the future process variables (and remembers the past variables). horizon, that is, after nµ steps, the manipulated variable is kept constant. That means that if the reference signal is a constant There is value, a fundamental then the last difference be manipulated variable is the steady-state value of the corresponding manipulated variable. 6.5). MPC GENERAL TUNING This Chapter can be summarized into the following points: Predictive thinking is natural in every day thinking, for example, during car driving one observes the future shape of the road, brakes if one is approaching curve, pushes the gas pedal if one is nearing a hill, and decreases the speed if another slower car appears in the field of vision. The aim of control is to follow the reference signal and reject (which means eliminate ) the effect of the disturbances. Therefore, the quality of the control depends on how these signals can be known in advance and also on the quality of the process model. Sometimes there is no information about the future course of the reference signal or disturbance. Then the signal is assumed to remain constant, which is also a prediction, though it is not optimal. 6.3). PREDICTION OF THE DISTURBANCE In some cases the course of the future disturbance is known. Examples are: Weather forecast Electrical consumption forecast(schedule of broadcasting an event, when many people switch on their TV, lights, or heating). Predictive control performs the following tasks: Minimizes the control error several steps ahead of the current time point(between k+n1 and k+n2) Takes into account limitations in the control, controlled, and other computed(e.g., state)variables. 6.4). COST FUNCTION OF PREDICTIVE CONTROL Any reasonable criterion can be defined to be achieved by the predictive controller. Some possible aims may be: Fastest control Fastest control without overshoot in the controlled signal Fastest control with limitation of the manipulated signal, and so on Introduction to the Prediction control is explained. Explains about minimization of the cost function The procedure to tune various parameters of MPC like receding horizon, control horizon, sampling time etc., is explained. Explains various differences between MPC and conventional controller. Demerits of MPC are discussed. 7). SIMULATION RESULTS AND DISCUSSIONS Simulations are software applications that enable a user to run a model of a system. Users can interact with computer systems, setting input variables and observing what changes occur to outputs. They can dynamically explore the model domain in real time, start and stop the model, make changes to test hypotheses, and experiment in a new way. A simulation can be done by using MATLAB environment. The results from different types of controllers that are designed for the Load frequency problem are presented in this section. The different control strategies that are designed are 1. Conventional PI controller 2. GA employed PID controller 3. BIA based MPLFCs controller 4. PSO employed PID controller 7.1). SYSTEM PARAMETERS Typical values of the system parameters are given as follows: T t1 = 0.3 s; T g1 = 0.2 s; T r1 = 10 s; K r1 = 0.333; T 1 = 48.7 s; T 2 = 0.513s; T 3 = 10 s; T w = 1 s; T P1 = 20 s; T P2 =13s; K p1 = 120 Hz/p.u.MW; K p2 = 80 Hz/p.u.MW; T 12 = MW/rad; a 12 =-1; R 1 =R 2 = 2.4 Hz/p.u.MW; B 1 = B 2 = p.u.mw/hz. Boiler (oil fired) data: K 1 = 0.85; K 2 = 0.095; K 3 = 0.92; C b = 200; T f = 10; K ib = 0.03; T ib =26; T rb = 69. The cost function consists of two parts: Costs due to control error during the control error horizon,which is also called the optimization or prediction horizon. Costs to penalize the control signal increments during the manipulated variable horizon, which is also called the control horizon. After the control 6

7 Table 4: Controller parameters for the system by using different controllers 7.2). SIMULATION DIAGRAM Fig.7 : Simulink diagram of GA based PID Controller for two area hydro-thermal power system Fig 6: Simulink diagram of Conventional PI Controller for two area hydro-thermal power system Fig.8 Simulink diagram of PSO based PID Controller for two area hydro-thermal power system 7

8 subjected to 2 s transport time delays Fig.9: Simulink diagram of BIA based MPLFCs Controller for two area hydro-thermal power system 7.3). RESULTS Scenario 1: The system undergoes 0.01p.u. SSLPs and it is subjected to 2 s transport time delays (c) tie-line power deviation(δp tie ) Fig.11 system response subject to Scenario 2 : In fig.11, fig a represents frequency change in area 1, fig b represents frequency change in area 2 and tie line power change is as shown in fig c. From fig.11. it is observed that Scenario 3: The system undergoes 0.01p.u. SSLPs and it is subjected to 15 s transport time delays (c) tie-line power deviation(δp tie ) Fig.10 system response subject to Scenario 1 In fig 10, fig a represents frequency change in area 1, fig b represents frequency change in area 2 and tie line power change is as shown in fig c. From fig.10. it is observed that Scenario 2: The system undergoes 0.015p.u. SSLPs and it is 8

