Efficient optimization technique for multiple DG allocation in distribution networks

Journal Pre-proof Efficient optimization technique for multiple DG allocation in distribution networks Ali Selim, Salah Kamel, Francisco Jurado

PII: DOI: Reference:

S1568-4946(19)30719-7 https://doi.org/10.1016/j.asoc.2019.105938 ASOC 105938

To appear in:

Applied Soft Computing Journal

Received date : 20 October 2018 Revised date : 15 September 2019 Accepted date : 11 November 2019 Please cite this article as: A. Selim, S. Kamel and F. Jurado, Efficient optimization technique for multiple DG allocation in distribution networks, Applied Soft Computing Journal (2019), doi: https://doi.org/10.1016/j.asoc.2019.105938. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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*Highlights (for review)

Journal Pre-proof Highlights

Integration of distributed generators into distribution networks Efficient optimization for allocation of multiple distributed generators

Stranded IEEE radial distribution feeders

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Sine cosine algorithm and chaos map theory

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The result shows that the proposed optimization technique is efficient

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Author’s name (Fist, Last)

1. Ali Selim

Date

______July 8, 2019_______

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2. _Salah Kamel_________ July 8, 2019_______

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3. Francisco Jurado_______ July 8, 2019_______

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Efficient Optimization Technique for Multiple DG Allocation in Distribution Networks

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Ali Selim1, Salah Kamel2,3, and Francisco Jurado1, 1

Department of Electrical Engineering, University of Jaén, 23700 EPS Linares, Jaén, Spain

2

Department of Electrical Engineering, Faculty of Engineering, Aswan University, 81542 Aswan, Egypt 3

State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing, China 400030

Abstract

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In the last few decades, interest in the integration of distributed generators (DGs) into distribution networks has been increased due to their benefits such as enhance power system reliability, reduce the power losses and improve the voltage profile. These benefits can be increased by determining the optimal DGs allocation (location and size) into distribution networks. This paper

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proposes an efficient optimization technique to optimally allocate the multiple DG units in distribution networks. This technique is based on Sine Cosine Algorithm (SCA) and chaos map theory. As any random search-based optimization algorithm, SCA faces some issues such as low convergence rate and trapping in local solutions during the exploration and exploitation phases.

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This issue can be addressed by developing Chaotic SCA (CSCA). CSCA is mainly based on the iterative chaotic map which used to change the random parameters of SCA instead of using the random probability distribution. The iterative chaotic map is applied for single and multiobjective SCA. The proposed technique is validated using the two stranded IEEE radial distribution feeders; 33 and 69-nodes. Comprehensive comparison among the proposed technique, the original SCA, and other competitive optimization techniques are carried out to

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prove the effectiveness of CSCA. Finally, a complete study is performed to address the impact of the intermittent nature of renewable energy resource on the distribution system. Hence, typical loads and generation (represented in PV power) profiles are applied. The result proves that the proposed CSCA is more efficient to solve the optimal multiple DGs allocation with minimum power loss and high convergence rate. *Corresponding author, Tel.: +34 953 648518; Fax: +34 953 648586. E-mail addresses: [email protected] (F. Jurado), [email protected] Kamel).

(A. Selim), [email protected] (S.

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Keywords: Distributed generations, optimal allocation, power loss minimization, Sine Cosine

Nomenclature Symbols Parameters of the Beta PDF at time Solar irradiance

s

Mean and standard deviation

,

Number of PV modules Voltage and current at the maximum power point Open-circuit voltage, the short circuit current Cell voltage and current

,

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,

, ,

,

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,

Voltage and current temperature coefficient Cell, ambient temperature Operating temperature Daily charging and discharging energies at bus Total output energies of the PV+BES The quantity of PV energy transporting to the grid at bus Efficiencies of roundtrip, discharging and charging Capacity factor Counter Current at bus Apparent power at bus

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,

,

z

Maximum number of iterations Normalized value of the nondonated solution of the objective function Maximum and minimum of the objective function Grey relation coefficient

,

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The hourly average output power Output power of the PV module

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Algorithm, Chaos theory.

Voltage at bus Resistance between bus Reactance between bus Refer to branches ID Branch current

Minimum and maximum values of the

Distinguishing coefficient Grey relation grad Mean of all

Acronyms DGs PV

Distributed Generators Photovoltaic

BES LSF PSI

Battery Energy Storage Loss sensitivity factor Power stability index

VSI

voltage stability index

GA

Genetic Algorithm

DE

Differential Evolution

PSO ABC HS BSOA

Particle Swarm Optimization Artificial bee colony Harmony search Backtracking search optimization algorithm Stud Krill herd Algorithm Whale optimization algorithm Sine Cosine Algorithm Simulated annealing Grey Wolf Optimizer

SKHA WOA SCA SA GWO

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Set of lines connected to branch z Refers to function Active power loss

FA KHA BOA

Total number of the branches Position of individual at iteration Random values

CSCA MOSCA

Destination position. Constant number Chaotic map variable Lower and upper limits Benchmarks function.

MOCSCA VD VSI PDF LR STD

Introduction

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1

Firefly Algorithm Krill-Herd Algorithm Butterfly Optimization Algorithm Chaotic Sine Cosine Algorithm Multi-objective Sine Cosine Algorithm Multi-objective Chaotic Sine Cosine Algorithm Voltage deviation Voltage stability index Probability distribution functions Loss reduction Standard deviation

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M

During the last decades, the structure of the traditional distribution network has been modified by

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integrating the distributed generators (DGs). In practical, most distribution networks have a radial configuration, where the power flows from the distribution substation to the load in unidirectional flow. However, the integration of distribution networks with small, medium, and large DGs sizes

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convert their passive structure to be an active distribution system with multi-directional powers flow. The integration of DGs into distribution network leads to reduce power losses, enhance voltage profile, and increase the reliability [1]. On the other hand, uncoordinated DGs integration could bring some technical issues if they are not suitably planned, controlled, and operated such as over-voltage, fluctuation, and system

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unbalance [2]. In addition, the injected DGs power may lead to an increase in the active and reactive power losses in the distribution network. Hence, numerous efforts have been made in the last few years to address the optimal DG allocation problem. Moreover, many research works have been concentrated on sizing the DG units at snapshots load demand and generated power. Consequently, many factors have been disregarded particularly when integrating DG units which depend on renewable energy resources, such as wind power and

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photovoltaic (PV). These renewable energy resources have intermittent nature where the generation levels of this kind of distributed generation are variable. Thereby, power losses and

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voltage level issues become a matter of concern in the case of load and generation variation. A few researchers have considered the time-varying of the load demand and the uncertainty of the DG power generation [3-6].

To overcome the intermittent nature of DGs units such as PV, a power curtailment and Battery Energy Storage (BES) has been applied in [7, 8]. However, BES is considered more efficient than the power curtailment due to its availability to charge or discharge the required energy during the

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demand and generation variation. To increase the benefits of the BES in the distribution system, it is important to determine its optimal size and location. Many algorithms for calculating the

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optimal size and location of BES have been developed [9-11]. As mentioned earlier, several optimization techniques have been developed to determine the optimal DG allocation into distribution networks in both single and multi-objective algorithms.

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These techniques can be classified as; analytical techniques, heuristic techniques, and hybrid techniques based on both of them [12].

