The optimal deployment of switches and tie lines (TLs) plays a vital role in enhancing distribution network (DN) reliability. However, existing methods are primarily designed for radially operated DNs and rely on simplified reliability assessments, which renders them unsuitable for flexible inter-connected DNs (FIDNs) with a complex fault response process. To this end, this paper proposes an explicit reliability-integrated co-planning approach for multi-type switches and TLs in soft open point (SOP)-based FIDNs. First, a novel explicit reliability assessment method for FIDNs is proposed, considering the specific locations, operating features, and interdependencies of various types of switches and TLs, and fully capturing the coupled multi-stage fault response process. In particular, to enable the analytical formulation of FIDN topology, a node-branch state-association model integrating the SOP equivalent model is proposed. To accurately characterize the fault blocking and seamless transfer in FIDNs, a tight circuit breaker tripping model is established. Then, a mixed-integer linear programming (MILP)-based co-planning approach for multi-type switches and TLs in FIDNs is developed, which integrates the proposed explicit reliability assessment method. Case studies are carried out on a 37-node system, a real-world 304-node system, and a large-scale IEEE 8500-node system to validate the accuracy and integrability of the proposed reliability assessment method, and show that the proposed co-planning approach achieves lower annualized costs while enhancing system reliability.

The optimal operation of electrical-heat integrated systems (EHISs) facilitates interactions and synergies between distribution networks (DNs) and district heating networks (DHNs). However, the nonlinear and nonconvex DHN models present significant challenges in obtaining optimal solutions. Most existing methods simplify DHN models by assuming constant hydraulic conditions, sacrificing optimality for computational simplicity. To address this issue, an EHIS optimal operation model was first established, avoiding hydraulic condition assumptions for the DHN, thereby enhancing the optimality of the solution. To reduce mathematical complexity, an input convex neural network (ICNN)-based machine learning model is employed to approximate the complex hydraulic equations of DHNs. Finally, a binary McCormick (B-MC) method is proposed to relax the EHIS nonconvex optimal operation model into a convex formulation, significantly enhancing the convexity accuracy and solving efficiency. The proposed method is validated on both practical and standard test systems, demonstrating superior optimality and efficiency compared to both constant-hydraulic models and existing convex relaxation approaches.

Flexible ramping product (FRP) trading has emerged as a highly effective solution to cope with the volatility and uncertainty introduced by the increasing integration of renewable energy sources. This paper proposes a bidding method for electric vehicle aggregators (EVAs) in the FRP trading market. To effectively articulate the spatiotemporal operational characteristics intrinsic to EVAs, a charging and swapping flexibility aggregation model is formulated. The model is developed by accurately simulating the charging and swapping demands of plug-in electric vehicles and battery-swapping electric vehicles in different charging modes. A novel bilevel optimization model is developed to address the conflicting objectives in the FRP trading market between the EVAs and electric vehicles (EVs), aiming to optimize the incentive prices and charging strategies. The upper level optimizes the bidding profits of EVAs, whereas the lower level models the EV charging behavior using the charging and swapping flexibility aggregation model. To solve the high computational complexity of the high-dimensional nonconvex optimization problem owing to the vast number of EVs, a data-driven evolutionary algorithm incorporated with a zebra optimization algorithm is adopted. Owing to the limited data available for training high-quality agent models in real scenarios, a semi-supervised learning-based tri-training algorithm is adopted to enhance the efficiency of data utilization. Case studies validate the effectiveness of the proposed method.

Internet data center integrated energy systems (IDC-IESs) integrate multiple energy sources with internet data centers (IDCs) to improve system operation efficiency. To account for the effects of information load features and server lifespan degradation on system performance, this paper proposes a novel multiple IDC-IES coordinated planning method. Firstly, a refined multi-layer coupled IDC model is developed. In contrast to existing models, it enables differentiated characterization of multi-type information loads and dynamic quantification of server lifespan degradation, leading to significant enhancements in both accuracy and engineering practicality. Based on this, a coordinated planning model for multiple IDC-IESs considering information load features and server lifespan degradation is developed. It co-optimizes energy device capacities within each IDC-IES, the information load spatiotemporal transfer strategy between them, and the thermal inertia regulation processes of each IDC, thereby enhancing the accuracy and optimality of the planning scheme. Finally, an adaptive two-dimensional surface planarization method is proposed to solve the non-convex planning model. This method combines convex reformulation techniques and adaptive solving strategies to enhance computational precision and efficiency. Case studies on both practical and test systems demonstrate the effectiveness of the proposed method. It achieves cost reductions of 7.00% and 6.95%, respectively, compared to existing models that neglect information load features and server lifespan degradation.

