Solar Powered Boat Design Optimization

Solar Powered Boat Design Optimization

Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 194 (2017) 260 – 267 10th International Conference on Marine Technology...

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Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 194 (2017) 260 – 267

10th International Conference on Marine Technology, MARTEC 2016

Solar Powered Boat Design Optimization Ahmad Nasirudina,b,*, Ru-Min Chaoa, I Ketut Aria Pria Utamab a National Cheng Kung University, Tainan, Taiwan 701, ROC Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia

b

Abstract This paper presents a methodology to design a solar power boat with the aim to determine the size of photovoltaic (PV) system with minimum cost. Two stages optimization procedures have been proposed. First stage is a simplified ship size optimization based on the existing ship design for obtaining minimum propulsion power by using Golden search section algorithm. Second stage is optimization of PV system size for obtaining the number of photovoltaic (PV) module and battery with minimum cost by using Simplex algorithm. A leisure passenger catamaran boat operated in Taiwan with 42 person capacity is chosen as a case study. The service speed of the boat is 5 knots with total duration of cruising around 5 hours. 280 watt Multi-crystalline PV module and 12 volt 90 Ah Lead-Acid Battery is chosen for this case. From the simulation, it is obtained that the optimal ship has 32 PV modules (8.96 kW), 32 batteries (34.56 kWh), 14.44 meter length of water line, 4.37 meter breadth, 0.852 meter draught, and 16.258 ton of total displacement with the PV system annual capital cost around USD3,557. 2017The TheAuthors. Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license © 2017 © Published by Elsevier Ltd. This (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 10th International Conference on Marine Technology. Peer-review under responsibility of the organizing committee of the 10th International Conference on Marine Technology. Keywords: Solar powered boat, photovoltaic (PV) system, optimization ;

1. Introduction Utilization of photovoltaic (PV) energy for marine vehicle application has been widely used either as main, auxiliary, or hybrid energy source [1-5]. In case of solar powered boat which PV energy used as the main source to provide energy required by propulsion power, then the ship design which requires low power is very important. Another issue in the designing of solar powered boat is regarding to PV system cost, with the appropriate determination of PV system size then the minimum cost can be reached.

* Corresponding author. Tel.: +886-972-981-084. E-mail address: [email protected]

1877-7058 © 2017 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/). Peer-review under responsibility of the organizing committee of the 10th International Conference on Marine Technology.

doi:10.1016/j.proeng.2017.08.144

Ahmad Nasirudin et al. / Procedia Engineering 194 (2017) 260 – 267

Nomenclature c1 c2 CRF Cbatt Eload Eprop Eserv EPV Ebatt GSTC Irr Lwl Pprop PPV r SOC Vbatt ws w1 w2 x1 x2 y 't

Kd Ks Kc

cost of PV module (USD) cost of battery (USD) capital recovery factor capacity of battery (Ah) energy demand (kWh) energy of propulsion (kWh) energy of service (kWh) energy of PV system (kWh) energy of battery (kWh) irradiance at Standard Test Condition (kW/m2) irradiation (Insolation) (kWh/m2) length waterline (m) propulsion power (kW) PV power (kW) interest rate (5) state of charge (%) voltage of battery (volt) weight of PV system (kg) weight of PV module (kg) weight of battery (kg) number of PV module number of battery life time (year) time duration (hr) efficiency of discharging process (%) efficiency of PV system (%) efficiency of charging process (%)

The study to minimize the PV system cost for marine vehicle application is very limited; most of them are for land application [6-14] where the load energy more stable and independent to the system weight. Groumpos and Papageorgiou [6] introduced a method to optimize the size of PV module and battery capacity for getting a minimum life-cycle cost for stand-alone PV power system. Soras and Makios [7] introduced a new method for determining the optimum size of stand-alone PV system to get minimum cost with involving tilt angle of PV modules into consideration. Arab et. al. [8] developed an optimization method for stand-alone PV system in term of minimum cost as a function of the system reliability. Notton et. al. [9] conducted an optimization procedure for an autonomous PV system by minimizing the constraints for getting minimal the use of the kilowatt-hour cost of the system. Shrestha and Goel [10] studied on optimal sizing of stand-alone PV station for getting minimum cost with the different schemes by considering the stochastic natures of the insolation and the load demand. Kaldellis [11] studied about optimum technoeconomic energy autonomous PV solution for remote consumers throughout Greece. Celik et. at. [12] conducted optimal sizing and life-cycle assessment including the cost of residential PV energy system with battery storage. Shen [13] studied to optimally sizing of solar array and battery for getting minimum cost in a standalone PV system in Malaysia. Arun et. al. [14] studied about optimum sizing of photovoltaic battery systems incorporating uncertainty through design space approach with the aim to obtain minimum cost. The recent study regarding to optimization of PV system for marine vehicle application was conducted in [4]. The optimization was applied to large Tanker ship for finding the optimal size of hybrid system. The size of PV module, combustion engine generator, and battery system is optimized to meet the minimum cost and gas emission. In current study, an optimization procedure for getting the PV system size (i.e. the number of PV module and battery) with minimum cost is proposed. An existing solar powered boat is chosen as a case study.

