Multiobjective Salp Swarm Algorithm Approach for Transmission Congestion Management

Agrawal, Anjali; Pandey, Seema N.; Srivastava, Laxmi; Walde, Pratima; Saket, R. K.; Khan, Baseem

doi:https://doi.org/10.1155/2022/8256908

International Transactions on Electrical Energy Systems

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Abstract Introduction Results and Discussion Conclusion Data Availability Conflicts of Interest References Copyright Related Articles

Research Article | Open Access

Volume 2022 | Article ID 8256908 | https://doi.org/10.1155/2022/8256908

Multiobjective Salp Swarm Algorithm Approach for Transmission Congestion Management

Anjali Agrawal,¹Seema N. Pandey,²Laxmi Srivastava,³Pratima Walde,⁴R. K. Saket,⁵and Baseem Khan⁶

Academic Editor: Kin Cheong Sou

Received23 Jun 2022

Revised03 Nov 2022

Accepted19 Nov 2022

Published07 Dec 2022

Abstract

In the newly emerged electric supply industry, the profit maximizing tendency of market participants has developed the problem of transmission congestion as the most crucial issue. This paper proposes a multiobjective salp swarm algorithm (MOSSA) approach for transmission congestion management (CM), implementing demand side management activities. For this, demand response (DR) and distributed generation (DG) have been employed. For willingly reducing the demand, demand response has been called by providing appropriate financial incentives that supports in releasing the congestion over critical lines. Distributed generation implementing wind plant as renewable independent power producer (RIPP) has also been included in order to reduce the load curtailment of responsive customers to manage transmission congestion. The proposed incentive-based demand response and distributed generation approach of CM, has been framed with various strategies employing different thermal limits over transmission lines and has resulted into significant reduction in congestion and in-turn improvement of transmission reliability margin. Diversity has been obtained in multiobjective optimization by taking two and three objective functions, respectively (minimization of overall operational cost, CO₂ emission, and line loading). The by-products of the proposed algorithm for multiobjective optimization are minimized demand reduction, optimum size, and location of DG. To examine the proposed approach, it has been implemented on IEEE 30-bus system and a bigger power system IEEE 118-bus system; as well as the proposed technique of MOSSA has been compared and found better than reported methods and two other meta heuristic algorithms (multiobjective modified sperm swarm optimization and multiobjective adoptive rat swarm optimization).

1. 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 profit 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) [4–6] 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 efficiently 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 flexible energy hub in electricity market [8] and DSM (demand side management) has proved itself as more promising tool for congestion management [9]. Thus, targeted DSM along with distributed generation (DG) can be an effective alternative of CM [10]. Under DSM, customers adjust their demands on the basis of awareness for energy conservation or by getting financial incentives [11–13].

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 conflicting towards DR. Thus, decrement in demand offered 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].

Distributed generation can be accomplished by any energy sources such as wind, solar, diesel, bio-gas, natural gas [16–21]. Out of these sources, wind (renewable energy sources) is supposed to be the most advisable distributed generation plant [22].

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 CO₂ and transmission line loading have been considered as objective functions.

The 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 differential evolution and particle swarm has overcome these issues and encourage the researchers to employ the multiobjective optimization in the field of power system [25]. The training of efficient 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. The gated spatial-temporal graph neural network-dependent short-term load forecasting for wide-area multiple buses was given by the authors in [28]. The distribution of centrally switched fault current limiters in the transmission system was given in [29]. The multistate approach for improving transmission network resilience against short-circuits faults brought on by extreme weather occurrences were presented by authors in [30]. The split-core magnetoelectric current sensor and wireless current measuring application were presented in [31]. The review of deep learning applications in frequency analysis and regulation of contemporary power systems was offered 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. The estimate of the probabilistic energy flow 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.

The performance of MOSSA for CM has been compared with two other meta heuristic algorithms, namely, multiobjective modified sperm swarm optimization and multi-objective adoptive rat swarm optimization. The 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]. The proposed approach of congestion management has been compared with similar reported methods shown in Table 1.

The contribution of the paper is as follows:(1)The 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)These three objective functions (minimization of overall operational cost, CO₂ 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)The performance of MOSSA has been compared and found better than two other nature inspired algorithms, namely, multiobjective modified sperm swarm optimization and multiobjective adoptive rat swarm optimization(5)Seven specific cases have been taken first time which have not been considered earlier

The 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. Third section describes the proposed multiobjective salp swarm algorithm, adoptive rat swarm optimization, and modified 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 fifth section, this paper has been concluded.

