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Economic dispatch (ED) is one of the key problem in power systems. ED tends to minimize the fuel/operating cost by optimal sizing of conventional generators (CG). Greenhouse/toxic gas emission is one of the major problem associated with the CG. Emission dispatch (EMD) deals with the reduction of greenhouse/toxic gas emissions by the optimal output of generators. The multi-objective economic emission dispatch (MOEED) problem has been formulated by considering both fuel cost and emission objectives. The main objective is optimization of fuel cost and environmental emissions from the CG in a compromised way. In this paper, CONOPT solver in General Algebraic modeling system (GAMS) has been proposed to find the the optimal solutions for ED, EMD, and MOEED problems of a microgrid. The microgrid consists of a wind turbine generator (WTG), a photovoltaic (PV) module, three CGs, and a battery energy storage system (BESS) option. The proposed algorithm has been implemented in four case studies, including all energy sources, without WTG, without PV module, and without renewable energy sources (RES). To establish the effectiveness of the proposed algorithm, it has been compared with various algorithms. The comparison result shows that proposed algorithm is more effective, novel, and powerful. Finally, result shows the effectiveness of proposed approach to optimize the objective function for all aforementioned case studies and the CONOPT solver in GAMS outperformed all the approaches in comparison. The impact of BESS on the operating/fuel cost of the microgrid has also been presented for ED. Paradigm is changing in terms of demand response in μG. Demand flexibility (DF) model has also been established with consumers demand variation in optimization process. Result with DF shows the reduction in cost and better management from demand side. [ABSTRACT FROM AUTHOR]

Abstract Before starting stability analysis of the multivirtual synchronous machine (n‐VISMA) power system, it is necessary to obtain the steady‐state operating points (SSOPs) of all dynamic nodes in the network. Modified traditional iterative schemes using the concept of droop bus technique in an islanded microgrid are not feasible for load flow analysis of VISMA microgrid incorporating non‐control dynamics. This paper proposes closed‐form steady‐state, fundamental‐frequency models for islanded VISMA microgrids using the concept of virtual swing buses. In this technique, the virtual internal buses of all VISMAs in the network are governed by the swing equation. The voltage at all buses is variable except the virtual buses in which the pole wheel voltages are prespecified. The algorithm was extended by a droop control localized to each VISMA. The suitability of the proposed algorithm to obtaining SSOPs of VISMA was tested on IEEE‐9 bus system with VISMA replacing electromechanical synchronous machines and also on a low‐voltage distribution system. To validate the applicability of the proposed algorithm and prove its accuracy, the case study systems were also modeled in the SIMULINK environment for detailed time domain analysis. The algorithm was found to be computationally effective for a load flow analysis of the VISMA microgrid. The results also reveal that the addition of external droop control improves the frequency stability of the system.

The low carbon park islanded microgrid faces operational challenges due to the high variability and uncertainty of distributed renewable energy sources. These sources cause severe random disturbances that impair the frequency control performance and increase the regulation cost of the islanded microgrid, jeopardizing its safety and stability. This paper presents a data-driven intelligent load frequency control (DDI-LFC) method to address this problem. The method replaces the conventional LFC controller with an intelligent agent based on a deep reinforcement learning algorithm. To adapt to the complex islanded microgrid environment and achieve adaptive multi-objective optimal frequency control, this paper proposes the quantum-inspired maximum entropy actor-critic (QIS-MEAC) algorithm, which incorporates the quantum-inspired principle and the maximum entropy exploration strategy into the actor-critic algorithm. The algorithm transforms the experience into a quantum state and leverages the quantum features to improve the deep reinforcement learning's experience replay mechanism, enhancing the data efficiency and robustness of the algorithm and thus the quality of DDI-LFC. The validation on the Yongxing Island isolated microgrid model of China Southern Grid (CSG) demonstrates that the proposed method utilizes the frequency regulation potential of distributed generation, and reduces the frequency deviation and generation cost. [ABSTRACT FROM AUTHOR]

Before starting stability analysis of the multivirtual synchronous machine (n‐VISMA) power system, it is necessary to obtain the steady‐state operating points (SSOPs) of all dynamic nodes in the network. Modified traditional iterative schemes using the concept of droop bus technique in an islanded microgrid are not feasible for load flow analysis of VISMA microgrid incorporating non‐control dynamics. This paper proposes closed‐form steady‐state, fundamental‐frequency models for islanded VISMA microgrids using the concept of virtual swing buses. In this technique, the virtual internal buses of all VISMAs in the network are governed by the swing equation. The voltage at all buses is variable except the virtual buses in which the pole wheel voltages are prespecified. The algorithm was extended by a droop control localized to each VISMA. The suitability of the proposed algorithm to obtaining SSOPs of VISMA was tested on IEEE‐9 bus system with VISMA replacing electromechanical synchronous machines and also on a low‐voltage distribution system. To validate the applicability of the proposed algorithm and prove its accuracy, the case study systems were also modeled in the SIMULINK environment for detailed time domain analysis. The algorithm was found to be computationally effective for a load flow analysis of the VISMA microgrid. The results also reveal that the addition of external droop control improves the frequency stability of the system. [ABSTRACT FROM AUTHOR]

The existence of imbalanced single- and two-phase loads, coupled with short-circuit faults, contributes to voltage imbalance. It is inevitable to use LCL filters to remove harmonics caused by converter switching. While effective in removing harmonic components, these filters may inadvertently amplify and propagate resonance. Both voltage imbalance and active resonance significantly degrade power quality. This paper proposes a multi-level hierarchical control system to mitigate both phenomena. At Level 1, the controller incorporates proportional-resonant regulators for current and voltage. Level 2 employs common droop control to establish microgrid voltage and frequency reference values. Level 3 introduces a washout filter with an adjustable Kd gain, capable of attenuating active resonance harmonics originating from the LCL filter. Finally, Level 4 integrates a controller based on extracting positive and negative sequence components using the dual decoupled synchronous reference frame (DDSRF) algorithm. This controller effectively compensates for negative sequence components of voltage in the load bus, balancing load voltage. Simulation results for a standalone microgrid demonstrate that the proposed 4-level hierarchical control algorithm can reduce the load bus voltage imbalance from 10% to 2.5% under the most challenging conditions. It diminishes harmonic distortion caused by active resonance from 11% to 2.5%. The presented control algorithm can perform optimally under dynamic changes of active and reactive power of nonlinear and imbalanced loads. The main merit of this approach is not to use physical devices and Flexible Alternative Current Transmission Systems (FACTS), such as Active Power Filters (APF), Distribution Static Synchronous Compensators (DsSTATCOM), SVC, etc.

