電力系統(tǒng)暫態(tài)分析報(bào)告典型習(xí)的題目

1-2、發(fā)電機(jī)F1和F2具有相同的容量，它們的額定電壓分別為 6.3kV和10.5kV，若以它們的額定值為基本條件的發(fā)電機(jī)電抗的標(biāo)么值是相同的， 問(wèn)這兩個(gè)發(fā)電機(jī)電抗的歐姆值的比值是多少？解：XG1*(N)＝XG1*SN1/UN12XG2*(N)＝XG2*SN2/UN22∵XG1*(N)＝XG2*(N) ∴XG1*SN1/UN12＝XG2*SN2/UN22故：XG1/XG2＝UN12/UN22＝6.32/10.52＝0.36GT1XLT2IIIIII50MVA0.4Ω/km30MVA60MVA1-4、10.5kV/121kV100km110kV/6.6kV10.5kVXd’’k%=10.5k=0.15UU%=10.5求：①準(zhǔn)確計(jì)算各元件電抗的標(biāo)么值，基本段取 I段UBI＝10.5kV。②工程近似計(jì)算各元件電抗的標(biāo)么值， SB＝100MVA。解：① 精確計(jì)算法UBI＝10.5kV SB＝100MVAUBII＝10.5121＝10.5kV10.5UBIII＝10.51216.6＝7.26kV10.5110Xd''*0.151000.35010.510.521000.175XT1*6010.521001000.273XL*0.4100121210.511021000.289XT2*301212100②近似計(jì)算法UB＝Uav SB＝100MVAXd''*0.151000.35010.51000.175XT1*60100XL*0.41001000.302115210.51000.35XT2*301001-5、某一線路上安裝一臺(tái) Xk%＝5的電抗器，其額定電流為 150A，額定電壓為6kV，若另一臺(tái)額定電流為 300A、額定電壓為10kV的電抗器來(lái)代替它，并要求保持線路的電抗歐姆值不變，問(wèn)這臺(tái)電抗器的電抗百分?jǐn)?shù)值應(yīng)是多少？XR1%UN1XR2%UN2解：∵XR1003IN21003IN1U∴XR2% XR1%U

N1IN256300IN1106N2150K(3)U|0|=115kV0.4Ω/km10MVA50km1-12、110kV/11kVUk%=10.5若短路前空載，計(jì)算短路電流的周期分量及短路電流最大有效值；(2)若A相非周期分量電流的初值為零及最大時(shí)，計(jì)算相應(yīng)的 B、C相非周期分量電流的初始值；若短路前變壓器滿負(fù)荷運(yùn)行，功率因數(shù)為0.9（低壓側(cè)），計(jì)算最大非周期分量電流的初始值，并與空載時(shí)短路比較。解：歸算在高壓側(cè)的參數(shù)：Xl0.4502010.51102XT127.0510010歸算到短路點(diǎn)所在電壓等級(jí)（低壓側(cè)）的參數(shù)為：2X147.05111.47110①短路電流周期分量：ipa

U

m

sin

t

2U

|0|

sin

t6.388sin

t短路電流最大有效值：IM1.52Im1.526.38826.863kA2②A相非周期分量電流初始值：ia0 Im|0|sin |0| Imsin Imsin6.388sin若ia0 0 0，則：ii

b0IMsin1205.53kAc0IMsin1205.53kA若ia0MAX90，則：iii

a0IM6.388kAb0IMsin120903.194kAc0IMsin120903..194kA③短路前變壓器滿負(fù)荷運(yùn)行，cos0.9則：Im|0|2SN2100.742kA3UN311|0|arccos0.925.84ia0Im|0|sin|0|ImsinImsin0.742sin25.846.388sin90方法1：dia000.742cos25.846.388cos900dttg0.11求得：6.28即：當(dāng)6.28時(shí)，非周期分量具有最大值，其值為：ia0 0.742sin6.28 25.84 6.388sin6.28 90=6.10kA方法2：Um|0|Im|0|Im-Im|0|Im由相量圖并根據(jù)余弦定理可得非周期分量最大值：ia00.74226.388220.7426.388cos9025.841-13、G115kVT6.3kVXRXL10.4Ω/km30MVA0.3kA40km6.3kVUk%=10.5XR%=4設(shè)：（1）SB＝100MVA（2）UB=Uav（3）KM=1.8

