Optimal DG Placement in Power Systems Using a Modified Flower Pollination Algorithm

Abstract

There is a huge requirement for power systems to reduce power losses. Adding distributed generators (DGs) is the most common approach to achieving lower power losses. However, several challenges arise, such as determining the ideal size as well as location of the utilized distributed generators. Most of the existing methods do not consider the variety of load types, the variety and size of the utilized DGs besides reducing the convergence time and enhancing the optimization results. The paper performed an optimization algorithm that integrated a golden search-based flower pollination algorithm and fitness-distance balance (FDB) to find out the optimal size as well as the location of the distributed generators. It was then compared with different optimization methods to determine the best optimization technique, and it was determined to be the best technique. In addition, different types of DGs are considered, including solar energy, wind energy, and biogas, along with optimizing the size of the utilized DGs to reduce the system cost. Testing with different types of bus systems, and different types of DGs in a radial distribution system was done to reveal that the modified flower pollination with golden section search was superior in comparison to others with regards to convergence and power loss reduction.

1. Introduction

Electricity demand has been increasing steeply due to the increase in population and industrialization. Bloomberg New Energy Finance’s (BNEF) recent reports showed a significant increase in the electricity demand to reach up to 38.7 billion Mega-Watt hours (MWh) from 25 billion in 2017 [1]. To meet the electricity requirements, it should be working on a twofold roadmap in which there is an increase in electrical power generation and a reduction in power losses as well. The first direction includes developing new central power plants and extending power grids [2,3]. However, this direction requires a huge operational cost as well as a high investment cost [4]. In addition, fossil fuel-based generation increases greenhouse gas (GHG) emissions. Another solution to meet the increased demand for electricity is integrating the DGs within the power systems [5]. The DG has many advantages, such as small-scale generation and cost-effectiveness. Photovoltaic (PV), wind turbines (WT), geothermal, hydrogen, biogas, ethanol, biodiesel, and biomass are clean energy sources DGs and are considered eco-friendly sources [6]. In radial distribution networks, the DG units must be appropriately linked since this enhances the voltage profile and lowers power loss. However, improper allocation of DG may provide serious results, such as power loss being high as well as low system stability and voltage rise. This leads to the need for optimal allocation of DG units, which should be determined to realize technical benefits, economic benefits, and environmental benefits in distribution network planning. There are many research contributions for optimizing the allocation of DGs in radial distribution systems, besides many analytical methods introduced that help to identify an ideal location for the DGs within the power systems [7].

Analytical methods and metaheuristic methods are adopted by researchers for the purpose of optimal DG placement. In [8], a new voltage stability index (VSI) was used to determine the ideal DG position, and the optimal DG size was determined by minimizing active losses. The impact of increased loads on optimum DG placement was also studied. In [9], a strategy for effective DG deployment in distribution networks is described utilizing voltage stability algorithms. Modal analysis and continuous power flow formed the basis of the voltage stability approach. The aim function also included minimizing network losses and lowering the voltage stability limit. The power stability index (PSI), a metric for measuring voltage stability, was adopted as a standard for DG installation in [10].Aside from minimizing power outages, this criterion was used to determine the ideal size of the DG to be installed. The complexity of the load flow rises as the number of system characteristics grows, despite the fact that analytical approaches rely mostly on load repetition. However, the performance of analytical procedures may be improved by including sensitivities. However, by taking into account the reduction of actual power losses, metaheuristic algorithms are able to successfully estimate the ideal allocation [11]. Optimal allocation of DGs has been calculated more efficiently due to metaheuristic algorithms [12]. Some of them considered single objective functions, while others considered multiple objective functions, besides considering the equality and inequality constraints of components in power systems [13]. Metaheuristic algorithms have a powerful searching capability to compute optimal solutions and are applicable to dealing with large-scale networks [14]. There are numerous types of metaheuristic algorithms that are used in the radial distribution systems that help in solving the problem of optimal allocations in the distributed generator systems, such as the Sine Cosine Algorithm (SCA), Polar Bear Optimization (PBO), and Ant Lion Optimization (ALO), respectively [10,13,15,16]. Moreover, adaptive metaheuristic as well as hybrid methods are used to achieve optimal DG locations as well as sizing in the radial distribution system.