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2. Optimization procedure and formulation The procedure consists of two step optimization process, first is optimizing ship size and second is optimizing the PV system. The general procedure is shown in Fig. 1.

PV system Optimization A Ship Displ. Prop. power

Ship Design Optimization Existing Design

PV. type

PV. En.

Prop. Energy

Serv. En.

Total Load Energy

Batt. type

Batt. En.

Ship size ENERGY BALANCE Prop. power No Min. power?

No

Yes OPTIMAL Size

Constaints; Min. FB Stability? Max. PV no. Min. battery no.

Yes

A

PV & Batt. number (x1 & x2) No

Min. cost? Yes W. Balance? Yes OPTIMAL x1 & x2

Fig. 1. Solar powered boat optimization design procedure

No

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2.1. Ship design optimization The aim of ship design optimization is to find an optimum size of a certain ship design with minimum power. An existing ship design is chosen for this optimization process. The existing ship is a leisure passenger boat with 42 person capacity. The hullform is catamaran type with 13.9 meter waterline length, 4.41 meter beam overall of water line, 1.21 meter demihull breadth, 3.20 meter demihull separation distance, 0.826 meter draught, 1.40 meter height, and 15.55 ton displacement. The service speed of the boat is 5 knot. The existing ship is equipped with 12 Multicrystalline PV modules (3.12 kW) and 392 Li-Ion batteries (67.72 kWh). To find the optimum size, the parametric analysis is conducted by re-sizing the boat with changing the length of water line and breadth of demihull ratio, while the ship displacement, block coefficient, draft, and demihull separation distance are kept constant. In this case, the propulsion power of several different ship length water line to breadth of demihull ratios are estimated. Slender body method is chosen in ship resistance estimation and 30% of total propulsion efficiency (assumption which is fit with seatrial results) is taken to obtain the propulsion power. Based on these data, the optimum ship size with minimum propulsion power can be found by using Golden search section optimization method. 2.2. PV system optimization The objective of PV system optimization is to find the number of PV module and battery with minimum cost. In this study, the effect of PV system weight to the propulsion power is taken into consideration. Minimum freeboard, ship stability, minimum battery, and the maximum number of PV module because of the space limitation are taken as constraint. The linear optimization programming by simplex method is chosen as optimization algorithm in this PV system optimization. 2.2.1. Effect of PV system weight to propulsion power To include the effect of PV system weight in the optimization process, the formulation which expresses the relation between PV system weight and propulsion power is required. The formulation is obtained by calculating the propulsion power with different ship displacement. 2.2.2. Total energy demand The total energy demand (Eload) consists of energy required by propulsion power (Eprop) and energy required by electrical equipment for service purpose (Eserv). The propulsion power energy is function of propulsion power and ship cruising duration, while the service energy is product of electrical equipments power and the usage duration of each equipment. In this case, ship is arranged for cruising 5 hours a day with five trips plan. One trip takes one hour cruising and before continue to the next trip, the ship needs one hour stop for berthing. The ship is planned to start from 08:00, so the last trip will be end at 17:00. For the service energy, 1.28 kWh is taken as constant value which is obtained from the existing boat data. The total energy demand is expressed by Eq. (1). t

Eload (t )

³P

prop

(t ) ˜ dt  Eserv (t );

t

0,1,2,.. 24

(1)

0

2.2.3. PV energy PV energy defines as solar energy harvested by PV modules which is expressed by Eq. (2). t

EPV (t )

