Power optimization of gas pipelines via an improved particle swarm optimization algorithm

Pet. Sci(2012)9:89-92DOI10.1007/s12182-0120187-8Power optimization of gas pipelines via an improvedparticle swarm optimization algorithmZheng zhiwei and wu Changchun*Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum, Beijing 102249,c China University of Petroleum(Beijing)and Springer-Verlag Berlin Heidelberg 2012Abstract: In past decades dynamic programming, genetic algorithms, ant colony optimization algorithmsand some gradient algorithms have been applied to power optimization of gas pipelines. In this paper apower optimization model for gas pipelines is developed and an improved particle swarm optimizationalgorithm is applied. Based on the testing of the parameters involved in the algorithm which need to bedefined artificially, the values of these parameters have been recommended which can make the algorithmreach efficiently the approximate optimum solution with required accuracy. Some examples have shownthat the relative error of the particle swarm optimization over ant colony optimization and dynamicprogramming is less than 1% and the computation time is much less than that of ant colony optimizationand dynamic programmingKey words: Gas pipeline, operation, optimization, particle swarm optimization algorithm1 Introductiongeneration. Because the convergence of PSo is fast and theaccuracy is high, the researchers pay much attention to theCompressors provide the pressure necessary to transport PSO. It is one of the most popular optimization algorithmsnatural gas via a pipeline. The prime mover consumes muchpresently (Van den Bergh and Engelbrecht, 2006; Liu et alpower when driving the compressor. So power optimization is 2007; Perez and Behdinan, 2007; Chen et al, 2010)very important for improying the operational economy of gasIn this paper an improved PSo is introduced. BecaupipelinesThe objective function of power optimization is northe colony information is very important, after evolution forone generation, the best position of the particle swarm willlinear and non-convex. Many constraints are non-linear. be sought again n times around itself. If a better positionIt is difficult to solve this kind of optimization problems. can be found, it will be the new best position of the particleDynamic programming DP)(Wong and Larson, 1968a; swarm. If no betteter position can be found, the best position1968b; Peretti and Toth, 1982; Carter, 1998; Rios-Mercado of the particle swarm will not be changed. It is good foret al, 2006), artificial intelligence(Sun et al, 2000)and some the algorithm to avoid local solutions effectively and thegradient algorithms(Percell and Ryan, 1987; Wu et al, 2000) accuracy can be improved. The improved PSO is applied tohave been applied to power optimization of gas pipelines. the power optimization of gas pipelines. Some parametersThese methods are effective. However, the application range of the algorithm are tested in order to get the most fittingof traditional algorithms is limited and the computation values for the power optimization. Some cases show that thetime is long. Particle swarm optimization(PSO)algorithm computation time can be significantly saved compared to antis a colony intelligence calculation technique developed bycolony optimization(ACO)and DP.Kennedy and Eberhart in 1995. It is inspired by the socialbehavior of organisms such as bird flocking(Yu et al, 2009). 2 Power optimization model of gas pipelinesThe Pso belongs to evolution algorithms. Like genetialgorithm it also begins with some random solutions andIn power optimization of a gas pipeline (as shown insearches for the optimum solution by iterative computation. FIig. 1), the objective function is minimizing the total energyThe pSo also evaluates solutions by the fitness function, but consumed by all the compressor units and the decisionit does not have the process of crossover and mutation. The variables are the discharge pressures of compressor stationsPSO searches for the optimum solution by tracking the best The constraint中国煤化--aints and thermalpositions of individual and colony after evolution for one constraints ofof compressorCN MH Discharge pressureand the minimum allowable suction pressure of compressorCorresponding author. email: wuchangchun @vip. sina. corstations, the minimum allowable delivery pressure at theReceived April 15, 2011delivery terminal, the flow rate and speed limits of every90Ptsi(20129992online compressor, etc. The