Optimization of Power System Stabilizers Using Proportional-Integral-Derivative Controller-Based Antlion Algorithm: Experimental Validation via Electronics Environment

Abstract

A robust, optimized power system stabilizer (PSS) is crucial for oscillation damping, and thus improving electrical network stability. Additionally, real-time testing methods are required to significantly reduce the likelihood of software failure in a real-world setting at the user location. This paper presents an Antlion-based proportional integral derivative (PID) PSS to improve power system stability during real-time constraints. The Antlion optimization (ALO) is developed with real-time testing methodology, using hardware-in-the-loop (HIL) that can communicate multiple digital control schemes with real-time signals. The dynamic power system model runs on the dSPACE DS1104, and the proposed PSS runs on the field programmable gate arrays (FPGA) (NI SbRIO-9636 board). The optimized PSS performance was compared with a modified particle swarm optimization (MPSO)-based PID-PSS, through different performance indices. The test cases include other step load perturbations and several short circuit faults at various locations. Twelve different test cases have been applied, through real-time constraints, to prove the robustness of the proposed PSS. These include 5 and 10% step changes through 3 different operating conditions and single, double, and triple lines to ground short circuits through 3 different operating conditions, and at various locations of the system transmission lines. The analysis demonstrates the effectiveness of ALO and MPSO in regaining the system’s stability under the three loading conditions. The integral square of the error (ISE), integral absolute of the error (IAE), integral time square of the error (ITSE), and integral time absolute of the error (ITAE) are used as performance indices in the analysis stage. The simulation results demonstrate the effectiveness of the proposed PSS, based on the ALO algorithm. It provides a robust performance, compared to the traditional PSS. Regarding the applied indices, the proposed PSS, based on the ALO algorithm, obtains significant improvement percentages in ISE, IAE, ITSE, and ITAE with 30.919%, 23.295%, 51.073%, and 53.624%, respectively.

1. Introduction

1.1. Motivation and Incitement

The dynamic stability of an electrical power system is defined as the system’s ability to regain a new equilibrium point after being subjected to a significant disturbance [1,2]. These disturbances adversely affect the system security and power transfer capability, which requires immediate countermeasures to alleviate. Blackouts—such as those notable incidents which have occurred in the United Kingdom (1980), the system separation in the western region of the USA/Canada (1996), the USA (14 August 2003), and Italy (28 September 2003)—involved a low frequency of oscillation (LFO) in the range of 0.1 to 0.7 Hz [3].

These countermeasures, mainly performed by the controlling devices, aim to cancel, or diminish the oscillations associated with disturbances. Typically, modifying the field excitation current reduces the electromechanical changes. However, the power system stabilizer (PSS) provides an additional control signal to the excitation system to enhance its ability to dampen the oscillation and, as a result, improve the system stability [4]. In this regard, the optimal design of the PSS parameters is a critical aspect of enhancing the performance of the modern PSS controller.

1.2. Literature Review

Over the last few years, many techniques have been used to optimize the PSS parameter. In [5], the genetic algorithm (GA) has been implemented to produce a bank of conventional PSS-optimized parameters under different operating points. The adaptive neuro-fuzzy inference system has been activated to select the most suitable parameter for each situation. In [6], the non-dominated sorting genetic algorithm II (NSGAII) has optimized the lead-lag PSS. The study has considered different operating points to solve a multi-objective optimization problem for increasing the damping ratios and shifting the electromechanical modes as much as possible toward the D-shape sector. However, in this model of [6], the power system has been linearized around the steady-state operational condition.

Similarly, in [7], the firefly algorithm has been developed to optimize the PSS parameters. In [8], an advanced population-based incremental learning (PBIL) technique has been combined with an adaptive learning rate and developed to overcome the premature convergence problems in PBIL for designing PSS. In [9], the steepest descent method has been integrated with three metaheuristic algorithms of a gravitational search optimizer (bat optimization technique and PSO) to optimize the PSS parameters. Moreover, the farmland fertility algorithm, which emulates farmers’ behavior when applying various fertilizers to farmlands with varying soil conditions, has been utilized to design the PSS’s proportional integral derivative (PID) controller [10]. In [11], The PSO was modified by converting the search space boundary to work as a reflecting wall. The revised edges prevent any particle from escaping the search space by absorbing part of its velocity by the edge and randomly reflecting it to the search space. In [12], an intelligent hybrid optimization version between the atom search algorithm and simulated annealing has been presented for designing a PSS damping controller.

Robust PSS requires an accurate design and many testing conditions to ensure and validate its robustness. The researchers have investigated the PSS performance through various test cases and diverse system structures. A three-phase short circuit (S.C.) for a six-cycle, through a single-machine infinite bus (SMIB) model, has been covered in [12]. In [13], a 5% step change in mechanical power, across a multi-machine power system (MMPS), has been simulated as a disturbance condition. Different loading conditions have been conducted, with the step load increasing within the MMPS in [14]. Additionally, the effects of a three-phase fault have been analyzed in [15]. The fault lasted for 0.1 s, using a SMIB power system. A 100 ms 3-phase to ground fault, using the MMPS model, was investigated in [16]. On the other hand, offline simulation tests have been analyzed, based on small perturbations within four different system structures (2, 3, 4, and 10 machine systems) in [17], or small step load changes in [18]. In [19], different test scenarios, covering various operating conditions, have been demonstrated to ensure the PSS’s robustness.

For the sake of adequate investigation of the robustness of the optimized PSS in electrical power systems, several performance indices were adopted with different objective functions to improve the optimization process. In [19,20,21], the inverse time absolute square of the error (ITAE) has been utilized. The ITAE is used as a single objective function. The robustness of the developed method was evaluated using a damping ratio, overshot, settling time, and eigenvalues as performance indices. The ITAE-based objective function has also been suggested in [12]. In [22], the minimum-maximum damping ratio and eigenvalues were employed as objective functions where both the damping ratio and eigenvalue performance were used as indices.

On the other hand, considering the adopted simulation environment, all study cases reported in [5,6] have relied on simulation packages. The simulation package-based verification methods have great potential and flexibility, but suffer heavily from biased and unrealistic assumptions imposed by researchers in other cases. In other words, the simulation results are as promising as the researchers are adept at using these packages. However, in [23], experimental validation methodologies were adopted to overcome the insufficiency related to simulation methods. A combination of both strategies was also employed [24]. On the other hand, researchers recently used contemporary technologies and techniques to verify the robustness of their PSS models. Rapid control prototyping (RCP), hardware-in-the-loop (HIL), and software-in-the-loop (SIL) are some of the prevailing techniques [25].

In the last few decades, electrical power networks have evolved and become more complicated. Therefore, relevant verification methodologies and related test devices have also made their share of progress. Real-time technology provides:

• High-speed processing powers;
• Higher computation capabilities;
• Faster operations.;
• Enhanced performance than other methods.

