# Reliability Assessment of Power Systems in High-Load Areas with High Proportion of Gas-Fired Units Considering Natural Gas Loss

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Reliability Modeling of the Natural Gas Supply Chain

#### 2.1. Natural Gas Supply Chain Reliability Modeling Based on Minimal Cut Set

**T**, where the column number of the matrix represents the transmission line number and the number of rows represents the minimum set of connections in the pipeline system. Each row represents a minimum set of connections, and the elements of the matrix

**T**

_{ij}are 0–1 variables, where “1” indicates that the pipeline is in the set and “0” indicates that it is not included in the set [17,18,19].

#### 2.2. Modeling of Key Influencing Factors in the Natural Gas Supply Chain

## 3. Power System Reliability Assessment Considering Natural Gas Supply Fluctuations

#### 3.1. Assessment of Gas Supply Capacity of Natural Gas Pipeline System Based on the Monte Carlo Simulation Method

_{k}= 0, which means the component is in the operational state. Otherwise, when $0<{\xi}_{k}\le {p}_{k}$, S

_{k}= 1, which means the component is in the failed state.

_{1}and l

_{2}, where ${l}_{1}$ represents lines that occur in more than one minimal cut set and ${l}_{2}$ represents lines that occur in only one cut set r.

_{1}in the i-th simulation after proportional allocation, R is the number of minimal cut sets, ${F}_{{l}_{2},i}^{aft}$ is the finalized gas loss of line l

_{2}in simulation i after proportional allocation, ${L}_{{l}_{2},i}^{bef}$ represents the gas loss of line l

_{2}in the i-th simulation due to component failure before proportional allocation, ${C}_{r}$ is the set of all lines that occur only in cut set r, and ${E}_{r}$ is the set of all lines in cut set r that also appear in other cut sets.

#### 3.2. Power System Reliability Assessment Considering Gas Losses

_{s}is the number of loads. The larger the EDNS, the larger the electrical load removed due to the fault and the lower the system reliability.

## 4. Case Studies

#### 4.1. Natural Gas Supply Chain and Power System Initial Parameter Setting

#### 4.2. Natural Gas Supply Chain Minimum Cut Set

**T**of Figure 5 is obtained as:

#### 4.3. Analysis of Power Balance of the Power System Considering the Impact of Gas Supply Fluctuations

#### 4.4. Power System Reliability Evaluation

^{3}) and obtain the corresponding reliability-assessment results of the power system, respectively, which is presented in Table 6.

^{3}, which means no gas supply loss event occurs, no power-load loss in the power system, EDNS, SI, and AENS equal 0, and ASAI equals 1. Then when the gas supply is 14,400 m

^{3}, that is, the gas supply is 80% of the original, EDNS equals 53.35 MW, SI increases to 0.21, ASAI decreases to 0.79, and AENS increases to 3.81. A gas supply reduction leads to an increase in SI and AENS, indicating that the severity of system faults gradually increases. Additionally, ASAI decreases, indicating that the power supply availability gradually decreases. These results demonstrate that the reliability of the power system decreases with the gas supply of the gas source, and the power system may not have enough energy to ensure the power balance of electricity.

## 5. Conclusions

^{3}to 7200 m

^{3}, EDNS increases to 61.15 MW, SI increases to 0.24, ASAI decreases to 0.76, and AENS increases to 4.37. When the negative impact increases to the point where the gas supply drops to zero, EDNS reaches 69 MW, SI increases to 0.27, ASAI decreases to 0.73, and AENS increases to 4.93, indicating that the severity of system faults is extremely high and the availability of power supply in the electric power system also greatly decreases.

