Optimization Of Transient Operation For A Gas Pipeline With Varying Gas Consumption

Due to delivery flow rate variation,starting up or shutting down a compressor,opening or closing a valve,etc.,gas pipelines often operate under transient states.For the ones caused by delivery flow rate variation,the corresponding operation optimization problem was addressed.Given the source supplying condition,the delivery flow rate variation,the pipeline parameters,the environment parameters,and the constraints,the operation scheme of the lowest energy cost is computed.The mathematical model describing the problem is first built,including a pipelinelevel model and a station-level model.The objective of the pipeline-level model is to minimize the total energy cost by computing the optimal discharge pressure for each compressor station.Assuming that compressor station discharge pressure stays constant with time,and regarding the gas pipeline transient-state optimization problem as a multistage decision making problem,a dynamic programming(DP)algorithm was proposed.In each stage,the discharge pressure of a station is decided,transient simulations carried out to tackle the pipe flow control equations,and the station-level model solved to compute the energy cost of a compressor station.Solving the sequential steady-state optimization problem transformed from the transient-state one,the state space of the DP algorithm is cut based on the results,and the algorithm accelerated.In addition to the DP approach,a hybrid simulated annealing(SA)algorithm was also proposed.Regarding minimizing the weighted sum of the energy cost and the accumulated variation of the compressor station discharge pressure during the transient process as the objective,the sequential steady-state optimization problem transformed from the transient-state optimization problem was solved by SA.The results were adjusted according to two heuristics,including cutting the compressor station discharge pressure variation,and keeping the compressor station pressure ratio within proper range,to yield feasible solution for the transient-state optimization problem.The station-level model describes the compressor station operation optimization problem: given the suction pressure,the inlet flow rate,and the discharge pressure of a compressor station,the problem is to compute the operating scheme of the lowest energy cost for the station.According to whether the station operating parameters vary with time,this problem falls into two categories: the steady-state optimization problem and the sequential operating scheme optimization problem.Regarding the steady-state problem as a problem allocating the total flow rate to the compressors,a dynamic programming(DP)algorithm capable of computing the global optimal solution is proposed.Given the suction pressure,the suction temperature,and the discharge pressure of a compressor,a linear model is adopted to approximate the relationship between its energy cost and flow rate.Then,a mixed integer linear programming(MILP)approach is proposed for the sequential operating scheme optimization problem.By regarding the problem as a multistage decision making problem,where in each stage the station operating scheme for a time step is decided,a DP algorithm is proposed to compute its global optimal solution.By testing the two algorithms,the computing time of the MILP algorithm is found to be 1.52%~67.20% of the of the DP method,whereas its solution is 0.22%-1.18% higher.