Multiobjective Salp Swarm Algorithm Approach for Transmission Congestion Management

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Introduction
Transmission congestion management has now become one of the most important issues of present deregulated power market [1]. In this open access power market scenario for getting more proft margins from the market, problem of congestion is enlarging day by day [2,3]. To mitigate congestion various CM methods have been reported from the generator side and from the demand side.
Generation rescheduling (GR) [4][5][6] and enhancement of ATC through FACTS devices [7] are the generation side management. In early stage of deregulation, customers were not directly involved in market operations and security maintaining issues. Only independent system operator and regulatory utilities were responsible for managing energy systems. If customers (who are increasing the load) are well informed about the reliability and security issues, then they may have participated efciently in maintaining operation of power markets. In newly developed power market environment, an incentive-based demand response program along with energy storage system and distributed generation has been suggested to achieve a fexible energy hub in electricity market [8] and DSM (demand side management) has proved itself as more promising tool for congestion management [9]. Tus, targeted DSM along with distributed generation (DG) can be an efective alternative of CM [10]. Under DSM, customers adjust their demands on the basis of awareness for energy conservation or by getting fnancial incentives [11][12][13].
DR is all about reducing the demand for alleviating congestion [14]. However, the inspiration of any commodity business is to increase the consumption as much as possible, which is conficting towards DR. Tus, decrement in demand ofered by DR has to be kept in limit to increase avoid customer facility. So in order to limit the DR amount, distributed generation (DG) has to be added for managing congestion [15].
In the present paper, the problem of CM has been formulated under the multiobjective optimization framework. However, in the literature most of the times CM problem has been solved with double objective optimization framework [23,24]; while in present approach overall operating cost, emission of CO 2 and transmission line loading have been considered as objective functions.
Te traditional techniques of solving multiobjective optimization problems have been outmoded because of their sluggishness due to large number of iterations, complexity, stagnation, and full of approximations. However, the involvement of evolutionary algorithms such as diferential evolution and particle swarm has overcome these issues and encourage the researchers to employ the multiobjective optimization in the feld of power system [25]. Te training of efcient deep reinforcement learning agents for in-the-moment life-cycle production optimization was carried out by the authors in [26]. For a parallel inverter system, the authors of [27] introduced a unique droop control mechanism to maximize photovoltaic power output. Te gated spatial-temporal graph neural networkdependent short-term load forecasting for wide-area multiple buses was given by the authors in [28]. Te distribution of centrally switched fault current limiters in the transmission system was given in [29]. Te multistate approach for improving transmission network resilience against short-circuits faults brought on by extreme weather occurrences were presented by authors in [30]. Te split-core magnetoelectric current sensor and wireless current measuring application were presented in [31]. Te review of deep learning applications in frequency analysis and regulation of contemporary power systems was ofered by the authors in [32]. Authors in [33] presented a hierarchical multiobjective optimal planning model for an active distribution system that takes demand-side responsiveness and distributed generation into account. Te estimate of the probabilistic energy fow for the regional integrated energy system taking into account the cross-system failures was published in [34]. An energy storage system based multiobjective congestion management has been presented by using GAMS software [35] and genetic algorithm [36]. Hence, in the present work the recently developed multiobjective salp swarm algorithm (MOSSA) [37] with number of strategies has been proposed for solving multiobjective optimization-based CM problem.
Te performance of MOSSA for CM has been compared with two other meta heuristic algorithms, namely, multiobjective modifed sperm swarm optimization and multi-objective adoptive rat swarm optimization. Te prescribed work in this paper have been examined on IEEE 30-bus system and IEEE 118-bus system and compared with methods reported (same power system) in literature [23,38]. Te proposed approach of congestion management has been compared with similar reported methods shown in Table 1.
Te contribution of the paper is as follows: (1) Te problem of congestion management has been handled as multiobjective and simulated by implementing multiobjective salp swarm algorithm for simultaneous optimization of three objective functions (2) Tese three objective functions (minimization of overall operational cost, CO 2 emission, and line loading) have not been found in the literature simultaneously (3) Transmission congestion has been relieved by employing generation rescheduling, demand response, and wind plant simultaneously (4) Te performance of MOSSA has been compared and found better than two other nature inspired algorithms, namely, multiobjective modifed sperm swarm optimization and multiobjective adoptive rat swarm optimization (5) Seven specifc cases have been taken frst time which have not been considered earlier Te structure of the present paper is as follows: in the second section, multiobjective CM problem has been formulated with three objective functions along with all constraints. Tird section describes the proposed multiobjective salp swarm algorithm, adoptive rat swarm optimization, and modifed sperm swarm optimization. In the fourth section, numerical results are presented and analysed for IEEE 30-bus system and IEEE 118-bus system. In the ffth section, this paper has been concluded. International Transactions on Electrical Energy Systems response, and cost of distributed generation. Te above said objective functions are as follows:

