Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 1 https://internationalpubls.com Smart SVC Placement for Loss Reduction in Power Systems: Tackling Generator Outages with IGEPO Optimization 1Muhammad Nurhazeeq Nor Helmy, 2Ismail Musirin*, 3Nagaletchumi Balasubramaniam, 4Nor Azwan Mohamed Kamari, 5Nur Farahiah Ibrahim, 6Fathiah Zakaria 7Ahmad Asrul Ibrahim 1,2,5,6Power System Operation Computational Intelligence Research Group (POSC), School of Electrical Engineering, College of Engineering, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia. 3Institute of Power Engineering (IPE), Universiti Tenaga Nasional, 43000 Kajang, Selangor, Malaysia. 4,7Department of Electrical, Electronic and Systems Engineering, Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia, Malaysia. 4,7Electric Mobility and Inteligent Vehicle Technologies, Centre for Automotive Research (CAR), Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia, Malaysia. *Correspondin author: 2ismailbm@uitm.edu.my. Email: 1hazeeq.helmy@gmail.com, 3nagaletchumi@uniten.edu.my, 4azwank@ukm.edu.my, 5nurfarahiahibrahim@uitm.edu.my 6fathiahz@uitm.edu.my, 7ahmadasrul@ukm.edu.my Article History: Received: 28-10-2024 Revised:12-11-2024 Accepted:19-12-2024 Abstract: Increasing load demand and generator outages in power transmission networks can cause significant power losses and voltage instability. Addressing these challenges requires an optimal installation strategy for Static Var Compensators (SVC), which involves determining the best locations and sizes for the SVCs to ensure efficient, reliable, and cost-effective operation. Traditional optimization techniques often struggle with issues like local optima and inadequate exploration. This paper presents a novel approach, the Integrated Grasshopper Evolutionary Programming Optimization (IGEPO), which combines the Grasshopper Optimization Algorithm with Evolutionary Programming. The IGEPO method is applied to optimize the placement and sizing of SVCs, with the goal of minimizing losses, particularly during generator outages. Comparative studies on the IEEE 30-Bus RTS demonstrate that IGEPO outperforms both standalone Evolutionary Programming and the Grasshopper Optimization Algorithm in power system planning under normal conditions and during contingencies due to generator outages. Results are presented for the pre-SVC installation under both normal conditions and during generator outages to observe the impact of the outages and the subsequent SVC installation. The proposed algorithm has potential for broader applications and could be explored further in future studies. Keywords: Optimization techniques, Grasshopper Optimization Algorithm, Power Loss Minimization, Integrated Optimization, Integrated Grasshopper Evolutionary Programming Optimization. I. INTRODUCTION Electricity consumption throughout the world has gradually increased over the decades following the demographic growth, increase in the number of people in urban areas, more economic development, and technological development [1]. The traditional ways of applying new plants and new transmission Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 2 https://internationalpubls.com lines Construction to meet this increasing demand is often impossible because of high cost, environmental concerns and technology constraints. Thus, when making tactical and operational decisions, one has to enhance the cost effectiveness of existing systems, a component of which is the reduction of losses as from active power through the management of reactive power through FACTs. In this regard, one has found the use of FACTs devices as one of the most common strategies for the particular kind. FACTs are another control tool that was proposed by Hingorani in 1998 [2] to improve flexibility and dynamism of electrical variables in power systems with maintaining their security, stability, and reliability. This leads to an efficient utilization of the existing resources since power loss together with costs is minimized to increase the overall efficiency of the grid [3]. FACTs consist of numerous kinds of compensation equipment including the UPFC, SVC, TCSC, and STATCOM. Of them, SVC is unique of being the parallel connected device which can act as a variable capacitance or variable inductance. As mentioned earlier, SVC is used in many applications, some of which are voltage control in weak networks, minimum transmission losses, increasing transfer capability, small disturbance rejection, voltage control, and control of fluctuating power [4]. The choice of SVC in this study is influenced by its flexibility in handling numerous operations. However, the problem of achieving the best placement and sizing is a key challenge in enforcing the improvement of voltage stability using SVCs [5], [6]. To counter such complications, many optimization techniques have been advanced to reduce the power system losses or control voltages to IEEE or IET standards. If power voltage is not well maintained, then it results in reduction of span of the transmission cable in the system. For electrical power systems, accurate positioning of Static VAR compensators or SVCs is critical to loss minimization and the stability of the system, especially where there has been generators’ trip. SVCs are very necessary for applications used in controlling the reactive power which in turn supports the compensation methods used to control fluctuations of the voltage and improve the sturdiness of the power grid. The proper application of optimization methods is essential for the identification of the right SVC locations and their capacities to enhance system efficiency [7]- [13]. The Grasshopper Optimization Algorithm (GOA) is a relatively recent metaheuristic that simulates grasshoppers’ social behavior; it has shown excellent performance as a search algorithm and in terms of convergence