Deep Learning-Accelerated Shapley Value for Fair Allocation in Power Systems at Real-World Grid Scale

Fairly allocating costs, benefits, and emissions among the entities of a power system is a recurring operational task, and the Shapley value is its axiomatic gold standard. It is rarely used because two costs compound: the number of coalitions grows as $2^n$, and computing the characteristic function of each coalition is itself expensive, since in power systems it is usually the outcome of an optimization such as an optimal power flow (OPF). We propose SurroShap, which pairs KernelSHAP coalition sampling with a deep neural network surrogate of the characteristic function and thereby addresses both costs at once for any cooperative game whose coalition values can be labeled offline. We derive a bound showing that time-averaged SurroShap allocations are $\varepsilon$-close to exact Shapley values, with $\varepsilon$ governed by the surrogate's mean bias, and give a practical estimator for the bound. Using carbon emission responsibility with an OPF characteristic function as the showcase, we evaluate on nine systems from 26 to 1,951 entities. On the IEEE 30-bus system, where exact Shapley values are tractable, the cumulative error of SurroShap falls to 0.17% after 336 allocation rounds, below the theoretical bound of 0.37%. On the 1,951-entity Texas 2000-bus system, SurroShap completes one allocation in 3.17 minutes, inside a 5-minute settlement window and $10^4$-$10^5\times$ faster than KernelSHAP with OPF evaluations. We verify the approach under full AC OPF and report where it is weaker: single-period and per-entity errors, and the fixed topology.