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This paper proposes a new comprehensive load restoration (LR) method for electrical distribution networks. Since two main technologies of switching equipment are there in the modern distribution networks, namely manual switches (MSs) and remote‐controlled switches (RCSs), this article has benefited from this concept effectively. A two‐stage algorithm that provides the system operators with the ability to recover part of the loads in the shortest possible time by RCSs is proposed. After this step, the remaining loads will be restored by a combination of MSs and RCSs. The other strength of this algorithm is to provide accurate and practical solutions so that the sequence of switching actions is clearly defined. Also, using an innovative index called expected weighted energy not supplied as the objective function of the main problem will ensure the operators recover the maximum amount of load in the shortest time possible. This novel method was applied on a sample standard IEEE distribution test network. The simulation results proved the effectiveness of this proposed method. [ABSTRACT FROM AUTHOR]

Abstract Resilience is one of the main features of smart distribution networks, and a microgrid (MG) access to the distribution network provides an effective way to improve resilience. MG and distribution network belong to different interests, so it is necessary that MGs and flexible resources are actively guided through price leverage. In this way, MGs take part in the post‐disaster restoration and enhance its resilience. Firstly, this paper proposes a dynamic restoration electricity price response mechanism after extreme disasters and constructs a power response model for loads and electric vehicles within the MGs. Secondly, the optimal scheduling model of the distribution network with multiple‐microgrids (MMG) is proposed to improve the restoration rate of critical loads (RRCL). Single microgrid achieves the largest microgrid revenue and restoration contribution, and MMG uses the power headroom index to optimize the dynamic restoration electricity price to achieve the smallest power purchase cost of distribution network. Finally, the optimal scheduling method for resilience enhancement of distribution networks with MMG considering dynamic restoration electricity price response mechanism is validated by dual microgrid access to an IEEE 33‐node distribution system. The simulation results show that the proposed optimization method effectively improves the RRCL of distribution network.

Abstract The hybrid AC/DC distribution network has become a research hotspot because of the wide access to multiple sources and loads. Meanwhile, extreme disasters in the planning period cause huge losses to the hybrid AC/DC distribution networks. A coupled PV‐energy storage‐charging station (PV‐ES‐CS) is an efficient use form of local DC energy sources that can provide significant power restoration during recovery periods. However, over investment will happen if too many PV‐ES‐CSs are installed. Therefore, it is important to determine the optimal numbers and locations of PV‐ES‐CS in hybrid AC/DC distribution networks balanced with economics and resilience. Firstly, the advantages of PV‐ES‐CS in normal operation and extreme disasters are analysed and the payment function is quantified accurately. Secondly, a bi‐level optimal allocation model of PV‐ES‐CS in hybrid AC/DC distribution networks is established. In this model, the payment function using Nash equilibrium to balance economics and resilience is addressed at the upper‐level, and the typical scenarios are simulated, and the optimal results are obtained using the genetic algorithm in lower level. Finally, a series of examples are analysed, which demonstrate the necessity of balancing economics and resilience, and advantages of DC lines in network restoration after disasters.

Abstract Extreme events bring great challenges to the safety and resilience of a distribution network, which makes it difficult for traditional static resources to provide enough operation support. The continuous enrichment of spatial‐temporal flexibility resources on both the power demand and supply sides provides a new idea for the dynamic dispatching of distribution network. This paper proposes a spatial‐temporal migration method of mobile power sources (MPSs) on the supply side and internet data centres (IDCs) on the demand side, based on the power‐transportation and power‐computation network coupling models respectively. Then, the dynamic dispatching potential of MPSs and IDCs is evaluated, and the dispatching models against extreme events of MPSs and IDCs are established. With the objective of maximizing system resilience and minimizing dispatching costs, an optimization model considering spatial‐temporal migration of data loads and MPSs dynamic dispatching strategy is formulated. Finally, the proposed method is tested in the modified IEEE 33‐node test system and IEEE 69‐node test system, and the economy and resilience enhancement are verified with comparison of different dispatching schemes.

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 FROM AUTHOR]

Resilience is one of the main features of smart distribution networks, and a microgrid (MG) access to the distribution network provides an effective way to improve resilience. MG and distribution network belong to different interests, so it is necessary that MGs and flexible resources are actively guided through price leverage. In this way, MGs take part in the post‐disaster restoration and enhance its resilience. Firstly, this paper proposes a dynamic restoration electricity price response mechanism after extreme disasters and constructs a power response model for loads and electric vehicles within the MGs. Secondly, the optimal scheduling model of the distribution network with multiple‐microgrids (MMG) is proposed to improve the restoration rate of critical loads (RRCL). Single microgrid achieves the largest microgrid revenue and restoration contribution, and MMG uses the power headroom index to optimize the dynamic restoration electricity price to achieve the smallest power purchase cost of distribution network. Finally, the optimal scheduling method for resilience enhancement of distribution networks with MMG considering dynamic restoration electricity price response mechanism is validated by dual microgrid access to an IEEE 33‐node distribution system. The simulation results show that the proposed optimization method effectively improves the RRCL of distribution network. [ABSTRACT FROM AUTHOR]

