Security constrained economic load dispatch using improved particle swarm optimization suitable for utility system

The objective of this paper is to evolve simple and effective methods for the economic load dispatch (ELD) problem with security constraints in thermal units, which are capable of obtaining economic scheduling for utility system. In the proposed improved particle swarm optimization (IPSO) method, a new velocity strategy equation is formulated suitable for a large scale system and the features of constriction factor approach (CFA) are also incorporated into the proposed approach. The CFA generates higher quality solutions than the conventional PSO approach. The proposed approach takes security constraints such as line flow constraints and bus voltage limits into account. In this paper, two different systems IEEE-14 bus and 66-bus Indian utility system have been considered for investigations and the results clearly show that the proposed IPSO method is very competent in solving ELD problem in comparison with other existing methods.     

Economic dispatch with prohibited operating zones using fast computation evolutionary programming algorithm

This paper presents an efficient and simple approach for solving the economic dispatch (ED) problem with units having prohibited operating zones. The operating region of the units having prohibited zones is broken into isolated feasible sub-regions which results in multiple decision spaces for the economic dispatch problem. The optimal solution will lie in one of the feasible decision spaces and can be found using the conventional λ–δ iterative method in each of the feasible decision spaces. But, this elaborate search procedure is time consuming and not acceptable for on-line application. In this paper, a simple and novel approach is proposed. In this approach, the optimal solution and the corresponding optimum system lambda are determined using an efficient fast computation evolutionary programming algorithm (FCEPA) without considering the prohibited operating zones. Then, a small set of advantageous decision spaces is formed by combining the feasible sub-regions of the fuel cost curve intervening the prohibited zones in the neighbourhood of the optimal system lambda. A penalty cost for each advantageous decision space is judiciously computed using participation factor. The most advantageous decision space is found out by comparing the penalty cost of the decision spaces. The optimal solution in the most advantageous decision space is obtained using the FCEPA. The proposed algorithm is tested on a number of sample systems with units possessing prohibited zones. The study results reveal that the proposed approach is computationally efficient and would be a competent method for solving economic dispatch problem with units having prohibited operating zones.     

Application of evolutionary programming for economic dispatch of cogeneration systems under emission constraints

This paper studies the economical operation of cogeneration systems under emission control with NO_x and SO_x from fossil-fueled thermal generation. The emission model is formulated as a function of fuel enthalpy dependent on the emission factor. The objective function includes fuel cost, emission cost, and tie-line energy cost, subject to the use of mixed fuels, operational limits, and emission constraints. An evolutionary programming was adopted to solve this problem. The steams, fuel mix, and generations will be found by considering the time-of-use dispatch between cogeneration systems and utility companies. A real cogeneration system is given to illustrate the proposed method.     

Multi-objective economic emission dispatch considering wind power using evolutionary algorithm based on decomposition

Due to the increasing deterioration of environmental problem, multi-objective Economic Emission Dispatch (EED) problem has become one of the active research areas in recent years. Meanwhile, the renewable energy such as wind energy is an important approach to reduce pollution emissions, as well as the dependence on fossil fuels. In this paper, a newly developed optimization technique, called Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D), has been applied to optimize the cost and emission of wind–thermal power system. MOEA/D provides a simple but efficient framework which decomposes a Multi-objective Optimization Problem (MOP) into a number of scalar optimization subproblems and optimizes them simultaneously. The stochastic nature of wind power is modeled by Weibull probability distribution function and the uncertainty of wind power is considered as system constraints with stochastic variables. To validate the effectiveness of the MOEA/D method, it is first applied to solve the traditional EED problem of standard IEEE 30-bus 6-generator system as the benchmark. Then, the effect of wind power penetration on cost and emission is analyzed by MOEA/D in a 6-generator system and a 40-generator system with wind farms based on the proposed EED model. A comparative analysis with other similar optimization methods reveals that the MOEA/D method is able to generate better performance in terms of both solution quality and computational efficiency.     