PPV I (t ) ˜K s ˜Kc ˜ x1 rr dt; 1000 GSTC 0

³

t

0,1,2,.. 24

(2)

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where PPV is peak watt power of PV module in watt; Irr is sun irradiance in kW/m2 and GSTC is irradiance at standard test condition which equals to 1 kW/m2. Ks is PV system efficiency which is energy losses due to converter, wiring, temperature, etc. Kc is charging efficiency which is energy losses due to PV energy charging process to battery, and x1 is number of PV module which will be optimized. In this case, Multi-crystalline PV module D6P-280-B3A with PPV 280 watt produced by Neo solar Power is used, while Ks is assumed 80% and Kc is 85%. Regarding to the sun irradiance, it depends on the ship operational location. In this case, Nantou county Taiwan is chosen as ship operational location. Taken from [15], the average of daily irradiation along one year is known. To present daily irradiation (kWh/m2) to be irradiance (kW/m2), an approach introduced by Jain [16] is used. 2.2.4. Battery energy The energy of battery is calculated by Eq. (3). The other affecting factors to the battery capacity such as temperature, current of charging or discharging are not considered.

Ebatt

Vbatt ˜ Cbatt ˜ x2 1000 ˜K d

(3)

where Vbatt is battery nominal voltage in volt and Cbatt is battery capacity in Ampere-hour, Kd is battery discharging efficiency that represents the energy losses during energy discharging process, and x2 is the number of battery which will be optimized. In this case, Lead-Acid battery by Master Volt, AGM 12/90 (12 volt and 90 Ah capacity) is chosen and 85% discharging efficiency is taken. 2.2.5. Energy balance The number of PV modules and batteries are determined base on the energy balance calculation. The energy is balance if battery energy (Ebatt) equals to the minimum difference (deficit) between PV energy (EPV) and energy demand (Eload). Since, the battery is not allowed to fully discharge (0% remaining capacity), then the percentage of minimum remaining battery capacity (SOC, state of Charge) is considered into this calculation. The energy balance is expressed in Eq. (4). In this case, SOC is taken 50% which is typical of Lead-Acid battery. E batt

min E PV  E load

1  SOC

(4)

2.2.6. Weight balance The number of PV module and battery determine the PV system weight while the PV system weight will affect to the propulsion power, and the power itself will affect to the number of PV module and battery. Therefore, the balance condition where the effect of PV system weight is not influence to the propulsion power anymore has to be fulfilled. This is an iteration process where the process will be stop after the balance condition is reached.

2.2.7. Objective Function The objective of this optimization is to find the optimum number of PV module and battery with minimum annual capital cost. Some constraints are applied to this optimization such as minimum freeboard, stability, maximum number of PV modules caused by space limitation, and minimum number of battery. The objective function formulations are expressed in Eq. (5). Min. Cost PV  Cost batt

(5)

Ahmad Nasirudin et al. / Procedia Engineering 194 (2017) 260 – 267

where CostPV and Costbatt are cost of PV modules and batteries respectively which expressed in Eq. (6) and (7) respectively. Cost PV

c1 ˜ x1 ˜ CRF PV

(6)

Cost batt

c 2 ˜ x 2 ˜ CRFbatt

(7)

c1 is the unit cost of PV module and c2 is the unit cost of battery. x1 and x2 are the variables which represent the number of PV module and battery respectively. While CRFPV and CRFbatt are the capital recovery factor for PV module and battery respectively. CRF for PV module or battery can be expressed as follows [4]. r 1  r (1  r ) y  1 y

CRF

(8)

where r is the interest rate and y is the life time of the PV and battery in year. For this case, c1 is USD 420 (D6P-280-B3A), c2 is USD 246 (AGM 12/90), r is assumed 10% for PV module and battery, and y is taken 25 years and 5 years for PV module and battery respectively. 2.2.8. Constraints The first constraint is related to the minimum freeboard. In this case, the regulation from Inland Waters Small Passenger Boat Code by The Association of Inland Navigation Authorities (AINA), UK is referred. By following this regulation, the allowed minimum freeboard for this boat is 532 mm which equal to 1960 kg of the maximum PV system weight. The freeboard constraint is expressed in Eq. (9), where w1 is PV module weight in kg and w2 is battery weight in kg. In this case, w1 is 18.5 kg (D6P-280-B3A) and w2 is 28 kg (AGM 12/90). w1 ˜ x1  w2 ˜ x2 d 1960 kg

