作业5

作业46-7有一条110kV输电线路如图6-20所示，由A向B输送功率。试求：（1）当受端B的电压保持在110kV时，送端A的电压应是多少？并绘出相量图。（2）如果输电线路多输送5MW有功功率，则A点电压如何变化？（3）如果输电线路多输送5Mvar无功功率，则A点电压又如何变化？20+j10MV·AABl=100kmr=0.125Ω/kmx＝0.4Ω/km解：电阻：5.12100125.01lrR电抗：401004.01lxX（1）MVAjjQPSBBB1020~kVUXQRPUBBBB91.511040105.1220kVURQXPUBBBB14.61105.12104020kVUUUUBBBA07.11614.6)91.5110(2222相量图为：AUBUBUdBUIRBUjIIjXabcd（2）MVAjjQPSBBB1025~kVUXQRPUBBBB48.611040105.1225kVURQXPUBBBB95.71105.12104025kVUUUUBBBA75.11695.7)48.6110(2222（3）MVAjjQPSBBB1520~kVUXQRPUBBBB73.711040155.1220kVURQXPUBBBB57.51105.12154020kVUUUUBBBA86.11757.5)73.7110(2222可见：多传输无功功率对电压损失的影响大。6-8一条额定电压为380V的三相架空线路，干线Ac为LJ-70(r1=0.46Ω/km，x1=0.316Ω/km)，支线be、af为LJ-50(r1=0.64Ω/km，x1=0.325Ω/km)。各点负荷和各段线路长度均标于图6-21中。求电力网的最大电压损耗。100m60m80m60m50m60mAabcdef20+j10kV·A18+j0kV·A8+j6kV·A10+j8kV·A解：由图可知：AkVjSbc810~；AkVjSbe018~；AkVjSab1436~；AkVjSaf1020~；AkVjSAa2456~VUXQRPUNbcbcbcbcbc50.138.008.0316.0808.046.010VUXQRPUNbebebebebe42.238.00)2/06.005.0(64.018VUXQRPUNababababab31.338.006.0325.01406.046.036VUXQRPUNafafafafaf53.238.006.0325.01006.064.020VUXQRPUNAaAaAaAaAa78.838.01.0316.0241.046.056各支路电压损失：VUUUUbeabAaAe51.1442.231.378.8VUUUUbcabAaAc59.1350.131.378.8VUUUafAaAf31.1153.278.8所以，最大的电压损失为支路Ae。%82.3%10038051.14%AeU【补充】某双回输电线路如图（a）所示，已知线路型号为LGJ－120，线路全长100km，参数为r1＝0.27Ω/km，x1＝0.423Ω/km，b1＝2.69×10-6S/km。线路末端连接的降压变电所有两台并列运行的变压器，其铭牌数据为：SN＝31500kV·A，△Pk＝190kW，△P0=31.05kW,Uk%＝10.5，I0％＝0.7，变比为110/11kV；已知变压器在“0”分接头运行。试求系统的潮流分布和电压分布。116kV2×31.5MV·A110/11kV25MW2×LGJ－120100km85.0cos（a）3~S2~S2~S1~S1~S13.5J21.25j2.69×10-4j2.69×10-4j20.171.16-j3.65×10-55.13×10-6123（b）网络接线图及其等值电路图（a）网络接线图；（b）等值电路图解：方法一：取全网电压为额定电压110kV。（1）首先计算归算到110kV侧的网络各元件参数，并画出等值电路图，如图6-10（b）所示。线路参数为5.132110027.0211lrRL15.2121100423.0211lxXLSlbBL4611069.221001069.2212212变压器参数为16.12110315001101902110322322NNkTSUPR17.202110315001105.102110%22NNkTSUUXSUPGNT6323201013.521011005.31210SUSIBNNT5525201065.3210110315007.0210%等值电路图如图（b）所示。（2）取全网电压为额定电压UN＝110kV，由末端向首端推算功率分布。