Optimal Location and Sizing of Distributed Generators Based on Renewable Energy Sources Using Modified Moth Flame Optimization Technique

Due to the great impact of the penetration and locations of distributed generators (DG) on the performance of the distribution system, this paper proposes a modified moth flame optimization (MMFO) algorithm. Two modifications are proposed in MMFO to enhance the exploration and exploitation balance and overcome the shortcomings of the original MFO. The proposed MMFO is used to find the optimal location and sizing of DG units based on renewable energy sources in the distribution system. The main objective function is to minimize the total operating cost of the distribution system by considering the minimization of the total active power loss, voltage deviation of load buses, the DG units cost, and emission. This multi-objective function is converted to a coefficient single objective function with achieving different constraints. Also, the bus location index is employed to introduce the sorting list of locations to accomplish the narrow candidate buses list. Based on the candidate buses, the proposed MMFO is used to get the optimal location and sizing of DG units. The proposed MMFO algorithm has been applied to the IEEE 69-bus test distribution system and the results are compared with other published algorithms to prove its effectiveness and superiority.

Nomenclature

AbbreviationExpansion

$C_{DG}$	cost of all DG units
$C_{P_{LOSS}}$	cost of total active power loss of the distribution system
$C_{E}$	cost of emission which targeted to minimize it
$C_{VD}$	reflection of the voltage deviation on the cost
$C_{c}$	capital cost $({\$}/KW)$
$F_{c}$	variable fuel cost $({\$}/KWh)$
$OM_{c}$	operating and maintenance cost $({\$}/KW-year)$
$r$	interest rate (9%)
$n$	investment life time $(20-years)$
$P_{L}$	total real power losses in all buses
$P_{k}, Q_{k}$	active and reactive power injected at bus $k$ , respectively
$P_{DGi}, Q_{DGi}$	generated active and reactive power of DG unit, respectively
$P_{DGi_{max}}$	maximum allowable active power generated from DG unit
$P_{Grid}$	active power injected from grid
$P_{d}, Q_{d}$	demand of active and reactive power, respectively
$Q_{LOSS}$	reactive power losses
$Q_{Grid}$	reactive power injected from grid
$V_{i}, V_{j}$	magnitudes of the voltage at buses $i$ and $j$ respectively
$V_{D}$	voltage deviation at load buses
$V_{M}$	maximum allowable voltage $V_{M}= 1.0\,\,p.u$
$V_{Li}$	voltage at load bus $i$
$V_{Li}^{max}$	maximum magnitude of voltage at load bus $i$
$V_{Li}^{min}$	minimum magnitude of voltage at load bus $i$
$\theta _{i}, \theta _{j}$	angles of the voltage at buses $i$ and $j$ respectively
$k_{i}$	group of buses that connected to bus $i$
$G_{ij}, beta_{ij}$	susceptance and conductance of bus admittance matrix, respectively
$\omega$	weight factor that can be determined based on the $\frac {r_{i}}{x_{i}}$
$\frac {r_{i}}{x_{i}}$	ratio of the feeder resistance to feeder reactance
$R_{k}$	resistance of branch $k$
$I_{k}$	current flow of branch $k$
$E_{DG}$	total emission released from all DG units
$CO_{2,DGi}$ , $NO_{x,DGi}, SO_{2,DGi}$	emission products of DG units
$W_{LOSS}$	factor of power loss $({\$}/MW)$
$W_{E}$	emission factor in $({\$}/KG)$
$W_{VD}$	voltage deviation economic operator
$S_{li}$	transmission line loading
$N_{DG}$	total available number of DG units
$N_{b}$	number of total branches
$N$	number of network buses
$N_{l}$	number of load buses
$MO_{i}$	the $i^{th}$ moth
$F_{k}$	the $k^{th}$ flame
${g}$	logarithmic spiral function
$D_{i}$	distance between the $i^{th}$ moth and and $k^{th}$ flame
$s$	constant indicates the shape of the logarithmic spiral
$\varepsilon$	random number $\in [-1,1]$
$c$	the convergence constant
$N_{f}$	maximum number of flames
$it$	current number of iteration
$max_{it}$	maximum number of iterations

SECTION I. Introduction

Recently, the distributed generators (DG) integrated into the distribution system have major positive impacts on the performance of the system, due to its ability to decrease the loss of transmission lines, improve the voltage stability, increasing the reliability and reducing the pollutant emission based on DG technology types [1]–​[3].