Problem Formulation
(1) Generation Cost. Conventional generation cost C G ($/hr) can be written as follows [23]: where a i , b i , and c i are the cost coefcients of i th generating unit.
In this paper wind plant has been considered as renewable independent power producer playing a role of DG. Cost function (C RIPP ) of RIPP can be expressed as follows [39]: where Ψ represents cost of wind power generation ($/MWhr), air d (kg/m 3 ) is presenting the air density factor, W t (m 2 ) representing the swept area of wind turbine, η WP shows the overall efciency of wind plant, and v wind (m/sec) shows the wind velocity.
(3) Demand Response Cost. Demand response program (DRP) is the process in which responsive customers are convinced to reduce their demands to bring down the loading over critical transmission lines. Some appropriate monetary incentive ($/MW) are ofered to these customers to curtail their demands. Tis is termed as DR cost. Demand response (DR) cost ($/hr) can be written as follows [20]: where µ k is the DR cost for k th responsive customer in $/hr and N DR ∈ N B . Equation (3) indicates that DR cost minimization is actually the minimization of load reduction or minimization of incentive paid to the customers. Demand response cost of k th responsive customer can be expressed as follows [23]: Customers participated in DRP that not modify the required demand adjustment, then they have to be penalised with certain penalty. Penalty can be formulated as follows [12]: where L k is the penalizing cost bore by k th responsive customer in $/hr. Te reduced demand d k can be expressed as follows [11]: First objective function cost can be given as follows: 2.1.2. CO 2 Emission. Te problem of CO 2 emission minimization can be modelled as follows:

Minimization of Line's Maximum Loading.
Tis objective function is purposely involved in solving the present CM problem. Loading highly congested line has been considered for this objective function and can be given by the following equation: where l is the most congested transmission line and l ϵ N BR .

Constraints.
For the proposed multiobjective CM problem all constraints can be given as follows:

Equality Constraints.
Power balance can be expressed as follows [23]: where G ij and B ij are the transmission conductance and susceptance between bus i and j, respectively, and δ i δ j are the voltage angles at i th and j th buses, respectively.

Inequality Constraints.
On the basis of minimum and maximum limits of power system inequality constraints can be given as follows: (a) Inequality constraints for generators [23].
(c) Demand response constraints. Financial incentive paid to the k th responsive customer for ensuring his contribution in managing congestion must be bounded within a lower and upper limit. Tis is the cost for demand response and has to be kept restricted to maintain DR within limits. Tis can be written as follows [20]: (d) Constraints for wind plant [30].

Optimization Algorithms
In the present work CM has been handled as multiobjective optimization problem. Hence, simultaneous minimization of all objective function have been carried out by the Multiobjective slap swarm algorithm, multiobjective modifed sperm swarm optimization, and multiobjective adoptive rat swarm optimization.

