(735c) An Economic Nonlinear Model Predictive Control Formulation for Gas Pipeline Optimization

The most common objective of model predictive control is to track a set-point by minimizing a least-squares objective function subject to future predictions from a dynamic model of the process. The set-point is provided by a real-time optimization (RTO) layer that operates on top of the MPC, and minimizes a desired objective using a steady state process model. However, for certain energy intensive processes like gas pipeline distribution networks, the optimal operating point needs to be changed frequently based on the time-varying demands of the consumers. In such cases, it might be both challenging and sub-optimal to apply the traditional two-layer MPC approach i.e. taking the pipeline operation to an RTO set-point might be sub-optimal when we consider information about the economics of the process. As a result, an economically oriented nonlinear model predictive control (NMPC) formulation which directly considers an economic objective function along with the nonlinear dynamic model of the process is a preferred approach.

In this work, we present an economic NMPC formulation for the optimal operation of gas pipeline networks subject to transient demands of the consumers. The compression of gas accounts for the most significant portion of the energy costs, and is the objective function minimized. A detailed fully open nonlinear model of the pipeline network [1] is considered, and a novel feature of the model is the smoothing operations to handle flow reversals (due to possible compressor outages) and flow transitions (between laminar and turbulent flow regimes), that are otherwise discontinuous and/or non-differentiable. The gas demands of the consumers are assumed to be sinusoidal in nature, which is an approximation to a real-demand curve. Due to the diurnal nature of the demands, the system goes towards not a fixed, but a cyclic-steady state. This requires an NMPC formulation with an appropriately defined terminal region to ensure nominal stability, and we use the approach described in [2].

Several case studies are presented, including the incorporation of time-varying electricity prices into the NMPC objective. We show how the pipeline inventory (linepack) can be manipulated to achieve significant compression cost savings. We also show how, in the presence of disturbances in the network, the NMPC scheme recalculates the optimal compression profiles while satisfying consumer flow demands and contract pressures. The results of this work are generalizable to any energy intensive process or a process with a variable inventory.

References

[1] B.T. Baumrucker and L.T. Biegler, MPEC strategies for cost optimization of pipeline operations, Computers & Chemical Engineering, 34(6), 900-913.

[2] R. Huang, E. Harinath and L. T. Biegler, Lyapunov stability of economically oriented NMPC for cyclic processes, Journal of Process Control, 21(4), 501-509.