Capacity Expansion in the Integrated Supply Network for an Electricity Market

IEEE Trans. Power Syst.

2014

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We develop a tri-level model of transmission and generation expansion planning in a deregulated power market environment. Due to long planning/construction lead times and concerns for network reliability, transmission expansion is considered in the top level as a centralized decision. In the second level, multiple decentralized GENCOs make their own capacity expansion decisions while anticipating a wholesale electricity market equilibrium in the third level. The collection of bi-level games in the lower two levels forms an equilibrium problem with equilibrium constraints (EPEC) that can be approached by either the diagonalization method (DM) or a complementarity problem (CP) reformulation. We propose a hybrid iterative solution algorithm that combines a CP reformulation of the tri-level problem and DM solutions of the EPEC sub-problem. KeywordsComplementarity problem, equilibrium problem with equilibrium constraints, generation expansion planning, mathematical program with equilibrium constraints, Nash equilibrium, transmission expansion planning Abstract-We develop a tri-level model of transmission andgeneration expansion planning in a deregulated power market environment. Due to long planning/construction lead times and concerns for network reliability, transmission expansion is considered in the top level as a centralized decision. In the second level, multiple decentralized GENCOs make their own capacity expansion decisions while anticipating a wholesale electricity market equilibrium in the third level. The collection of bi-level games in the lower two levels forms an equilibrium problem with equilibrium constraints (EPEC) that can be approached by either the diagonalization method (DM) or a complementarity problem (CP) reformulation. We propose a hybrid iterative solution algorithm that combines a CP reformulation of the tri-level problem and DM solutions of the EPEC sub-problem.

Section: B Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

A Tri-Level Model of Centralized Transmission and Decentralized Generation Expansion Planning for an Electricity Market—Part I

Jin

IEEE Trans. Power Syst.

2014

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“…For each single MPEC, we can reformulate the lower level problem by introducing the binary variables µz and and a big value M, and converting all the equilibrium constraints of the form 0 x y 0 into 0 x, 0 y, x Mµz, y M 1 µz as in our previous paper [13]. Upon this reformulation, the MPEC becomes a single level programming problem with mixed integer linear constraints and nonlinear objective function given by equation (2) in Part I.…”

Section: Nash Equilibrium (Ne) Solution Validationmentioning

confidence: 99%

A Tri-Level Model of Centralized Transmission and Decentralized Generation Expansion Planning for an Electricity Market—Part II

Jin¹,

IEEE Trans. Power Syst.

2014

Self Cite

We study a tri-level integrated transmission and generation expansion planning problem in a deregulated power market environment. The collection of bi-level sub-problems in the lower two levels is an equilibrium problem with equilibrium constraints (EPEC) that can be approached by either the diagonalization method (DM) or a complementarity problem (CP) reformulation. This paper is a continuation of its Part I, in which a hybrid iterative algorithm is proposed to solve the tri-level problem by iteratively applying the CP reformulation of the tri-level problem to propose solutions and evaluating them in the EPEC sub-problem by DM. It focuses on the numerical results obtained by the hybrid algorithm for a 6-bus system, a modified IEEE 30-bus system, and an IEEE 118-bus system. In the numerical instances, the (approximate) Nash equilibrium point for the sub-problem can be verified by examining local concavity. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/imse_pubs/7 1  Abstract-We study a tri-level integrated transmission and generation expansion planning problem in a deregulated power market environment. The collection of bi-level sub-problems in the lower two levels is an equilibrium problem with equilibrium constraints (EPEC) that can be approached by either the diagonalization method (DM) or a complementarity problem (CP) reformulation. This paper is a continuation of its Part I, in which a hybrid iterative algorithm is proposed to solve the trilevel problem by iteratively applying the CP reformulation of the tri-level problem to propose solutions and evaluating them in the EPEC sub-problem by DM. It focuses on the numerical results obtained by the hybrid algorithm for a 6 bus system, a modified IEEE 30 bus system and an IEEE 118 bus system. In the numerical instances, the (approximate) Nash equilibrium point for the sub-problem can be verified by examining local concavity.

“…Due to the progress towards deregulation and competition, the conventional GEP models in some studies have been replaced by decentralized ones. Several papers have compared the optimal investment in the centralized environment to that in the decentralized environment, and developed new models and algorithms by including game theory and uncertain factors [25][26][27][28]. However, even in a decentralized environment, a centralized planning process can provide targets.…”

Section: Relation To the Literaturementioning

confidence: 99%

“…However, even in a decentralized environment, a centralized planning process can provide targets. Once these targets are identified, incentives and regulations can be designed to encourage decentralized decision makers to approach one of them [28]. Because the restructuring procedure has not taken hold in all regions of the US and large utilities still develop their own expansion plans, we maintain focus on this paper on a cost-minimization formulation that involves several uncertain factors.…”

Section: Relation To the Literaturementioning

confidence: 99%

Scenario construction and reduction applied to stochastic power generation expansion planning

Feng

Computers & Operations Research

2013

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133

A challenging aspect of applying stochastic programming in a dynamic setting is to construct a set of discrete scenarios that well represents multivariate stochastic processes for uncertain parameters. Often this is done by generating a scenario tree using a statistical procedure and then reducing its size while maintaining its statistical properties. In this paper, we test a new scenario reduction heuristic in the context of long-term power generation expansion planning. We generate two different sets of scenarios for future electricity demands and fuel prices by statistical extrapolation of long-term historical trends. The cardinality of the first set is controlled by employing increasing length time periods in a tree structure while that of the second set is limited by its lattice structure with periods of equal length. Nevertheless, some method of scenario thinning is necessary to achieve manageable solution times. To mitigate the computational complexity of the widely-used forward selection heuristic for scenario reduction, we customize a new heuristic scenario reduction method named forward selection in wait-and-see clusters (FSWC) for this application. In this method, we first cluster the scenarios based on their wait-and-see solutions and then apply fast forward selection within clusters. Numerical results for a twenty year generation expansion planning case study indicate substantial computational savings to achieve similar solutions as those obtained by forward selection alone. Abstract:A challenging aspect of applying stochastic programming in a dynamic setting is to construct a set of discrete scenarios that well represents multivariate stochastic processes for uncertain parameters. Often this is done by generating a scenario tree using a statistical procedure and then reducing its size while maintaining its statistical properties. In this paper, we test a new scenario reduction heuristic in the context of long-term power generation expansion planning. We generate two different sets of scenarios for future electricity demands and fuel prices by statistical extrapolation of long-term historical trends. The cardinality of the first set is controlled by employing increasing length time periods in a tree structure while that of the second set is limited by its lattice structure with periods of equal length. Nevertheless, some method of scenario thinning is necessary to achieve manageable solution times. To mitigate the computational complexity of the widely-used forward selection heuristic for scenario reduction, we customize a new heuristic scenario reduction method named forward selection in wait-and-see clusters (FSWC) for this application. In this method, we first cluster the scenarios based on their wait-and-see solutions and then apply fast forward selection within clusters. Numerical results for a twenty year generation expansion planning case study indicate substantial computational savings to achieve similar solutions as those obtained by forward selection alone.