Voltage Regulation by Synchronous Impedance Method

1. Electrical Machines-II
6th Semester, EE and EEE
By
Dr. Binod Kumar Sahu
Associate Professor, Electrical Engg.
Siksha ‘O’ Anusandhan, Deemed to be University,
Bhubaneswar, Odisha, India
Lecture-10

2. 2
Learning Outcomes: - (Previous Lecture_09)
 To understand and analyse the equivalent circuit of an alternator.
 To determine the induced emf from the equivalent circuit.
 To determine the voltage regulation for different loading conditions.

3. 3
Learning Outcomes: - (Today’s Lecture_10)
 To determine the voltage regulation using Synchronous Impedance
Method.
 To solve numerical related to determination of voltage regulation.

4. 4
Determination of Voltage Regulation of an Alternator: -
 Voltage regulation of an alternator can be determined by:
a) Direct loading method.
b) Indirect method by conducting certain tests on the alternator. Various
indirect methods are:
i. Synchronous Impedance Method or, EMF method.
ii. Ampere Turn Method or, MMF method.
iii. Zero Power Factor Method or, Potier Method.
 In direct loading method, the alternator is loaded with its rated capacity at
rated voltage and speed (voltage can be varied by varying the field current
and speed can be changed by changing the mechanical power input).
 Then the load is suddenly removed and field excitation and speed are
brought back to their nominal values.
 Voltages at full load & no-load are measured to determine the voltage
regulation.
 Direct loading method is only used for small rated alternators.

5. 5
Determination of Voltage Regulation of an Alternator EMF Method: -
 The Synchronous Impedance Method or Emf Method is based on the concept of
replacing the effect of armature reaction by an imaginary reactance called
armature reaction reactance (xar).
 For calculating the voltage regulation using EMF method we need:
i. The armature resistance per phase.
ii. Open Circuit Characteristic (OCC).
iii. Short Circuit Characteristic (SCC).
Measurement of Armature Resistance: -
 Resistance of a winding can be measured by passing a DC current through it.
 This can be done by using a multimeter or a DC source.
 But multimeter measures the winding resistance by passing a very small current
through it. So, this resistance is called the cold resistance of the armature winding.
 Since resistance is temperature dependent, the accurate resistance (i.e. hot
resistance) value can be measured by passing rated DC current through the winding.

6. 6
Armature Winding
V
A
Ra
RaRa
Armature Winding
V
A
Ra
RaRa
Armature Winding
V
A
Ra Ra
Ra
Figure 1 Figure 2 Figure 3
In Figure 2,
a
Voltmeter reading
R
Ammeter reading

In Figure 1,
2 a
Voltmeter reading
R
Ammeter reading

In Figure 3,
 
2
|| 2
3
a a a
Voltmeter reading
Ammeter reading
R R R  
Impedance of any winding,
2 2 2 2
(2 )L
V
Z R X R fL
I
    

7. 7
 The measured armature resistance is its DC value.
 But armature winding carries AC current, so the actual resistance while carrying AC current
will be more than that while carrying DC current. This effect is due to skin effect.
 The tendency of the alternating current to concentrate near the surface of a conductor is
called skin effect.
- -
-
-
-
-
-
-
-
- - - -
-
--
-
- - -
--
-
---
-
--- - -------- -
--
- -
-
-
-
-
-
-
-
- - - -
-
--
-
- - -
--
-
---
-
-
-
--
--
-
- --
-
-
-
- -
-
 In AC, flux linking with the portion near the centre of the
conductor is more as compared to that linking near the
periphery.
 So the portion near the centre will offer more opposition for
the flow of current as compared to the portion near the
surface.
 So, the distribution of current is not uniform throughout the cross-section of the conductor.
 Current distribution is less near the centre of the conductor as compared to its periphery.
This reduces the effective area of the conductor as a result of which conductor resistance
increases.
 Whereas, in case of DC, the current is evenly distributed.
 So, the AC resistance is more then the DC resistance. Generally, (1.2 1.7)ac dcR to R
Conductor
carrying DC
Conductor
carrying AC