Multiobjective Salp Swarm Algorithm.
In the present work multiobjective salp swarm algorithm proposed by [37] has been employed to solve MOO-based CM problem. Salps belong to the category of Salpidae and have a barrel shaped transparent body seems such as jelly fsh. Teir forward movement is just such as jet propulsion. Te mathematical model for solving optimization problems is based on the most interesting swarming behaviour of salps. Salps made swarm which is called salp chain. Te frst salp at the front of the chain is called leader and the rest of the salps are called followers. Similarly to other swarm-based multiobjective techniques, MOSSA also has multidimensional search and objective space. Updated position of leader salp using three parameters c 1 , c 2 , and c 3 , can be given as follows: where x1/j presents the position of leader salp in j th search dimension, F j is the target food source in j th dimension, ub j and lb j are the upper and lower bounds of variables in j th dimension.
Parameters c 2 and c 3 are generated randomly between [0, 1] while c 1 is very important parameter which provides a balance between exploration and exploitation during optimization and depends upon size of iterations. It can be given as follows: where k and K are the iteration count and maximum number of iterations, respectively. Follower salps update their position on the basis of updated position of leader salp and can be given as follows: where i ≥ 2 indicating follower salps and x i j is the i th follower salp in j th dimension.
Multiobjective salp swarm optimization contains multiple optimum solution that can be termed as nondominated solutions. For extracting good compromise and best solutions among the set of nondominated solutions, membership function μ i can be given as follows [25]: Normalized fuzzy membership function μ i,j for multiple solutions can be given as follows:

Adoptive Rat Swarm Optimization (ARSO).
Te rat swarm optimization is a nature inspired meta-heuristic technique Figure 1 and it is based on following and attacking (social painful) behaviour of rats [40]. In this algorithm rat agents explore the optimum solution in search space and update their position on the basis of best rat position such as other swarm based optimization techniques. Its performance can be improved by adoptive version of RSO in which initial population is updated on the basis of opposition based learning [40]. Te steps for the ARSO are as follows [40]: Step 1. Generate initial rat population by using the following equation randomly under the upper and lower limits of search space.
where x k min and x k max are the lower and upper bounds of search space, respectively, and M is the population size.
Step 2. Select initial parameters A, R, and C.
Step 3. Generate opposite number based solutions ( x →k ) by using the following equation for these initial population on the basis of opposite number concept.
Step 4. Evaluate ftness function for both initial population f(x k ) and opposite number based solutions f( x →k ). If is better than f(x k ), then replace x k by x →k for starting the optimization. Now, rat agents explores best solution in search space.
Step 5. During optimization to avoid local minima worst solution, we replaced it by a best (new) solution in each iteration using following equation: where x worst is the worst solution, P r (x) is the best solution, and rand 1 and rand 2 are the random numbers between 0 and 1.
Step 6. Selected population update their position using the following equation by getting information from the greatest search agent (rat population) to get the optimal solution.
where P →r (x + 1) � denotes updated position of rat population, P →r (x) is the position of greatest search agent, and P → can be evaluated by using the following equation: where P →k (x) is the position of k th rat population and parameters A and C can be given by the following equations, respectively.
where iter max is the maximum iteration number and q is the current iteration number.
Step 7. Stop if stopping criteria has been reached otherwise go to step 5.

Modifed Sperm Swarm Optimization (MSSO).
Sperm swarm optimization is inspired by sperm swarm behaviour during fertilization of ovum [41]. In this algorithm a set of International Transactions on Electrical Energy Systems searching agents of sperm (potential solutions) levitate in search space to explore and achieve the optimum solution.
Te searching agents update their position on basis of their personal best and global best position of sperm swarm.
Mathematically searching sperms update their position according to following equation: where v k (t) is the current velocity of k th sperm and t is the iteration number. To avoid the premature convergence and improving the performance of MSSO chaotic dynamics are integrated.
Hence, damping factor has been modifed by the following equation: Finally, the current velocity of k th sperm can be given as follows [41]: v k (t) � θ * D * log 10 pH Rand 1 * v k + log 10 * pH Rand 1 * log 10 Temp Rand 2 * x best k − x k (t) + log 10 * pH Rand 1 * log 10 Temp where D is the damping factor can vary randomly between 0 and 1, pH Rand 1 is a random number [7,14] that shows the pH value, Temp Rand 2 is the random temperature [35.1 to 38.5] of visited location, x best k and x gbest k are the personal best position of k th sperm, t is the iteration number, and θ can be given by following equation: where μ is a control parameter and can vary between 0 and 4. Te detailed modelling of this algorithm can be seen in [41]. For applying demand response to manage transmission congestion, 7 receptive customers have been found through power transfer distribution factor [38]. Tese 7 load buses are, 8, 12, 17, 19, 21, and 30. In this work, load elasticity has been taken as − 0.1 [42]. Te market electricity price has been decided to be taken as same, before and after demand response. Te cost of wind power generation has been taken as 3.75 $/MWhr [39].