Among all meta-heuristic algorithms, the GA and PSO are the most prominent. The GA is a nature inspired algorithm, where Darwin’s theory that in evolution, the fittest are selected are used [17]. Similar to evolution, the GA has five phases namely initial population, fitness function, selection, crossover, and mutation. The PSO, on the other hand, is a bio-inspired algorithm based on the change in location of swarms [18]. It has the phases of initial population, evaluation of position, the updating of position, identification of best position, and the updating of velocity and position. The major advantage of PSO is that it has fewer parameters to tune. However, it does have the disadvantage of poor performance of local search. The FPA is a nature-inspired algorithm that has the phases of initial population, finding the best solution, probability switch generation, global pollination or local pollination of flowers, and finally determining the best flower [19]. Compared to PSO, the FPA has the advantage that the switchover criteria enable the algorithm to escape local minima while staying effective in local searches. The FPA is used in many applications, but it is mainly useful in transmission systems, power generation, and distribution systems [20]. In power generation, it is useful in solving the economic dispatch problem, scheduling of hydrothermal power stations, and renewable energy generation efficiency. In transmission systems, it is applied to transmission line planning, power system management, congestion management, and bus profile voltage improvement. In distributed systems, it is applied in distribution system planning, distribution system operation, distributed system operation, and reactive power control. We also explore the application of the FPA in optimal DG placement for reducing power losses. Figure 1 shows the different applications of the flower pollination algorithm.

By surveying this heuristic-based optimization, a considerable convergence time and power losses are still found. In addition, most of the research does not consider technical points, such as testing with different scale of loads’ power including residential, commercial, and industrial areas. In [21], two modes of DGs are investigated and applied on three different radial systems. In [22], power losses are minimized using an analytical method. In [23], the Combined Sensitivity Index is used to optimize DG placement. Though a lot of recent research works, such as the ones done in [21,22,23], do minimize power losses through optimizing DG placement, they do not consider multiple different types of DGs and optimization of DGs’ size for reducing the system cost. This paper considers different types of DGs, including PV, wind, and biogas, with optimization of the size of the utilized DGs. The optimization algorithm is implemented by using MATLAB and its performance parameters have been tested with different bus systems such as IEEE 33, and IEEE 69. Three different optimization algorithms are compared namely the particle swarm optimization algorithm [18], the genetic algorithm [17], and a modified flower pollination algorithm, which combines a golden search algorithm and utilizes the fitness-distance balance (FDB) method to control the selection of population from one generation to next generation. The inception of the idea of modifying the existing flower pollination by incorporating golden section search and the fitness-distance band was inspired from the work done in [24,25,26,27,28]. The comparison of various algorithms for solving multi-objectives was presented in [26].

This study presents a golden search-based technique for fault location that is based on the ideas of minimal fault reactance and the golden section. The aim of the approach is to solve the problem of fault location in distribution networks that contain distributed energy resources (DERs). The purpose of this research is to propose a method for locating faults that is predicated on the concepts of minimal fault reactance and the golden section. The purpose of the technique is to locate faults in distribution networks that are comprised of distributed energy resources, which has been a long-standing challenge (DERs). In [26], To achieve the goal of minimizing the phase current divergence across the phases, a phase switching method that is based on a hybrid version of the fuzzy flower pollination algorithm (FFPA) has been created. The flower pollination algorithm is utilized in order to maximize the value of fitness, and fuzzy logic is applied in order to structure the fitness function that incorporates many objectives. In [27], different search algorithms were used such as cuckoo search and the differential search algorithm in the flower pollination algorithm to optimize it. In [28], a fractional Choas FPA was proposed which differed in terms of initialization and switching probability factor.

The work done in [24,25,26,27,28] definitely gives the idea that golden section search is very useful for non-smooth univariate functions, but there are also reasons to consider the Fibonacci search because it is faster in small iterations [29]. However, a thorough analysis done in [30], shows that it is hard to apply Fibonacci search in problems that require stopping criteria while gold search is used to problems which require stopping criteria. Furthermore, the work done in [31] shows that the Fibonacci Search technique searches the whole current range, which means that very high and low currents are also searched. This caused torque ripple and high losses during the search procedure. For our case, Fibonacci Search could lead to the solutions getting stuck in local optimal point without finding the global optimal point.

The target of our paper is reducing the convergence time and improving the performance and efficiency. In this paper, a hybrid modified FPA algorithm is presented that uses FDB that is used to find the optimal global population, while golden search is used to evaluate the optimal local pollination. In this way, the problem of stucking in local optimal points is resolved and the FPA produces efficient solutions in less time, as will be shown in results section.

