Multistage Economic NMPC for Gas Pipeline Networks with Uncertainty

Gas pipelines form complex highly integrated networks to transport natural gas with dynamic operation due to time varying demands, composition, and ambient conditions. These can be modeled and optimized through non-linear optimal control problems with model equations, operation bounds and uncertainty descriptions. In this study, we use a multistage Economic Nonlinear Model Predictive Controller (eNMPC) to find optimal operational policies for networks with dynamic demands and uncertain parameters. This approach relies on constructing a scenario tree by generating extreme cases of the uncertain parameters with separate control sequences to address constraint violations in each case. For demonstration, we assume that the efficiency of the compressors is uncertain. Under this uncertainty we show that standard eNMPC, designed with a nominal value of compressor efficiency, violates constraints in the plant. We demonstrate that multistage eNMPC prevents constraint violations in all uncertain realizations and provides a promising robust control strategy for these networks.