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The increasing penetration of renewable energy sources in power systems presents frequency stability challenges, as power electronic-connected sources like photovoltaics and batteries inherently provide limited inertia and damping for frequency regulation. To address this issue, this paper proposes a distributed cooperative control method for secondary frequency regulation. Additionally, it achieves economic dispatch among generators and proportional power sharing among renewable energy sources. The proposed control system enables photovoltaics and battery energy storage systems to actively manage frequency in conjunction with power generators. It operates using a sparse communication network that mirrors the topology of the power network. Moreover, the cooperative control method can tolerate communication time delays while maintaining a stable frequency response. The frequency stability of the proposed control system, both with and without time delays, is assured through Lyapunov methods and eigenvalue analysis. Validation is performed on a modified IEEE 14-bus system with integrated photovoltaics and batteries, demonstrating the efficacy of the proposed secondary frequency control.

Microgrids (MGs) play an important role in enhancing the resilience of distribution systems (DSs). However, each MG has its own operation scheme and the ownership obstructs the coordination of restoration resources from different MGs. To address this problem, this paper proposes a bi-level coordinated restoration framework for the distribution system operators (DSOs) and the microgrid operators (MGOs). In the framework, MGOs report their surplus capacity to DSO once an extreme event occurs, and then DSO dispatches its own resources and orders MGOs’ supporting capacity. After receiving the order, MGOs dispatch distributed generators and energy storage systems to provide the surplus power. The proposed framework is capable of finding the optimal restoration scheme provided that the autonomy of MGs is retained. The stochastic programming is leveraged to model the uncertainty of renewable energy, and the coordinated restoration framework is formulated as a bi-level mixed integer linear programming (BMILP). The relaxation-based bi-level reformulation and decomposition (RBRD) algorithm is adopted to effectively achieve the global optimal solution. The effectiveness of the proposed method is validated on a test system comprised of the IEEE 33-bus system and three IEEE 13 node test feeders.

Abstract Distribution system (DS) communication failures following extreme events often degrade monitoring and control functions, thus preventing the acquisition of complete global DS component state information, on which existing post‐disaster DS restoration methods are based. This paper proposes methods of inferring the states of DS components in the case of incomplete component state information. By using the known DS information, the operating states of unobservable DS branches and buses can be inferred, providing complete information for DS performance restoration before full communication recovery.

Abstract Distributed energy resources (DERs) provide flexible load restoration strategies, which can effectively enhance the resilience of active distribution systems (ADSs). Whereas, the widespread DERs in ADSs complicates the supply‐demand relationship and make the system resilience difficult to access. Therefore, this paper proposes a simulation‐based resilience assessment algorithm of ADSs considering the microgrid formation based on grid‐edge DERs. Microgrid formation is used to depict the resilience gain of grid‐edge DERs on ADSs. Specifically, a resilience assessment framework for ADSs is firstly proposed, where the uncertainty of component state and supply‐demand is modelled based on probability statistics. Then the mixed integer linear programming is used to search for optimal load restoration strategies with microgrid formation. On this basis, a set of resilience indices are defined to quantitatively analyse the resilience of ADSs, and a resilience assessment algorithm with uncertainty scenario generation is proposed to obtain these indices. Furthermore, extensive numerical results based on a modified IEEE 123‐bus feeder validate the effectiveness of the proposed method.

The intermittency of distributed renewable energy resources (DRERs) and the fluctuation of load demand make the supply–demand scenario of active distribution systems significantly different from that of traditional radial distribution systems. Scenario generation is an effective tool for describing supply–demand uncertainty and is therefore of great significance for the planning and operation of active distribution systems with a high penetration of DRERs. This paper proposes a supply–demand scenario generation method for active distribution systems using conditional generation adversarial networks (CGANs). The proposed method is data-driven and utilizes neural networks to learn and represent distribution laws from data without revealing the expression probability distribution. Specifically, it first extracts the features information of historical scenarios as the conditional control vectors (CCVs), then embeds the CCVs to the input of the generator network and discriminator network to achieve conditional control. The proposed approach is verified by the actual time series wind power data and load profiles. Results show that the proposed method can efficiently generate supply–demand scenarios satisfying various statistical characteristics and capture complex spatial–temporal correlations.