## 6. Future Directions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Shan, W.G.; Li, Y.F.; Bai, H.; Zhang, X.Y. Major changes in the world oil and gas market in 2022 and outlook for 2023. Int. Pet. Econ.
**2023**, 31, 30–39. [Google Scholar] - World’s Third Largest Installed Capacity, Generates Only 3% of the Country’s Electricity. China Energy News. 2022. Available online: https://baijiahao.baidu.com/s?id=1741420174872212213&wfr=spider&for=pc (accessed on 17 August 2022).
- Huajing Information Network. Analysis of the Development Status and Frontier Technology Routes of Thermal Power Generation Industry in 2020. 2021. Available online: https://power.in-en.com/html/power-2385843.shtml (accessed on 31 March 2021).
- Zhao, Y. Problems and Operational Suggestions of Natural Gas Power Generation in China in the New Era. 2020. Available online: https://news.bjx.com.cn/html/20200918/1105370.shtml (accessed on 18 September 2020).
- Su, H.; Zhang, J.; Zio, E.; Yang, N.; Li, X.; Zhang, Z. An Integrated Systemic Method for Supply Reliability Assessment of Natural Gas Pipeline Networks. Appl. Energy
**2018**, 209, 489–501. [Google Scholar] [CrossRef] - Yuan, Z.Y.; Ou, X.M.; Peng, T.D.; Yan, X.Y. Life Cycle Greenhouse Gas Emissions of Multi-pathways Natural Gas Vehicles in China Considering Methane Leakage. Appl. Energy
**2019**, 253, 113472.1–113472.5. [Google Scholar] [CrossRef] - Cai, J.L.; Hao, L.L.; Xu, Q.S.; Zhang, K. Reliability Assessment of Renewable Energy Integrated Power Systems with an Extendable Latin Hypercube Importance Sampling Method. Sustain. Energy Technol. Assess.
**2022**, 50, 101792.1–101792.13. [Google Scholar] [CrossRef] - Gao, T.L.; Qu, L.P.; Zhang, J.; Liu, B.; Cui, W.C. Power System Reliability Evaluation Method Based on State Space Segmentation Non-Repeated Sampling. J. Beihua Univ. (Nat. Sci. Ed.)
**2022**, 23, 388–395. [Google Scholar] - Dong, Z.H.; Hou, K.; Meng, H.; Yu, X.; Jia, H. Data-driven Power System Reliability Evaluation Based on Stacked Denoising Auto-encoders. Energy Rep.
**2022**, 8, 920–927. [Google Scholar] [CrossRef] - Wang, H.Y.; Wang, Q.Y. Adaptive Cost-sensitive Assignment Method for Power System Transient Stability Assessment. Int. J. Electr. Power Energy Syst.
**2022**, 135, 107574.1–107574.9. [Google Scholar] [CrossRef] - Zhang, H.; Wang, X.L.; Zhang, Q.W.; Xuan, D.Z.; Shen, C.L.; Li, X. Reliability Assessment of Power System for Offshore Oil Field Cluster Considering Production Index. Power Grid Technol.
**2021**, 45, 649–656. [Google Scholar] - Juanwei, C.; Tao, Y.; Yue, X.; Xiaohua, C.; Bo, Y.; Baomin, Z. Fast Analytical Method for Reliability Evaluation of Electricity-gas Integrated Energy System Considering Dispatch Strategies. Appl. Energy
**2019**, 242, 260–272. [Google Scholar] [CrossRef] - Munoz, J.; Jimenez-Redondo, N.; Perez-Ruiz, J. Natural gas network modeling for power systems reliability studies. In Proceedings of the 2003 IEEE Bologna Power Tech Conference Proceedings, Bologna, Italy, 23–26 June 2003. [Google Scholar]
- Alemany, J.; Moitre, D.; Magnago, F. Power system reliability considering combined cycle plants. IEEE Lat. Am. Trans.
