Selecting Critical Scenarios of DER Adoption in Distribution Grids Using Bayesian Optimization

TL;DR

This work tackles the challenge of identifying which DER adoption scenarios will most stress a distribution grid over a long planning horizon. It develops a multi-objective Bayesian Optimization framework using Gaussian Process surrogates with a separable categorical kernel to predict bus voltage violations and line overloads across many potential behind-the-meter PV adopters, mapping critical scenarios to the Pareto frontier. The main contributions are a statistically guaranteed, efficient search method and empirical validation on feeders with hundreds of buses, illustrating that critical scenarios are not simply those with extreme aggregate PV but depend on locational patterns. The approach yields large speedups over exhaustive search while providing planners with a compact, action-oriented set of scenarios for robust upgrade planning and prioritization of grid investments.

Abstract

We develop a new methodology to select scenarios of DER adoption most critical for distribution grids. Anticipating risks of future voltage and line flow violations due to additional PV adopters is central for utility investment planning but continues to rely on deterministic or ad hoc scenario selection. We propose a highly efficient search framework based on multi-objective Bayesian Optimization. We treat underlying grid stress metrics as computationally expensive black-box functions, approximated via Gaussian Process surrogates and design an acquisition function based on probability of scenarios being Pareto-critical across a collection of line- and bus-based violation objectives. Our approach provides a statistical guarantee and offers an order of magnitude speed-up relative to a conservative exhaustive search. Case studies on realistic feeders with 200-400 buses demonstrate the effectiveness and accuracy of our approach.

Figures (12)

• Figure 1: Feeder p4rhs8 with $248$ buses, $202$ lines and $159$ potential PV adopters, cf. Table \ref{['tab:feeder']}. Left: partition of buses into 12 bus objectives (different colors) via the Louvain community algorithm. Right: A representative critical scenario of PV adoption; circle size is proportional to installed PV capacity.
• Figure 2: Pareto frontier $\mathcal{P}(\mathcal{S}_{n^*})$ projected on two representative bus objectives $f_3$ and $f_8$. Each point represents the stress objective values $(f_3(\mathbf{x}), f_8(\mathbf{x}))$ of a scenario $\mathbf{x}$. The three green points on the staircase are the critical non-dominated scenarios.
• Figure 3: Progression of the Pareto frontier projected onto two representative bus objectives. Each point represents the objective values ($f_3(\mathbf{x})$, $f_8(\mathbf{x})$) of a scenario $\mathbf{x} \in \mathcal{S}_{n^\star}$. Evaluated scenarios $\mathbf{x}_n$ (and respective Pareto fronts $\mathcal{P}_n$) are color-coded in terms of the step $n$ of the BO algorithm. Non-evaluated scenarios are shown in gray.
• Figure 4: Initial Pareto front $\mathcal{P}(\mathcal{S}_0)$ (dashed gray), Pareto front $\mathcal{P}(\mathcal{S}_{n})$ at step n = 55 (orange) and true front $\mathcal{P}(\mathcal{S}_{n^\star})$ (green) across two representative objectives $f_3(\mathbf{x})$, $f_8(\mathbf{x})$. We also plot 30 simulated fronts $\widetilde{\mathcal{P}}_i$ (solid gray curves) obtained by sampling the terminal GP across $M=500$ non-evaluated scenarios.
• Figure 5: Evolution of statistical stopping criteria $\tau_n^b$ for buses and $\tau_n^l$ for lines as a function of number of evaluations $n$. The overall stopping criterion $\tau_n = \max(\tau^b_n, \tau^l_n)$ is triggered at the threshold $\bar{\tau}=0.1$.