Question

On a $\mathbf{1000}\mathbf{MVA}$common base, a two-area system interconnected by a tie line has the following parameters:

The two areas are operating in parallel at the nominal frequency of $\mathbf{60}\mathbf{Hz}$. The areas are initially operating in steady state with each area supplying $\mathbf{1000}\mathbf{MW}$ when a sudden load change of$\mathbf{187}\mathbf{.}\mathbf{5}\mathbf{MW}$occurs in area 1. Compute the new steady-state frequency and change in tie-line power flow (a) without LFC, and (b) with LFC.

Short answer

(a) New steady state frequency is$59.7\text{\hspace{0.17em}Hz}$ and change in the tie line power flow is$-84.5\text{\hspace{0.17em}MW}$ .

(b) New steady state frequency is$60\text{\hspace{0.17em}Hz}$ and change in tie line power flow is $0$.

Step-by-step solution

Write the given data from the question:

The common base for the system,$S_{base}=1000\text{\hspace{0.17em}MVA}$

The nominal frequency,$f_0=60\text{\hspace{0.17em}Hz}$

Change in the load in area 1,$\Delta p_{L1}=187.5\text{\hspace{0.17em}MW}$

Write the area frequency response characteristics.

$\begin{array}{l}{\beta }_1=0.05\text{\hspace{0.17em}pu}\\ {\beta }_2=0.0625\text{\hspace{0.17em}pu}\end{array}$

Write the frequency dependent load characteristics.

$\begin{array}{l}{D}_1=0.6\text{\hspace{0.17em}pu}\\ D_2=0.9\text{\hspace{0.17em}pu}\end{array}$

Write the governor time constant.

$\begin{array}{l}{\tau }_{g1}=0.25\text{\hspace{0.17em}s}\\ {\tau }_{g2}=0.3\text{\hspace{0.17em}s}\end{array}$

Write the turbine constant.

$\begin{array}{l}{\tau }_{t1}=0.5\text{\hspace{0.17em}s}\\ {\tau }_{t2}=0.6\text{\hspace{0.17em}s}\end{array}$

Determine the equation to calculate the steady-state frequency and change in tie-line power flow with and without LFC.

The equation to calculate the per unit change in load in area 1 is given as follows.

${\mathbf{\left(}{\mathbf{\Delta p}}_{\mathbf{L}\mathbf{1}}\mathbf{\right)}}_{\mathbf{pu}}\mathbf{=}\frac{{\mathbf{\Delta p}}_{\mathbf{L}\mathbf{1}}}{{\mathbf{S}}_{\mathbf{base}}}$ …… (1)

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

${\mathbf{\Delta f}}_{\mathbf{pu}}\mathbf{=}\frac{\mathbf{-}{\mathbf{\Delta p}}_{\mathbf{L}\mathbf{1}}}{\left(\frac{1}{{\beta }_1}+D_1\right)\mathbf{+}\left(\frac{1}{R_2}+D_2\right)}$ …… (2)

The equation to calculate the frequency deviation in hertz is given as follows.

${\mathbf{\Delta f}}_{\mathbf{hertz}}\mathbf{=}{\mathbf{\Delta f}}_{\mathbf{pu}}{\mathbf{f}}_{\mathbf{0}}$ …… (3)

The equation to calculate the new steady state frequency is given as follows.

$\mathbf{f}\mathbf{=}{\mathbf{f}}_{\mathbf{0}}\mathbf{+}\mathbf{\Delta f}$ …… (4)

The equation to calculate the per unit change in the tie line power flow is given as follows.

${\mathbf{\left(}{\mathbf{\Delta p}}_{\mathbf{12}}\mathbf{\right)}}_{\mathbf{pu}}\mathbf{=}{\mathbf{\Delta f}}_{\mathbf{pu}}\left(\frac{1}{{\beta }_2}+D_2\right)$ …… (5)

The equation to calculate the change in the tie line power flow in MW is given as follows.

