Large-Load Demand Flexibility as Virtual Storage

Abstract: Water electrolysis plants, hyperscale data centers, and aluminum potlines represent gigawatts of demand-side flexibility for bulk power system balancing, operational planning, and procurement services. Such loads are scheduled through per-interval power bounds and horizon energy windows, whereas co-located battery energy storage systems (BESS) operate under state-of-charge dynamics. The two formulations share no common mathematical structure, and the joint procurement value of co-located loads and storage goes unrealized as a result. This paper establishes the connection between the two formulations through a virtual storage (VS) equivalence. Every feasible large-load trajectory under power-bound and energy-window constraints is a valid charge trajectory of a VS device that operates at unity accounting efficiency in the grid power balance. Production and service-level costs lie outside this abstraction and enter the dispatch through curtailment opportunity costs. For a portfolio co-located with a BESS, aggregation reduces the constraint count from O(NT) to O(T) and yields a co-dispatch price for both resources. Validation on the IEEE RTS-GMLC with three representative load classes shows that virtual storage delivers the dominant share of joint procurement savings. In the tested case, savings are additive because the two resources dispatch to non-overlapping intervals, and the curtailment shadow price tracks the peak-price band onset rather than the daily peak price.

• The paper establishes an exact equivalence between large-load curtailment trajectories and charge-only virtual storage, enabling unified linear-program co-dispatch with battery energy storage.
• The RTS-GMLC case study finds that coordinated virtual storage and battery dispatch reduces costs by 33.9% over 14 days, compared with 29.84% for virtual storage alone and 4.06% for batteries alone.
• The proposed aggregation reduces load-side constraints from O(NT) to O(T) under proportional flexibility profiles, while heterogeneous portfolios require disaggregation validation because aggregate flexibility may overstate deliverability.

Motivation and problem statement

Large flexible industrial loads—water electrolysis plants, hyperscale data centers, and aluminum potlines—constitute gigawatt-scale demand-side resources for bulk power system balancing. Yet they are scheduled through a formulation structurally incompatible with that used for battery energy storage systems (BESS): loads are governed by per-interval power bounds and horizon energy windows, while BESS operate under state-of-charge (SOC) dynamics. Because the two formulations share no common mathematical structure, day-ahead scheduling and resource-adequacy models cannot co-optimize them in a unified linear program, and market mechanisms that clear the two resource classes sequentially assign independent shadow prices, precluding joint intertemporal optimization and potentially incentivizing strategic capacity withholding by storage operators.

The paper's central claim is that this gap can be closed exactly, not approximately: every feasible large-load trajectory under power-bound and energy-window constraints is a valid charge trajectory of a virtual storage (VS) device operating at unity accounting efficiency in the grid power balance. Prior work on aggregate flexibility—polytope and polymatroid characterizations of thermostatically controlled load ensembles, flexibility envelopes for operational planning—had not established such an equivalence between curtailment trajectories and storage charge trajectories.

The virtual storage equivalence

The base model assumes each load draws power between a strictly positive process floor $\underline{p}$ and rated power $\bar{p}$, with total horizon energy confined to $[E_{\min}, E_{\max}]$. Defining curtailment as $\delta^t = \bar{p} - p^t$, the energy window converts to curtailment energy bounds $$\underline{D} \leq \sum_t \delta^t \Delta t \leq \bar{D}$$, where $\bar{D} = T\bar{p}\Delta t - E_{\min}$ is the maximum curtailment consistent with the throughput commitment. Because $\delta^t \geq 0$, the cumulative curtailment energy $s^t$ is nondecreasing—precisely the SOC trajectory of a charge-only device with capacity $C_{VS} = \bar{D}$, minimum terminal energy $\underline{D}$, and unity efficiency. Intermediate capacity bounds are automatically satisfied since $\bar{p}$0.

The equivalence is exact within the base abstraction and requires no approximation. Two caveats are stated plainly. First, unity efficiency is an accounting convention: one megawatt of verified load reduction reduces net demand by one megawatt, but production penalties, SLA violations, thermal recovery, and rebound effects are real costs outside the abstraction, representable through calibrated energy-window parameters or curtailment opportunity costs. Second, VS is charge-only; unlike a BESS it cannot inject energy back into the load process. Technology-specific extensions qualify the fit further: electrolyzers conform well (with a ~2% hot-standby mode), data centers fit only under delay-tolerant workloads with 5–10% sheddable depth depending on SLAs and cooling headroom, and potlines' rolling thermal sub-window constraints make the single-horizon model a conservative lower bound on their flexibility.

Portfolio aggregation and co-dispatch

For $\bar{p}$1 loads, aggregate flexibility is the Minkowski sum of individual deviation sets. Additive parameters ($\bar{p}$2, $\bar{p}$3, $\bar{p}$4) define an outer set that contains the true aggregate; equality holds under a proportionality condition requiring all loads to share identical normalized flexibility profiles. Under this condition, replacing disaggregated constraints reduces the load-side block from $\bar{p}$5 to $\bar{p}$6—from $\bar{p}$7 to $\bar{p}$8 constraints—independent of portfolio size. When profiles differ, the outer set overstates simultaneous deliverability and any aggregate dispatch requires ex-post disaggregation validation, with a second-stage disaggregation-constrained LP or tighter inner approximation as fallbacks.

The joint co-dispatch LP minimizes procurement cost plus curtailment opportunity cost $\bar{p}$9 over both the aggregate VS and the co-located BESS. Because VS carries no round-trip conversion penalty, it is preferred over BESS at the same interval when $[E_{\min}, E_{\max}]$0 and prices are positive. The dual variable of the aggregate energy budget, $[E_{\min}, E_{\max}]$1, provides a single value-based price for both resources—a candidate settlement signal analogous to a capacity price, though formal market mechanism design remains out of scope.