Compared to simulation studies, these modern technologies can validate newly created procedures where prototyping can considerably improve the entire process. Many simulation assumptions are not applicable in the physical world. Additionally, the simulated model is a simplified representation of the physical system, which means there is no guarantee that the well-optimized model, during simulation, will behave the same way in the field. Such a challenge necessitates more inquiry to match the academic outcomes to the real-world problem, resulting in more sophisticated yet unrealistic solutions [26].

Nowadays, HIL-based verification methodologies have received significant attention from power system researchers [27]. The typical structure of the HIL-based method consists of a real-time controller under investigation and a virtual simulation of the test system [4,28]. Recently, various platforms have been established via HIL, where the most attractive structure was found depending on a field programmable gate array (FPGA), as indicated in [28,29,30,31,32,33]. HIL-based verification methodology produces more tractability and replicability than simulation outcomes. Such advantages encourage researchers to use experimental investigation to validate their developed PSS model [30,34].

On the other hand, the rapid development of electronic chip manufacturing has also led to sophisticated technologies such as RCP. It usually uses a fixed-point processor and can incorporate any digital controller under testing, saving time and effort in the development. Such a technique accelerates the transition stage from research to production [35].

Alternatively, the SIL-based verification procedure utilizes the computational capability of a supercomputer, or vector processor framework, to investigate the developed PSS and the model under investigation on the same framework. SIL does not have any external input/output connections [36]. Modern solutions for experimental verification were adopted in [37], employing the real-time digital simulator platform (RTDS). In this structure, the RCP technology assimilates the newly developed PSS, and the test system under investigation is emulated through a supercomputer with MATLAB/SIMULINK and RTDS. RTDS is an excellent choice for large-scale laboratories and large companies in the power system field.

1.3. Contribution and Paper Organization

This paper gives several contributions to the research field, as described below:

• Proposing an ALO algorithm to optimize the gains of the PID-based PSS that improves the power system stability during real-time constraints;
• Presenting experimental validation of the proposed ALO-based PID-PSS controller via a real-time domain, using the dSPACE electronics environment;
• Several test cases, considering light, nominal, and heavy loadings, are performed, including different step load perturbations and several short circuit faults at various locations;
• The high effectiveness of ALO and MPSO is demonstrated to regain the system’s stability under the three loading conditions;
• The proposed ALO-based PID-PSS controller has a robust performance over the MPSO-based PID-PSS.

The rest of the paper is organized as follows: in Section 2, Single machine infinite bus (SMIB) model; in Section 3, Proposed HIL-Based Experimental Model-based Antlion Optimizer (ALO); in Section 4, Results and Analysis in Section 5, Conclusions.

2. SMIB Model

2.1. Block Diagram

The power system model used in this study is a SMIB. The state-space representation of the SMIB model has been summarized. The synchronous generator of the adopted SMIB model is mathematically represented using a fourth-order equation. Figure 1 shows the block diagram representation of the Heffron–Philips SMIB model [38]. The machine has been described in the direct and quadrature axis, while the field circuit is on the direct axis without damper windings. The SMIB model has been used for designing and calculating the constants of the developed PSS. The detailed technical specs of the SMIB model are listed in [38,39]. In this regard, a workbench MATLAB/SIMULINK dynamic model for PSS performance examination is shown in Figure 2 [39]. It illustrates the dynamic test model used throughout this case study [38]. Its dynamics and operating parameters are adapted to fit the model within the HIL method requirements.

The equations of the linear SMIB model without the proposed PID-PSS: -

$$X_1^{\prime }=-\frac{D}{M}{X}_1-\frac{K_1}{M}{X}_2-\frac{K_2}{M}{X}_3$$

(1)

$$X_2^{\prime }={\omega }_b{X}_1$$

(2)

$$X_3^{\prime }=-\frac{K_4}{T_{do}^{\prime }}{X}_2-\frac{1}{T_{do}^{\prime }{K}_3}{X}_3+\frac{1}{T_{do}^{\prime }}{X}_4$$

(3)

$$X_4^{\prime }=-\frac{K_A{K}_5}{T_A}{X}_2-\frac{K_A{K}_6}{T_A}{X}_3-\frac{1}{T_A}{X}_4$$

(4)

where, states:

$$X=\left[\Delta \omega \hspace{1em}\Delta \delta \hspace{1em}\Delta E_q^{\prime }\hspace{1em}\Delta E_{fd}\right]$$

(5)

The above fifth equations are applied only for optimization. In contrast, the testing process depends on the full dynamics.

2.2. Dynamic Model via dSPACE Electronics Environment

In this section, the experimental application of the developed PSS is accomplished by merging dSPACE and NI-single board in a unique configuration. The dynamic model of the SMIB is implemented on the dSPACE board and communicationally linked with the developed PSS, implemented on the NI SbRIO-9636 board via ADC/DAC port. Both boards have FPGAs inside, and accessible communication between the two is guaranteed. Additionally, the MATLAB/SIMULINK power system model’s configuration parameter is adopted, as shown in Figure 3, to effectively perform the dSPACE parameter for real-time links. The real-time controller and the generator 1 (G1) excitation device connection are adopted using MATLAB RTI blocks. The detailed dynamic model has been discussed in [39]. The dynamic test model parameters with the whole states are described in the Appendix A. This model was designed in MATLAB Simulink and then built in the DSPACE board to be used as the test system.

As shown in Figure 3, the path of the signals in Figure 3 can be illustrated in the following order:

• The block “gain 1” shifts the G1 speed deviation by k;
• Then, the signal is sent to the developed PSS on the NI-sbRIO-9636 through the DAC converter (DS1104DAC_C1) of dSPACE;
• The developed PSS receives the real-time signal from dSPACE through the analog pins of the NI-sbRIO-9636, and then compensates for the shift which retained before analyzing the signal;
• The correction signal was sent back from the PSS after being shifted to the dSPACE through the analog output pin of the NI-SbRIO board;
• The dSPACE analog input received the correction signal using the ADC converter, represented by the block DS1104ADC_C5.

Considering this,

Table 1. The parameter of dSPACE DS1104 controls ports [40].

Parameters	Ports
	8 Parallel DAC Channels One A/D Converter	(ADC1) Multiplexed to Four Channels. Four Parallel A/D	Converters with One Channel Each
Channels	DACH1:DACH8	ADCH1:ADCH4	ADC2:ADC5
Resolution	16-bit	16-bit	12-bit
Conversion time	-	2 µs	800 ns
Settling time	Max. 10 µs	-	-
I/O voltage ranges	±10 V	±10 V	±10 V
Offset error	±1 mV	±5 mV	±5 mV
Gain error	±0.1%	±0.25%	±0.5%
Signal-to-noise ratio (SNR)	>80 dB (At 10 kHz)	>80 dB (At 10 kHz)	>65 dB
Simulink I/O	−1: +1 (Double)	−1: +1 (Double)	−1: +1 (Double)
Offset drift	130 µV/K	40 µV/K	40 µV/K
Gain drift	25 ppm/K	25 ppm/K	25 ppm/K

reports the I/O characteristics of dSPACE ADC/DAC at different ports.

3. Proposed HIL-Based Experimental Model-based Antlion Optimizer (ALO)

3.1. HIL-Based Experimental Model via dSPACE DS1104 and NI SbRIO-9636 Board

Most implemented case studies push the controller to its limits, which cannot be achieved in the natural operation of physical networks. HIL verification methodology evaluates and validates the effectiveness of the developed controllers by running a set of virtual scenarios in a complex system before real-world implementation [41,42]. HIL simulation blends digital simulation’s speed with analog simulation’s real-time nature [41]. It provides many benefits, including shorter development times, the ability to run multiple tests on practical systems, and experience realization without causing damage to equipment [43]. Figure 4 displays the FPGA platforms of the experimental setup, which include dSPACE DS1104 and NI SbRIO-9636 boards.

Figure 4a demonstrates the essential connections between the power system dynamic model embedded on the dSPACE board, and the PSSs prototype embedded into the FPGA board. The dSPACE R&D real-time hardware platform RTI1104 control board is used widely as an obvious choice to test MATLAB/Simulink models in real-time (its specifications and system parameter modification on a Simulink model are described in Appendix A). The DS1104 I/O capabilities in MATLAB Simulink are available through the rtilib1104 library. The DS1104 has a configurable I/O port that can be programmed graphically, by inserting and connecting the blocks in a Simulink block diagram. Once the code designing is finished, according to the main goals, the MATLAB coder generates the model code in the real-time model, which is then compiled and downloaded on the board to achieve the minimum possible time for developing and implementing a digital controller.

Additionally, there are different configurations for National Instrument reconfigurable I/O boards. This paper uses the NI SbRIO-9636 board to assimilate the developed controller under investigation (its technical specifications are described in Appendix A [44]. As shown in Figure 4b, the board is comprised of an ARM architecture 32-bit microprocessor, compelling programable hardware, and a reconfigurable electronic component (FPGA).

3.2. Antlion Optimizer (ALO)

One of the most contemporary algorithms, rooted in nature, created by Mirjalili in 2015, is the Antlion optimization (ALO) technique. The ALO procedure, which imitates the natural hunting behavior of antlions, has been thoroughly surveyed in [45,46], along with a review of how it is applied to tackle optimizing issues in many domains. It shows great superiority, compared to several other algorithms, and validates several mathematical benchmark functions. The ALO method is appropriate for finding the optimal solution and achieving excellent convergence, because it is straightforward to implement, versatile, scalable, and has a sufficient level of exploring and exploiting abilities. As a result, several application fields—including global optimization, picture segmentation, load balancing, feature selection, and renewable energy integration—have been effectively implemented.

The Antlion optimizer was first proposed in 2015 by S. Mirjalili, miming the hunting behavior of antlions in nature [47]. It is mathematically modeled through two crucial phases in its lifecycle: the larval phase and adulthood. A natural lifespan can be up to 3 years, mostly in the larval stage (only 3–5 weeks are spent in adulthood) [47]. The larval stage is simulated where antlions build cone-shaped traps and then hide in the sand, waiting for prey ants. The size of the trap depends on the antlion’s hunger level and the phase which the moon is in at the time. The antlion purposefully throws sand towards the pit edge to slide the prey into the bottom of the hole. When a prey target falls into the pit, it is pulled under the soil and swallowed. After consuming the prey, antlions throw the remains outside the pit and then reconstruct it for the next hunt [48]. They have evolved and adapted this method to improve their chance of survival. Figure 5 depicts the flow chart of the ALO and highlights its mathematical model via five significant steps, as displayed in

Table 2. The ALO algorithm mathematical model.

Equation and Description
The random walking of ants in search of space
$X_{\left(t\right)}=\left[0,cusum\left(2r\left(t_1\right)-1\right),\dots cusum\left(2r\left(t_{max\text{\_}Iter}\right)-1\right)\right]$	(6)
Definition of Stochastic function
$r_{\left(t\right)}=\left\{\begin{array}{c}1ifR>0.5\\ 1ifR\le 0.5\end{array}\right.$	(7)
The normalized random walking of prey in search of space
$X_{i\left(t\right)}=\frac{(X_i^t-a_i)\times (d_i^t-C_i^t)}{{(b_i-a}_i)}+C_i^t$	(8)
The relationship between the random walks of the antlion and the traps
$C_i^t={Antlion}_j^t+C^t$	(9)
$d_i^t={Antlion}_j^t+d^t$	(10)
The prey ants sliding into the mouth of the antlion
$C^t=\frac{C^t}{I}$	(11)
$d^t=\frac{d^t}{I}$	(12)
$I={10}^w\frac{t}{max\text{\_}iter}$	(13)
Capturing the prey and rebuilding the trap in the same position or a new position
${Antlion}_j^t={Ant}_i^{t}iff\left({Ant}_i^t\right)>f\left({Antlion}_j^t\right)$	(14)
Elitism (the fittest antlion of each iteration)
${Ant}_i^t=\frac{R_A^t+R_E^t}{2}$	(15)

, which can be illustrated as follows:

Step 1: The random walking patterns of ants in search of space: it is necessary for the antlion and the ant to engage with one another, as part of the antlion’s hunting behavior. The ants must travel to an area in which they look for food and cover, and this is where the antlions set their traps for the ants. The stochastic ant’s behavior—while they look for food simulated by a random walking pattern—is selected as Equation (6), where t indicates the random walk’s steps; max_Iter addresses the highest numbers of iteration, cusum evaluates the cumulative sum, and $r_{\left(t\right)}$ refers to the stochastics expression specified by Equation (7). R is a random, uniformly distributed number inside the range [0, 1]. Therefore, the normalized random walking pattern is represented in Equation (8) where a_i and b_i show, respectively, related to every variable (i), the lower and higher values of the random walking pattern, and $C_i^t$ and $d_i^t$ symbolize the lowest and the highest values in every iteration (t) related to every variable (i).

Step 2: Traps, established where the fittest antlions with the best chance of capturing prey, are selected through this step. The ALO program uses the roulette wheel to find the fittest antlion during optimization.

Step 3: Ants become caught in nets where the antlion’s traps affect the random walking pattern. Equations (9) and (10) thus represent the formal relationship for this premise. In both equations, the hypersphere of randomly moving ants, around the chosen antlion, is indicated by C and D.

Step 4: Ants move toward the antlion, forcing the ant inside the trap. The sliding motion of an ant into the pit is represented by the two algebraic Equations (11) and (12), where I denotes the ratio specified in Equation (13), t indicates the current iteration, and w represents the constant that depends on the present iteration.

Step 5: This step mimics catching the targeted prey and reconstructing the trap where the antlion captures the ant. Consequently, the hunting process is complete, as described by Equation (14), based on the comparative assessment of their fitness value. In Equation (14), ${Antlion}_j^t$ and ${Ant}_i^t$ stand for, respectively, the positions of the chosen antlion (j) and ant (i). The functions $f\left({Ant}_i^t\right)$ and $f\left({Antlion}_j^t\right)$ demonstrate, respectively, the values of the goal of the ant and the antlion. The antlion then upgrades its location, or builds a new trap to capture a new target.

Step 6: Elitism enables the program to find the best solution at each stage of the refining process. In every iteration of the ALO, the best antlion is located and stored as an elite, since the top selection influences all ant movement throughout rounds. As a result, it is assumed that every ant travels through the selected antlion at random and concurrently, as in Equation (15), where ${Ant}_i^t$ indicates the position of an ant ($i$) in iteration (t); $R_A^t$ refers to the random walking pattern around the chosen antlion in this instance; and $R_E^t$ shows the random walking pattern close to the elite solution. The termination condition of a flowchart, of ALO in Figure 5, is achieved when the number of iterations reaches the maximum number.

3.3. Optimization Process Using the Proposed ALO in Handling the HIL-Based Experimental Model

The two optimization methods, ALO and MPSO, were exploited to optimize the parameters of the PID-PSS for the generator named G1 on the SMIB power system. Equations (16)–(19) demonstrate $J$’s objective function to optimize the PID-PSS gains. All the viewed objective functions have been applied within the two AI optimization tools, while objective $J_2$ provides the best performance with MPSO and $J_4$ gives the best performance with ALO.

$$J_1=\mathit{max}\left\{Real\left({\lambda }_i\right)\right\}$$

(16)

$$J_2=\mathit{min}\left\{\begin{array}{cc}Damping& ratio\end{array}\right\}$$

(17)

$$J_3=ITSE=\underset{0}{\overset{\infty }{\int }}t\left|e^2\left(t\right)\right|dt$$

(18)

$$J_4=ITAE=\underset{0}{\overset{\infty }{\int }}t\left|e\left(t\right)\right|dt$$

(19)

MPSO and ALO optimizes the PID parameters using the four objective functions J’s according to Equations (20)–(22).

$$K_P^{min}\le K_P\le K_P^{max}$$

(20)

$$K_I^{min}\le K_I\le K_I^{max}$$

(21)

$$K_d^{min}\le K_d\le K_d^{max}$$

(22)

The MPSO differs from the original PSO by modifying the search space boundary, which is used as a reflecting wake to reflect the particles into the search and prevent it from going out of the search space. These modifications of the original PSO algorithm improve the algorithm’s overall performance. The author used this method with a PD-based controller to enhance the performance of the PSS [11].

4. Results and Analysis

In this part, the performance of the developed PSS is illustrated. First, the proposed ALO is applied, and its performance is compared to one of the highly effective techniques, modified particle swarm optimization (MPSO). The MPSO technique is an effective modified version of the original PSO algorithm to improve the algorithm’s overall performance, which was first proposed in [49]. In this MPSO, the search space boundary is used as a reflecting wake to exhibit the particles in the search and prevent it from going out of the search space. This effective version has been employed with a PD-based controller to enhance the performance of the PSS [50]. In this study, the upper and lower boundaries of the PID gains are set from −50 to 50 for the two optimization processes. The proposed ALO is applied to tune the PID controller, and

Table 3. The parameters of the ALO.

Parameters	Values
Search agents	40
Maximum no. of iteration	500
Lower bound	−50
Upper bound	50
Best score	Elite antlion fitness
Best position	Elite antlion position

shows the ALO parameters.

Table 4. PID-PSS parameters of the developed ALO and MPSO.

Gains	MPSO-Based PID	Proposed ALO-Based PID *
$K_P$	28.958	42.7423
$K_I$	16.9831	18.9831
$K_D$	12.5603	8.5603

* The proposed PSS.

exhibits the proposed PID-PSS parameters, compared to MPSO.

The ALO is applied by the mentioned parameters in Table 3, on the m-file containing linearized SMIB with PID-PSS, according to the suggested objective function to compute the PSS gains shown in Table 4. Next, the performance is tested experimentally, as mentioned previously. Various case studies adopted optimization algorithms, as summarized in

Table 5. HIL testing map.

Test Types	Operating Conditions
	Light Loading	Nominal Loading	Heavy Loading
Step change 5%	Case No. 1	Case No. 6	Case No. 10
Step change 10%	Case No. 2	Case No. 7	-
Short circuit fault at the beginning of the line	Case No. 3	Case No. 8	Case No. 11
Short circuit fault at the middle of the line	Case No. 4	Case No. 9	Case No. 12
Short circuit fault at the end of the line	Case No. 5	-	-

. Different loading conditions are considered. These conditions are named according to the percentage of loading from light, nominal, and heavy loading conditions. Additionally, twelve distinct scenarios are addressed and evaluated, considering different step changes, single, double, and three-phase short circuits (S. C.) at various transmission line (TL) locations. All the graphs in the following sections were plotted from real-time test results.

4.1. Light Loading

In this case, the light loading condition is considered, and both controllers, previously optimized in the preceding section, are applied. Table 5 shows their impacts on the system, compared to the initial case. The eigenvalues, damping ratio, damped and undamped frequencies, and the synchronizing and damping torque coefficients are tabulated in

Table 6. Eigenvalues and stability parameters of the SMIB with different PSSs during light loading, compared to the initial condition.

Indices	Initial Operating Condition	PSSs
		MPSO-Based PID-PSS	ALO-Based PID-PSS
${\lambda }_1$	−963.6785	−964.2796	−964.0872
${\lambda }_{\mathrm{2,3}}$	0.0142 ± 5.3557i *	−27.2376 ± 21.4542i	−26.9996 ± 16.0385i
${\lambda }_{\mathrm{4,5}}$	−36.7372	−0.7802 ± 4.1830i *	−1.1504 ± 4.5691i *
${\lambda }_6$	0	0	0
${\lambda }_{\mathrm{7,8}}$	0	−20.00	−20.00
$\xi$ in (per unit speed change * MVA/MW)	−0.0027	0.1834	0.2442
${\omega }_n$ in (rad/s)	5.3557	4.2551	4.7117
${\omega }_d$ in (rad/s)	5.3557	4.1830	4.5691
$K_S$ in (per unit torque/rad)	0.6756	0.4265	0.5229
$K_D$ in (per unit torque/per unit speed change)	−0.2102	11.5470	17.0259

* An oscillatory mode.

