Optimal planning of hybrid photovoltaic/battery/diesel generator in ship power system

Received Jan 5, 2020 Revised Mar 30, 2020 Accepted Apr 16, 2020 In line with the increasing concern on the pollution release by marine ships, renewable energy technologies in ships power system has received so much attention. Recently, photovoltaic (PV) and energy storage system (ESS) are been integrated into conventional diesel generator in ships power system Nevertheless, improper sizing of the overall ship power station will result in a high investment cost and increase CO2 emission. This paper devised a methodology to compute the optimal size of the ESS, PV and diesel generator in a ship power system to minimize CO2 emission, fuel cost, and investment cost. It is a well-known fact that power generation in a sailing ship depend on the time zone, local time, date, latitude, and longitude along ship navigation route and the condition of the ship power system also differs from power systems on land. The devised method in this paper takes into accounts the geographical and season variation of solar insolation along the route from Lagos (Nigeria) to Conakry (Guinea) and accurately model the power output of PV modules is along the route.


INTRODUCTION
As the amount of CO 2 emission emitted by marine ships increases, the marine industries and international maritime organizations are under pressure from the United Nations and European Union framework convention on climate change to reduce CO 2 emissions [1]. Due to the fact that marine ships are powered by conventional DG, the cost of fuel has adversely affected the operational costs of ships. Consequently, efforts are been made to integrate renewable energy (RE) technologies, specifically photovoltaic (PV) and energy storage system (ESS) into the ship power system. The integration of the RE not only mitigates the CO 2 emission and fuel cost but also improves power quality, improve energy efficiency. Notwithstanding, the use of RE technologies increases the investment cost and makes the power generated fluctuates from time to time [2,3]. A wide range of research have proven that the used of ESS is one of the most effective methods to improve power quality and reliability of the power system and as well favours the penetration of RE technologies [4,5]. Nonetheless, the deployment RE technology may increase the investment cost and make the power system to be wobbly owing to the intermittent behavior of the resources [6]. Some works have confirmed that the optimal management of ESS with RE generators in the ship power system can reduce the cost of operating existing power system and reduce negative environmental impact [2,7]. 1528 A ship power system integrated with a RE system can be viewed as a special mobile and autonomous system. Previous studies have explored hybrid power system arrangements on ships [8][9][10]. In [9], a DG in conjunction with a lithium-ion battery has been examined for ship crane operation. To minimize fuel consumption, the battery storage system has been used to convert bulk carriers to all-electric ships [11]. Other study have elucidated different control control schemes to reduce fuel consumption and prolong the lifespan of ESS. Also available in the literature are studies related to hybrid PV/Wind/diesel and PV/diesel systems in conjunction with ESS on land for residential purpose [3,12,13]. Specifically, the optimal sizing of an autonomous PV/Wind/ESS/diesel generator system has been proposed to maximize reliability and minimize the cost of energy [3]. In [14] an optimum unit sizing method has been proposed for a standalone microgrid system. An optimum design for standalone diesel/wind/PV hybrid system under uncertainties of RE sources has been proposed to maximize reliability and the Levelized cost of energy To the best of our knowledge, hybrid PV/diesel with ESS on ships has not been discussed extensively in the literature [1,[15][16][17][18]. Different from the previous works, this study analyses a hybrid PV/diesel with ESS for an oil tanker ship navigating from Lagos in Nigeria to Conakry in Ghana. The shipload variations at full-speed sailing, regular sailing, anchoring, docking, and loading/unloading is been modelled. Finally, a comparison is made based on various system configurations in terms of CO 2 emission and cost for the ship power system. The rest of the paper is organized as follows: Section 2 presents the mathematical modelling of the component that composed the hybrid ship power system. Sections 3 present the formulation optimization problem. Section 4 presents the methodology. Section 5 demonstrates exemplary case studies to validate the proposed methodology and finally, the conclusion is drawn out in Section 6.

DESCRIPTION AND MATHEMATICAL MODELLING OF THE HYBRID SHIP POWER POWER SYSTEM 2.1. Difference between a ship power system and power system on land
This study is related to generation planning expansion in ship power system and it differs considerably from autonomous microgrid on land. A ship power system can be viewed as special mobile and autonomous microgrid [1]. The details description of the differences is described in Table 1. Table 1. Difference between a ship power system and power system on land Hybrid ship power system Standalone power system on land Power system is mobile Power system is fixed in one position. Irradiance on a sailing ship varies with the time, date and position of the ship; in addition, it relies on longitude and latitude.
Fixed irradiance is received.
Load varies with the operating modes of the ship (full-speed sailing, regular sailing, anchoring, docking and loading/unloading).

