Distributionally robust chance-constrained energy management of an integrated retailer in the multi-energy market

In this paper, we study an energy management problem of an integrated retailer in multi-energy systems considering both renewable generation and electricity demand uncertainties. The retailer equipped with an energy hub seeks to maximize its profit by managing multiple types of energy, e.g., electricity, natural gas, heat, cold, etc. We model the energy management problem as a stochastic optimization problem with a risk sensitive cost. In the proposed model, a chance constraint relating the supply and demand balance is introduced to capture the generation and demand uncertainties simultaneously. In addition, risk of the retailer's energy management profit is incorporated using the Markowitz framework to trade off the risk and the expected profit due to uncertainties. To tackle the intractable chance constraint, we first relax the problem to a risk-only minimization problem with guaranteed expected return. The analytical solution is obtained using the Karush- Kuhn-Tucker optimality conditions. A distributionally robust optimization method is further adopted to avoid dependencies on probability distribution information of uncertainties, and convert the original problem into a tractable second-order conic programming problem. Simulation results show that our method can drastically shift electricity loads from peak hours to off-peak periods of the day thereby reducing the peak load demand. Moreover, it outperforms the state of the art methods in producing less conservative and more effective results for the energy management problem in multi-energy markets under uncertainties.