Fractional Order PI Controller Research Articles

A novel scheme of load frequency control for a multi-microgrids power system utilizing electric vehicles and supercapacitors

Incorporation of renewable energy sources (RESs) into power systems has recently experienced a rapid surge, primarily driven by environmental concerns and the desire for more sustainable power generation. However, the replacement of traditional generating units with RESs lowers the system inertia significantly and causes intermittent generation. These issues make frequency stability a greater concern, particularly in microgrids (MGs), and produce mechanical stress on the conventional generation units. Moreover, in interconnected MGs, the complexity is further magnified owing to interaction between microgrids through the tie power which may increase the disturbance propagation among microgrids. This paper suggests a novel control scheme based on a centralized fractional order proportional integral controller cascaded with a virtual inertia emulator (C.FOPI+VI). The virtual inertia emulation is provided using a supercapacitor (SC) along with electric vehicles (EVs) controlled through a virtual inertia controller. However, the EV is suffering from uncertainty, hence the supercapacitor can mitigate this uncertainty. The control system is applied on three interconnected microgrids, each has a thermal plant, a supercapacitor, and an electric vehicle aggregator. The performance of the system incorporating the proposed control technique is compared with five different inertia emulation topologies known as virtual inertia (VI), virtual synchronous generator (VSG), distributed fractional order proportional integral controller cascaded with virtual inertia (D.FOPI+VI), distributed fractional order proportional integral controller cascaded with virtual synchronous generator (D.FOPI+VSG), and without synthetic inertia. To optimize the parameters of different controllers, the Transit Search (TS) optimization algorithm is employed considering the frequency deviation, the restoration time, and the tie power. The proposed C.FOPI+VI has proven its superiority in providing fast frequency restoration, less stress on the conventional generation units, and minimizing the spreading of the disturbance within the system. Furthermore, the proposed controller enhances the Gain Margin (G.M) to 21.1 dB compared to operation without inertia support (0.322 dB), VI (3.38 dB), VSG (5.23 dB), DFOPI+VI (8.25), and DFOPI+VSG (8.32).

Design of fractional MOIF and MOPIF controller using PSO algorithm for the stabilization of an inverted pendulum‐cart system

AbstractThe topic of this paper is the design of two fractional order schemes, based on a state feedback for linear integer order system. In the first one of the state feedback is associated with a fractional order integral () controller. In the second structure the state feedback is associated with a fractional order proportional integral () controller. With such controllers, the closed loop system with state feedback described by the state equations splits in n‐subsystems with different fractional orders derivatives of the state variable. In order to find the optimal parameters value of both controllers () and (), a multi‐objective particle swarm optimization algorithm is used, with the integral of absolute error, the overshoot , the Buslowicz stability criterion are considered as objective functions. The multi‐objective integral fractional order controller and the multi‐objective proportional integral fractional order controller are applied to stabilize the inverted pendulum‐cart system (IP‐C), and their performance is compared to the fractional order controller. The simulation results of these innovative controllers are also compared with those obtained by conventional proportional–integral–derivative and fractional order proportional–integral–derivative controllers. The robustness of the proposed controllers against disturbances is investigated through simulation runs, considering the non‐linear model of the IP‐C system. The obtained results demonstrate that our approach not only leads to high effectiveness but also showcases remarkable robustness, supported by both simulation and experimental results.

Driving an asynchronous motor powered by PV‐MPPT using equivalent RST controller of fractional order PI and IP, based on generalized predictive control

AbstractThe article introduces a new model of a Reference Signal Tracking (RST) controller for the fractional order quantities. The controller is applied to an indirect field‐oriented control (IFOC) system used for the speed control of an asynchronous motor powered by a photovoltaic (PV) generator with a maximum power point tracking (MPPT) algorithm. This model utilizes two fractional order controllers: the fractional order proportional‐integral (FOPI) regulator and the fractional‐order integral‐proportional (FOIP) regulator. These controllers are used with the generalized predictive control (GPC) technique. The first step in the approach is to derive the equivalent digital RST controller's model from the FOPI and FOIP controller's transfer functions. The GPC technique converts the continuous‐time FOPI (and FOIP) controller into a discrete‐time version. This conversion ensures a fast response and effective disturbance rejection. Simulation tests are conducted to analyze the rotor speed and stator current ripples to evaluate the performance of the proposed method. The results demonstrate the effectiveness of the introduced scheme in achieving improved control performance in terms of response speed and disturbance rejection. The article presents a modified RST controller model based on the fractional order approach applied to an IFOC system for motor speed control driven by a photovoltaic generator. Using FOPI, FOIP controllers, and GPC contributes to enhanced control performance, as evidenced by the simulation results.

Enhancing Microgrid Inverter-Integrated Charging Station Performance through Optimization of Fractional-Order PI Controller Using the One-to-One Sine Cosine Algorithm

This paper is dedicated to optimizing the functionality of Microgrid-Integrated Charging Stations (MICCS) through the implementation of a new control strategy, specifically the fractional-order proportional-integral (FPI) controller, aided by a hybrid optimization algorithm. The primary goal is to elevate the efficiency and stability of the MICCS-integrated inverter, ensuring its seamless integration into modern energy ecosystems. The MICCS system considered here comprises a PV array as the primary electrical power source, complemented by a proton exchange membrane fuel cell as a supporting power resource. Additionally, it includes a battery system and an electric vehicle charging station. The optimization model is formulated with the objective of minimizing the integral of square errors in both the DC-link voltage and grid current while also reducing total harmonic distortion. To enhance the precision of control parameter estimation, a hybrid of the one-to-one optimizer and sine cosine algorithm (HOOBSCA) is introduced. This hybrid approach improves the exploitation and exploration characteristics of individual algorithms. Different meta-heuristic algorithms are tested against HOOBSCA in different case studies to see how well it tunes FPI settings. Findings demonstrate that the suggested method improves the integrated inverters’ transient and steady-state performance, confirming its improved performance in generating high-quality solutions. The best fitness value achieved by the proposed optimizer was 3.9109, outperforming the other algorithms investigated in this paper. The HOOBSCA-based FPI successfully improved the response of the DC-link voltage, with a maximum overshooting not exceeding 8.5% compared to the other algorithms employed in this study.

Optimized fractional order PID controller with sensorless speed estimation for torque control in induction motor

With rising concern on environmental protection, the exploitation of EV has been widely focused. The IM is said to be the best in comparing varied electric motors for EV applications due to its lower price and robustness. In addition, sensor-less controlling schemes like DTC and FOC are found to be appropriate for crucial appliances owing to their energy savings, improved efficiency, and reliability. The “Optimized Fractional Order Proportional Integral Controller (FoPID)” with a sensor-less speed estimate mechanism is proposed in this work. Additionally, the parameters of FoPID are adjusted using a brand-new hybrid method called the Wolf based Elephant Herding method (W-EHA), which combines the ideas of Grey wolf optimization (GWO) model and Elephant herding optimization (EHO). The superiority of the recommended technique is finally shown in terms of controller performance and error. The RMSE obtained by the developed model at speed = 100 is 3.344, which is 53.89 %, 24.22 %, 1.09 %, and 38.96 % superior to existing approaches like P-controller, MFI-DA + FoPID, EHO-FoPID, and GWO-FoPID respectively.

Application of Fractional Order PI/PID Voltage Controllers for Three-Phase Voltage Source Inverter with Dynamic Load

Purpose: With the depletion of fossil fuels, the landscape of electrical energy generation has witnessed a transformative shift towards alternative sources such as fuel cells and photovoltaic (PV) systems that produce direct current (DC) electricity. In the realm of distributed power generation, three-phase voltage source inverters (VSIs) are extensively utilized for converting energy from DC sources to alternating current (AC) for the grid or loads. The pivotal objective of this study is to investigate and compare the performance of fractional-order Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) control structures against their integer-order counterparts in the voltage control loop of a VSI connected to a dynamic load system.
 Materials and Methods: The research employs frequency response analysis to design and implement both fractional-order PI/PID and integer-order PI/PID control structures for the voltage control loop. The simulation of the controlled system is conducted using MATLAB/Simulink, considering two distinct test scenarios – unstable and stable dynamic load conditions. The primary focus is on analyzing the inverter output voltage in the d-q axis under these scenarios.
 Findings: The analysis of the simulation results reveals noteworthy distinctions between the fractional-order and integer-order PI/PID controllers in the context of controlling the inverter system with dynamic loads. These findings shed light on the advantages of employing fractional order controllers, particularly in dynamic load scenarios, showcasing superior performance in comparison to their integer-order counterparts.
 Implications to Theory, Practice and Policy: The study's outcomes hold significant implications for the theory and practice of voltage control in distributed power generation systems. The superiority of fractional-order PI controllers underscores their potential for enhancing power quality, especially in systems with unstable and time-varying dynamic loads. These insights can inform the development of more effective control strategies for voltage source inverters, influencing both theoretical frameworks and practical applications. Policymakers may consider these findings when formulating regulations and incentives to promote the adoption of advanced control strategies in the evolving landscape of electrical energy generation.

Advanced modeling and control of wind conversion systems based on hybrid generators using fractional order controllers

AbstractThe focus of this study is on modeling and management of a Wind Energy Conversion System (WECS) based on a Hybrid Excitation Synchronous Generator (HESG). Using a wind simulator, two controllers, CRONE and H∞, are evaluated for Maximum Power Point Tracking (MPPT) and optimal rotation speed. The results show the CRONE controller's higher tracking capability, and robustness tests investigate the influence of parametric uncertainty. Space harmonic effects, commutation effects, and turbine shaft flexibility are all addressed in the sophisticated models. The introduction of Fractional Order Proportional‐Integral (FOPI) control for MPPT is a game changer. Although fractional calculus‐based accuracy and robustness are uncommon in WECS, they show promise for emissions reduction and increased energy efficiency. This work validates a dependable control approach inside an isolated HESG‐based WECS's power‐maximizing range. Extensive investigation of the parameters impacting FOPI control efficiency yields useful insights for effective MPPT control. A variable‐speed wind turbine (WT) is linked to a HESG through a multiplier, with a controller controlling generator coil excitation voltages and a rectifier connecting the WECS to a load. A thorough 3 kW HESG electrical model that includes generator space harmonics and converter commutation effects is among the contributions. For HESG‐based WECS stability, frequency analysis finds important resonant and anti‐resonant frequencies. These issues are addressed by a FOPI control technique, which ensures system stability and performance. The necessity of exact frequency analysis in HESG‐based WECS is highlighted by a step‐by‐step controller parameter tuning approach.

An optimal membership function based Fuzzy-[formula omitted] stabilizer design to suppress low frequency oscillation in synchronous generator

An optimal membership function-based fractional order fuzzy proportional integral (Fuzzy-PIλ) power system stabilizer (PSS) is designed to suppress low frequency oscillation (LFO) in a synchronous generator connected to an infinite bus power system. Speed deviation and the change in speed deviation of synchronous generator due to LFO are taken as inputs of the fuzzy controller, and the parameters of a fractional-order PI controller (proportional gain, integral gain, and the fractional term in integral control action) are taken as fuzzy output variables. The range, scaling, and shape of the membership functions of the fuzzy controller are optimized such that it can tune the fractional order proportional integral (PIλ) stabilizer under any disturbance or parametric uncertainty in the synchronous generator. The advantage of the proposed stabilizer is that it can handle a wide range of disturbances and adjust the gains of the control parameters for the system. A nonlinear dynamic acceleration coefficient-based class-topper optimization is applied to optimize the fuzzy settings. The robustness and sensitivity of the proposed optimal Fuzzy-PIλ stabilizer are verified under different scenarios for the synchronous generator and compared with available results.

Fault Tolerant Control of a Dual Star Induction Machine Drive System using Hybrid Fractional Controller

Abstract This paper presents a novel fault tolerant control (FTC) strategy for a dual star induction machine (DSIM) based on the combination of two types of robust controllers, namely a proportional resonant (PR) controller for current regulation and a fractional order PI (FOPI) for speed regulation. This FTC is associated with an indirect rotor indirect rotor field-oriented control (IRFOC) strategy. Fault feedforward compensation of the current components is introduced using the residual signal generated by the calculations passing through the PR controller. The fractional-order PI controller is applied as a feedforward fractional-order perturbation observer to the speed control loop, which attempts to minimise the error induced by the fault. In this context, a fault-tolerant control scheme is achieved. The performance characteristics of the proposed fault tolerant control for a dual star induction machine drive are compared with the fault tolerant control based on the conventional integer order IP (IOPI) to verify the effectiveness of the proposed FTC scheme under various conditions, by examining the robustness of the control in the presence of faults. To evaluate the performance of the proposed technique, simulation results are obtained using the Matlab/Simulink environment. According to the obtained simulation results, the proposed FTC system achieves significantly better responses than the conventional IRFOC system in terms of harmonics in the stator currents, and low oscillations in the electromagnetic torque response.

Design, implementation and empirical analysis of a cascaded hybrid MPPT controller for grid tied solar photovoltaic systems under partial shaded conditions

Solar Photovoltaic (PV) system based power generation is going to become the major power source in the following few decades. Because of the advantages such as reliability, cleanliness, feasibility in small scale to medium scale power generation etc., Solar Photovoltaic (PV) based power generation is developing very rapidly. Hybrid MPPT control methods are essential to track and achieve maximum power generation from solar PV systems under normal and Partially Shaded Conditions (PSC). The proposed Hybrid Grey Wolf Optimization (GWO) algorithm with Adaptive Neuro-Fuzzy Inference System (ANFIS) will effectively tracks the Maximum Power Point when compared to the conventional hybrid MPPT methods. Luo converter is employed as DC-DC converter to convert the variable DC output from solar panel into a nominal DC level. The Luo converter output is given to a single phase Voltage Source Inverter (VSI) and the inverter is connected to grid. The Arithmetic Optimization Algorithm (AOA) tuned Fractional order Proportional Integral controller (FOPI) is adopted to maintain the stability of the grid connected inverter. The tracking efficiency of the proposed system is maintained around 98 % even under different irradiance conditions with very less convergence time of 0.016 s.

Simulation of Different Control Strategies in Pumping Mode of Variable-speed Pumped Storage Unit

Because of the complex structure, the variable-speed pumped storage (VSPS) unit would face more stability problems in operation compared with conventional generators in the power grid. To overcome the shortcomings of the PI controller, the fractional order PI (FOPI) controller is applied for VSPS in pumping mode. To compare the quality of the two controllers, the WSCC 9-bus system with VSPS is studied under different disturbances. The dynamic performance is evaluated by calculating the integral of time multiplied absolute error criterion (ITAE) of rotor speed and active power of the stator. The result shows that the FOPI control strategy can effectively improve the dynamic performance of VSPS.

Power quality enhancement of hybrid renewable energy source-based distribution system using optimised uPQC

ABSTRACT Generally, the Battery Energy Storage Systems (BESS) may meet entire load requirements while the wind turbine and PV array are still not providing energy, which enhances the reliability of the power system's distribution. The primary aim of the presented research is to produce a framework for enhancing power quality in hybrid devices attached to renewable sources via an optimised fractional order proportional integral (FOPI) Controller in Unified Power Quality Conditioner (UPQC). The source input is made up of RES. To address the PQ difficulties, the UPQC employs series and shunt filter management techniques. Utilizing suggested Adaptive Bald Eagle optimisation algorithm (ABE-OA), the variables are ideally optimised for greater control. To confirm the effectiveness of the proposed method in PQ enhancement, the effectiveness of the developed system is evaluated to that of previous techniques. The proposed method achieved better rise time of 2042.5 and settling min of 19,999.

Enhanced Low-Speed Characteristics With Constant Switching Torque-Controller-Based DTC Technique of Five-Phase Induction Motor Drive With FOPI Control

The Classical hysteresis controller-based DTC (C-DTC) of an induction motor is a simple control scheme with better dynamics and steady-state characteristics when compared with the flux-oriented control (FOC) scheme. The major drawbacks of the C-DTC scheme are variable switching frequency and high average torque ripple under different rotor speeds. In this paper, the two-level five-leg inverter-controlled five-phase induction motor drive with constant switching torque controller-based DTC (PI-CST-DTC) scheme is introduced to improve the steady-state performance with constant switching frequency under various operating speeds. However, the proposed PI-CST-DTC exhibits slower torque and slower speed dynamics w.r.t C-DTC which is due to the periodic occurrence of zero vectors under transients. These slower dynamics are improved with the help of the proposed fractional order PI (FOPI) constant switching torque controller-based DTC (FOPI-CST-DTC) method. With the help of the hardware results, it has been verified that the proposed FOPI-based CST-DTC exhibits improved low-speed steady-state and dynamic performance of the five-phase induction motor drive. The proposed CST-DTC techniques with PI and FOPI controllers are compared with C-DTC for torque ripple reduction and %THD analysis and dynamics through hardware results.

