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Decision-Gated Surrogate-Assisted Stochastic Optimization with Independent High-Fidelity Certification for Photovoltaic Hosting-Capacity Planning

Ali Abubakar, Samuel Essamuah Assabil, Akhtar Hussain, Van-Hai Bui

arXiv:2609.30847v1eess.SYcs.SY

TL;DR

Stochastic PV penetration planning requires repeated nonlinear PV and power-flow evaluations under uncertain irradiance and demand, where surrogate errors can affect feasibility and trade-off decisions. The paper combines high-fidelity simulation with matched data-only and physics-informed surrogates, decision-gated enrichment, and independent certification. Despite nearly identical held-out errors, optimizer-realistic screening distinguishes the surrogates’ operational agreement, and the conclusion limits certified penetration to feeder-specific assessment.

  • Problem

    Surrogate prediction errors can be decision-critical near operational limits and Pareto regions, so held-out accuracy alone does not establish optimization reliability.

    Source: §1 · p. 2

  • Method

    The framework uses a calibrated PV and AC power-flow model as the high-fidelity authority, while matched data-only and physics-informed surrogates accelerate search and undergo decision-focused auditing.

    Source: §2.3 · p. 5, §4 · p. 13

  • Results

    44.4% for SNN-DATA versus 93.4% for PINS operational agreement separated their decision performance despite nearly identical frozen-test errors.

    Source: §4 · p. 13

  • Takeaways & Limitations

    Surrogate selection based on decision-level evidence favored PINS over selection by average predictive accuracy.

    Source: §4 · p. 13

    Certified penetration is a starting point for feeder-specific siting and capacity assessment, not a universally portable certificate.

    Source: §4 · p. 14

Abstract

from arXiv · show

High photovoltaic (PV) penetration planning requires repeated nonlinear PV and power-flow evaluations under uncertain irradiance and demand, particularly when two competing objectives, penetration and total electrical loss, are optimized simultaneously subject to reliability constraints. This paper develops a decision-focused, surrogate-assisted stochastic multiobjective framework in which a calibrated PV model coupled with a distribution-network simulator provides the high-fidelity reference, while matched data-only and physics-informed surrogates accelerate optimization and are evaluated empirically for decision reliability across the loss-penetration tradeoff. Although the two surrogates exhibit nearly identical held-out errors, optimizer-realistic screening yields markedly different operational validity rates of 44.4% and 93.4%, respectively, motivating selection of the physics-informed model on decision performance rather than test accuracy. Surrogate inference cuts the cost of a 60-scenario design evaluation from 286.0 to 0.46 ms, an approximately 620 time speedup. A decision-gated enrichment strategy further targets Pareto-critical, constraint boundary, and surrogate-disagreement regions, reducing prediction error by 39.1%. Independent 500 scenario certification verifies all 80 screened candidates and identifies 46 non-dominated designs; the selected compromise attains 70.74% expected penetration with 297.9 kW expected total electrical loss. Cross-feeder transfer eliminates baseline voltage violations on the 85- and 69-bus systems, but produces overvoltage and a 62.7% increase in feeder-network loss on the 33-bus system, demonstrating that certified penetration is topology-specific and demands decision-level auditing, independent certification, and feeder-specific validation.

1. Background

Stochastic PV planning combines costly nonlinear PV and AC power-flow evaluations with objectives and constraints sensitive to scenario variation. This paper addresses the gap between surrogate prediction accuracy and decision reliability through high-fidelity auditing, decision-gated enrichment, and independent certification.

