1-3电力系统的部分接线如题图1-3所示,网络的额定电压已在图中标明。试求:(1)发电机,电动机及变压器高、中、低压绕组的额定电压;(2)当变压器T-1高压侧工作于+2.5%抽头,中压侧工作于+5%抽头;T-2工作于额定抽头;T-3高压侧工作于-2.5%抽头时,各变压器的实际变比。解(1)发电机、电动机及变压器高、中、低压绕组额定电压。(a)发电机:网络无此电压等级,此电压为发电机专用额定电压,故VGN=13.8kV。(b)变压器T-1:一次侧与发电机直接连接,故其额定电压等于发电机的额定电压;二次侧电压高于网络额定电压10%,故T-1的额定电压为121/38.5/13.8kV。(c)变压器T-2:一次侧额定电压等于网络额定电压,二次侧额定电压高于网络额定电压10%,故T-2的额定电压为35/11kV。(d)变压器T-3:一次侧额定电压等于网络额定电压,二次侧与负荷直接连接,其额定电压应高于网络额定电压5%,因此T-3的额定电压为10/[(1+0.05)×0.38]kV=10/0.4kV。(e)电动机:其额定电压等于网络额定电压VMN=0.38kV。(2)各变压器的实际变比为T-1:068.3]5.38)05.01[(121)025.01()21(1Tk987.88.13121)025.01()31(1Tk929.28.135.38)05.01()32(1TkT-2:182.311352TkT-3:375.244.010)025.01(3Tk题图1-3系统接线图VGN=13.8kV2-2110kV架空线路长90km,双回路共杆塔,导线及地线在杆塔上的排列如图2.2所示,导线采用LGJ-120型钢芯铝线,计算半径r=7.6mm,试计算输电线路的等值电路参数。题图2-2导线在杆塔上的排列解取DS=0.8r=0.8×7.6mm=6.08mm。从题图2-2所示的导线排列看,它相当于水平排列,相间距离为m536.3m5.05.322D相间几何均距为m455.4m536.326.126.1eqDD813.11901205.312121210lSlrR629.186.78.01000455.4lg1445.09021lg1445.0902121e0SqDDlxXSSrDllbB466eq010929.4106.71000455.4lg58.790210lg58.7222-4有一台SFL1-31500/35型双绕组三相变压器,额定变比为35/11,查得kW300P,2.1%0I,kW2.177SP,8%SV,求变压器参数归算到高、低压侧的有名值。解(1)归算到高压侧的参数。SSVPG53232N0T10449.210353010SSVSIB53232NN0T1086.301035315001002.110100%2188.01031500352.1771032232N2NTSVPRS11.3103150035100810100%3223N2NTSSVVXS(2)归算到地压测的参数,按变压器额定变比归算。SSG425T10479.2113510449.2SSB425T10243.3111351086.300216.035112188.02TR3072.0351111.32TX2-8有一台三相双绕组变压器,已知:AkV31500NS,11/220TNk,kW590P,5.3%0I,kW208SP,14%SV。(1)计算归算到高压侧的参数有名值;(2)作出Π型等值电路并计算其参数;(3)当高压侧运行电压为210kV,变压器通过额定电流,功率因数为0.8时,忽略励磁电流,计算Π型等值电路各支路的电流及低压侧的实际电压,并说明不含磁耦合关系的Π型等值电路是怎样起到变压器作用的。解(1)计算归算到高压侧的参数有名值S10219.1S10220591063232N0TVPGS10779.22S10220315001005.310100%63232NN0TVSIB146.1010315002202081032232N2NTSVPRS111.21510315002201001410100%3223N2NTSVVXS(2)作出Π型等值电路及其参数。Π型等值电路如题图2-8(a)所示。20112202N1NTVVk,)111.215146.10(TTTjjXRZ756.0507.020111.215146.10TT12jjkZZ322.11534.0201111.215146.101TT10TjjkZZ3.875667.0566.0027.0)120(20111.215146.101TTT20TjjkkZZ(3)已知高压侧电压为210kV,相电压为kV244.121kV3210,取其为参考电压,即kV0244.1211V。忽略励磁电流,A2203315003NNN1VSIIA666.82。已知8.0cos,有87.36,6.0sin。