CHAPTER 5 PSO AND ACO BASED PID CONTROLLER

Transcription

1 128 CHAPTER 5 PSO AND ACO BASED PID CONTROLLER 5.1 INTRODUCTION The quality and stability of the power supply are the important factors for the generating system. To optimize the performance of electrical equipment, it is important to ensure the quality of the electric power. During the transportation, both the active power balance and the reactive power balance must be maintained between the generation and utilization of AC power. These two balances correspond to two equilibrium points: frequency and voltage. When either of the two balances is broken and reset at a new level, the equilibrium points will float. A good quality of the electric power system requires both the frequency and voltage to remain at standard values during operation. Control system plays an important role in maintaining these power system parameters. The first attempt in the area of AGC has been to control the frequency of a power system via the fly wheel governor of the synchronous machine. The turbine-governor technique was subsequently insufficient and a supplementary control was included to the governor with the help of a signal directly proportional to the frequency deviation. Based on the experiences with actual implementation of AGC schemes, modifications to the definition of Area Control Error (ACE) are suggested from time to time to cope with the change in a power system environment. The daily load cycle changes significantly and hence fixed gain controllers will fail to provide best performance under a wide range of operating conditions. Power systems are subject to constant changes due to loading conditions, disturbances or

2 129 structural changes. Controllers are designed to stabilize or enhance the stability of the system under these conditions. However, in general, each controller is designed for a specific situation or scenario and is effective under these particular conditions. Hence, it is desirable to increase the capability of PID controllers to suit the needs of present day applications. A PID controller improves the transient response of a system by reducing the overshoot and settling time of a system. The main reason to develop better methods to design PID controllers is because of the significant impact on the performance improvement. The performance index adopted for problem formulation is settling time, overshoot and oscillations. The primary design goal is to obtain a good load disturbance response by optimally selecting the PID controller parameters. Traditionally, the control parameters have been obtained by trial and error approach, which consumes more amounts of time in optimizing the choice of gains. To reduce the complexity in tuning PID parameters, Evolutionary computation techniques can be used to solve a wide range of practical problems including optimization and design of PID gains. It can obtain suboptimal solutions for very difficult problems which conventional methods fail to produce in reasonable time. Evolutionary algorithms can be a useful paradigm and provide promising results for solving complex optimization functions. Evolutionary computation refers to the study of computational systems that use ideas to draw inspirations from natural evolution. Evolutionary algorithms like Genetic Algorithm (GA), Simulated Annealing (SA), and Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO) has been employed in control applications to efficiently search global optimum solutions. Zwe-Lee Gaing(2004) have presented PSO for optimum design of PID controller in AVR system. The simulation results proved the proposed method was indeed more efficient and robust in improving the step response

3 130 of an AVR system. Yoshida et al (1999) proposed PSO for reactive power and voltage control considering voltage stability. The results reveal that the proposed method generates a solution very near to the global optimum solution. Miranda and Fonseca (2002) developed new Evolutionary PSO for voltage/avr control. The simulation results obtained indicate that it can obtain high quality solutions with shorter calculation time. Chatterjee et al (2006) incorporated PSO for intelligent control of AVR system. It has been revealed that PSO exhibits better transient performance and can be successfully applied to obtain on-line responses. Wong et al (2009) proposed PSO-PID controller design for AVR system with new fitness function. From simulation and comparison results, it can be seen that the proposed PSO algorithm finds high quality solutions and demonstrates better control performance. Yousuf et al (2009) developed PSO based predictive non-linear single area automatic generation control. The simulation results show improvement over the response characteristics and signify the strengths of the proposed scheme. Rohit Kumar (2003) presented PSO based approach to solve the economic load dispatch with line flows and voltage constraints, and concluded that the proposed approach is computationally faster than GA. Zhao et al (2005) proposed PSO approach based on the multi-agent system to solve reactive power dispatch problem. The results indicate the possibility of PSO as a practical tool for various optimization problems in the power system. Another meta-heuristic technique used for combinatorial optimization problems is the Ant Colony Optimization (ACO) algorithm that has been inspired by the foraging behaviour of real ants. Ying-Tung Hsiao (2004) proposed an optimum approach for designing of PID controllers using ACO to minimize the integral absolute control error. The experiment results demonstrate that better control performance can be achieved in comparison with conventional PID method. Duan Hai-bin (2006) presented a novel

4 131 parameter optimization strategy for PID controller using ACO Algorithm. The algorithm has been applied to the combinatorial optimization problem, and the results indicate high precision of control and quick response. Shyh-Jier Huang (2001) proposed ACO based optimization approach for enhancing hydroelectric generation scheduling. Test results demonstrated the feasibility and effectiveness of the method for the application considered. Boubertakh et al (2009) developed ACO for tuning PID controllers and illustrated the efficiency of the proposed method by simulation examples. Hong He et al (2009) designed ACO based PID parameter optimization to increase the search speed for PID parameter optimization. Simulation results show the validity of this algorithm, and the methodology adapted to overcome the drawbacks of traditional PID parameter optimization. Girirajkumar (2009) presented the application of ACO algorithm to optimize the PID parameters in the design of PID controller. The results presented prove the improvement of ACO-PID controller and its stability over different operating conditions. In this research, an efficient optimization algorithm is proposed using PSO and ACO for tuning the optimal gains of PID controllers used for LFC and AVR of Power generating systems. The primary aim of the controller is to maintain the frequency and voltage at an optimal level under varying operating conditions. The transient response of LFC and AVR is very important, because both the amplitude and time duration of the response must be within the prescribed limits. The performance of two area system with PSO and ACO tuned PID controllers is analysed for its validity and application worthiness. The proposed method has better adaptability towards changes in load than the conventional PID, Fuzzy, and Genetic Algorithm based controllers, thereby providing improved performance with respect to overshoot, settling time and oscillations.