Load
fluctuates continuously in standalone power system Loss of power supply probability (LPSP) must be zero.
It is not necessary to guarantee zero LPSP Sea water crashing on the deck in the ship power system has a great impact on the efficiency of PV models.
This phenomenon is not found in the PV modules on land.
The angle of incidence on the PV array changes due to fluctuation of the ship The angle of incidence on the PV array is fixed.

Modelling of the ship power system components 2.3.1. Photovoltaic system
During the navigation route from Lagos in Nigeria to Conakry in Guinea, solar irradiance varies with the time, date and position of the ship. The mathematical model to compute for the PV panel power output is defined by (1) [17,20]. The model estimates PV power output under varying ambient temperature and solar irradiance.
where is the total hourly PV panel output power ( ) generated at time ( ), is the PV panel rated power ( ), represent solar irradiance ( 2 ⁄ ), represents the solar irradiance at reference conditions having a value of 1000 ( 2 ⁄ ), denote the PV panel coefficient, it is set as −3.7 × 10 −3 (1 ℃ ⁄ ) for poly and mono-crystalline silicon [21]. denote the PV panel cell temperature, and lastly, is the PV panel cell temperature at standard test condition, normally set as 25℃ [22]. According to the model of PV proposed by Markvar [17,20], the cell temperature can be expressed as follows: where, represents ambient temperature in℃, depicts the nominal cell operating temperature in℃. It is important to note that the value depends on the PV module specification and it specified by its manufacturer. Solar irradiance plays an important role in a ship power system. This work, therefore, proposes a modification of the solar irradiance on the ship board. The modification is as follows [23].
where ( , ) , ( , ) , ( , ) and , ( , ) denote the sky diffuse radiation, ground reflection radiation, direct radiation and direct normal irradiance on a surface which is perpendicular to the sun's rays, respectively. The variables , and represent the zenith angle, diffuse portion constant and the reflection index, respectively. While represents the angle the solar rays and board and it is computed using 5 [24].
where ϕ denote the tilt angle from the horizontal surface and since PV modules are horizontally placed on the shipboard, therefore, ϕ is a constant 0. Ƈ and denote the plate azimuth and sun azimuth angle, respectively. The azimuth and sun zenith angle can be computed using 6 [25]. cos θ = cosχ = sinλsinδ + cosxcosλcosα (6) where denote the latitude in degrees, is the solar declination angle which can be computed using 7 and denote the solar angle, it is determined using (8)(9)(10)(11)(12)(13).
where denote the number of days, and denote the local time and local standard time, respectively.
represent the equation of time, taking into account the irregularity of the speed of earth around the sun.
represent the difference between GMT and the current time zone. denote the local longitude. Table 2 presents the specification of the PV that is used in this study [3].

Battery storage system and energy management strategy
Due to the sporadic nature of the PV power output, ESS is incorporated to the ship power system to manage the deficit or excess power produced, taking into account the state of charge (SOC) of the ESS. When the power generated by PV modules or the diesel generator exceeds the load demand of the ship, the ESS begins to charge. The charging energy of the battery bank at any given time can be computed as follows: (14) where ( ) denote the load demand, ( ) and ( −1) denotes the charging energy of the battery at time and − 1, ℎ is the charging efficiency of the battery. Similarly, when the oil tanker ship energy demand exceeds the generated power at time , the ESU discharges to fulfil the ship demand according to (16). Table 2 presents the specification of the battery that is used in this study [3].

Diesel generator
Following the deployment of the PV system to the ship power system, the diesel generator now acts as a backup source. It switched on when the total power generated from PV array and ESU is not sufficient to fulfil the demand of the ship. Consequently, the diesel generator is modelled according to its fuel consumption defined by [3]: where and denote the output and rated power of the diesel generator. and represent the coefficient of fuel consumption curve and are given as 0.246 (L/h) and 0.0845 (L/h) respectively.

Load demand
To achieve a reliable system that would fulfil the load requirement of the ship at all time, all the characteristics of the ship load profile must be considered. The hourly change in the ship load profile with respect to different operating modes of the ship is accounted for in this work. Figure 2a shows the ship load profiles and its different operating modes. The load conditions are 500 kW, 1290 kW, 1580 kW, 1650 kW, and 1790 kW which correspond to anchoring, unloading/loading, regular cruising, docking, and full-speed sailing, respectively. The plot of the hourly load condition along the route is given in Figure 2b.