. The second and third eigenvalues are positive (0.0142 ± 5.3557i), indicating that the system is initially unstable. Using the MPSO and proposed ALO-based PID-PSS controllers, the system achieves acceptable performance where the second and third eigenvalues are transformed to the negative side of (0.7802 ± 4.1830i) and (−1.1504 ± 4.5691i), respectively.

Moreover, the proposed ALO-based PID-PSS boosts the damping ratio and the synchronizing and damping torque more than the modified PSO-based PID-PSS. The natural frequency of the ALO-based PSS was found to be higher than the MPSO–PSS. On the other hand, MPSO-based PSS have a higher damped frequency, compared with ALO-based PSS. Consequently, under light loading conditions, the developed ALO-based PID-PSS is superior and more robust than the modified PSO-based PID-PSS.

The experimental validations are described for each scenario at this loading condition as follows:

4.1.1. Simulation of Case Study No. (1) during Light Loading

In this case, a 5% load step change is considered, where Figure 6 shows its impacts on the controlled machine speed deviation, rotor angle deviation, active power, and voltage at bus 1 (B1). As shown, the proposed ALO-based PID-PSS derives superior stability performance than the modified PSO-based PID-PSS for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1. The developed PSS improves the system stability with the lowest settling time and area under the curve. Furthermore, the adopted optimization algorithm supports the damping of the LFOs faster than the MPSO.

In accompanying those figures, the numerical analysis of the considered objectives is summarized in

Table 7. Performance indices at 5% load step change of case study No. (1) during light loading.

Signal	PSS	ISE	IAE	ITSE	ITAE
$\Delta \mathit{\omega }$ in (per unit)	MPSO-based PID-PSS	5.6141 × 10−8	7.5682 × 10−4	4.0514 × 10−7	7.9489 × 10−3
	Proposed ALO-based PID-PSS	4.2867 × 10−8	6.0334 × 10−4	2.7636 × 10−7	5.8924 × 10−3
	Improvement %	23.64	20.28	31.79	25.87
	Average improvement %	25.4
Δδ in (electrical radian)	MPSO-based PID-PSS	99.2272	73.3638	2722.6478	2002.0799
	Proposed ALO-based PID-PSS	90.7444	67.3441	2298.9890	1695.0494
	Improvement %	8.55	8.21	15.56	15.34
	Average improvement %	11.91
Active Power in (per unit)	MPSO-based PID-PSS	4.8840	1.6280	132.5225	441.7392
	Proposed ALO-based PID-PSS	4.4999	1.4999	112.5009	375.0011
	Improvement %	7.87	7.87	15.11	15.11
	Average improvement %	11.49
Positive Voltage B1 in (per unit)	MPSO-based PID-PSS	55.1833	54.7230	1496.6154	1484.4879
	Proposed ALO-based PID-PSS	50.8451	50.4205	1270.5249	1260.2205
	Improvement %	7.86	7.86	15.11	15.11
	Average improvement %	11.48

. From this table, regarding the ISE performance measures, the proposed ALO-based PID-PSS has a much lower value than the modified PSO-based PID-PSS, with the improvement of 23.64%, 8.55%, 7.87%, and 7.86% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively.

Similar findings are obtained, considering the IAE performance measures, the proposed ALO-based PID-PSS has a much lower value than the modified PSO-based PID-PSS with the improvement of 20.28%, 8.21%, 7.87%, and 7.86% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively. Additionally, considering the ITSE performance measures, the proposed ALO-based PID-PSS has a much lower value than the modified PSO-based PID-PSS, with the improvement of 31.79%, 15.56%, 15.11%, and 15.11% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively. Considering the ITAE performance measures, the proposed ALO-based PID-PSS has a much lower value than the modified PSO-based PID-PSS with the improvement of 25.87%, 15.34%, 15.11%, and 15.11% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively.

The developed PSS has the smallest ISE, IAE, ISAE, and ITAE, compared with the MPSO. On average, the proposed ALO-based PID-PSS has much lower objective metrics than the modified PSO-based PID-PSS, with an improvement of 25.4%, 11.91%, 11.49%, and 11.48% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively.

4.1.2. Case Study No. (2) during Light Loading

Similar to case No. 1, a 10% load step change has been considered. A significant load change directly affects the speed deviation, rotor angle deviation, active power, and voltage on bus B1 of the controlled machine.

Table 8. Performance indices at 10% load step change of case study No. (2) during light loading.

Signal	PSS	ISE	IAE	ITSE	ITAE
$\Delta \mathit{\omega }$ in (per unit)	MPSO-based PID-PSS	1.8618 × 10−7	1.2599 × 10−3	1.2429 × 10−6	1.2518 × 10−2
	Proposed ALO-based PID-PSS	1.4160 × 10−7	9.7225 × 10−4	8.3481 × 10−7	8.9427 × 10−3
	Improvement %	23.94	22.83	32.83	28.56
	Average improvement %	27.04
Δδ in (electrical radian)	MPSO-based PID-PSS	99.6772	73.5034	2751.3496	2012.3675
	Proposed ALO-based PID-PSS	90.8837	67.3758	2318.1264	1701.8895
	Improvement %	8.82	8.34	15.75	15.43
	Average improvement %	12.08
Active Power in (per unit)	MPSO-based PID-PSS	4.8842	16.2799	132.5242	441.7405
	Proposed ALO-based PID-PSS	4.5002	14.9997	125.0260	375.0021
	Improvement %	7.862	7.864	5.658	15.108
	Average improvement %	9.12
Positive Voltage B1 in (per unit)	MPSO-based PID-PSS	55.1986	54.7304	1496.4318	1484.3961
	Proposed ALO-based PID-PSS	50.8609	50.4281	1270.3843	1260.1499
	Improvement %	7.858	7.861	15.106	15.107
	Average improvement %	11.48

summarizes the effects of step load change, using step information performance indices on the PSS to show the robustness of the adopted optimization tools.

As shown, the proposed ALO-based PID-PSS has much lower objective metrics than the modified PSO-based PID-PSS, with an average improvement of 27.04%, 12.08%, 9.12%, and 11.48% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively.

4.1.3. Case Study No. (3) during Light Loading

In this case, a 3-phase S.C. is considered at the sending end of the TL at a time of 5 s. The fault lasts for five cycles. Figure 7 reveals the performance of the PSS to this stern test. The proposed ALO-based PID-PSS reduces the oscillation and makes the system regain the same equilibrium point faster than the MPSO-based PSS.

Table 9. Performance indices at three-phase S.C. at the sending end of the TL of case study No. (3) during light loading.

