微网调度；光伏储能协同；两阶段随机鲁棒优化；滚动模型预测控制；CVaR风险约束

… strategies, including load scheduling and efficient peer-to-peer … sources such as photovoltaic and battery storage systems. … optimal rational solution of the scheduling problem which is …

In this article, a decentralized photovoltaic (PV)–battery energy storage (BES) coordination control method for Plug-n-Play (PnP) dc microgrid (MG) is proposed. With the proposed control method, PV units can operate under dc bus voltage control when BES units are saturated due to state-of-charge (SoC) limit or charging/discharging power limit. The mode transition and power sharing are based on a communication-less manner. By bypassing communication, the MG system can become more flexible and reliable. The proposed control system contains controllers for PV converter and BES converter, respectively. The PV converter controller can achieve seamless mode transition between maximum power point tracking (MPPT) control and droop control. The BES converter controller has a decoupled feature that a high-pass-filter (HPF) path could improve MG dynamic performance under generation-dominating mode. The BES HPF compensation overcomes the issue of poor dynamic performance under PV-dominating mode and makes the system more resistive to PV parameter variation. The detailed design, analysis, and implementation of the proposed PV–BES coordination control are provided in this article. The simulation and experimental results have been provided to verify the concept and analytical study.

… and self-consumption of photovoltaic, this paper … photovoltaic consumption potential in village microgrid. An electric vehicles orderly charging scheduling model and an energy storage …

… for coordinated scheduling of combined heat and power units in micro grid considering wind turbine and photovoltaic units. … The type of the objective function, coordinated scheduling of …

The increasing deployment of photovoltaic-storage systems in distribution-level microgrids introduces a critical control conflict: traditional maximum power point tracking algorithms aim to maximize energy harvest, while grid-forming inverter control demands real-time power flexibility to deliver frequency and inertia support. This paper presents a novel two-layer co-optimization framework that resolves this tension by integrating adaptive traditional maximum power point tracking modulation and virtual synchronous control into a unified, grid-aware inverter strategy. The proposed approach consists of a distributionally robust predictive scheduling layer, formulated using Wasserstein ambiguity sets, and a real-time control layer that dynamically reallocates photovoltaic output and synthetic inertia response based on local frequency conditions. Unlike existing methods that treat traditional maximum power point tracking and grid-forming control in isolation, our architecture redefines traditional maximum power point tracking as a tunable component of system-level stability control, enabling intentional photovoltaic curtailment to create headroom for disturbance mitigation. The mathematical model includes multi-timescale inverter dynamics, frequency-coupled battery dispatch, state-of-charge-constrained response planning, and robust power flow feasibility. The framework is validated on a modified IEEE 33-bus low-voltage feeder with high photovoltaic penetration and battery energy storage system-equipped inverters operating under realistic solar and load variability. Results demonstrate that the proposed method reduces the frequency of lowest frequency point violations by over 30%, maintains battery state-of-charge within safe margins across all nodes, and achieves higher energy utilization than fixed-frequency-power adjustment or decoupled Model Predictive Control schemes. Additional analysis quantifies the trade-off between photovoltaic curtailment and rate of change of frequency resilience, revealing that modest dynamic curtailment yields disproportionately large stability benefits. This study provides a scalable and implementable paradigm for inverter-dominated grids, where resilience, efficiency, and uncertainty-aware decision making must be co-optimized in real time.

The increasing penetration of distributed energy resources and diverse load characteristics in interconnected multi-microgrid systems creates significant challenges for coordinated energy management and optimal resource planning. This study proposes a multi-objective optimization framework for the simultaneous sizing of photovoltaic (PV) systems and battery energy storage systems (BESSs), combined with coordinated energy management and bidirectional power exchange among residential, commercial, and industrial microgrids connected to the IEEE 33-bus distribution network. The framework incorporates 24 h load profiles, photovoltaic generation, time-of-use electricity pricing, and distribution network operational constraints. A Multi-Objective Particle Swarm Optimization (MOPSO) algorithm is employed to simultaneously minimize the total daily cost, network power losses, and grid dependency while satisfying the voltage, feeder loading, and battery state-of-charge constraints. The economic objective combines the equivalent daily investment costs of PV and BESSs with daily operating costs using a capital recovery factor (CRF)-based formulation to ensure dimensional consistency. The best compromise solution is selected using the minimum normalized Euclidean distance to the ideal Pareto solution. Simulation results demonstrate that the proposed framework achieves a total daily cost of $13,412.52/day, total network power losses of 4179.1 kW, and grid dependency of 3262.28 kWh while maintaining all operational constraints within acceptable limits. Furthermore, coordinated PV–BESS operation improves voltage regulation, reduces feeder loading and network power losses, enhances renewable energy utilization, and decreases the reliance on the utility grid. The results demonstrate that the proposed framework provides an effective techno-economic approach for the coordinated planning and operation of interconnected multi-microgrid systems with high renewable energy penetration.

Regional clusters of energy producers and consumers can be realized by integrating household Battery Energy Storage (BES) systems with Renewable Energy Sources (RES) and linking them to the main utility grid. These clusters, functioning as grid-connected microgrids (MGs), act as controllable units within the broader energy distribution network. As distribution systems evolve to include higher MG penetration, the need for efficient and scalable energy management becomes critical to ensure technical compatibility with grid objectives and operational constraints. Additionally, understanding the impact of battery usage patterns on degradation is essential for developing long-term, cost-effective energy management strategies. This paper presents a novel Grid-Connected Microgrid Energy Management (GCM-EM) model that incorporates both economic and technical constraints, with Battery Energy Storage (BES) as the central flexible resource. The proposed model supports both uncoordinated (microgrid-autonomous) and coordinated (DSO-integrated) scheduling schemes. The novelty lies in its ability to capture real-world BES degradation dynamics—including cycle aging and depth-of-discharge (DoD) effects—within an optimization-based energy scheduling framework. The scheduling model leverages mixed-integer programming, AC optimal power flow, and rolling-horizon control to achieve both local and system-level operational goals. The model’s performance was validated using simulations on two representative test systems: a university campus distribution grid and a standardized 33-bus power network. Results demonstrate that localized MG optimization can reduce energy costs by up to 2%. At the same time, coordination with the Distribution System Operator (DSO) further enhances grid-level cost efficiency—though sometimes at the expense of local MG economic optimality. Importantly, the model preserves data privacy during coordination and maintains compliance with distribution grid constraints. Furthermore, the model was implemented in a real building-level microgrid (BMG), where it effectively minimized BES operational and degradation costs. Compared to conventional EMS frameworks that ignore battery wear, the proposed model achieved a 3% reduction in combined annual energy and degradation costs. Integration into actual EMS platforms also enabled optimized BES dispatch, reduced municipal grid dependence, enhanced MG operational flexibility, and lowered overall network operating expenses. This research provides a comprehensive and practically validated energy management architecture for BES-integrated microgrids. By combining advanced scheduling strategies with accurate degradation modeling and multi-agent coordination, the proposed system represents a significant advancement toward economically sustainable and technically robust distributed energy networks.

