The optimal planning (sizing and siting) of the distributed generations (DGs) by using butterflyPSO/BFPSO technique to investigate the impacts of load models is presented in this work. The validity of the evaluated results is confirmed by comparing with wellknown Genetic Algorithm (GA) and standard or conventional particle swarm optimization (PSO). To exhibit its compatibility in terms of load management, an impact of different load models on the size and location of DG has also been presented in this work. The fitness evolution function explored is the multiobjective function (FMO), which is based on the three significant indexes such as active power loss, reactive power loss, and voltage deviation index. The optimal solution is obtained by minimizing the multiobjective fitness function using BFPSO, GA, and PSO technique. The comparison of the different optimization techniques is given for the different types of load models such as constant, industrial, residential, and commercial load models. The results clearly show that the BFPSO technique presents the superior solution in terms of compatibility as well as computation time and efforts both. The algorithm has been carried out with 15bus radial and 30bus mesh system.
The practical system comprises various kinds of loads. Many researchers have explored efficient siting and sizing methods for distribution system. However, most of them have assumed constant load models. Constant load shows insensitivity to variations of frequency as well as voltage profile of the system. This depicts the ideal situation of the system. Thus all those methods fail to present the practically sound solution. It is observed that actual practical system comprised industrial, residential, and commercial loads. The Genetic Algorithm (GA) is genetic based evolutionary search algorithm. The basic concepts and applications of the Genetic Algorithms (GAs) including the various fields of optimizing the complex problems in a practical way for different functions have been analyzed in [
This paper presents the optimal sizing and siting of distributed generation (DG) with the different type of load models. Then DG is considered as an active power source at load bus. The optimal site allocation and sizing of DG with the different objective indices such as active power loss index (PLI), reactive power loss index (QLI), and voltage deviation index (VDI) based multiobjective function have been evaluated as fitness function. The presented results exhibit the impacts of the different load models on the overall performance of the distributed system. The evaluated results show that the BFPSO leads GA and PSO in terms of computational time and efforts. In spite of that, the better performance characteristics can be obtained by using BFPSO.
To find the optimal sizing and siting of the distributed generation (DG) in the radial system with the various objectives is achieved by the accompanying multiobjective function (FMO) as
The active power loss index (PLI) is
The load models for the particular loads can be mathematically expressed as
The exponent values for load models.
Load type 



Constant  0  0 
Industrial load  0.18  6 
Residential load  0.92  4.04 
Commercial load  1.51  3.4 
The butterflyPSO (BFPSO) algorithm is essentially based on the nectar probability and the sensitivity of the butterfly swarm [
Then the equations of BFPSO technique given below for the velocity and position updating are
Read and input the systems data (bus data, line data, generation data, etc.).
Run and execute the NRpower flow results for noDG case including load models.
Initialize all the parameters of GA (population, selection rate, mutation rate, iterations, etc.), PSO (
where
Update the variables within the algorithm using the different operators (selection, crossover, and mutation) for GA, equations (velocity and positions/locations) for PSO, and equations (velocity, locations, inertia weight, sensitivity, and probability) for BFPSO.
After that, assign the DG size and location in the system excluding the slack and PV buses.
After that, call the NRpower flow and execute the results with DG condition including load models.
Calculate the all indices value for the multiobjective function with each technique.
Evaluate the fitness value for each technique of multiobjective function.
Compare the variables from previous variables for each technique.
Check for termination criteria; if otherwise, repeat algorithm from step
Repeat this procedure up to maximum number of iterations.
Record and save all the output data of the system.
This proposed algorithm has been tested on 15bus radial system [
The data of 15bus radial system is given in [
The convergence of multiobjective function (FMO) with iterations of 15bus radial system for (a) constant load, (b) industrial load, (c) residential load, and (d) commercial load.
Active power loss of 15bus radial system for (a) constant load, (b) industrial load, (c) residential load, and (d) commercial load.
The reactive power loss of 15bus radial system for (a) constant load, (b) industrial load, (c) residential load, and (d) commercial load.
The voltage profile of 15bus radial system for (a) constant load, (b) industrial load, (c) residential load, and (d) commercial load.
The impacts of load models on the active and reactive power losses of 15bus radial system are shown in Figures
The impact of different load models on the voltage profile using BFPSO is shown in Figure
Objective indices of 15bus radial system with different load models using GA, PSO, and BFPSO.
Load type  PLI  QLI  VDI  Technique 

Constant load  0.6123  0.5931  0.0324  BFPSO 
0.6133  0.594  0.0338  PSO  
0.6188  0.6001  0.0302  GA  