in a number of fields, including power systems [9]. The hormonal based most new creation has been attached with GOA latest GOA formation which has been categorized as the Integrated Grasshopper Evolutionary Programming Optimization (IGEPO). This integration of the two types of methods makes use of the advantages of each in generating more efficient solutions to reducing power losses and in SVC placement [10]. Thus, it can be seen that generator outages present a major threat to power system reliability and efficiency. Hence, they asserted that the implementation of generator outages management within optimization frameworks is vital for operation resilience [11]. In any optimization algorithm, the initialization process is a significant determinant of convergence rates and solution quality; thus, strategic initialization procedures are valuable for improving the system’s overall performance [12]. Some of the main goals include minimizing certain losses, increasing system availability, and adjusting operation costs based on multifaceted studies and comparisons with other techniques [13]-[15]. Despite these advancements, many metaheuristic algorithms struggle to balance exploration and exploitation, resulting in suboptimal solutions for real-world applications. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 3 https://internationalpubls.com This paper presents smart SVC placement for loss reduction in power systems: tackling generator outages with IGEPO optimization. In this study, one of the major objectives of the utility is the achievement of an efficient loss minimization scheme incorporating a feasible plan for generator outages by applying the IGEPO method on the suitable SVC. This study highlights a new proposed optimization algorithm, termed IGEPO, combining the advantages of GOA and EP, to optimize SVC installation for loss minimization in power systems validation, particularly under generator outage conditions. Comparative studies on the IEEE 30-Bus RTS will demonstrate the effectiveness of the proposed method. II. PROBLEM FORMULATIION Minimizing power losses in power systems is critical for achieving operational efficiency and reducing costs, as such losses lead to wasted energy and increased expenses. Static Var Compensators (SVCs) play a vital role in enhancing power system stability and efficiency by providing rapid reactive power compensation, stabilizing voltage levels, correcting power factor, and increasing transmission capacity. However, generator outages—whether planned or unplanned—pose significant challenges, resulting in power imbalances, voltage instability, and increased losses. To address these issues, determining the optimal placement and sizing of SVCs during generator outages is crucial. An increase in reactive power can significantly raise power losses in the system, as shown in Fig. 1. This phenomenon occurs both before and after a generator outage. Comparing the profiles of these two scenarios reveals that during a generator outage, the loss profile is higher than under normal conditions. The mathematical equations for power loss can be expressed starting with (1). The complex power injected into bus i can be expressed as: Vi : the voltage at bus i Vk ∗ : the complex conjugate of the voltage at bus k Yik : the admittance of the transmission line between bus i and bus k N : the total number of buses The power loss in the system is given by: Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 4 https://internationalpubls.com Fig. 1: The effect of generator outage under variations of reactive power in the system. Fig. 1 illustrates the effect of a generator outage under different reactive power variations in the system. This study focuses on optimizing power system performance by minimizing losses during generator outages. It addresses challenges such as power imbalances through the strategic placement and sizing of SVCs. Traditional optimization methods often struggle to balance objectives like minimizing losses. To overcome this, the study proposes the Integrated Grasshopper Evolutionary Programming Optimization (IGEPO) method, which combines the exploration capabilities of the Grasshopper Optimization Algorithm (GOA) with the exploitation strengths of Evolutionary Programming (EP). The goal is to enhance overall optimization effectiveness. Comparative studies on the IEEE 30-Bus RTS validate IGEPO, offering a robust solution for efficient and smooth power system operation. A. Conceptual Strategy for Loss Minimization Fig. 2 illustrates the conceptual strategy for minimizing losses in a power system. Initially, a random number generator generates numbers used to determine the locations and sizes. Fig. 2: Conceptual strategy for loss minimization These numbers are then transmitted to the control center and subsequently integrated into the power transmission system. Similarly, the techniques EP, GOA, and IGEPO utilize the same random numbers to assign the compensating devices, which are validated within the power transmission network. Random number generator generates random numbers which will be utilized by the power system network. The random numbers represent the random locations and sizing of the SVC to be installed in the system. The number of control variables is given by 2n, where n is the number of SVC units to be installed into the system. The same random numbers will be utilized by all the three optimization techniques, i.e. EP, GOA and IGEPO. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 5 https://internationalpubls.com III. OPTIMIZATION TECHNIQUES This section introduces the proposed IGEPO algorithm, followed by descriptions of EP and GOA as benchmark techniques. IGEPO integrates EP and GOA, where the mutation operator of GOA is embedded into the original EP mechanics. GOA and EP are taken as the benchmarked techniques for the purpose of comparative study in the effort to highlight the performance of the proposed IGEPO. A. Evolutionary Programming Evolutionary Programming (EP) was first introduced by L. J. Fogel in the early 1960s as a State Machine Model [16], [17]. In the late 1990s, D. B. Fogel extended EP into an optimization tool used to solve various real-world problems, especially in engineering. Over the years, EP has effectively addressed numerous combinatorial and numerical optimization challenges. Unlike genetic algorithms, which focus on gene analysis, EP emphasizes the relationship between species' behaviors during the evolutionary process. EP simulates the evolution of species, focusing on behavioral development and the connection between parents and offspring. This approach suggests that an exceptional offspring can emerge independently of its parent’s characteristics [18]. The mechanics of EP are depicted in the flowchart of Fig. 3, highlighting essential processes such as initialization, fitness calculation in two phases, mutation, combination, tournament and convergence test, which determines convergence [19]. Fig. 3: Flowchart for Evolutionary Programming in SVC installation scheme B. Grasshopper Optimization Algorithm The Grasshopper Optimization Algorithm (GOA) replicates the foraging behavior of grasshoppers to solve complex optimization problems [7]. GOA employs agents that mimic grasshoppers, adjusting their positions based on social interactions, gravity, and wind advection to balance exploration and exploitation. This methodology allows GOA to adeptly navigate engineering and computational intelligence domains, avoiding local optima and converging on global solutions. GOA's process is illustrated in the step-by-step procedures as follows: Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 6 https://internationalpubls.com Step 1: Declaration Process The first step in implementing GOA involves clearing the workspace and initializing essential parameters like bus numbers, load, and limit values to set initial conditions for the power system model. This includes loading the detailed bus and line data, assigning specified loads, and setting generator outage conditions to accurately prepare for the optimization process. Step 2: Random Parameter Generation In this stage, random individuals are generated to determine random locations or load buses and sizes for SVC installation. The power data for the selected buses is adjusted accordingly, setting up the initial state for the optimization process and enabling the algorithm to explore various configurations of reactive power injection. Step 3: Initialize Population for GOA After parameter generation, GOA initializes the population by defining variable boundaries and setting algorithm parameters such as iterations and population size. Agents' positions are randomly initialized within these bounds and sorted to identify the lowest loss values and corresponding bus locations. This diverse starting setup enhances the algorithm's ability to explore the search space effectively. During this initialization process, all the random individuals amounted of 20 values for each variable will ensure that all the fitness values are better than the preset fitness. These random individuals represent the random locations for the SVCs to be installed and the sizing of SVCs. In this study, fitness is power loss. Thus, the loss values computed using all the random individuals during initialization should be less than lossset, where it was computed using the normal load flow process. Step 4: Main Optimization Loop The main optimization loop calculates fitness values for the population in each iteration, identifying the best fitness value and position. Agents' positions are updated using GOA equations, mimicking grasshopper swarming behavior through social interaction, gravity, and wind advection. Adjustments keep positions within boundaries, enforcing integer constraints on specific variables. Progress is displayed to monitor the algorithm's performance. Step 5: Identify the Best Fitness, Optimal Sizing, and Location GOA outputs result that include fitness values, optimal sizing, and the best location for minimizing losses, along with the best position. This comprehensive output assesses the algorithm's effectiveness in optimizing SVC installation in power system. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 7 https://internationalpubls.com C. Proposed IGEPO Algorithm The Integrated Grasshopper Evolutionary Programming Optimization (IGEPO) method is formulated to enhance the performance of the original EP technique. This improvement aims to mitigate premature convergence when addressing highly complex problems and to boost EP's global search capability. The flowchart is illustrated in Fig. 4. The step-by-step process of the proposed method is as follows: Step 1: Set the Loading Condition Setting the loading conditions is crucial for simulating various operational scenarios that the power system might face in real-world situations. This involves determining the electrical power demand or consumption at different buses within the system, particularly for the IEEE 30-bus system in this context. Step 2: Initialization This stage generates individuals to represent random buses as the locations and sizes of the SVCs to be installed. Random parameters for reactive power injection are generated, ensuring that all three selected buses are distinct, as in this study three units of SVCs are installed in the system. Losses are then calculated based on these new parameters when the random locations and SVC sizing are inserted into the system. If the new loss value is lower than the previously established initial loss, the parameters are saved in a predefined matrix and added to the individual pool. If not, the solution is rejected, and the loop process continues until the