# Application of Jellyfish Search Algorithm for Reactive Power Planning-based Power Losses Minimization in Electrical Power Networks

Sultan Hassan Hakmi

► To cite this version:

Sultan Hassan Hakmi. Application of Jellyfish Search Algorithm for Reactive Power Planning-based Power Losses Minimization in Electrical Power Networks. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0332. hal-05073757

HAL Id: hal-05073757

https://utc.hal.science/hal-05073757v1

Submitted on 19 May 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Application of Jellyfish Search Algorithm for Reactive Power Planning-based Power Losses Minimization in Electrical Power Networks

Sultan Hassan Hakmi

Department of Electrical and Electronic Engineering, College of Engineering and Computer Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia;

shhakmi@jazanu.edu.sa

***Abstract***—This study investigates the application of the Jellyfish Search Optimization (JFSO) algorithm for Reactive Power Planning (RPP) to minimize power losses in electrical power networks. The RPP problem is formulated as a multi-objective optimization task that seeks to reduce active power losses and minimize the investment costs of reactive power compensators. The performance of the JFSO algorithm is benchmarked against Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms on the IEEE 30-bus test system under two case studies: (1) minimizing active power losses alone and (2) minimizing both losses and investment costs. For minimizing the losses in Case 1, JFSO reduced power losses from an initial 5.6 MW with 18.2% reduction, compared to 16.8% for DE and 11.0% for PSO. In Case 2, JFSO minimized the total costs to $2,391,466/year, outperforming DE and PSO, which resulted in $2,435,863/year and $2,629,826/year, respectively. The findings demonstrate that JFSO offers superior optimization performance with enhanced convergence properties. By effectively balancing investment and operational costs, the proposed algorithm provides a robust solution for efficient RPP.

***Keywords***— Jellyfish search algorithm; Reactive power planning; Power losses minimization; Electrical power networks.

## I. INTRODUCTION

As power systems evolve to accommodate increasing loads, renewable energy integration, and the demands of smart grid technologies, the need for efficient management of reactive power has become more pressing. Reliability and security are fundamental priorities for power system operators to ensure the effective transmission and distribution of electricity [1]–[3]. Reactive power planning (RPP), a critical component in maintaining this delicate balance, plays a vital role in stabilizing voltage levels and safeguarding system reliability. RPP focuses on optimizing the placement and sizing of reactive power sources, such as shunt power capacitors (SPCs), to meet operational objectives while adhering to technical constraints. These objectives typically include minimizing the investment cost of new reactive power devices, reducing system operation costs by lowering power losses, and improving the overall voltage profile and stability of the network [4], [5]. Managing reactive power is essential to mitigating voltage fluctuations and preventing grid instability. Historically, fixed compensating devices were utilized to regulate various parameters within interconnected power networks. However, advancements in technology have introduced Flexible Alternating Current Transmission System (FACTS) devices [6]–[8] revolutionizing traditional approaches to power control.

Conventional approaches to RPP frequently fail to address several practical considerations in managing reactive power. Notably, existing models often neglect the financial

advantages associated with freeing up transformer capacity through the deployment of SPCs. By releasing transformer capacity, system operators can mitigate overload conditions, enhance the efficiency of power transmission and distribution, and delay the need for expensive infrastructure expansions. To address active power losses and minimize voltage deviations in power systems, the study in [9] proposed a hybrid krill herd algorithm for solving the optimal RPP problem, incorporating FACTS devices. In [10], researchers developed an enhanced Genetic Algorithm, achieving substantial reductions in transmission congestion. Researchers in [11] introduced the Whale Optimization Algorithm (WOA) to tackle the RPP challenge, using the IEEE 30 and IEEE 57 bus systems as benchmark networks. Further advancements in solving RPP were made through methods such as a fuzzy-based procedure [12],[13], hybrid Harris Hawk Optimizer (HHO)-PSO [14], Differential Evolution (DE) [15], social network search [16], oppositional-based HHO [17] and backtracking searching [18]. The work in [19] utilized Particle Swarm Optimization (PSO) to analyze the impact of Static Var Compensators (SVC) and Thyristor-Controlled Series Compensators (TCSC) on active and reactive power flows within the IEEE 14-bus test system. Meanwhile, to mitigate voltage collapse, reduce load shedding, and improve system loadability, the authors in [20] introduced a methodology based on Improved Moth Flame Optimizer (IMFO). The MFO was employed to determine both the optimal size and placement of TCSC devices.

Additionally, [21] presented a performance evaluation of Fractional Order Darwinian PSO (FODPSO) with varying fractional orders for Optimal Reactive Power Dispatch (ORPD) on the IEEE 30, IEEE 57, and IEEE 118 bus systems, focusing on the strategic placement of TCSC and SVC devices. Meanwhile, the study in [22] introduced a hybrid DE-Crow Search Algorithm to solve RPP for India’s 62-bus and 191-bus systems. The RPP problem has been addressed by predefining locations for the installation of SVC and TCSC devices. In [23], the authors utilized the Ant Lion Algorithm and its modified variant to optimize the placement of FACTS devices for resolving the RPP problem. Similarly, [24] employed a hybrid CSA-JAYA algorithm to solve the RPP problem for the IEEE 30 and UPSEV 75 bus systems, analyzing system behavior under varying load conditions. To handle ORPP under unbalanced conditions, [25] introduced the Backtracking-Assisted Elephant Herding Optimizer (BAEHO) algorithm, incorporating UPFC devices into the optimization process. Furthermore, the study examined the impact of SVC devices on system performance across multiple operating scenarios. The RPP was also analyzed under normal load and elevated load conditions, as highlighted in [26], providing insights into the system’s response and improvements under these scenarios. The
gradual increase in system loading and the mitigating role of SVC installation in addressing these effects were examined in the same study. In [27], an Improved DE (IDE) algorithm was proposed to solve the RPP problem, with standard IEEE test systems utilized for validation. Similarly, [28] introduced an enhanced version of the IDE algorithm tailored to handle RPP challenges under varying load conditions.

