# Optimal Configuration of Multi-Energy Storage in an Electric–Thermal–Hydrogen Integrated Energy System Considering Extreme Disaster Scenarios

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## Abstract

**:**

## 1. Introduction

## 2. Refined Model of Multivariate Energy Storage

#### 2.1. Electricity Storage

#### 2.1.1. Life Degradation Model

#### 2.1.2. Basic Model

#### 2.2. Thermal/Hydrogen Storage

#### 2.3. Electro-Hydrogen Coupling Equipment

#### 2.3.1. Life Degradation Model

^{−7}, 2.75 × 10

^{−6}, and 5.50 × 10

^{−6}, respectively. ${D}_{1,t}^{EC/FC}$, ${D}_{2,t}^{EC/FC}$, and ${D}_{3,t}^{EC/FC}$ are the efficiency degradation of the electro-hydrogen coupling equipment during steady operation, fluctuating operation, and start–stop, respectively. ${D}^{EC/FC}$ and ${L}_{de}^{EC/FC}$ represent the total efficiency degradation and equivalent life degradation of the electro-hydrogen coupling equipment when running a scheduling cycle.

#### 2.3.2. Start–Stop Model

#### 2.3.3. Heat Transfer Model

#### 2.3.4. Output Model

#### 2.3.5. Power Model

#### 2.4. Sequential Monte Carlo Extraction Equipment Fault Model Based on Markov State Transition

#### 2.4.1. Markov State Transformation Model

#### 2.4.2. Equipment Fault Extraction Model Based on Sequential Monte Carlo

## 3. Two-Layer Capacity Optimization Configuration Model

#### 3.1. Capacity Configuration Model

#### 3.2. Capacity Configuration Constraints

#### 3.3. Optimal Operating Model

#### 3.4. Operational Constraints

#### 3.4.1. Wind Turbine Photovoltaic Output and Load Constraints

#### 3.4.2. Purchase and Sale Power Constraints

#### 3.4.3. System Equilibrium Constraints

## 4. Solution Method

- STEP 1: Input the system’s initial data.
- STEP 2: The initial particles selected by the device, which correspond to each device’s capacity, are generated and sent to the lower-level optimal operating model. Simultaneously, the lower-level optimum operation generates the wind and light vulnerability index using the Monte Carlo method and uses the Gurobi solver to solve it. The daily operating cost is obtained, and its value is returned to the upper layer.
- STEP 3: The current particle fitness value, i.e., the system daily investment cost plus the daily operation cost, is obtained.
- STEP 4: The average optimal position of the particles is calculated, the position is updated by the quantum algorithm, and the number of chaotic optimization iterations j is set to 0.
- STEP 5: This step is to determine whether the variance of the group position is less than the limit value; if not, step 6 is entered. If yes, the chaotic optimization is used to break up the particles and recalculate the fitness, and j = j + 1, until the position variance is no longer less than the limit value or the maximum number of iterations of the chaotic optimization enters step 6.
- STEP 6: The new particle fitness is compared with k – 1’s fitness, and the individual and global optimal positions and attractors are updated.
- STEP 7: A judgement is made regarding whether the current particle fitness is inferior to the individual optimal position; if the current particle fitness is inferior to the individual optimal position, it is proved that the particle quality is poor, and there is a greater probability of entrance into the tabu table; then, the attractor is cancelled, and step 9 is entered. If the current fitness is better than the individual’s optimal position, step 8 is entered.
- STEP 8: This step is to determine whether the particle fitness is inferior to the global optimal position. If the current particle fitness value is inferior to the global optimal position, it is proved that the particle quality is general, and there is a small probability of entrance into the tabu table; then, the attractor is cancelled, and step 9 is entered. If it is superior to the global optimal position, it directly enters step 9.
- STEP 9: This step is to determine whether to converge or to reach the maximum number of iterations. If so, the loop is ended, and the optimal design result is output. If not, step 4 is returned to, and the loop is started again.

## 5. Case Study

#### 5.1. Overview of Examples

#### 5.1.1. Parameters and Data

#### 5.1.2. Scene Setting

#### 5.2. Analysis of Example Results

#### 5.2.1. Upper Layer Capacity Configuration Results

- Case 1: Without considering the extreme disaster scenes, the four typical days are normal scenarios, which is a commonly used processing method in the existing research.
- Case 2: Considering the extreme scenarios, the penalty coefficients of the electrical, thermal, and hydrogen load losses are all set to 1000.
- Case 3: Considering the extreme scenarios, the penalty coefficients of the electrical, thermal, and hydrogen load losses are set at 1500-1000-1000.
- Case 4: Considering the extreme scenarios, the penalty coefficients of the electrical, thermal, and hydrogen load losses are set to 1000-1500-1000.
- Case 5: Considering the extreme scenarios, the penalty coefficients of the power, heat, and hydrogen losses are set at 1000-1000-1500.

#### 5.2.2. Optimal Operation Results of the Lower Layer

#### Load Loss Cost Analysis

#### Electric–Heat–Hydrogen Coupling Operation Analysis

#### Energy Storage Operation Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 11.**Electrical coupling operation results from fault scenarios without considering the configuration of extreme scenarios.

