Explain how the efficiency and regulation of a transformer can be assessed by open and short circuit tests.

What is meant by equivalent resistance?

Open Circuit Test and Short Circuit Test on Transformer

These two tests are performed on a transformer to determine

(i) equivalent circuit of transformer (ii)voltage regulation of transformer (iii) efficiency of transformer.

The power required for these Open Circuit test and Short Circuit test on transformer is equal to the power loss occurring in the transformer.

Open Circuit Test on Transformer

The connection diagram for open circuit test on transformer is shown in the figure. A voltmeter, wattmeter, and an ammeter are connected in LV side of the transformer as shown. The voltage at rated frequency is applied to that LV side with the help of a variac of variable ratio auto transformer. The HV side of the transformer is kept open. Now with help of variac applied voltage is slowly increase until the voltmeter gives reading equal to the rated voltage of the LV side. After reaching at rated LV side voltage, all three instruments reading (Voltmeter, Ammeter and Wattmeter readings) are recorded. The ammeter reading gives the no load current Ie. As no load current Ieis quite small compared to rated current of the transformer, the voltage drops due to this electric current then can be taken as negligible. Since, voltmeter reading V1 can be considered equal to secondary induced voltage of the transformer. The input power during test is indicated by wattmeter reading. As the transformer is open circuited, there is no output hence the input power here consists of core losses in transformer and copper loss in transformer during no load condition. But as said earlier, the no load current in the transformer is quite small compared to full load current so copper loss due to the small no load current can be neglected. Hence the wattmeter reading can be taken as equal to core losses in transformer. Let us consider wattmeter reading is Po.

Po = V1 2/Rm
Where Rm is shunt branch resistance of transformer.
If, Zm is shunt branch impedance of transformer.
Then, Zm = V1/ Ie.
Therefore, if shunt branch reactance of transformer is Xm 
Then, (1/ Xm)2 = (1/ Zm)2 - (1/ Rm)2

These values are referred to the LV side of transformer as because the test is conduced on LV side of transformer. These values could easily be referred to HV side by multiplying these values with square of transformation ratio.

Therefore it is seen that the open circuit test on transformer is used to determine core losses in transformer and parameters of shunt branch of the equivalent circuit of transformer.

Short Circuit Test on Transformer

The connection diagram for short circuit test on transformer is shown in the figure. A voltmeter, wattmeter, and an ammeter are connected in HV side of the transformer as shown. The voltage at rated frequency is applied to that HV side with the help of a variac of variable ratio auto transformer. The LV side of the transformer is short circuited . Now with help of variac applied voltage is slowly increase until the ammeter gives reading equal to the rated current of the HV side. After reaching at rated current of HV side, all three instruments reading (Voltmeter, Ammeter and Wattmeter readings) are recorded. The ammeter reading gives the primary equivalent of full load current IL. As the voltage, applied for full load current in short circuit test on transformer, is quite small compared to rated primary voltage of the transformer, the core losses in transformer can be taken as negligible here. Let’s, voltmeter reading is Vsc. The input power during test is indicated by wattmeter reading. As the transformer is short circuited, there is no output hence the input power here consists of copper losses in transformer. Since, the applied voltage Vsc is short circuit voltage in the transformer and hence it is quite small compared to rated voltage so core loss due to the small applied volate can be neglected. Hence the wattmeter reading can be taken as equal to copper losses in transformer. Let us consider wattmeter reading is Psc.

Psc = Re.IL2

Where Re is equivalent resistance of transformer.

If, Ze is equivalent impedance of transformer.

Then, Ze = Vsc/ IL.

Therefore, if equivalent reactance of transformer is Xe 

Then, Xe2 = Ze2 - Re2

These values are referred to the HV side of transformer as because the test is conduced on HV side of transformer. These values could easily be referred to LV side by dividing these values with square of transformation ratio.

Therefore it is seen that the Short Circuit test on transformer is used to determine copper loss in transformer at full load and parameters of approximate equivalent circuit of transformer.

Voltage Regulation of Transformer

What is Voltage Regulation?

Definition

The voltage regulation is the percentage of voltage difference between no load and full load voltages of a transformer with respect to its full load voltage.

Say a electrical power transformer is open circuited means load is not connected with secondary terminals. In this situation the secondary terminal voltage of the transformer will be its secondary induced emf E2. Whenever full load is connected to the secondary terminals of the transformer, rated current I2 flows through the secondary circuit and voltage drops comes into picture. At this situation, primary winding will also draw equivalent full load current from source. The voltage drop in the secondary is I2Z2 where Z2 is the secondary impedance of transformer. If now, at this loading condition any one measures the voltage between secondary terminals, he or she will get voltage V2 across load terminals which is obviously less than no load secondary voltage E2 and this is because of I2Z2voltage drop in the transformer.

Expression of Voltage Regulation of transformer

Expression of Voltage Regulation of Transformer, represented in percentage, is

Voltage regulation (%) =	E2 − V2	X 100%
	V2

Voltage Regulation of Transformer for lagging Power Factor

Now we will derive the expression of voltage regulation in detail, say lagging Power Factor of the load is cosθ2, that means angle between secondary current and voltage is θ2

Here, from the above diagram,

OC = OA + AB + BC

Here, OA = V2

Here, AB = AEcosθ2 = I2R2cosθ2

and, BC = DEsinθ2 = I2X2sinθ2

Angle between OC & OD may be very small so it can be neglected and OD is considered nearly equal to OC i.e.

E2 = OC = OA + AB + BC

E2 = OC = V2 + I2R2cosθ2 + I2X2sinθ2.....................1

Voltage Regulation of transformer at lagging power factor,

Voltage regulation (%) =	E2 − V2	X 100% =	I2R2cosθ2 + I2X2sinθ2	X 100%
	V2		V2

Voltage Regulation of Transformer for Leading Power Factor

Let's derive the expression of voltage regulation with leading current, say leading Power Factor of the load is cosθ2, that means angle between secondary current and voltage is θ2

Here, from the above diagram,

OC = OA + AB − BC

Here, OA = V2

Here, AB = AEcosθ2 = I2R2cosθ2

and, BC = DEsinθ2 = I2X2sinθ2

Angle between OC & OD may be very small so it can be neglected and OD is considered nearly equal to OC i.e.

E2 = OC = OA + AB − BC

E2 = OC = V2 + I2R2cosθ2 − I2X2sinθ2.....................2

Voltage Regulation of transformer at leading power factor,

Voltage regulation (%) =	E2 − V2	X 100% =	I2R2cosθ2 − I2X2sinθ2	X 100%
	V2		V2