Dynamic Congestion Pricing in Distribution Networks via a Convex-Analytic Bilevel Reformulation

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

With the high penetration of renewable energy, tapping the regulation potential of smart buildings in distribution networks plays a pivotal role in enabling orderly renewable energy accommodation. Customer directrix load-based demand response serves as an effective mechanism for guiding smart building interaction. However, its incentive price, derived as the equilibrium point of a leader-follower game between the operator and load entities, relies on a corresponding bilevel optimization model that suffers from low computational efficiency. To address this limitation, an efficient incentive pricing method is proposed. The proposed linear similarity metric and incentive revenue formulation ensure the linearity of the lower-level optimization problem. Subsequently, based on primal-dual feasibility, an aggregated strong-duality equality, and a discrete-price reformulation, the original bilevel model is accurately reformulated into a single-level mixed-integer linear programming problem, enabling a one-shot determination of the incentive price. Simulation results demonstrate that the proposed linear metric is highly consistent with traditional nonlinear metrics in terms of ranking monotonicity. Compared with time-of-use-only demand response and fixed incentive pricing strategies, the proposed method can identify an economically balanced incentive price that effectively guides smart building energy consumption behavior, improves renewable energy accommodation, and maintains favorable economic performance for both the distribution system operator and smart buildings. These findings support the use of the proposed single-level MILP framework for balancing renewable energy accommodation with the economic interests of the distribution system operator and smart buildings.

Distributed coordination for transmission-distribution systems with nonlinear flexibility aggregation

High shares of distributed energy resources (DERs) transform distribution systems into active participants in integrated transmission and distribution (ITD) operations. Linear models enable scalable distribution-level flexibility aggregation but can misclassify AC feasible operating points, whereas direct nonlinear aggregation becomes costly, especially in multiperiod ITD coordination. This paper reformulates transmission-distribution coordination within a hierarchical optimization framework and introduces a non-iterative predictor-corrector aggregation method. By leveraging path-following techniques from real-time optimal control, the approach achieves tractable computation with guaranteed error bounds. Across 24 radial distribution-network cases and seven meshed variants, including the real KIT Campus North grid, the proposed method yields substantially lower sampled false- and lost-flexibility rates than linear surrogates and a convex relaxation. On two 24-period ITD testcases, the formulation reduces end-to-end wall-clock time by factors of 6 relative to the corresponding centralized formulation, primarily through dimensionality reduction.

Congestion Management Strategy for Distribution Networks Considering Flexible Loads and Advanced Energy Storage under Renewable Energy Integration

: Large-scale integration of customer-side flexible resources and distributed resources can aggravate line congestion and voltage violations in active distribution networks, particularly under power supply guarantee scenarios. This paper develops a bi-level congestion management method that coordinates heterogeneous flexible resources through a Stackelberg game framework. Distributed energy storage, electric vehicles, interruptible loads, and time-shiftable loads are scheduled, and vehicle-to-grid capability is explicitly incorporated to enhance operational flexibility during critical supply periods. The model captures the interaction between the load aggregator (LA) and the distribution system operator (DSO): the LA optimizes the dispatch of aggregated flexible resources in response to price signals, while the DSO seeks to maximize social welfare subject to network security constraints. To solve the nested bi-level problem, an improved grey wolf optimizer (IGWO) with Tent chaotic initialization and nonlinear convergence control is employed. Simulations on a modified IEEE 33-bus system show that the proposed method can relieve line overloading, keep nodal voltages within allowable limits, smooth net-load fluctuations, and improve peak-shaving and valley-filling performance, thereby reducing social welfare losses. The results indicate that the method provides practical support for the secure and economic operation of active distribution networks and facilitates the effective integration of renewable generation and distributed storage.

Fair Dynamic Operating Envelopes using Distributed Multi-Period Optimal Power Flow and Jain Index for Active Distribution Networks

Dynamic operating envelopes (DOEs) are increasingly used to publish time-varying export limits that keep distribution networks within operational limits. Purely technical DOE allocation, however, can systematically privilege electrically favorable prosumers, while embedding fairness directly into a single-period optimal power flow (OPF) objective mixes network feasibility, equity and efficiency in a way that obscures the cost of fairness. This paper proposes a two-stage, multi-period framework that addresses both of these. Initially, a technical distributed OPF computes network-feasible export envelopes. The subsequent stage then applies a dynamic aggregate export budget and redistributes capacity through cumulative proportional fairness, limiting the additional curtailment by an admissible efficiency budget. The resulting fair DOEs are treated as first-stage decisions, while battery storage provides scenario-dependent recourse under demand and renewable uncertainty. The operational problem is solved by a calibrated regional alternating direction method of multipliers (ADMM) on a lossless LinDistFlow model and independently validated using AC power flow. On the IEEE 33-bus feeder over a 24-hour horizon, the technical benchmark yields 2.1097 MWh of renewable curtailment, whereas the fairness-constrained allocation increases curtailment to 5.7216 MWh but caps the maximum cumulative curtailment ratio at 11.20% and raises Jain fairness indices close to unity, with AC voltage deviations below 0.01 p.u. and no voltage or thermal violations under the adopted 0.90-1.05 p.u. limits. Results show that considering both storage (which alleviates curtailment impact) and multi-period fairness (which increases curtailment) is an interesting approach for modern DOE design, which in turn requires a multi-period, co-designed approach.

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

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.