(9)

The second constraint is ship stability. Maximum allowed KG (vertical distance of centre of gravity) is taken as stability requirement. The constraint regarding to the ship stability is expressed in Eq. (10). KG0 

h1 ˜ w1 ˜ x1  h2 ˜ w2 ˜ x2 d KGmax w1 ˜ x1  w2 ˜ x2

(10)

KG0 is the initial vertical distance of centre of gravity excluding PV system, KGmax is maximum KG refers to the regulation, and h1 and h2 are vertical distance of PV module and battery from G0 respectively. For this case, KG0 is 1.5 m., while h1 and h2 is 0.4 m and 3.4 m respectively. By using ISO 12217-1 stability criteria, the average KGmax with PV system weight up to 1960 kg is around 4.2 meter. The third and fourth constraints are the maximum number of PV module and the minimum number of battery. Maximum number of PV is calculated base on the availability space on the boat. In this case the maximum number of PV module is 32 modules. The constraint regarding to the maximum number of PV and the minimum number of battery are expressed in Eq. (11) and Eq. (12) respectively. 0 d x1 d 32

x2 t

min E PV  E load ˜K ˜1000 1  SOC ˜Vb ˜ C b d

(11) (12)

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3. Results and Discussion Based on the procedure as described in section 2, the results are shown in Figure 2 and summarized in Table 1. For ship design optimization, in this case, increasing ship length water line to demihull breadth ratio (Lwl/b) does not always give lower power (Figure 2a). The optimal Lwl/b is obtained at Lwl/b 12.44 which equals to 14.43 meter ship water line length and 1.16 meter demihull breadth. This configuration can reduce the propulsion power around 1.75%. From PV system optimization (Figure 2b), the optimal number of PV module is obtained around 32 modules (8.96 kW power) and the optimal number of battery is 32 batteries (34.56 kWh energy capacity). Comparing with the existing ship (Table 1), the optimum result tends to give a solution of higher PV power and reducing battery capacity. This means that the optimum ship utilizes more solar energy and reduces the dependency to grid energy. Regarding to the Lead-Acid battery choice for optimum ship, even though the PV system weight is heavier, the annual capital cost is much cheaper i.e. only 16% of PV system annual capital cost of the existing ship.

(a)

(b)

Fig. 2. (a) Ship design optimization (b) PV system optimization Table 1. Optimization results Item

Existing Ship

Optimum Ship

w/o PV syst.

w/ PV syst.

w/o PV syst.

w/ PV syst.

Length waterline, Lwl (m)

13.89

13.90

14.43

14.44

Breadth waterline, Bwl (m)

4.41

4.41

4.36

4.37

Breadth of demihull, b (m)

1.21

1.21

1.16

1.17

Lwl/b

11.48

11.49

12.44

12.34

Separation distance of demihull, S (m)

1.6

1.6

1.6

1.6

Depth, D (m)

1.4

1.4

1.4

1.4

Draught, d (m)

0.802

0.826

0.802

0.852

Block coefficient, Cb

0.549

0.558

0.549

0.565

Displacement (ton)

14.77

15.50

14.77

16.258

Power, (kW)

7.922

8.062

7.783

8.067

PV module spec

-

Multi-cryst. 260w

-

Multi-cryst. 280w

Number of PV module (power, kW)

-

12 (3.12)

-

32 (8.96)

Battery spec.

-

Li-Ion 3.2v 50Ah

-

Lead-Acid 12v 90Ah

Number of Battery (Energy, kWh)

-

392(62.72)

-

32 (34.56)

Annual Capital Cost of PV system (USD)

-

21,573

-

3,557

PV system weight (ton)

