# Multi-Objective Energy Optimal Scheduling of Multiple Pulsed Loads in Isolated Power Systems

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## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Related Works

- (1)
- In different modes, the optimization objectives and constraints of multiple pulsed load energy optimization scheduling in IPS are quite different. When the conditions such as pulsed load running time, running times, available power and real-time control performance are changed, the corresponding energy optimization scheduling method needs to be given to maximize the effectiveness of multi-pulsed loads.
- (2)
- In the IPS operation, a variety of complicated working conditions need to be considered, especially in special scenarios such as accelerated catch-up and rapid evacuation, and the mobility and suppression capabilities of the system need to be considered at the same time. Only in this way can we improve the survivability of ships and achieve multi-objective optimization of systems in special scenarios.

#### 1.3. Main Contribution

#### 1.4. Paper Organization

## 2. Problem Formulation

#### 2.1. Assumption

#### 2.2. The Typical Operation Model and Senarios of IPS

- A.
- Normal Mode

- B.
- Emergency Mode

- C.
- Suppression Mode

#### 2.3. The Chosen of Optimal Targets

#### 2.4. Mathematical Model

## 3. Solution Method

#### 3.1. Algorithm for General Situation

#### 3.2. Particular Solution Considering Typical Engineering Scenarios

#### 3.2.1. Accelerating the Catch-Up Situation

#### 3.2.2. Accelerating the Evacuation Situation

## 4. Case Study

#### 4.1. Case Settings

#### 4.2. Results and Analyses

#### 4.2.1. General Situation

#### 4.2.2. Typical Engineering Scenarios

#### Accelerating the Catch-Up Situation

#### Accelerating the Evacuation Situation

## 5. Conclusions and Prospects

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Appendix B

## References

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**Figure 4.**Constant power load curve corresponding to generator output, ship power consumption, available power and stability constraints.

**Figure 6.**Constant power load curve corresponding to generator output, ship power consumption, available power and stability constraints in the case of accelerated catch-up.

**Figure 7.**Multiple pulsed load DLES charging power and constraint curve under accelerated catch-up situation.

**Figure 8.**Constant power load curve corresponding to generator output, ship power consumption, available power and stability constraints in the case of accelerated evacuation.

**Figure 9.**Multiple pulsed load DLES charging power and constraint curve under accelerated evacuation.

Mode | Working Condition | Target | Variables and Means |
---|---|---|---|

Normal Mode | Berthing on shore | Economy | Long time scale: Load forecasting, Unit commitment |

Accelerating | |||

Decelerating | Middle time scale: Optimization of generator operating point | ||

Uniform Velocity | |||

Berthing at sea | Short time scale: Automatic generation control | ||

Emergency Mode | Emergency transfer | Safety, self-healing, Maneuverability | Regulating power distribution |

Comloss | Suppressive ability | Charging capacity | |

Suppression Mode | Attack | Maneuverability | Charging and discharging power regulation |

Defense | Suppressive ability | Power distribution |

No. | $\mathit{S}$ (MJ) | $\mathit{D}$ (s) | $\mathit{V}$ | No. | $\mathit{S}$ (MJ) | $\mathit{D}$ (s) | $\mathit{V}$ |
---|---|---|---|---|---|---|---|

1 | 80 | 5 | 10 | 5 | 145 | 8 | 16 |

2 | 160 | 7 | 25 | 6 | 130 | 9 | 20 |

3 | 120 | 10 | 18 | 7 | 90 | 6.5 | 8 |

4 | 105 | 6 | 13 | 8 | 110 | 11 | 19 |

${\mathit{v}}_{0}$ m/s | ${\mathit{m}}_{1}$ t | ${\mathit{v}}_{\mathit{T}}$ m/s | $\mathit{k}$ MW/(m/s) ^{3} | $\mathit{T}$ s | ${\mathit{P}}_{\mathit{S}\mathit{L}\mathit{E}\mathit{S}}$ MW | $\mathit{\beta}$ s/m |
---|---|---|---|---|---|---|

