Equitable DER Allocation

• Equitable DER allocation is the strategic distribution of distributed energy resources to optimize grid performance, cost, and fairness under varying uncertainty.
• Approaches combine pre-storm planning, dynamic pricing with Shapley value, and fairness constraints in ACOPF to improve load restoration and mitigate voltage deviations.
• Emerging methods harness decentralized control and reinforcement learning, enabling real-time, equity-aware management of power supply and demand.

Equitable DER (Distributed Energy Resource) allocation concerns the principled distribution of electricity generation, storage, and control assets across a power grid to optimally balance costs, physical constraints, and fairness among grid users or regions. This topic spans stochastic optimization under disaster scenarios, game-theoretic and market mechanisms, equity-aware control design, fair division algorithms, and reinforcement learning methods. Equitable approaches seek not only economic or physical optimality but also minimize disparities—whether in outage risk, economic burden, power curtailment, or resource access—across consumers and communities.

1. Stochastic Optimization Frameworks for DER Placement under Uncertainty

Equitable DER allocation in disaster-prone networks is modeled via two-stage stochastic mixed integer programs incorporating both physical uncertainty and resource constraints (Chang et al., 2018). In this methodology, failure probabilities for grid lines are first determined using a physics-based stochastic model: the Holland parametric wind field formula computes spatio-temporal wind speeds per grid cell, and a non-homogeneous Poisson process (NHPP)—activated past a critical wind speed threshold—yields line-specific failure rates: $$\lambda_{h, t} = \begin{cases} 1 + \left(\frac{v_{h,t}}{v_{crit}}\right)^2 - 1, & v_{h,t} \geq v_{crit} \ 0, & v_{h,t} < v_{crit} \end{cases}$$ Line failure probabilities are aggregated and scenarios sampled to form the uncertainty set.

The two stages consist of:

• Pre-storm DER Allocation (Stage I): Binary development and assignment variables select which nodes host DERs, optimizing fixed costs plus expected loss-of-load.
• Post-storm Dispatch & Repair (Stage II): After failures are realized, the model simultaneously schedules line repairs over multiple periods and dispatches DERs within microgrid islands such that the cost of repairs and the total unmet demand is minimized.

Constraints enforce that a DER can only be assigned to a developed site and total DER deployments do not exceed a budget. LinDistFlow-based models switch power flow equations on/off per repaired line, voltage droop control is activated for DERs in islanded microgrids, and repair crew maximums are enforced per period.

Sample Average Approximation (SAA) reduces computational burden by restricting optimization to a representative scenario set. Results on small test networks reveal that optimal placement of limited DER resources significantly improves load restoration rates and equity of recovery between islands and nodes, especially under severe weather and constrained crew availability.

2. Game-Theoretic and Market-Based DER Allocation Mechanisms

Coalitional game theory and nodal market mechanisms provide another axis for equity in DER allocation (Gautam et al., 2023, Balogun et al., 2023). In tertiary frequency regulation contexts, the worth of each DER coalition is formalized via composite characteristic functions—worthiness index (WI) and power loss reduction (PLR):

• WI: Encodes priced capacity, reserve bid price, and historical performance.
• PLR: Measures technical benefit as reduction in network losses.

Shapley value allocations consider each DER's marginal contribution in all coalitions, ensuring that reserves (or energy allocation) are distributed proportionally: $$\psi_j(V) = \sum_{S \subseteq N, j \in S} \frac{(|S|-1)!(n-|S|)!}{n!} [V(S) - V(S \setminus \{j\})]$$ Distribution factors derived from normalized Shapley values set the reserve obligations and thereby the active power setpoints for each DER.

Dynamic pricing with explicit equity penalties is addressed via pricing oracles termed Power Distribution Authorities (PDA) (Balogun et al., 2023). The total economic burden per node is

$\Lambda_k = \sum_{t=1}^T \lambda_k(t)$

while the equity metric penalizes variance: $$\Gamma(\lambda) = \min_k \left\{ \sum_{t=1}^T \lambda_k(t) \right\} - \max_k \left\{ \sum_{t=1}^T \lambda_k(t) \right\}$$ Two algorithms—Implicitly Constrained Dual (with dual variables as optimal nodal prices) and Subgradient Descent via Implicit Differentiation—iteratively update node-wise prices to minimize both voltage deviations and equity gap. Empirical results demonstrate at least 45% reduction in voltage deviations versus time-of-use pricing, with nearly perfect equity.