2. Problem Formulation

2.1. Objective Functions

Three objective functions for multiobjective CM problem have been formulated as follows:

2.1.1. Minimization of Overall Operational Cost

In the present work, overall operation cost minimization has been achieved by minimizing cost of generation, cost of demand response, and cost of distributed generation. The above said objective functions are as follows:

(1) Generation Cost. Conventional generation cost ($/hr) can be written as follows [23]:where , , and are the cost coefficients of i^th generating unit.

(2) Cost of Renewable Independent Power Producer (RIPP). In this paper wind plant has been considered as renewable independent power producer playing a role of DG. Cost function of RIPP can be expressed as follows [39]:where represents cost of wind power generation ($/MWhr), (kg/m³) is presenting the air density factor, (m²) representing the swept area of wind turbine, shows the overall efficiency of wind plant, and (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 ($/MW) are offered to these customers to curtail their demands. This is termed as DR cost. Demand response (DR) cost ($/hr) can be written as follows [20]:where is the DR cost for k^th responsive customer in $/hr and . 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 is the penalizing cost bore by k^th responsive customer in $/hr. The reduced demand can be expressed as follows [11]:

First objective function cost can be given as follows:

2.1.2. CO₂ Emission

The problem of emission minimization can be modelled as follows:

2.1.3. Minimization of Line’s Maximum Loading

This 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 is the most congested transmission line and l ϵ N_BR.

2.2. Constraints

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

2.2.1. Equality Constraints

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

2.2.2. 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].(b)Inequality constraints for security [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. This is the cost for demand response and has to be kept restricted to maintain DR within limits. This can be written as follows [20]:(d)Constraints for wind plant [30].

3. 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 modified sperm swarm optimization, and multiobjective adoptive rat swarm optimization.

3.1. 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 fish. Their forward movement is just such as jet propulsion. The mathematical model for solving optimization problems is based on the most interesting swarming behaviour of salps. Salps made swarm which is called salp chain. The first 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 c₁, c₂, and c₃, can be given as follows:where presents the position of leader salp in j^th search dimension, is the target food source in j^th dimension, and are the upper and lower bounds of variables in j^th dimension.

Parameters and are generated randomly between [0, 1] while 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 indicating follower salps and 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 can be given as follows [25]:

Normalized fuzzy membership function for multiple solutions can be given as follows:

3.2. Adoptive Rat Swarm Optimization (ARSO)

The 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]. The 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 and are the lower and upper bounds of search space, respectively, and is the population size.

Step 2. Select initial parameters , and .

Step 3. Generate opposite number based solutions by using the following equation for these initial population on the basis of opposite number concept.

Step 4. Evaluate fitness function for both initial population and opposite number based solutions . If is better than , then replace by 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 is the worst solution, is the best solution, and and 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 denotes updated position of rat population, is the position of greatest search agent, and can be evaluated by using the following equation: where is the position of k^th rat population and parameters and can be given by the following equations, respectively.where is the maximum iteration number and is the current iteration number.where and is a random number between [1, 5] and [0, 2].

Step 7. Stop if stopping criteria has been reached otherwise go to step 5.

Step 8. Optimum solution obtained.

3.3. Modified Sperm Swarm Optimization (MSSO)

Sperm swarm optimization is inspired by sperm swarm behaviour during fertilization of ovum [41]. In this algorithm a set of searching agents of sperm (potential solutions) levitate in search space to explore and achieve the optimum solution. The 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 is the current velocity of k^th sperm and is the iteration number. To avoid the premature convergence and improving the performance of MSSO chaotic dynamics are integrated.

Hence, damping factor has been modified by the following equation:

Finally, the current velocity of k^th sperm can be given as follows [41]:where is the damping factor can vary randomly between 0 and 1, is a random number [7, 14] that shows the value, is the random temperature [35.1 to 38.5] of visited location, and are the personal best position of k^th sperm, is the iteration number, and can be given by following equation:where is a control parameter and can vary between 0 and 4. The detailed modelling of this algorithm can be seen in [41].

