Fractional Order PI Controller Research Articles

A Combined Fractional Order Proportional Integral Derivative Controller for Automatic Generation Control Integrated with Wind and Small Hydropower Plant Using Crow Search Algorithm

A Combined Fractional Order Proportional Integral Derivative Controller for Automatic Generation Control Integrated with Wind and Small Hydropower Plant Using Crow Search Algorithm

Coordination of time delay and GCSC for frequency stabilization of dual‐area interlinked microgrid using non‐integer controller optimization

AbstractThis study presents a novel frequency regulation solution for renewables (wind‐solar tower)‐bio (biodiesel‐biogas) cogenerated independent dual‐area interlinked microgrid power system (IµPS) with collective effect of time delay and flexible gate‐controlled series capacitor (GCSC). As a component, a non‐integer proportional fractional integral fractional derivative (PFIFD) controller is introduced whose dynamic responses is compared with integer order PID (IOPID) and fractional order PI (FOPI) controllers. The findings demonstrate that the suggested non‐integer PFIFD controller performs better than IOPID and FOPI at giving superior dynamic properties, such as different decision parameters and minimum error function (J). Subsequently, to obtain the optimally tuned controllers’ parameters, a recently developed yellow saddle goatfish technique (YSGA) is leveraged. In this study, the comparative effect of time delay, interline power flow controller (IPFC) and GCSC scheme have been analyzed under real time wind data in IµPS. Further, a meticulous sensitivity assessment of YSGA tuned PFIFD controller is performed under different uncertainties. The improved results show that the recommended YSGA‐based PFIFD controller offers a wonderful improvement in system frequency stability under a variety of situations, including system uncertainties, physical constraints, and significant renewables penetration. Finally, real‐time hardware‐in‐the‐loop (HIL) simulation platform is utilized to validate the proposed control approach.

Non-Integer Order Proportional Integral Control for Time Delay Plant with Single Fractional Order

This paper studies the tuning of non-integer order proportional integral controller for time delay plants having one fractional order in its denominator polynomial. The well-known first order plus time delay plant is reorganized to have the order of the operator s to be an arbitrary real number. The main aim is to tune the parameters of the fractional order proportional integral controller to make the mentioned plant behavior to be stable and robust against unexpected changes in the gain of the system. The approach here is a graphical point of view on the Bode diagram. The two crossover points in the Bode diagram, the gain crossover frequency and the phase crossover frequency are tuned towards the desire of the researcher. This brought us to extend or to restrict the distance between these two crossover frequencies and thus, to provide the stability and robustness of the system. The design process is an analytical way from beginning to the end. Hence, the method is more reliable when compared with the methods based on optimization. This paper presents the findings of the first step in the research. The formulas to design the controller are found and the results are shown on an illustrative example.

Dynamic performance improvement of proton exchange membrane fuel cell system by robust loop shaping and artificial intelligence optimized fractional order PI controllers

ABSTRACT Due to inherent nonlinear behavior, the Proton Exchange Membrane (PEM) Fuel Cell system yields in poor power quality. The sudden change in stack current causes uncertainty in PEMFC behavior resulting in degraded output. This necessitates the control of supply manifold pressure on the cathode side to prevent oxygen starvation. In this work, three techniques, namely, robust loop shaping, smith predictor, and Fractional Order Proportional Integral (FOPI) controllers, are designed after incorporating parametric uncertainty in system description. Further, the Particle Swarm Optimization (PSO) artificial intelligence technique is implemented to optimize the parameters of smith predictor and Fractional Order PI controllers. By stabilizing the system across the entire parameterized uncertainty range, the proposed control strategies, namely, loop shaping, PSO-Smith Predictor, and PSO-FOPI controller effectively compensate uncertainty effects. The simulation result shows that the PSO-tuned FOPI controller has best overshoot at operating points 3, 4, and 5 having a value of 0.505% in comparison with PSO-Smith Predictor where overshoot (ranging from 19.88% to 40.141%) is too high; and loop shaping controller having high values of overshoot (more than 40% at every operating point) Thus, PSO-FOPI controller exhibits the best performance with far superior overshoot and steady-state stability.

