# Multiobjective Salp Swarm Algorithm Approach for Transmission Congestion Management

Authors: Anjali Agrawal; Seema N. Pandey; Laxmi Srivastava; Pratima Walde; R. K. Saket; Baseem Khan
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## 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).


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## Body

## 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.Table 1
Comparison of proposed CM approach with the reported methods.
Reported methodologiesCongestion management strategyAdvantagesDisadvantagesReferenceNSGA-II/DEDGMultiobjectiveTransmission expansion[1]Fitness distance ratio-PSO and fuzzy adaptive-PSOGRCM in hybrid power marketSingle objective[4]Gravitational search algorithmATC enhancementCM with TCSCCost not included/single objective[7]GAMS softwareDRCM with renewable energy sourceCost not included/Single objective[13]CPLEX (MATLAB)DRCM with renewable energy sourceCost not included/single objective[14]Differential evolutionDGCM with renewable energy sourceCost not included/single objective[15]Matpower toolboxDGCM based on flow gate marginal pricesingle objective[16]GA basedDGLMP difference based CMGeneration cost not included[17]DE-PSODGCM with renewable energy sourceMultiobjective problem handled as single objective[18]Flower pollinationDGCM with renewable energy sourceMultiobjective problem handled as single objective[19]MOPSODRP2-objective functionsHigh demand response[23]Jaya algorithmTransmission switching/DRHybrid power systemAll transmission lines cannot be switched off[24]GAMS softwareOptimal energy storage system chargingMultiobjectiveCost and emission are in single objective/load shedding[35]Hybrid bacterial foraging and nelder–mead algorithmTCSC placement2-objective functionsMultiobjective problem handled as single objective[38]MATPOWER (MATLAB)TCSC placementCM with renewable energy sourceCost not included/single objective[39]MOSSA [proposed]DR/RIPP3-objective functions/CM with renewable energy source[Proposed]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 earlierThe 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 CG ($/hr) can be written as follows [23]:(1)CG=∑i=1NGai+biPGi+ciPGi2i=1,2,3……….NG,where ai, bi, and ci are the cost coefficients of ith generating unit.(2) Cost of Renewable Independent Power Producer (RIPP). In this paper wind plant has been considered as renewable independent power producer playing a role of DG. Cost function CRIPP of RIPP can be expressed as follows [39]:(2)CRIPP=Ψ×PWP$hr,PWP=12aird×Wt×ηWP×vwind3.where Ψ represents cost of wind power generation ($/MWhr), aird (kg/m3) is presenting the air density factor, Wt (m2) representing the swept area of wind turbine, ηWP shows the overall efficiency of wind plant, and vwind (m/sec) shows the wind velocity.(3) Demand Response Cost. Demand response program (DRP) is the process in which responsive customers are convinced to reduce their demands to bring down the loading over critical transmission lines. Some appropriate monetary incentive ($/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]:(3)CDR=∑k=1NDRµk,where µk is the DR cost for kth responsive customer in $/hr and NDR∈NB. 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 ofkth responsive customer can be expressed as follows [23]:(4)µk=INC×d0k−dk.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]:(5)ℒk=PEN×LRk−d0k−dk,ℒk=PEN×LRk−Αdk,where ℒk is the penalizing cost bore by kth responsive customer in $/hr. The reduced demand dk can be expressed as follows [11]:(6)dk=d0k×1+ε×EPDR−EP0+INC−PENEP0.First objective function cost can be given as follows:(7)F1=minimizeCG+CDR+CRIPP.


#### 2.1.2. CO2 Emission

The problem ofCO2 emission minimization can be modelled as follows:(8)F2=minimizeE=minimize∑i=1NGαi+βiPGi+γiPGi2.


#### 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:(9)F3=minimizemaxSl,where l is the most congested transmission line and l ϵ NBR.


### 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]:(10)PGi−PDi−Vi∑j=1NBVjGijcosδi−δj+Bijsinδi−δj=0,QGi−QDi−Vi∑j=1NBVjGijsinδi−δj+Bijcosδi−δj=0,where Gij and Bij are the transmission conductance and susceptance between bus i and j, respectively, and δiδj are the voltage angles at ith and jth 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].(11)PGimin≤PGi≤PGimax,i=1,2,3……NG,QGimin≤QGi≤QGimax,i=1,2,3……NG,VGimin≤VGi≤VGimax,i=1,2,3……NG.(b)
Inequality constraints for security [23].(12)Vimin≤Vi≤ViMax,i=1,2,3…………….NLB,Smaxl≥Sl,l=1,2,3………….…NBR.(c)
Demand response constraints.Financial incentive paid to thekth 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]:(13)µkmin≤µk≤µkmax,k=1,2,3……NDR,DRkmin≤DRk≤DRkmax,k=1,2,3……NDR.(d)
Constraints for wind plant [30].(14)PWPmin≤PWP≤PWPmax.


## 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 CG ($/hr) can be written as follows [23]:(1)CG=∑i=1NGai+biPGi+ciPGi2i=1,2,3……….NG,where ai, bi, and ci are the cost coefficients of ith generating unit.(2) Cost of Renewable Independent Power Producer (RIPP). In this paper wind plant has been considered as renewable independent power producer playing a role of DG. Cost function CRIPP of RIPP can be expressed as follows [39]:(2)CRIPP=Ψ×PWP$hr,PWP=12aird×Wt×ηWP×vwind3.where Ψ represents cost of wind power generation ($/MWhr), aird (kg/m3) is presenting the air density factor, Wt (m2) representing the swept area of wind turbine, ηWP shows the overall efficiency of wind plant, and vwind (m/sec) shows the wind velocity.(3) Demand Response Cost. Demand response program (DRP) is the process in which responsive customers are convinced to reduce their demands to bring down the loading over critical transmission lines. Some appropriate monetary incentive ($/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]:(3)CDR=∑k=1NDRµk,where µk is the DR cost for kth responsive customer in $/hr and NDR∈NB. 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 ofkth responsive customer can be expressed as follows [23]:(4)µk=INC×d0k−dk.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]:(5)ℒk=PEN×LRk−d0k−dk,ℒk=PEN×LRk−Αdk,where ℒk is the penalizing cost bore by kth responsive customer in $/hr. The reduced demand dk can be expressed as follows [11]:(6)dk=d0k×1+ε×EPDR−EP0+INC−PENEP0.First objective function cost can be given as follows:(7)F1=minimizeCG+CDR+CRIPP.


### 2.1.2. CO2 Emission

The problem ofCO2 emission minimization can be modelled as follows:(8)F2=minimizeE=minimize∑i=1NGαi+βiPGi+γiPGi2.


### 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:(9)F3=minimizemaxSl,where l is the most congested transmission line and l ϵ NBR.


## 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 CG ($/hr) can be written as follows [23]:(1)CG=∑i=1NGai+biPGi+ciPGi2i=1,2,3……….NG,where ai, bi, and ci are the cost coefficients of ith generating unit.(2) Cost of Renewable Independent Power Producer (RIPP). In this paper wind plant has been considered as renewable independent power producer playing a role of DG. Cost function CRIPP of RIPP can be expressed as follows [39]:(2)CRIPP=Ψ×PWP$hr,PWP=12aird×Wt×ηWP×vwind3.where Ψ represents cost of wind power generation ($/MWhr), aird (kg/m3) is presenting the air density factor, Wt (m2) representing the swept area of wind turbine, ηWP shows the overall efficiency of wind plant, and vwind (m/sec) shows the wind velocity.(3) Demand Response Cost. Demand response program (DRP) is the process in which responsive customers are convinced to reduce their demands to bring down the loading over critical transmission lines. Some appropriate monetary incentive ($/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]:(3)CDR=∑k=1NDRµk,where µk is the DR cost for kth responsive customer in $/hr and NDR∈NB. 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 ofkth responsive customer can be expressed as follows [23]:(4)µk=INC×d0k−dk.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]:(5)ℒk=PEN×LRk−d0k−dk,ℒk=PEN×LRk−Αdk,where ℒk is the penalizing cost bore by kth responsive customer in $/hr. The reduced demand dk can be expressed as follows [11]:(6)dk=d0k×1+ε×EPDR−EP0+INC−PENEP0.First objective function cost can be given as follows:(7)F1=minimizeCG+CDR+CRIPP.