The penetration of DG units in the distribution system is becoming more widespread because of the growth of demand load, reduction of pollutant emission and deregulated of the electrical power market. Several DG units technologies are used and categorized according to fuel energy used into dispatchable and non-dispatchable units. The former includes, for example, diesel generators, micro-turbine, and fuel cell. While, the later includes, renewable energy sources based on DG units such as solar photovoltaic systems, wind turbine generators, biomass and micro-hydro generators [4]–​[7].

The effectiveness of DG performance is more related to the choice of their adequate location, types, and sizes, where the optimal selection will maximize the benefits of DG units used and avoid their drawbacks for the system such as increasing loss of the system, increasing the operating cost and voltage instability [8], [9]. Incorporating the DG units into the system has different impacts in the case of both steady-state and transient conditions. In the steady-state, there are some problems like reverse power flow, high power losses, voltage fluctuation, reactive power management, miscoordination of the protection scheme, poor power quality, regulation, and reliability of over-load tap changer (OLTC) [10]–​[13]. On the other hand, the impacts in the transient state appear due to the islanding of DG units and the phenomena of the uncertainty of the output of DG units such as occurring from the variation of wind speed and shading effects in zones with PV [14]. The severity of these impacts is based on the locations of DG units with the amount of DG penetrations and the DG’s technology. Also, due to the nature of renewable DG units, the simultaneous variations of DG’s generations for supplying the demand load may cause under or over voltage. The effects of such phenomenon may affect by DG unit locations and weather conditions [15]. In addition, at a specific penetration level of DG units, the performance of the system is improved, but in contrast, beyond this level, the system was subject to degradation by substation and feeder loading, voltage deviation and increased power losses. Moreover, by increasing the penetration of DG units, the operation of the automatic voltage regulator (AVR) inside the OLTC of the transformer becomes more sophisticated and incapable because of occurring the phenomena of reverse power flow and accompanied with high voltage and current which can be controlled by employing different methods summarized in [9], [16].

Consequently, the problem of determining the optimal location and sizes of DG units has subject to great interest recently in order to achieve many objectives such as minimization of real power loss, improvement voltage profile, improvement power system quality and increasing both efficiency and reliability of the distribution system. So, various approaches are proposed in the literature to solve this problem [3], [17]–​[21].

The authors in [3] proposed a novel method to determine the optimal size and location of DGs to not only reducing the power loss but ensuring the voltage stability of the system. The improved gravitational search algorithm is proposed in [19] to get the optimal placement and sizing of solar photovoltaic based DGs to minimize the total cost. A combined method of an intelligent water drop (IWD) and hybrid (GA) were proposed in [22] to determine the size and location of DGs in micro-grid for increasing voltage stability, reduce network losses and improve voltage profile. A hybrid fuzzy logic controller technique and ant-lion optimization algorithm’s with particle swarm optimization based combination is proposed in [23] to solve the optimal allocation of distributed generations in a radial distribution network to minimize the total cost of operation and deviation of voltage indexes. In [24] at different load levels, the objective function to find optimal location and sizing of DGs is reducing real and reactive power losses which solved by using biogeography-based optimization (BBO) algorithm. An efficient optimization algorithm to optimally allocate the multiple DG units in distribution systems based on sine cosine algorithm (SCA) and chaos map theory is proposed in [25] using three objective functions.

Nowadays, the DGs are planned optimally to achieve economic motive during the liberalized modern power market, so the optimally planning of distributed generators is very important for the operators in the distribution network [26]. In the real distribution network, there are different configurations with many huge buses. In addition to several load levels which may be taken into consideration at different periods, moreover, there are geographical and environmental constraints, this means a very large number of buses to be nominated for distributed generators. All of that may be making the choice of the optimal location and size is not easy and take a huge time. So it is better to use a technique reducing the nominated buses to save the time of searching according to network configuration. Therefore, the bus location index is employed in this paper to create a priority ranking list of candidate buses.

