Inclusion of price dependent load models in the Optimal Power Flow

In this paper we investigate the inclusion of price-dependent loads into the traditional Optimal Power Flow algorithm. The development of the model will be based on the solution of the OPF using an objective function for maximization of social welfare. The paper will show that a traditional OPF algorithm that minimizes supplier costs can be modified to solve the social welfare maximization problem by including price-dependent load models. This modification to the standard OPF is intuitive and very simple. We will show this modified OPF formulation facilitates simulation of a spot market for electricity. While the development in this paper will account for both real and reactive power supply and consumption, the examples in the paper will concentrate on real power markets. The algorithm will be demonstrated on a range of practical examples, including several small systems, and on a system with over a hundred buses. The impact of such price dependent loads on congestion and bus marginal costs is highlighted.