• Journal of Electrical Engineering and Technology
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• v.3 no.4
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• pp.509-513
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• 2008

In this paper, we investigate how generators' ramp-rate constraints may influence their equilibrium strategy formulation. In the market model proposed in this study, the generators' ramp-rate constraints are explicitly represented. In order to fully characterize the inter-temporal nature of the ramp-rate constraints, a dynamic game model is presented. The subgame perfect Nash equilibrium is adopted as the solution of the game and the backward induction procedure for the solution of the game is designed in this paper. The inter-temporal nature of the ramp-rate constraints results in the Markov property of the game, and we have found that the Markov property of the game significantly simplifies the subgame perfect Nash equilibrium characterization. Finally, a simple electricity market numerical illustration is presented for the successful application of the approach proposed.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.3
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• pp.509-516
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• 2011

This paper studies a novel method to find the profit-maximizing Nash Equilibriums in allocating generation quantities with consideration of ramp-rates under competitive market environment. Each GenCo in a market participates in a game to maximize its profit through competitions and play a game with bidding strategies. In order to find the Nash equilibriums it is necessary to search the feasible combinations of GenCos' strategies which satisfy every participant's profit and no one wants various constraints. During the procedure to find Nash equilibriums, the payoff matrix can be simplified as eliminating the dominated strategies. in each time interval. Because of the ramp-rate, generator's physically or technically limits to increase or decrease outputs in its range, it can restrict the number of bidding strategies of each generator at the next stage. So in this paper, we found the Nash Equilibriums for multi-stage generation allocation game considering the ramp-rate limits of generators. In the case studies, we analyzed the generation allocation game for a 12-hour multi-stage and compared it with the results of dynamic economic dispatch. Both of the two cases were considered generator's ramp-rate effects.

• Journal of Electrical Engineering and Technology
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• v.10 no.4
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• pp.1441-1452
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• 2015

This paper proposes a new Hybrid Particle Swarm Optimization (HPSO) method that integrates the Evolutionary Programming (EP) and Particle Swarm Optimization (PSO) techniques. The proposed method is applied to solve Economic Dispatch(ED) problems considering prohibited operating zones, ramp rate limits, capacity limits and power balance constraints. In the proposed HPSO method, the best features of both EP and PSO are exploited, and it is capable of finding the most optimal solution for the non-linear optimization problems. For validating the proposed method, it has been tested on the standard three, six, fifteen and twenty unit test systems. The numerical results show that the proposed HPSO method is well suitable for solving non-linear economic dispatch problems, and it outperforms the EP, PSO and other modern metaheuristic optimization methods reported in the recent literatures.

• Proceedings of the KIEE Conference
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• 2009.07a
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• pp.569_570
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• 2009

This paper presents a methodology to find the profit maximized Nash Equilibriums of each generator(or GenCo), which considers the Ramp-rate of each generator under a competitive market environment. The ramp-rate of a generator is one of the physical or technical constraints of a generator and means the ability to increase or decrease the output instantaneously. In this paper, we found several Nash Equilibriums of the generation allocation problem through Dynamic Programming in a competitive market. Individual generators participate in a game to maximize its profit through competitions and play a game with bidding strategies of its generation quantities in a spot market.

• Journal of Electrical Engineering and Technology
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• v.3 no.3
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• pp.320-330
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• 2008

This paper presents an improved dynamic programming (IDP) approach to solve the economic power dispatch problem including transmission losses in power systems. A detailed mathematical derivation of recursive dynamic programming approach for the economic power dispatch problem with transmission losses is presented. The transmission losses are augmented with the objective function using price factor. The generalized expression for optimal scheduling of thermal generating units derived in this article can be implemented for the solution of the economic power dispatch problem of a large-scale system. Six-unit, fifteen-unit, and forty-unit sample systems with non-linear characteristics of the generator, such as ramp-rate limits and prohibited operating zones are considered to illustrate the effectiveness of the proposed method. The proposed method results have been compared with the results of genetic algorithm and particle swarm optimization methods reported in the literature. Test results show that the proposed IDP approach can obtain a higher quality solution with better performance.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.4
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• pp.467-473
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• 1996

This Paper presents a new algorithm to solve Dynamic Economic Dispatch problem. Proposed algorithm is composed of two computational modules; one is dispatch, the other adjusting module. In the dispatch module based on the traditional Static Economic Dispatch method, the power dispatch of each unit is calculated. And in case the results of dispatch module violate ramp rate constraints, Lagrange multipliers are adjusted in the adjusting module. Tests and computer results on test systems are given to show the efficiency of the proposed algorithm. (author). 11 refs., 6 figs., 4 tabs.