In 2015, the moth flame optimization (MFO) is proposed as a new technique to solve optimization problem in [27]. The MFO which is considered as one of the novel nature-inspired algorithms simulates the navigation method of moths for travelling for long distances. The MFO is appropriate for solving many practical optimization problems because of its brilliant characteristics [28]–​[31].

As known, the balance between exploration and exploitation is the greatest significant features for any generalized approach. The exploration points to exploring the global search while the exploitation refers to the local search. According to the theory published in [32], no algorithm is the best appropriate for all the optimization problems. Therefore, there are different modifications are proposed by researchers to improve the characteristics of the MFO regarding the proper balance between exploitation and exploration capabilities.

The opposition based MFO method is proposed in [33] to overcome the disadvantages of the conventional MFO which are trapping in local optima and the slow convergence. In [34] the conventional MFO is combined with $\text{l}\acute {e}$ vy flights to gain their merits and to decrease the computational times, especially for the highly complex optimization problems. The chaotic MFO is proposed in [35] to enhance the balance between exploitation and exploration capabilities by employing two chaotic mechanisms.

This paper proposes a modified moth flame optimization (MMFO) algorithm. Two modifications are made in the original MFO to derive the proposed MMFO in order to improve the balance between the exploration-exploitation capabilities of the algorithm and speed up the convergence of the algorithm. Then, the proposed MMFO is employed to find the optimal location and sizing of DGs based on different dispatchable and non-dispatchable DGs units in order to minimize the total operating cost of the distribution system. The total objective function consists of the minimization of fuel cost, total real power loss, voltage deviation and pollution emission for some DGs is treated as weighted economic operators, where a multi-objective problem is converted to coefficient single objective function (CSOF) with considering some constraints of the system. The performance of the developed approach is tested using a standard test system and compared with other published methods to discover its notability for solving the problem described here. The contributions of this paper are to:

• Propose the MMFO algorithm which improves the complementary features of the original MFO by improving the balance between the exploration and exploitation and avoiding the problems of the original MFO.

• Introduce the problem formulation of finding the optimal location and sizing of DG units based on renewable energy sources to minimize the total operating cost considering four different objective functions.

• Use the proposed MMFO algorithm to solve the above problem by converting the multi-objective function consists of four different functions into a coefficient single objective function (CSOF).

• Enhance the solution of the above problem in comparison with the obtained results from published algorithms based on different cases and scenarios using the IEEE 69-bus test distribution system.

This paper is organized as follows: Section II introduces the bus location index (BLI) technique. The mathematical model of the objective problem is described in Section III. In Section IV the MMFO technique is discussed. The simulation results for the test system are presented with a discussion in Section V. Finally, Section VI presents the conclusions of the proposed work.

SECTION II. Bus Location Index (BLI)

It is known that any change in the injected active and reactive power at any bus of the distribution system will lead to a change in total real power losses. According to this concept, the bus location index (BLI) is formulated as described in [36]. The real power losses can be written as in [37] as following.

$$\begin{equation*} P_{L}=\sum _{i=1}^{N}\sum _{j\in {k_{i}}}V_{i}V_{j}[G_{ij}\cos (\theta _{i}-\theta _{j})+\beta _{ij}\sin (\theta _{i}-\theta _{j})]\tag{1}\end{equation*}$$

The power balance equations are written as follow:

$$\begin{align*} \Delta {P_{k}}=&P_{k}-V_{k}^{2}G_{kk}-V_{k}\sum _{j=1,j\neq {k}}^{N}V_{j}[G_{kj}\cos (\theta _{k}-\theta _{j}) \\&+\,\beta _{kj}\sin (\theta _{k}-\theta _{j})] \tag{2}\\ \Delta {Q_{k}}=&Q_{k}-V_{k}^{2}\beta _{kk}-V_{k}\sum _{j=1,j\neq {k}}^{N}V_{j}[G_{kj}\sin (\theta _{k}-\theta _{j}) \\&-\,\beta _{kj}\cos (\theta _{k}-\theta _{j})]\tag{3}\end{align*}$$

