Safety-Oriented Coordinated Operation Algorithms for Natural Gas Pipeline Networks and Gas-Fired Power Generation Facilities
Abstract
1. Introduction
2. Optimization Model of Coordinated Operation of Pipeline Networks and Gas-Fired Power Generation Facilities
2.1. Objective Function
2.2. Decision Variable
2.3. Key Constraints
- Constraints on the injection-withdrawal volume of gas storage: As shown in Equations (6)–(9), during the gas injection period, if the operating state of gas storage is = 1, the constraint Equations (6) and (9) take effect; if the operating state of gas storage during the gas withdrawal period is = 0, the constraint Equations (7) and (8) take effect. While maintaining compliant injection-withdrawal volumes, gas storage restricts the pipeline injection volume to zero during storage injection phases and the pipeline withdrawal volume to zero during storage withdrawal phases. In practical operations, gas storage typically sustains either injection or withdrawal states for prolonged duration. Thus, our intraday optimization model excludes transitions between injection and withdrawal states.
- Gas consumption constraints for gas-fired power generation facilities: the optimization model incorporates operation constraints for gas-fired power generation facilities, determined by the actual gas demand of end-users and technical operation constraints inherent to gas-fired power generation facilities.
2.4. Model Summary
3. Algorithm Design and Robustness Analysis
3.1. Controller Design
3.2. The Robustness and Computational Time of the Algorithm
4. Application of the Optimization Model of Coordinated Operation of Pipeline Networks and Gas-Fired Power Generation Facilities
4.1. Basic Parameters and Operation of the Regional Pipeline Network System
4.1.1. Basic Parameters of the System
4.1.2. Operating Parameters of the System
4.1.3. Gas and Electricity Prices
4.2. Analysis Results of Coordinated Operation of Gas Power Network–Gas Storage
4.2.1. Flow Directions in Pipeline Network Operation During Gas Injection When Gas Storages Are Considered
4.2.2. Analysis Results
4.3. Analysis Results of Coordinated Optimization Operation of Gas Power Network
4.3.1. Flow Directions in Pipeline Network Operation When Gas Storages Are Not Considered
4.3.2. Analysis Results
4.4. Contrastive Analysis
4.4.1. Analysis of Changes in Total Gas Consumption for Gas-Fired Power Generation Facilities
4.4.2. Analysis of Changes in Peak-Shaving Volume of Gas Offtake and Injection at Station N4
4.4.3. Analysis of Changes in Linepack
4.4.4. Summary
5. Conclusions
- (1)
- Given the significant nonlinearity and high dimensionality of the coordinated optimization model involving natural gas pipeline networks and gas-fired power generation facilities, we comparatively analyzed various optimization solvers to evaluate their advantages, disadvantages, and applicability to the coordinated optimization model. The IPOPT solver is ultimately selected as the primary tool for addressing the optimization problem. It can effectively address the model’s high nonlinearity and dimensionality while ensuring computational efficiency and practical feasibility while maintaining solution accuracy.
- (2)
- In this study, an integrated coordinated optimization model is established by focusing on natural gas users, pipeline networks, gas storage, compressor stations, gas sources, and gas-fired power generation facilities. The model sought to identify the optimal coordinated operation strategy while meeting the basic gas and electricity demands of users and ensuring safe and stable operation of equipment and pipelines, thereby maximizing the system’s overall operating benefits and achieving safe, stable, coordinated, and efficient system operations.
- (3)
- A comparative case analysis of this regional pipeline network reveals that the solution results correspond with actual operating conditions and predefined model constraints, yielding significant effects. The coordinated operation optimization technique for pipeline networks and gas-fired power generation facilities, as developed in this study, has proven its favorable applicability in this regional case.