## 2.1.2. CO2 Emission

The problem ofCO2 emission minimization can be modelled as follows:(8)F2=minimizeE=minimize∑i=1NGαi+βiPGi+γiPGi2.


## 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:(9)F3=minimizemaxSl,where l is the most congested transmission line and l ϵ NBR.


## 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]:(10)PGi−PDi−Vi∑j=1NBVjGijcosδi−δj+Bijsinδi−δj=0,QGi−QDi−Vi∑j=1NBVjGijsinδi−δj+Bijcosδi−δj=0,where Gij and Bij are the transmission conductance and susceptance between bus i and j, respectively, and δiδj are the voltage angles at ith and jth 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].(11)PGimin≤PGi≤PGimax,i=1,2,3……NG,QGimin≤QGi≤QGimax,i=1,2,3……NG,VGimin≤VGi≤VGimax,i=1,2,3……NG.(b)
Inequality constraints for security [23].(12)Vimin≤Vi≤ViMax,i=1,2,3…………….NLB,Smaxl≥Sl,l=1,2,3………….…NBR.(c)
Demand response constraints.Financial incentive paid to thekth 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]:(13)µkmin≤µk≤µkmax,k=1,2,3……NDR,DRkmin≤DRk≤DRkmax,k=1,2,3……NDR.(d)
Constraints for wind plant [30].(14)PWPmin≤PWP≤PWPmax.


## 2.2.1. Equality Constraints

Power balance can be expressed as follows [23]:(10)PGi−PDi−Vi∑j=1NBVjGijcosδi−δj+Bijsinδi−δj=0,QGi−QDi−Vi∑j=1NBVjGijsinδi−δj+Bijcosδi−δj=0,where Gij and Bij are the transmission conductance and susceptance between bus i and j, respectively, and δiδj are the voltage angles at ith and jth 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].(11)PGimin≤PGi≤PGimax,i=1,2,3……NG,QGimin≤QGi≤QGimax,i=1,2,3……NG,VGimin≤VGi≤VGimax,i=1,2,3……NG.(b)
Inequality constraints for security [23].(12)Vimin≤Vi≤ViMax,i=1,2,3…………….NLB,Smaxl≥Sl,l=1,2,3………….…NBR.(c)
Demand response constraints.Financial incentive paid to thekth 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]:(13)µkmin≤µk≤µkmax,k=1,2,3……NDR,DRkmin≤DRk≤DRkmax,k=1,2,3……NDR.(d)
Constraints for wind plant [30].(14)PWPmin≤PWP≤PWPmax.


## 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 parametersc1, c2, and c3, can be given as follows:(15)xj1=Fj+c1ubj−lbjc2+lbj,c3≥0,Fj−c1ubj−lbjc2+lbj,c3<0,where x1/j presents the position of leader salp in jth search dimension, Fj is the target food source in jth dimension, ubj and lbj are the upper and lower bounds of variables in jth dimension.Parametersc2 and c3 are generated randomly between [0, 1] while c1 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:(16)c1=2e−−4k/K2,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:(17)xji=12xji+xji−1,where i≥2 indicating follower salps and xji is the ith follower salp in jth 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 functionμi can be given as follows [25]:(18)μi=1,Fi<Fimin,Fimax−FiFimax−Fimin,Fimin<Fi<Fimax,0,Fi≥Fimax.Normalized fuzzy membership functionμi,j for multiple solutions can be given as follows:(19)μi,j=∑i=1NobjWiμi∑j=1NREPO∑i=1NobjWiμi.


### 3.2. Adoptive Rat Swarm Optimization (ARSO)

The rat swarm optimization is a nature inspired meta-heuristic technique Figure1 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]:Figure 1
Flow chart of proposed MOSSA algorithm.Step 1.
Generate initial rat population by using the following equation randomly under the upper and lower limits of search space.(20)xk=xkmin+rand∗xkmax−xkmin,k=1,2,3…..M.where xkmin and xkmax are the lower and upper bounds of search space, respectively, and M is the population size.Step 2.
Select initial parametersA,R, and C.Step 3.
Generate opposite number based solutionsx⟶k by using the following equation for these initial population on the basis of opposite number concept.(21)x⟶k=xkmax−xkmin−xk,k=1,2,3…….M.Step 4.
Evaluate fitness function for both initial populationfxk and opposite number based solutions fx⟶k. If fx⟶k is better than fxk, then replace xk 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:(22)xworst=rand1∗P⟶rx,ifrand2≤0.5,xkmax−xkmin−xk,ifrand2>0.5,where xworst is the worst solution, Prx is the best solution, and rand1 and rand2 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.(23)P→rx+1=P→rx−P→.where P⟶rx+1=denotes updated position of rat population, P⟶rx is the position of greatest search agent, and P⟶ can be evaluated by using the following equation: (24)P¯=A∗P⟶kx+C∗P⟶rx−P⟶kx,where P⟶kx is the position of kth rat population and parameters A and C can be given by the following equations, respectively.(25)A=R−q∗Ritermax,q=1,2,3….itermax,where itermax is the maximum iteration number and q is the current iteration number.(26)C=2∗rand,where R and C is a random number between [1, 5] and [0, 2].Step 7.
Stop if stopping criteria has been reached otherwise go to step5.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:(27)xkt+1=xkt+vkt,where vkt is the current velocity of kth 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 modified by the following equation:(28)CD=θ∗100∗e−20∗iter/itermax.Finally, the current velocity ofkth sperm can be given as follows [41]:(29)vkt=θ∗D∗log10pHRand1∗vk+log10∗pHRand1∗log10TempRand2∗xbestk−xkt+log10∗pHRand1∗log10TempRand2∗xgbestk−xkt,where D is the damping factor can vary randomly between 0 and 1, pHRand1 is a random number [7, 14] that shows the pH value, TempRand2 is the random temperature [35.1 to 38.5] of visited location, xbestk and xgbestk are the personal best position of kth sperm, t is the iteration number, and θ can be given by following equation:(30)θt+1=μ∗θt∗1−θt0≤θ≤1,where μ is a control parameter and can vary between 0 and 4. The detailed modelling of this algorithm can be seen in [41].


## 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 parametersc1, c2, and c3, can be given as follows:(15)xj1=Fj+c1ubj−lbjc2+lbj,c3≥0,Fj−c1ubj−lbjc2+lbj,c3<0,where x1/j presents the position of leader salp in jth search dimension, Fj is the target food source in jth dimension, ubj and lbj are the upper and lower bounds of variables in jth dimension.Parametersc2 and c3 are generated randomly between [0, 1] while c1 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:(16)c1=2e−−4k/K2,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:(17)xji=12xji+xji−1,where i≥2 indicating follower salps and xji is the ith follower salp in jth 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 functionμi can be given as follows [25]:(18)μi=1,Fi<Fimin,Fimax−FiFimax−Fimin,Fimin<Fi<Fimax,0,Fi≥Fimax.Normalized fuzzy membership functionμi,j for multiple solutions can be given as follows:(19)μi,j=∑i=1NobjWiμi∑j=1NREPO∑i=1NobjWiμi.


