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This paper proposes a two-level framework for the operation of a competitive market for reactive power ancillary services. It is argued that the first-level, i.e., reactive power procurement, be on a seasonal basis while the second-level, i.e., reactive power dispatch, be close to real-time operation. To this effect, a reactive power procurement market model is proposed here taking into consideration system security aspects. This procurement procedure is based on a two-step optimization model. First, the marginal benefits of reactive power supply from each provider with respect to system security are obtained by solving an optimal power flow (OPF) that maximizes system loadability subject to transmission security constraints imposed by voltage limits, thermal limits, and stability limits. Second, the selected set of generators is then determined by solving an OPF-based auction to maximize a societal advantage function comprising generators' offers and their corresponding marginal benefits with respect to system security, considering all transmission system constraints. The proposed procedure yields the selected set of generators and zonal price components, which would form the basis for seasonal contracts between the system operator and the selected reactive power service providers. Index Terms--Ancillary services, electricity markets, pricing, reactive power management, system operation, system security.

An affine supply function equilibrium (SFE) approach is used to discuss voltage constraints and reactive power issues in the modeling of strategic behavior. Generation companies (GenCos) can choose their bid parameters with no restrictions for both energy and spinning reserves. The strategic behavior of generators is formulated as a multi-leader single-follower game. Each GenCo is modeled as a leader, while the central market operator running a cost minimization process is the sole follower. An ac model is considered to represent the transmission system. A three-node system is used to illustrate several cases, and study the implications of the incentives of the strategic players to exploit active and reactive power, and spinning reserves in order to maximize profits. Results for a 14-node system are also presented. Index Terms--Ac system, complementarity, market power, mathematical problem with complementarity constraints, Nash equilibrium, oligopoly, spinning reserves, supply function equilibrium.

In this paper, oligopolistic competition in a centralized power market is characterized by a multi-leader single-follower game, and formulated as a nonlinear programming (NLP) problem. An ac network is used to represent the transmission system and is modeled using rectangular coordinates. The follower is composed of a set of competitive suppliers, demands, and the system operator, while the leaders are the dominant suppliers. The ac approach allows one to capture the strategic behavior of suppliers regarding not only active but also reactive power. In addition, the impact of voltage and apparent power flow constraints can be analyzed. Different case studies are presented using a three-node system to highlight the features of the formulation. Results on a 14-node system are also presented. Index Terms--Competition, complementarity, Cournot, mathematical problem with equilibrium constraints (MPEC), Nash equilibrium, oligopoly.