Why is transformer rated in KVA, but not in KW?

Transformers are rated in kVA (kilovolt-amperes) instead of kW (kilowatts) because kVA represents the apparent power, which includes both real and reactive power, while kW only represents the real power.

The power factor, which determines the proportion of real and reactive power, can vary depending on the load connected to the transformer. Since the transformer's losses (copper and core losses) depend on the current and voltage, not the power factor, kVA is a more consistent and accurate way to rate a transformer's capacity, regardless of the connected load. 

Here's a more detailed explanation:

Real Power (kW):

This is the power that is actually converted into work, like heat or mechanical energy, by the load. 

Reactive Power (kVAR):

This is the power that oscillates between the source and the load due to inductive or capacitive loads, and does not contribute to useful work. 

Apparent Power (kVA):

This is the vector sum of real and reactive power. It represents the total power that the transformer needs to handle, regardless of the power factor. 

Power Factor:

The power factor is the ratio of real power to apparent power (kW/kVA). It indicates how efficiently the power is being used. A power factor of 1 means all power is real power, while a power factor less than 1 means some power is reactive. 

Transformer Losses:

Transformer losses (copper and core losses) are primarily dependent on the voltage and current flowing through the transformer, not the power factor. Since kVA is directly related to voltage and current, it provides a more reliable measure of the transformer's capability to handle these losses. 

Load Variability:

When a transformer is designed, the manufacturer doesn't know what kind of load (resistive, inductive, or capacitive) will be connected to it in the future. Therefore, kVA is used as a universal rating that applies to all types of loads. 

In summary, kVA is used as the standard rating for transformers because it provides a more accurate and consistent measure of the transformer's capacity to handle power, regardless of the load's power factor.

If one phase power is 220V, why is three phase 220V, not 660V.

In a three-phase system, the voltage between two phases is not simply the sum of the individual phase voltages (220V + 220V = 440V) because the phases are shifted by 120 degrees from each other.

This means the voltages don't reach their peak values at the same time. When calculating the voltage between two phases, you must use vector addition (or phasor addition), which takes into account the phase difference. The resulting line-to-line voltage in a 3-phase system is approximately 1.732 (the square root of 3) times the phase voltage, which is why a 220V phase voltage results in a 380-400V line voltage, not 660V. 

Elaboration:

1. Phase Shift:

In a three-phase system, each phase voltage is 120 degrees out of phase with the others. This means they don't reach their peak positive or negative values simultaneously. 

2. Vector Addition:

When calculating the voltage between two phases (line-to-line voltage), you are essentially finding the resultant voltage of two vectors (phasors) that are 120 degrees apart. 

3. Square Root of 3:

The line-to-line voltage in a balanced three-phase system is calculated by multiplying the phase voltage by the square root of 3 (approximately 1.732). For example, if the phase voltage is 220V, the line voltage would be approximately 220 * 1.732 = 381V, which is typically rounded to 400V.

4. Why not 660V?

If you were to simply add the phase voltages arithmetically (220V + 220V + 220V = 660V), you would be ignoring the phase shift and assuming they all reach their peak values at the same time, which is not the case in a three-phase system.

5. Practical Considerations:

While the theoretical line-to-line voltage is 400V, the actual measured voltage can vary slightly due to factors like system loading and voltage drops, according to an electrical forum.