## 3.2. Adoptive Rat Swarm Optimization (ARSO)

The rat swarm optimization is a nature inspired meta-heuristic technique Figure1 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]:Figure 1
Flow chart of proposed MOSSA algorithm.Step 1.
Generate initial rat population by using the following equation randomly under the upper and lower limits of search space.(20)xk=xkmin+rand∗xkmax−xkmin,k=1,2,3…..M.where xkmin and xkmax are the lower and upper bounds of search space, respectively, and M is the population size.Step 2.
Select initial parametersA,R, and C.Step 3.
Generate opposite number based solutionsx⟶k by using the following equation for these initial population on the basis of opposite number concept.(21)x⟶k=xkmax−xkmin−xk,k=1,2,3…….M.Step 4.
Evaluate fitness function for both initial populationfxk and opposite number based solutions fx⟶k. If fx⟶k is better than fxk, then replace xk 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:(22)xworst=rand1∗P⟶rx,ifrand2≤0.5,xkmax−xkmin−xk,ifrand2>0.5,where xworst is the worst solution, Prx is the best solution, and rand1 and rand2 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.(23)P→rx+1=P→rx−P→.where P⟶rx+1=denotes updated position of rat population, P⟶rx is the position of greatest search agent, and P⟶ can be evaluated by using the following equation: (24)P¯=A∗P⟶kx+C∗P⟶rx−P⟶kx,where P⟶kx is the position of kth rat population and parameters A and C can be given by the following equations, respectively.(25)A=R−q∗Ritermax,q=1,2,3….itermax,where itermax is the maximum iteration number and q is the current iteration number.(26)C=2∗rand,where R and C is a random number between [1, 5] and [0, 2].Step 7.
Stop if stopping criteria has been reached otherwise go to step5.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:(27)xkt+1=xkt+vkt,where vkt is the current velocity of kth 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 modified by the following equation:(28)CD=θ∗100∗e−20∗iter/itermax.Finally, the current velocity ofkth sperm can be given as follows [41]:(29)vkt=θ∗D∗log10pHRand1∗vk+log10∗pHRand1∗log10TempRand2∗xbestk−xkt+log10∗pHRand1∗log10TempRand2∗xgbestk−xkt,where D is the damping factor can vary randomly between 0 and 1, pHRand1 is a random number [7, 14] that shows the pH value, TempRand2 is the random temperature [35.1 to 38.5] of visited location, xbestk and xgbestk are the personal best position of kth sperm, t is the iteration number, and θ can be given by following equation:(30)θt+1=μ∗θt∗1−θt0≤θ≤1,where μ 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.Table 2
Transmission line flows (MVA) after NRLF.
Line no.From busTo busNRLF (MVA)Line no.From busTo busNRLF (MVA)11212.092215189.221316.082318195.8832417.392419205.2843413.32510207.5152515.052610178.6962621.9927102111.9974625.222810229.4285715.3129∗212230.5196710.1130152310.4610∗6834.833122248.111696.743223247.14126103.843324254.271391103425264.27149106.773525277.54154122.643628278.8516∗121338.73727296.41712145.463827307.321812159.553929303.731912169.27408288.12014151.17416282.812116176.08For 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:StrategyA1: Only GR.StrategyA2: GR with DR.StrategyA3: 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 strategiesA1, 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 Table3 and considered as different case studies.Table 3
Weighting coefficients of objective functions for Group A.
Weighting coefficientsCase 1Case 2Case 3Case 4Case 5Case 6Case 7Cost1000.3330.50.50Emission0100.33300.50.5Line loading0010.3330.500.5Optimal solutions (optimal fronts) obtained by implementing MOSSA have been shown in Figure2, Figure 3, and Figure 4 for strategies A1, A2, and A3, respectively. Seven specific cases have also been shown in these Figures.Figure 2
Pareto-optimal front for strategyA1.Figure 3
Pareto-optimal front for strategyA2.Figure 4
Pareto-optimal front for strategyA3.The optimum values of three conflicting objective functions and control variables obtained by employing MOSSA for CM have been shown in Tables4–6.It can be seen from Table4 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 $/hr (Case 1), 246.069 tons/hr (Case 2), and 26.621 MVA (Case 3), respectively.The comparison among optimal solutions (pareto fronts) obtained for strategiesA1, A2, and A3 has been shown in Figure 5.Figure 5
Comparison of pareto-optimal fronts for all strategies of group A.Table 4
Optimized variables for strategyA1.
Case 1Case 2Case 3Case 4Case 5Case 6Case 7PG1 (MW)43.719823.700933.988015.011112.659729.44321.7909PG2 (MW)58.038527.920028.569044.573950.1839543.90126.8511PG3 (MW)17.518330.300017.994021.609122.4650125.13430.8579PG4 (MW)23.281833.990029.634027.275827.3077427.18427.8138PG5 (MW)17.035130.000027.839029.931024.4872525.31529.7888PG6 (MW)32.096445.380054.152253.694554.916040.46154.9710Cost ($/hr)574.835618.610634.705608.319606.426588.468620.637Emission (tons/hr)392.922282.537338.603314.062332.708306.550289.657Loading (MVA)34.448733.001532.258532.41032.394632.46232.2720Table 5
Optimized variables for strategyA2.
Case 1Case 2Case 3Case 4Case 5Case 6Case 7PG1 (MW)43.552621.627013.831923.497435.032234.273822.0440PG2 (MW)57.963628.300032.750738.476347.201037.652127.5273PG3 (MW)17.562729.155032.560326.721112.767325.002730.8975PG4 (MW)23.168229.476028.210325.430723.839126.021030.4195PG5 (MW)17.134027.530029.184224.575320.814621.660925.9777PG6 (MW)31.856143.743054.99952.783652.104446.755154.5817DR1 (MW)0.014002.714000.038710.044140.097600.064070.05061DR2 (MW)0.129802.650000.149730.149490.149180.146300.14894DR3 (MW)0.055901.65600.041510.046810.047630.044310.05490DR4(MW)0.045000.652100.044590.044180.038400.040990.04325DR5 (MW)0.047500.847500.046220.046350.046250.042080.04518DR6 (MW)0.087501.587500.087330.086860.083770.083940.07020DR7 (MW)0.052900.953000.052920.052830.052840.051670.05070Cost ($/hr)573.992590.449623.454599.692584.2237589.044617.512Emission (tons/hr)390.979249.080296.132298.334341.9832305.433288.365Loading (MVA)34.345032.828232.176732.461132.650032.976032.2386Table 6
Optimized variables for strategyA3.
Case 1Case 2Case 3Case 4Case 5Case 6Case 7PG1 (MW)41.953722.35617.8827126.776131.812534.617029.4501PG2 (MW)56.066528.265455.809340.843643.505041.630632.5137PG3 (MW)15.993831.04100.1773120.720614.927820.457826.3910PG4 (MW)22.764929.999931.020925.399824.077824.170323.7110PG5 (MW)15.676829.369629.998620.039617.702122.685820.8522PG6 (MW)28.734341.819454.999945.355449.369637.776548.7966DR1 (MW)0.053700.113980.029610.095940.110800.079600.10150DR2 (MW)0.129900.149890.150000.149810.149700.106000.02090DR3 (MW)0.035900.055910.036970.044260.049600.055800.01480DR4 (MW)0.014900.044980.032110.042870.044600.025500.02140DR5 (MW)0.047500.047440.047260.046860.045000.031700.02770DR6 (MW)0.087400.087470.079980.079830.087200.070600.01270DR7 (MW)0.030700.052970.052950.052290.052500.048600.02230PRIPP (MW)10.000010.00009.817809.970909.992109.842409.79230Cost ($/hr)573.515615.778623.207587.785584.056582.246596.118Emission (tons/hr)358.259246.069358.668271.466298.368286.632269.167Loading (MVA)28.123527.160426.621027.123027.758228.435327.8879Table7 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.Table 7
