Unit commitment for a compressor station by mixed integer linear programming

• The compressor station transient optimization problem, which is a MINLP problem, was solved.
• A dynamic programming (DP) method was proposed to compute the true optimum of the problem.
• Equivalent states were proposed to accelerate the DP method.
• A mixed integer linear programming (MILP) model was formulated to describe the problem and was then solved by CPLEX.
• The results of the MILP method were only 0.22%–1.18% higher than the true optimum, but its speed is 0.49–64.95 times faster.

When operating a compressor station, given its mass flow rate, inlet pressure and temperature, and discharge pressure, dispatchers need to decide which compressors to run and at what flow rates, i.e., the operating scheme of the station, to cut its energy costs. This paper addresses this problem under unsteady states. This means that at least one of the four given operating parameters is time-dependent, and therefore so is the operating scheme. The key constraints of the problem are the minimum uptime and downtime of each compressor, which interconnect the operating schemes at each time step and complicate the problem. The energy cost of a compressor unit is almost a linear function of its flow rate for a given inlet pressure, inlet temperature, and discharge pressure. Therefore, the optimization problem was formulated as a mixed integer linear programming (MILP) model, which was solved by CPLEX. The optimal operating schemes given by CPLEX were simulated to reevaluate the objective function, and the error of the linearized energy cost model was shown to be within 5%. The recalculated objective function values were 0.22%–1.18% higher than those of the true optimum. However, the MILP method was 0.49–64.95 times faster than the dynamic programming approach yielding global optimal solutions.