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In recent years, due to the increase in electricity consumption and environmental problems, power system expansion planning requires new technologies. In this regard, the incorporation of renewable energy sources (RESs) and utilization of demand response (DR) programs need disruptive variations in the present power system configurations. This paper proposes a mixed-integer linear robust multiobjective model for generation and transmission expansion planning (GEP-TEP) taking into account wind farms (WFs) and a DR program based on time-of-use pricing. The suggested model is presented via mixed-integer nonlinear programming (MINLP) at the first stage and then transformed into mixed-integer linear programming (MILP) using the Big M linearization technique. Moreover, long- and short-term uncertainties of load demand and WFs are incorporated into the recommended model to achieve more accurate results. The interval-based method is applied for taking into account long-term uncertainties while the scenario-based stochastic model is applied for modeling short-term uncertainties in the recommended GEP–TEP model. Lastly, the suggested model is investigated on various standard test systems to evaluate the effectiveness of the GEP-TEP model. [ABSTRACT FROM AUTHOR]

With the emergence of the Smart Grid concept, utility companies require more active participation of home users in the power sector. This changing paradigm is enabled by the wide deployment of multiple home assets such as small renewable‐based generators or storage facilities. In this context, consumers are no longer conceived as pure loads but also active agents that can exchange energy with the grid. To promote this active participation, utility companies promote different price‐based demand response programs to change the consumer patterns on pursuing a more efficient and economic system operation. In this regard, home energy management programs are becoming an essential tool for efficiently managing the different home users while addressing multiple demand response goals at minimum cost. In essence, a home energy management system is a computational optimization tool, which has to handle multiple uncertainties brought by weather forecast or energy pricing. This paper tackles this issue by developing a novel robust home energy management program based on interval optimization. In contrast to other related approaches, the proposal avoids the explicit use of interval arithmetic. Instead, the different uncertain parameters are sequentially incorporated into the scheduling task through different stages and interval‐based formulation. The developed methodology incorporates weather, load, energy pricing and plug‐in electric vehicle related uncertainties. A benchmark case study in a smart prosumer layout serves to prove the effectiveness of the new approach. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic transmission expansion planning (TEP) in the presence of wind farms under uncertain load and wind source conditions when reliability and N-1 contingency is taken into consideration is proposed. The main aim of the suggested TEP is to minimize the total planning cost while satisfying techno-economic constraints. In this paper, reliability cost is also incorporated as the loss of load cost (LOLC) into the objective function in addition to the investment cost. In order to provide more accurate and real results, the N-1 contingency is also considered as a constraint in the TEP problem. Uncertainties for the wind source and loads in the TEP problem are modeled using a scenario-based approach and Monte Carlo simulation. Grey wolf optimization (GWO) is applied to solve the TEP problem, and it is compared to other optimization techniques. The simulation results are provided in various scenarios to confirm the efficiency of the suggested stochastic TEP. [ABSTRACT FROM AUTHOR]

This paper proposes an improved probabilistic load and distributed energy resources (DERs) modeling as pseudo-measurements by considering the correlation to be used for distribution network state estimation. The two-point method (TPM) is applied for the modeling of pseudo-measurements. The proposed method has the ability to estimate the states of a distribution network with high accuracy and short computational time. To implement the proposed scheme, the probability density functions (PDFs) of uncertain loads and DERs at different buses are extracted using historical data. Then, the TPM achieves two concentration points at each bus from obtained PDFs. Finally, the weighted least squares state estimation method is utilized at these two concentration points to obtain the probabilistic distribution of output variables. To examine the effectiveness of the suggested model, simulations are carried out on IEEE 69-bus standard test system. The proposed TPM-based state estimation approach is then compared with other conventional methods such as the Gaussian-based model, Gaussian mixture model (GMM) and Monte Carlo simulation. The superiority of the proposed TPM-based state estimation model over the GMM and Gaussian model is confirmed by a significant decrease in the running time and a noteworthy increase in the accuracy of all estimated variables. [ABSTRACT FROM AUTHOR]

This study deals with multiobjective reactive power planning, considering the uncertainties of load demand and wind power generation. The main feature of the current study is to examine the impact of multiple uncertainties on Reactive Power Planning (RPP), while several objectives exist. To fulfill this goal, the Information Gap Decision Theory (IGDT) is used to handle the uncertainties of load demand and wind power production. In order to cope with the probabilistic optimal RPP problem and to create Pareto optimal solutions, the ε-Constraint method is utilized. Fuzzy Decision Maker (FDM) and min-max approach are jointly applied to find the Best Compromise Solution (BCS). To evaluate the efficiency and the proficiency of the proposed multiobjective RPP model, it is implemented on the IEEE-30 bus test system via the GAMS software environment. To prove the superiority of the proposed model, the obtained results are compared with the scenario-based approach. The results imply that for specific amounts of uncertainty, the IGDT method performs reasonably towards the scenario-based approach. • Using the IGDT technique to present a robust VAr planning scheme. • Developing a model for multi-objective reactive power planning. • Considering multiple uncertain input parameters. [ABSTRACT FROM AUTHOR]

This paper proposes an N -step ahead model predictive controller for a multilevel asymmetric cascade grid-connected inverter. To this goal, a predictive function controller has been designed based on the Lyapunov theory. First, the equations of the N -step ahead predictive sequence have been derived for the reference current as well as the reference voltage using first-order linear interpolation considering the mean of previous values. Second, the current, voltage, current error, and Lyapunov function have been calculated for the N-samples ahead. Then, the switching scenario has been determined such that it minimizes the derivation of the Lyapunov function. Moreover, the effect of the number of prediction steps on the unwanted harmonic reduction, switching average, grid power injection, and inverter efficiency has been investigated. Finally, The proposed controller is implemented on a 19-level asymmetric cascaded inverter. The results show that by increasing the prediction steps from 1 to 5, the harmonic distortion and the number of switches are reduced. • An N -step ahead model predictive controller for a cascade inverter is proposed. • A predictive function controller has been designed based on the Lyapunov theory. • The proposed scheme is applied for control the power injection in grid-tied mode. • The effect of prediction horizon on the system characteristics was studied. • Simulation and experimental results validate the operation of the proposed control. [ABSTRACT FROM AUTHOR]

One of the main barriers for the wide penetration of fuel cell electric vehicles is the lack of proper infrastructures for hydrogen transportation that hinders the implantation of refuelling stations. This barrier could be overcome by deploying onsite hydrogen generators based on mature electrolysis and hydrogen storage technologies. This way, the necessity of hydrogen transportation is avoided. In addition, electrolysers can be onsite supplied by means of renewable generators like photovoltaic panels, while the produced hydrogen can also be destined to generate electricity through fuel cells thus obtaining a monetary revenue. Thereby, the economy of the system may be improved in order to make viable this kind of infrastructures. However, the optimal coordination of the different assets is challenging and requires the use of energy management tools to pursue the optimal performance of the installation. In this kind of infrastructures, the energy management problem is performed under substantial uncertainties; moreover, these unknown parameters have a very different character. Thus, while energy pricing and renewable generation can be forecasted using conventional techniques, refuelling demand is highly unpredictable. To this end, this paper proposes a novel stochastic-interval model for the optimal scheduling of photovoltaic-assisted refuelling stations. The new proposal uses interval notation to model the inherent uncertainty of renewable generation and energy pricing, while the vehicle demand is modelled using a more suitable approach based on scenarios. In this regard, a comprehensive stochastic model for fuel cell electric vehicles is developed, which is based on reported driving behaviour and common characteristics of commercial vehicles. To solve the problem subjected to uncertainties, an iterative solution methodology is developed which allows adopting risk-seeker and risk-averse operational strategies. A case study is analysed to validate the new proposal and discussing the importance of the different economic activities that can be exploited in refuelling stations. Results reveal the importance of selling energy to the grid in order to complement the revenues obtained from refuelling; however, this process is highly impacted by uncertainties and the operational strategy, observing variations up to 50% in the total profit depending on the strategy adopted. [ABSTRACT FROM AUTHOR]

By placing distributed generation power sources beside a big nonlinear load, these sources can be used as a power quality enhancer, while injecting some active power to the network. In this paper, a new scheme to use the distributed generation power source in both operation modes is presented. In this scheme, a fuzzy controller is added to adjust the optimal set point of inverter between compensating mode and maximum active power injection mode, which works based on the harmonic content of the nonlinear load. As the high order current harmonics can be easily rejected using passive filters, the DG is used to compensate the low order harmonics of the load current. Multilevel transformerless cascade inverters are preferred in such utilization, as they have more flexibility in current/voltage waveform. The proposed scheme is simulated in MATLAB/SIMULINK to evaluate the circuit performance. Then, a 1kw single phase prototype of the circuit is used for experimental evaluation of the paper. Both simulative and experimental results prove that such a circuit can inject a well-controlled current with desired harmonics and THD, while having a smaller switching frequency and better efficiency, related to previous 3-phase inverter schemes in the literature. [ABSTRACT FROM AUTHOR]

Power‐Flow (PF) solution in isolated microgrids has attracted notable attention recently, because these systems present various particularities compared with the traditional PF solution in large meshed transmission networks. In this sense, this paper develops a novel Newton‐like PF solver for isolated microgrids. The new proposal is based on the Modified Midpoint method and shows high convergence order with relatively low computational burden. These characteristics bring superior theoretical performance compared with the standard Newton–Raphson (NR) method and other high order techniques, which has been conventionally used. Extensive simulations are performed on various small‐, and large‐scale benchmark Microgrids under different loading conditions and R/X ratios. Results provided serve to confirm the theoretical features of the developed solver, outperforming the NR technique as well as other recently developed solvers in all the studied systems with acceptable reliability even under high stressed conditions. [ABSTRACT FROM AUTHOR]

• Defining a distributed multi-agent approach to solve power system restoration problem. • Bus agents achieve the general agreement on load feeding sequence by using Dynamic Programming. • Considering uncertainty in the wind and photovoltaic sources by Monte Carlo simulation. • Demonstrating the outperformance of the multi-agent approach rather than the top-down method. In this paper, a decentralized multi-agent system (MAS) has been proposed to solve the power system restoration problem. In the proposed MAS, an agent with its own specific logic and interactions with other agents is devoted to any piece of equipment in the grid, including bus, black start, non-black start, photovoltaic and wind generating units. Power system restoration is devised as a single objective problem to minimize the energy not supplied (ENS), which is solved by bus agents using dynamic programming. The uncertainty of the wind and photovoltaic sources is considered in the corresponding agents, which is dealed by the Monte Carlo method. In addition, not only the genetic algorithm but also dynamic programming are employed in a top-down approach to solve the problem. The proposed algorithms are applied successfully to the IEEE 39-bus system. Comparing the results of both MAS and top-down approaches demonstrate that the proposed MAS outperforms the centralized method either optimized by genetic algorithm or dynamic programming in the sense of ENS. [ABSTRACT FROM AUTHOR]

This paper presents a model predictive control (MPC) and its application on a three‐phase four‐leg inverter in an islanded mini‐grid to compensate for unbalanced load conditions while minimizing the neutral‐to‐ground voltage (NGV). The proposed approach uses the novel discrete‐time model of the four‐leg inverter and LC filter to predict the control variables. These predictions are evaluated by using a multiobjective cost function. The proposed method is based on the minimization of the cost function to select the best vector state of the power converter to be applied in the next sampling instance. The cost function in this study has two objectives: the adequately tracked low voltage reference and minimization of the NGV, simultaneously. The stability analysis is also defined to investigate the stable dynamics of the proposed MPC. The effectiveness of the suggested method is verified through simulations considering the single/three‐phase and balanced/unbalanced loads. The distinguished results of the proposed work indicate that the proposed MPC algorithm provides high power quality under unbalanced and nonlinear load conditions with high stability. The robustness of the proposed controller is also studied with both inductive and capacitive filter parameter variations. [ABSTRACT FROM AUTHOR]

