Given the different contingencies or faults in a distribution system, the first obvious parameter of interest to be monitored for quality and security deg-radation is deviation of the node voltages from the prescribed statutory standards using the following techniques.
2.7.1 Capacitor Banks for Voltage Regulation and Power Factor Correction
To boost the voltage at the customer end of service, a capacitor bank is used as a regulating device. It is connected in parallel across the line to increase voltage by reducing the inductive VArs and is generally a lagging power factor. To correct the power factor appropriate for the substation load, VAr due to computation is reduced by using a lagging power factor, while the leading power factor substation increases VAr supply, which may reduce the quality of real power supply.
Balanced capacitor banks are installed on each phase of the 3φ power system for effective power factor correction. Capacitors can be switchable automatically, depending on voltage degradation. The convention of the center-tapping capacitor keeps the voltage at normal values.
2.7.1.1 Shunt Capacitor Installed in Parallel to Distribution Network Model
Consider a reduced feeder length, shown in Figure 2.7. The corresponding phasor diagram is presented in Figure 2.8.
VDrop = IR cos φ + IXL sin φ (2.76) To reduce the VDrop, we install a capacitor, as shown in Figure 2.9. The corresponding phasor diagram is shown in Figure 2.10.
VDrop = IR cos φ + I(XL – XC) sin φ (2.77) The series-connected capacitor effectively resolved the voltage drop in the reactive element.
Apago PDF Enhancer
FIGURE 2.7 Reduced feeder.
FIGURE 2.8
Phasor diagram for reduced feeder.
FIGURE 2.9
Reduced feeder with capacitor.
FIGURE 2.10
Phasor diagram for reduced feeder with capacitor.
VS VR
IS R jXL
ISR
VS
φ
VR jISXL
IS
VDrop
VS VR
IS R XL XC
ISR
VS
φ
VR
jIS(XL-XC)
IS
-jISXC) VS(old)
VDrop
Apago PDF Enhancer
2.7.1.2 Calculation of Voltage Drop for a Distribution Feeder
Consider a series-connected (radial) system, as shown in Figure 2.11. The voltage drop per unit length for each layer (lateral) is given as
V = I(Z1 + Z2 + Z3 + … + Zn) (2.78) S = VI* = II*(Z1 + Z2 + Z3 + … + Zn) (2.79)
Si = I2 Zi (2.80)
If Z is given per unit length,
Ztotal = z1(l1) + z2(l2) + z3(l3) + … + zn(ln) (2.81) Si = I2 zi(Δli)
(2.82)
2.7.2 Tap-Changing Method for Voltage Regulation
The tap-changing transformer schemes are operated manually or automati-cally to accommodate a variety of load types typiautomati-cally called ULTCs (unload tap-changing transformer). They are aimed at keeping voltages at proper levels in response to wide variations in the load and the primary voltage level.
The taps are connections on a transformer winding that change the turn ratio according to
FIGURE 2.11
Series-connected radial system.
Zn Z3
Z2 Z1
S=
∑
SiS Si Ii zi li i
n
total =
∑ ∑
= =1 2 (Δ )N N
V V
1 2
1 2
=
Apago PDF Enhancer
A new voltage obtained from a particular given setting relative to the pri-mary voltage varies from ±10% to ±2.5%. Taps are typically located on the primary side because they require less current than would be necessary on the secondary side (Figure 2.12).
2.7.3 Voltage-Regulating Transformers
We have several situations where voltage magnitude and current flows in a network need to be controlled using other devices. The automatic voltage regulation is designed to provide a boost of voltage magnitude along a line or change in phase to control flows of power between systems (Figure 2.13).
In Figure 2.13, the connections and polarity of the secondary windings are used to obtain ±5% or ±10% voltage regulation. Parallel connection of the secondary windings results in a 5% voltage regulation, and series connection results in a 10% voltage regulation for this example.
Single-phase buck-boost voltage regulation can also be obtained using a voltage-to-voltage transformer configuration, as shown in Figure 2.14. This
FIGURE 2.12
Tap-changing transformer.
FIGURE 2.13
Single-phase booster transformer connection for 10% boost.
Exciting Transformer
Reactor
Series Transformer
To Load From source of
Power
CB
2.4 kV 2.64 kV
120 V 120 V
Apago PDF Enhancer
is applicable to correcting voltage sag. The transformer is used to alter the output voltage by a converter with a duty cycle given by Vnominal − VS)(a/VS), where a is the turns ratio of the buck-boost transformer, and Vload = VS + Vsecondary.
Figure 2.15 presents a simplified diagram of a three-phase regulating trans-former. The output voltage of each phase is a fraction of the input voltage in either buck or boost operation. The tap changing is done using a ganged switch.
2.7.4 Phase Shifter or Regulating Transformer
The phase-shifter transformer is a special type of regulatory transformer that is primarily used to alter the current and voltage phase angles in a trans-mission or distribution system. It is used to control power flows and losses within power networks. This class of power transformer is characterized by a complex turn ratio that describes its mathematical behavior on the power
FIGURE 2.14
Voltage regulation using solid-state control.
FIGURE 2.15
Three-phase regulating transformer.
~
+
AC Voltage-Voltage Converter
Turns ratio a:1 Secondary Side
Primary Side
Load VS
Va
Vc
Vb
Va’ = Va + Δ Va
Vc’= V b + Δ Vb
V b’ = Vc + Δ Vc ΔVa
ΔVc
ΔVb
Apago PDF Enhancer
system. The network representation of the static phase-shifter transformer is shown in Figure 2.16.
The physical device consists of two sets of windings representing a booster transformer and a magnetizing transformer. The current through the mag-netizing transformer uses a small voltage on the primary side of the booster transformer. This voltage is quadrature to the phase voltage. Therefore, the sending end voltage is displaced in the vector space by the presence of the booster transformer and the “quadrature” voltage. Furthermore, when the reactance of the magnetizing transformer is referred to the primary side of the booster transformer, the resultant reactance is xs = xkb + n2xkm, as the booster transformer is at its nominal tap setting. A more exact representation is shown in Figure 2.17.
Now, by applying Kirchoff's current law to Figure 2.17,
Io = − Ij = Ii− Is (2.83)
(2.84)
where
k =
φ =
n = turns ratio of the magnetizing transformer
FIGURE 2.16
Network representation of the static phase-shifter transformer.
FIGURE 2.17
Equivalent circuit diagram of the phase-shifter transformer.
Ii Ij
Apago PDF Enhancer
Further, by Kirchoff's voltage law (KVL),
V′ = Vi + Vs (2.85)
(2.86)
Equation 2.85 and Equation 2.86 show the complex nature of the transfer characteristics of a phase-shifter transformer. The exact model will reflect this property, which is a drawback to the existing power system program-ming techniques and computations.