The power coordination control of a photovoltaic/battery microgrid is performed with a novel bio-computing model within the framework of membrane computing. First, a neural-like P system with state values (SVNPS) is proposed for describing complex logical relationships between different modes of Photovoltaic (PV) units and energy storage units. After comparing the objects in the neurons with the thresholds, state values will be obtained to determine the configuration of the SVNPS. Considering the characteristics of PV/battery microgrids, an operation control strategy based on bus voltages of the point of common coupling and charging/discharging statuses of batteries is proposed. At first, the SVNPS is used to construct the complicated unit working modes; each unit of the microgrid can adjust the operation modes automatically. After that, the output power of each unit is reasonably coordinated to ensure the operation stability of the microgrid. Finally, a PV/battery microgrid, including two PV units, one storage unit, and some loads are taken into consideration, and experimental results show the feasibility and effectiveness of the proposed control strategy and the SVNPS-based power coordination control models.

… wind, photovoltaic (PV), and energy storage systems has … Inter-microgrid coordination is emerging as a vital component … distributed robust scheduling [30], which allow each microgrid to …

With the integration of more microgrids in distribution networks, its optimal autonomous operation becomes more important to reduce its operating cost and its influence on the main grid. This paper proposes a bi-layer multi-time coordination method for optimal generation and reserve schedule and dispatch of a grid-connected microgrid to reduce the impact of uncertainties of renewable sources, loads, and random component failures on power balance, operating costs, and system reliability. The reserve is refined into positive and negative reserves related to power shortage and power surplus. In the days ahead schedule layer, generating units are committed, and relaxed bidirectional reserve boundaries are predicted for the next day. In the real-time dispatch layer, generation output is dynamically adjusted and the reserve is dispatched using a successive approximation based on real-time data. A test microgrid is analyzed to illustrate the effectiveness of the proposed approach.

… the coordinated development of multiple microgrids and … in shared energy storage operation, distributed PV consumption, and … energy storage studies focus on operation scheduling for …

… method for an independent wind-photovoltaic-diesel-storage microgrid. It combines a mixed-… paper proposes a closed-loop coordination framework for sizing and scheduling of island …

… to coordinated multi-microgrid operation, EV-based storage flexibility, and scheduling-… Each microgrid in the cluster hosts both PV and wind generation, but the installed capacities …

A multi-energy micro-grid (MEMG) consists of combined cooling, heat and power generation units, thermal energy storage systems, diesel generators, and renewable energy generators and it can simultaneously supply electric and thermal loads. The MEMG can operate in grid-connected or islanded mode depending on practical needs. However, uncertainties existing in the renewable power generation and multi-energy loads pose significant challenges to the operation of the MEMGs in terms of economic profits and conformity with operating constraints. To address the uncertainties, this paper proposes a robustly coordinated operation approach which coordinates multiple devices in different timescales to minimize the operating costs. Both the operation modes and the practical operating constraints are considered. In addition, this paper develops a robust optimization method to guarantee optimal and reliable multi-energy supply under the uncertainties. The proposed approach is verified and compared with existing methods, and simulation results show that it can achieve high energy utilization efficiency and high operating robustness against the uncertainties.

With the increasing integration of photovoltaic (PV) generation, short-term scheduling of hydro–PV–battery energy storage systems (HPBS) faces growing challenges due to the stochastic variability of PV output, the temporal coupling of hydropower operation, and the accumulation of deviations during the real-time execution of day-ahead schedules. This paper proposes a bi-level coordinated scheduling framework that integrates day-ahead mixed-integer quadratic programming (MIQP) with intraday Soft Actor–Critic (SAC)-based correction. In the upper layer, MIQP generates a 24 h baseline schedule subject to unit output limits, mutually exclusive charging/discharging logic, and operational constraints. In the lower layer, SAC performs bounded real-time residual correction for hydropower and battery storage around the MIQP baseline, while a deviation-triggered replanning mechanism forms a closed-loop process of planning, execution, correction, and replanning. Comparative experiments under the tested setting show that SAC achieves better overall performance than Deep Deterministic Policy Gradient (DDPG), Twin Delayed Deep Deterministic Policy Gradient (TD3), and Proximal Policy Optimization (PPO). Typical-day evaluations under dry-, normal-, and wet-season conditions show that, in the selected case studies, the proposed MIQP + SAC framework achieves better performance than standalone MIQP and MIQP-Replan, which refers to a deviation-triggered MIQP re-optimization strategy, in load tracking, PV curtailment reduction, and hydro-storage coordination. These results indicate the effectiveness of the proposed framework for short-term HPBS scheduling under representative operating conditions.

… —including distributed photovoltaics, electric vehicles, and energy storage systems—poses … This paper addresses the coordinated dispatch problem of main-distribution-microgrids …

To mitigate the mismatch between fluctuating renewable generation and load demand in highway service area multi-microgrid systems, this paper develops a day-ahead capacity optimization model based on the coordinated operation of fixed and mobile energy storage. A ring-structured multi-microgrid architecture is established, incorporating a “one-to-many” interaction mode of mobile storage stations. A coordinated control strategy is then proposed to enable flexible power dispatch and resource sharing among microgrids. The objective function minimizes both investment and operating costs of energy storage on a day-ahead timescale, and the model is solved using an optimization approach. Case study results demonstrate that introducing mobile energy storage significantly reduces the required capacity of local fixed storage, enhances energy interconnection among microgrids, and improves overall storage utilization and system economy.