6.10kAK(3)XL20.08Ω/km0.5km求：①K點(diǎn)發(fā)生三相短路時(shí)的沖擊電流是多少？短路電流的最大有效值是多少？短路功率是多少？②簡(jiǎn)述短路沖擊電流的意義，何種情況下短路，其沖擊電流最大。解：①XL1*400.41000.1211152XXX

10.51000.35T*301004IB4100R*IN1001.22210036.30.3L2*0.50.081000.10086.32X*XL1*XT*XR*XL2*1.7937所以：I*10.5575X*II*IB0.557510035.113kA6.3iM2.55I2.555.11313.01kAIM1.52I1.525.1137.766kASdS*SB0.557510055.75MVA②短路電流在最惡劣的情況下可能出現(xiàn)的最大瞬時(shí)值稱為沖擊電流，它用于檢驗(yàn)電氣設(shè)備或載流導(dǎo)體的動(dòng)穩(wěn)定。3-3、電力系統(tǒng)接線如圖所示，元件參數(shù)標(biāo)于圖中，發(fā)電機(jī)均裝有自動(dòng)電壓調(diào)節(jié)器，當(dāng)K點(diǎn)發(fā)生三相短路時(shí)，試計(jì)算：1）次暫態(tài)電流初始有效值I''；2）沖擊電流值iM。K(3)G1GsG2Ss=100MVA110kVs2×50MW2×60MVA0.4Ω/kmX=0.1Xd''=0.125U%=10.5kcosφ=0.8解：取SB100MVA,UBUpj，則各元件參數(shù)計(jì)算如下：G,G:XXX''SB0.1251000.80.212G1G2dS50NT1,T2:XT1UK%SB10.51000.175XT2SN10060100l:Xlx1lUB20.4601000.181SB1152Ss:Xs0.1系統(tǒng)等值電路如下：KS0.5XG1 0.5XT10.5XL XsXd1XG11XT1//1XLXs0.1875//0.19052220.1875 0.19050.0940.1875 0.1905Id*I*''110.58XdI''I*''?IB10.581005.31(kA)115M2.55I''13.54(kA)3-4、電力系統(tǒng)接線如圖所示， A系統(tǒng)的容量不詳，只知斷路器 S的切斷容量為3500MVA，B系統(tǒng)的容量為100MVA，電抗XB＝0.3，試計(jì)算當(dāng)K點(diǎn)發(fā)生三相35kV0.4Ω/km50km 40kmA B40km

40km短路時(shí)的起始次暫態(tài)電流 I''及沖擊電流iM。解：取SB100MVA,UBUpj，則系統(tǒng)的等值電路圖為：X1X3SXAXBX2X4X5K圖中：XA110.028SA*3500100X1X20.4501001.461372X3X4X50.4401001.169372XB0.3化簡(jiǎn)上圖如下：X7X8X9XBASX11X10X10KKX7XAX1//X20.0280.730.758X8X91.1691.169X1031.1690.39X11X7X8//X9XB1.1480.691.148//0.690.4311.1480.69XdX11X100.4310.390.821I*''11.218XdI''I*''IB1.2181001.9(kA)37M2.55I''4.85kA3-26、系統(tǒng)接線如圖所示，當(dāng) K點(diǎn)發(fā)生三相短路時(shí)，試計(jì)算：（1）次暫態(tài)電流初始有效值I''；250MVAXw＝0.4（2）0.2秒電流有效值I0.2；110kV（3）短路電流穩(wěn)態(tài)值I∞。50km（3）0.4Ω/kmK解：取SB1000MVA,UBUpj，系30km37kV統(tǒng)40km31.5MVA25km等值如下所示：150MVAUk%=10.5SB1000Xp＝0.3Xw*Xw0.4SN1.6250X110.45010000.75621152X20.44010001.211152X30.43010000.9071152X40.42510000.7561152XT10.510003.3310031.5Xp*0.310002150網(wǎng)絡(luò)化簡(jiǎn)過(guò)程如下：XwXwX1X3X1X2X4XTX7XTX5XpX6XpX11X8 X10X9 X13X12X5X2X31.210.907X2X3X41.210.9070.3820.756X6X2X41.210.756X2X3X41.210.9070.3180.756X7X4X30.7560.907X2X3X41.210.9070.2390.756X8Xw*X5X11.60.7560.3822.738X9Xp*X620.3182.318X10XTX73.330.2393.569X11X8X10X8X102.7382.7383.569X93.56910.522.318X12X9X10X9X102.3182.3183.569X83.5698.92.738XwjsX11SwN10.522502.63SB1000XpjsX12SpN1501.33SB8.91000I''0.751500.412503.35kA337337I0.20.71500.422503.28kA337337I0.81500.422503.51kA3373373-27、下圖所示系統(tǒng)，在 K點(diǎn)發(fā)生三相短路，試求 t＝0″、t＝0.6″時(shí)的短路電流周期分量。100km115kV0.4Ω/km60MVA60MVA無(wú)限大功50km10.5kV10.5/121kV率電源0.4Ω/kmXd＝0.12Uk%=10.5K（3）解：SB 120MVA各元件的參數(shù)計(jì)算如下：XG0.121200.2460XT10.51201000.2160XL11001200.360.42115XL2501200.180.41152系統(tǒng)的等值電路如下所示：GX1 XG0.855X2 XL1XGjs X1I02.5I0.61.86