In a renewable energy-based islanded microgrid system, frequency control is one of the major challenges. In general, frequency oscillations occur in islanded microgrids due to the stochastic nature of load and variable output power of distributed generating units (DGUs). In the presented research proposal, frequency oscillations are suppressed by implementing the proportional integral derivative (PID) controller-based control design strategy for an islanded microgrid. The modeling of the islanded microgrid is firstly presented in the form of a linearized transfer function. Further, the derived transfer function is approximated into its equivalent first-order plus dead time (FOPDT) form. The approximated FOPDT transfer function is obtained by employing the reaction curve method to calculate the parameters of the FOPDT transfer function. Furthermore, the desired frequency regulation is achieved for the manifested FOPDT transfer function by incorporating PID control design. For PID controller tuning, different rule-based methods are implemented. Additionally, comparative analysis is also performed to ensure the applicability of the comparatively better rule-based tuning method. The Wang–Chan–Juang (WCJ) method is found effective over other rule-based tuning methods. The efficacy of the WCJ method is proved in terms of transient response and frequency deviation. The tabulated data of tuning parameters, time domain specifications, and error indices along with responses are provided in support of the presented control strategy. [ABSTRACT FROM AUTHOR]

Ensuring accurate current sharing and regulating output voltage is challenging in DC microgrids. Conventional droop control has limitations in achieving voltage regulation and accurate current sharing. Unequal transmission line resistances, local loads, and constant power load (CPL) add to the complexity. To tackle this issue, this paper presents a novel consensus based distributed secondary control that determines the resistance of transmission lines by injecting an external pulse to the reference voltage of each converter, and then measuring the resulting changes in output voltage and current. The proposed secondary control signal, denoted as ψi, enables simultaneous proportional current sharing and voltage restoration in the DC microgrid. To guarantee the stability of the proposed method, a comprehensive stability analysis of the system is performed. In contrast to similar methods, the proposed method enables achieving precise proportional current sharing and voltage restoration, even when faced with varying resistive loads and CPLs. Furthermore, the proposed method exhibits remarkable features including, high convergence speed, the capability to determine transmission line resistances instead of assuming them to be known, and robustness in plug-and-play scenarios and communication system failures. The proposed method is validated through simulations in MATLAB and experimental tests, affirming its effectiveness. [ABSTRACT FROM AUTHOR]

Pre-synchronization control is needed when the microgrid changes from an off-grid state to a grid-connected state. Aiming to resolve the problems of frequency overstep and voltage fluctuation in traditional pre-synchronous grid-connection schemes, a micro-grid pre-synchronous grid-connection scheme is proposed that can solve both frequency overstep and voltage fluctuation at the same time. Firstly, the feedforward disturbance compensation V/f control strategy of the load voltage and current is introduced to the energy storage system to suppress voltage fluctuations caused by power changes. Then, the V/f control strategy of the energy storage system is improved to suppress voltage fluctuations caused by frequency fluctuations when the starting phase of pre-synchronization is enacted. Finally, PI parameters are optimized based on the golden jackal optimization algorithm to meet the requirements of frequency fluctuation and grid-connection speed in the pre-synchronization process. A large number of simulation experiments demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Optimal power flow (OPF) analysis enables the in-depth study and examination of islanded microgrid design and operation. The development of the analysis framework, including modeling, formulating, and selecting effective OPF solvers, however, is a nontrivial task. As a result, this paper presents a tutorial on an OPF modeling framework, offering a mathematical model that can be readily implemented using established open-source software tools such as OpenDSS, Pyomo, and IPOPT. The framework is versatile, capable of representing single-phase and unbalanced three-phase islanded microgrids. Various inverter models, such as those of grid forming and following equipped with their operating characteristics, can be incorporated. The efficacy of the proposed framework is demonstrated in studying the OPF of single-phase and three-phase microgrids. [ABSTRACT FROM AUTHOR]

The low carbon park islanded microgrid faces operational challenges due to the high variability and uncertainty of distributed renewable energy sources. These sources cause severe random disturbances that impair the frequency control performance and increase the regulation cost of the islanded microgrid, jeopardizing its safety and stability. This paper presents a data-driven intelligent load frequency control (DDI-LFC) method to address this problem. The method replaces the conventional LFC controller with an intelligent agent based on a deep reinforcement learning algorithm. To adapt to the complex islanded microgrid environment and achieve adaptive multi-objective optimal frequency control, this paper proposes the quantum-inspired maximum entropy actor-critic (QIS-MEAC) algorithm, which incorporates the quantum-inspired principle and the maximum entropy exploration strategy into the actor-critic algorithm. The algorithm transforms the experience into a quantum state and leverages the quantum features to improve the deep reinforcement learning’s experience replay mechanism, enhancing the data efficiency and robustness of the algorithm and thus the quality of DDI-LFC. The validation on the Yongxing Island isolated microgrid model of China Southern Grid (CSG) demonstrates that the proposed method utilizes the frequency regulation potential of distributed generation, and reduces the frequency deviation and generation cost.

In order to solve the problems such as significant frequency fluctuation and slow dynamic response under load disturbance in islanded microgrid which has a diesel generator (DG) as the primary source, an auxiliary frequency regulation method is proposed to improve the dynamic response process of the system. Firstly, the model of diesel generator system is established to analyze the impact on transient state due to main parameters, including inertia and response delay. Secondly, the energy storage system (ESS) with auxiliary frequency regulation based on droop control is proposed, and the engineering parameter and ESS′s power margin design method are given. In addition, a small signal model of the DG-ESS system is established to prove the stability of the system. Finally, the experimental platform of DG-ESS microgrid is built, and the results verify that the proposed control strategy effectively reduces the transient frequency fluctuation under the change of static or motor load.

