The robustness of real power systems results in extremely rare transient instability events, which inevitably causes severe sample imbalance issues in data-driven transient stability assessment (TSA). Training TSA models on such imbalanced datasets typically introduces significant assessment bias, which severely degrades model reliability. In existing solutions, samples quantity imbalance is considered, but quality imbalance is ignored. In response to this limitation, a dynamic imbalance correction method considering both quantity and quality imbalance is proposed. Firstly, samples exhibiting similar impacts are systematically categorized into different intervals based on the probability distribution of fault severity. Subsequently, the imbalance degree in each interval is accurately quantified by sample impact norm mean ratios. A cost-sensitive matrix is constructed based on the derived imbalance degree and dynamically adjusted during training process. Finally, the loss function is modified by using the cost-sensitive matrix to alleviate the assessment bias. The simulation results in the IEEE-39 bus system and the East China power grid system show that the corrected model achieves accuracies of 98.41% and 97.80% in the two power systems, respectively. Meanwhile, the proposed method is also applicable to other deep learning models with different structures. Compared with the traditional cost-sensitive method, it has better correction performance, and the training time is shortened by 38.81% and 46.79% in two system, while achieving better convergence effect and continuous stability update.
This study introduces a decentralized control framework for a shared battery energy storage system (SBESS) serving residential households, which can select among multiple tariff schemes offered by the utility company. The problem considered is the decentralized coordination of households’ use of the SBESS, with the objective of maximizing each household’s energy arbitrage while collectively satisfying battery operating constraints and grid power exchange limits. Because households’ battery-use decisions are coupled through a shared, limited resource and future demand and photovoltaic power generation are not known a priori, this control problem is formulated within a multi-agent reinforcement learning setting, where interactions among households are modeled as a Markov game. The proposed belief-based mean-field actor–critic (BBMFAC) learning framework integrates cluster-based mean-field approximation, parameter sharing, and a semi-decentralized training and decentralized execution (s-DTDE) architecture. Within this framework, agents selecting the same tariff option are grouped into clusters and share a parameterized cluster-level critic function, thereby improving scalability and learning efficiency in large multi-agent settings. To address the inherent non-stationarity of the multi-agent environment, agents within each cluster construct beliefs from the average behaviour of other clusters during training and incorporate this information into the update of their own cluster-level critic function. The performance of the proposed method is assessed through numerical simulations using historical data on demand, photovoltaic generation, and electricity tariffs. The results are compared with state-of-the-art approaches, specifically independent and multi-agent deep deterministic policy gradient, as well as mean-field actor–critic methods.
With the accelerating integration of distributed energy resources (DERs), multi-microgrid distribution systems (MMDSs) have become a promising paradigm for enhancing system flexibility and resilience. However, achieving efficient coordination between distribution network (DN) and microgrids (MGs), while coping with significant renewable energy resource (RES) uncertainty, remains a key challenge in MMDS operation. This paper proposes a non-iterative privacy-preserving distributionally robust chance-constrained scheduling model for MMDSs. The model co-optimizes DN controllable generation, reserve deployment, network topology, and DN–MGs power exchanges. To enable efficient and privacy-preserving coordination, we develop a binary-boundary outer approximation (BBOA) method to aggregate MG flexibility, allowing the distribution system operator (DSO) to conduct non-iterative coordination based solely on each MG’s aggregated feasible region (AFR). In addition, a hierarchical strategy is introduced to constrain the cardinality of AFR boundary coefficients, thereby further improving computational efficiency of BBOA. To address RES uncertainty, we propose a physically bounded Wasserstein-based distributionally robust chance-constrained (PBW–DRCC) method. The PBW–DRCC approach explicitly incorporates physical bounds on random variables, thereby preventing physically unrealistic reserve allocations that may arise from exact reformulations. A sequential convex optimization algorithm is developed to handle the nonconvex bilinear constraints introduced by the PBW–DRCC approach. Numerical experiments on a modified IEEE 33-bus MMDS demonstrate that the proposed framework enables secure and economical MMDS operation. The BBOA achieves an average AFR approximation error below 0.2085 %, and AFR-based scheduling yields only 0.0252 % optimality loss compared with centralized coordination. Moreover, the PBW–DRCC approach attains a favorable trade-off between cost efficiency and robustness while maintaining physical feasibility and avoiding unnecessary conservativeness.