A dynamic programming based fast computation Hopfield neural network for unit commitment and economic dispatch

This paper develops a new dynamic programming based direct computation Hopfield method for solving short term unit commitment (UC) problems of thermal generators. The proposed two step process uses a direct computation Hopfield neural network to generate economic dispatch (ED). Then using dynamic programming (DP) the generator schedule is produced. The method employs a linear input–output model for neurons. Formulations for solving the UC problems are explored. Through the application of these formulations, direct computation instead of iterations for solving the problems becomes possible. However, it has been found that the UC problem cannot be tackled accurately within the framework of the conventional Hopfield network. Unlike the usual Hopfield methods which select the weighting factors of the energy function by trials, the proposed method determines the corresponding factor using formulation calculation. Hence, it is relatively easy to apply the proposed method. The Neyveli Thermal Power Station (NTPS) unit II in India with three units having prohibited operating zone has been considered as a case study and extensive study has also been performed for power system consisting of 10 generating units.     

A mixed integer quadratic programming formulation for the economic dispatch of generators with prohibited operating zones

In this paper, an optimisation-based approach is proposed using a mixed integer quadratic programming model for the economic dispatch of electrical power generators with prohibited zones of operation. The main advantage of the proposed approach is its capability to solve case studies from the literature to global optimality quickly and without any targeting of solution procedures.     

An -dominance-based multiobjective genetic algorithm for economic emission load dispatch optimization problem

In this paper, a novel multiobjective genetic algorithm approach for economic emission load dispatch (EELD) optimization problem is presented. The EELD problem is formulated as a non-linear constrained multiobjective optimization problem with both equality and inequality constraints. A new optimization algorithm which is based on concept of co-evolution and repair algorithm for handling non-linear constraints is presented. The algorithm maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of -dominance. The use of -dominance also makes the algorithms practical by allowing a decision maker to control the resolution of the Pareto-set approximation by choosing an appropriate value.The proposed approach is carried out on the standard IEEE 30-bus 6-genrator test system. The results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto-optimal non-dominated solutions of the multiobjective EELD problem in one single run. Simulation results with the proposed approach have been compared to those reported in the literature. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.     

A security constrained environmental/economic power dispatch technique using F-MSG algorithm for a power system area including limited energy supply thermal units

A security constrained non-convex environmental/economic power dispatch problem for a lossy electric power system area including limited energy supply thermal units is formulated. An iterative solution method based on modified subgradient algorithm operating on feasible values (F-MSG) and a common pseudo scaling factor for limited energy supply thermal units are used to solve it. In the proposed solution method, the F-MSG algorithm is used to solve the dispatch problem of each subinterval, while the common pseudo scaling factor is employed to adjust the amount of fuel spent by the limited energy supply thermal units during the considered operation period. We assume that limited energy supply thermal units are fueled under take-or-pay (T-O-P) agreement.The proposed dispatch technique is demonstrated on IEEE 30-bus power system with six thermal generating units having non-convex cost rate functions. Two of the generating units are selected as gas-fired limited energy supply thermal units. Pareto optimal solutions for the power system, where the constraint on the amount of fuel consumed by the limited energy supply thermal units is not considered, are calculated first. Later on, the same Pareto optimal solutions for the power system, where the fuel constraint is considered, are recalculated, and the obtained savings in the sum of optimal total fuel cost and total emission cost are presented. The dispatch problem of the first subinterval of the test system was solved previously by means of differential evolution (DE), and a hybrid method based on combination of DE and biogeography based optimization (BBO) for the best cost and the best emission cases in the literature. The results produced by these methods are compared with those of produced by the proposed method in terms of their total cost rate, emission rate and solution time values. It is demonstrated that the proposed method outperforms against the evolutionary methods mentioned in the above in terms of solution time values especially when the exact model of the test system is considered.     

Analytical methods for determining a system configuration acceptable from viewpoints of both short circuit current and voltage stability

Generally, improving voltage stability to power demand increase tends to increase short circuit capacity. In this paper, two methods are proposed in order to obtain appropriate system separation points that minimize short circuit capacity increase and voltage stability decrease. Considering the Q-ϵ network that expresses the relation of voltage and reactive power, voltage sensitivity is equivalent to an element of the system impedance matrix. A fast calculation procedure for the change of the impedance matrix element due to bus connection changes has been proposed. It can be applied to the calculation of both the voltage sensitivities and the short circuit capacity. The results give information on the most appropriate separation points among the designated candidates, taking account of short circuit capacity problems and voltage stability considerations. The second method proposed uses a linear programming technique with variable line impedances and the objective function minimizing the short circuit capacity subject to bus voltage dip constraints. This gives information on the preferable separation points in large and complicated systems. Some practical procedures are also given. © 1998 Scripta Technica, Electr Eng Jpn, 124(3): 30–39, 1998