Power Reserve Capacity from Virtual Power Plants with Reliability and Cost Guarantees

The growing penetration of renewable energy sources is expected to drive higher demand for power reserve ancillary services (AS). One solution is to increase the supply by integrating distributed energy resources (DERs) into the AS market through virtual power plants (VPPs). Several methods have been developed to assess the potential of VPPs to provide services. However, the existing approaches fail to account for AS products’ requirements (reliability and technical specifications) and to provide accurate cost estimations. Here, we propose a new method to assess VPPs’ potential to deliver power reserve capacity products under forecasting uncertainty. First, the maximum feasible reserve quantity is determined using a novel formulation of subset simulation for efficient uncertainty quantification. Second, the supply curve is characterized by considering explicit and opportunity costs. The method is applied to a VPP based on a representative Swiss low-voltage network with a diversified DER portfolio. We find that VPPs can reliably offer reserve products and that opportunity costs drive product pricing. Additionally, we show that the product’s requirements strongly impact the reserve capacity provision capability. This approach aims to support VPP managers in developing market strategies and policymakers in designing DER-focused AS products.

💡 Research Summary

The paper addresses the growing need for reserve capacity ancillary services (AS) driven by the increasing penetration of renewable energy sources (RES) and distributed energy resources (DERs). Traditional reserve providers are declining, and system operators will require larger reserve volumes to maintain reliability. Virtual power plants (VPPs), which aggregate numerous small‑scale DERs, are proposed as a new source of reserve capacity. Existing literature evaluates VPP flexibility mainly through the feasible operating region (FOR) and either ignores the strict technical specifications of reserve products (duration, ramp time, reliability > 99 %) or treats forecasting uncertainty inadequately.

To fill these gaps, the authors develop a two‑step methodology that quantifies both the maximum amount of reserve a VPP can reliably offer and the associated cost curve.

Step 1 – Maximum Flexibility Assessment
A mixed‑integer linear program (MILP) is formulated to maximize the reserve quantity qₚ for a given realization of uncertain parameters z (e.g., renewable generation, EV charging demand, load forecasts). The MILP incorporates three groups of constraints: (i) product‑defining constraints that map power exchanges at the point of common coupling (PCC) to the reserve quantity and enforce duration and ramp‑time limits; (ii) network constraints based on a linearized DistFlow model that guarantee voltage, current, and branch‑capacity limits in a radial low‑voltage grid; (iii) DER constraints that capture the operating limits of generators, heat pumps, battery energy storage systems (BESS), and electric vehicles (EVs), including capacity factors, capability charts, and ramp‑rate limits.

Because reserve products are contracted ahead of delivery (lead time t_lead) and must meet a reliability target Rₚ (e.g., 99 %–99.9 %), the extreme quantile qₚ, max corresponding to αₚ = 1 − Rₚ must be estimated. Direct Monte‑Carlo simulation would require an infeasibly large number of MILP solves. The authors therefore adapt Subset Simulation (SS), a technique from structural reliability analysis, to estimate extreme quantiles efficiently. SS decomposes the rare‑event probability into a sequence of conditional events, dramatically reducing the required sample size while preserving accuracy. The result is a reliability‑adjusted maximum reserve quantity qₚ, max that satisfies the product’s reliability requirement.

Step 2 – Cost Assessment
The second step builds a supply curve Cₚ(q) that relates the reserve quantity to its marginal cost. Costs are split into:

Explicit costs – direct operating expenses of DERs (e.g., battery cycling cost, EV charging electricity price, heat‑pump electricity consumption).

Opportunity costs – the foregone profit from not participating in the energy market (e.g., selling energy in the spot market, providing demand‑response services). The opportunity cost is quantified by comparing the optimal dispatch without reserve provision to the dispatch required to honor the reserve commitment.

Summing both components yields a supply curve that reflects the minimum price a VPP would need to bid to be economically viable and the maximum price the market could tolerate before the VPP becomes uncompetitive.

Case Study
The methodology is applied to a realistic Swiss low‑voltage distribution network comprising:

• Distributed generators (≈150 kW total) with stochastic output.
• Electric‑vehicle charging stations (≈200 kW peak).
• Heat pumps (≈100 kW).
• Battery storage (≈300 kWh).

The network is modeled with linear DistFlow equations; DER constraints follow the formulations described in the paper. Three product types are examined: upward, downward, and symmetric reserves, each with varying ramp‑time (rₚ) and duration (tₚ) specifications.

Key findings:

1. Reliability Impact – Tightening the reliability requirement from 99 % to 99.9 % reduces the maximum feasible reserve by roughly 15 %–20 %, illustrating the sensitivity of reserve provision to extreme‑quantile estimation.

2. Cost Structure – Opportunity costs dominate the supply curve, accounting for 60 %–75 % of total cost across all product types. Batteries and EV charging contribute the largest opportunity cost because their alternative market revenues are high.

3. Product Specification Influence – Symmetric products (requiring both upward and downward capability) yield the smallest feasible reserve and the highest marginal cost, while unilateral (upward‑only or downward‑only) products are more economical.

4. Computational Efficiency – The SS‑based quantile estimator reduces the number of MILP solves by an order of magnitude compared with direct Monte‑Carlo, making the approach tractable for daily market participation studies.

Implications

For VPP Operators – The framework enables the design of bidding strategies that respect reliability contracts while minimizing total cost. By explicitly quantifying opportunity cost, operators can decide whether to offer reserve capacity or to pursue higher‑margin energy market transactions.

For Policymakers – The analysis shows that modest relaxations of product specifications (e.g., longer ramp times or slightly lower reliability thresholds) can substantially increase the amount of DER‑based reserve available and lower market prices. This insight supports the design of DER‑friendly ancillary service products and informs regulatory decisions on reserve market rules.

For Researchers – The integration of Subset Simulation with a MILP‑based flexibility model offers a novel, computationally efficient tool for extreme‑event quantile estimation in power system contexts, improving upon Monte‑Carlo, robust optimization, and chance‑constraint methods that either suffer from high computational burden or excessive conservatism.

Conclusion
The authors present a rigorous, two‑stage method that quantifies both the maximum reliable reserve capacity a VPP can provide and the full cost curve associated with that capacity. Applied to a realistic low‑voltage Swiss network, the method demonstrates that VPPs can meet stringent reliability requirements, that opportunity costs are the primary driver of reserve pricing, and that product technical specifications critically shape reserve provision capability. The approach equips VPP managers with actionable market‑participation tools, assists network planners in estimating DER‑derived reserves, and offers policymakers quantitative evidence for crafting ancillary‑service products tailored to the evolving DER landscape.