Metaheuristic-Based Algorithms for Optimizing Fractional-Order Controllers—A Recent, Systematic, and Comprehensive Review

Metaheuristic optimization algorithms (MHA) play a significant role in obtaining the best (optimal) values of the system’s parameters to improve its performance. This role is significantly apparent when dealing with systems where the classical analytical methods fail. Fractional-order (FO) systems have not yet shown an easy procedure to deal with the determination of their optimal parameters through traditional methods. In this paper, a recent, systematic. And comprehensive review is presented to highlight the role of MHA in obtaining the best set of gains and orders for FO controllers. The systematic review starts by exploring the most relevant publications related to the MHA and the FO controllers. The study is focused on the most popular controllers such as the FO-PI, FO-PID, FO Type-1 fuzzy-PID, and FO Type-2 fuzzy-PID. The time domain is restricted in the articles published through the last decade (2014:2023) in the most reputed databases such as Scopus, Web of Science, Science Direct, and Google Scholar. The identified number of papers, from the entire databases, has reached 850 articles. A Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology was applied to the initial set of articles to be screened and filtered to end up with a final list that contains 82 articles. Then, a thorough and comprehensive study was applied to the final list. The results showed that Particle Swarm Optimization (PSO) is the most attractive optimizer to the researchers to be used in the optimal parameters identification of the FO controllers as it attains about 25% of the published papers. In addition, the papers that used PSO as an optimizer have gained a high citation number despite the fact that the Chaotic Atom Search Optimization (ChASO) is the highest one, but it is used only once. Furthermore, the Integral of the Time-Weighted Absolute Error (ITAE) is the best nominated cost function. Based on our comprehensive literature review, this appears to be the first review paper that systematically and comprehensively addresses the optimization of the parameters of the fractional-order PI, PID, Type-1, and Type-2 fuzzy controllers with the use of MHAs. Therefore, the work in this paper can be used as a guide for researchers who are interested in working in this field.

Research on the side converter system of wind power grid based on fractional LCL filter

AbstractThe power electronic converters and grid‐connected filters were important components of the permanent magnet direct drive wind power generation system whose performance directly determines the quality of wind power generation. In past modeling, analysis, and control studies, capacitive and inductive components were often treated as integral‐order components. However, the inductance and capacitance components in the actual permanent magnet direct drive wind generator were fractional‐order components, and their electrical characteristics will change with the change of order, which had an important impact on the dynamic and static characteristics of the system. In this paper, the mathematical model of the fractional‐order LCL (FOLCL) filter was derived. Through simulation, it could be seen that the FOLCL filter can avoid resonance fundamentally. At the same time, the fractional‐order PI (FOPI) controller was introduced into the machine‐side current converter, and the parameters of the FOPI controller of the outer speed loop and the inner current loop were adjusted by using the time‐domain optimization method. The results showed that the efficiency of the FOPI controller was significantly better than that of the integer‐order PI controller in realizing maximum wind energy capture. It provides theoretical support and practical application value for the stable operation of the wind power generation system.

Optimization of fractional order PI controller to regulate grid voltage connected photovoltaic system based on slap swarm algorithm

Problems with voltage and stability have arisen as a result of the dramatic development in renewable energy generating units, notably solar energy systems linked to low and medium voltage networks, and the influence of active loads that vary rapidly from time to time during the day. Because reactive power is directly proportional to voltage, its use to renewable energy producing units can only improve their efficiency. Better performance for these controllers is possible via the usage of several controller types. In this paper, we use a salp swarm optimization algorithm (SSA) to design fractional order proportional-integral (FO-PI) controllers, whose job it is to regulate the active and reactive power of solar inverters by compensating for the overvoltage and undervoltage presented by the inverters' ability to absorb and produce reactive power. After that, we compared the FO-PI controller's results to those of the standard PI controller. Grid-connected photovoltaic (PV) system modeling and simulation were performed using the MATLAB/ Simulink modeling and simulation tools. After that, the full PV system was simulated in the most likely situations across a range of grid and weather conditions. We may infer from the simulation results that this model is credible, reliable, and applicable to the analysis of grid-connected PV systems.

Novel Fractional-Order Proportional-Integral Controller for Hybrid Power System with Solar Grid and Reheated Thermal Generator

This paper presents a new fractional-order proportional-integral, (PI)λ (FO[PI]) type structure to investigate the load frequency control (LFC) problem. In the literature, some controllers’ extensive tuning options may slow or complicate the optimization process. Due to the intricacy of the tuning, even if there are fewer tuning parameters, a robust structure can be obtained. The (PI)λ structure deviates from the standard FOPI, integer PID, or PI-PD controllers with the same or fewer tuning parameters. The efficacy of a tri-parametric fractional-order controller is examined on a two-area interconnected hybrid power system comprising a photovoltaic (PV) grid and a Reheated Thermal Generator (RTG). In order to obtain optimal performance with lower control efforts, a novel dual-performance index is developed for the LFC problem. Various analyses are also proven to perform better than other optimized controllers from the recent literature. The presented scheme is significantly robust to disturbance interruptions, non-linearities, and parameter perturbations. It is also observed that there are no stability issues due to communication time delays. It is highlighted that the improvement can be obtained without adding complex structure or controller parameters.

