Energy harvesting maximization by integration of distributed generation based on economic benefits

Indonesian Journal of Electrical Engineering and Computer Science
Vol. 25, No. 2, February 2022, pp. 610~625
ISSN: 2502-4752, DOI: 10.11591/ijeecs.v25.i2.pp610-625  610
Journal homepage: http://ijeecs.iaescore.com
Energy harvesting maximization by integration of distributed
generation based on economic benefits
Tarek A. Boghdady1
, Samar G. A. Nasser2
, Essam El-Din Aboul Zahab1
1
Department of Electrical power Engineering, Faculty of Engineering, Cairo university, Giza, Egypt
2
Department of Electrical Power Engineering, Institute of Aviation Engineering and Technology (I.A.E.T), Giza, Egypt
Article Info ABSTRACT
Article history:
Received Jan 27, 2021
Revised Dec 19, 2021
Accepted Dec 27, 2021
The purpose of distributed generation systems (DGS) is to enhance the
distribution system (DS) performance to be better known with its benefits in
the power sector as installing distributed generation (DG) units into the DS
can introduce economic, environmental and technical benefits. Those
benefits can be obtained if the DG units' site and size is properly determined.
The aim of this paper is studying and reviewing the effect of connecting DG
units in the DS on transmission efficiency, reactive power loss and voltage
deviation in addition to the economical point of view and considering the
interest and inflation rate. Whale optimization algorithm (WOA) is
introduced to find the best solution to the distributed generation penetration
problem in the DS. The result of WOA is compared with the genetic
algorithm (GA), particle swarm optimization (PSO), and grey wolf optimizer
(GWO). The proposed solutions methodologies have been tested using
MATLAB software on IEEE 33 standard bus system.
Keywords:
Distributed generation
Genetic algorithm
Grey wolf optimizer
Particle swarm optimization
Whale optimization algorithm
This is an open access article under the CC BY-SA license.
Corresponding Author:
Tarek A. Boghdady
Department of Electrical Power Engineering, Faculty of Engineering, Cairo University
El Gamma Street, Giza, Egypt
Email: Engtarek82@gmail.com
1. INTRODUCTION
In the last few years, society and electric power system utilities have met numerous economic,
environmental and technical power quality problems associated with power systems. So, with better energy
planning and the use of emerging smart technology, research is now making a great effort to pay attention to
the existing infrastructure. One of the most applicable solutions for improving DS performance is the
optimum allocation of distributed generation (DG) in the distribution system (DS). As the non-optimal
allocation of DG may consequence in an increase in energy loss, lower voltage profile than acceptable
boundaries in addition to high expends [1]. If real active power losses are far higher than the normal values,
DS companies in Egypt are economically penalized. Or, on the other hand, they gain a good profit [2]. Also,
high real active power losses decrease the transmission efficiency to the end user; therefore, its decrease
attracted much more attention from distribution companies [3]. Likewise, decreasing the reactive power loss
is also objective that should be taken into consideration during DG planning. Thus, reducing the reactive
power consumption, diminishing voltage drops and empowering system loadability are one of the most
common objectives [4]. Moreover, it aids active power flow through transmission and distribution (T&D)
lines to the end user [3].
The optimal DG size and site supports in decreasing the resistance losses (𝐼2
𝑅), the reactance losses
(𝐼2
𝑥) and consequently the voltage drop in the two components (IR and IX) in the DS [2]. Many research
objectives in DG planning based on the single objective index (SOI) almost as if it were real power or

Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 
Energy harvesting maximization by integration of distributed generation … (Tarek A. Boghdady)
611
minimizing the energy loss of the DS and not taking note of the merits of the sum of the weighted multi-
objectives index (MOI), such as energy loss minimization, voltage profile enhancement and total cost
reduction of the DS. A new proposed optimization technique is proposed for location and how to size the DG
in DS with a changed loading conditions for minimization of real power loss of the system, is proposed
in [5]-[7]. The MOI of performance for DS with DG, which includes a wide range of electric technical
problems, is proposed in [8]. The optimal MOI sizing and location of multiple DGS in addition to shunt
capacitor banks all together in view of load uncertainty by adjusted particle swarm optimization (PSO)
approach from dissimilar power system performances views, is presented in [9].
A technique on empowering the power system parameters systems by selecting the optimally
located DG in DS is proposed in [10]. States that the effect that was elevated because of the joining of DG
into the present network from different power system performances viewpoints [11]. The objective function
contains voltage profile enhancement and power losses minimization using ant colony algorithm, the
suggested method was confirmed on IEEE 33-bus test system, the results display a significant lessening in
the total power loss and enhanced voltage profiles of all the buses. Correspondingly, allocating of DGS and
optimal penetration of solid state fault current limiters (SSFCLs) have been applied [12]-[13]. It was also
discovered that adding DG units to the DS decreases the reactive and active power loss and enhance the
stability of voltage of the system. PSO has been presented in [14] for penetration of DGS for loss
minimization. Several researches motivated in decreasing the system losses neglecting the costs of losses,
DGS units' connection and its maintenance. Although particular papers [15]-[18] they took these costs into
account, but only concentrated on improving voltage stability without reducing system losses. This paper is
providing a complete review on the effect of connecting DG units in the DS. Comprehensive methodology
using genetic algorithm is proposed and other methods to determine:
− Optimum size DGs and maximization SOI of transmission efficiency.
− Optimum site DGs and maximization SOI of transmission efficiency.
− Allocation of DGs and maximization SOI of transmission efficiency.
− Allocation of DGs and minimization MOI of reactive power loss (Qloss), voltage deviation (VD) and
maximization of transmission efficiency.
− Allocation of DGs and minimization SOI of total cost and maximization of transmission efficiency.
The proposed 33-bus IEEE DS radial algorithms were applied and the results were compared with
other techniques. The backward/forward sweep (BFS) method is used here for lateral radial DS power flow
analysis because it is simple to implement, flexible, fast, and has extreme accuracy [19]-[20]. The rest of this
paper is arranged as follows. Section 2 discusses the problem formulation, while sections 3 present
methodology and 4 present simulation results, finally the paper conclusions explained in section 5.
2. PROBLEM FORMULATION
2.1. Power flow formulation
The BFS algorithm for Figure 1 measures the power flow estimates. Shows the DS segment,
provided that the N line is linked between the two ‘i’ and ‘j’ buses given. Three measures based on the
currents and voltage law of the Kirchhoff are used to evaluate the BFS technique Kirchhoff's current law
(KCL) and Kirchhoff's voltage law (KVL), correspondingly. The three stages are: (a) backward sweep, (b)
forward sweep, and (c) nodal current analysis. Such measures depend on concourse achievements if the
maximum mismatch between voltages is less than the epsilon acceptance provided.
Figure 1. A section of DS
It is easy to estimate the active and reactive power losses for the radial DS after the concourse.
The BFS power flow evaluations are presented as: the flow of active (P_ij) and reactive (Q_ij) powers from
node ‘i’ to node ‘j’ via branch ‘N’ can be obtained from the latest node in (a) backwards sweep path as:

 ISSN: 2502-4752
Indonesian J Elec Eng & Comp Sci, Vol. 25, No. 2, February 2022: 610-625
612
𝑃𝑖𝑗 = 𝑃𝑗
′
+ 𝑅𝑖𝑗
(𝑃𝑗
′2
+𝑄𝑗
′2
)
𝑉𝑗
2 (1)
𝑄𝑖𝑗 = 𝑄𝑗
′
+ 𝑋𝑖𝑗
(𝑃𝑗
′2
+𝑄𝑗
′2
)
𝑉𝑗
2 (2)
where, 𝑃𝑖𝑗
`
= 𝑃𝑗 + 𝑃𝐿𝑗 and 𝑄𝑖𝑗
`
= 𝑄𝑗 + 𝑄𝐿𝑗 . 𝑃𝐿𝑗 and 𝑄𝐿𝑗 are loads that are attached at node ‘j’. 𝑃𝑗 𝑎𝑛𝑑 𝑄𝑗
are the active and reactive power flowing from node ‘j’.
The magnitude and angle of voltage at each node are considered in (b) forward direction. take into
account a voltage 𝑉𝑖∠𝛿i at node ‘i’ and 𝑉𝑗∠𝛿𝑗 at node ‘j’, then the (c) the current flowing through the branch
‘N’ having an impedance, 𝑍𝑖𝑗 = 𝑅𝑖𝑗 + 𝑗𝑋𝑖𝑗 linked between ‘I’ and ‘j’ are given as:
𝐼𝑖𝑗 =
(𝑉𝑗∠𝛿𝑗−𝑉𝑗∠𝛿𝑗 )
𝑅𝑖𝑗 + 𝑗𝑋𝑖𝑗
(3)
𝐼𝑖𝑗 =
(𝑃𝑖−𝑗𝑄𝑖)
𝑉𝑗∠−𝛿𝑗
(4)
hence from (3) and (4) the bus voltage at ‘j’ can be calculated as:
𝑉
𝑗 = [𝑉𝑖
2
− 2 ∗ (𝑃𝑖𝑅𝑖𝑗 + 𝑗𝑄𝑖𝑋𝑖𝑗) + (𝑅𝑖𝑗
2
+ 𝑋𝑖𝑗
2
) ∗
𝑃𝑖
2
+𝑄𝑖
2
𝑉𝑖
2 ]0.5 (5)
the magnitude and phase angle equations can be suggested correspondingly in (b) the forward direction to
find the voltage and angle of all radial DS nodes. It is possible to present the active and reactive power losses
of line ‘N’ between buses ‘i’ and ‘j’ as:
𝑃𝑙𝑜𝑠𝑠(𝑖𝑗) = 𝑅𝑖𝑗
(𝑃𝑖𝑗
2
+𝑄𝑖𝑗
2
)
𝑉𝑖
2 (6)
𝑄𝑙𝑜𝑠𝑠(𝑖𝑗) = 𝑋𝑖𝑗
(𝑃𝑖𝑗
2
+𝑄𝑖𝑗
2
)
𝑉𝑖
2 (7)
the total active power loss of radial DS can be considered as:
𝑃𝑇𝑙𝑜𝑠𝑠 = ∑ 𝑃𝑙𝑜𝑠𝑠(𝑖𝑗)
𝑁
𝑗=1 (8)
where ‘N’ is the number of branches, i=1: n and ‘n’ is the number of buses.
2.2. Power loss estimation in case of existing DGS units
Then the power losses within a line sector in Figure 1 when putting DG units in the DS. It is:
𝑃𝐷𝐺,𝑙𝑜𝑠𝑠(𝑖𝑗) = 𝑅𝑖𝑗
(𝑃𝐷𝐺(𝑖𝑗)
2
+𝑄𝐷𝐺(𝑖𝑗)
2
)
𝑉𝑖
2 (9)
𝑃𝐷𝐺,𝑇𝐿𝑂𝑆𝑆 = ∑ 𝑃𝐷𝐺,𝑙𝑜𝑠𝑠(𝑖𝑗)
𝑁
𝑗=1 (10)
where, 𝑃𝐷𝐺,𝑙𝑜𝑠𝑠(𝑖𝑗) and 𝑄𝐷𝐺,𝑙𝑜𝑠𝑠(𝑖𝑗)is the active and reactive power loss when locating DGS between buses ‘i’
and ‘j’, 𝑃𝐷𝐺,𝑇𝐿𝑂𝑆𝑆 is the total power loss with locating DGS.
2.3. Index of power losses
The total power loss index 𝛥𝑃𝑙𝐷𝐺 is calculated as the division of total power loss with connecting
DGS by the total power loss without connecting DGS and it is presented as:
∆𝑃𝑙𝐷𝐺 =
𝑃𝐷𝐺,𝑇𝐿𝑂𝑆𝑆
𝑃𝑇𝐿𝑂𝑆𝑆
(11)
by minimizing, the total power loss in the system reduced by integration DGS.

