Optimal Siting and Sizing of SSSC Using Modified Salp Swarm Algorithm Considering Optimal Reactive Power Dispatch Problem

The Flexible alternating current transmission systems (FACTS) is considered one of the most developed technologies applied for enhancing the performance of system due to their ability of adjusting different parameters in the transmission systems such as the buses voltage, the transmission line impedance, the active and reactive powers flow in transmission lines. The static synchronous series compensator (SSSC) is an effective member of the FACTS which is connected in series with the transmission lines and it consists of a solid-state voltage source inverter coupled with a transformer which aims to control and secure the operation of the power system. The main function of SSSC is inserting a controllable voltage in series with the transmission line to control the active and reactive powers flow in transmission lines. Solving the optimal reactive power dispatch (ORPD) problem is nonlinear, non-convex and it becomes a complex problem with integration of the SSSC. The contributions of article include, 1) an efficient and reliable optimization algorithm is developed to solve the ORPD problem and identify the optimal location and ratings of the SSSC, 2) The proposed algorithm is based on modifying the salp swarm algorithm (SSSA) using Levy Flight Distribution and spiral movement of particles to enhance the searching capabilities of the SSA, 3) an efficient model of SSSC based on power injection approach is used for representation the SSSC in ORPD. The ORPD is solved with and without the SSSC controller to minimize power losses and voltage deviations as well as improve the voltage stability. The proposed algorithm for ORPD is tested on the standards IEEE 30-bus and 57-bus systems. The simulation results demonstrate that MSSA is more effective and superior for solving the ORPD compared with some other reported meta-heuristic techniques. Moreover, the system performance is enhanced considerably with optimal inclusion the SSSC.


INDEX TERMS
|V se | , θ se : Voltage mag, phase angle of SSSC injected voltage P Gi , P Di : Generated active and load demand power at bus i Q Gi , Q Di : Generated active and load demand power at bus i Y ij , θ ij : Admittance matrix magnitude and phase z 1 n : Leader position Q n : Food source position u n , l n : Upper, lower limits in n th dimension of search space r 1 , r 2 , r 3 : Random variables interval [0,1] e G , e Q , e V , e S , e F , e t : Penalty factors I. INTRODUCTION A. GENERAL In electric power system, the power flow intentions can be deliberated as fundamental of power scheme network calculations, since they are the most frequently accomplished program of power network designs which can be used in power scheme scheduling, operational forecasting, as well as operation/control. The optimal reactive power dispatch (ORPD) problem is a non-linear optimization problem related to optimal power flow. Solving the ORPD problem turns into a determined task in order to modify the power scheme for its secure and economical operation. The foremost aim to solve the ORPD problem is assigning the best operating set of control variables like voltages of the generators, transformer taps and the shunt compensator with satisfying operating constraints of the electric scheme [1]. The control variables remain enhanced for a definite fitness function. For example, boosting voltage stability as well as minimizing power losses and voltage deviation minimization.