Results and Discussion
In order to explore congestion over critical lines, maximum thermal limit of 35 MVA (3-objectives-group A) and 32 MVA (2-objectives-group B) have been considered so that at least one critical line gets congested and management of that congestion could be carried out. For that only line no 10, 16, and 29 have been considered as critical lines and the power fows over other lines have been observed.

Group "A": 3-Objectives (35 MVA Termal Rating).
In this group, thermal rating of transmission lines has been considered as 35 MVA and multiobjective (minimization of overall cost, minimization of CO2 emission and minimization of maximum line loading) CM has been carried out to mitigate congestion. For this group, generation rescheduling (GR), DR, and DG have been employed as congestion control strategies in following ways: Strategy A1: Only GR. Strategy A2: GR with DR. Strategy A3: GR and DR along with DG.
For each strategy by having several trials of implementation of the proposed algorithm MOSSA with diferent population size and generations, the fnal best results were tried to obtain. Population size and maximum number of generations are found to be 100 and 200, respectively, for which the proposed MOSSA algorithm is producing best results. For CM while implementing MOSSA out of 100 probable solutions (population size), 70, 72, and 75 nondominated solutions were obtained for strategies A 1 , A 2 , and A 3 , respectively.
For solving multiobjective congestion management problem, each objective function has been assigned weighting coefcient for seven specifc cases. Tese seven specifc cases have been shown in Table 3 and considered as diferent case studies.
Optimal solutions (optimal fronts) obtained by implementing MOSSA have been shown in Figure 2, Figure 3, and Figure 4 for strategies A 1 , A 2 , and A 3 , respectively. Seven specifc cases have also been shown in these Figures.
Te optimum values of three conficting objective functions and control variables obtained by employing MOSSA for CM have been shown in Tables 4-6.
It can be seen from Table 4 that the minimum cost, emission, and line loading obtained for strategy A 1 are 574.835 $/hr (Case 1), 282.537 tons/hr (Case 2), and 32.2585 MVA (Case 3), respectively. Table 5 shows the best (minimum) results for cost, emission, and line loading as 573.992 $/hr (Case 1), 259.08 tons/hr (Case 2), and 32.1767 MVA (Case 3), respectively, for strategy A 2 . Similarly, for strategy A 3 , best cost, emission, and line loading can be seen from Table 6  Te comparison among optimal solutions (pareto fronts) obtained for strategies A 1 , A 2 , and A 3 has been shown in Figure 5. Table 7 shows the optimized power fows on transmission lines of Case 1 for strategy A 1 (group A). From this Since pictorial representation is more efective as compared to numerals depiction, the bar chart for presenting transmission reliability margin over all three congested lines for all three strategies has been shown in Figure 6. Observation.
(1) Te optimum location of DG (RIPP) has been found, bus no. 8, which is suppling 30 MW maximum load.
International Transactions on Electrical Energy Systems  Figure 5 that maximum minimization of all objective functions (individual and simultaneous) has been achieved. (2) It is very clear from Table 8 that maximum optimized power fows have been found. (3) Figure 6 distinctly shows the highest transmission reliability margin for strategy A 3 .
(6) All above facts not only appreciate the use of DR for managing congestion but also indicates the importance of adding distributed generation (RIPP) along with DR.

