Applied Energy 158 (2015) 26–34

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Applied Energy

journal homepage: www.elsevier .com/ locate/apenergy

Optimal sizing of hybrid PV/diesel/battery in ship power systemq

http://dx.doi.org/10.1016/j.apenergy.2015.08.0310306-2619/� 2015 The Authors. Published by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

q The work was supported by Ministry of Industry and Information Technologycooperated with Ministry of Finance (GK110900004) and fundamental researchfunds for the central universities (HEUCFX41401).⇑ Corresponding author.

E-mail address: wenshuli2010@126.com (S. Wen).

Hai Lan a, Shuli Wen a,⇑, Ying-Yi Hong b, David C. Yu c, Lijun Zhang a

aCollege of Automation, Harbin Engineering University, Harbin 150001, ChinabDepartment of Electrical Engineering, Chung Yuan Christian University, Chung Li District 320, Taoyuan City, TaiwancDepartment of Electrical Engineering and Computer Science, University of Wisconsin-Milwaukee, Milwaukee 53211, USA

h i g h l i g h t s

� An optimal sizing method is developed for a hybrid PV/diesel/ESS ship power system.� The output of PV along a navigation route is explored for the ship power system.� Five operating conditions of the load in the ship power system are modeled.� The impact of various prices of PV on cost is studied.

a r t i c l e i n f o

Article history:Received 7 June 2015Received in revised form 8 August 2015Accepted 12 August 2015Available online 27 August 2015

Keywords:Photovoltaic generationShip power systemEnergy storage systemIrradiation

a b s t r a c t

Owing to the strict restrictions imposed by the Marine Pollution Protocol and the rapid development ofrenewable energy, the use of solar generation and energy storage systems in ship power systems hasbeen increasingly attracting attention. However, the improper sizing of a hybrid power generationsystem in a ship power system will result in a high investment cost and increased greenhouse gasemission. This paper proposes a method for determining the optimal size of the photovoltaic (PV)generation system, the diesel generator and the energy storage system in a stand-alone ship powersystem that minimizes the investment cost, fuel cost and the CO2 emissions. The power generationfrom PV modules on a ship relies on the date, local time, time zone, longitude and latitude along anavigation route and is different from the conditions of power systems on land. Thus, a method, whichtakes the seasonal and geographical variation of solar irradiations and temperatures along the routefrom Dalian in China to Aden in Yemen into account, for correcting the output of PV modules isdeveloped in this paper. The proposed method considers five conditions along the navigation routeto model the total ship load. Four cases are studied in details to demonstrate the applicability of theproposed algorithm.� 2015 The Authors. Published by Elsevier Ltd. This is anopenaccess article under the CCBY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

As the amount of greenhouse gas that is produced by the shipsystems increases, the International Convention for the Preventionof Pollution from Ships (MARPOL) [1] recently has made the claimthat the ships must find a new way to reduce their collective emis-sions of greenhouse gas. Serious environmental pollution and thelow energy efficiency of traditional ship systems whose power issupplied only by diesel generators can be mitigated by properlyintegrating renewable energy. Recently, photovoltaic (PV) energy

has been introduced into ship power systems to reduce theirgreenhouse gas emissions, improve energy efficiency and reinforcethe ship power system stability. However, the use of too muchsolar energy may increase investment cost and make the powersystem unstable owing to the uncertainty associated with solarpower [2,3]. Additionally, a wide range of investigations [4–9] havefound that the use of an energy storage system (ESS) is one of themost effective solutions for ensuring the reliability and powerquality of power systems and favors the increased penetration ofdistributed generation resources. Some studies [10,11] havedemonstrated that an optimal management of ESS with distributedgenerators in power systems can shave the peak load, decrease thecost of updating the power system and reduce negative impact onthe environment.

A ship power system with PV and ESS can be regarded as aspecial mobile and islanded microgrid. Previous studies have

H. Lan et al. / Applied Energy 158 (2015) 26–34 27

investigated hybrid power arrangements on ships [12–14]. Alithium-ion battery in conjunction with diesel generations hasbeen explored for ship crane operations in [14]. To maximize fuelsavings, battery storage systems have been utilized in convertingthe bulk carriers to all-electric ships in [15]. Other works haveelucidated various control strategies to prolong the battery lifeand reduce fuel consumption [13,16,17].

