Primal-Dual Decomposed State Estimation for Multi-Energy Systems Leveraging Variational Bayesian Approximation

This paper proposes a new methodology for the tracking state estimation (SE) of multi-energy systems containing electricity, gas and heat networks. The three networks are modelled via quasi steady-state models, whereby different gas components form the gas mixture. The SE Kalman filter framework is extended to allow the application of the primal-dual decomposed constrained optimization. The primal problem is further decomposed into three sub-problems, corresponding to electricity, gas and heat networks. It is also proposed to solve the dual problem with a Newton - type second-order method. Efficient detection of bad data, without further aggravation of the measurement redundancy, is achieved by incorporating the Variational Bayesian approximation into the decomposed Kalman filter SE and developing the computation algorithms. The proposed methodology is tested on the developed regional and national multi-energy systems and its advantages are highlighted.