B. LITERATURE SURVEY
The ORPD problem has been solved with different conventional techniques, for example, linear and non-linear programming, interior point method as well as the quadratic programming [2]- [5]. The foremost disadvantage of the conventional techniques is difficult to be implement with non-convex or nonlinear fitness functions. Moreover, these techniques can confine proceeding local minima of the objective functions.
Newly, numerous meta-heuristic optimization techniques have been applied to solve the optimization problem. These methods not only have been confirmed to overcome the foremost shortcomings in conventional methods but also are efficaciously applied to solve the ORPD problem for example particle swarm optimization (PSO) [6], genetic algorithm (GA) [7], whale optimization algorithm (WOA) [8], ant colony algorithm (ACA) [9], gravitational search algorithm (GSA) [10], lightning attachment procedure optimization [11], grey wolf optimization [12] and the conventional salp swarm algorithm [13].
In recent years, several available technologies have been produced and embedded in electric system to enhance their performance. FACTS are considered one of the most applied technology in electrical power systems to control different variables for example, the bus voltage magnitude, the active power, the reactive power, and the transmission line impedance. Therefore, the FACTS devices can enhance the security and stability of the power systems [14], [15]. Though, the foremost determination of ORPD problem is defining the control variables designed for the voltage profile enhancement, voltage stability improvement and power losses minimization. But it should be pointed out that solving the OPRD with incorporating the SSSC compensator in power system might considerably improve the performance of the system.
Although, the detail of FACTS is the submission of power electronic equipment in ways that regulate and control the electrical constraints through one or several functions to direct the operation of transmission schemes comprising voltage, current, impedance, phase angle and damping of oscillations [16]. FACTS controllers can cause quick alterations of the important scheme. Consequently, that can be able to considerably disturb the operation of traditional distance arrangements while moreover series or shunt connected FACTS devices present novel dynamic controls into the power schemes [43], [44]. They would predictably touch the features of a defensive relay in a transmission line towards approximately range.
The Static Synchronous Series Compensator (SSSC) controller is an elegant member of FACTS and it is inserted in series through transmission lines to control proceeding the active and reactive powers flow over transmission lines individually or instantaneously. SSSC provides the required controllability through inserting an AC voltage with wellregulated magnitude as well as phase angle in series with the transmission line [17], [18]. Ahmed et al. [19] discussed the ORPD problem considering SSSC on IEEE30 bus-system to improve the voltage profile with enhancing voltage stability using GWO. Marouani et al. [20] used multi-objective evolutionary algorithm (MOEA) for ORPD problem considering SSSC on 6 bus-system to minimize the real power losses with voltage deviation. Susanta et al. [21] solved ORPD problem by using chemical reaction optimization (CRO) using SSSC to minimize power losses of IEEE30 and IEEE57 bussystem. Mohamed, et al. [22] used improved harmony search algorithm considering SSSC in non-smooth cost functions on IEEE 30-bus system.
The novel nature inspired SSA is a simple and efficient optimization technique which simulate the swarm behavior of salps in nature and contains the iterative nature. Hence, it iteratively evolves and generates few random individuals 49250 VOLUME 9, 2021 salps inside the search space. Then entire salps update their location, the leader salp attack in direction of food while followers move towards the rest of salps [29]. Some of related applications of SSA used in various fields, such as feature selection [23], tunning of power system stabilizer [24], PID-fuzzy control seismic exited structural system against earthquake [25], fuel cell [26], machine learning [27] and etc. However, SSA has some limitations and is faced with premature convergence in some cases [28].

C. CONTRIBUTION TO THE RESEARCH
The aim of the research is to identify the size and the optimal location of SSSC controllers in the power systems using novel modified Salp Swarm Optimization (MSSA). A simple SSSC model is developed with ORPD solution to optimize the power losses and voltage deviations reduction as well as the voltage stability boosting on IEEE 30-bus and IEEE 57-bus systems.
This research is organized in different sections such as; Section II represents the simple modelling and formulation of SSSC, Section III defines the ORPD formulation, Section IV defines methodology of the conventional SSA and MSSA with their graphical abstract and pseudo code, Section V demonstrates the results and discussion, Section VI defines the main achievements while Section VII is the part of conclusion.

II. SSSC MODELS FORMULATION
The SSSC consists, voltage source converter which is linked to a common DC and depicted in the Fig. 1. While Fig.2 illustrates the SSSC equivalent circuit where the voltage source (V se ) is connected in series with the coupling transformer's impedance (Z se ). In Fig. 3, the simple model of SSSC is generally obtained by altering the voltage source V se into the current source I inj in parallel with impedance Z se . The related discussion related current source the formulation is given as follow: The current I inj can be injected at bus m and j. So, the new injected currents I inj can be computed as the function of specified active and reactive power flow of the transmission line by applying the concept of Kirchhoff current law at bus j.
where, S sp is depend on sum of P sp + jQ sp .I inj can also be injected as the complex loads at m and j buses, as shown in Fig. 3, as written as follows:

III. ORPD PROBLEM FORMULATION FOR DIFFERENT OBJECTIVE FUNCTIONS A. MINIMAZATION OF OBJECTIVE FUNCTIONS
The optimal reactive power dispatch (ORPD) problem is generally formulated as: Subject to where, F denotes the objective function, x and u represent the dependent and independent control variables, g j and h j are the equality and inequality constraints, while m and p are the number of equality and inequality constraints, respectively. The independent variables can be represented as follows: The dependent variables which include the generated power at slack bus, the voltages of the PQ buses, the generated reactive powers of the generators, the power flow in transmission VOLUME 9, 2021 lines, the magnitude and the angle of the injected voltage by the SSSC. The dependent variables can be indicted as follows: |V se | , θ se ] (9)

1) MINIMAZATION OF POWER LOSSES
Generally, the minimization of active power losses be represented as:

2) MINIMAZATION OF VOLTAGE DEVIATIONS
The 2 nd objective function is to reduce the voltage deviations (VD) and it is generally expression as follows: where, NL represents number of the transmission lines while V ref is reference voltage which commonly equals to 1.

3) ENCHANCEMENT OF VOLTAGE STABILITY
The 3 rd objective function is to improve the voltage stability (VSI) which is proportional to the minimization of voltage stability indicator called L-index. This enhanced objective can be achieved by reducing the maximum value of the L index in the power networks (12) where, L i represents the value of bus i, Y ij is the mutual admittance between bus i and j, while N BS represents the number of buses.
These constraints represent the balanced load flow equations as: 2

) INEQUALITY CONSTRAINTS
These constraints which represent the operating limits of system components include: (23) The system constraints which added to the objective function are taken into consideration by using the penalty factors related the constraints. Thereby, the objective function can be formulated as:

IV. METHODOLOGY
It is worth mentioning that the salp swarm algorithm (SSA) is an efficient optimization technique and it has been wildly applied in several optimization problems. However, it suffers from stagnation and prone to local optima for some cases. Therefore, a modified slap swarm algorithm (MSSA) is proposed to render and overcome the shortages of the standard SSA. The proposed MSSA is based on implementing two searching strategies for enhancing its searching capability. The first strategy is applying Levy Flight Distribution (LFD) for enhancing the exploration process which enables the populations to jump to new area. The second strategy is based on spiral motion of the populations around the best solution to enhance the exploitation process. The pseudocode of the conventional SSA and the modified MSSA are given in Algorithm I and II, while the graphical representation of MSSA to solve the ORPD problem using SSSC is given in Fig. 4.

