Event-Triggered Distribution System State Estimation: Sparse Kalman Filtering With Reinforced Coupling

A novel distribution system state estimation (DSSE) method is proposed for power distribution networks with low-observablity, where the measurements come from only a few distribution-level phasor measurement units (D-PMUs). The proposed DSSE method is event-triggered, which means the state variables are updated based on the information that is extracted from the events in the power distribution system. In this regard, the estimations of the state variables during the previous events are used as priori information to predict the state variables at the current event. Accordingly, a novel data-driven method based on elastic net regression analysis is proposed to learn the event-triggered state transition matrix. The DSSE problem is formulated as a generalized group Lasso problem, which is augmented based on the knowledge on the sparsity patterns of the state variables that are extracted from the analysis of the events. Here, in the absence of direct power measurements, we enhance our ability in sparse recovery by developing a new reinforced physics-based coupling method among the state variables, in which we add a novel set of linear differential power flow equations to the DSSE problem formulation in forms of virtual measurements. Finally, two different approaches are proposed to solve the formulated sparse event-triggered DSSE problem. The first approach is exact but computationally expensive, as it requires conducting a batch alternating direction method of multipliers (ADMM) analysis. The second approach is approximate, but it is much faster as it works based on a novel modified Kalman filter/smoother in the presence of
$\ell _{1}$
-norm.