A transformer transfers 220,000 W of the 250,000 W of energy supplied to it. How efficient is the transformer?
Answers
Answer:
Transformers form the most important link between supply systems and load. Transformer’s efficiency directly affects its performance and aging. The transformer’s efficiency, in general, is in the range of 95 – 99 %. For large power transformers with very low losses, the efficiency can be as high as 99.7%. The input and output measurements of a transformer are not done under loaded conditions as the wattmeter readings inevitably suffer errors of 1 – 2%. So for the purpose of efficiency calculations, OC and SC tests are used to calculate rated core and winding losses in the transformer. The core losses depend on the transformer rated voltage, and the copper losses depend on the currents through the transformer primary and secondary windings. Hence transformer efficiency is of prime importance to operate it under constant voltage and frequency conditions. The rise in the temperature of the transformer due to heat generated affects the life of transformer oil properties and decides the type of cooling method adopted. The temperature rise limits the rating of the equipment. The efficiency of transformer is simply given as:
The output power is the product of the fraction of the rated loading (volt-ampere), and power factor of the load
The losses are the sum of copper losses in the windings + the iron loss + dielectric loss + stray load loss.
The iron losses include the hysteresis and eddy current losses in the transformer. These losses depend on the flux density inside the core. Mathematically,
Hysteresis Loss :
Eddy Current Loss :
Where kh and ke are constants, Bmax is the peak magnetic field density, f is the source frequency, and t is the thickness of the core. The power ‘n’ in the hysteresis loss is known as Steinmetz constant whose value can be nearly 2.
The dielectric losses take place inside the transformer oil. For low voltage transformers, it can be neglected.
The leakage flux links to the metal frame, tank,etc. to produce eddy currents and are present all around the transformer hence called stray loss, and it depends on the load current and so named as ‘stray load loss.’ It can be represented by resistance in series to the leakage reactance.
Explanation:
efficiency = (energy transferred × 100) / energy supplied
in this case efficiency = (220000 × 100)/250000
=> efficiency = (22 × 100)/25
=> efficiency = 88%