J. S. Dhillon

Stochastic economic emission load dispatch

Abstract The economic emission load dispatch (EELD) problem is a multiple non-commensurable objective problem that minimizes both cost and emission together. In the paper a stochastic EELD problem is formulated with consideration of the uncertainties in the system production cost and nature of the load demand, which is random. In addition, risk is considered as another conflicting objective to be minimized because of the random load and uncertain system production cost. The weighted minimax technique is used to simulate the trade-off relation between the conflicting objectives in the non-inferior domain. Once the trade-off has been obtained, fuzzy set theory helps the power system operator to choose the optimal operating point over the trade-off curve and adjust the generation levels in the most economic manner associated with minimum emission and risk. The validity of the method is demonstrated by analysing a sample system comprising six generators.

Multiobjective load dispatch by fuzzy logic based searching weightage pattern

Abstract A multiobjective thermal power dispatch problem minimizes number of objectives viz cost and emission together while allocating the electricity demand among the committed generating units subject to physical and technological constraints. Such problems are solved to generate non-inferior solutions using weighting method or e-constraint method. Afterwards the decision maker is provided with a set of simple but effective tools to choose the best alternative among non-inferior solutions. The generation of non-inferior solution requires an enormous amount of computation time when the number of objectives is more than two. In the paper, the multiobjective problem has been solved a using weighted technique. The Evolutionary optimization technique has been employed in which the ‘preferred’ weightage pattern has been searched to get the ‘best’ optimal solution in non-inferior domain. Decision making theories attempt to deal with the vagueness or fuzziness inherent in subjective or impressive determination of goals. So fuzzy set theory has been exploited to decide the ‘preferred’ optimal operating point. The non-inferior solution that attains maximum satisfaction level from the membership functions of the participating objectives has been adjudged the ‘best’ solution. The proposed method requires few search moves to get the optimal operating point in the non-inferior domain for any number of goals. The validity of the proposed method has been demonstrated on a 25 nodes IEEE system comprising five generators.

Solution of non-convex economic load dispatch problem using Grey Wolf Optimizer

Abstract Grey Wolf Optimizer (GWO) is a recently developed meta-heuristic search algorithm inspired by grey wolves (Canis lupus), which simulate the social stratum and hunting mechanism of grey wolves in nature and based on three main steps of hunting: searching for prey, encircling prey and attacking prey. This paper presents the application of GWO algorithm for the solution of non-convex and dynamic economic load dispatch problem (ELDP) of electric power system. The performance of GWO is tested for ELDP of small-, medium- and large-scale power systems, and the results are verified by a comparative study with lambda iteration method, Particle Swarm Optimization algorithm, Genetic Algorithm, Biogeography-Based Optimization, Differential Evolution algorithm, pattern search algorithm, NN-EPSO, FEP, CEP, IFEP and MFEP. Comparative results show that the GWO algorithm is able to provide very competitive results compared to other well-known conventional, heuristics and meta-heuristics search algorithms.

Multiobjective optimal thermal power dispatch

Abstract A multiobjective thermal power dispatch problem is formulated using noncommensurable objectives such as operating costs and minimal emission. A sensitivity measure is chosen whereby the effects of variations in the nominal conditions describing a given multiobjective problem can be measured and incorporated as a performance index to be minimized. A nonlinear programming problem provides the framework for examining the objective constraint level in an ϵ-constant form of the multiobjective optimization problem. The dispersion index is chosen as the sensitivity measure for the investigation of the effects of random variations in the model parameters of the optimal solution. A sensitivity trade-off is exploited for the multiobjective problem that represents the trade-off between sensitivity and objective level. Validity of the method has been demonstrated by analysing a three-generator sample system.

Scheduling short-term hydrothermal generation using predator prey optimization technique

Abstract Paper presents predator–prey based optimization (PPO) technique to obtain optimal generation scheduling of short-term hydrothermal system. PPO is a part of the swarm intelligence family and is capable to solve large scale non-linear optimization problems. PPO based algorithm combines the idea of particle swarm optimization concept with predator effect that helps to, maintain diversity in the swarm and preventing premature convergence to local sub-optimal. In this paper first of all feasible solution is obtained through random heuristic search and then thermal and hydro power generations are searched for optimum hydrothermal scheduling problem using PPO. Variable elimination method is implemented to handle the equality constraint by eliminating variable explicitly. These eliminated variables are considered by penalty method restricts slack units with in limits. Slack thermal generating unit for each sub-interval handles power balance equality constraint and slack hydro units handle water equality constraint. The performance of the proposed approach is illustrated on, fixed-head and variable-head hydrothermal power systems. The results obtained from the proposed technique are compared with the existing technique. From the numerical results, it is experienced that the PPO based approach is able to provide a better solution.

