Question

For a large, $\mathbf{60}\mathbf{Hz}$ , interconnected electrical system assume that following the loss of two$\mathbf{1400}\mathbf{MW}$ generators (for a total generation loss of$\mathbf{2800}\mathbf{MW}$ ) the change in frequency is $\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{12}\mathbf{Hz}$. If all the on-line generators that are available to participate in frequency regulation have$\mathbf{R}$ of $\mathbf{0}\mathbf{.}\mathbf{04}$per unit (on their own MVA base), estimate the total MVA rating of these units.

Short answer

The MVA rating of the unit is $56000\text{\hspace{0.17em}MVA}$.

Step-by-step solution

Write the given data from the question:

Frequency of the system,$f=60\text{\hspace{0.17em}Hz}$

The change in the frequency,$\Delta f=-0.12\text{\hspace{0.17em}Hz}$

Total Generator losses,$\Delta P=2800\text{\hspace{0.17em}MW}$

Regulation constant,$R_{pu}=0.04\text{\hspace{0.17em}pu}$

Determine the equation to calculate the total MVA rating of the unit.

The equation to calculate the per unit frequency is given as follows.

${\mathbf{\Delta f}}_{\mathbf{pu}}\mathbf{=}\frac{\mathbf{\Delta f}}{\mathbf{f}}$ …… (1)

The equation to calculate the MVA rating is given as follows.

${\mathbf{\Delta P}}_{\mathbf{T}}\mathbf{=}\mathbf{\Delta P}\left(\frac{R_{\mathrm{pu}}}{{\mathrm{\Delta f}}_{\mathrm{pu}}}\right)$ …… (2)

Calculate the MVA rating of the unit.

Calculate the per unit frequency of the system.

Substitute$-0.12\text{\hspace{0.17em}pu}$for$\Delta f$and $60\text{\hspace{0.17em}Hz}$for$f$into equation (1).

$\begin{array}{l}\Delta f_{pu}=\frac{-0.12}{60}\\ \Delta f_{pu}=-0.002\text{\hspace{0.17em}pu}\end{array}$

Calculate the MVA rating of the unit.

Substitute$0.002\text{\hspace{0.17em}pu}$ for$\Delta f_{pu}$ ,$0.04\text{\hspace{0.17em}pu}$ for$R_{pu}$ and$2800\text{\hspace{0.17em}MW}$ for$\Delta P$ into equation (2).

$\begin{array}{l}\Delta P_T=2800\left(\frac{0.04}{0.002}\right)\\ \Delta P_T=56000\text{\hspace{0.17em}MVA}\end{array}$

Hence the MVA rating of the unit is$56000\text{\hspace{0.17em}MVA}$ .