The interest in the integration of distributed energy resources in microgrids increased significantly in the last decade. The stochastic nature of some energy sources and the dynamic power demand has brought difficulties regarding the optimal control of microgrids. This current study addresses the energy management challenge in an islanded hybrid energy microgrid that includes three types of renewable energy resources (photovoltaic, geothermal and biomass) and a battery storage system, using intelligent management methods that optimize energy production costs. The proposed intelligent management methods are based on cost function minimization. These ensure optimal energy management operation under uncertain weather conditions, keeping to the minimum the price of the energy produced by the microgrid. Due to the erratic nature of solar irradiance and considering that solar energy is cheaper than its counterparts (geothermal and biomass in this case), forecasting the photovoltaic power production is an essential task for guaranteeing optimal microgrid operation. Day-ahead photovoltaic power forecasts are issued based on solar irradiance forecasts provided by the Global Forecasting System and further integrated into the day-ahead scheduling of the microgrid. This algorithm, together with the cost-optimization algorithms, gives intelligence to the management protocol generating the input parameters (power and operating time for each generating unit) for the microgrid Energy Management Controller. Different cost optimization methods are studied and compared, including mathematical models, such as Mixed Integer Linear Programming, or nature-inspired optimization algorithms, such as Genetic Algorithm, Harmony Search Algorithm, and Particle Swarm Optimization. It is shown that these algorithms provided suitable solutions for the energy balance and scheduling ensuring minimal operation costs for the microgrid. The study also highlights the differences and limitations of these algorithms and shows a method on how these energy management methods can be integrated into a real-world microgrid providing a step forward in the development of intelligent microgrids.

The increasing interest in renewable energy-based power systems globally is driven by their abundance and environmentally friendly attributes. Islanded hybrid microgrid systems (IHMS) are a relatively new development in this field and involve the integration of two or more sustainable sources, such as wind turbines, solar photovoltaic (PV) systems, and other forms of renewable energy such as the ocean, wave, and geothermal energy. In order to ensure an uninterrupted power supply for the growing community and industrial sector of Perhentian Island, Malaysia, alternative power sources must be properly synchronized and managed through an energy management system. To this end, the main contribution of this study is the comprehensive analysis of various optimization methods in terms of net present cost (NPC) and convergence rate. The results of the analysis indicate that HOMER proved to be relatively faster in terms of convergence rate, with the NPC recorded as 387,185$ and the Levelized Cost of Energy (LCOE) recorded as 0.64$/kWh, which are the least among the other techniques evaluated. The hybrid energy system was designed to acquire the optimal quantity and size of power-generating modules, including PV systems, wind turbines, batteries, and diesel generators, while also meeting the load requirements. The optimization problem incorporated the LCOE and NPC into the cost function. Various optimization techniques were developed and tested. In addition, an advanced control method, which includes the use of Proportional–integral–derivative (PID) control and Fuzzy Logic Controller (FLC) with automated tuning, was applied to manage voltage and frequency. The control strategy was implemented in MATLAB Simulink, along with a full model of the islanded hybrid microgrid system. The simulation results demonstrate the effectiveness of the proposed FLC in maintaining the voltage and frequency within the acceptable range during various operating conditions. In conclusion, this manuscript provides a comprehensive study on the optimization and control of a solar-wind islanded hybrid microgrid. The proposed approach can be used as a valuable tool for the design and operation of solar-wind islanded hybrid microgrids in remote and islanded communities.

Islanded microgrids with low-inertia distributed energy resources (DERs) are prone to frequency fluctuations. With the increasing integration of DERs in microgrids, the complexity of control and stability has also increased. Moreover, the integration of DERs into microgrids may result in a power imbalance between energy supply and demand during sudden changes in load or energy generation. This can cause frequency variations in the microgrid, which could have disastrous consequences such as equipment damage or even blackouts. This paper proposes a control strategy to ensure the efficient operation of an islanded hybrid microgrid consisting of a PV generator, battery energy storage system (BESS), and emergency diesel generator. According to Energy Exchange Model proposed in this paper, the hybrid system presented operates independently without being connected to the electrical grid, where the PV system and BESS act as the main energy sources, while the emergency diesel generator provides active power backup with voltage and frequency regulation. The novel in this paper is also that DER aids in frequency regulation during active power transients by delivering and absorbing active power in accordance with the inverter's suggested P droop control strategy. In this way inverter droop control decreases system frequency nadir emulating so called "synthetic inertia". To design both the islanded hybrid system and the proposed control strategy, the MATLAB/Simulink environment is utilized. Based on the results, it can be concluded that the analyzed microgrid system is capable of maintaining stability and operating efficiently in a range of operating conditions. [ABSTRACT FROM AUTHOR]

Controlled power converters have found many applications in the power industry during the last decade. Virtual synchronous generator (VSG) is a truly good example of these converters that can be used to induce desired dynamics to the network. Despite the excellent performance of VSGs in balanced conditions, they do not carry the flexibility to suppress unbalanced components. To deal with this conflicting issue, a decoupled double synchronous reference frame-based VSG is proposed in this paper. Applying this method to the VSG structure under unbalanced voltage conditions by decoupling the positive and negative components, the oscillating terms are mostly eliminated, and DC values are extracted with the aim that the controllers can perform better. The benefits of the proposed scheme include higher accuracy, better controllability, effective component separation, and robust performance under heavy load conditions. The simulation results prove the validity and effectiveness of the proposed strategy against traditional VSG and previous techniques presented to enhance VSGs under unbalanced conditions in an islanded microgrid. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Proportional reactive power sharing among the distributed generators (DGs) is still a challenge in an islanded microgrid. The disparity in output voltage of each DG is the main cause of the error in reactive power sharing in DGs. The output voltage difference of DGs is caused by unequal line impedances and connected local loads. In order to reduce the error in reactive power sharing among the DGs, a Robust Volt-VAr control scheme (RVVCS) with an adaptive nominal voltage is proposed in this study. Since the suggested strategy is entirely decentralized, it does not need knowledge of feeder impedance or network configurations. Also, it does not require any communication link or optimization technique. The technique proposed is tested on several network configurations, including various loads, radial networks, reconfigured networks, and mesh networks, and is found satisfactory in each case. In one of the many cases presented in this study, with n q = 3 e - 4 V/VAr, β = 0.2, β add = 0.002 and local as well as common load is connected, the suggested RVVCS minimises the error in reactive power output of D G 1 , D G 2 and D G 3 to (42.68%, - 8.92%, - 33.82%), respectively, compared to the error obtained in RDCS (72.21 %, - 15.61%, - 56.6%), SADCS (72.6%, - 16%, - 56.6%) and CDCS (243.74%, - 69.87%, - 173.87%). A similar reduction pattern in reactive power output is also observed in all the case studies performed in this research. The stability of the proposed strategy is investigated in terms of eigenvalue analysis. The practicability of the proposed technique is validated in time-domain simulation in MATLAB/Simulink. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Engineering Technology is the property of Editorial Department of Electric Power Engineering Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract Modern electrical power system design will increase renewable energy sources (RES) dominance. Rotating masses, the main source of inertia in power systems, have been greatly decreased in renewable energy producing systems. Thus, load–frequency equilibrium is an important indicator of these systems' performance and safety. This work introduces a fractional‐order (FO) operator‐based cascade control structure for islanded microgrid (μG) load‐frequency control (LFC). The structure utilizes a tilt–FO derivative with filter (TFODn) in the first level to reduce noise. The second level implements the proportional integral (PI) controller's FO form (FOPI), making it a tilt–FO derivative with a filter cascaded to the FOPI controller (TOFDn‐FOPI). The optimal controller parameters for quick dynamic responses with low frequency fluctuation are determined using a unique cost function and prairie dog optimization (PDO) algorithm. The LFC control loops have frequency deviation‐based responsive loads (RL). Control signal delays, RES output changes, parameter uncertainties, and cyber vandalism are examined. Laboratory‐scale tests also assessed the controller's practicality. The proposed controller outperforms standard and FO type proportional integral derivative (PID) and PD‐PI controllers. The TFODn‐FOPI controller is suitable for complicated closed‐loop systems like islanded μGs due to its faster error clearing, reduced RL capacity, and superior time and frequency domain indicators.

