# Effects of harmonics - Increased losses

## Losses in conductors

The active power transmitted to a load is a function of the fundamental component I_{1} of the current.

When the current drawn by the load contains harmonics, the rms value of the current, I_{r.m.s}, is greater than the fundamental I_{1}.

The definition of THD_{i} being:

[math]\displaystyle{ THD_i= \sqrt {\left (\frac{I_{r.m.s} }{I1} \right)^2 - 1} }[/math]

it may be deduced that :

[math]\displaystyle{ I_{r.m.s} = I_1 \cdot \sqrt{1 +THD_i ^2} }[/math]

**Figure** M18 shows, as a function of the harmonic distortion:

- The increase in the r.m.s. current I
_{r.m.s.}for a load drawing a given fundamental current - The increase in Joule losses, not taking into account the skin effect. (The reference point in the graph is 1 for I
_{r.m.s.}and Joules losses, the case when there are no harmonics)

The harmonic currents cause an increase of the Joule losses in all conductors in which they flow and additional temperature rise in transformers, switchgear, cables, etc.

## Losses in asynchronous machines

The harmonic voltages (order h) supplied to asynchronous machines cause the flow of currents in the rotor with frequencies higher than 50 Hz that are the origin of additional losses.

### Orders of magnitude

- A virtually rectangular supply voltage causes a 20% increase in losses
- A supply voltage with harmonics u
_{5}= 8% (of U_{1}, the fundamental voltage),

- u
_{7}= 5%, u_{11}= 3%, u_{13}= 1%, i.e. total harmonic distortion THD_{u}equal to 10%, results in additional losses of 6%

## Losses in transformers

Harmonic currents flowing in transformers cause an increase in the “copper” losses due to the Joule effect and increased “iron” losses due to eddy currents. The harmonic voltages are responsible for “iron” losses due to hysteresis.

It is generally considered that losses in windings increase as the square of the THD_{i} and that core losses increase linearly with the THD_{u}.

In Utility distribution transformers, where distortion levels are limited, losses increase between 10 and 15%.

## Losses in capacitors

The harmonic voltages applied to capacitors cause the flow of currents proportional to the frequency of the harmonics. These currents cause additional losses.

### Example

A supply voltage has the following harmonics:

- Fundamental voltage U
_{1}, - harmonic voltages u
_{5}= 8% (of U_{1}), - u
_{7}= 5%, - u
_{11}= 3%, - u
_{13}= 1%,

i.e. total harmonic distortion THDu equal to 10%. The amperage of the current is multiplied by 1.19. Joule losses are multiplied by (1.19)^{2}, i.e. 1.4.