problem can be formulated as compressor units in each compressor station; Q is the volumefollowsflow rate in the pipeline, m /s; m is the gas adiabatic indexR is the gas constant, kJ/(kmol K); P, is the density of theminm=(∑∑Qpnatural gas at the suction condition of station i, kg/m; Z isRZ, I ((a)m-1)/na/n, )/Emin the gas compressibility factor; T is the gas temperature at thesuction condition of the stations. K: h is the adiabatic headkJ/kg; ik represents the adiabatic efficiency of compressork in station i;n, represents the efficiency of the gas turbine;Emin is the low calorific value of gas, kJ/m; Pa and Ps are theP4≤Pmsdischarge pressure and the suction pressure of a compressormini pstation,Pa;Pe is the end pressure of a pipe segment betweencompressor stations, Pa; Delivery is the supply pressure atPmin2≤Pthe delivery terminal, Pa; Pmax is the maximum allowableHn=a1(")2+a1Q"+adischarge pressure of a compressor station, Pa; Pmint is the(1) minimum allowable suction pressure of a compressor stationPa; Pmin? is the minimum allowable delivery pressure at then=bo+b,0-0+b, 0(0)2delivery terminal, Pa; f represents the resistance ofpipesegments between compressor stations; ao, aI, a,, bo, b,,b2Q-n≤Q4sgnare coefficients of characteristic equations for a centrifugalcompressor; nok and n k represent the rated speed and theactual speed of compressor k in station i, respectively, rpmnmin, i and nmax. k are the minimum speed and the maximumspeed of compressor k in station i, rpm; @minJk and @max& arewhere num sta represents the number of compressor stations the surge flow rate and the stonewall Aow rate of compressoralong the pipeline system; J represents the number of online k in station i, m/sCompressor stationGassourceterminalFig. 1 A gas pipeline system3 PSO algorithm3.2 An improved PSo algorithmBecause the traditional PSo may converge to a local3.1 Traditional Pso algorithmoptimum solution and the accuracy is poor Jiang et al, 2007)an improved PSO is introduced hereA particle swarm containing M particles flies in DFrom Eg.(2)it can be seen that the particles are updateddimensional space. x (a,xi2,xig,",xD) represents the by tracking the best positions of individuals and the colonyposition of particle i in the space. v(vu,V2,V13,",VD) So the two best positions are very important for the algorithmrepresents the velocity of particle i. P (Pu, Pa, Pia, ", PD) The acceleration constants c, and c, represent the biggestand Pg(Pgl,Pg2, Pg3,", PgD)are the best positions of step flying to the best positions of individuals and the colony,particle i and the particle swarm presently. The velocity respectively. The influence of individuals and the colony onand position of particle i in the space are adjusted by the the particles is decided by them. If c;= 0, the particles onlyfollowing equations( Du and Li, 2008)have colony experience, the convergence will be very fastVd,,=WVd, -1+Gi(Pd, t-l-xid -1)+C22 (Pgd, -1-xMd, t 1)not have colony experiences, the particles fly in the space(2) independently, the optimum solution can not be obtainedThe colony information is very important for the algorithmto obtain the global solution. So in the improved PSO afterid, t=xid.i-I +vid.(3) every iterativ中国煤化工 ition of the particleswarm willIf a better positionwhere i=1, 2, . M;d=1, 2, D; t represents the can be foundCNMHGiition of the particleevolution generation up to now; w represents the weight swarm. If no better position can be found after searching forfactor; c, and c2 are the acceleration constants; r, and r2 are n times, the best position of the particle swarm will not bethe random numbers between [0, 1changed. The searching process around Pg is as followsPet. Sci.(2012)9:8992Ped=Pga(l+(2rand-I)m)(4) With c,;=1,c2=1,n=30, when mint=0.5,1,2,3,4thptimal objective value obtained by the algorithm is smallestm=mint a+ mmin(5) It equals 43.45 MWSo the best combination of these parameters can be chosea=exp(-30×())(6)asc=1,e2=1,n=30,mm=1where rand is a random number between [0, 1]; t represents 5 Case analysisthe evolution generation up to now; T represents the set totalevolution generations; S belongs to [l, 20]; mmin can be set at Fig. 3 is the topological structure of the gas pipeline. The0.01; mint will be defined artificiallypipeline is composed of five pipe segments connected inIn the early stage, a is big, the searching step is large,series by five compressor stations and one deliverythe convergence is fast and is good for the algorithm to avoid The basic data of the pipeline is shown in Table Ithe local solution. In the late stage, a is small, the searchingstep is small, the searching around the best position of the Station 1 Station 2 Station 3 Station 4 Station 5 Delivery terminalcolony is accurate, so it is good for the algorithm to increasethe optimization accuracyFig. 