As microgrids are the main carriers of renewable energy sources (RESs), research on them has been receiving more attention. When considering the increase in the penetration of renewable energy sources/distributed generators (DGs) in microgrids, their low inertia and high stochastic power disturbance pose more challenges for frequency control. To address these challenges, this paper proposes a model predictive control (MPC) secondary control that incorporates an unknown input observer and where RESs/DGs use a deloading virtual synchronous generator (VSG) control to improve the system's inertia. An unknown input observer is employed to estimate the system states and random power disturbance from the RESs/DGs and load to improve the effect of the predictive control. The distributed restorative power of each DG is obtained by solving the quadratic programming (QP) optimal problem with variable constraints. The RESs/DGs are given priority to participate in secondary frequency control due to the proper weighting factors being set. An islanded microgrid model consisting of multiple photovoltaic and wind power sources was built. The simulation results demonstrate that the proposed method improves the system frequency, restoration speed, and reduces frequency deviations compared with the traditional secondary control method. [ABSTRACT FROM AUTHOR]

According to the characteristics of islanded microgrid with renewable energy and load uncertainty, a robust economic dispatch algorithm for islanded microgrid was proposed based on echelon deviation uncertainty set. The microgrid model was set up for its structural characteristics, and the uncertainty set was converted into the uncertainty set with echelon deviation. In the day-ahead scheduling stage, the outputs of each device of the microgrid were optimized to obtain the day-ahead scheduling scheme with the optimal solution for all scenarios feasible and performance of the expected set of scenarios optimal. In the intra-day scheduling stage, it maintains the power output of the energy storage system obtained in the day-ahead scheduling stage, and adjusts the day-ahead optimal solution of micro-gas turbine, curtailment of photovoltaic power and wind power, and shiftable load to improve the economic performance through a secondary optimization utilizing the real-time data of new energy and load. The results show that the proposed method achieves better control performance and improves the economy of microgrid dispatch. Finally, the effectiveness of the method is verified by a simulation case. [ABSTRACT FROM AUTHOR]

In a high percentage of new energy-islanded microgrids, the overall inertia of the system gradually decreases, and the transient stability requirements of the microgrid frequency and voltage become more and more demanding under low-inertia conditions. To improve the transient stability of low-inertia islanded microgrid frequencies and voltages, this paper proposes a transient stability enhancement strategy for islanded microgrids based on energy storage system (ESS)–virtual synchronous generator (VSG) control. Model predictive control (MPC) is added within the active control loop of the VSG to achieve dynamic correction of the active power reference value of the VSG; PI control link is added within the reactive control loop to achieve a fast dynamic response of the reactive power command value. The ESS achieves fast and accurate regulation of frequency and voltage according to the power reference value of the VSG active control loop and the power command value of the reactive control loop simultaneously. Considering the need to ensure the ability of VSG to operate stably during transients, a comprehensive current-limiting technique combining virtual impedance and phase limiting is used to limit the fault current of VSG and maintain its synchronization and stability. Finally, the simulation results verify the strategy's effectiveness and the superiority of the transient stability enhancement effect. [ABSTRACT FROM AUTHOR]

The percentage of renewable power in conventional power generation is gradually growing due to developments in power electronic converters (PECs). Renewable energy sources (RESs) can be integrated into the main grid through PECs, which are the most prevalent method to accomplish this. Virtual oscillator control (VOC) is a well-known time-domain method to regulate grid-forming inverters. VOC objective is to model the nonlinear dynamics of deadzone oscillator in a system of voltage source inverters to give a steady AC microgrid (MG). VOC is a self-synchronizing control method that just involves the current feedback signal. In contrast, classical droop and virtual synchronous machine (VSM) controllers both require the use of low pass filters to calculate real and reactive powers. The selection of control parameters in deadzone VOC is difficult and time-consuming. The VOC parameters are designed using different optimization techniques such as Particle Swarm Optimization (PSO), Sine Cosine Algorithm (SCA), modified Sine Cosine Algorithm (mSCA), African Vulture Optimization Algorithm (AVOA), and Artificial Jellyfish Search Optimization (AJSO). MATLAB and a real-time digital simulator (Opal RT-OP5142) were used to examine the system's performance with aforesaid controllers (droop, VSM, conventional VOC, VOC-PSO, VOC-SCA, VOC-mSCA, VOC-AVOA, and VOC-AJSO). In comparison to all control methods, the proposed VOC-AJSO provides faster synchronization. The effectiveness of the suggested VOC-AJSO control approach is proved by the hardware results. • Implementation of different grid-forming inverter control methods, such as droop, VSM, and VOC. • Different optimization methods (PSO, SCA, mSCA, AVOA, and AJSO) are presented to select the VOC parameters. • The three-phase VSI is tested in hardware for standalone condition with the aforesaid control methodologies. [ABSTRACT FROM AUTHOR]

