Frequency Regulation of Stand-Alone Synchronous Generator via Induction Motor Speed Control Using a PSO-Fuzzy PID Controller

Abstract

This paper introduces a novel approach to frequency regulation in stand-alone synchronous generators by combining particle swarm optimization (PSO) with a Fuzzy PID controller. This study compares three control methods: a programmable logic controller (PLC)-based PID, a Fuzzy PID, and a PSO-Fuzzy PID controller. An experimental setup is implemented using real physical equipment, including an asynchronous motor, a synchronous generator, and various power and control components. The system is monitored and controlled in real-time via an S7-1215 PLC with the TIA Portal V17 interface, and the controllers are designed using MATLAB/Simulink. PLC-MATLAB communication is implemented using the KEPServerEX interface and the OPC UA protocol. The PSO-Fuzzy PID controller demonstrates superior performance, reducing overshoot, undershoot, and settling time compared to the other methods. These results highlight the effectiveness and real-time applicability of the PSO-Fuzzy PID controller for industrial frequency control, especially under varying load conditions and the nonlinear characteristics of the synchronous generator.

1. Introduction

Maintaining grid stability in modern power systems is vital to ensure a reliable and high-quality electricity supply [1]. Power system stability refers to the ability of a power system to maintain operational equilibrium under normal conditions and to return to an acceptable equilibrium state after a disturbance [2]. Synchronous generators, which are pivotal in power plants, have to operate near their stability limits to meet fluctuating demand. Frequency stability is the balance between electrical demand and power generation [3,4,5]. A deviation from this balance can cause the system frequently to fall outside safe operating limits, threatening grid stability and security [6,7,8,9].

Load frequency control (LFC) is essential for maintaining power system stability, particularly under fluctuation load conditions, by regulating the power balance between interconnected regions [10]. LFC ensures that the power generation matches the demand, preventing frequency deviation from its nominal value [11]. When this balance is disturbed, the frequency deviates, endangering both the security and stability of the power grid [12,13,14]. Automatic generation control (AGC) or LFC is responsible for correcting these imbalances and keeping the frequency and power within predefined limits. It is essential to maintain a reliable and high-quality electricity supply for consumers [15,16,17].

Power-frequency control operates at three distinct levels: primary, secondary, and tertiary. Each level has its own response time and associated control variables [18]. Primary frequency control responds within seconds (typically 2–30 s) and adjusts the generator’s power output through droop control using speed governors [19]. This control mechanism helps stabilize the system by addressing the imbalance between generation and load. When the load increases, for example, the power output of the generator does not immediately adjust, and the required balance is achieved using the kinetic energy from the rotating generators. Speed controllers (governors) of each generator increase output to correct the speed drop and eliminate the imbalance [20].

Secondary control, operating between 30 s and 15 min, aims to bring the system back to its target value. It adjusts the frequency and power exchanges with neighboring regions using AGC [21]. Tertiary control works on a time scale of 10–30 min and involves adjusting unit commitments and the distribution of generation to restore primary and secondary reserves or optimize their distribution [22]. This level typically works on larger electrical systems, ensuring sufficient energy reserves and optimizing generation for economic reasons [23].

While traditional PI and PID controllers are widely used for their simplicity and efficiency, their performance can degrade in complex systems with fluctuating loads, leading to longer settling times and larger overshoots [24,25,26]. Various improvements to these controllers have been proposed to enhance their performance in LFC applications, including the use of hybrid algorithms like teaching-learning-based optimization (TLBO), imperialist competitive algorithm (ICA), and hybrid harmony search-cuckoo optimization to improve PID performance [27,28]. Additionally, metaheuristic algorithms, such as the GBMO algorithm, fractional PID controllers, and Fuzzy PID controllers, have been developed to address the nonlinear and uncertain nature of power systems and improve controller robustness [29]. Other approaches include model predictive control (MPC) and event-triggered LFC strategies, which offer adaptive solutions to LFC in nonlinear, isolated, and interconnected microgrids [30].

PLCs are widely utilized in industrial automation systems, acting as controllers in a variety of applications, including motor control, water pumping, and switched reluctance motor control [31,32,33,34]. Despite their simple design, PLCs can be combined with advanced control algorithms to handle complex control tasks efficiently [35].

Table 1. Comparison of control methods and technologies in power system control studies.

Factors	References							This Study
	[36]	[37]	[38]	[39]	[40]	[41]	[42]
Using Industrial Tools	No	No	No	Yes	No	No	Yes	Yes
Classical Controller	Yes	No	Yes	No	Yes	No	Yes	Yes
Using AI	Yes	No	Yes	No	Yes	No	No	Yes
Real-Time Operation	No	Yes	No	No	No	Yes	No	Yes
Implemented in a Real System	No	Yes	No	No	No	Yes	No	Yes

highlights the key differences between this study and previous research on frequency control of stand-alone synchronous generators. Unlike traditional studies that primarily rely on simulations, this research integrates AI optimization with fuzzy logic and demonstrates its effectiveness in real-world industrial systems. This study is motivated by the need for practical control solutions in industrial applications, where ensuring real-time performance, robustness, and reliability is essential. Existing approaches often lack real-world validation, limiting their applicability in dynamic industrial environments.