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2.4. Voltage deviation index (VDI)
The VDI can be presented as (12).
𝑉𝐷 = max (
𝑉1−𝑉𝑖
𝑉1
), ∀ 𝑖 = 1,2, … … … . , 𝑛 (12)
2.5. DGS cost evaluation
DS companies are mainly responsible for providing the demand of end user. So that, benefits and
costs of DGs site and size in a utility network may be proposed as shown:
− Cost of investment
Investment cost includes DG units cost, investigation fee, DG units installation, preparation of location.
It can be presented as:
𝐶1 = ∑ 𝐾𝐷𝐺𝑖
𝑁𝐷𝐺
𝑖=1 ∗ 𝐼𝐶𝑖 (13)
where, i=1, 2, 3 … NDG, no. of DGS that should be located. K_DGi Is the MW capacity of i DG. IC_i
is the initial cost of i DG in $/MW.
− Cost of operation
DG operating cost is mainly depending on DGs operation to produce power for end users can be
presented as:
𝐶2 = ∑ [𝐾𝐷𝐺𝑖
𝑁𝐷𝐺
𝑖=1 ∗ 𝑂𝐶𝑖] ∗ ∆𝑇 (14)
while, OCi is the cost of operation of i DG in $/MWh of i DG , ∆T is the operating hours during a year.
And if the inflation rate (IF) and the interest rate (IR), so that the present worth value (PWV) can be
signified as:
𝛽𝑡
= ∑𝑛
𝑡=1 (
1+𝐼𝐹
1+𝐼𝑅
)𝑡
(15)
where, 𝛽𝑡
is PWV, n is the planning period in years. PWV of operating cost in planning year can be
considered as:
𝑃𝑊𝑉(𝐶2) = ∑ [𝐾𝐷𝐺𝑖
𝑁𝐷𝐺
𝑖=1 ∗ 𝑂𝐶𝑖] ∗ ∆𝑇 ∗ 𝛽𝑡
(16)
− Maintenance cost
MCDGi Can be calculated as (percentage% of initial cost per year.
2.6. DGS benefits evaluation
− Real power demand decreases from DS network
In an energy efficient power system, transmission grid sold its power to DS company to achieve the
energy request of end users. DS corporation can resource demand of power with existing of DGS, then
obtain lower electrical power from transmission grid. DS company can create a market and sell the
energy to the grid as per agreed contract as shown:
𝐵1 = ∑ 𝐾𝐷𝐺𝑖
𝑁𝐷𝐺
𝑖=1 ∗ 𝐸𝑃𝐺 ∗ ∆𝑇 (17)
while, EPG is the price of electricity in ($/KWh), and ∆T is time segment in which energy is sold to grid.
PWV of the generated electricity from DG by the DS company can be considered as shown:
𝑃𝑊𝑉(𝐵1) = ∑ 𝐾𝐷𝐺𝑖
𝑁𝐷𝐺
𝑖=1 ∗ 𝐸𝑃𝐺 ∗ ∆𝑇 ∗ 𝛽𝑡
(18)
− Loss reduction revenue
Economic benefit is the main target of DS company for maximizing the profit. So, the revenue came
from the loss reduction in the existence of DGs estimated as:
𝐵2 = ∑ ∆ 𝐿𝑂𝑆𝑆𝑖𝑗
𝑁𝐷𝐺
𝑖=1 ∗ 𝐸𝑃𝐺 ∗ ∆𝑇 (19)
∆ LOSSij Is the active power loss reduction, when DGs is sited in the network and EPG is the electricity
price in the grid in $/kWh. The PWV of loss reduction revenue in a planned zone can be calculated as:

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614
𝑃𝑊𝑉(𝐵2) = ∑ ∆ 𝐿𝑂𝑆𝑆𝑖𝑗
𝑁𝐷𝐺
𝑖=1 ∗ 𝐸𝑃𝐺 ∗ ∆𝑇 ∗ 𝛽𝑡
(20)
3. METHODOLGY
It is commonly known that the MOF is mathematically modeled in order to optimize the obtained
benefits of the DG integration into the DS in terms of different indices. These indices importance appears
when planning and operation of DG because of their significant impact on the income of utilities', power
quality, security, environmental effect and system stability [4]. In our review we have two phases, the first
one was maximizing transmission efficiency, minimizing voltage deviation and reactive power loss. The
second phase was a single objective function (SOI) to minimize the total cost. The MOF can be stated as the
weighted sum of the transmission efficiency (TEI) and the voltage deviation index (VDI) and reactive power
loss reduction index (QLI). The weighted summation method is efficient, the development of a strongly non-
dominated solution that can be used as the initial solution for other approaches is simple and feasible [21].
MOF minimization can be stated from (21):
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 (𝑀𝑂𝐹) = 𝑚𝑖𝑛 [𝑊𝑝𝑙𝑃𝐿𝐼 + 𝑊𝑄𝐿 𝑄𝐿𝐼 + 𝑊𝑉𝐷 𝑉𝐷𝐼] (21)
𝑊𝑝𝑙 + 𝑊𝑄𝐿 + 𝑊𝑉𝐷 = 1 (22)
the reactive power loss reduction (WQL), voltage deviation (WVD ). The transmission efficiency are each
assigned with different weighting factors according to their importance.
3.1. Reactive and real power loss indices (𝑸𝑳𝑰, PLI)
In this approach, the benefits can be achieved when lowering the indices values. The reactive and
real power loss indices are well-defined as;
𝑃𝐿𝐼 =
𝑃𝐿𝐷𝐺
𝑃𝐿
(23)
𝑄𝐿𝐼 =
𝑄𝐿𝐷𝐺
𝑄𝐿
(24)
where, QLDG and PLDG are the total reactive and real power losses of the DS after presence of DG. QL and
PL are the total reactive and real losses without existing DG in the DS.
3.2. Voltage deviation index (𝑽𝑫𝑰)
In this approach, the better network performance can be achieved when this index is much lower.
Selecting the proper location of DG improves the voltage profile. This index maybe is used for finding the
DG locations taking into consideration the pre-established voltage deviation limit, and also for ensuring the
rated voltage concerned for each bus within the allowable limits. Where, V1 is the rated voltage
(normallyV1=100%), ‘n’ is the nodes number and Vi is the bus I voltage. The VDI can be estimated:
𝑉𝐷𝐼 = 𝑚𝑎𝑥 (
𝑉1−𝑉𝑖
𝑉1
), ∀ 𝑖 = 1,2, … … … . , 𝑛 (25)
3.3. Maximizing profit (𝐌𝐏)
In a few words, the view point of benefit and cost that have been shown in the previous sections are
worked in a one single objective function (SOF) that is expressed below for maximizing the distribution
company profit taking into consideration the constraints.
max profit = 𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠 − Investments (26)
Min cost = ∑ KDGi
NDG
i=1 ∗ EPG ∗ ∆T ∗ βt
+ ∑ ∆losss ∗ EPG
NDG
i=1 − ∑ KDGi
NDG
i=1 ∗ OCi ∆T ∗ βt
−
∑ [KDGi
NDG
i=1 ∗ ICi ∗ {1MCDG ∗ βt
}] (27)
3.4. Solution methodology for multiple DG connecting
The methodology of connecting for multi DG can be expressed in three stages. The first stage is
identifying the optimal DG location, then the optimal DG size and finally by optimizing the optimal
placement and size.

615
3.4.1. Identifying the optimal DG source’s location
This procedure is repetitive for multiple DGs connecting. The starting base system is reformed by
considering a fixed optimal DG size at the best locations in the DS configuration (DSC) firstly by injecting a
DG unit one-by-one in the DSC. The obtained DG will be located in the system so that developing a new
staring base case with repetitive steps of placing single DG. The best select of DG sizes cannot be the optimal
overall choices. It is reasonably illustrated that the optimal DG (size and placement) is optimum choice at the
time of adding of each DG, but not for the overall complete system. However, the optimum overall global
DG size choices are detected by using algorithms provided that the placement of DGs which are strong-
minded by single algorithms of placing DGs.
3.4.2. Identifying the global optimal DG sources sizes
The common procedure for obtaining the optimal sizing of multi-DG connecting is as follows:
1) Input probable buses that are the best optimal DG locations are given by single placement of DG and
applying genetic algorithm again.
2) In a random way selecting the initial GA population.
3) Applying the power flow for the DSC with the existing of the injected DG at the best optimal location.
4) Assess the needed objective function by the power flow with the existing of the inserted DG from the
GA search.
5) Repeating steps 3, 4 for all groupings populations of GA.
6) Giving values to the objective function as a fitness to GA.
7) Checking the criteria of GA convergence if it's satisfied then goes to step no 9.
8) Generating one a new generation and then go to step no 3.
9) Printing the result for all probable candidate buses.
3.4.3. Optimal sites and sizes of DG using GA
This process is repetitive for multiple locations and sizes of DGs. By using GA, simply we can
obtain both the optimal site and size for the following cases:
a) Consider existing of 1 DG.
b) Consider existing of 2 DG.
c) Consider existing of 3 DG.
4. RESULTS AND DISCUSSION
The test system is the standard 33 bus radial DS network given in Figure 2(a) and Figure 2(b), with
number of thirty -two branches and three laterals. The reactive and real powers of the connected loads for this
network are 2.3 MVAR and3.72 MW respectively. The active and reactive power losses for this radial DS
network without DGs are 201.893 kW and 134.641 kVAR respectively.
(a) (b)
Figure 2. The test system is the standard 33 bus radial DS network: (a) single line diagram of standard IEEE
33 bus DS and (b) magnitude of the node voltage of base case of 33-bus test DS
4.1. Using single objective function of transmission efficiency
4.1.1. Optimum size DGs
Assuming DG location as follows:
a) Existing one DG at bus 6 as it is the longest branch and near to load center.
b) The results as shown in Table 1 are approximately equal between optimization techniques and the
optimal size is 2588 kw at bus 6.
c) Existing two DG at bus 6 and 18 as it is near to load center and the end node of the longest branch.
d) The results as shown in Table 1 show the optimal size to achieve maximum transmission is 2079 kw at