${\mathrm{\Delta p}}_{12,\mathrm{MW}}={{\mathrm{\Delta p}}_{12,}}_{\mathrm{pu}}{\mathrm{S}}_{\mathrm{base}}$ …… (6)

Calculate the steady-state frequency and change in tie-line power flow without LFC

Calculate the per unit change in load of area 1.

Substitute $187.5\text{\hspace{0.17em}MW}$for $\Delta P_{L1}$and $1000\text{\hspace{0.17em}MVA}$for $S_{base}$into equation (1).

$\begin{array}{l}\Delta p_{L1}=\frac{187.5}{1000}\\ \Delta p_{L1}=0.1875\text{\hspace{0.17em}pu}\end{array}$

Calculate the per unit frequency deviation.

Substitute $0.6\text{\hspace{0.17em}pu}$for $D_1$, $0.9\text{\hspace{0.17em}pu}$for $D_2$, $0.05\text{\hspace{0.17em}pu}$for ${\beta }_1$, $0.0625\text{\hspace{0.17em}pu}$for ${\beta }_2$and $0.1875\text{\hspace{0.17em}pu}$for $\Delta p_{L1}$into equation (2).

$\begin{array}{l}\Delta f_{pu}=\frac{-0.1875}{\left(\frac{1}{0.05}+0.6\right)+\left(\frac{1}{0.0625}+0.9\right)}\\ \Delta f_{pu}=\frac{-0.1875}{37.5}\\ \Delta f_{pu}=-0.005\text{\hspace{0.17em}pu}\end{array}$

Calculate the steady state frequency deviation in hertz.

Substitute$60Hz$for$f_0$, $-0.005\text{\hspace{0.17em}pu}$for$\Delta f_{pu}$into equation (3).

$\begin{array}{l}\Delta f_{hertz}=(-0.005)\left(60\right)\\ \Delta f_{hertz}=-0.3\text{\hspace{0.17em}Hz}\end{array}$

Calculate the new steady state frequency.

Substitute$60\text{\hspace{0.17em}Hz}$ for$f_0$and$-0.3\text{\hspace{0.17em}Hz}$for$\Delta f_{hertz}$into equation (4).

$\begin{array}{l}f=60-0.3\\ f=59.7\text{\hspace{0.17em}Hz}\end{array}$

Calculate the per unit change in the tie line power flow

Substitute $-0.005\text{\hspace{0.17em}pu}$for $\Delta f_{pu}$, $0.9\text{\hspace{0.17em}pu}$for $D_2$and $0.0625\text{\hspace{0.17em}pu}$for ${\beta }_2$into equation (5)

$\begin{array}{l}\Delta p_{12,pu}=(-0.005)\left(\frac{1}{0.0625}+0.9\right)\\ \Delta p_{12,pu}=-0.005\times 16.9\\ \Delta p_{12,pu}=-0.0845\text{\hspace{0.17em}pu}\end{array}$

Calculate the change in the tie line power flow in MW.

Substitute$-0.0845\text{\hspace{0.17em}pu}$ for$\Delta p_{12,pu}$ and$1000\text{\hspace{0.17em}MVA}$ for$S_{base}$ into equation (6)

$\begin{array}{l}\Delta p_{12,MW}=0.0845\times 1000\\ \Delta p_{12,MW}=84.5\text{\hspace{0.17em}MW}\end{array}$

Hence the new steady state frequency is $59.7\text{\hspace{0.17em}Hz}$and change in the tie line power flow is $-84.5\text{\hspace{0.17em}MW}$.

Calculate the steady-state frequency and change in tie-line power flow with LFC.

The main objective of the LFC is the reduce the change in the frequency and net tiel line power flow to zero after the change in the load.

Therefore, change in the frequency is zero and new frequency is the same as the nominal frequency.

$\begin{array}{l}f=f_0\\ f=60\text{\hspace{0.17em}Hz}\end{array}$

The change in the net tie line power flow is zero.

$\Delta p_{12}=0$

Hence the new steady state frequency is$60Hz$ and change in tie line power flow is $0$.