Multi-objective optimization strategy for parallel tuning of multiple fractional order controllers in a PMSG based WECS

In this paper, a novel multi-objective optimization strategy is proposed for the parallel tuning of six fractional order controllers used in regulation loops of a PMSG based wind energy conversion system connected to the electric grid. The nonlinear nature of the WECS components has made controllers design challenging. To enhance the transient response of system variables, Fractional Order Proportional Integral (FOPI) controllers are considered as they are more suitable for such nonlinear physical systems. The additional parameters introduced by FOPI are normally tuned using a single objective, multi-dimensional particle swarm optimization algorithm. However, the inter-dependence of regulation loops introduces additional complexity that is solved in this work using a multi-objective optimization strategy based on a succession of Single-Objective PSO and Multi-Objective PSO. A simulation study has been conducted in order to demonstrate the higher performance and superior tracking accuracy of the proposed multi-objective optimization strategy in variable wind speed operating conditions.

Power quality improvement using rabbit optimization FOPID controlled photovoltaic- battery powered hybrid power filter

This paper presents the tuning of a fractional proportional controller (FOPI) using artificial rabbit optimization for the control of photovoltaic (PV) and battery power series active power filters along with a shunt passive filter which is known as a hybrid power filter. The PV power generation is combined into a series active filter to alleviate the problem of voltage sag and swell in the power system and also supply real power to the grid. Generally, the proportional controller is used to control the series active filter, but this is a linear controller and is not able to control the non-linear power system effectively. This problem is effectively controlled by non-linear control, i.e., a fractional-order proportional integral controller. Another problem in FOPI is finding the optimal value for proportional gain, integral gain, and fractional order. There are no standard rules for finding these values. This will make system design more complex. In this paper, artificial rabbit optimization is used to simplify the system design by finding optimal values of the FOPI controller for the series active filter and enhance the overall performance of the system. The MATLAB 2020b/Simulink environment is utilized to assess the recommended controller’s performance. According to the experimental findings, the suggested system has a total harmonic distortion (THD) value for load voltage of 0.10 % and a total harmonic distortion value for grid current of 1.87 %. The proposed artificial-rabbit optimized FOIPI controller effectively controls the system against voltage sag, swell, and non-linear loads and also obeys IEEE power quality standards.

Enhancement of a Grid-Connected DFIG Wind Turbine System Using Fractional Order PI Controllers

The wind velocities are unpredictable, and generating power with persistent speed is difficult which comprises mechanical stress at the rotor that leads to poor efficiency. So, variable wind power speed generation has ample significance with the Doubly Fed Induction Generator (DFIG). For a grid-connected DFIG, the governing of power is done conventionally by employing vector-controlled PI regulators. Yet, the performance of PI regulators depends on system parameters, which motivates the adoption of Fractional Order PI (FOPI) regulators. Presently FOPI regulators are seizing a lot of applications with the assistance of additional tuning parameters. However, tuning FOPI regulators by conventional methods is challenging. So, initially, the Particle Swarm Optimization (PSO) method was used for tuning FOPI regulators, but the disadvantages are low convergence rate, falling into local elucidation, entailing more variables to attune, and requiring a large number of iterations. Thus, this motivates introducing the Ant Lion Optimization (ALO) algorithm in this article due to its better performance and eligibility to overcome the limitations of conventional methods. Furthermore, in the validation of the proposed algorithm, the performance parameters like DC coupling capacitor voltage, rotor Speed, active power, and reactive power with PI, FOPI, PSO-FOPI, and ALO-FOPI regulators are compared and analysed using the bode plot are presented. The time response analysis of all the controllers with PI, FOPI, PSO-FOPI, and ALO-FOPI controllers were also observed with a voltage dip. Finally, the fractional order controllers with frequency response and time response analysis show superior performance in distributed generation with advanced heuristic controllers when compared to conventional controllers. The complete work has been simulated via MATLAB/ Simulation platform.