Summary: Nowadays, microgrids are emerging as an invaluable framework for the integration of renewable energy sources and demand response programs. In such systems, energy storage facilities are also frequently deployed to properly manage surplus energy from renewable sources on pursuing more efficient management of the system. Hybrid storage systems in which various storage facilities are combined may result in a more effective solution than only considering one storage technology. This way, the good features of the different technologies may be jointly exploited while their drawbacks are minimized. Due to the large‐scale integration of renewable energies in this kind of grid, coping with uncertainties becomes a critical issue. Moreover, the operation of microgrids frequently deals with other kinds of uncertainties related to energy pricing from the upscale grid (in the case of grid‐connected mode) or local demand. This way, proper modeling of uncertainties is essential for adequately operating these systems. This paper contributes to this pool by developing a novel interval‐based formulation, for optimal scheduling of microgrids considering battery and pumped‐hydro storage systems. To achieve this goal, the optimal scheduling of a microgrid with pumped‐hydro and battery energy storage considering demand response is modeled, firstly. Then, the new interval‐based formulation is used to cope with the uncertainties. Finally, the suggested model is verified using simulations in various cases, and the results confirm the effectiveness of the novel interval‐based formulation for the optimal scheduling of microgrid with pumped‐hydro and battery energy storage under uncertainty. [ABSTRACT FROM AUTHOR]

• A novel stochastic-robust approach is developed for energy communities. • Individual and collective assets are considered and analysed. • The problem is solved using a novel three-stage procedure. • Operating cost is incremented 77$ when the degree of robustness grows. • Collective storage systems help to reduce unserved demand and wasted generation. This paper presents an extended model for aggregation of operational settings of droop-controlled Distributed Energy Resources (DERs) in Microgrid (MG) planning, thus deriving in a novel problem named Optimal Siting, Sizing and Setting (OSSS) of DERs. The proposed approach precisely deals with the power flow formulation for autonomous MG as an essential constraint for accurate results. Furthermore, the proposed OSSS model considers the frequency and voltage dependence characteristic of loads. The problem casts in multi-objective formulation to consider different technical, power quality and controlling aspects. This will help the designer to provide efficient decision for allocation of DERs. The effects of realistic load model as well as power sharing error index are elaborately investigated in simulation results. The model is thus further validated and its usefulness demonstrated. Finally, the performance of multi-objective OSSS model is verified by comparing the results with the previous simplified models presented in the recently published literatures. [ABSTRACT FROM AUTHOR]

The main goal of generation expansion planning (GEP) and transmission expansion planning (TEP) is to expand the power system to satisfy the increasing demand of electricity while maintaining efficient operation of the system. The major objective of this study is to propose a dynamic, robust GEP–TEP expansion planning in the presence of wind farms considering both long‐ and short‐term uncertainties. The suggested model allows implementing information‐gap decision theory on multi‐year long‐term uncertainties, such as demand growth and future increase in production capacity to decrease the risk in long‐term decisions. Additionally, a scenario‐based approach is employed for short‐term uncertainties in demand and wind power production in a 1‐year time horizon. The main advantage of the proposed model is to enhance the power system robustness against the uncertainties corresponding to forecast errors. To verify the robustness of the suggested expansion planning model, it is applied to the Garver 6‐bus and IEEE 24‐bus test systems. [ABSTRACT FROM AUTHOR]