Optimized power flow for case 1 strategyA1 of group A.
Line no.Power flow (MVA)Line no.Power flow (MVA)Line no.Power flow (MVA)Line no.Power flow (MVA)121.041111.11213.59315.16220.55126.38228.06323.12319.24130.00234.763311.46418.161411.27245.63344.22514.331519.23257.973515.81621.8316∗20.86267.753625.06718.44175.102712.44376.32814.26186.83289.88387.18912.40197.2729∗30.22393.7110∗34.06201.603011.344010.384114.98Optimized power flows (only for highly congested lines) obtained by employing MOSSA, for all strategies of group A have been shown in Table8. 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.Table 8
Optimized power flow for all strategies of group A.
StrategyLine no.Optimum power flows in MVACase 1Case 2Case 3Case 4Case 5Case 6Case 7A11034.06133.05732.35932.45132.75533.33932.4041620.86431.74525.20724.08618.09024.79432.1002930.22434.10934.58632.76330.81832.28533.682A21034.05832.99332.27732.50532.54033.56732.3531621.26829.61126.93523.49915.69726.31028.3852930.73934.76131.50832.71230.77932.11433.823A31028.18927.16526.72926.97926.98028.43527.8881620.45826.58430.3922.82819.34323.51628.5542929.81033.05031.36231.70030.69131.21931.653Since 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 Figure6.Figure 6
Percentage Improvement in TRM over critical lines for group A.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 strategyA3 has been found better as compared to strategy A2 and A1.(5)
For strategyA3 of congestion management,(1)
This is very clear from Tables4–6 and Figure 5 that maximum minimization of all objective functions (individual and simultaneous) has been achieved.(2)
It is very clear from Table8 that maximum optimized power flows have been found.(3)
Figure6 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:StrategyB1: only GR.StrategyB2: GR with DR.StrategyB3: 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 strategiesB1, 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 Table9. On this basis 5 specific points have been identified.Table 9
Weighting coefficients of objective functions for group B.
Weighting coefficientsCase 1Case 2Case 3Case 4Case 5Cost10.750.50.250Emission00.250.50.751Figures7–9 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.Figure 7
Pareto-optimal front for strategyB1.Figure 8
Pareto-optimal front for strategyB2.Figure 9
Pareto-optimal front for strategyB3.Figure 10
Comparison of pareto-optimal fronts obtained by MOSSA, MMSSO, and MARSO for strategyB3.For CM the results (optimal control variables and objective function values) obtained by employing MOSSA have been shown in Tables10–12. 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 $/hr (Case 1) and 262.312 tons/hr (Case 5), respectively.Optimized power flows over highly congested lines for all strategies of group B have been shown in Table13. The optimized power flow over line no.10 for strategy B1 is found to be 31.850 MVA (Case 3), for strategy B2 is 31.783 MVA (Case 1), and for strategy B3 is 28.065MVA (Case 3).Table 10
Optimized variables for strategyB1.
Case 1Case 2Case 3Case 4Case 5PG1 (MW)40.624836.839233.712130.8682326.9647PG2 (MW)52.102548.265742.621138.161131.2577PG3 (MW)15.508118.097221.777126.577629.8260PG4 (MW)22.652523.452224.010022.228522.9801PG5 (MW)17.205918.617922.160124.554929.9999PG6 (MW)44.064046.801647.691149.603651.0395Cost ($/hr)578.083579.455583.188594.077600.318Emission (tons/hr)365.149339.162316.825297.529285.162Table 11
Optimized variables for strategyB2.
Case 1Case 2Case 3Case 4Case 5PG1 (MW)40.046235.666832.582730.456926.5898PG2 (MW)53.383547.155341.091235.946131.2685PG3 (MW)15.198518.681222.851828.893829.8184PG4 (MW)22.279423.270923.452622.107223.1169PG5 (MW)15.098519.153522.959124.917729.8332PG6 (MW)45.026447.691148.597049.190749.1780DR1 (MW)0.120000.090800.090640.089740.29100DR2 (MW)0.220000.119880.119880.119880.62000DR3 (MW)0.044700.044440.044410.043100.44800DR4 (MW)0.036000.035700.035560.035600.43660DR5 (MW)0.038000.037680.037700.037890.03800DR6 (MW)0.069900.069710.069610.069570.37000DR7 (MW)0.042400.042090.042080.042250.04240Cost ($/hr)576.083578.182582.98592.077598.318Emission (tons/hr)363.149331.053308.922295.529283.162Table 12
Optimized variables for strategyB3.
Case 1Case 2Case 3Case 4Case 5PG1 (MW)41.438437.688834.554228.856425.3077PG2 (MW)55.272750.661343.862536.183134.1679PG3 (MW)16.427919.046020.774725.161129.4997PG4 (MW)22.758823.709023.759524.060323.8601PG5 (MW)16.399718.152320.273125.103925.2513PG6 (MW)29.334832.218838.254342.140743.3897DR1 (MW)0.068340.066950.064990.063780.06165DR2 (MW)0.059580.055030.052470.034280.03577DR3 (MW)0.023620.031930.027060.022560.02064DR4 (MW)0.025030.024410.024950.022780.02669DR5 (MW)0.019750.016620.021180.015090.01534DR6 (MW)0.051320.048620.037640.034770.03407DR7 (MW)0.012600.031530.022530.021170.02368PWP (MW)9.880009.980009.890009.890009.89000Cost ($/hr)574.582576.071580.749592.464599.243Emission (tons/hr)353.437322.327293.331267.017262.312Table 13
Optimized MVA power flows over critical lines for all strategies of group B.
StrategyLine no.Case 1Case 2Case 3Case 4Case 5B11031.85031.84031.78031.73031.7101619.54021.59024.73028.90031.7202930.72031.28031.6831.7731.220B21031.78331.12231.00331.76231.6781619.92420.91824.07627.89228.5532930.10831.25931.93131.98031.988B31028.06528.86228.45728.22828.0831619.79722.78824.14727.97330.7752929.77430.32531.64631.89131.989The 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 Figure11 for all strategies of group B.Figure 11
Percentage Improvement in TRM over critical lines for Group B.Observations.(1)
Congestion control strategiesB1, 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)
Figure10 indicates better performance of MOSSA as compared to MMSSO and MARSO both for congestion control strategy B3.(3)
It can be seen from Table13 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 Figure11 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.Table 14
Result comparison between proposed approach and reported methods [23, 38].
S. No.`Line thermal ratingMethodBest solutionPreferred solutionOptimal flowDRDGCostEmissionLine loadingCostEmission(MVA)($/hr)(tons/hr)(MVA)($/hr)(tons/hr)(MVA)(MW)(MW)135MOPSO (scenario 1) [23]574.870282.590NA585.32311.04034.22NANAMOSSA (strategyA1)574.835282.53732.258588.47306.55034.061NANA235MOPSO (scenario 2) [23]574.020249.250NA623.57277.12034.150.44NAMOSSA (strategyA2)573.992249.08032.18589.04305.43034.0580.4326NAMOSSA (strategyA3)573.515246.06926.62582.25286.63228.1890.4010332BF-NM [29]648.860NANANANANANANAMOPSO (scenario 3) [23]579.180285.440NA588.33307.80031.99NANAMOSSA (strategyB1)578.083285.162NA583.188316.82531.85NANA432MOPSO (scenario 4) [23]577.900250.180NA624.80278.27031.960.6NAMOSSA (scenarioB2)576.083283.162NA580.98308.92231.7830.571NAMOSSA (strategyB3)574.582262.312NA580.749293.33128.0650.2609.88