Facing the challenges of climate deterioration, environmental pollution, and energy shortages, China has put forward the goals of “carbon dioxide peaking and carbon neutrality”, and the electricity sector will be the key area and the main direction of carbon emissions reduction. To prospect China’s power system and explore the potential for establishing China’s zero-coal power system in the future, this paper proposes a forecasting-test framework for long-term power system planning. We predict, evaluate, and analyze China’s power system from 2025 to 2060 using the proposed forecasting-test framework. During this process, the power capacity mix and the electricity generation mix of China’s power system will gradually transition from coal-fired generators dominated to wind and solar generators dominated. Moreover, the roles of different generators and energy storages are illustrated through the seasonal comparison and sensitivity analysis of the installed capacity of generators. The results indicate that coal-fired generators can be completely withdrawn from the power system, confirming the feasibility and possibility of achieving China’s zero-coal power system by 2060. Although the timing may be advanced or delayed in different scenarios, achieving China’s zero-coal power system will require exercising nationwide planning and making joint efforts of various sectors from now on.

Abstract Considering the limited information sharing between natural gas systems (NGS) and electrical power systems (EPS), this paper proposes a distributed resilience assessment method for NGS and EPS. First, a coordinated restoration framework is presented for incompletely integrated energy systems, and the collaborative benefit redistribution mechanism is proposed to motivate the participation of the cooperative restoration. Then fragility and recovery models for NGS and EPS components are developed, involving the impact of wind and rainfall during typhoons. An emergency load shedding model considering the conditional value at risk under typhoons is built, where the dynamic constraints of gas storage in NGS's pipelines is considered, and a linear approximation method is adopted to make the solution feasible. The modified alternating direction method of multipliers algorithm is used to solve the problem, and herein the self‐adaptive penalty factor is leveraged to boost the efficiency. Based on the valley‐shaped resilience model, the concept of skewness and kurtosis are introduced to give risk‐adverse metrics more systematically to the impact of extreme events. The proposed model and algorithm are validated by case studies. Except for the performance exploration, the weakness and enhancement suggestions are also concluded from the case analysis.

The modern power distribution systems are vulnerable to natural disasters and malicious attacks, while the uncertainty of a large amount of renewable energy sources (RESs) further increases their operational risk in extreme events. An adaptive probabilistic resilience assessment method is thus necessary to provide risk information and help decision making. To tackle the existing problems in uncertainty handling and computation efficiency of resilience assessment in operational stage, this paper establishes a systematic online probabilistic resilience assessment framework. A novel probabilistic modeling method is proposed to characterize the time-varying short-term uncertainty of RESs considering incomplete measurement information due to disasters-induced communication interruption. Moreover, the probabilistic optimal power flow (POPF) model is newly applied to the resilience assessment problem and solved by the cumulant method (CM), which can calculate the statistic information of load power and resilience indexes efficiently with only one optimization at basic operational point. The case study to a modified IEEE 37 node test feeder validates the advantage of the proposed method in reducing operational uncertainty degree, as well as its enough efficiency and accuracy to be applied to the online probabilistic resilience assessment for distribution systems operation.

Abstract Successive failure propagating through a power system, typically caused by extreme weather such as storm and lightning, can cause blackouts by means of a variety of processes. To address this issue, this paper proposes preventive control for successive failures of power system to mitigate the consequences of successive failures in extreme weather. First, based on the Poisson process theory, the authors model the successive failure propagation, and present the confidence interval estimation for the time interval between successive failures. Then, a failure pre‐control methodology that quantifies the grid regulating ability and actions is developed to make decisions for system operators on mitigating overloads of transmission lines. Furthermore, a systematic pre‐control framework for successive failures is first proposed to detect latent risks, eliminate predictable consequential outages, and secure power system stability. Results from IEEE‐9 bus and IEEE‐39 bus standard systems as well as a real‐world system show the feasibility and effectiveness of the proposed method. The proposed preventive control framework can provide a systematic pre‐control action scheme for system operators, and realize enhancement of stability and resilience to power system failures.

The frequent natural disasters caused by global warming have been threatening the safety of power systems for decades. A resilient power system has the ability to recover quickly following a disaster and has been continuously studied these years. However, with the progress of energy transition, a large quantity of renewable energy sources (RESs) has been integrated into the power distribution systems and the uncertainty has complicated the decision and operation of resilient distribution systems. This paper proposes an online resilience assessment method for islanded distribution systems considering the time-varying uncertainty of RESs and loads, based on only the measured data without any forecasting tools. An offline probabilistic modeling and online conditional probability distribution derivation method is proposed to generate short-term power scenarios of RESs and loads dynamically, and an online resilience assessment framework is established with an optimization-based system response model in different outage scenarios of distribution systems. The case study to a modified IEEE 37-node test feeder validates the advantages of the proposed method in generating accurate short-term scenarios of uncertainties and providing reliable resilience assessment results. The proposed framework can be used as a basic tool for the online operation of resilient distribution systems.