The hybrid AC/DC distribution network has become a research hotspot because of the wide access to multiple sources and loads. Meanwhile, extreme disasters in the planning period cause huge losses to the hybrid AC/DC distribution networks. A coupled PV‐energy storage‐charging station (PV‐ES‐CS) is an efficient use form of local DC energy sources that can provide significant power restoration during recovery periods. However, over investment will happen if too many PV‐ES‐CSs are installed. Therefore, it is important to determine the optimal numbers and locations of PV‐ES‐CS in hybrid AC/DC distribution networks balanced with economics and resilience. Firstly, the advantages of PV‐ES‐CS in normal operation and extreme disasters are analysed and the payment function is quantified accurately. Secondly, a bi‐level optimal allocation model of PV‐ES‐CS in hybrid AC/DC distribution networks is established. In this model, the payment function using Nash equilibrium to balance economics and resilience is addressed at the upper‐level, and the typical scenarios are simulated, and the optimal results are obtained using the genetic algorithm in lower level. Finally, a series of examples are analysed, which demonstrate the necessity of balancing economics and resilience, and advantages of DC lines in network restoration after disasters. [ABSTRACT FROM AUTHOR]

Extreme events bring great challenges to the safety and resilience of a distribution network, which makes it difficult for traditional static resources to provide enough operation support. The continuous enrichment of spatial‐temporal flexibility resources on both the power demand and supply sides provides a new idea for the dynamic dispatching of distribution network. This paper proposes a spatial‐temporal migration method of mobile power sources (MPSs) on the supply side and internet data centres (IDCs) on the demand side, based on the power‐transportation and power‐computation network coupling models respectively. Then, the dynamic dispatching potential of MPSs and IDCs is evaluated, and the dispatching models against extreme events of MPSs and IDCs are established. With the objective of maximizing system resilience and minimizing dispatching costs, an optimization model considering spatial‐temporal migration of data loads and MPSs dynamic dispatching strategy is formulated. Finally, the proposed method is tested in the modified IEEE 33‐node test system and IEEE 69‐node test system, and the economy and resilience enhancement are verified with comparison of different dispatching schemes. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a new comprehensive load restoration (LR) method for electrical distribution networks. Since two main technologies of switching equipment are there in the modern distribution networks, namely manual switches (MSs) and remote‐controlled switches (RCSs), this article has benefited from this concept effectively. A two‐stage algorithm that provides the system operators with the ability to recover part of the loads in the shortest possible time by RCSs is proposed. After this step, the remaining loads will be restored by a combination of MSs and RCSs. The other strength of this algorithm is to provide accurate and practical solutions so that the sequence of switching actions is clearly defined. Also, using an innovative index called expected weighted energy not supplied as the objective function of the main problem will ensure the operators recover the maximum amount of load in the shortest time possible. This novel method was applied on a sample standard IEEE distribution test network. The simulation results proved the effectiveness of this proposed method.

The reasonable generator start-up sequence (GSUS) strategy is beneficial to increasing the energy capacity of power systems after a blackout. Since the decision-making strategies of power systems are highly dependent on the cyber system, the denial of service (DoS) attack, as the most common type of cyber attacks, may prevent the generators from being re-started at their desired time and degrade performance of the optimal GSUS strategy in the power system restoration process, which has not been studied in the existing methods. To fill this gap, a bi-level GSUS optimization strategy against the DoS attack is proposed in this work. First, the effects of the DoS attack on the power generation of generators are analyzed and quantified by the generation energy loss. Then, a bi-level optimization model for the GSUS is proposed considering the DoS attack, where the upper-level model, referred to as the attacker model, aims to maximize the energy loss to prolong the restoration of generators by optimizing the time instant of the attack, while the lower-level model, referred to as the defender model, aims to maximize the energy generation by adjusting the optimal GSUS strategy in the restoration process. Both the upper-level and lower-level models are reformulated as mixed-integer linear programing problems, which can be efficiently solved by commercial solvers. Finally, the IEEE 39-bus power system and an actual power system in China are employed to verify the effectiveness of the proposed model.

The ability of fast restoration reflects power system resilience and safety. This paper proposes a partitioning decision-making method for parallel restoration based on the label propagation algorithm and the cooperative game theory. The topological and physical characteristics of blackout systems are considered as the edge weight and the node importance simultaneously for formulating the partitioning model. By the label propagation algorithm, various labels representing different subsystems mark all buses. To accelerate the speed of convergence and prevent the label oscillation, this paper proposes a game strategy of cooperation between buses and subsystems by evaluating the Shapley value of buses. The partitioning constraints are integrated into each label propagation process to assess the feasibility of the partitioning strategy. Finally, case studies on the IEEE 39- and 118-bus test systems and an actual urban power system in South China verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The decision-making of generator start-up sequence plays a pivotal role in the power system restoration process following the blackout. In this paper, an optimized deep Q-learning network (DQN) algorithm is proposed to address this challenge. The generator start-up process is modeled as a Markov Decision Process (MDP) based on its characteristics. The DQN is tasked with deciding both the generator start-up sequence and the corresponding restoration path. To address the limitations of DQN, such as low exploration efficiency and slow convergence, the study incorporates the Artificial Potential Field (APF) algorithm to refine the reward function of it. This integration results in the development of the F-DQN (APF-DQN) algorithm, which enhances training efficiency. The effectiveness of this proposed method is demonstrated through the IEEE 39-bus test system. The results reveal that the DQN algorithm is capable of efficiently solving the model of the generator start-up sequence after the blackout. Moreover, the F-DQN algorithm exhibits superior learning efficiency, faster convergence, and higher-quality optimal solutions compared to the DQN. This paper also discusses the applicability of this method under partial blackouts. When compared to other decision-making algorithms, the proposed method offers a restoration scheme that is both time-efficient and results in increased electricity generation. [ABSTRACT FROM AUTHOR]

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.