required number of accepted individuals is achieved. The iteration then stops, and the individual pool is populated with all the generated individuals. Step 3: Redefine the Initial Population The initial population stored in the accepted matrix is redefined for Fitness I calculation. This fitness calculation involves the parameters in power system model and analyzing the performance of each approach. The previously generated initial population, consisting of 20 individuals, as bus numbers as the random locations and reactive power to be injected into the buses represent the SVCs sizing. Step 4: Fitness I Calculation The loop for Fitness I calculation involves 20 iterations, corresponding to the number of individuals in the process. During each iteration, selected buses receive injections of reactive power, followed by a load flow analysis. Additionally, the power loss is computed, and all obtained fitness values are stored in the 'Fitness I' array. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 8 https://internationalpubls.com Step 5 Update the Position Using GOA Equation Optimization techniques are integrated with GOA to enhance the efficiency of reactive power support in power systems. Initially, random solutions are generated for bus positions and SVC values, followed by a fitness evaluation based on system losses. Mutation is introduced, controlled by parameters such as mutation strength and mutation probability, to explore new potential solutions. This process mitigates the risk of premature convergence, enabling the algorithm to find optimal configurations for reactive power compensation devices. Mutation is described as follows: Generate random displacement for each individual: Where N(0,1) is a normally distributed random variable with mean 0 and standard deviation 1. Calculate new values after mutation: Where Xi and Yi represent the initial position and SVC values, and Xi′ and Yi′ are the new values after mutation. Step 6: Fitness II Calculation Similar to Fitness I, Fitness II calculation involves 20 iterations, each corresponding to an individual in the population. New configurations from mutations are applied to the system, and load flow analysis is conducted to evaluate their fitness values. New loss values are computed, and the fitness values are stored in the 'Fitness II' array. Step 7: Combination and Tournament Populations from Fitness I and Fitness II are merged into a combined matrix, sorted in ascending order based on the fitness values stored in the 8th column. This column represents the fitness values, while columns 2 to 7 indicate the locations and sizes of the SVCs (3 variables each). Step 8: Convergence Check The maximum and minimum fitness values are determined from the combined matrix. If both values are less than or equal to 0.0001, the function halts the Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 9 https://internationalpubls.com optimization process, indicating convergence. If not, the process resumes at Step 3, incrementing the iteration counter to continue optimization. Fig. 4: Flowchart for the Proposed IGEPO in SVC installation optimization scheme IV. RESULTS AND DISCUSSION This section presents the results and discussion of the study. The outcomes for loss values when three load buses (Buses 20, 29, and 30) were subjected to reactive load increments are shown under various conditions: pre-generator outage, post-generator outage, pre-SVC installation, and post-SVC installation. Additionally, the initial randomness in the results for SVC locations and sizing are highlighted, illustrating the variability during the initialization phase. Comparative studies results on the optimal solutions are compared among the proposed IGEPO, GOA and EP in the effort to highlight the superiority of IGEPO technique. A. Test System Fig. 5 shows the single-line diagram of the IEEE 30-bus RTS, a widely used model in both industry and academic research for studying real power systems [20]. In this study, the IEEE 30-Bus RTS is used to optimize SVC placement and sizing for loss minimization. This system comprises six generator buses, 28 load buses, and 41 transmission lines. B. Initialization Process The initialization process assigns random parameters to represent the locations and reactive power settings of SVCs with the goal of minimizing system losses. The focus of this study is on installing three SVC units strategically to reduce overall system losses, as indicated by a reduction in the lossset value. Figs. 6 to 11 display the scatter plots of the initial random configurations of the Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 10 https://internationalpubls.com parameters. These figures visually demonstrate the diversity of configurations explored during the initialization phase, showing the variability in SVC placements and their effects on system losses. Specifically, the figures depict the random configurations during initialization at 𝑄𝑑20 = 20 MVAR, 𝑄𝑑29 = 10 MVAR and 𝑄𝑑30 = 10 MVAR respectively. Fig. 5: Single line diagram for IEEE 30-bus RTS Figs 6, 8, and 10 illustrate scatter plots representing the locations for at 𝑄𝑑20 = 20 MVAR, 𝑄𝑑29 = 10 MVAR and 𝑄𝑑30 = 10 MVAR respectively. Each variable is assigned 20 individuals, resulting in a total of 60 individuals for the three random locations. The values range between 1 and 30, indicating the random locations generated during the initialization process in the IEEE 30-Bus RTS. Additionally, the random parameters for reactive power injection must satisfy certain conditions prior to optimization process. For instance, Bus 1, Bus 2, and Bus 3 must be assigned distinct locations during initialization. The scatter plots in Figs. 6, 8, and 10 highlight the random nature of the locations selection. The data points are spread across the bus numbers, suggesting that the initialization process allows exploration