The movement trends of jellyfish have recently captivated a new optimisation strategy of the Jellyfish Search Optimisation (JFSO) algorithm introduced in [29]. They are separated into three groups. The jellyfish may first drift in the direction of the ocean flow or among its entire swarming. In the meantime, the jellyfishes are drawn to their areas whenever there is a sufficient amount of food. The quantity of food is also shown by the quantitative fitness indicator. JFSO has recently been utilized successfully across a variety of engineering applications, demonstrating its effectiveness in solving complex challenges [30]–[37].

Hence, in this paper, the JFSO algorithm is employed for reactive power planning-based power losses minimization in electrical power networks. For comparison purposes, the well-known population-based effective algorithms of DE and PSO besides the designed JFSO are implemented as well. The applications are performed on the standard IEEE 30-bus system. The minimization objective of power losses is addressed. Two cases studies are simulated with/without considering the investment costs of reactive power compensators. This novel application of the JFSO provides the following main contributions:

* **Distinctive Application to RPP:** The work optimizes JFSO algorithm for solving RPP problems by addressing unique constraints, transformer tap settings, and voltage profile enhancements, minimizing power losses and investment costs.

* **Performance Superiority Over Existing Algorithms:** The study benchmarks JFSO against established algorithms (DE and PSO). The results demonstrate that JFSO achieves significantly better performance in terms of minimizing active power losses (18.2% reduction compared to 16.8% for DE and 11.0% for PSO) and reducing investment costs in reactive power compensators.

* **Balancing Investment and Operational Costs:** The approach uses a dual-objective optimization framework to minimize operational losses and investment costs, ensuring cost-effectiveness and operational efficiency in modern power systems.

## II. RPP FORMULATION

The primary goal of the RPP problem is to minimize a composite objective function comprising two key components: the total cost of energy losses ($f_i$) and the investment cost associated with reactive power (VAr) production ($f_2$). The mathematical representation of the objective function is given as:

$$ \text{Min } F = f_1 + f_2 \qquad (1) $$

### A. Minimization of cost of energy loss

The first term ($f_i$) accounts for the operational costs associated with active power losses in the system. These losses are evaluated based on the tariff of active power generation ($H_{loss}$) and on annual basis with hour duration ($D_H$) of 8760 hr. The cost formulation is expressed as:

$$ \text{Min } f_i = H_{loss} \times D_H \times Ploss \qquad (2) $$

### B. Minimization of investment cost of VAr sources

The second term ($f_2$) represents the investment cost for installing reactive power (VAr) sources. This cost is calculated considering the depreciation rate, the expected operational lifetime of the VAr sources, and their average utilization rate. The formulation for this component is as follows:

$$ \text{Min } f_2 = \frac{\sum_{i=1}^{N_b} (e_i + C_{c_i} |Q_{c_i}|)}{\text{Average working rate} * \text{lifetime} * 8760} \qquad (3) $$

By optimizing both terms, the RPP framework ensures a balanced approach to minimizing operational and investment costs while maintaining efficient and reliable system performance.

### C. Equality and inequality constraints

To ensure the power system operates effectively, it must satisfy a set of constraints. These include equality constraints, which represent the load flow balance equations, and inequality constraints, which impose limits on the operational variables of the system. The equality constraints ensure that power generation and demand are balanced across the system, maintaining the fundamental load flow equations. These constraints account for factors such as the voltage angle difference ($\theta_{ij}$) between buses i and j, voltage magnitudes ($V_i$ and $V_j$), and the mutual conductance ($G_{ij}$) and susceptance ($B_{ij}$) between these buses. These constraints are mathematically formulated as follows:

$$ Q_{g,i} + Q_{c,i}^{n} - Q_{Li} - V_i \sum_{j=1}^{N_b} V_j (-B_{ij} \cos \theta_{ij} + G_{ij} \sin \theta_{ij}) = 0, \qquad (4) $$

$$ P_{g,i} - P_{Li} - V_i \sum_{j=1}^{N_b} V_j (B_{ij} \sin \theta_{ij} + G_{ij} \cos \theta_{ij}) = 0, \qquad (5) $$

The inequality constraints encompass various operational limitations, including:

* Voltage Magnitude Limits ($V_i$):

$$ V_i^{\min} \leq V_i \leq V_i^{\max}, \quad i=1, 2, \dots, N_b \qquad (6) $$

* Transformer Tap Settings ($T_k$):

$$ T_k^{\min} \leq T_k \leq T_k^{\max}, \quad k=1, 2, \dots, N_t \qquad (7) $$

* Apparent Power Flow Limits ($S_L^{flow}$):

$$ |S_L^{flow}| \leq S_L^{max}, \quad L=1, 2, \dots, N_L \qquad (8) $$

* Reactive Power Limits of Existing ($Q_{c,e}$) and New ($Q_{c^n}$) Sources:

$$ 0 \leq Q_{c,e} \leq Q_{c,e}^{max}, \quad e=1, 2, \dots, N_c \qquad (9) $$

$$ 0 \leq Q_{c,j}^{n} \leq Q_{c,j}^{max(n)}, \quad j \in \text{ candidate buses} \qquad (10) $$
* Active Power Limits of Slack bus machine ($P_s$):

$$P_s^{min} \leq P_s \leq P_s^{max} \qquad (11)$$

* Reactive Power Limits of all generators ($Q_{gi}$):

$$Q_{gi}^{min} < Q_{gi} < Q_{gi}^{max}, \quad i=1, 2, \dots, N_{pv} \qquad (12)$$

By adhering to these constraints, the system ensures reliable and efficient operation while maintaining compliance with physical and technical limits.

