Hybrid Physics- and Data-Driven Dynamic State Estimation of Electricity-Heat Integrated Energy Systems

State estimation (SE) can provide real-time, reliable, and complete operating state of the systems, supporting the subsequent collaborative scheduling and safe operation with credible data. For the dynamic SE of electric-heat integrated energy systems (EH-IESs), a hybrid physics- and data-driven SE method is proposed in this article with the consideration of the transient operation characteristics of the district heating system (DHS) and the coupling relationship between the electric power system (EPS) and DHS. By integrating the physics-driven and data-driven methods, the linear SE model of DHSs is first established, which captures the transient transmission characteristics and parameter variation characteristics of heat in the pipeline and the topological structure characteristics of the system under the guidance of the first principles. To solve the dynamic SE problem of DHSs, a breadth-first search-based Kalman filter algorithm is developed, which is combined with the weighted least squares-based static SE of EPSs to realize the real-time SE of EH-IESs. Numerical results of three systems with different scales in MATLAB show that the proposed method can accurately and efficiently estimate the state of EH-IESs, and the robustness of the SE of EH-IESs is effectively enhanced by combining the SE of the EPS and DHS.