This paper proposes a multi-time collaborative restoration model for integrated electricity-gas distribution systems (IEGDSs) considering multiple resources after extreme weather events. Based on the linearized power flow constraints of the unbalanced electrical distribution system (EDS) and gas distribution system (GDS), this problem can be formulated as a mixed-integer linear programming (MILP) model. To improve the efficiency and veracity of the solution, a rolling optimization based two-stage method is developed with the first stage solved by a linear approximation model, and the second stage solved by real-time updated rolling optimization. By solving the MILP problem using rolling optimization, the proposed model and solution method achieve efficient and reliable collaborative restoration of IEGDS considering multiple resources and unbalanced operation characteristics of EDS. The effectiveness of the proposed model and method is validated by using an IEGDS made of a 37-bus unbalanced EDS and 11-node GDS.

This article studies the Transmission Restoration Problem with Mobile Substation Resources, a novel mixed-integer linear programming model that prescribes the most effective usage of mobile-substation resources to enhance the resilience of a power transmission system against a particular, widespread flood event. The model is a two-stage stochastic program in which each scenario captures a different potential progression of flood heights at substations over the event horizon. The first stage concerns the pre-event selection and positioning of mobile-substation resources. The second stage concerns the coordination of mobile-substation resource deployment and permanent-substation restoration to maintain and recover service within the horizon. Experiments in the IEEE 24-Bus System and a synthetic Houston grid confirm the efficacy of the model. Even when isolated from effects related to restoration of permanent substations, the effect of four mobile transformers and eight mobile breakers for a realistic set of flood scenarios in the synthetic Houston grid was found to be an average total-cost reduction of approximately ${\$}$ 35MM (i.e., approximately 8% of a default optimal objective value). Additionally, a novel, parallel heuristic is designed that can efficiently solve the problem as well as, with minor modifications, similar stochastic problems on pre-selection of mobile resources or placement of static ones. For a 40-scenario model instance in the IEEE 24-Bus System, the extensive form was not able to find an integer-feasible solution in six hours, yet the heuristic achieved an optimality gap no worse than 4.5% in two hours.

A swift power system restoration in a post-blackout event is one the most important challenges faced by the transmission system (TS) operators (TSO), which is particularly essential in the presence of wind farms, as their potential can be great in a fast restoration. In this study, we propose a bi-level decentralized approach to examine the influence of natural gas network (NGN) constraints on the bulk power system restoration process, taking into account the concurrent effects of pump storage hydropowers (PSHs) and wind farms. At the upper level of the problem, the transmission system (TS) operator (TSO) submits the amount of natural gas fuel consumed by the gas-fired units (GFUs) to the NGN by observing the restoration, operational, and topological constraints. The objective of the TSO is to maximize load servicing in the power grid restoration process. The equilibrium of the proposed bi-level problem is calculated by the analytical target cascading (ACT) algorithm, preserving the privacy of both electricity and NGNs. In the proposed study, an investigation has been conducted into the impact of the gas storage system (GSS) and linepack technology on enhancing the restoration process. Moreover, a moment-based distributionally robust optimization (DRO) approach has been deployed to model the uncertain behavior of wind farms in the restoration process. The proposed approach comprehensively examines the effects of the decentralized interconnection between electricity and NGNs in the restoration process. This facet holds great significance for the advancement of future sustainable energy systems. The results show that ignoring the NGN model leads to 11.92% higher level of unserviced loads.

Abstract In recent decades, flash floods have become more common because of climate change and are considered a substantial risk for many cities worldwide. This catastrophic natural hazard presents a significant threat to critical infrastructure in urban areas, particularly the power distribution system. As modern societies are much more dependent on electrical energy these days, it is essential and imperative to make existing distribution systems resilient against flash flooding. Although researchers in this area have proposed various algorithms to impart resilience to a distribution system, however, the focus in these works is on wind‐related events such as hurricanes, cyclones, and windstorms. Therefore, here, the spatiotemporal effects of a flash flood on the distribution system are modelled using a grid‐based hydrodynamic model. The evolving line faults are then included in the proposed resilience‐oriented time horizon‐based service restoration model that also considers dynamic load demand, heavy uncertainties related to renewable generation, and interdependence among critical loads. Finally, the resilience of the distribution system's response is assessed using an operational resilience metric. The efficacy of the proposed framework is evaluated on IEEE 33‐bus and 69‐bus systems and the results show that the model provides an efficient restoration solution despite increased complexity caused by varying conditions.

Abstract The restoration control of the modern alternating current–direct current (AC–DC) hybrid power grid after a major blackout is difficult and complex. Taking into account the interaction between the line‐commutated converter high‐voltage direct current (LCC‐HVDC) and the AC power grid, this paper proposes a novel optimization method of restoration path to reconfigure the skeleton network for the blackout power grid. Based on the system strength, the supporting capability of the AC power grid for the LCC‐HVDC is first analysed from the aspects of start‐up and operation of LCC‐HVDCs. Subsequently, the quantitative relationship between the restoration path and the restoration characteristic of LCC‐HVDC is derived in detail based on the system strength indices of the short‐circuit capacity and the frequency regulation capability. Then, an optimization model of restoration path considering non‐tree paths is formulated and a feasible optimization algorithm is proposed to achieve the optimal path restoration scheme. A modified IEEE 39‐bus system and a partial power grid of Southwest China are simulated to show that the proposed method is suitable for the restoration of AC–DC power grids and can improve restoration efficiency. This research can be an important guidance for operators to rapidly restore the AC–DC power grid.