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bus 6 and 462 kw at bus 18.
e) Existing 3DG at bus 6.18, and 33 near to load center, the end node of the longest branch, and second far
end node at the second-largest branch.
f) The results as shown in Table 1 are the optimum size, in this case, obtained by GWO or WOA is
1396 kw at bus 6, 457 kw at bus 18, and 658 kw at bus 33.
Before installing the DG, the voltage profiles of some of the buses in all distribution systems exceed
the required constraint limitations. As a result, after using the genetic algorithm to identify the ideal size DG
as the base technique, the voltage profile of all buses in all systems moved to the suitable range, as shown in
Figure 3(a). After adding DG sources, there is the increase in the system's transmission efficiency. Compared
to single DG placement, the total DG capacity mounted in the device is smaller for multi DG positioning
after putting the optimal DG determined by the genetic algorithm as base technique as shown in Figure 3(b).
Table 1. Global optimum size of DGs for transmission efficiency maximization
CASE
NO.
BASE W/O
DG (kw)
201.893
Techniques
GA PSO WOA GWO
1 DG BUS NO. - 6 6 6 6
DG SIZE (kw) - 2818 2588 2588 2588
Power Loss (kw) - 103.05.00 102.08.00 102.08.00 102.08.00
P LOSS reduction % - 48% 49% 49% 49%
2 DG BUS NO. - 6 18 6 18 6 18 6 18
DG SIZE (kw) - 2856 338 2079 462 2099 456 2099 456
Overall Size (kw) - 3194 2541 2555 2555
Power Loss (kw) - 97 90.08.00 90.08.00 90.08.00
P LOSS reduction % - 52% 55% 55.1% 55.1%
3 DG BUS NO. - 6 18 33 6 18 33 6 18 33 6 18 33
DG SIZE (kw) - 1804 250 617 1510 442 708 1383 459 663 1396 457 658
Overall Size (kw) - 2671 2660 2505 2511
Power Loss (kw) - 81.01.00 78.71 78.33.00 78.32.00
P LOSS reduction% - 59.8% 61% 61.2% 61.2%
(a) (b)
Figure 3. Optimum allocation of DGs: (a) magnitude of the node voltage and (b) transmission efficiency
4.1.2. Optimum site DGs
Assuming DG size from the results as follows in Table 1:
− Existing one DG with size 2588 kw.
− The results are witten in Table 2 are approximately equal between optimization techniques and the
optimal site is bus 6. The loss reduction percentage, in this case, is 49%.
− Existing two DG with size 2079 kw and 462 kw as in WOA.
− The results are shown in Table 2 illustrate the optimal site to achieve maximum transmission at bus 6
and bus 18. The loss reduction percentage, in this case, is 55.6%.
− Existing 3DG for example from different techniques with sizes 1510, 442, and 708 kw as in PSO.
− The results shown in Table 2 are the optimum site at bus 29, bus 16, and bus 25. The loss reduction
percentage, in this case, is 62.4%.
Before installing the DG, the voltage profiles of some buses in the distribution system exceed the
required constraint limitations. As a result, after using the different optimization algorithmes to identify the
optimum site DG for the three cases (1 DG, 2 DG, and 3 DG). The voltage profile of all buses in all systems
moved to the suitable range, as shown in Figure 4(a). There is the increase in the system's transmission

617
efficiency after adding DG sources, when compared to the base case without DG and the single DG
installation. After using the genetic algorithm to select the optimum DG site, as shown in Figure 4(b).
(a)
(b)
Figure 4. Optimum site of DGs: (a) magnitude of the node voltage and (b) transmission efficiency
Table 2. Global optimum site of DGs for transmission efficiency maximization
CASE
NO.
BASE W/O DG
(kw)
201.893
Techniques
GA PSO WOA GWO
IDG DG SIZE (kw) - 2818 2588 2588 2588
BUS NO. - 6 6 6 6
Power Loss (kw) - 103.05.00 102.08.00 102.08.00 102.08.00
P LOSS reduction
%
- 48% 49% 49% 49%
2DG DG SIZE (kw) - 2856 338 2079 462 2079 462 2079 462
BUS NO. - 6 16 26 15 6 15 7 15
Overall Size (kw) - 3194 3541 2541 2541
Power Loss (kw) - 96.07.00 89.07.00 89.06.00 91.02.00
P LOSS reduction
%
- 51.9% 55.5% 55.6% 54.8%
3DG DG SIZE (kw) - 1804 250 617 1510 442 708 459 663 1383 1396 457 658
BUS NO. - 6 17 31 29 16 25 14 25 30 7 15 31
Overall Size (kw) - 2671 2660 2505 2511
Power Loss (kw) - 80.34.00 75.94 75.34.00 76.05.00
P LOSS reduction
%
- 60.2% 62.4% 62.3% 62%
4.1.3. Optimum allocation of DGs
This section looks at the problem for one, two, and three DGs existing. The different techniques
determine the appropriate position of the DG unit, in addition to its size. But the previous sections determine
the size only or position of the units. The results of this section are summarized in Table 3. The voltage
profile of all buses is enhanced and is within the acceptable range in all three cases (after inserting the
optimum location and capacity of the one, two, and three DG units) as shown in Figure 5(a). It illustrates that
the better voltage profile, the greater the number of DG units. The increasing in the system's transmission
efficiency after adding DG sources is shown in Figure 5(b).