**2010**, 8, 547–556. [Google Scholar] [CrossRef] - Zhang, G.Z.; Yang, Z.H.; Cheng, W.H. Description and Computation of Complex System Reliability Based on Minimum path and Minimal Cut Set. Math. Stat. Manag.
**2009**, 28, 811–825. [Google Scholar] - Wang, X.L.; Luo, S.; Xie, S.Y.; Wang, X.; Zhang, Y.L. Reliability Assessment of Distribution System with Ring Network Based on Minimal Cut Set. Power Syst. Prot. Control
**2011**, 39, 52–58. [Google Scholar] - Liu, S.Y.; Lin, Z.Z.; Zeng, C.J.; Li, H.Y.; Wang, W.K.; Hu, X.T.; Liu, Y.L. Data-driven event identification in the U.S. power systems based on 2D-OLPP and RUSBoosted trees. IEEE Trans. Power Syst.
**2022**, 37, 94–105. [Google Scholar] [CrossRef] - Ghatasheh, N.; Faris, H.; AlTaharwa, I.; Harb, Y.; Harb, A. Business Analytics in Telemarketing: Cost-Sensitive Analysis of Bank Campaigns Using Artificial Neural Networks. Appl. Sci.
**2020**, 10, 2581. [Google Scholar] [CrossRef] - Bosisio, A.; Berizzi, A.; Lupis, D.; Morotti, A.; Iannarelli, G.; Greco, B. A Tabu-search-based Algorithm for Distribution Network Restoration to Improve Reliability and Resiliency. J. Mod. Power Syst. Clean Energy
**2023**, 11, 302–311. [Google Scholar] [CrossRef] - Wang, F.; Xu, H.; Xu, T.; Li, K.; Shafie-Khah, M.; Catalão, J.P. The Values of Market-based Demand Response on Improving Power System Reliability Under Extreme Circumstances. Appl. Energy
**2017**, 193, 220–231. [Google Scholar] [CrossRef] - Wang, Q.; Zhang, G.; Wen, F. A Survey on Policies, Modelling and Security of Cyber-physical Systems in Smart Grids. Energy Convers. Econ.
**2021**, 2, 197–211. [Google Scholar] [CrossRef] - Chen, C.M.; Li, Y.; Qiu, W.Q.; Liu, C.; Zhang, Q.; Li, Z.Y.; Lin, Z.Z.; Yang, L. Cooperative-game-based Day-ahead Scheduling of Local Integrated Energy Systems with Shared Energy Storage. IEEE Trans. Sustain. Energy
**2022**, 13, 1994–2011. [Google Scholar] [CrossRef] - Park, H.; Huang, B.; Baldick, R. Enhanced Flexible Ramping Product Formulation for Alleviating Capacity Shortage in Look-ahead Commitment. J. Mod. Power Syst. Clean Energy
**2022**, 10, 850–860. [Google Scholar] [CrossRef] - He, Z.; Hou, K.; Wang, Y.; Jia, H.; Zhu, L.; Lei, Y.; Liu, X.; Yu, X. Reliability Modeling for Integrated Community Energy System Considering Dynamic Process of Thermal Loads. IET Energy Syst. Integr.
**2019**, 1, 173–183. [Google Scholar] [CrossRef] - Bao, M.; Ding, Y.; Shao, C.; Yang, Y.; Wang, P. Nodal Reliability Evaluation of Interdependent Gas and Power Systems Considering Cascading Effects. IEEE Trans. Smart Grid
**2020**, 11, 4090–4104. [Google Scholar] [CrossRef] - Zhang, A.A.; Li, J.; Lin, D.; Yang, W.; Li, X.; Qu, G.-L. Interlocking Failure Model of Coupled Electric-gas System Considering the Influence of the Limit Risk of Natural Gas Pipeline Network. Chin. J. Electr. Eng.
**2021**, 41, 7275–7285. [Google Scholar] - Zhao, S.P.; Lu, J.L.; Huang, C.; Liu, L.F. Construction of Natural Gas Supply Capacity Measurement Method and Analysis of Software Development. Nat. Gas Ind.
**2021**, 41, 144–151. [Google Scholar] - Xie, K.; Hu, B.; Karki, R. Tracing the Component Unreliability Contributions and Recognizing the Weak Parts of a Bulk Power System. Eur. Trans. Electr. Power
**2011**, 21, 254–262. [Google Scholar] [CrossRef] - Ni, W.; Lv, L.; Xiang, Y.; Liu, J.Y.; Huang, Y.; Wang, P.F. Reliability Assessment of Integrated Energy Systems Based on Markov Process Monte Carlo Method. Power Grid Technol.
**2020**, 44, 150–158. [Google Scholar] - Zhao, Y.; Guo, Y.; Xie, K.G. Characteristics of Probability Distribution of Grid Reliability Considering Parameter Uncertainty. Power Grid Technol.
**2013**, 37, 2165–2172. [Google Scholar] - Bakht, M.P.; Salam, Z.; Gul, M.; Anjum, W.; Kamaruddin, M.A.; Khan, N.; Bukar, A.L. The Potential Role of Hybrid Renewable Energy System for Grid Intermittency Problem: A Techno-Economic Optimisation and Comparative Analysis. Sustainability
**2022**, 14, 14045. [Google Scholar] [CrossRef] - Lai, S.