• 대한전기학회논문지:전력기술부문A
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• 제54권2호
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• pp.97-106
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• 2005

This paper presents a method for evaluating the nash equilibrium of the Cournot model for N-Gencos in wholesale electricity market. In wholesale electricity market, the strategies of N-Gencos can be applied to the game model under the conditions, which the Gencos determine their strategies to maximize their benefit. Generally, the Lemke algorithm has known as the approach to evaluate the mixed nash equilibrium in the only two-player game model. In this paper, we have developed the necessary condition for obtaining the mixed nash equilibrium of N-player by using the Lemke algorithms. However, it is difficult to find the mixed nash equilibrium of two more players by using the analytic method since those have the nonlinear characteristics. To overcome the above problem, we have formulated the object function satisfied with the proposed necessary conditions for N-player nash equilibrium and applied the modified particle swarm optimization (PSO) method to obtain the equilibrium for N-player. To present the effectiveness the proposed necessary condition and the evaluation approach, this paper has shown the results of equilibrium of sample system and the cournot game model for 3-players.

• 전기학회논문지
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• 제61권2호
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• pp.187-193
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• 2012

Nash Equilibrium (NE) is as useful tool for investigating a participant's strategic generation quantity in a competitive electricity market. Cournot model may give a mixed strategy NE instead of a pure strategy when transmission constraints are considered. A mixed strategy is difficult to compute, complicated to understand conceptually, and hard to implement in an electricity market practically. This paper presents that a mixed strategy does not appear in Stackelberg leader-follower model even under a transmission congestion. A solution method is proposed for the leader-follower model under a nondifferentiable space of a strategy variable. Based on the pure strategy NE with a transmission line congested, the merit of leader-follower model is shown from a social welfare point of view.

• Journal of Electrical Engineering and Technology
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• 제9권1호
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• pp.90-97
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• 2014

Nash Cournot Equilibrium (NCE) has been widely used in a competitive electricity market to analyze generation firms' strategic production quantities. Congestion on a transmission network may lead to a mixed strategy NCE. Mixed strategy is complicated to understand, difficult to compute, and hard to implement in practical market. However, Stackelberg model based equilibrium does not have any mixed strategy, even under congestion in a transmission line. A guide to understanding mixed strategy equilibrium is given by analyzing a cycling phenomenon in the players' best choices. This paper connects the concept of leader-follower in Stackelberg model with relations between generation firms on both sides of the congested line. From the viewpoint of social welfare, the surplus analysis is presented for comparison between the NCE and the Stackelberg equilibrium (SE).

• Journal of Electrical Engineering and Technology
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• 제2권4호
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• pp.494-499
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• 2007

In this paper, we have investigated how transmission network constraints can be modeled in an electricity market equilibrium model. Under Cournot competition assumption, a game model is set up considering transmission line capacity constraints. Based on locational marginal pricing principle, market clearing is formulated as a total consumers# benefit maximization problem, and then converted to a conventional optimal power flow (OPF) formulation with a linearized transmission model. Using market clearing formulation, best response analysis is formulated and, finally, Nash equilibrium is formulated. In order for illustration, a numerical study for a four node system with two generating firms and two loads are presented.

• 전기학회논문지
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• 제56권7호
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• pp.1199-1204
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• 2007

In a cost based pool market, the generation capacity can be used as strategic bids by generation companies (Gencos) with the cost functions open to the market. Competition using strategic capacities is modeled by Cournot and Perfect Competiton (PC) model, and transformed into two by two payoff matrix game with Gencos' decision variables of Cournot and PC model. The payoff matrices vary when capacity payments are given to Gencos in accordance with their capacity bids. Nash Equilibrium (NE) in the matrices also moves with capacity price changes. In order to maximize social welfare of the market, NE should locate in a certain position of the payoff matrices, which corresponds to a PC NE. A concept of a critical capacity price is proposed and calculated in this paper that is defined as a minimum capacity price leading to PC NE. The critical capacity price is verified to work as a tool for suppressing a strategic capacity withholding in simulations of a test system.

