Solar Fairness Evaluation Framework

• Solar Fairness Evaluation Framework is a structured quantitative toolkit that measures equity in solar resource allocation using metrics such as the Gini coefficient and Jain’s index.
• It integrates fairness objectives into optimization models for unit commitment, hosting capacity, and P2P market mechanisms, balancing technical efficiency with equitable outcomes.
• Empirical analyses reveal trade-offs between operating costs and fairness gains, providing actionable insights for regulatory policies and system planning.

A Solar Fairness Evaluation Framework is a structured, quantitative set of tools and methodologies designed to measure, optimize, and report the equity of solar photovoltaic (PV) resource allocation, benefit distribution, curtailment policies, and operational mechanisms in modern electricity networks. Such frameworks are being deployed at multiple layers of the power system, from distribution network hosting capacity and market trading, to robust generation scheduling and energy community sharing, with fairness metrics adapted to the specific context and optimization objective. The following exposition synthesizes frameworks and methods from recent research, with a focus on technical rigor and comparative analysis.

1. Fairness Notions and Quantitative Indicators

Solar fairness in power systems is articulated through a combination of distributional, procedural, and meritocratic perspectives, linked to operational and economic outcomes. The principal quantitative fairness indicators employed in recent frameworks include:

• Gini coefficient: Measures the disparity in an allocation (energy delivered, hosting capacity, financial benefit). $G=0$ indicates equality, $G\to 1$ extreme inequality (Toyoshima et al., 10 Mar 2026, Rubbers et al., 22 Aug 2025, Couraud et al., 22 Aug 2025).
• Jain's Index: $J=\frac{(\sum_i u_i)^2}{n\sum_i u_i^2}$ used for outcomes (bill reductions, hosting capacity), with $J=1$ indicating perfect equality (Couraud et al., 22 Aug 2025, Rubbers et al., 22 Aug 2025).
• Variance of per-unit capacity: For spatial fairness of PV hosting, $$\mathcal{M}^U = \frac{1}{N-1}\sum_n (x_n - \bar x)^2$$, where $x_n = \alpha_n/\bar p_n$ (Ali et al., 11 Jul 2025).
• Entropy of allocations: Normalized entropy of market shares (e.g., FBS metric, see Section 3) (Jadhav et al., 26 Aug 2025).
• Fairness-to-Grid (FTG), Fairness-Between-Sellers (FBS), Fairness-of-Pricing (FPP): Slot-level fairness metrics in P2P trading (Jadhav et al., 26 Aug 2025).
• Min-max ratio: Ratio $\min_i u_i / \max_i u_i$, emphasizing the position of the least-advantaged agent (Couraud et al., 22 Aug 2025).
• Meritocratic index: Root-mean-square deviation between realized and “ideal” reward-by-contribution (Couraud et al., 22 Aug 2025).

These metrics are selected and normalized according to context, supporting both real-time shaping (incentive-guided) and post-hoc evaluation.

2. Methodologies for Fairness-Embedded Network and Market Optimization

Solar fairness frameworks typically embed equity objectives into either optimization models or learning environments, producing allocations that satisfy technical constraints while quantifying or directly optimizing fairness properties.

2.1 Robust Unit Commitment with Fairness (RE-RPᵃⁱʳ)

A two-stage robust mixed-integer program augments classic unit commitment with robust PV output suppression and an explicit fairness penalty. The first stage selects thermal and PV-suppression binaries; the second dispatches under worst-case uncertainty. The fairness penalty uses the $L^1$-distance of per-unit deliveries about their mean, enforced via auxiliary linear constraints. The objective reads:

$$\min_{x\in\{0,1\}^n} \left\{ c^\top x + \chi L^1(a^+,a^-) + \max_{(\zeta,\eta)\in\mathcal{D}\times\mathcal{Z}}\min_{y\in\Omega(x,\zeta,\eta)} b^\top y \right\}$$

The Gini index $G$ computed on the resulting delivered energies quantifies equity after optimization. This approach captures a trade-off tunable by $G\to 1$0, supports large uncertainty budgets, and is directly extendable to wind, hydro, and storage suppression fairness (Toyoshima et al., 10 Mar 2026).

2.2 Hosting Capacity with Fairness Criteria

Distribution network hosting capacity (HC) optimization incorporates both physical constraints (power flow, security limits) and fairness constraints or objectives, parameterized by selectable fairness paradigms:

• Utilitarian: Maximizes total DG capacity, disregards disparity.
• Egalitarian (max-min): Maximizes the minimum allocation across all users.
• Bounded: Constrains each user’s allocation within $G\to 1$1-bounds of egalitarian and utilitarian references.
• Bargaining, Nash-style: Trades off total capacity against maximum deviation from the mean via parameter $G\to 1$2.

Inequality metrics (Gini, Jain) and “Price of Fairness” PoF are reported across parameter sweeps, tracing the Pareto front of capacity versus disparity. Fairness can be mandated operationally (DSO policy) or via regulatory incentives (Rubbers et al., 22 Aug 2025).

2.3 Data-Validated Spatial Fairness for PV Distribution

Large-scale frameworks commence with automated grid data extraction, rule-based and load-flow validation (topology, geographic, and electrical checks), enabling reliable downstream optimization. Fair per-unit PV capacity is enforced by appending a variance penalty to the OPF objective:

$G\to 1$3

Intensive validation and scalable convex optimization enable the quantification of economic cost and capacity sacrifice for imposed variance targets, supporting DSO planning (Ali et al., 11 Jul 2025).