### 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.Table 15
Weighting coefficients of objective functions for IEEE 118-bus system.
Objective functionCase 1Case 2Case 3Cost10.50Emission00.51To 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 Table16.Table 16
Power flows of case 1 for IEEE 118-bus system.
Line noFrom busTo busBase caseThermal line ratingWithout CMAfter CM(MVA PF)55688.05132.07140.87136.9041233291.77137.65146.82129.4662454636.7155.0758.7455.8992616228.8343.2446.1340.69121777845.9168.8773.4663.00The Pareto-optimal front obtained by MOSSA has been drawn in Figure12 and three specific cases (Case 1, Case 2, and Case 3) have been marked in Figure 12.Figure 12
Pareto-optimal fronts obtained for IEEE 118-bus system.The optimized apparent power flows over critical lines (line no. 5, 41, 62, 92, and 121) have been shown in Table16. 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.Table17 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 $/hr. Therefore, the proposed approach has provided congestion management with lower operation cost and DR cost.Table 17
Optimized parameters for IEEE 118-bus system.
DRRIPPDR costRIPP costFuel costCostEmission(MW)(MW)($/hr)($/hr)($/hr)($/hr)(tons/hr)Case 15.934526.8940.82936100.837570826.33709684463Case 26.884526.0247.3653697.57581893.06820384253Case 38.654325.44059.5418495.490750.06908994220


