## Transformer loss

The increased use of non linear modern loads that use high frequency switching generate harmonics in distribution system.

The existence of high level harmonics causes several undesirable effects such as transformer overheating, increase of running losses, increase in loading profile of transformer, nuisance tripping of protection devices and loss of life of transformer.

## Components of transformer losses & effects of harmonics        Transformer losses are categorized as no load losses and load losses. The no load losses are excitation losses caused by eddy currents in magnetic core & hysteresis loss of the core.

Since the no load losses are dependent on excitation voltage and the total harmonic voltage distortion (THDv) in most power system falls below 5% and the magnitudes of harmonic voltages are near to 2 to 3% of the fundamental component.

The extra no load loss caused by voltage harmonics is insignificant. But when the voltage distortion level is large enough, the no load loss can be evaluated by using the following equation (2).

Where, P & PM are no load losses at distorted and sinusoidal voltages,

• Ph = Hysteresis loss
• Pec = Eddy current loss
• V_hrms =  RMS values of distorted
• V_rms = Sinusoidal voltages

The load losses P_load (3), which are also known as impedance losses are sum of I2R (ohmic loss) and stray loss.

• Total stray loss = Winding stray loss* + other stray losses

The Winding stray loss caused by eddy current in the strands of winding conductor.

The Other stray losses caused by time variation of leakage flux in the structural parts such as tank walls, core clamps, etc.

Existence of harmonics causes an increase in both ohmic loss and stray loss and these losses under harmonic current can be evaluated by using the following formulae:

• P_DC is Ohmic loss(4)

where P_(DC-R)is the rated ohmic loss and IR is the rated fundamental frequency current of transformer.

• P_EC is eddy current loss (5)

The winding eddy current loss in the case of transformer supplying non linear loads can be given by the equation(5).

where

• P_(EC-R ) is the rated eddy current loss at rated fundamental frequency current of transformer.

The winding eddy current losses (P_EC) in the case of harmonic rich loads should be multiplied by harmonic loss factor(HLF) to correct the loss value(6).

The variation of other stray losses in the presence of harmonics can be evaluated from the  equation(7).

• P_OSL is the stray losses
• P_OSL-R is the rated stray losses at rated fundamental frequency current of transformer.

The loss correction factor for other stray losses is expressed in equation (8). The stray losses (P_OSL) in the case of harmonic rich loads should be multiplied by harmonic loss factor(H_LF-OSL) to correct the loss value(8).

The distribution transformer under study is an oil filled one 90% of load loss is assumed to be ohmic loss and 10% of the load loss is assumed to be total stray loss. Furthermore, 33% stray loss is assumed to winding eddy current loss and 67% of total stray loss is other stray loss.

Example: