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Abstract

To stabilize frequency in a power system, this research study suggests a novel modified Gorilla Troops Optimizer (mGTO) technique, which builds on the original technique, and offers notable gains in effectiveness and efficiency when solving real-world optimization problems. A thorough comparative analysis reveals that the mGTO algorithm is the best option, outperforming its counterparts in terms of stability and overall performance. Interestingly, mGTO performs better than any of its competitors in terms of stability, making it the best option. The mGTO algorithm significantly reduces implementation time and enhances solution quality compared to the conventional GTO algorithm. A new linearized Phillips–Heffron model with an IPFC was developed to investigate power systems’ stability. To effectively dampen low-frequency oscillations, an auxiliary controller for modeling the IPFC is proposed. It provides four options for damping controllers, and the recommended mGTO algorithm is used to adjust the controller parameters. This method is superior to traditional controllers in stability control and has undergone extensive validation. It is a crucial instrument for controlling the frequency of an SMIB power system based on IPFC. Based on the simulation results, the updated strategy that has been suggested is the most effective way to define the mentioned damping controller by considering the percentage improvement in the goal function value.

Keywords

Power system oscillations modified Gorilla Troops Optimizer algorithm (mGTO)flexible AC transmission systems (FACTS)interline power flow controller (IPFC)damping controller benchmark functions

Introduction

Low-frequency oscillations are observed when relatively weak tie lines link large power networks. Until the synchronism loss occurs, these oscillations’ size may rise (Kundur, 1994). Flexible AC transmission systems (FACTS) devices have emerged as a viable concept for power system applications over the last decade due to the rapid and constant advancement of power electronics technology (Sahoo et al., 2023). Within the FACTS family, the IPFC is considered one of the most adaptable gadgets (Ahmed et al., 2022). In addition to providing voltage support and reducing system oscillation, this device also regulates the power flow of the line (Prakash et al., 2023). The IPFC uses two or more VSCs that share a DC link. Every VSC can exchange reactive power with its gearbox system and offer a range of compensation for the chosen line in the gearbox system (Singh and Singh, 2022).

The efficacy of FACTS-based damping controllers in enhancing system stability is intimately linked to their performance (Banaei and Kami 2011). Therefore, numerous control techniques have been proposed to optimize the performance of these FACTS-based controllers (Dhurvey and Chandrakar 2016). Countless trials have shown how IPFC affects power system stability using various controllers. The IPFC controllers were designed using fuzzy logic and artificial neural networks (Naga Sai Kalyan and Rao, 2016). The damping control approach, which uses a fuzzy logic controller that is not ideal, causes the unexplainable settling time of the system's reaction, as explained in (Bento, 2020). Additionally, a certain amount of trial and error is necessary when modifying the initial values of this controller (Kazemi and Karimi 2006; Rajbongshi and Saikia, 2019). To lessen interarea oscillations, a PI supplemental damping controller for the IPFC has been suggested; however, the controller settings have not been optimized (Khan et al., 2024; Martins et al., 2017).

The power system utilities choose a typical lead-lag controller structure due to its ease of online tuning, and other adaptive or variable structure solutions do not guarantee stability (Kumar and Rajan, 2024; Sahu et al., 2022). The Phillips–Heffron linear model has been a standard for small signal stability investigations of power systems for many years (Agrawal et al., 2023; Farhang and Mazlumi, 2014), and tuning the controller parameters is a challenging task (Khadanga et al., 2024). Numerous traditional methods, including the gradient approach for optimization, Eigenvalue assignment, mathematical programming, and current control theory, have been documented in the literature (Aref et al., 2023). Regretfully, the traditional methods take a long time since they are iterative, computationally demanding, and have a slow convergence rate (Singh et al., 2023). Another way to address the stability difficulties is to employ nature-inspired algorithms (NIAs) (Ustun, 2023). Effective NIA applications for power system problems include the Grasshopper Optimization Algorithm (Srivastava et al., 2022), Flower Pollination optimization (Hussain et al., 2020), Sine cosine algorithm (Latif et al., 2021), African Vulture Optimization (Nayak et al., 2023), Particle swarm optimization (Abdolrasol et al., 2023), satin bowerbird optimization (Farooq et al., 2022), drone squadron optimization (Mazumdar et al., 2024), artificial bee colony (Singh et al., 2021a), Chaotic Evolutionary programming (Singh et al., 2021b), Shuffled frog-leaping optimization algorithm (Khadanga and Panda, 2022), COVID-19-based optimization Algorithm (Safiullah et al., 2022), and others. Despite their success in power system design, these approaches usually have a disadvantage: they often become trapped in local optima and have a slow rate of convergence.