With the increasing penetration of renewable energy sources (RES) in distribution network, the coordination of demand-side electric vehicle (EV) becomes crucial for RES accommodation. By introducing the concept of customer directrix load, this paper proposes a novel closed-loop corrective strategy to enhance the effectiveness of EV demand response. Firstly, a robust composite customer directrix load (CCDL) model is constructed to enhance resilience against uncertainties in EV responses, which integrates control characteristics and response fluctuations to provide tailored full-time guidance for heterogeneous EVs. On the basis, considering that the implementation of demand response is a sequential coupled process, a closed-loop correction mechanism is further proposed to facilitate the multi-stage coordination across RES prediction, CCDL optimization, and deviation feedback. By developing a direction-aware combined prediction model to cope with asymmetric prediction effects, and designing a policy-based gradient descent method for closed-loop refinement, the proposed mechanism enables self-correction against uncertain deviations for demand response implementation. Numerical comparison using real-world case demonstrates that the constructed CCDL model could effectively promote the EV-coordinated RES accommodation, while the proposed deviation correction mechanism can improve the demand response accuracy by 17.88 % over traditional sequential mode.

Climate change has led to an increase in both the frequency and severity of weather-related power outages globally. The inherent stochasticity of extreme weather phenomena has substantially disrupted power grid operations, intensifying vulnerabilities arising from computational complexity, uncertainty, and reduced system inertia, particularly in networks with high penetration of distributed energy resources (DERs). To mitigate these challenges, this study introduces a resilience enhancement framework for distribution systems based on robust safe reinforcement learning (RSRL), which exploits the aggregated flexibility of DERs under frequency security constraints. Initially, acknowledging the spatiotemporal effects of typhoons on distribution networks, a flexibility aggregation model is developed employing linear approximation and adaptive robust optimization (ARO) to reliably define the safe dispatchable range of DERs under both normal and extreme weather scenarios. Subsequently, a novel grid resilience enhancement model is formulated, integrating analytically derived and linearized frequency security constraints that comprehensively incorporate frequency security margins to effectively alleviate typhooninduced impacts. Moreover, to address the dynamic and timevarying solution space encountered during disaster events, a robust safe reinforcement learning methodology is proposed, facilitating efficient resolution of models characterized by complex constraints and uncertainties related to source-load coupling. Validation through simulations on the modified IEEE 30-bus system demonstrates the efficacy of the proposed approach in substantially improving system resilience and stability, while effectively managing challenges associated with extreme weather conditions and frequency stability.

This study presents a data-driven distributionally robust optimization method for the operation of port distribution network (PDN). Capturing the interplay between the PDN and the overall logistics system, the proposed approach integrates crucial operational aspects including berth allocation, quay crane allocation, and electric truck charging tactics. To quantify the uncertainty within a certain confidence region of renewable power forecasting error, an ambiguity set, parameterized based on historical data, is established. Building upon this ambiguity set, a distributionally robust optimization model has been developed for the operation of a PDN. Subsequently, by utilizing duality techniques, the internal maximization problem is converted into a minimization problem, which ensures the tractability of the model. Case studies are conducted on a modified 27-bus distribution network in southern China. The results verify the model's effectiveness in managing port logistics system loads, mitigating renewable power forecasting errors, and reducing PDN operational costs.

While battery-powered propulsion represents a promising pathway for inland waterway freight, its widespread adoption is hindered by range anxiety and high investment costs. Strategic energy replenishment has emerged as a critical and cost-effective solution to extend voyage endurance and mitigate these barriers. This paper introduces a novel approach to optimize energy replenishment strategies for inland electric ships that considers the possibility of adopting multiple technologies (charging and battery swapping) and partial replenishment. The proposed approach not only identifies optimal replenishment ports but also determines the technology to employ and the corresponding amount of energy to replenish for each operation, aimed at minimizing total replenishment costs. This problem is formulated as a mixed-integer linear programming model. A case study of a 700-TEU electric container ship operating on two routes along the Yangtze River validates the effectiveness of the proposed approach. The methodology demonstrates superior performance over existing approaches by significantly reducing replenishment costs and improving solution feasibility, particularly in scenarios with tight schedules and limited technology availability. Furthermore, a sensitivity analysis examines the impacts of key parameters, offering valuable strategic insights for industry stakeholders.