2.4 P2P Electricity Market Fairness with LLM-Guided MARL

In prosumer-centric P2P markets, fairness is enforced at each trading slot via a Large-Language-Model (LLM) “critic.” The LLM receives the executed trade ledger, returns normalized scores for FTG (peer-to-peer trade share), FBS (entropy of seller share), and FPP (price spread). These shape the MARL reward:

$G\to 1$4

Ramp-up schedules for $G\to 1$5 mitigate learning instability. The approach achieves robust convergence, supports scaled communities, and delivers tradeable fairness-efficiency outcomes measurable by slot-level and aggregate metrics (Jadhav et al., 26 Aug 2025).

2.5 Community Self-Consumption Mechanisms

Within local energy markets (LEMs), mechanisms such as pro rata, glass-filling (standard or prioritized), and uniform-price double auction are directly assessed via fairness indicators—Jain’s index, min-max, and a scalable meritocratic index based on historical marginal contribution. Mechanism choice induces trade-offs among fairness objectives, which are quantified in simulation across representative community ensembles (Couraud et al., 22 Aug 2025).

3. Comparative Summary of Solar Fairness Metrics and Mechanisms

Below is a comparison of salient metrics and their application:

Metric/Mechanism	Integrable (optimization)	Post-hoc (evaluation)	Context/References
Gini Index	✓	✓	(Toyoshima et al., 10 Mar 2026, Rubbers et al., 22 Aug 2025, Couraud et al., 22 Aug 2025)
$G\to 1$6 Deviation	✓	—	(Toyoshima et al., 10 Mar 2026)
Jain’s Index	—	✓	(Rubbers et al., 22 Aug 2025, Couraud et al., 22 Aug 2025)
Seller-entropy (FBS)	—	✓	(Jadhav et al., 26 Aug 2025)
FTG, FPP (slot scores)	✓	✓	(Jadhav et al., 26 Aug 2025)
Spatial variance	✓	✓	(Ali et al., 11 Jul 2025)
Meritocratic index	—	✓	(Couraud et al., 22 Aug 2025)

Algorithmic mechanisms that support fairness shaping include Benders decomposition (for robust UC), convex QP solvers (for HC), PPO in MARL (for market trading), and prescriptive LEM allocation logic.

4. Empirical Results and Trade-Offs

Framework validation across synthetic and real networks/communities yields the following insights:

• Unit commitment (RE-RPᵃⁱʳ): Small increases in total operating cost or curtailment enable large reductions in Gini ($G\to 1$7 is feasible with modest penalty $G\to 1$8). As PV penetration scales, computational costs grow but remain tractable (Toyoshima et al., 10 Mar 2026).
• Distribution network HC: Star/branched topologies improve fairness at minimal cost; chain/radial feeders or large LV networks entail difficult trade-offs (PoF up to 0.65 for perfect equality). Bounded and bargaining criteria identify operational “knees” where small efficiency sacrifices produce substantial fairness gains (Rubbers et al., 22 Aug 2025).
• Data-validated spatial fairness: Halving per-unit capacity variance requires <1% of profit over 20 years. Near-perfect fairness entails a larger reduction in total installable PV (up to 60%) but may be justified by regulatory pressures (Ali et al., 11 Jul 2025).
• P2P market fairness: Stable convergence to FTG ≈ 0.8–0.85, FBS ≈ 0.9, FPP > 0.95, with consumer bill cuts >30% in deployed scenarios. The system responds robustly to ±20% PV and ±10% demand shocks (Jadhav et al., 26 Aug 2025).
• Community allocation mechanisms: Prioritized glass-filling maximizes egalitarian/min-max indices, double auction is meritocratic-optimal, standard glass-filling balances all metrics. Mechanism selection thus can be matched to community justice priorities (Couraud et al., 22 Aug 2025).

5. Practical Implications, Extensions, and Recommendations

• Regulatory and operational policy: DSOs and regulators can set caps on Gini/variance, optimize or constrain for fairness targets, and implement incentives (e.g., connection charge discounts, targeted feed-in tariffs) (Rubbers et al., 22 Aug 2025, Ali et al., 11 Jul 2025).
• Planning and auditing: Systematic validation pipelines ensure that fairness analyses are based on accurate physical models; optimization frameworks support real-world adoption and auditing at scale (Ali et al., 11 Jul 2025).
• Technological extensions: All main frameworks readily generalize to wind, hydro, and other DERs by addition of analogous fairness penalties or constraints (Toyoshima et al., 10 Mar 2026, Rubbers et al., 22 Aug 2025).
• Methodological outlook: Future research includes temporal fairness (across adoption windows), unbalanced/three-phase modelling, integration of storage, and automated correction of grid databases (Ali et al., 11 Jul 2025). In LEMs, socioeconomic and real-time flexibility dimensions represent key expansions (Couraud et al., 22 Aug 2025).

This suggests that modern Solar Fairness Evaluation Frameworks enable systematic, technically grounded, and operationally actionable assessment or enforcement of equity in solar resource integration, providing essential tools for both system operators and policy-makers across scales and regulatory contexts.