Download EXPERIMENT NO 3

EXPERIMENT NO: THREE
AIM: Voltage Profile Enhancement of the Power System
Theory: In a modern power system, electrical energy from the generating station is
delivered to the ultimate consumers through a network of transmission and distribution.
For satisfactory operation of motors, lamps and other loads, it is desirable that consumers
are supplied with substantially constant voltage. Too wide variations of voltage may cause
erratic operation or even malfunctioning of consumers’ appliances. To safeguard the
interest of the consumers, the government has enacted a law in this regard. The statutory
limit of voltage variation is ± 6% of declared voltage at consumers’ terminals. The principal
cause of voltage variation at consumer’s premises is the change in load on the supply
system. When the load on the system increases, the voltage at the consumer’s terminals
falls due to the increased voltage drop in (i) alternator synchronous impedance (ii)
transmission line (iii) transformer impedance (iv) feeders and (v) distributors. The reverse
would happen should the load on the system decrease. These voltage variations are
undesirable and must be kept within the prescribed limits (i.e., ± 6% of the declared
voltage). This is achieved by installing voltage regulating equipment at suitable places in
the power system. The purpose of this chapter is to deal with important voltage control
equipment and its increasing utility in this fast-developing power system.
Methods of Voltage Control
There are several methods of voltage control. In each method, the system voltage is
changed in accordance with the load to obtain a fairly constant voltage at the consumer’s
end of the system. The following are the methods of voltage control in an A.C power
system:
1)
2)
3)
4)
5)
6)
By excitation control
By using tap changing transformers
Auto-transformer tap changing
Booster transformers
Induction regulators
By synchronous condenser
Voltage Control by Synchronous Condenser
The voltage at the receiving end of a transmission line can be controlled by installing
specially designed synchronous motors called synchronous condensers at the receiving end
of the line. The synchronous condenser supplies wattless leading kVA to the line depending
upon the excitation of the motor. This wattless leading kVA partly or fully cancels the
wattles lagging kVA of the line, thus controlling the voltage drop in the line. In this way,
voltage at the receiving end of a transmission line can be kept constant as the load on the
system changes. For simplicity, consider a short transmission line where the effects of
capacitance are neglected. Therefore, the line has only resistance and inductance. Let V 1
and V2 be the per phase sending end and receiving end voltages, respectively. Let I2 be the
load current at a lagging power factor of cos φ2.
(i)
Without synchronous condenser: - Fig. 1 (i) shows the transmission line with
resistance R and inductive reactance X per phase. The load current I 2 can be resolved into
two rectangular components via Ip in phase with V2 and Iq at right angles to V2 [See Fig.1
(ii)]. Each component will produce resistive and reactive drops; the resistive drops being
in phase with and the reactive drops in quadrature leading with the corresponding currents.
The vector addition of these voltage drops to V2 gives the sending end voltage V1.
Figure 1
(ii)
With synchronous condenser: - Now suppose that a synchronous condenser
taking a leading current Im is connected at the receiving end of the line. The vector diagram
of the circuit becomes as shown in Fig. 2.2. Note that since I m and Iq are in direct opposition
and that Im must be greater than Iq, the four drops due to these two currents simplify to:
Figure 2
(𝐼𝑚 − 𝐼𝑞 ) R
and
in phase with Im
(𝐼𝑚 − 𝐼𝑞 ) X in
quadrature leading with Im
From the vector diagram, the relation between V 1 and V2 is given by.
𝑂𝐸 2 = (𝑂𝐴 + 𝐴𝐵 − 𝐷𝐸 ) 2 + (𝐵𝐶 + 𝐶𝐷) 2
or
2
2
𝑉12 = [ 𝑉2 + 𝐼𝑝 𝑅 − (𝐼𝑚 − 𝐼𝑞 ) 𝑋] + [ 𝐼𝑝 𝑋 + (𝐼𝑚 − 𝐼𝑞 )𝑅]
𝑉1
From this equation, the value of Im can be calculated to obtain any desired ratio of
𝑉2
for a
given load current and power factor.
3 𝑉2 𝐼𝑚
kVAR capacity of condenser =
1000
Calculations: Voltage Profile Enhancement using Synchronous Condenser
A 3-phase overhead line has resistance and reactance per phase of 5Ω and 20Ω respectively.