To address transient grid impacts and high operating costs caused by high-frequency, high-power charging of new-energy locomotives in locomotive depot microgrids, this paper innovatively proposes a timetable-driven spatiotemporal-energy decoupling collaborative scheduling method. First, a locomotive spatiotemporal state correlation matrix and a discrete energy mapping model are established, reconstructing the rigid traffic load into a virtual energy storage system with great large-capacity temporal translation potential. Second, a multi-objective optimal scheduling model is constructed to minimize microgrid comprehensive operation and maintenance costs and main grid interactive power fluctuation, considering locomotive smooth ramping and battery safe operation boundaries. For the high-dimensional, discontinuous mixed-integer nonlinear programming problem, an improved multi-objective particle swarm optimization–mantis shrimp optimization algorithm integrated with physical constraint masking is proposed, which reduces dimension via the underlying temporal feasible region filtering mechanism and achieves efficient coordination between global exploration and local exploitation. Multi-scenario simulations show the strategy guides locomotive clusters to form refined temporal peak-shifting. Compared with unordered charging, system comprehensive operation and maintenance costs decrease by 59.6%, main grid interactive power fluctuation by 85.2%, achieving high economic benefits, new-energy local consumption rate and grid-connection friendliness while ensuring transportation rigid demand.

Photovoltaic‐storage‐charging microgrids (PSCMs) are being increasingly deployed in extreme environments, including desert, polar, coastal and high‐altitude regions, to provide a reliable and sustainable power supply. However, these harsh environments significantly accelerate the degradation of photovoltaic arrays, battery storage systems and electric vehicle charging infrastructures. Effectively managing PSCMs under these conditions requires energy management systems with control strategies that explicitly account for environment‐dependent degradation dynamics. This paper provides a comprehensive review of degradation‐aware energy management for PSCMs operating in extreme environments. First, extreme operating environments are classified using quantitative thresholds, and their specific degradation effects on PSCM components are systematically analysed. Next, degradation modelling approaches comprising analytical models, data‐driven approximations and physics‐informed enhancements are reviewed and compared. Current energy management strategies, ranging from model‐based methods to data‐driven reinforcement learning and hybrid architectures, are then examined. Finally, future research directions are outlined, focusing on generalizable multi‐stress degradation models, principled degradation‐aware control frameworks and comprehensive datasets and digital twin testbeds.

… Scheduling strategy of the proposed microgrid The primary goal of the microgrid scheduling … of PV and WT operating under the specified power factors φ PV,j and φ WT,j .(22) P grid , j , …

Robust sizing of rural micro-grids is hindered by uncertainty associated with the expected load demand and its potential evolution over time. This study couples a stochastic load generation model with a two-stage stochastic micro-grid sizing model to take into account multiple probabilistic load scenarios within a single optimisation problem. As a result, the stochastic-optimal sizing of the system ensures an increased robustness to shocks in the expected load compared to a best-case (lowest-demand) sizing, though with a lower cost and better dispatch flexibility compared to a worst-case (highest-demand) sizing. What is more, allowing just a 1% unmet demand enables to significantly improve the cost-competitiveness and the renewables penetration as all the not supplied energy is located in a negligible fraction of the unlikeliest highest demand scenarios.

… microgrids, thereby alleviating the very generation-side fluctuations caused by WT power integration. In this paper, a twostage robust optimization … Antarctic islanded microgrid validate …

As the increasing penetration of wind and PV generations in island microgrids, the intermittent nature of renewable energy resources and randomness of load demands are inevitable, therefore, maintaining system stability and reliability has become a challenging issue for microgrid operators. In addition, energy storage unit and demand side management technology are widely utilized in the island microgrids to alleviate the passive impacts introduced by renewable energy resources. Nevertheless, they produce uncertainties as well. To accommodate the combined uncertainties, a two-stage robust model predictive control based optimization approach is proposed in this paper. The mixed integer quadratic programming model is established in the first operation stage to minimize the operation cost under the joint worst case of uncertainty, then an economic dispatch model is used to minimize the adjustment cost after obtaining actual data in the second operation stage. Robust linearization methods with the consideration of three types of uncertainty scenarios and uncertainty budgets are utilized in the first operation stage. Finally, the case study indicates that the proposed approach is more robust and economical than the conventional two-stage robust optimization approach, then the sensitivity of typical parameters and important units are analyzed and discussed.

With the rapid transition towards carbon neutrality and the integration of high-penetration renewable energy, zerocarbon multi-energy microgrids (MEMGs) coupled with reversible solid oxide cells (RSOCs) have become critical solutions for fully autonomous energy supply. This paper first proposes a microgrid-oriented electro-thermal-hydrogen cogeneration architecture, integrating parabolic trough solar thermal collectors and local heat networks to optimize the multi-modal switching logic of the RSOC and maintain its precise thermal management. Second, an R-Vine Copula function and conditional Wasserstein distance are employed to accurately capture the high-dimensional, asymmetric cascade correlations among distributed sources and multi-energy loads, thereby constructing a robust data-driven fuzzy set. Finally, a two-stage distributionally robust optimization (DRO) scheduling model is established to account for extreme local uncertainties, utilizing an adaptive McCormick envelope method and Benders decomposition to efficiently solve the system's complex nonlinear electro-thermal physical constraints. The results demonstrate that the proposed strategy effectively ensures the reliability and economic efficiency of the microgrid under extreme source-load scenarios, providing new insights into the resilient scheduling of zero-carbon multi-energy systems.

