BASIC ELECTRICAL TECHNOLOGY

DET 211/3

Chapter 6: Single Phase Transformer (Continued)

• Open circuit test– Provides magnetizing reactance and core loss

resistance– Obtain components are connected in parallel

Parameter determination of the transformer

Experiment Setup:

In the open circuit test, transformer rated voltage is applied to the primary voltage side of the transformer with the secondary side left open. Measurements of power, current, and voltage are made on the primary side.Since the secondary side is open, the input current IOC is equal to the excitation current through the shunt excitation branch. Because this current is very small, about 5% of rated value, the voltage drop across the secondary winding and the winding copper losses are neglected.

oc

ococ V

IY

ococ

oc

IV

PcosPF

ococ

oc

IV

Pcos 1

MCMC

oc

ococ X

jR

jBGV

IY

11

Admittance

Open circuit Power Factor

Open circuit Power Factor Angle

Angle of current always lags angle of voltage by

Short circuit test– Provides combined leakage reactance and winding

resistance– Obtain components are connected in series

Experiment Setup:

In the short circuit test, the secondary side is short circuited and the primary side is connected to a variable, low voltage source. Measurements of power, current, and voltage are made on the primary side. The applied voltage is adjusted until rated short circuit currents flows in the windings. This voltage is generally much smaller than the rated voltage.

sc

scsc I

VZ

scsc

sc

IV

PcosPF

scsc

sc

IV

Pcos 1

spspeqeqsc XaXjRaRjXRZ 22

Impedances referred to the primary side

Power Factor of the current

Angle Power Factor

00

00

sc

sc

sc

scsc I

V

I

VZ

Therefore

Exercise

The equivalent circuit impedances of a 20-kVA, 8000/240-V, 60-Hz transformer are to be determined. The open circuit test and the short circuit test were performed on the primary side of the

transformer and the following data were taken:

Find the impedances of the approximate equivalent circuit referred to the primary side and sketch that circuit

Open- circuit test (on primary)

Short- circuit test (on primary)

Voc = 8000 V Vsc = 489 V

Ioc = 0.214 A Isc = 2.5 A

Poc = 400 W Psc = 240 W

Per unit System

quantity of valueBase

Quantity Actual pu Per Unit,

The per unit value of any quantity is defined as

Quantity – may be power, voltage, current or impedance

1. It eliminates the need for conversion of the voltages, currents, and impedances across every transformer in the circuit; thus, there is less chance of computational errors.

2. The need to transform from three phase to single phase equivalents circuits, and vise versa, is avoided with the per unit quantities; hence, there is less confusion in handling and manipulating the various parameters in three phase system.

Two major advantages in using a per unit system:

Per Unit (pu) in Single Phase System

basebasebasebasebase IVS,Q,P

base

basebase I

VZ

base

basebase V

IY

base

basebase S

)V(Z

2

Voltage Regulation (VR)

The voltage regulation of a transformer is defined as the change in the magnitude of the secondary voltage as the current changes from full load to no load with the primary held fixed.

%100,

,, XV

VVVR

flS

flSnlS

%100,

,

XV

Va

V

VRflS

flSp

aVV P

S At no load,

I s

V p /a

R eq X eq

V s

+

-

+

-

V s

I sR eq

jI sX eq

V p /a

I s

Phasor Diagram

Lagging power factor

V s I sR eq

jI sX eq

V p /a

I s

Unity power factor

I s

V s

I sR eq

jI sX eq

V p /a

Leading power factor

Efficiency

The efficiency of a transformer is defined as the ratio of the power output (Pout) to the power input (Pin).

%100XP

P

in

out

%100XPP

P

lossesout

out

%100cos

cosX

PPIV

IV

corecuss

ss

Pcore = Peddy current + Physteresis

And

Pcu=Pcopper losses

Copper losses are resistive losses in the primary and secondary winding of the transformer core. They are modeled by placing a resistor Rp in the primary circuit of the transformer and resistor Rs in the secondary circuit.

Core loss is resistive loss in the primary winding of the transformer core. It can be modeled by placing a resistor Rc in the primary circuit of the transformer.

Assignment 5

A 15-kVA, 2400/240-V transformer is to be tested to determine its excitation branch components, its series impedances and its voltage regulation. The following test data have been taken from the primary side of the transformer:

Open- circuit test Short- circuit test

Voc = 2400 V Vsc = 48 V

Ioc = 0.25 A Isc = 6.0 A

Poc = 50 W Psc = 200 W

Assignment 5

The data have been taken by using the connections of open-circuit test and short-circuit test:

a) Find the equivalent circuit of this transformer referred to the high-voltage side.

b) Find the equivalent circuit of this transformer referred to the low-voltage side

c) Calculate the full-load voltage regulation at 0.8 lagging power factor and 0.8 leading power factor

d) What is the efficiency of the transformer at full load with a power factor of 0.8 lagging?