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This paper analyzes the notion of resilience in power systems from a fundamental viewpoint and thoroughly examines its practical implications. This paper aims to describe and classify different high-impact rare (HR) events, provide a more technical definition of power system resilience, and discuss linkages between resilience and other well-established concepts, such as security and reliability. Most relevant decisions of system operators in the face of HR events involve a significant level of stress and strain. In order to make informed decisions within this context, it is crucial to have an all-inclusive picture of the state of the system. This paper provides an appropriate framework that not only characterizes the various states of the system but also derives informed decisions from a resilience-oriented perspective. It also describes and analyzes diverse resilience improvement strategies. Comprehensive models and classifications are provided to clearly capture various aspects of power system resilience.

With increasing power consumption and the number of active units, such as distributed generators (DGs), energy storage systems (ESSs), and transportable ESSs (TESSs), in the distribution system, the requirements for the operability of the power system restoration service increase as well. In this study, the authors propose a new bi‐level optimisation strategy for service restoration (SR) to minimise the final cost of the restoration process and to re‐energise the maximum number of customers. The proposed method considers different power resupply methodologies, such as topology reconfiguration‐based restoration, islanding operation of DG, and the application of TESS for SR, along with their optimal combination, to minimise the financial costs. The primary level comprises a reconfiguration approach and a genetic algorithm to optimise the islanding partition of an active distribution system; the second level consists of the fuzzy logic procedure to set up the combination of energy resources. In addition, this study considers the objective problem formulation as a combination of different subtasks, which represent the financial costs of various components during the restoration process. Case studies are conducted on a modified IEEE 39‐bus distribution network, where the validity and effectiveness of the proposed strategy are demonstrated. [ABSTRACT FROM AUTHOR]

Owing to the important role of the power system in modern societies, its resilience against natural disasters has become a top priority for power system operators and planners. Moreover, in recent years, due to the increasing number and severity of weather-related events, several operational solutions have been proposed to increase the resilience of power systems. For instance, in the distribution part of power systems, dynamic micro-grid (MG) formation can enhance resilience by means of distributed energy resources (DERs) when the main grid is unavailable. Following this concept, the capabilities of electric vehicles (EVs) such as vehicle-to-grid make it possible to use the energy stored inside them to restore critical loads. Therefore, the aggregation of EVs in the distribution system can be seen as a DER from the system operator viewpoint, and operators can benefit from this limited energy resource in MG formation. This study uses two types of EV aggregation for this purpose, i.e. a public parking lot and a residential parking. To improve system performance when using these resources, two steps should be taken: (i) employing a master–slave control technique in each MG and (ii) using a demand-side management programme. [ABSTRACT FROM AUTHOR]

Service restoration is considered as one of the most staple functions of distribution automation, which executes the fault location, isolation and service restoration (FLISR) function in case of contingency occurrence. The first part of the FLISR function is the fault location that can be improved through fault indicators (FIs) employment in electricity distribution system (EDS). On the other hand, the advanced metering infrastructure (AMI) is widely proliferated in EDSs in order to gather the consumers' consumption data for the operational purposes. In this study, FIs are deployed in the EDS considering available AMI data, using a metaheuristic optimisation method. The economic objective function of the optimisation problem consists of the total customers' interruption cost and the total cost of FI deployment. In addition, the technical objective function of the problem is the system average interruption duration index. In order to investigate the effectiveness of the proposed method, it is implemented on bus number four of the Roy Billinton test system. The results show that the number of deployed FIs reduces when the electric utility uses the proposed method. [ABSTRACT FROM AUTHOR]

The service restoration is a vital measurement to enhance the resilience of the electrical distribution network. With the integration of distributed generations (DGs) in the distribution network, the uncertainties are introduced, which have a considerable impact on service restoration. Meanwhile, the soft open points (SOPs) are electronic devices installed in the tie‐line of the distribution networks. They have the ability to control the branch power flow, which can be utilised to assist the service restoration. This study proposes a data‐driven stochastic and robust service restoration method to handle the uncertainties of DGs outputs, which is modelled as a two‐stage conic optimisation programming problem. The non‐parametric estimation method is introduced to estimate the probability density function of forecasted error based on historical data. Furthermore, the nonlinear constraints of the SOPs are reformulated into conic forms so that the proposed model could be solved efficiently. Numerical tests are carried out on the IEEE 33‐bus and 123‐bus distribution networks to show the effectiveness of the proposed method, and the results show the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In cloud computing, it is crucial to maintain service continuity, while power outage is one of the most common and serious threats. To improve the resilience of cloud against power outage, a service provider usually deploys emergency energy supply (e.g., UPSs and generators) in a data center. When a power outage at a data center happens, the cloud service provider needs to make the operation decision on which subset of VMs to keep running and which servers to host such VMs to minimize its loss (or maximize its profit) using the emergency energy supply while the selected VMs are running in the affected data center until they are finished, migrated to other data centers, or normal power supply of the affected data center has been restored. No prior research has theoretically studied such a cloud service continuity problem under power outage. In this paper, we tackle this challenge and investigate the cloud service continuity problem. Specifically, we consider that a profit is associated with maintaining the continuity of a service, denoted as service continuity profit. Based on that we first formulate an optimization problem that aims to maximize the total profit subject to energy constrains. After showing the hardness of the problem, we focus on the design of approximation algorithms for solving the problem, where we consider two practical cases. In the first one with sufficient number of servers for re-provisioning, we develop a constant approximation algorithm of which the worst-case performance approaches the optimal solution within a constant factor ($\approx$ ≈ 4.5-6.4). In the second one, we consider the general case with limited number of servers, and we develop an approximation algorithm with an approximation ratio of around 5.7-8. By combining these two algorithms together, we can achieve both good worst-case performance and average performance. Simulation results demonstrate the efficiency in terms of maximizing the service continuity profit of the proposed algorithms. [ABSTRACT FROM AUTHOR]

