Optimal Proportional-integral Controller Research Articles

Design of hybrid optimized PI controller for power conditioning circuit of piezoelectric energy harvester

Abstract Piezoelectric Energy Harvesters (PEH) are vital in the present day to encourage advancing technology through producing sustainable energy and dealing with economic and ecological issues associated with batteries. The required stable energy production from the PEH is challenging due to its erratic behaviour with input. As such, a power conditioning circuit with an optimized controller is proposed in this paper. The Proportional Integral (PI) controller is utilized to control the boost converter of the PEH system. The conventional approach of selecting the controller parameters, such as Proportional gain (KP) and Integral gain (Ki), fails to produce optimal outcomes and is time-consuming. Metaheuristic optimization techniques such as Aquila Optimization (AO), African Vulture’s Optimization Algorithm (AVOA) and Hybrid Aquila Optimizer-based African Vulture’s Optimization Algorithm (HAOAVOA) are used to optimize the controller parameter. The different stages of PEH system (Rectifier, boost converter without controller, boost converter with un optimized controller and boost converter with optimized controller) are simulated and analysed using MATLAB-SIMULINK® software. An experimental study is executed to validate the performance of the PEH system with optimized controller. The experimentally obtained response is compared with simulation results. In which the HAOAVOA optimized PI controller gives the better response. Furthermore, the power conditioning circuit with a hybrid optimized controller produces an output of 12 V for the input of 6 V.

Determination of Attacking Angle of Aircraft in Bio Inspired Optimized Technique

This paper deals with the design of a proportional–integral (PI) controller for controlling the angle of attack of flight control system. For the first time teaching–learning based optimization (TLBO) algorithm is applied in this area to obtain the parameters of the proposed PI controller. The design problem is formulated as an optimization problem and TLBO is employed to optimize the parameters of the PI controller. The superiority of proposed approach is demonstrated by comparing the results with that of the conventional methods like GA and PSO. It is observed that TLBO optimized PI controller gives better dynamic performance in terms of settling time, overshoot and undershoot as compared to GA and PSO based PI controllers. The various performance indices like Mean Square Error (MSE), Integral Absolute Error (IAE), and Integral Time absolute Error (ITAE) etc. are improved by using the TLBO soft computing techniques. Further, robustness of the system is studied by varying all the system parameters from −50% to +50% in step of 25%. Analysis also reveals that TLBO optimized PI controller gains are quite robust and need not be reset for wide variation in system parameters.

Marine Predator Algorithm-Based Optimal PI Controllers for LVRT Capability Enhancement of Grid-Connected PV Systems.

Photovoltaic (PV) systems are becoming essential to our energy landscape as renewable energy sources become more widely integrated into power networks. Preserving grid stability, especially during voltage sags, is one of the significant difficulties confronting the implementation of these technologies. This attribute is referred to as low-voltage ride-through (LVRT). To overcome this issue, adopting a Proportional-Integral (PI) controller, a control system standard, is proving to be an efficient solution. This paper provides a unique algorithm-based approach of the Marine Predator Algorithm (MPA) for optimized tuning of the used PI controller, mainly focusing on inverter control, to improve the LVRT of the grid, leading to improvements in the overshoot, undershoot, settling time, and steady-state response of the system. The fitness function is optimized using the MPA to determine the settings of the PI controller. This process helps to optimally design the controllers optimally, thus improving the inverter control and performance and enhancing the system's LVRT capability. The methodology is tested in case of a 3L-G fault. To test its validity, the proposed approach is compared with rival standard optimization-based PI controllers, namely Grey Wolf Optimization and Particle Swarm Optimization. The comparison shows that the used algorithm provides better results with a higher convergence rate with overshoot ranging from 14% to 40% less in the case of DC-Link Voltage and active power and also settling times in the case of MPA being less than PSO and GWO by 0.76 to 0.95 s.