5 132 The chapter is organized as follows: Section 5.2 describes the evolutionary algorithms for power system control. Section 5.3 demonstrates the basic concepts of ACO algorithm, Section 5.4 explains the concepts of PSO algorithm, Section 5.5 deals with Simulink models of proposed controllers, Simulation results are presented in Section 5.6, Comparative analysis is briefed in section 5.7 and conclusion is derived in Section EVOLUTIONARY ALGORITHMS FOR POWER SYSTEM CONTROL In general, an electric power network is a large and complex system consists of synchronous generators, transformers, transmission lines, relays and switches, etc... Various control objectives such as operating conditions, actions, and design decisions requires solving one or more linear or non-linear optimization problems. Evolutionary Algorithm (EA) is considered as a useful promising technique for deriving the global optimization solution for complex problems. Since the loads are switched on and off, the power system is prone to sudden changes to its configuration. Under these circumstances, keeping voltage and frequency within the allowable range is one of the important tasks for power system control. An online control strategy to achieve this is referred to as real and reactive power control, using LFC and AVR. Essentially, LFC takes care of frequency, and AVR ensures voltage of the generating system. The PID control system with plant indicating LFC/AVR and EA based PID is shown in Figure 5.1. The K p, K i and K d are respectively the proportional, integral and derivative gains of the PID controller that are tuned by EA. In the proposed system, PSO and ACO algorithms are used to optimize set of PID parameters in the system to achieve desired output y d. The control output u from EA-PID is based on the error signal e, which is the difference between actual output y and the desired output y d. The objective on the PSO and ACO based optimization is to seek a set of PID

6 133 parameters such that the feedback control system has a minimum performance index. A set of optimal PID parameters can yield good frequency and voltage characteristics of LFC and AVR. EA is considered as a useful and promising technique for deriving the global optimum solution of complex functions. Hence, application of these algorithms yields improved performance characteristics in terms of settling time, oscillations and frequency. Figure 5.1 PID Control System with Evolutionary Algorithm The LFC/AVR is subjected to different operating characteristics like, varying load and regulation parameters to verify the validity of the proposed algorithm. Stochastic techniques like Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) are applied to tune the controller gains to ensure optimal performance at nominal operating conditions. PSO and ACO are used in offline to tune the gain parameters and applied to PID controller in the secondary control loop of the plant. 5.3 BASIC CONCEPTS OF ACO ALGORITHM Ant Colony Optimization (ACO) was introduced around by M. Dorigo and colleagues as a novel nature-inspired meta-heuristic for the

7 134 solution of hard combinatorial optimization problems (Dorigo and Blum 2005), (Dorigo et al 1999). In this algorithm, computational resources are allocated to a set of relatively simple agents that exploit a form of indirect communication mediated by the environment to find the shortest path from the ant nest to a set target. While walking, Ants can follow through to a food source because, they deposit pheromone on the ground, and they have a probabilistic preference for paths with a larger amount of pheromone. Figure 5.2 Behavior of Real Ants in Finding Shortest Path As shown in Figure 5.2, ants arrive at a point where they have to decide whether to turn left or right. Since they have no clue of which is the better choice, they choose randomly. It can be expected that, on an average, half of the ants decide to turn left and the other half to turn right. This happens both to ants moving from left to right and to those moving from right

8 135 to left Figure 5.2(a) and (c) show what happens in the immediate instants, supposing all ants walk at approximately the same speed. The number of lines is roughly proportional to the amount of pheromone that the ants have deposited. Since the lower path is shorter than the upper one, more ants will visit it on average, and therefore, pheromone accumulates faster. After a short period, the difference in the amount of pheromone on the two paths is large enough to influence the decision of new ants coming into the system (Figure 5.2(d)), from this point on, new ants will prefer the lower path, since at the decision point they perceive a greater amount of pheromone on this lower path. In turn, this increases the positive feedback and the numbers of ants are choosing the lower and shorter path. Very soon all ants will use the shorter path. This process is thus characterized by a positive feedback loop, where the probability with which an ant chooses a path increases with the number of ants that previously chose the same path. This behavior inspired the ACO algorithm in which a set of artificial ants cooperate in the solution of a problem by exchanging information via pheromone deposited on graph edges. The ACO algorithm is developed using artificial ants, which are designed based on the behaviour of real ants. The artificial ants walk through this graph, looking for food paths; each ant has a rather simple behaviour so that it will typically only find rather poor-quality paths on its own. Better paths are found as the emergent result of the global cooperation among ants in the colony. The behaviour of artificial ants is inspired from real ants. They lay pheromone trails on the graph edges and chooses their path with respect to probabilities that depend on pheromone trails and this pheromone trails progressively decrease by evaporation.