## 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.Table 2
Transmission line flows (MVA) after NRLF.
Line no.From busTo busNRLF (MVA)Line no.From busTo busNRLF (MVA)11212.092215189.221316.082318195.8832417.392419205.2843413.32510207.5152515.052610178.6962621.9927102111.9974625.222810229.4285715.3129∗212230.5196710.1130152310.4610∗6834.833122248.111696.743223247.14126103.843324254.271391103425264.27149106.773525277.54154122.643628278.8516∗121338.73727296.41712145.463827307.321812159.553929303.731912169.27408288.12014151.17416282.812116176.08For 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:StrategyA1: Only GR.StrategyA2: GR with DR.StrategyA3: 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 strategiesA1, 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 Table3 and considered as different case studies.Table 3
Weighting coefficients of objective functions for Group A.
Weighting coefficientsCase 1Case 2Case 3Case 4Case 5Case 6Case 7Cost1000.3330.50.50Emission0100.33300.50.5Line loading0010.3330.500.5Optimal solutions (optimal fronts) obtained by implementing MOSSA have been shown in Figure2, Figure 3, and Figure 4 for strategies A1, A2, and A3, respectively. Seven specific cases have also been shown in these Figures.Figure 2
Pareto-optimal front for strategyA1.Figure 3
Pareto-optimal front for strategyA2.Figure 4
Pareto-optimal front for strategyA3.The optimum values of three conflicting objective functions and control variables obtained by employing MOSSA for CM have been shown in Tables4–6.It can be seen from Table4 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 $/hr (Case 1), 246.069 tons/hr (Case 2), and 26.621 MVA (Case 3), respectively.The comparison among optimal solutions (pareto fronts) obtained for strategiesA1, A2, and A3 has been shown in Figure 5.Figure 5
Comparison of pareto-optimal fronts for all strategies of group A.Table 4
Optimized variables for strategyA1.
Case 1Case 2Case 3Case 4Case 5Case 6Case 7PG1 (MW)43.719823.700933.988015.011112.659729.44321.7909PG2 (MW)58.038527.920028.569044.573950.1839543.90126.8511PG3 (MW)17.518330.300017.994021.609122.4650125.13430.8579PG4 (MW)23.281833.990029.634027.275827.3077427.18427.8138PG5 (MW)17.035130.000027.839029.931024.4872525.31529.7888PG6 (MW)32.096445.380054.152253.694554.916040.46154.9710Cost ($/hr)574.835618.610634.705608.319606.426588.468620.637Emission (tons/hr)392.922282.537338.603314.062332.708306.550289.657Loading (MVA)34.448733.001532.258532.41032.394632.46232.2720Table 5
Optimized variables for strategyA2.
Case 1Case 2Case 3Case 4Case 5Case 6Case 7PG1 (MW)43.552621.627013.831923.497435.032234.273822.0440PG2 (MW)57.963628.300032.750738.476347.201037.652127.5273PG3 (MW)17.562729.155032.560326.721112.767325.002730.8975PG4 (MW)23.168229.476028.210325.430723.839126.021030.4195PG5 (MW)17.134027.530029.184224.575320.814621.660925.9777PG6 (MW)31.856143.743054.99952.783652.104446.755154.5817DR1 (MW)0.014002.714000.038710.044140.097600.064070.05061DR2 (MW)0.129802.650000.149730.149490.149180.146300.14894DR3 (MW)0.055901.65600.041510.046810.047630.044310.05490DR4(MW)0.045000.652100.044590.044180.038400.040990.04325DR5 (MW)0.047500.847500.046220.046350.046250.042080.04518DR6 (MW)0.087501.587500.087330.086860.083770.083940.07020DR7 (MW)0.052900.953000.052920.052830.052840.051670.05070Cost ($/hr)573.992590.449623.454599.692584.2237589.044617.512Emission (tons/hr)390.979249.080296.132298.334341.9832305.433288.365Loading (MVA)34.345032.828232.176732.461132.650032.976032.2386Table 6
Optimized variables for strategyA3.
Case 1Case 2Case 3Case 4Case 5Case 6Case 7PG1 (MW)41.953722.35617.8827126.776131.812534.617029.4501PG2 (MW)56.066528.265455.809340.843643.505041.630632.5137PG3 (MW)15.993831.04100.1773120.720614.927820.457826.3910PG4 (MW)22.764929.999931.020925.399824.077824.170323.7110PG5 (MW)15.676829.369629.998620.039617.702122.685820.8522PG6 (MW)28.734341.819454.999945.355449.369637.776548.7966DR1 (MW)0.053700.113980.029610.095940.110800.079600.10150DR2 (MW)0.129900.149890.150000.149810.149700.106000.02090DR3 (MW)0.035900.055910.036970.044260.049600.055800.01480DR4 (MW)0.014900.044980.032110.042870.044600.025500.02140DR5 (MW)0.047500.047440.047260.046860.045000.031700.02770DR6 (MW)0.087400.087470.079980.079830.087200.070600.01270DR7 (MW)0.030700.052970.052950.052290.052500.048600.02230PRIPP (MW)10.000010.00009.817809.970909.992109.842409.79230Cost ($/hr)573.515615.778623.207587.785584.056582.246596.118Emission (tons/hr)358.259246.069358.668271.466298.368286.632269.167Loading (MVA)28.123527.160426.621027.123027.758228.435327.8879Table7 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.Table 7
Optimized power flow for case 1 strategyA1 of group A.
Line no.Power flow (MVA)Line no.Power flow (MVA)Line no.Power flow (MVA)Line no.Power flow (MVA)121.041111.11213.59315.16220.55126.38228.06323.12319.24130.00234.763311.46418.161411.27245.63344.22514.331519.23257.973515.81621.8316∗20.86267.753625.06718.44175.102712.44376.32814.26186.83289.88387.18912.40197.2729∗30.22393.7110∗34.06201.603011.344010.384114.98Optimized power flows (only for highly congested lines) obtained by employing MOSSA, for all strategies of group A have been shown in Table8. 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.Table 8
Optimized power flow for all strategies of group A.
StrategyLine no.Optimum power flows in MVACase 1Case 2Case 3Case 4Case 5Case 6Case 7A11034.06133.05732.35932.45132.75533.33932.4041620.86431.74525.20724.08618.09024.79432.1002930.22434.10934.58632.76330.81832.28533.682A21034.05832.99332.27732.50532.54033.56732.3531621.26829.61126.93523.49915.69726.31028.3852930.73934.76131.50832.71230.77932.11433.823A31028.18927.16526.72926.97926.98028.43527.8881620.45826.58430.3922.82819.34323.51628.5542929.81033.05031.36231.70030.69131.21931.653Since 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 Figure6.Figure 6
Percentage Improvement in TRM over critical lines for group A.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 strategyA3 has been found better as compared to strategy A2 and A1.(5)
For strategyA3 of congestion management,(1)
This is very clear from Tables4–6 and Figure 5 that maximum minimization of all objective functions (individual and simultaneous) has been achieved.(2)
It is very clear from Table8 that maximum optimized power flows have been found.(3)
Figure6 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:StrategyB1: only GR.StrategyB2: GR with DR.StrategyB3: 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 strategiesB1, 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 Table9. On this basis 5 specific points have been identified.Table 9
Weighting coefficients of objective functions for group B.
Weighting coefficientsCase 1Case 2Case 3Case 4Case 5Cost10.750.50.250Emission00.250.50.751Figures7–9 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.Figure 7
Pareto-optimal front for strategyB1.Figure 8
Pareto-optimal front for strategyB2.Figure 9
Pareto-optimal front for strategyB3.Figure 10
Comparison of pareto-optimal fronts obtained by MOSSA, MMSSO, and MARSO for strategyB3.For CM the results (optimal control variables and objective function values) obtained by employing MOSSA have been shown in Tables10–12. 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 $/hr (Case 1) and 262.312 tons/hr (Case 5), respectively.Optimized power flows over highly congested lines for all strategies of group B have been shown in Table13. The optimized power flow over line no.10 for strategy B1 is found to be 31.850 MVA (Case 3), for strategy B2 is 31.783 MVA (Case 1), and for strategy B3 is 28.065MVA (Case 3).Table 10
Optimized variables for strategyB1.
Case 1Case 2Case 3Case 4Case 5PG1 (MW)40.624836.839233.712130.8682326.9647PG2 (MW)52.102548.265742.621138.161131.2577PG3 (MW)15.508118.097221.777126.577629.8260PG4 (MW)22.652523.452224.010022.228522.9801PG5 (MW)17.205918.617922.160124.554929.9999PG6 (MW)44.064046.801647.691149.603651.0395Cost ($/hr)578.083579.455583.188594.077600.318Emission (tons/hr)365.149339.162316.825297.529285.162Table 11
Optimized variables for strategyB2.
Case 1Case 2Case 3Case 4Case 5PG1 (MW)40.046235.666832.582730.456926.5898PG2 (MW)53.383547.155341.091235.946131.2685PG3 (MW)15.198518.681222.851828.893829.8184PG4 (MW)22.279423.270923.452622.107223.1169PG5 (MW)15.098519.153522.959124.917729.8332PG6 (MW)45.026447.691148.597049.190749.1780DR1 (MW)0.120000.090800.090640.089740.29100DR2 (MW)0.220000.119880.119880.119880.62000DR3 (MW)0.044700.044440.044410.043100.44800DR4 (MW)0.036000.035700.035560.035600.43660DR5 (MW)0.038000.037680.037700.037890.03800DR6 (MW)0.069900.069710.069610.069570.37000DR7 (MW)0.042400.042090.042080.042250.04240Cost ($/hr)576.083578.182582.98592.077598.318Emission (tons/hr)363.149331.053308.922295.529283.162Table 12
Optimized variables for strategyB3.
Case 1Case 2Case 3Case 4Case 5PG1 (MW)41.438437.688834.554228.856425.3077PG2 (MW)55.272750.661343.862536.183134.1679PG3 (MW)16.427919.046020.774725.161129.4997PG4 (MW)22.758823.709023.759524.060323.8601PG5 (MW)16.399718.152320.273125.103925.2513PG6 (MW)29.334832.218838.254342.140743.3897DR1 (MW)0.068340.066950.064990.063780.06165DR2 (MW)0.059580.055030.052470.034280.03577DR3 (MW)0.023620.031930.027060.022560.02064DR4 (MW)0.025030.024410.024950.022780.02669DR5 (MW)0.019750.016620.021180.015090.01534DR6 (MW)0.051320.048620.037640.034770.03407DR7 (MW)0.012600.031530.022530.021170.02368PWP (MW)9.880009.980009.890009.890009.89000Cost ($/hr)574.582576.071580.749592.464599.243Emission (tons/hr)353.437322.327293.331267.017262.312Table 13
Optimized MVA power flows over critical lines for all strategies of group B.
StrategyLine no.Case 1Case 2Case 3Case 4Case 5B11031.85031.84031.78031.73031.7101619.54021.59024.73028.90031.7202930.72031.28031.6831.7731.220B21031.78331.12231.00331.76231.6781619.92420.91824.07627.89228.5532930.10831.25931.93131.98031.988B31028.06528.86228.45728.22828.0831619.79722.78824.14727.97330.7752929.77430.32531.64631.89131.989The 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 Figure11 for all strategies of group B.Figure 11
Percentage Improvement in TRM over critical lines for Group B.Observations.(1)
Congestion control strategiesB1, 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)
Figure10 indicates better performance of MOSSA as compared to MMSSO and MARSO both for congestion control strategy B3.(3)
It can be seen from Table13 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 Figure11 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.Table 14
Result comparison between proposed approach and reported methods [23, 38].
S. No.`Line thermal ratingMethodBest solutionPreferred solutionOptimal flowDRDGCostEmissionLine loadingCostEmission(MVA)($/hr)(tons/hr)(MVA)($/hr)(tons/hr)(MVA)(MW)(MW)135MOPSO (scenario 1) [23]574.870282.590NA585.32311.04034.22NANAMOSSA (strategyA1)574.835282.53732.258588.47306.55034.061NANA235MOPSO (scenario 2) [23]574.020249.250NA623.57277.12034.150.44NAMOSSA (strategyA2)573.992249.08032.18589.04305.43034.0580.4326NAMOSSA (strategyA3)573.515246.06926.62582.25286.63228.1890.4010332BF-NM [29]648.860NANANANANANANAMOPSO (scenario 3) [23]579.180285.440NA588.33307.80031.99NANAMOSSA (strategyB1)578.083285.162NA583.188316.82531.85NANA432MOPSO (scenario 4) [23]577.900250.180NA624.80278.27031.960.6NAMOSSA (scenarioB2)576.083283.162NA580.98308.92231.7830.571NAMOSSA (strategyB3)574.582262.312NA580.749293.33128.0650.2609.88