across the entire bus system. This distribution of locations increases the diversity of potential solutions in the optimization process, laying the groundwork for effective SVC placement that minimizes system losses. Fig. 6: Random Locations during Initialization at 𝑄𝑑20 = 20 MVAR Fig. 7: Random Sizing during Initialization at 𝑄𝑑20 = 20 MVAR Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 11 https://internationalpubls.com On the other hand, Figs. 7, 9 and 11 illustrate the scatter plot for the sizing of SVC1, SVC2 and SVC3 for 𝑄𝑑20 = 20 MVAR, 𝑄𝑑29 = 10 MVAR and 𝑄𝑑30 = 10 MVAR respectively. These values are random in nature which ensure that the fitness value of each individual is better than fitnessset. The random sizes are filtered such that the fitness value of each individual is better than the predefined fitness threshold. This indicates that every configuration in the scatter plots has undergone a selection process to ensure that it contributes positively to loss minimization. The filtering mechanism serves to eliminate unfit individuals from the population, optimizing the sizing of SVC units from the outset. The scatter plots from Figs. 6 to 11 collectively demonstrate the diversity of initial solutions explored during the optimization process. By generating a wide range of random locations and sizes, the initialization phase sets the foundation for robust and effective optimization. The fact that only configurations with better fitness than the set threshold are selected ensures that subsequent optimization steps, such as those using IGEPO, EP, or GOA, start with a well-rounded pool of potential solutions. This improves the convergence rate and the quality of the final SVC placement and sizing solutions, directly contributing to loss minimization and overall system efficiency. Tables 1, 2, and 3 present the random values for locations and sizing corresponding to 𝑄𝑑20 = 20 MVAR, 𝑄𝑑29 = 10 MVAR and 𝑄𝑑30 = 10 MVAR, respectively. In these tables, the random locations and sizing of the SVCs intended for installation within the system are initially generated. These values are selected to ensure that the fitness values are lower than the loss values before the SVCs are installed. Each individual in the table must exhibit a loss value lower than the predetermined Fig. 8: Scatter Plot for Random Locations during Initialization at 𝑄𝑑29 = 10 MVAR Fig. 9: Scatter Plot for Random Sizing during Initialization at 𝑄𝑑29 = 10 MVAR Fig. 10: Scatter Plot for Random Locations during Initialization at 𝑄𝑑30 = 10 MVAR Fig. 11: Scatter Plot for Random Sizing during Initialization at 𝑄𝑑30 = 10 MVAR Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 12 https://internationalpubls.com loss setpoint. If any individual's loss value exceeds this threshold, the individual is discarded, and new random parameters are generated until the conditions are met and the pool is populated. Similar observations apply to Tables 2 and 3, where the random locations and sizing ensure that all loss values are below the set threshold. The same approach applies to the tabulation of Table 2 and Table 3, where each individual must have a loss value below the respective loss setpoint. This process will continue until the pool of 20 individuals is fully populated. The loss value plays a critical role in the initialization process, ensuring that all conditions are met before the parameters are saved and the individual pool is filled. Table 1: Results during Initialization at 𝑄𝑑20 = 20 MVAR Individual number Bus 1 Bus 2 Bus 3 SVC1 (MVAR) SVC2 (MVAR) SVC 3 (MVAR) Losses (MW) 1 13 6 27 13.8260 24.3298 10.6595 20.9198 2 9 4 5 78.9507 24.0125 77.6561 20.8891 3 9 4 14 70.8570 43.4650 15.7454 20.8759 4 22 9 13 12.1508 68.9644 34.9300 20.7732 5 9 22 13 30.0967 34.8911 65.4144 20.8774 6 11 4 18 72.7929 30.3723 17.1712 20.5544 7 20 12 13 32.2574 49.6937 2.6678 20.5592 8 11 19 6 56.0493 19.9940 39.2794 20.4981 9 4 30 25 62.0369 4.7758 16.2073 20.9166 10 21 19 8 30.0604 24.5905 42.1181 20.5563 11 11 5 4 103.5479 29.2506 65.0043 20.8198 12 4 10 13 38.5129 35.7691 121.5653 20.7905 13 5 13 3 18.4838 7.0878 24.7200 20.8638 14 18 27 10 8.9261 21.2454 71.0483 20.8953 15 2 8 4 62.5811 0.0009 15.7967 20.8724 16 21 19 21 3.9472 40.6722 27.2335 20.8852 17 13 20 12 65.7334 31.2674 61.2674 20.6977 18 2 7 5 78.9602 34.4887 50.8100 21.0025 19 10 4 6 1.5120 61.8258 55.4426 20.9298 20 12 20 12 0.0366 15.3980 43.8577 20.5739 Note: lossset = 21.0056 MW Table 2: Results during Initialization at 𝑄𝑑29 = 10 MVAR Individual number Bus 1 Bus 2 Bus 3 SVC1 (MVAR) SVC2 (MVAR) SVC 3 (MVAR) Losses (MW) 1 13 6 27 13.826 24.3298 10.6595 20.6346 2 22 9 13 12.1508 68.9644 34.93 20.8619 3 11 4 18 72.7929 30.3723 17.1712 20.7822 4 4 30 25 62.0369 4.7758 16.2073 20.5038 5 28 7 2 26.4459 26.7228 29.7079 20.805 6 27 21 8 25.552 2.4112 24.8121 20.5907 7 27 3 29 8.0628 61.4937 24.5326 20.7664 8 11 5 4 103.5479 29.2506 65.0043 20.7106 9 4 10 13 38.5129 35.7691 121.5653 20.8554 10 5 13 3 18.4838 7.0878 24.72 20.7313 11 2 8 4 62.5811 0.0009 15.7967 20.7363 12 9 13 30 23.2867 29.4977 17.7529 20.6137 13 5 4 29 39.0676 58.3613 29.1629 20.8034 14 6 11 29 81.4159 57.5576 20.2141 20.6683 15 10 4 6 1.512 61.8258 55.4426 20.8317 16 3 5 22 21.0308 65.3124 4.8827 20.7024 17 4 13 19 22.8371 123.7435 7.7486 20.7773 18 4 12 10 72.0421 10.7639 9.2549 20.7946 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 13 https://internationalpubls.com 19 8 11 22 5.2398 15.3611 24.8087 20.8438 20 18 11 29 7.4172 10.3622 8.2225 20.3958 Note: lossset = 20.8632 MW Table 3: Results during Initialization at 𝑄𝑑30 = 10 MVAR Individual number Bus 1 Bus 2 Bus 3 SVC1 (MVAR) SVC2 (MVAR) SVC 3 (MVAR) Losses (MW) 1 13 6 27 13.826 24.3298 10.6595 20.6432 2 22 9 13 12.1508 68.9644 34.93 20.8503 3 11 4 18 72.7929 30.3723 17.1712 20.776 4 4 30 25 62.0369 4.7758 16.2073 20.4383 5 28 7 2 26.4459 26.7228 29.7079 20.8098 