Resilient enhancement measures are crucial for increasing systems' capacities to deal with extreme natural disasters. However, in the pre-disaster prevention stage of hurricanes, research that simultaneously considers load importance, vulnerable lines, and multiple resilience enhancement measures is lacking. To address this issue, a novel resilience-oriented transmission expansion planning (ROTEP) model is proposed that incorporates two resilience assessment indices: the combined loss of loads (CLL) and the vulnerable line survival proportion (VLSP). In addition, the novel function of the proposed model meets the requirements of normal and hurricane damage scenarios based on the collaborative implementation of three resilience enhancement measures (expansion planning, hardening, and unit commitment). The proposed ROTEP model is structured in two stages. The first-stage model aims to meet the load growth demand while minimizing the total planning cost of transmission lines, the operating cost of generators, and the penalty cost of wind power and load shedding across several normal scenarios. Based on the scheme obtained from the first-stage model, damage scenarios are constructed, and a fault chain set is formulated using a hurricane simulation model. Then, a cascading fault graph is constructed to identify vulnerable lines. The second-stage model further enhances the CLL and VLSP (if necessary) under several damage scenarios by hardening the highest-contributing or most vulnerable line. Finally, the efficacy of the proposed ROTEP model for enhancing resilience is validated with a modified IEEE RTS-24 system and a two-area IEEE RTS-1996 system.

With distributed photovoltaics access massively, which is characterized by stochasticity and volatility, has posed new technical challenges to the safe and reliable operation of the distribution network. To evaluate and improve the hosting capacity of distributed photovoltaics in distribution network, the article proposed a robust optimization method for the hosting capacity of distributed photovoltaics in the distribution network, which considers adjustable characteristics of 5G base stations. Firstly, a 5G base station adjustable characteristics model is constructed, which considers the communication load migration and the dynamic power backup of the energy storage. Secondly, a robust optimization model of the maximum hosting capacity of distributed photovoltaics in the distribution network with 5G base stations is established. Then, the model is solved using an increasingly tight linear cut algorithm combined with a column-and-constraint generation algorithm. Finally, the effectiveness of the model is verified on an improved IEEE 33-node distribution network, and the effects of source-load uncertainty, 5G base station communication load migration, and dynamic energy storage backup on the maximum access capacity of distributed photovoltaics in distribution network are analyzed.

Existing resilience-oriented offshore wind farms and transmission network integrated planning (ROWF&TNIP) models lack detailed characterization of the uncertainties associated with wind power and grid faults during typhoon disasters, and tend to be relatively conservative in enhancing resilience. To address these limitations, this paper proposes a multi-scenario distributionally robust model for ROWF&TNIP considering typhoon disasters. This model accounts for multiple uncertainties in wind power and grid faults under both normal operation scenario (NOS) and typhoon disaster scenario (TDS), and enhances resilience in a less conservative manner. Firstly, the multi-scenario distributionally robust uncertainty sets for offshore wind farms (OWF) output and grid fault are established: a conditional value-at-risk (CVaR) based multi-scenario budget uncertainty set to capture the uncertainties of wind turbine outputs and turbine failures under NOS and TDS, and a 1-norm grid fault uncertainty set to represent the uncertain probability distribution of four types of fault: high-probability faults, high-loss faults, cascading faults under TDS and fault-free state under NOS. Subsequently, a multi-scenario distributionally robust ROWF&TNIP model is formulated, utilizing the worst-case expected load-shedding cost under TDS as resilience index, the planning and expected generation cost under TDS and NOS as economic index. This model coordinates resilience and economic efficiency under the most adverse realization of uncertain OWF outputs and grid faults. To further mitigate the conservatism of the ROWF&TNIP model, short-term source-gridload measures, including preventive unit commitment, differential load-shedding and an innovative differential hardening model, are integrated to the planning model. A column and constraint generation (C&CG) based decomposition algorithm is developed to solve the model. In case study section, a series of comparative and sensitivity analyses are conducted on the IEEE-30 bus system and a Chinese 81-bus system to demonstrate the effectiveness of the proposed model and reveal how key parameters of the model influence the resilience and economy of the planning results.