The variation in real power losses based on the previous concept may be described as follow in [37]

$$\begin{align*} \begin{bmatrix} \dfrac {\partial {P_{L}}}{\partial {P}}\\[0.8pc] \dfrac {\partial {P_{L}}}{\partial {Q}} \end{bmatrix}=J^{-1} \begin{bmatrix} \dfrac {\partial {P_{L}}}{\partial {\theta }}\\[0.8pc] \dfrac {\partial {P_{L}}}{\partial {V}} \end{bmatrix}\tag{4}\end{align*}$$ where $\frac {\partial {P_{L}}}{\partial {P}}$ and $\frac {\partial {P_{L}}}{\partial {Q}}$ are the power loss derivative with respect to injected active and reactive power at bus $i$ respectively. $\frac {\partial {P_{L}}}{\partial {\theta }}$ and $\frac {\partial {P_{L}}}{\partial {V}}$ are the power loss derivative with respect to angle and the voltage of bus $i$ respectively. $J$ is the jacobian matrix, $$\begin{align*} J=\begin{bmatrix} \dfrac {\partial {\Delta {P}}}{\partial {\Theta }} &\quad \dfrac {\partial {\Delta {P}}}{\partial {V}}\\[0.7pc] \dfrac {\partial {\Delta {Q}}}{\partial {\Theta }} &\quad \dfrac {\partial {\Delta {Q}}}{\partial {V}} \end{bmatrix}\tag{5}\end{align*}$$ where $\frac {\partial {\Delta {P}}}{\partial {\Theta }}$ and $\frac {\partial {\Delta {P}}}{\partial {V}}$ are the partial derivatives of injected active power with respect to angle and voltage magnitude respectively. $\frac {\partial {\Delta {Q}}}{\partial {\Theta }}$ and $\frac {\partial {\Delta {Q}}}{\partial {V}}$ are the partial derivatives of injected reactive power with respect to angle and voltage magnitude respectively.

The BLI can be expressed as follow in [38] for each bus.

$$\begin{align*} BLI=&\omega \frac {\partial {P_{L}}}{\partial {P}}+(1-\omega)\frac {\partial {P_{L}}}{\partial {Q}} \tag{6}\\ \omega _{i}=&\frac {\frac {r_{i}}{x_{i}}} {\frac {r_{i}}{x_{i}}+1}\tag{7}\end{align*}$$

The weight factor may be a unique value and is calculated as the mean value of all weight factors of buses. This value is accepted particularly and can be used in BLI equation due to the $\frac {r_{i}}{x_{i}}$ variation will be very small because all feeders have the same parameters and the same voltage level. According to the values calculated by BLI, the priority ranking list can be constructed in descending order, which means that the greater values of BLI are more favorable to connect DGs.

SECTION III. Objective Problem Formulation

The target of the objective problem proposed here is finding the optimal location and sizing of DGs based on renewable energy sources to minimize the total operating cost with considering equality and inequality constraints. Where some coefficients are utilized to integrate different objective functions for creating only CSOF which used to minimize the total cost of the system.

A. Cost Formulation of Dg Units

The total cost of DG units contains capital installation cost, fuel cost, operating and maintenance cost. It may be formulated as follow [39]

$$\begin{align*} C_{DG}=&\sum _{i=1}^{N_{DG}}C(P_{DGi}) \tag{8}\\ C(P_{DGi})=&C_{c}P_{DGi_{max}}+\frac {(1+r)^{n}-1}{r(1+r)^{n}}(F_{c}+OM_{c})P_{DGi}\tag{9}\end{align*}$$

B. Total Power Loss Formulation

The active power losses of the distribution system can be described as follow [40]

$$\begin{equation*} P_{LOSS}=\sum _{k=1}^{N_{b}}|{I_{k}}|^{2}R_{k}\tag{10}\end{equation*}$$

The cost of active power losses can be formulated as following:

$$\begin{equation*} C_{P_{LOSS}}=P_{LOSS}W_{LOSS}\tag{11}\end{equation*}$$

C. Pollution Emission Formulation of Dg Units

According to DGs technologies, there are some types of DGs that generate $CO_{2}$ , $SO_{2}$ and $NO_{x}$ , to deliver the required output power. The reflect of emission on the cost of DG units can be expressed as following in [41]

$$\begin{align*} E_{DG}=&\sum _{i=1}^{N_{DG}}E(P_{DGi}) \tag{12}\\ E(P_{DGi})=&(CO_{2,DGi}+NO_{x,DGi}+SO_{2,DGi})P_{DGi}\tag{13}\end{align*}$$