Industrial load  0.3782  0.3404  0.0187  BFPSO 
0.402  0.3662  0.02  PSO  
0.5006  0.4483  0.022  GA  


Residential load  0.5453  0.5093  0.0195  BFPSO 
0.5637  0.5303  0.0212  PSO  
0.644  0.6003  0.0229  GA  


Commercial load  0.6603  0.6285  0.0198  BFPSO 
0.6715  0.6379  0.0188  PSO  
0.7387  0.7034  0.0227  GA 
Multiobjective function and DG size at optimal bus location with different load models for 15bus radial system using GA, PSO, and BFPSO.
Load Type  Fitness (FMO)  PDG  Bus  Technique 

Constant load  0.4335  1.0355  3  BFPSO 
0.4346  0.9703  3  PSO  
0.4375  1.1596  3  GA  


Industrial load  0.2609  0.8549  3  BFPSO 
0.2785  0.7232  4  PSO  
0.3439  0.5862  15  GA  


Residential load  0.3786  0.672  3  BFPSO 
0.3926  0.5697  4  PSO  
0.4467  0.4502  15  GA  


Commercial load  0.4602  0.5505  3  BFPSO 
0.4673  0.644  3  PSO  
0.5151  0.363  15  GA 
The all data information about the 30bus mesh system data have given in [
Objective indices of 30bus mesh system with different load models using GA, PSO, and BFPSO.
Load type  PLI  QLI  VDI  Technique 

Constant load  0.3073  −0.2643  −0.0048  BFPSO 
0.3071  −0.2634  −0.0046  PSO  
0.3185  −0.2528  −0.006  GA  


Industrial load  0.3111  −0.2296  0.0004  BFPSO 
0.3155  −0.2266  −0.0002  PSO  
0.3197  −0.2215  −0.0004  GA  


Residential load  0.3078  −0.2032  −0.001  BFPSO 
0.3085  −0.2034  −0.0012  PSO  
0.317  −0.1799  0.0001  GA  


Commercial load  0.3059  −0.1791  −0.0016  BFPSO 
0.3068  −0.179  −0.0018  PSO  
0.3061  −0.1765  −0.0012  GA 
Multiobjective function and DG size at optimal bus location with different load models for 30bus mesh system using GA, PSO, and BFPSO.
Load type  Fitness function (FMO)  PDG  Bus  Technique 

Constant load  0.0708  202.9922  6  BFPSO 
0.0710  199.2922  6  PSO  
0.0784  226.1614  6  GA  


Industrial load  0.0827  203.2873  7  BFPSO 
0.0853  216.8522  7  PSO  
0.0884  223.5097  6  GA  


Residential load  0.0874  206.3894  7  BFPSO 
0.0876  210.8828  7  PSO  
0.0977  179.2814  7  GA  


Commercial load  0.0924  210.0633  6  BFPSO 
0.0925  215.0907  6  PSO  
0.0932  201.9343  6  GA 
The comparative analysis of 30bus radial system.
Cases  Parameter  

Active power loss (MW)  Active power loss reduction (%)  Reactive power loss 
Reactive power loss reduction (%)  
WithoutDG (base case)  17.557  —  67.69  — 
WithDG  
Existing (7.5% DG penetration)  7.0973 [ 
59.57%  NA  NA 
Proposed (DGBFPSO)  5.396  69.27%  26.32  61.11% 
The convergence of multiobjective function (FMO) with iterations of 30bus mesh system for (a) constant load, (b) industrial load, (c) residential load, and (d) commercial load.
Active power loss of 30bus mesh system for (a) constant load, (b) industrial load, (c) residential load, and (d) commercial load.
The reactive power loss of 30bus mesh system for (a) constant load, (b) industrial load, (c) residential load, and (d) commercial load.
The voltage profile of 30bus mesh system for (a) constant load, (b) industrial load, (c) residential load, and (d) commercial load.
The result for convergence of multiobjective function (FMO) with iterations for the constant, industrial, residential and commercial loads are shown in Figure
The voltage profiles of the system are dissimilar for the particular load models of the system. The change in voltage profiles of the system occurs due to variations in the size and location of DG. The impact of different load models on the voltage profile of 30bus mesh system using BFPSO is shown in Figure
The comparative analysis of the proposed and the existing methodology is given in Table
The proposed methodology is implemented on the 15bus radial and 30bus mesh system and the comparative analysis for 30bus mesh system with proposed and the existing methodology is given in Section
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors wish to acknowledge the MANIT, Bhopal, and MHRD for financial support. Furthermore, the authors want to extend acknowledgment to those who have supported them directly or indirectly.