-L.; Cao, K.-K.; Xie, K.G.; Wang, L.; Huang, Y.; Xu, S. Reliability Sensitivity Analysis of High-voltage DC Transmission System Based on Least Squares Method. Power Syst. Autom.
**2009**, 33, 12–16. [Google Scholar] - Zhou, J.Q.; Chen, W.J.; Xie, K.G.; Liu, Y.; Jin, X. Sensitivity Analysis Model for Reliability of High-voltage DC Transmission System. Power Grid Technol.
**2007**, 31, 18–23. [Google Scholar] - Cao, Y.J.; Chen, X.G.; Sun, K. Identification of Vulnerable Lines in Large Power Systems Based on Complex Network Theory. Power Autom. Equip.
**2006**, 26, 1–5, 31. [Google Scholar] - Kumar, A.; Ridha, S.; Ganet, T.; Vasant, P.; Ilyas, S.U. Machine Learning Methods for Herschel–Bulkley Fluids in Annulus: Pressure Drop Predictions and Algorithm Performance Evaluation. Appl. Sci.
**2020**, 10, 2588. [Google Scholar] [CrossRef] - Xie, K.; Billiton, R. Tracing the Unreliability and Recognizing the Major Unreliability Contribution of Network Components. Reliab. Eng. Syst. Saf.
**2009**, 94, 927–931. [Google Scholar] [CrossRef] - Hou, H.; Liu, P.; Xiao, Z.; Deng, X.; Huang, L.; Zhang, R.; Xie, C. Capacity Configuration Optimization of Standalone Multi-energy Hub Considering Electricity, Heat and Hydrogen Uncertainty. Energy Convers. Econ.
**2021**, 2, 122–132. [Google Scholar] [CrossRef] - Wang, X.B.; Huang, W.H.; Lou, H.H.; Ying, K.; Guo, R.P. Application of System State Space Partitioning Method in Power System Reliability Assessment. Power Grid Technol.
**2011**, 35, 124–129. [Google Scholar] - Chen, C.M.; Wu, X.Y.; Li, Y.; Zhu, X.; Li, Z.; Ma, J.; Qiu, W.; Liu, C.; Lin, Z.; Yang, L.; et al. Distributionally robust day-ahead scheduling of park-level integrated energy system considering generalized energy storages. Appl. Energy
**2021**, 302, 117493.1–117493.13. [Google Scholar] [CrossRef] - Yu, W.C.; Huang, W.W.; Gong, J.; Wen, K.; Li, Y.C.; Dang, F.H.; Xiong, J.Y. Research on the Reliability Evaluation Index of Natural Gas Pipeline Network System. Pet. Sci. Bull.
**2019**, 4, 184–191. [Google Scholar] - Santos, M.; Huo, D.; Wade, N.; Greenwood, D.; Sarantakos, I. Reliability Assessment of Island Multi-energy Microgrids. Energy Convers. Econ.
**2021**, 2, 169–182. [Google Scholar] [CrossRef] - Li, W.; Zhou, J.; Lu, J.; Yan, W. Incorporating a Combined Fuzzy and Probabilistic Load Model in Power System Reliability Assessment. IEEE Trans. Power Syst.
**2007**, 22, 1386–1388. [Google Scholar] [CrossRef] - Fan, M.W.; Gong, J.; Wu, Y.; Kong, W.H. Reliability Analysis of Gas Supply in Shaanxi-Beijing Natural Gas Pipeline Network Based on Simplified Topology. Nat. Gas Ind.
**2017**, 37, 123–129. [Google Scholar] - Araki, K.; Tawa, H.; Saiki, H.; Ota, Y.; Nishioka, K.; Yamaguchi, M. The Outdoor Field Test and Energy Yield Model of the Four-Terminal on Si Tandem PV Module. Appl. Sci.
**2020**, 10, 2529. [Google Scholar] [CrossRef] - Liang, Y.Z.; Hui, C.W. Convexification for Natural Gas Transmission Networks Optimization. Energy
**2018**, 158, 1001–1016. [Google Scholar] [CrossRef] - Dundulis, G.; Žutautaitė, I.; Janulionis, R.; Ušpuras, E.; Rimkevičius, S.; Eid, M. Integrated failure probability estimation based on structural integrity analysis and failure data: Natural gas pipeline case. Reliab. Eng. Syst. Saf.
**2016**, 156, 195–202. [Google Scholar] [CrossRef] - Zhang, T.H.; Liu, S.Y.; Qiu, W.Q.; Lin, Z.Z.; Zhu, L.; Zhao, D.; Qian, M.; Yang, L. KPI-based Real-time Situational Awareness for Power Systems with a High Proportion of Renewable Energy Sources. CSEE J. Power Energy Syst.
**2022**, 8, 1060–1073. [Google Scholar]