Enhanced Randomized Harris Hawk Optimization of PI controller for power flow control in the microgrid with the PV-wind-battery system

Microgrids, characterized by their ability to work individually or in combination with the main power system, play a pivotal role in addressing the growing demand for reliable and sustainable energy solutions. This work concentrates on the integration of sustainable energy sources, specifically photovoltaic (PV), and wind generation and a battery storage system within a microgrid framework. Additionally, a power flow control strategy is implemented to enhance the dynamic behaviour and stability of the microgrid. The proportional-integral (PI) controller is a fundamental component in regulating the microgrid’s power flow, ensuring optimal performance under varying operating conditions. However, tuning the PI controller parameters is a difficult task because of the dynamic and nonlinear nature of renewable energy sources. In this work, the application of the Enhanced Randomized Harris Hawk Optimization (ERHHO) to fine-tune the PI controller is proposed, using the algorithm’s ability to mimic the hunting behaviour of hawks in finding optimal solutions. The PV-Wind-Battery microgrid system is modelled, and the proposed algorithm is employed to optimize the PI controller parameters for efficient energy management. The ERHHO algorithm’s exploration-exploitation balance is harnessed to navigate the complex solution space and converge to optimal PI controller settings, thereby enhancing the microgrid’s stability and performance. The study evaluates the effectiveness of the proposed ERHHO-based PI controller tuning through comprehensive simulations. Performance metrics such as transient response, overshoot, settling time, and steady-state error are analysed to validate the robustness and efficiency of the proposed method. Compared to its nearest optimization algorithm, with the proposed algorithm rise time is reduced by 50%, overshoot is reduced by 75%, settling time is reduced by 66%, and finally, a percentage of reduction of steady-state error is 45%. The outcomes of this research contribute to the advancement of microgrid control strategies, offering a novel approach to PI controller tuning in the context of diverse renewable energy sources. The integration of the Harris Hawk Optimization algorithm provides a promising avenue for enhancing the operational efficiency and reliability of microgrids, paving the way for sustainable and resilient energy systems in the aspect of growing energy landscapes.

Volterra LMS/F Based Control Algorithm for UPQC With Multi-Objective Optimized PI Controller Gains

This paper describes Volterra expansions filter with Least Mean Square (LMS) and Least Mean Fourth (LMF) control algorithm on Unified Power Quality Controller (UPQC). The adaptive models based on the LMS provide a simplified structure to approximate the necessary parameters for a particular PQ interruption. However, these algorithms are ineffective in the case of time-varying perturbations. Besides that, LMF is a comparatively better solution for multiple PQ disruptions with high computational complexity than LMS. So the LMS/Fourth (LMS/F) algorithm is a mixture of LMS and LMF to improve the error convergence quality of a given filter. The Volterra expansions filter has the advantageous characteristic of estimating fundamental components at any PQ conditions without any delay and less computational calculation. Furthermore, an optimization approach named Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is used to calculate Proportional integral (PI) controller gains in the Volterra LMS/F control algorithms. The PI controller gains of dc link voltage control loop and ac terminal voltage control loop are optimized in a coordinated manner using the multi-objective NSGA-II. The applied algorithms deliver Pareto’s set of optimal global solutions. This complete algorithm is implemented through MATLAB in four-wire UPQC for mitigation of power quality problems.

Design of optimal PI controller for torque ripple minimization of SVPWM-DTC of BLDC motor

Conventional direct torque control (CDTC) for brushless DC motor (BLDCM) using proportional integral (PI) controller suffers from torque ripple minimization and speed regulation issues. A novel method in fusion with space vector pulse width modulation (SVPWM) with DTC using optimal PI controller is developed to minimize these issues. In this method, SVPWM replaces switching table and hysteresis controllers in CDTC. To get better performance in steady state, conventional PI controllers are preferred in SVPWM-DTC for BLDCM. However, uncertainty arises due to PI controller tuning as well as load variations. In such a case, optimal PI controller tuned properly can minimize these uncertainties. Here, JAYA algorithm is used to tune controller gain parameters. Simulations of proposed PI controller of SVPWM-DTC for BLDCM are carried away in Simulink. To appreciate the performance of proposed optimal controller of SVPWM-DTC for BLDCM, the simulation results are compared with Conventional PI controller and particle swarm optimization (PSO) technique based tuned PI controller. This proposed technique reduces the toque ripple by 63.1% when compared to conventional PI and 58.5% when compared to PSO-PI controller. It also improves the settling time by 43.9% when compared to conventional PI and 46.79% when compared to PSO-PI controller.

An highly efficient optimized PI controller fed SEPIC converter for hybrid renewable sources based microgrid system

This paper proposes an electric power generation that is self-sufficient with the adopting of Hybrid Renewable Energy Sources (HRES) including solar and wind which in turn contributes a cleaner and sustainable environment. The proposed system provides uninterrupted power supply during any weather conditions and the excess energy is stored in battery which energizes the grid at times of deficit power supply from HRES. The incorporation of converter and control approach ensures the balanced flow of power in the grid connected system. A Single-Ended Primary Inductance-Converter (SEPIC) is employed in this work for the enhancing of voltage from the PhotoVoltaic (PV) system. An improved Grey Wolf Optimized (GWO) Proportional Integral (PI) controller facilitates the effective control of SEPIC thereby improving the transient response. A Doubly Fed Induction Generator (DFIG) based wind system is integrated as an alternate source with PI based control. The control of the battery is carried out by the Artificial Neural Network (ANN) and grid synchronization is accomplished with the aid of PI based dq theory. The simulation of the proposed work is carried out by Matlab and the proposed work generates improved outputs with efficiency 95.8% and a reduced THD of 1.3%.