In the field of optimization, a novel technique called Gorilla Troops Optimizer (GTO) algorithm has recently acquired popularity. Numerous optimization difficulties have been addressed by this approach, which has been widely used (Patil et al., 2022). The GTO algorithm is not without its limits, despite its wide range of applications. The GTO algorithm's vulnerability to local minima is one of its main problems (Mostafa et al., 2023; Natarajan et al., 2022). Therefore, to overcome the constraints above constraints, the GTO algorithm is improved by modifications, leading to the creation of the modified Gorilla Troops Optimizer (mGTO) algorithm. With these modifications, the algorithm should operate more efficiently and be able to overcome issues like local minima, providing a stronger and more reliable optimization tool.

Motivation research gap and paper organization

Research gap

The following are the main conclusions drawn from the literature review indicated above:

The impact of the modified Philips–Heffron technique on an SMIB power system equipped with IPFC has hardly been studied.

The lead-lag controller for the IPFC-based SMIB power system is not being executed, as far as the author is aware.

The traditional GTO algorithm has many drawbacks that must be modified to achieve a better effect.

Motivation

The analyzed literature concludes that numerous holes still need to be filled for the SMIB power system to operate consistently. Therefore, it is imperative to spearhead a top-to-bottom focus on frequency support for various system components. Motivated by the circumstances, a unique approach is implemented to examine the dynamic performances of an IPFC-based SMIB power system: the lead-lag damping controller. Like how a system tuned using an advanced improvement technique can ensure promising results for controlling complex power systems is planned using a recently mGTO algorithm. The optimal tuning of the lead-lag controller boundaries has been achieved using the proposed mGTO.

Innovations

The key innovations of the paper are summarized as follows:

The Modified Heffron–Phillips modeling of an SMIB power system with IPFC has been developed.

The impact of a lead-lag controller in the said system is examined.

It has been demonstrated that the suggested lead-lag controller, built with the recently determined modified GTO computation, provides better frequency regulation than several other controllers.

By considering a few benchmark functions, the advantages of the proposed method over several alternative approaches are also evaluated in terms of operation time.

Paper organization

This paper is divided into six primary sections for the remaining portion. “Motivation research gap and paper organization” section describes the idea behind the research in terms of the research gap and Motivation, while “System under study” section presents the modeling of the IPFC in an SMIB power system. “Problem formulation” section describes the objective function and the IPFC controller's structure. “Modified artificial GTO algorithm” section provides an overview of the GTO and mGTO optimization techniques. “Simulation results with discussions” section explains the findings, and last section offers “Conclusions.”

System under study

This study considers an SMIB power system equipped with an IPFC, as seen in Figure 1.

Figure 1.

IPFC-based SMIB power system.

Linearized equations

The nonlinear equations can be linearized around an operational condition to provide these system linear equations which can be expressed as (Prakash et al., 2023): $\overset{∙}{Δ δ} = ω_{0} Δ ω$ (1) $Δ ω^{∙} = \frac{(Δ P_{m} - Δ P_{e} - D Δ ω)}{M}$ (2) $Δ \overset{∙}{E^{'} = \frac{(- Δ E_{q} + Δ E_{f d})}{T_{d o}^{'}}}$ (3) $Δ E_{f d}^{∙} = \frac{- Δ E_{f d} + K_{A} (Δ V_{r e f} - Δ V_{t})}{T_{A}}$ (4) $Δ V_{d c}^{∙} = K_{c δ e} Δ δ_{E} + K_{c δ b} Δ δ_{B} + K_{7} Δ δ + K_{c e} Δ m_{E} + K_{c b} Δ m_{B} + K_{8} Δ E_{q}^{'} - K_{9} Δ V_{d c}$ (5)where $Δ P_{e} = K_{p δ 2} Δ δ_{2} + K_{1} Δ δ + K_{p d} Δ V_{d c} + K_{p 1} Δ m_{1} + K_{p δ 1} Δ δ_{1} + K_{p 2} Δ m_{2} + K_{2} Δ E_{q}^{'}$ $Δ E_{q}^{'} = K_{q δ 2} Δ δ_{2} + K_{4} Δ δ + + K_{q d} Δ V_{d c} + K_{q δ 1} Δ δ_{1} + K_{q 2} Δ m_{2} + K_{3} Δ E_{q}^{'} + K_{q 1} Δ m_{1}$ $Δ V_{s} = K_{6} Δ E_{q}^{'} + K_{v 1} Δ m_{1} + K_{v δ 1} Δ δ_{1} + K_{v δ 2} Δ δ_{2} + K_{v d} Δ V_{d c} + K_{5} Δ δ + K_{v 2} Δ m_{2}$ $Δ V_{d c} = K_{c δ 2} Δ δ_{2} + K_{8} Δ E_{q}^{'} - K_{9} Δ V_{d c} + K_{c 1} Δ m_{1} + K_{c 2} Δ m_{2} + K_{7} Δ δ + K_{c δ 1} Δ δ_{1}$ Figure 2 displays the block diagram model of the SMIB power system installed with IPFC where m₁, δ₁, m₂, and δ₂ are the input control signals.