A. THE SALP SWARM ALGORITHM (SSA)
The traditional SSA algorithm is the population based metaheuristic introduced by Mirjalili in 2017 [29]. SSA simulates mechanism of swarm salps which will be scavenged in oceans. In ocean, the salp at the front of chain will be the leader while the remain salps will consider as the followers.
Likewise, other meta-heuristic approaches the position of the salp can be explain in s dimension, where s is the number of the variable for a given problem. Therefore, the positions of entire salps are keeping in a two-dimensional matrix called z. For example, in a search space there is a food source called Q and considered as the swarms' target. So, the expression of the SSA will be given as follows.
where, z i n and Q n represent the leader position and food source position, respectively. u n and l n are the upper and Step (2) Initialize a population of (S) salps' position randomly Step (3) Run the load flow and calculate the fitness evaluation for each salp Step (4) Set iteration t = 1 Step (5) Update r 1 according to Eq. (26) Step ( Repeat steps 5 to 7 until (t = T max ) is satisfied Step (7) Return the best solution (Z * ) and its fitness value f(Z * ) End SSA lower limits in n-th dimension of search space.
In order to change the position of followers, the following expression is used.
The simulation time is depending on the iterations and the conflict between iteration is equal to 1 while considering v o = 0, the Equation (25) will be as followed. The MSSA is proposed to overcome the shortages of the conventional SSA which include its tendency to local optima VOLUME 9, 2021 Algorithm 2 Pseudocode of Modified MSSA Algorithm Start MSSA Step (1) Set the parameters of MSSA technique including maximum number of iteration (T max ), number of populations, the upper and lower limits of the control variables Step (2) Initialize a population of (S) salps' position randomly Step (3) Run the load flow and calculate the Fitness evaluation for each salp Step (4) Set iteration t = 1 Step (5) Update r 1 according to Eq. (26) Step ( Step (9) Compare the value of k with a random value r 4 .
If the value of k is less than r 4 Update the salp positions based on the spiral orientation according to Eq. (33) Else Update the salp positions based on Levy distribution according to Eq. (29) End Step (10) Calculate the fitness function of the updated salps. Then, include the new solutions if these solutions are better than the solutions of the previous steps Increment t to 1.
Repeat steps 5 to 7 until (t = T max ) is satisfied Step (7) Return the best solution (Z * ) and its fitness value f(Z * ) End MSSA and stagnation for some cases. Two search strategies are presented for enhancing capability of the conventional SSA. The first modification is utilized for boosting the exploration process by updating the locations of salps using the Levy flight distribution (LFD) to aid population to find new areas to overcome its stagnation. While the second modification depends upon modifying and updating the locations of salps in the spiral path around the best solution to enhance its exploitation. The first modification which based on the LFD is expressed as follows: where ∝ refers to a step size parameter which is assigned as follows: where u and v are determined using (29) and (30) as follows: where represents the standard gamma function. The second modification is based on modifying the locations of salps in the spiral path around the best solution which can be expressed as follows: where b denotes a constant to describe the logarithmic spiral shape. To balance the exploration and the exploitation process an adaptive operator k is utilized to achieve this task.
where, k max and k min are the maximum and the minimum k limits. Finally, it is worth mentioned that searching capability of the MSSA is improved by enhancing the exploration phase using the LFD by applying Eq. (27) at the first iteration when the value of k is small while the exploitation phase is enhanced using the variable bandwidth transition by applying Eq. (31) at the final iteration when the value of k is large.

V. RESULTS AND DISCUSSION
In order to demonstrate the effectiveness of proposed MSSA algorithm compared simple SSA, the simulation is run on MATLAB on Window 10 Professional Lenovo E-480 Model Intel R Core TM i7-8550U CPU @ 1.80 GHz 8GB RAM. The ORPD problem is solved with optimal site and sizing of the SSSC to minimize transmission line losses, voltage deviations and enhancing the voltage stability index. The MSSA is employed to determine the parameters setting and location of SSSC controller. The proposed algorithm is tested on IEEE30 and IEEE57 standard bus systems and the simplified SSSC model is used to represent the SSSC into power flow solution. The data of system as well as the upper and the lower limits of the control variables are taken from [30], [31] and [32].  To better understand the article, the simulation outcomes of MSSA and conventional SSA for IEEE 30-bus and IEEE 57bus systems are given into different cases with and without SSSC controller. The detail studied cases are presented as follows: • CASE I: Solving the ORPD without inclusion the SSSC on IEEE30-bus system.
• CASE II: Solving the ORPD with optimal inclusion the SSSC on IEEE30-bus system.
• CASE III: Solving the ORPD without inclusion the SSSC on IEEE 57-bus system.
• CASE IV: Solving the ORPD with optimal inclusion the SSSC on 57-bus system. In case of comparison the results without using SSSC, the values of base case are considered such as 5.811 MW for IEEE 30-bus system and 27.86 MW for IEEE 57-bus system [42], respectively.

A. CASE I: SOLVING THE ORPD WITHOUT INCLUSION THE SSSC ON IEEE30-BUS SYSTEM 1) MINIMAZATION OF POWER LOSSES
In this case, MSSA and SSA techniques are applied for minimizing the power losses without optimal inclusion of SSSC controller. The selected of parameters of MSSA are given in the Table. 1. Fig. 5 shows the convergence plot of the power loss by applying the SSA and MSSA. Fig. 5 demonstrated that the better convergence response getting from the MSSA algorithm. The outcomes of MSSA and SSA including the best, the average, the worst, and the standard values with simulation time are given in Table. 2.
The best achieved value for this case by application of the MSSA is 4.5902 MW while the worst value reported by SSA is 4.6137 MW. The MSSA'S best outcome is reported 0.51% less reported compared with conventional SSA. The best outcomes getting by MSSA and SSA techniques are further compared with the base case 5.811 MW which gives 21.01% and 20.60% less in reduction in power losses.