- (4)
- This optimization model relies on the actual gas price, electricity price, and the actual gas consumption of natural gas users in this region and is constrained by the restrictions of this region. In the next step, the above actual values shall be set as range values for the calculation and solution of the optimization algorithm, and this optimization algorithm can be extended to more complex regions.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Kashani, A.H.A.; Molaei, R. Techno-economical and environmental optimization of natural gas network operation. Chem. Eng. Res. Des. 2014, 92, 2106–2122. [Google Scholar] [CrossRef]
- Pratt, K.F.; Wilson, J.G. Optimization of the operation of gas transmission systems. Trans. Inst. Meas. Control 1984, 6, 261–269. [Google Scholar] [CrossRef]
- Sekirnjak, E. Practical experiences with various optimization techniques for gas transmission and distribution systems. In Proceedings of the PSIG Annual Meeting, San Francisco, CA, USA, 23–25 October 1996. PSIG-9603. [Google Scholar]
- Rømo, F.; Tomasgard, A.; Hellemo, L.; Fodstad, M.; Eidesen, B.H.; Pedersen, B. Optimizing the Norwegian natural gas production and transport. Interfaces 2009, 39, 46–56. [Google Scholar] [CrossRef]
- Pepper, W.; Ring, B.J.; Read, E.G.; Starkey, S.R. Implementation of a scheduling and pricing model for natural gas. In Handbook of Networks in Power Systems II; Springer: Berlin/Heidelberg, Germany, 2012; pp. 3–35. [Google Scholar]
- Bermúdez de Castro López-Varela, A.; González Díaz, J.; González Diéguez, F.J.; González Rueda, Á.M.; Pérez Fernández de Córdoba, M. Simulation and optimization models of steady-state gas transmission networks. Energy Procedia 2015, 64, 130–139. [Google Scholar] [CrossRef]
- Žácik, T.; Somora, P.; Hajossy, R. Modeling and optimizing in Slovak gas transmission network. In Proceedings of the PSIG Annual Meeting, Prague, Czech Republic, 16–19 April 2013. PSIG-1319. [Google Scholar]
- Zavala, V.M. Stochastic optimal control model for natural gas networks. Comput. Chem. Eng. 2013, 64, 103–113. [Google Scholar] [CrossRef]
- Zhang, X.; Wu, C.; Zuo, L. Minimizing fuel consumption of a gas pipeline in transient states by dynamic programming. J. Nat. Gas Sci. Eng. 2016, 28, 193–203. [Google Scholar] [CrossRef]
- Behrooz, H.A.; Boozarjomehry, R.B. Dynamic optimization of natural gas networks under customer demand uncertainties. Energy 2017, 134, 968–983. [Google Scholar] [CrossRef]
- Hoppmann-Baum, K.; Hennings, F.; Lenz, R.; Gotzes, U.; Heinecke, N.; Spreckelsen, K.; Koch, T. Optimal operation of transient gas transport networks. Optim. Energy 2021, 22, 735–810. [Google Scholar] [CrossRef]
- Wen, K.; Lu, Y.; Lu, M.; Zhang, W.; Zhu, M.; Qiao, D.; Meng, F.; Zhang, J.; Gong, J.; Hong, B. Multi-period optimal infrastructure planning of natural gas pipeline network system integrating flow-rate allocation. Energy 2022, 257, 124745. [Google Scholar] [CrossRef]