The accelerated growth of distributed energy resources (DERs) is pushing low-voltage (LV) distribution networks towards their hosting capacity limits, leading to voltage violations, transformer overloading, and increased photovoltaic (PV) curtailment. Dynamic export limits (DELs) can improve network utilization compared with static export limits. However, centralized DEL schemes can be difficult to scale, require detailed prosumer data, and introduce communication and single-point-failure risks. This paper proposes a co-operative two-layer prosumer control architecture for unbalanced three-phase four-wire LV networks, where the distribution network operator (DNO) provides network information and operating limits, while prosumer-side controllers compute feasible DELs using anonymized real-time measurement exchange. The calculated DELs are then used by local home energy management systems (HEMS) to optimize PV, battery energy storage, and electric vehicle charging. Two DEL allocation strategies are developed: equal addition/reduction and phase-wise proportional curtailment. Base-case simulations on an unbalanced 49-prosumer LV network show that the phase-wise proportional curtailment method reduces total curtailment by 13.5%, compared with the equal addition/reduction method, while maintaining a Jain’s fairness index of 0.9663. Model validation against power flow results shows a maximum voltage estimation error of 1.31 V in the base-case and below 1.98 V under severe phase unbalance conditions. The HEMS-integrated framework increases the mean daily net financial return of prosumers by 33.7%, and decreases network-wide PV curtailment by 39.4% compared with day-ahead DEL scheduling. Case studies on multiple LV networks show that the proposed framework maintains all customer voltages and transformer loading within their operational limits.
Accurate accounting of carbon emissions within virtual power plants (VPP) scheduling is critical to ensure environmentally responsible and economically efficient operation in today’s low-carbon energy landscape. VPPs have become key platforms for aggregating distributed energy resources through advanced control and communication technologies. However, existing studies treat carbon accounting (CA) as a post-scheduling exercise, ignoring its real-time impact on operational decisions, and the carbon penalty strategies adopted are often overly simplistic, especially in the presence of energy storage. To address this limitation and enable cost-effective carbon emission reduction during the scheduling phase, this paper proposes an integrated CA-informed VPP optimal scheduling framework that includes a nonconvex problem formulation, McCormick relaxation to make the problem solvable, and an iterative algorithm to alleviate significant relaxation error. To account for uncertainty in renewable energy output, we formulated the problem as a scenario-based stochastic optimization problem after obtaining a set of representative scenarios through the use of a modified distance-based scenario reduction algorithm. A stepped carbon penalty pricing strategy is incorporated into the problem formulation to represent the realistic carbon market in China. Furthermore, a profit-oriented framework has been developed to determine the marginal cost of carbon for VPP, enabling informed participation in carbon markets. Compared with the original scheme, the proposed CA-informed scheduling reduces carbon emissions by 4.56%, demonstrating its effectiveness in guiding low-carbon operational decisions. Additionally, the proposed carbon market participation strategy increases the daily profit of the VPP by 14.85%, indicating that emission reduction and economic improvement can be achieved simultaneously.
The increasing integration of renewable generation, electrified freight mobility, and carbon policy mechanisms requires computationally robust scheduling strategies for modern eco‑industrial energy networks. Existing approaches typically treat energy dispatch, transportation logistics, and carbon‑certificate markets as separate layers and do not capture the coupled cyber‑physical interactions driven by travel congestion, stochastic renewable patterns, and multi‑market compliance requirements. This study develops a blockchain oracle ‑enabled stochastic energy settlement intelligence framework for travel‑congestion‑aware eco‑industrial parks operated as sustainable energy communities that participate in tokenized twin carbon–green certificate markets while coordinating heavy‑duty electric mobility resources. A multi‑layer stochastic optimization model is formulated to represent uncertainty in renewable outputs, market prices, and logistics behavior through scenario‑based risk management, while ensuring transparent and tamper‑resistant carbon accounting via blockchain‑backed transactional integrity. Heavy‑duty electric vehicles are modeled as mobile storage units that support coordinated power–logistics operations and enhance system flexibility within the integrated energy–mobility ecosystem. Numerical results show that dual‑market participation combined with congestion‑aware mobility coordination reduces operating cost by 1.52%, lowers carbon emissions by 12.59%, and increases renewable utilization by 20.69% relative to baseline operation. The findings indicate that incorporating ICT‑enabled coordination, spatiotemporal mobility dynamics, and market‑coupled decarbonization mechanisms strengthens system efficiency, regulatory compliance, and resilience. The proposed framework provides a transferable computational basis for smart, low‑carbon industrial grid operation and supports advanced planning of sustainable energy–transport infrastructures aligned with future cyber‑physical energy systems.