Motivation

  • Under uncertainty, repeated two-diode PV and nonlinear AC power-flow evaluations make stochastic optimization computationally costly, while reducing physical fidelity can compromise engineering estimates.Irradiance and demand vary, and surrogate errors near operational limits or Pareto regions can change feasibility classifications and trade-off decisions.Source: §1 · pp. 1–2

Research gap

  • Comparable held-out errors do not ensure comparable decision reliability, so surrogate evaluation should include feasibility agreement, false-feasibility, and Pareto-structure preservation.The literature review identifies no single prior formulation combining all seven listed attributes in a unified stochastic multiobjective PV-planning framework.Source: §1 · p. 2

Study contributions

  • The framework couples a calibrated two-diode PV model with balanced AC power flow to optimize expected PV penetration and total electrical loss under a reliability requirement.The high-fidelity model remains the authority for feasibility, loss, and penetration.Source: §1 · p. 3
  • The framework compares matched data-only and physics-informed models using predictive accuracy and optimizer-realistic high-fidelity evidence, and supports stochastic multiobjective PV penetration–loss planning through periodic decision-aware enrichment and independent reliability verification.Enrichment targets Pareto-critical, constraint-boundary, and surrogate-disagreement regions; candidate updates are retained only when prediction-error, false-feasibility, and decision-agreement gates are simultaneously satisfied, otherwise the previous surrogate is restored.Source: §1 · p. 3
  • Independent high-fidelity certification evaluates screened candidates on 500 scenarios with a one-sided 95% Clopper–Pearson lower confidence bound.The study then selects a compromise from the certified non-dominated set and tests transfer across feeder topologies.Source: §1 · p. 3

2. Methodology

The methodology retains high-fidelity PV and network simulation as the authority while using matched surrogates to accelerate stochastic optimization. Periodic enrichment targets decision-critical regions, updates pass explicit gates, and final candidates undergo independent high-fidelity verification.

2.1. High-Fidelity PV–Distribution-Network

  • A calibrated two-diode PV model and balanced radial AC network define the high-fidelity model, with a mixed-integer design covering array, inverter, conductors, PCC, and row geometry.Scenario-level constraints include power-flow validity, voltage limits, a PV-current cap, and inverter-power compliance.Source: §2.1 · p. 4

2.2. Stochastic Formulation

  • Search minimizes expected operational loss and maximizes expected PV penetration subject to a joint operational-safety probability of at least 0.90.Scenarios preserve within-weather dependence but independently sample demand; search and screening use raw safe-outcome fractions, while certification applies a one-sided confidence bound.Source: §2.2 · pp. 4–5

2.3. Neural Surrogate for Stochastic Evaluation

  • Matched surrogate variants predict decision-relevant physical outputs directly; PINS adds a two-diode current-residual penalty and voltage-ordering consistency penalty to the data-only loss.The comparison holds architecture, data, and training budget constant, while the PV residual is asinh-compressed to limit training instability.Source: §2.3 · pp. 5–6

2.4. Periodic Decision-Gated High-Fidelity

  • Periodic enrichment re-evaluates Pareto-critical, constraint-boundary, and surrogate-disagreement candidates against the high-fidelity model.An update is retained only if prediction-error, false-feasibility, and decision-agreement gates pass; otherwise, the previous surrogate is restored.Source: §2.4 · p. 6

2.5. Statistical Protocol and Validation

  • The validation protocol separates sampling, surrogate, and search uncertainty, estimates search variability over eight independent seeds, and compares certified Pareto-design recovery with high-fidelity cost.Physical solvers are validated before stochastic optimization, and model parameters are fixed in the reproducibility record.Source: §2.5 · p. 7

2.6. Independent High-Fidelity Verification

  • Final candidates are independently evaluated by the high-fidelity model, and certification uses an exact one-sided Clopper–Pearson lower bound.The retained surrogate’s screened Pareto set is re-verified on an independent certification scenario set; reported final quantities are recomputed by the high-fidelity model.Source: §2.6 · pp. 7–8

3. Simulations, Analyses and Discussions of Results

This results section audits the 34-bus reference and stochastic setup, then evaluates physical-model validation, stochastic adequacy, and matched-surrogate performance. Under optimizer-induced screening, PINS substantially outperforms SNN-DATA operationally despite a near tie in held-out error.