The restoration of the modern alternating current-direct current (AC–DC) hybrid power grid after a blackout is difficult and complex. By using the partitioning restoration strategy and the support of high voltage direct current (HVDC) system, the restoration speed of the blackout power grid can be greatly accelerated. Aiming at this problem, this paper proposes a partitioning method for the power grid restoration with multiple line commutated converter-based HVDC (LCC-HVDC) systems. Firstly, by introducing the system strength indices to quantify the interaction between AC and LCC-HVDC systems in the restoration process, a partitioning model considering multiple LCC-HVDCs is proposed. Wherein, the transmission power is optimized to make full use of LCC-HVDCs’ support capability. Then, by combining the system strength characteristic and community structure characteristic of the power grid, a partitioning method based on an improved Girvan Newman (GN) algorithm is proposed. Finally, the results are studied based on a modified IEEE 39-bus system and a realistic partial power grid of southwest China. Compared with two typical partitioning methods for the AC power grid restoration, the results show that the proposed method can effectively use the DC support power and speed up the restoration progress.

Abstract In this modern era of cyber–physical–social systems, there is a need of dynamic coordination strategies for electric vehicles (EVs) to enhance the resilience of modern power distribution networks (MPDNs). This paper proposes a two‐stage EV coordination framework for MPDN smart restoration. The first stage is to introduce a novel proactive EV prepositioning model to optimize planning prior to a rare event, and thereby enhance the MPDN survivability in its immediate aftermath. The second stage involves creating an advanced spatial–temporal EV dispatch model to maximize the number of available EVs for discharging, thereby improving the MPDN recovery after a rare event. The proposed framework also includes an information system to further enhance MPDN resilience by effectively organizing data exchange among intelligent transportation system and smart charging system, and EV users. In addition, a novel bidirectional geographic graph is proposed to optimize travel plans, covering a large penetration of EVs and considering variations in traffic conditions. The effectiveness is assessed on a modified IEEE 123‐node test feeder with real‐world transportation and charging infrastructure. The results demonstrate a significant improvement in MPDN resilience with smart restoration strategies. The validation and sensitivity analyses evidence a significant superiority of the proposed framework.

In recent decades, flash floods have become more common because of climate change and are considered a substantial risk for many cities worldwide. This catastrophic natural hazard presents a significant threat to critical infrastructure in urban areas, particularly the power distribution system. As modern societies are much more dependent on electrical energy these days, it is essential and imperative to make existing distribution systems resilient against flash flooding. Although researchers in this area have proposed various algorithms to impart resilience to a distribution system, however, the focus in these works is on wind‐related events such as hurricanes, cyclones, and windstorms. Therefore, here, the spatiotemporal effects of a flash flood on the distribution system are modelled using a grid‐based hydrodynamic model. The evolving line faults are then included in the proposed resilience‐oriented time horizon‐based service restoration model that also considers dynamic load demand, heavy uncertainties related to renewable generation, and interdependence among critical loads. Finally, the resilience of the distribution system's response is assessed using an operational resilience metric. The efficacy of the proposed framework is evaluated on IEEE 33‐bus and 69‐bus systems and the results show that the model provides an efficient restoration solution despite increased complexity caused by varying conditions. [ABSTRACT FROM AUTHOR]

The restoration control of the modern alternating current–direct current (AC–DC) hybrid power grid after a major blackout is difficult and complex. Taking into account the interaction between the line‐commutated converter high‐voltage direct current (LCC‐HVDC) and the AC power grid, this paper proposes a novel optimization method of restoration path to reconfigure the skeleton network for the blackout power grid. Based on the system strength, the supporting capability of the AC power grid for the LCC‐HVDC is first analysed from the aspects of start‐up and operation of LCC‐HVDCs. Subsequently, the quantitative relationship between the restoration path and the restoration characteristic of LCC‐HVDC is derived in detail based on the system strength indices of the short‐circuit capacity and the frequency regulation capability. Then, an optimization model of restoration path considering non‐tree paths is formulated and a feasible optimization algorithm is proposed to achieve the optimal path restoration scheme. A modified IEEE 39‐bus system and a partial power grid of Southwest China are simulated to show that the proposed method is suitable for the restoration of AC–DC power grids and can improve restoration efficiency. This research can be an important guidance for operators to rapidly restore the AC–DC power grid. [ABSTRACT FROM AUTHOR]

In this modern era of cyber–physical–social systems, there is a need of dynamic coordination strategies for electric vehicles (EVs) to enhance the resilience of modern power distribution networks (MPDNs). This paper proposes a two‐stage EV coordination framework for MPDN smart restoration. The first stage is to introduce a novel proactive EV prepositioning model to optimize planning prior to a rare event, and thereby enhance the MPDN survivability in its immediate aftermath. The second stage involves creating an advanced spatial–temporal EV dispatch model to maximize the number of available EVs for discharging, thereby improving the MPDN recovery after a rare event. The proposed framework also includes an information system to further enhance MPDN resilience by effectively organizing data exchange among intelligent transportation system and smart charging system, and EV users. In addition, a novel bidirectional geographic graph is proposed to optimize travel plans, covering a large penetration of EVs and considering variations in traffic conditions. The effectiveness is assessed on a modified IEEE 123‐node test feeder with real‐world transportation and charging infrastructure. The results demonstrate a significant improvement in MPDN resilience with smart restoration strategies. The validation and sensitivity analyses evidence a significant superiority of the proposed framework. [ABSTRACT FROM AUTHOR]

