# Optimal Tilt Angle of Photovoltaic Arrays and Economic Allocation of Energy Storage System on Large Oil Tanker Ship

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}emissions. Unlike on land, power generation using a PV on a ship depends on the date, latitude and longitude of the navigation. Accordingly, this work considers a route from Dalian in China to Aden in Yemen, accounting for the seasonal and geographical variations of solar irradiation. This proposed method adopts five conditions associated with the navigation route to model the total shipload. Various cases are discussed in detail to demonstrate the effectiveness of the proposed algorithm.

## 1. Introduction

_{2}emission is challenging so ESSs play a critical role in ensuring the stability of the hybrid ship system and the quality of the power output. Studies [20,21,22,23] have found that the use of an ESS is one of the most effective ways to ensure the reliability and power quality of power systems and favors the increased penetration of distributed generation resources. Some investigations [24,25,26] have demonstrated that the optimal management of ESS with distributed generators in power systems can reduce the cost and loss of power; improve the voltage profile; shave the peak load; and reduce the negative impact of power generation on the environment.

_{2}emissions.

## 2. Hybrid Ship Power System and Components

#### 2.1. Problem Description

^{2}.

#### 2.2. Models of System Components

#### 2.2.1. PV System

^{2}), and I

_{(t)}is the hourly total solar radiance (W/m

^{2}).

_{b(t)}, I

_{d(t)}, I

_{r(t)}, I

_{bh(t)}, I

_{dh(t)}, and I

_{o(t)}denote the direct radiation, sky diffuse radiation, the ground reflected radiation, the direct radiation on horizontal surfaces, the diffuse radiation on horizontal surfaces, and the direct normal irradiance on a surface perpendicular to the sun’s rays, respectively. Note that the different types of irradiation (I

_{b(t)}, I

_{d(t)}and I

_{r(t)}) are all influenced by the direct radiation on the horizontal surface (I

_{bh(t)}). The variables ρ and β represent the albedo, which is taken to be 0.2 [29] in this paper, and the angle between the PV panel and the board, respectively. The variable R

_{b}is the ratio of the radiation that hits the tilt surface to that which hits the horizontal surface, which is given by Equation (3).

_{s}), affecting the installation of all PV modules and the detailed relationship behind this is described as follows.

Items | Parameters | Items | Parameters |
---|---|---|---|

Life Time | 25 years | Efficiency | 14.5% |

Cost of Investment | $1800/kW | Length of PV Panel | 1.47 m |

Cost of Replacement | $1800/kW | Width of PV Panel | 0.68 m |

Cost of Brackets | $1100/kW | Cost of Inverter | $655/kW |

#### 2.2.2. Battery

Item | Parameters |
---|---|

Life Time | 8 years |

Charge Efficiency | 75% |

Discharge Efficiency | 100% |

Cost of Investment | $100/kWh |

Cost of Replacement | $100/kWh |

#### 2.2.3. Diesel Generator

_{d}(L/h), depends on the output power and is defined as [35].

_{d}is the output power of the diesel generator; P

_{dN}is the rated power; and a = 0.246 (L/kwh) and b = 0.0845 (L/kwh) are the coefficients of the consumption curve.

#### 2.2.4. Load

Operating Mode | Dalian in China | Shanghai in China | Hong Kong in China | Singapore | Matara in Sri Lanka | Aden in Yemen |
---|---|---|---|---|---|---|

Docking | 2 h | 2 h | 2 h | 2 h | 2 h | 2 h |

Loading and unloading | 6 h | 8 h | 14 h | 12 h | 7 h | 6 h |

Anchoring | 4 h | 0 h | 4 h | 5 h | 6 h | 4 h |

## 3. Problem Formulation

#### 3.1. Objective Function

_{1}(t), S

_{2}(t), , S

_{3}(t), and S

_{4}(t) denote Boolean variables that take the value 0 or 1, based on the ship’s operating situation; $Price$ is the price for wasted power that is generated by the PV system; ${C}_{\text{capital}}^{\text{ESS}}$ and ${C}_{\text{replacement}}^{\text{ESS}}$ denote the costs of installation and replacement for the lead-acid battery; ${C}_{\text{ESS}}$ is the capacity of the ESS (kWh); and $\text{\Delta}P$ is the difference between the expected and real output power of the PV system.

_{1}and F

_{2}) but increase the capital and replacement fee for ESS. As a consequence, an optimal capacity of ESS is necessary in a hybrid ship power system.

#### 3.2. Constraints

## 4. Solution Method

## 5. Simulation Result and Discussion

#### 5.1. Optimal Tilt Angle of PV Arrays

#### 5.2. Economic Analysis

_{2}emissions.

Item | Case 1 | Case 2 | Case 3 |
---|---|---|---|

PV size (kW) | 0 | 292 | 292 |

ESS size (kW) | 0 | 0 | 140 |

ESS capacity (kWh) | 0 | 0 | 110 |

PV installation cost ($) | 0 | 522,000 | 522,000 |

PV replacement cost ($) | 0 | 522,000 | 522,000 |

ESS installation cost ($) | 0 | 0 | 583,975 |

ESS replacement cost ($) | 0 | 0 | 583,975 |

Total NPC ($) | 2,320,645 | 1,258,245 | 1,105,975 |

Emission (kg) | 55,314,000 | 49,557,769 | 29,853,731 |

Total diesel output (kWh) | 8,720,000 | 2,766,500 | 2,070,326 |

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Lan, H.; Dai, J.; Wen, S.; Hong, Y.-Y.; Yu, D.C.; Bai, Y. Optimal Tilt Angle of Photovoltaic Arrays and Economic Allocation of Energy Storage System on Large Oil Tanker Ship. *Energies* **2015**, *8*, 11515-11530.
https://doi.org/10.3390/en81011515

**AMA Style**

Lan H, Dai J, Wen S, Hong Y-Y, Yu DC, Bai Y. Optimal Tilt Angle of Photovoltaic Arrays and Economic Allocation of Energy Storage System on Large Oil Tanker Ship. *Energies*. 2015; 8(10):11515-11530.
https://doi.org/10.3390/en81011515

**Chicago/Turabian Style**

Lan, Hai, Jinfeng Dai, Shuli Wen, Ying-Yi Hong, David C. Yu, and Yifei Bai. 2015. "Optimal Tilt Angle of Photovoltaic Arrays and Economic Allocation of Energy Storage System on Large Oil Tanker Ship" *Energies* 8, no. 10: 11515-11530.
https://doi.org/10.3390/en81011515