Distributionally robust planning for integrated energy systems incorporating electric-thermal demand response

Demand response (DR) can achieve the optimal planning of integrated energy systems (IESs) for improving the economic performance and sustainable development of IESs. However, the integration of renewable energy imposes great uncertainties on IESs planning. In this context, electric-thermal DR is implemented to maximize the net annual profit during the planning period of electric-thermal IES. For avoiding the new electric load peak, electric price-based DR is modified by integrating the peak-valley difference constraint and cost. Meanwhile, the inertia of thermal loads measured by the predicted mean vote (PMV) is considered as the thermal DR measure. In order to deal with uncertainties of wind power, distributionally robust optimization (DRO) method is developed. Especially, the first- and second-moment uncertainties of wind power are considered in the uncertainty set. Further, based on the conditional value at risk (CVaR) and duality theories, the DRO planning model is reformulated to a tractable second order conic programming problem. Finally, the whole planning model is solved by the CPLEX solver. Case studies and comparative analysis are performed based on a representative test system. Numerical results show that the proposed model is effective in improving the net annual profit and solution robustness, and it significantly outperforms other methods.