Extended matrix modeling of integrated energy systems considering network dynamic characteristics and source–load uncertainty

A refined and efficient modeling approach is indispensable for enhancing the timeliness of scheduling strategies for the integrated energy system (IES). Non-flowing variables such as pressure and temperature introduced by energy devices, however, worsen the complexity while improving the completeness for models. Nonlinear and uncertain variables associated with network dynamic characteristics and source–load uncertainty in the systems seriously postpone the modeling processes. An extended matrix modeling approach is proposed in this paper to tackle such issues. New nodes, branches, definition rules and topological matrices are first presented to create an extended matrix model that is compatible with both flowing and non-flowing variables. To boost the modeling efficiency, adaptive piecewise linearization (APL) with extended matrix form and modified Taylor expansion are applied to approximate various nonlinear characteristics. The convex approximation based on Kullback–Leibler (KL) divergence and the strong duality theory characterized by Wasserstein distance are adopted to deal with uncertain variables, which adapt to combine with the above matrix model. A linearized matrix modeling framework applicable to highly automated by computers is thus established. The distributionally robust optimization (DRO) scheduling strategy is verified in a standard test system with the proposed modeling. The effect of dynamic characteristics and uncertain factors on the strategy is discussed. The results show that the extended matrix model simulates the response for real physical systems more effectively, which exhibits the better performances in modeling, objectives and scheduling strategies.