### III. JFSO ALGORITHM

A novel optimisation framework called the JFSO algorithm was put out in [29]. The jellyfish may first drift in the direction of the ocean flow or among its entire swarming. In the meantime, the jellyfishes are drawn to their areas whenever there is a sufficient amount of food. The volume of food is also shown by the numeric fitness function. The following is an arithmetic representation of the original population:

$$X_i(t+1) = 4 \times (1-X_i) \times P_0, \quad 0 \leq P_0 \leq 1 \qquad (13)$$

where $P_o$ is a randomised value that falls between 0 and 1 and does not correspond to {0,0.0,0.25,0.75,0.5,1.0}, and $X_i(t+1)$ denotes the ith jellyfish chaotic counterpart. Eq. (14) is used to assess the outcome of the time-varying regulation factor $CF(t)$, which varies over time from 0 to 1:

$$CF(t) = \left| (-1 + (2 \times r_i)) \times \left( \frac{-t}{T^{\text{max}}} + 1 \right) \right| \qquad (14)$$

where $r_i$ is a randomised result inside the interval [0,1], $t$ represents a count of iterations, and $T^{max}$ indicates the greatest length of iterations. Each jellyfish's new location could be created using Eq. (15) if the $CF$ level exceeds 0.5.

$$X_i(t+1) = X_i(t) + R \times (X^* - 3 \times \mu \times R) \qquad (15)$$

where $R$ is a randomly selected quantity, $X^*$ reflects the jellyfishes' optimal location amongst the group, and $\mu$ provides the jellyfishes' average. Either Eq. (16), which represents the passive type, or Eq. (17), which follows the passive type, might be used to determine each jellyfish's new location if the $CF$ value is less than 0.5, depending on how it moves within the swarm:

$$X_i(t+1) = X_i(t) + \frac{(U_b - L_b)}{10} \times R \qquad (16)$$

$$X_i(t+1) = \begin{cases} X_i(t)(1+R \times (X_j(t)-1)) & \text{if } f(X_i) \geq f(X_j) \\ X_i(t)(1+R \times (1-X_j(t))) & \text{if } f(X_i) < f(X_j) \end{cases} \qquad (17)$$

where $f$ represents the amount of food, and $U_b$ and $L_b$ represent the upper and lower bounds of the governing variables. The examination mechanism for each position to be restored in the closest boundary is described by Eq. (18).

$$\begin{cases} X'_{i,d} = L_b(d) + (X_{i,d} - U_{b,d}) & \text{if } X_{i,d} > U_{b,d} \\ X'_{i,d} = U_b(d) + (X_{i,d} - L_{b,d}) & \text{if } X_{i,d} < L_{b,d} \end{cases} \qquad (18)$$

where the ith jellyfish's location in the dth dimension is indicated by $X_{i,d}$. The main phases of the JFSO are shown in Figure 1.

### IV. NUMERICAL RESULTS

The standardized IEEE 30-bus electrical system is taken into consideration in order to assess the execution and efficiency of the suggested JFSO algorithm to address the RPP issue. In contrast to the popular PSO and DE algorithms, which have 200 peak iterations and search groups of 50 members, 20 simulation runs are conducted using the designed JFSO. Also, the initial populations for all algorithms (JFSO, DE, and PSO) were generated randomly within the boundaries of the control variables. This ensures a consistent basis for comparison. The investigated standardized system includes 41 transmission lines, 30 buses, 4 tap changers, 6 generators and 9 reactive power devices, is shown in Fig. 2. This system's entire set of data is taken from [38]. Generator voltages range from 1.1 to 0.95 p.u., which are the greatest and lowest values, respectively. Table I displays the parameters used in the economic cost functions and also the parameters of DE, PSO and JFSO algorithms.

<table><caption>TABLE I Parameters used in the cost functions and the applied algorithms</caption><thead><tr><th colspan="2">Parameters used in the economic cost functions</th></tr></thead><tbody><tr><td>e<sub>i</sub></td><td>1000 $</td></tr><tr><td>c<sub>ci</sub></td><td>30,000 $/MVAr</td></tr><tr><td>h<sub>loss</sub></td><td>60 $/MWhr</td></tr><tr><th colspan="2">Parameters used in the applied algorithms</th></tr><tr><td>DE</td><td>Mutation Factor = 0.5; Crossover = 0.5; Population Size=50 and Iterations =200</td></tr><tr><td>PSO</td><td>Cognitive parameter = 2; Social parameter = 0.5; Population Size=50 and Iterations =200</td></tr><tr><td>JFSO</td><td>Population Size=50 and Iterations =200</td></tr></tbody></table>

The study evaluates two distinct scenarios, described as follows:

* Case 1: Focuses solely on minimizing active power losses, treating this as a standalone objective function.