Figure 2.

IPFC-based modified Heffron–Phillips model.

Problem formulation

Controller structure

This study uses the widely known lead-lag structure as the IPFC-based extradamping controller, as shown in Figure 3 (Khan et al., 2024). The said structure comprises three blocks as phase correction block with T₁, and T₂ as time constants; gain block (K_s); and the signal washout block (Ahmed et al., 2022). The gain block comes first, giving the controller the proper gain. Next is the phase compensation block. This block compensates for the phase lag between the input and output signals from the controller, helping to provide the required phase lead. The final component is a high-pass filter called a signal washout block. This screen allows the signals that are connected to the input oscillations signal to flow through it without any changes. The change in the control vector is the output, while the speed deviation is the input signal. The literature study suggests that the washout time constant for the controller can be varied between 1 and 20, and for the proposed research, it is taken as 10. Once the controller gets K_T, it is necessary to determine the controller constants T₁ and T₂.

Figure 3.

Damping controller structure.

Objective function

The objective function J in the current study is an ITAE error of the speed deviations, which is represented as Rai and Das (2022): $J = \int_{0}^{t_{1}} t | e (t) | d t$ (6)where t₁ is the simulation's time range and “e” is the error signal (Δω). Gorilla Troops Optimizer and mGTO are used to determine the damping controller's parameters.

The objective function can be expressed as a design problem and is assessed in a bounded region as Khadanga et al. (2024):

Minimize J

Subject to $K_{i}^{X} \leq K_{i} \leq K_{i}^{Y}$

$T_{1}^{X} \leq T_{1} \leq T_{1}^{Y}$ $T_{2}^{X} \leq T_{2} \leq T_{2}^{Y}$ where the temporal constants T₁^X and T₁^Y represent the lower and upper boundaries for the damping controller, respectively, and K_i^X and K_i^Y represent the lower and upper bounds of the gains. The controller's parameters are obtained using the GTO and the proposed mGTO techniques mentioned above.

Modified artificial GTO algorithm

Artificial GTO algorithm

The group behaviors seen in gorillas serve as an inspiration for the GTO algorithm. This clever program uses signals from the relationships and behaviors of gorilla battalions to create an optimization strategy that is effective and flexible. The main benefit of the GTO algorithm is its ease of use in engineering applications. The gorilla tracking approach (GTO) is divided into three main segments: exploitation, exploration, and initialization. These segments are based on different gorilla behaviors. These activities include exploring new areas, returning to well-known areas, approaching other gorillas, respecting the Silverback's choices, and competing with them for the attention of adult female gorillas. The exploration phase starts when the initialization phase is over. Moving to new habitats, returning to known locations, and approaching other gorillas are its three primary behaviors. Similarly, two basic gorilla behaviors are included in the exploitation phase of GTO: hunting silverbacks and fighting for older females. The following is a description of the three stages of GTO (Singh et al., 2021a):

Initialization phase

The n^th gorilla's position is described as: $Y_{s} = r a n d (1, N) \times (u_{b} - l_{b}) + l_{b}$ (7)where $s \in N$ is the total gorilla population. The location vector for the above study can be expressed as $Y = {Y_{1}, \dots \dots Y_{n}, \dots . ., Y_{n}} .$

Exploration phase

At each step, all N gorillas are considered as possible answers, with the silverback being the best choice. One important way to improve the algorithm's exploration part is to move gorillas to areas that have not been explored yet, like finding uncharted territory in the solution space to find potentially better solutions. Conversely, visiting different gorillas strikes a balance between exploitation and exploitation. It will take a variety of search space enhancements to move to the selected location. The following mathematical description of the exploration phase is based on these three strategies (Khadanga and Panda, 2022): $P_{s} (i t + 1) = {\begin{matrix} (u_{b} - l_{b}) \times s_{2} \times l_{b}, s_{1} < α \\ (s_{3} - D) \times Y_{A} (i t) + M \times N \times Y_{s} (i t), s_{1} \geq 0.5 \\ Y_{A} (i t) - S \times (S \times Y_{s} (i t) - Y_{B} (i t) + s_{4} \times Y_{n} (i t) - Y_{B} (i t)) s_{1} < 0.5 \end{matrix}$ (8)The variables D, M, and N can be expressed as: $D = (\cos (2 \times s_{5})) \times (1 - \frac{i t}{i t_{max}})$ (9) $M = D \times z z \in [- 1, 1]$ (10) $N = Z \times Y_{s} (i t), y \in [- C, C]$ (11)

