ECE 441 1

Voltage Regulation

% 100%

nl rated

rated

E Vreg per unit regulation

V

regulation per unit

ECE 441 2

Voltage Regulation (continued)

• Enl = no-load output voltage– Measure with a voltmeter when no load is

connected to the transformer

• Vrated = voltmeter reading at the output terminals when the transformer

is supplying the rated apparent power

• These voltages are all either High-side or Low-side voltages!

ECE 441 3

Voltage Regulation (continued)

• Measurements are not always easy to make, so use the equivalent circuit.

ECE 441 4

When the breaker is open, no current flows in Req,LS , jXeq,LS , or ZLOAD,LS , therefore

Vout = VLS = E’LS = Enl

ECE 441 5

With rated load on the secondary, E’LS = ILSZeq,LS + VLS

ILS = rated low-side current at a specified power factor

VLS = rated low-side voltage

Zeq,LS = equivalent impedance of the transformer referred to the low-side

E’LS = no-load low-side voltage

ECE 441 6

Example 2.7

• The equivalent low-side parameters of a 250kVA, 4160 – 480V, 60 Hz transformer areReq,LS = 0.00920 Ω and Xeq,LS = 0.0433 Ω. The transformer is operated in the step-down mode and is delivering rated current at rated voltage to a 0.840 power-factor lagging load.

• Determine

ECE 441 7

– the no-load voltage – The actual input voltage on the high-side– The high-side current– The input impedance– The voltage regulation– The voltage regulation if the power factor of

the load is 0.840 leading– Sketch the tip-to-tail phasor diagram of the

secondary circuit for the 0.840 power factor lagging load. Show all voltage drops.

ECE 441 8

1

250,000520.83

480

cos (0.840) 32.86 32.86 ( )

480 0

520.83 32.86

LS

LS

LS

kVAI A

V

lagging

V V

I A

ECE 441 9

Low-Side Output

ECE 441 10

', ,

'

'

'

'

520.83 32.86 (0.0092) 520.83 32.86 ( 0.0433) 480 0

4.79 32.86 22.55 57.14 480 0

4.024 2.599 12.235 18.94 480 0

496.53 1.886

LS LS eq LS LS eq LS LS

LS

LS

LS

LS

E I R I jX V

E j

E

E j j j

E V

ECE 441 11

'

'

' '

41608.667

480

8.667(496.53 1.886 )

4303.4 1.886

HS HS

LS LS

T HS LS

T

E Va

E V

V E aE

V V

ECE 441 12

The high-side current

520.83 32.86

8.66760.09 32.86

LSHS

HS

II

aI A

The input impedance

'

'

4304.4 1.886

60.09 32.86

71.62 34.74

Tin

HS

in

VZ

I

Z

ECE 441 13

The voltage regulation

496.53 4800.0344 3.44%

480nl rated

rated

E Vreg

V

ECE 441 14

Voltage Regulation if the power factor is 0.840 leading

'

520.83 32.86

.............

472.28 2.61

472.28 4800.0161 1.61%

480

LS

LS

nl rated

rated

I

E

E Vreg

V

Regulation is negative because of a voltage rise in the transformer due to resonant effects.

ECE 441 15

The “tip-to-tail” phasor diagram for the 0.840 power factor lagging load.

,

,

520.83 32.86 (0.0092) 4.79 32.86

520.83 32.86 ( 0.0433) 22.6 57.14

LS eq LS

LS eq LS

I R V

I X j V

ECE 441 16

Component Phasors

ECE 441 17

Tip-to-Tail Addition