Signal	PSS	ISE	IAE	ITSE	ITAE
$\Delta \mathit{\omega }$ in (per unit)	MPSO-based PID-PSS	1.04 × 10−5	1.05 × 10−2	8.71 × 10−5	1.18 × 10−1
	Proposed ALO-based PID-PSS	8.97 × 10−6	9.21 × 10−3	6.95 × 10−5	9.85 × 10−2
	Improvement %	13.62	12.42	20.25	16.88
	Average improvement %	15.79
Δδ in (electrical radian)	MPSO-based PID-PSS	132.1931	82.1348	3055.509	2090.912
	Proposed ALO-based PID-PSS	136.3286	80.0167	2841.141	1850.655
	Improvement %	−3.13	2.58	7.02	11.49
	Average improvement %	4.49
Active power in (per unit)	MPSO-based PID-PSS	4.9663	16.3013	132.947	441.8534
	Proposed ALO-based PID-PSS	4.5831	15.0222	112.9271	375.116
	Improvement %	7.716	7.847	15.059	15.104
	Average improvement %	11.43
Positive voltage B1 in (per unit)	MPSO-based PID-PSS	54.8311	54.4937	1493.386	1482.835
	Proposed ALO-based PID-PSS	50.5184	50.2043	1267.963	1258.669
	Improvement %	7.865	7.871	15.095	15.117
	Average improvement %	11.49

summarizes the performance indices related to the three-phase S.C. at the beginning of the TL. As shown, the proposed ALO-based PID-PSS has much lower objective metrics than the modified PSO-based PID-PSS, with an average improvement of 15.79%, 4.49%, 11.43%, and 11.49% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively.

4.1.4. Case Study No. (4) during Light Loading

In this case, a single-phase S.C. to the ground occurred in the middle of the TL.

Table 10. Performance indices at single-phase S.C. to ground at the middle of the line of case study No. (4) during light loading.

Signal	PSS	ISE	IAE	ITSE	ITAE
$\Delta \mathit{\omega }$ in (per unit)	MPSO-based PID-PSS	4.94 × 10−6	7.28 × 10−3	4.22 × 10−5	8.25 × 10−2
	Proposed ALO-based PID-PSS	4.06 × 10−6	6.23 × 10−3	3.20 × 10−5	6.70 × 10−2
	Improvement %	17.82	14.43	24.24	18.74
	Average improvement %	18.81
Δδ in (electrical radian)	MPSO-based PID-PSS	122.3997	80.097	2960.332	2072.018
	Proposed ALO-based PID-PSS	122.4022	76.8583	2678.378	1812.301
	Improvement %	0.00	4.04	9.52	12.53
	Average improvement %	6.53
Active power in (per unit)	MPSO-based PID-PSS	4.8865	16.2812	132.5237	441.7258
	Proposed ALO-based PID-PSS	4.5029	15.0019	112.5045	374.9918
	Improvement %	7.850	7.858	15.106	15.108
	Average improvement %	11.48
Positive voltage B1 in (per unit)	MPSO-based PID-PSS	54.9084	54.5824	1494.37	1483.347
	Proposed ALO-based PID-PSS	50.5927	50.2913	1268.54	1259.168
	Improvement %	7.860	7.862	15.112	15.113
	Average improvement %	11.49

summarizes performance indices of the developed PSS based on adopted optimization tools to show the robustness of the developed method. As shown, the proposed ALO-based PID-PSS has much lower objective metrics than the modified PSO-based PID-PSS, with an average improvement of 18.81%, 6.53%, 11.48%, and 11.49% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively.

4.1.5. Case Study No. (5) during Light Loading

In this case, a three-phase S.C. to ground fault occurred at the end of the TL.

Table 11. Performance indices at three-phase S.C. to ground fault at the end of the line of case study No. (5) during light loading.

Signal	PSS	ISE	IAE	ITSE	ITAE
$\Delta \mathit{\omega }$ in (per unit)	MPSO-based PID-PSS	4.8497 × 10−6	7.0375 × 10−3	3.9695 × 10−5	7.8472 × 10−2
	Proposed ALO-based PID-PSS	4.2507 × 10−6	6.1757 × 10−3	3.2162 × 10−5	6.5195 × 10−2
	Improvement %	12.35	12.25	18.98	16.92
	Average improvement %	15.12
Δδ in (electrical radian)	MPSO-based PID-PSS	117.9186	78.9027	2902.6561	2054.6824
	Proposed ALO-based PID-PSS	116.7623	75.3083	2600.7211	1788.6808
	Improvement %	0.98	4.56	10.40	12.95
	Average improvement %	7.22
Active Power in (per unit)	MPSO-based PID-PSS	4.9262	16.2894	132.7317	441.7767
	Proposed ALO-based PID-PSS	4.5425	15.0098	112.7113	375.0399
	Improvement %	7.789	7.855	15.083	15.106
	Average improvement %	11.46
Positive Voltage B1 in (per unit)	MPSO-based PID-PSS	54.9541	54.5859	1495.1461	1483.6358
	Proposed ALO-based PID-PSS	50.6308	50.2909	1269.0789	1259.3816
	Improvement %	7.867	7.868	15.120	15.115
	Average improvement %	11.49

summarizes the system response to this fault using performance measures. As illustrated, the performance indices emphasize the robustness of the proposed PSS, compared with the MPSO-based PSS since it has a smaller ISE, IAE, ITSE, and ITAE than the other assessed PSS. The proposed ALO-based PID-PSS has much lower objective metrics than the modified PSO-based PID-PSS, with an average improvement of 15.12%, 7.22%, 11.46%, and 11.49% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively.

4.2. Nominal Loading

The nominal loading situation is considered in this instance, and both previously optimized controllers are used.

Table 12. Eigenvalues and stability parameters of the SMIB with different PSSs during Nominal loading.

Indices	Normal Operating Condition	PSSs
		MPSO-Based PID-PSS	ALO-Based PID-PSS
${\lambda }_1$	−966.47668	−968.1181	−967.5935
${\lambda }_{\mathrm{2,3}}$	0.1646 $\pm$ 5.5081i *	−25.0930 $\pm$ 38.1149i	−24.4835 $\pm$ 30.2602i
${\lambda }_{\mathrm{4,5}}$	−34.2399	−1.0417 $\pm$ 3.1403i *	−1.9135 $\pm$ 3.3986i *
${\lambda }_6$	0	−20.00	−20.00
${\lambda }_{\mathrm{7,8}}$	0	0	0
$\xi$ in (per unit speed change * MVA/MW)	−0.0290	0.3148	0.4906
${\omega }_n$ in (rad/s)	5.5123	3.3086	3.9003
${\omega }_d$ in (rad/s)	5.5100	3.1403	3.3986
$K_S$ in (per unit torque/rad)	0.7157	0.2578	0.3583
$K_D$ in (per unit torque/per unit speed change)	−2.3680	15.4172	28.3198

* An oscillatory mode.

compares their effects on the system to the original model and displays the results. The fact that the second and third eigenvalues are positive (0.1646 $\pm$ 5.5081i), as shown, implies that the system is inherently unstable. The system obtains adequate performance when the second and third eigenvalues are transformed to the negative side of (−25.0930 ± 38.1149i) and (−24.4835 ± 30.2602i), respectively, using the MPSO and proposed ALO-based PID-PSS controllers.