Exploitation phase

The silverback displays specific behaviors when it trails when the GTO algorithm executes the phase using one of two tactics for adult females. If so, the silverback gorilla's choice is respected. The following mathematical assertion demonstrates the behavior (Safiullah et al., 2022): $P_{s} (i t + 1) = M \times R \times (P_{s} (i t) - Y_{s i l v e r b a c k}) + P_{s} (i t)$ (12)where $Y_{s i l v e r b a c k}$ represents the best answer. The parameter R can be expressed as: $R = ({| \sum_{n = 1}^{N} Y_{n} (i t) / P |}^{2^{L}}) 2^{\frac{1}{L}}$ (13)If C < Z, which can be expressed as $P_{s} (i t + 1) = Y_{s i l v e r b a c k} - (Y_{s i l v e r b a c k} \times I - Y_{n} (i t) \times I) \times J$ (14)

I = 2 \times s_{6} - 1

(15a)

J = φ \times W

(15b)

W = {\begin{matrix} N_{1}, r_{7} \geq 0.5 \\ N_{2}, r_{7} < 0.5 \end{matrix}

(15c)

Equations (15a), (15b), and (15c) illustrate the fierce rivalry amongst juvenile gorillas in their pursuit of older females. I represents impact force, while S6 is a randomly generated value between 0 and 1. The intensity of the violence is represented by the constant J. The random value of S7 ranges from 0 to 1.

Modified artificial GTO algorithm

In the original GTO method, the variables M and N depend on the variable D, which is computed as the algorithm runs. Equation (9), which is used in the optimization process, is probably used to find the value of C depending on attributes. An optimization algorithm that has a high degree of exploration capability is less likely to become stuck in local minima. Excessive exploration capability can be detrimental, but it can also help prevent local minima and expand the search space by introducing extra randomness.

Excessive exploitation leads to less unpredictability since the algorithm focuses too much on refining and utilizing preexisting solutions. As a result, there is a possibility that the algorithm will fail to identify the global minimum and become stuck in local minima. Consequently, striking a balance between the exploitation and exploration phases is essential to the algorithm's efficacy. D can be updated using Equation (9) as: $D = (\cos (2 \times s_{5})) \times (1 - \frac{i t^{α}}{i t_{max}^{α}})$ (16)Equation (16) demonstrates how the presence of a parameter causes the variation in C to change from linear to nonlinear. The suggested mGTO algorithm's step-by-step process is shown in Figure 4, which encourages the proposed mGTO to be implemented in the suggested power system. To choose values correctly, several values higher or lower than one are attempted.

Figure 4.

Flowchart for the proposed modified Gorilla Troops Optimizer (mGTO) algorithm.

Simulation results with discussions

Modified GTO algorithm's performance evaluation

Using a few benchmark test functions, the suggested mGTO approach's performance was first examined. The basic algorithm parameters are displayed in Table 1. The study's population size is set at 30. All algorithms’ dimensions are set to 30 (n = 30), and the maximum number of iterations is set to 50 to minimize the function displayed in Table 1. All algorithms have the same number of function evaluations to provide a fair comparison. Thirty iterations of the algorithm's simulation were run, and the results were noted.

Table 1.

Algorithm parameters.

Parameters	Values
Population size (N)	30
Number of iteration	50
φ	3
W	0.8
P₁	0.03
P₂	3
P₃	0.8

The statistical analysis of the recorded results is summarized in Table 2. From the recorded values attained, the mean, best, and worst were computed, tabulated, and compared. The mean of each of the 30 recorded and simulated fitness values is calculated and tabulated. The statistical results for a few unimodal (f1–f7) and multimodal (f8–f10) functions are also shown in Table 2 (Khadanga et al., 2023). Table 2 presents the results from SCA-AOA (Khadanga et al., 2023), ASO (Singh et al., 2021a), MGWO-CS (Khadanga et al., 2022), and GTO (Patil et al., 2022) to support the claim that the method is superior. The proposed improved method outperforms rival algorithms for nearly all test functions.

Table 2.

Benchmark function testing.

