The compressor fuel cost minimization problem (FCMP) for natural gas pipelines is a relevant problem because of the substantial energy consumption of compressor stations transporting the large global demand for natural gas. The common method for modeling the FCMP is to assume key modeling parameters such as the friction factor, compressibility factor, isentropic exponent, and compressor efficiency to be constants, and their nonlinear relationships to the system operating conditions are ignored. Previous work has avoided the complexity associated with the nonlinear relationships inherent in the FCMP to avoid unreasonably long solution times for practical transportation systems. In this paper, a mixed-integer linear programming (MILP) based method is introduced to generate piecewise-linear functions that approximate the previously ignored nonlinear relationships. The MILP determines the optimal break-points and orientation of the linear segments so that approximation error is minimized. A novel FCMP model that includes the piecewise-linear approximations is applied in a case study on three simple gas networks. The case study shows that the novel FCMP model captures the nonlinear relationships with a high degree of accuracy and only marginally increases solution time compared to the common simplified FCMP model. The common simplified model is found to produce solutions with high error and infeasibility when applied on a rigorous simulation.Processes 2018, 6, 198 2 of 31 constraints and physical equipment limitations. With an estimated 3-5% of all natural gas transported by transmission pipelines consumed by the compressor stations responsible for maintaining gas flow, substantial energy and cost savings can be realized through optimizing the FCMP. It has been estimated that at least a 20% reduction in compressor station fuel consumption can be obtained through global optimization of pipeline operation [2].The FCMP is a difficult optimization problem because real pipeline systems have complex network topographies, integer variables are required to represent the pipeline binary operating states (bi-directional flow, ON/OFF compressor units), and gas and compressor physics are governed by highly nonlinear equations. The FCMP is most appropriately modeled as a nonlinear program (NLP) or mixed-integer nonlinear program (MINLP), depending on whether bi-directional flow or ON/OFF compressor units are considered [3]. Given the complexity of the FCMP model, current algorithms can only solve simplified versions for networks large enough to have practical importance. With this, there are numerous simplifications of model parameters that are broadly accepted across FCMP literature because of the computational savings they provide. However, upon inspection of the error such simplifications introduce to the model, the ability for the model to provide a useful representation of the real system is brought into question.There has been virtually no previous work done on methods of approximating the nonlinear relationships inherent in...

Combined heat and power (CHP) systems are attracting increasing attention for their ability to improve the economics and sustainability of the electricity system. Determining how to best operate these systems is difficult because they can consist of many generating units whose operation is governed by complex nonlinear physics. Mathematical programming is a useful tool to support the operation of CHP systems, and has been the subject of substantial research attention since the early 1990s. This paper critically reviews the modeling and optimization work that has been done on the CHP economic dispatch problem, and the CHP economic and emission dispatch problem. A summary of the common models used for these problems is provided, along with comments on future modeling work that would beneficial to the field. The majority of optimization approaches studied for CHP system operation are metaheuristic algorithms. A discussion of the limitations and benefits of metaheuristic algorithms is given. Finally, a case study optimizing five classic CHP system test instances demonstrates the advantages of the using deterministic global search algorithms over metaheuristic search algorithms.

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