Multiple scenarios multi-objective salp swarm optimization for sizing of standalone photovoltaic system

Journal Pre-proof Multiple scenarios multi-objective salp swarm optimization for sizing of standalone photovoltaic system Hussein Mohammed Ridha, Chandima Gomes, Hashim Hizam, Seyedali Mirjalili PII:

S0960-1481(20)30202-0

DOI:

https://doi.org/10.1016/j.renene.2020.02.016

Reference:

RENE 13037

To appear in:

Renewable Energy

Received Date: 15 September 2019 Revised Date:

26 December 2019

Accepted Date: 5 February 2020

Please cite this article as: Ridha HM, Gomes C, Hizam H, Mirjalili S, Multiple scenarios multi-objective salp swarm optimization for sizing of standalone photovoltaic system, Renewable Energy (2020), doi: https://doi.org/10.1016/j.renene.2020.02.016. 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. © 2020 Published by Elsevier Ltd.

Hussein Mohammed Ridha: Conceptualization, Methodology, Formal analysis, Writing- Reviewing and Editing Chandima Gomes: Formal analysis, Data Curation, Writing- Reviewing and Editing Hashim Hizam: Visualization, Investigation, Formal analysis, Writing- Reviewing and Editing Seyedali Mirjalili: Software, Writing- Reviewing and Editing, Supervision, Project administration

Multiple Scenarios Multi-objective Salp Swarm Optimization for Sizing of Standalone Photovoltaic System Hussein Mohammed Ridha1,2, Chandima Gomes3, Hashim Hizam1,2, Seyedali Mirjalili*,4 1,*

Department of Electrical and Electronics Engineering, Faculty of Engineering, Universiti

1

Putra Malaysia, 43400 Serdang, Malaysia

2 3

2

Advanced Lightning, Power and Energy Research, Faculty of Engineering, Universiti Putra Malaysia, 43400 Serdang, Malaysia

4 3

5

School of Electrical and Information Engineering, University of Witwatersrand, 1 Jan Smuts Avenue, Braamfontein, Johannesburg 2000, South Africa

6 4

Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Fortitude Valley, Brisbane, 4006 QLD, Australia E-mail: [email protected] & [email protected], [email protected], [email protected], [email protected].

Abstract 7

The paper presents a new multiple scenario multi-objective salp swarm optimization (MS-

8

MOSS) algorithm to optimally size a standalone PV system. An accurate estimation of the

9

number of PV modules and storage battery is crucial as it affects the system reliability and cost.

10

Three scenarios have been presented focusing on Pareto optimal solutions by minimizing two

11

conflicting objectives. Loss of load probability (LLP) and life-cycle cost (LLC) are considered to

12

obtain the Pareto front. The iterative method is employed for validation of the superiority results

13

of the proposed MS-MOSS algorithm. The results show that the scenarios are able to find Pareto

14

optimal configuration at a high level of accuracy and at a very low cost. The proposed three

15

scenarios are faster than iterative approach approximately by 158, 194.2, and 141.6 times,

16

respectively. The third scenario outperforms other scenarios in terms of coverage and

17

convergence of the distribution of solution to the Pareto front. As a conclusion, The MS-MOSS

18

algorithm is found to be very effective in sizing of SAPV system.

1

19

Keywords: Standalone PV system; Multiple scenarios; Multi-objectives optimization; Salp

20

swarm algorithm; LLP; LCC.

1. Introduction 21

Due to the increasing energy demands and the determinations of fossil fuel resources

22

motivate renewable energy system designers to rise up with optimum designers. Solar energy is

23

considered one of the cleanest, abundant, and never-ending of all of the renewable energy

24

resources until date [1,2]. Standalone PV (SAPV) system is one of the most important

25

applications of photovoltaic (PV) systems in both remote and resident areas [3]. However, the

26

low conversion of energy and the high initial cost are the main obstacles of the SAPV systems

27

[4]. Therefore, an optimal configuration must be chosen to fulfill the load demand and achieve a

28

tradeoff between techno-economic criteria.

29

Multi-objective optimization methods have been carried out by the researchers and become an

30

active area of study to the optimum size of the SAPV systems [5–7]. Stochastic sizing methods

31

of a standalone PV system can be further categorized into single and multi-objective methods.

32

Only one objective is optimized in single-objective methods whereas, two or more than

33

objectives are considered in multi-objective methods. In the case of multi-objective, the problem

34

can be solved in two ways: combining the objectives into a single or simultaneously optimizing

35

all the objectives. Single-objective methods can be criticized because they evaluate only

36

availability or cost of the system [8,9]. Whilst, the availability, and cost are optimized

37

synchronously in multi-objective optimization [10]. Before installing the SAPV system, a high

38

level of reliability and minimum cost are important to be calculated accurately using more than

39

one scenario. Regarding that, in [11] a sizing methodology of a SAPV system using stochastic

40

analysis is presented in Brazil. Loss of power supply probability (LPSP) is used to select an

41

optimum PV/battery configuration. Then, the minimum total life-cycle cost (TLCC) is utilized to

42

choose an optimal design of the SAV system from a set of configurations. The result showed that

43

the utilized method in [11] is more reliable and realistic. However, the proposed method is

44

complex (needs more statistical processing for simulation) and time-consuming. The authors of

45

[12] proposed a techno-economic numerical sizing methodology of the SAPV system in France.

2

46

Hourly meteorological data and load demand were utilized for this purpose. The reliability of the

47

system is evaluated by using LPSP due to the highly sensitive to the random nature of cloud

48

cover. LPSP is obtained for various scenarios and the minimum annualized cost of the SAPV

49

system is selected for the best scenario. In addition to that, Ibrahim et al. [13] developed a

50

technique for modeling the output power of a standalone PV system. Then, the iterative

51

numerical method is utilized to optimally size of SAPV system for the set of configurations

52

based on loss of the load probability (LLP). After that, the best configuration is chosen based on

53

minimum ALCC. Moreover, the levelized cost of the energy (LCE) is used to find the total

54

power energy generated by the PV/battery system. In Ref. [14], the authors studied the impact of

55

increasing suppressed demand (SD) by 20% and 50% in three remote applications: household, a

56

school, and a health centre in Bolivia. LPSP was employed to calculate the reliability of the

57

system and the cost of the PV system hardware was set to be 2.5 $/
 . The authors of Ref. [14]

58

claimed that for the household and school, increasing the PV capacity is more cost-effective but

59

this leads to raise the battery ageing rate using lithium-ion battery. However, the supplied energy

60

to the load demand depends on the energy generated by the PV arrays to the storage battery. The

61

used energy management process may lead to reduce the lifetime of the battery with increasing

62

the capital cost. Moreover, the cost of the of the system’s components were assumed to be

63

constant.

64

In 2018, Sadio et al. [15] used two conflicting objectives to find appropriate numbers of

65

PV modules and storage battery using average monthly metrological data. Sarhan et. Al. [16]

66

proposed an improved numerical method for optimal sizing of a SAPV system in Yemen. LLP is

67

used for reliability evaluation. Whilst, the net present cost (NPC) and LCE are employed as

68

economic parameters. However, a simple PV model is obtained for the output prediction of the

69

system. In [17], combined PV and storage battery for the various value of LLP, but there was no

70

consideration for time-execution and amount of the lost energy during its operation.

71

A multi-objective methodology was proposed in [18] to find an optimal sizing for the off-grid

72

PV system in a rural area in Uganda. The energy balance and state of the charge (SOC) for each

73

time step, loss of load (LL) were considered as technical parameters. While the value of the lost

74

cost (VOLL), levelized cost of supplied and cost energy (LCoSLE) as economic parameters were

75

computed based on the numerical method to choose an optimum configuration. Bin-Juine et al. 3

76

in [19] proposed sizing of the SAPV system to supply power to the air conditioner. The variables

77

an operation probability (OPB), daily overall runtime fraction (RF), and (LLP) were used to

78

characterize the loss of power. Whilst, the capital cost of the system was obtained as an

79

economic parameter based on the analytical method. However, the simplicities of the

80

mathematical models were used which may affect on the result power generated.

81

Several techno-economic criteria must be taken into account in the SAPV system design

82

process. Therefore, the multi-objective evaluation is necessary to achieve the trade-off between

83

the objectives. Meta-heuristic methods are employed to overcome the drawbacks of other

84

methods and have the ability to deal with more than two objectives at the same time [10,20]. For

85

instance, a genetic algorithm was utilized in [13] to choose an optimal configuration based on the

86

unmet load with computing the system’s capital cost. In addition, a techno-economic

87

optimization was designed in [14] based on the LLPand LCC. Iman et al. [21] proposed a multi-

88

objective optimization using a hybrid method by combining numerical with the genetic algortihm

89

to minimize three objective functions.

90

Another similar work conducted by Muhsen in 2016, in which a Pareto optimization

91

approach was employed to optimize a weighted objective function [22]. However, it is difficult

92

to identify the relative importance of individual objective in the objective space as discussed by

93

Talbi in 2009 [23]. Therefore, a Pareto multi-objective optimization based on the non-dominated

94

set of the solutions is essential which can give a more informative picture of the objective space.

95

The authors of [24] proposed a hybrid method by combining differential evolution multi-

96

objective optimization (DEMO) and multi-criteria decision making (MCDM) for sizing of a

97

SAPV system. Non-dominated sorting and crowding distance using NSGA-II [25] concepts were

98

employed for distribution optimal solutions on the Pareto front. Then, the ideal solution was

99

selected by using the Analytic hierarchy process (AHP) based concept to arrange the preference

100

of configurations between LLP and LCC. Hussein et. al [26] proposed an optimal design of the

101

SAPV system using multi-objective particle swarm optimization (MOPSO) in Malaysia. Two

102

104

adaptive weights PSO (
 ) using techno-economic criteria. The performance results

105

configuration in term of accuracy. However, the main demerit of the proposed method in Ref.

103

variants of PSO algorithm were presented referred to as sigmoid function PSO ( ) and demonstrated that  algorithm has a trivial superiority in selecting an optimal

4

106

[26] is by using a non-scale (NS) approach which can conduct only one solution based on given

107

weights. In addition, the proposed algorithm cannot cover all Pareto front (PF) solution when all

108

possible status of weighs within [0,1] are considered.

109

It can be concluded based on the above literature review that most research papers used

110

iterative method for calculating multi-objective function which takes a very long execution time.

111

In meanwhile, other research woks obtained only single objective using metaheuristic method

112

after aggregation of the individual objective. Therefore, obtaining a set optimal solution using PF

113

is important to enable choosing most appropriate optimal configuration to the user-costumer. The

114

contributions of this pepper can be summarized by follows:

115

•

functions are presented.

116 117

• • •

124

The CPU-execution time of three SS-PBI, SS-NS, and MOSS-NDRW methods are 65.2 s, average 53 s, and 72 s, respectively, which is notably faster than iterative method 10295.7 s.

122 123

The analysis performance of the SAPV system is presented utilizing resulted by optimal configurations of different scenarios.

120 121

Various Pareto optimal solutions are obtained based on SS-PBI, SS-NS, MOSS-NDRW methods.

118 119

Optimally designs of the proposed SAPV system using multiple scenario multi-objective

•

The proposed MOSS-NDRW method outperformed well-regarded DEMO-NSGA-II algorithm in terms of diversity, convergence, coverage, and computational time.

125

The rest of the paper is organized as follow. Section 2 presents the definitions, concepts, steps of

126

modeling the SAPV systems. The Salp Swarm Algorithm and the details of the proposed multi-

127

objective optimization approach are given in Section 3. Section 4 presents the results and

128

discussions. Finally, Section 5 concludes the work and suggests future directions.

129 130

2. Modeling of the SAPV system

131

2.1 Photovoltaic model

132

A standalone PV (SAPV) system comprises mainly of four parts which are PV arrays,

133

storage battery, DC/DC converter, and DC/AC inverter [27]. Before installing the PV array in a 5

134

SAPV system, efficient and cost-effective PV model is essential. Therefore, the single-diode PV

135

model is utilized in this research due to its simplicity and accuracy [28]. For instance, the single-

136

diode PV model offers high ability in reflecting the reality behavior when it is dealing with non-

137

linearity and stochastic nature among other mathematical models [29]. The mathematical

138

equation of the single-diode PV model is given by,

139

=  −   

140

 

 − 1 −

 

,

(1)

where and ! are the output current (A) and voltage (V) of PV cell,  is the photocurrent (A),

142

 shows the reverse current (saturation current) of the diode (A), "# and " indicate series and

143

following equation:

141

144 145

parallel resistances of the PV cell, the voltage thermal of the diode is !$ and expressed by the !$ =

%&' (

,

(2)

where ) is the diode’s ideality factor, * indicates the cell temperature in (K), + refers to the

147

constant of Boltzmann (1.3806503*10-19 J/K), and , is the electron charge (1.60217646*10-19

148

of PV array is expressed by

146

149

150

Coulombs). Since the PV array consists of parallel - and series -# modules, the output current = -  − - / 0 1 3 2



 4

+

  4

67 − 18 −

4 

3





+

  4

6,

(3)

The five parameters (  , / , "# , " and )) the of single-diode PV model are extracted

151

using improved electromagnetism (IEM) algorithm. The output I-V and PV curves at seven

152

environmental conditions are shown in Fig. 1. (A) and (B). To simulate the output power of the

153

PV array, a maximum power point tracker (MPPT) is employed in this study.

154 155

Table 1. Extracted five parameters of single-diode PV model at MPPT. Solar Radiation (W/m2)

Cell Temperature (k)

978

328.56

Parameters

Values

"#

1.3257

)

0.2140

6

"

38.5131



5.9134E-06

Average value of RMSE

0.0589

6.3930



156

157 158

(A)

7

159 160

(B)

161

Fig. 1. Shows the output characteristics under seven weather condition of PV cell (A) I-V curve

162

and (B) P-V curve.

163 164

2.2 The mathematical model of storage battery The lead-acid battery is used for simulating SAPV system due to its reliability and cost-

165

effective [30,31]. The capacity of the storage battery can be computed by [32,33]

166

:;%$ =

<=>?@ ∗BC

CC∗DE∗DFGH

,

(4)

168

where :;%$ is the capacity of the battery (KW), IJ%K shows the energy of the load demand, L

169

efficiencies of battery (85%) and inverter (95%), respectively. The minimum discharge value of

167

170 171 172

is the number of autonomy days which is chosen to be 3 days in this study, MNOP and MQ are the

the battery LRL is (80%). The state of charge (SOC) and minimum energy to be stored in the storage battery can be expressed as follows [34]: I;%$ = : (O − 1) + S (O) − J (O )T,

(5)

8

173

174

:VFG , I;%$ < :VFG : (O) = UI;%$ , :VG < I;%$ < :V%X , :V%X , I;%$ > :V%X IVFG = :V%X ∗ (1 − LRL),

(6)

(7)

176

where I;%$ is the hourly capacity of the battery, : (O − 1) and : (O) are the SOC of the

177

the amount of energy to be stored in the battery for one year can be written in the following

178

equation:

175

179 180 181 182 183

184

battery at initial and final points of discharging and charging, respectively [35]. In meanwhile,

`ab I;%$ = (∑`ab Gc2 I[\\ O]^_ − ∑Gc2 LdN[Ne O]^_ ). M:ℎ,

(8)

where M:ℎ is battery’s charging efficiency. To increase the reliability of the storage battery, the

number of batteries to be connected in parallel (;%$ ) and series (;%$ ) are considered using the DC bus nominal voltage (!;h# ) and the nominal voltage of batteries (!;%$ ). -;%$ = -;%$ =

('i? ) (ji? )

il i?

× :;%$ ,

(9)

,

(10)

185 186

2.3 Proposed criteria for the sizing of SAPV system

187

The performance of the SAPV system can be evaluated by the selected configuration, the

188

optimal configuration requires to be chosen in the design of the system to fulfill the load

189

demand. In this paper, a Multiple Scenario Multi-objective Salp Swarm algorithm (MS-MOSS)

190

algorithm is proposed as an optimization problem for finding optimal sizing of a SAPV system.

191

Therefore, the optimal configuration is based on minimizing two conflicts objectives with

192

multiple parameters, the reliability of the system and the economic cost. The system’s reliability

193

can be described by many technical parameters such as loss of load probability (LPSP), loss of

194

load expected (LOLE), total energy loss (TEL), equivalent loss factor (ELF), state of charge

195

(SOC), and loss of load probability (LLP). In contrast, the economic parameters such as net

196

present value (NPV), the annualized cost of a system (ACS), capital recovery factor (CRF), the

197

average generation cost of energy (:%H ), levelized cost of energy (LCE), and total life-cycle cost 9

198

(TLCC) [5]. Based on this paper [5], we consider the LLP as the parameter stability of the

199

system. In addition to that, the LCC as economic parameters.

200

2.3.1

First objective: loss of load probability

201

In order to calculate the reliability of the proposed SAPV system, loss of load probability

202

(LLP) is used for this purpose which defines as the ratio of the annual energy deficits to annual

203

energy of load demand over a period of time and is expressed by [36],

204

rwx mm = ∑stuv

∑stuv

(11)

205 206 207 208 209 210 211

2.3.2

Second objective: Life cycle cost The life cycle cost (LCC) is used for the cost analysis of the SAPV system [10]. LLC is

composed of summation of three parts which are initial capital cost ( :#$ ), operating and

maintenance cost for an item over a period of time (&{#$ ), and value of replacement cost ("#$ ) in (USD). The following equations are utilized to calculate LCC [37], mm: (|L) = :#$ + &{#$ + "#$

(12)

212

The calculation of the initial capital cost of each component for the SAPV system must

213

be considered such as components price, installation and the connections, and the cost of the

214 215 216 217 218 219 220 221 222 223

civil work. The initial cost of the off-grid SAPV system ( :% ) is given by:

:#$ ($) = : × |#$, + :;%$ × |#$,;%$ + :~ × |#$,~ + :GH × |~#$,GH + :FHF (13)

where (:,|#$, ) are the capacity and unit cost of the PV array in (W), :;%$ , |#$,;%$ are the capacities of the battery and unit cost in (W), :~ , |#$,~ are the capacity and unit cost of the DC-DC converter in (W), :GH , |~#$,GH are the capacity and unit cost of the DC-AC inverter in

(W), and :FHF is the initialization cost and civil work. Two variables need to be calculated which are the inflation rate ( d ) and interest rate ( O ). In order to calculate the value of operating and

maintenance cost (&{#$ ) over a period of time (m*), this can be performed by following [38]:

10

224

&{,#$ G

2„ J'

6 dR] O ≠ d ?‚ ƒ &{#$ ($) = € &{,#$ × m* dR] O = d 2

 31 − „

(14)

226

where (&{,#$ ) denotes to the operation and maintenance cost through first year in ($). In

227

which are DC-DC converter, storage battery, and DC-AC inverter which have a shorter lifetime

225

228

229

the standalone PV system, three components are required for replacement during a period of time than PV arrays. Thus, the "#$ equation can be expressed by the following [37]: n

=†‡∗r

2 ‚ ˆl‰ Šx 7  2G

"#$ ($) = | × 1∑Fc2 ˆl‰ 

(15)

231

where | is the initial costs of the three components that need for replacement ($), and "Ghy

232

shows the number of the component replaced in m*. Table 2 summarizes different financial data evaluation for the proposed SAPV system [13,39].

233

Table 2. Various components and financial data of the SAPV system [40].

230

Components PV arrays Converter Storage battery Inverter

Unit cost in ($) 1W 0.5 W 0.125 W 0.5 W

‹Œ 20 10 5 10

Ž& 1% 0% 5% 0%

‘’“”• 0 1 3 1

–— 8%

–“ 4%

234 235

3. Optimal sizing of the proposed standalone PV system

236

3.1 Salp swarm optimization algorithm (SSA)

237

Before choosing an optimal configuration, it is important to consider a multi-objective

238

optimization to find Pareto optimal solutions. Recently, a novel meta-heuristic population-based

239

Salp Swarm Algorithm (SSA) proposed by Mirjalili et. al. [41] that has been proven its superior

240

performance in solving multi optimization problems. SSA algorithm works on a group of

241

solutions that allows us to find a tradeoff between multiple, often conflicting objectives with fast

242

convergence and high diversity. Inspiring by the swarm behavior of salps in oceans, SSA uses

243

slaps within a group (salp chain) for exploration and exploitation phases. The salp chain is

244

dividing into two parts: leader and follows. The leader at first chain guides the flowers for

245

discovering new search region and the reminder flowers flow the leader as shown in Fig. 2. [42]

246

SSA likewise particle swarm optimization (PSO), which the salps’ position defined as a d-

247

dimensional search space, where d refers to the number of variables for the sizing of a SAPV 11

248

system problem. Therefore, the position is stored in 2-dimensional matrixes called X. During the

249

optimization process, the leader position and food source (F) are updated in each iteration.

250

Fig. 2. Salp swarm algorithm with leader and follower concept.

251 252 253 254

255 256

The leader’s position can be adaptive by follows: ™ + :2 ›(œ − m): + mž :` Ÿ 0.5 ˜™2 = š , ™ − ›(œ − m): + mž :` < 0.5

(16)

where ˜™2 is the leader’s position, ™ is the food source (F) position in Nth dimension, œ and m are

258

the upper and lower bounds, : and :` are randomly distributed with the interval [0,1], and :2

259

equation:

257

260

plays the main role in exploration and exploitation phases and expressed in the following

:2 = 2

ƒ3

 £† 6 †¤¥¦

,

(17)

12

262

where * is the current iteration and *VB§ is the maximum number of iterations. Therefore, :2 is

263

stages of optimization. The followers’ positions are updated using the follows:

264

˜™F = 0.5 )*  + !¨ *,

261

265 266 267 268 269

employs the diversification in the early stages. Meanwhile, emphases on intensification in later

(18)

where N Ÿ 2 and ˜™F is the position’s follower salp, !¨ is the initial speed, * is time, and ) = ©rˆ?ª >

, where ! =

§ƒ§> '

. In this algorithm, the discrepancy between iteration is equal 1 and

considering ! =0, the reason for that is because the time in optimization is iteration. The equation can be given by, ˜™F = 0.5›˜™F + ˜™Fƒ2 ž,

(19)

270

In this research study, both single and multi-objective SSA were used to find the optimal

271

size of the SAPV system. In the single objective salp swarm (SOFSS) algorithm, the SSA

272

algorithm starts by initializing randomly multiple salps. Then, the best fitness function is chosen

274

after calculating the fitness of each salp and stored in (F) as a food source. The parameter :2 is

275

for the i-th dimension using Eq. (16), and the followers’ positions are updated utilizing Eq. (18).

276

Penalty boundaries are used if any of salp extracts outside of search space.

273

updated based on Eq. (17). As mentioned above, the leader’s position is updated in each iteration

277

The SSA algorithm based on single-objective function (SOF) is considered to minimize

278

the two conflicts objective LLP and LCC. Several approaches have been employed in order to

279

reach for uniform distributions to the Pareto front (PF). For brevity, the most commonly utilized

280

approaches to enable the directions in the design space are the weighted sum (WS) approach and

281

Tchebycheff (TCH) approach [43]. However, these approaches are limited to cover all PF and

282

the complexity in local minima avoidance. Thus, we consider three variants approaches in order

283

to obtain various optimal solutions for sizing of a SAPV system:

284

3.1.1

285

Penalty-Based Boundary Intersection (PBI) PBI method is commonly utilized for scalarizing two conflicting and nonlinear

286

dimensional objectives, which can be expressed as follows [44]:

287

^; (˜|
, ¬) = ­2 + ¬­ , 13

288

289

­2 =

®((§)ƒ¯ ∗ )† °® ‖°‖

,

­ = ²d (˜ ) − ­2 ‖°‖ + ³ ∗ ², °

291

where ¬(¬ Ÿ 0), ¬ a penalty parameter,
and ³ ∗ are the direction vector and ideal point,

292

3.1.2

290

respectively.

Non-Scale approach (NS) In this approach, the two conflicting objectives are weighted and aggregated then

293 294

converted into a mono-objective function, which can be written by [23],

295

F (˜) =

¨„r (§)ƒ¨„r¤rˆ (§)

¨„r¤?´ (§)ƒ¨„r¤rˆ (§)

,

(20)

297

where FV%X (˜) is the upper bounds and FVFG (˜) is the lower bounds of the Nth individual

298

objective function. The weights coefficients range are between 0 >
F < 1, where the summation of weights for all objectives must equal to 1.

299

3.1.3

296

Multi-objective Salp Swarm Non-dominated Roulette Wheel (MOSS-NDRW)

300

method

301

The multi-objective salp swarm algorithm (MOSSA) maintains multi-objective formation

302

of the problem as opposed to the previous two methods. In MOSSA, the best non-dominated

303

solutions are stored in the repository. For excellent convergence to pareto front, each salp is

304

compared against all salps in repository using dominance Pareto operator. When the salps

305

dominate the solution in the repository, they will be replaced and added in the repository. It is

306

important to note that, if there is no salp dominated in comparison with solutions in the

307

repository, the new salp will be moved to the archive. By this way, it can be guaranteed that the

308

non-dominated solutions are stored in the repository.

309

A special case may be occurred when the salp is non-dominated and the archive is full in

310

comparison with solutions in the repository. Then, one solution of the similar non-dominated in

311

the repository residents will be deleted. For finding non-dominated solutions with the populated

312

neighborhood, the neighborhood solutions’ number with maximum distance is calculated. For

14

313 314 315

each objective, minimum and maximum values are stored by calculating the distance which is µµµµµµµµµµ¶ƒV4 µµµµµµµµµ¶ VB§

given by L = n#F$q #F¯n. The segment with one solution will be chosen as the best solution in the repository. The solutions in the repository are ranked based on the number of neighboring

316

solutions and a roulette wheel is used for selecting one of them. When MOSSA faces a large

317

number of neighboring solutions (crowded neighborhood), one of them will be excluded from

318

the repository. The steps of single-objective and multi-objective SSA methodologies are depicted

319

in Fig. 3.

320

15

Fig. 3. The main steps of SOFSSA and MOSSA.

321 322

3.2 Validation of the proposed methods using iterative method

323

In order to validate the accuracy of proposed methods for sizing of a SAPV system, an

324

iterative method is used. The numerical method is time-consuming which is considered the main

325

obstacle of this method. Thus, the intuitive method is used to give an initial evaluation and

326

reducing the execution time [16]. After defining the ranges of serial and parallel number of PV

327

modules and storage battery by the initial method, the simulation is started by incrementing each

328

variable. During the iterative process, each number of PV modules and storage battery are stored

329

in the matrix until the desired value of LLP is reached. Then, the calculation of LLC is

330

performed for all stored configurations stored within the desired LLP values. The optimal

331

configuration is chosen based on the desired value of LLP and minimum LLC.

332 333

3.3 Multiple scenario multi-objective salp swarm algorithm (MS-MOSSA)

334

In practice, the optimization problems must be considered for their performance over various

335

operating conditions and scenarios. Therefore, a resilient optimal solution must be feasible under

336

all scenarios [45]. In this paper, we proposed multiple scenarios based on MOSSA (MS-

337

MOSSA) in order to achieve two requirements as follows:

338

•

Trade-off solution corresponding to multi-objective.

339

•

Comprising solutions corresponding to multiple scenarios.

340

These two points make multiple scenarios, multi-objective sizing optimization of SAPV system

341

challenging. The authors of [46,47] proposed a multi-scenario, multi-objective optimization

342

problem into a series of sub-problems and it has the ability to operate on one or more

343

optimization problem on each sub-problem until finding an acceptable solution. As pre-

344

mentioned, the various scenarios have been considered in this study in order to achieve the best

345

trade-off among these scenarios. The process from defining the system’s components to the final

346

set of optimal configurations is shown in Fig. 4. The three scenarios will be discussed in the

347

result and discussion section for SS-PBI method, SS-NS method, MSMOSS-NDRW method.