Fractional-Order Model-Free Predictive Control for Voltage Source Inverters

Currently, a two-level voltage source inverter (2L-VSI) is regarded as the cornerstone of modern industrial applications. However, the control of VSIs is a challenging task due to their nonlinear and time-varying nature. This paper proposes employing the fractional-order controller (FOC) to improve the performance of model-free predictive control (MFPC) of the 2L-VSI voltage control in uninterruptible power supply (UPS) applications. In the conventional MFPC based on the ultra-local model (ULM), the unknown variable that includes all the system disturbances is estimated using algebraic identification, which is insufficient to improve the prediction accuracy in the predictive control. The proposed FO-MFPC uses fractional-order proportional-integral control (FOPI) to estimate the unknown function associated with the MFPC. To get the best performance from the FOPI, its parameters are optimally designed using the grey wolf optimization (GWO) approach. The number of iterations of the GWO is 100, while the grey wolf’s number is 20. The proposed GWO algorithm achieves a small fitness function value of approximately 0.156. In addition, the GWO algorithm nearly finds the optimal parameters after 80 iterations for the defined objective function. The performance of the proposed FO-MFPC controller is compared to that of conventional MFPC for the three loading cases and conditions. Using MATLAB simulations, the simulation results indicated the superiority of the proposed FO-MFPC controller over the conventional MFPC in steady state and transient responses. Moreover, the total harmonic distortion (THD) of the output voltage at different sampling times proves the excellent quality of the output voltage with the proposed FO-MFPC controller over the conventional MFPC controller. The results confirm the robustness of the two control systems against parameter mismatches. Additionally, using the TMS320F28379D kit, the experimental verification of the proposed FO-MFPC control strategy is implemented for 2L-VSI on the basis of the Hardware-in-the-Loop (HIL) simulator, demonstrating the applicability and effective performance of our proposed control strategy under realistic circumstances.

A universal stability quantification method for grid-connected hydropower plant considering FOPI controller and complex nonlinear characteristics based on improved GWO

The stable operation of the hydropower plant is an important guarantee for power delivery quality and the security of power grids. Nevertheless, the current stability analysis is only focused on simplified models, leading to an inaccuracy result. Therefore, a novel nonlinear model of the grid-connected hydropower plant system with fractional order PI controller considering nonlinear characteristics is taken as the research object. Then, a new universal stability quantification method for complex nonlinear systems is proposed to overcome the application limitations of traditional methods. Finally, the stability and parameter sensitivity of the system are investigated. The results demonstrate that the proposed method is highly accurate and robust, whose errors fall within the range of [-0.0025,0.0005]. The results show that the governor nonlinearity and integral order of fractional order PI controller have an obvious negative influence on the stability of the hydropower plant.

An analytical solution of fractional order PI controller design for stable/unstable/integrating processes with time delay

This paper aims to put forward an analytical solution for tuning parameters of a fractional order PI (FOPI) controller for stable, unstable, and integrating processes with time delay. Following this purpose, the analytical weighted geometrical center (AWGC) method has been extended to the design of fractional order PI controllers. To apply AWGC, the stability equations of the closed-loop system are written in terms of process and fractional order PI controller parameters. With the proposed method, the centroid can be calculated analytically, and the controller parameters can be easily calculated without the need of repetitive drawings of the stability boundary regions. Additionally, analytical equations are derived to calculate fractional integral order, ?, using the integral of squared error (ISE) objective function. The proposed analytical equations are simple and time-saving which might attract controller engineers for applying them on the industrial level. To show the efficiency of the suggested method compared to the given methods in the literature, several simulation examples are considered. Comparisons between the reported methods are figured out in terms of unit step responses for nominal and perturbed cases. Also, rise time, settling time, maximum sensitivity (Ms), integral of squared error (ISE), and total variation (TV) values are considered to compare the performance and robustness issues. Also, a real-time application of an inverted pendulum setup is deemed to prove the feasibility of the suggested method.