In analytical techniques, a mathematical formulation for the distribution networks is fully expressed to investigate the effect of the DG injected power on the system performance based on the objective function. In this regard, many indices have been developed using derivative

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equations [13]. Loss sensitivity factor (LSF) is one of the most common indices that has been used in the analytical technique to obtain the optimal DG allocation into the distribution network. LSF is used to find the most sensitive bus in the system subject to the change in the active or reactive power [14]. In addition, the power stability index (PSI) and voltage stability index (VSI) have been proposed to allocate DG in the distribution network. These two stability indices have been used to detect the most sensitive buses which could cause instability with increasing the load

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in the system [15]. However, some of the analytical techniques are not suitable to find the optimal size and location of multiple DGs due to their dependency on the topology of the system. Also,

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many of these techniques use the exact loss formula which requires to construct Zbus matrix [13]. In consequence, many researchers have turned towards using metaheuristic-based optimization techniques due to their ability to solve the optimization problem without going so far in the details of the problem. In the last few years, numerous heuristic optimization algorithms have been established and applied to solve the optimal DG allocation problem. These algorithms can be classified as the nature of its inspiration such as evolutionary phenomena which utilizes

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exploration and exploitation phases to find the optimal local solution from different global solutions to corporate behavior of creatures (swarm techniques), physical rules, and human-

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related concepts. Some of the evolutionary phenomena algorithms have been used to determine the optimal size and location of DG units such as Genetic Algorithm (GA) [16, 17], Differential Evolution (DE) [18, 19], Particle Swarm Optimization (PSO) technique[20], Artificial bee colony

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(ABC) [21], Harmony search (HS) [22], backtracking search optimization algorithm (BSOA) [23], Stud Krill herd Algorithm (SKHA) [24], and Whale optimization algorithm (WOA) [25]. In [26], a new Sine Cosine Algorithm (SCA) has been proposed. In this technique, a set of agents are randomly initialized then the mathematical formulations of the sine and cosine are used to update the initial positions by oscillating far or close to the best solution. The SCA has been used

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in the optimal power flow problem in [27]. The heuristic optimization techniques proved their effectiveness and feasibility in allocating the DG units into the distribution networks. However, there are some problems associated with using the heuristic optimization techniques due to the random initialization of the search agents such as low convergence rate and falling in a local solution.

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Various techniques have been proposed to enhance the performance of heuristic optimization techniques such as a hybridization approach such as hybrid WOA with simulated annealing (SA)

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[28], WOA with Grey Wolf Optimizer (GWO) [29], GA and PSO [30]. SCA has been used to improve other metaheuristic optimization like GWO-SCA [31], SCA with DE [32], and WOASCA[33], In addition, a hybrid between the analytical techniques and heuristic techniques have been developed in [12], and VSI with SCA in [34].

Newly, the Chaotic theory has been widely used for enhancing the performance of the metaheuristic optimization algorithms. The main idea behind using chaotic theory in

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metaheuristic optimization algorithms that the chaotic can generate a chaotic variable instead of the random initial variables [35]. The performance of GA, HS, ABC, FA, KHA, BOA, and GWO

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have been improved using different chaotic maps [36].

The main contribution of this paper is to develop an efficient optimization algorithm for optimally allocating the multiple DG units into distribution networks based on single and multi-

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objective functions. The proposed CSCA is based on the chaotic map to minimize the total active power loss and improve the voltage profile. The proposed CSCA utilizes the iterative chaos map to change the original SCA parameters rather than using the random probability. The proposed approach aims to enhance the overall SCA performance in the exploration and exploitation phases. For the single-objective algorithm, the proposed CSCA is used to minimize the total

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power loss in the distribution system. However, Multi-objective CSCA (MOCSCA) is applied to minimize the power loss, voltage deviation (VD), and maximize the voltage stability index (VSI). The performance of the proposed algorithms has been validated and tested using the standard IEEE test distribution systems and compared with other well-known optimization techniques. Finally, the problem of sitting and sizing distributed generation is addressed considering the PV generation typical profiles with the load profiles of the distribution network consumers.

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The rest of the paper is arranged as follows. Section 2 presents the uncertainty modeling of PV power, Section 3 shows the PV and BES modeling. Section 4 provides the mathematical

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formulation for the objective functions, the SCA, and the chaotic theory. Section 5 describes the proposed CSCA. Section 6 presents the optimal allocation of DGs using CSCA. Section 7 describes the implementation of MOCSCA for allocation of DG. Section 8 discusses various studied cases and numerical results. Finally, the conclusions are presented in Section 9.

2

Modeling of PV Power Generation

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A probability distribution functions (PDF) is used to demonstrate the stochastic behavior of the PV [3, 37]. To generate a typical day for a PV power generation, Beta PDF is applied to the

Solar irradiance model

At each

hour of the normal day, Beta PDF is utilized to characterize the probabilistic nature of

solar irradiance

and

are the parameters of the Beta PDF which are estimated with the mean

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where,

(kW/m2) as follows:

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2.1

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accumulated historical data of solar irradiance at the period as follows:

the standard deviation

(1)

and

of the solar irradiance at time as: (2)

(3)

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2.2

PV Power Generation

To estimate the PV power generation, the continuous PDF at specific time hour

time segment

where,

can be calculated as follows:

(4)

is the output power of the PV module and it can be expressed as [3]:

is the number of PV modules,

maximum power point, respectively,

and

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where,

(5)

are the voltage and current at the

is the open-circuit voltage,

is the short circuit current,

are the cell voltage and current, respectively, which can be calculated using the following

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,

array corresponds to a specific

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divided into many states. The hourly average output power

has been

where,

,

respectively,

(6)

(7)

are the voltage and current temperature coefficient (V/⁰ C), (A/⁰ C)

is the cell temperature ⁰ C which can be determined using the ambient and the nominal operating temperature

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temperature

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equations:

In this work, the solar irradiance data for

as follows: (8)

and

during three years are given in [5].

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3

Modeling of PV and BES

BES is used to maintain the PV power at the required power generation by converting the PV

and discharging

Therefore, the total output energies

energies at bus are obtained as:

of the PV+BES and

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Hence the daily charging

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power from non-dispatchable to dispatchable over the day using the charging/discharging BES.

(9)

(10)

of the PV generation unit

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at bus in case of BES discharging and charging can be calculated as:

where,

(11)

(12)

is the quantity of PV energy transporting to the grid at bus . The charging and

expressed as:

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discharging energies of the BES unit at bus

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Using (11) to (12), the

with a roundtrip efficiency (

=

) is

(13)

of the PV generation unit is calculated as: (14)

To find the maximum PV unit output power at bus , a capacity factor for the module unit can be used as follows: (15)

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where, (16)

over a 24-hr day. Consequently, the

can be calculated using the following equation:

Problem formulation

(17)

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4

is the amount of PV generated energy

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is the maximum output of a PV module unit, and

Integration of DGs in the distribution networks has excessive impacts on system performance. These impacts are completely observed using power flow calculation. Several methods have been

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introduced to solve the power flow problem in power systems. Forward/ backward load flow considers the most efficient power flow method used in the radial distribution systems. 4.1

Forward/backward power flow method

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Forward/backward power flow method is mainly based on Kirchhoff’s voltage and current laws. The simple equivalent circuit for the radial distribution network is shown in Fig. 1. The Forward/backward power flow algorithm for this system can be achieved by applying the

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following steps [38]:

Fig. 1 Equivalent circuit for radial distribution network

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Step 1: Calculate the load currents in the phasor format each bus i based on the active and reactive powers and the initial buses voltage as:

Where, ,

, and

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(18)

are current, voltage, and apparent power respectively at bus i.

Step 2 (backward step): Calculate the total branch currents

starting from sub-lines P

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moving to the main feeder at node #1 as given in (2).

(19)

Step 3 (forward step): Update the buses voltage starting from the main feeder node #1 toward

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the last node n in the system as follows:

Objective function

(20)

Many objective functions are used to optimally allocate the DG into the distribution system, in

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this work, the following three main objective functions are considered: 4.2.1 Total power loss:

The main objective of optimal DG allocation into the distribution networks is considered to :

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minimize the total power losses

(21)

where the power loss in each branch is calculated as:

where,

(22)

is the magnitude value of branch current.

