文档名：基于改进交替方向乘子法的电气综合能源系统优化调度
摘要：在电-气综合能源系统分布式优化调度中,非线性非凸的Weymouth方程给问题求解带来了巨大挑战.一方面,目前许多研究采用二阶锥松弛Weymouth方程,较为复杂;另一方面,主流分布式算法即交替方向乘子法(ADMM)的计算效率并不高.对此,该文提出一种精确近似的Weymouth方程线性化模型和多参数规划改进ADMM算法以解决上述两个问题.Weymouth方程线性化模型基于泰勒展开,利用一簇切线松弛Weymouth方程.特别地,增加了惩罚项以收紧松弛间隙,通过变量替换的方法减少切线的数量,并给出了一种有效的切线选取方法.对于多参数规划改进ADMM算法,其通过多参数规划得到子问题最优解的解析式.迭代过程中,若参数落在临界域内,可直接将参数代入最优解解析式获得子问题的最优解,无需求解子问题,提高了迭代速度.此外,该文还对多参数规划中难以避免的退化问题进行了处理,提升了算法的通用性.最后在两个不同规模的系统中验证了Weymouth方程线性化模型的精确性和多参数规划改进ADMM算法的高效性.
Abstract：ItischallengingfordistributedoptimaldispatchofintegratedelectricityandgassystemsduetothenonlinearandnonconvexWeymouthequation.Atpresent,manystudiesusethesecond-orderconetorelaxtheWeymouthequation,whichisrelativelycomplicated.Ontheotherhand,themainstreamdistributedalgorithmalternatingdirectionmethodofmultipliers(ADMM)isnotcomputationallyefficient.Inthispaper,anexactapproximateWeymouthequationlinearizationmodelandamulti-parameterprogrammingmodifiedADMMalgorithmareproposedtoaddresstheaforementionedtwoconcerns.TheWeymouthequationlinearizationmodelisbasedonTaylorexpansion,whichusesaclusteroftangentstorelaxtheWeymouthequationandreplacesthecurvewithtangentsapproximately.Inparticular,apenaltytermisaddedtotightentheslackgap,andthenumberoftangentsisreducedbyvariablesubstitution.ThenaneffectivetangentselectionmethodisgiventoobtainanaccurateapproximationoftheWeymouthequationlinearizationmodel.Themulti-parameterprogrammingmodifiedADMMalgorithmimprovesADMMbymulti-parameterprogramming,toimprovethecomputationalefficiencyofdistributedoptimaldispatch.IntheADMMsubproblem,theanalyticalexpressionoftheoptimalsolutionofthesubproblemisobtainedbymulti-parameterprogramming.Duringtheiteration,aslongastheparametersfallinthecriticalregions,theparameterscanbedirectlysubstitutedintotheanalyticequationoftheoptimalsolutiontoobtaintheoptimalsolutionofthesubproblemwithoutsolvingthesubproblem,toimprovetheiterationspeed.Inaddition,thispaperalsodealswiththeunavoidabledegradationprobleminmulti-parameterprogrammingbythemethodbasedonQRdecomposition,whichenhancesthegeneralityofthemulti-parameterprogrammingmodifiedADMMalgorithm.Thesimulationresultsofthesmall-scalesystemshowthattheaveragerelativeerroroftheWeymouthequationlinearizationmodelis0.49%,andthemaximumrelativeerroris2.75%,whichachievesagoodapproximationeffect.Comparedwiththepiecewiselinearizationmethod,theproposedlinearizationmethodhashigheraccuracyandcomputationalefficiency.Inthedistributedoptimaldispatch,thenumberofiterationsofthemulti-parameterprogrammingmodifiedADMMalgorithmandclassicADMMisthesame,butthetimeconsumptionoftheproposedalgorithmisonly63.43%ofclassicADMM,whichisequivalenttoa57.66%increaseincomputationalefficiency.ForthevaryingpenaltyparameterADMM,althoughthenumberofiterationsofthevaryingpenaltyparameterADMMisonelessthanthatoftheproposedalgorithm,thetimeconsumptionoftheproposedalgorithmisstilllessthanthatofthevaryingpenaltyparameterADMM,andthecomputationalefficiencycanalsobeimprovedby44.53%.Inaddition,thesimulationresultsofthelarge-scalesystemalsoverifytheaccuracyoftheWeymouthequationlinearizationmodelandtheefficiencyofthemulti-parameterprogrammingmodifiedADMMalgorithm.Throughsimulationanalysis,thefollowingconclusionscanbedrawn:(1)TheWeymouthequationlinearizationmodelcanaccuratelydescribethepipelinegasflow,andithasadvantagesincomputationalefficiency.(2)Themulti-parameterprogrammingmodifiedADMMalgorithmimprovestheefficiencyofdistributedoptimaldispatchoftheintegratedelectricityandgassystem,whichisconducivetoreal-timedynamiceconomicdispatch.
作者：罗清局 朱继忠Author：LuoQingju ZhuJizhong
作者单位：华南理工大学电力学院广州510641
刊名：电工技术学报
Journal：TransactionsofChinaElectrotechnicalSociety
年，卷(期)：2024, 39(9)
分类号：TM732
关键词：电-气综合能源系统 分布式优化调度 Weymouth方程线性化 多参数规划 交替方向乘子法
Keywords：Integratedelectricityandgassystem distributedoptimaldispatch Weymouthequationlinearization multi-parameterprogramming alternatingdirectionmethodofmultipliers
机标分类号：TM71F224.0TP273
在线出版日期：2024年5月13日
基金项目：国家自然科学基金，高端外国专家人才项目基于改进交替方向乘子法的电-气综合能源系统优化调度[
期刊论文] 电工技术学报--2024, 39(9)罗清局 朱继忠在电-气综合能源系统分布式优化调度中,非线性非凸的Weymouth方程给问题求解带来了巨大挑战.一方面,目前许多研究采用二阶锥松弛Weymouth方程,较为复杂;另一方面,主流分布式算法即交替方向乘子法(ADMM)的计算效率并不...参考文献和引证文献
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