Many works related to hybrid PV/diesel systems in electricalpower systems with ESS on land have been published in[18–24]. In particular, the economic and environmental meritsof a hybrid PV/diesel system with flywheel energy storage havebeen analyzed in [22]. An optimal design for a standalonewind/PV/diesel hybrid system under uncertainties of renewableenergy has been proposed to minimize the levelized cost ofenergy and maximize reliability [23]. An optimal unit sizingmethod for a stand-alone microgrid has also been proposed[24].

To the best of the authors’ knowledge, the hybrid PV/diesel/battery ship power system has not been extensively discussed[25–27]. In [25], the PV system applied to merchant marinevessels has been discussed to reduce the fuel cost. A stabilityassessment and economic analysis of a hybrid PV/diesel shipsystem has been studied in [26]. The authors in [27] have pro-posed a preliminary analysis to reduce the emission of electricalship at berth. In addition, the integration of a significantamount of PV power into a ship power system to reduce CO2

emission is challenging. The PV power generation in a shippower system depends on its position in the ocean. Previousstudies [28–34] on the use of PV systems have considered thedate, local time, time zone, longitude and latitude to formulatethe power generated by PV on a moving shipboard. In [28], theoptimal sizing of hybrid PV/battery/diesel power system wasproposed, taking into account various tilt angles of PV panels.Owing to the strong dependency of the performance and ratingof a solar-based system on climatic conditions [29], parameterssuch as date, local time, longitude and latitude were consideredand corrections for the output of PV modules were made fordifferent locations. The authors in [30] have proposed theoptimal design for hybrid PV/wind system which consideredvarious environmental conditions. Particle swarm optimizationwas used in [31] to optimize a hybrid system that includedPV panels, wind turbine, diesel generator, batteries, fuel cell,electrolyzer, and hydrogen tank. A detailed PV system modelhas been established and optimized in [32,33], which tookactual environmental conditions and uncertain operatingsituations into consideration. A method has been developed in[34] to estimate the global tilted irradiance which consideredtemperature and solar spectrum distribution.

This paper presents a novel method for optimally sizing ahybrid PV/diesel/ESS in a standalone ship power system for atypical navigation route from Dalian in China to Aden inYemen. Specifically, this work proposes an approach togenerating power from PV arrays on the shipboard alongthat route. Variations of the load under five conditions aremodeled; these are regular cruising, full-speed sailing, docking,loading/unloading and anchoring. For economic analysis,Multi-Objective Particle Swarm Optimization (MOPSO) is usedto determine the optimal sizes of various sources of powerand to minimize CO2 emissions.

The rest of this paper is organized as follows: Section 2 modelsthe hybrid ship power system. Section 3 formulates the problem.Section 4 proposes solution method. Section 5 describes four casestudies to verify the proposed algorithm and Section 6 drawsconclusions.

2. Mathematical model of hybrid ship power system

2.1. Difference between standalone power systems on land and hybridship power systems

The studied problem related to the generation expansion plan-ning in ship power systems differs considerably from that in stan-dalone power systems on land. The details are described as follows.

(1) The standalone power system on land is still; however, aship power system usually operates in a mobile mode.

(2) The PV array receives fixed irradiations in the standalonepower system on land. The irradiation on a sailing shipchanges continuously even though the magnitude of solarradiation is fixed. That’s, the irradiation in the ship powersystem also relies on the longitude and latitude, in additionto the date and time.

(3) The load changes continuously in the standalone power sys-tem on land. However, the total load varies with some oper-ating conditions (regular cruising, full-speed sailing,docking, load/unloading and anchoring) in a ship. Pleasenote that the steam engine of an oil tanker ship is used todrive ship propellers, which are independent from the oiltanker ship power system.

(4) The angle of incidence on the PV array in the standalonepower system on land is fixed at a moment; however, fluc-tuations of the ship result in changes of angle of incidence.