With the gradually increase of power system load and renewable energy resources, the Thevenin equivalencebased voltage stability assessment methods have garnered significant attention. Due to the nonlinearity and time-varying nature of power systems, the Thevenin equivalent (TE) parameters are variable. Neglecting the variation during the calculation of voltage stability margin leads to inaccurate calculation results. Meanwhile, it is theoretically incorrect to apply the impedance matching condition to calculate voltage stability margin when the parameters of the TE model are variable. Regarding these two issues, this paper proposes an improved coupled single-port (CSP) model to calculate voltage stability margin based on a novel limit condition. Firstly, an improved CSP model based on Taylor expansion is introduced. The voltages at all buses can be expanded into Taylor series functions of the studied bus's load impedance modulus parametric variable, obtaining the TE voltage and TE impedance of the studied bus. Subsequently, propose a novel voltage stability limit condition, which is used to replace the impedance matching condition. Finally, a voltage stability margin solution framework is established. Experimental results on extensive standard IEEE test systems demonstrate effectiveness of the proposed voltage stability limit condition. The accuracy and efficiency of the proposed improved CSP model is validated by comparisons with the conventional CSP model and continuous power flow (CPF) approach.

Multi-district integrated energy systems (IESs) can achieve cross-district synergy and efficient energy resource utilization by coordinating and managing various energy subsystems. To effectively capture and utilize the dynamic characteristics of gas and heat interconnected pipes (GHIPs), this paper proposes a novel coordinated operation method for multi-district IESs. Firstly, novel gas and heat virtual energy storage (VES) models are developed to accurately characterize and quantify the dynamic characteristics of GHIPs. Based on these, a coordinated operation model for multi-district IESs is established, which can jointly optimize the energy device outputs within each IES, the multi-energy interaction power between districts, and the storage and release processes of VES for GHIPs. Finally, a two-dimensional piecewise linearization (TDPL) method is proposed to relax the nonconvex coordinated operation problem into a convex model, significantly improving the convexification accuracy and solving efficiency. A case study in northern China demonstrates the effectiveness of the proposed method. It reduces the operation cost by 4.03 % compared to existing multi-district IES models without considering the VES of GHIPs. It is important to note that the cost savings can vary based on factors such as system configuration, pipe parameters, and load dynamics.

In this paper, we propose a two-stage transmission hardening and planning (TH&P) model that can meet the load growth demand of normal scenarios and the resilience requirements of hurricane-induced damage scenarios. To better measure the resilience requirements, the proposed TH&P model includes two resilience assessment indexes, namely, the load shedding (LS) under the damage scenario and the average connectivity degree (ACD) at different stages. The first-stage model, which aims to meet the load growth demand while minimizing the LS, is formulated as a mixed-integer linear program (MILP) to minimize the total planning and hardening cost of transmission lines, the operating cost of generators, and the penalty cost of wind power and load shedding in both normal and damage scenarios. The second-stage model aims to further improve the ACD when the ACD of the scheme obtained from the first-stage model cannot reach the target. Specifically, the contribution of each transmission line to the ACD is calculated, and the next hardened line is determined to increase the ACD. This process is repeated until the ACD meets the requirements. Case studies of the modified IEEE RTS-24 and two-area IEEE reliability test system-1996 indicate the proposed TH&P model can meet the requirements for both normal and damage scenarios.