* Case 2: Aims to minimize both the investment costs associated with installing new reactive power compensators and the operational costs arising from active power losses. This case is formulated mathematically as described in Equation 1.

#### 1) Case 1: Power losses minimization

The proposed JFSO algorithm has been run for Case 1 in contrast to the popular PSO and DE algorithms. For the standardized IEEE 30-bus system, the maximum number of installed Var devices is limited to six and each capacity is limited to thirty MVAr. Their optimal outcomes of the control variables and its corresponding losses are shown in Table II while Fig. 3 depicts the convergences of DE, PSO and JFSO for Case 1. The results in Table II reveal that JFSO achieves the most significant reduction in power losses, outperforming both DE and PSO. While the initial power losses of the system were 5.6 MW, JFSO reduces these losses to 4.581 MW, representing an 18.2% reduction. In comparison, DE achieves a 16.8% reduction, lowering the losses to 4.66 MW, and PSO delivers a more modest 11.0% reduction, reaching 4.986 MW. This demonstrates that JFSO is not only highly effective in minimizing losses but also surpasses the established benchmarks of DE and PSO.
<figure><img src="image_2.png" /><figcaption>Fig. 1. Applied JFSO Flowchart for solving the RPP.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. IEEE 30-bus network [39].</figcaption></figure>

Another critical factor is the allocation of reactive power (QC) across the buses. JFSO employs a more strategic and balanced distribution of reactive power devices compared to DE and PSO. It adheres to the constraint of using a maximum of six devices, each with a capacity limit of 30 MVAr. For example, JFSO allocates 11.31 MVAr at Bus 12 and 11.44 MVAr at Bus 21, ensuring a well-balanced system response. In contrast, DE and PSO allocate higher capacities to higher buses, which could lead to underutilization of available resources.

<table><caption>TABLE II Results of DE, PSO and JFSO for Case 1</caption><thead><tr><th></th><th>DE</th><th>PSO</th><th>JFSO</th></tr></thead><tbody><tr><td>Vg1</td><td>1.099986</td><td>1.075</td><td>1.099502</td></tr><tr><td>Vg2</td><td>1.096608</td><td>1.064944</td><td>1.091037</td></tr><tr><td>Vg5</td><td>1.074824</td><td>1.057913</td><td>1.068822</td></tr><tr><td>Vg8</td><td>1.072298</td><td>1.063223</td><td>1.071374</td></tr><tr><td>Vg11</td><td>1.062538</td><td>1.029959</td><td>1.063012</td></tr><tr><td>Vg13</td><td>1.085611</td><td>1.029623</td><td>1.098061</td></tr><tr><td>T6-9</td><td>1.061611</td><td>1.1</td><td>0.999985</td></tr><tr><td>T6-10</td><td>0.960753</td><td>1</td><td>0.995743</td></tr><tr><td>T4-12</td><td>1.005084</td><td>1</td><td>1.008459</td></tr><tr><td>T28-27</td><td>0.970507</td><td>1</td><td>0.972953</td></tr><tr><td>QC1</td><td>10.57 (Bus 4)</td><td>5.11 (Bus 5)</td><td>9.06 (Bus 7)</td></tr><tr><td>QC2</td><td>5.42 (Bus 5)</td><td>26.00 (Bus 8)</td><td>11.31 (Bus 12)</td></tr><tr><td>QC3</td><td>12.05 (Bus 9)</td><td>15.26 (Bus 12)</td><td>7.66 (Bus 15)</td></tr><tr><td>QC4</td><td>3.49 (Bus 11)</td><td>6.00 (Bus 17)</td><td>11.44 (Bus 21)</td></tr><tr><td>QC5</td><td>9.38 (Bus 12)</td><td>18.80 (Bus 21)</td><td></td></tr><tr><td>QC6</td><td>6.16 (Bus 22)</td><td>2.34 (Bus 23)</td><td></td></tr><tr><td>Loss (MW)</td><td>4.66053</td><td>4.986577</td><td>4.581072</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Fig. 3. Convergences of DE, PSO and JFSO for Case 1</figcaption></figure>
Not only that, Fig. 4 illustrates the significant improvement of voltages at all buses using the proposed RPP allocation compared to the initial case. Also, as shown in Fig.

5, the designed JFSO achieves the lowest maximum, mean and minimum objective ratings of the power losses compared to DE and PSO.

<figure><img src="image_5.png" /><figcaption>Fig. 4. Voltage Profiles of DE, PSO and JFSO for Case 1 compared to the initial case</figcaption></figure>

## 2) Case 2: Investment costs of new VAr compensators and operational costs of losses minimization

The proposed JFSO algorithm has been run for Case 2 in contrast to the popular PSO and DE algorithms. Their optimal outcomes of the control variables and its corresponding losses are shown in Table III while Fig. 6 depicts the convergences of DE, PSO and JFSO for Case 2. As shown, JFSO achieves the most significant reduction in power losses and the investment costs as well, outperforming both DE and PSO. JFSO reduces the costs to 2391466 $/year while DE and PSO achieve counterparts of 2435863 and 2629826 $/year. Simultaneously, JFSO reduces the losses from 5.6 MW to 4.55 MW, representing an 18.75% reduction. In comparison, DE achieves a 17.24% reduction, lowering the losses to 4.634 MW, and PSO delivers a more modest 10.65% reduction, reaching 5 MW. Also, as shown in Fig. 7, the designed JFSO achieves the lowest maximum, mean and minimum objective ratings of the power losses compared to DE and PSO.