(5) The crashing of sea water onto the deck in a ship power sys-tem has impacts on the efficiency of PV modules. This phe-nomenon does not occur in the PV module on land.

(6) It is not necessary to ensure that loss of load probability(LOLP) is zero in the standalone power system on land; how-ever, the LOLP in a ship power system must be zero.

To simplify the studies, the above descriptions (4) and (5) willnot be addressed in this work.

2.2. Problem description

The focus of this work is to optimize the size of a hybrid PV/die-sel/ESS system in a ship power system which is based on the pro-ject named ‘‘Study on the Application of Photovoltaic Technologyin the Oil Tanker Ship” in China [35]. The detailed parameters ofthis oil tanker are that the length, width, and height are332.95 m, 60 m and 30.5 m, respectively. The total area for PVarray installation is 2000 m2. The deadweight of this oil tanker is100,000 tons.

This study analyzes the cost and emissions of a hybrid PV/die-sel/ESS power system in an oil tanker ship which is presented inFig. 1. The system consists of a generating PV array, a diesel gener-ator to supply the main power and an ESS to store excess energyand improve the reliability of the system. The diesel generatormust be able to supply the whole load all the time since the ship’spower system always operates in stand-alone mode.

Navigating the ship route in Fig. 2 from Dalian in China to Adenin Yemen takes 20 days. The oil tanker sails four times annually.Specifically, the ship sets sail at 8:00 am on January 1st, April 1st,July 1st and October 1st separately from Dalian and returns on Jan-uary 25th, April 25th, July 25th and October 25th respectively fromAden. Consequently, the optimization involves 3840 h in a yearand the irradiation, temperature and the load profile are sampledevery hour. The impacts of fluctuations of the ship and the crashingof sea water onto the deck on PV arrays are not taken into account.

DC/DC

Control Strategy

Diesel Generator

ACLoad

PV Battery

Transformer

DCBus

ACBus

DCLoad

DC/DC

DC/AC

Fig. 1. Hybrid ship power system.

Fig. 2. Route map.

28 H. Lan et al. / Applied Energy 158 (2015) 26–34

2.3. Models of system components

2.3.1. PV systemSolar irradiation varies with the position of the ship, the date

and the time, as the oil tanker sails along the route. The originaldata on global horizontal irradiation and ambient temperaturewere obtained from seven meteorological sites owned by the Geo-Model Solar Company [36]. These data, which are sampled everyhour, are allocated to different hours according to when and wherethe ship sails along the route. Consequently, the power that is gen-erated by the PV arrays on board can be estimated by the hourlydata that are the date, local time, time zone, longitude, latitudeand environmental temperature. Furthermore, various actual envi-ronmental conditions are taken into account to improve the accu-racy of the proposed method. In this paper, a mathematical modelfor estimating the power output of PV modules is considered and

the output power of each PV system at time t (t = 1, 2, . . ., 960)in season s (s = 1, 2, 3, 4) is obtained from the solar radiation usingthe following formula.

PPVðs;tÞ ¼ gpv � Apv � Gðs;tÞ ð1Þ

where gpv is the instantaneous PV generator efficiency, Apv is thearea of modules used in the PV system (m2) and G(s,t) is the hourlytotal solar radiance (W/m2).

The instantaneous PV generator efficiency is given by the fol-lowing equation [37].

gpv ¼ gpv ref � gMPPT ½1� bðTc � Tc-ref Þ� ð2Þ

where gpv_ref is the PV generator reference efficiency; gMPPT is theefficiency of power tracking equipment, which is 1 in this paper;Tc is the temperature of the PV cell (�C); Tc-ref is the PV cell reference

H. Lan et al. / Applied Energy 158 (2015) 26–34 29

temperature, which is taken as 25 �C in this paper, and b is thetemperature coefficient of efficiency, which ranges from 0.004 to0.006 per �C for silicon cells and is set to 0.0048 herein.

Based on the PV model that was proposed by Markvar [38], thePV cell temperature Tc can be expressed as follows.