负荷功率)(49.1525)85.0(cos2525~13AMVjtgjS变压器阻抗支路的功率损耗)(442.1083.017.2016.111049.1525~22222323AMVjjXRUQPSTTNTZ变压器高压侧的功率AMVjjjSSSTZ932.16083.25442.1083.049.1525~~~32变压器导纳支路的功率损耗AMVjjSIjPSNTY441.0062.025.311007.01005.312100%~300线路末端电纳的功率损耗var255.31101069.222422MjjUBjjQNY线路阻抗支路末端功率)(118.14145.25255.3)441.0062.0()932.16083.25(~~~222AMVjjjjjQSSSYTY线路阻抗支路的功率损耗AMVjjjXRUQPSLLNLZ454.1928.015.215.13110118.14145.25~22222222线路阻抗支路首端功率AMVjjjSSSLZ572.15073.26454.1928.0118.14145.25~~21线路首端电纳的功率损耗var255.321MjjQjQYY电源侧高压母线输出功率为AMVjjjQSSY317.12073.26255.3572.15073.26~~111（3）根据给定首端电压和求得的首端功率，由首端向末端推算电压分布。电源侧高压母线电压kVU1161线路阻抗支路的电压损耗（注意：流过线路阻抗支路的功率为1~S，而不是1~S）kVUXQRPULLL87.511715.21572.155.13073.26111线路末端电压为kVUUUL13.11087.511612变压器阻抗支路的电压损耗kVUXQRPUTTT37.313.11017.20932.1616.1083.25222归算到110kV的变压器低压侧电压为kVUUUT76.10637.313.11023当变压器在“0”分接头运行时，其变比为1011110Tk则变压器低压侧母线实际电压为kVkUUT68.101076.10633方法二：3~S2~S2~S1~S1~S13.5J21.25j2.69×10-4j2.69×10-4j20.171.16-j3.65×10-55.13×10-6123（b）等值电路图3~S2~S2~S1~S1~S13.5J21.25j2.69×10-4j20.171.1612320Y10Y5.13×10-6+2.325×10-412Z23Z（c）简化电路取全网电压为额定电压110kV。（1）首先计算归算到110kV侧的网络各元件参数，并画出等值电路图，如图6-10（b）所示。线路参数为5.132110027.0211lrRL15.2121100423.0211lxXLSlbBL4611069.221001069.2212212变压器参数为16.12110315001101902110322322NNkTSUPR17.202110315001105.102110%22NNkTSUUXSUPGNT6323201013.521011005.31210SUSIBNNT5525201065.3210110315007.0210%等值电路图如图（b）所示。化简电路：)(15.215.1312jjXRZLL)(17.2016.123jjXRZTT)(1069.22410SjBjYL)(10325.21013.5)1065.31013.5(1069.2)(24656420SjjjjBGBjYTTL　　（2）取全网电压为额定电压UN＝110kV，由末端向首端推算功率分布。负荷功率)(49.1525)85.0(cos2525~13AMVjtgjS)(442.1083.017.2016.111049.1525~22223232232323AMVjjjXRUQPSNAMVjjjSSS932.16083.25442.1083.049.1525~~~2332)(814.2062.0110)10325.21013.5(~246220*20AMVjjUYSNY)(118.14145.25)814.2062.0()932.16083.25(~~~2022AMVjjjSSSYAMVjjjXRUQPSN454.1928.015.215.13110118.14145.25~22212122222212AMVjjjSSSLZ572.15073.26454.1928.0118.14145.25~~21)(255.31101069.2~24210*10AMVjjUYSNYAMVjjSSSY317.12073.26255.3572.15073.26~~~1011（3）根据给定首端电压和求得的首端功率，由首端向末端推算电压分布。电源侧高压母线电压kVU1161线路阻抗支路的电压损耗（注意：流过线路阻抗支路的功率为1~S，而不是1~S）kVUXQRPULLL87.511715.21572.155.13073.26111线路末端电压为kVUUUL13.11087.511612变压器阻抗支路的电压损耗kVUXQRPUTTT37.313.11017.20932.1616.1083.25222归算到110kV的变压器低压侧电压为kVUUUT76.10637.313.11023当变压器在“0”分接头运行时，其变比为1011110Tk则变压器低压侧母线实际电压为kVkUUT68.101076.10633