<table><caption>TABLE III Results of DE, PSO and JFSO for Case 2</caption><thead><tr><th></th><th>DE</th><th>PSO</th><th>JFSO</th></tr></thead><tbody><tr><td>Vg1</td><td>1.097085</td><td>1.075</td><td>1.099661</td></tr><tr><td>Vg2</td><td>1.092176</td><td>1.075</td><td>1.092276</td></tr><tr><td>Vg5</td><td>1.079097</td><td>1.050125</td><td>1.071207</td></tr><tr><td>Vg8</td><td>1.074341</td><td>1.048499</td><td>1.074414</td></tr><tr><td>Vg11</td><td>1.073935</td><td>1.092109</td><td>1.08488</td></tr><tr><td>Vg13</td><td>1.091221</td><td>1.025999</td><td>1.091644</td></tr><tr><td>T6-9</td><td>1.012065</td><td>1</td><td>0.981912</td></tr><tr><td>T6-10</td><td>1.018529</td><td>1.1</td><td>1.018379</td></tr><tr><td>T4-12</td><td>1.005079</td><td>1</td><td>1.004505</td></tr><tr><td>T28-27</td><td>0.974972</td><td>1</td><td>0.962021</td></tr><tr><td>QC1</td><td>6.79 (Bus 6)</td><td>4.70 (Bus 6)</td><td>7.30 (Bus 7)</td></tr><tr><td>QC2</td><td>7.07 (Bus 7)</td><td>3.79 (Bus 8)</td><td>12.14 (Bus 10)</td></tr><tr><td>QC3</td><td>3.18 (Bus 15)</td><td>4.00 (Bus 9)</td><td>20.84 (Bus 12)</td></tr><tr><td>QC4</td><td>6.39 (Bus 20)</td><td>7.36 (Bus 11)</td><td>8.01 (Bus 15)</td></tr><tr><td>QC5</td><td>6.91 (Bus 21)</td><td>9.87 (Bus 12)</td><td>7.32 (Bus 17)</td></tr><tr><td>QC6</td><td>6.66 (Bus 22)</td><td>4.24 (Bus 30)</td><td>8.18 (Bus 21)</td></tr><tr><td>f1 (MW)</td><td>4.634443</td><td>5.003474</td><td>4.549974</td></tr><tr><td>f2 ($/year)</td><td>2435863</td><td>2629826</td><td>2391466</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>Fig. 5. Maximum, mean and objective ratings of DE, PSO and JFSO for Case 1</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6. Convergences of DE, PSO and JFSO for Case 2</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 7. Maximum, mean and minimum objective ratings of DE, PSO and JFSO for Case 2</figcaption></figure>

In order to assess the convergence time of the DE, PSO and JFSO in the two investigated cases, Table IV displays their computing time in each iteration. As shown, in the first case, where the focus is solely on minimizing power losses, JFSO exhibits a convergence time of 1.097 seconds per iteration. This is slightly faster than DE (1.101618 seconds) and comparable to PSO (1.066 seconds). The negligible differences in convergence times among the three algorithms indicate that all methods handle the simpler optimization task with similar computational efficiency. In the second case, which incorporates the dual objectives of minimizing power losses and investment costs, JFSO demonstrates a significant advantage with a convergence time of 1.1838 seconds per iteration. This is markedly faster than both DE (1.2725 seconds) and PSO (1.3515 seconds).

<table><caption>TABLE IV Convergence time/iteration of DE, PSO and JFSO algorithms for RPP problem</caption><thead><tr><th></th><th>DE</th><th>PSO</th><th>JFSO</th></tr></thead><tbody><tr><th>Case 1</th><td>1.101618 s</td><td>1.066 s</td><td>1.097 s</td></tr><tr><th>Case 2</th><td>1.2725 s</td><td>1.3515 s</td><td>1.1838 s</td></tr></tbody></table>

### 3) Sensitivity Analysis of JFSO Algorithm

To evaluate the robustness of the JFSO algorithm, a sensitivity analysis was conducted by varying key algorithm parameters, such as population size and maximum number of iterations. Table IV summarizes the results, including statistical indicators such as minimum, mean, average, and standard deviation (STD) of the solutions obtained for different combinations of population size and maximum iterations.

As shown, the sensitivity analysis reveals that increasing the population size and maximum number of iterations consistently improves the minimum, mean, and average costs. For instance, the minimum cost decreased from 2,474,529 (population size of 100 and 20 iterations) to 2,391,466 (population size of 200 and 50 iterations), demonstrating better optimization results with more comprehensive searches. The STD decreases as the population size and iterations increase, indicating improved convergence stability. For example, the STD drops from 87,939.38 (population size of 150, 20 iterations) to 26,552.19 (population size of 150, 50 iterations), reflecting more consistent solutions. While larger population sizes and iteration counts yield better results, the improvements diminish at higher values. For instance, increasing the population size from 150 to 200 results in smaller gains compared to the improvement observed between 100 and 150.

