Generation bidding game with flexible demand

Game theoretic approaches to the study of electricity markets have been explored for decades [2], [7], [10]. Recently problems associated with variations of the optimal power flow problem with static (inelastic) demand for an electrical power grid [5], [21], [22], have been considered by several authors, e.g., [15], [17]. Indeed, demand elasticity for electricity is motivated by the onset of potentially enormous load from plugin electric and hybrid-electric vehicles, see e.g., [1], [14] and the references therein. We consider a noncooperative, iterated Bertrand-type game played by the generators based on information from the grid (independent system operator (ISO)). That is, the grid is assumed to provide sufficient information so that the generators can modify their prices to improve upon their net utility. The game is a “discriminatory” sealed-bid auction in that the generators earn at the price they bid but in a quantity determined by the ISO [7], [10]. To simplify matters herein, we do not consider strategic bidding by the generators wherein they may infer demand and/or the bidding strategies of their competitors via a probabilistic model, nor multipart bidding to account for start-up/ramp-up costs, secure contracts involving minimum and maximum supply per generator, and the like1, nor peak-power consumption penalties [8], [11]. Also, we assume a continuously differentiable and convex cost of supply [2], quadratic in particular. Also, rather than demand-side bidding, we assume a simple “passive” linear demand response based on average cost of supply, i.e., the ISO ensures that its customers pay the same rates irrespective of their location or demand volume. Here we attempt to understand demand-response on the wholesale (generation-level) market2. As such, we are focusing here on how a demand-response consumers (load) can influence the wholesale generation market [4], [20]. In summary, in this paper, we are interested in studying the optimum power-flow (economic dispatch) in the presence of flexible elastic demand for a mean clearing-price based