Risk analysis of bidding strategies in an electricity pay as bid auction: A new theorem

Considering the uncertainties in the power market, the bidding problem has an important role for the power supplier to reach his goals, and using risk management methods to protect against the market risk is unavoidable. Thus, in this paper, the bidding decision making problem is formulated from a supplier’s viewpoint in a spot market. The spot market works based on a pay as bid auction or a discriminatory price auction. The market clearing price (MCP) is uncertain, and we consider a probabilistic model for it. Regarding the literature of the bidding problem and forecasting methods of MCP, a normal probability density function, pdf (N(μm, σm)), is a proper distribution for the MCP. The statistical parameters of MCP vary on different times (peak and off peak), and considering the concept of supplier risk, their effects on the supplier expected benefit and expected sell from selling energy will be discussed analytically. An important section of this research work concerns the optimal bidding strategy when μm and σm vary in different conditions of the power market. Thus, the coefficient of variation index (CV), as a proper measure, mathematically defined as σm divided by μm, is introduced to measure the market risk index. In this paper, the CV index is used to analyze and manage the supplier risk and introduce the optimal strategy. Then, for a constant amount of the CV as a theorem, it is proved that: (1) the maximum of the expected sell occurs at a constant level of the supplier risk and (2) the optimal bid price linearly depends on the standard deviation of the MCP. This theorem is generalized for the case that the expected value of the supplier benefit is considered as an objective function in the bidding process. Some numerical examples are presented, and application of the proposed theorem is discussed.