2) MINIMAZATION OF VOLTAGE DEVIATIONS
In this case, the simulation is run to minimize the voltage deviations (VD) by using the MSSA and SSA techniques without inclusion the SSSC controller. Fig. 6 illustrates the best convergence response getting by the MSSA algorithm over the conventional SSA. Table. 2 shows the best, average, worst, standard deviation, and the simulation time for minimization the VD.
The minimum VD that obtained by application of the MSSA and SSA are 0.1286 p.u. and 0.1288 p.u., respectively. In other words, the VD is reduced by 0.1553 % with application of the MSSA compared with the SSA. According to the comparisons in Table 3, the obtained VD by application of the MSSA is better than HSA [34], SGA [34], PSO [34], and PSO-TVAC [40] by 4.6701 %, 14.3238 %, 9.6910 %, and 37.6938 %, respectively. The optimal values of the control parameters for this case are tabulated in APPENDIX 2. Figure 6 shows the trends of the VD with application of the SSA and the MSSA, it is clear that the proposed algorithm has stable convergence characteristics.

3) ENHANCEMENT OF VOLTAGE STABILITY
In this case, the simulation is run by MSSA and SSA techniques for the enhancement of voltage stability index (VSI ) without incorporating the SSSC. The best, worst, average and the standard deviation values of the VSI that obtained by MSSA and SSA techniques are reported in Table. 2. The obtained VSI by application of MSSA and SSA are 0.1140 p.u. and 0.1166 p.u., respectively. In other words, the VSI is enhanced by 2.2298 % compared with SSA. Table 3 shows the values obtained by other algorithms, it is evidently that the obtained VSI by MSSA is better than HSA [34], SGA [34], PSO [34] PG-PSO [40], CMAES [39] and PSO-TVAC [40] Figure 7 shows the stable convergence characteristics of the proposed algorithm for the VSI . In this case, the proposed MSSA and the conventional SSA are used to minimize the power losses with optimal inclusion the SSSC on IEEE 30-bus system. TABLE 2 shows the best, worst, mean and the standard deviation of the power losses. Judging from this table the best results are obtained by the proposed algorithm with optimal incorporating the SSSC compared with the conventional algorithm. The power loss is reduced to 4.3541 MW and 4.4361 MW by application the SSA and the MSSA or it is reduced by 5.1436 % and 3.3572 % compared to without incorporating the SSSC. Fig. 8 depicts the trends of the power losses using MSSA and SSA with optimal allocation the SSSC. It is obvious that the MSSA has stable convergence characteristics. The values of the control variables for this case are given in APPENDIX. 1. The optimal location of the SSSC is at 14 th line while the optimal specified active and reactive power of the SSSC 39.63 MW and 17.09 MVar, respectively.

2) MINIMAZATION OF VOLTAGE DEVIATIONS
In this case, the simulations are carried out by using both MSSA and SSA algorithms to minimize the voltage deviations (VD) with optimal inclusion the SSSC. The outcomes for this case are reported in Table 2 with its average, best, worst and the standard deviations values with the simulation time. The minimum values of the VD that obtained by MSSA and SSA with optimal incorporating the SSSC are 0.1160 p.u. and 0.1279 p.u., respectively.
In other words, the voltage deviations are reduced with optimal incorporating the SSSC by 9.937% and 9.979% using MSSA and SSA respectively compared to without SSSC. The optimal values of the control variables as well as the optimal location and size of the SSSC by MSSA and SSA are listed in APPENDIX 2. The optimal location of the SSSC is at 29 th line while the optimal specified active and reactive power of the SSSC −3.82 MW and 4.39 MVar, respectively. Fig. 9 verifies that the proposed algorithm has well convergence characteristics in terms of the VD minimization.