The cost of emission released by DG units may be formulated as follow:

$$\begin{equation*} C_{E}= E_{DG}W_{E}\tag{14}\end{equation*}$$

D. Voltage Deviation Formulation

The penetration of DG units may be cause variation in the distribution system voltage. Therefore, the voltage violation should be limited. The voltage deviation can be defined as follow [39]

$$\begin{equation*} V_{D}=\sum _{i=1}^{N_{l}}|V_{i}-V_{M}|\tag{15}\end{equation*}$$

The reflection of the voltage deviation on the cost can be expressed as follow:

$$\begin{equation*} C_{VD}= V_{D}W_{VD}\tag{16}\end{equation*}$$

E. Equality and Inequality Constraints

According to the objective problem proposed, there are two types of constraints as following:

1) Equality Constraints

Power balance equation with considering DG units in the distribution system can be defined as follow [42]

$$\begin{align*} P_{Grid}+\sum _{i=1}^{N_{DG}}P_{DGi}=&\sum _{j=1}^{N_{l}}P_{d}(j)+P_{LOSS} \tag{17}\\ Q_{Grid}+\sum _{i=1}^{N_{DG}}Q_{DGi}=&\sum _{j=1}^{N_{l}}Q_{d}(j)+Q_{LOSS}\tag{18}\end{align*}$$

2) Inequality Constraints

a: Voltage Limit Constraints

The voltage at each bus of the distribution system should be limited as following [42]:

$$\begin{equation*} V_{Li}^{min}\leq V_{Li} \leq V_{Li}^{max}\tag{19}\end{equation*}$$

b: Dg Limit Constraints

The minimum and maximum allowable values of the active and reactive output power of DG units in the distribution system can be defined as follow:

$$\begin{align*} P_{DGi}^{min}\leq P_{DGi}\leq&P_{DGi}^{max} \tag{20}\\ Q_{DGi}^{min}\leq Q_{DGi}\leq&Q_{DGi}^{max}\tag{21}\end{align*}$$

c: Feeder Constraints

The loading for each branch of distribution system should be limited using the following equation:

$$\begin{equation*} S_{li} \leq S_{li}^{max}\tag{22}\end{equation*}$$

F. Total Objective Function

In this paper, the above four objective functions which are the minimization of fuel cost, total real power loss, voltage deviation and pollution emission for some DGs are combined and converted into CSOF based on some coeficients. Therefore, the total objective function can be expressed as follows:

$$\begin{align*} \mathcal {F}=&C_{DG}+C_{P_{LOSS}}+ C_{E}+C_{VD} \\=&C_{DG}+P_{LOSS}W_{LOSS}+E_{DG}W_{E}+V_{D}W_{VD}\tag{23}\end{align*}$$

SECTION IV. Proposed Optimization Algorithm

A. Moth Flame Optimization Overview

Moth-Flame Optimization (MFO) recently proposed in [27] is a population-based algorithm which mimics the moth’s navigation way in nature. It is based on the navigation way named transverse orientation of the moths. The main idea of the transverse orientation method is employing a fixed angle with respect to the moon by moths during flying. The moths attempt to keep the fixed angle when they see an artificial light that is very close in comparison with the moon, but they fail. So, they fly in a logarithmic spiral mechanism during convergence with the flame [27], [34].

The model of the MFO algorithm consists of two important components. They are moth and flame. The moths represent the members (solutions) which move around the search space, while the flames represent the best position (problem’s variables) found for these members. The MFO begins with an initial population of moths and flames which are randomly generated. The moth movement is oriented by the flames. The fitness value of each moth is then calculated based on the problem objective function. In the next iteration, the number of flames is decreased by removing the unfit flames which guide the moths to move to the fittest flame. These processes are repeated until only one flame remains which means that the best solution for the problem is obtained.