To bridge this gap, this study implements a PSO-Fuzzy PID controller on a real system, using industrial tools such as PLCs for real-time monitoring and control. The reasons for choosing this approach are as follows:

• Limitations of classical controllers: While classical controllers are widely used, they struggle with adaptability to varying operating conditions. AI-based methods, particularly PSO-Fuzzy PID, offer online tuning capabilities that enhance stability and performance.
• Industrial applicability: Many studies do not consider the constraints of industrial environments where computational efficiency and real-time execution are essential. This study addresses this challenge by offloading complex calculations to external computers while ensuring real-time operation via PLCs.
• Experimental design justification: The experiment involves controlling the frequency of a synchronous generator through an induction motor and a frequency converter. This setup mimics real industrial scenarios, making the findings directly applicable to power system automation and industrial control.

This paper provides a comparative analysis of three control strategies for frequency regulation of a stand-alone synchronous generator: a classical PLC-PID controller, a Fuzzy PID controller, and a PSO-Fuzzy PID controller. The main contributions of this study are as follows:

• Optimization-based dynamic control design: Implementing an optimization-driven control strategy for frequency regulation, ensuring robust performance under industrial operating conditions.
• Effective use of metaheuristic algorithms in industrial applications: demonstrating that PSO combined with Fuzzy PID can be practically applied in automation, even with simple PLC-based control systems.
• Reliable convergence with PSO-Fuzzy PID: Validating the performance improvement and reliable convergence with PSO-Fuzzy PID, the PSO-Fuzzy PID controller enables efficient parameter tuning, improves dynamic response, and ensures stable frequency control.
• Expansion to large interconnected and multi-area power systems: Presenting a framework that extends to primary and secondary frequency control in interconnected power networks.
• This approach can be applied to develop advanced real-time controllers for use in both academic and industrial applications.

This study provides a practical implementation framework, ensuring its applicability in real-world industrial settings.

This article is organized as follows. Detailed information about the system established as the experimental setup and its modeling are presented in Section 2. Section 3 describes the proposed controller designs. Results obtained from experimental studies are discussed in Section 4. Finally, Section 5 presents the conclusion and future work.

2. System Modeling

2.1. Experimental Setup

The experimental setup consists of a PLC, a 1 kW brushed synchronous generator (SG), a frequency converter (FC), a 4 kW asynchronous motor, an encoder, an analog DC converter, two DC power supplies (24 V and 72 V), three current transformers (CTs), and 6 contactors. Figure 1 shows the experimental setup used in the study.

SG is driven by an asynchronous (induction) motor that is mechanically coupled to its shaft. The asynchronous motor is powered by the frequency converter (drive), which controls its speed and, consequently, the frequency of the SG. The control device used in the system is an S7-1215C DC/DC/DC PLC. The system can be monitored and controlled through software and SCADA within the TIA Portal interface.

An AI/AQ module (SM1234) and an Energy Meter module (SM1238) are integrated into the PLC. The AQ module regulates the frequency and voltage of SG via the drive and DC converter, while the Energy Meter module measures all electrical parameters of the SG, including phase-to-phase voltages, phase-to-neutral voltages, power factors, active power, apparent power, reactive power, etc.

The PLC and encoder operate on a 24 V DC power supply, while the rotor (field) windings of the SG use a separate 0–85 V DC supply. Moreover, the system includes an incremental rotary encoder with a PPR value of 1024, mechanically coupled to the SG shaft, which measures the speed of the generator to regulate its frequency. Current transformers facilitate the electrical connection between the SG and the energy meter, while contractors enable the connection and disconnection of various load groups. In the experimental setup, the nominal values of the SGs are as follows:

• Power: 1 kW;
• Voltage: 380 V AC (220 V phase-neutral);
• Frequency: 50 Hz;
• Speed: 1500 rpm;
• Excitation current: 2.1 A DC
• Excitation voltage: 72 V DC;
• Current: 2.3 A AC;

The system components are shown in Figure 2.

2.2. Obtaining of the Transfer Function

To implement optimization processes in frequency control of an SG using PSO, the transfer function of the system must first be identified. This research selected offline optimization to ensure robust and efficient controller tuning before real-time implementation. Given the complexity of the system and the need for stability in industrial applications, obtaining the transfer function allows for precise parameter tuning and performance validation under various operating conditions. This approach minimizes computational overhead during real-time execution and enhances the adaptability of the controller to dynamic changes.