A Potent Fractional-Order Controller for Interconnected Multi-Source Microgrids

Frequency deviations and the capability to cope with demand are two of the main problems in isolated or interconnected microgrids, especially with the increase in the penetration level of renewable energy sources. Those two problems call for new improved controllers and methods able to suppress frequency deviations while keeping a balance between supply and demand. This study focuses on the implementation of a filtered fractional-order PDF controller in series with a one plus fractional-order PI controller (FOPDF-(1+FOPI)) for the frequency regulation of three-area multi-source interconnected microgrids. The proposed controller is optimized via the coot optimization algorithm. The proposed microgrids incorporate various sustainable units, renewable energy sources and a hybrid energy storage system in each area. The microgrids consist solely of sustainable and renewable sources and aim to provide possible microgrid configurations for 100% sustainable microgrids, which could be farms or small communities. The proposed controller is compared with the PIDF, integer-order PDF-(1+PI), and FOTDF-(1+TI) controllers in various scenarios. The first scenario involved evaluating the proposed controller in an isolated microgrid, where it achieved the best ITAE value, outperforming the second best by 29.5%. The second scenario considered three-area interconnected microgrids without RES penetration. The results revealed that the FOPDF-(1+FOPI) controller reduced the settling time in area one by 79.13% and 52.26% compared to that of the PIDF and FOTDF-(1+TI) controllers. Next, RES penetration was introduced into each microgrid in the form of steps or varied changes. Subsequently, performance evaluation was conducted in the presence of a communication time delay and noise in the control channels. Finally, a robustness assessment was conducted for the proposed controller in the interconnected microgrids with respect to parameter uncertainties. The simulations showed a maximum deviation in the settling time and maximum overshoot in area 1 of 66.6% and 38.74%, respectively

Neural Fractional Order PID Controllers Design for 2-Link Rigid Robot Manipulator

The robotic manipulator is considered one of the complex systems that include multi-input, multi-output, non-linearity, and highly coupled. The uncertainty in the parameters and external disturbances have a negative influence on the performance of the system. Therefore, the controllers that will be designed for these systems must be able to deal with these complexities and difficulties. The Proportional, Integral, and Derivative (PID) controller is known to be simple and well robust, while the neural network has a solid ability to map complex functions. In this paper, we propose six control structures by combining the benefits of PID controller with integer and fractional order and the benefits of neural networks to produce hybrid controllers for a 2-Link Rigid Robot Manipulator (2-LRRM) handling with the problem of trajectory tracking. The Gorilla Forces Troops Optimization algorithm (GTO) was used to tune the parameters of the proposed controller schemes to minimize the Integral of Time Square Error (ITSE). In addition, the robustness of the performance of the suggested control systems is tested by altering the initial position, external disturbances and parameters and carried out using MATLAB. The best performance of the proposed controllers was the Neural Network Fractional Order Proportional Integral Derivative Controller (NNFOPID).

Optimization of fractional order PI controller using meta-heuristics algorithms applied to multilevel inverter for grid-connected PV

Optimization of fractional order PI controller using meta-heuristics algorithms applied to multilevel inverter for grid-connected PV

Optimal Fractional-Order Controller for the Voltage Stability of a DC Microgrid Feeding an Electric Vehicle Charging Station

Charging stations are regarded as the cornerstone of electric vehicle (EV) development and utilization. Electric vehicle charging stations (EVCSs) are now energized via standalone microgrids that utilize renewable energy sources and reduce the stress on the utility grid. However, the control and energy management of EVCSs are challenging tasks because they are nonlinear and time-varying. This study suggests a fractional-order proportional integral (FOPI) controller to improve the performance and energy management of a standalone EVCS microgrid. The microgrid is supplied mainly by photovoltaic (PV) energy and utilizes a battery as an energy storage system (ESS). The FOPI’s settings are best created utilizing the grey wolf optimization (GWO) method to attain the highest performance possible. The grey wolf is run for 100 iterations using 20 wolves. In addition, after 80 iterations for the specified goal function, the GWO algorithm almost discovers the ideal values. For changes in solar insolation, the performance of the proposed FOPI controller is compared with that of a traditional PI controller. The Matlab/Simulink platform models and simulates the EVCS’s microgrid. The results demonstrate that the suggested FOPI controller significantly improves the transient responsiveness of the EVCS performance compared to the standard PI controller. Despite all PV insolation disruptions, the EV battery continues to charge while the ESS battery precisely stores and balances PV energy changes. The results support the suggested FOPI control’s robustness to parameter mismatches. The microgrid’s efficiency fluctuations with the insolation level and state of charge of the EV battery are discussed.