**Figure 12.**Electrical coupling operation results from fault scenarios considering the configuration of extreme scenarios.

**Figure 13.**Electrical coupling operation results from normal scenarios without considering the configuration of extreme scenarios.

**Figure 14.**Electrical coupling operation results from normal scenarios considering the configuration of extreme scenarios.

**Figure 15.**Thermal coupling operation results from fault scenarios without considering extreme scenario configuration.

**Figure 16.**Thermal coupling operation results from fault scenarios considering extreme scenario configuration.

**Figure 17.**Thermal coupling operation results from normal scenarios without considering extreme scenario configuration.

**Figure 18.**Thermal coupling operation results from normal scenarios considering extreme scenario configuration.

**Figure 19.**Hydrogen coupling operation results from fault scenarios without considering extreme scenario configuration.

**Figure 20.**Hydrogen coupling operation results from fault scenarios considering extreme scenario configuration.

**Figure 21.**Hydrogen coupling operation results from normal scenarios without considering extreme scenario configuration.

**Figure 22.**Hydrogen coupling operation results from normal scenarios considering extreme scenario configuration.

Equipment Variables | Electrolyzer | Hydrogen Fuel Cell |
---|---|---|

hydrogen/electricity production efficiency | 0.65 | 0.45 |

heat production efficiency | 0.3 | 0.5 |

lower limit of temperature/°C | 50 | 25 |

upper limit of temperature/°C | 80 | 100 |

upper/lower limit of output | 1/0.05 | 1/0.05 |

upper climbing limit | 100%/30 min | 100%/30 min |

maximum number of start-ups | 2 | 2 |

maximum number of shutdowns | 2 | 2 |

start-up delay | 0 h | 0 h |

Equipment | Investment Cost | Upper Limit of Capacity | Lower Limit of Capacity | Term for Year |
---|---|---|---|---|

AEC | 2400 (CNY/kW) | 15 (MW) | 5 (MW) | 10 |

PEMEC | 4000 (CNY/kW) | 15 (MW) | 5 (MW) | 8 |

SOEC | 6400 (CNY/kW) | 15 (MW) | 5 (MW) | 5 |

PEMFC | 4200 (CNY/kW) | 5 (MW) | 2 (MW) | 5 |

SOFC | 6300 (CNY/kW) | 5 (MW) | 2 (MW) | 5 |

electric storage tank | 1071 (CNY/kW) | 20 (MW) | 2 (MW) | 10 |

heat storage tank | 56 (CNY/kW) | 30 (MW) | 10 (MW) | 25 |

hydrogen storage tank | 65 (CNY/kg) | 1000 (kg) | 100 (kg) | 35 |

Equipment | Charge/Discharge Efficiency | Energy Storage Range (%) | The Upper Limit of Charging/Discharging Rate (%) |
---|---|---|---|

electric storage tank | 0.95/0.95 | 20–90 | 20 |

heat storage tank | 0.95/0.95 | 10–90 | 20 |

hydrogen storage tank | 0.95/0.95 | 30–80 | 10 |

Extreme Fault Scenarios | Normal Working Hours of PV | Fault Time of PV | Normal Working Hours of WT | Fault Time of WT |
---|---|---|---|---|

1 | 1–7 h, 19–24 h | 8–18 h | 1–7 h, 22–24 h | 8–21 h |

2 | 1–4 h, 24 h | 5–23 h | 1–4 h, 20–24 h | 5–19 h |

Case | AEC (MW) | PEMEC (MW) | SOEC (MW) | PEMFC (MW) | SOFC (MW) | HST (MW) | ESS (MW) | HSS (MW) |
---|---|---|---|---|---|---|---|---|

1 | 11 | 10 | 10 | 3 | 5 | 31 | 11 | 12 |

2 | 14 | 10 | 15 | 3 | 5 | 31 | 40 | 32 |

3 | 15 | 10 | 15 | 2 | 4 | 39 | 40 | 25 |

4 | 14 | 11 | 15 | 5 | 5 | 42 | 22 | 30 |

5 | 13 | 10 | 13 | 5 | 5 | 27 | 39 | 37 |

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**MDPI and ACS Style**

Chen, Z.; Sun, Z.; Lin, D.; Li, Z.; Chen, J.
Optimal Configuration of Multi-Energy Storage in an Electric–Thermal–Hydrogen Integrated Energy System Considering Extreme Disaster Scenarios. *Sustainability* **2024**, *16*, 2276.
https://doi.org/10.3390/su16062276

**AMA Style**

Chen Z, Sun Z, Lin D, Li Z, Chen J.
Optimal Configuration of Multi-Energy Storage in an Electric–Thermal–Hydrogen Integrated Energy System Considering Extreme Disaster Scenarios. *Sustainability*. 2024; 16(6):2276.
https://doi.org/10.3390/su16062276

**Chicago/Turabian Style**

Chen, Zhe, Zihan Sun, Da Lin, Zhihao Li, and Jian Chen.
2024. "Optimal Configuration of Multi-Energy Storage in an Electric–Thermal–Hydrogen Integrated Energy System Considering Extreme Disaster Scenarios" *Sustainability* 16, no. 6: 2276.
https://doi.org/10.3390/su16062276