To overcome the challenges of conventional power systems, such as increasing power demand, requirements of stability and reliability, and increasing integration of renewable energy sources, the concept of microgrids was introduced and is currently one of the most important solutions for solving the mentioned problems. Generally, microgrids have two operating modes, namely grid-connected and islanded modes. Based on the literature and its unique characteristics, the islanded mode is more challenging than the other one. In this paper, a new self-adaptive comprehensive differential evolution (SACDE) algorithm is proposed for solving economic load dispatch (ELD) and combined economic emission dispatch (CEED) problems, achieving optimal power consumption in isolated microgrids. Initially, SACDE is employed for solving the ELD problem as a single-objective function, meaning that the operational cost is just considered as the objective function, and thereby, the resources are scheduled accordingly. Then, a multi-objective platform based on SACDE is also proposed to solve the CEED problem. It means two objective functions, including operational cost and emission, are simultaneously optimized. For evaluating the performance of the proposed method, three different scenarios under various cases are considered. According to the results, when SACDE is employed to solve the single objective function (cost minimization) problem, it has better performance than other methods. In terms of the bi-objective scheme (cost and emission minimization), SACDE is significantly superior to the price penalty factor technique which is frequently used in previous studies. [ABSTRACT FROM AUTHOR]

This paper proposes a homotopy-based approach to solve the power flow problem (PFP) in islanded microgrid networks with droop-controlled distributed generation (DG) units. The technique is based on modifying an "easy" problem solution that evolves with the computation of intermediate results to the PFP solution of interest. These intermediate results require the solution of nonlinear equations through Newton–Raphson (NR) method. In favor of convergence, the intermediate solutions are close to each other, strengthening the convergence qualities of the technique for the solution of interest. The DG units are modeled with operational power limits and three types of droop-control strategies, while the loads are both magnitude voltage- and frequency-dependent. To evaluate the method performance, simulations are performed considering the proposed and classical NR methods, both departing from a flat start estimation. Tests are carried out in three test systems. Different load and DG unit scenarios are implemented for a 6-, 38-, and 69-bus test system. A base case is studied for all systems, while for the two larger models, a loading factor is used to simulate the load augmenting up to the maximum value. The results demonstrated that for the largest-size model system, only the homotopy-based approach could solve the PFP for stringent requirements such as the diversification of the load profile and hard loading operation point. [ABSTRACT FROM AUTHOR]

When multiple paralleled distributed generation (DG) units operate in an islanded microgrid, accurate power sharing of each DG unit cannot be achieved with a conventional droop control strategy due to mismatched feeder impedance. In this paper, a small AC signal (SACS)-injection-based modified droop control method is presented for accurate active and reactive power sharing among DG units. The proposed control method adjusts the voltage amplitude of each DG unit by injecting small AC signals to form a reactive power control loop. This strategy does not need communication links or to specifically obtain the physical parameter of the feeder impedance and only requires the local information. Moreover, the parameter design procedure and stability analysis are given full consideration. Finally, simulation and experimental results verify the effectiveness of the proposed control scheme, and accurate active and reactive power sharing can be achieved. [ABSTRACT FROM AUTHOR]

Modern electrical power system design will increase renewable energy sources (RES) dominance. Rotating masses, the main source of inertia in power systems, have been greatly decreased in renewable energy producing systems. Thus, load–frequency equilibrium is an important indicator of these systems' performance and safety. This work introduces a fractional‐order (FO) operator‐based cascade control structure for islanded microgrid (μG) load‐frequency control (LFC). The structure utilizes a tilt–FO derivative with filter (TFODn) in the first level to reduce noise. The second level implements the proportional integral (PI) controller's FO form (FOPI), making it a tilt–FO derivative with a filter cascaded to the FOPI controller (TOFDn‐FOPI). The optimal controller parameters for quick dynamic responses with low frequency fluctuation are determined using a unique cost function and prairie dog optimization (PDO) algorithm. The LFC control loops have frequency deviation‐based responsive loads (RL). Control signal delays, RES output changes, parameter uncertainties, and cyber vandalism are examined. Laboratory‐scale tests also assessed the controller's practicality. The proposed controller outperforms standard and FO type proportional integral derivative (PID) and PD‐PI controllers. The TFODn‐FOPI controller is suitable for complicated closed‐loop systems like islanded μGs due to its faster error clearing, reduced RL capacity, and superior time and frequency domain indicators. [ABSTRACT FROM AUTHOR]

Abstract The high proportion of nonlinear and unbalanced loads results in power quality issues in islanded microgrids. This paper presents a novel control strategy for harmonic and unbalanced power allocation among distributed generators (DGs) in microgrids. Different from the existing sharing strategies that allocate the harmonic and unbalanced power according to the rated capacities of DGs, the proposed control strategy intends to shape the lowest output impedances of DGs to optimize the power quality of the microgrid. To achieve this goal, the feasible range of virtual impedance is analyzed in detail by eigenvalue analysis, and the findings suggest a simultaneous adjustment of real and imaginary parts of virtual impedance. Because virtual impedance is an open-loop control that imposes DG to the risk of overload, a new closed-loop structure is designed that uses residual capacity and absorbed power as feedback. Accordingly, virtual impedance can be safely adjusted in the feasible range until the power limit is reached. In addition, a fuzzy integral controller is adopted to improve the dynamics and convergence of the power distribution, and its performance is found to be superior to linear integral controllers. Finally, simulations and control hardware-in-the-loop experiments are conducted to verify the effectiveness and usefulness of the proposed control strategy.