-

0.73

-

1.488

Ahmad Nasirudin et al. / Procedia Engineering 194 (2017) 260 – 267

4. Conclusion The two stages solar powered boat optimization procedure has been introduced. A simplified ship size optimization base on the existing ship design for obtaining minimum propulsion power by using Golden search section algorithm has been applied. An optimization of PV system size for obtaining the number of photovoltaic (PV) module and battery with minimum cost by using Simplex algorithm has been proposed. Regarding to the ship design optimization, the optimum ship is more slender and has lower propulsion power around l.75% than the existing ship. Regarding to the PV system optimization, the optimum PV system has 32 PV modules (8.96 kW), 32 batteries (34.56 kWh). Comparing to the existing ship, the optimum ship gives higher PV power and smaller battery capacity which means that the optimum ship utilizes more solar energy and reduces the dependency to grid energy. While, by using Lead-Acid battery, even though the PV system weight is heavier, the annual capital cost of the PV system is much cheaper i.e. around 16% of existing ship annual capital cost. This is a preliminary study where the results depend on some factors such as ship weight, cost of PV module, and cost of battery. For the next study, the sensitivity of these matters will be evaluated. Acknowledgements This work is supported by the Ministry of Science and Technology under MOST-104-2221-E-006-255-MY3 and partially supported by the Research Center for Energy Technology and Strategy, NCKU, under the project of The Aim for the Top University by Ministry of Education, Taiwan, R.O.C. References [1] A. Nasirudin, R-M. Chao, S-X. Chen, Energy Harvesting and Battery Management Systems Development for a Solar Powered Boat Application, MARTEC, Surabaya, Indonesia, 2014. [2] I.K.A.P. Utama, P.I., Santosa, R.M. Chao, A. Nasirudin, New Concept of Solar Powered Catamaran Fishing Vessel, the 7th Int. Conf. on Asian and Pacific coasts (APAC), Bali, Indonesia, 2013. [3] S. Babu and J. V. Jain, On-Board Solar Power for Small-Scale Distant-water Fishing Vessels, Global Humanitarian Technology Conference, San Jose, CA, 2013. [4] H. Lan, S. Wen, Y.-Y Hong, D.C. Yu, L. Zhang, Optimal Sizing of Hybrid PV/Diesel/Battery in Ship Power System, J. Applied Energy, 158, 2015, pp. 26-34. [5] K. J. Lee, D. S. Shin, J. P. Lee, D. W. Yoo, H. K. Choi and H. J. Kim, Hybrid Photovoltaic/Diesel Green Ship Operating in Standalone and Grid-Connected Mode in South Korea - Experimental investigation, IEEE Vehicle Power and Propulsion Conference, Seoul, 2012. [6] P.P. Groumpos, G. Papageorgiou, An Optimal Sizing Method for Stand-alone Photovoltaic Power System, Solar Energy, Vol. 38, No.5, 1987, pp. 341-351. [7] C. Soras, V. Makios, A Novel Method for Determining The Optimum Size of Stand-alone Photovoltaic Systems, Solar Cell, 25, 1988, pp. 127-142. [8] A.H. Arab, B.A. Driss, R. Amimeur, E. Lorenzo, Photovoltaic Systems Sizing for Algeria, J. Solar Energy, Vol. 54, No. 2, 1995, pp. 99-104. [9] G. Notton, M. Muselli, P. Poggi, A. Louche, Autonomous Photovoltaic Systems: Influences of Some Parameters on The Sizing: Simulation Timestep, Input and Output Power Profile, J. Renewable Energy, Vol. 7, No. 4, 1996, pp. 353-369. [10] G.B. Shrestha, L. Goel, A Study on Optimal Sizing of Stand-alone Photovoltaic Stations, IEEE Trans. on Energy Conversion, Vol. 13, No. 4, 1998, pp. 373-378. [11] J.K. Kaldellis, Optimum Technoeconomic Energy Autonomous Photovoltaic Solution for Remote Consumers Throughout Greece, J. Energy Conversion and Management, 45, 2004, pp. 2745-2760. [12] A.N. Celik, T. Muneer, P. Clarke, Optimal Sizing and Life Cycle Assessment of Residential Photovoltaic Energy Systems with Battery Storage, Prog. Photovolt: Res. Appl., 16, 2008, pp. 69-85. [13] W.X. Shen, Optimally Sizing of Solar Array and Battery in A Standalone Photovoltaic System in Malaysia, J. Renewable Energy, 34, 2009, pp. 348-352. [14] P. Arun, R. Banerjee, S. Bandyopadhyay, Optimum Sizing of Photovoltaic Battery Systems Incorporating Uncertainty Through Design Space Approach, J. Solar Energy, 83, 2009, pp. 1013-1025. [15] Solarelectricityhandbook.com, Solar Electricity Handbook, 2016 Edition. [16] P. C. Jain, Estimation of monthly average hourly global and diffuse irradiation, J. Solar and Wind Technology, vol.5, no.1, 1988, pp.7–14.

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