Tc ¼ Ta þ ½ðNCOT � 20Þ=800�Gðs;tÞ ð3Þ

where the normal operating cell temperature (NCOT) is defined as45 �C and Ta is the ambient temperature (�C), which is assumed tobe 25 �C in this study.

Solar irradiation plays an essential role in a hybrid ship powersystem. This work proposes a modification of the hourly total solarradiance on board, which is shown as follows.

Gðs;tÞ ¼ Gbðs;tÞ þ Gdðs;tÞ þ Grðs;tÞ

¼ Gb;nðs;tÞ cosðhÞ þ cos2/2

� �sinðvÞ þ qðcosvþ CÞsin2 /

2

� �� �ð4Þ

where Gb(s,t), Gd(s,t), Gr(s,t), and Gb,n(s,t) denote the direct radiation, skydiffuse radiation, ground reflected radiation, and direct normal irra-diance on a surface perpendicular to the sun’s rays, respectively.The variables C, q and v represent the diffuse portion constant,the reflection index and the zenith angle, respectively. The variableh is the angle between the board and the solar rays and is calculatedusing Eq. (5).

cosh ¼ ½cos/cosvþ sin/sinvcosðn� fÞ� ð5Þ

where / is defined as the tilt angle from the horizontal surface.Since the PV array on the shipboard is horizontal, / is a constant0. n and f are the sun azimuth and plate azimuth angles, respec-tively. Eq. (6) is used to calculate the sun zenith and azimuth angles[39]:

cosh ¼ cosv ¼ sindsinkþ cosdcoskcosa ð6Þ

where d is the solar declination angle, which is calculated by Eq. (7);k is the latitude in degrees and a is the solar angle which is deter-mined using Eqs. (8)–(13).

d ¼ 23:44sin 360d� 80365:25

� �� �ð7Þ

a ¼ 36024

ðLST � 12Þ ð8ÞLST ¼ LT þ TC=60 ð9ÞTC ¼ 4ðLlocal � LSTMÞ þ EOT ð10ÞLSTM ¼ 15� � tzone ð11ÞEOT ¼ 9:87sinð2BÞ � 7:53cosðBÞ � 1:5sinðBÞ ð12ÞB ¼ 360ðd� 81Þ=364 ð13Þ

where d is the number of the day (for example, on January 1st,d = 1); LST and LT denote the local standard time and the local time,respectively. EOT stands for ‘‘equation of time” and accounts for theirregularity of the earth’s speed around the sun (minutes). Llocal islocal longitude (degrees East > 0 andWest < 0) and tzone is the differ-ence between the current time zone and GMT (East > 0 andWest < 0).

Table 1 presents the PV data that are used in this study [40].

Table 1PV data.

Life time 25 yr Efficiency 17%Cost of investment $ 1800/kW Length of a PV panel 1.66 mCost of replacement $ 1500/kW Width of a PV panel 0.99 m

2.3.2. Diesel generatorAs a main power source in a hybrid ship power system, a diesel

generator meets the load demand in case that the total power gen-erated by both the PV modules and the ESS is insufficient. The fuelconsumption of the diesel generator, Fd (L/h), depends on the out-put power and is defined as [19]:

Fd ¼ a � Pd þ b � Pratedd ð14Þ

where Pratedd is the rated power; Pd is the output power of the diesel

generator, and a = 0.246 (L/h) and b = 0.0845 (L/h) are the coeffi-cients of the consumption curve.

2.3.3. BatteryBecause of the intermittence of the output power of the PV sys-

tem [41], LiFePO4 battery is adopted as the ESS to regulate anyexcess or deficit produced power taking the state of charge (SOC)into account.

When the total power generated by the diesel generator and PVmodules exceeds the load, the battery bank is charged. The charg-ing energy of the ESS at time t in season s can be obtained asfollows.

EESSðs;tÞ ¼ EESSðs;t�1Þ þ ðEdieselðs;tÞ þ EPVðs;tÞ � Eloadðs;tÞÞ � gch

¼ EESSðs;t�1Þ þ DP � h � gch

ð15Þ

where EESS(s,t) and EESS(s,t�1) are the charging energy of the ESS attimes t and t � 1; Eload(s,t) is the load demand, and gch is the chargeefficiency of the battery bank.

