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Three Phase Power

In this article, we will begin a discussion of three phase power. The name “three phase” comes from the fact that there are three distinct line-to-neutral voltages: $$ V_a = V_{LN}cos(\omega_0 t + 0) \\ V_b = V_{LN}cos(\omega_0t + \frac{2\pi}{3}) \\ V_c = V_{LN}cos(\omega_0t - \frac{2\pi}{3}) $$

It is also possible to measure the voltage difference across two lines, for example: $$ V_{ab} = V_a - V_b = \sqrt{3}V_{LN}cos(\omega_0t + \frac{\pi}{6})$$

There are several benefits to using three phase power in comparison to single phase power. Firstly, power dissipation in transmission lines is proportional to $ I_L^2R $. For a three phase system, there are three conductors, each carrying $ \frac{1}{3} $ of the current required, therefore reducing power loss and improving efficiency. Additionally, the use of three phases causes the torque of rotating electrical machinery to be smoother.

Common Connections in Three Phase Circuits

The two common configurations in three phase circuits are delta (Also written as $\Delta$): and wye (also known as star):

Relations between Line and Phase Voltage and Currents

For Wye Circuits: $$ V_{line} = \sqrt{3} V_{phase} \\ I_{line} = I_{phase} $$

For Delta Circuits: $$ V_{line} = V_{phase}\\ I_{line} = \sqrt{3}I_{phase} $$

Where $V_{line}$ is the line to line voltage, $V_{phase}$ is the voltage across one phase of the load, $I_{line}$ is the current conducted by one line, and $I_{phase}$ is the current through one phase of the load.

wiki/power/three_phase_power.txt · Last modified: 2016/10/01 13:49 by jdlenz2