6 27 21 8 25.552 2.4112 24.8121 20.6123 7 11 5 4 103.5479 29.2506 65.0043 20.7072 8 4 10 13 38.5129 35.7691 121.5653 20.8445 9 5 13 3 18.4838 7.0878 24.72 20.725 10 2 8 4 62.5811 0.0009 15.7967 20.7298 11 9 13 30 23.2867 29.4977 17.7529 20.3631 12 10 4 6 1.512 61.8258 55.4426 20.8345 13 3 5 22 21.0308 65.3124 4.8827 20.6958 14 4 13 19 22.8371 123.7435 7.7486 20.768 15 4 12 10 72.0421 10.7639 9.2549 20.7899 16 8 11 22 5.2398 15.3611 24.8087 20.8355 17 18 11 29 7.4172 10.3622 8.2225 20.5395 18 5 14 4 48.239 2.6355 44.6505 20.7044 19 28 11 22 5.115 17.3233 1.9047 20.8093 20 13 17 26 140.8439 12.6472 10.9834 20.8245 Note: lossset = 20.8558 MW C. Optimal Location and Sizing Table 4 summarizes the results for optimal locations when 𝑄𝑑20 is increased from 20 MVAR to 100 MVAR, using EP, GOA, and the proposed IGEPO, before a generator outage occurs in the system. For instance, at 𝑄𝑑20 = 100 MVAR, the optimal locations determined by EP are Bus 17, Bus 5, and Bus 20. Under the same reactive power loading, IGEPO identifies Bus 19, Bus 20, and Bus 5 as the optimal locations with the corresponding SVC sizing to be installed into the system of 52.9373 MVAR, 30.1033 MVAR and 108.8579 MVAR before the generator outage. Table 4: Optimal Location for Loading Variation at Bus 20 before Generator Outage Technique 𝑄𝑑20 (MVAR) Optimal location Optimal sizing Bus 1 Bus 2 Bus 3 SVC1 (MVAR) SVC2 (MVAR) SVC3 (MVAR) EP 20 11 19 6 56.0194 19.9756 39.2452 40 20 12 13 32.2572 49.6918 2.6555 60 5 8 20 104.3461 119.1607 104.3813 80 20 19 24 37.1281 71.4052 58.3412 100 17 5 20 62.3643 105.1364 136.502 GOA 20 6 19 7 40.7875 15.9058 28.0966 40 7 19 15 6.5981 43.5271 9.9388 60 21 19 4 38.1404 75.7811 3.6478 80 2 7 20 81.2306 93.4049 106.8923 100 10 20 17 11.34 92.2045 30.2478 IGEPO 20 13 11 20 26.3041 8.6606 25.3855 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 14 https://internationalpubls.com 40 20 13 5 56.9045 17.6416 127.0478 60 13 19 4 47.3036 47.9579 61.9262 80 20 13 3 129.7316 6.3166 119.6156 100 19 20 5 52.9373 30.1033 108.8579 Additionally, Table 4 presents the results for optimal sizing under the same reactive power loading. The optimal sizing determined by EP requires 62.3643 MVAR for SVC1, 105.1364 MVAR for SVC2, and 136.502 MVAR for SVC3 which need to be installed at Buses 17, 5 and 20. In comparison, the GOA technique suggests installing 11.34 MVAR, 92.2045 MVAR, and 30.2478 MVAR into the system for the same reactive power loading which need to be installed at Buses 10, 20 and 17. Detailed results for other reactive power loadings are also included in the table. Table 5 provides the results for optimal locations and sizing for SVCs when 𝑄𝑑20 is varied from 20 MVAR to 100 MVAR during a generator outage at Bus 2. IGEPO identifies Bus 22, Bus 4, and Bus 20 as the optimal locations under this loading condition, with the corresponding SVC installation values of 52.9373 MVAR, 30.1033 MVAR, and 108.8579 MVAR, respectively. Table 5: Optimal Location for Loading Variation at Bus 20 with Generator Outage at Bus 2 Technique 𝑄d20 (MVAR) Optimal location Optimal sizing Bus 1 Bus 2 Bus 3 SVC1 (MVAR) SVC2 (MVAR) SVC3 (MVAR) EP 20 11 19 6 56.0143 19.9741 39.2421 40 20 19 12 33.679 34.9933 97.8911 60 2 10 20 81.8807 137.6307 39.9576 80 20 19 24 37.1271 71.4041 58.3404 100 17 5 20 62.3629 105.1348 136.5008 GOA 20 11 17 20 0.7339 34.9923 115.2514 40 16 19 3 80.8806 60.2989 43.778 60 11 19 8 66.5885 3.0993 39.6884 80 19 8 3 12.6391 25.6815 79.3858 100 20 9 28 111.201 105.0463 13.572 IGEPO 20 20 24 13 26.3041 8.6606 25.3855 40 20 8 11 56.9045 17.6416 127.0478 60 13 4 20 47.3036 47.9579 61.9262 80 20 6 12 129.7316 6.3166 119.6156 100 22 4 20 52.9373 30.1033 108.8579 Meanwhile, GOA identifies Bus 20, Bus 9, and Bus 28 as the optimal locations, while EP identifies Bus 17, Bus 5, and Bus 20. Table 5 also presents the optimal sizing for these conditions. For instance, the optimal sizing determined by EP is 62.3629 MVAR, 105.1348 MVAR, and 136.5008 MVAR, which need to be installed at Bus 17, Bus 5, and Bus 20, as highlighted in the table. Table 6: Optimal Location for Loading Variation at Bus 20 with Generator Outage at Bus 13 Technique 𝑄𝑑20 (MVAR) Optimal location Optimal sizing Bus 1 Bus 2 Bus 3 SVC1 (MVAR) SVC2 (MVAR) SVC3 (MVAR) EP 20 11 19 6 56.0194 19.9756 39.2452 40 20 12 13 32.2572 49.6918 2.6555 60 5 8 20 104.3461 119.1607 104.3813 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 15 https://internationalpubls.com 80 20 19 24 37.1281 71.4052 58.3412 100 17 5 20 62.3643 105.1364 136.502 GOA 20 4 20 13 0.7339 34.9923 115.2514 40 13 6 20 80.8806 60.2989 43.778 60 19 2 16 66.5885 3.0993 39.6884 80 6 20 17 12.6391 25.6815 79.3858 100 20 2 15 111.201 105.0463 13.572 IGEPO 20 11 20 17 114.3041 27.1081 24.3782 40 12 5 20 40.9334 5.4685 45.4552 60 20 19 14 24.923 28.707 26.5299 80 20 21 20 71.0908 -11.2741 32.7062 100 14 20 20 -5.7137 36.0838 77.2096 Similarly, Table 6 presents the results for optimal locations and sizing for SVCs when 𝑄𝑑20 is varied from 20 MVAR to 100 MVAR during a generator outage at Bus 13. IGEPO identifies Bus 11, Bus 20, and Bus 17 as the optimal locations at 𝑄𝑑20 = 20 MVAR, with corresponding SVC installation values of 114.3041 MVAR, 27.1081 MVAR, and 24.3782 MVAR, respectively. In contrast, GOA identifies Bus 4, Bus 20, and Bus 13 as the optimal locations, while EP identifies Bus 11, Bus 19, and Bus 6. The same approach is applied to the loading conditions at Bus 29 and Bus 30, with the optimal locations and sizing identified as shown in Table 7 and Table 8. For instance, under a loading variation of 𝑄𝑑29 = 10 MVAR before a generator outage, EP defines Bus 4, Bus 30, and Bus 25 as the optimal locations, with corresponding optimal sizing of 7.4172 MVAR, 10.3622 MVAR, and 8.2225 MVAR, as shown in Table 7. Table 7: Optimal Location for Loading Variation at Bus 29 before Generator Outage Technique 𝑄d29 (MVAR) Optimal location Optimal sizing Bus 1 Bus 2 Bus 3 SVC1 (MVAR) SVC2 (MVAR) SVC3 (MVAR) EP 10 4 30 25 7.4172 10.3622 8.2225 15 27 3 29 81.3662 57.53 20.185 20 27 3 29 8.0267 61.4508 24.4714 25 4 30 25 62.0369 4.7758 16.2073 30 5 29 4 75.066 57.5757 41.5239 GOA 10 5 18 29 19.8944 14.8692 6.2817 15 11 13 29 22.4482 36.1503 78.7168 20 29 10 3 14.8694 10.5678 13.1169 25 13 6 29 18.3064 25.3139 50.7389 30 14 16 29 17.8422 23.98 132.2493 IGEPO 10 20 16 29 76.9856 10.8446 27.6903 15 29 5 24 15.8619 18.5635 123.5997 20 4 11 29 22.1947 30.3332 13.5563 25 29 4 11 139.9012 33.3262 127.2227 30 29 5 2 13.6046 50.165 121.0529 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 16 https://internationalpubls.com Table 8: Optimal Location for Loading Variation at Bus 29 with Generator Outage at Bus 2 Technique 𝑄𝑑29 (MVAR) Optimal location Optimal sizing Bus 1 Bus 2 Bus 3 SVC1 (MVAR) SVC2 (MVAR) SVC3 (MVAR) EP 10 18 11 29 7.4172 10.3622 8.2225 15 6 11 29 81.3662 57.53 20.185 20 27 3 29 8.0267 61.4508 24.4714 25 4 30 25 62.0369 4.7758 16.2073 30 5 29 4 75.066 57.5757 41.5239 GOA 10 29 23 4 19.8944 14.8692 6.2817 15 29 8 4 22.4482 36.1503 78.7168 20 29 24 12 14.8694 10.5678 13.1169 25 4 15 29 18.3064 25.3139 50.7389 30 19 29 13 17.8422 23.98 132.2493 IGEPO 10 9 29 12 76.9856 10.8446 27.6903 15 17 29 13 15.8619 18.5635 123.5997 20 29 8 16 22.1947 30.3332 13.5563 25 8 29 9 139.9012 33.3262 127.2227 30 10 29 2 13.6046 50.165 121.0529 This approach is also applied to the other two techniques to identify optimal locations for the loading condition at Bus 29. For the same reactive power loading solved using IGEPO, the optimal locations after the generator outage at Generator 2 in the system for 𝑄𝑑29 = 10 MVAR are identified as Bus 9, Bus 29, and Bus 12, with corresponding optimal sizing of 76.9856 MVAR, 10.8446 MVAR, and 27.6903 MVAR, respectively, as highlighted in the table. Table 9 presents the results for optimal locations and sizing for SVCs when 𝑄𝑑29 is varied from 10 MVAR to 30 MVAR during a generator outage at Bus 13. EP identifies Bus 5, Bus 29, and Bus 4 as the optimal locations, while GOA identifies Bus 14, Bus 29, and Bus 13. Detailed results for other reactive power loadings are provided in the same table. Table 9: Optimal Location for Loading Variation at Bus 29 with Generator Outage at Bus 13 Technique 𝑄d29 (MVAR) Optimal location Optimal sizing Bus 1 Bus 2 Bus 3 SVC1 (MVAR) SVC2 (MVAR) SVC3 (MVAR) EP 10 4 30 25 61.9937 4.748 16.728 15 27 3 29 8.0255 61.4613 24.5001 20 27 3 29 8.0227 61.4498 24.4842 25 4 30 25 62.0369 4.7758 16.2073 30 5 29 4 75.065 57.5754 41.5294 GOA 10 8 27 11 27.6411 14.4026 114.019 15 7 30 29 8.7111 7.8013 16.4172 20 29 20 16 38.2434 6.9192 41.6205 25 29 13 17 47.8899 135.9531 13.5845 30 14 29 13 8.7234 64.9786 95.2836 IGEPO 10 3 29 7 28.838 14.4239 6.5461 15 5 7 29 47.2654 7.2383 21.3549 20 29 2 17 23.1187 105.8557 15.9843 25 29 13 8 9.7797 31.922 28.3125 30 5 29 4 71.2597 53.775 37.7159 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 17 https://internationalpubls.com Table 10: Optimal Location for Loading Variation at Bus 30 before Generator Outage Technique 𝑄𝑑30 (MVAR) Optimal location Optimal sizing Bus 1 Bus 2 Bus 3 SVC1 (MVAR) SVC2 (MVAR) SVC3 (MVAR) EP 10 9 13 30 23.2415 29.4662 17.726 15 9 13 30 23.2867 29.4977 17.7529 20 4 30 25 62.0369 4.7758 16.2073 25 4 30 25 62.0369 4.7758 16.2073 30 29 6 8 47.8434 94.3393 18.9707 GOA 10 2 29 9 22.0278 20.7151 8.5245 15 15 30 15 18.7707 29.855 23.414 20 30 20 8 126.6807 23.3393 13.7491 25 30 21 19 47.1259 45.4744 38.2877 30 29 27 6 13.2276 15.981 92.1754 IGEPO 10 30 8 9 21.5984 27.8094 16.0646 15 9 13 30 23.5395 29.7505 18.0057 20 9 13 30 25.9117 36.4536 64.3652 25 28 3 30 120.3978 77.5099 10.7773 30 10 29 4 47.4582 15.6005 82.6972 Table 10 presents the results for optimal locations when 𝑄𝑑30 is increased from 10 MVAR to 30 MVAR, solved using EP, GOA, and the proposed IGEPO technique, before a generator outage is experienced in the system. For example, at 𝑄𝑑30 = 10 MVAR, the optimal locations identified using EP are Bus 9, Bus 13, and Bus 30. In contrast, under the same reactive power loading, IGEPO identifies Bus 30, Bus 8, and Bus 9 as the optimal locations before the generator outage. Detailed results for other reactive power loadings are provided in the same table. Table 11 provides the results for optimal locations and sizing of SVCs when 𝑄𝑑30 is varied from 10 MVAR to 30 MVAR during a generator outage at Bus 2. IGEPO identifies Bus 30, Bus 9, and Bus 28 as the optimal locations at Qd30 = 30 MVAR. The corresponding SVC installation values are 47.4582 MVAR, 15.6005 MVAR, and 82.6972 MVAR, respectively. Table 11: Optimal Locations and Sizing for 𝑄𝑑30 during Generator Outage at Bus 2 Technique 𝑄d30 (MVAR) Optimal location Optimal sizing Bus 1 Bus 2 Bus 3 SVC1 (MVAR) SVC2 (MVAR) SVC3 (MVAR) EP 10 9 13 30 23.2415 29.4662 17.726 15 9 13 30 23.2867 29.4977 17.7529 20 4 30 25 62.0369 4.7758 16.2073 25 4 30 25 62.0369 4.7758 16.2073 30 29 6 8 47.8434 94.3393 18.9707 GOA 10 27 7 22 22.0278 20.7151 8.5245 15 30 9 12 18.7707 29.855 23.414 20 11 27 29 126.6807 23.3393 13.7491 25 3 30 4 47.1259 45.4744 38.2877 30 30 30 13 13.2276 15.981 92.1754 IGEPO 10 9 13 30 21.5984 27.8094 16.0646 15 9 13 30 23.5395 29.7505 18.0057 20 30 5 11 25.9117 36.4536 64.3652 25 11 2 30 120.3978 77.5099 10.7773 30 30 9 28 47.4582 15.6005 82.6972 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 18 https://internationalpubls.com Table 12 outlines the results for optimal locations and sizing for SVCs when 𝑄𝑑30 is varied from 10 MVAR to 30 MVAR during a generator outage at Bus 13. At 𝑄𝑑30 = 20 MVAR, EP identifies Bus 4, Bus 30, and Bus 25 as the optimal locations, while GOA identifies Bus 30, Bus 20, and Bus 12. The optimal sizing determined by IGEPO are 66.288 MVAR, -4.6007 MVAR, and 19.4587 MVAR, which need to be installed at Bus 28, Bus 3, and Bus 