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Renewable distributed generations are associated with generation intermittency. Exacerbated by the consumption and demand uncertainty and their resulting mismatch, its energy trading suffers similar uncertainty. The situation is severe in the standalone distributed generations (SDG) for lacking transaction access to the utility grid. This paper proposes the energy transaction time determination and minimization algorithm for consumers in the SDG arena. First, blockchain technology is adopted for transaction enhancement and transaction data acquisition. The acquired blockchain data includes the hourly nodes (number of blockchain members), transaction sizes, and corresponding transaction durations. Next, the blockchain-recorded transaction data are fitted using the linear regression (LR) algorithm to obtain their fitting formula. The fitting formula was subsequently optimized in hourly intervals to obtain the optimal transaction time (energy delivery time) using particle swarm optimization (PSO). Finally, the optimal results are presented in a decision tree (DT) to energy consumers in the blockchain platform. Consequently, their transaction decision-making is guided by the result against the inherent transaction time uncertainty. Consumers can thus correctly adjust their transaction habits to suitably adapt to the transaction duration fluctuations in the energy trading arena. Energy transaction delays and transaction costs are consequently minimized leading to greater penetration of renewables and bridging the generation and consumption gap.

This paper presents a novel approach for grid-injected current control of DC-AC converters using a robust model reference adaptive controller (RMRAC) with deep symbolic optimization (DSO). Grid voltages are known to be time-varying and can contain distortions, unbalances, and harmonics, which can lead to poor tracking and high total harmonic distortion (THD). The proposed adaptive control structure addresses this issue by enabling or disabling harmonics compensation blocks based on the grid voltage’s characteristics. The DSO framework is implemented to generate an equivalent mathematical expression of the grid voltages, which is then incorporated into the RMRAC-based controller. The controller is then able to reconfigure itself to adequately compensate for high harmonics present in the grid, reducing computational complexity and improving performance. A controller-hardware-in-the-loop (C-HIL) environment with a Typhoon HIL 604 and a TSM320F28335 DSP is implemented to demonstrate that the proposed RMRAC-based structure with DSO outperforms both the same adaptive structure without DSO and a superior RMRAC-based controller. The proposed approach has potential applications in less-inertia power grids, where efficient and accurate control of grid-connected converters is crucial.

Transportation electrification is considered a green alternative to internal combustion vehicles. However, higher penetration of electric vehicles (EVs) can cause several technical challenges to the power systems, including local equipment overloading. This is especially challenging for distribution systems due to the direct connection of EVs with them. To mitigate equipment overloading, by managing EV loads locally, a dynamic pricing model is proposed in this study. First, a satisfaction function is devised for EVs considering the sensitivity of different EV owners to the battery state of charge and urgency of recharge. Then, a welfare function is developed for the EV fleet operator (EFO) considering the net load of EVs and the electricity price of the upstream grid. To this end, a welfare maximization problem is formulated considering the welfare of EVs and EFO. The problem is then decomposed into the EFO sub-problem and EV sub-problem to preserve privacy. Finally, a distributed mechanism is developed to solve the sub-problems iteratively without revealing private information. The performance of the proposed method is analyzed for a residential apartment complex in terms of load management and convergence for different day types (working days and holidays). Simulation results have shown the efficacy of the proposed method in mitigating the overloading of transformers during peak load hours.

