(457h) Multistage Economic Nonlinear Model Predictive Control of Gas Pipeline Networks Under Uncertainty

Natural gas networks are the cornerstone of energy-based operations. Transport of gas over large distances is an inherently dynamic process with uncertainties such as fluctuating demands, changing compositions and ambient conditions. Operating complex gas networks requires energy to overcome losses due to friction and changes in elevation. Owing to decarbonization, it is desired to minimize the energy consumption in natural gas transportation while meeting the demands. Implementing dynamic optimization to determine optimal operational policies for transport of natural gas has great potential in terms of cost reduction and energy savings [1, 2] .

Mathematical models of gas networks consist of non-linear model equations, operational bounds and uncertain parameters which require advanced control strategies. Optimal control approaches, both stochastic [1] and robust [2] have been studied in the past for gas pipeline networks with demand and composition uncertainties. Gopalkrishnan et. al. [3] employed an economic model predictive control (E-NMPC) framework to optimize operating costs. However, none of these approaches explicitly consider uncertainty in an E-NMPC framework. Under uncertainty, a standard E-NMPC fails to meet the demands or the terminal constraints leading to line pack depletion.

To address this, we embed dynamic gas network models into a multistage E-NMPC to optimize operational costs. The uncertainty in demands is explicitly considered by constructing a scenario tree based on extreme cases in demands. A separate control sequence is generated for each uncertain scenario while ensuring a common control action using non-anticipativity constraints. The advantage of this approach is that it is less conservative than the standard robust NMPC and prevents constraint violation in all realizations of uncertainty [4]. To demonstrate this approach, we show that a standard E-NMPC fails to meet demands in the presence of uncertainty while a multistage E-NMPC provides a promising control strategy by making cost-effective decisions without violating any constraints.

In this talk we describe our model formulation [5], give details on the multistage E-NMPC approach, and describe our results obtained on instances from the gaslib [6] library using PyomoDAE [7] and IPOPT [8]. Future directions including parallelization to achieve computational efficiency and simultaneously considering multiple uncertainties are also discussed.

References

[1] V. M. Zavala, “Stochastic optimal control model for natural gas networks,” Computers & Chemical Engineering, vol. 64, pp. 103–113, May 2014, doi: 10.1016/j.compchemeng.2014.02.002.

[2] K. Liu, L. T. Biegler, B. Zhang, and Q. Chen, “Dynamic optimization of natural gas pipeline networks with demand and composition uncertainty,” Chemical Engineering Science, vol. 215, p. 115449, Apr. 2020, doi: 10.1016/j.ces.2019.115449.

[3] A. Gopalakrishnan and L. T. Biegler, “Economic Nonlinear Model Predictive Control for periodic optimal operation of gas pipeline networks,” Computers & Chemical Engineering, vol. 52, pp. 90–99, May 2013, doi: 10.1016/j.compchemeng.2012.11.011.

[4] S. Naik, R. Parker, and L. T. Biegler, “Multistage Economic NMPC for Gas Pipeline Networks with Uncertainty,” in Computer Aided Chemical Engineering, vol. 52, A. C. Kokossis, M. C. Georgiadis, and E. Pistikopoulos, Eds., in 33 European Symposium on Computer Aided Process Engineering, vol. 52., Elsevier, 2023, pp. 1847–1852. doi: 10.1016/B978-0-443-15274-0.50293-6.

[5] L. M. P. Ghilardi, F. Casella, D. Barbati, R. Palazzo, and E. Martelli, “Optimal operation of large gas networks: MILP model and decomposition algorithm,” in Computer Aided Chemical Engineering, vol. 52, A. C. Kokossis, M. C. Georgiadis, and E. Pistikopoulos, Eds., in 33 European Symposium on Computer Aided Process Engineering, vol. 52. , Elsevier, 2023, pp. 915–920. doi: 10.1016/B978-0-443-15274-0.50146-3.

[6] M. Schmidt et al., “GasLib—A Library of Gas Network Instances,” Data, vol. 2, no. 4, Art. no. 4, Dec. 2017, doi: 10.3390/data2040040.

[7] B. Nicholson, J. D. Siirola, J.-P. Watson, V. M. Zavala, and L. T. Biegler, “pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations,” Math. Prog. Comp., vol. 10, no. 2, pp. 187–223, Jun. 2018, doi: 10.1007/s12532-017-0127-0.

[8] A. Wächter, L. Biegler, Y. Lang, and A. Raghunathan, IPOPT: An interior point algorithm for large-scale nonlinear optimization. 2002.