30, as highlighted in the table. Detailed results for other reactive power loadings are also available. Table 12: Optimal Locations and Sizing for 𝑄𝑑30 during Generator Outage at Bus 13 Technique 𝑄𝑑30 (MVAR) Optimal location Optimal sizing Bus 1 Bus 2 Bus 3 SVC1 (MVAR) SVC2 (MVAR) SVC3 (MVAR) EP 10 9 13 30 23.2504 29.4537 17.7262 15 9 13 30 23.2867 29.4977 17.7529 20 4 30 25 62.0369 4.7758 16.2073 25 4 30 25 62.0369 4.7758 16.2073 30 29 6 8 47.8427 94.3393 18.9722 GOA 10 6 4 30 6.9627 22.4195 4.136 15 5 30 8 89.5627 30.202 5.021 20 30 20 12 14.6199 16.4513 47.7941 25 6 27 4 20.593 57.0328 49.7719 30 29 27 10 14.0338 66.2988 84.3964 IGEPO 10 13 3 27 149.1441 14.6735 17.5478 15 9 13 30 23.5835 29.7945 18.0498 20 28 3 30 66.288 -4.6007 19.4587 25 5 30 26 108.1328 33.6528 -0.8637 30 17 27 8 17.9425 55.0943 15.5303 Table 13 summarizes the loss values (in MW) for various reactive power loadings, both before and after SVC installation, and under both normal and generator outage conditions, using the three optimization techniques: EP, GOA, and IGEPO. For instance, at 𝑄𝑑20 = 20 MVAR, the loss without a generator outage before SVC installation is 18.2559 MW, which reduces to 17.6566 MW after SVC installation optimized by EP. In the event of a generator outage, the loss before SVC installation is 21.0056 MW, which decreases to 20.4981 MW after SVC installation using EP. Similarly, under the same reactive power loading, GOA reduces the loss from 18.2559 MW to 18.0014 MW after SVC installation. For the IGEPO technique with 𝑄𝑑20 = 20 MVAR, the loss without a generator outage drops from 18.2559 MW before SVC installation to 17.5563 MW after SVC installation. During a generator outage, IGEPO reduces the loss from 21.0056 MW to 20.3919 MW after SVC installation. The results indicate that IGEPO consistently demonstrates substantial loss reduction after SVC installation across all loading conditions, underscoring its effectiveness in minimizing losses. Additionally, the result shows that the proposed IGEPO method achieves the lowest loss values for all loading variations at Bus 20, Bus 29, and Bus 30, demonstrating that IGEPO outperforms both GOA and traditional EP, regardless of the loading conditions. Table 13: Losses Value with and without Generator Outage at Bus 20 before and after SVC Installation Technique 𝑄𝑑20 (MVAR) Loss without Generator outage Loss with Generator outage Before After Before After Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 19 https://internationalpubls.com (MW) (MW) (MW) (MW) EP 20 18.2559 17.6566 21.0056 20.4981 40 19.7678 17.8953 22.7643 21.3836 60 22.7897 19.3242 25.8874 22.1345 80 28.962 20.4412 31.7932 23.3497 100 42.6276 19.4661 46.2123 22.3974 GOA 20 18.2559 18.0014 21.0056 20.939 40 19.7678 19.2832 22.7643 21.7151 60 22.7897 22.7529 25.8874 24.5546 80 28.962 22.7252 31.7932 28.9067 100 42.6276 17.8337 46.2123 22.4353 IGEPO 20 18.2559 17.5563 21.0056 20.2893 40 19.7678 17.6726 22.7643 20.461 60 22.7897 18.6306 25.8874 20.4302 80 28.962 18.3941 31.7932 22.0156 100 42.6276 19.115 46.2123 20.8532 IV. CONCLUSION This paper presents a novel optimization technique, Integrated Grasshopper Evolutionary Programming Optimization (IGEPO), developed to improve the installation of static var compensators (SVCs) for efficient loss minimization in power systems, especially during generator outages. IGEPO integrates the strengths of two powerful algorithms: the Grasshopper Optimization Algorithm (GOA), which excels at exploring a wide search space, and Evolutionary Programming (EP), which focuses on refining solutions. This hybrid approach provides a comprehensive search mechanism, reducing the risk of getting stuck in local optima, a common problem in conventional optimization methods. By blending these two approaches, IGEPO ensures more balanced and efficient optimization. The primary objective of IGEPO is to determine the optimal placement and sizing of SVCs, which are crucial for controlling reactive power and reducing loss in power system. Finding the best locations and sizes for SVCs is challenging, especially in power systems experiencing generator outages that disrupt normal operations. IGEPO addresses this challenge by offering optimal solutions that minimize power system losses under varying loading conditions. A standout feature of IGEPO is its adaptability to the complexities of power systems with generator outages, which can cause increased system losses. IGEPO has shown its capability to adapt to these dynamic conditions, consistently finding the most effective SVC configurations, regardless of changing system demands. Tested on the IEEE Reliability Test System (RTS), IGEPO consistently outperformed traditional EP and GOA techniques, achieving the lowest power loss values across all loading scenarios. Beyond SVC installation, IGEPO’s potential applications extend to optimizing power flow, enhancing voltage stability, and integrating renewable energy sources into the grid. Its adaptability makes it well-suited for modern power systems, which face increasingly complex network structures and the need for more efficient energy management. IGEPO could also be expanded to optimize energy storage systems, distributed generation units, and other critical components, ensuring that power systems remain efficient, reliable, and resilient as they evolve. Acknowledgment The authors would like to acknowledge the contribution and support by Universiti Teknologi MARA, Universiti Tenaga Nasional (UNITEN) and Universiti Kebangsaan Malaysia (UKM). This project is Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 20 https://internationalpubls.com partially supported by the Innovation and Research Management Centre (iRMC) at Universiti Tenaga Nasional (UNITEN) under the project code BOLD2025 (J510050951). REFERENCES [1] W. Wu and Y. 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