• 한국지능시스템학회논문지
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• 제24권4호
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• pp.379-384
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• 2014

이 논문은 불완전 경쟁시장의 형태를 가지고 있는 전력시장과 탄소배출권시장에서 수익 극대화를 추구하는 발전회사의 전략적 입찰행위를 분석하는데 사용할 수 있는 쿠르노(Cournot) 기반의 전력시장 모델링 기법을 제안한다. 제안된 전력시장의 모델은 크게 두 부분으로 구성되어있다. 첫 번째 모델은 쿠르노 모델을 이용한 발전회사의 전략적 행위에 대한 모델이며, 두 번째 모델은 환경적 후생을 고려하여 전체 사회적 후생을 극대화하기 위한 시장운영자에 대한 모델이다. 두 모델의 결합을 통하여 배출권 거래를 고려한 전력시장의 모델이 구성되었으며, 이에 대한 내쉬균형점(Nash Equilibrium)을 계산하기 위하여 2단계 최적화 기법(Two-level optimization)을 사용하였다. 제안된 모델을 3개의 발전회사가 존재하는 샘플 전력시장에 적용하여 그 효용성을 검토하였다.

• Journal of Electrical Engineering and Technology
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• 제8권4호
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• pp.675-685
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• 2013

Generation capacities and transmission line constraints in a competitive electricity market make it troublesome to compute Nash Equilibrium (NE) for analyzing participants' strategic generation quantities. The NE can cause a mixed strategy NE rather than a pure strategy NE resulting in a more complicated computation of NE, especially in a multiplayer game. A two-level hierarchical optimization problem is used to model competition among multiple participants. There are difficulties in using a mathematical programming approach to solve a mixed strategy NE. This paper presents heuristics applied to the mathematical programming method for dealing with the constraints on generation capacities and transmission line flows. A new formulation based on the heuristics is provided with a set of linear and nonlinear equations, and an algorithm is suggested for using the heuristics and the newly-formulated equations.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 하계학술대회 논문집 A
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• pp.639-642
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• 2003

This paper presents a method for evaluating the mixed nash equilibria of the Cournot model for N-Gencos. in wholesale electricity market. In the wholesale electricity market, the strategies of N-Genco. can be applied to the game model under the conditions which the Gencos. determine their stratgies to maximize their benefit. Generally, the Lemke algorithm is evaluated the mixed nash equlibria in the two-player game model. However, the necessary condition for the mixed equlibria of N-player are modified as the necessary condition of N-1 player by analyzing the Lemke algorithms. Although reducing the necessary condition for N-player as the one of N-1 player, it is difficult to and the mixed nash equilibria participated two more players by using the mathmatical approaches since those have the nonlinear characteristics. To overcome the above problem, this paper presents the generalized necessary condition for N-player and proposed the object function to and the mixed nash equlibrium. Also, to evaluate the mixed equilibrium through the nonlinear objective function, the Particle Swarm Optimization (PSO) as one of the heuristic algorithm are proposed in this paper. To present the mixed equlibria for the strategy of N-Gencos. through the proposed necessry condition and the evaluation approach, this paper proposes the mixed equilibrium in the cournot game model for 3-players.

• 전기학회논문지
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• 제58권2호
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• pp.264-269
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• 2009

Marginal Loss Factor(MLF) is represented as the sensitivity of transmission loss, which is computed from the change of the generation at slack bus by the change of the load at the arbitrary bus. The MLF dependent on the selection of slack bus is one of the key factors affecting nodal pricing, Genco's profits, social welfare(SW) and Nash Equilibrium in a competitive electricity market. This paper addresses the methodology of slack bus selection by using Cournot model of Cost Based Pool market. Numerical results from sample cases show that the slack bus of MLF of the highest average is beneficial from the view points of SW.

• 대한전기학회논문지:전력기술부문A
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• 제51권8호
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• pp.403-408
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• 2002

As the electricity industry undergoes a process of fundamental restructuring, horizontal market power appears as a potential obstacle to a fully competitive wholesale electricity market. Market power is the ability profitably to maintain prices above competitive levels by restricting output below competitive levels. In models for imperfect competition under the consideration of the transmission constraints, the Nash equilibrium has the form of a mixed strategy. In this paper, the models for analyzing imperfect competition are compared using the solution of pure and mixed equilibria. The relation between market power and the capacity of a transmission line is investigated by imperfect competition analysis methods: Cournot, Bertrand, and Supply Curve model.