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Reliability Value of Long-Duration Energy Storage against Extreme Events in High-Renewable Grids: A Full-Year AC-OPF Assessment

Jeongdong Kim, Jonggeol Na, Sungho Shin

arXiv:2609.06864v1eess.SYcs.SY

TL;DR

High-renewable grids need LDES reliability assessed under prolonged scarcity, full-year uncertainty, nonlinear network constraints, and line outages. The paper evaluates this with full-year multi-period AC-OPF and a multi-day security-constrained extension. LDES reduces load shedding and supports feasible operation under the considered N−1 contingencies.

  • Problem

    Existing LDES studies simplify transmission physics or use short operational horizons, leaving its network-level reliability under full-year uncertainty and N−1 contingencies insufficiently assessed.

    Source: §1 · p. 6

  • Method

    The study combines full-year load-shedding-minimizing multi-period AC-OPF with a seasonally anchored, multi-day SC-AC-OPF for line outages and restoration.

    Source: §1 · p. 3, §2.1.1 · p. 8

  • Results

    LDES reduces load shedding versus the base network and enables feasible N−1 corrective operation where the network without LDES or with standalone BESS has no feasible solution.

    Source: §4 · p. 33

  • Takeaways & Limitations

    LDES can substitute for generation or transmission expansion otherwise needed for N−1-secure operation while remaining actively used in normal operation.

    Source: §4 · p. 33

    Candidate storage technologies are represented by a common model parameterized by round-trip efficiency, duration, and power capacity rather than technology-specific characteristics.

    Source: §2.1.2 · p. 10

Abstract

from arXiv · show

Long-duration energy storage (LDES) can mitigate prolonged renewable--load imbalances during Dunkelflaute events, but existing studies rely on zonal or linearized DC network models and inadequately analyze the operational feasibility of the grid across a wide range of full-year renewable, load, and contingency scenarios. To address this gap, this paper introduces a multi-period alternating-current optimal power flow (AC-OPF) formulation that captures the full nonlinear network physics and assesses the reliability value of LDES in high-renewable grids. To evaluate scarcity events spanning multiple days to weeks, full-year operation is modeled as an 8,760-h load-shedding minimization over scenarios sampled from a Gaussian copula model, fitted to 2010--2025 historical wind and bus-level load data, that represents both typical variability and tail events. On a synthetic 200-bus Illinois transmission network, a hybrid fleet of battery energy storage (BESS) and LDES with 50 MW total power reduces annual load shedding by 83.0% on average relative to the base network, versus 68.5% for short-duration BESS alone at equal power. To further account for unexpected line outages throughout the year, the formulation is extended to a multi-day security-constrained AC-OPF. Under N-1contingencies, no feasible operating solution is obtained for the base network, whereas the LDES-equipped network remains feasible in all considered cases, thereby saving the cost of additional generation and transmission capacity. During the contingency period, LDES acts as a backup power supply, requiring only 5.5% more generation on average than the no-contingency base case.

1. Introduction

The paper asks whether LDES can improve reliability in high-renewable grids when assessed with nonlinear network physics, full-year uncertainty, and line contingencies. It proposes full-year multi-period AC-OPF and a seasonally anchored security-constrained extension to quantify that value.

1. Introduction

  • Short-duration BESS cannot mitigate renewable–load mismatches lasting multiple days, while network reliability also depends on voltage, reactive-power, and transmission constraints.Dunkelflaute shortages can persist for several days to weeks.Source: §1 · pp. 2–3
  • Prior studies either simplify transmission physics or assess AC-constrained storage over short horizons, leaving full-year network-level LDES reliability under uncertainty and N−1 contingencies unquantified.The paper argues that seasonal storage durations of 10–100 hours or longer require full-year evaluation.Source: §1 · p. 6
  • The proposed 8,760-h multi-period AC-OPF minimizes load shedding while coupling storage inter-temporal constraints with nonlinear AC network physics.The authors report solving full-year-scale problems with GPU-based nonlinear optimization solvers.Source: §1 · p. 7
  • A multi-day seasonally anchored SC-AC-OPF tests N−1 outages across the year while accounting for the seasonal LDES energy state and post-contingency restoration.Outage timing spans the year, including Dunkelflaute-driven scarcity periods.Source: §1 · pp. 3, 4, 7
  • The study uses 99th-percentile annual apparent load shedding and constraint-binding-hour attribution to assess reliability across LDES parameters and identify secure configurations.The stated contribution includes configurations that eliminate load shedding and sustain operation under all considered contingencies without additional generation or transmission expansion.Source: §1 · p. 7