## 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:StrategyA1: Only GR.StrategyA2: GR with DR.StrategyA3: 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 strategiesA1, 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 Table3 and considered as different case studies.Table 3
Weighting coefficients of objective functions for Group A.
Weighting coefficientsCase 1Case 2Case 3Case 4Case 5Case 6Case 7Cost1000.3330.50.50Emission0100.33300.50.5Line loading0010.3330.500.5Optimal solutions (optimal fronts) obtained by implementing MOSSA have been shown in Figure2, Figure 3, and Figure 4 for strategies A1, A2, and A3, respectively. Seven specific cases have also been shown in these Figures.Figure 2
Pareto-optimal front for strategyA1.Figure 3
Pareto-optimal front for strategyA2.Figure 4
Pareto-optimal front for strategyA3.The optimum values of three conflicting objective functions and control variables obtained by employing MOSSA for CM have been shown in Tables4–6.It can be seen from Table4 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 $/hr (Case 1), 246.069 tons/hr (Case 2), and 26.621 MVA (Case 3), respectively.The comparison among optimal solutions (pareto fronts) obtained for strategiesA1, A2, and A3 has been shown in Figure 5.Figure 5
Comparison of pareto-optimal fronts for all strategies of group A.Table 4
Optimized variables for strategyA1.
Case 1Case 2Case 3Case 4Case 5Case 6Case 7PG1 (MW)43.719823.700933.988015.011112.659729.44321.7909PG2 (MW)58.038527.920028.569044.573950.1839543.90126.8511PG3 (MW)17.518330.300017.994021.609122.4650125.13430.8579PG4 (MW)23.281833.990029.634027.275827.3077427.18427.8138PG5 (MW)17.035130.000027.839029.931024.4872525.31529.7888PG6 (MW)32.096445.380054.152253.694554.916040.46154.9710Cost ($/hr)574.835618.610634.705608.319606.426588.468620.637Emission (tons/hr)392.922282.537338.603314.062332.708306.550289.657Loading (MVA)34.448733.001532.258532.41032.394632.46232.2720Table 5
Optimized variables for strategyA2.
Case 1Case 2Case 3Case 4Case 5Case 6Case 7PG1 (MW)43.552621.627013.831923.497435.032234.273822.0440PG2 (MW)57.963628.300032.750738.476347.201037.652127.5273PG3 (MW)17.562729.155032.560326.721112.767325.002730.8975PG4 (MW)23.168229.476028.210325.430723.839126.021030.4195PG5 (MW)17.134027.530029.184224.575320.814621.660925.9777PG6 (MW)31.856143.743054.99952.783652.104446.755154.5817DR1 (MW)0.014002.714000.038710.044140.097600.064070.05061DR2 (MW)0.129802.650000.149730.149490.149180.146300.14894DR3 (MW)0.055901.65600.041510.046810.047630.044310.05490DR4(MW)0.045000.652100.044590.044180.038400.040990.04325DR5 (MW)0.047500.847500.046220.046350.046250.042080.04518DR6 (MW)0.087501.587500.087330.086860.083770.083940.07020DR7 (MW)0.052900.953000.052920.052830.052840.051670.05070Cost ($/hr)573.992590.449623.454599.692584.2237589.044617.512Emission (tons/hr)390.979249.080296.132298.334341.9832305.433288.365Loading (MVA)34.345032.828232.176732.461132.650032.976032.2386Table 6
Optimized variables for strategyA3.
Case 1Case 2Case 3Case 4Case 5Case 6Case 7PG1 (MW)41.953722.35617.8827126.776131.812534.617029.4501PG2 (MW)56.066528.265455.809340.843643.505041.630632.5137PG3 (MW)15.993831.04100.1773120.720614.927820.457826.3910PG4 (MW)22.764929.999931.020925.399824.077824.170323.7110PG5 (MW)15.676829.369629.998620.039617.702122.685820.8522PG6 (MW)28.734341.819454.999945.355449.369637.776548.7966DR1 (MW)0.053700.113980.029610.095940.110800.079600.10150DR2 (MW)0.129900.149890.150000.149810.149700.106000.02090DR3 (MW)0.035900.055910.036970.044260.049600.055800.01480DR4 (MW)0.014900.044980.032110.042870.044600.025500.02140DR5 (MW)0.047500.047440.047260.046860.045000.031700.02770DR6 (MW)0.087400.087470.079980.079830.087200.070600.01270DR7 (MW)0.030700.052970.052950.052290.052500.048600.02230PRIPP (MW)10.000010.00009.817809.970909.992109.842409.79230Cost ($/hr)573.515615.778623.207587.785584.056582.246596.118Emission (tons/hr)358.259246.069358.668271.466298.368286.632269.167Loading (MVA)28.123527.160426.621027.123027.758228.435327.8879Table7 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.Table 7
Optimized power flow for case 1 strategyA1 of group A.
Line no.Power flow (MVA)Line no.Power flow (MVA)Line no.Power flow (MVA)Line no.Power flow (MVA)121.041111.11213.59315.16220.55126.38228.06323.12319.24130.00234.763311.46418.161411.27245.63344.22514.331519.23257.973515.81621.8316∗20.86267.753625.06718.44175.102712.44376.32814.26186.83289.88387.18912.40197.2729∗30.22393.7110∗34.06201.603011.344010.384114.98Optimized power flows (only for highly congested lines) obtained by employing MOSSA, for all strategies of group A have been shown in Table8. 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.Table 8
Optimized power flow for all strategies of group A.
StrategyLine no.Optimum power flows in MVACase 1Case 2Case 3Case 4Case 5Case 6Case 7A11034.06133.05732.35932.45132.75533.33932.4041620.86431.74525.20724.08618.09024.79432.1002930.22434.10934.58632.76330.81832.28533.682A21034.05832.99332.27732.50532.54033.56732.3531621.26829.61126.93523.49915.69726.31028.3852930.73934.76131.50832.71230.77932.11433.823A31028.18927.16526.72926.97926.98028.43527.8881620.45826.58430.3922.82819.34323.51628.5542929.81033.05031.36231.70030.69131.21931.653Since 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 Figure6.Figure 6
Percentage Improvement in TRM over critical lines for group A.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 strategyA3 has been found better as compared to strategy A2 and A1.(5)
For strategyA3 of congestion management,(1)
This is very clear from Tables4–6 and Figure 5 that maximum minimization of all objective functions (individual and simultaneous) has been achieved.(2)
It is very clear from Table8 that maximum optimized power flows have been found.(3)
Figure6 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:StrategyB1: only GR.StrategyB2: GR with DR.StrategyB3: 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 strategiesB1, 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 Table9. On this basis 5 specific points have been identified.Table 9
Weighting coefficients of objective functions for group B.
Weighting coefficientsCase 1Case 2Case 3Case 4Case 5Cost10.750.50.250Emission00.250.50.751Figures7–9 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.Figure 7
Pareto-optimal front for strategyB1.Figure 8
Pareto-optimal front for strategyB2.Figure 9
Pareto-optimal front for strategyB3.Figure 10
Comparison of pareto-optimal fronts obtained by MOSSA, MMSSO, and MARSO for strategyB3.For CM the results (optimal control variables and objective function values) obtained by employing MOSSA have been shown in Tables10–12. 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 $/hr (Case 1) and 262.312 tons/hr (Case 5), respectively.Optimized power flows over highly congested lines for all strategies of group B have been shown in Table13. The optimized power flow over line no.10 for strategy B1 is found to be 31.850 MVA (Case 3), for strategy B2 is 31.783 MVA (Case 1), and for strategy B3 is 28.065MVA (Case 3).Table 10
Optimized variables for strategyB1.
Case 1Case 2Case 3Case 4Case 5PG1 (MW)40.624836.839233.712130.8682326.9647PG2 (MW)52.102548.265742.621138.161131.2577PG3 (MW)15.508118.097221.777126.577629.8260PG4 (MW)22.652523.452224.010022.228522.9801PG5 (MW)17.205918.617922.160124.554929.9999PG6 (MW)44.064046.801647.691149.603651.0395Cost ($/hr)578.083579.455583.188594.077600.318Emission (tons/hr)365.149339.162316.825297.529285.162Table 11
Optimized variables for strategyB2.
Case 1Case 2Case 3Case 4Case 5PG1 (MW)40.046235.666832.582730.456926.5898PG2 (MW)53.383547.155341.091235.946131.2685PG3 (MW)15.198518.681222.851828.893829.8184PG4 (MW)22.279423.270923.452622.107223.1169PG5 (MW)15.098519.153522.959124.917729.8332PG6 (MW)45.026447.691148.597049.190749.1780DR1 (MW)0.120000.090800.090640.089740.29100DR2 (MW)0.220000.119880.119880.119880.62000DR3 (MW)0.044700.044440.044410.043100.44800DR4 (MW)0.036000.035700.035560.035600.43660DR5 (MW)0.038000.037680.037700.037890.03800DR6 (MW)0.069900.069710.069610.069570.37000DR7 (MW)0.042400.042090.042080.042250.04240Cost ($/hr)576.083578.182582.98592.077598.318Emission (tons/hr)363.149331.053308.922295.529283.162Table 12
Optimized variables for strategyB3.
Case 1Case 2Case 3Case 4Case 5PG1 (MW)41.438437.688834.554228.856425.3077PG2 (MW)55.272750.661343.862536.183134.1679PG3 (MW)16.427919.046020.774725.161129.4997PG4 (MW)22.758823.709023.759524.060323.8601PG5 (MW)16.399718.152320.273125.103925.2513PG6 (MW)29.334832.218838.254342.140743.3897DR1 (MW)0.068340.066950.064990.063780.06165DR2 (MW)0.059580.055030.052470.034280.03577DR3 (MW)0.023620.031930.027060.022560.02064DR4 (MW)0.025030.024410.024950.022780.02669DR5 (MW)0.019750.016620.021180.015090.01534DR6 (MW)0.051320.048620.037640.034770.03407DR7 (MW)0.012600.031530.022530.021170.02368PWP (MW)9.880009.980009.890009.890009.89000Cost ($/hr)574.582576.071580.749592.464599.243Emission (tons/hr)353.437322.327293.331267.017262.312Table 13
Optimized MVA power flows over critical lines for all strategies of group B.
StrategyLine no.Case 1Case 2Case 3Case 4Case 5B11031.85031.84031.78031.73031.7101619.54021.59024.73028.90031.7202930.72031.28031.6831.7731.220B21031.78331.12231.00331.76231.6781619.92420.91824.07627.89228.5532930.10831.25931.93131.98031.988B31028.06528.86228.45728.22828.0831619.79722.78824.14727.97330.7752929.77430.32531.64631.89131.989The 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 Figure11 for all strategies of group B.Figure 11
Percentage Improvement in TRM over critical lines for Group B.Observations.(1)
Congestion control strategiesB1, 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)
Figure10 indicates better performance of MOSSA as compared to MMSSO and MARSO both for congestion control strategy B3.(3)
It can be seen from Table13 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 Figure11 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.Table 14
Result comparison between proposed approach and reported methods [23, 38].
S. No.`Line thermal ratingMethodBest solutionPreferred solutionOptimal flowDRDGCostEmissionLine loadingCostEmission(MVA)($/hr)(tons/hr)(MVA)($/hr)(tons/hr)(MVA)(MW)(MW)135MOPSO (scenario 1) [23]574.870282.590NA585.32311.04034.22NANAMOSSA (strategyA1)574.835282.53732.258588.47306.55034.061NANA235MOPSO (scenario 2) [23]574.020249.250NA623.57277.12034.150.44NAMOSSA (strategyA2)573.992249.08032.18589.04305.43034.0580.4326NAMOSSA (strategyA3)573.515246.06926.62582.25286.63228.1890.4010332BF-NM [29]648.860NANANANANANANAMOPSO (scenario 3) [23]579.180285.440NA588.33307.80031.99NANAMOSSA (strategyB1)578.083285.162NA583.188316.82531.85NANA432MOPSO (scenario 4) [23]577.900250.180NA624.80278.27031.960.6NAMOSSA (scenarioB2)576.083283.162NA580.98308.92231.7830.571NAMOSSA (strategyB3)574.582262.312NA580.749293.33128.0650.2609.88


