Integral Of Time Multiplied Absolute Error Research Articles

Pareto design of Load Frequency Control for interconnected power systems based on multi-objective uniform diversity genetic algorithm (MUGA)

In this study, it is tried to employ a state-of-the-art multi-objective uniform-diversity genetic algorithm (MUGA) for Pareto optimization of PI/PID controllers in Load Frequency Control (LFC) of power systems. At first, multi objective optimization of a linear non-reheat two-area interconnected power system is conducted with respect to three conflicting objective functions. Gains of PI and PID controllers are considered as design variables while the objective functions are Integral Time multiply Absolute Error (ITAE), minimum damping ratio of dominant eigenvalues, and settling times in frequency and tie-line power deviations. To illustrate superiority of MUGA in finding optimum values of the deign variables, the proposed designs by MUGA are compared with those proposed by single and multi-objective optimization methods such as BFOA, hBFOA-PSO, and NSGA-II; the results indicate there is a noticeable improvement in response of the system. Further, robustness of the proposed designs is demonstrated by varying the system parameters from their nominal values and monitoring sensitivity of the system response to the variations. At the end, to take nonlinearities and physical constraints into account and to evaluate performance of MUGA in more complex system, a three unequal area hydro thermal system with generation rate constraints is considered.

Design of intelligent load frequency control strategy using optimal fuzzy-PID controller

This paper proposes a robust control strategy involving a novel optimised fuzzy-PID controller tuning by particle swarm optimisation (PSO) algorithm. The proposed control strategy was suggested to design an intelligent load frequency control (LFC) scheme in multi-area interconnected power system. The PSO algorithm was employed to optimise the fuzzy-PID controller parameters including the scaling factors of fuzzy logic and the PID controller gains for minimisation of both system frequency deviation and tie-line power changes during load disturbances using the integral time multiply absolute error (ITAE) as objective function. To demonstrate the effectiveness of the proposed control strategy, the three-area 9-unit interconnected power system was used for the simulation. The superiority of the proposed approach was shown by comparing the obtained results to other strategies available in literature. Initially, the simulation was performed using the same controllers in each area, and then was extended with different controllers in each area. The comparative study demonstrates the potential of the proposed control strategy and shows its robustness to enhance frequency stability.

Design and analysis of tilt integral derivative controller with filter for load frequency control of multi-area interconnected power systems

In this paper, a novel Tilt Integral Derivative controller with Filter (TIDF) is proposed for Load Frequency Control (LFC) of multi-area power systems. Initially, a two-area power system is considered and the parameters of the TIDF controller are optimized using Differential Evolution (DE) algorithm employing an Integral of Time multiplied Absolute Error (ITAE) criterion. The superiority of the proposed approach is demonstrated by comparing the results with some recently published heuristic approaches such as Firefly Algorithm (FA), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) optimized PID controllers for the same interconnected power system. Investigations reveal that proposed TIDF controllers provide better dynamic response compared to PID controller in terms of minimum undershoots and settling times of frequency as well as tie-line power deviations following a disturbance. The proposed approach is also extended to two widely used three area test systems considering nonlinearities such as Generation Rate Constraint (GRC) and Governor Dead Band (GDB). To improve the performance of the system, a Thyristor Controlled Series Compensator (TCSC) is also considered and the performance of TIDF controller in presence of TCSC is investigated. It is observed that system performance improves with the inclusion of TCSC. Finally, sensitivity analysis is carried out to test the robustness of the proposed controller by varying the system parameters, operating condition and load pattern. It is observed that the proposed controllers are robust and perform satisfactorily with variations in operating condition, system parameters and load pattern.

Load frequency control of interconnected power system using grey wolf optimization

In this article an attempt has been made to solve load frequency control (LFC) problem in an interconnected power system network equipped with classical PI/PID controller using grey wolf optimization (GWO) technique. Initially, proposed algorithm is used for two-area interconnected non-reheat thermal-thermal power system and then the study is extended to three other realistic power systems, viz. (i) two-area multi-units hydro-thermal, (ii) two-area multi-sources power system having thermal, hydro and gas power plants and (iii) three-unequal-area all thermal power system for better validation of the effectiveness of proposed algorithm. The generation rate constraint (GRC) of the steam turbine is included in the system modeling and dynamic stability of aforesaid systems is investigated in the presence of GRC. The controller gains are optimized by using GWO algorithm employing integral time multiplied absolute error (ITAE) based fitness function. Performance of the proposed GWO algorithm has been compared with comprehensive learning particle swarm optimization (CLPSO), ensemble of mutation and crossover strategies and parameters in differential evolution (EPSDE) and other similar meta-heuristic optimization techniques available in literature for similar test system. Moreover, to demonstrate the robustness of proposed GWO algorithm, sensitivity analysis is performed by varying the operating loading conditions and system parameters in the range of ±50%. Simulation results show that GWO has better tuning capability than CLPSO, EPSDE and other similar population-based optimization techniques.

