[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

I S2 = K I S1 (I S2 assumed I S1 , K 1), kA
I bt = I L , the rated current of the bus-tie reactor, kA
number of feeders on the section of the bus with the highest number of feeders
Therefore, the required reactor impedance, in Ohms, in each configuration, their ratio, and the ratio of
the rated power of the reactors are given by Equations 2.9.15a–d:
FIGURE 2.9.31 Simplified radial system.
X
bt
VLL
3 I
S2
K ( 1)
1
K 1
(2.9.15a)
X
fd
VLL
3
S2
K ( 1)
1
( 1
K)
(2.9.15b)
X
X
bt
fd
MVAbt
Total MVA
( 1
K)
K 1
fd
2
( 1
K)
n
K 1
(2.9.15c)
(2.9.15d)
From the above, it is apparent that bus-tie reactors are a good solution where a relatively small reduction
in fault level is required on a number of downstream feeders. However, bus-tie reactors increase rapidly
in size and cost when (1) the fault contributions on either side of the reactor are significantly different
(i.e., as K moves away from 1.0) and (2) when the largest fault contribution (I S1 ) approaches the breaker
rating I b . Conversely, bus-tie reactors decrease rapidly in size and cost when the reactor can be given a
low continuous rating due to low normal power transfer across the tie.
FIGURE 2.9.32 Power-line-balance phasor diagram.
2.9.3.3 Power-Line Balance
Consider the radial system shown in Figure 2.9.31, in which the sending-end bus is fed from an infinite
power source. By inspection of Figure 2.9.32, the following equations can be written:
V = V 1 – V 2 (2.9.16)
V = Z I (2.9.17)
FIGURE 2.9.29 Bus-tie-reactor connection.
V = [(R I cos ) + (X I sin )] + j [(X I cos ) – (RI sin )] (2.9.18)
where
= tan –1 (Q/P)
V 1 = sending end voltage, kV
V 2 = receiving end voltage, kV
V = line voltage drop, kV
R = line resistance,
X = line reactance,
I = line current, kA
P = real power, kW
Q = reactive power kVA
= transmission angle, deg.
= current phase angle, deg.
Since P = V 2 I cos and Q = V 2 I sin , then
V = [(P R + Q X) + j (P X – Q R)]/V 2 (2.9.19)
FIGURE 2.9.30 Phase-reactor connection.
where
V f = in phase component of V, kV
V q = quadrature component of V, kV
V = V f + j V q (2.9.20)
© 2004 by CRC Press LLC
© 2004 by CRC Press LLC