**Figure 5.**Simplified topology diagram of natural gas pipe network system and the power grid of an area.

Line Name | Maximum Gas Delivery Volume/m^{3} | Gas Delivery Volume during Operation/m^{3} |
---|---|---|

A | 5000 | 4500 |

B | 6000 | 5400 |

C | 7000 | 6300 |

D | 6000 | 5400 |

E | 7000 | 6300 |

Equipment Components | Failure Probability |
---|---|

Compressor station | 0.14 |

Sub-transmission substation | 0.20 |

Compressor and sub-transmission station | 0.15 |

Independent pipeline | 0.10 |

Collinear pipeline | 0.13 |

Nodes | Gas Unit Output/MW | Coal-Fired Unit Output/MW | The Upper Limit of Gas Unit Output/MW | The Upper Limit of Coal-Fired Unit Output/MW | Load/MW |
---|---|---|---|---|---|

1 | \ | 100 | \ | 140 | 0 |

2 | 8.8 | \ | 30 | \ | 21.7 |

3 | 4 | \ | 50 | \ | 94.2 |

6 | 6.73 | \ | 20 | \ | 11.2 |

8 | \ | 90 | \ | 100 | 0 |

Load Number | Electric Load Loss at 100% Supply/MW | Electric Load Loss at 80% Supply/MW | Electric Load Loss at 60% Supply/MW | Electric Load Loss at 40% Supply/MW | Electric Load Loss at 20% Supply/MW | Electric Load Loss with No Supply/MW |
---|---|---|---|---|---|---|

1 | 0 | 0 | 0 | 0 | 0 | 0 |

2 | 0 | 4.47 | 4.79 | 5.12 | 5.45 | 5.78 |

3 | 0 | 19.40 | 20.80 | 22.24 | 23.67 | 25.10 |

4 | 0 | 9.85 | 10.55 | 11.28 | 12.01 | 12.73 |

5 | 0 | 1.57 | 1.68 | 1.79 | 1.91 | 2.02 |

6 | 0 | 2.31 | 2.47 | 2.64 | 2.81 | 2.98 |

7 | 0 | 0 | 0 | 0 | 0 | 0 |

8 | 0 | 0 | 0 | 0 | 0 | 0 |

9 | 0 | 6.08 | 6.51 | 6.96 | 7.41 | 7.86 |

10 | 0 | 1.85 | 1.99 | 2.12 | 2.26 | 2.40 |

11 | 0 | 0.72 | 0.77 | 0.83 | 0.88 | 0.93 |

12 | 0 | 1.26 | 1.35 | 1.44 | 1.53 | 1.63 |

13 | 0 | 2.78 | 2.98 | 3.19 | 3.39 | 3.60 |

14 | 0 | 3.07 | 3.29 | 3.52 | 3.74 | 3.97 |

Gas Supply Volume/m^{3} | EDNS/MW | SI | ASAI | AENS |
---|---|---|---|---|

0 | 69.00 | 0.27 | 0.73 | 4.93 |

3600 | 65.07 | 0.25 | 0.75 | 4.65 |

7200 | 61.15 | 0.24 | 0.76 | 4.37 |

10,800 | 57.19 | 0.22 | 0.78 | 4.09 |

14,400 | 53.35 | 0.21 | 0.79 | 3.81 |

18,000 | 0.00 | 0.00 | 1.00 | 0.00 |

EDNS/MW | SI | ASAI | AENS | |
---|---|---|---|---|

MCS | 57.19 | 0.22 | 0.78 | 4.09 |

LHS | 57.48 | 0.22 | 0.78 | 4.11 |

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**MDPI and ACS Style**

Zeng, K.; Wang, Y.; Yu, S.; Jiang, X.; Ma, Y.; Ma, J.; Lin, Z.
Reliability Assessment of Power Systems in High-Load Areas with High Proportion of Gas-Fired Units Considering Natural Gas Loss. *Appl. Sci.* **2023**, *13*, 6012.
https://doi.org/10.3390/app13106012

**AMA Style**

Zeng K, Wang Y, Yu S, Jiang X, Ma Y, Ma J, Lin Z.
Reliability Assessment of Power Systems in High-Load Areas with High Proportion of Gas-Fired Units Considering Natural Gas Loss. *Applied Sciences*. 2023; 13(10):6012.
https://doi.org/10.3390/app13106012

**Chicago/Turabian Style**

Zeng, Kaile, Yunchu Wang, Shuyang Yu, Xinyue Jiang, Yuanqian Ma, Jien Ma, and Zhenzhi Lin.
2023. "Reliability Assessment of Power Systems in High-Load Areas with High Proportion of Gas-Fired Units Considering Natural Gas Loss" *Applied Sciences* 13, no. 10: 6012.
https://doi.org/10.3390/app13106012