2. Methodology

The methodology assesses LDES in nominal full-year operation and under N−1 line outages using AC-OPF, combining renewable and load scenarios, storage parameter sweeps, and shifted contingency windows on a modified synthetic 200-bus high-renewable network.

2. Methodology

  • The study evaluates nominal full-year operation with load-shedding-minimizing AC-OPF and N−1 security with multi-day SC-AC-OPF, quantifying capacity buildout avoided by LDES.It sweeps LDES capacity, round-trip efficiency, and duration, then shifts contingency timing through the year to sample operating conditions including peak load.Source: §2 · pp. 7–8

2.1.1. Multi-period AC-OPF

  • The full-year AC-OPF models 8,760 hourly periods with renewable generators, BESS, and LDES, relaxing power-balance constraints to assess AC-feasible network operation.The formulation extends standard AC-OPF with storage and renewable generation.Source: §2.1.1 · p. 8

2.1.2. Energy storage modeling

  • Storage is represented by co-located BESS and LDES using a common model parameterized by power capacity, duration, and round-trip efficiency.The inverter-based grid interface also models reactive-power capability; its apparent-power rating is set to 1.05 times storage power capacity.Source: §2.1.2 · pp. 10, 12

2.1.3. Objective function

  • Load-shedding variables relax active and reactive power balance, keeping the full-year optimization solvable while quantifying deviation from AC-feasible operation.The objective minimizes load shedding across the full-year scenarios.Source: §2.1.3 · p. 12

2.2. Multi-day security-constrained AC-OPF with LDES

  • The multi-day SC-AC-OPF evaluates line-outage cases without load shedding and couples contingency dispatch to a nominal full-year storage-energy trajectory.Storage discharges during contingencies to support corrective redispatch, with its terminal energy-state deviation constrained during restoration.Source: §2.2 · pp. 12–14

2.3. Uncertainty modeling of load and renewable generation

  • A Gaussian copula models wind and load uncertainty by sampling residuals while preserving historical trend and daily and weekly periodic components.Wind series are decomposed into trend, periodic, and residual components; the same decomposition and copula-based sampling procedure is applied to load profiles.Source: §2.3 · p. 15

2.4. Case study setup

  • The case study uses a 200-bus synthetic Illinois network and adds renewable capacity at five selected thermal-generator sites to represent high renewable penetration.At a capacity ratio of 0.6, thermal capacity is retired without compensating investment, defining a counterfactual reliability gap for storage configurations.Source: §2.4 · p. 17
  • For full-year AC-OPF, 100 scenarios combine 2017 load data with renewable profiles from 2010–2025, reconstructing years from sampled historical years and residual vectors.Load scenarios use 2017 data because other load profiles are unavailable; renewable profiles come from NASA POWER API data.Source: §2.4 · p. 17
  • SC-AC-OPF uses 24-hour contingency and restoration periods, with occurrence times shifted weekly through 2020 and line outages restricted to the top 50% of lines by thermal capacity.The nominal energy-state trajectory is obtained from a full-year AC-OPF using 2020 historical load and renewable profiles; only line-outage contingencies are considered.Source: §2.4 · pp. 17–18
  • Optimization uses ExaModelsPower.jl with MadNLP.jl, a 10^-6 termination tolerance, and a 500-iteration maximum.Computations run on a 56-core Intel Xeon server with 2.01 TB RAM and one NVIDIA H200 GPU.Source: §2.4 · p. 18

3. Results and discussion

Across the tested scenarios, hybrid BESS–LDES reduces load shedding more than equal-power standalone BESS, and LDES-equipped operation remains feasible across the considered N−1 contingency cases. The results also show seasonal energy shifting and lower thermal generation with storage, alongside scenario validation and sensitivity to LDES parameters.