- Wen, K.; Qiao, D.; Nie, C.; Lu, Y.; Wen, F.; Zhang, J.; Miao, Q.; Gong, J.; Li, C.; Hong, B. Multi-period supply and demand balance of large-scale and complex natural gas pipeline networks: Economy and environment. Energy 2023, 264, 126104. [Google Scholar] [CrossRef]
- Hong, B.; Qiao, D.; Li, Y.; Sun, X.; Yang, B.; Li, L.; Gong, J.; Wen, K. Supply-demand balance of natural gas pipeline network integrating hydraulic and thermal characteristics, energy conservation and carbon reduction. Energy 2023, 283, 128427. [Google Scholar] [CrossRef]
- Wen, K.; Gao, W.; Hui, X.; Li, L.; Yang, B.; Nie, C.; Miao, Q.; Li, Y.; Li, C.; Hong, B. Allocation of transportation capacity for complex natural gas pipeline networks under fair opening. Energy 2024, 291, 130330. [Google Scholar] [CrossRef]
- Orazbayev, B.; Moldasheva, Z.; Orazbayeva, K.; Makhatova, V.; Kurmangaziyeva, L.; Gabdulova, A. Development of mathematical models and optimization of operation modes of the oil heating station of main oil pipelines under conditions of fuzzy initial information. East. Eur. J. Enterp. Technol. 2021, 6, 147–162. [Google Scholar] [CrossRef]
- Yong, T.; Jefeerson, J.T. Shell pipeline calls it dynamic programming. Oil Gas J. 1961, 59, 8–12. [Google Scholar]
- Gopal, V.N. Optimization pipeline operation. J. Pet. Technol. 1980, 32, 2063–2067. [Google Scholar] [CrossRef]
- Cheng, W.; Liu, Q. Sufficient descent nonlinear conjugate gradient methods with conjugacy condition. Numer. Algorithms 2010, 53, 113–131. [Google Scholar] [CrossRef]
- Neculai, A. Another hybrid conjugate gradient algorithm for unconstrained optimization. Numer. Algorithms 2008, 47, 143–156. [Google Scholar]
- Andrei, N. Hybrid conjugate gradient algorithm for unconstrained optimization. J. Optim. Theory Appl. 2009, 141, 249–264. [Google Scholar] [CrossRef]
- Pandey, H.M.; Chaudhary, A.; Mehrotra, D. A comparative review of approaches to prevent premature convergence in GA. Appl. Soft Comput. 2014, 24, 1047–1077. [Google Scholar] [CrossRef]
- Guria, C.; Bhattacharya, P.K.; Gupta, S.K. Multi-objective optimization of reverse osmosis desalination units using different adaptations of the non-dominated sorting genetic algorithm (NSGA). Comput. Chem. Eng. 2005, 29, 1977–1995. [Google Scholar] [CrossRef]
- Ripon, K.S.N.; Kwong, S.; Man, K.F. A real-coding jumping gene genetic algorithm (RJGGA) for multi-objective optimization. Inf. Sci. 2006, 177, 632–654. [Google Scholar] [CrossRef]
- Roshani, A.; Roshani, A.; Roshani, A.; Salehi, M.; Esfandyari, A. A simulated annealing algorithm for multi-manned assembly line balancing problem. J. Manuf. Syst. 2013, 32, 238–247. [Google Scholar] [CrossRef]
- Roshani, A.; Nezami, F.G. Mixed-model multi-manned assembly line balancing problem: A mathematical model and a simulated annealing approach. Assem. Autom. 2017, 37, 34–50. [Google Scholar] [CrossRef]
- Patriksson, M. The Traffic Assignment Problem: Models and Methods; Dover Publications: New York, NY, USA, 2015. [Google Scholar]
Steps | Procedure |
---|---|