8 | 500,000 | 10 | 0.03 | 1200 | 3 | 10 |

${\mathit{\lambda}}_{\mathit{i}}^{\mathit{d}}$ MW/s | ${\mathit{p}}_{\mathit{G},\mathbf{max}}$ MW | ${\mathit{\gamma}}^{\mathit{u}}$ MW/s | ${\mathit{\lambda}}_{\mathit{i}}^{\mathit{u}}$ MW/s | ${\mathit{\gamma}}^{\mathit{d}}$ MW/s | ${\mathit{v}}_{\mathit{T}\mathbf{min}}$ m/s | ${\mathit{v}}_{\mathit{T}\mathbf{max}}$ m/s |
---|---|---|---|---|---|---|

0.4 | 22 | 0.15 | 0.4 | 0.15 | 8.06 | 8.67 |

${\mathit{v}}_{0}$ m/s | ${\mathit{m}}_{1}$ T | ${\mathit{v}}_{\mathit{T}}$ m/s | $\mathit{k}$ MW/(m/s) ^{3} | $\mathit{T}$ S | ${\mathit{P}}_{\mathit{S}\mathit{L}\mathit{E}\mathit{S}}$ MW |
---|---|---|---|---|---|

8 | 500,000 | 10 | 0.03 | 1200 | 3 |

${\mathit{\lambda}}_{\mathit{i}}^{\mathit{d}}$ MW/s | ${\mathit{p}}_{\mathit{G},\mathbf{max}}$ MW | ${\mathit{\gamma}}^{\mathit{u}}$ MW/s | ${\mathit{\lambda}}_{\mathit{i}}^{\mathit{u}}$ MW/s | ${\mathit{\gamma}}^{\mathit{d}}$ MW/s |
---|---|---|---|---|

0.4 | 22 | 0.15 | 0.4 | 0.15 |

${\mathit{v}}_{0}$ m/s | ${\mathit{m}}_{1}$ t | ${\mathit{f}}_{\mathit{m}}$ | $\mathit{k}$ MW/(m/s) ^{3} | $\mathit{T}$ s | ${\mathit{P}}_{\mathit{S}\mathit{L}\mathit{E}\mathit{S}}$ MW |
---|---|---|---|---|---|

8 | 500,000 | 1800 | 0.03 | 1200 | 3 |

${\mathit{\lambda}}_{\mathit{i}}^{\mathit{d}}$ MW/s | ${\mathit{p}}_{\mathit{G},\mathbf{max}}$ MW | ${\mathit{\gamma}}^{\mathit{u}}$ MW/s | ${\mathit{\lambda}}_{\mathit{i}}^{\mathit{u}}$ MW/s | ${\mathit{\gamma}}^{\mathit{d}}$ MW/s |
---|---|---|---|---|

0.4 | 22 | 0.15 | 0.4 | 0.15 |

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**MDPI and ACS Style**

Li, F.; Liu, D.; Qin, B.; Sun, K.; Wang, D.; Liang, H.; Zhang, C.; Tao, T.
Multi-Objective Energy Optimal Scheduling of Multiple Pulsed Loads in Isolated Power Systems. *Sustainability* **2022**, *14*, 16021.
https://doi.org/10.3390/su142316021

**AMA Style**

Li F, Liu D, Qin B, Sun K, Wang D, Liang H, Zhang C, Tao T.
Multi-Objective Energy Optimal Scheduling of Multiple Pulsed Loads in Isolated Power Systems. *Sustainability*. 2022; 14(23):16021.
https://doi.org/10.3390/su142316021

**Chicago/Turabian Style**

Li, Fan, Dong Liu, Boyu Qin, Ke Sun, Dan Wang, Hanqing Liang, Cheng Zhang, and Taikun Tao.
2022. "Multi-Objective Energy Optimal Scheduling of Multiple Pulsed Loads in Isolated Power Systems" *Sustainability* 14, no. 23: 16021.
https://doi.org/10.3390/su142316021