The overall contribution is summarized as:

• Evaluation the optimal DG location and size while satisfying all the network constraints.
• Comparing different state-of-the-art techniques in terms of their efficiency and power loss.
• Testing the method on different bus systems.

This paper is divided into four sections. Section 1 is the introduction and review of previous work done. Section 2 is the material and methods. It has two subsections. Section 2.1 presents the system model and the optimization problem, including the objective function and the system constraints of each power system, while Section 2.2 introduces the design and parameters and the narrative logic flow of the modified flower pollination algorithm, which has later been determined to be the best technique. The Section 3 deals with results and outcomes of the proposed technique. The Section 4 provides a conclusion of the presented work.

2. Materials and Methods

2.1. Problem Formulation with System Model

The proposed method aims to determine the location of DG placement as well as the optimal size and optimal power factor by solving the optimization problem. The objective functions should meet the power system constraints in the radial distribution system. Additionally, different types of DGs are considered in calculation including PV, wind, and biogas. The normal system parameters, which are the deviation in voltage and loss in power, are computed, and the normal system parameters are to be optimized by selecting optimal size of the distributed generators and allocation of various radial distribution system to minimize the power losses and obtaining optimal power factor. The core calculation of the optimization procedure loop is the power flow calculation of the radial distribution system. The power flow calculations are introduced in the following sub-sections.

2.1.1. Power Flow Calculation

The power flow of the radial distribution network is calculated based on the equations below to find the system’s power loss [32,33]. Notably, general load flow analysis can be carried out by considering a single line diagram, which is illustrated in Figure 2.

Real and reactive power is derived from Figure 1. The real power can be computed by Equation (1) while the reactive power can be computed by Equation (2).

$$P^{P+1}=P^P-P^{L\left(P+1\right)}-R^{p,p+1}\ast \frac{\left(P_P^2+Q_P^2\right)}{{\left|V^P\right|}^2}$$

(1)

$$Q^{P+1}=Q^P-Q^{L\left(P+1\right)}-X^{p,p+1}\ast \frac{\left(P_P^2+Q_P^2\right)}{{\left|V^P\right|}^2}$$

(2)

After that, the line voltage is computed based on the below equations,

$${\left|V^{p+1}\right|}^2={\left|V^p\right|}^2-2\left(R^{p·p+1}{P}^P+X^{p·p+1}·Q^P\right)+\left(R^{p·p+1}{}^2+X^{p·p+1}{}^2\right)\ast \frac{\left(P^P{}^2+Q^P{}^2\right)}{{\left|V^P\right|}^2}$$

(3)

The real power loss of the radial distribution system in each line can be computed as follows,

$$P^{LOSS}{}^{\left(p·P+1\right)}=R^{p·p+1}\ast \frac{\left(P^P{}^2+Q^P{}^2\right)}{{\left|V^P\right|}^2}$$

(4)

The complete system power loss can be computed by the below equation,

$$P_{loss}^{Total}={\displaystyle \sum }_{P=1}^{N-1}{P}^{LOSS}{}^{\left(p·P+1\right)}$$

(5)

where:

• $P^p$ is the real power flow which is flowing from bus p;
• $P^{Lp}$ is the real power load which is at bus p;
• $P^{L\left(p+1\right)}$ is the real power load which is at bus p + 1;
• $Q^p$ is the reactive power flow which is flowing from bus p;
• $Q^{Lp}$ is the reactive power load which is at bus p;
• $Q^{L\left(p+1\right)}$ is the reactive power load which is at bus p + 1;
• $X^{P·p+1}$ is the reactance which is between the buses p and p + 1;
• $R^{P·p+1}$ is the resistance which is between the buses p and p + 1;
• $V^{P+1}$ is the voltage which is at bus p + 1;
• $V^P$ is the voltage which is at bus p;
• $P_{loss}^{Total}$ is the total power loss which is in the system.

The system’s real power loss is computed from the forward-backward process, which provides a detailed study about it. In order for the system to operate steadily and dependably, the general power loss should be kept to a minimum. The overall process flow for power loss minimization is charted in Figure 3.

