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

Opportunities for Price Manipulation by Aggregators in Electricity Markets

Aggregators are playing an increasingly crucial role in the integration of renewable generation in power systems. However, the intermittent nature of renewable generation makes market interactions of aggregators difficult to monitor and regulate, raising concerns about potential market manipulation by aggregators. In this paper, we study this issue by quantifying the profit an aggregator can obtain through strategic curtailment of generation in an electricity market. We show that, while the problem of maximizing the benefit from curtailment is hard in general, efficient algorithms exist when the topology of the network is radial (acyclic). Further, we highlight that significant increases in profit are possible via strategic curtailment in practical settings

Network-constrained models of liberalized electricity markets: the devil is in the details

Numerical models for electricity markets are frequently used to inform and support decisions. How robust are the results? Three research groups used the same, realistic data set for generators, demand and transmission network as input for their numerical models. The results coincide when predicting competitive market results. In the strategic case in which large generators can exercise market power, the predicted prices differed significantly. The results are highly sensitive to assumptions about market design, timing of the market and assumptions about constraints on the rationality of generators. Given the same assumptions the results coincide. We provide a checklist for users to understand the implications of different modelling assumptions

Network-constrained models of liberalized electricity markets: the devil is in the details

Numerical models for electricity markets are frequently used to inform and support decisions. How robust are the results? Three research groups used the same, realistic data set for generators, demand and transmission network as input for their numerical models. The results coincide when predicting competitive market results. In the strategic case in which large generators can exercise market power, the predicted prices differed significantly. The results are highly sensitive to assumptions about market design, timing of the market and assumptions about constraints on the rationality of generators. Given the same assumptions the results coincide. We provide a checklist for users to understand the implications of different modelling assumptions.Market power, Electricity, Networks, Numeric models, Model comparison

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

Impacts of Strategic Behavior and Consumer Requirements on the Promise of Demand Response

Demand response (DR) is envisaged to be of significance for enhancing the flexibility of power systems. The distributed nature of demand-side resources necessitates the need of an aggregator to represent the flexible demand in the electricity market. This paper presents a bilevel optimization model considering the optimal operation of a strategic aggregator in a day-ahead electricity market. Additionally, consumers’ requirements in terms of comfort satisfaction and cost reduction are considered by integrating detailed demand models and retail contract constraints. The results on the considered test system reveal that centralized optimization models would tend to over-estimate the capabilities of DR in an electricity market with strategic participants. Also, the flexibility value of DR for the power system and the profitability of the aggregator are significantly dependent on the retail contracts between the aggregator and the consumers, highlighting the need for careful contract design

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