Study of Fractional Order PI DC-DC Converter Based on Dual Closed-loop Control

In this paper, the dual closed-loop control strategy with fractional-order PI is applied to the field of the DC-DC converter, which effectively improves the dynamic performance and static performance of the output voltage of the power electronic DC chopper converter. The open-loop transfer function of the Boost converter is obtained by modeling and analyzing the operating principle and small-signal model of the Boost converter, and the fractional-order PI parameters of the double closed-loop control are obtained by combining the frequency-domain analysis design method of control theory. The Simulink simulation model is built, and the fractional-order PI control model is compared and analyzed with the single-voltage loop control and the integer-order PI control model. The results show that the fractional-order PI-controlled Boost converter has a faster response and stronger anti-interference capability, which effectively improves the dynamic performance and static performance index of the DC-DC converter and provides a theoretical basis for the research of dual closed-loop control strategy of the DC-DC converter.

Decentralized frequency control of restructured energy system using hybrid intelligent algorithm and non‐linear fractional order proportional integral derivative controller

AbstractThe emergence of micro‐sources in the energy market to reduce carbon emissions and exploit more renewable generations increases the frequency oscillations of the system. Hence, this paper attempts to develop a robust nonlinear fractional order proportional integral derivative (NLFOPID) controller for frequency regulation of restructured energy systems. A hybrid atom search‐particle swarm optimization (AS‐PSO) is proposed to optimize the gain values of the NLFOPID controller. The proposed control approach enhances flexibility by providing robustness against the RE intermittency. The optimization technique is coded in MATLAB and applied for frequency regulation of a multi‐area energy system developed in Simulink. Initially, the effectiveness of the hybrid algorithm is validated for standard benchmark functions and then implemented for frequency control. The results demonstrate that the proffered AS‐PSO technique performs significantly for various types of transactions in a deregulated energy market than state‐of‐the‐art. The real‐time applicability of the proposed controller is validated using hardware‐in‐the‐loop simulation of the open energy market in OPAL‐RT. The frequency response obtained from the AS‐PSO optimized NLFOPID controller is remarkable compared to other techniques. Furthermore, the closed‐loop stability of the system is examined using bode analysis through an improved Oustaloup approximation technique.

Optimal Fractional Order Proportional Integral Controller for Dual Star Induction Motor Based on Particle Swarm Optimization Algorithm

Optimal Fractional Order Proportional Integral Controller for Dual Star Induction Motor Based on Particle Swarm Optimization Algorithm

Active hybrid energy storage management in a wind-dominated standalone system with robust fractional-order controller optimized by Gases Brownian Motion Optimization Algorithm

Accessibility to sustainable and reliable electrical energy for remote area power supply (RAPS) systems under high penetration levels of wind energy requires adopting appropriate technologies and controllers. In recent years, energy storage has gained significant attention for smoothing inherent voltage and power fluctuations of standalone systems. This paper presents a filtration-based fractional-order PI (FOPI) controller optimized by Gases Brownian Motion Optimization (GBMO) algorithm to manage an active battery-supercapacitor hybrid energy storage system (HESS) in a wind-dominated RAPS system. The GBMO algorithm has a high accuracy and convergence rate among optimization algorithms introduced in recent years. Moreover, a fuzzy logic controller (FLC) guarantees the wind turbine generator's maximum power point tracking (MPPT) at any wind condition while mitigating its fluctuating torque. The proposed RAPS system uses the advantages of the FOPI controller, the GBMO optimization algorithm, the FLC-based MPPT algorithm, and a high-pass filter to manage precise coordination between different components of the RAPS system. The high-pass filter decouples high and low-frequency voltage oscillations to modify the HESS performance and relieve battery stress, thereby extending its lifespan. The proposed controller's performance and robustness are verified in comparison with an optimal PI controller based on GBMO under turbulent wind speed and load step changes in a detailed model of the system. The results demonstrate the superiority of the optimal FOPI controller over the optimal PI controller.

Automatic Generation Control of Simplified Egyptian Power System Using Fractional Order PI Controller Based on PSO

In this Paper, Fraction Order (FO) PI controller is tested in order to find the optimized gains for Automatic Generation Control (AGC) controller by Particle Swarm Optimization (PSO) algorithm to represent the Simplified Egyptian Power System (SEPS) to achieve the development of power grid for the sustainable growth of Egypt. The mission of AGC is to return primary frequency regulation capability, bring back the frequency to its predefined set point in addition to reduce power fluctuation due to unplanned tie-line power flows among nearby control zones. The suggested controller is built using actual statistical records of SEPS for minimum and maximum loading situations of the SEPS in Winter and Summer of 2019-2020. The strength of the proposed controller is illustrated by implement the suggested controller and verify the outcomes of trip of the biggest generation unit in this Simplified Egyptian Power System (SEPS) on the grid frequency. The gains of fractional order FO-PI controller parameters such as proportional, integral, order of integrator (λ) are elevated by different Particle Swarm Optimization (PSO) and compared with another conventional supplementary Proportional Integral (PI) based on PSO also. The results display that the suggested FO-PI controller-built on PSO provides finest dynamic performance for a step load variation. The used software for gaining the results is MATLAB-Simulink.