<table><caption>TABLE V Sensitivity analysis results of JFSO algorithm for RPP problem</caption><thead><tr><th>Statistical Indicators</th><th>Population Size/Maximum Number of Iterations</th><th>20</th><th>30</th><th>40</th><th>50</th></tr></thead><tbody><tr><td>Minimum</td><td>100</td><td>2474529</td><td>2469248</td><td>2461060</td><td>2460138</td></tr><tr><td>Mean</td><td>100</td><td>2605511</td><td>2562967</td><td>2536481</td><td>2526578</td></tr><tr><td>Average</td><td>100</td><td>2743465</td><td>2674989</td><td>2668078</td><td>2625408</td></tr><tr><td>STD</td><td>100</td><td>77486.12</td><td>55736.43</td><td>46054.82</td><td>50612.25</td></tr><tr><td>Minimum</td><td>150</td><td>2443347</td><td>2435394</td><td>2406193</td><td>2424445</td></tr><tr><td>Mean</td><td>150</td><td>2549107</td><td>2499851</td><td>2484510</td><td>2472451</td></tr><tr><td>Average</td><td>150</td><td>2726784</td><td>2583111</td><td>2547754</td><td>2524024</td></tr><tr><td>STD</td><td>150</td><td>87939.38</td><td>41120.58</td><td>44686.26</td><td>26552.19</td></tr><tr><td>Minimum</td><td>200</td><td>2417816</td><td>2415632</td><td>2401397</td><td>2391466</td></tr><tr><td>Mean</td><td>200</td><td>2528936</td><td>2469440</td><td>2457913</td><td>2441443</td></tr><tr><td>Average</td><td>200</td><td>2674283</td><td>2619753</td><td>2568650</td><td>2505060</td></tr><tr><td>STD</td><td>200</td><td>76080.99</td><td>50949.62</td><td>41942.1</td><td>29545.83</td></tr></tbody></table>

### 4) Limitations and Perspectives

While the JFSO algorithm has demonstrated superior performance in addressing the RPP problem, this study is subject to several limitations. The research was conducted on the IEEE 30-bus system, which, although a standard benchmark, does not fully capture the complexity of large-scale power networks. The scalability of JFSO to larger and more complex systems, such as the IEEE 118-bus or real-world grids, remains unexplored. Furthermore, the study does not consider dynamic scenarios like load variations, seasonal changes, or grid reconfigurations, which are critical for modern, adaptive power systems. Additionally, while the

dual-objective optimization of power loss and investment cost provides valuable insights, the study does not address broader objectives, such as environmental impacts, which are increasingly significant in the context of sustainable energy systems.

Based on these findings, several perspectives can be inferred for future research. First, the JFSO algorithm could be enhanced or hybridized with other metaheuristic techniques to further improve its efficiency and adaptability in solving RPP problems. Second, extending the application to larger-scale systems and varying operational conditions would validate its robustness and scalability. Third,
incorporating dynamic scenarios would enhance the algorithm's practical applicability, addressing the challenges of evolving power systems. Finally, integrating economic objectives with environmental considerations, such as minimizing greenhouse gas emissions, could align the research with global sustainability goals and broaden its impact. These perspectives offer a pathway to addressing current limitations while advancing the state-of-the-art in RPP optimization.

## V. CONCLUSION

This study presented the application of the Jellyfish Search Optimization (JFSO) algorithm for Reactive Power Planning (RPP) in electrical power networks. The main objectives were to minimize active power losses and reduce the investment costs associated with reactive power compensators while adhering to operational constraints. The JFSO algorithm was tested on the IEEE 30-bus test system and benchmarked against DE and PSO algorithms under two distinct case studies. In Case 1, JFSO demonstrated a significant reduction in power losses compared to DE and PSO. Similarly, in Case 2, which considered both operational losses and the investment costs of reactive power compensators, JFSO highlighted superior ability to enhance system efficiency by optimizing reactive power distribution. The findings reveal that JFSO not only offers superior optimization capabilities but also provides better convergence characteristics compared to DE and PSO.

## VI. REFERENCES

[1] A. Shaheen, R. El-Seheimy, S. Kamel, and A. Selim, "Reliability enhancement and power loss reduction in medium voltage distribution feeders using modified jellyfish optimization," *Alexandria Eng. J.*, vol. 75, pp. 363-381, Jul. 2023, doi: 10.1016/J.AEJ.2023.05.084.

[2] A. A. Abou El-Ela, R. A. El-Sehiemy, A. M. Shaheen, A. S. Shalaby, and M. T. Mouwafi, "Robust generation expansion planning in power grids under renewable energy penetration via honey badger algorithm," *Neural Comput. Appl.*, vol. 36, no. 14, 2024, doi: 10.1007/s00521-024-09485-5.

[3] M. H. Alqahtani, S. Z. Almutairi, A. M. Shaheen, and A. R. Ginidi, "Enhanced Kepler Optimization Method for Nonlinear Multi-Dimensional Optimal Power Flow," *Axioms*, vol. 13, no. 7, p. 419, Jun. 2024, doi: 10.3390/axioms13070419.

[4] A. Aljumah, M. Alqahtani, A. Shaheen, and A. Elsayed, "Enhancing Power System Performance via TCSC Technology Allocation with Enhanced Gradient-Based Optimization Algorithm," *IEEE Access*, vol. 12, pp. 97806-97832, 224AD, doi: 10.1109/ACCESS.2024.3428328.

[5] H. Alnami, A. M. El-Rifaie, G. Moustafa, S. H. Hakmi, A. M. Shaheen, and M. A. Tolba, "Optimal allocation of TCSC devices in transmission power systems by a novel adaptive dwarf mongoose optimization," *IEEE Access*, pp. 1-1, Dec. 2023, doi: 10.1109/ACCESS.2023.3346533.