On the other hand, when the load demand exceeds the availableenergy generated, the battery bank is discharged, according to Eq.(16).

EESSðs;tÞ ¼ EESSðs;t�1Þ � ðEloadðs;tÞ � Edieselðs;tÞ � EPVðs;tÞÞ=gdis

¼ EESSðs;t�1Þ � DP � h=gdis

ð16Þ

Table 2 presents the parameters of the LiFePO4 battery [42].

2.3.4. LoadThe characteristics of the load profile are critical in planning a

reliable hybrid ship power system. Fig. 3 presents the total loadin five operating situations of the oil tanker, which are specifiedin detail in Table 3. Specifically, the five different load conditionsare 1580 kW, 1790 kW, 1650 kW, 1290 kW and 500 kW that corre-spond to regular cruising, full-speed sailing, docking, loading/unloading and anchoring, respectively. Furthermore, the ship stopsin 6 cities that are Dalian (China), Shanghai (China), Hong Kong(China), Singapore, Matara (Sri Lanka), and Aden (Yemen) for trad-ing and maintenance. When the ship sails on the ocean, it is alwaysat full speed; when it sails in the Strait of Malacca, the ship is in itsregular cruising mode.

The peak load is 1790 kW when the ship is at full speed and theoff-peak load which is 500 kW, pertains when the ship is at anchor.Fig. 4 plots the hourly load profile along the route, which areattained by [35].

Table 2Battery data (LiFePO4 battery).

Life time 5 yrCharge efficiency 85%Discharge efficiency 100%Cost of investment $ 42/kW hCost of replacement $ 42/kW h

Regula cruising Full speed sailing Docking Loading and unloading Anchoring0

200

400

600

800

1000

1200

1400

1600

1800

Ship operating situation

Load

(kW

)

Fig. 3. Five different load conditions.

30 H. Lan et al. / Applied Energy 158 (2015) 26–34

3. Problem formulation

3.1. Objective function

Based on the above description, the objective of the studiedproblem is to minimize the investment and operating costs ofthe ship’s power system and the emissions from the diesel gener-ators, while satisfying the operational constraints. More specifi-cally, the number of control variables for this multi-objectiveproblem is 3842, which contains the diesel generator outputs for3840 h, an optimal PV size and a capacity of ESS. The multi-objective functions are as follows (17).

min f 1 ¼ Costfuel þ CostPV � CRFPV þ CostESS � CRFESS

min f 2 ¼ Emissioni ¼X4s¼1

X960t¼1

ECOx ðPGjÞ ¼X4s¼1

X960t¼1

Emfuel � ða � Pdðs;tÞ þ b � Pratedd Þ

9>=>;

ð17ÞThe total cost is composed of fuel cost and the costs of installa-

tion and replacement of PV and ESS, specified as net present values.These costs are defined as follows.

Costfuel ¼X4s¼1

X960t¼1

Pricefuel � ða � Pdðs;tÞ þ b � Pratedd Þ

CostPV ¼ ðCPVcapital þ CPV

replacementÞ � PPV

CostESS ¼ ðCESScapital þ CESS

replacementÞ � Eess

8>>>>><>>>>>:

ð18Þ

Table 3Duration associated with load conditions.

Dalian in China Shanghai in China Hong K

Docking 2 h 2 h 2 hLoading and unloading 6 h 8 h 14 hAnchoring 4 h 0 h 4 h

Fig. 4. Ship load profile al

where Pricefuel is the fuel price (0.709 $/L); CPVcapital, C

PVreplacement , C

ESScapital

and CESSreplacement denote the installation and replacement prices for

PV and the LiFePO4 battery; PPV is the size of PV (kW) and Eess isthe capacity of the LiFePO4 battery.

In order to convert the initial cost to an annual capital cost, thecapital recovery factor (CRF), defined by Eq. (19) is applied.