3.1. Statistical evaluation of synthetic scenarios

  • Sampled scenarios closely reproduce historical wind and load distributions and temporal dependence; percentile errors were within 5% for wind and 1% for load.Low autocorrelation errors were reported from 1-hour to 168-hour lags.Source: Table 1 · p. 19, §3.1 · p. 19

3.2. Full-year network feasibility improvement with LDES

  • 83.0% average annual load-shedding reduction with 50 MW hybrid BESS–LDES, versus 68.5% with equal-power standalone BESS, relative to the base network.The hybrid configuration uses 37.5 MW BESS and 12.5 MW LDES.Source: §3.2 · p. 21, Figure 5 · p. 22
  • The hybrid configuration pairs frequent BESS cycling for short-term balancing with LDES seasonal shifting, which discharges during the summer peak period.The LDES state of charge reaches unity before the peak period and falls to 0.1 during it.Source: §3.2 · p. 21, Figure 6 · p. 23
  • With 50 MW and 50 h duration, increasing RTE from 0.3 to 0.8 reduced load shedding by only 5.1%, while 100 MW power capacity achieved a 76.3% reduction across RTE settings.Beyond 50 h duration, further increases in RTE or duration did not noticeably reduce load shedding.Source: §3.2 · p. 24, Figure 7 · p. 25
  • At 50 MW and 100 h, increasing RTE from 0.3 to 0.8 reduced average binding hours by 27.4% at ESS sites and 10.3% at other generators.At 100 MW and 0.8 RTE, binding hours at ESS sites fell by approximately 66.9%, and most remaining generators' binding hours approached zero.Source: Figure 9 · p. 27, §3.2 · p. 27

3.3. Curtailment reduction and nominal operation with LDES

  • 21.2% average reduction in annual thermal generation with BESS–LDES versus the original network across scenarios.LDES shifts energy seasonally, while BESS supports short-term energy balancing.Source: §3.3 · p. 28, Figure 10 · p. 29

3.4. Corrective redispatch and LDES operation under N −1 contingencies

  • The LDES-equipped network was feasible for all considered N−1 contingency windows, whereas the base and standalone-BESS networks had no feasible solutions.The contingency configuration used 150 MW total ESS power, 0.5 RTE, and 100 h LDES duration.Source: §3.4 · p. 30
  • During contingencies, generation was only 5.5% higher on average than the no-contingency base case, with LDES supplying backup power.During restoration, the LDES energy depleted in the contingency period is recovered toward its nominal terminal state.Source: §3.4 · p. 30, Figure 12 · p. 32

4. Conclusion

The full-year and contingency analyses show that LDES improves reliability across prolonged scarcity and N−1 outages. Its value depends on storage duration, efficiency, power capacity, and seasonal energy state.

4. Conclusion

  • Across full-year scarcity and N−1 contingencies, LDES reduces load shedding and preserves feasible operation where networks without BESS–LDES or with standalone BESS do not.The contingency response also allows full recovery of depleted energy within the subsequent 24 h restoration period.Source: §4 · p. 33
  • Higher round-trip efficiency reduces load shedding at limited durations, but its benefit saturates beyond approximately 50 h as storage power becomes the binding constraint, especially at the summer peak.With adequate capacity to serve full load, LDES also reduces renewable curtailment and thermal generation.Source: §4 · p. 33
  • LDES can reduce the additional flexible generation or reserve capacity needed for reliable high-renewable operation while remaining actively utilized during normal operation.Corrective redispatch and restoration generation vary with contingency timing and the LDES energy state.Source: §4 · pp. 33–34
  • The analyses inform LDES planning by clarifying the trade-off between round-trip efficiency and duration, the growing importance of power capacity at longer durations, and the role of seasonal energy state in contingency recovery.The assessment uses a modified 200-bus synthetic network and a full-year multi-period AC-OPF with copula-based tail-event characterization.Source: §4 · pp. 33–34
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