348

The best optimal solution will be validated using the iterative method. 16

349

350 351

Fig. 4. Description of the proposed multiple-scenario process design of the SAPV system.

352 353

3.4 Management of energy flow for the proposed SAPV system

354

In the proposed SAPV system, energy flow management is necessary to calculate the output

355

power of the PV panels, set the maximum and minimum capacity of the storage battery, and for

356

securing case when the SAPV system is not capable for needing energy for the load electrical

357

demand. After obtaining the required specifications which are tabulated in Table 3, the

358

simulation firstly begins to check the status of the net power of the PV system. Secondly, three

359 360

stages can be considered for describing the I4n$ and expressed by following:

Table 3. components’ specifications of the standalone PV system. Components Kyocera +:120-1 PV panels

Battery

DC-DC controller DC-AC inverter

Characteristics Maximum power at STC. Open circuit voltage Short circuit current Voltage at MPP Current at MPP No. of cells connected in series Nominal operation cell temperature Lead acid Efficiency Maximum LRL Bus voltage Battery voltage Efficiency Efficiency

17

Value 120 (W) 21.5 (V) 7.45 (A) 16.9 (V) 7.1 (A) 36 43.6 (℃) 85 % 80 % 24 (V) 12 (V) 95 % 90 %

AC voltage

Electrical load AC

230 (V)

361 362 363 364 365 366 367 368

Stage 1:

If the I4n$ is equal to zero, the IJ%K is supplied directly by the I . There is no

deficit or excess energy. Stage 2:

If the I4n$ is larger than zero, the I supplies the IJ%K and the excess energy

will be used for charging the storage battery if it is not at :V%X . Otherwise, the excess energy is considered as dump energy.

Stage 3:

If the I4n$ is less than zero, the I will supply the IJ%K with/without storage

battery depending on the SOC of the battery. If the SOC is larger than :VFG , then

370

the energy in the storage battery will be used for providing IJ%K . Whilst, if the SOC

371

is less than :VFG , then the system is not capable to meet the IJ%K and there is deficit energy. The two objective LLP and LCC are computed in each iteration. The

372

energy flow management of the SAPV system is illustrated in Fig. 5.

369

18

373 374 375

Fig. 5. The energy flow management of the standalone PV system. 3.5 Metrological data and Load demand profile

376

Hourly solar radiation and ambient temperature for one year are proposed in this study which

377

is in Klang Valley registered by Subang Meteorological Station with 101.6o longitude east and

378

3.12o latitude north as shown in Fig. 6. The load electrical demand profile of this study is

379

selected using hourly hypothetical data for one year in a rural area in Malaysia [13] as shown in

380

Fig. 7. The maximum load demand is proposed to be 5KW, which is efficient to meet the

381

customer needs such as lights, fans, TV, refrigerator, computer, etc. However, considering

382

hourly load demand based on real data can affect the reliability behavior of the SAPV system

383

and the price of the conducted electricity [48].

19

384 385

Fig. 6. Monthly meteorological data for one year.

386

387 388

Fig. 7. Hourly hypothetical load demand of a typical house in rural area.

389 390

In the next section the results and discussions are presented.

391 20

392

4. Results and discussion

393

The MS-MOSS algorithm has been considered for finding sets of optimal solutions to the

394

proposed standalone PV system. The decision variables of the search space are within range the

396

[4,80] for the PV modules (series -# and parallel - ), and the range of storage battery is [4, 60].

397

several attempts to reach of acceptance level of stability to optimal solutions. Three scenarios are

398

used for finding the trade-off between techno-economic objectives.

395

The population size is chosen to be 30 and the maximin iteration for all scenarios is 50 after

399

In the first scenario, the SSA algorithm based on PBI method is used for finding the optimal

400

solution. In SS-PBI scenario, only one optimal solution can be chosen in each execution as

401

depicted in Fig. 8 [49]. From Fig. 9, It is evident that the SS-PBI based method tries to obtain the

402

optimal solution of the LLP and LCC (USD) objectives. The best-found value of LLP is

403

0.000447 and LCC is 57183.76, respectively. Meanwhile, the best number of PV models and

404

storage batteries are given in Table 4. The SS-PBI method shows its ability to find an optimal

405

solution between the two conflicts objective. However, the main obstacle of this method is

407

giving an appropriate value of ¬. According to [50], the best values of ¬ and
are chosen to be

408

PBI method is that ideal solution of the PF’s position is required to be known. In addition to that,

409

the complexity of finding an optimal solution when the objectives are more than two [51].

406

0.5 for achieving a balance between LLP and LCC objectives [50]. The major obstacle of the SS-

410 411

Fig. 8. Obtained optimal PF solution using SSA based on PBI method. 21

412 413

Fig. 9. Evaluation of LLP and LCC (USD) during the optimization process of PBI method.

414 415

¸¹

¸º

¸

¸»¼½

»¼½

º»¼½

Table 4. Optimized numbers of PV modules and storage battery based on SSA-PBI method, 256

4

64

48

24

2

Time 65.2187

416 417

The second scenario is to select an optimal solution for the SAPV system based on SS-

418

NS method. In this scenario, the individual objective can significantly be influenced by the given

419

value of weight. Therefore, a wide range of weights is chosen with step size 0.05 to overcome

420

the difficulty of initializing weights process and increasing number of solutions on Pareto

421

optimal set. The Pareto optimal set using SSA-NS method is illustrated in Fig. 10. As can be

422

seen in this figure, the distribution of Pareto optimal solutions is low across both objectives. This

423

is because of the limitations accompanied by various given weights. Moreover, the SS-NS

424

method is similar to SS-PBI method by identifying only one solution at each run time.