Combined cooling, heating, and power (CCHP) microgrids are a special form of a microgrid that is attracting increasing attention. This study contributes to the goal of minimising the operation cost of CCHP microgrids by proposing a hierarchical two-stage robust optimisation dispatch model for multiple CCHP microgrid systems. The uncertainties associated with wind power output, electric power, heating, and cooling loads, and transmission line failures are considered in the proposed model. Moreover, the electricity purchasing and selling prices of each microgrid are independently determined. The proposed model applies the outputs of fuel cells, energy storage devices, and gas turbines, the distribution factor of waste heat, and the power transmission between the microgrids and an external grid as control variables. The optimised dispatch problem is solved using McCormick envelopes relaxation and a novel column and constraint generation algorithm that provides enhanced optimisation performance by implementing co-evolutionary theory. In this way, the microgrid system is divided into several sections, and each section is represented as an individual min–max–min problem. The rationality and validity of the proposed model and the superiority of the solution performance of the improved algorithm are verified through simulation case studies involving a system composed of four CCHP microgrids.

… Consequently, nonanticipativity is not satisfied in two-stage robust optimization methods and counterexamples have been given in [24]. Meanwhile, multi-stage robustness cannot be …

To improve the reliability of microgrid operation and the capability for off-grid autonomous operation, this study proposes a robust reliability-based optimal configuration method for microgrid hybrid energy storage systems. Firstly, the operational characteristics of the hydrogen energy storage system are analyzed, and combined with the cooperative mechanism of the hydrogen energy storage and distributed power supply systems, the operation architecture of the microgrid electro-hydrogen coupling system is constructed. Secondly, according to the electro-hydrogen coupling characteristics and adjustment capability, a two-stage distributionally robust optimization configuration model of electro-hydrogen hybrid energy storage is constructed. In the first stage, the minimum investment and operation cost of the microgrid is the optimization goal. The optimal configuration model for the equipment capacity in the microgrid is constructed, and the distributed photovoltaic, wind turbine, battery, hydrogen storage tank, hydrogen fuel cell and electrolytic cell in the microgrid are fixed. In the second stage, according to the results of the capacity optimization configuration in the first stage, the operation reliability of the microgrid is taken as the optimization objective; 168 h is set as the operation cycle, and the extreme operation scenario for the new energy output from the microgrid is assumed to provide the capacity optimization boundary for the upper layer. Finally, the model is solved by the constraint generation algorithm and analyzed by an actual microgrid in a given area. The quantitative results demonstrate the validity of the proposed method: compared to systems without hydrogen energy storage, the duration of the continuous islanded operation is increased from approximately 302 h to 529 h (an improvement of approximately 75.2%), and the load-shedding duration is reduced from approximately 35 h to 7 h (an approximately 80% reduction).

Coordinated planning is an effective method to balance investment costs and benefits in achieving high renewable target under the renewable-driven power system expansion wave. This paper proposes a coordinated planning model to support the efficient achievement of renewable target considering economy of the system by accounting for the interaction among source, grid, and energy storage system. An adaptive two-stage min-max-min robust optimization model is formulated to take into account renewable target as well as the uncertainty associated with renewable production and load demand. To reduce the conservatism of robust optimization, uncertain budget, multiple uncertain sets, and data-driven method are used to design uncertain sets. The resulting model is transformed into a tractable bi-level programming through strong duality theory and big-M method. A customized column-and-constraint generation algorithm is used to solve the bi-level programming. Simulation results presented for the modified IEEE 30-bus test system corroborates the effectiveness of the methodology, which finds siting and sizing of renewable energy sources and energy storage systems as well as transmission expansion schemes. It is capable to provide a flexible planning tool driven by renewable target under a reasonable computational burden.

ABSTRACT By clustering multiple microgrids (MGs), a multi-microgrid (MMG) system plays a significant role in integrating a large amount of renewable generation. However, the large-scale utilization of renewable energy also brings uncertainties to MMG energy management. In this work, a novel comprehensive bi-level MMG energy management model considering uncertainties of renewable energy is first developed which includes unit commitment (UC) problem and other models in the lower MG level. Then considering the non-convexity of the bi-level problem, a decomposition method called analytical target cascading (ATC) is employed to deal with it by decentralization. With regard to the energy management of each individual MG, a two-stage distributionally robust model is developed which describes the uncertainties from probability distribution of renewable generation with a metric-based ambiguity set. Moreover, an efficient solution scheme based on column and constraint generation (CCG) algorithm and a decomposition method without duality is designed to handle the MG energy management problem. Finally, we implement extensive experiments to corroborate the effectiveness of the proposed approach. Particularly, the optimal solution from the proposed method can attain 2.98% less cost compared with that from robust optimization (RO) method and achieve 86.17% less energy trading amount than that in independent mode.

… , two-stage robust optimization has been used to deal with equality constraints in microgrid … order to cope with the min-max-min optimization objectives embedded in two-stage robust …

Introduction of renewable energy sources (RESs) and independently operated multi-microgrid (MMG) systems have led to new issues in the management of power systems. In this context, uncertainty associated with RESs as well as intense ramps inflicted on the network called system flexibility constraints have raised new challenges in power systems. The new condition necessitates the implementation of novel frameworks that enable local system operators to efficiently manage the available resources to cope with the flexibility-ramp constraints. Moreover, the new framework should facilitate energy management in a system with an MMG structure considering uncertainty of RESs. Consequently, in this article, we aim to provide a novel framework that composes of a two-level stochastic optimization procedure to optimize the energy management in an MMG, considering uncertainty of RESs as well as grid flexibility constraints. In the proposed scheme, resource scheduling in microgrids (MGs) is conducted in the first level by their control units, while the second-level procedure focuses on the coordination of MGs, considering flexibility constraints. Furthermore, interaction with gas grid as a potential flexible resource is optimized in the second-level procedure. Finally, the provided flexibility-oriented management scheme is implemented to schedule the local resources in a three-MG test system, considering flexibility constraints.

With the increasing integration of distributed renewable energy into distribution networks, challenges arise due to the variability and uncertainty associated with renewable energy sources, such as power flow reversals and voltage violations. Consequently, enhanced flexibility is required in the distribution network. This paper proposes a distributionally robust optimization (DRO) scheduling model that considers demand-side flexibility resources, such as controllable distributed generation (DG), energy storage systems (ESS), soft open points (SOP), smart loads (SL), and electric vehicles (EV). The model utilizes probabilistic scenario reduction to generate typical scenarios for wind generation, solar generation, and loads. It formulates a two-stage three-layer DRO model, optimizing day-ahead scheduling and worst-case scenario probability distribution to minimize intra-day adjustment costs. The proposed model is validated using an enhanced IEEE 33-bus distribution system. The results show that the proposed model can ensure a balanced supply-demand relationship and effectively cope with scenarios of insufficient flexibility.