Initially, the dataset of bus systems is obtained from the open-source system. The collected bus data is utilized to analyze the variation of voltage, normal power loss, and operational cost functions for bus systems. The normal power loss and normal voltage deviations are reduced with the help of the modified FPA algorithm, which is elucidated in detail in the next subsection. A single-objective function is used in the proposed method to reduce power loss, lower voltage variation, lower operating costs, and achieve the best power factor, respectively. The single objective function-based optimal DG location is identified using the proposed algorithm. The algorithm suggested reduces loss of power in the systems and ensures that there is continuous monitoring of constraint limits. The limits are satisfied; the maximum iteration condition is checked. Once the condition is checked, the optimal results are saved and stop the procedure. The sub-sections below formulate and explain the single-objective function and constraints.

2.1.2. Power Loss Minimization

The primary function is to ensure that there is a reduction of the total power loss by developing distributed generators and placing them in optimal locations [34]. The minimization (Min) of power loss is formulated as follows:

$$P_{loss min}={\displaystyle \sum }_{I=1}^{N^{BR}}{R}^I\times \frac{P_I^2+Q_I^2}{V_I^2}$$

(6)

where:

• $P_{loss min}$ is the minimization of power loss;
• $P_I^2$ is the Ith bus’s active powers load;
• $Q_I^2$ is the Ith bus’s reactive powers load;
• $N^{BR}$ is the number of branches in the distribution network;
• $V_I^2$ is the Ith bus’s voltage magnitude;
• $R^I$ is the Ith branch’s resistance.

The suggested approach, which must adhere to the power system’s limits, aids in achieving the best possible placement of the DG.

2.1.3. Real Power Balance and Reactive Power Balance

Real and reactive power both operate in the power system within their mathematically defined boundaries, which are as follows:

$$P^{SLACK}+{\displaystyle \sum }_{I=1}^{N^{DG}}{P}^{DG,I}={\displaystyle \sum }_{I=1}^{N^B}{P}^{D,J}+{\displaystyle \sum }_{I=1}^{N^{BR}}{P}^{L,K}$$

(7)

$$Q^{SLACK}+{\displaystyle \sum }_{I=1}^{N^{DG}}{Q}^{DG,I}={\displaystyle \sum }_{I=1}^{N^B}{Q}^{D,J}+{\displaystyle \sum }_{I=1}^{N^{BR}}{Q}^{L,K}$$

(8)

where:

• $P^{DG,I}$ is the Ith DG unit’s active power output;
• $P^{D,J}$ is the Jth bus’s active power load demand;
• $P^{L,K}$ is the Kth branch’s active power loss;
• $P^{SLACK}$ is the slack bus’s active power provided;
• $Q^{DG,I}$ is the Ith DG unit’s reactive power output;
• $Q^{D,J}$ is the Jth bus’s reactive power load demand;
• $Q^{L,K}$ is the Kth branch’s reactive power loss;
• $Q^{SLACK}$ is the slack bus’s reactive power provided;
• $N^B$ is the distribution network’s number of buses;
• $N^{DG}$ is the total number of DG units presented in the power system.

2.1.4. Radial Configuration Constraint

A distributed network is operated as a radial network with the aim of saving energy to protect devices as well as reduce faulty levels. Thus, it is mandatory and crucial for operators to determine the accurate radial configuration, especially in the optimal DG placement problem that usually occurs in the distribution networks. The number of branches and tie switches could be fixed as follows [35]:

$$N^{Br}=\left(N^B-1\right)$$

(9)

$$N^{TS}=N_L^{loop}-N_L^{radial}$$

(10)

where:

• $N^{TS}$ is the total number of tie switches in the distribution network;
• $N_L^{loop}$ is the number of lines in the loop network;
• $N_L^{radial}$ is the number of lines in the radial network.

The distribution network should provide clarity about radial configuration and supply complete loads after DG placement. The mentioned constraints should meet by the proposed system, while selecting the optimal location of DG in the power system. The proposed algorithm is made to compute the best location of DG for reducing the system’s power loss. A detailed description of the proposed algorithm is presented in the section below.

2.2. Detailed Description of Algorithm

The modified flower pollination algorithm aims to solve a single objective optimization problem of determining the optimal DG placement with optimum size for minimizing the power losses, calculating the optimal power factor, and minimizing the cost of the power system. For highlighting the advantages of the proposed method over dozens of optimization methods that have been presented in the literature to solve the same problem. The algorithm combines the golden search algorithm with a modified FPA, which utilizes the FDB method for optimizing the population selection, therefore increasing the efficiency and accelerating the convergence speed. For optimal DG placement, the golden search algorithm is adopted in the FPA. The specific characteristics of the combination of the golden search-based FPA and FDB are presented in the next section.