Vernier permanent magnet (VPM) machines have been widely used in the last two decades due to their high torque density resulting from their magnetic gearing effect. In this paper, we present a new design of VPM machine with higher efficiency and power/weight ratio than their conventional counterparts. The proposed design is a combination of discrete-pole and hybrid-pole VPM machines, which incorporates the attractive characteristics of both types to improve the distribution of air-gap flux density and reduce construction costs. The arrangement of the magnets in the stator is spoke type, and their magnetization is peripheral. In order to determine the performance characteristics of the proposed machine, an analytical model based on the subdomain method is presented. The proposed method employs a quasi-Cartesian coordinates system to express the Laplace's and Poisson's equations, as well as to determine the solution for each region. Then, the solution of the equations is written in the form of hyperbolic functions and the mathematical expression of the coefficients of the equations will be simpler. To validate the proposed analytical model, a Vernier machine is designed and fabricated and the results of the experimental experiments are compared with numerical (machine simulation in finite element analysis software) and analytical results. The comparison of these results shows that the proposed model is highly accurate. [ABSTRACT FROM AUTHOR]

In this paper, a new control strategy and power management for a stand-alone PV/battery hybrid power system has been suggested. The solar cell arrays provide energy in the steady-state and the battery provides energy in transient states. Here, a charge controller system based on the MPP tracking technology, suitable for using in the islanded micro grid that contains a solar panel and a battery is designed. The charge controller includes a unidirectional DC-DC converter as an interface circuit between the solar panel and the DC bus, a bidirectional DC-DC converter as an interface circuit between the battery and the DC bus with a control system and power management in different states of irradiance and state of charge (SOC). A 200-W prototype system is designed and simulated in MATLAB/Simulink software. Also, a microcontroller DSP TMS320F2812 is applied to construct the charge controller circuit. The simulation and experimental results are showing better performance of the proposed charge controller compared with previous examples. [ABSTRACT FROM AUTHOR]

Doubly fed induction generators are widely used in wind power plants, yet their performance is vulnerable to grid voltage faults. Recent regulations require the wind generator to have the capability of fault crossing to stay connected even in faulty conditions. This paper investigates the problem of stabilizing the rotor current when the stator voltage is affected by the faults that occurred at the nearby grid. The proposed controller consists of 2 terms: the first is responsible for the internal stability of generator dynamics and the second compensates for the effect of the fault on the stator voltage. The stability of generator circuit is verified by using linear quadratic regulator and pole placement criteria. Also, to enhance the performance of the stabilizers, genetic algorithm is used to adjust the stabilizers. To detect the stator voltage disorders and to determine the suitable time for switching in fault stabilizers, a fault observer is also suggested. The fault detection and stabilization structure is simulated and shows higher levels of performance in faulty conditions than in conventional rotor side converter controllers in faulty grid conditions. [ABSTRACT FROM AUTHOR]

• Power flow Analysis of droop-controlled islanded AC microgrids is proposed. • The full detail of MG network modeling is provided. • The effect of parallel elements is considered in the proposed formulation. • A novel index named Power Sharing Error Index is developed. • Detailed modeling of droop-controlled islanded microgrids. One of the essential studies in the planning and operation of a microgrid is Power Flow (PF). Traditional PF methods are not applicable for droop-controlled islanded microgrids due to the absence of a slack bus in the system. The steady state characteristics of the system such as frequency, bus voltages, Distributed Generators' (DG) output power, and actual loads' demand are obtained based on the droop characteristics of the DGs, and also, the frequency and voltage dependency of the load. Therefore, in this paper, an Enhanced Newton Raphson (ENR) method is proposed for PF in the droop-controlled islanded microgrids. The proposed method is based on the well-known NR method but with a more comprehensive model that considers different droop schemes (resistive, inductive, and complex), load demand dependency on voltage and frequency, π line model, and shunt compensators. Moreover, a new index for selecting proper droop characteristics for any droop-controlled islanded microgrid is proposed. Five test systems with different scales, topologies, droop control strategies, and various load models are considered to evaluate the performance of the proposed method. The results are compared with the recently developed methods and steady-state results of Time-Domain simulations conducted in PLECS software. The results show that the proposed technique has excellent accuracy with low computational time and can be easily integrated into the currently available power system analysis tools. [ABSTRACT FROM AUTHOR]