A well-functioning smart grid is an essential part of an efficient and uninterrupted power supply for the key enablers of smart cities. To effectively manage the operations of a smart grid, there is an essential requirement for a seamless wireless communication system that provides high data rates, reliability, flexibility, massive connectivity, low latency, security, and adaptability to changing needs. A contemporary review of the utilization of emerging 6G wireless communication for the major applications of smart grids, especially in terms of massive connectivity and monitoring, secured communication for operation and resource management, and time-critical operations, are presented in this paper. This article starts with the key enablers of the smart city, along with the necessity of the smart grid for the key enablers of it. The fundamentals of the smart city, smart grid, and 6G wireless communication are also introduced in this paper. Moreover, the motivations to integrate 6G wireless communication with the smart grid system are expressed in this article as well. The relevant literature overview, along with the novelty of this paper, is depicted to bridge the gap of the current research works. We describe the novel technologies of 6G wireless communication to effectively perform the considered smart grid applications. Novel technologies of 6G wireless communication have significantly improved the key performance indicators compared to the prior generation of the wireless communication system. A significant part of this article is the contemporary survey of the considered major applications of a smart grid that is served by 6G. In addition, the anticipated challenges and interesting future research pathways are also discussed explicitly in this article. This article serves as a valuable resource for understanding the potential of 6G wireless communication in advancing smart grid applications and addressing emerging challenges.

The optimal design of power converters often requires a huge number of simulations and numeric analyses to determine the optimal parameters. This process is time-consuming and results in a high computational cost. Therefore, this paper proposes a deep reinforcement learning (DRL)-based optimization algorithm to optimize the design parameters for power converters using a deep neural network (DNN)-based surrogate model. The surrogate model of power converters can quickly estimate the power efficiency from input parameters without requiring any simulation. The proposed optimization model includes two major steps. In the first step, the surrogate model is trained offline using a large dataset. In the second step, a soft actor-critic-based optimization model interacts with the surrogate model from step 1 to determine the optimal values of design parameters in power converters. Unlike deep Q learning-based methods, the proposed method is able to handle large state and action spaces. In addition, using entropy-regularized reinforcement learning, our proposed method can accelerate and stabilize the learning process and also prevent trapping in local optima. Finally, to show the effectiveness of the proposed method, the performance of different optimization algorithms is compared, considering over ten power converter topologies.

The existing distributed operation schemes for microgrids lack the ability to determine the power selling to the grid during normal operation mode and are unable to provide service reliability to critical loads, during islanded operation mode. In order to overcome these issues, in this study, we have proposed a distributed operation method for both grid-connected and islanded modes of microgrids. Unlike the existing studies, where the utility grid is considered as a dispatchable generator, the bi-directional flow of power with the grid is considered in this study. Similarly, different load agents are considered for different priority loads to assure the service reliability to the critical loads during islanding. A two-step operation method is proposed for both grid-connected and islanded mode operations. During the first step, each agent in the network shares information with its neighboring agents to determine the total load and available renewable power in the network. Whereas, in the second step, each agent in the network determines the optimal operation points based on the local information received from the neighboring agents. Moreover, a modified cost function for the battery is also proposed in this study, which utilizes the information of market price and load to enhance the battery operation. A comparison is made between the centralized method, conventional distributed method, and the proposed distributed operation method. Simulation results have proved the effectiveness of the proposed method for realizing distributed operation for microgrids in both grid-connected and islanded modes.

In the conventional operation of a wind farm (WF) system, the operation point of each wind turbine generator (WTG) is determined to capture maximum energy individually using maximum power point tracking (MPPT) algorithm. However, this operation strategy might not ensure the maximum output power of WF due to wake effect among WTGs. Therefore, this paper develops a multi-agent-based cooperative learning strategy among WTGs using deep reinforcement learning to enhance the overall efficiency of WF by minimizing the wake effect. WTG agents are learnable units and they interact with others as an extensive-form game based on a cooperative model to achieve a common goals (i.e. maximum output power of the WF). In this game, WTG agents carry out their actions sequentially and measure a common reward which is used to update the knowledge of all agents. During the training process, WTG agents use different deep neural networks (DNNs) to improve their actions for achieving the higher reward in the long run by optimizing the weights of DNNs in each learning step. After the training process, WTG agents are able to determine optimal set-points with different input information to minimize the wake effect and to maximize the output power of the WF. Moreover, an operation strategy for the entire WF system is proposed to ensure that the WF always complies with grid-code constraints from transmission system operators, including the requirement of limited power and reserve power. In order to show the effectiveness of the proposed method, a comparison between the results using the proposed method and the conventional MPPT method is also presented in different cases, and the results show that the proposed method can increase the output power of the WF in the range of 1.99% to 4.11% with different layouts.