The total power losses in the distribution network can be calculated by summation the power losses of all branches

in the system as follows:

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(23)

for distribution system can be calculated using the voltage at bus

specified voltage

where,

as:

is taken 1.00 p.u.

based on a

(24)

(25)

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4.2.3 Voltage stability index (VSI)

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The total

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4.2.2 Total voltage deviation (VD)

Voltage stability considered one of the most significant indices used to indicate the intensity of the system to withstand abnormal conditions. Hence, it is required to maximize the minimum

4.3

SCA

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VSI. The voltage stability index (VSI) for each branch ik can be described as follows: (26) (27)

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SCA considers a new metaheuristic algorithm that has been presented for the first time in [26]. The main idea behind this technique is to use the sine and cosine functions to find the optimal global solution. In the SCA, a set of individual solutions are randomly distributed then the fitness function for each individual solution is calculated. Then, the updating equation for the incoming solutions can be computed as follows:

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(28) (29)

is the current position of

values,

is the goal position.

dimension at

iteration and

are random

pro of

where,

The circular characteristic of sine and cosine functions as provides the possibility for the individual solutions to update their positions in the circumference of another solution as shown in Fig. 2.a, in this way, the exploitation phase can be easily accomplished. On the other hand, in the exploration phase, the area of the search space can be chosen to formulate the boundary of the

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sine and cosine functions to move in the direction of the local optima or move out as seen in Fig. 2.b. 1

0.6

-0.2 -0.2

0.20

0.2

0.6

1

0.00 -0.20

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-0.6

-0.6

-0.60

-1

-1.00

1

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π 1.00

3π/2 1.50

2π 2.00

Sine cosine functions Sine Cosine

out

0.60

0.2

-0.6

a)

π/2 0.50

1.00

0.6

-1

Sine Cosine

0.60

0.2 -1

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1.00

0.2

0.20 0.6

1

0.00 -0.20

in

π/2 0.50

π 1.00

out

-0.6

-0.60

-1

-1.00

out

b) Sine cosine with a search space area Fig. 2 Sine cosine circular characteristics

3π/2 1.50

2π 2.00

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Equations (28) and (29) can be combined to evaluate the updated position in one equation where the switching between sine and cosine function is achieved by involving new parameter as suggested in [26]:

pro of

has a random value between

which

The purpose of the parameters

(30)

is to keep the search within the search space,

is

considered the guide to the next position region. To ensure the balance between exploration and

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where,

can be calculated using the following equation as written in [26]:

is the maximum number of the iterative process, and

illustrate the role that

(31)

is a constant. To

plays in the SCA, Fig. 3 shows an example of the variation of the

updated value at c=1 and

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exploitation,

=10. The figure shows that the individual position goes beyond the

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destination point while the number of iterations reaches to the maximum limit number.

Fig. 3 Impact of the parameter

Furthermore, the parameter

on the sine cosine functions at c=1,

is adapted to move the individual positions toward or outward

from the destination as explained earlier in Fig. 2. The value of Finally, when

=10

varies between

.

is a random weighting parameter used for giving the designation value more concern or unconcern

.

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In general, the pseudocode of the SCA is written as presented in Fig. 4: Initialize a set of random search agents

.

.

Calculate the objective function for each search agent Store the best solution as a destination point While (k < ) for each search agents Update the parameters using (31)

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within the limits

end while return the final best solution stored

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if Update the agents position using sine function (28) else Update the agents position using cosine function (29) end if Calculate the objective function Update the destination if there is a better solution

4.4

Chaotic maps

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Fig. 4 Pseudocode of SCA

Chaos maps are introduced as a solution for predicting the unpredictable behaviors such as

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climate, brain states or unsteady movement of air or water, these attitudes can be transferred to set of chaotic equation so-called chaotic maps. Lately, many chaotic maps have been utilized in optimization algorithms. The main advantage of using chaotic maps in the optimization is to improve the convergence rate of the algorithm using different chaotic maps as a replacement for using random variables [36, 39]. TABLE I presents the chaotic maps which are commonly used

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for enhancing the performance of optimization algorithms. In this work, these chaotic maps are involved in the developed algorithm to enhance its convergence rate. From TABLE I, it can be noted that the behavior of any chaotic map depends on the initial value , hence it is important to set a suitable initial value. However, the initial value is chosen at for all chaotic maps as used in [36, 39].

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TABLE I Chaotic maps Chaotic map formula

Name Chebyshev Circle

3

Gauss/mouse

4

Iterative

5 6

Logistic Piecewise

8

Singer

9 10

Sinusoidal Tent

5

Proposed CSCA

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Sine

,

,

, ,

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7

pro of

No 1 2

This section presents the proposed CSCA and how the chaotic maps employed in the original

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SCA optimization algorithm. As mentioned in the previous section, there are four parameters used in the SCA (

). The parameter

is updated at each iteration using (10),

however, the other three parameters are randomly updated as highlighted by the red color in Fig. 4. Hence, instead of using a random variation, a particular chaotic map can be used to adjust

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those three parameters. So, the ten chaotic maps are tested separately in each parameter and then a combination between them is implemented. In consequence, the chaotic maps are numbered from 1 to 10 as displayed in TABLE I, also the numbering for using the chaotic map with the parameters is investigated in TABLE II. Name Parameter Name

TABLE II Arrangement of the proposed CSCA algorithms SCA CSCA_1 CSCA_2 NA CSCA_4 CSCA_5 CSCA_6

CSCA_3 CSCA_7

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Parameter

To study the impact of the chaotic maps on SCA parameters, ten maps are applied to each arrangement of the proposed CSCA algorithms, for instance when chaotic map 1 (Chebyshev)

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involves with CSCA_2, a case study called CSCA_21 is resulted and so on.

The pseudocode of the proposed chaotic SCA algorithm is presented in Fig. 5 Initialize a set of random search agents

within the limits

.

.

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Calculate the objective function for each of the search agents Store the best solution as a destination point While (k < ) Update for the selected chaotic map using the mapping formula for each search agents Update the parameter Eq. (31) Update the parameters using the selected chaotic map if Update the agents position using sine function (28) else Update the agents position using cosine function (29) end if Calculate the objective function Update the destination if there is a better solution

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end while return the final best solution stored

Fig. 5 Pseudocode of CSCA algorithm

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Optimal allocation of DGs using proposed CSCA The optimal size and location of DG into radial distribution network can be achieved using

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the proposed CSCA as described in the following steps: Step 1: Read the system data (line data and load data) and define the objective function. Step 2: Randomly initialize a set of search agents, SCA parameters, and Max. number of iterations

.

Step 3: Initialize the chaotic map parameter

.

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Step 4: Run power flow and calculate the objective function for each of the search agents and store the best solution.

Step 6: For each search agent, update the parameters Step 7: Using the chaotic

.

pro of

Step 5: Update the selected chaotic map parameter

.

, update the parameters

Step 8: Check the value of

.

and update the position of the current search agents using

equation (31).

Step 10: Update the best solution. Step 11: Check if

<

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Step 9: Calculate the objective function for each search agent.

, repeat Step 5.

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Step 12: Return the stored best solution obtained so far.

Step 13: Use the search agents position obtained at the best solution as the optimal size and location for the DGs.

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Step 14: Run the power flow and obtain the voltage profile.

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Initialize the CSCA population Xi(i = 1, 2, .., n)

Start

Initialize 𝒚1 for the selected chaotic map

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Enter power system data

Run power flow and Calculate the objective functions of each search agent

Define the objective function

Store the best solution 𝑫 = 𝑿

Run the CSCA to find the optimal Size and location of DG

Set k = 1

Update 𝒚𝒌 for the selected chaotic map

For each search agent 𝑿𝒊 Update the parameter 𝒓𝟏 Eq. (31)

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Identify the optimal size and location of DG units

Update the parameters 𝒓𝟐 , 𝒓𝟑 𝒂𝒏𝒅 𝒓𝟒 using the selected chaotic map

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Run Power Flow and find the voltage profile

End

If 𝒓𝟒 < 𝟎. 𝟓

No

Yes

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Update the agents position using Cosine

Update the agents position using Sine

Calculate the objective function Update the best solution 𝑫 = 𝑿

k No

k 1

If 𝒌 > 𝑲𝒎𝒂𝒙

Yes Output the optimal Size and location of DG

Fig. 6 Proposed CSCA algorithm for optimal allocation of DGs

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7

Multi-objective CSCA with grey relation analysis

In this section, the MOCSCA based on the original SCA and chaotic map is presented. A grey

7.1

pro of

relation analysis is employed to find the best compromise solution among the Pareto optimal set. Multi-objective CSCA

Two structures namely archive and leader selection are used to formulate the Pareto optimal solutions of the MOCSCA as used with MOGWO [40]. The archive is responsible to arrange the non-dominate solutions obtained so far and the leader selection applied to guide the SCA agents to

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update their position directly to the destination. The following steps establish the MOCSCA formulation:

Step 1: Randomly initialize a set of search agents, SCA parameters, and Max. number of .