Application of Whale Optimization Algorithm Based FOPI Controllers for STATCOM and UPQC to Mitigate Harmonics and Voltage Instability in Modern Distribution Power Grids

In recent modern power systems, the number of renewable energy systems (RESs) and nonlinear loads have become more prevalent. When these systems are connected to the electricity grid, they may face new difficulties and issues such as harmonics and non-standard voltage. The proposed study suggests the application of a whale optimization algorithm (WOA) based on a fractional-order proportional-integral controller (FOPIC) for unified power quality conditioner (UPQC) and STATCOM tools. These operate best with the help of their improved control system, to increase the system’s reliability and fast dynamic response, and to decrease the total harmonic distortion (THD) for enhancing the power quality (PQ). In this article, three different configurations are studied and assessed, namely: (C1) WOA-based FOPIC for UPQC, (C2) WOA-based FOPIC for STATCOM, and (C3) system without FACTS, i.e., base case, to mitigate the mentioned drawbacks. C3 is also considered as a base case to highlight the main benefits of C1 and C2 in improving the PQ by reducing the %THD of the voltage and current system and improving the systems’ voltage waveforms. With C2, voltage fluctuation is decreased by 98%, but it nearly disappears in C1 during normal conditions. Additionally, during the fault period, voltage distortion is reduced by 95% and 100% with C2 and C1, respectively. Furthermore, when comparing C1 to C2 and C3 under regular conditions, the percentage reduction in THD is remarkable. In addition, C1 eliminates the need for voltage sag, and harmonic and current harmonic detectors, and it helps to streamline the control approach and boost control precision. The modeling and simulation of the prepared system are performed by MATLAB/Simulink. Finally, it can be concluded that the acquired results are very interesting and helpful in the recovery to the steady state of wind systems and nonlinear loads, thereby increasing their grid connection capabilities.

Microgrid Frequency Regulation Based on a Fractional Order Cascade Controller

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

Modified Whale Algorithm-Based Optimization for Fractional Order Concurrent Diminution of Torque Ripple in Switch Reluctance Motor for EV Applications

This work proposes a new multi-objective optimization technique for concurrent diminution of torque ripple with the regulation of the speed of a 75 Kilowatt, 8/6, 4-phase SRM based on a double close loop, modified whale algorithm optimized fractional order proportional integral (MWAO FO-PI) control with a commutation angle controller. The system is analyzed and designed in MATLAB/SIMULINK environment. First, the performance of MWAO is tested on 30-dimensional standard benchmark functions. It is found that MWAO performance is better when examined on 30-dimensional standard benchmark functions, compared with WOA, and another six recently proposed state-of-art functions. Then, a double loop control based on the MWAO FO-PI controller is designed and implemented for concurrent diminution of torque ripple with the regulation of the speed of a 75 Kilowatt, 8/6, 4-phase SRM with a commutation angle controller. It was found that the percentage improvement achieved in the combined objective optimization function with the MWAO FO-PI controller was 10.044% in comparison with the MWAO PI controller, and 9.0597% compared with the WOA PI controller. It is also proved that MWAO FO-PI-based double close loop control of SRM provides less torque ripple, better tracking of speed with a reference value of speed and a better current profile in comparison with the MWAO PI controller and WOA PI controller. From all the above analysis, the conclusion is reached that the MWAO FO-PI controller provides very good overall system operational performance compared with MWAO PI and WOA PI controllers. The conclusion is reached based on simulation analysis and experimental validation is lacking.

Controller Design based on Fractional Calculus for AUV Yaw Control

This research presents a fractional order integral controller strategy, which improves the steering angle for Autonomous Underwater Vehicles (AUVs). The AUV mathematical modeling is presented. A Fractional Order Proportional Integral (FOPI) control scheme is implemented to ensure the yaw angle stability of the AUV steering under system uncertainty. The FOPI controller is validated with MATLAB/Simulink and is compared to the conventional Integer Order PI (IOPI) controller to track the yaw angle of the structure. The simulation results show that the proposed FOPI controller outperforms the IOPI controller and improves the AUV system steering and the overall transient response while ensuring the system's stability with and without external disturbances such as underwater current and different loading conditions.