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Recently, microgrids (MGs) present a vital role in the transformation of the existing power networks to the smart grids. Connecting MGs to construct the multi-microgrid (MMG) system enhances the robustness of the system against disturbances and upgrades overall network performance. In this paper, the MMG, as a source of self-healing support to the distribution networks, is analysed extensively. In fact, the MMG strengthens the self-healing of the network by participating in the restoration of disturbed loads. In this study, an operational framework is proposed for the self-healing problem in radial interconnected MGs based on two-stage cyber communication network architecture. In the first stage, the local control system (LCS) within each MG, schedules the accessible resources according to the local power consumption target. In the second stage, a number of LCSs are communicated globally to perform self-healing action. The communication of LCSs is accomplished using a consensus algorithm. Nevertheless, when a fault takes place in MG and a line is eliminated, the healthy MGs, due to demand and supply information in the first stage, supply the on-outage loads as far as possible. To validate the effectiveness of the proposed framework, two benchmark distribution networks (the 33-bus and the 119-bus) are employed. [ABSTRACT FROM AUTHOR]

Voltage source converter (VSC)–high-voltage direct current (HVDC) has become a new trend for achieving an efficient and reliable bulk power transmission. The main challenges in VSC-HVDC link are the "soft-start-up" or the restoration of power after the system blackout, with over voltage and less response delay. In this paper, VSC-HVDC link with firefly Levenberg–Marquardt-trained artificial neural network (ANN), termed as ANN-FLM, is proposed to restore the power quickly. The simulation is performed by creating blackout in the system through the introduction of a three-phase fault. The performance analysis is made on VSC-HVDC with ANN-FLM in existing proportional integral controller. The simulated results provide faster restoration and independent control of real and reactive powers. The proposed method minimizes the over voltage to 98% in maximum point, 84% in phase A, 61% in phase B and 82% in phase C, when simulated. [ABSTRACT FROM AUTHOR]

Several parallel restored subsystems exist in the last stage of the build-up restoration process of bulk power systems. The whole system restoration is completed when these subsystems are reconnected and their internal loads are recovered. This paper proposes a robust distributed coordination scheme to achieve reconnection and load recovery of parallel restored subsystems in wind power penetrated transmission systems. First, robust distributed restoration models are constructed considering individual subsystems under uncertain conditions. Then, an inner-outer nested upper-lower (IOUL) iterative algorithm is developed to solve the constructed models. The robust distributed coordination can be realized according to convergence. The proposed algorithm solves the complex non-convex model with uncertain variables by iteratively solving the small-scale mixed-integer linear programming (MILP) problem. The robust distributed restoration scheme allows independent decision-making within subsystems and ensures the feasibility of the distributed restoration strategy under uncertain conditions. The effectiveness of the proposed method is validated using three interconnected 6-bus systems and the IEEE 118-bus system, showing improved computational efficiency and restoration acceleration. [ABSTRACT FROM AUTHOR]

In many China's enterprise‐owned power grids (EPGs), the frequently changing operation state and the poor reliability of some outdated facilities may lead to inaccuracy or even malfunctions of the traditional pre‐decision‐making emergency control systems, which have already caused several blackouts in EPGs. To solve this problem, a real‐time decision‐making emergency control system based on the detailed time‐domain transient stability simulation is designed. Based on the trajectory characteristics of the stability restoration process of EPGs, the stability restoration criteria are proposed to significantly shorten the simulation time needed to judge the elimination of a certain stability problem. Fast decision‐making algorithms for frequency instability, rotor angle instability and branch overload with relatively low computational cost are introduced. Control strategies can be determined within a specific time after faults are detected. The corresponding countermeasures are directly executed when the strategy is obtained. The system configuration is designed to be capable of dealing with complicated and unanticipated faults, such as cascading outages and unexpected grid splitting. The test results of a 31‐node practical EPG show that the proposed algorithms and the system configuration are practical and efficient. This work is a meaningful exploration of the real‐time decision‐making emergency control system. [ABSTRACT FROM AUTHOR]

This study validates an alternative restoration of a critical load area using remote black‐start units. Using the conventional restoration, switching actions on a nominal system voltage create switching transients, especially when energising a transformer. The transients maybe close to the resonance frequencies of a weak island system, which may induce high voltages, delay the restoration and damage the equipment in the grid. This study proposes an alternative restoration procedure where, to avoid switching transients, hundreds of kilometres of transmission lines and several transformers are energised using a gradually increasing voltage, which is controlled by the synchronous generator exciter. This study presents detailed procedure flowcharts, a proof of concept for the proposed procedure using a Finnish and an Austrian field tests and theoretical analyses of the tests. The results show that with the gradually increased voltage, harmonic resonances and switching transients during the initial system energisation maybe avoided. In addition, the study shows that variations in the system frequency may cause voltage problems in a weak system during restoration since the system reactance is dependent on the system frequency. Thus, large frequency variations and the unstable operation regions of turbine governors should be avoided during the restoration. [ABSTRACT FROM AUTHOR]

