短路容量及短路电流的计算1、计算公式:同步电机及发电机标么值计算公式:rjd d S S x X ⋅=100%""* (1-1) 变压器标么值计算公式: rTjk T S S u X ⋅=100%* (1-2)线路标么值计算公式: 2*jj L L US L X X ⨯⨯= (1-3)电抗器标么值计算公式: j jr r k k U I I U x X ⋅⋅=100%* (1-4) 电力系统标么值计算公式:sj s S S X =* (1-5)异步电动机影响后的短路全电流最大有效值:2""2""])1()1[(2)(M M ch s s ch M s ch I K I K I I I -+-++=•• (1-6)其中:%"d x 同步电动机超瞬变电抗百分值j S 基准容量,100MV A j U 基准容量,10.5kV j I 基准电流,5.5kAr S 同步电机的额定容量,MV A rT S 变压器的额定容量,MV A%k u 变压器阻抗电压百分值L X 高压电缆线路每公里电抗值,取0.08km /Ω高压电缆线路每公里电抗值,取0.4km /ΩL 高压线路长度,kmr U 额定电压,kVr I 额定电流,kA %k x 电抗器的电抗百分值s S 系统的短路容量,1627MV A"s I 由系统送到短路点去的超瞬变短路电流,kA"M I 异步电动机送到短路点去的超瞬变短路电流,kA ,rM qM M I K I 9.0"=rM I 异步电动机的额定电流,kAqM K 异步电动机的启动电流倍数,一般可取平均值6s ch K •由系统馈送的短路电流冲击系数M ch K •由异步电动机馈送的短路电流冲击系数,一般可取1.4~1.72、接线方案图1 三台主变接线示意图3、求k1点短路电流的计算过程 3.1网络变换(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)图2 求k1点短路电流网络变换图3.2用标么值计算各线路电抗根据图1中所给数值,用标么制计算个电抗值:X1=s X *+L X *=sj S S +2jj L U S L X ⨯⨯=0.061+0.015=0.076X2=X3=X4=rTjk T S S u X ⋅=100%*=1.125 X5=X6=jjr r k kU I I U x X ⋅⋅=100%*=0.52 X7=X9=X12=r jd L d S S x X X ⋅=+100%""**+2jj L U S L X ⨯⨯=1.353(2.03)+0.029=1.382(超瞬变电抗百分值14%,功率因数为0.87;电缆均长400米)X8=X10=X11=2*jj L L U S L X X ⨯⨯==0.015X13=X14=X15=2*jj L L US L X X ⨯⨯==0.007X16=X17=X18=rjd d S S x X ⋅=100%""*=0.378 X19=X20=X21=X8+X13+X16=X10+X14+X17=X11+X15+X18=0.4 X22=X23=X24=X7//X19=X9//X20=X12//X21=0.31X25=X28=X2+X5+2252X X X ⨯=3.531X26=X29= X22+X5+2522X X X ⨯=0.974X27=X30= X2+X22+5222X X X ⨯=2.106X31=X3//X25//X28=0.687 X32=X26//X29//X23=0.189 X33=X27//X30=1.053 X34=X1//X33=0.071 X35=X34+X31=0.758因为电网与发电机属于不同类型电源,要用分布系数法求出两种电源支路的等值电抗X36、X37。
分布系数:C1=134X X =0.933 C2=3334X X =0.067X36=135C X =0.813X37=235C X =11.262X38=X32//X37=0.186 3.3求短路电流值:I *S ”= I *0.1=I *0.2=I *k =361X =1.23 765.65.523.1*42.01.0"=⨯=⨯=====j S k S I I I I I I I (kA ) 221.17765.68.122"..=⨯⨯==S s ch s ch I K i (kA )发电机支路的等值电抗换算的以发电机容量为基准值的标么值为:X *C =X38j RG S S ⨯=10039330186.0⨯+⨯⨯=0.218 根据X *C ,查《》,第二版,第108页,表4-18得到各电流的标么值为:I *0=4.987,I *0.1=4.019,I *0.2=3.51,I *4=I *k =2.446换算到短路点电压发电机额定电流:jRGRG U S I 3=5.10339330⨯⨯+⨯==6.433(kA )081.32433.6987.40*"=⨯=⨯=RG G I I I (kA )854.25433.6019.41.0*1.0=⨯=⨯=RG G I I I (kA ) 58.22433.651.32.0*2.0=⨯=⨯=RG G I I I (kA ) 735.15433.6446.24*=⨯=⨯=RG kG I I I (kA )933.83081.3285.122"..=⨯⨯==G G ch G ch I K i (kA )考虑到异步电动机对短路电流的影响,假定每段母线上参与反馈的异步电动机的等效容量为10000kW ,其额定功率因数为0.87,启动电流倍数取平均值6,则由异步电动机送到短路点的超瞬变短路电流:rM qM M I K I 9.0"==3.584(kA )629.987.01031069.19.0229.0..=⨯⨯⨯⨯⨯⨯=⨯=rM qM M ch M ch I K K i (kA )则k 1点的总短路电流:43.42584.3081.32765.6""""=++=++=∑M G S I I I I (kA )783.110629.9933.83221.17...