The application of the four-leg inverter as an effective interface for renewable and sustainable distributed energy resources (DERs) is gaining more attention with the advances in power electronics technology. One of the key technologies in inverter-based distributed generation (DG) systems is the four-leg voltage source inverter (VSI) that is utilized to operate in autonomous four-wire microgrids. Four-leg VSIs are becoming increasingly popular in four-wire microgrid, because they can not only achieve a proper control scheme in autonomous mode but also cope with the prescribed power quality requirements. The aim of this paper is to provide an overview of the main characteristics of recently used control strategies for four-leg VSIs operating in autonomous microgrids. First, two commonly-used four-wire inverter configurations are discussed, and their advantages and disadvantages are compared. Afterwards, the most up to date control techniques for three-phase four-leg VSIs operating in islanded microgrid from the reference frame point of view are described. Lastly, a comparative analysis is carried out where the benefits and drawbacks of each strategy are assessed, and then some suggestions are put forward for the future research. [ABSTRACT FROM AUTHOR]

Multi-functional voltage source inverters (VSIs) have attracted increasing attention in recent years for their advantageous auxiliary services for power quality enhancement in autonomous microgrids. These types of VSIs can not only achieve a proper control scheme in autonomous mode but also cope with the prescribed power quality and stability requirements. These functionalities are integrated within the same device, thereby significantly improving the cost-effectiveness of microgrids while decreasing the investment and bulk compared with those of multiple devices with independent functionalities. Control strategies for power quality enhancement in autonomous microgrids using multi-functional VSIs are comprehensively reviewed in this paper. In addition, such VSIs are discussed in detail, and comparisons of which are also provided. Lastly, a number of future research directions for multi-functional VSIs are recommended. [ABSTRACT FROM AUTHOR]

In recent years, multi-energy microgrids (MEMGs) have emerged as an invaluable framework for enabling the use of clean and efficient electro-thermal resources as well as the integration of multi-energy storage facilities. Uncertainties modelling in such systems is a challenge because of the heterogeneity of the resources and consumers involved. This paper tackles this issue by proposing a hybrid robust energy management tool for MEMGs encompassing electric, heat, hydrogen and gas sub-networks. The variety of uncertainties brought by unpredictable demand and renewable generation are managed using adequate techniques. This way, renewable generation is modelled using the Hong 2m + 1 approach, the electrical and heat demands are managed using the information gap decision theory and the fuel-cell electric vehicles refueling demand is modelled via scenarios. The novel methodology is validated on a benchmark case study, in which extensive simulations are performed. The obtained results demonstrate the accurateness of the novel proposal and its effectiveness to manage a wide variety of uncertainties. The evidence for accurateness is that the difference in the objective function with the Monte Carlo and Hong 2m + 1 uncertainty modelling approaches only differs by ∼0.2%. Moreover, the new proposal is computationally competitive with the Monte Carlo simulation, improving its computation time by 2–3 times. [ABSTRACT FROM AUTHOR]

• A new method introduced for solving the power flow problem in droop-controlled islanded microgrids. • The method iteratively utilizes the conventional power flow solution methods. • A new adjustment procedure for frequency and voltage magnitude of the virtual slack bus is proposed. This paper proposes a new method for solving the power flow problem (PFP) in droop-controlled islanded microgrids (DCIMGs). The method is utilizing the conventional power flow (CPF) solution methods. A virtual slack bus (VSB) including a dummy generator/load (DGL) is set to fulfill the necessity of using the CPF methods. This bus emulates the treatment of the main grid for fulfilling the load demand to equalize the production and consumption in the microgrid and maintaining constant the frequency. Solving the problem is done to tend injective active and reactive powers to zero by DGL, which is expressing the islanded operation properties of the microgrid which is solved by an iterative process. The system frequency and the VSB's voltage magnitude are adjusted in this iterative process simultaneously. The proposed method is applied to a small 7-bus system and a big 41-bus system. Validation of the developed method is performed using the obtained results comparing with the steady-state results of time-domain (TD) simulations by PSIM. Besides the accuracy and computational burden of the required calculation is compared with (modified Newton-Raphson) MNR and the other relevant iterative methods. [ABSTRACT FROM AUTHOR]