The primary function of hybrid direct current circuit breakers (HCBs) is to quickly interrupt fault currents to protect high-voltage direct current (HVDC) systems. To enhance the reliability and stability of HVDC systems, optimal design of HCBs is required to minimize the peak fault current, interruption time, and recovery time. Therefore, this study develops a multi-objective genetic algorithm (MOGA)-based optimization model to identify the optimal parameters for HCBs. The MOGA model consists of three objective functions that provide trade-offs among reductions in the peak fault current, the interruption time, and the recovery time. The proposed algorithm is verified with a novel HCB topology using inverse current injection techniques. The performance of the HCB topology with the optimal parameters is validated in the MATLAB/Simulink environment. In addition, a comparison study between the optimal design of an HCB using the proposed algorithm and a typical HCB model is presented in this study to show the effectiveness of the proposed optimization method. Our simulation results show that the optimal parameter design of HCBs significantly reduces the magnitude of the peak fault current and operating time, thus maintaining the safe and stable operation of the entire system.

In wind farm (WF) systems, the set-points of wind turbine generators (WTGs) is determined by the wind farm operator. A change in the value of set-point in two consecutive intervals leads to power fluctuations in the WF system, i.e. power deviation. A large amount of power deviation may adversely affect the operation of the WF system. Therefore, this paper proposes a strategy for operation of a WF system to minimize the power deviation of WTGs during operation time. By using the proposed strategy, the change in set-points of WTGs is minimized and the output power of WTGs is therefore smoother and avoids unnecessary fluctuations. Several grid-code constraints are also considered for operation of the WF system. This ensures the WF system to operate in compliance with the requirements from transmission system operator. Besides, an additional strategy is also proposed to monitor all events in the WF system. Whenever an event occurs in the system, the set-points of WTGs are rescheduled considering the event. Therefore, the proposed operation strategy is also capable of handling events in the WF system. Finally, the simulation results with and without the proposed method are compared to show the effectiveness of the proposed method.

Energy management system (EMS) is responsible for the optimal operation of microgrids. EMS adjusts its operational schedule for near future by using the available information. Market price signals are generally used for the operation of microgrids, which are obtained by using estimation/ forecasting methods. However, it is difficult to precisely predict the market prices due to the involvement of various complex factors like weather, policy, demand, errors in forecasting methods, and fuel cost. Therefore, in this paper, the uncertainties associated with the real-time market price signals (buying and selling) are realized via a robust optimization method. In addition to market price signals, uncertainties associated with renewable power sources and forecasted load values are also considered. Initially, a deterministic model is formulated for an ac/dc hybrid microgrid. Then a min-max robust counterpart is formulated by considering the worstcase uncertainties. Finally, an equivalent mixed integer problem is formulated by using linear duality and other optimality conditions. The developed model can provide feasible solutions for all the scenarios if the uncertainties fluctuate within the specified bounds. The effect of market price uncertainties on internal power transfer and external power trading, operation cost, the state-of-charge of energy storage elements, and unit commitment of dispatchable generators is analyzed. Taguchi's orthogonal array (OA) method is used to find the worst-case scenario within the specified uncertainty bounds. Then, Monte Carlo method is used to generate various scenarios within the uncertainty bounds to evaluate the robustness of the selected scenario via Taguchi's OA method. Finally, a violation index is formulated to evaluate the robustness of the proposed approach against the deterministic model. Simulations results have validated the robustness of the proposed optimization strategy.

