Efficiency of Transformer

Introduction of Efficiency of Transformer

Transformer efficiency is output power divided by input power at a stated load and power factor. Transformers lose part of their input energy as heat in the core, windings, insulation and surrounding metalwork. These losses affect temperature rise, cooling requirements and insulation life. Efficiency is high, with values around 98 to 99% typical for large power transformers. Open-circuit (OC) and short-circuit (SC) tests measure no-load and load losses without a direct full-load efficiency test. At rated voltage, core loss changes little with load, while winding loss rises approximately with the square of the currents. The test result must use the stated voltage, frequency, load and power factor. The efficiency of transformer ratio is given as:

• Output power equals the load fraction multiplied by rated apparent power and the load power factor.
• Total loss includes winding copper loss, core loss, dielectric loss and stray load loss.
• Core loss includes hysteresis loss and eddy-current loss. Both depend on core flux density. The simplified relationships are:
  Hysteresis Loss :
  
  Eddy Current Loss :
  
  Here k_h and k_e are material and construction constants, B_max is peak magnetic flux density, f is supply frequency and t is core-lamination thickness. The power ‘n’ is an empirical Steinmetz exponent that depends on the core material and operating range.
  
• Dielectric loss occurs in the oil and solid insulation. It is often small enough to omit from a simplified low-voltage calculation.
• Leakage flux can induce eddy currents in the frame, tank and other conducting parts around the transformer. This stray load loss varies with load current. In the equivalent circuit, its active component can be included as resistance in series with leakage reactance.

Efficiency Calculation of the Transformer

The equivalent circuit below is referred to the primary side. R_c represents core loss. The short-circuit (SC) test gives the equivalent resistance used to calculate winding loss:


Let x be the per-unit load relative to rated apparent power S in VA. Let P_cufl in watts be full-load copper loss, cosθ be the load power factor and P_i in watts be core loss. A common efficiency calculation keeps the two dominant terms, core loss and copper loss. The efficiency of transformer is then:

Here x²P_cufl is copper loss P_cu at per-unit load x.
Maximum efficiency (η_max) occurs when the load-dependent copper loss equals the nearly constant core loss at the stated voltage and frequency.

The maximum-efficiency expression is:

Full-load maximum efficiency occurs only when full-load copper loss equals core loss. If full-load copper loss is greater than core loss, the equality occurs below full load.
The figure below shows efficiency against load:

For a given load, a higher power factor raises output power without changing the loss terms in this simplified model. It raises the efficiency value, but the load fraction at maximum efficiency remains set by the equality of copper loss and core loss.

All Day Efficiency of Transformer

All-day efficiency is an energy ratio commonly used for distribution transformers, whose load changes over the day. Unlike a power transformer‘s efficiency stated at one load point, it divides total output energy by total input energy over 24 hours. No-load loss continues whenever the transformer is energised, while copper loss changes with the load cycle. A design with lower core flux density and a larger core cross-section can reduce the no-load energy loss over that period.