Non-Technical Losses (NTLs), such as electricity theft or metering irregularities, remain a persistent challenge for power distribution systems, leading to substantial financial losses and operational inefficiencies. In this study, we extend previous work on NTL detection by incorporating explainable machine learning (ML) techniques and evaluating emerging model architectures. Using a real-world dataset from the Hellenic Electricity Distribution Network Operator (HEDNO), we perform an in-depth analysis of consumption data collected from traditional meters. Beyond conventional models, we evaluate the potential of modern transformer-based architectures in capturing complex sequential trends in consumption. A key novelty of this work lies in its focus on explainability: we integrate Shapley values and Permutation Importance to interpret model predictions, offering actionable insights to utility providers and domain experts. Our experimental results demonstrate that ensemble models, particularly CatBoost, achieve strong performance in detecting NTLs, with confirmed NTL cases accounting for over 60% of the top-ranked 10% of users. Furthermore, we show that comparable predictive performance can be maintained using a reduced set of carefully selected features, enhancing both efficiency and explainability.
This study proposes a new decentralized transactive energy market (TEM) framework for the coordinated energy market interactions between distribution system operators (DSOs) and networked microgrids (NMGs) by utilizing stochastic power-based distribution locational marginal pricing (SPDLMP). The proliferation of distributed energy resources (DERs) and the advent of NMGs have initiated a transformative paradigm in the architectural evolution of future distribution system (DS) design. In transactive energy (TE) environments, the strong interdependence between DSO decisions and MG activities necessitates advanced coordination mechanisms, since DER scheduling influences both market-clearing outcomes and distribution system operation. To this end, this paper, as the leading one, proposes a transactive market framework for planning of networked MGs by using SPDLMP mechanism as a dynamic price signal. Rather than relying on explicit coordination signals or fixed pricing mechanisms, the DSO facilitates a SPDLMP-based transactive energy market to enable dynamic and efficient cooperation with NMGs for efficient energy management during operation. The performance of the developed framework is evaluated using a modified IEEE 33-bus test system comprising three MGs; it is subsequently extended to the IEEE 69-bus system with five MGs to rigorously assess its scalability. The results demonstrate that the proposed PDLMP-based TE framework effectively coordinates MG energy scheduling.
This paper presents a metamodel-assisted stochastic Stackelberg framework for dynamic pricing and dispatch coordination between a Distribution System Operator (DSO) and multiple VPPs under joint wind, load, and price uncertainty. To preserve the bilevel information barrier while limiting repeated lower-level solves, the leader search uses adaptive Kriging with Expected Improvement (EI). On the RTS-GMLC test system, the scenario-aware solution yields a 9.7% lower expected DSO profit and a 0.68% lower aggregate VPP cost than the deterministic mean-profile benchmark, indicating redistribution of uncertainty burden rather than uniform economic gain. Robustness checks preserve that interpretation: a budget-matched rerun with five scenarios per VPP shifts the best expected DSO profit from 15.23 to 14.44 kSAR and the total VPP portfolio cost from 116.25 to 113.95 kSAR, while a study with 10 scenarios reaches 14.36 kSAR. A focused network-aware search raises the weighted pre-reconciliation minimum voltage from 0.892 to 0.908 pu and reduces the reconciliation adjustment share from 5.76% to 5.20%, while retaining a positive reconciled DSO profit. Under the full adaptive-search budget, the same penalty setting preserves that physical trend, reaching 0.910 pu and a 4.65% adjustment share after 19 exact evaluations, although not yet a network-cleared economic optimum. A tetra-VPP study with ex-post feeder screening on IEEE 33- and 69-bus benchmarks illustrates scalability. Under a matched evaluation budget, the surrogate-assisted workflow remains competitive with direct heuristic search while reducing exact bilevel evaluations by 97.7%.
Renewable energy curtailment has become a significant operational challenge in power systems with high penetration of variable renewable generation. Unlike generation forecasting, curtailment reflects grid-level balancing conditions and operational constraints in addition to renewable availability, and therefore remains comparatively underexplored. This paper develops a wavelet-augmented Transformer framework for short-term, system-level forecasting of joint solar and wind curtailment in the California Independent System Operator (CAISO) grid over the period 2019–2024. The proposed approach relies exclusively on historically observable system-level operational and temporal inputs, including aggregate load, generation by resource type, interchange flows, and lagged curtailment indicators, and enriches these features with multi-scale representations extracted from historical curtailment windows using discrete wavelet decomposition. A systematic comparison across seven wavelet families identifies a level-2 coif1 basis as providing the most balanced performance across both solar and wind resources. Relative to a non-augmented baseline, wavelet feature enrichment reduces solar mean absolute error by approximately 33% and wind mean absolute error by about 25%, with corresponding improvements in the coefficient of determination. When integrated with an attention-based Transformer encoder, the proposed model achieves the strongest overall performance for solar curtailment forecasting and competitive performance for wind curtailment under identical training and input conditions. Robustness is evaluated using both a held-out multi-year test set and a leakage-aware five-fold time-series cross-validation scheme, confirming stable performance under evolving system conditions. Additional operational analyses indicate that elevated curtailment is consistently associated with low-net-load and renewable-oversupply conditions, supporting the operational interpretability of the proposed forecasting framework under CAISO operating conditions. Local/System decomposition further suggests that localized curtailment behaviour often occurs within broader system-level operating regimes. Overall, the results demonstrate that combining multi-scale signal representations with attention-based sequence modeling enables accurate and robust curtailment forecasting using system-level operational data, while providing useful insight into the operating conditions associated with renewable curtailment. The proposed framework therefore offers a flexible foundation for curtailment-aware grid analysis and operational decision support under increasing renewable penetration.
To address the problems that the support potential of microgrid power restoration is not fully utilized and the multi-level coordination efficiency is insufficient in the main-distribution-microgrid multi-level coordinated power restoration, this paper proposes a robust multi-level coordinated power restoration method for main-distribution-microgrid based on equivalent projection. Firstly, the fast approximation progressive vertex enumerations (FAPVE) method is used to transform the high-dimensional operation constraints inside the microgrid into low-dimensional constraints of the interactive power boundary between the microgrid and the distribution network(DN), so as to provide boundary support for the microgrid output in the multi-level coordinated power restoration. Secondly, a multi-level coordinated power restoration framework and optimization model for main-distribution-microgrid systems are constructed, and the power restoration process is divided into two stages: reconstruction level identification and reconstruction area power restoration. In the reconstruction level identification stage, the optimal reconstruction level is determined with the objective of maximizing the difference between the load restoration amount and the reconstruction cost. In the reconstruction area’s power restoration stage, the optimal load restoration strategy is determined according to reconstruction level identification outcomes, with the goal of maximizing the gap between restored load and the comprehensive costs. Next, the Kullback-Leibler (KL) divergence is utilized to build a characteristic scenario probability set for source-load uncertainty, developing a robust multi-level coordinated power restoration optimization model for main-distribution-microgrid systems, which is solved via the column and constraint generation (C&CG) algorithm. Finally, case studies are conducted on a revised 78-node distribution system to confirm the proposed method’s effectiveness.
The rapid expansion of residential photovoltaic (PV) systems and electric vehicles (EVs) is fundamentally reshaping household electricity demand, charging behaviour, and energy economics. In response, this study develops a unified optimisation framework that jointly integrates PV generation, household load, EV charging behaviour, and both home and public fast-charging options, enabling a realistic assessment of PV–EV systems across diverse behavioural and technical conditions. To capture variability in real-world usage, 3000 distinct scenarios are constructed by combining six representative household demand profiles, five widely used EV models, and 100 scenarios of travel patterns. Optimal PV capacities are determined using a CPLEX-based optimisation model that explicitly accounts for time-varying electricity tariffs and charging availability. The results demonstrate that optimal PV sizing and system configuration are highly sensitive to mobility behaviour and EV characteristics, with required PV capacity varying by up to 50% for the same household. While PV–EV integration consistently reduces electricity costs, financial outcomes depend strongly on the alignment between PV generation, charging opportunities, and daily travel schedules. By explicitly modelling both home and public charging, the analysis quantifies when public fast charging becomes financially advantageous, providing actionable insights for EV users and system planners. Sensitivity analysis further reveals that changes in EV type after system installation can increase annual electricity costs by up to 44%, highlighting the importance of robust PV–EV planning under evolving user behaviour. Battery capacity emerges as the dominant factor: upgrading to an EV with a larger battery generally improves economic performance by absorbing surplus PV generation, whereas switching to an EV with a battery approximately 10 kWh smaller can significantly worsen outcomes by increasing reliance on peak-tariff grid imports and public charging.
Generation Expansion Planning (GEP) in hazard-prone power systems is often conducted under Normal-condition assumptions or fixed scenario weights. These choices can bias prioritization by inflating performance and underweighting high-severity disruptions. We develop a climate-informed RSGEP indicator for renewable-integrated GEP prioritization. Its core novelty is a single end-to-end indicator that combines severity-dependent performance, vulnerability penalties, and climate-informed posterior scenario relevance. Resilience and sustainability variables are evaluated jointly. Performance is assessed using a novel two-stage Slack-Based Measure DEA model with consistent handling of variable directionality. This design reduces self-evaluation bias and limits efficiency inflation under disruption. Disruption impacts are represented through disruption-severity scenarios. Scenario probabilities are updated using a climate-informed Bayesian mechanism that links forward-looking multi-hazard signals to severity transitions. The proposed RSGEP aggregates scenario-wise efficiency and vulnerability penalties using the resulting posterior probabilities. We apply the framework to 74 expansion alternatives in Sistan and Baluchestan, Iran, and validate it against conventional aggregation rules. Excluding sustainability variables overestimates resilience by about 30%. Historical weights also shift prioritization toward low-severity conditions. In contrast, RSGEP separates disruption-fragile designs from plans that sustain efficiency under Severe stress and reshapes the ranking toward robust alternatives.
With the rapid increase in the proportion of distributed renewable energy in rural areas, surplus electricity urgently needs to be transmitted and consumed through the electricity market, with microgrids as the main entity. At the same time, the stable operation of rural microgrids faces multi-type and cross-timescale flexibility demands, such as energy balance, power ramping, and frequency fluctuations, due to renewable energy volatility and load uncertainty. This paper proposes an optimal dispatch method for rural microgrids with high renewable energy penetration, considering three-level flexibility supply-demand balance. First, flexibility is categorized into three levels—energy-type, ramping-type, and frequency-type—based on resource response characteristics. Second, conditional generative adversarial networks (cGAN) are used to generate typical daily scenarios for each season. Within a framework aimed at minimizing annual operating costs, a three-layer nested Dynamic Programming (DP) model at the second-minute-hour levels is constructed to achieve coordinated allocation and refined scheduling of multi-timescale, multi-type flexibility resources. Furthermore, the model integrates a collaborative participation mechanism between the energy market and the ancillary service market, enabling the microgrid to utilize surplus flexibility for market transactions and revenue generation while completing internal regulation. Finally, simulation analysis reveals that the proposed scheme increases market electricity sales by 51.21%, reduces the probability of flexibility shortages from 8.3% to 0.62%, and boosts net revenue by 42.07%, validating the effectiveness and advantages of this method in enhancing flexibility utilization efficiency and economic performance in rural microgrids.
The traditional passive energy consumption model does not adequately address the distribution network security constraints, and fair benefit distribution required for prosumers with distributed renewable energy and adjustable loads in the distribution grid. To address these gaps, this paper proposes an optimal energy transaction strategy to enhance distribution grid security while incentivizing prosumers. A bi-level Stackelberg game optimization model is developed between a virtual power plant (VPP) and an energy-sharing alliance. At the upper level, the VPP sets transaction prices to guide energy trading while ensuring grid security. At the lower level, prosumers form a peer-to-peer energy-sharing alliance, responding to VPP price signals. The model is transformed into a two-stage optimization problem using generalized Nash bargaining theory. The existence of a globally optimal solution is proven, and the bisection method is employed for solving the upper-level problem. The consensus alternating direction multiplier method is used for decentralized peer-to-peer transactions, preserving privacy and independence. By reformulating the model with Karush–Kuhn–Tucker conditions, a fully decentralized iterative solution is achieved. Simulations on the IEEE-33 node distribution grid confirm that the proposed model converges in six iterations. Multi-scenario analysis further validates the effectiveness of the benefit distribution mechanism, which accounts for prosumer contributions in the energy-sharing alliance.
This paper proposes a risk-averse three-stage stochastic programming approach to develop the day-ahead market bidding and offering curves of a virtual power plant participating in a manual frequency restoration reserve-based demand response program. This participation requires that the virtual power plant should comply with the requests from the system operator to decrease its energy consumption from the grid by a specified capacity for a given time. The day-ahead market scheduling strategy of the virtual power plant is, therefore, determined considering the participation in the demand response program and the operation of the assets under its control, i.e., conventional and renewable generating units, a battery, inelastic and flexible demands, and an electrolyzer. Scenarios are used to model the uncertainty in the day-ahead electricity market prices and the activations of the demand response program. The performance of the proposed model is analyzed under a realistic case study based on the Spanish power system. Results show that providing the manual frequency restoration reserve-based demand response program leads to increases in the net day-ahead market participation costs and the rescheduling costs of the virtual power plant due to the program’s activations. Nevertheless, these increases are negligible in comparison with the remunerations obtained. Furthermore, it is concluded through sensitivity analyses that the power assigned in the demand response program and the risk-aversion level significantly influence the operation of the virtual power plant. Lastly, computational times lower than 1 h are obtained, which motivates extending the proposed approach to medium- and long-term models in future works.