3.1. Simulation Configuration, Data Audit, and Reproducibility

  • 250 audited weather–demand scenarios were all HF-valid, 98.0% jointly safe, and 85.2% within the prescribed penetration and loss windows.Complete empirical weather rows preserve within-weather dependence, while an independently sampled mean-one truncated-lognormal multiplier introduces demand uncertainty.Source: §3.1 · p. 8, Figure 5 · p. 8
  • The no-PV 34-bus feeder converged with minimum voltage 0.9566 pu at bus 27 and network I2R loss of 163.45 kW (3.53%).Source: §3.1 · p. 9, Figure 6 · p. 9

3.2. High-Fidelity Physical-Model Validation

  • On 80 independent curves, held-out current fit reached R2 = 0.99999966, RMSE = 0.615 mA, and MAE = 0.504 mA; the nearest STC maximum-power point differed by −0.013%.Two of the eight fitted parameters reached imposed bounds, indicating limited identifiability for those parameters despite strong predictive agreement.Source: §3.2 · p. 9, Figure 7 · p. 9

3.3. Stochastic Adequacy and SAA Budget

  • The optimization used 60 scenarios per generation, refreshed every 20 generations, while independent 500-scenario HF sampling was reserved for final reliability certification.The study also used 24 scenarios as an evidence-checked diagnostic reference size.Source: §3.3 · p. 9

3.4. Matched Surrogates: Predictive Performance and Robustness

  • Frozen-test NRMSE was 0.350842 for SNN-DATA and 0.353172 for PINS, a difference under 1%; PINS had lower mean test NRMSE in six of eight degraded-data conditions.Source: §3.4 · p. 9
  • 93.4% operational HF agreement for PINS exceeded the 60% decision-validity floor, versus 44.4% for SNN-DATA under common-batch screening.False infeasibility was 6.6% for PINS and 55.6% for SNN-DATA; both models had zero false feasibility.Source: §3.5 · p. 10, Table 2 · p. 10
  • All 72 SNN-DATA search-stage designs were dominated by a PINS candidate, while none of 183 PINS designs was dominated by SNN-DATA.This is a geometric property of the evaluated candidate sets.Source: §3.5 · p. 10, Figure 9 · p. 10
  • 286.0 ms per design for 60-scenario HF evaluation versus 0.46 ms per design-equivalent for PINS inference yields an approximately 620× speedup, though PINS underpredicts HF 95th-percentile TL by approximately 30%.Source: §3.5 · p. 10

3.6. Periodic Decision-Gated High-Fidelity

Decision-gated high-fidelity enrichment reduces local prediction error, while independent high-fidelity certification establishes a feasible Pareto set for final planning decisions.

3.6. Periodic Decision-Gated High-Fidelity

  • 39.1%: decision-gated enrichment reduced mean normalized prediction error from 0.1829 to 0.1113 on the protected audit set.It returned Pareto-critical, constraint-boundary, and surrogate-disagreement designs to the high-fidelity model.Source: §3.6 · p. 10

3.7. Independent HF Certification and Final

  • The certified Pareto front spans expected total loss of 264.49–300.64 kW and expected penetration of 53.15–71.58%.Every plotted non-dominated design was recomputed using the independent high-fidelity certification stage.Source: Figure 10 · p. 11, §3.7 · p. 11
  • 80/80 screened candidates met high-fidelity validity, penetration, loss, and 0.90 reliability requirements; non-dominated filtering retained 46 certified designs.Reliability was assessed on a disjoint 500-scenario set using an exact one-sided 95% Clopper–Pearson lower confidence bound.Source: §3.7 · pp. 10–11, Table 3 · p. 11
  • The selected compromise had empirical safety probability 0.982 and a one-sided 95% lower bound of 0.9688, above the required 0.90.TOPSIS was applied only after certification, and every other certified Pareto design remained an admissible alternative.Source: §3.7 · p. 11
  • Seven tested loss–penetration weight pairs selected five distinct certified designs spanning approximately 53.2–71.6% expected penetration.The certified Pareto front, rather than one TOPSIS point, is the fundamental decision product.Source: §3.7 · p. 11

3.8. Representative Operational-Loss

Operational-loss decomposition identifies feeder-network losses as the largest component at the representative operating point, while transfer tests and robustness checks show that planning outcomes depend on topology and decision-level validation.