The system’s transfer function was obtained employing the input (normalized frequency converter signal from 0 to 2000 as the required speed) and output data (actual speed of synchronous generator). The System Identification Toolbox in MATLAB/Simulink R2021a was employed to derive the transfer function. System identification is the process of determining a dynamic system model using input–output measurements from real systems. Identifying such a dynamic system involves several steps: designing experiments, estimating unknown system characteristics from experimental data, collecting data, creating models, and validating the discovered model. Ensuring a high-performance controller design requires key facilities, which are provided through the formulation of the system model and its attributes.

By employing offline optimization, the controller is optimized under controlled conditions before real-time operation, reducing uncertainties and enhancing system performance in real industrial environments.

To obtain the transfer function that defines the nonlinear dynamic behavior of the system, the voltage signal from the frequency converter was used as the input variable, while the actual speed of the SG, taken from the encoder, was used as the output variable. Both input and output data were measured and saved in an Excel file using the data logging function of the SCADA system. For this purpose, 126 measurements were used during the experiment, with a sampling time of 1 s (Ts) for both input and output data. Figure 3 illustrates the data collected from the test, showing the time (in seconds) on the x-axis, the input signal as voltage (V) on the y-axis, and the system output as speed (in rpm) on the y-axis.

As depicted in Figure 4, the measured value of the system is represented by the black line, while the green line corresponds to the output of the simulation model. The best fit of the model, determined using the System Identification Toolbox, is 93.86%. Since the model meets the stability criterion—having all poles and zeros within the unit circle, as illustrated in Figure 5—it is considered valid. This confirms that the model is both stable and performs satisfactorily. The transfer function, identified through system identification (SI), is presented in Equation (1) below.

$$G_s={\displaystyle \frac{10.09s+0.3434}{s^3+4.772s^2+10.22s+0.3205}}$$

(1)

3. Controller Design

Due to its simplicity in development and installation and its capability to function effectively even in the presence of system uncertainty, the PID controller continues to be one of the most commonly used controllers in recent years. The PID transfer function is shown in Equation (2) below.

$$C\left(s\right)={\displaystyle \frac{U\left(s\right)}{E\left(s\right)}}=K_p+{\displaystyle \frac{K_i}{S}}+K_{d}S$$

(2)

where K_p represents proportional gain, K_i represents integral gain, and K_d represents derivative gain. While PID controllers offer several advantages, they may not always achieve the desired performance, especially in nonlinear systems.

This study proposes three strategies for controlling the frequency of stand-alone synchronous generators: a PLC-PID controller, a fuzzy PID controller, and a PSO-fuzzy PID controller. These strategies are validated through both simulations and real-time experiments.

In the classical (PLC-PID) control scheme, the control structure is implemented directly in PLC using TIA Portal instructions. In the second scheme, Fuzzy PID and PSO-Fuzzy PID in MATLAB/Simulink are used with PLC to implement frequency control. Communication between PLC and MATLAB is conducted via the OPC server, with the PLC acting as a monitoring and measurement unit. Figure 6 shows the PLC-PID control structure, while Figure 7 illustrates Fuzzy PID and PSO-Fuzzy PID control structures.

3.1. PLC-PID Controller

In the experimental setup, the rpm value is achieved using the encoder. Based on this value, frequency control is performed. If the rpm value differs from the set value of 1500, the speed of the asynchronous motor is adjusted as a result. Since the SG is mechanically connected to the asynchronous motor, the speed (rpm) of the SG also changes. This adjustment is achieved by sending a proportional 0–10 V signal from the analog output of PLC to the analog input of the drive. When the SG reaches 1500 rpm, the drive frequency is set to 50 Hz, as illustrated in Figure 8.

Frequency control of SG under varying load conditions is conducted using the PID_Compact function of the TIA Portal V17 interface. The PID controller works according to Equation (3).

$$y=K_p\left[\left(b·w-x\right)+{\displaystyle \frac{1}{T_I·s}}\left(w-x\right)+{\displaystyle \frac{T_D·s}{a·T_D·s+1}}(c·w-x)\right]$$

(3)

where y is the output value of the PID controller, K_p is the proportional gain, s is the Laplace operator, b is proportional action weighting, w is the setpoint, x is the process value, T_I is the integral action time, T_D is the derivative action time, a is derivative delay coefficient, and c is the derivative action weighting [43]. Figure 9 shows the PID block diagram for speed control using the PLC.

The compact PID controller for the SG implemented in the OB30 cyclic interrupt block is shown in Figure 10.

In the TIA Portal interface, the PID compact function was used for speed regulation. The settings were configured based on the working scenario. Within the PID compact configuration window, the basic settings were defined. The controller type was set to ‘speed’. In the Input/Output parameters section, ‘Input’ and ‘Output_PER (analog)’ were selected, as the speed is continuously measured by the encoder, and the control signal for regulating frequency is analog. The setpoint for speed regulation was set to 1500 rpm.

After configuring the settings, the real/physical system was initialized. The setup window in PID compact was accessed, where initial and fine-tuning processes were performed. During system operation, the PLC calculated the appropriate Kp, Ki, and Kd values. The final values, after the initial setup and fine-tuning, are shown in Figure 11.

