User:Tonypetelo/sandbox

$$ slope = -R = \frac{\Delta f}{\Delta P_{m}} $$

If we have a graph for a generator where frequency is on the vertical axis and power is on the horizontal axis: slope = -R = $$ \frac{\Delta f}{\Delta P_{m}} <\math> where $P_{m}$ is the change in power of the system. \par

If we have multiple generators, each can have its own R. Beta can be found by: \[ \beta = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n} \] The change in frequency due to a change in power can be found with: \[ \Delta f = \frac{\Delta P_{m}}{\beta} \] It should be noted that this simple equation can be rearranged to find the change in power due to a change in frequency. $$