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iterations

Step 2: For each search agent, calculate the objective functions Step 3: Prepare archive for the non-dominate solutions and select the leader. Step 4: Update the parameters

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agent's position

using the chaotic map, then, Update the

Step 5: Check the archive, if it is full, apply grid mechanism to delete current archive agent and insert the new solution.

Step 6: Perform the leader selection. Step 7: If

<

, repeat Step 2.

Step 8: Return the stored final non-dominated solutions in the archive Grey Relational Analysis

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7.2

To achieve the best compromise solution among the Pareto optimal set, a suitable decision making is required [41]. In this work, a grey relational analysis is implemented to find the optimal solution using the following steps [42].

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7.2.1 Grey relational generation To obtain the grey relational, all non-dominated solution

for all objective functions

are

where,

pro of

normalized within the maximum and minimum values as follows:

is the normalized value of the nondominated solution

(32)

of the objective function ,

are the maximum and minimum of the objective function values, respectively. 7.2.2 Reference sequence definition

value for all objective function is 1.

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7.2.3 Grey relational coefficient

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Now all objective functions are normalized between [0,1], hence the reference sequence

To present how close the solution

where,

and

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as:

to the reference

, a grey relation coefficient

are the minimum and maximum values of the

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distinguishing coefficient

is used

(33)

(34) , respectively, and

is

.

7.2.4 Grey relational grade Finally, the grey relation grad

for all nondominated solutions is calculated as: (35)

where

is the number of objective functions.

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According to the above steps, the best compromise solution is the one has a highest-grade value subject to all non-dominated solutions. Optimal DG allocation using MOCSCA

pro of

7.3

Fig. 7. shows the flowchart for allocating DG unit into the distribution system using the MOSCA with grey relation analysis.

Initialize the MOCSCA population Xi(i = 1, 2, .., n) Set k = 1 Start

Define the objective functions

Run the MOCSCA to find DG sizes and locations

Run power flow and Calculate the objective functions of each search agent

Run the grid mechanism to omit one of the current archive members

Find the non-dominated solutions and put in the archive

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Enter power system data

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Update 𝒚𝒌 for the selected chaotic map

add the new solution to the archive

Yes

If the archive is full

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Output the Pareto optimal solutions

Identify the best compromise solution using Grey relation analysis Output the optimal size and location for DGs

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End

No

No

Select Leader from (archive)

If new added solutions located outside the hypercubes

Yes Update the parameters 𝒓𝟏 , 𝒓𝟐 , 𝒓𝟑 𝐚𝐧𝐝 𝒓𝟒

For each search agent the position of the current search agent k

k 1

No If k > kmax Yes Output the non-dominated solutions

Update the grids to cover the new solution(s)

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Fig. 7 Flowchart for the MOSCA with Grey relation decision making for optimal DG unit allocation Spacing metric (SP-metric)

pro of

7.4

The performance of the multi-objective optimization techniques is deliberated using spacing

where,

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metric which calculates the divergence scale of nearby trajectories in the Pareto front as [43]:

, m is the number of objective functions and

is the mean of all

(36)

(37) . The

8

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SP-metric value indicates how close the solutions in the Pareto to each other.

Results and discussions

In this section, the proposed techniques (CSCA and MOCSCA) are applied for two standard

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IEEE 33-node and 69-node distribution systems. The optimal sizing and sitting of multiple DGs unit are determined to minimize the total power loss as a single objective optimization problem, in addition, minimizing the total VD and maximizing VSI are considered for the multi-objective problem. To prove the feasibility and efficiency of the proposed techniques, a comprehensive

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comparison with other well-known optimization techniques is carried out. All simulations are performed using MATLAB M-files. CSCA parameters are set as; number of agents = 100, maximum number of iterations = 100. To assess the performance of proposed CSCA compared with the original SCA, 30 runs are carried out to evaluate the best, worst and average costs for the single objective function and calculate the SP-metric for the multi-objective. The following four cases have been considered for the single objective problem in the two studied systems:

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Case #1: Base case (without DG); Case #2: Integrating 1 DG;

pro of

Case #3: Integrating 2 DGs; Case #4: Integrating 3 DGs.

The results of the above four cases obtained by CSCA are compared with those obtained by the other optimization techniques. However, for Multi-objective problem, Case 4 is studied and compared with other multi-objective algorithms. Also, typical load and PV power profiles in different seasons of the year (summer, spring, winter, and fall) are used with Case 4. The

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proposed MOCSCA is applied for optimally setting the PV and BES to minimize the total energy loss and enhance the voltage profile during a year. Performance of CSCA

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8.1

The performance of the SCA has been demonstrated in [26] and the results have been verified with

well-known optimization techniques such as GA, PSO, and FA.however, to check the

follows: 8.2

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performance of the SCA with the chaotic maps, two performance analysis is performed as

Mathematical application

To demonstrated the performance of using the chaotic maps with the standard SCA technique, two benchmarks are used as given in TABLE III. These benchmarks function are chosen to

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represent two different types of functions (unimodal and multimodal). The unimodal functions have only one optima solution while the multimodal has more than one optima.

Function

TABLE III Benchmark functions

Type

Dim Range

Unimodal

20

[−100,100]

Optimal value 0

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[−32,32]

0

pro of

Multimodal 20

The combinations of CSCA presented in TABLE II are used with the ten chaotic maps to solve the benchmarks function. Due to the stochastic nature of the SCA, 30 runs are performed and the best, average, worst, and standard deviation (STD) value are calculated and summarized in TABLE IV and TABLE V. From these tables, it can be seen that for

, CSCA_72 gives the best solution through all

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chaotic maps as well as the standard SCA. Also, three chaotic namely CSCA_23, CSCA_63, and CSCA_67 prove their superiority in case of

. Consequently, it clear that chaotic maps

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SCA CSCA_11 CSCA_12 CSCA_13 CSCA_14 CSCA_15 CSCA_16 CSCA_17 CSCA_18 CSCA_19 CSCA_110 CSCA_21 CSCA_22 CSCA_23 CSCA_24 CSCA_25 CSCA_26 CSCA_27 CSCA_28 CSCA_29 CSCA_210 CSCA_31 CSCA_32