9 136 Ants prefer to move to nodes, which are connected by short edges with a high mount of pheromone. In addition, artificial ants have some extra features that do not find in their counterpart, real ants. In particular, they live in a discrete world, and their moves consist of transitions from nodes to nodes. Furthermore, they are usually associated with data structures that contain the memory of their previous action. Finally, the probability for an artificial ant to choose an edge often depends not only on pheromone, but also on some problem-specific local heuristics. The variables which are used in ACO algorithm and their definitions are tabulated in Table 5.1. Table 5.1 Variables and their Definitions used in ACO Algorithm Variable Definition ij ij Heuristic factor Pheromone factor P ij Transition probability and Constants greater than 0 Coefficient of the persistence of the trail At each generation, each ant generates a complete tour by choosing the nodes according to a probabilistic state transition rule. Every ant selects the nodes in the order in which they will appear in the permutation. For the selection of a node, an ant uses a heuristic factor as well as a pheromone factor. The heuristic factor, denoted by ij, and the pheromone factor, denoted by i, are indicators of how good it seems to have node j at node i of the permutation.

10 137 The heuristic value is generated by the problem dependent heuristics, whereas the pheromone factor stems from former ants that have found good solution. The next node is chosen by an ant according to the Pseudo Random Proportional Action Choice rule. With Probability q 0, (where 0 q 0 < 1) the ant chooses a node from the set of nodes (s) that have not been selected and which maximizes the Equation (5.1). [ ij ] [ ij ] (5.1) where 0 and 0 are constants that determine the relative influence of pheromone values and heuristic values on the decision of ant. With probability (1 q 0 ) the next node is chosen from the set S according to the probability distribution that is determined by P ij h ij ij S ij ij (5.2) Therefore, the transition probability is a trade-off between the heuristic and pheromone factor. For the heuristic factor, the close nodes (low cost of path) should be chosen with high probability, thus implementing greedy constructive heuristic. As the pheromone factor is on an edge (i, j) there has been a lot of traffic then it is highly desirable to implement the autocatalytic process. The heuristic factor ij j is computed according to the rule, ij 1 (5.3) F(X ), j S j where, F(X) represents the cost function of X. It is in favour that the choice of edges, which are shorter (with low cost) and, which have a greater amount of

11 138 pheromone. The ant lays a trial substance along the path from i to j as mentioned in Equation (5.4), k ij Q Lk (5.4) if K th ant uses edge (I,j) in its tour then, k ij = 0. where Q is a constant related to the quality of pheromone trails laid by ants and L K is the cost of the tour performed by the k th ant. In other words, pheromone updating is intended to allocate a greater amount of pheromone with low cost (shorter tours). This value is evaluated when the ant has completed a tour and consisting of a cycle of n iterations (generations). It is used to update the amount of substance previously laid on the trail, on the following rules ij (t+n)=. ij (t)+ ij (t) (5.5) m ij (t) ij(t) (5.6) k 1 where, m denotes the number of ants,, (0,1) is a coefficient of persistence of the trial during a cycle such that (1- )represents the evaporation of the trail between generation n g and n g+1. The pheromone updating rule was meant to simulate the change in the amount of pheromone due to both the addition of new pheromone deposited by ants on the visited edges and to pheromone evaporation. The algorithm stops iterating either when an ant found a solution or when a maximum number of generations has been performed.

12 ACO-PID Controller Design The Conventional fixed gain PID controller is well known technique for industrial control process. The design of this controller requires the three main parameters, Proportional gain (K p ), Integral time constant (K i ) and derivative time constant (K d ). The gains of the controller are tuned by trial and error method based on the experience and plant behaviour. This process will consume more time and will be suitable only for particular operating condition. In this research, ACO algorithm is used to optimize the gains, and the values are transferred to the PID controller of the plant representing LFC and AVR of the power generating system as shown in Figure 5.3. Figure 5.3 ACO-PID Controller The proportional gain makes the controller respond to the error while the integral gain help to eliminate steady state error and derivative gain to prevent overshoot. The plant is replaced by LFC and AVR models developed using simulink in MATLAB. With the optimum gains generated by the proposed algorithm the models are simulated for various operating conditions to validate the performance. The flowchart for ACO based PID controller is shown in Figure 5.4.

13 140 Figure 5.4 Flow Chart of ACO Algorithm The design steps of ACO based PID controller for AVR is as follows. 1. Initialize the algorithm parameters like number of iterations, number of ants, strength of pheromone and decay rate. 2. Initialize the ranges of PID controller gain values. 3. For each ant the transition probability is calculated using the Equation (5.2).