Group "B": 2-Objectives (32 MVA) Termal Rating.
In this group only two objective functions (minimization of overall operational cost and minimization of CO 2 emission) have been considered for solving multiobjective optimization problem of CM. Termal rating of transmission lines have been considered 32 MVA. In this group, congestion control strategies are taken as follows: Strategy B1: only GR. Strategy B2: GR with DR.
Strategy B3: GR and DR along with DG.
For this strategy of CM, performance of the proposed MOSSA has been compared with two nature inspired metaheuristic optimization algorithms named as multiobjective modifed sperm swarm optimization and multiobjective adoptive rat swarm optimization.
Te fnal population size and maximum number of iterations of proposed algorithm MOSSA that are producing best results for cost and emission are found to be 120 and 200. Tese parameters have been obtained by having several trials. In this group out of 120 probable solutions, 70, 72, and 78 nondominated solutions have been determined for strategies B 1 , B 2 , and B 3 , respectively. After having several trials population size and the number of iteration for MMSSO and MARSO have been found 100 and 180 for strategy B 3 . Te optimal solutions obtained by MMSSO and MARSO are 62 and 48, respectively.
For solving 2-objective congestion management problem, each objective function has been assigned some specifc values these are mentioned in Table 9. On this basis 5 specifc points have been identifed. Figures 7-9 show the optimal solutions (pareto fronts) obtained by MOSSA for strategy B 1 , B 2 , and B 3 , respectively. Out of these nondominated solutions, fve specifc cases given in Table 9 have been recognized and marked on these pareto-optimal fronts. For strategy B 3 the multiobjective congestion management has been carried out by employing multiobjective salp swarm algorithm, multiobjective modifed sperm swarm optimization, and multiobjective adoptive rat swarm optimization. Te paretooptimal fronts obtained by these three algorithms have been shown in Figure 10. It is very clear from this Figure that the performance of MMSSO (shown by blue colour) is better than MARSO (shown by green colour) and the proposed MOSSA (shown by red colour) is better than MMSSO and MARSO both.
For CM the results (optimal control variables and objective function values) obtained by employing MOSSA have been shown in Tables 10-12. It can be seen from Table 10 that the minimum cost and emission obtained for strategy B 1 are 578.083 $/hr (Case 1) and 285.162 tons/hr (Case 5), respectively. Table 11 shows the best (minimum) results for cost and emission as 576.083 $/hr (Case 1) and 283.162 tons/ hr (Case 5), respectively, for strategy B 2 . Similarly, for strategy B 3 , best cost and emission can be seen from Table 12 as 574.582 $/hr (Case 1) and 262.312 tons/hr (Case 5), respectively.
Optimized power fows over highly congested lines for all strategies of group B have been shown in Table 13. Te optimized power fow over line no.10 for strategy B 1 is found to be 31.850 MVA (Case 3), for strategy B 2 is 31.783 MVA (Case 1), and for strategy B 3 is 28.065MVA (Case 3).
Te percentage transmission reliability margins have been calculated with respect to imposed thermal limit over lines. Tis enhancement of TRM in terms of percentage improvement has been shown in Figure 11 for all strategies of group B. Observations.
(1) Congestion control strategies B 1 , B 2 , and B 3 all possess same thermal limit but Tables 10-12 clearly shows that the cost and emission both found better in strategy B 3 . (2) Figure 10 indicates better performance of MOSSA as compared to MMSSO and MARSO both for congestion control strategy B 3 . (3) It can be seen from Table 13 that the optimum power fow over transmission line no. 10 has remarkably reduced for strategy B 3 as compared to strategies B 1 and B 2 . (4) It is clear from Figure 11 that the reliability margin is strategy in B 3 is higher as compared to other two schemes B 1 and B 2 . (5) Tis clearly establishes the signifcance of implementation of DG along with DR towards managing congestion.
Te proposed approach of CM has been compared with reported methods [23,38] on the basis of result obtained. Tis comprehensive comparison has been presented in Table 14. Tis comparison has been carried out for the same power system i.e., IEEE 30-bus system. Line thermal limits have been considered as 32 and 35 MVA, which are taken by the proposed approach and [23], while a thermal limit of 32 MVA has been considered by [38]. For comparison "various control strategies to manage congestion have been considered. Te strategies of this paper have been compared to scenarios of [23]. Te strategy B 1 has been compared with [38]. In Table 14 NA has been mentioned for "not applicable" cases.

