Equilibria in the competitive retail electricity market considering uncertainty and risk management

• Presenting an equilibrium problem formulation for the retailer's decision-making.
• Modeling consumer's retail choice behavior with an econometric model.
• Managing the retailer's risk caused by rivals' strategy through CVaR.
• Approximating the nonlinear price-quota curve with a piecewise-linear function.
• Decomposing the nonlinear optimization problem using Lagrangian relaxation method.

In a medium term planning horizon, a retailer should determine its forward contracting and pool participating strategies as well as the selling price to be offered to the customers. Considering a competitive retail electricity market, the number of clients being supplied by any retailer is a function of the selling prices and some other characteristics of all the retailers. This paper presents an equilibrium problem formulation to model the retailer's medium term decision making problem considering the strategy of other retailers. Decision making of any single retailer is formulated as a risk constraint stochastic programming problem. Uncertainty of pool prices and clients' demands is modeled with scenario generation method and CVaR (conditional value at risk) is used as the risk measure. The resulting single retailer planning problem is a quadratic constrained programming problem which is solved using the Lagrangian relaxation method and the Nash equilibrium point of the competitive retailers is achieved by successive solving of this problem for all the retailers. The performance of the proposed method is demonstrated using a realistic case study of Texas electricity market.