4.2.1. Case Studies No. (6) and (7) during Nominal Loading

The first 2 cases in this loading condition consider 5% and 10% load changes, respectively. The impacts of the proposed ALO-based PID-PSS and the modified PSO-based PID-PSS are assessed on the controlled machine using speed deviation, rotor angle deviation, active power, and voltage at bus 1 (B1). Figure 8 displays the valuable improvement percentages of the proposed ALO controller versus MPSO. As shown, the proposed ALO-based PID-PSS has much lower objective metrics than the modified PSO-based PID-PSS with an average improvement of 33.57%, 11.69%, 11.49%, and 11.48% at 5% step load change, and 17.76%, 6.51%, 11.48%, and 11.49% at 10% step load change for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively.

4.2.2. Case Study No. (8) during Nominal Loading

In this case, a double-line-to-ground fault at the sending end of the TL is considered. The performance indices are calculated and summarized in

Table 13. Performance indices at double-line to ground fault at the sending end of the line of case study (8) during nominal loading.

Signal	PSS	ISE	IAE	ITSE	ITAE
$\Delta \mathit{\omega }$ in (per unit)	MPSO-based PID-PSS	3.0812 × 10−5	1.4898 × 10−2	2.2519 × 10−4	1.3995 × 10−1
	Proposed ALO-based PID-PSS	2.6185 × 10−5	1.2706 × 10−2	1.7327 × 10−4	1.1421 × 10−1
	Average improvement %	17.79
Δδ in (electrical radian)	MPSO-based PID-PSS	73.4539	59.6633	1612.1012	1505.4544
	Proposed ALO-based PID-PSS	79.4138	59.5458	1541.2948	1347.6912
	Average improvement %	1.74
Active Power in (per unit)	MPSO-based PID-PSS	49.0806	51.5533	1329.4346	1398.8343
	Proposed ALO-based PID-PSS	45.2330	47.5007	1128.6774	1187.5008
	Average improvement %	11.48
Positive Voltage B1 in (per unit)	MPSO-based PID-PSS	53.7099	53.9568	1460.3439	1466.2232
	Proposed ALO-based PID-PSS	49.8328	49.7099	1239.6082	1244.6283
	Average improvement %	11.33

. The performance indices clearly show the superiority of the developed PSS, compared with the conventional PSS. This conclusion is based on the performance indices that are lower in the case of the proposed PSS. The proposed ALO-based PID-PSS has much lower objective metrics than the modified PSO-based PID-PSS, with an average improvement of 17.79%, 1.74%, 11.48%, and 11.33% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively.

4.2.3. Case Study No. (9) during Nominal Loading

Likewise, the double-line-to-ground fault is addressed in this case study. The fault is initiated at 5 s in the middle of the TL. Figure 9 shows the speed deviation, rotor angle deviation, active power, and B1 positive sequence voltage. As shown, the four signals emphasize the significant impact of the developed PSS to dampen the LFO better than the modified PSO-based PSS. In accompanying those figures, the numerical analysis of the considered objectives is summarized in

Table 14. Performance indices at double-phase S.C. on the middle of the line of case study No. (9) during nominal loading.

Signal	PSS	ISE	IAE	ITSE	ITAE
$\Delta \mathit{\omega }$ in (per unit)	MPSO-based PID-PSS	2.10 × 10−5	1.23 × 10−2	1.54 × 10−4	1.15 × 10−1
	Proposed ALO-based PID-PSS	1.74 × 10−5	1.03 × 10−2	1.15 × 10−4	9.19 × 10−2
	Average improvement %	19.72
Δδ in (electrical radian)	MPSO-based PID-PSS	68.7602	58.5991	1569.719	1495.881
	Proposed ALO-based PID-PSS	72.115	57.6263	1463.141	1325.248
	Average improvement %	3.74
Active Power in (per unit)	MPSO-based PID-PSS	49.0306	51.5537	1329.163	1398.829
	Proposed ALO-based PID-PSS	45.1818	47.5008	1128.402	1187.496
	Average improvement %	11.48
Positive Voltage B1 in (per unit)	MPSO-based PID-PSS	53.7112	53.9735	1460.347	1466.309
	Proposed ALO-based PID-PSS	49.4829	49.7257	1239.607	1244.711
	Average improvement %	11.49

. From this table, the proposed ALO-based PID-PSS has much lower objective metrics than the modified PSO-based PID-PSS, with an average improvement of 19.72%, 3.74%, 11.48%, and 11.49% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively.

4.3. Heavy Loading

The third and final step toward validating the robustness of the developed PSS covers the heavy loading condition. Both previously adjusted controllers are used.

Table 15. Eigenvalues and stability parameters of the SMIB with different PSSs during heavy loading.

Indices	Heavy Loading Condition	PSSs
		MPSO-Based PID-PSS	ALO-Based PID-PSS
${\lambda }_1$	−966.7365	−968.4387	−967.8947
${\lambda }_{\mathrm{2,3}}$	0.1843 $\pm$ 5.5145i *	−24.9295 $\pm$ 38.8812i	−24.3121 $\pm$ 30.9152i
${\lambda }_{\mathrm{4,5}}$	−34.0196	−1.0449 $\pm$ 3.0970i *	−1.9342 $\pm$ 3.3408i *
${\lambda }_6$	0	−20.00	−20.00
${\lambda }_{\mathrm{7,8}}$	0	0	0
$\xi$ in (per unit speed change MVA/MW)	−0.0334	0.3197	0.5010
${\omega }_n$ in (rad/s)	5.5176	3.2685	3.8603
${\omega }_d$ in (rad/s)	5.5145	3.0970	3.3408
$K_S$ in (per unit torque/rad)	0.7171	0.2516	0.3510
$K_D$ in (per unit torque/per unit speed change)	−2.7276	15.4645	28.6262

* An oscillatory mode.

compares their effects on the system to the original instance and displays the results. The fact that the second and third eigenvalues are positive (0.1843 ± 5.5145i), as shown, implies that the system is inherently unstable. The system obtains adequate performance when the second and third eigenvalues are transformed to the negative side of (−24.9295 ± 38.8812i) and (−24.3121 ± 30.9152i), respectively, using the MPSO and proposed ALO-based PID-PSS controllers.

4.3.1. Case Study No. (10) during Heavy Loading

The load step change disturbance is applied in this case, where 5% of the load is suddenly added after 4.1 s. Figure 10 shows the controlled machine speed deviation, rotor angle deviation, active power, and the bus B1 system response voltage in this case study. This figure reveals that the system’s response to the proposed PSS has a shorter settling time, oscillation range, area under the curve, and higher rise time than the other PSS. In this regard,

Table 16. Performance indices at three-phase S.C.-to-ground fault at the end of the line of case study no. (10) during light loading.