3.8. Representative Operational-Loss

  • At the representative high-fidelity operating point, feeder-network loss contributed 111.57 kW, or 72.3% of total operational loss, while inverter conversion contributed 23.30 kW, or 15.1%.The operating point used an array MPP of 1,301.3 kW and instantaneous penetration of 27.1%, distinct from the stochastic TOPSIS expectation.Source: §3.8 · p. 11

3.9. Multi-Feeder Engineering Validation

  • On the 85- and 69-bus feeders, PV cleared all baseline voltage violations and reduced network loss; on the 33-bus feeder, loss rose 62.7% and voltage exceeded 1.05 pu.On the 33-bus feeder, the violation count fell from 21 to 3 despite the overvoltage; on the 34-bus system, network loss increased 25.3%.Source: Figure 11 · p. 12, Figure 12 · p. 12, §3.9 · p. 12

3.10. Robustness and Secondary Planning Checks

  • PCC location was the dominant local design sensitivity, with re-siting changing loss by up to approximately 26%.Across four completed optimizers, normalized hypervolume differences were not significant (Friedman p = 0.392); MOEA/D completed none of eight runs.Source: §3.10 · p. 13
  • SNN-DATA and PINS differed by less than 1% in frozen-test NRMSE, yet their high-fidelity decision agreement was 44.4% and 93.4%, respectively.Residual upper-tail loss error of approximately 30% supports retaining high-fidelity evaluation for final decisions.Source: §3.10 · p. 13

4. Conclusion

The conclusion presents a decision-focused framework that uses surrogates for speed while retaining high-fidelity simulation for certification. Its certified loss–penetration trade-off is feeder-specific, not universally portable.

4. Conclusion

  • Despite similar frozen-test NRMSEs (0.3508 and 0.3532), operational agreement was 44.4% for SNN-DATA versus 93.4% for PINS, selected on decision-level evidence.Every one of the 72 SNN-DATA search-stage designs was dominated by at least one PINS design.Source: §4 · p. 13
  • At the Ngen = 60 scenario budget, surrogate inference reduced evaluation time from 286.0 to 0.46 ms per design-equivalent, an approximately 620× speedup.Periodic targeted high-fidelity enrichment reduced audited mean normalized prediction error by 39.1%.Source: §4 · p. 13
  • Independent 500-scenario high-fidelity evaluation certified all 80 screened candidates and retained 46 non-dominated designs; the compromise attained E[Π] = 70.74% and E[TL] = 297.92 kW.Its empirical safety probability was 0.982, with a one-sided 95% Clopper–Pearson lower bound of 0.9688.Source: §4 · p. 13
  • Transfer removed severe baseline voltage violations and reduced network losses on the 85- and 69-bus feeders, but the 33-bus system developed local overvoltage and a 62.7% network-loss increase.The conclusion describes certified penetration as a network-specific planning result and a starting point for feeder-specific siting and capacity assessment, not a universally portable certificate.Source: §4 · pp. 13–14
  • The framework integrates high-fidelity evaluation, surrogate optimization, targeted enrichment, independent certification, and cross-feeder assessment.Source: Figure 13 · p. 14

Appendix A. Supporting Physical, Statistical, and Reproducibility Details

Appendix A collects supporting physical definitions, stochastic-sampling assumptions, enrichment settings, and diagnostic evidence without duplicating the principal results.

Appendix A. Supporting Physical, Statistical, and Reproducibility Details

  • Appendix A records supporting physical definitions, stochastic-sampling assumptions, enrichment settings, and diagnostic evidence for interpreting or reproducing the main study.Source: Appendix A · p. 14
  • The appendix is intentionally limited to material that supports, but does not duplicate, the principal results.Source: Appendix A · p. 14

A.1. Notation and Reliability Terminology

This section distinguishes key notation and reliability terminology, clarifies how penetration and evaluation stages are described, and records the surrogate’s physical-residual role.