Improving the performance of grid connected wind generator with a PI control scheme based on the metaheuristic golden eagle optimization algorithm

• A novel Golden Eagle optimization algorithm (GEOA) is proposed. • GEOA is used to improve the Transient and Dynamics stability of wind farm. • Transient and Dynamics stability of grid-tied PMSG-VSWT is investigated during symmetrical, unsymmetrical faults and Stochastics wind variation at that site. • The results of GEOA are compared with the results of NR, PSO and GOA. • The results shown that the GEOA is robust and competitive. Wind power installations are globally established thoroughly, resulting in significant electrical power penetration into power grids. Consequently, tremendous efforts are expended to improvise the performance of the grid-connected Permanent Magnet Synchronous Generator driven by a Variable-Speed Wind Turbine (PMSG-VSWT). In this work, eight cascaded Proportional Integral (PI) controllers in the machine side and grid side converters are optimally tuned by the golden eagle optimization algorithm with the purpose of enhancing the dynamics and transient stability performances of the grid connected PMSG-VSWT.The integration of the square error criterion was utilised as a fitness function in the optimization process, which was processed using the simulation-based optimization technique. The proposed control technique's efficacy was compared to various optimal PI controllers under symmetrical and unsymmetrical fault conditions. This study also employed the measured real-time events collected at the Coimbatore wind farm in Tamil Nadu (India) to produce realistic results and aid in the pursuit of higher performance. The wind farm modelling and simulation were processed using the DIgSILENT power factory/MATLAB Simulink environment and was utilized to test the proposed control approach's achievability. Finally, the study demonstrates that the golden eagle optimization technique improves the wind farm's performance when compared to observed events and other techniques.

Improved Interleaved Single-Ended Primary Inductor-Converter for Single-Phase Grid-Connected System

The generation of electricity based on renewable energy sources, particularly Photovoltaic (PV) system has been greatly increased and it is simply instigated for both domestic and commercial uses. The power generated from the PV system is erratic and hence there is a need for an efficient converter to perform the extraction of maximum power. An improved interleaved Single-ended Primary Inductor-Converter (SEPIC) converter is employed in proposed work to extricate most of power from renewable source. This proposed converter minimizes ripples, reduces electromagnetic interference due to filter elements and the continuous input current improves the power output of PV panel. A Crow Search Algorithm (CSA) based Proportional Integral (PI) controller is utilized for controlling the converter switches effectively by optimizing the parameters of PI controller. The optimized PI controller reduces ripples present in Direct Current (DC) voltage, maintains constant voltage at proposed converter output and reduces overshoots with minimum settling and rise time. This voltage is given to single phase grid via Voltage Source Inverter (VSI). The command pulses of VSI are produced by simple PI controller. The response of the proposed converter is thus improved with less input current. After implementing CSA based PI the efficiency of proposed converter obtained is and the Total Harmonic Distortion (THD) is found to be . The dynamics and closed loop operation is designed and modeled using MATLAB Simulink tool and its behavior is performed.

A theoretical demonstration for reinforcement learning of PI control dynamics for optimal speed control of DC motors by using Twin Delay Deep Deterministic Policy Gradient Algorithm

To benefit from the advantages of Reinforcement Learning (RL) in industrial control applications, RL methods can be used for optimal tuning of the classical controllers based on the simulation scenarios of operating conditions. In this study, the Twin Delay Deep Deterministic (TD3) policy gradient method, which is an effective actor-critic RL strategy, is implemented to learn optimal Proportional Integral (PI) controller dynamics from a Direct Current (DC) motor speed control simulation environment. For this purpose, the PI controller dynamics are introduced to the actor-network by using the PI-based observer states from the control simulation environment. A suitable Simulink simulation environment is adapted to perform the training process of the TD3 algorithm. The actor-network learns the optimal PI controller dynamics by using the reward mechanism that implements the minimization of the optimal control objective function. A setpoint filter is used to describe the desired setpoint response, and step disturbance signals with random amplitude are incorporated in the simulation environment to improve disturbance rejection control skills with the help of experience based learning in the designed control simulation environment. When the training task is completed, the optimal PI controller coefficients are obtained from the weight coefficients of the actor-network. The performance of the optimal PI dynamics, which were learned by using the TD3 algorithm and Deep Deterministic Policy Gradient algorithm, are compared. Moreover, control performance improvement of this RL based PI controller tuning method (RL-PI) is demonstrated relative to performances of both integer and fractional order PI controllers that were tuned by using several popular metaheuristic optimization algorithms such as Genetic Algorithm, Particle Swarm Optimization, Grey Wolf Optimization and Differential Evolution.