9 (c) tie-line power deviation(δp tie ) Fig.12 system response subject to Scenario 3: In fig.12, fig a represents frequency change in area 1, fig b represents frequency change in area 2 and tie line power change is as shown in fig c. From fig.12. it is observed that Scenario 4:System response subjected to robustness study T 12 (0.4444) (c) tie-line power deviation(δp tie In fig.14, fig a represents frequency change in area 1, fig b represents frequency change in area 2 and tie line power change is as shown in fig c. From fig.14. it is observed that Scenario 6: System response subjected to robustness study T 12 (0.6666) (c) tie-line power deviation(δp tie ) Fig.13. system response subject to robustness study In fig.13, fig a represents frequency change in area 1, fig b represents frequency change in area 2 and tie line power change is as shown in fig c. From fig.13. it is observed that Scenario 5:System response subjected to robustness study T 12 (0.2222) (c) tie-line power deviation(δp tie ) Fig.15 system response subject to robustness study : In fig 7.10, fig a represents frequency change in area 1, fig b represents frequency change in area 2 and tie line power change is as shown in fig c. From fig.15. it is observed that 9

10 Simulation is used for tuning of Controller parameters and for load frequency control of multi source multi area power system by using PSO optimization techniques are shown and compared with PI, GA, MPC based optimization techniques in this chapter. 8). CONCLUSION AND FUTURE SCOPE 8.1).Conclusion: In this work time response analysis is evaluated for a two area load frequency control problem by considering one area as thermal and another area as hydro. To verify the time domain analysis of proposed PSO method six scenarios are considered. In the first scenario transport delay is chosen as 2s and step input is chosen as 0.01 p.u (Fig.10) In the second scenario transport delay is chosen as 2s and step input is chosen as p.u(fig.11) In the third scenario transport delay is choosen as 15s and step input is chosen as 0.01p.u(Fig.12) To evaluate robustness of the proposed controller the system time domain specifications are observed with ±50% variations in time consatants. In the fourth Scenario System response subjected to robustness study T 12 (0.444)(Fig.13) In the fifth Scenario System response subjected to robustness study T 12 (0.2222)(Fig.14) In the sixth Scenario System response subjected to robustness study T 12 (0.6666)(Fig.15) The entire simulation is carried out using four control methods Conventional controller GA based optimization BIA based MPC controller PSO based optimization From all the simulation results it is observed that PSO based optimization and GA based optimization produces better transient and steady state values compared with other optimization methods. 8.2).Future Scope: Other optimization techniques such as Cuckoo search algorithm, Fire Fly algorithm and Bacterial foraging optimization algorithm may give better optimization results. These can be implemented so that the system performance can be improved. REFERENCES [1] Kundur P. Power system stability and control. McGraw-Hill ; [2] Saadat H. Power system analysis. Tata Mcgraw-Hill ; [3] Elgard OI. Electrical energy system theory: an introduction. NewDelhi: McGraw-Hill; [4] Surya P, Sinha SK. Load frequency control of three area interconnected hydro-thermal reheat power system using artificial intelligence and PI controllers. IntJ Eng Sci Technol 2012;4(1): [5] Elgard OI, Fosha CE. Optimum megawatt-frequency control of multi area electric energy systems. IEEE Trans Power Apparatus Syst 1970;PAS-89(4): [6] Ahmed B, Abdel Ghany AM. Performance analysis and comparative study of LMI-based iterative PID load-frequency controllers of a single-area power system. WSEAS Trans Power Syst 2010;5(2): [7] Ghoshal SP. Application of GA/GA-SA based fuzzy automatic generation control of a multi-area thermal generating system. Electr Power Syst Res2004;70: [8] Ismayil C, Kumar RS, Sindhu TK. Optimal fractional order PID controller for automatic generation control of two-area power systems. Int Trans Electr Energy Syst 2015;25(12): [9] Gozde H, Taplamacioglu MC, Kocaarslan I, Senol MA. Particle swarm optimization based PI-controller design to load frequency control of a two area reheat thermal power system. J Therm Sci Technol 2010;30(1): AUTHOR S PROFILE A. HIMA BINDU received her B.Tech in EEE from K.S.R.M College of Engineering, Kadapa, S.V.University, Tirupati, Andhra Pradesh, in India 2009 & M.Tech in Electrical power systems (EPS) from S.V.University, Tirupati, in Inidia She is currently working as Assistant Professor in B.I.T Institute of Technology, A.P, India. Her areas of interest are Power System Operation and Control, Power Distribution Systems & Distributed Generation. V.Lakhma Naik received his B.Tech in EEE from MeRITS, JNTU, Hyderabad, Andhra Pradesh, in india 2007 & M.Tech in Electrical power systems (EPS) from SVEC, JNTUA, in inidia And pursuing Phd in dept. of EEE in JNTUCEA, JNTUA, A.P, india. He is currently working as Assistant Professor in BIT Institute of Technology, A.P, India. His areas of interest are Renewable energy sources, Power System operation and control, Power distribution systems & Distributed Generation. 10