After the initial population of moths and flames are generated randomly, the mathematical model of transverse orientation behaviour can be expressed. The position of each moth which is guided by the flames can be updated as follows [27]:

$$\begin{equation*} MO_{i}={g}(MO_{i},F_{k})\tag{24}\end{equation*}$$

The logarithmic spiral function can be expressed using the following equation [27]:

$$\begin{equation*} {g}(MO_{i},F_{k})=D_{i}\cdot \exp (s\varepsilon)\cdot \cos (2\pi \varepsilon)+F_{k}\tag{25}\end{equation*}$$

$D$ can be expressed as follows [27]:

$$\begin{equation*} D_{i}=|F_{k}-MO_{i}|\tag{26}\end{equation*}$$

The parameter $\varepsilon$ is a very important parameter in (25) where it controls the flying direction of the moth around the flame. Equation (25) permits a moth to navigate around a flame and not essentially within the space between them. To confirm exploitation property, the parameter $\varepsilon$ is chosen as a random number $\in [c,1]$ . The parameter $c$ which called the convergence constant is linearly decreased from −1 to −2 over the iterations.

Also, to improve the exploitation property, the number of flames is decreased progressively with the iterations as follows [27]:

$$\begin{equation*} \textrm {Flame number}=\textrm {round}\left ({N_{f}-it*\frac {N_{f}-it}{max_{it}}}\right)\tag{27}\end{equation*}$$

More details and the pseudo code of the original MFO algorithm can be found in [27].

B. Modified Moth Flam Optimization (MMFO)

To derive the proposed MMFO method, two modifications are made in the conventional MFO. In the conventional MFO, the convergence constant ($c$ ) is linearly decreased from −1 to −2 over the iterations. Although this decrement emphasizes the exploitation property of the algorithm, it reduces the convergence rate of the conventional MFO. Thus, the convergence constant is decreased exponentially from −1 to −2 in this paper to guarantee the exploration-exploitation balance and increase the convergence rate of the conventional MFO as follows:

$$\begin{equation*} c=\exp \left ({-\left ({\frac {it}{max_{it}/2}}\right)^{2}}\right)-2\tag{28}\end{equation*}$$

It is clear from (27) that the number of flames will reduce with iterations. This reduction in the flames’ number makes the balance between the exploitation and exploration. Therefore, equation (27) is modified in the proposed MMFO to enhance the balance between exploitation and exploration of the algorithm as follows:

$$\begin{equation*} \textrm {Flame number}=\textrm {round}\left ({N_{f}*\exp \left ({-\frac {it}{max_{it}/4}}\right)}\right)\tag{29}\end{equation*}$$

SECTION V. Simulation Results and Discussions

The developed method presented in the previous section is applied to the IEEE-69 bus radial distribution test system which described in [43] and shown in Fig. 1. The system consists of the main root bus represent the utility grid at bus 69, 70 branches where the system voltage is 12.66 kV. The system load active and reactive power are 3.86 MW and 2.69 MVAR, respectively. While the maximum and minimum voltage limits are 0.95 and 1.05 p.u., respectively [41], [44].

FIGURE 1.

Single line diagram of IEEE-69 bus radial distribution test system.

The notability of the developed MMFO method in determining the optimal location and sizing of different DG units is proved in this paper compared with other published algorithms. These algorithms are ant lion optimizer (ALO) [45], grey wolf optimizer (GWO) [46], dragonfly algorithm (DA) [47], conventional MFO [27], modified JAYA (MJAYA) algorithm [48], and Salp swarm algorithm (SSA) [49].

In the implementation of the proposed MMFO and other meta-heuristic methods, many parameters should be chosen. In this paper, the appropriate values of these parameters are obtained based on empirical tests. All the numerical studies have been run on 2.9-GHz i7 PC with 8 GB of RAM using MATLAB 2014a.

Firstly, the sorting list of buses is obtained using the BLI method described in section II to create narrow candidate buses as shown in Fig. 2. Table 1 shows candidate buses sorting in descending order, accordingly, the first twenty buses from the table were chosen for primary locations of DG units. Then the MMFO method is used to find optimal placement and sizing of DG based on the proposed objective function.

TABLE 1 BLI Values for the IEEE-69 Bus System

FIGURE 2.

BLI values for the IEEE-69 bus radial distribution test system.

The simulation results are executed with consideration of the system maximum load. Moreover, the maximum capacity of DG power is limited to 30 % of the total load demand. In addition, the DG units can deliver active power and reactive power where the DG units are represented as PQ model at power factor 0.9 [41], [44], [50].

