Source-linked AI summary
Real-Time Operation Strategy of Virtual Power Plants With Optimal Power Disaggregation Among Heterogeneous Resources
Qixin Chen, Ruike Lyu, Hongye Guo, Xiangbo Su
TL;DR
VPP regulation requires real-time allocation across heterogeneous resources despite temporal coupling, uncertain signals, and fast-response constraints. The paper develops a stochastic optimal operation framework with reduced-scale, solver-free disaggregation, and reports higher profits with minimal online computation.
Problem
Optimal disaggregation is difficult because heterogeneous resources have temporal coupling, regulation signals are uncertain, and deployment requires fast response.
Method
The paper models heterogeneous VPP resources in a unified framework, prioritizes low-cost resources, and uses an equivalent reduced-scale problem with a solver-free algebraic algorithm.
Results
Numerical results demonstrate substantial improvements in VPP profits while incurring minimal online computational costs.
Takeaways & Limitations
The strategy exploits heterogeneous resource characteristics for optimal real-time regulation disaggregation without online optimisation solvers.
Takeaways & Limitations
The model neglects uncertainties in resource parameters and owner behaviour, including EV uncertainty, and assumes predetermined EV arrival and departure times.
Abstract
from arXiv · showhide
The virtual power plant (VPP) can aggregate flexible resources on the demand side to provide frequency regulation for the grid, helping address the supply-demand balance challenges. When deploying regulation, the VPP disaggregates the requested power adjustment in real time among its internal heterogeneous resources. Achieving optimal power disaggregation in this process is challenging due to the temporal coupling characteristics of the resources, the uncertain regulation signals, and the requirement for fast response. Therefore, existing research relies on heuristic methods, such as proportional disaggregation, and fails to leverage the heterogeneity of multiple resources. Here, we propose an optimal operation strategy for VPPs to provide regulation, exploiting the complementary characteristics of heterogeneous resources by prioritizing the use of low-cost resources while considering temporal coupling. To reduce the computational overhead of online deployment, we further propose a fast disaggregation algorithm to eliminate the reliance on optimisation solvers. We conducted case studies on the operation of a VPP composed of resources including thermostatically controlled loads and industrial production processes. The results verified the reduced operation cost and increased profit of the VPP under the proposed strategy, with only milliseconds of online computation time. We believe that our work can help better exploit demand-side flexibility.
Real-Time Operation Strategy of Virtual Power Plants With Optimal Power Disaggregation Among Heterogeneous Resources
This paper presents a real-time VPP operation strategy for regulation services, combining optimal power disaggregation among heterogeneous resources with a fast solver-free deployment algorithm.
- The paper targets VPP regulation operation with optimal power disaggregation among heterogeneous resources.
- The proposed strategy prioritizes low-cost resources while accounting for temporally coupled operating characteristics over a specified horizon.
- The disaggregation problem is reduced in scale to facilitate online deployment.
- A fast disaggregation algorithm eliminates the need for an optimisation solver during online operation.
1. Introduction
The introduction motivates optimal real-time disaggregation for heterogeneous VPP resources and presents a framework that models temporal coupling, uncertainty, and resource differences while reducing online computational demands.
- Motivation: Increasing renewable generation creates supply-demand balance challenges that motivate using flexible demand-side resources for frequency regulation.
- Problem: VPPs must allocate regulation adjustments among heterogeneous resources, ideally prioritizing low-cost resources to improve net profit.
- Problem: Temporal coupling makes current disaggregation decisions affect later resource operation and potential regulation income.
- Related limitations: Proportional disaggregation and current-signal optimization simplify implementation but fail to guarantee optimization over the entire horizon.
- Proposed approach: The proposed framework unifies models for RES, ES, EV, TCL, and IPP resources and prioritizes low-cost responses while considering temporal coupling.
- Proposed approach: An equivalent reduced-scale disaggregation problem and solver-free algorithm support rapid online response while preserving theoretical optimality.
- Results: Case studies verify that the proposed strategy can improve VPP profits in regulation services.
2. Overall Framework
The VPP operates across market bidding and real-time regulation deployment, modeling uncertain signals and controlling heterogeneous resources. Its lower layer aims to disaggregate power quickly while accounting for impacts on future feasible operation and revenue.
- Secondary frequency regulation corrects persistent frequency and power mismatches over seconds to minutes, enabling demand-side resource participation.
- After market clearing, the VPP receives accepted regulation capacity and responds to operator signals by adjusting its output by δr.