Studying the Applicability of Swarm Intelligence in Designing Optimized PI Controller for DC-DC Zeta Converter: A MATLAB-Based Approach

Studying the stability of power converters and improving the performance is a major concern for researchers in the domain of power electronics. In this context, the DC-DC Zeta converter is studied in this paper and the closed-loop operation is comprehensively investigated by employing swarm intelligence (SI) algorithms with a view to design an optimized proportional-integral (PI) controller. These algorithms have been increasingly used to develop and optimize power converters in recent years. The state-space averaging technique was used to design the converter’s closed-loop transfer function. Hence, the traditional and SI algorithm-based PI controllers are inspected, and comparative analysis is presented. Four objective functions termed as integral absolute error, integral time absolute error, integral square error, integral time squared error, gain values, and different performance parameters such as percentage of overshoot, rise time, settling time, and peak amplitude are tabulated to examine the stability of the system. Furthermore, eigenvalues have been analyzed for determining the stability of the system extensively. Finally, a detailed comparative study is shown to provide a detailed evaluation of the performances where ant colony optimization for continuous domains (ACOR)-based PI controller has shown promising results than other SI-based controllers in terms of percentage of overshoot (2.27%), rise time (1.54 μs), and settling time (0.103 μs). All the simulation results and analysis are obtained using the MATLAB-Simulink.

Stability Analysis of the Dual Half-Bridge Series Resonant Inverter-Fed Induction Cooking Load Based on Floquet Theory

Induction heating (IH) applications aided power electronic control and becomes most attractive in recent years. Power control plays a vital role in any IH applications in which the stability of the converter is still a research hot spot due to variable frequency operation. In the proposed work, the stability of the converter is carried out based on the Floquet theory for dual-frequency half-bridge series inverter-fed multiload IH system. The dynamic behaviour of the converter is analyzed by developing a small-signal model of the converter. The system with a dynamic closed-loop controller results in poles and zeros lying outside the unit circle, which has poor closed-loop stability and up-down glitches in the frequency response plot. Hence, a proportional-integral (PI) compensator is used to mitigate the said issue, which results in a better response when compared with the open system and works satisfactorily. However, the system becomes unstable when the frequency is varied and the system also possesses a poor time domain response. Hence, the values of the controller gain are optimized with the Floquet theory, which is based on the Eigenvalues of the time domain model. For the optimized gains, the system possesses better stability for the variations in the switching frequency (20 kHz to 24 kHz), and also, the frequency response of the system is better with minimum time domain specifications. The performance of the system is simulated in MATLAB, and the response is noted for various switching frequencies in open loop, with a PI compensator, and with an optimized PI compensator. The output power is varied from 500 W to 18 W at load 1 and 250 W to 9 W at load 2. It is noted from the output response that the rise time is 0.0085 s, the peak time is 0.0001 s, and the peak overshoot is 0.1% with minimum steady-state error. Furthermore, the IH system is validated using a PIC16F877A microcontroller with the optimized PI controller, and the thermal image is recorded using a FLIR thermal imager.

Chaotic-Billiards Optimization Algorithm-Based Optimal FLC Approach for Stability Enhancement of Grid-Tied Wind Power Plants

