CLC number: V27

On-line Access: 2013-01-02

Received: 2012-06-05

Revision Accepted: 2012-11-08

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Jian Liu, Quan-bao Wang, Hai-tao Zhao, Ji-an Chen, Ye Qiu, Deng-ping Duan. Optimization design of the stratospheric airship’s power system based on the methodology of orthogonal experiment[J]. Journal of Zhejiang University Science A, 2013, 14(1): 38-46.

@article{title="Optimization design of the stratospheric airship’s power system based on the methodology of orthogonal experiment",

author="Jian Liu, Quan-bao Wang, Hai-tao Zhao, Ji-an Chen, Ye Qiu, Deng-ping Duan",

journal="Journal of Zhejiang University Science A",

volume="14",

number="1",

pages="38-46",

year="2013",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.A1200138"

}

%0 Journal Article

%T Optimization design of the stratospheric airship’s power system based on the methodology of orthogonal experiment

%A Jian Liu

%A Quan-bao Wang

%A Hai-tao Zhao

%A Ji-an Chen

%A Ye Qiu

%A Deng-ping Duan

%J Journal of Zhejiang University SCIENCE A

%V 14

%N 1

%P 38-46

%@ 1673-565X

%D 2013

%I Zhejiang University Press & Springer

%DOI 10.1631/jzus.A1200138

TY - JOUR

T1 - Optimization design of the stratospheric airship’s power system based on the methodology of orthogonal experiment

A1 - Jian Liu

A1 - Quan-bao Wang

A1 - Hai-tao Zhao

A1 - Ji-an Chen

A1 - Ye Qiu

A1 - Deng-ping Duan

J0 - Journal of Zhejiang University Science A

VL - 14

IS - 1

SP - 38

EP - 46

%@ 1673-565X

Y1 - 2013

PB - Zhejiang University Press & Springer

ER -

DOI - 10.1631/jzus.A1200138

**Abstract: **The optimization design of the power system is essential for stratospheric airships with paradoxical requirements of high reliability and low weight. The methodology of orthogonal experiment is presented to deal with the problem of the optimization design of the airship’s power system. Mathematical models of the solar array, regenerative fuel cell, and power management subsystem (PMS) are presented. The basic theory of the method of orthogonal experiment is discussed, and the selection of factors and levels of the experiment and the choice of the evaluation function are also revealed. The proposed methodology is validated in the optimization design of the power system of the ZhiYuan-2 stratospheric airship. Results show that the optimal configuration is easily obtained through this methodology. Furthermore, the optimal configuration and three sub-optimal configurations are in the Pareto frontier of the design space. Sensitivity analyses for the weight and reliability of the airship’s power system are presented.

**
**

1. Introduction

To meet the requirement of long endurance, a regenerative power system is usually applied in the stratospheric airship to generate the needed power. The power system is expected to be sufficiently strong and have no failures during operation. In other words, the power system must have high reliability. Furthermore, as the total net buoyancy of an airship is limited, the power system has the limitation of weight. High reliability usually means redundancy in the power system, which adds weight to the power system. It is contradictory to minimize weight while setting redundancy in the airship’s power system. Therefore, a critical aspect in the optimization design of the power system is how to satisfy both requirements of maximum reliability and minimum weight.

To date, a lot of effort has been taken on the design of the airship’s power system (Naito et al.,

The purpose of this paper is to propose an optimization design method for the power system of the stratosphere airship. Reliability and weight models of the power system are created based upon the configuration and redundancy of the power system. The methodology of orthogonal experiment is discussed. The ZhiYuan-2 (ZY-2) is used as a demonstration problem to show the capability of this reliability-based optimization method. The sensitivity analyses for the weight and the reliability of the airship’s power system are also presented.

2. Airship’s power system and its reliability and weight model

The thin-film solar cell array, which lies on the surface of the airship, converts the solar energy into the electrical energy in the daytime. The electrical energy is regulated by the PMS and distributed to electronic equipment in the airship. The superfluous energy is stored in the fuel cell to supplement the energy released in the night. When there is no solar energy in the nighttime, the fuel cell discharges its energy and the PMS converts the energy to the electrical energy used by payloads of the airship.

The PMS consists of a switching regulator (SR), a battery discharging regulator (BDR), and a power management central unit (PMCU). The output voltage of the solar cell array is regulated by the SR. BDR performs as a DC/DC converter when transforming the fuel cell’s voltage to the bus’s voltage. PMCU supervises and coordinates the running state of the SR, RFC and BDR to maintain the continuous operation of the power system.

The weight model of SA is given as

The area of SA is calculated on the condition of the required power

The reliability of one solar cell string

As one solar cell string usually connects in series with one solar shunt regulator circuit, the reliability of the solar array should be considered with the reliability of the solar shunt regulator circuit. It will be shown in the subsection 2.4.1.

Assuming various parts of the RFC are independent of each other, the reliability block diagram is in series. If failure rates of all components are obtained, the formula for calculating the reliability of one RFC module is expressed as

The reliability of a shunt regulating circuit of SR is shown as follows:

The method of parallel redundancy is usually applied in SR to improve the reliability. In this regard, the calculation of the weight is given in Eq. (

The reliability model of a paralleled shunt regulating circuit is given by

As each shunt regulating circuit connects to one solar cell string, the total reliability of the solar array and the shunt regulator is

The total reliability of one shunt regulating circuit and one solar cell string is calculated by

BDR usually uses the method of parallel redundancy to improve reliability. Thus, the weight and reliability model of BDR is shown as follows. In Eq. (

As one RFC module usually connects to one BDR, the total reliability of an RFC module and a BDR module can be calculated by Eq. (

If PMCU is paralleled, it has the weight of 1.8

The reliability of the power system can be calculated by

3. Methodology of orthogonal experiment

The flow chart of the methodology of orthogonal experiment is shown in Fig.