=++=++=M ch G ch S ch ch i i i i (kA )短路全电流最大有效值:2"""2"""])1())(1[(2)(M M ch G s s ch G M s ch I K I I K I I I I -++-+++=••=63.123(kA )4、求k2点短路电流的计算过程 4.1网络变换(a ) (b )(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)(m)(n)图2 求k2点短路电流网络变换图4.2用标么值计算各线路电抗根据图1中所给数值,用标么制计算个电抗值:X1=s X *+L X *=sj S S +2jj L U S L X ⨯⨯=0.061+0.015=0.076X2=X3=X4=rTjk T S S u X ⋅=100%*=1.125 X5=X6=jjr r k kU I I U x X ⋅⋅=100%*=0.52 X7=X9=X12=r jd L d S S x X X ⋅=+100%""**+2jj L U S L X ⨯⨯=1.353+0.029=1.382(超瞬变电抗百分值14%,功率因数为0.87,电缆均长400米)X8=X10=X11=2*jj L L U S L X X ⨯⨯==0.015X13=X14=X15=2*jj L L US L X X ⨯⨯==0.007X16=X17=X18=rjd d S S x X ⋅=100%""*=0.378 X19=X20=X21=X8+X13+X16=X10+X14+X17=X11+X15+X18=0.4 X22=X23=X24=X7//X19=X9//X20=X12//X21=0.31X25=X2+X5+2252X X X ⨯=2.874X26= X22+X5+2522X X X ⨯=0.793X27= X2+X22+5222X X X ⨯=2.359X28=64343X X X X X ++⨯=0.482X29=64363X X X X X ++⨯=0.162X30=64346X X X X X ++⨯=0.162X31= 2928252825X X X X X ++⨯=0.393X32=2928252925X X X X X ++⨯=0.132X33=2928252829X X X X X ++⨯=0.022X34=X33+X30=0.184 X35=X1//X27=0.074 X36=X23//X26=0.223 X37=X31+X35=0.468 X38=X32+X36=0.355 因为电网与发电机属于不同类型电源,要用分布系数法求出两种电源支路的等值电抗X39、X40。
分布系数:C1=2735X X =0.031 C2=135X X =0.969X39=137C X =11.87X40=237C X =0.483X41=X38//X39=0.347 X42=X40//X41=0.202 X43=X34+X42=0.386 不同类型电源,要用分布系数法求出两种电源支路的等值电抗X44、X45。
分布系数:C3=4142X X =0.582 C4=4042X X =0.418X44=343C X =0.663X45=443C X =0.923X46=X24//X44=0.211 4.3求短路电流值:I *S ”= I *0.1=I *0.2=I *k =451X =1.084 962.55.5084.1*42.01.0"=⨯=⨯=====j S k S I I I I I I I 177.15962.58.122"..=⨯⨯==S s ch s ch I K i (kA )发电机支路的等值电抗换算的以发电机容量为基准值的标么值为:X *C =X46j RG S S ⨯=10039330211.0⨯+⨯⨯=0.247 根据X *C ,查《工业与民用配电设计手册》,第二版,第108页,表4-18得到各电流的标么值为:I *0=4.404,I *0.1=3.639,I *0.2=3.223,I *4=I *k =2.418换算到短路点电压发电机额定电流:jRGRG U S I 3=5.10339330⨯⨯+⨯==6.433(kA )331.28433.6404.40*"=⨯=⨯=RG G I I I (kA )41.23433.6639.31.0*1.0=⨯=⨯=RG G I I I (kA ) 734.20433.6223.32.0*2.0=⨯=⨯=RG G I I I (kA ) 555.15433.6418.24*=⨯=⨯=RG kG I I I (kA )122.74331.2885.122"..=⨯⨯==G G ch G ch I K i (kA )考虑到异步电动机对短路电流的影响,假定每段母线上参与反馈的异步电动机的等效容量为10000kW ,其额定功率因数为0.87,启动电流倍数取平均值6,则由异步电动机送到短路点的超瞬变短路电流:rM qM M I K I 9.0"==3.584(kA )629.987.01031069.19.0229.0..=⨯⨯⨯⨯⨯⨯=⨯=rM qM M ch M ch I K K i (kA )则k 2点的总短路电流:877.37584.3331.28962.5""""=++=++=∑M G S I I I I (kA )928.98629.9122.74177.15...=++=++=M ch G ch S ch ch i i i i (kA ). .word .. 短路全电流最大有效值:2"""2"""])1())(1[(2)(M M ch G s s ch G M s ch I K I I K I I I I -++-+++=••=56.25(kA )。