A resilience-constrained operation strategy is proposed in this paper using a battery energy storage system (BESS) as a resilience resource. A proactive operation scheme is proposed for the pre-disturbance phase by formulating resiliency cuts for the state of charge (SoC) of BESS units. These resiliency cuts can assure the survivability of critical loads for n intervals after the occurrence of an event. A resilience constraint index is formulated to access the feasibility of the operation model for each selected value of n. In the emergency mode, different possible scenarios are analyzed and a unified survivability enhancement strategy is proposed, which comprises of dynamic penalty costs and target SoC. Dynamic penalty costs can potentially avoid the unnecessary load shedding by shifting it toward the possible end of the scheduling horizon. Similarly, the inclusion of target SoC for the last interval of the scheduling horizon can mitigate the load shedding of critical loads on the following day. A two-step adaptive robust optimization scheme is adopted to incorporate the prevailing uncertainties in loads and renewables in the operation model. Finally, the impact of various decision parameters, involved in the problem formulation, is analyzed with reference to the proposed resilience-constrained operation strategy for hybrid microgrids.

Transmission system operators impose several grid-code constraints on large-scale wind farms to ensure power system stability. These constraints may reduce the net profit of the wind farm operators due to their inability to sell all the power. The violation of these constraints also results in an imposition of penalties on the wind farm operators. Therefore, an operation strategy is developed in this study for optimizing the operation of wind farms using an energy storage system. This facilitates wind farms in fulfilling all the grid-code constraints imposed by the transmission system operators. Specifically, the limited power constraint and the reserve power constraint are considered in this study. In addition, an optimization algorithm is developed for optimal sizing of the energy storage system, which reduces the total operation and investment costs of wind farms. All parameters affecting the size of the energy storage systems are also analyzed in detail. This analysis allows the wind farm operators to find out the optimal size of the energy storage systems considering grid-code constraints and the local information of wind farms.

In order to minimize the peak load of electric vehicles (EVs) and enhance the resilience of fast EV charging stations, several sizing methods for deployment of the stationary energy storage system (ESS) have been proposed. However, methods for assessing the optimality of the obtained results and performance of the determined sizes under different conditions are missing. In order to address these issues, a two-step approach is proposed in this study, which comprises of optimality analysis and performance evaluation steps. In the case of optimality analysis, random sizes of battery and converter (scenarios) are generated using Monte Carlo simulations and their results are compared with the results of sizes obtained from sizing methods. In order to carry out this analysis, two performance analysis indices are proposed in this study, which are named the cost index and the power index. These indices respectively determine the performance of the determined sizes in terms of total network cost and performance ratio of power bought during peak intervals and investment cost of the ESS. During performance evaluation, the performance of the determined sizes (battery and converter) are analyzed for different seasons of the year and typical public holidays. Typical working days and holidays have been analyzed for each season of the year and suitability of the determined sizes is analyzed. Simulation results have proved that the proposed method is suitable for determining the optimality of results obtained by different sizing methods.

In this paper, a multi-objective optimization method is proposed to determine trade-off between conflicting operation objectives of wind farm (WF) systems, i.e., maximizing the output power and minimizing the output power fluctuation of the WF system. A detailed analysis of the effects of different objective’s weight values and battery size on the operation of the WF system is also carried out. This helps the WF operator to decide on an optimal operation point for the whole system to increase its profit and improve output power quality. In order to find out the optimal solution, a two-stage optimization is also developed to determine the optimal output power of the entire system as well as the optimal set-points of wind turbine generators (WTGs). In stage 1, the WF operator performs multi-objective optimization to determine the optimal output power of the WF system based on the relevant information from WTGs’ and battery’s controllers. In stage 2, the WF operator performs optimization to determine the optimal set-points of WTGs for minimizing the power deviation and fulfilling the required output power from the previous stage. The minimization of the power deviation for the set-points of WTGs helps the output power of WTGs much smoother and therefore avoids unnecessary internal power fluctuations. Finally, different case studies are also analyzed to show the effectiveness of the proposed method.