In recent years, integrating renewable energy sources (RESs) has achieved significant attention due to the growing demand for sustainable energy solutions. Inverter-interfaced Islanded Microgrids (IGs) have appeared as an advantageous approach to integrating RESs into the power grid. Grid-forming inverters (GFIs) are a critical component of IGs, and their synchronization is essential for stable and reliable operation. The literature has widely proposed soft transition, pre-synchronization, and re-synchronization to synchronize IGs to the main grid. However, methods for synchronizing GFIs in the islanded microgrid are restricted. Parallel operation of GFIs is required to guarantee the high-power demand of IG and improve voltage-frequency stability. For parallel operation, GFIs must be synchronized with each other. In the conventional synchronization control systems that are highly nonlinear, the linear proportional-integral (PI) controllers are commonly used in synchronization loops without considering the nonlinearity resulting from the initial condition dependency and cross-coupling. Thus, conventional synchronization methods can be exposed to concerns of stable operation, narrow operation area, and performance degradation. This study proposes a new linearized synchronization control system for GFIs in IGs. In this way, it is possible to analytically design robust linear controllers and ensure a stable operation, high performance, and wide (full) operation area. In addition, a new soft-commissioning method is proposed to deactivate synchronization loops and soft-start the synced GFI. The proposed system has been tested in real-time and CHIL hardware setups for two 550 kW GFIs operating in parallel, and the results in the perfect agreement are presented in this study.

This article provides insights into the dynamic performance of indirect and direct control strategies for grid-forming (GFM) inverters. The indirect method for grid-forming inverters utilizes three cascaded stages to produce the reference signal sent to the PWM generator. However, the direct method has only one stage. The indirect method consists of the outer loop, which controls the power, the middle loop, which regulates voltage, and the inner loop, which controls the output current. The direct method does not require the middle and inner control loops. The article compares the performance and sensitivity of both indirect and direct control methods under various conditions, including static, inductive and dynamic loads, by adjusting controller gain parameters. A virtual reactance inrush current mitigation technique is implemented with the direct method to provide momentary control over inrush caused by the dynamic loads. The direct method incorporates a feedforward technique known as virtual reactance inrush current mitigation to outperform the performance of the direct control method in the presence of dynamic and inductive loads. The performance of both control methods is experimentally compared, and the direct method outperforms the indirect method. Experimental analyses are performed in a laboratory-scaled microgrid supplied by a 208V, one 5kVA SiC inverter, and one 10kVA Si-based inverter to compare the performance of the indirect and direct methods under different test scenarios, and the outcomes are presented in this article.

In a renewable energy-based islanded microgrid system, frequency control is one of the major challenges. In general, frequency oscillations occur in islanded microgrids due to the stochastic nature of load and variable output power of distributed generating units (DGUs). In the presented research proposal, frequency oscillations are suppressed by implementing the proportional integral derivative (PID) controller-based control design strategy for an islanded microgrid. The modeling of the islanded microgrid is firstly presented in the form of a linearized transfer function. Further, the derived transfer function is approximated into its equivalent first-order plus dead time (FOPDT) form. The approximated FOPDT transfer function is obtained by employing the reaction curve method to calculate the parameters of the FOPDT transfer function. Furthermore, the desired frequency regulation is achieved for the manifested FOPDT transfer function by incorporating PID control design. For PID controller tuning, different rule-based methods are implemented. Additionally, comparative analysis is also performed to ensure the applicability of the comparatively better rule-based tuning method. The Wang–Chan–Juang (WCJ) method is found effective over other rule-based tuning methods. The efficacy of the WCJ method is proved in terms of transient response and frequency deviation. The tabulated data of tuning parameters, time domain specifications, and error indices along with responses are provided in support of the presented control strategy.

In this paper, a control strategy for a combination PV-BESS-SC hybrid system in islanded microgrid with a DC load is designed and analyzed using a new topology. Although Battery Energy Storage System (BESS) is employed to keep the DC bus voltage stable; however, it has a high energy density and a low power density. On the other hand, the Supercapacitor (SC) has a low energy density but a high-power density. As a result, combining a BESS and an SC is more efficient for power density and high energy. Integrating the many sources is more complicated. In order to integrate the SC and BESS and deliver continuous power to the load, a control strategy is required. A novel method for controlling the bus voltage and energy management will be proposed in this paper. The main advantage of the proposed system is that throughout the operation, the State of Charging (SOC), BESS current, and SC voltage and current are all kept within predetermined ranges. Additionally, SC balances fastchanging power surges, while BESS balances slow-changing power surges. Therefore, it enhances the life span and minimizes the current strains on BESS. To track the Maximum Power Point (MPP) or restrict power from the PV panel to the load, a unidirectional boost converter is utilized. Two buck converters coupled in parallel with a boost converter are proposed to charge the hybrid BESS-SC. Another two boost converters are used to manage the discharge operation of the BESS-SC storage in order to reduce losses. The simulation results show that the proposed control technique for rapid changes in load demand and PV generation is effective. In addition, the proposed technique control strategy is compared with a traditional control strategy. [ABSTRACT FROM AUTHOR]

Reliable droop-controlled islanded microgrids are necessary to expand coverage and maximize renewables potential. Nonetheless, due to uncertainties surrounding renewable generation and load forecast, substantial power mismatch is expected at off-peak hours. Existing energy management systems such as storage and demand response are not equipped to handle a large power mismatch. Hence, utilizing dump loads to consume excess power is a promising solution to keep frequency and voltage within permissible limits during low-load hours. Considering the uncertainty in wind generation and demand forecast during off-peak hours, the dump load allocation problem was modeled within a scenario-based stochastic framework. The multi-objective optimization with uncertainty was formulated to minimize total microgrid cost, maximum voltage error, frequency deviation, and total energy loss. The mixed-integer distributed ant colony optimization was utilized in a massive parallelization framework for the first time in microgrids to solve the decomposed deterministic problem of the most probable scenarios. Moreover, a flexible and robust load-flow method called general backward/forward sweep was used to obtain the load-flow solution. The optimization problem was applied to the IEEE 69-bus and 118-bus systems. Furthermore, a cost benefit analysis was provided to highlight the proposed method's advantage over battery-based power management solutions. Lastly, the obtained results further demonstrate the fundamental role of dump load as power management solution while minimizing costs and energy losses. [ABSTRACT FROM AUTHOR]

