Jochen Cremer

Betül Mamudi, Jochen Stiasny, Jochen Cremer

Pseudo-measurements are the dominant source of uncertainty in distribution system state estimation (DSSE), yet their distributional assumptions are treated as fixed inputs by existing uncertainty quantification methods. This paper investigates whether the uncertainty bounds assumed by weighted least squares (WLS)-based DSSE are sensitive to these distributional assumptions, and whether this sensitivity is quantifiable using the Fisher Information Matrix (FIM). We propose a diagnostic framework that compares the true Cramér-Rao Bound (CRB) against the WLS-assumed CRB via a per-bus, per-scenario ratio, computed directly from the converged WLS solution. Pseudo-measurement distributions are varied across five types in 22 variants matched at equal spread to isolate shape effects from variance. Experiments on the CIGRE MV network across 100 operating scenarios yield three findings. First, heavy-tailed and skewed distributions show consistently that WLS systematically overstates its uncertainty bounds. Second, the degree of miscalibration varies across buses and operating scenarios, confirming that distributional sensitivity is not uniform. Third, the CRB ratio is structurally blind to mean-shift bias, exposing a fundamental limitation of variance-based uncertainty diagnostics. Together, these results confirm the hypothesis and show that the choice of pseudo-measurement distribution directly distorts the confidence limits under WLS-based assumptions, which must be explicitly accounted for in any uncertainty-aware DSSE method.

Jochen Stiasny, Jochen Cremer

The energy transition challenges operational tasks based on simulations and optimisation. These computations need to be fast and flexible as the grid is ever-expanding, and renewables' uncertainty requires a flexible operational environment. Learned approximations, proxies or surrogates -- we refer to them as Neural Solvers -- excel in terms of evaluation speed, but are inflexible with respect to adjusting to changing tasks. Hence, neural solvers are usually applicable to highly specific tasks, which limits their usefulness in practice; a widely reusable, foundational neural solver is required. Therefore, this work proposes the Residual Power Flow (RPF) formulation. RPF formulates residual functions based on Kirchhoff's laws to quantify the infeasibility of an operating condition. The minimisation of the residuals determines the voltage solution; an additional slack variable is needed to achieve AC-feasibility. RPF forms a natural, foundational subtask of tasks subject to power flow constraints. We propose to learn RPF with neural solvers to exploit their speed. Furthermore, RPF improves learning performance compared to common power flow formulations. To solve operational tasks, we integrate the neural solver in a Predict-then-Optimise (PO) approach to combine speed and flexibility. The case study investigates the IEEE 9-bus system and three tasks (AC Optimal Power Flow (OPF), power-flow and quasi-steady state power flow) solved by PO. The results demonstrate the accuracy and flexibility of learning with RPF.