A.1. Notation and Reliability Terminology

  • HF denotes the two-diode-plus-AC-power-flow reference simulator; PINS and SNN-DATA are the physics-penalized and data-only surrogates, respectively.SAA denotes sample-average approximation, PCC point of common coupling, and CP95 the one-sided 95% Clopper–Pearson lower confidence bound.Source: §A.1 · p. 14
  • PV penetration is not interpreted as a ratio against fixed historical peak demand or installed feeder capacity.Source: §A.1 · p. 14
  • Search-time statistics use Ngen = 60, comparative operational screening uses Nscr = 100, and only independent Ncert = 500 high-fidelity results are described as certified.Source: §A.1 · p. 14

A.2. Two-Diode Residual Used by the Physics-Penalized Surrogate

  • Array-level voltage and current predictions are transformed before evaluating the two-diode residual, which contributes to PINS loss alongside a voltage-ordering term.These penalties target physically inconsistent predictions without requiring reproduction of the complete AC bus-state vector.Source: §A.1 · p. 15

A.3. Interconnection and Network-Loss

The interconnection and network-loss details separate inverter constraints from the accounting of distinct electrical loss elements.

A.3. Interconnection and Network-Loss

  • Satisfying the DC inverter-current limiter does not imply satisfaction of the AC apparent-power rating, which is checked separately.Source: §A.3 · p. 15
  • The DC cable, dedicated AC interconnection cable, and feeder-network branches are evaluated as distinct physical elements to avoid counting the same resistance or dissipation mechanism more than once.Source: §A.3 · p. 15

A.4. Scenario Independence and Clopper–Pearson

Each Monte Carlo scenario combines a historical weather state with an independently sampled demand multiplier. Independence applies across scenario draws, not among weather variables within a scenario.

A.4. Scenario Independence and Clopper–Pearson

  • Each scenario pairs one complete historical weather state with an independently sampled demand multiplier truncated to [0.70, 1.30].Weather variables within a scenario retain the dependencies in the sampled historical row; scenario draws are generated independently with replacement.Source: §A.4 · p. 15
  • Figure A.1 compares high-fidelity and surrogate TL quantiles over probabilities from 0.50 to 0.99.Source: Figure A.1 · p. 15
  • For the Clopper–Pearson calculation, final safety indicators are treated as independent Bernoulli observations across Monte Carlo scenario draws.This independence assumption does not require irradiance, temperature, solar geometry, and albedo within a scenario to be independent.Source: §A.4 · p. 15

A.5. Periodic HF-Enrichment Configuration

Periodic enrichment samples Pareto-critical, constraint-boundary, and surrogate-disagreement regions, while update acceptance requires all three decision gates to pass. Supplementary diagnostics also qualify the selected surrogate's tail accuracy and report sensitivity and algorithm comparisons.

A.5. Periodic HF-Enrichment Configuration

  • At each scheduled audit, the optimization population is sampled from Pareto-critical, constraint-boundary, and surrogate-disagreement regions.Table A.1 reports the configuration of a representative audited round.Source: §A.5 · p. 15
  • The audited round's quotas do not imply exactly 117 unique points at every audit, because acquisition-set overlap can vary.Candidate updates are accepted only if prediction-error, false-feasibility, and decision-agreement gates all pass simultaneously.Source: §A.5 · p. 15

A.6. Supplementary Physical, Robustness, and Sensitivity Diagnostics

  • PINS underpredicts the high-fidelity TL 95th percentile by approximately 30%, so final objectives and reliability statistics are recomputed using high-fidelity simulation.Superior operational feasibility agreement does not imply uniformly accurate tail reproduction.Source: §A.5 · p. 15
  • PCC placement dominates every other tested perturbation in maximum absolute expected-loss change relative to the TOPSIS-selected design.Source: Figure A.2 · p. 16
  • Mean normalized hypervolume differences among four successfully paired algorithms are not statistically significant (Friedman p = 0.392).Source: Figure A.3 · p. 16
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