Integration of demand response programs in microgrids can be beneficial for both the microgrid owners and the consumers. The demand response programs are generally triggered by market price signals to reduce the peak load demand. However, during islanded mode, due to the absence of connection with the utility grid, the market price signals are not available. Therefore, in this study, we have proposed a distributed demand response program for an islanded multi-microgrid network, which is not triggered by market price signals. The proposed distributed demand response program is based on welfare maximization of the network. Based on the welfare function of individual microgrids, the optimal power is allocated to the microgrids of the network in two steps. In the first step, the total surplus power and shortage power of the network is determined in a distributed way by using the local surplus/shortage information of each microgrid, which is computed after local optimization. In the second step, the total surplus of the network is allocated to the microgrids having shortage power based on their welfare functions. Finally, the allocated power amount and the initial shortage amount in the microgrid is used to determine the amount of load to be curtailed. Diffusion strategy is used in both the first and the second steps and the performance of the proposed method is compared with the widely used consensus method. Simulation results have proved the effectiveness of the proposed method for realizing distributed demand response for islanded microgrid networks.

Energy management systems (EMSs) of microgrids (MGs) can be broadly categorized as centralized or decentralized EMSs. The centralized approach may not be suitable for a system having several entities that have their own operation objectives. On the other hand, the use of the decentralized approach leads to an increase in the operation cost due to local optimization. In this paper, both centralized and decentralized approaches are combined for managing the operation of a distributed system, which is comprised of an MG and a community battery storage system (CBESS). The MG is formed by grouping all entities having the same operation objective and is operated under a centralized controller, i.e., a microgrid EMS (MG-EMS). The CBESS is operated by using its local controller with different operation objectives. A Q-learning-based operation strategy is proposed for optimal operation of CBESS in both grid-connected and islanded modes. The objective of CBESS in the grid-connected mode is to maximize its profit while the objective of CBESS in islanded mode is to minimize the load shedding amount in the entire system by cooperating with the MG. A comparison between the Q-learning-based strategy and a conventional centralized-based strategy is presented to show the effectiveness of the proposed strategy. In addition, an adjusted epsilon is also introduced for epsilon-greedy policy to reduce the learning time and improve the operation results.

In this paper, an optimal energy management scheme for islanded building microgrid networks is proposed. The proposed building microgrid network comprises of several inter-connected building microgrids (BMGs) and an external energy supplier. Each BMG has a local combined heat and power (CHP) unit, energy storage, renewables and loads (electric and thermal). The external energy system comprises of an external CHP unit, chillers, electric heat pumps and heat pile line, for thermal energy storage. The BMGs can trade energy with other BMGs of the network and can also trade energy with the external energy supplier. In order to efficiently utilize the components of the BMGs and the network, the concept of adjustable power is adopted in this study. Adjustable power can reduce the operation cost of the network by increasing/decreasing the power of dispatchable units. In addition, the failure/recovery of components in the BMGs and the external system are also considered to analyze the performance of the proposed operation method. In order to optimally utilize the available resources during events, precedence among loads of BMGs and the external energy supplier is considered. Simulation results have proved the applicability of the proposed method for both normal islanded mode and with outage/recovery of equipment during the operation horizon. Finally, sensitivity analysis is carried out to analyze the impact of change in components’ parameters values on the saved cost of the network.

In this paper, an optimal energy management scheme for building microgrids with rooftop greenhouse is proposed. A building energy management system (BEMS) is utilized for the optimal fulfilment of energy demands in the building and the greenhouse. The exhaust heat generated due to the operation of air conditioners in the building is used for fulfilling the cooling demands of the greenhouse via chillers. In addition to thermal and cooling demands, the four major control parameters (temperature, humidity, light intensity, and CO2 concentration) are also considered for optimal growth of crops in the greenhouse. A multi-agent system (MAS) is adopted to realize the interaction among several households of the building, the greenhouse, and the BEMS. The MAS comprises of several inner-level, intermediate level, and upper-level agents, which are responsible for their respective tasks. The performance of the proposed optimization strategy is evaluated for two seasons of a year, i.e., summer and winter. Numerical simulations have demonstrated the effectiveness of the proposed operation scheme for optimal operation of building microgrids with rooftop greenhouses.

