Voltage Regulation, in
general, is defined as change in magnitude of Secondary Terminal Voltage per unit Rated Secondary Terminal Voltage when load at a given Power Factor is
reduced to zero while maintain the Primary Voltage constant.

Lets us assume that,

V

_{2}= Secondary Terminal Voltage at any Load
E

_{2}= Secondary Terminal Voltage at no load
Then from the definition,

Change in Secondary Terminal
Voltage from any load to no load,

= E

_{2}– V_{2}_{}

Also, Rated Secondary
Terminal Voltage of a Transformer is equal to Secondary Terminal Voltage at no
load. Therefore, as per definition of Voltage Regulation,

Voltage Regulation = (E

_{2}– V_{2}) / E_{2}in pu
= (E

_{2}– V_{2}) x100 / E_{2}in percentage.
The change in magnitude of
Secondary Terminal Voltage with loading of Transformer is because of Primary
and Secondary leakage impedance. The magnitude of this change in voltage
depends on the load current, load power factor, total leakage reactance and total
resistance of Transformer.

As the consumer need their
terminal voltage to be within a prescribed limit, the Voltage Regulation of a
Distribution Transformer shall be less i.e. good. For better Voltage Regulation
of a Distribution Transformer, it is quite important that their leakage
impedance shall be less.

**Calculation of Voltage Regulation:**

The Voltage Regulation of a
Transformer can be obtained from its equivalent circuit model when referred to
Primary or Secondary side. Figure below shows the equivalent circuit of a
Transformer when referred to Secondary side and its phasor diagram for load of lagging
power factor.

In the figure above,

re2 = Equivalent resistance
referred to Secondary

xe2 = Equivalent reactance
referred to Secondary

It can be seen from the
above phasor diagram that,

E

_{2}≈ OC
= OA
+ AB + BC

But from the right angled
Triangle ABE,

CosƟ

_{2}= AB / AE
So, AE = ABCosƟ

_{2}_{}

= I

_{2}r_{e2}CosƟ_{2}_{}

Similarly from the right
angled Triangle DEF,

Therefore BC = EF = I

_{2}x_{e2}SinƟ_{2}_{}

E

_{2}= V_{2}+ I_{2}r_{e2}CosƟ_{2}+I_{2}x_{e2}SinƟ_{2}_{}

Hence,

(E

_{2}– V_{2}) = I_{2}r_{e2}CosƟ_{2}+I_{2}x_{e2}SinƟ_{2}
Now, per unit Voltage Regulation
for any load current I

_{2},
(E

_{2}– V_{2}) / E_{2}= I_{2}r_{e2}CosƟ_{2}/ E_{2}+I_{2}x_{e2}SinƟ_{2}/ E_{2}_{}

In case I2 is rated current then,

I

_{2}r_{e2}/ E_{2}= Voltage drop across re2 at rated current / Rated Voltage
= pu resistance drop

= ε

_{r }………………..(1)
Similarly,

I

_{2}x_{e2}/ E_{2}= Voltage drop across reactance / Rated or Base Voltage
= pu reactance drop

= ε

_{x }………………………(2)
Therefore pu Voltage
Regulation VR at rated current,

**VR = ε**

_{r}CosƟ_{2}+ ε_{x}SinƟ_{2}

And percentage Voltage
Regulation VR at rated current,

**VR = (ε**

_{r}CosƟ_{2}+ ε_{x}SinƟ_{2}) x 100 %

The above calculation for
Voltage Regulation has been carried out assuming lagging power factor load but
for leading power factor load we only need to replace

**Ɵ2**by**- Ɵ2.**Therefore Voltage Regulation VR for leading power factor load for rated current will be as below.**VR**

**= ε**

_{r}CosƟ_{2}- ε_{x}SinƟ_{2}in pu.

**= (ε**

_{r}CosƟ_{2}- ε_{x}SinƟ_{2}) x 100 %

Now we will investigate some
conditions based on Voltage Regulation which are very important.

**Condition for Zero Voltage Regulation:**

As can be seen from the
expression of Voltage Regulation, that VR varies as the Power factor of load is
varied keeping load current constant. Thus for a particular Power Factor, we
can get zero Voltage Regulation.

As VR = 0

ε

_{r}CosƟ_{2}+ ε_{x}SinƟ_{2}= 0
So,

tanƟ

_{2}= - ε_{r}/ ε_{x}_{}

From equation (1) and (2),

**tanƟ2**

_{ }= -r_{e2}/ x_{e2}

Therefore Magnitude of Power
Factor CosƟ

_{2}= x_{e2}/ z_{e2}_{}

Here negative sign in the
value of tanƟ

_{2}means that power factor of load is leading. Thus zero Voltage Regulation is achieved by leading load of power factor x_{e2}/ z_{e2}and if we increase the power factor of load beyond this value then Voltage Regulation will become negative. Negative Voltage Regulation means that Secondary Terminal Voltage V_{2}is more than the no load generated EMF E_{2}.**Condition for Maximum Voltage Regulation:**

For Maximum Voltage Regulation,

d(VR) / dƟ

_{2}= 0 assuming load current constant.
Thus,

-ε

_{r}SinƟ_{2}+ ε_{x}CosƟ_{2}= 0
This implies that, tanƟ

_{2}= ε_{x}/ ε_{r}_{}

Thus, CosƟ

_{2}= r_{e2}/ x_{e2}_{}

Here tanƟ

_{2}is positive, which means that maximum Voltage Regulation occurs for lagging power factor load and at a power factor of r_{e2}/ x_{e2}.
One important thing to note
here that,

Leakage Impedance Angle = Ø

= Ɵ

_{2}_{}

Thus we can say that, maximum
Voltage Regulation occurs when load power factor is equal to leakage impedance
angle.

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