The ability of fast restoration reflects power system resilience and safety. This paper proposes a partitioning decision-making method for parallel restoration based on the label propagation algorithm and the cooperative game theory. The topological and physical characteristics of blackout systems are considered as the edge weight and the node importance simultaneously for formulating the partitioning model. By the label propagation algorithm, various labels representing different subsystems mark all buses. To accelerate the speed of convergence and prevent the label oscillation, this paper proposes a game strategy of cooperation between buses and subsystems by evaluating the Shapley value of buses. The partitioning constraints are integrated into each label propagation process to assess the feasibility of the partitioning strategy. Finally, case studies on the IEEE 39- and 118-bus test systems and an actual urban power system in South China verify the effectiveness of the proposed method.

Abstract Power systems are currently experiencing a transition towards decarbonisation through the large‐scale deployment of renewable energy sources. These are gradually replacing conventional thermal power plants which today are the main providers of black start services. Consequently, in case of a total/partial blackout, conventional black‐start resources may not be ready for operation. Offshore wind farms (OWFs), with their large capacity and fast controllers, have potential as innovative black‐start units, thus, the need for a new design for OWFs. Here, challenges and possible solutions in integrating black start services into offshore wind farms will be presented. The first challenge is represented by the self‐start capability. The self‐start unit should be capable of forming the wind farm power island and withstanding transient phenomena due to the equipment energisation. The investigated solution comprises grid‐forming (GFM) converters in the wind farm design, which could be battery energy storage systems (BESSs) to also increase the service availability. The challenges are analysed using simulations on a wind farm, and the proposed solutions are discussed. It can be concluded that a hybrid system comprised of a BESS and an OWF, with GFM control, applying soft‐charging, etc., represents a good proposal to provide black start services by OWFs.

Abstract This paper proposes an approach for segmentation of power systems to prevent uncontrolled islanding. With the development of microgrids (MGs) and increased penetration of renewable energy sources (RESs) in the power system, it is necessary to consider the effect of MGs and the stochastic behaviour of RESs in the controlled islanding process. First, the enormous search space for finding the boundary points is reduced by the clustering of the coherent generators and the buses which are placed in sections that cannot be separated from the coherent groups. Then, linear AC power flow is defined as a sub‐problem and solved by linear programming to satisfy the power system and MG constraints. In this step, an optimization model is defined, and a mixed‐integer linear programming (MILP)‐based model is suggested to find cut‐sets and islands arrangement with reduced load shedding. In view of the fact that the fluctuation of RESs may have the significant effects on the power imbalance, to cover the uncertainties a scenario based stochastic simulation is considered. Finally, the effect of uncertainties on cut‐sets and load curtailment is evaluated. The effectiveness of the proposed methodology is demonstrated by the simulation on the test system.

Abstract The existing static voltage stability margin evaluation methods cannot meet the actual demand of current power grid well in terms of calculation speed and accuracy. Thus, this paper proposes a static voltage stability margin prediction method based on a graph attention network (GAT) and a long short‐term memory network (LSTM) to predict the static voltage stability margin of a power system accurately, fast, and effectively, considering new energy uncertainty. First, an innovative machine learning framework named the GAT‐LSTM is designed to extract highly representative power grid operation features considering the spatial‐temporal correlation of the power grid operation. Then, a static voltage stability margin prediction method based on the GAT‐LSTM is developed. Particularly, considering the influence of new energy power uncertainty, two loss functions of certainty and uncertainty are used in the proposed method to predict the voltage stability margin and voltage fluctuation range. Finally, the IEEE39‐bus power system and a practical power system are employed to verify the proposed method. The results show that the computational speed of the proposed method is greatly improved compared to the traditional methods not based on machine learning; the computation results are more accurate and reliable than the existing machine learning methods. Compared with the existing methods, the proposed method has higher scalability and applicability.

Despite the extensive studies that have been done regarding the restoration problems and issues of power systems, the impact of the topological extent of the power grid structure on power system restoration has not been analyzed or assessed. This objective, which is neglected in the process of planning and development of transmission systems, could make operators encounter more challenges during the restoration process and prolongation of the restoration procedures. In this study, an attempt is made to evaluate the desirability of a power system network structure according to the main requirement of the restoration process, i.e. restoration time. To address this concern, a systematic approach on the basis of a fractal-based quantitative index is introduced to measure the topological extent of a power system network as a representative of restoration time. The proposed approach combines the feeding point condition, topological extent, and support routes to deliver an index associated with the time and success probability of the power system restoration process.

Abstract Power outages in urban area carry heavy social and economic costs. Although social cost, especially public sentiment, is concerned by engineers and managers, it has been only qualitatively investigated without a rigorous model in the state‐of‐the‐art research and practice of service restoration (SR) for a long time. To fill this gap, this paper investigates a hybrid model which takes public sentiment into consideration by quantifying public sentiment triggered by power outage. Furthermore, conventional SR method focused on the optimization model with ideal conditions, which leaves a large room for improvement in complex environment. To improve the robustness of the model, the authors propose a reinforcement learning framework to analyze emergency management process without prior rules. At each time step, the optimal decision can be made automatically by a learned model. The numerical simulations with modified IEEE 33‐bus and IEEE 123‐bus systems demonstrate the effectiveness of the proposed method.