8. 8
Open circuit characteristic of an Alternator: -
 It is the graph between the open circuit voltage (E0) and field current (If) at rated
speed of the alternator.
 Under no-load condition armature current is zero. So, there is no internal voltage drop
in the armature winding, i.e. .
 The field current (If) is gradually varied and for every field current the respective no-
load voltage (E0) is noted.
0E V
 

 Finally, a graph is plotted
between E0 and If which is
called Open Circuit
Characteristic (OCC).
fV
fI
Field Winding
A
Armature Winding
ar sx
ar sx
ar sx
E0 V V

9. 9
Short circuit characteristic (SCC) of an Alternator: -
 It is the graph between the short circuit armature current (ISC) and field current (If) at
rated speed of the alternator.
 Under short circuit condition, terminal voltage is zero. So the induced EMF (E)
circulates the short circuited armature current (ISC).
 In short circuit test, the field current (If) is gradually varied and for every field
current the respective short circuited armature current (ISC) is noted.
 Finally, a graph is plotted
between ISC and If which is
called Short Circuit
Characteristic (SCC).
fV
fI
Field Winding
A
Armature Winding
ar sx
ar sx
ar sx
E0 VV A SCI

10. 10
OCC
SCC
Field Current (If)
OpenCircuitVoltage(E0)
ShortCircuitCharacteristic(ISC)
Rated Voltage (V)
Rated Current (Ia)

11. 11
 From the OCC and SCC, it is clear that for a particular field current, the induced
voltage can be obtained from OCC and the corresponding short circuit current can be
obtained from SCC.
 So, the synchronous impedance,
 After knowing the values of ra and xs, we can determine the induced emf/phase i.e.
the no-load induced emf/phase for any loading condition by using the relation:
 And finally, percentage voltage regulation can be obtained as:
fV
fI
Field Circuit Armature Circuit
aIar sx
VEs
SC forthesame field current
E
Z
I

2 2
s s ax Z r 
 0 a a sE V I r jx
  
  
 Armature resistance (ra) already we have
measured, so the synchronous reactance,
0
100
E V
PercentageVoltage Regulation
V

 

12. 12
Numerical on voltage regulation by EMF Method: -
1. From the following test results, determine the voltage regulation of a 2000 V, three
phase, star connected alternator delivering a load current of 100 A, at 0.8 pf
leading. Test results: An excitation of 2.5 A produces a current of 100 A in the
stator winding on short circuit and an emf/phase of 500 V on open circuit. Assume
Ra = 0.8 Ω.
Solution: -
A field current of 2.5 A produces an open circuit EMF/phase of 500 V and short circuit
current of 100 A.
So, the synchronous impedance, Zs = 500/100 = 5 Ω.
Rated terminal voltage, V = 2000/√(3) = 1154.7 V.
Armature current, Ia = 100 A.
Power factor 0.8 leading. So, the power factor angle is 36.870.
No-load voltage/phase,
2 2 2 2
5 0.8 4.9356s s sx Z X     
   0 0 0
0 1154.7 0 100 36.87 0.5 4.9356 993.94 25.31a a sE V I r jx j
  
          

13. 13
Percentage voltage regulation,
= (|E0|-|V|) / |V| x 100 = (993.94 – 1154.7)/1154.7 x 100 = – 13.92 %.
2. A 3-phase, star-connected synchronous generator is rated at 1200 kVA, 11 kV. On
short-circuit a field current of 55 A gives full-load current. The OC voltage with the
same excitation is 1580 V/phase. Calculate the voltage regulation at 0.8 lagging.
Neglect armature resistance.
Solution: -
Rated armature current, Ia = 1200 x 103 /(√3 x 11 x 103) = 62.98 A. (As S = √3VL x IL)
Rated terminal voltage, V = (11 x 103)/ √3 = 6350.85 V.
Power factor is 0.8 lagging. So the power factor angle is 36.870.
Synchronous Impedance = Synchronous Reactance (as the armature resistance is
neglected)
xs = 1580 / 62.98 = 25.087 Ω.
So, the generated emf/phase,
Percentage voltage regulation = (|E0|-|V|) / |V| x 100 = (7407.48 – 6350.85)/6350.85 x 100
= 16.64 %.
   0 0 0
0 6350.85 0 62.98 36.87 0 25.087 7407.48 9.82a a sE V I r jx j V
  
           

14. 14
Thank you