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Table 3. Global Optimum allocation of DGs for transmission efficiency maximization
CASE
NO.
BASE W/O
DG (kw)
201.893
Techniques
GA PSO WOA GWO
I DG DG SIZE (kw) - 2588 2455 2588 2588
BUS NO. - 6 26 6 6
Power Loss
(KW)
- 102.08 104.03 102.08 102.08
P LOSS
reduction %
- 49% 48.3% 49% 49%
2DG DG SIZE (kw) - 1192 850 850 1192 850 1192 1000 1126
BUS NO. - 13 30 13 30 14 30 12 30
Overall Size
(kw)
- 2042 2042 2042 2126
Power Loss
(KW)
- 82.09 82.09.00 83 83.02.00
P LOSS
reduction %
- 59% 59% 58.9% 58.8%
3DG DG SIZE (kw) - 725 1070 1119 759 1071 1100 759 1071 1100 1383 1000 1000
BUS NO. - 14 24 30 14 24 30 15 24 31 3 12 30
Overall Size
(kw)
- 2914
293
0
2930 3383
Power Loss
(KW)
- 69.04 69.4 71.03 76.06
P LOSS
reduction %
-
65.6
%
56.6
%
64.8% 62%
(a)
(b)
Figure 5. Global optimum allocation of DGs: (a) magnitude of the node voltage and
(b) transmission efficiency
4.2. Optimum allocation of DGs and minimization of total cost as SOI
The total cost can be minimized by selecting the optimum allocation of DGs taking into
consideration the interest and inflation rate, thus we can extract the maximum profit, and certain assumptions
are considered. The effect of DG placement and capacity in a 33-bus test system was demonstrated in Table 4
as a result of the simulation. The price list of DG units from generator joe company, the cost of service and
maintenance are shown in Table 5, and the benefit earned during the planning period. For serval study
duration, optimum positioning and size are carried out with DG. Table 4 presents the financial and technical
benefits and profits of DG size and placement, based on the results of simulation by the proposed GA as base
algorithm compared with other techniques of algorithms, and presents the best Global optimal location and
size of DG sources for minimizing total cost in case of injecting three DGs with overall capacity 600 kw only
at bus bar (15, 18, 32), the profit 1.5508*10^6 $ and the loss reduction percentage 52.9% taking into
consideration interest and inflation rates. In the case of injecting two DGs with an overall capacity of 400
KW only at the bus bar (32, 17), the profit 0.92471*10^6 $ and the loss reduction percentage 23%. In the

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case of injecting one DG with an overall capacity of 200 kw only at the bus bar (17), the profit 0.88717*10^6
$ and the loss reduction percentage 12.5%.
The voltage profile is shown in Figure 6(a) as an obtained by genetic algorithm and this is the worst
solution technique for optimum allocation of DGs for minimizing total cost as SOI. The values of voltage
profile at some buses in the non-acceptable range. The Transmission efficiency of this case is shown in
Figure 6(b). The transmission efficiency is not sufficiently improved like in previous cases, in addition to the
economic profit was higher because this is from the economic point of view.
Table 4. Global optimum allocation of DGs for minimizing total cost
CASE
NO.
BASE W/O DG
(kw)
201.893
Techniques
GA PSO WOA GWO
I DG DG SIZE (kw) - 200 200 200 200
BUS NO. - 33 17 17 17
Power Loss (KW) - 178.07 176.06 176.06 176.06
P LOSS reduction % - 11.5% 12.5% 12.5% 12.5%
Profit*10^6 - 0,613194444 0,615972222 0,615972222 0,615972222
2 DG DG SIZE (kw) - 200 200 200 200 200 200 200 200
BUS NO. - 17 15 17 32 17 33 32 17
Power Loss (KW) - 167.05 155.02 155.03 155.02
P LOSS reduction % - 17% 23.2% 23.1% 23.2%
Profit*10^6 0.90324 0.92471 0.92466 0.92471
3 DG DG SIZE (kw) - 200 200 200 200 200 200 200 200 200 200 200 200
BUS NO. - 7 20 29 14 17 32 15 18 32 14 17 32
Power Loss (KW) - 164.09 137.06 95.02 137.06
P LOSS reduction % - 18.3% 31.9% 52.9% 31.9%
Profit*10^6 - 14.294 14.770 15.508 14.770
(a)
(b)
Figure 6. Optimum allocation of DGs for minimizing total cost: (a) magnitude of the node voltage and
(b) transmission efficency
Table 5. The sample of price list of DG units from generator joe company
Diesel
generators
list price of
Generator
joe co,
Sets 60 HZ 200 KW 210 KW 250 KW 275 KW 280 KW 300 KW 350 KW 400 KW 450 KW
investment
cost ($)
46,705.6 51,823.6 53,673.9 57,902.5 54,310.7 61,708.1 65,791.3 68,253.2 76,978.8
fuel cost 5g/hr-
13.4
15.5 g/h 18.5 g/h 19.5 g/h 19.5 g/h 23 g/h 23 g/h 25.8 g/h 29.9 g/h
40.2$/h 46.5$/h 55.5 $/h 58.5 $/h 58.5$/h 69 $/h 69 $/h 77.4 $/h 89.7 $/h
4.2. Optimum allocation of DGs and minimization MOI of reactive power loss (Qloss), voltage
deviation (VD) and maximization of transmission efficiency
It is presented as a case study in the first and then changed the weights, which the reactive power
loss reduction, voltage deviation, and the transmission efficiency. Each index is assigned with different
weighting factors according to their importance to get the best global performance index:

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620
a) Case study
From the utility point of view, is enhancing transmission efficiency to deliver energy to end-users
with high transmission efficiency and high power quality. So, assume the weight factors to be W1=0.5,
W2=0.25, and W3=0.25 from (21), (22). When changed the weights in this case study as according to some
ref [22]-[25] with optimum size and site of DGs for existence one, two, and three DGs, the results are
summarized in Table 6. The voltage profile of all buses is enhanced and is within the acceptable range in
three cases as shown in Figure 7(a). The transmission efficiency of optimum allocation of DGs for
minimizing MOI is shown in Figure 7(b).
Table 6. Global optimum allocation of DGs for minimizing MOI
CASE
NO.
BASE W/O
DG (kw)
201.893
Techniques
GA PSO WOA GWO
I DG BUS NO. - 6 6 6 6
DG SIZE
(kw)
- 2959 2952 2952 2952
Power Loss
(KW)
- 104.07 104.06 104.06 104.06
P LOSS
reduction%
- 48% 48.2% 48.2% 48.2%
2DG BUS NO. - 13 30 30 13 13 31 6 15
DG SIZE
(kw)
- 991 1203 1270 957 957 1270 2266 563
Overall Size
(kw)
- 2221 2227 2227 2829
Power Loss
(KW)
- 83.08 38.83 86.67 90.01
P LOSS
reduction %
- 58% 58.5% 57% 55.4%
3DG BUS NO. - 14 24 30 30 14 24 25 15 31 30 4 14
DG SIZE
(kw)
- 852 1066 1192 1113 794 1050 1084 852 1188 1070 1112 901
Overall Size
(kw)
- 3110 2957 3124 3083
Power Loss
(KW)
- 70.03 69.05 74.07 77.05
P LOSS
reduction %
- 65% 65.6% 63% 61.6%
(a)
(b)
Figure 7. Optimum allocation of DGs for minimizing MOI: (a) magnitude of the node voltage and
(b) transmission efficiency
b) Changing the weight factors by parito method to achieve the best MOI
− Allocation by (constant weight of transmission efficiency equal to 0.1) and changing other weights from
0.1 to 0.8 So that it is equal to 1. The best case that appeared when W1=0.1, W2=0.1, and W3=0.8,

621
when allocated DGs for minimizing MOI by using this weights factor. So, the voltages profile is
dominant. The end node voltage is improved and arrived at 1pu approximately because of the largest
weight comparing to another weight as shown in Figure 8(a). The transmission efficiency of optimum
allocation of DGs for minimizing MOI taking into consideration voltage profile is shown in Figure 8(b).
When changed the weights of this case study as according to the largest problem in the grid (VD) with
optimum size and site of DGs for existence one, two, and three DGs, the results are summarized in
Table 7.
(a)
(b)
Figure 8. Optimum allocation of DGs for minimizing MOI taking into consideration voltage profile:
(a) magnitude of the node voltage and (b) transmission efficiency
Table 7. Global optimum allocation of DGs sources for minimizing MOI taking into consideration
voltage profile
CASE
NO.
BASE W/O
DG (kw)
201.
893
Techniques
GA PSO WOA GWO
I DG BUS NO. - 6 6 6 26
DG SIZE
(kw)
- 4047 4222 4222 4061
Power Loss
(KW)
- 130.07 137.06 137.06 104.09
P LOSS
reduction %
- 35.3% 31.8% 31.8% 30.2%
2DG BUS NO. - 13 30 6 14 13 31 30 14
DG SIZE
(kw)
- 991 1203 1270 957 957 1270 2266
56
3
Overall Size
(kw)
- 2761 3683 2761 2772
Power Loss
(KW)
- 95.05 106.02 101.09 96.09
P LOSS
reduction %
- 52.7% 47.4% 49.5% 51.9%
3DG BUS NO. - 13 24 30 31 14 6 4 31 13 2 16 6
DG SIZE
(kw)
- 1079 1187 1481 962 824 1480 2061 1399 1030 3608 492
31
81
Overall Size
(kw)
- 3747 3266 4490 7281
Power Loss
(KW)
- 81.72 85.98 102.6 113
P LOSS
reduction %
- 59.5% 57.4% 49% 44%
− Allocation by (constant weight of reactive power loss equal to 0.1) and changing other weights from 0.1
to 0.8 so that it is equal to 1. The best case that appeared when W1=0.8, W2=0.1, and W3=0.1, When