3.2. Fuzzy PID Controller

Traditionally, PID adjusts frequency but struggles with large and rapid changes. The fuzzy algorithm, combining PID fuzzy control, improves performance and was implemented in this research for fast, stable frequency control.

Using the fuzzy logic module in the MATLAB/Simulink platform, the proposed fuzzy PID controller was designed. Mamdani fuzzy inference system and the Centroid method were employed for fuzzification and defuzzification, respectively, as shown in Figure 12.

A Fuzzy PID controller is employed to automatically adjust the parameters of the PID controller—Kp, Ki, and Kd—in real-time operation based on the system’s error signals. This adjustment allows the performance of the controller to meet specific system requirements. As shown in Figure 13, the fuzzy logic controller takes two inputs—the error (e(t)) and the change in error (∆e(t))—and gives three outputs: Kp, Ki, and Kd.

The error signal is generated by comparing the actual speed with the desired speed of the stand-alone SG, while the change in error is calculated by differentiating the error signal. Both signals are then fed into the fuzzy logic controller block. The fuzzy logic controller generates correction coefficients (∆K_p, ∆K_i, and ∆K_d) to adjust the parameters of the PID controller accordingly, which subsequently adjusts the set point in the plant block.

The fuzzy design, depicted in Figure 14, uses seven linguistic membership functions (MF) for both the error and change in error inputs, along with the outputs (∆K_p, ∆K_i, and ∆K_d). These membership functions are ‘Negative Small’ (NS), ‘Negative Medium’ (NM), ‘Negative Big’ (NB), ‘Zero’ (ZE), ‘Positive Small’ (PS), ‘Positive Medium’ (PM), and ‘Positive Big’ (PB). Trapezoidal membership functions (trapmf) were employed for the ‘NB’ and ‘PB’ values of all the variables, while triangular membership functions (trimf) were used for the remaining variables. The input MF range for both inputs was normalized between [−0.5, 1], while the output ranges for (∆K_p, ∆K_i, and ∆K_d) were normalized within [−6, 6], [−10, 10], and [−1, 1], respectively.

In fuzzy control systems, the performance of membership functions has been widely investigated. In both industry-based applications, such as process control, motor control, and PLC-oriented control, and literature studies aimed at performance improvement, triangular and trapezoidal membership functions are commonly preferred. In [44], the impact of membership functions on the performance of fuzzy controller systems has been reviewed in detail. The step responses of controllers with different types of membership functions, including triangular, trapezoidal, and Gaussian, have been compared in terms of maximum overshoot, settling time, Integral of Absolute Error (IAE), and Integral of Squared Error (ISE). The fuzzy controller with a triangular membership function has been observed to perform better in these comparisons.

In [45], five popular methods for online tuning of PID controllers were compared. Experimental simulation results demonstrated that the fuzzy logic approach was the most successful method, enabling the dynamic adjustment of PID gain parameters over time and enhancing system robustness. This method significantly reduced both the settling time and the Integral of Time-weighted Absolute Error (ITAE).

In an Automatic Voltage Regulator (AVR) system, a fuzzy PID filter (FPIDF) controller was proposed in [46] to maintain the output voltage of the generation unit within permissible limits despite unexpected variations. Triangular membership functions were preferred in this controller. Similarly, in [47], a metaheuristic-based fuzzy PID method for AVR control also utilized triangular membership functions. The performance of the proposed method was evaluated based on two different objective functions, namely the Integral of Absolute Error (IAE) and the Integral of Time-weighted Absolute Error (ITAE), and it was found to be superior to the other compared methods.

In [48,49,50,51,52,53,54], fuzzy logic controllers utilizing triangular and trapezoidal membership functions were preferred for controlling various systems due to their simplicity, robustness, and effectiveness in producing reliable results.

In this study, triangular and trapezoidal membership functions were selected primarily due to computational efficiency and compatibility with industrial PLC-based implementations [55,56]. PLCs often have limited processing power and memory, making it impractical to use computationally complex functions such as generalized bell and Gaussian membership functions. Triangular and trapezoidal membership functions provide a good balance between accuracy and efficiency, ensuring real-time performance without excessive computational burden. Furthermore, systematic analyses [57,58] have proven triangular membership functions provide optimal performance for fuzzy control systems, particularly in induction motor drives and similar applications. Their simplicity and efficiency make them well-suited for applications requiring fast and adaptive response under limited computational resources. The fuzzy logic controller operates with 49 rule bases, derived from a detailed analysis of the dynamic behavior of SG and requirements for PID parameter adjustment, as described in

Table 2. Fuzzy controller design linguistic rules.