## 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.Table 15
Weighting coefficients of objective functions for IEEE 118-bus system.
Objective functionCase 1Case 2Case 3Cost10.50Emission00.51To 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 Table16.Table 16
Power flows of case 1 for IEEE 118-bus system.
Line noFrom busTo busBase caseThermal line ratingWithout CMAfter CM(MVA PF)55688.05132.07140.87136.9041233291.77137.65146.82129.4662454636.7155.0758.7455.8992616228.8343.2446.1340.69121777845.9168.8773.4663.00The Pareto-optimal front obtained by MOSSA has been drawn in Figure12 and three specific cases (Case 1, Case 2, and Case 3) have been marked in Figure 12.Figure 12
Pareto-optimal fronts obtained for IEEE 118-bus system.The optimized apparent power flows over critical lines (line no. 5, 41, 62, 92, and 121) have been shown in Table16. 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.Table17 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 $/hr. Therefore, the proposed approach has provided congestion management with lower operation cost and DR cost.Table 17
Optimized parameters for IEEE 118-bus system.
DRRIPPDR costRIPP costFuel costCostEmission(MW)(MW)($/hr)($/hr)($/hr)($/hr)(tons/hr)Case 15.934526.8940.82936100.837570826.33709684463Case 26.884526.0247.3653697.57581893.06820384253Case 38.654325.44059.5418495.490750.06908994220


## 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 Table18 and Table 19.Table 18
Nomenclature.
ai, bi and ciCost coefficients ofith thermal generating unitαi, βi and γiEmission coefficients ofith thermal generating unitCGGeneration cost for thermal generators ($/hr)PGimin and PGimaxMinimum and maximum active power limit ofith generating unit (MW)QGimin and QGimaxMinimum and maximum reactive power limit ofith generating unit (MVAR)PGiActive power generated byith generating unit (MWQGiReactive power generated byith generating unit (MVAR)PDiActive power demand atith load bus (MW)QDiReactive power demand atith load bus (MVAR)VGimin and VGimaxMinimum and maximum voltage limits ofith generating unit (volt)NGTotal number of generatorsNBRTotal number of transmission linesNBTotal number of total busesNLBTotal number of load busesCRIPPCost of power generated by wind power plant as renewable independent power producer ($/hr)PWPActive power generated by wind plant (MW)PWPmin and PWPmaxMinimum and maximum power generated by wind plant (MW)CDRTotal demand response cost ($/hr)d0kInitial demand ofkth receptive customer (MW)dkReduced demand ofkth receptive customer (MW)µkmin and µkmaxMinimum and maximum incentive paid tokth receptive customerEP0 and EPDRElectricity prices in$/hr before and after demand response programDRkminandDRkmaxMinimum and maximum demand reduction ofkth receptive customerϵSelf-elasticity of customer demandINCIncentive rate at which incentive paid to the receptive costumers ($/MWhr)PENPenalty rate at which penalty is imposed on defaulter customers ($/hr)LRkContracted load reduction ofkth receptive customer (MW)µkIncentive in$/hr paid to the kth responsive customerℒkPenalty paid bykth defaulter receptive customer ($/hr)Vimin and VimaxMinimum and maximum voltage limit atith load bus (volt)ΔdkChange in demand ofkth receptive customer before and after demand response program (MW)Smaxl and SlMaximum line loading and power flow oflth transmission line (MVA)NDRTotal number of receptive customers take part in demand responseFimin and FimaxMinimum and maximum value ofith objective functionTable 19
Generation and emission coefficients for generators IEEE 30 bus-system.
Generatora ($/hr)b ($/MWhr)c ($/MWhr2)(ton/hr)(ton/MWhr)(ton/MWhr2)G1020.020.04091−0.055540.0649G201.750.01750.02543−0.060470.05638G13030.0250.06131−0.055550.05151G22010.06250.04258−0.050940.04586G23030.0250.04258−0.050940.04586G2703.250.008340.05326−0.03550.0338



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*Source: 8256908-2022-12-07.xml*