3) ENHANCEMENT OF VOLTAGE STABILITY
In this case, the objective function enhances the voltage stability index (VSI ) by using MSSA and SSA techniques considering with optimal inclusion the SSSC in solving ORPD problem. Fig. 10   which is 10.93% less than the conventional SSA considering with the optimal inclusion the SSSC. In addition, to enhance the VSI , the MSSA considering optimal inclusion the SSSC is reported 35.68% and 34.21% less compared to the case without optimal inclusion the SSSC by using SSA and MSSA techniques. The best values of the control variables for this case are reported in the APPENDIX. 3. The optimal location of the SSSC is at 36 th line while the optimal specified active and reactive power of the SSSC 28.97 MW and 18.11 MVar, respectively. In this case, to solve the ORPD problem without optimal inclusion the SSSC controller to minimize the power losses by using MSSA and SSA techniques tested on IEEE 57-bus system. Fig. 11 illustrated the best convergence response achieved by the proposed MSSA technique and conventional SSA for power loss reduction. The simulation outcomes reported by both techniques are given in Table. 4  including the average, the best, the worst and the standard  deviation values with the simulation time. Judging from  Table. 4, the minimum power losses obtained by MSSA is 24.6969 MW while the power losses obtained by conventional SSA technique is 25.3207 MW. The results indicated that the best reported values getting from the MSSA is 2.46% less than the conventional SSA. In addition, compared with the base case of 27.86 MW [45], the MSSA and the conventional SSA are reported to 11.35% and 9.11%, respectively. Judging from Table 4, the power losses that obtained by the proposed MSSA technique is also less than the reported than PSO [41], SGA [34], PSO-EE [38], CGA [33], FODPSO [37], L-SaDE [36], ICA [41], PSO-ICA [41], MOALO [9], and FODPSO [38] by 8.1063 %, 1.2453%, 4.3115%, 1.6443%, 5.0948%, 9.2952%, 6.2185%, 1.0369%, 4.0708%, and 4.2297%, respectively. The best values of the control variables for this case are reported in APPENDIX. 4. The Fig. 11, Table 4 and Table 5 indicated the efficient performance reported by the proposed MSSA technique to minimize the power losses without optimal inclusion of SSSC.

2) MINIMAZATION OF VOLTAGE DEVIATIONS
In this case, the ORPD problem is solved without inclusion the SSSC to minimize the voltage deviations (VD) by using MSSA and conventional SSA techniques on IEEE 57-bus system. Figure. 12 illustrated the best convergence performance achieved by the proposed MSSA over conventional SSA.
The outcomes computed by both optimization techniques are given in Table. 4 with their average, best, worst and the standard deviation values with the simulation time. According to the Table. 4, the best value of MSSA and conventional SSA are reported to 0.9402 p.u. and 0.9424 p.u., respectively. The results indicated that the proposed MSSA technique is reported 0.23% less than the conventional SSA.
In addition, Judging from the Table. 5, the proposed MSSA is also less than the other optimization techniques such as; PSO, ICA and hybrid PSO-ICA, respectively. The best control values for this case are given in APPENDIX. 5. The results towards the best performance achieved by the proposed MSSA technique are indicated from Fig. 12, Table. 4 and 5.

3) ENHANCEMENT OF VOLTAGE STABILITY
In this case, the ORPD problem is considered without optimal inclusion the SSSC controller to enhance the voltage stability index (VSI ) by using the proposed MSSA and conventional SSA techniques applied on IEEE 57bus-system. The values of the parameter settings for the proposed MSSA technique are taken from Table. 1. The Figure. 13 illustrated the best convergence response getting from the proposed MSSA technique.
The simulation results for both techniques are given in Table. 4, with average, best, worst and the standard  In this case, the minimization of the power losses is achieved by the proposed MSSA and conventional SSA techniques considering the optimal inclusion of SSSC to ORPD problem applied on IEEE 57-bus system. Fig. 14, illustrated the best convergence performance obtained by the proposed MSSA technique over SSA. The simulation outcomes are given in Table. 4 for this case including the average, the best, the worst, the standard deviation values, and the simulation VOLUME 9, 2021 Moreover, the power losses obtained by MSSA with optimal inclusion the SSSC are reduced by 2.911% and 5.30% compared to the case where MSSA and SSA are considered without inclusion the SSSC to the system.
The best values of the control variables for this case are given in APPENDIX. 4. The optimal location of the SSSC is at 18 th line while the optimal specified active and reactive power of the SSSC are 36.29 MW and 10.33 MVar, respectively. It has also been observed that the consideration of the optimal inclusion of SSSC in ORPD gives the minimum the power losses while Fig. 14