TABLE IV Stochastic calculation of different CSCA algorithms applied on Best Average Worst STD Method Best Average Value Value Value Value Value 7.9E-34 5.5E-26 1.1E-24 2.0E-25 1.9E-27 5.7E-21 5.9E-20 1.3E-20 CSCA_51 4.1E-10 9.4E-07 2.1E-51 7.3E-41 7.9E-40 1.8E-40 CSCA_52 2.1E-30 5.8E-23 1.1E+03 4.5E+03 1.4E+04 2.8E+03 CSCA_53 1.9E+03 5.2E+03 1.5E-39 9.8E-32 2.8E-30 5.0E-31 CSCA_54 1.1E-15 2.7E-10 2.1E-22 9.1E-15 1.3E-13 2.7E-14 CSCA_55 3.1E-06 1.1E-03 2.4E-28 4.0E-22 6.9E-21 1.4E-21 CSCA_56 1.2E-15 4.8E-10 1.8E-19 7.1E-13 9.0E-12 2.1E-12 CSCA_57 2.3E-02 2.9E-01 2.1E-08 3.1E-06 2.1E-05 5.0E-06 CSCA_58 8.5E-18 1.0E-13 1.3E-02 4.0E+00 3.5E+01 7.9E+00 CSCA_59 4.9E-84 4.0E-74 5.0E-19 9.4E-12 2.2E-10 4.0E-11 CSCA_510 5.9E-24 6.6E-18 5.3E-46 1.5E-31 3.9E-30 7.1E-31 CSCA_61 2.1E-40 2.5E-30 2.6E-45 2.1E-37 4.1E-36 7.5E-37 CSCA_62 1.2E-46 3.2E-38 1.5E-94 1.8E-80 2.2E-79 4.7E-80 CSCA_63 6.3E-91 2.1E-74 6.3E-45 1.9E-33 3.5E-32 6.5E-33 CSCA_64 5.3E-43 1.9E-32 1.4E-48 9.6E-34 2.9E-32 5.2E-33 CSCA_65 1.4E-48 1.4E-38 4.3E-45 9.8E-30 2.5E-28 4.6E-29 CSCA_66 5.4E-39 1.1E-30 4.7E-47 3.3E-36 8.3E-35 1.5E-35 CSCA_67 2.9E-45 2.2E-34 1.0E-20 1.2E-11 2.0E-10 4.2E-11 CSCA_68 8.9E-22 4.3E-12 8.8E-14 1.1E-05 2.2E-04 4.3E-05 CSCA_69 6.6E-16 2.3E-04 8.4E-44 3.1E-33 8.7E-32 1.6E-32 CSCA_610 3.8E-42 7.3E-33 1.2E-33 1.6E-22 4.8E-21 8.5E-22 CSCA_71 5.1E-38 1.5E+03 2.3E-36 6.8E-27 1.9E-25 3.4E-26 CSCA_72 2.3E-214 3.8E-122

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Method

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improve the performance of the standard SCA.

Worst Value

STD

7.9E-06 1.3E-21 1.1E+04 3.2E-09 9.0E-03 9.0E-09 1.3E+00 1.1E-12 8.8E-73 1.0E-16 7.4E-29 7.2E-37 6.3E-73 5.2E-31 3.6E-37 3.2E-29 3.2E-33 1.3E-10 6.8E-03 2.1E-31 6.9E+03 1.1E-120

1.8E-06 2.4E-22 1.8E+03 6.3E-10 1.8E-03 1.7E-09 3.0E-01 2.3E-13 1.6E-73 2.1E-17 1.3E-29 1.3E-37 1.1E-73 9.2E-32 6.5E-38 5.7E-30 7.5E-34 2.3E-11 1.2E-03 3.7E-32 2.6E+03 2.1E-121

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CSCA_73 CSCA_74 CSCA_75 CSCA_76 CSCA_77 CSCA_78 CSCA_79 CSCA_710

1.2E+03 9.8E-28 6.3E-05 1.6E-88 5.9E+01 1.0E-12 1.2E-56 1.3E-189

4.8E+03 2.6E+02 8.0E+03 7.6E-04 4.7E+03 9.9E+01 7.2E+03 5.7E+03

pro of

1.9E-26 1.4E-23 6.0E-26 2.3E-25 7.8E-25 1.8E-26 4.9E-26 3.6E-24 5.4E-12 3.2E-47 8.7E+02 8.5E-16 3.2E-03 1.1E-24 3.9E-02 5.7E-01 5.7E+03 1.4E-22

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1.0E-25 7.6E-23 3.3E-25 1.0E-24 4.2E-24 1.0E-25 2.6E-25 2.0E-23 3.0E-11 1.8E-46 4.0E+03 3.8E-15 1.7E-02 6.2E-24 2.2E-01 2.6E+00 1.8E+04 7.9E-22

TABLE V Stochastic calculation of different CSCA algorithms applied on Best Average Worst STD Method Best Average Value Value Value Value Value 4.4E-15 9.4E-07 2.8E-05 5.1E-06 5.8E-14 8.2E-11 1.6E-09 2.9E-10 CSCA_51 1.3E-05 4.3E-04 8.9E-16 3.8E-15 4.4E-15 1.3E-15 CSCA_52 8.9E-16 2.0E-12 9.3E+00 1.7E+01 2.0E+01 2.5E+00 CSCA_53 1.4E+01 1.7E+01 8.9E-16 4.3E-15 4.4E-15 6.4E-16 CSCA_54 6.3E-08 2.3E-06 1.4E-11 8.2E-09 1.5E-07 2.8E-08 CSCA_55 1.3E-03 1.7E-02 4.4E-15 6.0E-12 1.7E-10 3.0E-11 CSCA_56 2.5E-08 2.9E-06 8.1E-10 2.3E-07 1.5E-06 3.8E-07 CSCA_57 7.2E-02 3.3E-01 9.2E-06 3.3E-04 1.0E-03 2.5E-04 CSCA_58 2.7E-11 4.8E-08 3.2E-03 2.4E+00 2.0E+01 5.0E+00 CSCA_59 8.9E-16 3.3E-15 4.7E-10 4.4E-07 9.4E-06 1.7E-06 CSCA_510 5.9E-12 2.1E-10 8.9E-16 3.4E-15 8.0E-15 1.9E-15 CSCA_61 8.9E-16 3.0E-15 8.9E-16 3.8E-15 4.4E-15 1.3E-15 CSCA_62 8.9E-16 3.3E-15 8.9E-16 8.9E-16 8.9E-16 0.00 CSCA_63 8.9E-16 8.9E-16 8.9E-16 3.5E-15 4.4E-15 1.6E-15 CSCA_64 8.9E-16 3.8E-15 8.9E-16 1.6E-15 4.4E-15 1.4E-15 CSCA_65 8.9E-16 2.0E-15 8.9E-16 4.4E-15 8.0E-15 1.3E-15 CSCA_66 8.9E-16 4.3E-15 8.9E-16 1.0E-15 4.4E-15 6.4E-16 CSCA_67 8.9E-16 8.9E-16 5.5E-12 1.3E-07 2.1E-06 3.8E-07 CSCA_68 7.1E-13 4.8E-08 7.7E-06 9.8E-01 2.0E+01 3.9E+00 CSCA_69 6.8E-07 1.7E+00 8.9E-16 2.2E-15 4.4E-15 1.7E-15 CSCA_610 8.9E-16 2.7E-15 4.4E-15 9.4E-15 4.4E-14 8.8E-15 CSCA_71 8.9E-16 4.1E+00 4.4E-15 1.2E-13 3.2E-12 5.7E-13 CSCA_72 8.9E-16 6.7E-01 4.4E-15 1.7E-14 1.1E-13 2.5E-14 CSCA_73 1.2E+01 1.6E+01 8.9E-16 2.1E-14 3.0E-13 5.3E-14 CSCA_74 8.9E-16 6.6E-03 8.9E-16 3.8E-14 4.3E-13 8.3E-14 CSCA_75 6.6E-04 1.6E+01

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SCA CSCA_11 CSCA_12 CSCA_13 CSCA_14 CSCA_15 CSCA_16 CSCA_17 CSCA_18 CSCA_19 CSCA_110 CSCA_21 CSCA_22 CSCA_23 CSCA_24 CSCA_25 CSCA_26 CSCA_27 CSCA_28 CSCA_29 CSCA_210 CSCA_31 CSCA_32 CSCA_33 CSCA_34 CSCA_35

5.4E-27 2.6E-24 1.3E-26 9.0E-26 2.1E-25 4.5E-27 1.3E-26 7.2E-25 1.1E-12 5.9E-48 2.1E+03 2.8E-16 9.3E-04 2.1E-25 9.9E-03 1.7E-01 1.0E+04 3.1E-23

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Method

1.1E-34 3.9E-32 1.3E-34 3.9E-36 1.5E-36 6.1E-35 1.9E-34 3.7E-37 7.4E-21 6.5E-75 5.8E+02 9.0E-27 1.2E-08 1.2E-41 1.0E-11 6.1E-07 1.3E+00 2.5E-46

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CSCA_33 CSCA_34 CSCA_35 CSCA_36 CSCA_37 CSCA_38 CSCA_39 CSCA_310 CSCA_41 CSCA_42 CSCA_43 CSCA_44 CSCA_45 CSCA_46 CSCA_47 CSCA_48 CSCA_49 CSCA_410

