Continuous-Time Optimization of Integrated Networks of Electricity and District Heating Under Wind Power Uncertainty

The integrated operation of the electricity and district heating systems (EDHS) attracted lots of attention in recent years due to considerable impacts on the power system’s flexibility. The time intervals and mathematical methods used in the optimization procedure are essential, especially when flexible operation in the presence of intermittent renewable resources is an objective because of the sub-hourly dynamics. Due to the intrinsic deficiencies of the traditional discrete-time hourly models in handling the sub-hourly variation of the load and renewable generation, in this paper, a new continuous-time optimization model is proposed to model the look-ahead operation of EDHS. The proposed continuous-time model is approximated by the linear spline-based trajectories and represented by the cubic splines of Bernstein function space to capture EDHS’s sub-hourly load and wind generation fluctuations. The EDHS of Barry Island is employed to investigate the proposed model and obtain results compared with the discrete-time procedure. Also, to measure the impact of uncertainties on both the continuous-time and discrete-time models, the information gap decision theory (IGDT) is utilized. The examination results illustrate that the proposed continuous-time model brings a saving of 0.91% in the costs when compared with the discrete-time model on a small test system. In addition, the results of the IGDT technique show more opportunities by wind increasing and fewer threats by wind reduction using the proposed continuous-time optimization problem compared to the discrete-time model.