14 Incrementally builds a solution and local pheromone updating is done by using the Equation (5.5). 5. Record the best solution found so far. 6. A global pheromone update is done by using the Equation (5.6). 7. Repeat the steps 3 to 6 until the maximum iteration is reached. The algorithm is tested for different values of parameters by simulating the model for different operating conditions. According to the trials, the optimum parameters used for verifying the performance of the ACO-PID controller is listed in Table 5.2. Table 5.2 ACO Parameters Parameters LFC AVR Number of ants Number of nodes Number of generations Pheromone strength Decay rate The ACO algorithm design steps for LFC is 1. Initialize the population size, the initial search steps of all variables and number of ants, t = 0, and count t = Initialize the PID parameters. 3. For each ant (j = 1,2, n), select the j th solution component with a probability P ij.

15 Evaluate the candidate solution and get the best individual ant and the path. 5. Update the trial matrix as in Equation (5.4). Evaluate the local and global pheromone using Equations (5.5) and (5.6). If no improvement occurs, adjust the current searching step scheme according to the path. 6. Repeat the process until the best searching step is reached or the maximum iteration is performed. Since the model parameters of LFC are identical, the optimized parameters are used in the PID controller for single and two area interconnected LFC system. The system is stable and the control task is to minimize the system frequency deviation f 1 in area 1, f 2 in area2 and tieline power deviation P tie. The performance of the system can be tested by applying load disturbance P D1 to system and observing the change in frequency in both areas. To assess the effectiveness of the optimized parameters, the models are tested for different load and regulation parameters. 5.4 OVERVIEW OF PSO ALGORITHM In PSO algorithm, each particle in the swarm represents a solution to the problem, and it is defined with its position and velocity. PSO is initialized with a group of random particles (solutions) and then searches for optima by updating the particles in each generation. In every iteration, each particle is updated by two "best" values. The first one is the best solution (fitness) achieved so far (the fitness value is also stored) called pbest. 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 a global best and called gbest. After finding the two best values, the particle updates its velocity and positions. The above mentioned overview of PSO is depicted as shown in Figure 5.5.

16 143 Figure 5.5 Representation of PSO The variables which are used in PSO algorithm and their definitions are given in Table 5.3. Table 5.3 Variables and their Definitions used in PSO Algorithm Variable Definition itermax Maximum number of iterations X Position of the particle X i Position of i th particle V Velocity of the particle V i Velocity of i th particle P Best position of the particle P i Best position previously visited by i th particle P g Best position visited by a particle W Inertia weight W max Maximum value of inertia weight W min Minimum value of inertia weight C 1 Cognitive coefficient C 2 Social coefficient R and r Random number between 0 and 1

17 144 In D-dimensional search space, the position of the ith particle can be represented by a D-dimensional vector, X i = (X i1,, X id,, X id ). The velocity of the particle v i can be represented by another D-dimensional vector V i = (V i1,, V id,, V id ). The best position visited by the ith particle is denoted as P i =(P i1,,p id,,p id ), and P g as the index of the particle visited the best position in the swarm, then P g becomes the best solution found so far, and the velocity of the particle and its new position will be determined according to the Equations (5.6) and (5.7). V id =WV id +C1R (P id -X id ) + C2R (P gd X id ) (5.6) X id =X id + V id (5.7) The parameter W in Equation (5.6) is inertia weight that increases the overall performance of PSO. It is reported that a larger value of W can favour higher ability for global search while lower value of W implies a higher ability for local re-search. To achieve a higher performance, we linearly decrease the value of inertia weight W over the generations to favour global re-search in initial generations and local re-search in the later generations. The linearly decreasing value of inertia is expressed in Equation (5.8). W W W iter * W min min max (5.8) itermax where itermax is the maximum of iteration in evolution process, W max is maximum value of inertia weight, Wmin weight, and iter is current value of iteration. is the minimum value of inertia PSO-PID Controller Design With the advancement of computational methods in the recent times, optimization techniques are often proposed to tune the control

18 145 parameters. Stochastic Algorithm can be applied for tuning of PID controller gains to ensure optimal control performance at nominal operating conditions. In Conventional PID controller, the gains are randomly selected and the results are verified for every set of random gain values. PSO algorithm finds the Proportional, Integral and Derivative gains of the PID controller and the values are passed to the PID controller of single area LFC and AVR as shown in Figure 5.6. The gain values are tested for two area LFC to optimize the change in frequency in both areas. Figure 5.6 PSO Algorithm Based PID Controller generating system is The design steps of PSO based PID controller for LFC of a power 1. Initialize the algorithm parameters like number of generations, population, inertia weight, cognitive and social coefficients. 2. Initialize the values of the parameters K P, K i and K D randomly. 3. Calculate the fitness function of each particle in each generation.