Summary: The observability of power systems during the parallel restoration of subsystems is one of the most important issues for system operators to accomplish the restoration task as quick as possible. Thus, this article proposes a coordinated optimal plan to solve the observability and sectionalizing problems by determining the locations of phasor measurement units (PMUs) and subsystems. Also, the impact of renewable energy resources on power system sectionalizing and the reliability value of power generation are taken into account in the proposed model. The objective functions that are considered in the optimization problem are the cost of wide‐area measurement system (WAMS), the worst observability index among all subsystems and the lowest value of quality among all subsystems based on the reliability of subsystems. Since there are three contradictory objective functions, a multi‐objective problem (MOP) is proposed as a mixed‐integer nonlinear problem (MINLP). The Pareto curve of the proposed MOP is extracted by using a particle swarm optimization (PSO) algorithm. Two standard power grids are considered to validate the suggested technique. The outcomes of simulations confirm that the observability value of all sections is enhanced during the parallel restoration of the system. Also, the results show that the quality of subsystems in the presence of renewable energy resources is enhanced. [ABSTRACT FROM AUTHOR]

With the increase in a number of online high‐voltage direct current (HVDC) systems in China, a big question for their use as black‐start and restoration of power system outages arises. Line‐commutated converters (LCC)–HVDC systems can significantly reduce recovery time. The black‐start‐up and recovery conditions for LCC–HVDC systems and the connected AC systems are discussed in this study. The appropriate start‐up and recovery modes are identified and the results of the control characteristics of LCC–HVDC systems are analysed in detail. The stability requirements of AC systems in terms of LCC–HVDC system effects are evaluated. Furthermore, the restoration using LCC–HVDC systems, including the priority sequence index of the multi‐HVDC links and the optimisation model of the mentioned problem, is discussed in detail. Compared to the conventional black‐start strategy, the applicability and effectiveness of the proposed method are illustrated using a part of the actual Guangzhou power system as a test system. [ABSTRACT FROM AUTHOR]

Multi‐carrier energy systems (MCESs) can be formed by the integration of various energy infrastructures including power and natural gas systems. The proliferation of bidirectional energy conversion units in an MCES can set the stage for a more resilient and robust system. This study shows how bidirectional energy conversion units and storage devices can be optimally scheduled within an MCES for provision of various regulation services to the grid operator. To that end, a new model is proposed for optimal scheduling of power‐to‐gas (PtG), gas‐fired generation, and gas storage units in an MCES. The model aims to facilitate integration of renewables, utilise gas, and power price arbitrage, provide regulation services to the real‐time (RT) market, and contribute to the system restoration. New indices that quantify the contribution of the MCES operator to RT and ancillary service markets are proposed. The proposed model is validated technically and economically by using a test system historical operating data. Numerical results demonstrate that while the proposed model is technically feasible, it also enhances the economic viability of the grid operator. [ABSTRACT FROM AUTHOR]

Intentional controlled islanding (ICI) and black start allocation (BSA) are two examples of problems in the power systems literature that have been formulated as mixed integer programs (MIPs) and allow reconfiguration of the power system topology. A key consideration in both of these problems is that each island that appears after a reconfiguration must have at least one energized generator. In this paper, we examine three alternative MIP formulations for this restriction, show their equivalence, and prove that two of them are stronger in terms of their linear programming relaxation than the formulation most commonly used in the power systems literature. Since the time to solve MIPs can vary significantly between equivalent formulations, we also present computational experiments on the IEEE test systems for the ICI and BSA problems. We observe that a polynomially separable, exponential in size, strong formulation yields the best performance for the BSA problem and exhibits a comparable performance to a linear in size, weak formulation for the ICI problem. [ABSTRACT FROM AUTHOR]

A resilient power system is capable of providing fast and efficient recovery from outages caused by natural or man-made attacks. After a major blackout, transmission, and distribution system operators (TSOs and DSOs) coordinate to restore the system in a timely and reliable manner. However, these two systems are usually operated separately without considering capabilities and limitations of each individual network, or their mutual impacts. This could prolong the restoration process and lead to unpractical outcomes. Therefore, a distributed strategy for integrated transmission and distribution systems restoration (ITDSR) has been developed in this paper. Based on the alternating direction method of multipliers (ADMM), the distributed algorithm is able to provide the coordinated restoration for both TSOs and DSOs by sharing limited information of boundary buses in an iterative procedure. The ADMM-ITDSR model includes convex ac power flow model and three-phase unbalanced branch flow model. The ITDSR strategy coordinates the operation of distributed energy resources in terms of serving high priority loads across different networks. The effectiveness and advantage of developed models and algorithms are validated and demonstrated through testing of the integrated IEEE test cases, such as 14-bus transmission with 13-node distribution systems, and 39-bus transmission with 123-node distribution systems. [ABSTRACT FROM AUTHOR]