A)6.49133.66(A87.36666.821jIA)13.106859.503(A7.9210697.10A10322.11534.00244.1213310T111jjZVI题图2-8变压器的Π型等值电路1V2V1V2VTGTB1I0I12I11I2I22I12I0ITTjBGTTTkZZ110)1(20TTTTkkZZTTTjXRZTTkZZ12A96.8685.10749A)73.10734033.570(A)]13.106859.503()6.49133.66[(11112jjjIIIV148.7257.5535V)]756.10507.0()73.10734033.570(121244[121212jjZIVV线电压V346.9587V257.5535332)L(2VV,或kV5874.9)L(2V。(4)由于Π型等值电路的三个阻抗Z12、ZT10、ZT20都与变压器的变比有关,且0]566.0027.0)322.11534.0(756.0507.0[201012jjjZZZZTT构成了谐振三角形,这个谐振三角形在原、副方电压差作用下产生很大的顺时针方向的感性环流(实际上ZT10为即发有功,又发无功的电源),这一感性环流流过Z12产生了巨大的电压降纵分量,从而完成了原、副方之间的电压变换。A488.9453.9767A3.875667.0148.7257.553520T222ZVIA896.36005.11660A)618.996543.1327(A)]112.973851.757()73.10734033.570[(22122jjjIII2008.20666.82005.1660Tk(5)与不用Π型等值电路比较,同样忽略励磁电流,其等值电路如题图2-8(b)所示。由上已知)111.215146.10(TjZA)6.49133.66(A87.36666.82121jIIV01212441VV117.791.110756V)694.1372251.109903(V]111.215146.10)6.49133.66(121244[T1212jjjZIVV归算到二次侧V117.7846.5537V117.72091.110756N1N222VVVV线电压V8.9591V846.55373)L(2V或kV5918.92V212T82.66620A1653.32AIIk2-9系统接线如题图2-9(a)所示,一直各元件参数如下。发电机G:N30MVAS,N10.5kVV,G%27x变压器T-1:N31.5MVSA,T10.5/121k,S%10.5V变压器T-2:、T-3:N15MVAS,T110/6.6k,S%10.5V线路L:100kml,0.4/kmx电抗器R:N6kVV,s1.5KAI,R%6x试做不含磁耦合关系的等值电路并计算其标幺值参数。解:选B100MVAS,B(1)10kVV,则B(2)B(1)T1121/10V115.238kV10.5VVkkB(3)B(2)T26.6/115.238kV6.914kV110VVk22GGNBG22GNB(1)%2710010.50.99231001003010xVSXSV22ST1T1NBT122T1NB(1)%10.510010.50.367510010031.510VVSXSVB22B(2)1000.41000.3012115.238lSXxlV10.15062lX22ST2T2NBT2T322T2NB(2)%10.51001100.637810010015115.238VVSXXSVRNRBR22B(3)RN%661000.28981001006.914331.5VxSXVI等值电路如题图2-9(b)所示。kV10kV110kV69923.0GX3675.01TX1506.021lX6378.02TX6378.03TX2898.0RX)(a)(b题图2-9系统接线图及等值电路3-1同步电机定子A、B、C三相分别通以正弦电流iA,iB,iC,转子各绕组均开路,已知ABC0iii,试问0和90时A相绕组的等值电感AAA(/)Li等于多少?解:(1)当0时AaaababcaciLiLiL。(P48之式(3-3)并注意到转子各绕组均开路)由aa0202cos2Lllll(P48之式(3-7))ab02[cos2(30)]Lm+m(P48之式(3-9))ac02[cos2(150)]Lm+m(P48之式(3-9))计及22ml及abc0iii,因而有bcaiii。将代入A中便得A02a02b02c02a02a002a()[cos60][cos(60)]11()[](]22llim+mim+millim+milm+li故2AA002amaddA33[][]22Llm+lwLi(2)当90时A02a02b02c002a113()[][](]222llim+lim+lilmli故2AA002amaqq33[][]22ALlmlwLi3-4同步电机定子三相通入直流A1i,BC0.5ii,求转换到d、q、0坐标系的id,iq和i0。解:(1)dABC2[coscos(120)(120)]3iiiicos题给A1i,BC0.5ii,代入得d211[coscos(120)cos(120)]322i因为113coscos(120)cos(120)cos222故dcosi(2)qABC2[sinsin(120)sin(120)]3iiii211[sinsin(1