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

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

Using EPECs to model bilevel games in restructured electricity markets with locational prices

CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal prices. Each player faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. This gives an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for existence of pure strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e. congestion, on existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We model the latter via complementarity problems, CPs. Finally, we present numerical examples of methods that attempt to find local Nash or Nash stationary equilibria of randomly generated electricity market games. The CP solver PATH is found to be rather effective in this context

Electricity System Expansion Studies to Consider Uncertainties and Interactions in Restructured Markets

This dissertation concerns power system expansion planning under different market mechanisms. The thesis follows a three paper format, in which each paper emphasizes a different perspective. The first paper investigates the impact of market uncertainties on a long term centralized generation expansion planning problem. The problem is modeled as a two-stage stochastic program with uncertain fuel prices and demands, which are represented as probabilistic scenario paths in a multi-period tree. Two measurements, expected cost (EC) and Conditional Value-at-Risk (CVaR), are used to minimize, respectively, the total expected cost among scenarios and the risk of incurring high costs in unfavorable scenarios. We sample paths from the scenario tree to reduce the problem scale and determine the sufficient number of scenarios by computing confidence intervals on the objective values. The second paper studies an integrated electricity supply system including generation, transmission and fuel transportation with a restructured wholesale electricity market. This integrated system expansion problem is modeled as a bi-level program in which a centralized system expansion decision is made in the upper level and the operational decisions of multiple market participants are made in the lower level. The difficulty of solving a bi-level programming problem to global optimality is discussed and three problem relaxations obtained by reformulation are explored. The third paper solves a more realistic market-based generation and transmission expansion problem. It focuses on interactions among a centralized transmission expansion decision and decentralized generation expansion decisions. It allows each generator to make its own strategic investment and operational decisions both in response to a transmission expansion decision and in anticipation of a market price settled by an Independent System Operator (ISO) market clearing problem. The model poses a complicated tri-level structure including an equilibrium problem with equilibrium constraints (EPEC) sub-problem. A hybrid iterative algorithm is proposed to solve the problem efficiently and reliably

A Comparison of Electricity Market Designs in Networks

In the real world two classes of market designs are implemented to trade electricity in transmission constrained networks. Analytical results show that in two node networks integrated market designs reduce the ability of electricity generators to exercise market power relative to separated market designs. In multi node networks countervailing effects make an analytic analysis difficult. We present a formulation of both market designs as an equilibrium problem with equilibrium constraints. We find that in a realistic network, prices are lower with the integrated market design.

A Bilevel Game-Theoretic Decision-Making Framework for Strategic Retailers in Both Local and Wholesale Electricity Markets

This paper proposes a bilevel game-theoretic model for multiple strategic retailers participating in both wholesale and local electricity markets while considering customers\u27 switching behaviors. At the upper level, each retailer maximizes its own profit by making optimal pricing decisions in the retail market and bidding decisions in the day-ahead wholesale (DAW) and local power exchange (LPE) markets. The interaction among multiple strategic retailers is formulated using the Bertrand competition model. For the lower level, there are three optimization problems. First, the welfare maximization problem is formulated for customers to model their switching behaviors among different retailers. Second, a market-clearing problem is formulated for the independent system operator (ISO) in the DAW market. Third, a novel LPE market is developed for retailers to facilitate their power balancing. In addition, the bilevel multi-leader multi-follower Stackelberg game forms an equilibrium problem with equilibrium constraints (EPEC) problem, which is solved by the diagonalization algorithm. Numerical results demonstrate the feasibility and effectiveness of the EPEC model and the importance of modeling customers\u27 switching behaviors. We corroborate that incentivizing customers\u27 switching behaviors and increasing the number of retailers facilitates retail competition, which results in reducing strategic retailers\u27 retail prices and profits. Moreover, the relationship between customers\u27 switching behaviors and welfare is reflected by a balance between the electricity purchasing cost (i.e., electricity price) and the electricity consumption level

A Bilevel Game-Theoretic Decision-Making Framework for Strategic Retailers in Both Local and Wholesale Electricity Markets

This paper proposes a bilevel game-theoretic model for multiple strategic retailers participating in both wholesale and local electricity markets while considering customers\u27 switching behaviors. At the upper level, each retailer maximizes its own profit by making optimal pricing decisions in the retail market and bidding decisions in the day-ahead wholesale (DAW) and local power exchange (LPE) markets. The interaction among multiple strategic retailers is formulated using the Bertrand competition model. For the lower level, there are three optimization problems. First, the welfare maximization problem is formulated for customers to model their switching behaviors among different retailers. Second, a market-clearing problem is formulated for the independent system operator (ISO) in the DAW market. Third, a novel LPE market is developed for retailers to facilitate their power balancing. In addition, the bilevel multi-leader multi-follower Stackelberg game forms an equilibrium problem with equilibrium constraints (EPEC) problem, which is solved by the diagonalization algorithm. Numerical results demonstrate the feasibility and effectiveness of the EPEC model and the importance of modeling customers\u27 switching behaviors. We corroborate that incentivizing customers\u27 switching behaviors and increasing the number of retailers facilitates retail competition, which results in reducing strategic retailers\u27 retail prices and profits. Moreover, the relationship between customers\u27 switching behaviors and welfare is reflected by a balance between the electricity purchasing cost (i.e., electricity price) and the electricity consumption level

Economic Engineering Modeling of Liberalized Electricity Markets: Approaches, Algorithms, and Applications in a European Context: Economic Engineering Modeling of Liberalized Electricity Markets: Approaches, Algorithms, and Applications in a European Context

This dissertation focuses on selected issues in regard to the mathematical modeling of electricity markets. In a first step the interrelations of electric power market modeling are highlighted a crossroad between operations research, applied economics, and engineering. In a second step the development of a large-scale continental European economic engineering model named ELMOD is described and the model is applied to the issue of wind integration. It is concluded that enabling the integration of low-carbon technologies appears feasible for wind energy. In a third step algorithmic work is carried out regarding a game theoretic model. Two approaches in order to solve a discretely-constrained mathematical program with equilibrium constraints using disjunctive constraints are presented. The first one reformulates the problem as a mixed-integer linear program and the second one applies the Benders decomposition technique. Selected numerical results are reported