2.2.1. Process of Flower Pollination Algorithm

The FPA was developed in 2012 by Xin-She Yang. The pollination process in flowering plants can serve as an inspiration for this algorithm [36]. In order to solve optimization issues, the FPA was slowly being extended and used [37,38,39]. The four rules are considered in the FPA for optimization procedure which is presented below,

• Rule 1: Global pollination refers to cross-pollination process and biotic pollination. Based on levy flight operation, it moves away to carry pollinators.
• Rule 2: Local pollination utilizes both self-pollination as well as abiotic pollination.
• Rule 3: Insects or pollinators with developed flower constancy equates to a reproduction probability. The probability of reproduction is directly proportional to the similarity function involved.
• Rule 4: Based on switch probability, the switching or interaction of both the global and local pollination is controllers, which lightly biased to local pollination.

The above four rules can be generally used for developing the proper model for the algorithm, as mentioned in [36], where pollination occurs with the help of insects. In addition to that, an insect can fly or move over long distances, making the pollen also move over long distances. As such, the first ule is mathematically formulated as follows,

$$X_I^{T+1}=X_I^T+\gamma L\left(\lambda \right)\left(g^{*}-X_I^T\right)$$

(11)

where,$L\left(\lambda \right)$ and $\gamma$ represents the step size and control factor to stabilize step size $g^{*}$ can be considered as a current ideal solution form the completed solutions at the current iteration/generation and $X_I^T$ can be described as pollen $I$ or solution vector $X_I$ at iteration $T$ [40].

In the FPA, insects may fly that replicate the behavior of flying animals and is named a levy flight of dynamic steps which can be modeled as,

$$L~\frac{\lambda \Gamma \left(\lambda \right)\sin \left(\frac{\pi \lambda }{2}\right)}{\pi } \frac{1}{M^{1+\lambda }}, \left(M\gg M_0>0\right)$$

(12)

where $\Gamma \left(\lambda \right)$ stands for gamma function and its distribution are very large that is $M>0$. However, in a real world solution, its values is small and considered close to 0.1.

2.2.2. Process of Golden Search Algorithm

The main objective of the golden search algorithm is to find minimum $F\left(X\right),XϵR$, within the period $\left[l,u\right]$. It is used because of generalization capability and modeling of the dynamic model [28]. At the beginning of the algorithm, two points were evaluated which were:

$$C=\frac{-1+\sqrt{5}}{2}$$

(13)

$$X_1=C_l+{\left(1-C\right)}_u$$

(14)

$$X_2=C_l+C_u$$

(15)

The objective function is commuted at those points and if $F\left(X_1\right)<F\left(X_2\right)$, then the solution is in the range of $\left[l,u\right]$. Otherwise, they will be in the range $\left[X_1,u\right]$. Until the termination conditions become satisfactory, the search process does not stop.

We can clearly notice two search sections $\left[l,u\right]$ and $\left[X_1,u\right].$ The sections $\left[l,u\right]$ and $\left[X_1,u\right]$ can be identified from the search for every single iteration. After an iteration is complete, the next iteration has one of these sections. This is possible, as both of the sections would have the same width. The optimization of convergence speed also takes place as the larger section, which is used in various different conditions.

$$P+Q=Q+R$$

(16)

$$\frac{P}{Q}=\frac{R}{Q}=\frac{\left(Q+R\right)}{P}=\frac{1}{C}={\varnothing }_N$$

(17)

To summarize, the very first step of the GSA is to find the minimum point within the interval. The convergence speed is minimized. ${\varnothing }_N$ is the convergence speed, with N as the number of iterations. P represents the distance between l and x₁, Q represents the distance between x₁ and x₂, while R represents the distance between x₂ and u. The algorithm finally stops when the algorithm is in the best bound. Figure 4 illustrates the flow chart of the golden section search.