Abstract The large‐scale blackouts of distribution systems (DS) caused by extreme natural disasters have aroused a lot of attention. To enhance the resilience of DSs, a novel service restoration and recovery model to minimize the system‐wide load loss is proposed here, where reconfiguration systems and two kinds of moveable resources, that is, mobile sources (MS) and repair crews (RC), are considered. Then, time‐space network (TSN) is applied to model the movement of MSs and RCs over the real‐world transportation networks (TN). However, the introduction of TSN makes solving the model become a time‐consuming task as plenty of variables are involved by it. To tackle this challenge which may lead to the impracticability of the model, a Floyd‐algorithm based TN simplification method is proposed to reduce the variables without sacrificing the equivalence of the TNs before and after the transformation. Finally, the applicability and effectiveness of the proposed model are verified on a 33‐bus test DS and a real‐world DS with complicated TNs.

Abstract Composed of multiple integrated energy systems (IESs) belonging to different stakeholders, multi‐agent IESs (MA‐IESs) are widely concerned because of data privacy protect. As the basis of planning design and reliability evaluation for MA‐IESs, distributed energy resource coordination (DERC) problem is studied in this paper. First, a DERC model for MA‐IESs is established, which considers energy conversion process specifically. Meanwhile, a novel distributed accelerated descent (DAD) algorithm is proposed to realize fully distributed solving. Different from most of the existing researches that investigate the DERC with box constraints, the presented algorithm is able to solve the DERC with general convex constraints. Moreover, the backward operators in the method improve the convergence rate to the best of distributed first‐order optimization algorithm with fixed step size, O(1/T). Furthermore, the presented approach is initialization robustness when the load fluctuations suddenly happened in MA‐IESs. The convergence property, computing, and communication complexity are strictly proved. Finally, the effectiveness of DERC model and DAD algorithm are demonstrated by some modified case studies.

Abstract Extreme weather events, such as hurricanes, impose severe impacts on power systems. A rapid repair for power systems is desired after hurricanes pass to mitigate load‐shedding losses. This study proposes a proactive repair crew deployment model to prepare for post‐disaster repair and restoration. A two‐stage stochastic optimisation framework is designed. In the first stage, the repair crews are allocated to candidate locations ahead of a hurricane. In the second stage, the repair dispatch and load restoration are implemented under several damage scenarios to support the first‐stage decision‐making. A novel repair crew routing method is proposed which considers repair crew cooperation on important damaged components to enable earlier restoration of critical load. A linear‐programming approximation of AC power flow is applied to model the restoration of the transmission system in which the generator start‐up characters and security constraints are incorporated. A scenario‐based decomposition algorithm is applied to solve the stochastic problem and a preprocessing method to identify necessary components is proposed to further reduce computation time. Case studies validate the effectiveness of the proposed model in improving transmission system resilience.

The surging electricity consumption and energy cost have become a primary concern in the planning of the upcoming 5G systems. The integration of distributed renewable energy sources (RESs), such as solar and wind, is considered to be a viable solution for cutting energy bills and greenhouse gas (GHG) emissions of 5G base stations (BSs). Meanwhile, battery swapping (BSW) service for electric two-wheelers (E2Ws) is a burgeoning method to address the issue of E2Ws refueling in urban areas. The authors spotted potentials in the integration and cooperation of 5G BSs, distributed RES generations, and BSW systems for E2Ws. This paper proposes a simulation-based optimization framework for cooperative planning of the integrated system of 5G BS, RES generations, and BSW systems. A multi-paradigm simulation model is presented to mimic all the heterogeneous components contained in the integrated system, as well as their complex interconnections, and to take the involved uncertainties and distributive characteristics into account. Then an optimization model is developed based on the presented simulation model under different scenarios, to minimize the comprehensive annualized expense, with consideration of all the operation and planning constraints of the integrated system. Finally, the proposed simulation-based optimization framework is applied to practical cases under different scenarios. Numerical results and comparison analysis reveal how the integration of RES generations and BSW systems benefit 5G BS in expense cutting and RES accommodating.