4. Results and Discussion

MOSSA based multiobjective congestion management have been evaluated on IEEE 30-bus [23] system and IEEE 118 [23] bus system. To manage congestion, demand response and wind plant-based distributed generation have been employed. The obtained results of the proposed approach have also been compared with reported results in literature [23, 38]. Simulations have been performed using MATLAB platform.

4.1. IEEE 30 Bus-System

This bus system consists of 6 generator buses (at bus no. 1, 2, 13, 22, 23, and 27), 24 load buses and 41 transmission lines [38]. Base case results of transmission line flows employing Newton Raphson load flow (NRLF) have been shown in Table 2. The highly loaded lines (10, 16, and 29) have been identified as congested (critical) lines.

For applying demand response to manage transmission congestion, 7 receptive customers have been found through power transfer distribution factor [38]. These 7 load buses are, 8, 12, 17, 19, 21, and 30. In this work, load elasticity has been taken as −0.1 [42]. The market electricity price has been decided to be taken as same, before and after demand response. The cost of wind power generation has been taken as 3.75 $/MWhr [39].

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 flows over other lines have been observed.

4.1.1. Group “A”: 3-Objectives (35 MVA Thermal 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 different population size and generations, the final 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 A₁, A₂, and A₃, respectively.

For solving multiobjective congestion management problem, each objective function has been assigned weighting coefficient for seven specific cases. These seven specific cases have been shown in Table 3 and considered as different case studies.

Optimal solutions (optimal fronts) obtained by implementing MOSSA have been shown in Figure 2, Figure 3, and Figure 4 for strategies A₁, A₂, and A₃, respectively. Seven specific cases have also been shown in these Figures.

The optimum values of three conflicting 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 A₁ 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 A₂. Similarly, for strategy A₃, best cost, emission, and line loading can be seen from Table 6 as 573.515 $/hr (Case 1), 246.069 tons/hr (Case 2), and 26.621 MVA (Case 3), respectively.

The comparison among optimal solutions (pareto fronts) obtained for strategies A₁, A₂, and A₃ has been shown in Figure 5.

Table 7 shows the optimized power flows on transmission lines of Case 1 for strategy A₁ (group A). From this Table it is very clear that the MVA power flows over line no. 10, 16, and 29 are 34.06 MVA, 20.86 MVA, and 30.22 MVA, respectively, which are higher. Hence, these lines have been considered as critical lines (denoted by sign). The power flows over other lines are very low as compared to thermal rating (35 MVA) therefore only critical lines have been considered for congestion management analysis.

Optimized power flows (only for highly congested lines) obtained by employing MOSSA, for all strategies of group A have been shown in Table 8. The optimum flows over line no. 10 was found to be 32.359 MVA (Case 3) for strategy A₁, 32.277 MVA (Case 3) for strategy A₂, and 26.729 MVA (Case 3) for strategy A₃.

Since pictorial representation is more effective 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)The optimum location of DG (RIPP) has been found, bus no. 8, which is suppling 30 MW maximum load.(2)The MVA power flow at critical transmission line no. 10 that is connected between buses 6 and 8 has been found, 26.6210 MW (strategy B3, case3).(3)The proposed multiobjective approach of CM MOSSA has eliminated congestion efficiently over all critical lines.(4)The congestion management performance of strategy A₃ has been found better as compared to strategy A₂ and A₁.(5)For strategy A₃ of congestion management,(1)This is very clear from Tables 4–6 and 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 flows have been found.(3)Figure 6 distinctly shows the highest transmission reliability margin for strategy A₃.(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.

4.1.2. Group “B”: 2-Objectives (32 MVA) Thermal Rating

In this group only two objective functions (minimization of overall operational cost and minimization of CO₂ emission) have been considered for solving multiobjective optimization problem of CM. Thermal 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 modified sperm swarm optimization and multiobjective adoptive rat swarm optimization.

The final 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. These 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 B₁, B₂, and B₃, respectively. After having several trials population size and the number of iteration for MMSSO and MARSO have been found 100 and 180 for strategy B₃. The 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 specific values these are mentioned in Table 9. On this basis 5 specific points have been identified.

Figures 7–9 show the optimal solutions (pareto fronts) obtained by MOSSA for strategy B₁, B₂, and B₃, respectively. Out of these nondominated solutions, five specific cases given in Table 9 have been recognized and marked on these pareto-optimal fronts.

