Linear Relaxation-Based Robust Interval State Estimation for Low Voltage Networks With Photovoltaic and Measurement Uncertainties

Distribution system state estimation (DSSE) poses significant challenges for low voltage (LV) networks due to the uncertainties of distributed generations and measurements. While interval state estimation (ISE) is developed to address them, the existing ISE methods face two significant challenges: i) the non-convex nature of nonlinear ISE can lead to convergence issues and lack guaranteed optimality, ii) they do not adequately address robustness against bad data. This paper proposes a linear relaxation-based robust ISE method for LV networks. First, a three-phase unbalanced nonlinear interval measurement model is formulated to minimize and maximize state variables subject to measurement uncertainty constraints. Then, the non-convex nonlinear ISE model is relaxed to a linear optimization problem by introducing the McCormick enclosures of the bilinear terms, enabling efficient solutions while ensuring approximate global optimality. Inspired by sparse state recovery optimization method, an$L_{1}$-norm is proposed to suppress sparse bad data in the measurements. The optimality-based bound tightening (OBBT) algorithm is also developed to determine near-global solutions. Numerical results on two realistic LV networks demonstrate the advantages of the proposed robust ISE method compared to the existing ISE approaches.