Comparison of transmission pricing models

In this paper we make a comparison of three transmission pricing models: the Wangensteen model, the optimal power flow model and the Hogan model. The similarities among the models are that all can be used in locational pricing systems. In these systems the prices are calculated as the marginal cost that in turn equals the marginal benefit to load. In the Wangensteen model and the original optimal power flow model, the locational prices are equal to the Lagrange multipliers associated with the power flow equations. On the contrary, Hogan’s model and the modified optimal power flow model express the locational prices as equal to the reference bus (node) price, the marginal costs of losses, and the marginal costs of congestion. The Wangensteen model is used for educational purposes and considers elastic load. The optimal power flow model has been widely used in electrical engineering and dispatch of power systems. Load is assumed to be inelastic. Hogan’s model is an economist’s version of the optimal power flow model and considers elastic load. It also gives an expression for the locational prices in terms of an equilibrium equation.