Counterfactual Explanations for Power System Optimisation

TL;DR

The paper tackles the explainability gap in power-system optimisation by introducing counterfactual explanations (CEs) that identify minimal input changes needed to move a solution into a region aligned with user expectations. It formulates CE generation as a bilevel optimization problem and develops methods for linear (KKT-based) and MILP lower levels, including decomposition (DECOMP) and data-driven cuts (DECOMP+cut). Through extensive numerical experiments on DCOPF and UC problems, it demonstrates that exact solutions become challenging for large networks, but data-driven heuristics can dramatically speed up explanations with modest impacts on minimality. The results highlight practical pathways to provide transparent, need-driven rationale for dispatch decisions and propose future work to broaden perturbation types and integrate natural-language interfaces.

Abstract

Enhanced computational capabilities of modern decision-making software have allowed us to solve increasingly sophisticated optimisation problems. But in complex socio-economic, technical environments such as electricity markets, transparent operation is key to ensure a fair treatment of all parties involved, particularly regarding dispatch decisions. We address this issue by building on the concept of counterfactual explanations, answering questions such as "Why was this generator not dispatched?" by identifying minimum changes in the input parameters that would have changed the optimal solution. Both DC Optimal Power Flow and Unit Commitment problems are considered, wherein the variable parameters are the spatial and temporal demand profiles, respectively. The thereby obtained explanations allow users to identify the most important differences between the real and expected market outcomes and observe which constraints have led to the solution. The framework uses a bilevel optimisation problem to find the counterfactual demand scenarios. State-of-the-art methods are compared with data-driven heuristics on the basis of computational efficiency and explanation accuracy. Results show that leveraging historical data from previously solved instances can provide significant speed benefits and allows us to derive explanations in cases where conventional methods would not be tractable.

Figures (5)

• Figure 1: 5-bus toy network (all units in MW). In the factual scenario (left), $g_5$ -- the cheapest unit -- is not fully dispatched. The user is interested in why $g_5$ was not dispatched at least 400 MW. The counterfactual scenario (right) shows the minimum nodal demand variations that satisfy this solution requirement.
• Figure 2: Demand and associated optimal generation profiles for factual scenario (0) and counterfactual scenario (CE). It reveals that a slower demand ramp between 6:00 AM and 8:00 AM would have allowed the commitment of $g_2$ during the morning peak.
• Figure 3: Hourly demand profile samples with empirical probability density for an exemplary bus in case14
• Figure 4: Cumulative proportions of runtimes and empirical distributions of peak-normalised distances ($\Delta_{{k\rm{NN1}}}^{{\mathrm{D}}}$) of DCOPF CE problems on selected test cases
• Figure 5: Cumulative proportions of runtimes and empirical distributions of peak-normalised distances ($\Delta_{{k\rm{NN1}}}^{{\mathrm{D}}}$) of UC CE problems on selected test cases

Theorems & Definitions (3)

• Proposition 1
• proof
• proof : Proof of Proposition \ref{['proposition']}