Single-level MILP incentive pricing for customer directrix load-based demand response in smart buildings

Bilevel Metaheuristic Optimization of Price–Incentive Based Demand Response with Aggregator Coordination for Profit Maximization of Retailer and End User

Optimization of virtual power plant aggregation based on the differentiated adjustment ability of demand-side resource

Two-Stage Optimization Scheduling Model for Flexible Resource Aggregation in High-Share Renewable Energy Power Systems Considering Multi-Type Demand Response

: Aiming at the prominent problems of insufficient coordination of multi-type flexible resources and insufficient utilization of demand response potential in high-proportion renewable energy power systems, this paper proposes a two-stage optimal scheduling model for flexible resource aggregation that integrates price-based and segmented incentive-based demand response. In the first stage, the price-based demand response is adopted to optimize the time distribution of elastic loads with the goal of minimizing the net load fluctuation, so as to smooth the net load curve. In the second stage, based on the optimized net load, the segmented incentive-based demand response market mechanism is combined with electrochemical energy storage, pumped storage and flexibility-transformed thermal power units to construct a scheduling model with the minimum system operation cost as the goal. The quadratic terms in the model are linearized by SOS2 constraints, and the Gurobi solver is used for efficient solution. The results show that the proposed model can reduce the net load variance by 46.5%, reduce the system operation cost by 2.33%, avoid the frequent start-stop of thermal power units, significantly enhance the system flexibility and renewable energy consumption capacity, and provide an effective scheduling solution for the safe and economic operation of new power systems.

Stackelberg Game-Based Optimal Clearing Mechanism for Heterogeneous Energy Storage in Frequency Regulation Markets

The surging integration of volatile renewable energy severely exacerbates power grid frequency fluctuations, yet conventional frequency regulation (FR) market clearing mechanisms fail to efficiently coordinate heterogeneous energy storage systems (ESSs) due to the complete decoupling of multi-dimensional physical performance from economic dispatch. To resolve this critical industry bottleneck, this paper proposes a novel Stackelberg game-based clearing mechanism tailored for diverse ESS participation. A bi-level optimization framework is constructed to internalize physical FR characteristics into market economics; the upper level minimizes the system operator’s total procurement costs by transforming multi-dimensional physical metrics—including dynamic response rates, time delays, and control accuracy—into endogenous performance penalty factors. Concurrently, the lower level maximizes the individual revenues of heterogeneous ESS aggregators under a Gini coefficient-based fairness constraint to mitigate profit monopolization and promote a more sustainable market ecology. To address the computational challenges of high-dimensional non-convexity, an enhanced hybrid Genetic Algorithm and Quadratic Programming (GA-QP) solver is developed to secure robust convergence to the Stackelberg equilibrium. Comprehensive simulation results confirm that the proposed Stackelberg game-based clearing mechanism enables a highly rational, quality-driven allocation of frequency regulation capacity. By dynamically linking physical performance metrics with economic benefit factors, it successfully achieves an optimal balance of interests between heterogeneous energy storage aggregators and the overarching market. Crucially, compared to conventional purely economic models, this mechanism structurally prevents absolute technology monopoly—drastically reducing the market Gini coefficient from a hazardous 0.85 to a healthy 0.32—while sustaining multi-party equity at a negligible system cost increase of only 1.64%. Ultimately, this framework offers a highly feasible and resilient solution for the efficient clearing of multi-type energy storage in modern power systems.

Optimal Scheduling Model for Master-Slave Game Considering Demand-Side Incentives

Day-ahead Coordination of Virtual Power Plants within Active Distribution Networks using Deterministic Bi-Level Optimization

This paper proposes a deterministic bilevel optimization framework for the coordinated operation of Virtual Power Plants (VPPs) embedded in an active distribution network. The Distribution System Operator (DSO) acts as the upper-level leader, minimizing a weighted combination of expenditure, active losses and voltage deviation subject to nonlinear AC power flow constraints, while each VPP operates as a lower-level follower that maximizes its profit under the uniform price signal issued by the DSO. Unlike most existing formulations, which linearize the lower-level subproblem to obtain a Mixed-Integer Linear Program (MILP), the proposed model retains the full AC Optimal Power Flow (AC-OPF) equations, producing a bilevel Mixed-Integer Nonlinear Program (MINLP). The lower-level problem is replaced by its Karush-Kuhn-Tucker (KKT) optimality conditions and the Strong Duality Theorem, yielding a single-level Mathematical Program with Equilibrium Constraints (MPEC). Complementarity conditions are then linearized via the Fortuny-Amat big-M transformation. The framework is validated on the IEEE 33-bus feeder over a 24-hour horizon, with four distributed resources aggregated into a single VPP. Compared with individual dispatch against a regulated time-of-use tariff, aggregation reduces active losses by 10.5 %, the accumulated voltage deviation by 18.3 %, and the bus-hours below 0.95 p.u. from 132 to 29. These gains cost 0.31 % in social cost and 0.26 % in DSO expenditure, while the rent of the aggregator is preserved.