In recent years, severe outages caused by natural disasters such as hurricanes have high-lighted the importance of boosting the resilience level of distribution systems. However, due to the uncertain characteristics of natural disasters and loads, there exists a research gap in the selection of optimal planning strategies coupled with provisional microgrid (MG) formation. For this purpose, this study proposes a novel three-stage stochastic planning model considering the planning step and emergency response step. In the first stage, the decisions on line hardening and Distributed Generation (DG) placement are made with the aim of maximising the distribution system resilience. Then, in the second stage, the line outage uncertainty is imposed via the given scenarios to form the provisional MGs based on a master-slave control technique. In addition, the non-anticipativity constraints are presented to guarantee that the MG formation decision is based on the line damage uncertainty. Last, with the realisation of the load demand, the cost of load shedding in each provisional MG is minimised based on a demand-side management program. The proposed method can consider the step-by-step uncertainty realisation that is near to the reality in MG formation strategy. Two standard distribution systems are utilised to validate the correctness and effectiveness of the presented model.

As an emerging energy allocation method, shared energy storage devices play an important role in modern power systems. At the same time, with the continuous improvement in renewable energy penetration, modern power systems are facing more uncertainties from the source side. Therefore, a robust optimization algorithm that considers both shared energy storage devices and source-side uncertainty is needed. Responding to the above issues, this paper first establishes an optimal model of a regional integrated energy system with shared energy storage. Secondly, the uncertainty problem is transformed into a dynamic optimization problem with time-varying parameters, and a modified robust optimization over time algorithm combined with scenario analysis is proposed to solve such optimization problems. Finally, an optimal scheduling objective function with the lowest operating cost of the system as the optimization objective is established. In the experimental part, this paper first establishes a dynamic benchmark test function to verify the validity of proposed method. Secondly, the multi-mode actual verification of the proposed algorithm is carried out through a regional integrated energy system. The simulation results show that the modified robust optimization over time (ROOT) algorithm could find solutions with better robustness in the same dynamic environment based on the two-stage evaluation strategy. Compared with the existing algorithms, the average fitness and survival time of the robust solution obtained by the modified ROOT algorithm are increased by 94.41% and 179.78%. At the same time, the operating cost of the system is reduced by 11.65% by using the combined optimization scheduling method proposed in this paper.

… , a two-stage distributionally robust optimization (DRO) … robust optimization models of microgrid were proposed in Refs. [17,18] which considered the multiple uncertainties in microgrid…

Microgrids face significant challenges due to the unpredictability of distributed generation (DG) technologies and fluctuating load demands. These challenges result in complex power management systems characterised by voltage/frequency variations and intricate interactions with the utility grid. Model predictive control (MPC) has emerged as a powerful technique to effectively address these challenges. By applying a receding horizon control strategy, MPC offers promising solutions for optimising constraints and enhancing microgrid operations. The purpose of this review paper is to comprehensively analyse the application of MPC in microgrids, covering various levels of the hierarchical control structure. Furthermore, this paper explores the emerging trend of employing MPC across microgrid applications, ranging from converter control levels for power quality to overarching energy management systems. It also investigates the future research perspectives by considering the challenges associated with establishing MPC-based microgrid control. The key conclusion derived from this review paper is that the implementation of MPC techniques in microgrid operations can greatly improve their overall performance, efficiency, and resilience. This paper thoroughly examines the various challenges faced in MPC-based microgrid operations, underscoring the significance of conducting research in advanced artificial intelligence (AI)-based MPC methods. It highlights how these cutting-edge AI techniques can bring about economic benefits in microgrid operations, addressing the complex demands of efficient energy management in a rapidly evolving landscape. The presented insights strive to enhance the comprehension and adoption of MPC techniques in microgrid settings, actively contributing to the ongoing improvement of their operational processes. By shedding light on key aspects and offering valuable guidance, this work aims to propel the advancement and effective utilisation of MPC methodologies in microgrids, ultimately leading to optimised performance and enhanced overall operations.

… framework for reliable microgrid energy management based on receding horizon control. A … here to use Model Predictive Control (MPC) for handling control and state constraints while …

This paper presents a two-level hierarchical energy management system (EMS) for microgrid operation that is based on a robust model predictive control (MPC) strategy. This EMS focuses on minimizing the cost of the energy drawn from the main grid and increasing self-consumption of local renewable energy resources, and brings benefits to the users of the microgrid as well as the distribution network operator (DNO). The higher level of the EMS comprises a robust MPC controller which optimizes energy usage and defines a power reference that is tracked by the lower-level real-time controller. The proposed EMS addresses the uncertainty of the predictions of the generation and end-user consumption profiles with the use of the robust MPC controller, which considers the optimization over a control policy where the uncertainty of the power predictions can be compensated either by the battery or main grid power consumption. Simulation results using data from a real urban community showed that when compared with an equivalent (non-robust) deterministic EMS (i.e., an EMS based on the same MPC formulation, but without the uncertainty handling), the proposed EMS based on robust MPC achieved reduced energy costs and obtained a more uniform grid power consumption, safer battery operation, and reduced peak loads.

Model predictive control (MPC) facilitates online optimal resource scheduling in electrical networks, thermal systems, water networks, process industry to name a few. In electrical systems, the capability of MPC can be used not only to minimise operating costs but also to improve renewable energy utilisation and energy storage system degradation. This work assesses the application of MPC for energy management in an islanded microgrid with PV generation and hybrid storage system composed of battery, supercapacitor and regenerative fuel cell. The objective is to improve the utilisation of renewable generation, the operational efficiency of the microgrid and the reduction in rate of degradation of storage systems. The improvements in energy scheduling, achieved with MPC, are highlighted through comparison with a heuristic based method, like Fuzzy inference. Simulated behaviour of an islanded microgrid with the MPC and fuzzy based energy management schemes will be studied for the same. Apart from this, the study also carries out an analysis of the computational demand resulting from the use of MPC in the energy management stage. It is concluded that, compared to heuristic methods, MPC ensures improved performance in an islanded microgrid.