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622
made the penetration DG for minimizing MOI by using this weights factor. So, transmission efficiency
is dominant because of the largest weight comparing to another weight. When changed the weights of
this case as according to the largest problem (PL) in the grid with optimum size and site of DGs for
existence one, two, and three DGs, the results are summarized in Table 8. The voltage profile of all
buses is enhanced and is within the acceptable range in three cases as shown in Figure 9(a). The
transmission efficiency of optimum allocation of DGs for minimizing MOI is shown in Figure 9(b).
(a)
(b)
Figure 9. Optimum allocation of DGs for minimizing MOI taking into consideration maximizing
transmission efficiency: (a) magnitude of the node voltage and (b) transmission efficiency
Table 8. Global optimum allocation of DGs for minimizing MOI
CASE
NO.
BASE W/O
DG (kw)
201.893
Techniques
GA PSO WOA GWO
I DG BUS NO. - 6 6 6 6
DG SIZE
(kw)
- 2707 2723 2723 2723
Power Loss
(KW)
- 102.09 103 103 103
P LOSS
reduction %
- 49% 48.9% 48.9% 48.9%
2DG BUS NO. - 13 30 30 13 13 30 27 14
DG SIZE
(kw)
- 893 1222 1222 893 893 1222 1823 638
Overall
Size (kw)
- 2115 2115 2115 2461
Power Loss
(KW)
- 83.01.00 83.01 83.01 88.03
P LOSS
reduction %
- 58.9% 58.9% 58.9% 56.3%
3DG BUS NO. - 14 24 30 14 30 3 14 25 30 14 30 25
DG SIZE
(kw)
- 797 1000 1124 770 1083 1626 797 1075 1134 911 1071 464
Overall
Size (kw)
- 2921 3479 3006 2446
Power Loss
(KW)
- 69.52 75.06 70.85 73.03
P LOSS
reduction %
- 65.6% 62.8% 64.9% 63.7%
− Allocation by (Constant weight of voltage deviation equal to 0.1) and changing other weights from 0.1
to 0.8 so that it is equal to 1. The best case that appeared when W1=0.1, W2=0.8, and W3=0.1, When
made the penetration DG for minimizing MOI by using this weights factor. So, reactive power loss is
the dominant because of the largest weight comparing to other weights. The voltage profile of all buses
is enhanced and is within the acceptable range in three cases as shown in Figure 10(a). The transmission

623
efficiency of optimum allocation of DGs for minimizing MOI is shown in Figure 10(b). When changed
the weights of this case as according to the largest problem (QL) in the grid with optimum size and site
of DGs for existence one, two, and three DGs, the results are summarized in Table 9.
Table 9. Global optimum allocation of DGs for minimizing MOI taking into consideration reactive power
CASE
NO.
BASE W/O
DG (kw)
201.89
3
Techniques
GA PSO WOA GWO
I DG BUS NO. - 6 6 6 6
DG SIZE (kw) - 2710 2676 2676 2675
Power Loss
(KW)
- 102.09 102.08 102.08 102.08
P LOSS
reduction %
- 48.9% 49% 49% 49%
2DG BUS NO. - 13 30 30 13 13 30 6 3
DG SIZE (kw) - 991 1170 1070 900 900 1170 2469 1627
Overall Size
(kw)
- 2070 1970 2070 4096
Power Loss
(KW)
- 82.09 38.03 82.09 100.09
P LOSS
reduction %
- 58.9% 58.7% 58.9% 50%
3DG BUS NO. - 13 24 30 13 30 24 32 7 15 12 3 6
DG SIZE (kw) - 852 1041 1090 852 1090 1041 730 1128 666 1222 915 1233
Overall Size
(kw)
- 2983 2983 2524 3370
Power Loss
(KW)
- 69.65 69.65 76.35 92.96
P LOSS
reduction %
- 65.5% 65.5%
62.2
%
53.9%
(a)
(b)
Figure 10. Optimum placement and size for minimizing MOI taking into consideration reactive power:
(a) magnitude of the node voltage and (b) transmission efficiency
5. CONCLUSION
This paper has introduced an intensive review for obtaining the optimal DG Site, Size and
Penetration between them for single and multiple DGs to fulfill economic, environmental and technical
benefits using single and Multi objective indices based on a comparison between the best performance
existed by GA, PSO, GWO, and WOP algorithms. The proposed algorithm techniques were tested on 33-bus
radial DS and the results can be summarized as presented.
By Allocating DG units at the optimal location the system loadability is enhanced. The voltage
profile is enhanced at all nodes in which DG units are best located while compared to the case that no

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624
allocation for DG units. While increasing the DGs penetration level, at a Particular point the increasing in
reduction of losses is not much noticeable when compared to the cost increase due to this highly penetration
level. The GWO has presented the best Global optimal location and size of DG sources for minimizing total
cost in case of injecting three DGs taking into consideration interest and inflation rates.
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BIOGRAPHIES OF AUTHORS
Tarek A. Boghdady received the B. S., M. S and Ph. D degrees in electrical
power engineering from the faculty of engineering Cairo University, in 2004, 2010 and 2016.
From 2004 to 2016, he was a teaching assistant in electrical power engineering department in
the same university. Since 2016, he has been an assistant professor in the electrical power
engineering department, Cairo University. He is an author and supervisor of more than thirty
scientific papers. His research interests include wind energy, optimization, power quality,
neural network, fuzzy control, solar energy, sliding mode control, HVDC, and Harmonics. He
can be contacted at email: Engtarek82@gmail.com.
Samar G. A. Nasser received her B. S. degree from Institute of aviation
engineering and technology (I.A.E.T), Giza, Egypt, in 2016. After graduation, she worked
four years as a teaching assistant at I.A.E.T from 2016 to 2020. She is currently working
towards the M. S. degree at the department of electrical power engineering at the faculty of
engineering, Cairo University, Giza, Egypt. She can be contacted at email:
eng_samar_gamal@yahoo.com.
Essam El-Din Aboul Zahab received the B. S., M. S degree in electrical
engineering from Cairo University, faculty of engineering in 1970, 1974 and the Ph. D.
degree in electrical engineering from Paul Sabatier University, France, in 1979. He is
promoted in the academic degrees starting from teaching assistant till being professor
emeritus in electri cal engineering at Cairo University. He is an author and supervisor of
hundreds scientific papers. His research interest switch gear and protection, electrical
distribution system, illumination engineering and electrical power systems. He can be
contacted at email: Zahab0@yahoo.com.

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