In the event of a major power outage in the power systems, there is an urgent need to investigate entire-process coordinated restoration strategies for the transmission systems (TSs) and distribution systems (DSs), aiming to accelerate the restoration speed of generating units, network reconfiguration, and load restoration. Furthermore, it is imperative to address the multiple uncertainties that arise during the restoration process to mitigate potential security risks associated with the restoration. Hence, an adaptive ADMM-based entire-process distributed restoration method of TSs and DSs considering CVaR is proposed in this paper. Firstly, an entire-process distributed restoration model of TSs and DSs considering CVaR is proposed to maximize the total restoration benefits of TSs and DSs. Then, an adaptive ADMM-based distributed solving algorithm for the coordinated restoration model of the TSs and DSs is introduced, which incorporates adaptive penalty parameter adjustments, leading to faster convergence compared to the standard ADMM. Finally, case studies on an improved 179-bus transmission system are employed to verify that the proposed restoration method can achieve higher restoration benefits and faster convergence speed compared to existing restoration models.

Power systems are currently experiencing a transition towards decarbonisation through the large‐scale deployment of renewable energy sources. These are gradually replacing conventional thermal power plants which today are the main providers of black start services. Consequently, in case of a total/partial blackout, conventional black‐start resources may not be ready for operation. Offshore wind farms (OWFs), with their large capacity and fast controllers, have potential as innovative black‐start units, thus, the need for a new design for OWFs. Here, challenges and possible solutions in integrating black start services into offshore wind farms will be presented. The first challenge is represented by the self‐start capability. The self‐start unit should be capable of forming the wind farm power island and withstanding transient phenomena due to the equipment energisation. The investigated solution comprises grid‐forming (GFM) converters in the wind farm design, which could be battery energy storage systems (BESSs) to also increase the service availability. The challenges are analysed using simulations on a wind farm, and the proposed solutions are discussed. It can be concluded that a hybrid system comprised of a BESS and an OWF, with GFM control, applying soft‐charging, etc., represents a good proposal to provide black start services by OWFs. [ABSTRACT FROM AUTHOR]

This paper proposes an approach for segmentation of power systems to prevent uncontrolled islanding. With the development of microgrids (MGs) and increased penetration of renewable energy sources (RESs) in the power system, it is necessary to consider the effect of MGs and the stochastic behaviour of RESs in the controlled islanding process. First, the enormous search space for finding the boundary points is reduced by the clustering of the coherent generators and the buses which are placed in sections that cannot be separated from the coherent groups. Then, linear AC power flow is defined as a sub‐problem and solved by linear programming to satisfy the power system and MG constraints. In this step, an optimization model is defined, and a mixed‐integer linear programming (MILP)‐based model is suggested to find cut‐sets and islands arrangement with reduced load shedding. In view of the fact that the fluctuation of RESs may have the significant effects on the power imbalance, to cover the uncertainties a scenario based stochastic simulation is considered. Finally, the effect of uncertainties on cut‐sets and load curtailment is evaluated. The effectiveness of the proposed methodology is demonstrated by the simulation on the test system. [ABSTRACT FROM AUTHOR]

The existing static voltage stability margin evaluation methods cannot meet the actual demand of current power grid well in terms of calculation speed and accuracy. Thus, this paper proposes a static voltage stability margin prediction method based on a graph attention network (GAT) and a long short‐term memory network (LSTM) to predict the static voltage stability margin of a power system accurately, fast, and effectively, considering new energy uncertainty. First, an innovative machine learning framework named the GAT‐LSTM is designed to extract highly representative power grid operation features considering the spatial‐temporal correlation of the power grid operation. Then, a static voltage stability margin prediction method based on the GAT‐LSTM is developed. Particularly, considering the influence of new energy power uncertainty, two loss functions of certainty and uncertainty are used in the proposed method to predict the voltage stability margin and voltage fluctuation range. Finally, the IEEE39‐bus power system and a practical power system are employed to verify the proposed method. The results show that the computational speed of the proposed method is greatly improved compared to the traditional methods not based on machine learning; the computation results are more accurate and reliable than the existing machine learning methods. Compared with the existing methods, the proposed method has higher scalability and applicability. [ABSTRACT FROM AUTHOR]

Power outages in urban area carry heavy social and economic costs. Although social cost, especially public sentiment, is concerned by engineers and managers, it has been only qualitatively investigated without a rigorous model in the state‐of‐the‐art research and practice of service restoration (SR) for a long time. To fill this gap, this paper investigates a hybrid model which takes public sentiment into consideration by quantifying public sentiment triggered by power outage. Furthermore, conventional SR method focused on the optimization model with ideal conditions, which leaves a large room for improvement in complex environment. To improve the robustness of the model, the authors propose a reinforcement learning framework to analyze emergency management process without prior rules. At each time step, the optimal decision can be made automatically by a learned model. The numerical simulations with modified IEEE 33‐bus and IEEE 123‐bus systems demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Despite the extensive studies that have been done regarding the restoration problems and issues of power systems, the impact of the topological extent of the power grid structure on power system restoration has not been analyzed or assessed. This objective, which is neglected in the process of planning and development of transmission systems, could make operators encounter more challenges during the restoration process and prolongation of the restoration procedures. In this study, an attempt is made to evaluate the desirability of a power system network structure according to the main requirement of the restoration process, i.e. restoration time. To address this concern, a systematic approach on the basis of a fractal-based quantitative index is introduced to measure the topological extent of a power system network as a representative of restoration time. The proposed approach combines the feeding point condition, topological extent, and support routes to deliver an index associated with the time and success probability of the power system restoration process. [ABSTRACT FROM AUTHOR]

