# Advanced State Estimation Approach for Partially Observable Shipboard Power Systems

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## Abstract

**:**

## 1. Introduction

- (1)
- This paper presents a state estimation approach capable of rapidly and accurately locating fault positions within a partially observable SPS, thereby determining the current state of the system.
- (2)
- The state estimation approach is proposed based on distributed fault-tolerant control, which fully leverages the zonal distribution structure of SPS and ensures that subsystems do not enter invalid states.
- (3)
- Simulation cases are conducted to show that a state estimation approach significantly reduces computational workload and time, surpassing traditional fault localization methods by achieving a computational time reduction of two orders of magnitude, thus enhancing the efficacy of fault recovery strategies and overall system management.

## 2. Distributed Fault-Tolerant Control of an SPS

#### 2.1. Distributed Control System

#### 2.2. SPS Distributed Control Model

#### 2.3. Fault-Tolerant Control Method

- Does not enter invalid states in the fault structure; or
- Recovers to the normal operating structure.

- ${Q}_{0,j}\cap {Q}_{il,j}^{\uparrow}=\varnothing $;
- Based on 1, it holds that ${Q}_{0,j}\cap {Q}_{re,j}^{\uparrow}\ne \varnothing $.

## 3. State Estimation for the SPS

#### 3.1. State Estimation Flowchart

#### 3.2. State Estimation under Partial Observability

- The system’s language is live, meaning that every state in the system has at least one corresponding state transition function;
- There are no closed-loop paths consisting solely of unobservable events in the system:$$(\exists {n}_{0}\in N)(\forall ust\in L)[(s\in {\Sigma}_{uo}^{\ast})\Rightarrow |s|<{n}_{0}]$$

## 4. Simulation and Results Analysis

^{−4}s.

#### 4.1. Case 1

#### 4.2. Case 2

#### 4.3. Comparison and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Operation status of the SPS under the fault condition in Case 1. (

**a**) Busbar voltage. (

**b**) Busbar current. (

**c**) Main generator and propulsion motor power. (

**d**) Main generator and propulsion motor current. (

**e**) Auxiliary generator power. (

**f**) Auxiliary generator current. (

**g**) Radar and regional load power. (

**h**) Radar and regional load current. (

**i**) System total power.

**Figure 6.**Operation status of the SPS under the fault condition in Case 2. (

**a**) Busbar voltage. (

**b**) Busbar current. (

**c**) Main generator and propulsion motor power. (

**d**) Main generator and propulsion motor current. (

**e**) Auxiliary generator power. (

**f**) Auxiliary generator current. (

**g**) Radar and regional load power. (

**h**) Radar and regional load current. (

**i**) System total power.

Equipment | Zone 1 | Zone 2 | Zone 3 | Zone 4 |
---|---|---|---|---|

PGM | BDG 0.55 MW | ATG 4 WM MTG 36 MW | ATG 4 WM MTG 36 MW | ATG 4 MW |

PMM | - | PM 36 MW | PM 36 MW | - |

Mission load (ML) | - | Radar 1 MW EMRG 20 MW | Radar 1 MW | - |

VL | 0.5 MW | 0.5 MW | 0.5 MW | 0.5 MW |

SL | 1 MW | 1 MW | 1 MW | 1 MW |

NL | 1 MW | 1 MW | 1 MW | 1 MW |

Event | Initial State | Transferred State |
---|---|---|

e1 | 1111 | 2111 |

e2 | 1111 | 3111 |

e3 | 1111 | 1211 |

e4 | 1111 | 1121 |

e5 | 1111 | 1112 |

Zone | System Status before Fault | State Estimation Result | Total Generator Power (MW) | Total Load Power (MW) | State Estimation Time (s) |
---|---|---|---|---|---|

1 | 3222 | 1111 | 0 | 0 | 0.000434 |

2 | 44,332,222 | 44,112,222 | 40 | 2.5 | 0.001368 |

3 | 44,223,222 | 44,213,222 | 40 | 38.5 | 0.001291 |

4 | 42,222 | - | 4 | 2.5 | - |

Zone | System Status before Fault | State Estimation Result | Total Generator Power (MW) | Total Load Power (MW) | State Estimation Time (s) |
---|---|---|---|---|---|

1 | 3222 | - | 0 | 2.5 | - |

2 | 44,332,222 | - | 40 | 39.5 | - |

3 | 44,223,222 | 24,123,222 | 38 | 3.5 | 0.001063 |

4 | 42,222 | 42,222 | 4 | 2.5 | 0.000469 |

Case | Node Status before the System Failure | Fault Location Result | Fault Location Result | Fault Location Time |
---|---|---|---|---|

1 | 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,−1,−1,1,0 | 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,1,0 | 24 | 0.447650 s |

2 | 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,1,1,−1,1 | 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0 | 21 | 0.438440 s |

Research | Configuration | Fault Type | Number of Faults | Simulation Platform | Computation Time (s) |
---|---|---|---|---|---|

[24] | Centralized | Electrical faults | 2 | DIgSILENT | Above 0.3 |

[25] | Centralized | Electrical faults | 136 | Matlab | 0.1 |

[26] | Centralized | Communication faults | 6 | - | Above 2.4 |

[27] | Distributed | Electrical faults | 11 | Matlab | - |

[28] | Distributed | Electrical faults | 34 | OpenDSS | - |

Our work | Distributed | Electrical + Communication faults | 4 | Matlab | About 0.001 |

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## Share and Cite

**MDPI and ACS Style**

Zhu, W.; Gu, T.; Wu, J.; Liang, Z.
Advanced State Estimation Approach for Partially Observable Shipboard Power Systems. *J. Mar. Sci. Eng.* **2023**, *11*, 2380.
https://doi.org/10.3390/jmse11122380

**AMA Style**

Zhu W, Gu T, Wu J, Liang Z.
Advanced State Estimation Approach for Partially Observable Shipboard Power Systems. *Journal of Marine Science and Engineering*. 2023; 11(12):2380.
https://doi.org/10.3390/jmse11122380

**Chicago/Turabian Style**

Zhu, Wanlu, Tianwen Gu, Jie Wu, and Zhengzhuo Liang.
2023. "Advanced State Estimation Approach for Partially Observable Shipboard Power Systems" *Journal of Marine Science and Engineering* 11, no. 12: 2380.
https://doi.org/10.3390/jmse11122380