… An integrated model predictive control (MPC) scheme enforces binary and logical constraints through mixed-integer programming (MIP). Convex relaxation techniques address …

Abstract The development of microgrids is an advantageous option for integrating rapidly growing renewable energies. However, the stochastic nature of renewable energies and variable power demand have created many challenges like unstable voltage/frequency and complicated power management and interaction with the utility grid. Recently, predictive control with its fast transient response and flexibility to accommodate different constraints has presented huge potentials in microgrid applications. This paper provides a comprehensive review of model predictive control (MPC) in individual and interconnected microgrids, including both converter-level and grid-level control strategies applied to three layers of the hierarchical control architecture. This survey shows that MPC is at the beginning of the application in microgrids and that it emerges as a competitive alternative to conventional methods in voltage regulation, frequency control, power flow management and economic operation optimization. Also, some of the most important trends in MPC development have been highlighted and discussed as future perspectives.

Optimization of economic aspects of microgrid operation in both grid-connected and islanded mode leads to contradictive definitions of optimality for both modes. There is no general agreement on how to cope with this duality. To address this issue, as well as modern energy market requirements and a better renewable energy utilization necessity in the case of large facilities, a comprehensive control solution utilizing the appropriate model is needed. In response, the authors propose a hybrid microgrid model covering fundamental features and designed to work in conjunction with two switched receding horizon control laws. A relevant controller is chosen according to the current microgrid operation mode and its cost function tailored to specific demands of the islanded or grid-connected operation. Performed research led to a new switched hybrid model predictive control approach focused on microgrid economic optimization. This approach utilizes an appropriate hybrid microgrid model also contributed by the authors. The introduced solution turned out to be effective in overall energy cost reduction in the case of large commercial facilities, regardless of grid-connection and renewable generation scenarios. Furthermore, it also provides satisfactory renewable energy and storage capabilities utilization in changing grid connection conditions.

This paper proposes an Adaptive Model-based Receding Horizon Control Scheme (AMRHCS), which allows taking into consideration the uncertainty power production of renewable energy resources, demand response, the variance of real-time electricity price, load demand and as well as respecting the special constraints for optimal performance and economic benefits of the micro-grids. The essence of this study is to propose a control scheme for the interconnected power microgrids so as to minimize the operating costs of the individual micro-grid, the power purchased by each micro-grid, the pollutant gas emissions, energy procured from the host grid and from the other micro-grids. Therefore, in order for these objectives to be achieved, an adaptive MPC controller is utilized to locate the best patterns for power exchange and state of energy storage system among micro-grids. More so, to investigate the optimal control action of the interconnected power micro-grids under the proposed control framework, we iteratively formulated a finite horizon Mixed Integer Linear Programming (MILP) problem. The MATLAB simulation results demonstrated the superiority of the proposed control technique in terms of excellent performance and economic benefits of the micro-grids.

… We recall that the vector of disturbances profiles, ˆw(k+j), is assumed to be known over the prediction horizon, for j = 0,...,T − 1. According to the receding horizon strategy, only the first …

… The aim of this paper is to present a robust model predictive control technique based on … in this approach is that the controller is implemented in a receding horizon scheme, so the …

Microgrids (MGs) are presented as a cornerstone of smart grids. With the potential to integrate intermittent renewable energy sources (RES) in a flexible and environmental way, the MG concept has gained even more attention. Due to the randomness of RES, load, and electricity price in MG, the forecast errors of MGs will affect the performance of the power scheduling and the operating cost of an MG. In this paper, a combined stochastic programming and receding horizon control (SPRHC) strategy is proposed for microgrid energy management under uncertainty, which combines the advantages of two-stage stochastic programming (SP) and receding horizon control (RHC) strategy. With an SP strategy, a scheduling plan can be derived that minimizes the risk of uncertainty by involving the uncertainty of MG in the optimization model. With an RHC strategy, the uncertainty within the MG can be further compensated through a feedback mechanism with the lately updated forecast information. In our approach, a proper strategy is also proposed to maintain the SP model as a mixed integer linear constrained quadratic programming (MILCQP) problem, which is solvable without resorting to any heuristics algorithms. The results of numerical experiments explicitly demonstrate the superiority of the proposed strategy for both island and grid-connected operating modes of an MG.

… According to the receding horizon strategy, only the first element of the optimal sequence u(k) is applied. The optimization problem (17) is repeated at time k +1, with the new measured/…

In this work, we propose a hierarchical distributed model predictive control strategy to operate interconnected microgrids (MGs) with the goal of increasing the overall infeed of renewable energy sources. In particular, we investigate how renewable infeed of MGs can be increased by using a transmission network allowing the exchange of energy. To obtain an model predictive control scheme, which is scalable with respect to the number of MGs and preserves their independent structure, we make use of the alternating direction method of multipliers leading to local controllers communicating through a central entity. This entity is in charge of the power lines and ensures that the constraints on the transmission capacities are met. The results are illustrated in a numerical case study.

… In this study, a model predictive control scheme integrated with two-layer moving-horizon … to the secondary frequency control of a PV high-penetration microgrid. The local observer …

This paper proposes an optimal power dispatch by taking into account risk management and renewable resources. In particular, it examines how control engineering and risk management techniques can be applied in the field of power systems through their use in the design of risk‐based model predictive controllers. To this end, this paper proposes a two‐layer control scheme for microgrid management where both levels are based on model predictive control (MPC): the higher level is devoted to risk management while the lower layer is dedicated to power dispatching. In particular, the high‐level controller is based on a risk‐based approach where potential risks have been identified and evaluated. Mitigation actions are the decision variables to be optimized to reduce the consequences of risks and costs. The MPC‐based algorithm decides the appropriate frequency of mitigation actions such as changes in references, constraints, and insurance contracting, by relying on a model that includes integer variables, identifiable risks, their costs, and the cost/benefit assessment of mitigating actions. On the other hand, the low‐level controller drives the plant to suitable values to satisfy demands. A series of simulations on a nonlinear model of a real laboratory‐scale power plant located in the facilities of the University of Seville are conducted under varying conditions to demonstrate the effectiveness of the algorithm when risks are explicitly considered.