• Journal of Electrical Engineering and Technology
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• v.9 no.1
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• pp.15-26
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• 2014

This paper proposes a Modified Particle Swarm Optimization with Time Varying Acceleration Coefficients (MPSO-TVAC) for solving economic load dispatch (ELD) problem. Due to prohibited operating zones (POZ) and ramp rate limits of the practical generators, the ELD problems become nonlinear and nonconvex optimization problem. Furthermore, the ELD problem may be more complicated if transmission losses are considered. Particle swarm optimization (PSO) is one of the famous heuristic methods for solving nonconvex problems. However, this method may suffer to trap at local minima especially for multimodal problem. To improve the solution quality and robustness of PSO algorithm, a new best neighbour particle called 'rbest' is proposed. The rbest provides extra information for each particle that is randomly selected from other best particles in order to diversify the movement of particle and avoid premature convergence. The effectiveness of MPSO-TVAC algorithm is tested on different power systems with POZ, ramp-rate limits and transmission loss constraints. To validate the performances of the proposed algorithm, comparative studies have been carried out in terms of convergence characteristic, solution quality, computation time and robustness. Simulation results found that the proposed MPSO-TVAC algorithm has good solution quality and more robust than other methods reported in previous work.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.25 no.10
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• pp.28-37
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• 2011

Though Korea has introduced CBP(Cost Based pool) power trading system since 2001, long-term Generation system planning has been executed by government for Cost minimization every 2 years. Until currently the model which is used for Generation system planning and best-mix only considers cost minimization and total yearly or quarterly electricity demand every year. In a view point of one day power supply operation, technical characteristics, like the ramp up/down rate of total generation system, minimum up/down time and GFRQ(Governor Free Response Quantity), are very important. this paper analyzes Optimal Fuel-Mix for 2022 Korea generation system satisfying these constraints of each fuel type and considering pump storage plants, construction cost and $CO_2$ emission charge Using MILP(Mixed Integer Linear Programming) method. Also the sensitivity analysis which follows in future power industry environmental change accomplished.

• Journal of Electrical Engineering and Technology
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• v.3 no.1
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• pp.52-59
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• 2008

This paper describes the secant method for solving the economic dispatch (ED) problem with generator constraints and transmission losses. The ED problem is an important optimization problem in the economic operation of a power system. The proposed algorithm involves selection of minimum and maximum incremental costs (lambda values) and then the evaluation of optimal lambda at required power demand is done by secant method. The proposed algorithm has been tested on a power system having 6, 15, and 40 generating units. Studies have been made on the proposed method to solve the ED problem by taking 120 and 200 units with generator constraints. Simulation results of the proposed approach were compared in terms of solution quality, convergence characteristics, and computation efficiency with conventional methods such as lambda iterative method, heuristic methods such as genetic algorithm, and meta-heuristic methods like particle swarm optimization. It is observed from different case studies that the proposed method provides qualitative solutions with less computational time compared to various methods available in the literature.

• Journal of Electrical Engineering and Technology
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• v.8 no.5
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• pp.959-968
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• 2013

This paper presents a new approach with artificial immune system algorithm to solve the profit based unit commitment problem. The objective of this work is to find the optimal generation scheduling and to maximize the profit of generation companies (Gencos) when subjected to various constraints such as power balance, spinning reserve, minimum up/down time and ramp rate limits. The proposed hybrid method is developed through adaptive search which is inspired from artificial immune system and genetic algorithm to carry out profit maximization of generation companies. The effectiveness of the proposed approach has been tested for different Gencos consists of 3, 10 and 36 generating units and the results are compared with the existing methods.