1 | Given an initial value , initial penalty factor , penalty factor magnification factor , set ; |
2 | Using the iteration point as the initial point, solve the unconstrained optimization problem to yield the local minimum ; |
3 | If , the termination condition is met and is the optimal solution to the original problem, output and stop iteration; otherwise, go to Step 4; |
4 | Let , go to Step 2. |
Scenario | 10-Node Convergence | 30-Node Convergence | 50-Node Convergence |
---|---|---|---|
IPOPT | 100 | 97 | 93 |
CONOPT | 94 | 88 | 79 |
KNITRO | 96 | 91 | 85 |
Bonmin | 87 | 74 | 63 |
Scenario | 10-Node Convergence | 30-Node Convergence | 50-Node Convergence |
---|---|---|---|
IPOPT | 1.3 | 4.3 | 11.6 |
CONOPT | 1.7 | 6.5 | 17.9 |
KNITRO | 1.5 | 5.6 | 14.8 |
Bonmin | 2.9 | 10.7 | 29.4 |
Scenario | Max Objective Fluctuation (%) | Constraint Violations (100 Trials) |
---|---|---|
IPOPT | 5.2 | 3 |
CONOPT | 6.8 | 8 |
KNITRO | 5.9 | 6 |
Bonmin | 8.1 | 11 |
Flow Directions | Contents |
---|---|
Condition 1 | (‘N1’, ‘N2’), (‘N2’, ‘N3’), (‘N3’, ‘N4’), (‘N1’, ‘N5’), (‘N5’, ‘N6’), (‘N6’, ‘N7’), (‘N7’, ‘N8’), (‘N8’, ‘N9’), (‘N9’, ‘N10’), (‘N10’, ‘N11’), (‘N10’, ‘N12’), (‘N9’, ‘N13’), (‘N13’, ‘N4’) |
Condition 2 | (‘N1’, ‘N2’), (‘N2’, ‘N3’), (‘N3’, ‘N4’), (‘N1’, ‘N5’), (‘N5’, ‘N6’), (‘N6’, ‘N7’), (‘N7’, ‘N8’), (‘N9’, ‘N8’), (‘N9’, ‘N10’), (‘N10’, ‘N11’), (‘N10’, ‘N12’), (‘N9’, ‘N13’), (‘N13’, ‘N4’) |
Condition 3 | (‘N1’, ‘N2’), (‘N2’, ‘N3’), (‘N3’, ‘N4’), (‘N1’, ‘N5’), (‘N5’, ‘N6’), (‘N6’, ‘N7’), (‘N8’, ‘N7’), (‘N9’, ‘N8’), (‘N9’, ‘N10’), (‘N10’, ‘N11’), (‘N10’, ‘N12’), (‘N9’, ‘N13’), (‘N13’, ‘N4’) |
Condition 4 | (‘N1’, ‘N2’), (‘N2’, ‘N3’), (‘N3’, ‘N4’), (‘N1’, ‘N5’), (‘N5’, ‘N6’), (‘N7’, ‘N6’), (‘N8’, ‘N7’), (‘N9’, ‘N8’), (‘N9’, ‘N10’), (‘N10’, ‘N11’), (‘N10’, ‘N12’), (‘N9’, ‘N13’), (‘N13’, ‘N4’) |
Condition 5 | (‘N1’, ‘N2’), (‘N2’, ‘N3’), (‘N3’, ‘N4’), (‘N1’, ‘N5’),(‘N6’, ‘N5’), (‘N7’, ‘N6’), (‘N8’, ‘N7’), (‘N9’, ‘N8’), (‘N9’, ‘N10’), (‘N10’, ‘N11’), (‘N10’, ‘N12’), (‘N9’, ‘N13’), (‘N13’, ‘N4’) |
Condition 6 | (‘N1’, ‘N2’), (‘N2’, ‘N3’), (‘N3’, ‘N4’), (‘N5’, ‘N1’), (‘N6’, ‘N5’), (‘N7’, ‘N6’), (‘N8’, ‘N7’), (‘N9’, ‘N8’), (‘N9’, ‘N10’), (‘N10’, ‘N11’), (‘N10’, ‘N12’), (‘N9’, ‘N13’), (‘N13’, ‘N4’) |
Name of Gas Storage Areas | Gas Injection Pressure (MPa) | Scheduled Injection Volume (10,000 m3/d) |
---|---|---|
A | 3.20 | 220 |
B | 3.00 | 250 |
Name of Gas-Fired Power Generation Facilities | Maximum Gas Consumption at Rated Output (m3/h) | Minimum Gas Consumption at Rated Output (m3/h) |
---|---|---|
Project N | 167,647 | 41,912 |
Project L | 247,058 | 61,765 |
Project Y | 86,470 | 43,235 |
Clock | Gas Sales Revenues for Gas-Fired Power Generation Facilities (CNY) | Offtake and Injection Costs at Station N4 (CNY) | Gas Injection Costs of Gas Storage (CNY) | Total Revenues (CNY) |
---|---|---|---|---|
0:00 | 352,244 | 13,186 | 7788 | 331,270 |
1:00 | 292,289 | 1561 | 7874 | 282,854 |
2:00 | 232,335 | 0 | 7875 | 224,460 |
3:00 | 182,015 | 0 | 7839 | 174,176 |
4:00 | 213,858 | 0 | 7777 | 206,081 |