The fixed-time secondary control problem for an islanded microgrid (MG) through an event-triggered communication mechanism is investigated in this paper. A distributed event-triggered fixed-time control strategy is proposed to achieve frequency and voltage secondary restoration. And a proportional active power-sharing is also achieved through an undirected topology. The given control protocol using frequency, voltage magnitude and active power measurement values of neighboring distributed generations only when the predefined event-triggered condition is satisfied. In comparison with the periodic communication way, the presented method exhibits excellent performance in alleviating communication burden and promoting control efficiency. Moreover, compared with conventional asymptotic control algorithms, the objectives of islanded MG secondary control are obtained within a fixed settling time by using the presented fixed-time control approach. The estimation of settling time is unrelated to any initial states. Several simulation experiments are conducted to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Islanded rural microgrid require continuous resource monitoring. Demand response schemes have been phenomenal in managing loads. However, urban demand response schemes are well equipped with market prices and peak time penalties to control deferrable loads. In rural microrids, regular loads such as fans, lights and water pumps are normally used that do not fall under category of deferrable loads. In addition, full liberty of utilizing regular load at any time, lack of awareness and no information of storage reserves make task of load management more complex. In this research fully automated two layered demand response scheme is designed for regular operating loads. The first layer control is load mode control. The mode of operation is decided on the state of charge (SoC) of battery. In second layer, fuzzy controller is designed on the consumer's routines, SoC and ambient temperature as membership function. Results are assessed in terms of consumers comfort and availablity of SoC. The load operation in automated demand response remained indentical to actual rutine operation as per consumer's desire with 5 to 7% deviation. In all modes of operation SoC levels remained 15% higher and heavy load operated 13.5% more compare to relevant study. [ABSTRACT FROM AUTHOR]

Nowadays, the participation of renewable energy sources (RESs) and the integration of these sources with traditional power plants in microgrids (MGs) for providing demand-side power has rapidly grown. Although the presence of RESs in MGs reduces environmental problems, their high participation significantly affects the system's whole inertia and dynamic stability. This paper focuses on an islanded MG frequency regulation under the high participation of RESs. In this regard, a novel fractional order cascade controller (FOCC) is proposed as the secondary frequency controller. In the proposed FOCC controller structure, a fractional order proportional-integral controller is cascaded with a fractional order tilt-derivative controller. The proposed FOCC controller has a greater degree of freedom and adaptability than integer order controllers and improves the control system's efficiency. The adjustable coefficients of the proposed controller are tuned via the kidney-inspired algorithm. An energy storage system equipped with virtual inertia is also employed to improve the system inertia. The proposed FOCC controller efficiency is compared with proportional-integral-derivative (PID), tilt-integral-derivative (TID), and fractional order proportional-integral-derivative (FOPID) controllers under different disturbances and operating conditions. The results demonstrate that the presented controller provides better frequency responses compared to the other controllers. Moreover, the sensitivity analysis is performed to show the proposed controller robustness versus the parameters' changes in the system. [ABSTRACT FROM AUTHOR]

Renewable-energy-based hybrid microgrids can aid in achieving one of the United Nations Sustainable Development Goals, i.e. 'Affordable and clean energy'. However, experts may be faced with the challenge of selecting the best one for the electrification of an area. To avoid the challenge and realize the ultimate goal of the United Nations, the present study, therefore, proposes a novel prospect theory-based decision-making approach to help experts in opting for the best microgrid scenario. The proposed decision-making framework considers the risk appetite of the decision-maker, a quintessential aspect of the process. Linear diophantine uncertain linguistic sets are used to model the linguistic evaluations from the experts. The information from different experts is aggregated using a linear diophantine uncertain linguistic power Einstein-weighted geometric operator. Finally, the prospect-theory-based TOmada de Decisao Interativa Multicriterio approach is employed to evaluate the performance of the available microgrid scenarios and hence opt for the best microgrid scenario. The proposed framework has been used to evaluate the performance of seven possible microgrid scenarios and hence select the best one that can be implemented for rural electrification of a remote village in Assam, India. The microgrid scenario consisting of a photovoltaic–wind turbine–fuel cell–battery converter (MG3) has been revealed to be the best scenario among the seven considered microgrid scenarios. The validity of the obtained ranking results has been adjudged through a comprehensive evaluation regarding the attenuation factor and the weights of the criteria. Moreover, previous case studies have also been solved using the proposed methodology and the results reveal a good correlation between the obtained ranking results. [ABSTRACT FROM AUTHOR]

Virtual synchronous generator control (VSG) is an attractive method for the grid-tied inverter to provide inertia and frequency support. However, it brings some troubles on DC-link voltage control when it is applied to two-stage photovoltaic (PV) power generation. This study proposes a DC-Side synchronous active power Control for two-stage photovoltaic (PV) power generation without energy storage. Synchronous active power Control is applied to DC–DC converters, while the grid-tied inverter still maintains the DC-link voltage constant. The DC–DC converters flexibly regulate active power to provide the simultaneous inertial and primary frequency response like a synchronous generator. A simple sensorless iterative maximum power estimation method is introduced and integrated into the DC-side VSG strategy. It can estimate a rough MAP based on one sample point and converge to an accurate value along with the VSG control. The effectiveness and advantages of the control strategy are validated through case studies on an islanded microgrid that included PV generations with a DC-bus collection system. The results show that the proposed strategy significantly improves the frequency nadir and the steady frequency and maintains DC-link voltage stability during irradiance change conditions.

The high proportion of nonlinear and unbalanced loads results in power quality issues in islanded microgrids. This paper presents a novel control strategy for harmonic and unbalanced power allocation among distributed generators (DGs) in microgrids. Different from the existing sharing strategies that allocate the harmonic and unbalanced power according to the rated capacities of DGs, the proposed control strategy intends to shape the lowest output impedances of DGs to optimize the power quality of the microgrid. To achieve this goal, the feasible range of virtual impedance is analyzed in detail by eigenvalue analysis, and the findings suggest a simultaneous adjustment of real and imaginary parts of virtual impedance. Because virtual impedance is an open-loop control that imposes DG to the risk of overload, a new closed-loop structure is designed that uses residual capacity and absorbed power as feedback. Accordingly, virtual impedance can be safely adjusted in the feasible range until the power limit is reached. In addition, a fuzzy integral controller is adopted to improve the dynamics and convergence of the power distribution, and its performance is found to be superior to linear integral controllers. Finally, simulations and control hardware-in-the-loop experiments are conducted to verify the effectiveness and usefulness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Recent advances in electric grid technology have led to sustainable, modern, decentralized, bidirectional microgrids (MGs). The MGs can support energy storage, renewable energy sources (RESs), power electronics converters, and energy management systems. The MG system is less costly and creates less CO2 than traditional power systems, which have significant operational and fuel expenses. In this paper, the proposed hybrid MG adopts renewable energies, including solar photovoltaic (PV), wind turbines (WT), biomass gasifiers (biogasifier), batteries' storage energies, and a backup diesel generator. The energy management system of the adopted MG resources is intended to satisfy the load demand of Basra, a city in southern Iraq, considering the city's real climate and demand data. For optimal sizing of the proposed MG components, a meta-heuristic optimization algorithm (Hybrid Grey Wolf with Cuckoo Search Optimization (GWCSO)) is applied. The simulation results are compared with those achieved using Particle Swarm Optimization (PSO), Genetic Algorithms (GA), Grey Wolf Optimization (GWO), Cuckoo Search Optimization (CSO), and Antlion Optimization (ALO) to evaluate the optimal sizing results with minimum costs. Since the adopted GWCSO has the lowest deviation, it is more robust than the other algorithms, and their optimal number of component units, annual cost, and Levelized Cost Of Energy (LCOE) are superior to the other ones. According to the optimal annual analysis, LCOE is 0.1192 and the overall system will cost about USD 2.6918 billion. [ABSTRACT FROM AUTHOR]