To date, numerous concepts for converter station designs for use in voltage source converter (VSC)‐based high‐voltage direct current (HVDC) systems have been proposed. These differ not only in converter circuit topology, sub‐module design, and control scheme but also in AC‐or‐DC switchgear and other auxiliary equipment. In the main, the existing literature categorises these converter stations according to just the converter circuit technologies and controls. However, for the development of network codes and to enable systematic network studies, a system‐focused and technology‐independent classification is needed. As such a classification does not yet exist, this study proposes a new framework, which categorises VSC station designs according to their capabilities during a DC‐side fault and the method by which post‐fault restoration may be achieved, given that these are the main differentiating factors from a system perspective. The classification comprises six converter station types and three time‐intervals through which to fully characterise a design. Many well‐known forms of converters are used as case studies, and simulation results are used to exemplify the classification framework. The outcome is a generic and technology‐independent way of characterising converter station designs that is useful in wider power‐system analysis but also for putting proposed converter stations into context. [ABSTRACT FROM AUTHOR]

• For grid resilience and real-time scenarios, a unique measure of capacity accessibility during severe events is developed. This metric is designed for real-time system adaptation. • By treating the three phases of PSR as a single, two-stage strategy and using the ADMS with two types of functions—ORP and ORO—at different times, optimal restoring and operating performance can be achieved. • The PSR process ensures global optimality and optimal operational performance. • Formulating the first stage ORP as a MILP problem with practical constraints to maximize restored load capacity for improving computational performance. • The interior point method solves AC optimal power flow for the second stage (ORO) by re-dispatching generators in a step-by-step manner for real-time operation. Large-scale power outages can affect the economy of the country and jeopardize the lives of millions of people, so there is a need for a fast, reliable, and self-healing tool to reduce these losses. Hence, the power system restoration performance can be improved by considering both restoring and operating performance, however, current restoration strategies only consider the restoring performance but ignore the operational performance which can enhance the power system resiliency. Given this background, challenging tasks such as optimal restoration planning (ORP) and optimal real-time operation (ORO) are planned to be tackled by developing an adaptive decision-making strategy (ADMS). In order to reduce the effects of emergency power outages on power systems, this study presents the ADMS, a two-stage self-healing restoration approach. Moreover, a novel metric of capacity accessibility (NMCA) is developed to determine the capacity adequacy status during severe events. The proposed ADMS has two steps, each of which is conducted at a certain time, and is referred to as ORP for the first stage and ORO functions for the second stage. The goal of the ORP optimization model is to maximize system-wide power capacity for electricity demand under extreme events by considering practical constraints, including non-black-start generators (NBSGs) constraints, network topology constraints, and power balance constraints. In order to reduce generation costs, the ORO optimization model adjusts the generated output power to enhance one or more operating performance metrics. The first stage problem is formulated using mixed-integer linear programming (MILP), and it is resolved using the branch-and-bound technique. Moreover, the interior point method solves AC optimal power flow for the second stage. Finally, simulation studies are performed on the modified IEEE 118-bus power systems. The outcomes demonstrate the effectiveness of the proposed strategy for planning (ORP) and real-time operation (ORO); the proposed two-stage strategy is capable of providing an optimal solution for a high-performance online restoration decision support system; the proposed strategy can adapt against the system conditions and contingencies. [ABSTRACT FROM AUTHOR]

• A novel generator start-up sequence optimization strategy is proposed in this work, taking the integration time of wind-solar hybrid systems into account. • The proposed model requires fewer variables compared with other models, therefore the computational efficiency can be greatly improved. • The confidence gap decision theory based generator start-up sequence strategy is proposed to address the generation uncertainty of wind-solar hybrid systems. • Better generator start-up sequence solutions with higher computational efficiency and less conservatism can be attained by employing the proposed strategy. A reasonable start-up sequence of generators considering renewable energy generation integration can effectively improve the restoration efficiency of the power system concerned. The restoration strategy of generators is time-sensitive, however, the computation procedure of existing methods is not fast enough to meet the requirements of practical applications. In this paper, the generator start-up sequence optimization (GSSO) problem is addressed with the integration of wind-solar hybrid systems (WSSs) considered in bulk power systems. Specifically, a deterministic model for GSSO is formulated to maximize the total generation capability during the restoration procedure, in which fewer auxiliary variables are required to promote the computational efficiency. On this basis, in order to deal with the inherent and significant uncertainties of WSSs, a confidence gap decision theory (CGDT) based approach is proposed combining the advantages of stochastic optimization and the information gap decision theory based method while considering the worst-case realization of unknown probability distributions, so that a chance-constrained robust generator start-up solution is thereby attained. Moreover, the formulated CGDT based model is transformed into a mixed integer linear programming problem. Finally, the IEEE 39-bus power system and a modified version of an actual power system in China are employed to demonstrate the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

• Analytical estimation of power low frequency oscillations observed during power system restorations; • Mutual coupling between two overhead lines operating at two different frequencies; • Experimental tests to restore power systems from black-out; • Instantaneous power behaviour of two electromagnetically coupled power systems. This paper derives an analytical formulation to estimate the period and the amplitude of power low frequency oscillations originated by the mutual coupling of two power systems operating at two slightly different frequencies. This is the typical case of the power system restoration tests, in which the restoration backbone involves two overhead lines installed on the same tower. These oscillations have been detected during several real-world power system restoration tests with a non-negligible amplitude. In some cases, the active power exchanged between the two systems could damage the control and protection equipment of the elements involved in the test, leading to the failure of the restoration test itself. For these reasons, the analytical prediction of the period and the magnitude of these oscillations could constitute a useful and reliable tool for the planning and the simulation of the restoration tests. [ABSTRACT FROM AUTHOR]