Functions	f₁	f₂	f₃	f₄	f₅	f₆	f₇	f₈	f₉	f₁₀
MGWO-CS (Khadanga et al., 2022)
Best	8.812*10⁻⁵⁰	1.699*10⁻⁴⁹	2.807*10⁻¹⁶	2.125*10⁻⁰⁹	26.312	8.988 × 10⁻⁷	0.00043	−7401.05	0	7.993 × 10⁻¹⁵
Average	5.886*10⁻⁴⁹	8.545*10⁻²⁹	8.856*10⁻¹²	2.1*10⁻⁰⁹	26.998	9.452 × 10⁻⁵	0.00986	−7125.12	0	2.895 × 10⁻¹⁴
Mean Deviation	1.699*10⁻⁴⁹	8.012*10⁻³⁰	2.1*10⁻⁰⁹	4.501*10⁻¹⁴	0.4254	0.398	0.00085	754.120	0	3.499 × 10⁻¹⁵
SCA-AOA (Khadanga et al., 2023)
Best	0	0	4.621 × 10^‒26	0	3.554 × 10^‒4	6.856 × 10^‒6	5.654 × 10^‒6	4.741 × 10³	0	0
Average	0	0	5.457 × 10^‒26	0	3.569 × 10^‒4	5.872 × 10^‒6	5.180 × 10^‒6	2.560 × 10³	0	8.824 × 10^‒20
Mean Deviation	0	0	5.982 × 10^‒32	0	2.251 × 10^‒10	2.345 × 10^‒12	2.895 × 10^‒12	4.569 × 10³	0	5.215 × 10^‒30
ASO (Singh et al., 2021a)
Best	3.625 × 10^‒22	5.254 × 10¹¹	23.789	2.785 × 10^‒10	16.21	0	0.04001	−5562.12	0	1.251 × 10^‒11
Average	2.587 × 10^‒21	3.354 × 10^‒10	1.897 × 10^‒02	3.898 × 10^‒09	24.52	0	0.03401	−7428.65	0	3.098 × 10^‒11
Mean Deviation	3.765 × 10^‒21	1.998 × 10^‒10	79.001	6.458 × 10^‒09	0.5987	0	0.01852	423.001	0	2.158 × 10^‒11
GTO (Patil et al., 2022)
Best	0	0	0	0	0	0.003 × 10⁻⁶	0.141 × 10⁻⁴	−1.256 × 10⁴	0	0.888 × 10⁻¹⁵
Average	0	0.186 × 10⁻¹⁹⁰	0	0.222 × 10⁻¹⁹⁰	3.2514	0.165 × 10⁻⁶	0.878 × 10⁻⁴	−1.256 × 10⁴	0	0.888 × 10⁻¹⁵
Mean Deviation	0	0	0	0	8.3191	0.211 × 10⁻⁶	0.661 × 10⁻⁴	0	0	0
Proposed mGTO
Best	0	0	0	0	0	0.001 × 10⁻⁸	0.003 × 10⁻⁴	−1.256 × 10⁴	0	0.888 × 10⁻¹⁵
Average	0	0.525 × 10⁻²⁹⁷	0	0.943 × 10⁻²⁹³	4.5466	0.228 × 10⁻⁸	0.427 × 10⁻⁴	−1.256 × 10⁴	0	0.888 × 10⁻¹⁵
Mean Deviation	0	0	0	0	9.2516	0.511 × 10⁻⁸	0.399 × 10⁻⁴	0	0	0

The convergence characteristics for both the suggested mGTO algorithm for the f₁ to f₄ standard benchmark functions and the conventional GTO approach using the Grey Wolf Optimizer algorithm (Khadanga et al., 2022) are displayed in Figure 5. To run the simulation parameters of all the algorithm is kept constant and the parameters are dimensions (n) = 30, and the maximum iterations = 50. The response curves show that the suggested mGTO method performs significantly better than the conventional and other published methods, suggesting that the mGTO approach should be adopted going forward.

Figure 5.

Convergence profile for modified Gorilla Troops Optimizer (mGTO) algorithm.

The computation times for the mGTO and GTO approaches for 30 iterations of each benchmark function are also included in Table 3. It demonstrates that for all functions (f₁–f₁₀), the recommended mGTO algorithm performs worse than the original GTO method. Thus, the study shows that the suggested method yields better results and might be used in future studies. Because the research shows that the customized method performs better than the benchmark algorithm, it will be used in the study being presented.

Table 3.

Computational time comparison.