Globally,wind power plants (WPPs) installations are dramatically increasing, leading to a large-scale integration into the power grids. Huge endeavors are devoted to achieving an efficient operation of WPPs. This paper offers a novel chaotic-billiards optimizer (C-BO) algorithm to properly design the fuzzy logic control (FLC) strategy for stability enhancement of grid-integrated WPPs. The C-BO algorithm has distinct features such as simple construction, low numbers of parameters required to design, high convergence speed, and low computational burden. The permanent-magnet synchronous generator (PMSG)-based WPP is interlinked into the electric power grid through power converters. A cascaded FLC approach, which is optimally fine-tuned by the C-BO, is offered as the control methodology for these converters. The C-BO algorithm fine-tunes the gain factors of multiple FLCs at a rapid convergence speed. A simulation-based optimization approach is applied, in which the integrated square error criterion is chosen as an objective function. For the sake of preciseness, the PMSG-based WPP is connected to the IEEE 39-bus New England test system. The effectiveness of the optimal FLC using the C-BO algorithm is compared with that achieved using the water cycle algorithm-based optimal FLC, the genetic algorithm-based optimal FLC, and the marine predator algorithm-based optimal proportional-integral controller, taking into account severe grid disturbances. Moreover, real wind speed measured data captured from Zaafarana Station in Egypt are extensively performed in the system studies. The validity of the offered control approach is widely verified by the simulation analyses using the MATLAB/Simulink environment.

EPLL Control Technique Optimum Controller Gains to Control Voltage and Frequency in Standalone Wind Energy Conversion System

This study describes how to regulate the frequency and terminal voltage of a freestanding wind energy conversion system using an Enhanced Phase Locked Loop (EPLL)-based strategy to supply power to varied loads regardless of wind speed. In a standalone wind turbine energy conversion system, the EPLL control scheme extracts the reference source currents (SWECS). The control algorithm employs two proportional-integral (PI) controllers to create the active and reactive power components of the consumers' load currents, estimate reference source currents, and connect the zigzag transformer to PCC with VSC for neutral current compensation. To obtain optimal PI controller gains and most-suited settings to apply to SWECS, optimization approaches are used. The control algorithm is the most significant aspect of the system, and the speed with which it calculates, evaluates, and guesstimates determines the generation of source currents based on the algorithm's ideal controller PI gains. By properly estimating source currents, the EPLL control method improves dynamics and power quality issues, and the optimization technique is employed to acquire the gains of PI controllers. The proposed system employs the EPLL algorithm on a three-phase, four-wire system with changing loads to achieve ideal total harmonic distortion of source currents and voltages on the PCC, as defined by IEEE-519 standards. A battery energy storage device coupled to the VSC dc link keeps the load's necessary power constant. If the generator output exceeds the consumer demand, the excess power is delivered to BESS for temporary storage. When consumer demand exceeds generated power, a BESS delivers deficit power to the load, which adjusts and the frequency under various load conditions. The suggested system simulated results were tested with 3-phase 4-wire for harmonics reduction, load balancing, neutral wire current compensation, frequency and voltage control using MATLAB / Simulink.

A Novel Controller for Microgrid Interactive Hybrid Renewable Power Sources

In this paper, a self-sufficient electric power generation is proposed by using hybrid renewable sources like solar and wind turbines to favor a smart and green environment. This distributed generation unit is connected to the grid through an 3Φ inverter. The power drawn from the hybrid unit is stored in the batteries to transfer power during the non-availability of power sources. This standalone power conversion and storage system are developed by using power electronic converters and controllers to ensure balanced power flow operation. A PI (Proportional Integral) controller is utilized for generating the PWM (Pulse Width Modulation) pulses for the wind side converter. The GWO (Grey Wolf Optimization) optimized PI controller is used to control the PV (Photovoltaics) side SEPIC (Single-Ended Primary-Inductor Converter) for improvising the transient response of the system. The generated power is interfaced with grid through a three phase inverter, which is controlled by dq (Direct-axis and Quadrature-axis) theory. The power quality problems are effectively eliminated with the proposed converters. Thus, a continuous stable power is fed into the grid through the proposed approach. An automatic control is enabled for easy operation. The system is modeled in MATLAB and a prototype is developed to verify the simulation results.

Optimal PI controller based PSO optimization for PV inverter using SPWM techniques

This paper deals with the inverter controller utilizing Sinusoidal Pulse Width Modulation (SPWM) to control the three-phase off-grid system’s modulation index. Particle Swarm Optimization (PSO) algorithm has been used to improve the controller performance by automatically finding its parameters in order to reduce the error in the proportional Integral (PI) controller. The system is included with photovoltaic and battery storage to supply power to a local load of 3 kW. Control was on voltage by measuring load voltage to be feedback to the controller to evaluate the best modulation index value needed for SPWM pulse. Therefore, the inverter is based on load change to adjust the system to be stable at any time because of the proportional and integral controller (PI). The PI Controller provides better results than a system without a controller, especially when applying faults in phase. This shows how the robustness of the controller is. This model is explained in detail. All simulation results show that the modulation index controller acts so that total harmonic distortion (THD) is less after using the optimal PI controller parameters.