The load at the receiving end is 25MW at 66kV with power factor of 0.8 lagging. Find the
capacity of the synchronous condenser required for this load condition if it connected at
the receiving end and if the line voltage at both ends is to be maintained at 66kV. Present
numerical solution and develop MATLAB program to fill relevant data in observat ion
Table.
Given:
Load = 25MW; Line Voltage = 66kV; Power Factor = 0.8; R = 5Ω; X = 20Ω.
Solution:
𝑃
𝐼2 =
√3𝑉𝐿 𝑐𝑜𝑠𝜑
𝐼2 =
25 ∗ 106
√3(66000)( 0.8)
𝐼2 = 273.367𝐴
𝐼𝑝 = 𝐼2 𝑐𝑜𝑠𝜑2 = ( 273.367)( 0.8) = 218.693𝐴
𝐼𝑞 = 𝐼2 𝑆𝑖𝑛𝜑2 = (273.367)(0.6) = 164.02𝐴
Sending End Voltage: (V1 = Receiving End Voltage per phase = V2)
𝑉2 =
𝑉𝐿
√3
=
66000
√3
= 38.105𝑘𝑉
Let Im be the current taken by the synchronous condenser. Then,
2
2
𝑉12 = [𝑉2 + 𝐼𝑝 𝑅 − (𝐼𝑚 − 𝐼𝑞 ) 𝑋] + [ 𝐼𝑝 𝑋 + (𝐼𝑚 − 𝐼𝑞 )𝑅 ]
(38.105𝑘𝑉 )2 = [(38.105𝑘𝑉 ) + (218.693 ∗ 5) − (20𝐼𝑚 − (20)164.02)]2 + [(218.693 ∗ 20)
2
+ (5𝐼𝑚 − ((5)(164.02))]
(38.105𝑘𝑉 )2 = [ 38.105𝑘𝑉 + 1093.465 − 20𝐼𝑚 + 3280.4] 2 + [4373.86 + 5𝐼𝑚 − 820.1]2
Now:
𝐼𝑚 = 233.369𝐴
And:
Capacity of Synchronous Condenser:
=
=
3𝑉2 𝐼𝑚
106
𝑀𝑉𝐴𝑅
3 ∗ 38.105𝑘𝑉 ∗ 233.369
106
= 26.678 𝑀𝑉𝐴𝑅
MATLAB Program: close all
clc
kw=25e3;
pf=0.8;
v=66e3;
r=5;
x=20;
i2=kw*1000/sqrt(3)/v/1000/pf;
ip=i2*pf;
iq=i2*sind(acosd(pf));
v1=v/sqrt(3);
im=233.369;
capacity=3*v1*im/10^6;
fprintf("Load current = %d A \n", i2);
fprintf("Ip = %.2 f A \n", ip);
fprintf("Iq = %.2 f A \n", iq);
fprintf("Sending end voltage per phase = %d V \n", v1 );
fprintf("Im = %d A \n", im);
fprintf("Capacity of synchronous condenser = %.2f MVAR \n", capacity);
Observation Table:
Sr. No.
Data
Value
Unit (V,A)
1.
Load Current
273.367
A
2.
Ip
218.693
A
3.
Iq
164.02
A
4.
Sending end voltage\phase
𝟑𝟖. 𝟏𝟎𝟓
kV
5.
Im
233.369
A
6.
Capacity of Syn. Condenser
26.678
MVAR
Table 1
Conclusion:
Voltage variations that are too large may cause consumer appliances to malfunction. The difference in
voltage at the consumer's location is caused by a change in supply load. The system's load is inversely
proportional to the voltage at the customers' terminals. The calculated results are like the simulated
results. The load current, phase current, Iq, sending end voltage and Im are similar.
Questions: 1. A synchronous condenser is generally installed at the receiving end of the transmission
line.
2. The principal cause of voltage variation is the change of load on the system.
3.
Describe the synchronous condenser method of voltage control for a transmission line.
Illustrate your answer with a vector diagram.
The voltage at the receiving end of a transmission line can be controlled by installing specially designed
synchronous motors called synchronous condensers at the receiving end of the line. The synchronous
condensers provide wattless reading KVA to the line depending upon the excitation of the motor. The
wattless leading KVA then partly or fully cancels the wattless lagging KVA of the line, thus controlling
the voltage drop in the line. This then results to voltage at the receiving end of a transmission line can
be kept constant as the load on the system changes.