Function	% reduction in implementation time	Proposed mGTO	GTO
Function	% reduction in implementation time	Execution time (s)	Execution time (s)
f₁	45.94	4.0986	7.4989
f₂	37.08	5.0551	7.9856
f₃	13.04	15.263	17.489
f₄	36.57	4.8651	7.4986
f₅	37.89	5.9745	9.5891
f₆	28.79	5.651	8.3612
f₇	9.41	10.212	11.282
f₈	25.62	7.7192	10.365
f₉	27.12	5.3312	7.3126
f₁₀	43.39	5.2241	9.3251

Implementation of the proposed modified GTO algorithm

By using GTO and mGTO to minimize the fitness given in Equation (6), the suggested IPFC-based additional damping controller parameters are optimized. An increase in mechanical power input of 10% is considered while calculating the goal function. The fitness function is recorded after 20 iterations of the optimization process (Feleke et al., 2023). Table 4 presents the top 50 runs, indicating that the suggested method yields superior outcomes concerning the objective function. Now, taking these conclusions into account, the following research has been done:

Table 4.

Value of different controller parameters.

Controller	GTO-based lead-lag controller	Objective function	Proposed mGTO-based lead-lag controller	Objective function
δ₁-based	K_T= 420.1299, T₁= 0.0009, T₂= 0.0007	0.004884	K_T= 499.5633, T₁= 0.00096, T₂= 0.00094	0.004017
m₁-based	K_T= 50.1807, T₁= 0.0525, T₂= 0.0837	0.0003899	K_T= 50.4707, T₁= 0.0518, T₂= 0.0653	0.000323
δ₂-based	K_T= 346.7541, T₁= 0.0006, T₂= 0.0008	0.002959	K_T= 462.8537, T₁= 0.0007, T₂= 0.0005	0.002017
m₂-based	K_T= 47.7851, T₁= 0.0673, T₂= 0.0527	0.0002729	K_T= 55.9537, T₁= 0.0983, T₂= 0.0810	0.000231

Δ₁ damping controller

Using an IPFC damping controller based on δ₁, the system's performance is showcased under the considered contingency. The system response depicted in Figure 6 indicates that the system performs marginally better when using the suggested mGTO optimized δ₁-based IPFC damping controller.

Figure 6.

Response of δ₁ controller.

m₁ damping controller

At t = 1.0 s, a 10% step increase in mechanical power input is expected. Figure 7 illustrates the system speed deviation response for the said contingency. It is evident from the figure that in the absence of a controller, the system oscillates and becomes unstable. With the help of an m₁-based IPFC damping controller, system stability is preserved and power system oscillations are successfully reduced.

Figure 7.

Response of m₁ controller.

Δ₂ damping controller

The system response for the same change in mechanical input contingency with an IPFC damping controller based on δ₂ is shown in Figure 8, from which the suggested method outperforms the alternative damping controller.

Figure 8.

Response of δ₂ IPFC controller.

m₂ damping controller

With an m₂-based IPFC damping controller, the system's performance is confirmed under the same condition, and Figure 9 illustrates the system's response. The suggested mGTO-optimized damping controller outperforms the GTO-designed controller in terms of system performance.

Figure 9.

Response of m₂ IPFC controller.

Comparison of all IPFC damping controllers

Another disturbance is considered to evaluate the robustness of the suggested method and compare the performance of all IPFC-based damping controllers. Figures 10 and 11 display the system's dynamic response with each of the four alternate damping controllers. At t = 1.0, there is a 5% change in the reference voltage. The figures demonstrate that the damping efficacy of each of the four alternate damping controllers is sufficient for the current circumstance.

Figure 10.

Response of all controllers with change in reference voltage using GTO parameter.

Figure 11.

Response of all controllers with change in reference voltage using modified Gorilla Troops Optimizer (mGTO) parameter.

Conclusions

This study significantly enhances the original GTO algorithm by incorporating scaling variables, thereby giving rise to the mGTO algorithm. The efficacy of this proposed algorithm is meticulously evaluated by subjecting it to a battery of standard benchmark functions. Furthermore, both the modified and original GTO algorithm strategies are harnessed for the design of a FACTS-based controller. The design problem of an IPFC-based controller is meticulously examined to assess performance. Parameters of the controller are fine-tuned utilizing both GTO and mGTO optimization techniques. It is strikingly evident that when the proposed modified GTO algorithm is applied, there is a notable reduction in the objective function (J) for the IPFC-based damping controller. Moreover, simulation results unequivocally establish that the mGTO-based IPFC controllers yield superior results to other standard controllers, solidifying its position as a pioneering advancement in controller design methodologies.

The main flaw in the suggested approach is that it derives a Small-Signal model of an SMIB system by ignoring the following:

The resistances of every system component, including the generator, transmission lines, transformer, and series converter transformer.

The transients associated with the transformers, synchronous generator stator, fixed series capacitor, and transmission lines.

Moreover, linear approaches are unable to accurately depict the intricate dynamics of the system, particularly during significant disruptions.

