Results show that considering both storage and multi-period fairness is an interesting approach for modern DOE design, which in turn requires a multi-period, co-designed approach.
Abstract
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.
Decentralized energy communities (DECs) allow households, prosumers, and small generators to trade electricity locally, improving grid flexibility and supporting renewable integration. However, local market designs often face a trade-off between efficiency and fairness. Efficiency-oriented settlement rules can produce payment outcomes that are perceived as unfair, while strongly redistribution-based approaches may weaken incentives and reduce operational performance. This paper proposes a hybrid Vickrey-Clarke-Groves (VCG)-Shapley payment framework designed to balance an efficiency-oriented VCG settlement baseline, contribution-based fairness, and settlement stability. The VCG mechanism forms the efficiency-oriented settlement base, and a Shapley-inspired redistribution layer incentivizes meaningful community contributions beyond net energy supply. We develop a 14-factor contribution score to operationalize this approach, covering reliability, flexibility, self-consumption, demand response, renewable integration, transparency, and other supportive behaviors. Scores are evaluated every 30 minutes using time-varying weights to reflect the changing system conditions. A 24-hour simulation with generators, prosumers, and consumers compares the VCG-only settlement, the score-based redistribution, a convex combination payment and the proposed hybrid mechanism. The results show that the hybrid method produces the lowest SD and MAD-based payment dispersion among the evaluated post-VCG alternatives, preserves the VCG settlement anchor, and satisfies interval-level budget balance.
Kaung Si Thu, Pikkanate Angaphiwatchawal, S. Chaitusaney· IEEE Access· 0 citations
As the share of distributed energy resources (DERs) increases in the distribution network, maintaining compliance with network constraints has become a challenge. In this context, dynamic operating envelopes (DOEs) have emerged as a promising solution, where the distribution network operator (DNO) computes and imposes a dynamically varying import and export limit on power exchange between prosumers and the distribution network. Existing DOE approaches often require the prosumers to report their desired power exchange to the DNO, which then computes DOE limits that typically do not exceed the reported values. However, due to uncertain renewable generation and load demand, such DOE limits can potentially result in unnecessary curtailment of generation and load during real-time operation. This work addresses this limitation by computing flexible DOEs using a flexible optimization framework that trades off optimality with flexibility. The proposed approach computes both upper and lower limits on the active and reactive power exchange between each prosumer and the grid, and tries to contain the reported values between the upper and lower limits. As long as the power exchange resides within the DOE limits, network constraints are satisfied. The proposed flexible DOE is validated on a modified Australian low-voltage distribution network. Compared to non-flexible DOE, the proposed framework demonstrates superior performance in reducing curtailment and total operational costs while consistently maintaining voltage magnitudes within desired limits.
Abhishek Mishra, A. Hota, Gayan Lankeshwara et al.· arXiv.org· 0 citations
High penetration of distributed energy resources and uncertain loads creates financial and operational challenges for distribution networks. To address these challenges, this paper proposes a risk-averse, two-stage stochastic coordination framework for a distribution network interacting with the main grid. The day-ahead stage determines the procurement schedule, whereas the real-time stage corrects deviations through real-time market transactions and demand response (DR) mobilization. DR availability is explicitly modeled as scenario-dependent uncertainty. The physical network is formulated using a second-order cone programming (SOCP)-relaxed branch-flow model, which enables an exact mathematical decomposition of distribution locational marginal prices (DLMPs). A Conditional Value-at-Risk (CVaR) metric is integrated to manage extreme tail-risk penalties. Simulations on the IEEE 33-bus system show that the proposed framework reduces the expected daily power shortage by over 10% compared with the risk-neutral baseline. Stronger risk aversion leads to more conservative day-ahead procurement. This forward over-procurement reduces expected real-time marginal scarcity, decreases the expected reliance on local DR during most hours, and dampens absolute DLMP levels at high-priced downstream nodes over a large portion of the operating horizon. These results indicate that tail-risk management reshapes both real-time flexibility utilization and localized economic signals in distribution networks.
Chao Lu, Yu Lu, Meng-Hua Deng et al.· Frontiers in Energy Research· 0 citations
In transitional electricity markets that operate without explicit financial or physical transmission rights but retain priority generation schedules and rigidly executed medium- and long-term (MLT) contracts, network congestion gives rise to settlement imbalance funds that are difficult to allocate fairly. This paper proposes an allocation framework that couples proportional-sharing power-flow tracing with priority-based implicit transmission rights (PBITRs). Flow tracing quantifies each transaction’s contribution to the realized flows on constrained lines, while the priority rank converts dispatch and contract-execution rules into a direction-dependent settlement weight. The clearing inputs are produced by a joint 24-period DC optimal power flow over a modified IEEE 30-bus system, and representative off-peak, peak, and flat periods are recalculated by AC optimal power flow to test the robustness of constrained-line identification, contribution ranking, and allocation shares. In the recalculated case study, the daily congestion-surplus pool is CNY 19,380 and the proposed method assigns 60.6% of it to the MLT A-to-C transaction that physically dominates the constrained corridor, compared with 21.1% under energy-proportional allocation. For the balancing congestion charge pool of CNY 42,492, the fund-specific responsibility set excludes the LMP-settled spot increment and the proposed method assigns 81.2% to the MLT A-to-C transaction. Across the three AC-OPF checks, the constrained-line sets coincide with the DC results at the 0.95 loading threshold, the transaction contribution rankings are identical, and the maximum DC-AC share differences are 1.01 percentage points for congestion surplus and 0.72 percentage points for balancing congestion charge. Sensitivity tests over the priority exponent and loading threshold show smooth and interpretable changes. The framework contributes an ex-post, settlement-neutral tool for markets that clear energy with LMPs before tradable transmission rights are introduced.
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.
Zhe-Kai Xu, Chun-Xiang Yang, Zi-Fen Han et al.· Energies· 0 citations
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.
Laura M. Barajas-Arguello, R. A. Núñez-Rodríguez, Daniel Gebbran et al.· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
