Dynamic Interval State Estimation for Integrated Electricity and Heating Systems

The role of a state estimator within integrated electricity and heating systems (IEHSs) is to infer unknown states from available measurements to enable monitoring and control functions. However, the classical estimation methods based on point measurements struggle to effectively capture diverse uncertainties originating from renewable generation and multi-energy loads. Besides, the complex thermal dynamics and the multi-timescale nature of IEHSs also impose significant challenges on estimation accuracy and computational efficiency. To this end, this paper proposes a novel dynamic interval state estimation (DISE) framework, which quantifies both measurement inputs and state outputs as intervals to characterize the uncertainty impacts in IEHSs. The proposed DISE method utilizes the iterative interval arithmetic, which is prone to overestimating the true state ranges, known as the conservatism issue. Therefore, the DISE method is further enhanced by the model reformulation to strategically address this issue. Furthermore, a multi-rate coordinated estimation (MRCE) scheme is developed, which estimates state intervals of electric power and district heating systems in parallel and coordination at different time rates. The proposed MRCE algorithm significantly increases computing efficiency while accommodating distinct timescales inherent in power and heating systems. Case studies based on test systems of different sizes demonstrate the effectiveness of the DISE method over benchmarks. The estimated intervals provide intuitive quantification of the state deviations induced by intricate uncertainties, paving the way toward resilient operation of IEHSs.