Signal	PSS	ISE	IAE	ITSE	ITAE
$\Delta \mathit{\omega }$ in (per unit)	MPSO-based PID-PSS	4.8497 × 10−6	7.0375 × 10−3	3.9695 × 10−5	7.8472 × 10−2
	Proposed ALO-based PID-PSS	4.2507 × 10−6	6.1757 × 10−3	3.2162 × 10−5	6.5195 × 10−2
	Improvement %	12.35	12.25	18.98	16.92
	Average improvement %	15.12
Δδ in (electrical radian)	MPSO-based PID-PSS	117.9186	78.9027	2902.6561	2054.6824
	Proposed ALO-based PID-PSS	116.7623	75.3083	2600.7211	1788.6808
	Improvement %	0.98	4.56	10.40	12.95
	Average improvement %	7.22
Active Power in (per unit)	MPSO-based PID-PSS	4.9262	16.2894	132.7317	441.7767
	Proposed ALO-based PID-PSS	4.5425	15.0098	112.7113	375.0399
	Improvement %	7.789	7.855	15.083	15.106
	Average improvement %	11.46
Positive Voltage B1 in (per unit)	MPSO-based PID-PSS	54.9541	54.5859	1495.1461	1483.6358
	Proposed ALO-based PID-PSS	50.6308	50.2909	1269.0789	1259.3816
	Improvement %	7.867	7.868	15.120	15.115
	Average improvement %	11.49

summarizes the system response to this fault using the performance measures.

As illustrated, the performance indices emphasize the robustness of the proposed PSS, compared with the MPSO-based PSS, since it has a smaller ISE, IAE, ITSE, and ITAE than the other assessed PSS. The proposed ALO-based PID-PSS has much lower objective metrics than the modified PSO-based PID-PSS, with an average improvement of 15.12%, 7.22%, 11.46%, and 11.49% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively.

4.3.2. Case Study No. (11) during Heavy Loading

In this case, a three-line-to-ground fault has been applied to evaluate the robustness of the proposed PSS. The fault has been involved at the sending end of the TL. The performance indices of this case study are reported in

Table 17. Performance indices at three-phase S.C.-to-ground fault at the end of the line of case study no. (11) during light loading.

Signal	PSS	ISE	IAE	ITSE	ITAE
$\Delta \mathit{\omega }$ in (per unit)	MPSO-based PID-PSS	3.61 × 10−5	1.39 × 10−2	2.38 × 10−4	1.27 × 10−1
	Proposed ALO-based PID-PSS	3.35 × 10−5	1.22 × 10−2	2.05 × 10−4	1.06 × 10−1
	Average improvement %	12.28
Δδ in (electrical radian)	MPSO-based PID-PSS	64.1097	56.4723	1466.215	1443.575
	Proposed ALO-based PID-PSS	68.3277	55.8618	1382.389	1284.358
	Average improvement %	2.81
Active Power in (per unit)	MPSO-based PID-PSS	54.4781	54.2652	1473.608	1472.48
	Proposed ALO-based PID-PSS	50.2158	49.9989	1251.161	1250.018
	Average improvement %	11.47
Positive Voltage B1 in (per unit)	MPSO-based PID-PSS	53.6238	53.8894	1457.186	1464.516
	Proposed ALO-based PID-PSS	49.4051	49.6465	1236.963	1243.178
	Average improvement %	11.49

. As can be seen, the proposed PSS enhances the overall system stability more than the modified PSO-based PID-PSS. The proposed ALO-based PID-PSS has much lower objective metrics than the modified PSO-based PID-PSS, with an average improvement of 12.28%, 2.81%, 11.47%, and 11.49% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively.

4.3.3. Case Study No. (12) during Heavy Loading

To fully assess the resilience of the optimized PSS, a three-line-to-ground fault is planned to occur in the center of the TL. Five cycles of the test are conducted. The deviations of the governed machine speed, the rotary angle, the active power, and the voltage are shown in Figure 11 for bus B1. This finding confirms the results of the other case studies in this work. In contrast to the modified PSO-based PID PSS, Figure 11 demonstrates that the system responses, using the suggested PSS, have superior performance.

To emphasize the amount of participation of the optimized controller, Figure 12 displays the performance metrics of both MPSO-based PID-PSS and the proposed ALO-based PID-PSS controllers. As shown in Figure 12, with an average increase of 10.73%, 8.86%, 11.48%, and 11.49% for stabilizing the machine speed deviation, rotor angle deviation, active power, and voltage at B1, respectively, the suggested ALO-based PID-PSS has significantly lower objective metrics than the modified PSO-based PID-PSS.

5. Conclusions

This paper proposed an advanced, ALO-based PID-PSS to improve the power system stability. In this study, the adoption of powerful optimization tools, in combination with hardware-in-the-loop (HIL), provides real-time experimental validation. The developed PSS, via the ALO algorithm, has complied with a reconfigurable input/output single-board (SbRIO-9636), made by the National Instrument considering software package, MATLAB/SIMULINK. A total of 12 case studies were simulated under different loading conditions and disturbances to ensure the robustness and effectiveness of the developed ALO-based PID-PSS over the MPSO-based PID-PSS. Under the various loading conditions, the proposed ALO-based PID-PSS successfully demonstrated a high ability to regain power system stability.

Several disturbances were investigated, which were symmetrical and unsymmetrical faults, different fault locations, and step load changes. The performance indices of ALO-based PID-PSS and MPSO-based PID-PSS were compared to assess the developed PSS’s superiority under all test cases. The comparison results showed that the developed PSS improved the rise time, settling time, oscillation range, and the area under the curve for all cases by 22.031%, 12.894%, 19.859%, and 267.849%, respectively. The average scores of ISE, IAE, ITSE, and ITAE were 30.919%, 23.295%, 51.073%, and 53.624%, respectively.

The current study tested ALO’s ability to produce PSS which is able improve the power system stability through real-time constraints. The valuable part of this paper is that the system is configured with low-cost electronics boards, which is a new development in HIL tests, since existing HIL tests depend on costly real-time digital simulator systems or costly boards and high-speed, high-cost computers. However, one of the disadvantages of ALO is that it may become caught in premature convergence. The ALO technique in this paper was developed to handle the problem of PSS design, via a PID-based controller, to improve the power system stability of a single machine infinite bus model. The assessment of the ALO algorithm is compared to one of the improved and efficient versions of PSO technique. The applications show the significant performance of the ALO in solving the considered problems. Additionally, experimental validations, through the DSPACE electronics environment, using several scenarios of fault types and locations, provides great validation of the ALO in solving the considered problems.

The authors currently study how the current system can test the system with a higher number of generators, which may be a significant challenge with the same boards—especially the DSPACE board—since it runs the system in real time. This issue needs more investigation and work, which may depend on the cost of the system components.