To enhance the resilience of power grids against typhoon disasters, this study proposes a novel preventive scheduling method by coordinating source, network, and load resources. An evaluation index for unexpected load shedding that considers the importance of load is provided on the basis of the utility function and employed as the objective function. Moreover, the piecewise function based objective function is transformed into a mixed-integer linear formulation by introducing auxiliary variables with clear physical meanings. The startup and shutdown arrangements of units and the optimal scheduling of their outputs, as well as the opening and closing of line switches, for protecting the power supply of important loads and various demand-side management measures are comprehensively modeled. In response to the difficulty in solving the problem caused by numerous factors considered in the model, an identification method for variable and constraint reduction by narrowing the range of switchable lines is proposed to verify the effectiveness of the switchable lines in optimal transmission switching (OTS) in reducing the congestion caused by typhoon disasters. The proposed method is applied to the modified IEEE two-area system and the IEEE-118 system. Results indicate that the utility function based collaborative preventive scheduling method can effectively reduce the loss of important loads during disasters, without excessively cutting off other loads, compared with the widely used load shedding based method. Furthermore, the model dimensionality reduction method based on the effectiveness identification of switchable lines can greatly improve the solving efficiency with on decrease in the accuracy.

Nowadays, power sector is faced with the challenge of low-carbon transition by reducing carbon emissions while ensuring sufficient electricity supply. However, the prolonged transition process may present long-term uncertainties related to the concurrent tasks of regulating total carbon emissions and providing abundant electricity. The variation of these tasks poses a potential threat to the success of low-carbon transition. To confront this challenge, this study proposes a power system expansion planning model which integrates transmission expansion, renewable generation expansion, energy storage systems deployment coordinated with the retirement of coal-fired power plants and retrofit of coal-fired power plants to carbon capture power plants in compliance with transition targets. Then, a risk-averse planning strategy countering the long-term uncertainties of transition tasks is adopted to constitute a two-level multi-objective planning framework based on information gap decision theory. And the second-level risk-averse model is reformulated with an augmented normalized normal constraint method to obtain the Pareto frontier. Numerical results indicate that integrating the retirement and retrofit of coal-fired power plants yields a significant reduction in total cost (4.71 %), compared to a case without such integration. And the transition tasks can be accomplished in a robust way by preferred risk-averse approach.

Against the backdrop of the “double carbon” target, large-scale clean power feeds into the receiving system, and the contradiction of insufficient flexibility resources is becoming more and more prominent. Existing schemes are characterized by subjectivization, homogenization of dimensions, and inappropriate response to data demand, which easily lead to a series of problems such as low computational efficiency. In view of this, this paper proposes an extreme scenario extraction method based on feature selection and isolated forest algorithm for power system flexibility shortage, which solves the common subjectivity problem of extreme selection in the existing schemes, and improves the computational efficiency through the feature selection module to ensure that the extreme scenarios are in line with the demand. The extreme nature of the selected scenarios and the fit of the reconstructed scenarios to the original data are also verified through case analysis.

Emerging prosumers are driving changes in the way traditional distribution systems operate. With the increase in the penetration of renewable energy, the energy management of prosumers has created new challenges. This paper proposes a novel peer-to-peer (P2P) transaction strategy for coupling distributed energy resources (DERs) and electric vehicles (EVs) to achieve optimal energy transaction in high-penetration distribution systems. Firstly, the model of a prosumer aggregate is established. Secondly, the economic models of prosumers and P2P transaction are constructed. Prosumers can evaluate the response benefits of internal distributed generation (DG), energy storage systems (ESSs), flexible load, EVs, and external P2P benefits and propose a joint response mechanism with mutual benefit priority to solve the problem of joint optimization. In addition, to ensure compliance with network constraints, a P2P transaction negotiation algorithm considering network charges is proposed. This algorithm guides prosumers to reach a transaction by modifying the transaction price, enabling fast negotiation without intermediaries. Finally, the proposed method is validated on an IEEE 33-bus test system, demonstrating its ability to reduce internal energy imbalances and improve economic benefits for prosumers.

This paper proposes an interval prediction technology of photovoltaic (PV) power based on parameter optimization of extreme learning machine (ELM) model. First, the weighted Euclidean distance is proposed as the evaluation index of PV power prediction interval. The historical sample units are screened and the ELM training set is optimized. Then, a hybrid optimization algorithm for ELM parameters is proposed. The hidden layer input and output weights and biases parameters of the ELM model are optimized by using the elitist strategy genetic algorithm and quantile regression, and the trained model is used to predict the PV power range. Finally, an actual calculation example is constructed based on the historical data of PV power plants and weather stations. The PV power interval is predicted, and the results are compared with those obtained by other methods. The results of the calculation example show that the method proposed can greatly improve the accuracy of interval prediction while increasing the reliability of interval prediction.