An orthogonal experiment contains a number of orthogonal trials which can be generated by the orthogonal array. The form of the orthogonal array is

For the orthogonal array of

Trial | Factor |
||||||||

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |

1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

2 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |

3 | 1 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |

4 | 1 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |

5 | 1 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |

6 | 1 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 |

7 | 1 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 |

8 | 1 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |

9 | 2 | 1 | 2 | 5 | 7 | 8 | 4 | 6 | 3 |

… | … | … | … | … | … | … | … | … | … |

62 | 8 | 6 | 3 | 7 | 1 | 8 | 5 | 2 | 4 |

63 | 8 | 7 | 2 | 6 | 4 | 5 | 8 | 3 | 1 |

64 | 8 | 8 | 1 | 5 | 3 | 6 | 7 | 4 | 2 |

In this study, two responses of weight and reliability of the power system are selected for the optimization problem. The step of performing the experiment and measuring the response is replaced by estimating the weight and reliability index through the mathematical model previously depicted in section 2.

Factor | Level |

Quantity of redundant strings in SA | 0, 1, 2, 3, 4, 5, 6, 7 |

Minimum quantity of required modules in RFC | 1, 2, 3, 4, 5, 6, 7, 8 |

Quantity of redundant modules in RFC | 0, 1, 2, 3, 4, 5, 6, 7 |

Redundant configuration of PMS | 000, 001, 010, 011, 100, 101, 110, 111 |

To improve the reliability of SA, paralleled redundant cell strings are usually set. With the increase of redundant strings, the weight and reliability are also increased. Hence, the quantity of redundant strings is chosen as a factor. Eight levels, i.e., from zero to seven, are selected for analysis in which zero represents no redundancy.

With different rating modules, the minimum quantity of required modules in RFC is varied. When considering different combinations of the minimum quantity of required modules and the quantity of redundant modules, the weight and reliability of RFC are varied intricately. Thus, in RFC, the minimum quantity of required modules and the quantity of redundant modules are both chosen as factors. There are eight levels in the factor of the quantity of minimum required modules. Also, eight levels, i.e., from zero to seven, are chosen for the factor of the quantity of redundant modules. The number of each level in these two factors represents the quantity of modules.

The redundant configuration of PMS is chosen as a factor. There are eight levels, i.e., from ‘000’ to ‘111’, in a factor. The digit ‘0’ in each place means that there is no redundancy in SR, BDR, or PMCU and the digit ‘1’ means that redundancy is applied.

In the optimization problem of the airship’s power system, low weight and high reliability are equally expected and share the same importance. Hence,

4. Results

Parameter | Value | |

Solar array | Area density (kg/m^{2}) |
0.12 |

Efficiency | 12% | |

RFC | Efficiency of fuel cell | 65% |

Efficiency of electrolyzer | 85% | |

Specific weight (W/kg) | 500 | |

PMS | Efficiency of BDR | 95% |

The orthogonal table

Configuration | Redundant strings in SA | Required modules in RFC | Redundant modules in RFC | Redundancy in SR | Redundancy in BDR | Redundancy in PMCU | Weight (kg) | Reliability | Weighted score | |

Baseline | 0 | 1 | 0 | No | No | No | 4897.36 | 0.46198 | 413.00 | |

Optimization | 3 | 8 | 4 | Paralleled | Paralleled | No | 6917.00 | 0.99495 | 895.74 | |

Sub-optimization | No. 1 | 2 | 7 | 5 | Paralleled | Paralleled | Paralleled | 7713.42 | 0.99883 | 921.70 |

No. 2 | 6 | 6 | 4 | No | Paralleled | Paralleled | 7523.38 | 0.99596 | 920.73 | |

No. 3 | 4 | 8 | 6 | No | No | No | 7807.95 | 0.99865 | 920.57 |

Fig.

5. Sensitivity analyses

Fig.

Fig.

Fig.

6. Conclusions

The optimization design of the ZY-2 power system is used as a validation. Results show that the optimal configuration has an increase of 115.3% in reliability and 41.23% increase in weight. It also shows that the optimal configuration is the best solution for all combination of different configurations in the Pareto frontier. The results of optimal configuration and three sub-optimal configurations have verified the feasibility of the methodology of orthogonal experiment applied in the optimal design of the airship’s power system.

The sensitivity analyses for the weight and reliability of the airship’s power system on various variables are also performed. It shows that the weight of the airship’s power system increases linearly in proportion to the area density of the solar cell. The weight decreases inversely to the efficiency of the solar cell, the efficiency of the fuel cell and the specific weight of the RFC. The reliability of the power system remains constant when the area density of the solar cell or the specific weight of the RFC varies. The reliability increases as the efficiency of the solar cell or the efficiency of the fuel cell increases.

* Project supported by the National Hi-Tech R&D Program (863) of China (No. 2011AA7051001), and the National Nature Science Foundation (No. 51205253) of China

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