5:00 | 213,858 | 0 | 7719 | 206,139 |
6:00 | 248,983 | 0 | 7697 | 241,286 |
7:00 | 308,938 | 0 | 7648 | 301,290 |
8:00 | 357,432 | 0 | 7716 | 349,716 |
9:00 | 447,364 | 0 | 7655 | 439,709 |
10:00 | 537,295 | 0 | 7652 | 529,643 |
11:00 | 627,227 | 0 | 8607 | 618,620 |
12:00 | 717,159 | 0 | 8667 | 708,492 |
13:00 | 767,358 | 0 | 8743 | 758,615 |
14:00 | 771,112 | 0 | 8812 | 762,300 |
15:00 | 711,158 | 0 | 8867 | 702,291 |
16:00 | 635,783 | 0 | 8973 | 626,810 |
17:00 | 545,851 | 0 | 8034 | 537,817 |
18:00 | 472,565 | 0 | 8051 | 464,514 |
19:00 | 442,588 | 0 | 8077 | 434,511 |
20:00 | 532,520 | 0 | 9073 | 523,447 |
21:00 | 502,434 | 0 | 9095 | 493,339 |
22:00 | 412,502 | 0 | 8113 | 404,389 |
23:00 | 322,570 | 0 | 8091 | 314,479 |
Clock | Gas Sales Revenues of Gas-Fired Power Generation Facilities (CNY) | Injection Cost of the Downstream Pipeline of N4 (CNY) | Total Revenues (CNY) |
---|---|---|---|
0:00 | 412,211 | 25,214 | 386,997 |
1:00 | 442,189 | 13,564 | 428,625 |
2:00 | 472,166 | 11,565 | 460,601 |
3:00 | 502,143 | 11,537 | 490,606 |
4:00 | 532,120 | 11,507 | 520,613 |
5:00 | 622,052 | 11,483 | 610,569 |
6:00 | 711,984 | 11,465 | 700,519 |
7:00 | 801,916 | 11,455 | 790,461 |
8:00 | 863,747 | 12,061 | 851,686 |
9:00 | 923,702 | 12,076 | 911,626 |
10:00 | 953,590 | 15,455 | 938,135 |
11:00 | 923,613 | 28,381 | 895,232 |
12:00 | 893,636 | 24,398 | 869,238 |
13:00 | 863,658 | 12,518 | 851,140 |
14:00 | 833,681 | 25,098 | 808,583 |
15:00 | 803,704 | 37,729 | 765,975 |
16:00 | 773,726 | 45,461 | 728,265 |
17:00 | 803,704 | 31,958 | 771,746 |
18:00 | 805,568 | 19,711 | 785,857 |
19:00 | 805,568 | 12,298 | 793,270 |
20:00 | 777,436 | 25,349 | 752,087 |
21:00 | 687,504 | 22,423 | 665,081 |
22:00 | 597,573 | 14,070 | 583,503 |
23:00 | 507,641 | 26,353 | 481,288 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Wang, X.; Wang, F.; Bie, Q.; Jia, W.; Jiang, Y.; Liu, Y.; Tian, Y.; Zheng, Y.; Sun, J. Safety-Oriented Coordinated Operation Algorithms for Natural Gas Pipeline Networks and Gas-Fired Power Generation Facilities. Processes 2025, 13, 2184. https://doi.org/10.3390/pr13072184
Wang X, Wang F, Bie Q, Jia W, Jiang Y, Liu Y, Tian Y, Zheng Y, Sun J. Safety-Oriented Coordinated Operation Algorithms for Natural Gas Pipeline Networks and Gas-Fired Power Generation Facilities. Processes. 2025; 13(7):2184. https://doi.org/10.3390/pr13072184
Chicago/Turabian StyleWang, Xinyi, Feng Wang, Qin Bie, Wenlong Jia, Yong Jiang, Ying Liu, Yuanyuan Tian, Yuxin Zheng, and Jie Sun. 2025. "Safety-Oriented Coordinated Operation Algorithms for Natural Gas Pipeline Networks and Gas-Fired Power Generation Facilities" Processes 13, no. 7: 2184. https://doi.org/10.3390/pr13072184
APA StyleWang, X., Wang, F., Bie, Q., Jia, W., Jiang, Y., Liu, Y., Tian, Y., Zheng, Y., & Sun, J. (2025). Safety-Oriented Coordinated Operation Algorithms for Natural Gas Pipeline Networks and Gas-Fired Power Generation Facilities. Processes, 13(7), 2184. https://doi.org/10.3390/pr13072184