This paper proposes a two‐layer method for restoring service. Firstly, a new strategy is used to obtain binary variables relating to closed switches and tie switches. In addition, after the fault occurs it is also possible to obtain optimal islands online. Secondly, a non‐linear model is solved to optimally determine the islands created in the first step, in which distributed generation resources (DGRs), energy storages (ESs) and load shedding (LSH) are reprogrammed. When LSH is performed, the sensitive loads must experience the least amount of outage possible. Therefore, the loads are categorized into residential, industrial, and sensitive categories. In order to demonstrate the validity and effectiveness of the proposed method, a modified IEEE 33‐bus system is simulated. In simulations, the proposed strategy has been compared with one of the important existing methods. Based on these results, the proposed method can reduce the cost function by modifying the critical load less than other methods. In this method, the critical LSH is 220 kW, which is 105 kW less than the compared method. By reducing the amount of load, 46,000 dollars have been saved in system expenses. The results confirm that the proposed strategy is considerably superior to the existing method. [ABSTRACT FROM AUTHOR]

This paper deals with the simulation and the experimental confirmation of electromagnetic events that could interfere with the successful formation of the restoration path during the power system restoration procedure. The studied phenomena are more relevant for bulk power systems characterized by a low short circuit power as the restoration backbone. In particular, two case studies have been simulated and analyzed: one related to a transformer energization during the formation of the restoration path, and the other one occurred after the de-energization of some transmission lines and one autotransformer belonging to the restoration path. From the simulation results, it emerged that such events are related to the resonant effects between the supplying transformer and the restored network. Such resonances could have negative effects on the restoration if they are not effectively managed. In order to evaluate the impact of such phenomena in real networks, the measurement recordings of on-field tests were compared with the simulation results. It is worth noting that the performed analyses require the knowledge of several parameters that were not always available in practice. Hence, the exact magnitude of the described resonant phenomena was not easy to foresee for the restoration of real networks. The performed comparison confirms the preliminary simulation results and highlights that detailed electromagnetic models are particularly important to support the power system restoration management, in particular the planning of recovery procedures. [ABSTRACT FROM AUTHOR]

This paper explores the potential of distributed ledger technology (DLT) to improve fault-tolerant grid operations by leveraging its core features as an immutable, decentralized ledger, a distributed, consensus-based agreement process, and a distributed state-replication engine. Distribution power systems deliver electricity to millions of customers; however, they are susceptible to various threats that can result in customer interruptions. These include faults caused by adverse weather conditions, natural disasters, vegetation growth, equipment failure, and malicious attacks. To minimize the effects of these faults, fault-handling approaches rely on network knowledge to isolate affected areas and reconnect unaffected areas, reducing the number of affected customers while maintaining safety. Here, we present a trusted data-sharing architecture that enables independent, distributed actors to reconstruct the pre-fault system state by enabling distributed resources to make appropriate decisions with limited network/system information. Although the process requires some data sharing between switch-delimited areas, the approach limits the amount of private information shared, preserving customers’ privacy and business-sensitive information. We include three use cases that form a foundation for third parties to develop functional solutions that can eventually be deployed in the field. The gross error detection method used within switch-delimited areas can identify sensor errors and accurately detect circuit breaker states. The evaluation of possible reconnection while preserving data ownership resulted in a voltage magnitude difference smaller than 0.01% from the OpenDSS power flow solution that has full system knowledge, which is below the expected power flow tolerance. The approach offers a promising opportunity for improving fault-tolerant distribution grid operations.

Fault restoration techniques have always been crucial for distribution system operators (DSOs). In the last decade, it started to gain more and more importance due to the introduction of output-based regulations where DSO performances are evaluated according to frequency and duration of energy supply interruptions. The paper presents a tabu-search-based algorithm able to assist distribution network operational engineers in identifying solutions to restore the energy supply after permanent faults. According to the network property, two objective functions are considered to optimize either reliability or resiliency. The mathematical formulation includes the traditional feeders, number of switching operation limit, and radiality constraints. Thanks to the DSO of Milan, Unareti, the proposed algorithm has been tested on a real distribution network to investigate its effectiveness.

Abstract With the rapid development of renewable energy generation and multi‐energy system technologies, reviewing and discussing the emerging power system restoration methods and key technologies suitable for renewable‐dominated electric power systems and the Energy Internet are important. Based on this, the backgrounds of renewable‐dominated electric power systems and the Energy Internet are first introduced here. Subsequently, the power system restoration process is divided into three phases: the black‐start, network reconfiguration, and the load restoration phases; relative restoration strategy research on these three phases is reviewed. Moreover, the boundaries between these three phases are occasionally not sufficiently apparent or even cross in most cases owing to the severity of blackouts and other various factors. Therefore, the key technologies for power system restoration considering multiple phases are analysed in detail. Moreover, the major gaps between existing research and real‐world applications and the outlooks on the restoration technologies under renewable‐dominated electric power systems are discussed.

