# Phase resistance

*Electrical resistance of the winding conductors in one phase.*

The phase resistance $R_{ph}$ is proportional to the total conductor length $l_{cond}$ and inversely proportional to the conductor area $A_{cond}$ and the number of parallel paths $N_{pp}$: $$R_{ph} = \rho _T \frac{l_{cond}}{A_{cond} N_{pp}},$$ where the total conductor length $l_{cond}$ is twice the average conductor length times the number of turns per coil times the number of coils per parallel path. A large phase resistance causes large conductor losses, which reduces the electrical energy efficiency of the electrical machine. The phase resistance can be decreased by improving the winding technique in order to be able to increase the cross-sectional area of the conductors and thus the slot fill factor, or by using conductor materials with a high electrical conductivity (such as copper).

The resistivity of copper and aluminum conductors is largely temperature dependent: $$\rho _T = \rho _{20^\circ\mathrm{C}} \left[ 1+\alpha \left( T-20^\circ\mathrm{C}\right) \right],$$ where $\rho$ is the resistivity and $\alpha$ is the temperature coefficient of the resistivity. Therefore, you need to provide an accurate estimate of the temperature of conductors $T$ in order to get an accurate estimate of the phase resistance.

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