7.6E+03 7.9E+03 1.7E+04 9.6E-03 1.1E+04 1.9E+03 1.9E+04 1.3E+04

1.7E+03 1.4E+03 4.8E+03 2.4E-03 3.0E+03 3.6E+02 6.6E+03 4.7E+03

Worst Value

STD

1.8E-03 2.7E-11 1.9E+01 1.3E-05 2.0E-01 2.0E-05 7.0E-01 1.9E-07 4.4E-15 2.3E-09 4.4E-15 4.4E-15 8.9E-16 8.0E-15 4.4E-15 8.0E-15 8.9E-16 4.6E-07 2.0E+01 4.4E-15 2.0E+01 2.0E+01 1.9E+01 1.4E-01 2.0E+01

4.1E-04 5.4E-12 1.5E+00 3.0E-06 3.5E-02 5.3E-06 1.6E-01 4.9E-08 1.7E-15 4.2E-10 1.7E-15 1.7E-15 0.00 1.6E-15 1.6E-15 1.1E-15 0.00 1.0E-07 5.0E+00 1.8E-15 7.1E+00 3.6E+00 1.6E+00 2.5E-02 4.9E+00

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8.3

1.5E-09 9.0E-14 1.9E-13 2.4E-14 6.2E-14 6.4E-08 2.7E-15 1.4E+01 4.8E-11 3.6E-03 3.6E-14 1.9E-02 1.1E-01 1.8E+01 1.9E-12

4.5E-08 2.2E-12 5.3E-12 2.2E-13 1.2E-12 6.6E-07 4.4E-15 2.0E+01 6.9E-10 5.6E-02 6.4E-13 2.4E-01 1.3E+00 2.0E+01 3.1E-11

8.2E-09 4.0E-13 9.5E-13 4.4E-14 2.2E-13 1.4E-07 1.8E-15 2.1E+00 1.3E-10 1.0E-02 1.2E-13 4.5E-02 2.6E-01 3.2E+00 6.1E-12

Electrical engineering application

CSCA_76 CSCA_77 CSCA_78 CSCA_79 CSCA_710

8.9E-16 1.9E+00 2.5E-07 8.9E-16 8.9E-16

3.7E-03 1.6E+01 2.1E+00 9.7E+00 1.1E+01

3.0E-02 2.0E+01 1.6E+01 2.0E+01 2.0E+01

7.4E-03 3.5E+00 4.4E+00 9.1E+00 8.7E+00

pro of

4.4E-15 4.4E-15 4.4E-15 4.4E-15 4.4E-15 2.8E-11 8.9E-16 1.1E+01 4.4E-15 2.2E-06 8.9E-16 1.9E-06 5.7E-06 6.5E+00 8.9E-16

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CSCA_36 CSCA_37 CSCA_38 CSCA_39 CSCA_310 CSCA_41 CSCA_42 CSCA_43 CSCA_44 CSCA_45 CSCA_46 CSCA_47 CSCA_48 CSCA_49 CSCA_410

In this subsection, the seven CSCAs based on different chaotic maps are simulated to find the

engineering application.

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optimal size and location of the DG unit in IEEE 33-node tests system as an electrical

Fig. 8.a shows the convergence characteristics of the different combination algorithms between

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the original SCA parameters with iterative chaos maps. From this figure, it can be observed that CSCA_6 gives the highest convergence rate compared with the other proposed algorithms. However, among the ten chaos maps, the iterative chaotic map proves its efficiency as shown in Fig. 8.b. It can be concluded that the CSCA_64 is the efficient chaotic technique for SCA and it can be used to optimally allocate DG units in the distribution systems. Consequently, the

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CSCA_64 is used to find the optimal size and location in IEEE 33 and 69 nodes systems.

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106.50 106.50

106.5

SCA

106.00 106.00 106.0 105.50 105.50 105.5 105.00 105.00 105.0

SCA

104.21

CSCA_1

104.16

CSCA_2

104.11

CSCA_3 CSCA_4

104.06

CSCA_6

103.96 1

2

3

4

5

CSCA_5

CSCA_7

CSCA_7

0 0

10 10 10

2020 20

106.50 106.5

106.5

106.00 106.0

106

30 30 30

40 40 40

Iteration Number Iteration Number

a)

50 50 50

SCA parameter combination

CSCA_61 CSCA_62 CSCA_63

104.26

105.5

105.50 105.5

CSCA_64

104.21 104.16

105

105.0 105.00

CSCA_65

104.11 104.06

CSCA_66

104.01

104.5 104.50

104.5

104.0 104.00

104

103.5 103.50

103.5

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Power losses (kW)

CSCA_4

CSCA_6

104.0 104.00 104.00 103.5 103.50 103.50 0

CSCA_3

CSCA_5

104.01

104.5 104.50 104.50

CSCA_2

pro of

Power losse (kW)

Power losses (kW)

CSCA_1 104.26

1

0

0 0

CSCA_67

103.96

20

10 10

2

40

20 20

3

60

4

5

80

30 30

100

CSCA_68 CSCA_69 CSCA_610 120

40 40

50 50

Iteration Number

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b) Chaotic map convergence

Fig. 8 Convergence characteristics for the combination of SCA parameters using chaotic maps

8.4

IEEE 33- nodes system

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The proposed CSCA_64 is tested using the IEEE 33-node test system (Fig. 9). The full description of this test system including the line and load data is given in [44]. The base kV = 12.66 and MVA=100.

8.4.1 Single objective analysis

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The power flow results for the base case indicate that the active and reactive power losses are 202.68 kW and 134.14 kVAR, respectively. To reduce the total power losses and enhance voltage profiles, CSCA-64 is applied to determine the optimal locations and sizes of DGs according to the previously mentioned cases (1 DG, 2 DGs, and 3 DGs). The obtained results for each case including the DG location, size, active, and reactive power losses are summarized in TABLE VI. From this table, it can be observed that the active power losses decrease to 103.966 kW when a

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DG unit is integrated at bus 6 with a total capacity of 2575.26 kW. However, significant decreasing in the active power loss reach to 71.94 kW is obtained when 3 DG units are connected

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at 13, 24, and 30 buses. In addition, the reactive power losses decrease from 135.14 kVAR at the base case to 74.79 kVAR, 58.49 kVAR, and 49.54 kVAR when integrating 1 DG, 2 DGs, and 3 DGs, respectively. The voltage profiles of IEEE 33-node system for the four studied cases are shown in Fig. 10. As can be seen, the voltage profiles are significantly improved when 2 DGs and 3 DGs are optimally integrated. Also, it can be observed that the obtained voltage profiles are still

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kept within the limits.

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Fig. 9 Single line diagram of IEEE 33-node test system. TABLE VI Results of IEEE 33-node test system obtained by proposed CSCA-64 Location Size (kW) Total power loss (kW) Total reactive power loss (kVAR) NA NA 202.68 135.14 Base case 6 2575.26 103.966 74.79 Case #2: 1 DG 12 973.82 85.96 58.49 Case #3: 2 DGs 30 1106.22 13 871.00 24 1091.47 71.94 49.54 Case #4: 3 DGs 30 954.08

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Base Case

1 DG

2 DGs

3DGs

1.02

Voltage (p.u)

1.00 0.98 0.96 0.94

0.92 0.90 1

3

5

7

9 11 13 15 17 19 21 23 25 27 29 31 33 Bus number

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Case 2: Integrating 1 DG

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a)

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Fig. 10 Voltage profiles of IEEE-33 nodes test system

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b) Case 3: Integrating 2 DGs

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c) Case 4: Integrating 3 DGs Fig. 11 Convergence characteristics of SCA and CSCA-64 for DG integration in IEEE 33-node test system

It is important to investigate the enhancement in the convergence rate obtained by the proposed CSCA-64 compared with the original SCA. Hence, the convergence characteristics of the three DGs integration cases are shown in Fig. 11, and it is clear that the CSCA-64 reaches the optimal solution faster than the original SCA. To ensure the feasibility of obtained results, statistical analysis including the best, average, and the worst values of the cost function for 30 runs for each

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studied case is calculated and presented in TABLE VII. From this table, it can be observed the superiority of proposed CSCA-64 over the original SCA for all studied cases.

