Answer to Question #225498 in Electrical Engineering for Zoe

Question

Question 4
4.1 An interconnected 50 Hz power system consisting of one area has two
turbine-generator units, rated 600 and 800 MVA, with regulation constants
of 0.04 and 0.06 per unit, respectively, based on their respective ratings.
When each unit carries a 350 MVA steady-state load, let the area load
suddenly increase by 250 MVA. Determine:
4.1.1 The area frequency response characteristic on a 1000 MVA base. (5)
4.1.2 ∆

Answer 1

The regulation constant

$R_{1}{new}= 0.04* \frac{1000}{600}=0.0667p.u\\ R_{2}{new}= 0.06* \frac{1000}{800}=0.075$

The value of unit area frequency response characteristic

$\beta= \frac{1}{0.0667}+\frac{1}{0.075}= 28.33p.u$

Per unit value

$\Delta p_m = \frac{250}{1000}= 2.5 p.u$

Consider the expression for the steady state frequency power relation.

$\Delta p= \Delta p_{ref}- \beta\Delta f$

For the steady state operation, the value of $\Delta p_{ref}$ is 0

$\Delta p= - \beta\Delta f\\ \Delta f = -\frac{2.5}{28.33}=-0.0882$

The negative sign represents a decrease in the value of frequency. Therefore, the steady-state value of the area frequency is 0.0882

The steady-state area value of the area frequency in hertz

$\Delta f _{hertz} =-0.0882*50=-4.4123Hz$