19 Calculate the local best of each particle and the global best of the particles. 5. Update the position, velocity, local best and global best in each generation. 6. Repeat the steps 3 to 5 until the maximum iteration reached or the best solution is found. The objective function represents the function that measures the performance of the system. The fitness function (objective) function for PSO is defined as the Integral of Time multiplied by the Absolute value of Error (ITAE) of the corresponding system. Therefore, it becomes an unconstrained optimization problem to find a set of decision variables by minimizing the objective function. The AGC performance of a two area test system has been tested with a PSO tuned optimal PID controller. The main objectives of the AGC in multi-area power system are maintaining zero steady state errors for frequency deviation and accurate tracking of load demands. Hence, the optimal parameters obtained by the proposed algorithm, guarantee both stability and desired performance in both areas of interconnected system. Each area consists of three first-order transfer functions, modelling the turbine, governor and power system. In addition, all generators in each area are assumed to form a coherent group. For PID controller, the objective function is defined as f N N j 1 i 1 0 j t f i dt where, N is the number of areas in the power system and j f i is the frequency deviation in area i for step load changes in area j. The flowchart for PSO based PID controller is shown in Figure 5.7. To design the LFC for two area, the change in load in both areas must be taken into account along with the parameters of the governor, turbine, and load. Two identical areas with non-

20 147 reheat type turbine with similar parameters are considered for implementation. Furthermore, the generators tend to have the same response characteristics are said to be coherent. Then it is possible to let the LFC loop represent the whole system, which is referred to as a common area. The prime mover control must have drooping characteristics to ensure proper division of load, when generators are operating in parallel. In many cases, a group of generators are closely coupled internally and swing in unison. The Automatic Generation Control (AGC) of a multi area system can be realized by analyzing AGC for a two area system. Tie line power appears as a load increase in one area and a load decrease in the other area, depending on the direction of the flow. The optimum values used for various parameters in PSO implementation are listed in Table 5.4. Figure 5.7 PSO Algorithm for PID Controller

21 148 Table 5.4 PSO Parameters Parameters LFC AVR Population size 5 50 Number of generations Inertia weight cognitive coefficient social coefficient for AVR. The following procedure is used for implementing the PSO algorithm 1. Initialize the swarm by assigning a random position in the problem hyperspace to each particle. 2. Evaluate the fitness function for each particle. 3. For each individual particle, compare the particle s fitness value with its Pbest. If the current value is better than the Pbest value, then set this value as the Pbest and the current particle s position, xi and pi. 4. Identify the particle that has the best fitness value. The value of its fitness function is identified as gbest and its best position as pg. 5. Update the velocities and positions of all the particles using Equations (5.6) and (5.7). 6. Repeat steps 2 5 until the stopping criteria is reached. Maximum iterations or when the optimum solution is reached.

22 SIMULINK MODEL OF ACO AND PSO BASED PID CONTROLLER Simulink Model of an AVR The AVR model consists of a step input, PID controller based on PSO, an amplifier that amplifies the signal to the exciter which in turn controls the voltage of the generator and a scope to display the terminal voltage. It also contains a sensor that senses the voltage rise or fall due to the difference between load demand and power generated and feeds it to the controller based on the load changes. The AVR model shown in Figure 5.8 is simulated with system parameter values indicated in Table 5.5. Figure 5.8 Simulink Model of Automatic Voltage Regulator with PID Controller Table 5.5 Values for constants in AVR model Symbol Parameters Optimum Values Ka Amplifier gain 10 a Amplifier time constant 0.1 Kg Generator gain 1 g Generator time constant 1 Kr Sensor gain 1 r Sensor time constant 0.05

23 Simulation Model for LFC PID controllers are parametric controllers that affect the behaviour of the LFC system, if the parameters are not optimized. Designing an optimum controller ensures improved performance by minimizing the performance index. To illustrate the importance of proposed PSO and ACO algorithms, the LFC model designed using simulink in MATLAB is considered. It consists of a step input, PID controller based on PSO, a governor that controls the speed of the turbine that drives the generator and the scope that shows the frequency deviation. The optimum parameters used in LFC model in Figure 5.9 are indicated in Table 5.6. Figure 5.9 Simulink Model of LFC with PID Controller Table 5.6 Values for constants in LFC model Symbol Parameters Optimum Values g Governor time constant 0.2 t turbine time constant 0.5 R Regulation parameter 20, 30 H and D Inertia constants of the load 10 and 0.8

24 Simulation model for LFC in a Two Area Power System The normal operation of the multi-area interconnected power system requires that each area maintain the load and generation balance. This system experiences deviations in nominal system frequency and schedules power exchanges to other areas with change in load. AGC tries to achieve this balance by maintaining the system frequency and the tie line flows at their scheduled values. The AGC action is guided by the Area Control Error (ACE), which is a function of system frequency and tie line flows. The ACE represents a mismatch between area load and generation taking into account any interchange agreement with the neighboring areas (Ibraheem et al 2005), (Kothari and Nagrath 2007). Since both areas are connected together, a load perturbation in one area affects the output frequencies of both areas. The controller employed in each area needs the status about the transient behavior of both areas in order to maintain the frequency to optimal value. The tie-line power fluctuations and frequency fluctuations is sensed, and the signal is fed back into both areas (Ertugrul and Kocaarslan 2005) (Yesil and Eksin 2004). The primary speed controller employed makes initial course of adjustment, but it is limited by the time lags of the turbine and the system. Hence, an intelligent and efficient secondary controller is required to adjust the system frequency by reducing the error. The model of LFC for two areas interconnected system is represented in Figure 5.10 with PSO and ACO based PID controller. This model depicts the interconnection of two power systems with LFC, and the results are analysed from the scope that displays the combined output of the frequencies of the two systems.