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TABLE VII Performance comparison between original SCA and CSCA-64 (IEEE 33-node test system) Algorithm Best Cost Average Cost Worst Cost SCA 103.98 104.40 105.81 Case #2: 1 DG CSCA-64 103.97 103.97 103.97 SCA 86.03 88.82 94.36 Case #3: 2 DGs CSCA-64 85.96 87.39 91.52 SCA 72.51 80.36 89.67 Case #4: 3 DGs CSCA-64 71.94 76.07 84.67

The proposed CSCA-64 is compared with different well-known optimization algorithms and the

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results are given in TABLE VIII. From this table, it can be observed that the proposed CSCA-64 is able to significantly improve the loss reduction (LR) compared with the other optimization techniques; LSF [14], Fuzzy -IAS[45], BFOA[46], SKHA [24]. LR reaches to 47.7%, 57.6%, and

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64.5% in case of integrating 1 DG, 2 DGs, and 3 DGs, respectively.

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TABLE VIII Loss reduction obtained by different optimization techniques (IEEE 33-node test system) Method Case #2: 1 LR % Case #3: 2 LR % Case #4: 3 LR % DG (Bus/Size DG (Bus/Size DG (Bus/Size (kW)) (kW)) (kW)) #18/ 743 30.48 #18/ 720; 52.32 #18/720; 59.72 LSF [14] #33/0.900 #33/0.810; #25/ 900 #32/1931 37.71 #32/383.6; 42.43 #32/2071; 42.45 Fuzzy #30/1150.6 #30/1113.8; IAS[45] #31/150.3 #8/ 1858 43.98 #13/ 880; 57.62 #13/632; 57.76 BSOA[23] #31/ 924 #28/486; #31/550 NA NA NA NA #14/652; 57.62 BFOA[46] #18/198.4; #32/1067.2 #6/2590 47.38 #13/851.6; 58.7 #30/1054; 65.40 SKHA[24] #30/1157.6 #24/1091; #13/802 #6/ 2575 #12/973.82; #30/954.1; CSCA-64 48.70 57.60 64.5 #30/1106.2 #24/1091.5; #13/871

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8.4.2 Multi-objective analysis The multi-objective problem considering the optimal allocation of three DG units is presented in

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this section. The main target is to minimize power loss, VD, and maximize VSI. TABLE IX presents the achieved results of the proposed MOCSCA based on iterative chaos map compared with the MOSCA and other optimization algorithms. It is clear that the proposed MOCSCA gives the minimum power loss and maximum VSI (88.43 kW and 0.9572 p.u respectively) which are better than 89.92 kW and 0.9502 p.u obtained by MOSCA. However, the minimum VD has been obtained using TLBO [46] and QOTLBO [46].

PSO [47]

GA/PSO [47]

TLBO [48]

QOTLBO [48]

TM [49]

MOSCA

MOCSCA

‐ 11 29 30 8 13 32 11 16 32 12 28 30 13 26 30 15 26 33 7 14 30 13 25 32 13 24 30

‐ 1.5000 0.4228 1.0714 1.1768 0.9816 0.8297 0.9250 0.8630 1.2000 1.1826 1.1913 1.1863 1.0834 1.1876 1.1992 0.7199 0.7199 1.4397 0.9800 0.9600 1.3400 1247.61 1061.68 1223.50 1098.02 986.57 1584.90

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MOTA [49]

Size (MW)

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esaB esaB GA [47]

Bus

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Method

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TABLE IX Multi-objective results obtained by different optimization techniques (IEEE 33-node test system) (kW)

(p.u)

(p.u)

202.68 106.3

0.1337 0.0407

0.6691 0.949

105.3

0.0335

0.9255

103.4

0.0124

0.9508

124.7

0.0011

0.9503

103.4

0.0011

0.9530

102.30

0.0040

0.9371

96.30

0.0014

0.9551

89.92

0.0023

0.9502

88.43

0.0016

0.9572

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Fig. 12 shows the nondominated solution achieved by the proposed MOCSCA and the original MOSCA. The comparison between the original MOSCA and the proposed MOCSCA is exhibited

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in Fig. 13 which shows the advantage of using the chaotic map for decreasing the SP-metric of

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the proposed algorithm.

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Fig. 12 Pareto optimal set for MOCSCA and MOSCA in IEEE 33-node test system

Fig. 13 SP-metric for MOCSCA and MOSCA in IEEE 33-node test system

8.4.3 Impact of PV and BES

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In this study, the impact of the renewable energy sources in the distribution system is observed using a typical PV power generation based on the uncertainty and daily load profile during a year (Summer, Spring, Winter, and Fall). The daily load is shown in Fig. 14 is applied. The overall data can be found in [50]. The mean and standard deviation of the solar irradiance of the PV model is given in [51]. Fig. 15 shows four typical days presented in 96 hr sampling time. The power generation obtained by the Beta PDF for one PV module is demonstrated in Fig. 16.

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Fig. 17 displays the voltage profile of the IEEE 33-node during a typical day for each season without PV power. The figure indicates that a significant decrease in the voltage has been

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happened in the summer, however in the winter and the fall some buses exceeded the lower

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limits.

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Fig. 14 Typical daily load profile

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Fig. 15 Mean and Standard deviation of the solar irradiation

Fig. 16 PV power

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Fig. 17 Voltage profile of IEEE 33-node for four typical days of the four seasons in the year without PV

To enhance the voltage profile of the IEEE 33-node and reduce the power losses, three DG units are optimally located, using the MOCSCA, into the system with their maximum capacity given in

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TABLE IX. Fig. 18 reveals the impact of the PV power on the voltage profile, the voltage is

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improved in the presence of the PV power and decreased when the PV power is low.

Fig. 18 Voltage profile of IEEE 33-node for four typical days of the four seasons in the year with PV

A sequential MOCSCA is applied at each sampling time to determine the optimal power setting of the PV and BES to maintain the voltage profile within the limits and decrease the power

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losses. Fig. 19 exhibits the enhancement of the voltage profile when using three BESs at the same PV locations. It is clear that considerable improvement has been achieved using the BES. The energy loss minimization appears in Fig. 20 in the three studied cases, the minimum energy loss is obtained using the PV and BES.

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Finally, the optimal BES capacities are given in TABLE X, the maximum capacity of the PV and

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BES is achieved in the summer due to the high load demand and low PV power generation.

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Fig. 19 Voltage profile of IEEE 33-node for four typical days of the four seasons in the year with PV and BES

Fig. 20 Power loss minimization in IEEE 33-node for four typical days of the four seasons in the year

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BES 13 (MW h) BES 24 (MW h) BES 30 (MW h) PV 13 size (MW) PV 24 size (MW) PV 30 size (MW)

TABLE X Optimal size of PV and BES for IEEE 33-node Summer Fall Winter 9.88 6.14 7.29 13.01 9.98 11.32 14.60 9.12 10.85 3.06 1.92 2.25 3.59 2.78 3.34 4.60 2.84 3.36

Spring 6.70 10.01 9.58 2.06 3.06 2.96

IEEE 69-node system

In this subsection, the results of the IEEE 69-node test system obtained by the proposed CSCA64 and other optimization techniques are discussed. The overall data of this system are given in [52]. Its single line diagram is shown in Fig. 21.

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8.5.1 Single objective analysis The optimal locations, sizes, and active power losses are given in TABLE XI. From this table, it

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can be observed that the total power losses decreased to 63.03%, 68.14%, and 68.86% by integrating (1 DG, 2 DGs, and 3 DGs), respectively. There is no significant decrease in the power losses by integrating 3 DGs (70.07 kW) compared with only 2 DGs (71.67 kW). The voltage profiles for all studied cases are shown in Fig. 22. It can be noted that the voltage profile is obviously improved compared with the base case. All obtained voltages are still within the

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allowable limits.