- Possible regulation-signal values are represented by discrete scenarios with representative signal values and probabilities estimated from historical data.
- Upper layer: The upper layer maximises market bidding profit while considering resource constraints, signal uncertainty, and the selected deployment disaggregation strategy.
- Lower layer: The lower layer rapidly controls each resource, recognizing that heterogeneous resources and state variables can affect future feasible operation and overall revenue.
3. Upper Layer: VPP Bidding in the Market
The bidding formulation models heterogeneous resource operation, aggregate regulation tracking, reliability requirements, costs, profits, and the consequences of disaggregation choices. It contrasts this horizon-aware formulation with proportional disaggregation and notes scope assumptions about uncertainty and nonresponsive resources.
- 3.1.1. Individual Operation Constraints: Resource states evolve across time through operating actions and coupled units, capturing storage, thermal inertia, and interdependent industrial production processes.
- 3.1. Standardised Operation Model: The standardized model represents heterogeneous resources including renewable generation, storage, electric vehicles, thermostatically controlled loads, deferrable loads, and industrial production processes.
- 3.1.1. Individual Operation Constraints: Resources unable to provide regulation are modeled with constant power over a specified period and fixed at reference power during deployment.
- 3.1.2. Aggregate Power Balance: Aggregate resource power must follow the grid command, whose adjustment combines the VPP baseline energy bid with regulation capacity and the regulation signal.
- 3.1.3. Regulation Capacity Constraints: Regulation capacity reliability requires representative extreme-signal scenarios to sustain maximum output for the required duration Δt_req.
- 3.1.4. Operation Costs and Profits: The VPP optimizes expected market profit using piecewise-linear resource costs and energy, regulation, capacity, and mileage revenues.
- 3.2. Consideration of Disaggregation Strategy in Bidding: Proportional disaggregation preallocates resource-level regulation capacity and adjusts each resource proportionally, but it does not prioritize low-cost resources and increases control burden.
- 3.2. Consideration of Disaggregation Strategy in Bidding: The formulation treats disaggregation choices as decision variables so the bidding problem can directly optimize the associated strategy over its horizon.
4. Lower Layer: Power Disaggregation Optimisation
The lower layer formulates real-time disaggregation as a cost-minimisation problem that combines immediate operating costs with future-profit impacts from resource-state changes. Its solver-free algorithm prioritises the lowest-cost feasible power segments, preserving the optimal strategy while enabling fast online response.
- 4.1. Optimal Disaggregation Problem: The VPP minimises regulation-response cost over the signal duration, combining immediate operating costs with future-profit effects caused by changed resource states.Ignoring the future-profit term produces a myopic greedy strategy.
- 4.2. Optimality Analysis: Under strict feasibility, the optimal disaggregation solution corresponds to the optimal bidding-problem solution for every regulation-signal scenario.The result is stated as the paper’s optimality proposition.
- 4.2. Optimality Analysis: If signal occurrences match forecast probabilities, the optimal bidding solution remains unchanged within the current period as regulation signals arrive.When actual signals deviate significantly from forecasts, the bidding problem can be resolved to update the state shadow prices.
- 4.3. A Fast Optimal Disaggregation Algorithm: The disaggregation problem is reduced to current-period power segments whose costs and bounds are decoupled, with segments coupled only by the required total output.This structure supports adjusting the least-cost segment first until the required net output is reached.
- 4.3. A Fast Optimal Disaggregation Algorithm: The fast algorithm sorts power segments by marginal adjustment cost and fills low-cost segments within their bounds until the required power adjustment is satisfied.Marginal costs combine immediate resource costs with opportunity costs derived from the optimal operation problem.
- 4.3. A Fast Optimal Disaggregation Algorithm: The fast disaggregation algorithm has linear complexity O(5K) after one-time parameter calculation, where K is the number of power segments.Previous segment outputs can initialise later responses, further reducing computation.
- 4.3. A Fast Optimal Disaggregation Algorithm: When forecast deviations require more adjustment than available resource capacity, the algorithm moves all resources to their maximum and terminates at k = K.The paper notes that conservative reported regulation capacity reduces the likelihood of this case.
5. Case Study
The case study evaluates the strategy on a VPP containing PV, storage, EVs, TCLs, and industrial production resources under PJM market conditions. Across the reported comparisons, optimal disaggregation improves profit, prioritises low-cost resources, accounts for resource-state effects, and achieves regulation-compatible computation time.
