**1. Regulation**The voltage regulation is a measure of the variation in the secondary voltage when the load is varied from zero to rated value at a constant power factor.It is typically expressed as a percentage, or per unit, of the rated output voltage at rated load. A general expression for the regulation can be written as:

**% regulation = { ( V**

_{NL}- V_{FL})/V_{FL }} x 100where V

_{NL}is the voltage at no load and V_{FL}is the voltage at full load. The regulation is dependent upon the impedance characteristics of the transformer, the resistance (r), and more significantly the ac reactance (x), as well as the power factor of the load. The regulation can be calculated based on the transformer impedance characteristics and the load power factor using the following formulas:**%regulation = pr + qx + [(px – qr)**

^{2}/200]**q = SQRT (1 – p**

^{2})- Where p is the power factor of the load and r and x are expressed in terms of per unit on the transformer base. The value of q is taken to be positive for a lagging (inductive) power factor and negative for a leading (capacitive) power factor.

- It should be noted that lower impedance values, specifically ac reactance, result in lower regulation, which is generally desirable. However, this is at the expense of the fault current, which would in turn increase with a reduction in impedance, since it is primarily limited by the transformer impedance. Additionally, the regulation increases as the power factor of the load becomes more lagging (inductive).

**2. Transformer losses**a) Copper losses (or I

^{2}R losses or ohmic losses) in the primary and secondary windings.b) Iron losses or core losses) in the core. This again has tow component:

i) Hysteresis losses and ii) Eddy current lossesThe copper losses (Pc) also have have tow components i) The primary winding copper loss and ii) The secondary winding copper loss

Copper losses, (P

_{c}) = I

_{1}

^{2}R

_{1}+ I

_{2}

^{2}R

_{2 }

= I

_{1}

^{2}R

_{1}+ I

_{1}

^{2}R

_{2}

^{'}= I

_{1}

^{2}R

_{01}

Also P

_{c }= I

_{2}

^{2}R

_{2}+ I

_{2}

^{2}R

_{1}

^{'}= I

_{2}

^{2}R

_{02}

( assume that R

_{02 }= R

_{eq2}

**= equivalent resistance referred to secondary side)**

_{ }(For correct determination of copper losses, the winding resistance should be determined at the operating temperature of windings)

When alternating current flows through the winding, the core material under goes cycle processes of magnetisation and demagnetisation

This process is called hysteresis.

The hysteresis losses (in watts) is given as :

**P**

_{h}**= K**

_{h}B_{m}^{n}f v_{h }= Hysteresis coefficient whose value depends up on the material (K

_{h }is 0.025 for cast steel, 0.001 for silicon steel and 0.0001 for permalloy)

B

_{m }= Maxium flux density (in tesla)

n = a constant 1.5 ≤ n ≤ 2.5 depending upon the material

f = Frequency ( in hertz)

v = Volume of the core material (in m

^{2 })

The eddy currents are the circulating currents set up in the core. These are produced due to magnetic flux being cut by the core. The loss due these eddy current is called eddy current losses this loss (in watts) is given by,

**P**

_{e }

**= K**

_{e}B_{m}^{2}f^{2 }t^{2 }v_{e}= Constant dependent up on the material

t = Thickness of laminations (in meter)

A comparison of the expression of hysteresis and eddy current losses reveals that the eddy current varies as the square of the frequency. Whereas the hysteresis loss varies directly with the frequency. The hysteresis losses can be minimized by selecting suitable ferromagnetic material for the core. The eddy current losses can be minimized by using thin laminations in building the core.

The total iron losses is given as,

**P**

_{i}_{ }= P_{h}+ P_{i}

**3. Efficiency**The efficiency of a transformer, like any other device, is defined as the ratio of useful output power to input power.

Input power = P

_{1}Output power = P

_{2}_{}- The percentage efficiency of a transformer is in the range of 95 to 99%. For large power transformers with low loss designs, the efficiency can be as high as 99.7%.

- If we deal with the transformer as referred to the secondary side, we have

**P**

_{2}= V_{2}I_{2}cosθ2where I

_{2}is the load current. The input power P_{1}is the sum of the output power and power loss in the transformer. Thus**P**

_{1}= P_{2}+ P_{L }The power loss in the transformer is made of two parts: the I

^{2}R loss and the core loss Pc' Thus**P**

_{L}= Pc + I_{2}^{2}

_{}R_{eq2}As a result, the efficiency is given by

OR

.........(1.1)

**the condition for maximum efficiency**, at a given load power factor, can be derived by differentiating the expression for η with respect to I

_{2}and equating it to zero:

...........(1.2)

Solving it further, we get

**Pc = I**

_{2}^{2}

_{}R_{eq2} ............(1.3)

Thus, the maximum efficiency occurs at a load at which variable load loss equals the constant core (no-load) loss. Further,

...........(1.4)

where I

_{2FL}is the full-load (rated) current and I^{2}_{2FL}R_{eq2}**is the load loss at the rated load conditions. Therefore, the per-unit load at which the maximum efficiency occurs is**_{ } .........(1.5)

The value of maximum efficiency can be found out by substituting the value of I

_{2}from equation 1.1 in equation 1.5. Similarly, it can easily be shown that the maximum efficiency, for a given load, occurs at unity power factor (cosθ=1).__Related articles :__**Electromagnetism****Magnetic Circuit in Transformer****Transformer Theory and Operation****Open Circuit and Short Circuit Tests of Transformer****Types of Transformer**

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