Abstract This paper proposes a two‐layer method for restoring service. Firstly, a new strategy is used to obtain binary variables relating to closed switches and tie switches. In addition, after the fault occurs it is also possible to obtain optimal islands online. Secondly, a non‐linear model is solved to optimally determine the islands created in the first step, in which distributed generation resources (DGRs), energy storages (ESs) and load shedding (LSH) are reprogrammed. When LSH is performed, the sensitive loads must experience the least amount of outage possible. Therefore, the loads are categorized into residential, industrial, and sensitive categories. In order to demonstrate the validity and effectiveness of the proposed method, a modified IEEE 33‐bus system is simulated. In simulations, the proposed strategy has been compared with one of the important existing methods. Based on these results, the proposed method can reduce the cost function by modifying the critical load less than other methods. In this method, the critical LSH is 220 kW, which is 105 kW less than the compared method. By reducing the amount of load, 46,000 dollars have been saved in system expenses. The results confirm that the proposed strategy is considerably superior to the existing method.

After a blackout event, power system restoration is an essential activity for grid resilience; operators restart generators, re-establish transmission paths, and restore loads. With a goal of restoring electric service in the shortest time, the core decisions in restoration planning are to partition the grid into subnetworks, each of which has an initial power source for black-start (called sectionalization problem), and then restart all generators in each network (called generator startup sequencing (GSS) problem) as soon as possible. Due to their complexity, the sectionalization and GSS problems are usually solved separately, often resulting in a suboptimal solution. Our paper develops models and computational methods to solve the two problems simultaneously. We first study the computational complexity of the GSS problem and develop an efficient integer linear programming formulation. We then integrate the GSS problem with the sectionalization problem and develop an integer linear programming formulation for the parallel power system restoration (PPSR) problem to find exact optimal solutions. To solve larger systems, we then develop bounding approaches that find good upper and lower bounds efficiently. Finally, to address computational challenges for very large power grids, we develop a randomized approach to find a high-quality feasible solution quickly. Our computational experiments demonstrate that the proposed approaches are able to find good solutions for PPSR in up to 2,000-bus systems. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This research was supported by the Visiting Faculty Program of Argonne National Laboratory and the U.S. Department of Energy Advanced Grid Modeling Program [Grant DE-OE0000875]. [ABSTRACT FROM AUTHOR]

This paper proposes a novel repair rule set (RRS) for scheduling the power system infrastructure repair after the occurrence of extreme events. RRS is made up of multiple repair rules, each of them can be applied in arbitrary post-disaster failure scenarios to rank the repair actions by priority. A learning-to-rank technique called AdaRank is used to train the repair rules by combining the weak learners derived from the dynamic repair scheduling model. Then, RRS is constructed by iteratively clustering the training cases and retraining the repair rule for each cluster. Increasing the number of repair rules within RRS allows it to differentiate various types of failure scenarios, thereby improving its performance. Further combined with multi-label K nearest neighbor (ML-KNN) technique, RRS is able to schedule the repair without the full knowledge of real-time failure information, such as the estimated repair time. The results of case studies on IEEE-118 test systems show that the proposed method has a desirable performance compared to the exact mathematical optimization model. Moreover, it reduces the requirement for failure information while significantly improving the computational efficiency. [ABSTRACT FROM AUTHOR]

• proposing a MESS-assisted bulk power system parallel restoration framework. • Utilizing MESSs to transform non-black start (BS) units to MESS-assisted BS units. • Formulating a MESS mobility model in the transportation networks. • Developing an integrated restoration model considering optimal MESS dispatch. During bulk power system restoration, black-start (BS) units are used to crank non-BS units in such a way that the over system generation capability is maximized. However, traditional power system restoration methods rely on stationary BS units, whose number is limited due to high investment and geographic conditions, impeding a fast system restoration. To enhance restoration efficiency, this paper proposes an integrated power system parallel restoration method considering the support of mobile energy storage systems (MESSs), which can provide cranking power to non-BS units and transform them into MESS-assisted BS units. MESSs are routed and scheduled via transportation network, along with restoration planning in power network by integrating them into a mixed integrated linear programming model. Specifically, to describe the interactive behavior between MESSs and the power system, a mobility model for MESSs is proposed, which indicates the travel path, travel time and connection nodes. Then, an integrated optimization model involving BS unit location, zone partitioning, network reconfiguration and generator start-up is formulated. The proposed method was simulated in the modified IEEE 30-bus transmission system coupled with 11-node transportation system. The results show that, in contrast with a decoupled restoration method, the proposed method increases system generation capability by 6.3%. [ABSTRACT FROM AUTHOR]

The article presents the method of remote micro-grid synchronization with the utility grid in the presence of voltage disturbances. The proposed algorithm and control devices synchronize different power systems on the basis of the instantaneous voltage phase angle in spite of voltage quality problems and without need of access to point of common coupling. In the presence of grid voltage disturbances, instantaneous grid voltage phase angle is estimated and transmitted remotely with a certain accuracy, which is varies in presence of disturbances of grid voltages or depends on the synchronization algorithm and data transmission rate. The paper focuses on the influence of voltage disturbances on the proposed remote synchronization strategy and the shape of the output current of the synchronized power converter on the micro-grid. The four types of grid voltage disturbances are presented: harmonics, one-phase sag, two-phase sag, and phase voltage jump. The final conclusions present the possibility of using the proposed remote synchronizations algorithm in micro-grid power converter applications in the presence of typical utility grid voltage disturbances.