For strategy B₃ the multiobjective congestion management has been carried out by employing multiobjective salp swarm algorithm, multiobjective modified sperm swarm optimization, and multiobjective adoptive rat swarm optimization. The pareto-optimal 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 B₁ 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 B₂. Similarly, for strategy B₃, 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 flows over highly congested lines for all strategies of group B have been shown in Table 13. The optimized power flow over line no.10 for strategy B₁ is found to be 31.850 MVA (Case 3), for strategy B₂ is 31.783 MVA (Case 1), and for strategy B₃ is 28.065MVA (Case 3).

The percentage transmission reliability margins have been calculated with respect to imposed thermal limit over lines. This 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 B₁, B₂, and B₃ all possess same thermal limit but Tables 10–12 clearly shows that the cost and emission both found better in strategy B₃.(2)Figure 10 indicates better performance of MOSSA as compared to MMSSO and MARSO both for congestion control strategy B₃.(3)It can be seen from Table 13 that the optimum power flow over transmission line no. 10 has remarkably reduced for strategy B₃ as compared to strategies B₁ and B₂.(4)It is clear from Figure 11 that the reliability margin is strategy in B₃ is higher as compared to other two schemes B₁ and B₂.(5)This clearly establishes the significance of implementation of DG along with DR towards managing congestion.

The proposed approach of CM has been compared with reported methods [23, 38] on the basis of result obtained. This comprehensive comparison has been presented in Table 14. This 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. The strategies of this paper have been compared to scenarios of [23]. The strategy B₁ has been compared with [38]. In Table 14 NA has been mentioned for “not applicable” cases.

4.2. 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 This system comprises of 99 load buses, 54 generator buses, and 186 transmission lines. Bus no. 69 is the reference bus. The 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 flows 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.

To relieve overloading of these critical transmission lines multiobjective (minimization of overall cost and CO₂ 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.

The 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 pareto-optimal solutions out of 200 probable solutions.

Three specific cases by giving individual weightage to each objective function have been mentioned in Table 16.

The Pareto-optimal front obtained by MOSSA has been drawn in Figure 12 and three specific cases (Case 1, Case 2, and Case 3) have been marked in Figure 12.

The optimized apparent power flows over critical lines (line no. 5, 41, 62, 92, and 121) have been shown in Table 16. This table also shows the base case apparent power flows, 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 specific cases. The 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 specific cases.

The results obtained by proposed approach have been compared with reported [23] results. The 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. Therefore, the proposed approach has provided congestion management with lower operation cost and DR cost.

5. Conclusion

In the present work CM problem has been handled as multiobjective optimization and three objective functions, minimization of overall cost, minimization of CO₂ 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 flaw, distributed generation using renewable independent power producer has also been employed to relieve congestion over congested lines. To show the efficacy 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 different thermal limits.

During the CM congestion management, important findings 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.

The 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. The present approach of congestion management can be employed for hybrid power market as well Table 18 and Table 19.

Appendix. A

Data Availability

The data will be available on request. For the data related queries, kindly contact to Baseem Khan, [email protected].

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Copyright © 2022 Anjali Agrawal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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International Transactions on Electrical Energy Systems

Multiobjective Salp Swarm Algorithm Approach for Transmission Congestion Management

Abstract

1. Introduction

2. Problem Formulation

2.1. Objective Functions

2.1.1. Minimization of Overall Operational Cost

2.1.2. CO2 Emission

2.1.3. Minimization of Line’s Maximum Loading

2.2. Constraints

2.2.1. Equality Constraints

2.2.2. Inequality Constraints

3. Optimization Algorithms

3.1. Multiobjective Salp Swarm Algorithm

3.2. Adoptive Rat Swarm Optimization (ARSO)

3.3. Modified Sperm Swarm Optimization (MSSO)

4. Results and Discussion

4.1. IEEE 30 Bus-System

4.1.1. Group “A”: 3-Objectives (35 MVA Thermal Rating)

4.1.2. Group “B”: 2-Objectives (32 MVA) Thermal Rating

4.2. IEEE 118-Bus System

5. Conclusion

Appendix. A

Data Availability

Conflicts of Interest

References

Copyright

2.1.2. CO₂ Emission