Error Rate	Error e(t)
∆e(t)	NB	NM	NS	ZE	PS	PM	PB
NB	NB	NB	NM	NM	NS	NS	ZE
NM	NB	NM	NM	NS	NS	ZE	PS
NS	NB	NM	NS	NS	ZE	PS	PS
ZE	NM	NS	NS	ZE	PS	PS	PM
PS	NS	NS	ZE	PS	PS	PM	PM
PM	NS	ZE	PS	PS	PM	PM	PB
PB	ZE	PS	PS	PM	PM	PB	PB

. Although some previous studies have utilized fewer rules [59,60], decreasing the number of rules in this study would compromise the adaptability and accuracy of the controller, which are essential for frequency regulation in highly dynamic power systems.

By prioritizing efficiency and feasibility within industrial applications, this design ensures the Fuzzy-PID controller remains adaptable and effective under practical constraints while maintaining the computational efficiency suitable for PLC-based environments. Experimental results confirm that the chosen membership functions are sufficient in terms of accuracy and robustness without overloading computational complexity.

The fuzzy logic controller operates with 49 rule bases derived from a detailed analysis of the dynamic behavior of SG and PID parameter adjustment, as described in Table 2. These rules are essential for ensuring the performance of the controller across a range of operating conditions. The Mamdani-type inference system was used for fuzzification, and the “Centroid” method was applied for defuzzification. This design ensures that the Fuzzy PID controller adapts effectively to different system conditions. Figure 15 displays the surface viewer of the fuzzy logic system.

The implementation of the fuzzy logic system in MATLAB’s Fuzzy Logic Toolbox allowed the dynamic adjustment of PID parameters based on the error and error change, making the controller more adaptable to varying conditions. The 49-rule base, composed of seven membership functions per input, ensures a smooth and precise adaptation, maintaining control system stability. Reducing the number of rules could negatively impact the system’s adaptability and performance, especially in high-dynamic applications such as frequency control in stand-alone synchronous generators.

3.3. PSO-Fuzzy PID Controller

PSO was selected for its simplicity, fast convergence, and suitability for real-time implementation in industrial environments, efficiently tuning controller parameters without high computational overhead. While Fuzzy PID enables real-time adjustment of PID control parameters, its reliance on fixed fuzzy rules limits its ability to enhance optimal control. To enhance system stability and robustness, this paper employs PSO to adaptively optimize fuzzy control settings, resulting in a fuzzy PID coordination control approach. Through the optimization process, PSO determines the best parameters for the Fuzzy PID controller, ensuring an optimal control signal to the plant.

3.3.1. Particle Swarm Optimization Algorithm

PSO is a metaheuristic optimization technique inspired by the collective behavior of birds, iteratively refining candidate solutions to achieve optimal performance. Each particle in the swarm updates its position based on both its personal best-known position and the globally best-known position, facilitating the efficient exploration of large solution spaces [61]. The PSO method, widely used in nonlinear and power system applications [62,63], was initially proposed in 1995 [64] and later improved in 1998 with the introduction of an inertia weight coefficient to enhance performance [65]. In the swarm, each particle searches for an optimal position by continuously updating its location according to its best-found position and the global best position. In the PSO algorithm, each particle searches for an optimal position by continuously updating its velocity and position according to its best-found position and the global best position. The velocity and position updates follow these equations [66].

$$vi(k+1)=W vi\left(k\right)+C1R1(gbest-Xi(k\left)\right)+C2R2(Pbest-Xi(k\left)\right)$$

(4)

$$\begin{array}{c}xi(k+1)=xi\left(k\right)+vi(k+1)\\ i=1, 2,\dots , n\end{array}$$

(5)

where

• vi is the velocity of the ith particle,
• $w$ is the inertia weight factor,
• $k$ is the iteration number,
• $C1$ and $C2$ are cognitive and social coefficients,
• $R1$ and $R2$ are random variables from 0 to 1,
• xi is the position of the ith particle,
• $pbest$ is the individual best position of particle $i$,
• $gbest$ is the best global position of all particles in the swarm,
• $n$ is the total number of particles.

The position of a particle is updated if the following condition is met:

$$f\left(xik\right)<f\left(P_{best}\right)$$

(6)

If it is true, the position update is given by

$${xik=P}_{best}$$

(7)

In optimization methods, system performance is typically assessed using a variety of fitness criteria, including integral square errors (ISE), integral absolute errors (IAE), integral time absolute errors (ITAE), and integral time square errors (ITSE). Parameters such as overshoot, undershoot, steady-state error, settling time, and general tightness of the control system are all considered by these fitness criteria [67].

The minimization objective fitness function, donated as $f$, is used to evaluate the performance of the system. In this study, the output response performance of the system is assessed using the ITAE fitness function, as given in Equation (8).

$$\mathrm{I}\mathrm{T}\mathrm{A}\mathrm{E}={\int }_0^{t}t |e(t)|·dt$$

(8)

where $e\left(t\right)$ is the error signal at time t, and the integral is computed over the entire time period of interest. This fitness function is used to guide the optimization process in PSO. To enhance clarity, Algorithm 1 provides a step-by-step illustration of the PSO algorithm.