In off-grid dwellings, proper energy management of different appliances, onsite generators and storage facilities is crucial to meet some monetary goals and environmental premises such as CO 2 emissions and diesel consumption reduction. Nowadays, this task may be performed by home energy management systems, which are able to efficiently coordinate the operation of the different home assets to achieve some predefined goals. In such cases, the operation of thermostatically controlled appliances such as heating-ventilation-air conditioning systems, electric water heaters and freezers, plays a vital role as this kind of devices allow certain degree of flexibility. This way, some thermal premises (such as thermal comfort, frozen food conservation or hot water temperature set-point) can be relaxed in order to achieve other complementary goals. This work analyses this aspect by proposing a home energy management model which incorporates flexible operational modes of various typical thermostatically controlled devices. Various results are presented on a benchmark isolated home which counts with a diesel engine as backup generator. Results show that energy generated by the backup generator can be reduced by 15% by operating the thermal-based appliances in a flexible way, while other relevant indicators such as fuel consumption, fuel cost and CO 2 emissions can be also improved by 12%. Other relevant aspects such as the impact of the photovoltaic array size and storage capacity are also investigated. [ABSTRACT FROM AUTHOR]

The restructuring of the electrical market, improvement in the technologies of energy production, and energy crisis have paved the way for increasing applications of distributed generation (DG) resources in recent years. Installing DG units in a distribution network may result in positive impacts, such as voltage profile improvement and loss reduction, and negative impacts, such as an increase in the short-circuit level. These impacts depend on the type, capacity, and place of these resources. Therefore, finding the optimal place and capacity of DG resources is of crucial importance. Accordingly, this paper is aimed at finding the optimal place and capacity of DG resources, in order to improve the technical parameters of the network, including the power losses, voltage profile, and short-circuit level. The proposed formulation of this paper significantly increases the convergence and the speed of the finding the answers. Furthermore, to select the optimal weighting coefficients, an algorithm is proposed. The weighting coefficients are decided on according to the requirements of each network and deciding on them optimally prevents the arbitrarily selection of these resources. The genetic algorithm is used to minimize the objective function and to find the best answers during the investigation. Finally, the proposed algorithm is tested on the Zanjan Province distribution network in Iran and the simulation results are presented and discussed. [ABSTRACT FROM AUTHOR]

This paper suggests an enhanced control scheme for a four-leg battery energy storage systems (BESS) under unbalanced and nonlinear load conditions operating in the isolated microgrid. Simplicity, tiny steady-state error, fast transient response, and low total harmonic distortion (THD) are the main advantages of the method. Firstly, a new decoupled per-phase model for the three-phase four-leg inverter is presented. It can eliminate the effect of power stage coupling on control design; thus, the three-phase four-leg power inverter can be viewed as three single input single output (SISO) control systems. Then, using an improved orthogonal signal generation method, the per-phase model of the four-leg inverter in the stationary and synchronous frame is derived. As the second step, a per-phase multi-loop control scheme for the four-leg inverter under unbalanced load conditions is suggested. The proposed control strategy has the ability to provide balanced output voltages under unbalanced load conditions by avoiding the need to deal with the symmetrical components. Finally, a multi-resonant harmonic compensator is used to actively prevent low-order harmonic currents to distort the output voltages of the three-phase four-leg grid-forming power converter. Simulations results are also presented to verify the performance of the suggested control strategy. [ABSTRACT FROM AUTHOR]