In future research, a large-scale power system can be used to evaluate the effectiveness of the proposed technique. Only IPFC is considered in this work; other FACT devices may be evaluated in the SMIB system in a subsequent iteration. Integration of distributed energy sources like wind power plants, and photovoltaic systems can also be considered for further study. Moreover, the writers aim to integrate sophisticated soft computing methods for intricate optimization issues. Investigating how the mGTO algorithm performs in scenarios involving renewable energy integration or grid stability enhancement could provide valuable insights into its effectiveness in addressing contemporary challenges in power system control. Additionally, exploring the potential for incorporating real-time data and adaptive strategies into the mGTO algorithm could further enhance its applicability in dynamic power system environments, ultimately contributing to more robust and efficient control solutions.

Footnotes

Author contribution

All authors contributed equally to this work. RKK, DD, SP, SRM, MKK, TSU, and AK—Conceptualization, Investigation, Writing—original draft, Writing—review & editing.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Taha Selim Ustun

References

Abdolrasol

Ayob

Mutlag

(2023) Optimal fuzzy logic controller based PSO for photovoltaic system. Energy Reports 9: 427–434.

Agrawal

Khan

Gowda

(2023) Advanced Heffron-Phillips model for improving power system stability. International Journal of the Energy-Growth Nexus 1: 63–89.

Ahmed

Magdy

Khamies

, et al. (2022) An efficient coordinated strategy for frequency stability in hybrid power systems with renewables considering interline power flow controller and redox flow battery. Journal of Energy Storage 52: 104835.

Aref

Abdelaziz

Geem

, et al. (2023) Oscillation damping neuro-based controllers augmented solar energy penetration management of power system stability. Energies 16: 2391.

Banaei

Kami

(2011) Interline power flow controller (IPFC) based damping recurrent neural network controllers for enhancing stability. Energy Conversion and Management 52: 2629–2636.

Bento

(2020) Fixed low-order wide-area damping controller considering time delays and power system operation uncertainties. IEEE Transactions on Power Systems 35(5): 3918–3926.

Dhurvey

Chandrakar

(2016) Improvement of power system performance using fuzzy logic based interline power flow controller [IPFC]. Journal of Power and Energy Engineering 4: 67–77.

Farhang

Mazlumi

(2014) Low-frequency power system oscillation damping using HBA-based coordinated design of IPFC and PSS output feedback controllers. Transactions of the Institute of Measurement and Control 36: 184–195.

Farooq

Rahman

Hussain

SMS

(2022) Power generation control of renewable energy based hybrid deregulated power system. Energies 15: 517.

10.

Feleke

Pydi

Satish

, et al. (2023) DE-based design of an intelligent and conventional hybrid control system with IPFC for AGC of interconnected power system. Sustainability 15: 5625.

11.

Hussain

Das

Sinha

, et al. (2020) Performance assessment of an islanded hybrid power system with different storage combinations using an FPA-tuned two-degree-of-freedom (2DOF). Controller Energies 13: 5610.

12.

Kazemi

Karimi

(2006) The effect of interline power flow controller (IPFC) on damping inter-area oscillations in the interconnected power systems, industrial electronics. IEEE International Symposium 3: 1911–1915.

13.

Khadanga

Das

Kumar

, et al. (2023) Sine augmented scaled arithmetic optimization algorithm for frequency regulation of a virtual inertia control based microgrid. ISA Transactions 138: 534–545.

14.

Khadanga

Kumar

Panda

(2022) A modified grey wolf optimization with cuckoo search algorithm for load frequency controller design of hybrid power system. Applied Soft Computing 124: 109011.

15.

Khadanga

Panda

(2022) A modified local input signal for SSSC-based damping controller design. Electric Power Components and Systems 49: 978–989.

16.

Khadanga

Panda

Sahu

, et al. (2024) Design and analysis of IPFC-based damping controller. In: 2024 International Conference on Signal Processing, Computation, Electronics, Power and Telecommunication (IConSCEPT), pp.1–5: IEEE.

17.

Khan

Mokhlis

Mansor

, et al. (2024) Load frequency control in power systems with high renewable energy penetration: A strategy employing PIλ (1+ PDF) controller, hybrid energy storage, and IPFC-FACTS. Alexandria Engineering Journal 106: 337–366.

18.

Kumar

Rajan

(2024) Modelling of IPFC with multifunctional VSC for low-frequency oscillation damping and system stability improvement. International Journal of Electrical and Electronics Research 12: 428–434.

19.

Kundur

(1994) Power System Stability and Control. New York: McGraw-Hill.

20.

Latif

Hussain

SMS

Das

(2021) Optimization of two-stage IPD-(1 + I) controllers for frequency regulation of sustainable energy based hybrid microgrid network. Electronics 10: 919.

21.