2) MINIMAZATION OF VOLTAGE DEVIATIONS
This case represents, the consideration of optimal inclusion the SSSC to the ORPD problem to minimize the voltage deviations (VD) by using the proposed MSSA and the conventional SSA algorithms applied on IEEE 57-bus system.  Moreover, the proposed MSSA technique considering with optimal inclusion of SSSC, is also reported 7.99% and 8.21% less than the case of without optimal inclusion the SSSC to ORPD problem using MSSA and SSA techniques. The best values of the control variables for this case are reported in APPENDIX. 5. The optimal location of the SSSC is at 1th line while the optimal specified active and reactive power of the SSSC −16.71 MW and −32.34 MVar, respectively. It has been observed that solving the ORPD with optimal incorporating the SSSC can reduce the voltage deviations while Fig. 15 and Table. 4 demonstrated the better performance getting by the proposed MSSA technique for this case.

3) ENHANCEMENT OF VOLTAGE STABILITY
This case is considered with optimal inclusion of SSSC into the ORPD problem to enhance the voltage stability index (VSI ) by applying the proposed MSSA and the conventional SSA techniques on IEEE 57-bus system. Fig. 16 illustrated the best convergence performance achieved by the proposed MSSA technique over the conventional SSA. The simulation results are given in  15.56 MVar, respectively. The overall outcomes getting for this case, indicated that the consideration of the optimal inclusion the SSSC for ORPD gives the better response and help to improve the voltage stability (VSI ). the proposed algorithm for this case which are given in Table. 4. The best outcomes the proposed algorithm for this case which are given in Table. 4 and Fig. 16 indicated the best response getting by the proposed MSSA to enhance the (VSI ) considering optimal inclusion the SSSC.
It should be lighted here is that the proposed MSSA algorithm shows inferior results in early stages of iterations for some cases. This is due to its searching mechanism where in the earlier stages of iteration is that the populations (salps) updated their positions based on Levy distribution which enables the salps to jump to new areas for boosting exploration process. Thus, a randomness process will be high in the earlier stages and it may lead to inferior results. While in the final stages, the populations will update their positions around the best solution in spiral path to boost the exploitation process. In sequent, the results in final stages of iterations are enhanced considerably.

VI. OBTAINED RESULTS AND MAIN ACHIEVEMENTS
The outcomes and achievement of the article can be summarized as follows: • In application case of the MSSA for the IEEE 30-bus without SSSC, the power losses are reduced by 0.51%, the voltage deviations are reduced by 0.1553% and the voltage stability is enhanced by 2.2298% compared with application the SSA.

VII. CONCLUSION
This article presented MSSA for solving ORPD problem with optimal allocation of the SSSC controller. The exploration and exploitation processes of the conventional salp swarm algorithm (SSA) is enhanced by updating the positions of the salps using the Levy flight distribution (LFD) and a spiral movement of the salps around the best solution. The aim of incorporating the SSSC controller with ORPD in the power system is to reduce the power losses and voltage deviations as well as enhance voltage stability. A simplified power injection model is utilized to represent the SSSC. Consequently, the modifications in Jacobian matrix are avoided. The proposed algorithm was tested on standard IEEE 30-bus and IEEE 57-bus test systems. The yielded results were compared with those computed with some other algorithms to verify its effectiveness. The obtained results demonstrated that the superiority of the proposed algorithm for solving the ORPD.