Fuzzy decision making in multiobjective long-term scheduling of hydrothermal system

Abstract In the paper, a fuzzy decision making methodology is presented to decide the generation schedule of long-term hydrothermal problems with explicit recognition of statistical uncertainties in system production cost data, NOx emission data, system load demand and hydro reservoir water inflows. In deciding the optimal operation, three objectives operating cost, NOx emission and unsatisfied load demand over the whole of the planning period are simultaneously minimised. Specific technique is put forth to convert the stochastic models into their deterministic equivalents. The weighted minimax method is used to simulate the tradeoff relation between the conflicting objectives in the non-inferior domain. The fuzzy set theory is exploited to choose the best operating point over the tradeoff curve. An efficient decomposition technique is applied to reduce the complexity of the problem. In each subproblem, thermal generations are obtained by using simplified method and water discharges are adjusted using Conjugate gradient method. The validity and effectiveness of the method has been demonstrated by analysing a power system consisting of 3-hydro and 4-thermal plants.

Multi-objective Short-term Hydrothermal Generation Scheduling Using Predator–Prey Optimization

Abstract In this article, a predator–prey-based optimization technique is applied to obtain the scheduling of a hydrothermal system with cascaded reservoirs, minimizing economic and gaseous pollutants and emission objectives. These objectives are mutually conflicting and are equally important. Predator–prey optimization is a stochastic optimization technique based on the particle swarm optimization concept having an additional predator effect that helps to explore the search area more efficiently due to the fear created by the predator. A heuristic search technique is applied for generating an initial feasible solution. The direct substitution method is implemented to handle the equality constraints, whereby dependent variables are determined from the equality constraint. Inequality constraints of dependent variables are taken care by incorporating an additional objective function represented by the fuzzy membership index, and other variables are set to their limits on violation. Fuzzy methodology has been exploited for solving a decision-making problem involving the multiplicity of objectives and selection criterion for the best compromised solution. The solutions obtained from the proposed technique are compared with other existing techniques, and results are found to be satisfactory. The proposed method has the capability to escape from local optimum solutions due to its predator effect, and it is easy to implement.

MULTIOBJECTIVE DECISION MAKING IN STOCHASTIC ECONOMIC DISPATCH

ABSTRACT Recently, multiple objective decision making has been well established as a practical approach to seek satisfactory solutions to decision making problems in limited resources, information and cognitive ability of the Decision Maker (DM). In the past, it was normal to assume well behaved and deterministic system data. Now the trend is to assume them variable and uncertain for more realistic approach. This paper deals with decision making methodology based on fuzzy set theory in order to determine the optimal generation dispatch with due consideration of uncertainties in system production cost and randomness of load demand. The classical economic dispatch problem is formulated as stochastic multiobjective optimisation problem where operating cost and variance of generation mismatch are two non-commensurable objectives. Such problems are solved to generate non-inferior solutions. Weighted sum technique is used to simulate trade_off relation among the conflicting objectives in the non-inferior domain...

Hybrid heuristic search method for design of digital IIR filter with conflicting objectives

The design of digital IIR filter design by using evolutionary algorithms has gained much attention in the previous years. Most of the researchers treated the design problem as a single objective optimization problem and applied the techniques for minimizing the magnitude response error. In this paper the design of filter is treated as a multi-objective problem by simultaneously minimizing the magnitude response error, linear phase response error and optimal order along with meeting the stability criterion. A hybrid heuristic search technique having differential evolution (DE) method as a global search technique and binary successive approximation based evolutionary search method as a local search technique has been proposed. Based on mean value of population, new mutation strategies have been proposed. The above proposed hybrid heuristic search technique has been applied effectively to solve the multi-parameter and multi-objective optimization problem of low-pass, high-pass, band-pass and band-stop digital IIR filter design. The obtained results reveal that the proposed technique with new proposed mutation strategies performs better than the already existing mutation strategies of DE and other algorithms applied by other researchers for the design of digital IIR filter.

Fuzzy Satisfying Multiobjective Thermal Power Dispatch Based on Surrogate Worth Trade-off Method

Abstract In multiobjective optimization, trade-off analysis plays an important role in determining the best search direction to reach a most preferred solution. As in many cases, the objectives contradict with each other and cannot be handled by conventional scalar optimization techniques. This article deals with the multiobjective optimization problem relating to real and reactive power scheduling of thermal power generating units. In deciding the most preferred solution, operating cost, emission pollutants are the objectives undertaken to be minimized simultaneously while satisfying the security constraints. The real and reactive power line flows are obtained with the help of generalized Z-bus distribution factors (GZBDF). The non-inferior solutions, along with the trade-off functions between the conflicting objectives, are generated by implementing the ε-constraint method. Exploiting fuzzy set theory to access the indifference band, interaction with the decision maker is obtained via surrogate worth trade-off (SWT) functions of the membership functions of the objectives. The surrogate worth trade-off functions are constructed in the functional space and then transformed into the decision space, so the surrogate worth trade-off functions of objectives relate the decision makers preferences to non-inferior solutions. The goal/objectives being of fuzzy nature can be quantified by defining their membership functions. The effectiveness of the method is demonstrated on IEEE 11-bus system, which comprises 3-generators.