Algorithm 1: Strategy for the PSO algorithm

Additionally, the parameters of the PSO algorithm, including the number of agents (Np), iterations (Ni), cognitive, social coefficient, and inertia weight, are summarized in

Table 3. The parameters of the PSO algorithm.

Parameter	No. Iteration	No. Particles	Social Coefficient	Cognitive Coefficient	Inertia Weight
Value	100	50	2	2	0.7

. The PSO algorithm parameters listed in Table 3 were obtained from extensive experimentation with the mathematical model in Simulink (MATLAB). The decision for the number of agents (Np) and iterations (Ni) was made after testing various values to find the optimal configuration that balances computational efficiency with fast convergence. These chosen values were based on the performance consistency observed in various experimental runs, where these values led to optimal controller parameters (Kp, Ki, Kd) and exhibited improved response of the system. These hyperparameters were not arbitrary but were determined after a thorough process of experimentation to ensure the best results. These values ensure optimal control performance, with improved system stability and response time, as shown in Figure 16.

Figure 17, which includes a block diagram of the process, illustrates the optimization process for the PSO-Fuzzy PID system. The MATLAB program was used to find the optimal values of Fuzzy PID parameters. To search the domain of position and velocity of particles, the program uses a minimization algorithm. After 100 iterations, the optimal values of Fuzzy PID controller parameters are obtained.

As shown in the dashed box of Figure 17, the update and iteration of particles were separated into two sections in MATLAB. In the first section (A), the control system model of the Simulink platform was used, and the performance index was obtained for each sampling period. The second section (B) involved programming the PSO optimization in MATLAB executable code file (.m file). In this section, the particle position and velocity were updated based on the fitness value. The gBest, which represents the historical best position of the swarm, corresponds to the values for the three proportional and quantitative factors.

3.3.2. System Simulation for PSO-FPID Tuning of Frequency Control

This section presents the simulation results for frequency control of stand-alone synchronous generators. The simulation was performed using a mathematical model of the proposed method, with MATLAB/Simulink as the platform. The primary objective of the simulation was to optimize the Fuzzy PID controller using the PSO algorithm to determine appropriate values for Kp, Ki, and Kd and to implement the PSO-Fuzzy PID controller in real industrial systems for real-time operations.

The parameters of the PSO algorithm, including the number of agents (Np), iterations (Ni), cognitive, social coefficient, and inertia weight, are summarized in Table 3. The hyperparameters used for the PSO algorithm were selected through rigorous experimentation with the mathematical model in Simulink (MATLAB). Specifically, the PSO algorithm was executed with 50 agents (Np = 50) for 100 iterations (Ni = 100). These values were chosen because they provided a balance between computational efficiency and convergence speed, yielding optimal values for Kp, Ki, and Kd, as presented in

Table 4. Optimal parameter values found via PSO for Fuzzy PID controllers.

Criteria	Kp	Ki	Kd
PSO-Fuzzy PID	4.858	9.751	0.849

.

Figure 18 illustrates the Simulink block diagram, where the controller block consists of the Fuzzy PID controller and the system model. A step trajectory was used as the reference input signal to evaluate the synchronous generator speed control system.

In this study, PSO was used to adjust the controller parameters, balancing optimization efficiency with low computational cost. The most significant PSO parameters—number of particles, cognitive and social coefficients, and inertia weight—were carefully chosen based on established optimization guidelines and validated through empirical tests. To evaluate the performance of the controller, the ITAE function was employed as the objective function. Figure 19 illustrates the effectiveness of the PSO-based optimization, as the ITAE values gradually decrease over successive generations, indicating improved control accuracy. A summary of optimal parameter values obtained through PSO for Fuzzy PID controllers is presented in Table 4.

4. Experimental Results and Discussion

After implementing the three different controller designs outlined in Section 3, experiments were conducted, including no-load operation (step response), loading, and unloading tests. The results obtained from the experiments were recorded through the PLC/SCADA interface, and corresponding graphs were generated. For the loading and unloading experiments, instantaneous loading and unloading were conducted instead of gradual changes. This approach aimed to evaluate the response parameters of the SG and controllers under more challenging operating conditions. This section presents the results of the following experiments: initial no-load operation, resistive 1100 W (110%) instantaneous loading and unloading, 550 W (55%) instantaneous loading and unloading, and inductive load 500 VA (pf = 0.8) instantaneous loading and unloading.

The results of the initial no-load operation (step response) experiment are shown in Figure 20. For the experiment using the conventional PID (PLC-PID) controller, the maximum frequency observed was 63.03 Hz, with a maximum overshoot of 26.06% relative to the nominal frequency (50 Hz), and the settling time was 28 s. For the experiment using the Fuzzy PID controller, the maximum frequency was 51.03 Hz, with a maximum overshoot of 2.06%, and the settling time was 17 s. In the experiment using the PSO-Fuzzy PID, no overshoot could be observed, and the settling time was reduced to 6 s.