25 152 Figure 5.10 Simulink Model of LFC for a Two Area Power System with PID Controller 5.6 SIMULATION RESULTS The main purpose of the simulations under the normal conditions is to evaluate the performance of the LFC/AVR and to achieve improvements in the performance in the transient response of the system. To view a complete picture about the performance of the proposed controller a set of simulations are conducted to assure the robustness of the LFC/AVR under different disturbance magnitude. Load disturbances of 0.1, 0.2, 0.5, 0.6pu are applied to area 1 each at a time. For robustness, regulation constant is tuned according to load and system changes. The overshoot, oscillations, settling time are adapted as a standard set of performance indices to compare the time response of f1, f2 of the controllers. As it is observed from the results, the controllers will learn to bring the system to a stable operating point and the

26 153 transient oscillations are finally converged close to zero. The PID controller is configure ured with the auto-tuned parameters K P, K I, K D and the transient response of LFC and AVR are presented in this section PSO Based PID Controller The model for LFC and AVR with PSO based PID controller is designed in the simulink. The K p, K I and K d values for the PID controller were obtained by running the M-file. The simulation was performed for different regulations and loads to validate the robustness of the proposed controller. The terminal voltage response for a change in load of 0.1 p.u and regulation of 10 is shown in Figure Figure 5.11 AVR with PSO Based PID Controller for P L =0.1 p.u From Figure 5.11, it is observed that the settling time of AVR with PSO based PID controller is 9.03 seconds and there is no transient peak overshoot.

27 154 Figure 5.12 LFC with PSO Based PID Controller for R=10 and P L = 0.1 p.u From Figure 5.12, it is inferred that the settling time of LFC with PSO based PID controller is 8.2 seconds, and the peak overshoot is The simulation results for AVR and LFC with PSO based PID controller under various load changes and regulations are tabulated in Table 5.7 and Table 5.8, respectively. These results show that the proposed algorithm can search optimal PID controller parameters quickly and efficiently. The PSO method does not perform the selection and crossover operation in evolutionary processes; the computation time is reduced by 47% when compared with GA method. Table 5.7 Performance Analysis of PSO Based PID Controller for AVR Parameters Computational time (sec) Change in Load P L =0.2 P L =0.4 P L =0.6 P L = Settling Time(sec) Overshoot (V) Oscillation (V) 0 to to to to 0.204

28 155 Table 5.8 Performance Analysis of PSO Based PID Controller for LFC Parameters R1=10 R2=20 P L =0.2 P L =0.7 P L =0.2 P L =0.7 Computational time (sec) Settling Time(sec) Overshoot(Hz) Oscillation(Hz) 0 to to to to It is observed from the results that, when compared to the conventional controller the settling time, peak overshoots and oscillations of LFC are reduced by 73%, 77% and 77%, respectively. The settling time of AVR is reduced by 66% as compared to the conventional controller for a change in load of 20%. The objective function (ITAE) used for the PSO algorithm is same for AVR and LFC, hence the computational time is similar as mentioned in Table ACO Based PID Controller The simulink model for LFC and AVR with ACO based PID controller was simulated. The optimum gain values obtained by the M-file are transferred to the simulink model and tested for different loads and regulation parameters. The frequency deviation and terminal voltage response for a change in load of 0.1 p.u and regulation of 10 is shown in Figures 5.13 and 5.14, respectively.

29 156 Figure 5.13 LFC with ACO-PID controller for R=10 and P L = 0.1 p.u From Figure 5.13, it is observed that the frequency deviation and the peak overshoot is minimum. The settling time for frequency deviation is 9 seconds, and the oscillation varies between to , which is very less compared to PID controllers. Figure 5.14 AVR with ACO-PID Controller for P L = 0.1 p.u

30 157 From Figure 5.14, it is found that the settling time of AVR with ACO based Integral controller is 5.2 seconds and there is a transient overshoot of about The LFC and AVR models are simulated for different load conditions in order to replicate the daily load curve of the power system. The computational time taken by the proposed algorithm in generating the optimum values of PID gains is obtained and tabulated. To show the effectiveness of the proposed algorithm, the settling time for different operating conditions of LFC is presented in Table 5.9. As witnessed from the table, the merits of ACO are the response characteristics and computational efficiency. The computational time is reduced by 21.6% when compared to GA based PID controller. Since the population of ants is operated simultaneously, the computational efficiency is improved. It is achieved because of the parallel search and optimization capabilities inspired by the behaviour of ant colonies. Table 5.9 Performance Analysis of ACO Based PID Controller for LFC Parameters R1=10 R2=20 P L =0.2 P L =0.7 P L =0.2 P L =0.7 Computational time (sec) Settling time(sec) Overshoot(Hz) Oscillation(Hz) to to to to Owing to the randomness of heuristic algorithms, their performance cannot be judged by a single run. Many trials with different initialization should be made to acquire useful conclusion about the performance. An algorithm is robust, if it gives a consistent result during all the trials. The simulation results for LFC and AVR with ACO based PID controller under