English

An interval type-2 fuzzy logic controller (T2FLC) for nonlinear dead time process is proposed in this paper. Then PI & PID of T2FLC are applied to dynamic nonlinear system to analysis and comparative study of different performance parameter. Hence to comparative study of T2FLC with conventional T1FLC of different performance parameter such as rise time(tr),peak overshoot(% mp),settling time(ts) integral absolute error (IAE) and integral-of-time multiplied absolute error(ITAE) are taken . In this work an improved performance of T2FLC is observed. A type-2 fuzzy controller is designed by blurried the membership function based on foot print of uncertaintities (FOU) and embedded four T1FLC.

A comparative study of MPC and optimised PID control

The paper presents a comparative study between the performance of model predictive control (MPC) and optimised proportional-integral-differential (PID) control on different systems. An objective function derived from rise time, settling time, percentage overshoot, and steady-state error is minimised in order to obtain the gains of the PID controller. The bacterial foraging (BF) algorithm is used to tune the parameters of the PID controller through performance optimisation of the system. System performance characteristics are compared to another controller designed based on MPC. The rise time, settling time, percentage overshoot, integral absolute error (IAE), and integral time-multiplied absolute error (ITAE) of the controllers are compared when acting on systems of different orders. Controller testing and performance comparison are carried out on first, second, third, forth, and fifth order systems. Results indicate that MPC consistently outperforms optimised PID control in all cases.

Optimal fractional order PID controller for automatic generation control of two-area power systems

This paper proposes a fractional order PID (FOPID) controller for the supplementary automatic generation control (AGC) of two area thermal power systems. To establish the effectiveness of the proposed controller, its dynamic performance is compared with integral/PI controllers. The parameters of the PI controllers are determined using genetic algorithm (GA) and fuzzy logic-based approaches. These comparisons are performed in terms of two time domain performance indices viz., settling time and maximum overshoot/undershoot of the dynamic response and three error indices, viz., Integral of Time multiplied Absolute Error (ITAE), Integral of the Absolute Error (IAE) and Integral of the square error (ISE). Copyright © 2014 John Wiley & Sons, Ltd.

A new adaptive configuration of PID type fuzzy logic controller

In this paper, an adaptive configuration for PID type fuzzy logic controller (FLC) is proposed to improve the performances of both conventional PID (C-PID) controller and conventional PID type FLC (C-PID-FLC). The proposed configuration is called adaptive because its output scaling factors (SFs) are dynamically tuned while the controller is functioning. The initial values of SFs are calculated based on its well-tuned counterpart while the proceeding values are generated using a proposed stochastic hybrid bacterial foraging particle swarm optimization (h-BF-PSO) algorithm. The performance of the proposed configuration is evaluated through extensive simulations for different operating conditions (changes in reference, load disturbance and noise signals). The results reveal that the proposed scheme performs significantly better over the C-PID controller and the C-PID-FLC in terms of several performance indices (integral absolute error (IAE), integral-of-time-multiplied absolute error (ITAE) and integral-of-time-multiplied squared error (ITSE)), overshoot and settling time for plants with and without dead time.

Comparative performance analysis of teaching learning based optimization for automatic load frequency control of multi-source power systems

• Application of teaching learning based optimization to AGC problems. • PID controller gains have been optimized by teaching learning based optimization. • Dynamic performance is analyzed for single area system and multi area with HVDC link. • Dynamic performances of TLBO based PID controller are better than DE-PID controller. • Sensitivity analysis is done to load changes and different cost functions. This paper presents a new population based parameter free optimization algorithm as teaching learning based optimization (TLBO) and its application to automatic load frequency control (ALFC) of multi-source power system having thermal, hydro and gas power plants. The proposed method is based on the effect of the influence of teacher on the output of learners and the learners can enhance their knowledge by interactions among themselves in a class. In this extensive study, the algorithm is applied in multi area and multi-source realistic power system without and with DC link between two areas in order to tune the PID controller which is used for automatic generation control (AGC). The potential and effectiveness of the proposed algorithm is compared with that of differential evolution algorithm (DE) and optimal output feedback controller tuning performance for the same power systems. The dynamic performance of proposed controller is investigated by different cost functions like integral of absolute error (IAE), integral of squared error (ISE), integral of time weighted squared error (ITSE) and integral of time multiplied absolute error (ITAE) and the robustness of the optimized controller is verified by its response toward changing in load and system parameters. It is found that the dynamic performance of the proposed controller is better than that of recently published DE optimized controller and optimal output feedback controller and also the proposed system is more robust and stable to wide changes in system loading, parameters, size and locations of step load perturbation and different cost functions.

