S. Baskar

Evolutionary algorithms based design of multivariable PID controller

In this paper, performance comparison of evolutionary algorithms (EAs) such as real coded genetic algorithm (RGA), modified particle swarm optimization (MPSO), covariance matrix adaptation evolution strategy (CMAES) and differential evolution (DE) on optimal design of multivariable PID controller design is considered. Decoupled multivariable PI and PID controller structure for Binary distillation column plant described by Wood and Berry, having 2 inputs and 2 outputs is taken. EAs simulations are carried with minimization of IAE as objective using two types of stopping criteria, namely, maximum number of functional evaluations (Fevalmax) and Fevalmax along with tolerance of PID parameters and IAE. To compare the performances of various EAs, statistical measures like best, mean, standard deviation of results and average computation time, over 20 independent trials are considered. Results obtained by various EAs are compared with previously reported results using BLT and GA with multi-crossover approach. Results clearly indicate the better performance of CMAES and MPSO designed PI/PID controller on multivariable system. Simulations also reveal that all the four algorithms considered are suitable for off-line tuning of PID controller. However, only CMAES and MPSO algorithms are suitable for on-line tuning of PID due to their better consistency and minimum computation time.

Hybrid real coded genetic algorithm solution to economic dispatch problem

This paper presents a new, two-phase hybrid real coded genetic algorithm (GA) based technique to solve economic dispatch (ED) problem with multiple fuel options. The proposed hybrid scheme is developed in such a way that a simple real coded GA is acting as a base level search, which makes a quick decision to direct the search towards the optimal region, and local optimization by direct search and systematic reduction in size of the search region method is next employed to do the fine tuning. Constraint satisfaction technique has been employed to improve the solution quality and reduce the computational expenses. In order to validate the effectiveness of the proposed hybrid real coded genetic algorithm, the result of 10-generation unit ED problem with multiple fuel options is considered. The result shows that the proposed hybrid algorithm not only improves the solution accuracy and reliability but also makes the algorithm more efficient in terms of number of function evaluations and computation time. The simulation study clearly demonstrates that the proposed hybrid real coded genetic algorithm is practical and valid for real-time applications.

Application of NSGA-II Algorithm to Generation Expansion Planning

This paper describes use of a multiobjective optimization method, elitist nondominated sorting genetic algorithm version II (NSGA-II), to the generation expansion planning (GEP) problem. The proposed model provides for decision maker choice from among the different trade-off solutions. Two different problem formulations are considered. In one formulation, the first objective is to minimize cost; the second objective is to minimize sum of normalized constraint violations. In the other formulation, the first objective is to minimize investment cost; the second objective is to minimize outage cost (or maximize reliability). Virtual mapping procedure is introduced to improve the performance of NSGA-II. The GEP problem considered is a test system for a six-year planning horizon having five types of candidate units. The results are compared and validated.

A novel concurrent particle swarm optimization

In this paper, a concurrent PSO (CONPSO) algorithm is proposed to alleviate the premature convergence problem of PSO algorithm. It is a type of parallel algorithm in which modified PSO and FDR-PS algorithms are simulated concurrently with frequent message passing between them. This algorithm avoids the possible crosstalk effect of pbest and gbest terms with nbest term in FDR-PSO. Thereby, search efficiency of proposed algorithm is improved. In order to demonstrate the effectiveness of the proposed algorithm, experiments were conducted on six benchmarks continuous optimization problems. Results clearly demonstrate the superior performance of the proposed algorithm in terms of solution quality, average computation time and consistency. This algorithm is very much suitable for the implementation in parallel computer.

Application of modified NSGA-II algorithm to multi-objective reactive power planning

This paper discusses the application of Modified Non-Dominated Sorting Genetic Algorithm-II (MNSGA-II) to multi-objective Reactive Power Planning (RPP) problem. The three objectives considered are minimization of combined operating and VAR allocation cost, bus voltage profile improvement and voltage stability enhancement. For maintaining good diversity in nondominated solutions, Dynamic Crowding Distance (DCD) procedure is implemented in NSGA-II and it is called as MNSGA-II. The standard IEEE 30-bus test system, practical 69-bus Indian system and IEEE 118-bus system are considered to analyze the performance of MNSGA-II. The results obtained using MNSGA-II are compared with NSGA-II and validated with reference pareto-front generated by conventional weighted sum method using Covariance Matrix Adapted Evolution Strategy (CMA-ES). The performance of NSGA-II and MNSGA-II are compared with respect to best, mean, worst and standard deviation of multi-objective performance measures namely gamma, spread, minimum spacing and Inverted Generational Distance (IGD) in 15 independent runs. The results show the effectiveness of MNSGA-II and confirm its potential to solve the multi-objective RPP problem. A decision-making procedure based on Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method is used for finding best compromise solution from the set of pareto-solutions obtained through MNSGA-II.

Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization

In this paper, two lbests multi-objective particle swarm optimization (2LB-MOPSO) is applied to design multi-objective robust Proportional-integral-derivative (PID) controllers for two MIMO systems, namely, distillation column plant and longitudinal control system of the super maneuverable F18/HARV fighter aircraft. Multi-objective robust PID controller design problem is formulated by minimizing integral squared error (ISE) and balanced robust performance criteria. During the search, 2LB-MOPSO can focus on small regions in the parameter space in the vicinity of the best existing fronts. As the lbests are chosen from the top fronts in a non-domination sorted external archive of reasonably large size, the offspring obtained can be more diverse with good fitness. The performance of various optimal PID controllers is compared in terms of the sum of ISE and balanced robust performance criteria. For the purpose of comparison, 2LB-MOPSO, NSGA-II as well as earlier reported Riccati, IGA and OSA methods are considered. The performance of PID controllers obtained using 2LB-MOPSO is better than that of others. In addition, Hypervolume-based comparisons are carried out to show the superior performance of 2LB-MOPSO over NSGA-II. The results reveal that 2LB-MOPSO yields better robustness and consistency in terms of the sum of ISE and balanced robust performance criteria than various optimal PID controllers.

Efficient constraint handling for optimal reactive power dispatch problems.

Abstract In power engineering, minimizing the power loss in the transmission lines and/or minimizing the voltage deviation at the load buses by controlling the reactive power is referred to as optimal reactive power dispatch (ORPD). Recently, the use of evolutionary algorithms (EAs) such as differential evolution (DE), particle swarm optimization (PSO), evolutionary programming (EP), and evolution strategies (ES) to solve ORPD is gaining more importance due to their effectiveness in handling the inequality constraints and discrete values compared to that of conventional gradient-based methods. EAs generally perform unconstrained searches, and they require some additional mechanism to handle constraints. In the literature, various constraint handling techniques have been proposed. However, to solve ORPD the penalty function approach has been commonly used, while the other constraint handling methods remain untested. In this paper, we evaluate the performance of different constraint handling methods such as superiority of feasible solutions (SF), self-adaptive penalty (SP), e -constraint (EC), stochastic ranking (SR), and the ensemble of constraint handling techniques (ECHT) on ORPD. The proposed methods have been tested on IEEE 30-bus, 57-bus, and 118-bus systems. Simulation results clearly demonstrate the importance of employing an efficient constraint handling method to solve the ORPD problem effectively.

Application of NSGA-II Algorithm to Single-Objective Transmission Constrained Generation Expansion Planning

This paper presents an application of elitist nondominated sorting genetic algorithm version II (NSGA-II), a multiobjective algorithm to a constrained single objective optimization problem, the transmission constrained generation expansion planning (TC-GEP) problem. The TC-GEP problem is a large scale and challenging problem for the decision makers (to decide upon site, capacity, type of fuel, etc.) as there exist a large number of combinations. Normally the TC-GEP problem has an objective and a set of constraints. To use NSGA-II, the problem is treated as a two-objective problem. The first objective is the minimization of cost and the second objective is to minimize the sum of normalized soft constraints violation. The hard constraints (must satisfy constraints) are treated as constraints only. To improve the performance of the NSGA-II, two modifications are proposed. In problem formulation the modification is virtual mapping procedure (VMP), and in NSGA-II algorithm, controlled elitism is introduced. The NSGA-II is applied to solve TC-GEP problem for modified IEEE 30-bus test system for a planning horizon of six years. The results obtained by NSGA-II are compared and validated against single-objective genetic algorithm and dynamic programming. The effectiveness of each proposed approach has also been discussed in detail.

Application of extreme learning machine for series compensated transmission line protection

This paper proposes a new approach based on combined Wavelet Transform-Extreme Learning Machine (WT-ELM) technique for fault section identification (whether the fault is before or after the series capacitor as observed from the relay point), classification and location in a series compensated transmission line. This method uses the samples of fault currents for half cycle duration from the inception of fault. The features of fault currents are extracted by first level decomposition of the current samples using discrete wavelet transform (DWT) and the extracted features are applied as inputs to ELMs for fault section identification, classification and location. The feasibility of the proposed method has been tested on a 400kV, 300km series compensated transmission line for all the ten types of faults using MATLAB simulink. On testing 28,800 fault cases with varying fault resistance, fault inception angle, fault distance, load angle, percentage compensation level and source impedance, the performance of the proposed method has been found to be quite promising. The results also indicate that the proposed method is robust to wide variation in system and operating conditions.

Intelligent approaches using support vector machine and extreme learning machine for transmission line protection

This paper proposes two approaches based on wavelet transform-support vector machine (WT-SVM) and wavelet transform-extreme learning machine (WT-ELM) for transmission line protection. These methods uses fault current samples for half cycle from the inception of fault. The features of the line currents are extracted by first level decomposition of the current samples using discrete wavelet transform (DWT) and extracted features are applied as inputs to SVM and ELM for faulted phase detection, fault classification, location and discrimination between fault and switching transient condition. The feasibility of the proposed methods have been tested on a 240-kV, 225-km transmission line for all the 10 types of fault using MATLAB Simulink. Upon testing on 9600 fault cases with varying fault resistance, fault inception angle, fault distance, pre-fault power level, and source impedances, the performance of the proposed methods are quite promising. The performance of the proposed methods is compared in terms of classification accuracy and fault location error. The results indicate that SVM based approach is accurate compared to ELM based approach for fault classification. For fault location, the maximum error is less with SVM than ELM and the mean error of SVM is slightly higher than ELM.