2.2.3. Proposed Methodology Process

The proposed methodology (PM) is developed to the optimal allocation of DG in the power system for reducing the power loss with the minimum DG size. The optimal placement of DG is selected with the consideration of the objective function of power loss minimization. The proposed algorithm is a combination of FPA and the golden search method with optimum population selection based on FDB. By optimizing the selection process, the time of convergence is reduced by reducing the number of iterations and also increasing the efficiency by selecting the fittest individuals throughout the process [41,42,43,44,45,46]. The worst selection of population will cause the solution to be trapped in a local minimum optimal point. To avoid such scenarios, the GSFPA is developed. The local pollination in the FPA is enhanced through the proposed algorithms and is presented in Equation (18). $ϵ$ is factor by which scaling is performed and it is dependent on two variables which are $X_1$ and $X_2$, respectively. The main aim of this algorithm to determine the optimal scale factor to find the best generation.

To produce a superior solution, the scale factor puts the golden section method into effect. The method produces two intermediate points that are presented, as follows, as it moves through the interval [S = −1, T = 1].

$${ϵ}^1=b-\frac{b-a}{c}; {ϵ}^2=a+\frac{b-a}{c}$$

(18)

The golden search algorithm helps in optimally selecting a scaling factor. The fitness function is formulated by considering the function of FDB in optimizing the selection process [39]. The mathematical formulation of the FDB is presented as follows,

$$SP={\left[\begin{array}{c}S1\\ \dots \\ SN\end{array}\right]}_{N\times 1}$$

(19)

The initial population is created based on the above equation,

$${\forall }_{I=1}^N=PI\ne Pbest, DPI=\sqrt{{\left(X1PI-X1Pbest\right)}^2+{\left(X2PI-X2Pbest\right)}^2+\dots +{\left(XMPI-XMPbest\right)}^2}$$

(20)

where $Pbest$ can be described as the best solution and $P$ can be described as population. Based on this, the population vector can be presented as follows,

$$DP={\left[\begin{array}{c}D1\\ \dots \\ DN\end{array}\right]}_{N\times 1}$$

(21)

The score calculation is formulated as follows,

$${\forall }_{I=1}^N=PI,SPI=W\ast norm FPI+\left(1-W\right)\ast normDPI$$

(22)

Here, $W$ can be described as the weighting factor. Based on the FDB function, the optimal solutions are achieved in the optimization algorithm. Figure 5 illustrates the flowchart of the modified flower pollination algorithm.

3. Results

This section evaluates the different optimization algorithms that have been implemented using MATLAB for different bus systems, including IEEE 33 and IEEE 69. The different algorithms are utilized to find the optimal allocation of DG in a radial distribution system with the aim of having minimal power loss and determining the optimal power factor. The modified FPA, PSO, and GA are evaluated and their performances are compared. The main objective is to find the best optimization algorithm that can enable efficient operation by reducing the power loss of the whole system. Different scenarios are analyzed, and results are analyzed compared in order to determine the best optimization algorithm. The parameters for implementing the GA, PSO, FPA, and the proposed method are listed in

Table 1. Implementation parameters of GA, PSO, FPA and PM.

Genetic Algorithm (GA)
No	Description	Notation	Value
1	Population/Generation Combination	P/G	60:20
2	Probability of Crossover	%C	0.9
3	Probability of Mutation	%M	0.2
4	Maximum number of iterations	Niter	350
5	Population Size	Ns	60
Particle Swarm Optimistion (PSO)
No	Description	Notation	Value
1	Cognitives Constant	C1	2
2	Social Constant	C2	2
3	Inertia Weight	w	Linear reduction from 0.9 to 0.4
4	Probability Switch	P	0.8
5	Maximum number of iterations	Niter	350
6	Population Size	Ns	60
Flower Pollination Algorithm (FPA)
No	Description	Notation	Value
1	Maximum number of iterations	Niter	350
2	Golden ratio	C	0.618
3	Probability switch	P	0.8
4	Population	Ns	60
Proposed Method (PM)
No	Description	Notation	Value
1	Maximum number of iterations	Niter	350
2	Golden ratio	C	0.618
3	Probability switch	P	0.8
4	Population	Ns	60

. The convergence for each of them are represented in Figure 6 and

Table 2. Stopping Criteria of GA, PSO, FPA, and PM.

No	Algorithm	Stopping Criteria	Time Convergence
1	Genetic Algorithm	Exhaustion-based Stopping Criteria	110.65
2	Particle Swarm Algorithm	Movement-based Stopping Criteria	117.245
3	Flower Pollination Algorithm and	Movement-based Stopping Criteria	119.255
4	proposed method	Movement-based Stopping Criteria	100

.