3. Equity-Aware Control and Learning for DER Dispatch

Unsupervised learning frameworks can generate decentralized controllers that approximate OPF solutions and explicitly mitigate disparity in DER curtailment and service (Yuan et al., 17 Mar 2024). Neural controllers map local voltage and demand $(v_n, d_n)$ to active/reactive setpoints $(\gamma_n, \xi_n)$, trained by minimizing a loss comprising both network performance

$f_v(p, q, d) = \|v(p, q, d) - 1\|^2$

and an equity penalty inspired by orthogonality to “protected features” (e.g., electrical distance from substation): $$f_{eq}(p, q, d) = \|\langle \gamma(v_C, d_C), z_C \rangle\|$$ Controllers are updated incrementally, with stability guaranteed when their derivatives with respect to local voltage are non-positive and bounded by derived expressions. Simulations confirm the approach alleviates locational bias in curtailment and maintains tight voltage regulation.

4. Fair Division Algorithms and Existence Results for Equitable Allocations

Algorithms for equitable division of indivisible items (DER units, time slots) provide existence and computational guarantees for near-equity allocations even under complex utility models (Bilò et al., 7 Mar 2025, Bhaskar et al., 9 May 2025). Fairness and equity notions include:

• EQ1 (Equitable-up-to-one-item): Any inequity between bundles can be rectified by removing a single item.
• EQX* (Equitable-up-to-any-good-or-any-chore): For any pair of agents, removal of one "good" from the higher-valued bundle or one "chore" from the lower-valued bundle eliminates the gap.

Algorithmic results include:

• Pseudo-polynomial local-search for EQX* allocations using potential functions.
• Polynomial-time greedy EQ1 algorithms: sequentially assign goods to least-valued bundles and chores to the most-valued.
• Dynamic programming for path-constrained bundles and Sperner's Lemma-based rounding for existence proofs of EQ1* allocations.

Randomized "Best of Both Worlds" allocations are shown to always exist for two agents and binary valuations, achieving exact equity in expectation and EQ1 ex post (Bhaskar et al., 9 May 2025). The geometric characterization for existence is: $$\forall \boldsymbol{\ell} \in \mathbb{R}^n, \ \sum_i \ell_i = 0: \ \exists \ A \text{ (EQ1)} \text{ s.t. } \sum_i \ell_i v_i(A_i) \geq 0$$ These results transfer to DER contexts (e.g., in discrete battery or solar panel assignments), ensuring that average benefit is equitable and realized allocations remain nearly fair even when indivisibility or connectivity constraints (e.g., feeder topology) apply.

5. Equity Indicators and Constraints in Grid Optimization

Explicit equity indicators such as the grid Gini coefficient for outage risk, defined via the Outage Risk Indicator (ORI),

$ORI_i = \frac{P_{LS, i}}{P_{L, i}}$

and grid Gini coefficient

$$GGC_{oei} = \frac{\sum_{i=1}^n \sum_{j=1}^n |ORI_i - ORI_j|}{2n(n-1) ORI_{mean}}$$

are integrated into ACOPF optimization as constraints on allowable dispersion ($GGC_{oei} \leq \beta$), thus ensuring the risk of load shedding is distributed fairly across buses (Fang et al., 25 Jun 2024). Lower $\beta$ values induce more uniform curtailment profiles, which may slightly increase cost but achieve better risk equity in the population.

Analogous equity metrics can extend to DER allocation, such as an allocation Gini coefficient applied to DER capacity-to-demand ratios, balancing technical efficiency with social equity.

6. Reinforcement Learning Approaches for Equitable Real-Time Resource Deployment

Adaptive RL methods employing context-rich state vectors (encoding deficiencies, candidate features, and inefficiency deltas) and attention-based actor–critic architectures offer real-time, scalable solutions for equitable resource deployment (Tonwe, 18 Aug 2025). The RL agent selects DER sites by evaluating operational costs, technical feasibility, local need, and equity metrics, with a precision reward function penalizing suboptimal and inequitable allocations: $r_k(a_j) = 1.0 - \alpha \cdot (e_{kj} - e_{k}^*)$ Attention mechanisms prioritize candidates balancing efficiency with equity, while generated infrastructure deficiency maps and equity dashboards support continual monitoring and strategic planning for minimizing disparities in energy access.

7. Implementation Considerations, Trade-offs, and Future Directions

Equitable DER allocation integrates stochastic optimization, game theory, AI, control, and combinatorial fair division. The choice of method must balance solution tractability (SAA for scenario reduction, greedy vs. DP algorithms), performance (voltage stability, cost, outage risk), and equity guarantees (formal metrics, algorithmic existence proofs). In practice, computational complexity (e.g., Shapley value enumeration, NP-completeness for several allocation problems) and data requirements (wind field models, network topology, load and demand forecasting) inform feasible solution deployment.

Future work involves extending equity notions to long-term DER planning, developing scalable algorithms under path and topology constraints, quantifying the impact of fairness metrics on physical performance, integrating multi-dimensional protected features, and combining AI-based policies with optimization-based control for adaptive grid management.

Equitable DER allocation underscores the necessity of balancing grid reliability, economic optimality, and fairness across diverse consumers and regions, ensuring just and resilient operation under both routine and adverse conditions.