XG XT XL1 G X1SX3XL2X2KSXGXTXL20.240.210.18XTXL20.240.210.18XL10.36XL2XL1XL20.360.360.18XGXT0.180.6840.240.21SGN600.428SB0.8551206011201.634(kA)31150.684311560112031150.68431.44(kA)1155-2、圖示系統(tǒng)中K點(diǎn)發(fā)生單相接地故障，試組成復(fù)合序網(wǎng)，圖中發(fā)電機(jī)中性點(diǎn)經(jīng)Xpg接地。Xg XT1 K XT2XL1 XL2Xpg解：正序網(wǎng)絡(luò)圖如下：Xg1XT1XL1Uf|0|Uf(1)X∑(1)=X+X+XL1g1T1負(fù)序網(wǎng)絡(luò)圖如下：Xg2 XT1 XL1Uf(2)X∑(2)=Xg2+XT1+XL1零序網(wǎng)絡(luò)圖如下：Xg0XT1XL10XL20XT23XpgUf(0)X∑(0)=(3Xpg+Xg0+XT1+XL10)//(XL20+XT2)復(fù)合序網(wǎng)圖：X∑（1）Uf|0|X∑（2）X∑（0）5-8、設(shè)A、B發(fā)電機(jī)暫態(tài)電勢(shì)E’=1.0，當(dāng)在F點(diǎn)發(fā)生K(1)，K(2)，K(1,1)短路時(shí)，試計(jì)算故障處的A、B、C三相電流。（圖中各元件參數(shù)均為歸算到統(tǒng)一基準(zhǔn)值后FXT2的標(biāo)幺值）x=x=0.3xT2=0.1x1=0.25x1=0.3xT1=0.1212x=0.2單回線x0=0.7x2=0.152x=0.0500x=0.03解：正序網(wǎng)絡(luò)圖：

j0.3 j0.12 j0.15j0.1 j0.25j0.2 j0.12 j0.15j0.1 j0.15負(fù)序網(wǎng)絡(luò)圖：j0.05 j0.12 j0.35j0.1 j0.03零序網(wǎng)絡(luò)圖：由各序序網(wǎng)圖可求出各序等值電抗：X10.30.12//0.150.10.250.228X20.20.12//0.150.10.150.178X00.050.12//0.350.10.030.126單相接地短路????Uf|0|1If(1)If(1)If(1)X2X0)j1.88j(X1j0.2280.1780.126??Ifa3If(1)j5.64?Ifb0?Ifc0兩相接地短路??Uf|0|1If(1)j(X1X2//X0)j3.314j0.228j(0.178//0.126)??X00.126If(2)If(1)j3.314X2X0j1.3740.1780.126???If(0)(If(1)If(2))j1.94?Ifa0????Ifba2If(1)aIf(2)If(0)5.0144.3????IfcaIf(1)a2If(2)If(0)5.035.7兩相短路??Uf|0|1If(1)j2.463j(X1X2)j(0.2280.178)??If(2)If(1)j2.463?0Ifa???Ifba2If(1)aIf(2)4.266???IfcaIf(1)a2If(2)4.2665-10、系統(tǒng)接線如圖所示，變壓器采用Y0/-11接線方式，各元件標(biāo)幺值參數(shù)標(biāo)于圖中，當(dāng)高壓母線上 K點(diǎn)發(fā)生兩相接地短路時(shí)，試求：、計(jì)算短路點(diǎn)K處A相的電流、電壓序分量；、計(jì)算變壓器低壓側(cè)各相短路電流和電壓值，并作其相量圖。x1=0.2x2=0.3x0=0.1解：計(jì)算各序等值阻抗：X10.20.120.32X20.30.120.42X00.12?j1ej30Uf|0|160