The increased penetration of renewables is beneficial for power systems but it poses several challenges, i.e., uncertainty in power supply, power quality issues, and other technical problems. Backup generators or storage system have been proposed to solve this problem but there are limitations remaining due to high installation and maintenance cost. Furthermore, peak load is also an issue in the power distribution system. Due to the adjustable characteristics of loads, strategies on demand side such as demand response (DR) are more appropriate in order to deal with these challenges. Therefore, this paper studies how DR programs influence the operation of the multi-microgrid (MMG). The implementation is executed based on a hierarchical energy management system (HiEMS) including microgrid EMSs (MG-EMSs) responsible for local optimization in each MG and community EMS (C-EMS) responsible for community optimization in the MMG. Mixed integer linear programming (MILP)-based mathematical models are built for MMG optimal operation. Five scenarios consisting of single DR programs and DR groups are tested in an MMG test system to evaluate their impact on MMG operation. Among the five scenarios, some DR programs apply curtailing strategies, resulting in a study about the influence of base load value and curtailable load percentage on the amount of curtailed load and shifted load as well as the operation cost of the MMG. Furthermore, the impact of DR programs on the amount of external and internal trading power in the MMG is also examined. In summary, each individual DR program or group could be handy in certain situations depending on the interest of the MMG such as external trading, self-sufficiency or operation cost minimization.

Monitoring the status of existing devices and identification of newly added devices is required in microgrids to adjust the operation schedule followed by any event or integration of a new device. Therefore, in this paper, automatic reconfiguration of microgrids is considered after the addition of a new device or change in the operation status of an existing device by using a multiagent system. This capability of the microgrid is named as auto-configuration function, which is performed by the auto-configurator agent. In case of addition of a new device, the auto-configurator agent is responsible for authorization and registration of the newly added device. In case of change in status of any existing device, the status information is updated. After integration of a new device or change in status of an existing device, re-optimization is carried out by the energy management system (EMS) agent. Agent communication language (ACL) is used to develop a modified contract net protocol (MCNP) for communication among different agents. EMS agent and auto-configurator agent exchange information for economic rescheduling of the microgrid components. Simulation results have shown that the proposed method can be used for optimal operation of microgrids when the configuration changes due to the addition/removal of a device.

In distributed operation, each unit is operated by its local controller instead of using a centralized controller, which allows the action to be based on local information rather than global information. Most of the distributed solutions have implemented the consensus method, however, convergence time of the consensus method is quite long, while diffusion strategy includes a stochastic gradient term and can reach convergence much faster compared with consensus method. Therefore, in this paper, a diffusion strategy-based distributed operation of microgrids (MGs) is proposed using multiagent system for both normal and emergency operation modes. In normal operation, the MG system is operated by a central controller instead of the distributed controller to minimize the operation cost. If any event (fault) occurs in the system, MG system can be divided into two parts to isolate the faulty region. In this case, the MG system is changed to emergency operation mode. The normal part is rescheduled by the central controller while the isolated part schedules its resources in a distributed manner. The isolated part carries out distributed communication using diffusion between neighboring agents for optimal operation of this part. The proposed method enables peer-to-peer communication among the agents without the necessity of a centralized controller, and simultaneously performs resource optimization. Simulation results show that the system can be operated in an economic way in both normal operation and emergency operation modes.

