表4.3 小阻抗支路导致的病态问题节点电压计算结果
节点号 节点电压幅值 节点电压相角 节点号 节点电压幅值 节点电压相角 1 1.000 0 6 1.0041 2.7728 2 1.000 10.9976 7 0.9894 1.7893 3 1.000 5.6163 8 1.0021 5.1625 4 0.9833 -2.4029 9 0.9833 -2.4029 5 0.9728 -3.7246
这类病态问题可以根据病态特性从节点或者支路进行针对性处理，或是采用数学类方法解决。例如，小阻抗病态问题可以用两个串联阻抗来模拟该阻抗，如图4.3所示，在支路4-9之间插入一个节点10，用两个阻抗合适的串联阻抗来模拟该小阻抗。其中，节点10的参数和节点4一样。
G1x?0.057690?j30?MVA?1r?0.2x??0.02b?0.176/24r?0.017x?0.092b?0.1585r?0.039x?0.17b?0.358x?0.0586G36r?0.0119x?0.1008b?0.2093P=85MW10r?0.032x?0.161b?0.306r?0.00857x?0.072b?0.149r??0.2-9x?0.02?10b?0.176/29125?j50?MVA?8x?0.0625100?j35?MVA?2G2P=163MW图4.3 小阻抗支路导致的病态问题系统单线图
得到如下结果：
MATPOWER Version 5.1, 20-Mar-2015 -- AC Power Flow (Newton) Newton's method power flow converged in 4 iterations. Converged in 0.02 seconds
================================================================================ | System Summary | ================================================================================ How many? How much? P (MW) Q (MVAr) --------------------- ------------------- ------------- -----------------
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Buses 10 Total Gen Capacity 820.0 -900.0 to 900.0 Generators 3 On-line Capacity 820.0 -900.0 to 900.0 Committed Gens 3 Generation (actual) 318.2 32.1 Loads 3 Load 315.0 115.0 Fixed 3 Fixed 315.0 115.0 Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0 Shunts 0 Shunt (inj) -0.0 0.0 Branches 10 Losses (I^2 * Z) 3.24 48.56 Transformers 0 Branch Charging (inj) - 131.5 Inter-ties 0 Total Inter-tie Flow 0.0 0.0 Areas 1
Minimum Maximum
------------------------- -------------------------------- Voltage Magnitude 0.906 p.u. @ bus 10 1.004 p.u. @ bus 6 Voltage Angle -3.83 deg @ bus 5 10.36 deg @ bus 2 P Losses (I^2*R) - 6.12 MW @ line 10-4 Q Losses (I^2*X) - 16.62 MVAr @ line 8-2
================================================================================ | Bus Data | ================================================================================ Bus Voltage Generation Load # Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) ----- ------- -------- -------- -------- -------- -------- 1 1.000 0.000* 70.24 31.52 - - 2 1.000 10.360 163.00 5.27 - - 3 1.000 5.242 85.00 -4.70 - - 4 0.983 -2.360 - - - - 5 0.973 -3.829 - - 90.00 30.00 6 1.004 2.398 - - - - 7 0.989 1.261 - - 100.00 35.00 8 1.002 4.524 - - - - 9 0.983 -3.294 - - 125.00 50.00 10 0.906 2.556 - - - - -------- -------- -------- -------- Total: 318.24 32.09 315.00 115.00
================================================================================ | Branch Data | ================================================================================
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Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z) # Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr) ----- ----- ----- -------- -------- -------- -------- -------- -------- 1 1 4 70.24 31.52 -70.24 -28.10 0.000 3.41 2 4 5 27.77 -1.56 -27.62 -12.77 0.142 0.77 3 5 6 -62.38 -17.23 63.98 -10.75 1.604 6.99 4 3 6 85.00 -4.70 -85.00 8.94 0.000 4.25 5 6 7 21.02 1.80 -20.95 -21.97 0.070 0.59 6 7 8 -79.05 -13.03 79.60 2.88 0.546 4.62 7 8 2 -163.00 11.35 163.00 5.27 -0.000 16.62 8 8 9 83.40 -14.23 -81.19 -4.74 2.218 11.16 9 9 10 -43.81 -45.26 36.35 38.15 -7.461 0.75 10 10 4 -36.35 -38.15 42.47 29.67 6.118 -0.61 -------- -------- Total: 3.238 48.56
由此可见，使用具有正常X和R的两个串联支路来模拟小阻抗支路，一般可以得到正确的牛顿迭代法潮流计算结果。另外，改善后的系统雅克比矩阵的条件数在100左右，远小于之前的2.26?109。 （完）
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