Probabilistic Optimal Distribution Grid Design Considering Demand Correlations

Abstract

The rising adoption of electric vehicles, heat pumps and rooftop photovoltaics is reshaping residential electricity consumption, exposing low-voltage grids to new load patterns that are often more variable and statistically dependent across neighboring households. Conventional network planning, however, typically relies on a single deterministic peak estimate and ignores these dependencies, resulting in capacity margins that are either wasteful or insufficient depending on how strongly consumer loads happen to be correlated. This thesis presents an optimization framework for low-voltage grid planning that treats consumer demand as a jointly distributed random vector, explicitly capturing both the variability of individual households and the correlation structure between them through a multivariate normal distribution. Three planning problems are cast as Mixed-Integer Second-Order Cone Programs on this basis: assigning consumers to transformers without regard to network topology, extending this assignment to respect the physical switching structure of the grid via a flow-based connectivity formulation, and replacing the estimated peak load objective with a convex approximation of long-term transformer aging. Model parameters are estimated from a Belgian residential smart-meter dataset spanning 2400 households in eight consumption categories. The approach is tested on a small, analytically verifiable configuration, a network of a more realistic size, and a Monte Carlo simulation covering five chain topologies with 1000 randomly sampled household combinations each. Across these experiments, incorporating load correlations is found to shift the optimal transformer assignment in ways that a mean-only or correlation-blind model would miss, with the effect being most pronounced for transformer aging. Here, the proposed model tracks the assignment obtained from real measured load data substantially more closely than the tested benchmark methods.