CRF ¼ rð1þ rÞ yð1þ rÞ y � 1

ð19Þ

where r is the interest rate and y denotes the life span of the PVmodel or ESS.

3.2. Constraints

For a hybrid PV/diesel/ESS ship power system, the followingoperational constraints should be satisfied.

Pdmin 6 Pdðs;tÞ 6 Pdmax ð20ÞPPVðs;tÞ 6 PPV 6 PPV max ð21ÞEESSðs;tÞ 6 EESS 6 EESSmax ð22Þwhere Pd(s,t), PPV(s,t), EESS(s,t) represent the outputs of the diesel gen-erator, PV and ESS respectively, at time t in season s.

Furthermore, the active power should be balanced at time t inseason s as follows.

Pdðs;tÞ þ PPVðs;tÞ þ PESSðs;tÞ ¼ PLoadðs;tÞ ð23Þwhere PLoad(s,t) is the load demand at time t in season s.

4. Methodology

Since the optimal sizing problem is formulated as a constrainednonlinear optimization problem, Multi-Objective Particle SwarmOptimization (MOPSO) combined with elitist non-dominated sort-ing genetic algorithm (NSGA-II) [43] is utilized in this paper tosolve the multi-objective optimization problem.

PSO is a heuristic optimization technique first developed in1995 by Kennedy and Eberhart [44–46]. Its underlying idea is thata population of individuals called a swarm of particles is randomlygenerated. Each particle, representing a potential solution to theoptimization problem, flies through an n-dimensional search spaceat a random velocity, and updates its position based on its ownbest exploration, best swarm global experience, and its previousvelocity vector, using the following equations.

ong in China Singapore Matara in Sri Lanka Aden in Yemen

2 h 2 h 2 h12 h 7 h 6 h5 h 6 h 4 h

ong route of interest.

H. Lan et al. / Applied Energy 158 (2015) 26–34 31

vkþ1i ¼ wvk

i þ c1r1ðpbestki � xki Þ þ c2r2ðgbestk � xki Þxkþ1i ¼ xki þ vkþ1

i

)ð24Þ

where w is the inertia weight; c1 and c2 are acceleration constants;

r1 and r2 are two random numbers within [0, 1]; pbestki is the besthistoric position of particle i based on its own experience,pkbest i ¼ ½xpbesti1 ; xpbesti2 ; . . . ; xpbestiN � and gbestk is the best particle position

based on experience history of the entire swarm,gkbest ¼ ½xgbest1 ; xgbest2 ; . . . ; xgbestN �.To improve the algorithmic performance, a linearly decreasing

inertia weight from maximum wmax value to wmin is applied toupdate the inertia weight [47]:

wk ¼ wmax �wmax �wmin

kmax� k ð25Þ

where wmax and wmin are the initial and final inertia weights, andkmax is the maximum number of iterations.

The MOPSO algorithm integrated with NSGA-II starts with arandom population of N particles for initializing the diesel genera-tors’ output power Pd(s,t) for 3840 h, the size of PV PPV, and thecapacity of the battery Eess. A random swarm of particles consider-ing constrains and corresponding velocity for each particle is ini-tialized. Each particle is evaluated by multi-objective functions,and recalls its best positions associated with the best fitness value.The values of pbest and gbest are determined and preserved; then,if the algorithm has not yet found the minimum cost and emission,the position and velocity of each particle are continuously updated.

Randomly generate N particles within constraints

Iteration=Iterraion+1

Randomly initialize a velocity vector for each particle and initialize Pbest

and Gbest

Evaluate the fitness value of each particle

Check for pbest and gbest

Yes

Update Pbest and Gbest

Sort the individual by NSGA-II

Select the best solution as the final result

No

According to the navigation route,modify the solar irradiation

Calculate the total load for five operating situations

Minimum cost and emission

Check constraints for each particle

Fig. 5. Flowchart of proposed method.

Then, all the particles are sorted by NSGA-II to select the best solu-tion from the Pareto frontiers. The flowchart in Fig. 5 illustrates theproposed MOPSO methodology.