A hybrid firefly algorithm and pattern search technique for automatic generation control of multi area power systems

In this paper, a novel hybrid Firefly Algorithm and Pattern Search (hFA–PS) technique is proposed for Automatic Generation Control (AGC) of multi-area power systems with the consideration of Generation Rate Constraint (GRC). Initially a two area non-reheat thermal system with Proportional Integral Derivative (PID) controller is considered and the parameters of PID controllers are optimized by Firefly Algorithm (FA) employing an Integral Time multiply Absolute Error (ITAE) objective function. Pattern Search (PS) is then employed to fine tune the best solution provided by FA. The superiority of the proposed hFA–PS based PID controller has been demonstrated by comparing the results with some recently published modern heuristic optimization techniques such as Bacteria Foraging Optimization Algorithm (BFOA), Genetic Algorithm (GA) and conventional Ziegler Nichols (ZN) based PI/PID controllers for the same interconnected power system. Furthermore, sensitivity analysis is performed to show the robustness of the optimized controller parameters by varying the system parameters and operating load conditions from their nominal values. Finally, the proposed approach is extended to multi area multi source hydro thermal power system with/without considering the effect of physical constraints such as time delay, reheat turbine, GRC, and Governor Dead Band (GDB) nonlinearity. The controller parameters of each area are optimized under normal and varied conditions using proposed hFA–PS technique. It is observed that the proposed technique is able to handle nonlinearity and physical constraints in the system model.

Multiobjective optimization using weighted sum Artificial Bee Colony algorithm for Load Frequency Control

This paper presents the implementation of multiobjective based optimization of Artificial Bee Colony (ABC) algorithm for Load Frequency Control (LFC) on a two area interconnected reheat thermal power system. The ABC algorithm is currently being applied in many research works due to the local and global search capability of the algorithm. This paper uses the weighted sum approach of the ABC to optimize the PID controller’s gains to provide a compromise between the frequency response’s settling time and maximum overshoot. The composite objective function comprising both objectives is characterized by the performance criterions – Integral of Time Multiplied Absolute Error (ITAE) and Integral of Time Weighted Squared Error (ITSE). Analysis is carried out to determine the best weightage set for this investigation. A performance index based on Least Average Error (LAE) is formulated to calculate the index of each weightage set. In order to ensure effective compensation in the system output, the PID controllers for both areas are tuned simultaneously. The tuning performance of the algorithm is evaluated by comparing the performance of the proposed controller with conventional PI and PID controller. The robustness of the proposed algorithm is further investigated by evaluating the response of the system under simultaneous step load perturbation (SLP), changing load demand and collectively varying system parameters in the range of ±50%. The simulation result shows the dynamic response of the controller emphasizes on the compromise between the settling time and maximum overshoot of the frequency response. Furthermore, the proposed algorithm is robust enough to operate under different operating conditions and system parameter variations.

Suppression of Chaotic Behavior in Duffing-holmes System using Back-stepping Controller Optimized by Unified Particle Swarm Optimization Algorithm

The nonlinear behavior analysis and chaos control for Duffing-Holmes chaotic system is discussed in this paper. In order to suppress the irregular chaotic motion, an optimal back-stepping controller is designed. The back-stepping method consists of parameters with positive values. The improper selection of the parameters leads to inappropriate responses or even may lead to instability of the system. In this paper, the Unified particle swarm optimization (UPSO) algorithm is utilized to determine the convenient and optimal values of the parameters. The minimized objective function via UPSO algorithm is a weighted sum of the Integral of Time multiplied Absolute Error (ITAE) and squared control signal. Fast control of chaos in a very short time and having more limited control signal for this purpose, are the great advantages of the proposed controller. Numerical simulations show the high performance of this method for chaos elimination in Duffing-Holmes system.