Dump load (DL) utilization at low demand hours in highly penetrated islanded microgrid is of great importance to offer voltage and frequency regulation. Additionally, load flow (LF) convergence is vital to optimize the working states of the DL allocation problem. Hence, more analysis is necessary to highlight the significance of DL in power regulation while observing the influence of LF on solution accuracy. This article proposes two LF techniques derived from backward/forward sweep (BFS), viz., general BFS (GBFS) and improved special BFS (SBFS-II). The latter is based on global voltage shared between generating units, while the former has a more general approach by considering generating bus's local voltage. The optimal sizing and sitting of DL with optimum droop sets are determined using the mixed-integer distributed ant colony optimization (MIDACO) with the two new LF methods. The optimization problem was formulated to minimize voltage and frequency deviations as well as power losses. The problem was validated on IEEE 69- and 118-bus systems and compared with established metaheuristics. Results show that DL allocation using MIDACO with SBFS-II and GBFS has improved the solution speed and accuracy, respectively. Furthermore, the enhanced voltage and frequency results highlight DL as an efficient power management solution. [ABSTRACT FROM AUTHOR]

Methods for optimization of islanded microgrid systems are usually based on hourly models where each subcomponent is described by a simple algebraic model. There are many studies on this topic, which are usually based on the minimization of total lifetime cost by determining the number of required batteries, wind turbines, PV panels, the positioning of PV panels, etc. In this paper, we further improve the modeling of the microgrid system optimization process by developing a simplified algebraic model that uses one parameter to simulate accelerated battery degradation with respect to depth of discharge. The model consists of simply linearly increasing the degradation of the battery when the state of charge (SOC) becomes lower than a fixed value, and the only model constant is the factor of degradation f. The objective of the paper is to examine the effect of the degree of degradation on the obtained optimal microgrid system parameters. The analysis was performed for several different systems, and the results show that optimal parameters of the system and the overall system cost strongly depend on battery degradation characteristics. The overall system cost can be reduced by 1–6% for lower battery degradation rates and up to 20% for high degradation factor cases. Increasing the degradation factor also has an influence on the ratio of wind turbines to PV panels, and the optimal size of the battery system. [ABSTRACT FROM AUTHOR]

With increasing the penetration rate of microgrids in power networks, their control becomes more and more important, and microgrid frequency control in islanded mode is one of the most important recent approaches which are studied. With the aim of fast microgrid frequency adjustment, this study presents a novel robust approach using fuzzy and reset techniques. Therefore, this paper firstly describes the model of an islanded microgrid consisting of various elements such as renewable resources, variable loads, storage resources and distributed energy resources, and then designs and presents a robust hybrid control technique based on switching. The planned control method consists of three parts, which are: 1-Fuzzy control technique, 2- Fuzzy reset control technique, and 3- Switching between the two techniques. Due to the robust feature of the reset technique, which in addition to quickly reducing the frequency error, it is able to overcome the limitations of linear controllers, and also due to the intelligence of the innovative fuzzy technique, the planned technique is able to quickly remove frequency errors and restore the islanded microgrid frequency in the fastest possible time and with the least ups and downs and fluctuations. As the results of simulation and comparison in MATLAB environment show, the planned technique has a high and undeniable ability to overcome the uncertainty of the model and disturbances on the system even of the most severe type. [ABSTRACT FROM AUTHOR]

Microgrid provides a promising solution to consume more distributed renewable energies. To coordinate the increasingly developed distributed renewable generators in a high flexibility and high efficiency way, distributed event-triggered mechanisms have been widely investigated in the literature to reduce the communication requirement and hence improve the control performance of microgrids. However, most of the event-triggered mechanisms mandate continuous calculation of complicated triggering conditions, which may in turn impose the computation burden of the controller and increase additional energy cost. To this end, this paper presents a distributed self-triggered control strategy for the frequency restoration in islanded microgrids with the aid of a linear clock. With this self-triggered solution, each distributed generator’s controller decides its own control and communication actions based on monitoring the linear clock, which excludes continuous calculation of any triggering conditions. Thus, the communication and computation costs can be reduced simultaneously. Moreover, Zeno behavior can be naturally excluded by the above design. The results of theoretical analysis and simulations show that the proposed distributed self-triggered control scheme can effectively coordinate distributed renewable generators with very low communication and computation requirements. Therefore, this research can improve the coordination efficiency of microgrids greatly, which is very useful for guiding the efficient operation of large-scale distributed renewable generators.

Optimal power flow (OPF) analysis enables the in-depth study and examination of islanded microgrid design and operation. The development of the analysis framework, including modeling, formulating, and selecting effective OPF solvers, however, is a nontrivial task. As a result, this paper presents a tutorial on an OPF modeling framework, offering a mathematical model that can be readily implemented using established open-source software tools such as OpenDSS, Pyomo, and IPOPT. The framework is versatile, capable of representing single-phase and unbalanced three-phase islanded microgrids. Various inverter models, such as those of grid forming and following equipped with their operating characteristics, can be incorporated. The efficacy of the proposed framework is demonstrated in studying the OPF of single-phase and three-phase microgrids.