5. Simulation result and discussion

5.1. Correction coefficient for PV module

Owing to the significant effect of solar radiation on the optimalsizing problem, this paper analyzes the correction coefficient(cosh) of the PV module with respect to parameters that appearin Eqs. (4)–(13). The correction coefficient in four seasons is pre-sented in Fig. 6.

As seen in Fig. 6, the correction coefficients in the summer (Julyto September) are much larger than those in the other three sea-sons indicating that the irradiation in the summer has a greatimpact on the output of the PV arrays. More specifically, the cor-rection coefficient reaches its maximum value at 12:00 on July4th at E 118. 492�, N 118. 492�.

5.2. Sensitivity analysis

Five parameters – date, local time, time zone, longitude and lat-itude importantly affect the radiation of the PV modules. Followingthe calculation of the correction coefficient, Eq. (26) is used to ana-lyze the sensitivity of the correction coefficient.

s ¼ DG=Dp ð26Þwhere s is the sensitivity; DG is the variation of solar irradiation,and Dp is the variation of a parameter of interest.

The maximum correction coefficient is taken as an example forsensitivity analysis and the result is shown in Table 4. The sensitiv-ity of correction coefficient is calculated through perturbing eachparameter by one unit. As a consequence, it is the local time andtime zone that have the largest influence on the output of the PVsystem. Specifically, the correction coefficient is reduced by0.019138 as the local time is increased by one unit and the correc-tion coefficient is reduced by 0.038419 as the local time isdecreased by one unit.

The hourly solar irradiation along the route from Dalian inChina to Aden in Yemen, based on data from the GeoModel SolarCompany [36], is modified using the method that was discussedin Section 2, yielding data that are presented in Fig. 7.

It can be seen from Fig. 7 that the solar radiation reaches itshighest value on April 19th when the ship sails in the Gulf of Aden(57.296� E, 12.143� N) and Fig. 8 presents the solar radiation onthat day.

5.3. Economic analysis

The impacts of the integration of solar power into a ship’spower system, different loading conditions, and energy storagesystems are studied to demonstrate the effectiveness of the pro-posed MOPSO method.

Case 1: A cost study considering the diesel generator only.Case 2: A cost only considering the diesel generator and PVarray only.Case 3: An optimal cost study considering the diesel generator,PV and ESS.Case 4: Multi-objective optimization considering costs of dieselgenerator, PV, ESS and CO2 emissions.

Table 5 presents the total costs of the ship system and emis-sions in Case 1, Case 2, Case 3, and Case 4.

0 200 400 600 8000

0.2

0.4

0.6

0.8

1Correction coefficient in winter

Time (h)0 200 400 600 800

0

0.2

0.4

0.6

0.8

1Correction coefficient in spring

Time (h)

0 200 400 600 8000

0.2

0.4

0.6

0.8

1Correction coefficient in summer

Time (h)0 200 400 600 800

0

0.2

0.4

0.6

0.8

1Correction coefficient in autumn

Time (h)

Fig. 6. Correction coefficients in four seasons.

Table 4Sensitivity of maximum correction coefficient to different parameters.

Variation Julian days Local time Time zone Altitude Longitude

+1 5.19E�05 0.019138 0.038419 3.67E�04 5.21E�04�1 4.8E�05 0.038419 0.019138 6.29E�05 7.79E�04

0 500 1,000 1,500 2,000 2,500 3,000 3,500 38400

200

400

600

800

1000

1200

Time (h)

Mod

ified

irra

diat

ion

(w/m

2) Winter Spring Summer Autumn

Fig. 7. Modified solar irradiation along the route.

0

200

400

600

800

1000

1200

1 3 5 7 9 11 13 15 17 19 21 23

Rad

iatio

n (W

/m2)

(h)

Fig. 8. Maximum solar radiation on April 19th.

Table 5Net present cost and emission in four cases.

