Electricity market equilibrium analysis based on nonlinear interior point algorithm with complementarity constraints

This paper presents an interior point algorithm based on a.c. network model for determining the Nash supply function equilibrium (SFE) of bid-based electricity markets. The SFE problem is considered as a bi-level game. At the first level, the problem begins with the formulation of an optimal power flow (OPF) interior point-based algorithm to handle the independent system operator (ISO) problem for maximising social welfare. This algorithm is based on the OPF with a.c. network transmission model taking into account all the operating aspects such as the generation capacity limits, bus voltage limits, transmission line constraints, network losses and especially the effect of the reactive power. The resulting Karush-Kuhn-Tucker (KKT) conditions of the problem at the first level are then reformulated using nonlinear complementarity constraints and incorporated as equality constraints in the second-level formulation for maximising the individual profit for each strategic generating firm. By employing a special nonlinear complementarity function, the complementarity constraints are then transformed into nonlinear algebraic expressions, thus the KKT conditions of the resulting combined problem can be derived. The final problem is then solved iteratively based on the solution techniques of the interior point algorithm. Numerical examples of a three-bus system, the IEEE 14-bus system and the IEEE 30-bus system, show that the algorithm can successfully determine the electricity market equilibrium with the a.c. network model.     

Electricity market equilibrium of nonlinear power systems with reactive power control

The impact of reactive power control on the electricity market equilibrium is investigated. The effects of limitations on the reactive power generation and absorption, and load power factor adjustments, are examined using a novel electricity market equilibrium model that solves large-scale nonlinear power systems with asymmetric strategic firms. The algorithm implemented employs the linear supply function theory for bid-based pool markets. AC power flow analysis is used to represent the electricity network, incorporating variable price-responsive active and reactive load demands. The significance of the reactive power modeling in the electricity market equilibrium is demonstrated using the IEEE 14-bus and IEEE 118-bus systems. It is shown that variations on the reactive power in the system result in different market outcomes, as incentives are given to the strategic generating firms to alter their bidding strategies. The convergence characteristics of the IEEE 118-bus system are graphically presented and discussed to demonstrate the superior computational performance of the proposed algorithm in producing results under strict binding constraints and heavy transmission congestion conditions.