[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

Therefore,
Line reactive losses = (S i /V i ) 2 X (2.9.33)
Line charging (at each end) = V i2 (Y/2) , i = 1, 2 (2.9.34)
Line - surge impedance, Z
S
= X / Y L / C
(2.9.35)
Surge-impedance loading (SIL) = V LL2 /Z S (2.9.36)
FIGURE 2.9.33 Transmission system equivalent circuit.
The phasor diagram in Figure 2.9.32 illustrates the meaning of Equation 2.9.19 and Equation 2.9.20.
By inspection of Figure 2.9.32, it is clear that sin = V q /V 1 . Therefore
and
P = [(V 1 V 2 sin )/X] + [Q (R/X)] (2.9.21)
= tan –1 {(P X – Q R)/[V 2 + (P R + Q X)]} (2.9.22)
In transmission systems, the X/R ratio is large, and the grid usually operates with power factor close
to unity. Thus, assuming R = 0 and Q = 0,
V = j P (X/V 2 ) (2.9.23)
P = (V 1 V 2 sin /X (2.9.24)
= tan –1 [P (X/V 2 )] (2.9.25)
Therefore, apart from the voltage magnitude, which must be kept within regulated limits, control of
power flow can only be achieved by variation of the line reactance (X), the transmission angle (), or both.
2.9.3.4 Reactive Power Balance
Figure 2.9.33 shows a transmission system represented by its equivalent. By inspection, the following
expressions can be derived:
V 1 = V 2 + V (2.9.26)
(V 1 cos + j(V 1 sin = V 2 + (X I sin + j(X I cos 2.9.27)
X I cos = P L (X/V 2 ) = V 1 sin (2.9.28)
P L = (V 1 V 2 sin )/X (2.9.29)
X I sin = Q L (X/V 2 ) = (V 1 cos – V 2 (2.9.30)
Q L = V 1 V 2 cos – (V 22 /X) (2.9.31)
S i
2 2
( P Q
)
i
I
(2.9.32)
Power balance = total line charging – line reactive losses
2.9.4 Shunt Reactors Switching Transients
Since the amount of the reactive compensation needed in a power system varies with the loading of the
transmission line, shunt reactors are typically switched daily. Shunt reactors will thus experience a large
number of switching transients. Transient overvoltages occur, mainly while disconnecting the reactor
from the circuit, due to the following two phenomena in the switching device.
1. Current chopping
2. Single or multiple restrikes
The behavior of these overvoltages depends on a number of factors, such as:
• Circuit connection (wye or delta)
• Method of neutral grounding (floating neutral, solidly grounded, or grounded through a reactor)
• Rated MVAR of the reactor
• Construction of the reactor (air core, iron core with three legs or five legs), which impacts the
high-frequency characteristics
• Type of connection to the system (tertiary winding or direct connection)
• Type and ratings of circuit breaker
• Characteristics of neighboring equipment
2.9.4.1 Current Chopping
When the contacts of a breaker part, current in the circuit is not interrupted immediately. Current
continues to flow through the arc established between the contacts right after the instant of contact
parting. Normally the arc extinguishes when the ac current crosses zero. In some cases, however, due to
arc instability caused by the circuit parameters and the breaker characteristics, the arc extinguishes
abruptly and prematurely ahead of the natural zero crossing of the ac current. When this happens, the
energy trapped in the magnetic field of the reactor transfers to the electric field of the stray capacitances
in the circuit, thus initiating a resonant response. The resonance frequency is typically a few kHz, and
its magnitude is directly proportional to the chopped current and the surge impedance of the circuit,
and it may exceed the dielectric withstand of the reactor. Figure 2.9.34 shows a single-phase equivalent
circuit that can be used to simulate the chopping overvoltages for a star-connected and solidly grounded
shunt-reactor bank with negligible coupling between phases. The legend for Figure 2.9.34 is as follows:
L L = reactor reactance (For gapped iron-core shunt reactors, the manufacturer should be
consulted to obtain the core saturation level at high transient frequencies and thus the
resultant inductance; for air-core shunt reactors, the inductance can always be considered
a constant value equal to the 60-Hz rated value.)
C L = equivalent capacitance at the reactor side of the circuit breaker, F
R(f) = reactor frequency-dependent resistance,
L S = system equivalent reactance, H
© 2004 by CRC Press LLC
© 2004 by CRC Press LLC