31 158 various load changes and regulations are tabulated in Table 5.9 and Table 5.10, respectively. From the Tables, it is observed that the settling time, peak overshoots and oscillations of LFC are reduced by 37%, 21% and 50%, respectively. The settling time of AVR is reduced by 53% when compared to the conventional controller for a sudden increase in load of 0.2p.u. The fitness function of the algorithm to generate optimum gain value is same; hence the execution time for LFC and AVR is similar as tabulated. From the results, it is revealed that ACO method is a potential alternative to be developed in solving LFC and AVR problems. Table 5.10 Performance Analysis of ACO based PID Controller for AVR Change in Load P L =0.2 P L =0.4 P L =0.6 P L =0.8 Computational time (sec) Settling Time(sec) Overshoot (V) Oscillation (V) 0 to to to to Two Area Interconnected System In order to emphasize the advantages of the proposed controller, the two area LFC has been implemented and compared with conventional controllers. In multi area power networks the active power generation within each area should be controlled to maintain scheduled power interchanges. Control and balance of power flows at tie line are required for supplementary frequency control. For successful control of frequency and active power generation, the damping of oscillation at tie-line is important. The simulation result is plotted in Figure 5.15 for a change in load of 20% in area1 and 60% in area2.

32 159 Figure 5.15 PSO-PID based LFC for Area 1 Loaded by 0.2p.u and Area 2 Loaded by 0.6p.u It can be shown from the Figure 5.15 that, the proposed secondary controller damps the frequency oscillations in both areas by achieving power balance between them and increasing the tie-line power flow. Initial oscillation is due to time delay in governor control but then the proposed secondary controller starts acting and decreases the oscillations. The deviation in frequency is further investigated due to change in load from 20% to 80% in both areas and the results are tabulated in Table For comparing the performance of the algorithm, the computational time for different operating conditions is specified in Table This approach can be a useful alternative when compared to GA, since the computational time taken for convergence of particles is reduced by 46.5%.

33 160 Table 5.11 Performance Analysis of PSO-PID for Two Area LFC Parameters Settling Time (s) Overshoot (Hz) Oscillation (Hz) Computational time = 29.6 sec R1=20, R2=15 Computational time = 30.4 sec Computational time = 31 sec P L1 =0.2 P L2 =0.6 P L1 =0.3 P L2 =0.7 P L1 =0.4 P L2 =0.8 Area1 Area2 Area1 Area2 Area1 Area to to to to to to As can be seen from the simulation result, the PSO method has prompt convergence and good evaluation value. The results indicate that the PSO-PID controller is efficient in arresting the frequency oscillation of both areas. The settling time, oscillations and overshoot are reduced by 76%, 70.8%, and 63.6 % respectively when compared to conventional PID controller for change in load of 0.2 and 0.6 p.u. In the application of ACO algorithm for two areas LFC system, the initial population of the colony is randomly generated within the search space. Then, the fitness of ants is individually assessed based on their corresponding objective function. In order to examine the dynamic behaviour and convergence characteristics of the proposed method, simulation is carried out for the different load and regulation parameters. Figure 5.16 shows the frequency response of the two area interconnected system for change in load of 20% in area1 and 40% in area2.

34 161 Figure 5.16 ACO-PID based LFC for Area 1 Loaded by 0.2p.u and Area2 Loaded by 0.4p.u The low frequency oscillations if not damped immediately after a sudden load in a power system, will drive the system to instability. Hence the secondary controller employed in LFC has to manage efficiently for the increase in load and act dynamically to reduce the frequency oscillations. Table 5.12 shows the simulation results of a two area system for loads varying from 0.02 to 0.08p.u with R value of 20 and 15. The effectiveness of the algorithm is evaluated by comparing it with conventional PID and found that settling time, oscillations and overshoot are reduced by 75%, 82.9% and 61.8% respectively for change in load of 0.2 and 0.4 in both areas. The computational efficiency of the proposed ACO-PID controller is found to be improved since the execution time is reduced by 20.8% when compared to GA-PID controller. The computational time taken by the algorithm in generating optimum gain values are indicated in Table 5.12 for different load and regulation parameters.

35 162 Table 5.12 Performance Analysis of ACO-PID for Two Area LFC Parameters Settling Time (s) Overshoot (Hz) Oscillation (Hz) R1=20, R2=15 Computational time =43.6 sec Computational time = 44.9sec Computational time = 45.2 sec P L1 =0.2 P L2 =0.4 P L1 =0.3 P L2 =0.6 P L1 =0.2 P L2 =0.8 Area1 Area2 Area1 Area2 Area1 Area to to to to to to COMPARATIVE ANALYSIS A statistical analysis is performed to show that the proposed PSO and ACO algorithms allow the search process to be more efficient in finding feasible solutions and global minimum as compared with the conventional PID, fuzzy, and GA based controllers. This section deals with the performance evaluation of Conventional and EC based controllers for LFC and AVR of the generating system. The settling time, oscillations and overshoot are compared for a change in load of 0.10 and regulation of 10 for all types of controllers Performance Analysis of PSO Based Controller Table 5.13 Performance Comparison of PSO Based AVR Fixed Parameters: K a = 10, a = 0.1, K e = 1, e = 0.1, k g = 1, g = 1, K r = 1, 6 = 0.05 Methods Settling Time (sec) Overshoot (V) Oscillations (V) Conventional PID to 0.1 Fuzzy Controller to 0.1 GA-PID to 0.1 PSO-PID to 0.1

