By Carson W. Taylor
Voltage balance is an important obstacle within the making plans and operation of electrical energy platforms. This e-book offers a transparent, in-depth clarification of voltage balance, overlaying either temporary and longer-term phenomena and proposing confirmed ideas to instability difficulties. The e-book describes gear features for transmission, new release, and distribution/load subsystems of an influence procedure, including equipment for the modelling of apparatus. Readers will locate static and dynamic desktop simulation examples for small identical energy structures and for a truly huge energy procedure, plus an account of voltage balance linked to HVDC hyperlinks. they'll additionally get invaluable making plans and working guidance, laptop tools for energy circulate and dynamic simulation, and outlines of exact voltage instability incidents.
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Extra resources for Power System Voltage Stability
22), ✂ g✄ jwL ✂ G ✠ ✠ jwC ✂ ✂ 139 ☞ 10 ✍ 9 H/m✂ ✠ 9 ✌ 1 ☞ 10 ✍ 3 S/m ✂ j 2p ☞ 109 s ✍ 1 ✂ 362 ☞ 10 ✍ 12 F/m ✂ ☞ ✠ ✄ 109 ☞ 10 ✍ 3 j44 ✌ 5 ✂ m ✍ 1 ✌ ✠ Thus, from Eqs. 25b), a ✄ 0 ✌ 109 Np/m and b ✄ 44 ✌ 5 rad/m. ✄ R 0 ✌ 788 W/m ✂ From Eq. 29), Z0 ✄ R G ✠ ✠ jwL jwC j 2p ☞ 109 s ✍ ✄ 1 ✄ 19 ✌ 6 From Eq. 6 In addition to not dissipating power, a lossless line has two important features: (1) it is dispertionless (µp is independent of frequency) and (2) its characteristic impedance Z0 is purely real. Sometimes, it is not possible to design a transmission line such that R ✁ wL and G✁ wC , but it is possible to choose the dimensions of the line and its material properties so as to satisfy the condition RC ✄ LG (distortionless line) ✌ Such a line is called a distortionless line because despite the fact that it is not lossless, it does nonetheless possess the previously mentioned features of the loss line.
Zin jXinsc . Solving Eq. 68) for the line length, l ✄ 1 tan ✍ b ✞ 1 Xinsc ✡ Z0 1 tan ✍ 8 ✌ 38 rad/m ✄ ✞ 1 40 W ✡ 50 W ✄ 0 ✌ 675 np ✂ rad ✠ 8 ✌ 38 rad/m ✁ for which the smallest positive solution is 8 ✌ 05 cm (with n ✄ 0). 25 A lossless transmission line is terminated in a short circuit. How long (in wavelengths) should the line be in order for it to appear as an open circuit at its input terminals? sc Solution: From Eq. 68), Zin Hence, l ✄ ✄ jZ0 tan bl. If bl ✄ l p ✑ np✒ 2p 2 ✠ ✄ p☛ 2 l nl 4✠ 2 ✠ sc np ✂ , then Zin ✄ j¥ W ✂ .
Using Eq. 31 A generator with Vg ✄ 300 V and Zg ✄ 50 W is connected to a load ZL ✄ 75 W through a 50-W lossless line of length l ✄ 0 ✌ 15l. (a) Compute Zin , the input impedance of the line at the generator end. (b) Compute Ii and Vi . (c) Compute the time-average power delivered to the line, Pin ✄ 12 Vi Ii ✁ . (d) Compute VL , IL , and the time-average power delivered to the load, PL ✄ 12 VL IL ✁ . How does Pin compare to PL ? Explain. (e) Compute the time average power delivered by the generator, Pg , and the time average power dissipated in Zg .