3 Compressor stations over the gas pipeline4 Testing about parameters of the algorithmThe improved PSO is coded by FORTRAN90. SomeTable 1 Basic data for the pipelineparameters of the algorithm need to be set artificially andthe values of the parameters should be fit for the problems toPipe segment resistances(14824,1.7154,14613,be solved. A case of gas pipeline power optimization with a2.1601,2.3296)×10simple topological structure is taken to test the parametersGas constant R, kJ/(kmol K)8.314Fig. 2 is the topological structure of the gas pipelineThe gas pipeline is composed of three compressor stationsand one delivery terminal. The gas source pressure is 6.1pressure Pea, MP&eMaximum allowable discha7.2MPa at the suction of station 1. For every compressor stationthe maximum allowable discharge pressure is 10 MPa, and Minimum allowable suction pressure mini,MPa4.7the minimum allowable suction pressure is 4.7 MPa. Theminimum allowable delivery pressure is 4 MPa at the endMinimum allowable delivery pressure pmin?, MPa4.2of the pipeline. The design flow rate is 32. 7x10 m/d. TheAccording to the Pso, the optimal operation schepipeline is 1,016 mm in outside diameter, 14.6 mm in wall the flow rate of 1. 15x10 kg/h can be obtainedthickness and 0.01 mm in pipe roughness. The objective Table 2 indicates that the discharge pressures of allfunction is minimizing the total power of all the compressor stations except Station 5 are 7.2 MPa, the maximum dischargeunits and the decision variables are the discharge pressures of pressure, and the discharge pressure of Station 5 only needsall the compressor stationsto assure that the pressure at the delivery terminal equals theminimum allowable delivery pressureStation 1Station 2Station 3 Delivery termTable 2 Optimal operation schemeDischarge pressure, MPaTotal gas consumption200km250km180kmStation 1 Station 2 Station 3 Station 4 Station 5I/dFig. 2 Topological structure of the gas pipel7.2727.26.43278×105The parameters required to test include cu, C2, n, and mTo test the performance of the PSo the optimizationAccording to the properties of the algorithm, the best possible results of five flow rates obtained by PSo are compared withvalue of these parameters can be defined With CI, C2E(0.2, ACO and DP0.4,0.6,0.8,1,2,3},n∈{5,10,20,30,40,50},mm2∈{0.5,Table 3 shows for 5 stations the relative error of pso over1, 2, 3, 4,103, the optimal objective function values will be ACO and DP is less than 0.5%, but the computation time is 8observed to select the best combination of these parameters. to 9 times less than that of A co and more than 60 times lessFirstly we can choose n=40, mint=1, when c C2=0.6, 0.8, than that of DP1, 2 the optimal objective value obtained by the algorithmWhen the stations are increased to ll, the optimizationsmallest, it equals 43. 45 MW.ci=l, C2=l can be definedresults of thi中国煤化With c=l,c2l, mint=l, when n=30, 40, 50 the optimalTabllative error of psoobjective value obtained by the algorithm is smallest, it equals over ACOHCN MH Ge computation time43.45 MW. To pursue the shortest computation time n=30 is is 4 to 7 times less than that of ACo and about 100 times lessdefinedthan that of dpPet. Sci(2012)9:8992Table 3 The optimization results of three algorithms for 5 stations design a fast and effective decision aid tool to assist operatorsto make appropriate decisions within a shorter time. ForFlow rateComputation time, sGas consumption, 10m/ddifferent kinds of optimization problems the parameterskg/hPSO ACOPSo ACo DP involved in the algorithm need to be tested, the values9.5×10209172713531.3501.350adopted are those that can get better results. This researchencourages us to apply Pso to gas network optimization and1.00x 10 23 203 1170 1.849 1.853 1.852 other difficult optimization problems19914462262.2322.23References1.10×10°2319515442.6792.6902.689Carter R G. 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Computers and Mathematics withobtained by the algorithm differ from those from ACO and Applications. 2009.57: 2022-2029DP by less than 1%, but the computation time can be savedgreatly compared with ACO and DP. This will enable us to(Edited by Sun Yanhua)中国煤化工CNMHG