Figure 21 and Figure 22 show the results of no-load to 1100 W load (0–110% loading) and 1100 W load to no-load (unloading) experiments, respectively.

In the 1100 W loading experiment with the PLC-PID controller, the minimum frequency observed was 48.1 Hz, with a maximum undershoot of 1.9 Hz and a settling time of 20 s. In the experiment with the Fuzzy PID controller, the minimum frequency was 49.07(Hz), with a maximum undershoot of 0.93 Hz and a settling time of 7 s. For the experiment using the PSO-Fuzzy PID controller, the minimum frequency was 49.17(Hz), with a maximum undershoot of 0.83 Hz and a settling time of 6 s.

In the 1100 W unloading experiment, the maximum frequency values were 52.3 Hz (maximum overshoot of 2.3 Hz) for the PLC-PID controller, 51.63 Hz (maximum overshoot of 1.63 Hz) for the Fuzzy PID controller, and 51.3 Hz (maximum overshoot of 1.3 Hz) for the PSO-Fuzzy PID controllers. The corresponding settling times were 19 s for the PLC-PID, 9 s for the Fuzzy PID, and 8 s for the PSO-Fuzzy PID controller.

Figure 23 and Figure 24 show the results of the no-load to 550 W load (0–55% loading) and 550 W load to no-load (unloading) experiments, respectively. In the 550 W instantaneous loading experiment, conducted with the PLC-PID, Fuzzy PID, and PSO-Fuzzy PID controllers, the minimum frequency values observed were 49.13 Hz (with a maximum undershoot 0.87 Hz), 49.3 Hz (with a maximum undershoot 0.7 Hz) and 49.37 Hz (with a maximum undershoot 0.63 Hz), respectively. The settling time for PLC-PID, Fuzzy PID, and PSO-Fuzzy PID controllers were 13 s, 5 s, and 4 s, respectively.

In the 550 W instantaneous unloading experiment, the maximum frequency values for PLC-PID, Fuzzy PID, and PSO-Fuzzy PID controllers were 51.1 Hz (with a maximum overshoot of 1.1 Hz), 50.87 Hz (with a maximum overshoot of 0.87 Hz) and 50.57 Hz (with a maximum overshoot of 0.57 Hz), respectively. The settling times for PLC-PID, Fuzzy PID, and PSO-Fuzzy PID controllers were 13 s, 6 s, and 5 s, respectively.

Figure 25 and Figure 26 display the results of the no-load to 500 VA (pF = 0.8) load and 500 VA (pF = 0.8) load to no-load (unloading) experiments, respectively. In the 500 VA instantaneous loading experiment, performed with PLC-PID, Fuzzy PID, and PSO-Fuzzy PID controllers, the minimum frequency values were 49.17 Hz (with a maximum undershoot of 0.83 Hz), 49.37 Hz (with a maximum undershoot of 0.63 Hz), and 49.5 Hz (with a maximum undershoot of 0.5 Hz), respectively. The settling times for PLC-PID, Fuzzy PID, and PSO-Fuzzy PID controllers were 15 s, 9 s, and 7 s, respectively.

In the 550 VA instantaneous unloading experiment, the maximum frequency values for PLC-PID, Fuzzy PID, and PSO-Fuzzy PID controllers were 50.83 Hz (with a maximum overshoot of 0.83 Hz), 50.67 Hz (with a maximum overshoot of 0.67 Hz), and 50.63 Hz (with a maximum overshoot of 0.37 Hz), respectively. The settling times for PLC-PID, Fuzzy PID, and PSO-Fuzzy PID controllers were 16 s, 12 s, and 8 s, respectively.

The results obtained using PLC-PID, Fuzzy PID, and PSO-Fuzzy PID controllers are given in

Table 5. PID and aABC Fuzzy PID comparison for loading experiments.

Experiment	Settling Time (s)			Max. Undershoot (%)
	PLC- PID	Fuzzy PID	PSO-Fuzzy PID	PLC- PID	Fuzzy PID	PSO-Fuzzy PID
0–1100 W	20	7	6	3.8	1.86	1.66
0–550 W	13	5	4	1.74	1.4	1.26
0–500 VA	15	9	7	1.66	1.26	1

and

Table 6. PID and aABC Fuzzy PID comparison for unloading experiments.

Experiment	Settling Time (s)			Max. Overshoot (%)
	PLC- PID	Fuzzy PID	PSO-Fuzzy PID	PLC- PID	Fuzzy PID	PSO-Fuzzy PID
1100–0 W	19	9	8	4.6	3.26	2.6
550–0 W	13	6	5	2.2	1.74	1.14
500–0 VA	16	12	8	1.66	1.34	1.26

for loading and unloading, respectively.