An integrated energy system (IES) is a regional energy system incorporating distributed multi-energy systems to serve various energy demands such as electricity, heating, cooling, and gas. The reliability analysis plays a key role in guaranteeing the safety and adequacy of an IES. This paper aims to build a capacity reliability model of an IES. The multi-energy correlation in the IES can generate the dependent capacity outage states, which is the distinguished reliability feature of an IES from a generation system. To address this issue, this paper presents a novel analytical method to model the dependent multi-energy capacity outage states and their joint outage probabilities of an IES for its reliability assessment. To model the dependent multi-energy capacity outage states, a new multi-dimen-sional matrix method is presented in the capacity outage probability table (COPT) model of the generation system. Furthermore., a customized multi-dimensional discrete convolution algorithm is proposed to compute the reliability model, and the adequacy indices are calculated in an accurate and efficient way. Case studies demonstrate the correctness and efficiency of the proposed method. The capacity value of multi-energy conversion facilities is also quantified by the proposed method.

The emerging multi-energy system has brought new challenges and opportunities to energy business worldwide. To address the issues in multi-energy trading, this paper proposes an electricity, heating, and cooling trading model for the interaction between the multi-energy service provider (MESP) and multi-energy consumer (MEC) by using bi-level programming. In the upper level, the model instructs the MESP to make decisions on the optimal energy purchasing scheme and energy economic dispatch. In the lower level, optimal consuming patterns of different energies with the given retail prices are modeled for the MEC. Specifically, a novel multi-energy demand response (DR) program that employs energy conversion devices is proposed. Numerical results show that MEC can reduce its consumption cost via the multi-energy DR. Meanwhile, MESP benefits greatly from the flexibilities of energy conversion. This research can provide theoretical support for the future development of multi-energy trading.

A fast Monte Carlo reliability evaluation method for composite power system based on support vector machine (SVM) was proposesd.Firstly,sample data for training the SVM model was obtained by enumerating component failures and calculating the corresponding minimum load shedding.Then,the SVM algorithm was used to mine the nonlinear mapping relationship between component failures and minimum load shedding,and the minimum load shedding estimation model was trained.Finally,the model was combined with the Monte Carlo simulation.By randomly sampling component states,for each state,the estimation model obtained by the training directly gave the minimum load shedding,thereby achieving a rapid assessment of the reliability of the composite power system.The proposed method is applied to the IEEE RTS 79 system,which verifies its effectiveness.

Increasingly frequent natural disasters and man-made malicious attacks threaten the power systems. Improving the resilience has become an inevitable requirement for the development of power systems. The importance assessment of components is of significance for resilience improvement, since it plays a crucial role in strengthening grid structure, designing restoration strategy, and improving resource allocation efficiency for disaster prevention and mitigation. This paper proposes a component importance assessment approach of power systems for improving resilience under wind storms. Firstly, the component failure rate model under wind storms is established. According to the model, system states under wind storms can be sampled by the non-sequential Monte Carlo simulation method. For each system state, an optimal restoration model is then figured out by solving a component repair sequence optimization model considering crew dispatching. The distribution functions of component repair moment can be obtained after a sufficient system state sampling. And Copeland ranking method is adopted to rank the component importance. Finally, the feasibility of the proposed approach is validated by extensive case studies.

The world is witnessing increasing frequency of extreme events. The power system is the backbone critical infrastructure of our economy and is under treat of such events. The resilient power system is intended to cope with low probability, high risk extreme events including extreme natural disasters and man-made attacks. Realizing resilience in the power system has been an unprecedented mission. Equipped with today’s smart grid technologies, power system can be rendered more resilient by the strategies taken before, during and after a disruptive event erupts. Based on a thorough review of existing works, we present the most-investigated problems and solving measures according to their application stage. In the preparation stage, innovative planning frameworks considering disaster scenarios are discussed; after the event, the system can alter the topology and integrate resource allocation to alleviate load shedding. The characteristics of different disasters are investigated to facilitate enhancing resilience. The review provides a summary of resilience strategies in the power system and can shed light to future research and application. Keywords: Power system, Resilience, Critical infrastructure, Extreme event, Natural disaster

Abstract The natural gas system and electricity system are coupled tightly by gas turbines in an integrated energy system. The uncertainties of one system will not only threaten its own safe operation but also be likely to have a significant impact on the other. Therefore, it is necessary to study the variation of state variables when random fluctuations emerge in the coupled system. In this paper, a multi-slack-bus model is proposed to calculate the power and gas flow in the coupled system. A unified probabilistic power and gas flow calculation, in which the cumulant method and Gram–Charlier expansion are applied, is first presented to obtain the distribution of state variables after considering the effects of uncertain factors. When the variation range of random factors is too large, a new method of piecewise linearization is put forward to achieve a better fitting precision of probability distribution. Compared to the Monte Carlo method, the proposed method can reduce computation time greatly while reaching a satisfactory accuracy. The validity of the proposed methods is verified in a coupled system that consists of a 15-node natural gas system and the IEEE case24 power system.

