The optimal hourly electricity price considering wind electricity uncertainty based on conditional value at risk

Wind generation fluctuation results in the electricity supply uncertainty of the company in electricity market. And this uncertainty has an important impact on hourly electricity price. In our paper, we use game models to optimize hourly price for different risk appetites' companies considering the uncertainty. For the risk-neutral company, we solve the optimal electricity price by maximizing the expected profit. For the risk-averse or risk-preferring company, we consider wind electricity generation as a Weibull distribution and obtain the optimal electricity price based on conditional value at risk. In numerical examples, we find that the risk-preferring company sets the highest electricity price, demonstrating the importance of modeling risk appetites of the company in electricity price. And the results indicate that a risk-averse (risk-preferring) company will set a higher (lower) electricity price for a larger risk confidence level. Besides, we find that the company will lower electricity price with the decrement of users' price elasticity. Furthermore, our finding shows that the profit of the company increases with the wind penetration due to the decreased cost, which supports the observed and investigated results in electricity market.