Power system restoration must be accomplished as soon as possible after a blackout. In this process, available black-start (BS) units are used to provide cranking power to non-black-start (NBS) units so as to maximize the overall power system generation capacity. This procedure is known as the generation start-up problem, which is intrinsically combinatorial with complex non-linear constraints. This paper presents a new mixed integer linear programming (MILP) formulation for the generation start-up problem that integrates non-conventional renewable energy sources (NCRES) and battery energy storage systems (BESS). The main objective consists of determining an initial starting sequence for both BS and NBS units that would maximize the generation capacity of the system while meeting the non-served demand of the network. The nature of the proposed model leads to global optimal solutions, clearly outperforming heuristic and enumerative approaches, since the latter may take higher computational time while the former do not guarantee global optimal solutions. Several tests were carried out on the IEEE 39-bus test system considering BESS as well as wind and solar generation. The results showed the positive impact of NCRES in the restoration processes and evidenced the effectiveness and applicability of the proposed approach. It was found that including NCRES and BESS in the restoration process allows a reduction of 24.4% of the objective function compared to the classical restoration without these technologies.

During power system restoration following a blackout, it is necessary to quickly restore as many generator units as possible to accelerate the speed of the system restoration. Considering that wind power of large capacity has the advantages of fast start-up speed, flexible access method etc., its participation in power system restoration can speed up grid recovery. However, due to wind power fluctuations, the integration of wind power during system restoration may impact the frequency of the restored system. In severe cases, the frequency of the restored system will exceed the limit, which will threaten the safety of the restored system. Consequently, the power reference of the wind farm needs to be optimised during the system restoration. Therefore, an optimisation model of power reference of the wind farm in power restoration based on the fuzzy chance constraints model was proposed in this study. The model maximises the power support of a wind farm on the basis of the safety of the restored system. Simulation results show that this method can provide more power under the condition that the system safety is guaranteed.

In recent years, major power outages caused by extreme natural disasters have incurred large economic losses in distribution systems. This study proposes a transient simulation and verification method for resilience-enhancement strategies and proposed a graphics processing unit-based parallel simulation method. The proposed method can be used to verify the transient feasibility of the distribution system before a strategy is actually executed. Simulations are performed to verify the proposed method.

The increasing wind power penetration makes it necessary for wind power to participate in system restoration, while the maturing wind power control technology makes it possible. To characterise the security level of the system accommodating a certain amount of wind power during black start, the security margin evaluation indexes of wind power particpating in black start were put forward, based on the influence of wind power on the system recovery. Then, the law of wind speed prediction error was analysed, the representative sample set of future wind conditions was generated by historical simulation method, the worst future wind conditions were obtained at a certain level of confidence, and the solution method of the security margin based on time-domain simulation was given. Additionally, with a specific black-start scheme, general steps to solve the security margin were demonstrated, the ‘wind power integration capacity – security margin’ curves were obtained, and the influence of wind power on system restoration security was analysed from multi-views. At last, the impact of wind speed prediction accuracy on system security margin was explored, and other applications of the presented method were given.

This study proposes a service restoration strategy for an AC/DC hybrid distribution system. A mathematical model for voltage source converter with different control strategies in service restoration is developed. Power storage system scheduling strategy is also designed for restoring more power supply. A mixed-integer second-order cone programming is developed for network reconfiguration, and constraint express can make sure the distribution network operates in a radial manner. With the conditions of power balance in islands as the constraints, the islands are then divided. It adopts minimum loss in the object makes it not only stable but also economically acceptable. Simulation results show that the purposed strategy is feasible and effective to reduce lost load, distribution generation curtailments, and network loss.

Once blackouts occur the system operators should re‐energise the affected system in the shortest time. To attain this, restoration plans should be developed beforehand. A deliberate restoration plan considers the supply duration of the cranking power to non‐black‐start units (NBSUs), besides the static and dynamic constraints of the power system. Hence, there should be a method to estimate the restoration duration of NBSUs considering the failure in breakers operating mechanism and the stochastic nature of restoration actions. Accordingly, in this study, generally distributed transition stochastic Petri net is employed to calculate the supply duration of NBSUs, critical loads and the execution time of restoration actions. This is significant because the planners can validate their restoration plans from the NBSUs critical times' point of view or determine energisation time of critical loads. The proposed method has been applied in three test cases, two of these are used for benchmarking, and the other one is a part of Iran bulk power system, which includes a real black‐start test. The results show the effectiveness of the method in estimating the restoration duration. [ABSTRACT FROM AUTHOR]

Distribution system reconfiguration is a complex combinatorial optimisation problem. Finding a globally optimal solution to this problem in a short span of time is a challenging task. Two different network reconfiguration methodologies, namely a look‐up table‐based algorithm and a Pareto‐optimisation‐based algorithm have been discussed. Power loss minimisation and reliability maximisation are taken as objectives for both the methodologies when the system is in the normal operating state. The same algorithms also work for maximum service restoration under the post‐fault condition. For reliability assessment in the presence of distributed generators (DGs), an algorithm is also proposed using the probabilistic model of components. In the other algorithm, reconfiguration is performed in the presence of DGs using a look‐up table. The look‐up table is prepared with the help of the proposed Pareto‐optimisation‐based reconfiguration algorithm to train the system for various loading conditions. The feasibility and effectiveness of the proposed methods are demonstrated using the IEEE 34‐ and IEEE 123‐bus unbalanced radial distribution systems under normal and faulty conditions. The algorithms are also tested on a 13‐bus practical distribution system in the field. [ABSTRACT FROM AUTHOR]