To evaluate the MMFO method, different scenarios are carried out as follows:

• Location and sizing for one DG unit

• Location and sizing for two DG units

• Location and sizing for three DG units

In all scenarios, there are six types of DG units (fuel cell, micro-turbine, photovoltaic, wind, hydro and biomass). The specifications of these types can be found in [39], [51]. Table 2 shows the capital costs, variable fuel cots, average operating and maintenance costs, and emission factors for $NO_{x}$ , $SO_{2}$ and $CO_{2}$ [39], [41], [52]. Also, the maximum capacity of all DG power is limited to 30 % of the total load demand in the range of 0.1 MVA to 1.48 MVA [53], [54].

TABLE 2 Economic and Emission Factors of DG Units

A. Location and Sizing for One DG Unit

According to different technologies of renewable energy sources as DG units, the simulation results for locating and sizing one DG unit using a developed MMFO in comparison with other techniques are shown in Table 3. In addition, the effect of using one DG unit on the voltage profile using the developed MMFO is shown in Fig. 3.

TABLE 3 Results for Using One DG Unit

FIGURE 3.

The effect of using one DG unit on voltage profile using the developed MMFO.

The results show that the minimum total cost of the system was obtained by using the proposed MMFO compared with other meta-heuristic optimization techniques. A great benefit is obvious of the proposed MMFO when using one micro-turbine at optimal bus 60 with optimal sizing of 0.6144 MVA where the total cost of the system is $1.7690~M{\$}$ with a reduction of the total power losses to 0.1001 MW which represents percentage reduction 55.15 % from the real power loss without any DG unit. The minimum voltage is increased from 0.9092 p.u to 0.9446 and 0.9488 p.u when using one micro-turbine and one fuel cell, respectively. In addition, Fig. 3 shows that the best voltage profile can be obtained when one fuel cell is used.

B. Location and Sizing for Two DG Units

To confirm the efficiency of the developed MMFO to obtain the best location and size of DG, it is applied for two units of DG. The simulation results for locating and sizing two DG units using a developed MMFO in comparison with other recently published techniques are shown in Table 4. Also, the effect of using two DG units on voltage profile based on the developed MMFO is shown in Fig. 4.

TABLE 4 Results for Using Two DG Units

FIGURE 4.

The effect of using two DG units on voltage profile using the developed MMFO.

These results prove that the minimum total cost of the system may be obtained using the proposed MMFO compared with other meta-heuristic techniques, based on employing two micro- turbines at optimal buses 60 and 63 with optimal sizing of 0.4423 and 0.6 MVA, respectively where the total cost of the system is equal to $2.0555M{\$}$ . In addition, the total real power loss is reduced to 0.0628 MW which represents a percentage reduction of 72.08% from the real power loss without any DG unit. The minimum voltage is increased from 0.9092 p.u to 0.9635 upon using two micro-turbines. In addition, Fig. 4 shows that the best voltage profile obtained when two micro-turbines are used.

C. Location and Sizing for Three DG Units

In this case, to prove the superiority of the developed MMFO for finding the optimal location and size of DG, it is applied for three units of DG. The simulation results for locating and sizing three DG units based on developed MMFO in comparison with other published techniques are shown in Tables 5 and 6. Furthermore, the effect of using three DG units on the voltage profile based on proposed MMFO is shown in Fig. 5.

TABLE 5 Results for Using Three DG Units: Part A

TABLE 6 Results for Using Three DG Units: Part B

FIGURE 5.

The effect of using three DG units on voltage profile using the developed MMFO.

The results clearly indicate that the superiority of the proposed MMFO over other methods, where it gives the minimum total cost. The minimum total cost obtained using the proposed MMFO with inserting three micro-turbines at buses 60, 61 and 63 with optimal sizing of 0.6477, 0.3185 and 0.2293 MVA, respectively and the total cost of the system equal to $2.3064~M{\$}$ . By inserting three micro-turbines in the system, the total power loss is decreased to 0.0576 MW which represents a percentage reduction of 74.4 % from the real power loss without any DG unit. While the minimum voltage can be increased from 0.9092 p.u to 0.9666 while using three units of the fuel cell. In addition, Fig. 5 shows that the best voltage profile can be obtained when three units of the fuel cells are used.