FORMULATION OF THE OPTIMIZATION PROBLEM 3.1. Objective functions and constraints
Based on the system description above, the main objective is to minimize the operating costs and investment of the ships power system and as well the greenhouse emissions from the convention diesel generator system, while satisfying all other operational constraints. Thus, the objective functions are as follows: where , , , denotes the replacement and installation cost for the ESS and PV. denote the fuel cost (0.39 $/L), denotes the capacity of the battery and denote the size o the PV (kW). To convert the initial system capital cost to annual capital, (19) for capital recovery factor (CRF) is applied for the purpose.  (19) where denote the real interest rate and is the life span of the ESS and PV. For the hybrid ship power station, the following operational constraints must be fulfilled. And most importantly, the active power should be balanced in such a way that, where , , denote the output of ESS, PV and diesel generator respectively, considering the time (t) and seasonal variation (s).
represent the ship load demand.

METHODOLOGY
Since the formulation of the sizing design problem is formulated as a constrained nonlinear optimization problem, particle swarm optimization is used to solve the optimization problem in this paper. PSO was first developed by Kennedy and Eberhart in 1995 [2] [7]. The basic concept involves in the PSO is the random generation of swarm of particles also known as the population of individuals. Each particle in the swarm is representing a potential solution to the optimization problem flies via an n-dimensional search landscape at a random velocity. The position of each swarm is updated based on its best global experience, its best exploration, and its previous velocity vector, using the following formulae. Figure 3 presents the flowchart of the proposed methodology.
Where denote the inertia weight, 1 and 2 denote random number between 0 and 1, 1 and 2 denote acceleration constant, denote the best historic position attain by particle .

SIMULATION RESULTS AND DISCUSSION
Bearing in mind the influence of solar radiation on the optimal sizing design problem, the correction coefficient cos( )of the PV modules is investigated in this paper and taking into account the parameters of (4)- (12). In this regard, the solar irradiation is sampled along the route from Lagos in Nigeria to Conakry in Guinea. Thus, the solar irradiance obtained for the PV system on the ship board is given in Figure 4a. To strengthen the study, an economic analysis on the impact of integrating PV and ESS into the ship power system considering different loading condition is analyzed to demonstrate the effectiveness of the proposed PSO method. For comparison purpose, three cases are considered: Case 1: The cost considering the ship power system with diesel generator only. Case 2: The cost of ship power system with PV and diesel generator only. Case 3: The cost ship power system considering ESS, PV and diesel generator. Table 3 present the CO 2 that would be emitted and the total cost of the ship power system for Case 1, Case 2, and Case 3. It can be seen in Table 3, the output of the DG power is reduced with the deployment of PV in both Case 2 and Case 3. The emission is also reduced in since the diesel generator operation is compensated with PV and ESS. In case 1, the ship energy demand is continuously supplied by DG. Therefore, it results in high cost and the problem of CO 2 emission is much higher. In case 2, even though the PV is installed into the system, the system configuration has the highest cost of about ($ 1,216,300), this implies that ESS is essential in the power system and optimization process must be performed. Outstandingly, when ESS is incorporated the fuel cost and system cost drastically reduce to $522,905 and $1,003,600 respectively. A fuel price of 0.39 $/L is used for the estimation. Figure 4b depicts the summary of the comparison for the three different scenarios.

CONCLUSION
A methodology to compute for the optimum size of hybrid PV/ESS/DG in a ship power system has been presented in this paper. Hourly loads profile of the ship is modelled with respect to the ship five operating conditions namely, anchoring, unloading/loading, regular cruising, docking, and full-speed sailing. Navigation route from Lagos in Nigeria to Conakry in Guinea is considered as a case study. Followed by the application of PSO to compute for the best size of ESS and PV, and to optimize diesel generator output so as to reduce emission and total cost. The simulation result obtained shows that the net present cost of the ship power system that constitutes PV/ESS/diesel generator is less than that of the ship power system that constitutes PV/diesel generator. Some of the findings attained are as follows: (i) the time zone and as well the local time has a great influence on the correction coefficient for PV power in the ship power system. (ii) Solar irradiance greatly affects the PV power generation during summer than in any other season. The proposed methodology can be improved and applied to other microgrids that are mobile, such as a high-speed train and container ship.