Identification of Position DC Motor and Control Using Fuzzy Type 2 Based PSO

This paper presents identification of a position DC motor using least squares analysis to estimate the parameters of an ARX model .Type-2 fuzzy logic controllers is proposed as an alternative solution in the literature when a system has a large amount of uncertainties. This paper proposed an algorithm of interval fuzzy type 2 logic controller(PSOIT2FLC)with the optimized parameters using particle swarm optimization in the design of fuzzy controller for the position control of DC Motor. The performance of the proposed PSOIT2FLC is compared with that of its corresponding conventional PSO algorithm type -1 FLC in terms of several performance measures such as rise time, peak overshoot, settling time, integral absolute error (IAE) and integral of time multiplied absolute error (ITAE) and in each case, the proposed scheme shows improved performance over its conventional counterpart. . Extensive simulation studies are conducted to compare the response of the given system with the conventiona genetic algorithm type -1 fuzzy controller to the response given with the proposed PSOIT2FLC scheme. Simulation works in MATLAB environment demonstrate that the PSO optimized fuzzy position controller became very strong, gives better results and possesses good robustness.

Hybrid BFOA–PSO algorithm for automatic generation control of linear and nonlinear interconnected power systems

In the bacteria foraging optimization algorithm (BFAO), the chemotactic process is randomly set, imposing that the bacteria swarm together and keep a safe distance from each other. In hybrid bacteria foraging optimization algorithm and particle swarm optimization (hBFOA–PSO) algorithm the principle of swarming is introduced in the framework of BFAO. The hBFOA–PSO algorithm is based on the adjustment of each bacterium position according to the neighborhood environment. In this paper, the effectiveness of the hBFOA–PSO algorithm has been tested for automatic generation control (AGC) of an interconnected power system. A widely used linear model of two area non-reheat thermal system equipped with proportional-integral (PI) controller is considered initially for the design and analysis purpose. At first, a conventional integral time multiply absolute error (ITAE) based objective function is considered and the performance of hBFOA–PSO algorithm is compared with PSO, BFOA and GA. Further a modified objective function using ITAE, damping ratio of dominant eigenvalues and settling time with appropriate weight coefficients is proposed to increase the performance of the controller. Further, robustness analysis is carried out by varying the operating load condition and time constants of speed governor, turbine, tie-line power in the range of +50% to −50% as well as size and position of step load perturbation to demonstrate the robustness of the proposed hBFOA–PSO optimized PI controller. The proposed approach is also extended to a non-linear power system model by considering the effect of governor dead band non-linearity and the superiority of the proposed approach is shown by comparing the results of craziness based particle swarm optimization (CRAZYPSO) approach for the identical interconnected power system. Finally, the study is extended to a three area system considering both thermal and hydro units with different PI coefficients and comparison between ANFIS and proposed approach has been provided.

Automatic generation control of multi-area power system using multi-objective non-dominated sorting genetic algorithm-II

Controllers design problems are multi objective optimization problems as the controller must satisfy several performance measures that are often conflicting and competing with each other. In multi-objective approach a set of solutions can be generated from which the designer can select a final solution according to his requirement and need. This paper presents the design and analysis Proportional Integral (PI) and Proportional Integral Derivative (PID) controller employing multi-objective Non-Dominated Shorting Genetic Algorithm-II (NSGA-II) technique for Automatic Generation Control (AGC) of an interconnected system. To minimize the effect of noise in the input signal, a filter is employed with the derivative term. Integral Time multiply Absolute Error (ITAE), minimum damping ratio of dominant eigenvalues and settling times in frequency and tie-line power deviations are considered as multiple objectives and NSGA-II is employed to generate Pareto optimal set. Further, a fuzzy-based membership value assignment method is employed to choose the best compromise solution from the obtained Pareto solution set. The proposed approach is first applied to a linear two-area power system model and then extended to a non-linear power system model by considering the effect of governor dead band non-linearity. The superiority of the proposed NSGA-II optimized PI/PID controllers has been shown by comparing the results with some recently published modern heuristic optimization approaches such as Bacteria Foraging Optimization Algorithm (BFOA), Genetic Algorithm (GA) and Craziness based Particle Swarm Optimization (CPSO) based controllers for the similar interconnected power systems.

DE optimized parallel 2-DOF PID controller for load frequency control of power system with governor dead-band nonlinearity

