Synchronous Machines

Operation Characteristics

The frequency-speed relation of a synchronous generator is given by,

f = \frac{p n}{120}

$\large E_a$ is given by,

E_{a} = π \sqrt{2} N ϕ f = 4.44 N ϕ f, ϕ = B A

Phasor Diagram

V_{a} = E_{a} - I_{a} (R_{a} + X_{s} j)

where,

The complex power of a synchronous generator is given by,

S = 3 V_{a} I_{a}^{*}

$\large R_a$ , the active and reactive power are given by,

\begin{matrix} P = 3 \frac{| E_{a} | | V_{a} |}{X_{s}} \sin δ \\ Q = 3 [\frac{| E_{a} | | V_{a} |}{X_{s}} \cos δ - \frac{V_{a}^{2}}{X_{s}}] \end{matrix}