PI control based on parameter space approach supported metaheuristic optimization algorithms and ANFIS in a natural gas combined cycle power plant

AbstractIn this article, proportional‐integral (PI) control to ensure stable operation of a steam turbine in a natural gas combined cycle power plant is investigated, since active power control is very important due to the constantly changing power flow differences between supply and demand in power systems. For this purpose, an approach combining stability and optimization in PI control of a steam turbine in a natural gas combined cycle power plant is proposed. First, the regions of the PI controller, which will stabilize this power plant system in closed loop, are obtained by parameter space approach method. In the next step of this article, it is aimed to find the best parameter values of the PI controller, which stabilizes the system in the parameter space, with artificial intelligence‐based control and metaheuristic optimization. Through parameter space approach, the proposed optimization algorithms limit the search space to a stable region. The controller parameters are examined with Particle Swarm Optimization based PI, artificial bee colony based PI, genetic algorithm based PI, gray wolf optimization based PI, equilibrium optimization based PI, atom search optimization based PI, coronavirus herd immunity optimization based PI, and adaptive neuro‐fuzzy inference system based PI (ANFIS‐PI) algorithms. The optimized PI controller parameters are applied to the system model, and the transient responses performances of the system output signals are compared. Comparison results of all these methods based on parameter space approach that guarantee stability for this power plant system are presented. According to the results, ANFIS‐ PI controller is better than other methods.

Design of a Pitch Controller for a Wind Turbine Using Hybrid Mean-Variance Mapping Optimization

A variable-speed wind energy conversion system (WECS) has the advantage of extracting more power from the time-varying wind. To achieve this, the pitch angle is controlled to maintain the speed of the turbine and hence the generated power at a constant level, while reducing mechanical stress on the turbines. In this work, a proportional-integral (PI) controller is used for pitch angle control. The optimal PI control gains and are tuned by the hybrid mean-variance mapping optimization (MVMO-SH) technique, particle swarm optimization (PSO), and a genetic algorithm (GA). Different fitness evaluation criteria and optimization techniques are compared, and the performances of optimal controllers presented in the time domain. The results reveal that MVMO-SH achieves the minimum error criteria within a shorter time. The optimal controller design gives an error of less than in the region for which it is tuned. The performance of the optimal PI controller is designed for one operating condition in different cases of wind gust, random variation of wind, and disturbance from the grid side to mitigate line to ground fault. The performance of the controller is shown to be satisfactory in all the cases studied.

Optimization and H∞ Performance Analysis for Load Frequency Control of Power Systems With Time-Varying Delays

With the development and expansion of the power grid, the load frequency control (LFC) scheme receives sensor signals and outputs control signals through an open communication network with a mass of data and extensive information exchange, which may introduce constant, and time-varying delays. This paper considers the optimization andH∞performance problem for LFC of power systems with time-varying delays. Some improved criteria for guaranteeing the stability andH∞performance of the closed-loop system with unknown external load disturbances via the Lyapunov stability theory application. An unique delay-dependent proportional-integral (PI) controller and an optimized PI controller are designed for a specifiedH∞performance index and set, respectively. The criteria proposed in this paper are based on linear matrix inequalities (LMIs), which can be easily solved by the MATLAB LMI-Toolbox. Finally, in case studies, the effectiveness of our method is demonstrated.

Development of Optimal PI controllers of an Inverter–Based Decentralized energy generation System Based on Equilibrium Optimization Algorithm

The microgrid model gained considerable interest in the electricity industry due to increased financial and environmental benefits. The microgrid views decentralized generation (DG) and associated loads as a subsystem. The controlling methodology is the voltage source converter (VSC) cascaded-type converters technique, which depends on the Proportional-Integral (PI) controller. In this paper, the optimal tuning of the PI controller parameters is formulated as a constrained optimization problem for the system under different conditions (i) The system is converted from on-grid to off-grid mode at Time = 2 s. (ii) The system is subjected to three lines to earth fault in an off-grid mode. (iii) The system is subjected to load variation in an off-grid mode. The equilibrium optimization algorithm (EO) is physics-based optimization to tune the gains of the PI controller. The proposed approach (EO) has been compared with results from other approaches such as Genetic Algorithm (GA) which is inspired by a natural evolution process, Salp Swarm Algorithm (SSA) which is inspired by the swarming behavior of salp in oceans. Simulations are conducted using MATLAB/Simulink software. The EO performs perfectly and has a fine ability to tune controller gains with smaller errors than other approaches.