Integration of demand response (DR) programs and battery energy storage system (BESS) in microgrids are beneficial for both microgrid owners and consumers. The intensity of DR programs and BESS size can alter the operation of microgrids. Meanwhile, the optimal size for BESS units is linked with the uncertainties associated with renewable energy sources and load variations. Similarly, the participation of enrolled customers in DR programs is also uncertain and, among various other factors, uncertainty in market prices is a major cause. Therefore, in this paper, the impact of DR program intensity and BESS size on the operation of networked microgrids is analyzed while considering the prevailing uncertainties. The uncertainties associated with forecast load values, output of renewable generators, and market price are realized via the robust optimization method. Robust optimization has the capability to provide immunity against the worst-case scenario, provided the uncertainties lie within the specified bounds. The worst-case scenario of the prevailing uncertainties is considered for evaluating the feasibility of the proposed method. The two representative categories of DR programs, i.e., price-based and incentive-based DR programs are considered. The impact of change in DR intensity and BESS size on operation cost of the microgrid network, external power trading, internal power transfer, load profile of the network, and state-of-charge (SOC) of battery energy storage system (BESS) units is analyzed. Simulation results are analyzed to determine the integration of favorable DR program and/or BESS units for different microgrid networks with diverse objectives.

In this paper, an optimal energy management strategy for a cooperative multi-microgrid system with combined cooling, heat and power (CCHP) is proposed and has been verified for a test case of building microgrids (BMGs). Three different demand types of buildings are considered and the BMGs are assumed to be equipped with their own combined heat and power (CHP) generators. In addition, the BMGs are also connected to an external energy network (EEN), which contains a large CHP, an adsorption chiller (ADC), a thermal storage tank, and an electric heat pump (EHP). By trading the excess electricity and heat energy with the utility grid and EEN, each BMG can fulfill its energy demands. Seasonal energy demand variations have been evaluated by selecting a representative day for the two extreme seasons (summer and winter) of the year, among the real profiles of year-round data on electricity, heating, and cooling usage of all the three selected buildings. Especially, the thermal energy management aspect is emphasized where, bi-lateral heat trading between the energy supplier and the consumers, so-called energy prosumer concept, has been realized. An optimization model based on mixed integer linear programming has been developed for minimizing the daily operation cost of the EEN while fulfilling the energy demands of the BMGs. Simulation results have demonstrated the effectiveness of the proposed strategy.

The resiliency of power systems can be enhanced during emergency situations by using microgrids, due to their capability to supply local loads. However, precise prediction of disturbance events is very difficult rather the occurrence probability can be expressed as, high, medium, or low, etc. Therefore, a fuzzy logic-based battery energy storage system (BESS) operation controller is proposed in this study. In addition to BESS state-of-charge and market price signals, event occurrence probability is taken as crisp input for the BESS operation controller. After assessing the membership levels of all the three inputs, BESS operation controller decides the operation mode (subservient or resilient) of BESS units. In subservient mode, BESS is fully controlled by an energy management system (EMS) while in the case of resilient mode, the EMS follows the commands of the BESS operation controller for scheduling BESS units. Therefore, the proposed hybrid microgrid model can operate in normal, resilient, and emergency modes with the respective objective functions and scheduling horizons. Due to the consideration of resilient mode, load curtailment can be reduced during emergency operation periods. Numerical simulations have demonstrated the effectiveness of the proposed strategy for enhancing the resiliency of hybrid microgrids.

Scheduling of multi-microgrids (MMGs) is one of the important tasks in MMG operation and it faces new challenges as the integration of demand response (DR) programs and renewable generation (wind and solar) sources increases. In order to address these challenges, robust optimization (RO)-based scheduling has been proposed in this paper considering uncertainties in both renewable energy sources and forecasted electric loads. Initially, a cost minimization deterministic model has been formulated for the MMG system. Then, it has been transformed to a min-max robust counterpart and finally, a traceable robust counterpart has been formulated using linear duality theory and Karush–Kuhn–Tucker (KKT) optimality conditions. The developed model provides immunity against the worst-case realization within the provided uncertainty bounds. Budget of uncertainty has been used to develop a trade-off between the conservatism of solution and probability of unfeasible solution. The effect of uncertainty gaps on internal and external trading, operation cost, unit commitment of dispatchable generators, and state of charge (SOC) of battery energy storage systems (BESSs) have also been analyzed in both grid-connected and islanded modes. Simulations results have proved the robustness of proposed strategy.