… The influence of disturbances on renewable energy is mitigated by the receding horizon optimization strategy. In this way, the whole nonlinear mix-integer optimization problem is …

The world is rapidly integrating renewable energy resources into the existing grid systems. However, the unpredictable nature of renewables and uncertain load profiles cause issues such as poor power quality, lower system reliability, complex power management, battery degradation, high operating costs, and lower efficiency. Microgrids can help smart grid technology overcome several problems associated with renewable energy integration. Distant locations can obtain electricity without building extensive transmission infrastructure, cutting development costs, or transmission losses. The intermittent nature of renewable energy sources contributes to microgrid problems such as poor power quality, decreased reliability, and high operating costs. Model predictive control (MPC) is an effective method to address challenging industrial and scientific issues. Advancements in MPC that accept different system constraints have solved multiple concerns in uncertain microgrid systems. MPC applied to three hierarchal control layers in a microgrid resolves the problems of power quality, power sharing, energy management, and economic optimization. This study demonstrates that MPC microgrid control is suitable for low-cost operation, improved management, and reliable control. The shortcomings of recent model predictive control techniques for microgrids are reviewed, and future research directions for MPC microgrids are identified.

… under uncertainties of renewable resources, demand load … by using the conditional value-at-risk (CVaR) method. The … , CVaR, expected energy not served and scheduled reserves of …

… reserve scheduling of MG is formulated as a risk-constrained … uncertainties and proposes a risk-constrained two-stage … In this paper, CVaR method is applied to model risk aversion …

The unpredictable and volatile nature of renewable energy sources will increase the burden of a system operator for maintaining the system reliability in different conditions. In this article, a stochastic risk-constrained framework is proposed for short-term optimal scheduling of autonomous microgrids to evaluate the influence of demand response (DR) programs on reliability and economic issues, simultaneously. The objective is to maximize the expected profit of the microgrid operator through optimal scheduling of resources in a more reliable manner considering both supply and demand side uncertainties. In the proposed approach, the microgrid operator's risk aversion is modeled by using the conditional value-at-risk method to control and avoid nondesirable profit distributions due to various system uncertainties. Moreover, ac optimal power flow technique is employed to calculate the amount of energy and reserve of dispatchable distributed generation (DG) units and responsive loads for the operational hour of the next day. Eventually, the applicability of the proposed method is studied on different test systems and impacts of various parameters such as level of DR participants and values of lost load as well as risk aversion parameter on the system's economy and reliability indices are investigated deeply.

The integration of high levels of renewable energy into microgrids introduces significant volatility. This demands energy management systems (EMS) that balance economic efficiency with resilience. This work proposes a Resilient Constraint Energy Management System (RCEMS) that combines Wasserstein Distributionally Robust Optimization (DRO) and Conditional Value-at-Risk (CVaR)-constrained Model Predictive Control (MPC). The proposed framework helps communities achieve energy independence, reduce carbon footprints, and enhance climate resilience. The proposed two-layer architecture handles non-Gaussian uncertainties in renewable generation and load demand. The day-ahead layer uses Wasserstein DRO for scheduling, while the real-time layer employs risk-aware MPC with CVaR constraints to ensure probabilistic resilience. The proposed RCEMS is validate on a modified IEEE 34-node microgrid with solar PV, wind, and storage. Results show that the proposed method reduces daily operational costs by 12–18% compared to reinforcement learning (RL) and stochastic EMS methods. It also maintains voltage stability within 0.95–1.05 pu during extreme conditions. Key resilience metrics include a 98% islanding success rate which is 8–13% higher than benchmarks and only 2% state-of-charge violations compared to 28% in RL-based approaches. The system demonstrates Pareto-optimal performance, balancing costs i.e., ${\$}$ 500–550/day and resilience with 95–98% success across 100 Monte Carlo trials. Tests under hurricanes, cyberattacks, and multi-contingency outages confirm the framework’s adaptability to spatio-temporal uncertainties and its ability to take rapid corrective actions using Phasor Measurement Unit (PMU) feedback. The results highlight RCEMS as a scalable solution for microgrids with high renewable penetration, offering robust trade-offs between cost efficiency and survivability. The framework does not rely on restrictive parametric assumptions, thus providing a foundation for climate-resilient and sustainable energy infrastructures.

Abstract Recent years have witnessed a growing trend in the participation of renewable energy on the generation side and relatively high peak loads on the demand side, which makes it gradually challenging for traditional methods concentrating separately on the generation side to maintain system balance. Load resources, with potentialities to provide faster and more economical responses to balance signals, are able to make contributions to system balance through demand response(DR) programs in addition. With the reformation and development of the electricity market, load aggregators(LAs) pear as representatives of small-scale customers and generations to meet response limitations and participate in DR programs. The LA in this paper, which aggregates residential customers and a PV system with battery energy storage(BES) units, balances the power by optimal scheduling and bidding in Day-ahead(DA) and real-time(RT) markets based on real-time electricity price(RTP). And the objective of this paper is to maximize the profits of LA. A majority of papers use deterministic methods for the modeling of renewable generations and residential loads. However, influenced by multiple factors, the actual renewable outputs and residential responsive loads towards real-time electricity prices are unavoidably uncertain. These uncertainties bring risks to LA’s scheduling and bidding strategies, which results in the reduction of LA’s profits. A stochastic model based on the scenario generation method is adopted to reflect the uncertainties of customers’ responsive loads and the PV system’s outputs. The objective profit function turns out to be a risk function influenced by uncertain factors and the risk control method conditional risk at value(CVaR) is integrated to obtain optimal solutions for this maximization problem. Case studies have verified the effectiveness of the proposed strategy.