425

The evaluation of fitness function () for all status of weights is shown in Fig. 11. The

427

value of  at first status of weights (0.05, 0.95) is 0.0342 and the minimizing of  at the end

428

For convenience, the sets of weights, number of PV modules, storage batteries, and the two

426

of generations with the final status of weights (0.95,0.05) reached to 0.0025 as shown in Fig. 11.

22

429

objectives are tabulated in Table 5. It’s clear that the LLP values corresponding proportionally

430

with W1 values and inversely related to W2.

431 432

Fig. 10. Obtained optimal PF solutions using SSA based on non-scale method.

433

434 435

Fig. 11. Evolution of fitness function () for various sets of weights.

23

436 437

Table 5. Pareto optimal set configurations and performance with various weight sets Status 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

W1 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

W2 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05

¸¹ 152 180 192 200 209 208 210 220 228 228 230 231 235 228 240 234 236 234 256

¸º 4 4 4 4 11 4 30 55 4 57 23 7 5 4 30 26 59 6 64

¸ 38 45 48 50 19 52 7 4 57 4 10 33 47 57 8 9 4 39 4

¸»¼½ 28 32 34 37 39 40 45 48 48 48 51 54 54 59 52 60 59 60 53

Ž¾ 0.032790983 0.034701423 0.03455516 0.033886349 0.032755567 0.031417664 0.029917 0.028086922 0.025951335 0.023804139 0.021736879 0.019532971 0.017169598 0.014866625 0.012465012 0.009998479 0.007524628 0.005044092 0.002551142

LLP 0.126866937 0.047312627 0.027942083 0.018177516 0.011703162 0.011613826 0.008139217 0.004152678 0.002331942 0.002331942 0.001522993 0.000918299 0.000530064 0.000485458 0.000529892 8.97E-05 8.97E-05 8.97E-05 0

LCC 35848.0288 41203.8152 43579.3084 45630.5482 47552.4414 47681.788 49386.9211 51740.5609 52950.1609 52950.1609 54094.2007 55087.0405 55691.8405 56036.1735 55886.7473 57223.9201 57245.7735 57223.9201 58586.4939

Time 51.578125 57.390625 57.46875 51.96875 52.34375 57.09375 59.5 52.625 51.25 52.4375 50.609375 51.125 51.484375 62.140625 52.390625 51.4375 55.796875 57.578125 54.046875

438 439 440

For results validation, we compared our proposed MOSS-NDRW method with well-

441

regarded algorithm proposed by Dhiaa. et. al. [24]. The optimal PF solutions obtained are

442

illustrated in Fig. 12 and Fig. 13. The best optimal set PF solutions have been achieved by using

443

the third scenario which is based MOSS-NDRW concept as shown in Fig. 12. The minimum

444

LLP value found is 0.0007 and the maximum value is 0.85. Hence, the desired value of LLP is

445

0.01 for sizing of a SAPV system [35]. As mentioned before, the non-dominated solutions

446

always added to the repository and deleted the crowded neighborhood by employing roulette

447

wheel selection. Thus, the solutions are successfully distributed is each region of the PF. In

448

contrast, the DEMO-NSGA-II method failed in establishing accurate PF solutions as it is shown

449

in Fig 13. The reason of that is because of obtaining PF solutions is always challenging for

450

aggregation method. This means that the employed comparison crowding distance technique

451

cannot choose all solutions to fill up the PF [52]. The minimum value of LLP corresponding

452

with LCC obtained by DEMO-NSGA-II are 0 and 120029.29 $ at 378 number of PV modules

453

(42 in series and 9 in parallel) and 60 number of the storage battery. On contrast, the worst value

454

of LLP with correlated with LCC are 0.9008 and 67206.91 $ at 167 number of PV modules (24 24

455

in series and 7 in parallel) and 54 number of the storage battery. The gap can clearly be observed

456

in the PF solutions obtained by the SS-NS method. Moreover, the sizing of a SAPV system

457

based on the third scenario demonstrates a high ability in term of convergence and coverage

458

among the previous scenario [41]. These results can efficacy demonstrate the superiority of

459

MOSS-NDRW method which is able to drives the salps uniformly among different regions of the

460

PF. The CPU_execution time of the MOSS-NDRW and DEMO-NSGA-II methods are 72.75 s

461

and 421.62 s, respectively. It is clear that the MOSS-NDRW method is faster than proposed

462

method in Rf. [24]. by 5.79 times.

463 464

Fig. 12. Obtained optimal PF solutions using MOSS-NDRW method.

465

25

466 467

Fig. 13. Obtained optimal PF solutions using DEMO-NSGA-II method.

468

For demonstrating the effective are of the PF between the LLP and LLC objectives, the

469

circled dashed on the right bottom of the Fig. 14 shows the various desired configurations at

470

favorable levels of LLP values. It’s worth to mention that the stored solutions in the repository

471

are based on minimum values of the LLP and LCC among other solutions. However, according

472

to optimally size of the SAPV system, the priority is given to the LLP objective.

26

473

Fig. 14. Effective area of the optimal PF solutions using MOSS-NDRW method.

474 475 476

The validation of the previous three scenarios can be performed by using the iterative

478

method. Thus, the validation of the numerical method will be within ranges of 0.02 Ÿ LLP Ÿ

479

0.001 for more excellent availability values as presented in Table 6. It is worth to note that, the iterative method is very sensitive to the design space which can meet the total number of PV

480

module in some iterations and we can observe that in Table 6 and Table 5. The CPU-execution

481

time of the iterative method is very longer than others which is about 10295.71875 s. The reason

482

for that the iterative method went through all possible configurations less than 0.001 of the LLP

483

value. The number of configurations is 59502 which is very difficult to be figured or tableted.