Case 1 Case 2 Case 3 Case 4

PV size (kW) 0 306 150 298ESS capacity (kW h) 0 0 181 113Total NPC ($) 1,575,700 1,615,200 1,571,000 1,200,828Fuel cost ($) 1,575,700 1543400 1533400 1,126,600PV installation cost ($) 0 39,145 19,131 38,109PV replacement cost ($) 0 32,621 15,943 31,758ESS installation cost ($) 0 0 732 457ESS replacement cost ($) 0 0 1755 1096Emission (kg) 22,192,000 6,857,100 6,812,900 5,005,990Total diesel output

(kW h)6,396,176 6,211,010 6,156,300 3,822,100

32 H. Lan et al. / Applied Energy 158 (2015) 26–34

From Table 5, it can be found that (a) the total diesel outputpower is reduced with the application of solar energy and batteryand (b) the emissions are reduced from 22,192,000 kg in Case 1 to5,005,990 kg in Case 4. In Case 1, the total load demand is suppliedby diesel generators only so that the cost is high and the problemof emissions is serious. Even though the ship’s power systemincludes PV generation, Case 2 is associated with the highest totalsystem cost ($1,615,200), implying that the ESS is required in shippower system and optimization method must be performed. Nota-bly, when the LiFePO4 battery and MOPSO algorithm are used, thesystem cost and the total fuel cost are the lowest in Case 4, being$1,200,828 and $1,126,600, respectively. The fuel cost is estimatedby the oil price (0.709 $/L) and the fuel cost equation in Eq. (18) byconsidering the total output 3,822,100 kW h of diesel generator inone year (160 days or 3840 h). The total fuel cost in the hybrid shipsystem is reduced dramatically which is 28.5% reduction withrespect to that in Case 1. This result demonstrates that the sizeof the PV generation and the capacity of the LiFePO4 batteryselected by the proposed MOPSO algorithm are much better thanin the other cases. Furthermore, even though the total size of PV

generation in Case 4 is 148 kW more than in Case 3, the total sys-tem cost and CO2 emissions are lower.

The PV system with a capacity of 298 kW in Case 4 needs1939.21 m2 estimated using the data in Table 1. The required areais smaller than the maximum limit 2000 m2.

5.4. Impact of price of PV on cost

The price of PV importantly affects the cost of a ship’s powersystem and the planning strategy that will be developed by

1400 1500 1600 1700 1800 1900 2000 2100 22001.18

1.19

1.2

1.21 x 106

Price of PV panels ($/kW)

Tota

l NPC

($)

1400 1500 1600 1700 1800 1900 2000 2100 2200220240260280300320

Price of PV panels ($/kW)

Size

of P

V (k

W)

Fig. 9. Total cost and PV capacity for various prices of PV.

H. Lan et al. / Applied Energy 158 (2015) 26–34 33

decision-makers, because the price of PV affects net present costand the size of the ESS. Fig. 9 shows that when the price of PV fallsfrom $2160/kW to $1440/kW, the total net present cost of thewhole system decreases from $12,006,649 to $1,184,465 and thetotal installed size of PV increases from 234 kW to 309 kW.

6. Conclusion

In this paper, a novel methodology is proposed to find the opti-mal size of hybrid PV/diesel/ESS generators in a ship’s power sys-tem. Hourly loads are modeled with five operation conditions,which are regular cruising, full-speed sailing, docking, load/unloading and anchoring. A navigation route from Dalian in Chinato Aden in Yemen serves a route for decision makers consideringfour different seasons to allocate the sizes of PV and ESS herein.The MOPSO algorithm integrated with NSGA-II is developed tosearch the best sizes for the PV system and ESS and to optimizethe outputs of the diesel generator for reducing the total costand emission. The simulation results show that the acquired netpresent cost of hybrid PV/diesel/ESS power generation is less thanthat of PV/diesel power generation. Some findings can be attainedas follows: (i) the local time and time zone that have the largestinfluence on the correction coefficient for PV generation in a shippower system; (ii) the irradiation has a great impact on the PV gen-eration on the shipboard in the summer than in other seasons; (iii)as the price of PV panels falls, the ship’s power system can incorpo-rate more solar generation. The proposed method can be enhancedto study other mobile microgrids such as container ship and high-speed train.

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