Martins

LFB

de Araujo

de Vargas Fortes

, et al. (2017) Design of the PI–UPFC–POD and PSS damping controllers using an artificial bee colony algorithm. Journal of Control, Automation and Electrical Systems 28(6): 762–773.

22.

Mazumdar

Biswas

Sain

, et al. (2024) Performance analysis of drone sqadron optimisation based MPPT controller for grid implemented PV battery system under partially shaded conditions. Renewable Energy Focus 49: 100577.

23.

Mostafa

Gaheen

Abd ElAziz

, et al. (2023) An improved gorilla troops optimizer for global optimization problems and feature selection. Knowledge-Based Systems 269: 110462.

24.

Naga Sai Kalyan

Rao

(2016) Combined frequency and voltage stabilization of multi-area multisource system by DE-AEFA optimized PID controller with coordinated performance of IPFC and RFBs. International Journal of Ambient Energy 43: 3815–3831.

25.

Natarajan

Kaviarasan

Lim

, et al. (2022) Gorilla troops optimizer combined with ANFIS for wire cut EDM of aluminium alloy. Advances in Materials Science and Engineering 3072663: 14.

26.

Nayak

Khadanga

Panda

, et al. (2023) Participation of renewable energy sources in the frequency regulation issues of a five-area hybrid power system utilizing a sine cosine-adopted African vulture optimization algorithm. Energies 16: 926.

27.

Patil

Mulla

Dawn

(2022) Profit maximization with imbalance cost improvement by solar PV-battery hybrid system in deregulated power market. Energies 15: 5290.

28.

Prakash

El Moursi

Parida

, et al. (2024) Design of adaptive damping controller with wide-area measurements considering unknown power system dynamics. IEEE Transactions on Power Systems 39: 5150–5162.

29.

Rai

Das

(2022) Adaptive quantum class topper optimization tuned three degree of freedom-PID controller for automatic generation control of power system incorporating IPFC and real-time simulation. Soft Computing 26: 3273–3291.

30.

Rajbongshi

Saikia

(2019) Performance of coordinated interline power flow controller and power system stabilizer in combined multiarea restructured ALFC and AVR system. International Transactions on Electrical Energy Systems 29: 2822.

31.

Safiullah

Rahman

Lone

, et al. (2022) Novel COVID-19 Based Optimization Algorithm (C-19BOA) for performance improvement of power systems. Sustainability 14: 14287.

32.

Sahoo

Hota

Sahu

, et al. (2023) Optimal congestion management with FACTS devices for optimal power dispatch in the deregulated electricity market. Axioms 12: 614.

33.

Sahu

Lenka

Khadanga

, et al. (2022) Power system stability improvement of FACTS controller and PSS design: A time-delay approach. Sustainability 14: 14649.

34.

Singh

Slowik

Bishnoi

(2023) Review on soft computing-based controllers for frequency regulation of diverse traditional, hybrid, and future power systems. Energies 16: 1917.

35.

Singh

Chopra

, et al. (2021a) Chaotic evolutionary programming for an engineering optimization problem. Applied Sciences 11: 2717.

36.

Singh

Koley

Gope

, et al. (2021b) An economic risk analysis in wind and pumped hydro energy storage integrated power system using meta-heuristic algorithm. Sustainability 13: 13542.

37.

Singh

(2022) Power system transient stability improvement with FACTS controllers using SSSC-based controller. Sustainable Energy Technologies and Assessments (53): 102664.

38.

Srivastava

Latif

Shaoo

, et al. (2022) Analysis of GOA optimized two-stage controller for frequency regulation of grid integrated virtual power plant. Energy Reports 8: 493–500.

39.

Ustun

(2023) Microgrids imitate nature for improved performance—Use of nature-inspired optimization techniques in future power systems. Energies 16: 1522.

A Novel Modified Gorilla Troops Optimizer Algorithm for Interline Power Flow Controller-Based Damping Controller Design

Abstract

Keywords

Introduction

Motivation research gap and paper organization

Research gap

Motivation

Innovations

Paper organization

System under study

Linearized equations

Problem formulation

Controller structure

Objective function

Modified artificial GTO algorithm

Artificial GTO algorithm

Initialization phase

Exploration phase

Exploitation phase

Modified artificial GTO algorithm

Simulation results with discussions

Modified GTO algorithm's performance evaluation

Implementation of the proposed modified GTO algorithm

Δ1 damping controller

m1 damping controller

Δ2 damping controller

m2 damping controller

Comparison of all IPFC damping controllers

Conclusions

Footnotes

Author contribution

Declaration of conflicting interests

Funding

ORCID iD

References

Δ₁ damping controller

m₁ damping controller

Δ₂ damping controller

m₂ damping controller