Finding the optimal black-start alternative plays an important role in speeding up the restoration process of a power system after a complete blackout. In this article, a clustering method, affinity propagation, is adopted to deal with the black-start decision making problem. A novel black-start decision making method based on affinity propagation and TOPSIS is proposed. The standard deviation method is used to calculate the weights of the indexes, and a weighted normalized decision matrix is constructed. Then affinity propagation is used to cluster the black-start schemes of the weighted normalized decision matrix, and the optimal cluster is determined. Finally, for each black-start scheme in the optimal cluster, the relative closeness value is computed according to the TOPSIS method, and the best black-start scheme is selected. Compared with the existing black-start decision making methods, the proposed method can not only rank the black-start schemes but also determine which grade each black-start scheme should belong to. Based on the data of an actual power system, experiments were carried out to evaluate the performance of the proposed method. The results show that the proposed method is effective. [ABSTRACT FROM AUTHOR]

• Proposed an improved two-stage optimization method for network and load recovery. • Decouples integer and continuous decision variables and solves them separately. • Proposed method significantly can improve the computational efficiency. • Verified the advantage in computational efficiency and plan optimality. • Demonstrated potential application through simulation in a practical system. Network and load recovery (NLR) during power system restoration is a multi-step mixed-integer nonlinear programming (MINP) problem. The NLR is difficult to be solved as it is NP-hard. Thus, NLR is commonly solved step by step, which is short-sighted and will result in longer restoration time. To obtain a far-sighted NLR plan, this paper proposes an improved two-stage optimization method for NLR. The first stage adopts a mixed-integer linear programming (MILP) model to obtain optimal solutions of integer variables in NLR, namely the load pick-up schedules and transmission line charging schedules. Then in the second stage, a continuous non-linear optimization method based on AC power flow with frequency constraints and load model is established to minimize the restoration duration of the plan generated in the first stage step by step. Case studies are undertaken on a 10-machine 39-bus system and Southeast Hubei Provincial power system of China. Simulation results indicate that the restoration plan obtained from the improved two-stage optimization method is highly effective, while the computational efficient meets the intensive need for restoration scheduling after blackouts. [ABSTRACT FROM AUTHOR]

This paper analyzes synchronous generator self-excitation during power system restoration, caused by a large capacitive load and the impact of generator voltage control on the voltage rise. The paper analyzes measurements from a recent self-excitation incident in the Finnish 400-kV transmission system, models the system using an electromagnetic transient model and a linear d-axis generator model, validates the models using the measurements and analyzes the impact of generator voltage control during self-excitation. Self-excitation is rare during a normal system operation but may occur in a weak system during system restoration after a blackout. Since high voltages caused by the self-excitation may delay the restoration or even damage the equipment, self-excitation should be taken into account in restoration planning. This paper shows that the voltage controller and especially the under-excitation limiter settings of the generator have significant impact on the voltage during self-excitation. This paper also shows that details in the excitation system response influence the simulations significantly and reference measurements from the specific generator are required for detailed modeling. However, all measured incidents with digital static excitation systems are important references for simulations. In addition, special attention should be given to protection relays during the restoration. [ABSTRACT FROM AUTHOR]

This paper proposes a new decentralized restoration scheme in order to realize efficient coordinated restoration of the coupled transmission and distribution (TS-DS) system. First, considering the separated operation of the TS operator (TSO) and DS operators (DSOs) and to avoid the TSO data processing burden, the TS-DS system is divided into several subsystems according to their physical connection. Then, in order to implement the independent but coordinated decision-making of the subsystems, a decentralized decision-making framework is constructed by model decoupling and iterative interaction between TS and DS. Furthermore, for the sake of the convergence of the iterative process with non-convex models, a new decentralized optimization method is developed to obtain the optimal coordinated restoration strategy of the TS-DS system. The proposed decentralized restoration scheme achieves independent decision-making of the TSO and DSOs in the coupled TS-DS system, and solves the non-convergence problem of the decentralized optimization method. The effectiveness of the proposed method is validated using two IEEE standard test systems and a real-world power system. [ABSTRACT FROM AUTHOR]

Service restoration (SR) through network configuration in power systems is a highly investigated problem. In SR, utilities reconfigure the transmission and distribution networks to supply the consumer load demands. However, the advancements in distributed energy storage (DES) systems at the consumer side define a new dimension for SR. In this paper, we approach the network reconfiguration for SR in the presence of DES through mathematical modeling. We present a mathematical model that captures the properties of the power system, and reconfigures the network to supply consumer demand over available lines. This model considers power supply from DES, and proposes the least cost SR plan. We evaluate the proposed approach on the IEEE 14-, 30-, and 57-Bus systems, and report on the collected results. The collected results demonstrate the importance of the available DES in power SR. [ABSTRACT FROM AUTHOR]

To achieve fast power system restoration with high penetration of wind power, using wind farm (WF) as black‐start (BS) source is a promising choice. An energy storage system (ESS) sizing method with the minimum investment cost is proposed to enable WF to be a reliable BS source. The proposed method covers three aspects: (i) providing WF self‐starting power, (ii) dealing with frequency deviation when starting up ancillary machines and (iii) smoothing WF output power while starting up generator unit. During BS progress, ESS power sizing and capacity sizing are both considered as random variables and their marginal distributions are estimated by kernel density estimation to avoid the distribution model mismatch. The correlation between these two random variables is discussed, which shows that these two variables are not independent. To model the dependence structure between ESS power sizing and capacity sizing, copula theory is applied to build the joint probability distribution. A tail dependence analysis and goodness‐of‐fit test included copula selection procedure is conducted to choose the most suitable copula function. A case study with real WF data demonstrates that a better‐fitted copula has lower ESS sizing cost. [ABSTRACT FROM AUTHOR]

