Application of the HHI in a probabilistic framework for a parametric approach to determine possible market power

This paper presents the utilization of the Hirschman-Herfindahl Index (HHI) within a probabilistic framework to arrive at a parametric trend indicating the possible market power in a given system. The traditional Optimal Power Flow (OPF) algorithm for obtaining the least-cost generation dispatch trend for the resources in a power system is modified to include a nonlinear constraint incorporating the HHI. The solution of the modified OPF yields the generation dispatch for each resource in the system, which is used to model the market share of each resource in the system. Market shares of each market participant are modeled as joint normal random variables with their specific statistical properties obtained by solving the modified OPF. The problem of market power acquisition or potential is then formulated as one involving a conditional joint cumulative distribution of the market shares of all participants in the market. The solution of this problem provides the potential of market power or market abuse at that instant for a given value of HHI subject to various network constraints incorporated in the nonlinear optimization problem. A sample 5-bus, 5-generator network from the PJM system is presented to demonstrate this approach applied to a practical power system network.