… and scheduling decisions under multiple correlated uncertainties, including electricity prices, renewable … This paper proposes a synergistic Transformer-CVaR risk-averse scheduling …

This paper studies a risk-averse stochastic unit commitment framework for an energy aggregator, operating a portfolio of conventional generators, renewable units, and battery energy storage in a network-constrained environment. Renewable generation and demand uncertainty are represented through a scenario based extensive-form mixed-integer linear program. To avoid exposure to rare but high cost events, the model incorporates Conditional Value-at-Risk as part of the objective function. The approach captures key market interactions, including day-ahead commitments, imbalance penalties, and power exchange with a neighboring network, while respecting generator constraints, storage dynamics, line flow limits, and bus voltage security. A comprehensive parametric study is conducted to quantify the influence of two risk parameters: the Conditional Value-at-Risk confidence level α and the risk-aversion weight λ. Using a 300-scenario test set on a modified IEEE 9-bus system, the results show that risk-neutral scheduling exposes the aggregator to larger operational costs in extreme scenarios. Minor levels of risk aversion (0.1–0.5) reduce CVaR and tighten the distribution of costs. Increasing λ further yields diminishing returns, while higher α values focus risk mitigation on the most severe outcomes. The results demonstrate how CVaR-based stochastic scheduling can support aggregator decision-making by quantifying downside risk under renewable uncertainty.

… , this paper proposes a new risk-constrained two-stage stochastic … formulated using the conditional value-at-risk measure, … Strong motivations toward the use of the renewable energy …

… intermittency and availability of renewable resources on energy hub … scheduling problem, risk of energy hub operation cost variation is included using the conditional value at risk (CVaR…

This paper presents a risk-constrained scheduling optimization model for a grid-connected hybrid microgrid including demand response (DR), electric vehicles (EVs), variable wind power generation and dispatchable generation units. The proposed model determines optimal scheduling of dispatchable units, interactions with the main grid as well as adjustable responsive loads and EVs demand to maximize the expected microgrid operator’s profit under different scenarios. The uncertainties of day-ahead (DA) market prices, wind power production and demands of customers and EVs are considered in this study. To address these uncertainties, conditional value-at-risk (CVaR) as a risk measurement tool is added to the optimization model to evaluate the risk of profit loss and to indicate decision attitudes in different conditions. The proposed method is finally applied to a typical hybrid microgrid with flexible demand-side resources and its applicability and effectives are verified over different working conditions with uncertainties.

… of REH with and without consideration of the CVaR term are analyzed in this chapter. At the … the optimal scheduling of renewable-based energy hub considering a risk-constrained two-…

… -time operational risks driven by renewable uncertainty, including load-shedding, … risk-constrained decision support for dispatch schemes [19]. In long-term expansion planning, CVaR is …

Home energy management systems (HEMSs) encourage participation of residential consumers into the demand response programs. This paper proposes a robust Conditional Value at Risk (CVaR) optimization approach for day ahead HEMS to reduce the effect of risk of real-time exposure to energy price and solar power generation uncertainties. Initially, the CVaR method is integrated with the two-point Estimation (2PE) analysis to approximate the solar power, modeled as Beta probability distribution function, in low computation effort compared to conventional Monte Carlo simulation (MCS) based CVaR approach. Then the optimization constraints are revised to their robust counterparts by accounting a certain amount of uncertainty in the energy prices from their nominal values. Unlike the previous literatures, the optimization problem is developed to minimize the risk value of the energy cost. Again to maximize the life of the plug-in electric vehicle (PEV) a pseudo cost function for the PEV battery degradation is proposed. The entire optimization portfolio is developed as a mixed integer linear programming for its easy execution. Simulation is demonstrated on a smart home, designed as an ac–dc microgrid, having practical appliance data sets, to prove the efficacy of the proposed method.

… MG scheduling … risk-constrained stochastic scheduling (RSS) model is used to minimize the MG operation cost. The uncertainties associated with the real-time market price, renewables, …

Integrated energy system is a very important way to improve energy efficiency. Based on the combined heating cooling and power system, combined with energy storage equipment, a cross‐regional integrated energy system scheduling optimization problem is studied. An integrated energy system scheduling optimization model is established that meets the requirements of electrical, heating, and cooling load under a variety of energy sources while both considering the interaction of electrical, heating, and cooling load between regions, and complementation of them within one region. Meanwhile, the value at risk (VaR) theory is introduced and the operating constraints of equipment in the integrated energy system fully considered, the integrated energy system scheduling model with VaR is established. The example shows that the model can realize multi‐type electrical, heating, and cooling load optimized by schedule across regions under the premise of satisfying the balance of energy supply and demand, which can reduce the system operation cost. The sensitivity analysis of the minimum expected cost and the influencing factors of conditional VaR is carried out to verify the validity and feasibility of the proposed model.

… In the next section, hydropower-scheduling model in … Then, risk-constrained optimal stochastic solution considering hydro-… , since CVaR is greater than VaR, schedules with low CVaR …

With the increasing integration of variable renewables, cascade hydro–photovoltaic (PV) systems face growing challenges in scheduling under PV output uncertainty. This paper proposes a risk-aware bi-level scheduling model based on the Information Gap Decision Theory (IGDT) to maximize renewable energy utilization while accommodating different risk preferences. The upper level optimizes the uncertainty horizon based on the decision-maker’s risk attitude (risk-neutral, opportunity-seeking, or risk-averse), while the lower level ensures operational feasibility under corresponding deviations in the PV and hydropower schedule. The bi-level model is reformulated into a single-level mixed-integer linear programming (MILP) problem. A case study based on four hydropower plants and two photovoltaic (PV) clusters in Southwest China demonstrates the effectiveness of the model. Numerical results show that the opportunity-seeking strategy (OS) achieves the highest total generation (68,530.9 MWh) and PV utilization (102.2%), while the risk-averse strategy (RA) improves scheduling robustness, reduces the number of transmission violations from 38 (risk-neutral strategy) to 33, and increases the system reserve margin to 20.1%. Compared to the conditional value-at-risk (CVaR) model, the RA has comparable robustness. The proposed model provides a flexible and practical tool for risk-informed scheduling in multi-energy complementary systems.

… policies for the original risk-constrained MDPs. In this paper, we employ risk-constrained MDPs to study the economic and safety operation of renewable energy systems. Specifically, …