IEEE 118-Bus System.
For congestion management the proposed approach has also been evaluated on a big power system i.e., IEEE 118-bus system Tis system comprises of 99 load buses, 54 generator buses, and 186 transmission lines. Bus no. 69 is the reference bus. Te details of this system have been taken from [23]. To create congestion in transmission line 20% load has been increased at each load bus. Consequently, apparent power fows over congested transmission lines (shown in Table 15) have been found higher as compared to their thermal ratings. Hence, these lines have been considered as critical lines.

International Transactions on Electrical Energy Systems
To relieve overloading of these critical transmission lines multiobjective (minimization of overall cost and CO 2 emission) CM has been carried out. Demand response along with RIPP has been employed to manage congestion. Customers at bus number 6, 32, 45, 62, 77, and 78 (sensitive buses) take part in DR. 10% reduction in demand has been considered.
Te maximum capacity of wind plant has been considered, 10 MW (individual). For CM in a big power system optimum location of wind plant (RIPP) have been found at bus number 59, 90, and 116.
For managing congestion as multiobjective optimization problem, the proposed MOSSA has obtained 80 paretooptimal solutions out of 200 probable solutions.      International Transactions on Electrical Energy Systems       Tree specifc cases by giving individual weightage to each objective function have been mentioned in Table 16.
Te Pareto-optimal front obtained by MOSSA has been drawn in Figure 12 and three specifc cases (Case 1, Case 2, and Case 3) have been marked in Figure 12.
Te optimized apparent power fows over critical lines (line no. 5, 41, 62, 92, and 121) have been shown in Table 16. Tis table also shows the base case apparent power fows, thermal ratings, and overloading of the 5 critical lines. A remarkable observation of this Table is that the proposed       approach has eliminated the congestion over these congested lines. Table 17 shows the optimum DR, DG as RIPP, DR cost, DG cost, and two objective functions i.e., cost and emission for three specifc cases. Te total operation cost for Case 1, Case 2, and Case 3 are 70968 $/hr, 82038 $/hr, and 90905 $/hr while the emission for these three cases are 4463 tons/ hr, 4253 tons/hr, and 4225 tons/hr, respectively. For managing congestion optimum reduction in demand (MW) and size of RIPP (MW) along with its cost ($/hr) have been    shown in Table 17. Total operation cost is the summation of fuel cost, DR cost, and RIPP cost, which also has been shown in Table 17 for all three specifc cases. Te results obtained by proposed approach have been compared with reported [23] results. Te proposed approach has handled the problem of congestion as multiobjective optimization while reported method [23] has considered only one objective function i.e., cost. Total operation cost and demand response cost obtained by the proposed approach are 70968 $/hr and 40.82936 $/hr, while in reported results, total operation cost and demand response cost are 71015.2 $/hr and 151 $/hr. Terefore, the proposed approach has provided congestion management with lower operation cost and DR cost.

Conclusion
In the present work CM problem has been handled as multiobjective optimization and three objective functions, minimization of overall cost, minimization of CO 2 emission, and minimization of maximum line loading, have been taken. For this purpose, multiobjective salp swarm algorithm has been proposed.
For alleviating congestion over recognized transmission lines, incentive based demand response has been implemented.
However, asking more reduction in demand may create dissatisfaction among customers. For overcoming this faw, distributed generation using renewable independent power producer has also been employed to relieve congestion over congested lines. To show the efcacy of demand response and distributed generation in managing congestion, the whole work presented in this paper has been conducted for various control strategies framed under two groups with diferent thermal limits.
During the CM congestion management, important fndings of this paper are cost, emission, and line loading, which have become minimum when DG has been implemented along with DR. In this strategy load curtailment has also been reduced.
Te proposed MOSSA based approach of CM has been implemented on two test systems IEEE 30-bus system and IEEE 118-bus system and found better when compared with other techniques and control strategies, which are already reported in the literature. Te present approach of congestion management can be employed for hybrid power market as well Table 18 and Table 19.

Data Availability
Te data will be available on request. For the data related queries, kindly contact to Baseem Khan, baseem.khan04@ gmail.com.

Conflicts of Interest
Te authors declare that they have no conficts of interest.