- 5. Case Study: The test VPP includes PV, ES, EVs, TCLs, and IPP resources, with 2.5 MW photovoltaic capacity and 1 MW/2 MWh storage capacity.PJM real-time energy and frequency-regulation prices from July 2022 provide market boundary conditions.
- 5.1. Results and Comparisons: Regulation uncertainty is represented by 22 signal scenarios over [-1, 1], with probabilities estimated from the same time periods during the previous 14 days.Actual signals may differ from the predicted distribution, so future-period bids are updated every half hour using recent resource states.
- 5.1. Results and Comparisons: Optimal disaggregation increases market income, decreases operational costs, and produces higher VPP profits than greedy and proportional disaggregation in the reported July 15–28 averages.Greedy disaggregation yields the lowest VPP profits because it minimises only immediate response costs.
- 5.2. Regulation Deployment Results: Optimal disaggregation uses low-cost resources first, whereas proportional disaggregation makes all resources respond simultaneously regardless of their cost characteristics.For an up-regulation command, EVs respond before ES; increased EV power can represent reduced charging rather than discharging.
- 5.3. Sensitivity Analysis: Greedy disaggregation leaves EV state of charge low later in the day, forcing maximum charging before departure and contributing to higher optimal-strategy profits in the final hours.The state trajectories illustrate the effect of temporal coupling on later resource operation and VPP profit.
- 5.3. Sensitivity Analysis: Across ES degradation prices from 0.25 to 4 times the default value, market income decreases as degradation price rises, while the proposed approach consistently outperforms alternatives.The comparison covers both market income and operational costs.
- 5.4. Calculation Time: The fast disaggregation algorithm reduces computation time by several orders of magnitude beyond the subsecond optimal disaggregation problem and meets regulation response-time requirements.The optimal disaggregation problem still relies on powerful solvers and computing platforms.
6. Conclusion
The study presents an optimal VPP regulation strategy that exploits heterogeneous resources and temporal coupling while enabling fast real-time disaggregation. It reports improved VPP profits with minimal online computational cost and identifies practical constraints for future work.
- The strategy optimizes regulation power disaggregation by exploiting heterogeneous resource characteristics and temporal coupling.
- The method transforms the stochastic optimization problem into an equivalent smaller-scale linear program and uses a solver-free rapid disaggregation algorithm.
- Replacing proportional disaggregation enables complementary use of diverse resource types within VPP operation.
- Future work should incorporate practical constraints such as resource ramping-rate limits and examine VPP profit-allocation strategies.
Appendix A. Compact Formulation of the Standardised Operation Model
The appendix gives a compact matrix-form representation of the standardized VPP operation model. It defines matrices and vectors for resource states, transitions, limits, and uncertain regulation scenarios.
- The compact matrix-form model has the same meaning as the earlier element-wise standardized VPP operation model.
- The power matrix contains regulation-signal scenarios and resources indexed at time t.
- Hdis contains incidence matrices describing power-state transitions among resources, while Θ is the state-state transition matrix.
- The vectors δ and Πt represent regulation-signal values and probabilities of corresponding regulation-signal scenarios.
- Underlined and overlined symbols denote lower and upper parameter limits, and 1I denotes an all-ones vector.
Appendix B. Proof of Proposition 1
The proof verifies Proposition 1 by showing that a bidding problem solution satisfies the optimality conditions of the optimal disaggregation problem. Convexity then establishes uniqueness of the optimal value.
- The proof uses KKT conditions to establish that the bidding solution also satisfies the optimal disaggregation problem’s optimality conditions.
- Primal feasibility is checked through constraints (1b) and (3), while dual feasibility and complementary slackness are treated in parallel forms.
- The argument is made at the optimum of a strictly feasible bidding problem under Assumption 1.
- Because the two problems are convex, the optimal value is unique, completing the proposition’s proof.
Appendix C. Proof of Proposition 2
The proof shows that the optimal solution at one time point remains optimal after regulation-response-induced state changes and the resulting change in remaining period duration. It establishes this by preserving feasibility and KKT conditions.
- The proof compares Bid(t̂) and Bid(t̂′), where regulation responses change resource states and the remaining current-period duration.
- Substitution shows that the transformed state constraints at t̂′ remain identical to the corresponding constraints at t̂.
- The same transformation applies to relevant objective-function terms, so the primal constraints of Bid(t̂′) are satisfied.
- Scaling dual variables by the remaining-duration ratio preserves the KKT conditions for Bid(t̂′).