A max–min–max robust optimization model for multi-carrier energy systems integrated with power to gas storage system

The volatile nature of the electricity market prices and renewable resources imposes remarkable challenges for multi-energy systems operators to make the appropriate decisions. Therefore, this paper offers a linear max–min–max robust optimization-based decision-making tool that incorporates both uncertainties of the electricity market price and the wind generation. Besides interaction with the electricity market, the EH purchases natural gas to feed the combined heat and power (CHP) and boiler units and supply gas demands. An electrical storage system is also used to smooth the unfavorable volatility nature of the electricity market price. Besides, an uncertainty budget model is proposed to consider both negative and positive deviation of electricity market prices, which gives the capability to increase the robustness of the system against the error of forecasting uncertainty sources. The nonlinearities arisen from the model are linearized using effective approaches and the resulted linear mathematical model is solved by GAMS. Moreover, the power to gas (P2G) storage system is integrated with the EH in order to create a link between the electrical and natural gas networks by converting the electricity to hydrogen and then to natural gas. Simulation results demonstrate that using P2G saves 6.9% in gas purchase cost and 2.13% in total cost.