[6] A. M. Shaheen, A. M. Elsayed, R. A. El-Sehiemy, A. R. Ginidi, and E. Elattar, "Optimal management of static volt-ampere-reactive devices and distributed generations with reconfiguration capability in active distribution networks," *Int. Trans. Electr. Energy Syst.*, 2021, doi: 10.1002/2050-7038.13126.

[7] G. Moustafa, M. Elshahed, A. R. Ginidi, A. M. Shaheen, and H. S. E. Mansour, "A Gradient-Based Optimizer with a Crossover Operator for Distribution Static VAR Compensator (D-SVC) Sizing and Placement in Electrical Systems," *Mathematics*, vol. 11, no. 5, p. 1077, Feb. 2023, doi: 10.3390/math11051077.

[8] M. Alqahtani, S. Almutairi, A. Aljumah, A. Ginidi, A. Shaheen, and, "Enhanced power grid performance through Gorilla Troops Algorithm-guided thyristor controlled series capacitors allocation," *Heliyon*, vol. 10, no. 24, p. E34326, 2024, doi: https://doi.org/10.1016/j.heliyon.2024.e34326.

[9] V. K. Gupta, S. K. Mishra, R. Babu, and A. K. Singh, "Solution

of Reactive Power Planning with TCSC and UPFC Using Improved Krill Herd Algorithm," *Trans. Indian Natl. Acad. Eng.*, vol. 9, no. 1, 2024, doi: 10.1007/s41403-023-00428-5.

[10] S.-C. Kim and S. R. Salkuti, "Optimal power flow based congestion management using enhanced genetic algorithms," *Int. J. Electr. Comput. Eng.*, vol. 9, no. 2, 2019, doi: 10.11591/ijece.v9i2.pp875-883.

[11] S. Raj and B. Bhattacharyya, "Optimal placement of TCSC and SVC for reactive power planning using Whale optimization algorithm," *Swarm Evol. Comput.*, vol. 40, 2018, doi: 10.1016/j.swevo.2017.12.008.

[12] R. El Sehiemy, A. A. El-Ela, and A. A. Shaheen, "Multi-Objective fuzzy-based procedure for enhancing reactive power management," *IET Gener. Transm. Distrib.*, vol. 7, no. 12, 2013, doi: 10.1049/iet-gtd.2013.0051.

[13] R. A. El-Sehiemy, A. A. A. El Ela, and A. Shaheen, "A multi-objective fuzzy-based procedure for reactive power-based preventive emergency strategy," *Int. J. Eng. Res. Africa*, vol. 13, 2015, doi: 10.4028/www.scientific.net/JERA.13.91.

[14] S. Shekarappa G, S. Mahapatra, and S. Raj, "Voltage Constrained Reactive Power Planning Problem for Reactive Loading Variation Using Hybrid Harris Hawk Particle Swarm Optimizer," *Electr. Power Components Syst.*, vol. 49, no. 4-5, 2021, doi: 10.1080/15325008.2021.1970060.

[15] A. M. Shaheen, R. A. El-Sehiemy, and S. M. Farrag, "A novel adequate bi-level reactive power planning strategy," *Int. J. Electr. Power Energy Syst.*, vol. 78, pp. 897-909, 2016, doi: 10.1016/j.ijepes.2015.12.004.

[16] S. Sarhan, A. Shaheen, R. El-Sehiemy, and M. Gafar, "An Augmented Social Network Search Algorithm for Optimal Reactive Power Dispatch Problem," *Mathematics*, vol. 11, no. 5, p. 1236, Mar. 2023, doi: 10.3390/math11051236.

[17] S. S. Gudadappanavar and S. Mahapatra, "Metaheuristic nature-based algorithm for optimal reactive power planning," *Int. J. Syst. Assur. Eng. Manag.*, vol. 13, no. 3, 2022, doi: 10.1007/s13198-021-01489-x.

[18] A. M. Shaheen, R. A. El-Sehiemy, and S. M. Farrag, "Optimal reactive power dispatch using backtracking search algorithm," *Aust. J. Electr. Electron. Eng.*, vol. 13, no. 3, 2016, doi: 10.1080/1448837X.2017.1325134.

[19] J. G. Jamnani and M. Pandya, "Coordination of SVC and TCSC for management of power flow by particle swarm optimization," in *Energy Procedia*, 2019, vol. 156, doi: 10.1016/j.egypro.2018.11.149.

[20] F. Sayed, S. Kamel, M. A. Taher, and F. Jurado, "Enhancing power system loadability and optimal load shedding based on TCSC allocation using improved moth flame optimization algorithm," *Electr. Eng.*, vol. 103, no. 1, 2021, doi: 10.1007/s00202-020-01072-w.

[21] Y. Muhammad, R. Akhtar, R. Khan, F. Ullah, M. A. Z. Raja, and J. A. T. Machado, "Design of fractional evolutionary processing for reactive power planning with FACTS devices," *Sci. Rep.*, vol. 11, no. 1, 2021, doi: 10.1038/s41598-020-79838-2.

[22] N. Karmakar and B. Bhattacharyya, "Techno-Economic Model for Reactive Power Planning Using Series-Shunt Compensation Devices Under Load Demand in Power Transmission Network," *Energy Technol.*, vol. 9, no. 7, 2021, doi: 10.1002/ente.202100156.

[23] B. Mahdad, "Improvement optimal power flow solution considering SVC and TCSC controllers using new partitioned ant lion algorithm," *Electr. Eng.*, vol. 102, no. 4, 2020, doi: 10.1007/s00202-020-01033-3.