36 163 Table 5.14 Performance Comparison of PSO Based LFC Methods Fixed Parameters: g = 0.2, T =0.5,k g =1, H = 5,D=0.8 Settling Time (sec) Overshoot (Hz) Oscillations (Hz) Conventional PID to Fuzzy Controller to GA-PID e006 to PSO-PID to The results in comparison table shows that, for a load of 0.1 p.u and regulation of 10 the settling time of LFC is reduced by a factor of 59.5%, the oscillations are decreased by 75%, reduction of 75% in overshoot and the settling time of AVR is reduced by 44.87% as compared to fuzzy controllers. When compared GA based controller the settling time of LFC is reduced by 20.9%, the oscillations are decreased by 50%, reduction of 50% in the overshoots and the settling time of AVR is reduced by a factor of 22.49%. It is clear from the results that the proposed PSO method can avoid the drawback of the premature convergence problem in GA and obtain a high reliable solution with reduced computational time. The bar chart in the Figure 5.17 shows the comparative analysis of LFC and AVR with conventional controllers and PSO based controller.

37 164 Figure 5.17 Comparative Analysis of Conventional Controllers with PSO Based Controller for LFC and AVR Performance Analysis of ACO Based Controller To assess the effectiveness of the ACO-PID controller, the simulation results are compared with the conventional PID, fuzzy and GA based controllers in Tables 5.15 and The settling time of ACO based AVR is reduced by 54.3% when compared to GA-PID and 67.5% when compared to the fuzzy controller. The simulation results demonstrate the adaptability of ACO algorithm and its advantage in solving power system optimization problem. Table 5.15 Performance Comparison of ACO based AVR Fixed Parameters: K a = 10, a = 0.1, K e = 1, e = 0.1, k g = 1, g = 1, K r = 1, r = 0.05 Methods Settling Time (sec) Overshoot(V) Oscillations(V) Conventional PID to 0.1 Fuzzy Controller to 0.1 GA-PID to 0.1 ACO-PID to 0.15

38 165 Table 5.16 Performance Comparison of ACO based LFC Methods Fixed Parameters: g = 0.2, T =0.5, k g =1, H = 5, D=0.8 Settling Time (sec) Overshoot(Hz) Oscillations(Hz) Conventional PID to Fuzzy Controller to GA-PID to ACO-PID to The settling time, oscillations and overshoot of proposed LFC with ACO based controller is reduced by 63.6%, 88.9% and 66.3%, respectively when compared to conventional PID controller. The settling time of AVR with ACO based controller is decreased by a factor of 86.2%. Hence, ACO based controller gives improved performance characteristics when compared to the conventional controllers. When compared to the fuzzy controller, the proposed ACO-PID controller is reduced by 57%, 42.3%, and 3.8% with respect to settling time, overshoot and oscillations respectively. When compared GA based controller the settling time of LFC and AVR is reduced by 16% and 54.3% respectively. With respect to oscillations and overshoot, the performance of ACO based controller is found to be very close with GA- PID controller and can be varied by optimum tuning of regulation. The bar chart in Figure 5.18 can be used to visually analyse the impact of ACO based controller for LFC and AVR applications.

39 166 Figure 5.18 Comparative Analysis of Conventional Controllers with ACO Based Controller for LFC and AVR In standard numerical engineering analysis, the CPU time is less important than the effort of the engineer preparing the data. Therefore, the contemporary commercial finite element systems do not attach primary importance to the decrease of the computational time. In optimization algorithms, it is entirely different, since then the gradually modified solution must here be repeated even thousand times in the optimization loops. Hence, the time complexity of different evolutionary algorithms used in the optimization of PID gains are analyzed. To show the effectiveness of the ACO and PSO algorithms the mean CPU time taken to generate optimum parameters for a uniform load of 0.2pu and regulation value of 100 is considered. The comparison of average computation time or time complexity of GA, ACO and PSO are shown in Figure As it can be seen from the bar chart, since the PSO does not perform selection and crossover operation it can save some computation time when compared to GA and ACO.

40 167 Figure 5.19 Comparative Analysis of Execution Time for Different Evolutionary Algorithms 5.8 SUMMARY An efficient and intelligent computation based techniques such as PSO, and ACO is designed for determining the PID controller parameters for efficient control of frequency and voltage of the power generating system. The proposed method is effectively applied to the different optimization problem of the power system and can converge to produce an optimal solutions. The premature convergence problems of conventional controllers are avoided and hence obtain a high quality solution with better computational efficiency. The LFC and AVR models with PSO and ACO based controllers were simulated for different load changes and regulations to validate the efficiency of the proposed algorithms. From the simulation results it can be found that the EA based controllers can produce relatively better results with faster convergence rate and higher precision. As evident from the graphs and