In this paper, design and performance analysis of Differential Evolution (DE) algorithm based parallel 2-Degree Freedom of Proportional-Integral-Derivative (2-DOF PID) controller for Load Frequency Control (LFC) of interconnected power system is presented. A two area thermal system with governor dead-band nonlinearity is considered for the design and analysis purpose. The design problem is formulated as an optimization problem and DE is employed to search for optimal controller parameters. Conventional and modified objective functions are used for the design purpose. Conventional objective functions employed in the paper are Integral of Time multiplied by Squared Error (ITSE) and Integral of Squared Error (ISE). In order to further increase the performance of the controller, a modified objective function is derived using Integral Time multiply Absolute Error (ITAE), damping ratio of dominant eigenvalues, settling times of frequency and peak overshoots with appropriate weight coefficients. The superiority of the proposed approach has been demonstrated by comparing the results with a recently published technique, i.e. Craziness based Particle Swarm Optimization (CPSO) for the same interconnected power system. Further, sensitivity analysis is performed by varying the system parameters and operating load conditions from their nominal values. It is observed that the proposed controllers are quite robust for a wide range of the system parameters and operating load conditions from their nominal values. Finally, the proposed approach is extended to a more realistic power system model by considering the physical constraints such as time delay, reheat turbine, Generation Rate Constraint (GRC) and governor dead band.

Type-2 Fuzzy Logic Controllers Based Genetic Algorithm for the Position Control of DC Motor

Type-2 fuzzy logic systems have recently been utilized in many control processes due to their ability to model uncertainty. This research article proposes the position control of (DC) motor. The proposed algorithm of this article lies in the application of a genetic algorithm interval type-2 fuzzy logic controller (GAIT2FLC) in the design of fuzzy controller for the position control of DC Motor. The entire system has been modeled using MATLAB R11a. The performance of the proposed GAIT2FLC is compared with that of its corresponding conventional genetic algorithm type-1 FLC in terms of several performance measures such as rise time, peak overshoot, settling time, integral absolute error (IAE) and integral of time multiplied absolute error (ITAE) and in each case, the proposed scheme shows improved performance over its conventional counterpart. Extensive simulation studies are conducted to compare the response of the given system with the conventional genetic algorithm type-1 fuzzy controller to the response given with the proposed GAIT2FLC scheme.

Design and analysis of differential evolution algorithm based automatic generation control for interconnected power system

This paper presents the design and performance analysis of Differential Evolution (DE) algorithm based Proportional-Integral (PI) controller for Automatic Generation Control (AGC) of an interconnected power system. A two area non-reheat thermal system equipped with PI controllers which is widely used in literature is considered for the design and analysis purpose. The design problem is formulated as an optimization problem control and DE is employed to search for optimal controller parameters. Three different objective functions using Integral Time multiply Absolute Error (ITAE), damping ratio of dominant eigenvalues and settling time with appropriate weight coefficients are derived in order to increase the performance of the controller. The superiority of the proposed DE optimized PI controller has been shown by comparing the results with some recently published modern heuristic optimization techniques such as Bacteria Foraging Optimization Algorithm (BFOA) and Genetic Algorithm (GA) based PI controller for the same interconnected power system.

Bees Algorithm Based Intelligent Backstepping Controller Tuning For Gyro System

In this paper, an intelligent nonlinear controller is presented by intelligent tuning of the backstepping method parameters using Bees Algorithm. The proposed controller is utilized to control of chaos of Gyro system. The backstepping method consists of parameters which could have positive values. The parameters are usually chosen optional by trial and error method. The improper selection of the parameters leads to inappropriate responses or even may lead to instability of the system. The proposed optimal backstepping controller without trial and error determines the parameters of backstepping controller automatically and intelligently by minimizing the Integral of Time multiplied Absolute Error (ITAE) and squared controller output. Finally, the efficiency of the proposed intelligent backstepping controller is illustrated by implementing the method on the Gyro chaotic system.

Comparative performance analysis of Artificial Bee Colony algorithm in automatic generation control for interconnected reheat thermal power system

This study extensively presents the Automatic Generation Control (AGC) application of Artificial Bee Colony (ABC) algorithm. This algorithm is one of the new population based optimization algorithms which have been developed since 2005. In this study, the algorithm is applied to the interconnected reheat thermal power system in order to tune the parameters of PI and PID controllers which are used for AGC. The tuning performance of the algorithm is compared with that of Particle Swarm Optimization (PSO) algorithm through transient response analysis method. In addition to these, the robustness analysis is applied to the power system which is optimized by ABC algorithm so as to determine its response towards changing in the load and the system parameters, varied in the range of ±50%. The behavior of the system is also investigated with this analysis towards the different cost functions such as integral of absolute error (IAE), integral of squared error (ISE), integral of time weighted squared error (ITSE) and integral of time multiplied absolute error (ITAE). At the end of the study, it is seen that the ABC algorithm is successfully applied to the AGC in the application of interconnected reheat thermal power system, and it shows better tuning capability than the other similar population based optimization algorithm. Furthermore, it is also seen that the proposed system is robust and is not affected by changing in the load, the power system parameters and the cost functions.