K(1,1)xT=0.12故障點(diǎn)處的電流和電壓序分量：??Uf|0|160If(1)2.4230j(X1X2//X0)j(0.320.42//0.12)??X0If(2)If(1)0.54150X0X2???If(0)(If(1)If(2))1.88150???Uf(1)Uf|0|jIf(1)X1160j0.322.42300.22660??Uf(2)jIf(2)X2j0.420.541500.22660???Uf(0)Uf(1)Uf(2)0.22660低壓側(cè)各相短路電壓和電流：??ej30Ia(1)If(1)2.42??Ia(2)If(2)ej300.54120?Ia(0)0???ej302.420.1260)ej30Ua(1)Uf(1)jIf(1)XT(0.22660j0.516???j30Ua(2)Uf(2)jIf(2)XTe0.139j0.08?0Ua(0)????IaIa(1)Ia(2)Ia(0)2.15j0.4682.212.28?a2???IbIa(1)aIa(2)Ia(0)1.48j2.5632.96240????IcaIa(1)a2Ia(2)Ia(0)0.67j2.0962.2107.73????UaUa(1)Ua(2)Ua(0)0.139j0.5960.61276.87????Uba2Ua(1)aUa(2)Ua(0)0.308j0.1780.35630????UcaUa(1)a2Ua(2)Ua(0)0.447j0.4180.612136.97-3、下述電力系統(tǒng)參數(shù)標(biāo)幺值如下：Uc隱極機(jī) XT1 XL XT2Xd1.21,Xd'0.4,XT10.169,XT20.14,XL0.373，運(yùn)行參數(shù)為Uc=1,發(fā)電機(jī)2向系統(tǒng)輸送功率P0.8,cos0.98,試計(jì)算當(dāng)E、E'及UG為常數(shù)時(shí)，此系統(tǒng)的靜cq態(tài)穩(wěn)定極限及靜態(tài)穩(wěn)定儲(chǔ)備系數(shù)Kp。解：XdXdXT1XLXT21.210.1690.3730.141.8922Xd'Xd'XT1XLXT20.40.1690.3730.141.0822XeXT1XLXT20.1690.3730.140.6822Pc0.8,QcPctgc0.162(1)EqconstQcXd2PcXd222EqUc10.1621.8920.81.8921.999UcUcPMEqUc1.99911.057(2)Xd1.892KpPMP0100%1.0570.8100%32.1%P00.8E'constQX'2PX'2'22EUccdcd10.1621.0820.81.0821.46UcUcPME'Uc1.4611.349Xd'1.082KpPMP0100%1.3490.8100%68.6%P00.8(3)UGconst2PcXe2UGUcQcXe22UcUc10.1620.6820.80.6821.237PMUGUc1.23717-4、Xe0.6821.814KpPMP0100%1.8140.8P00.8100%126.8%某電廠有 4臺(tái)汽輪發(fā)電機(jī)，變壓器單元機(jī)組并列運(yùn)行，每臺(tái)發(fā)電機(jī)的參數(shù)為：PN

100MW,cos

N

0.85,U

N

10.5kV,Xd

1.63；每臺(tái)變壓器的參數(shù)為：SN

120MVA,Uk%

11,10.5/242kV

。該電廠經(jīng)輸電線與無(wú)窮大系統(tǒng)并列，系統(tǒng)維持電壓 220kV。從靜態(tài)穩(wěn)定的角度看，在發(fā)電機(jī)額定運(yùn)行的條件下，為保證有Kp=15%的儲(chǔ)備系數(shù)，輸電線的電抗允許多大？解：選取SB100MVA,UBUav，則：UG*10.52201,Us*0.95610.5230XTUk%SB11100100SN1000.0917120Xe1XTXL0.023XL4P0*PN400SB4100PMUGUs0.956XeXeKpPMP0100