Question

Consider the single-line diagram of a power system shown in Figure 342 With equipment ratings given:

Generator$G_1$$50MVA,13.2kV,x=0.15p.u$

Generator$G2$$20MVA,13.8kV,x=0.15p.u$

Three-phase$\Delta -Y$transporter $T_1$:$80MVA,13.2\Delta /165YkV,X=0.1p.u$

Three-phase$Y-\Delta$ transformer $T_2$:$40MVA,165Y/13.8\Delta kV,X=0.1p.u$

Load: $40MVA,0.8PF$ lagging, operating at

$150kVA$

Choose a base of 100 MVA for the system and 132-kV base in the transmission-line circuit. Let the load be modeled as a parallel combination of resistance and inductance Neglect transformer phase shifts. Draw a per-phase equivalent circuit of the system showing all impedances in per unit.

Short answer

Therefore, the per phase equivalent circuit of the system in per unit quantities as shown below.

Step-by-step solution

Determine the formulas to calculate the value of the quantities.

The per unit of reactance on the new base is given by,

${\mathit{X}}_{\mathbf{n}\mathbf{e}\mathbf{w}}\mathbf{=}{\mathit{X}}_{\mathbf{o}\mathbf{l}\mathbf{d}}\left(\frac{V_{baseold}}{V_{basenew}}\right)\left(\frac{S_{basenew}}{S_{baseold}}\right)$ ……(1)

The base impedance of transmission line is given by,

${\mathit{Z}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}}\mathbf{=}\frac{{\mathbf{V}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}}^{\mathbf{2}}}{{\mathbf{S}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}}}$ ……(2 )

The per unit impedance of the transmission line is given by,

${\mathit{Z}}_{\mathbf{p}\mathbf{.}\mathbf{u}}\mathbf{=}\frac{{\mathbf{Z}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}}}{{\mathbf{Z}}_{\mathbf{s}\mathbf{y}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{m}}}$ ……(3)

The base resistance of the load is given by,

$\mathit{R}\mathbf{=}\frac{{\mathbf{V}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}}^{\mathbf{2}}}{\mathbf{P}}$ ……(4)

The base reactance of the load is given by,

${\mathit{X}}_{\mathbf{l}\mathbf{o}\mathbf{a}\mathbf{d}}\mathbf{=}\frac{{\mathbf{V}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}}^{\mathbf{2}}}{\mathbf{Q}}$ ……(5)

Determine the values of the quantities and draw the per equivalent circuit of the system. 

The base voltage of the transformer 1 and generator 1 can be calculated as

$\begin{array}{l}{V}_{base1}=132\times \left(\frac{13.2}{165}\right)\\ V_{base1}=10.56\text{\hspace{0.17em}kV}\end{array}$

Calculate the per unit reactance of the transformer 1 by using the equation (1),

Calculate the per unit reactance of the generator 1 by using the equation (1),

The base value for the transformer 2 and generator 2 can be calculated as

Calculate the per unit reactance of the transformer 2 by using the equation (1),

Calculate the per unit reactance of the generator 2 by using the equation (1),

Calculate base impedance of the transmission line by using equation (2),

Calculate the per unit impedance of the transmission line by using equation (3),

Calculate the per unit impedance of the transmission line between the transformer 1 and load by using equation (3),

The power of the load can be written as

Calculate the base value of the resistance by using equation (4),

Calculate the base reactance of the load by using equation (5),

Calculate the per unit impedance of the load by using equation (3),

Hence the per phase equivalent circuit of the system in per unit is shown below.