3.1. IEEE 33 Bus System Performance Analysis

The IEEE 33 bus system is considered for performance evaluation. The performance of modified FPA, GA, and PSO have been evaluated. The normal real as well as reactive power loss of these system is mainly 202.67 kW and 135.14 kVAr, respectively. Initially, the loss of the system is identified as well as minimized with the assistance of DG optimal placement in a power system. After that, performance and power losses with DG allocation are evaluated for GA, PSO, FPA and modified FPA.

Table 3. Analysis of power loss with DG allocation with IEEE 33 Bus.

			GA	PSO	FPA	Modified FPA
DGs location (bus number)		Solar	30	14	10	9
		Wind	24	24	29	29
		Biogas	14	30	14	13
DG optimal size	P (kW)	Solar	492	340	400	396
		Wind	627	701	580	567
		Biogas	349	396	400	555
	Q (kVar)	Solar	40	19	19	23
		Wind	111	72	32	31
		Biogas	83	121	80	63
	Power factor	Solar	0.99677	0.8688	0.97677	0.99839
		Wind	0.98459	0.99477	0.98689	0.99851
		Biogas	0.97273	0.95624	0.96564	0.99368
Best power loss (kW)			205.968	275.565	275.565	193.363677
Worst Power loss			319.045	346.881	346.469	248.385615
Mean Power loss			242.491	310.469	310.469	200.95
Standard deviation			29.9714	24.5554	24.5554	8.71297325

list the results of all methods for the 33 bus system. The results clearly show the superiority of the modified FPA in reducing the power losses, including the best, worst, and mean power losses, besides the standard deviation.

Three distinct load circumstances have been used to assess the suggested approach. Figure 7 and Figure 8 show each bus’s power loss for the two types of loads used to evaluate the IEEE 33 bus system. According to the investigation, when compared to all other approaches, the modified FPA produced the best results in terms of power loss and standard deviation.

3.2. IEEE 69 Bus System Performance Analysis

Similarly, the modified flower pollination algorithm’s performance is evaluated by taking into consideration the bus system IEEE 69 with five cases. The normal real loss of power of the system is 226 kW.

Table 4. Analysis of power loss with DG allocation for IEEE 69 bus.

			GA	PSO	FPA	Modified FPA
DGs location (bus number)		Solar	18	11	15	12
		Wind	51	18	64	62
		Biogas	61	61	30	36
DG optimal size	P (kW)	Solar	199	431	440	238
		Wind	315	846	370	184
		Biogas	805	966	890	819
	Q (kVAr)	Solar	48	196	45	21
		Wind	49	38	50	15
		Biogas	94	633	83	75
	Power factor	Solar	0.97262	0.9105	0.97568	0.99607
		Wind	0.98801	0.99899	0.97546	0.99649
		Biogas	0.99332	0.8366	0.98453	0.99589
Best power loss (kW)			133.878	162.212	141.235	126.383916
Worst Power loss			181.364	192.529	160.458	152.611128
Mean Power loss			151.8	170.166	145.128	134.67
Standard deviation			15.8572	14.9133	6.235494	5.69932973

list the results of all methods. The bus system’s loss of power is noticed to be significantly less with the modified FPA compared to the GA, FPA, and PSO. Initially, the system’s power loss is identified and minimized with the assistance of DG optimal placement in a power system. It demonstrates that the novel technique greatly reduces the amount of power loss and, thus, the DG operating cost as compared to the system’s typical methods.

4. Conclusions

In this paper, the comparison of the optimization algorithms—the PSO, GA, FPA, and modified FPA for optimal DG placement for reducing power losses in power system—was conducted. Through the research, it was determined that the modified FPA algorithm was the most efficient algorithm to minimize loss of power by determining the optimal placement as well as sizing of DGs. A technical novelty is present in which different load type and size in power systems, including residential, industrial, and commercial loads is conducted. Additionally, different types of DGs are considered, including PV, wind, and biogas. The paper combines the merits of the FPA and GS algorithms and it optimizes the selection process of populations based on the FDB to assure moving forward with the best individuals through generations. As a result, there are significant improvements in speed and efficiency in terms of the power loss reductions. The performance parameters of the new method have been verified coherently using different bus systems, including IEEE 33, and IEEE 69. The results obtained proved that the modified flower pollination algorithm has significant improvements with respect to convergence speed and reduction in power loss as compared with all other methods.