A novel optimal scheduling method considering demand response is proposed for power systems incorporating with large scale wind power. The proposed method can jointly dispatch the energy resources and demand side resources to mitigate the fluctuation of load and wind power output. It is noticed in practical operation that, without customer's satisfaction being considered, customers might reject the too frequent or violent demand response all together. In this case, two indices that measure the customer satisfaction are then introduced as constraints to reduce the impact to end-users and avoid extreme demand adjustment. To make the model solvable, a proximate decoupling technique is used to dispose the concave constraint introduced by the customer satisfaction constraints. Results from the case studies show that the proposed model can significantly reduce the operation cost of power system while the demand response meets customer satisfaction. Especially, the total start-up costs of conventional thermal units decreases dramatically due to less startup times. Moreover, compared to the consumption way satisfaction constraint, the payment satisfaction constraint has a heavier influence on the cost.

How to restore the load of power system after disasters, especially to guarantee the power supply of the important load, is a significant segment of the research on power system resilience. Nowadays, quantities of research existing has been done to reduce the load loss after disasters. However, there is no clear methodologies or metrics available to evaluate the effects of restoration strategies. Here, a method for evaluating the recovery and economic efficiency of the power system post-disaster recovery strategy is explored, and assessment metrics related are defined. The method considers the repair and recovery process of transmission lines, generators, and the distributed generation at load nodes. After given the repair strategies, components state sampling and system power flow calculation will be conducted to analyse the running state of the system, then simulate the component repair and the load recovery procedure, and finally calculate corresponding metrics. This novel method can obtain and compare the expected effects of different restoration strategies in advance, providing more reliable reference information for system decision makers. Finally, the proposed method is applied to IEEE 14-bus system and verifies its effectiveness and application value.

High-voltage direct current (HVDC) grids are emerging, and their reliability has been an increasing concern for the utilities. HVDC grids are different from typical two-terminal HVDC transmission systems due to the loops in their topology, which makes it difficult to evaluate the reliability by conventional analytical methods. This paper proposes an innovative hybrid method to evaluate the reliability of meshed HVDC grids. First, steady-state models and reliability models are established for the components in HVDC grids, especially for converters and power flow controllers. In the models, virtual buses are introduced to represent the external AC connections to the HVDC grid. Then a hybrid reliability evaluation method is proposed based on an analytical approach and Monte Carlo simulation. One innovation of the paper is the application of an analytical analysis method to accelerate state evaluation in Monte Carlo simulation by skipping unnecessary optimization. The proposed models and methods are verified on two HVDC grids. Test results show that HVDC grids under most failure states (approximately 70%) tend to shed no load except on buses connected to faulted converters, and the application of the analytical method could promote evaluation efficiency significantly.

Asset management of distribution systems is an important issue for smart grid. Maintenance scheduling, as an important part of asset management, affects the reliability of distribution equipment and power supply. This research focuses on long-term distribution system maintenance scheduling aided by available operation information, which is a prominent advantage of smart grid over conventional distribution systems. In this paper, the historical and future operation information in smart grid is taken into account through a decoupled time-varying reliability model of equipment. Based on distribution system reliability assessment, a maintenance scheduling model is proposed to determine the optimal implementation time of maintenance activities to minimize distribution systems’ total cost, while satisfying reliability requirements. A combined algorithm that consists of particle swarm optimization and tabu search is designed and applied to the optimization problem. Numerical result verifies that the proposed method can schedule long-term maintenance of distribution systems in smart grid economically and effectively.

In order to consider the uncertainty and correlation of wind power in multiobjective transmission network expansion planning (TNEP), this paper presents an extended point-estimation method to calculate the probabilistic power flow, based on which the correlative power outputs of wind farm are sampled and the uncertain multiobjective transmission network planning model is transformed into a solvable deterministic model. A modified epsilon multiobjective evolutionary algorithm is used to solve the above model and a well-distributed Pareto front is achieved, and then the final planning scheme can be obtained from the set of nondominated solutions by a fuzzy satisfied method. The proposed method only needs the first four statistical moments and correlation coefficients of the output power of wind farms as input information; the modeling of wind power is more precise by considering the correlation between wind farms, and it can be easily combined with the multiobjective transmission network planning model. Besides, as the self-adaptive probabilities of crossover and mutation are adopted, the global search capabilities of the proposed algorithm can be significantly improved while the probability of being stuck in the local optimum is effectively reduced. The accuracy and efficiency of the proposed method are validated by IEEE 24 as well as a real system.