[24] N. Karmakar and B. Bhattacharyya, "Optimal reactive power planning in power transmission system considering facts devices and implementing hybrid optimisation approach," *IET Gener. Transm. Distrib.*, vol. 14, no. 25, 2020, doi: 10.1049/iet-gtd.2020.1356.

[25] S. Sharma, B. Sabitha, A. Prabhakaran, M. Chavan, and R. Srivastava, "A hybrid swarm intelligence approach for resolving reactive power dispatch issues in power system: Optimal placement and sizing of UPFC," *Adv. Eng. Softw.*, vol. 170, 2022, doi: 10.1016/j.advengsoft.2022.103149.

[26] B. Mahdad, "Optimal reconfiguration and reactive power planning based fractal search algorithm: A case study of the Algerian distribution electrical system," *Eng. Sci. Technol. an Int. J.*, vol. 22, no. 1, 2019, doi: 10.1016/j.jestch.2018.08.013.

[27] L. Kumar, M. K. Kar, and S. Kumar, "Reactive Power
Management of Transmission Network Using Evolutionary
Techniques,” *J. Electr. Eng. Technol.*, vol. 18, no. 1, 2023, doi:
10.1007/s42835-022-01185-1.

[28] E. Muthukumaran and S. Kalyani, “Development of smart controller for demand side management in smart grid using reactive power optimization,” *Soft Comput.*, vol. 25, no. 2, 2021, doi: 10.1007/s00500-020-05246-3.

[29] J. S. Chou and D. N. Truong, “A novel metaheuristic optimizer inspired by behavior of jellyfish in ocean,” *Appl. Math. Comput.*, vol. 389, 2021, doi: 10.1016/j.amc.2020.125535.

[30] R. EL-Sehiemy, A. Shaheen, A. Ginidi, S. Ghoniem, M. Alharthi, and A. Elsayed, “Quasi-Reflection Jellyfish Optimizer for Optimal Power Flow in Electrical Power Systems,” *Stud. Informatics Control*, vol. 31, no. 1, pp. 49–58, 2022.

[31] A. M. Shaheen, A. M. Elsayed, R. A. El-Sehiemy, S. S. M. Ghoneim, M. M. Alharthi, and A. R. Ginidi, “Multi-dimensional energy management based on an optimal power flow model using an improved quasi-reflection jellyfish optimization algorithm,” *Eng. Optim.*, pp. 1–23, Mar. 2022, doi: 10.1080/0305215X.2022.2051021.

[32] A. M. Shaheen, R. A. El-Sehiemy, A. R. Ginidi, S. S. M. Ghoneim, and M. M. Alharthi, “Multi-objective jellyfish search optimizer for efficient power system operation based on multi-dimensional OPF framework,” *Energy*, p. 121478, Jul. 2021, doi: 10.1016/J.ENERGY.2021.121478.

[33] A. M. Shaheen, A. M. Elsayed, A. R. Ginidi, E. E. Elattar, and R. A. El-Sehiemy, “Effective Automation of Distribution Systems With Joint Integration of DGs/ SVCs Considering Reconfiguration Capability by Jellyfish Search Algorithm,” *IEEE Access*, 2021, doi: 10.1109/ACCESS.2021.3092337.

[34] H. Youssef, M. H. Hassan, S. Kamel, and S. K. Elsayed, “Parameter estimation of single phase transformer using jellyfish search optimizer algorithm,” in *2021 IEEE International Conference on Automation/24th Congress of the Chilean Association of Automatic Control, ICA-ACCA 2021*, 2021, doi: 10.1109/ICAACCA51523.2021.9465279.

[35] A. Ginidi, A. Elsayed, A. Shaheen, E. Elattar, and R. El-Sehiemy, “An Innovative Hybrid Heap-Based and Jellyfish Search Algorithm for Combined Heat and Power Economic Dispatch in Electrical Grids,” *Mathematics*, vol. 9, no. 17, p. 2053, 2021, doi: 10.3390/math9172053.

[36] A. Shaheen, R. El-Sehiemy, S. Kamel, and A. Selim, “Optimal Operational Reliability and Reconfiguration of Electrical Distribution Network Based on Jellyfish Search Algorithm,” *Energies*, vol. 15, no. 19, p. 6994, Sep. 2022, doi: 10.3390/en15196994.

[37] A. M. Shaheen, R. A. El-Sehiemy, E. Elattar, and A. R. Ginidi, “An Amalgamated Heap and Jellyfish Optimizer for economic dispatch in Combined heat and power systems including N-1 Unit outages,” *Energy*, p. 123351, Feb. 2022, doi: 10.1016/J.ENERGY.2022.123351.

[38] A. Shaheen, A. Ginidi, R. El-Sehiemy, A. Elsayed, E. Elattar, and H. T. Dorrah, “Developed Gorilla Troops Technique for Optimal Power Flow Problem in Electrical Power Systems,” *Math. 2022*, Vol. 10, Page 1636, vol. 10, no. 10, p. 1636, May 2022, doi: 10.3390/MATH10101636.

[39] A. M. Shaheen, R. A. El-Sehiemy, A. M. Elsayed, and E. E. Elattar, “Multi-objective manta ray foraging algorithm for efficient operation of hybrid AC/DC power grids with emission minimisation,” *IET Gener. Transm. Distrib.*, vol. 15, no. 8, 2021, doi: 10.1049/gtd2.12104.