The increased frequency of power outages due to natural disasters in recent years has highlighted the urgency of enhancing distribution grid resilience. The effective distribution service restoration (DSR) is an important measure for a resilient distribution grid. In this work, the authors demonstrate that DSR can be significantly improved by leveraging the flexibility provided by the inclusion of demand response (DR). The authors propose a framework for this by considering integrated control of household‐level flexible appliances to vary the load demand at the distribution‐grid level to improve DSR. The overall framework of the proposed system is modelled as a three‐step method considering three optimization problems to (i) calculate feasible controllable aggregated load range for each bus, (ii) determine candidate buses to perform DR and their target load demand, and (iii) maintain the load level in each house through home energy management during the DSR, considering uncertainties in load and solar generation sequentially. The optimization problems are formulated as linear programming, mixed‐integer linear programming, and multistage stochastic programming (solved using the stochastic dual dynamic programming) models. Case studies performed in the IEEE 123‐node test feeder show improvements in resilience in terms of energy restored compared to the restoration process without DR. [ABSTRACT FROM AUTHOR]

The increasing penetration of renewable generation poses several challenges to the operation of distribution networks under emergency conditions. This study proposes a service restoration method that exploits active management of the distribution network. The proposed active network management (ANM) method considers the coordinated control of the available switches, distributed generation, and the operation of on‐load tap changer (OLTC) to determine the optimal service restoration plan. The objectives of the proposed model are the minimisation of (i) the out of service area considering customer priorities, (ii) the number of switch operations, (iii) the number of tap changes of the OLTC, and (iv) the injected power from the substations considering the variation of load demand and renewable generation. The service restoration problem is formulated as a mixed‐integer second‐order cone programming problem, which is efficiently solved by commercial branch and bound solvers. Results on a 135‐bus distribution system and a 540‐bus distribution system highlight the importance and the benefits of incorporating ANM into the solution of the service restoration problem. [ABSTRACT FROM AUTHOR]

The resilience in critical infrastructures context indicates the capability to anticipate, absorb, resist and recover from an event or adversity. In a power distribution system, as the frequency of severe weather event increases, this characteristic becomes mandatory, considering the impact in the society when a blackout occurs. This study proposes the analysis of power distribution systems resilience through two stochastic resilience indexes. Given several simulated weather scenarios and several numbers of available repair crews, the resilience indexes estimate the probability of a waiting crew time greater than a threshold as well as for the impact in the total time to restore the entire distribution system. These indexes, together with a costs and losses estimation methodology help the utilities in the decision support process as it demonstrates how the number of available repair crews will impact in the restoration process and costs for each possible weather scenario. The result for a real Brazilian power distribution system indicates its feasibility and benefits for the utilities. [ABSTRACT FROM AUTHOR]

This study proposes an agent‐based approach to have a reliable service restoration scheme, which is vital to restore as many loads as possible after a permanent fault. The proposed multi‐agent system (MAS) has four different types of agents: feeder agents, zone agents, switch agents and DG agents. The agents can communicate and cooperate with each other in order to supply services to out‐of‐service customers. An artificial neural network has been considered to handle DG uncertainties. The restoration plan is built in a distributed manner, based on local data considering system conditions, operational constraints and fault location. The result of the proposed MAS is a switching sequence. After defining this sequence, the command for opening will be received by circuit breaker agents. In case of one switch failure, the plan cannot be implemented, and hence the restoration plan will fail. To have a reliable restoration plan, the main feeder agent has to handle malfunction in order to operate the system at an acceptable range without violating system constraints. Different loading conditions have been considered under different scenarios and the results of the proposed approach for each scenario have been compared. Simulation results show the efficiency of the proposed agent architecture. [ABSTRACT FROM AUTHOR]

Microgrids may suffer from full blackouts when confronted with unexpected disruptions due to man‐made faults or natural disasters. How to quickly restore the power supply of microgrids by making use of local distributed energy resources (DERs) is therefore a practical issue to help microgrids ride through full blackouts. Accordingly, this study proposes a novel black start strategy for microgrids to determine the restoration sequence and optimally allocate the DERs after full blackouts. In particular, the uncertainty of power output of renewable energy sources is considered using a data‐driven chance‐constrained approach when renewable energy sources are integrated. The proposed approach only utilises historical data and does not need any prior knowledge about the true probability distribution of the uncertainty. In addition, affine‐based techniques and sample‐dependent band functions are developed to convert the chance‐constrained problem into a tractable mixed‐integer linear programming problem. Finally, numerical experiments based on two microgrid test systems are performed to validate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology to repair crews dispatch during distribution feeders restoration immediately after remotely controlled actions have been taken. Our method determines the sectors patrol sequence using the expected number of faults for each sector considering a previously calculated fault probability. Next, a road graph mapping of the buses is obtained by associating each bus with its real-world position. The crews' route inside each sector is determined by the application of the nearest neighbor algorithm on that mapping. The case studies analyzed 24 real faults available in the database of a Brazilian power distribution company, and, a comparison was made between the time spent to locate the failures by simulating both the proposed methodology and the usual greedy strategy. The average time spent in localizing all the failures was from 9.49 % to 41.81 % shorter than in the usual method. Moreover, the speed and distance of repair crews showed weak influence in the crew dispatch methodology efficiency. Such results indicate an enhancement of the power distribution QoS indicators by using the proposed methodology to deal with faults. [ABSTRACT FROM AUTHOR]