Fig. 21 Single line diagram of IEEE-69 node

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TABLE XI Results of IEEE 69-node test system obtained by proposed CSCA-64 Location Size (kW) Total power loss kW Total reactive power loss (kVAR) NA NA 224.95 102.15 Base case. 61 1872.60 83.19 40.52 Case #2: 1 DG 18 511.28 71.67 35.95 Case #3: 2 DGs 61 1794.11 17 365.97 61 1675.85 70.07 35.14 Case #4: 3 DGs 67 652.52

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Base Case

1 DG

2 DGs

3DGs

1.02

0.98 0.96

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Voltage (p.u)

1.00

0.94

0.92 0.90 1

11

21

31 41 Bus number

51

61

71

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Fig. 22 Voltage profiles of IEEE-69 nodes system

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Case 3: Integrating 2 DG

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a)

Case 2: Integrating 1 DG

a) Case 4: Integrating 3 DG Fig. 23 Convergence characteristics of SCA and CSCA-64 for DG integration in IEEE 69-node test system

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Similarly, it is worthy to track the performance of the proposed CSCA-64 with increasing the system size to prove the feasibility of the algorithm. The convergence characteristics of proposed

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CSCA-64 and original SCA are shown in Fig. 23. From this figure, it can be observed that the chaotic map enhances the convergence of the original SCA algorithm. The statistical analysis is summarized in TABLE XII. The effectiveness of the proposed technique is compared with the other optimization algorithms (Analytical, GAPSO, BFOA, MBFOA, and SKHA) used for allocating the DGs in IEEE 69-node system and the results are presented in TABLE XIII. It can be noted that the proposed CSCA-64 has the ability to improve the LR compared to other

DG, 2 DGs, and 3 DGs, respectively.

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optimization techniques where the LRs are 63.03%, 68.14%, and 68.86% in case of integrating 1

Method

Analytical [24] GAPSO [24]

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TABLE XII Performance comparison between original SCA and CSCA-64 in IEEE-69 nodes for minimizing the power losses (kW) Algorithm Best Cost Average Cost Worst Cost SCA 83.19 83.23 83.73 Case #2: 1 DG CSCA-64 83.19 83.19 83.21 SCA 71.73 78.67 86.20 Case #3: 2 DGs CSCA-64 71.67 76.06 83.23 SCA 70.40 76.55 87.09 Case #4: 3 DGs CSCA-64 70.07 74.67 83.00 TABLE XIII Comparison of IEEE-69 nodes result with other optimization methods Case #2: 1 LR % Case #3: 2 LR % Case #4: 3 DG (Bus/Size DG (Bus/Size DG (Bus/Size (kW)) (kW)) (kW)) #61/1800 62.95 NA NA NA NA

NA

NA

NA

NA

NA

NA

NA

MBFOA[24] SKHA[24]

#61/1879 #61/1865

63.00 63.00

NA #17/5229.; #61/1778.9

NA 68.07

CSCA-64

#61/1873

63.03

#18/511.3; #61/1794.1

68.14

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BFOA [24]

#63/884.9; #61/1196; #21/910.5 #27/295.4; #65/446; #61/1345.1 NA #61/1719.1; #17/371; #11/527.1 #67/652.5; #61/1675.9; #17/366

LR %

NA 63.96

66.56

NA 69.10

68.86

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8.5.2 Multi-objective analysis The MOCSCA is applied for the IEEE 69-node system, the results of the optimal size and

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location of the multiple DG are given in TABLE XIV. The proposed MOCSCA donates the minimum power loss, VD, and maximum VSI which reached to 79.69 kW, 0.0002 p.u, and 0.9798 p.u, respectively. These values are considered the best results obtained compared with the other optimization techniques.

The comparison between the original MOSCA and the proposed MOCSCA is carried out using the Pareto optimal set and the SP-metric as shown in Fig. 23 and Fig. 24, respectively. The

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proposed algorithm still gives better performance due to the chaotic iterative map. TABLE XIV Multi-objective results obtained by different optimization techniques (IEEE 69-node test system)

PSO [47]

GA/PSO [47]

TLBO [48]

QOTLBO [48]

SIMBO‐ Q [53]

MOSCA

MOCSCA

‐ 21 62 64 17 61 63 21 61 63 13 61 62 15 61 63 15 61 62 15 61 63 21 61 61 21 61 67

‐ 0.9297 1.0752 0.9848 0.9925 1.1998 0.7956 0.9105 1.1926 0.8849 1.0134 0.9901 1.1601 0.8114 1.1470 1.0022 0.7722 1.3526 0.8232 0.7754 1.4385 0.7235 785.77 1126.53 1071.26 453.12 2190.70 676.30

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QOSIMBO‐ Q]35[

Size (MW)

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esaB esaB GA [47]

Bus

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Method

(kW)

(p.u)

(p.u)

224.95 89.0

0.0992 0.0012

0.6852 0.9705

83.2

0.0049

0.9676

81.1

0.0031

0.9768

82.2

0.0008

0.9745

80.6

0.0007

0.9769

80.0

0.0007

0.9770

79.7

0.0007

0.9768

83.12

0.0010

0.9782

79.69

0.0002

0.9798

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Fig. 24 Pareto optimal set for MOCSCA and MOSCA in IEEE 69-node test system

8.5.3 Impact of PV and BES

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Fig. 25 SP-metric for MOCSCA and MOSCA in IEEE 69-node test system

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Similarly, the impact of the PV and BES is studied with the IEEE 69-node. The voltage profiles at base case (without PV) and its improvement due to using the PV and PV with BES are presented in Fig. 26, Fig .27, and Fig. 28, respectively. It can be observed a significant increase in

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the voltage profile is gained using the PV and BES through the year.

Fig. 26 Voltage profile of IEEE 69-node for four typical days of the four seasons in the year without PV

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Fig. 27 Voltage profile of IEEE 69-node for four typical days of the four seasons in the year with PV

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Fig. 28 Voltage profile of IEEE 69-node for four typical days of the four seasons in the year with PV and BES

Fig. 29 Power loss minimization in IEEE 69-node for four typical days of the four seasons in the year

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Finally, TABLE XV gives the optimal sizes of the PV and BES in the IEEE 69-bus system. It is clear that the maximum sizes of the PV and BES at buses 21 and 61are achieved in summer due to the high load. However, for BES connected at bus 67, the maximum capacity is obtained in spring.

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9

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BES 21 (MW h) BES 61 (MW h) BES 67 (MW h) PV 21 size (MW) PV 61 size (MW) PV 67 size (MW)

TABLE XV Optimal size of PV and BES for IEEE 69-node Summer Fall Winter 4.09 3.32 3.49 19.61 15.59 16.91 7.89 6.80 7.11 1.30 0.82 1.00 6.08 4.09 4.87 2.24 1.74 1.93

Conclusion

Spring 4.08 17.90 8.44 0.92 4.33 1.92

In this paper, efficient optimization techniques, CSCA and MOCSCA, have been proposed and applied for determining the optimal allocation of multiple DG units into radial distribution

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networks. The main target of the integration of DG units in the distribution system is to minimize power loss, VD, and maximize VSI. In CSCA, the chaotic maps theory has been used to update the parameters of original SCA. CSCA is able to enhance the convergence rate of original SCA

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and avoid its trapping in the local optima. The different combination of SCA parameters has been tested with several chaos maps. The results showed that a suitable and efficient combination is to use the iterative chaotic map to change the values of r3, and r4 instead of using a random

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variation. The CSCA and MOCSCA have been applied for two standard radial distribution test systems and compared with other well-known optimization techniques. The results proved the efficiency and robustness of the proposed technique compared with the other optimization techniques in terms of minimum power losses, VD, and maximum VSI with fast convergence characteristics. The impact of renewable energy resources has been addressed considering the

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typical PV power generation profiles as well as the load profiles of the distribution network consumers at different seasons.

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