Numerical evaluation on IEEE RTS-GMLC

The case study places a 200 MW PEM electrolyzer, 250 MW data center, and 300 MW aluminum potline at the highest-load buses of the three RTS-GMLC areas, with a 200 MW / 400 MWh BESS ($[E_{\min}, E_{\max}]$2) at bus 118. A 14-day summer window (July 5–18, 2020) uses exogenous day-ahead LMPs from the PLEXOS allTX solution, with prices spanning $[E_{\min}, E_{\max}]$3111.59/MWh and roughly 15% of hours at zero <a href="https://www.emergentmind.com/topics/language-model-programming-lmp" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">LMP</a> from midday solar oversupply. All <a href="https://www.emergentmind.com/topics/state-dependent-local-projections-lps" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">LPs</a> solve via HiGHS in under 25 iterations (&lt;1 ms each).</p> <p>On the July 5 reference day (baseline $376,650/day), results are:

Scenario

Daily cost ($[E_{\min}, E_{\max}]$4)</th> <th>Savings (%)</th> </tr> </thead><tbody><tr> <td>Baseline</td> <td>376,650</td> <td>—</td> </tr> <tr> <td>Load-only (VS)</td> <td>275,473</td> <td>101,177</td> </tr> <tr> <td>BESS-only</td> <td>365,252</td> <td>11,398</td> </tr> <tr> <td>Co-dispatch</td> <td>264,075</td> <td>112,575</td> </tr> </tbody></table></div> <p>Over 14 days, co-dispatch saves $[E_{\min}, E_{\max}]$55,475,478 baseline—a mean reduction of 33.9%, versus 29.84% for VS alone and 4.06% for BESS alone. Three findings stand out: VS dominates joint savings under zero opportunity cost, delivering nearly ten times the BESS contribution. This follows because the aggregate VS budget (3,720 MWh) exceeds the BESS capacity (400 MWh) by nearly an order of magnitude, and because VS avoids the $[E_{\min}, E_{\max}]$6 round-trip loss—an efficiency advantage of 362.7 MWh/day on the full curtailment budget. Savings are additive in the tested case because VS concentrates curtailment in peak-price hours while the BESS arbitrates the zero-to-peak spread, so the two serve non-overlapping intervals. The paper explicitly warns this additivity is not guaranteed: nonzero curtailment cost, network constraints, or different BESS sizing could induce resource competition. The shadow price $[E_{\min}, E_{\max}]$7 stays in a narrow $[E_{\min}, E_{\max}]$826.32/MWh band across all 14 days</strong>, even as daily peaks range from $[E_{\min}, E_{\max}]$9112/MWh. It tracks the curtailment-onset hour rather than the daily peak, implying a contract priced at $\delta^t = \bar{p} - p^t$0 would be self-triggering on standard summer days without spike forecasting. The paper notes this stability is established only for the selected summer window; other seasons and price distributions remain untested. A notable negative result: disaggregation of the aggregate dispatch is infeasible on all 14 days, because the inter-area portfolio deliberately violates the proportionality condition—the three loads have structurally dissimilar flexibility signatures. The authors frame this as diagnostic rather than fatal: matching normalized flexibility signatures across constituent loads (actionable through production-contract negotiation) would collapse the outer approximation to exactness and eliminate the disaggregation step entirely. Limitations and open questions Several assumptions bound the reported results. LMPs are exogenous and dispatch does not feed back into network flows, so the quantified savings represent price-taking economic value rather than network-constrained feasibility; a DC optimal power flow embedding is proposed but not implemented. Curtailment opportunity costs are set to zero throughout, which inflates the VS advantage relative to any setting where production economics matter. Only a single BESS site is modeled, leaving multi-site co-location unexamined. The potline uses the conservative base model without rolling thermal constraints. Strategic behavior under the joint settlement signal, full market mechanism design, and seasonal robustness of the $\delta^t = \bar{p} - p^t$1 band are all explicitly deferred. Conclusion The paper establishes an exact equivalence between large-load curtailment feasibility sets and charge-only virtual storage trajectories, enabling unified LP co-dispatch of flexible loads and BESS with load-side constraint complexity independent of portfolio size. On the RTS-GMLC, co-dispatch reduced procurement costs by 33.9% over 14 days, with VS contributing the dominant share due to its absence of round-trip losses, and produced a stable curtailment-budget shadow price tracking peak-band onset. The practical significance is that VS capacity derives from production commitments operators already hold, so the flexibility resource grows without additional grid capital expenditure—though the zero-opportunity-cost, price-taking assumptions mean the reported savings should be read as upper-bound economic value pending network-constrained and nonzero-cost extensions. Paper to Video (Beta) No one has generated a video about this paper yet. Whiteboard No one has generated a whiteboard explanation for this paper yet. Paper Prompts Sign up for free to create and run prompts on this paper. Top Community Prompts Explain it Like I'm 14  off on Knowledge Gaps  off on Practical Applications  off on Glossary  off on Conceptual Simplification  off on Open Problems We haven't generated a list of open problems mentioned in this paper yet. Continue Learning How does virtual storage differ mathematically and operationally from battery energy storage systems?  What assumptions determine whether an aggregate portfolio of flexible loads can be represented exactly by a virtual storage model?  How would nonzero curtailment opportunity costs and network constraints change the reported 33.9% savings?  What market mechanisms could use the virtual storage energy-budget shadow price to coordinate flexible loads and batteries?  Find recent papers about virtual storage for industrial demand flexibility.  Tweets Sign up for free to view the 1 tweet with 0 likes about this paper. 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