D. Discussion

By employing the reduced sorting list of buses based on the BLI method, the computational time can be minimized. In addition, the efficiency of the investigation is improved whereas preserving the equilibrium through exploitative and exploratory.

From the simulation results, the optimal location and sizing of DG’s are different for all cases according to different technologies of DG’s based on the suggested objective function. However, the proposed MMFO technique offering great performance compared with other meta-heuristic optimization techniques. The main benefits of the proposed technique are achieved when using multiple DG units.

The outstanding performance of MMFO proposed is assigned through the locations of multiple DG units with different technologies simultaneously. The verification of the proposed method is achieved by considering the elaborate investigation for the location and sizing of two and three DG units with different technologies.

In case of using one DG with different technologies, the most optimal location bus has been 60 based on the proposed MMFO results with sizing varying between 0.6144 MW to 0.7975 MW.

It is seen that the locations of DGs are sequentially take placed by applying the proposed method for the PV, wind, and micro-turbine where the optimal location bus calculated in case of single DG is repeated in case of two DG units, finally the case of three DG units will contain the buses selected in previous cases.

When using three DG units, the proposed method gives better results in comparison with using one or two DG units referring to the reduction of power loss and voltage deviation. For example, Figures 6 and 7 show the relation between the size (number of DG units), power losses and voltage deviation, respectively when one, two or three micro-turbines are used. These figures indicate that the reduction of power loss is increased from 55.15 % and 72.08 % using one or two micro-turbine units, respectively to 74.4% using three micro-turbine units. Moreover, the voltage deviation is reduced from 1.3666 and 1.1205 using one or two micro-turbine units, respectively to 1.0607 % using three micro-turbine units.

FIGURE 6.

The relation between the size and power losses when one, two or three micro-turbines are used based on MMFO.

FIGURE 7.

The relation between the size and voltage deviation when one, two or three micro-turbines are used based on MMFO.

The multiple locations of DG units might be useful but should be inspected firstly economically as seen from results for different types of DG technology where the increasing number of DG units will increase the total system cost.

To show the convergence property of the developed MMFO in comparison with other methods, Figs. 8 and 9 illustrate the convergence curves of the developed MMFO and other methods in case of using three DG units. From these figures, one can observe that the objective function of the developed MMFO converges smoothly to the optimum solution without any unexpected oscillations which approves the convergence dependability of the developed MMFO. In addition, the developed MMFO needs fewer iterations in comparison with other methods to obtain the solution. This is due to the improved exploration and exploitation mechanism in the developed MMFO.

FIGURE 8.

Comparison between the convergence characteristics of the developed MMFO and other methods in case of use three DG units: Part A.

FIGURE 9.

Comparison between the convergence characteristics of the developed MMFO and other methods in case of use three DG units: Part B.

To further prove the effectiveness of the developed MMFO method over other methods, Figs. 10–​12 show the computational time for the developed MMFO method and other algorithms for one, two, and three DG units, respectively. These results prove that the developed MMFO method is more effective than others when computational time is considered. The computational time of the developed MMFO is quite less and better than other optimization methods in most cases while it is comparable with other optimization methods in a few cases. As a whole, the developed MMFO is computationally efficient than the conventional MFO and other methods as a result of using the improved exploration and exploitation mechanism which accelerates the convergence of the MMFO method.

FIGURE 10.

The computational time of all methods for using one DG unit.

FIGURE 11.

The computational time of all methods for using two DG units.

FIGURE 12.

The computational time of all methods for using three DG units.

SECTION VI. Conclusion

The MMFO algorithm is proposed in this paper to find the optimal location and sizing of DG units based on renewable energy sources to minimize the total operating cost considering four different objective functions. The MMFO is developed to overcome the disadvantages of the conventional MFO, by improving the balance between the exploration and exploitation and speed up the convergence of the algorithm. Also, the total objective function which consists of four different functions is converted to coefficient single objective function. The performance of the developed MMFO algorithm is verified using a standard test system and compared with some meta-heuristic methods to discover its notability based on different scenarios. It can be noticed from the results that the MMFO algorithm provided a better reduction of the objective function for all scenarios over other meta-heuristic methods used in the comparison. The comparisons’ results with other meta-heuristic methods evidently demonstrate that the MMFO algorithm outperformed these meta-heuristic methods whatever the number of DG units.