477

484 485

¸ 200 209 208

¸’ 5 11 8

Table 6. validation of the optimal configurations using iterative method.

¸Á 40 19 26

»¼½ 37 39 40

LLP 0.018177516 0.011703162 0.011613826

Def (KWh) 405.3195276 260.9553544 258.9633428

Excess (KWh) 6804.276718 8037.628937 7893.43167

27

LCC 45630.54823 47552.44144 47681.78804

Cost year 2281.527412 2377.622072 2384.089402

210 228 242 216

30 6 11 18

7 38 22 12

45 48 48 42

0.008139217 0.002331942 0.001102284 0.00819904

181.4870435 51.99729484 24.57856956 182.820959

8103.286516 10771.88942 12781.47489 9023.822404

49386.92106 52950.16087 55066.96087 49452.48125

2469.346053 2647.508044 2753.348044 2472.624063

486 487

For analyzing the performance of the SAPV system, the optimal configurations based on

488

three scenarios are considered as illustrated in Table 7. Despite of the stochastic of nature, there

489

can find optimal configurations of the SAPV system. However, achieving a high level of

490

reliability and decreasing the total cost of the system is essential for the optimization design of a

491

SAPV system. Inspecting the results in Table 7, the numbers of hours which system is not

492

capable to meet the load demand for the SS-PBI, SS-NS, MOSS-NDRW scenarios are 87.6, 175,

493

and 210, respectively. In fact, decreasing the unmet load corresponding to raising the system’s

494

total cost.

Scenario SS-PBI SS-NS MOSS-NDRW

495

¸ 256 231

¸Á 4 7

¸’ 64 33

»¼½ 48 54

242

11

22

48

Def (KWh) 10.6063656 20.4760854 24.5785695

Excess (KWh) 148310.698845 11237.0871886 12781.4748919

LCC

LLP 0.0004756 0.0009183

57183.7608 55087.0404

0.0011022

55066.9608

Table 7. Chosen optimal configuration based on three scenarios.

496 497

The performance design of the system is taken for the 15 days of March based on optimal

498

configurations of the three scenarios and presented in Fig. 15. A, B, and C. The sum of the

499

conducted energy of the PV modules through one year for the three scenarios are 35288 KWh,

500

31842 KWh, and 33358 KWh.

28

501 502

(A)

503

504 505

(B)

29

506 507 508 509

(C) Fig. 15. Shows the performance of the SAPV system at various scenario: (A) SS-PBI method, (B) SS-NS method, and (C) MOSS-NDRW method.

510

Inspecting to the previous results, the obtaining PF solutions in terms of convergence,

511

coverage and diversity is a very challenging for multi-objectives optimization. As it was stated

512

that PBI method can only provide a single solution. Whist, NS method is strongly depended on

513

the given weighted value for the individual objective and has a lack in coverage and convergence

514

to the PF. The worst PF solution has been obtained by NSGA-II algorithm. It can be noticed that

515

the proposed methods are able to find single or set of optimal solutions for the two conflicting

516

objectives. However, the MOSS-NDRW algorithm demonstrated better performance than others

517

in terms of convergence and coverage. This is because the MOSS-NDRW updates slaps’ position

518

around the best obtained non-dominated solutions. Moreover, the adaptive mechanism can

519

always speed up the motion of salps toward the best non-dominated solutions obtained in the

520

achieve. The efficient coverage of the MOSS-NDRW algorithm is because of the solutions

521

selection mechanisms by the leader and the maintenance of the repository. It means that the

522

solutions are discarded in population regions and replace their positions by other solutions that

523

are not found in PF. The described phases of the MOSS-NDRW algorithm not only leads to

524

discover new regions in design space but also keep the best non-dominated solutions in the

30

525

repository. In other words, the MOSS-NDRW algorithm inherits significance local optima

526

avoidance, fast convergence rate, and reliable exploitation mechanism.

527 528

5. Conclusion

529

Considering a reliable design with a minimum cost of the system is essential for any community

530

and can increase the investment in installing of the renewable energy sources which lead to

531

improving the standard of living by reducing global warming, suitable applications in a

532

residential and rural area, and mitigate the dependency on fossil fuels sources. In this work, MS-

533

MOSS algorithm was proposed to find the optimal set of PF solutions considering conflicting

534

objectives for sizing of SAPV system. Three scenarios used are salp swarm Penalty-Based

535

Boundary Intersection (SS-PBI), SS Non-Scale (SS-NS), and Multi-objective Salp Swarm Non-

536

Dominated Roulette Wheel (MOSS-NDRW) algorithms. According to results, the optimal

537

configurations are 256, 231, and 242 PV modules and 48, 54, and 48 storage battery,

538

respectively. In meanwhile, the LLP values are 0.0004, 0.0009, and 0.0011. The LCC values that

539

correlate LLP values for the three scenarios are 14310.69 (USD), 11237.08 (USD), and 12781.47

540

(USD). The validation of the optimal solutions was verified by using the iterative approach. The

541

results indicated that the three scenarios can obtain optimal solution of the SAPV system. It was

542

observed that the MOSS-NDRW scenario outperforms DEMO-NSGA and other scenarios in

543

terms of converge and convergence. The authors believe that the MOSS-NRW algorithm is

544

reliable, efficient and can be applied for designing other systems in the field of energy

545

applications.

546

Conflict of interest

547

The author declares that there is no conflict of interest regarding the publication of this paper.

31

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•

A new multiple scenario multi-objective salp swarm optimization (MS-MOSS) is proposed

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An optimal size for a standalone PV system is found using MS-MOSS

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Three scenarios have been presented to obtain on Pareto optimal solutions

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The results demonstrate the efficiency of MS-MOSS for sizing of SAPV system