The experimental results demonstrate that the PSO-Fuzzy PID controller is better than the Fuzzy PID and PLC-PID controllers. In the 1100 W (110%) instantaneous loading experiment, the PSO-Fuzzy PID controller achieved a settling time of 6 s and a maximum overshoot of 0.83 Hz, while the PLC-PID controller had values of 20 s and 1.9 Hz, respectively, and the Fuzzy PID controller showed 7 s and 0.93 Hz. Furthermore, the PSO-Fuzzy PID controller exhibited the lowest maximum oscillation and settling time in the 550 W (55%) and 500 VA inductive load experiments compared to all the methods.

During the experiments, loading and unloading experiments were conducted under harsh conditions with instantaneous and large load fluctuations (55% and 110% of nominal power). Such instantaneous load fluctuations in real power systems are rarely observed at these levels. With the proposed control method, under smaller or gradual load fluctuations (10% or 20% of nominal power), frequency fluctuations (overshoot and undershoot values) were observed to be 0.5 Hz or less, and the settling times were 3 s or more. It was observed that overshoot and settling time values were higher in experiments performed with inductive loads compared to experiments performed with resistive loads of the same or similar values.

Standard frequencies are defined in the IEC 60196-2009 standard [68]. Although national regulations may vary, power systems generally allow frequency fluctuations of ±1% (0.5 Hz). Therefore, frequency values ranging from 49.5 to 50.5 (Hz) are considered acceptable. Based on this, a settling time of less than 3 s is acceptable, even under the most challenging conditions (110% instantaneous load). In the 110% instantaneous load experiment conducted using the PSO-Fuzzy PID controller, the frequency was consistently maintained within the acceptable range. Additionally, the SGs used in the experiments were specifically designed for research purposes rather than commercial applications. Given the superior stability, efficiency, and optimized design of commercial SGs, even better frequency regulation can be expected when implementing the proposed controller in real-world applications.

The comparison of the results obtained from the use of PSO-Fuzzy PID in loading and unloading tests reveals that the system performance is significantly enhanced system performance compared to traditional PLC-PID and Fuzzy PID methods. Specifically,

Reduction in settling time:

• In loading experiments, PSO-Fuzzy PID reduced settling time by 30% compared to Fuzzy PID and 50% compared to PLC-PID.
• In unloading experiments, PSO-Fuzzy PID reduced settling time by 30% compared to Fuzzy PID and 42% compared to PLC-PID.

Reduction in maximum undershoot:

• PSO-Fuzzy PID reduced the maximum undershoot by 10% compared to Fuzzy PID and 56% compared to PLC-PID.

Reduction in maximum overshoot:

• In unloading experiments, PSO-Fuzzy PID reduced the maximum overshoot by 20% compared with Fuzzy PID and 43% compared with PLC-PID.

These results emphasize that PSO-Fuzzy PID is superior in performance and has a faster response time when compared to other control methods. Applying this technique to optimize the parameters of the Fuzzy PID controller can enhance the stability and performance of the system under changing loading and unloading conditions.

5. Conclusions and Future Work

This study successfully implemented an experimental framework to evaluate the frequency control of a stand-alone synchronous generator using a PSO-Fuzzy PID controller. Unlike previous studies that relied on purely simulation-based validation, this research incorporated real industrial hardware, utilizing a Siemens S7-1200 PLC and TIA Portal V17 software for real-time monitoring and control. Communication between the PLC and MATLAB was successfully established using the KEPServerEX interface and OPC UA protocol, ensuring precise data exchange and operational efficiency.

The proposed PSO-based metaheuristic algorithm proved to be highly effective in optimizing controller parameters and balancing computational efficiency with optimization accuracy. The selection of the ITAE function as the fitness criterion enabled the systematic determination of the best control parameters, significantly improving system stability and performance. Comparative analysis with conventional PLC-PID and Fuzzy PID controllers highlighted the superiority of the PSO-Fuzzy PID method, demonstrating the following:

• A 30–50% reduction in settling time compared to PLC-PID and Fuzzy PID.
• A 10–56% reduction in maximum undershoot under dynamic load conditions.
• A 20–43% reduction in maximum overshoot during unloading experiments.

Considerable reductions in the overshoot, undershoot, and settling time under dynamic load variations are observed. By integrating an advanced yet computationally efficient optimization technique with an industrially viable control system, this research bridges the gap between theoretical development and practical application. The findings emphasize the potential of PSO-driven controller optimization for enhancing control precision in real-world industrial environments, paving the way for further research into adaptive and intelligent control techniques.

These improvements indicate the ability of the PSO-Fuzzy PID method to enhance control precision, robustness, and versatility under varying load conditions. While this study focused primarily on comparisons with conventional PID-based controllers, future research will investigate comprehensive and detailed comparative performance with other optimized control approaches, such as GA-PID and ANFIS-PID, for a broader perspective of optimization techniques.

Future research will also focus on further improving the controller’s performance under more challenging conditions and for higher-power SGs. The integration of predefined-time and event-triggered control strategies will be explored, to achieve maximum responsiveness of the system. Additionally, hybrid optimization approaches involving other metaheuristic algorithms, machine learning, and deep learning will be investigated to further enhance system performance and robustness for real-world industrial applications.