Power system restoration after a major blackout is a complex process, in which selection of energising paths is a key issue to realise unit and load restoration safely and efficiently. In general, the energising path scheme made beforehand may not be executed successfully due to the possible faults on the related lines under the extreme system condition, so it is necessary to provide alternative path schemes for system restoration. In view of this, the energising path optimisation based on the minimum cost flow model is investigated, then an iterative searching method for alternative path schemes based on mixed integer linear programming is proposed. The iterative method for alternative path schemes could determine more than one scheme with minimal charging reactive power efficiently. In order to make a comprehensive evaluation of the alternative schemes, an evaluation index set is established, and the method based on similarity to ideal grey relational projection is introduced to achieve the final evaluation. The New England 10‐unit 39‐bus system and the southern Hebei power system of China are employed to demonstrate the effectiveness of the proposed method. The proposed method can provide more efficient and comprehensive decision support for the dispatchers to select reasonable energising paths. [ABSTRACT FROM AUTHOR]

Fast load restoration based on network reconfiguration is a key step to enhance the resilience of distribution systems (DSs). For DSs equipped with remote‐controlled switches (RCSs), the reconfiguration can be completed promptly. However, when the branch is equipped with manual switches only, it cannot be operated immediately, and its post‐event state is determined by its pre‐event state. Considering these facts, this study proposes a unified two‐stage reconfiguration method for the resilience enhancement of DSs. In the pre‐event stage, the allocation of RCSs and the reconfiguration of the network are determined to prepare the system for a set of possible fault scenarios caused by upcoming extreme weather. In the post‐event stage, network reconfiguration based on the placed RCSs is performed for fast load restoration to minimise the loss of load expectation (LOLE). A new mathematical expression is proposed to ensure the radial operation of DSs with islanded DSs and islanded microgrids. To improve the computational efficiency, the scenario decomposition algorithm is employed to decompose the proposed model into several subproblems, which can be solved in parallel. The results show that the proposed method can significantly reduce the LOLE caused by extreme weather events, thus enhancing the resilience of DSs. [ABSTRACT FROM AUTHOR]

Generator start-up is a pivotal step of transmission system self-healing after large-scale blackouts. Considering the uncertainty of initial power system situation after blackouts and line restoration during power system restoration, an online generator start-up algorithm based on Monte Carlo tree search (MCTS) and sparse autoencoder (SAE) is proposed for real-time decision making. First, an online decision support system and a generator start-up efficiency indicator involving the total generation capability and number of restored lines are proposed. Then, the SAE is deployed to learn the data relevant to generator start-up offline to establish a value network, which is used to rapidly estimate the optimal generator start-up efficiency indicator. Next, MCTS used for the online generator start-up is improved by the modified upper confidence bound apply to tree algorithm, move pruning technique, and value network. It is used to search the next line to be restored based on real-time situation. Finally, root parallelization computation is adopted and a decision-making method is proposed to improve the reliability of decision making. Simulation results of the New England 10-unit 39-bus power system and Western Shandong Power Grid of China demonstrate that the proposed algorithm can accomplish generator start-up step by step reliably. [ABSTRACT FROM AUTHOR]

This paper proposes a restorability improvement strategy to accelerate system restoration through the implementation of a wind farm-battery energy storage system (WF-BESS) system. The concept of restorability is introduced and a restorability improvement model (RIM) is proposed and formulated as a mixed integer linear programming problem. To simulate the cylinder temperature drop during outages, the cranking time of a unit is modeled as a stepwise function of its startup time in the RIM. The WF might fail to meet its scheduled generation outputs optimized by the RIM due to the intermittency of wind. To tackle this problem, a linearized control strategy for the BESS (CSBESS) is proposed to minimize the difference between the scheduled wind power outputs and the combined power of the WF-BESS system. An iterative method is employed to efficiently solve the RIM and CSBESS by introducing optimality cuts. An actual power system case is employed to illustrate the effective performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Power system restoration comprises of three stages, i.e., the preparation stage, system restoration stage, and load restoration stage. This paper addresses the first two stages by a new skeleton-network restoration strategy considering the generator start-up sequence (GSUS) and load pickup. The proposed restoration strategy consists of three mathematical models: 1) GSUS model; 2) transmission line restoration (TLR) model; and 3) load pickup (LDP) model. The GSUS model aims to maximize the overall system generated energy considering the actual power system topology. The TLR model is to attain an optimal skeleton-network by identifying the restoration sequence of transmission lines. Critical loads are restored to keep the voltage within a specified respective threshold, and the load amounts are optimized in the LDP model. The proposed GSUS model and TLR model are both solved by the branch-and-bound method, while the LDR model is solved by the interior point method as well as the branch-and-cut method. Finally, the performance of the proposed method is demonstrated by two case studies on the New England 10-unit 39-bus system and an actual power system in Guangdong, China, respectively. [ABSTRACT FROM AUTHOR]