Question

Rework problem 3.4 if the load connected to the $\mathbf{240}\mathbf{}\mathit{v}\mathit{o}\mathit{l}\mathit{t}\mathit{s}$secondary winding absorbs $\mathbf{110}\mathbf{}\mathit{k}\mathit{V}\mathit{A}$under short term overload conditions at an 0.8 power factor leading and at $\mathbf{230}\mathbf{}\mathit{v}\mathit{o}\mathit{l}\mathit{t}\mathit{s}$.

Short answer

Answer

(a)The primary voltage is $2300V$.

(b)The load impedance is $0.48\Omega$

(c)The load impedance referred to the primary is $48\Omega$

(d)The real and reactive power is $88kW$and $-66kVAR$.

Step-by-step solution

Determine the formulas of transformer ratio, load impedance, active power, reactive power and apparent power.

Write the formula of transformer ratio.

$\frac{{\mathbf{V}}_{\mathbf{2}}}{{\mathbf{V}}_{\mathbf{1}}}\mathbf{=}\frac{{\mathbf{N}}_{\mathbf{2}}}{{\mathbf{N}}_{\mathbf{1}}}$ ……. (1)

Write the formula of apparent power

$\mathit{S}\mathbf{=}{\mathit{V}}_{\mathbf{2}}\left(\frac{V_2}{Z_2}\right)$ ……. (2)

Write the formula of load impedance referred to the primary

${\mathit{Z}}_{\mathbf{2}}^{\mathbf{\text{'}}}\mathbf{=}{\mathit{Z}}_{\mathbf{2}}{\left(\frac{N_1}{N_2}\right)}^{\mathbf{2}}$ ……. (3)

Write the formula of active power

$\mathit{P}\mathbf{=}\mathit{S}\mathbf{·}\mathit{p}\mathit{f}$ ……. (4)

Write the formula of active power

$\mathit{Q}\mathbf{=}\mathit{S}\mathbf{·}\mathit{s}\mathit{i}\mathit{n}\left(co{s}^{-1}pf\right)$ ……. (5)

Determine the primary voltage.

(a)

Determine the primary voltage.

Substitute $230V$for $V_2,2400for{N}_{1}and240for{N}_2$in equation (1).

$$\begin{gathered} \frac{230}{v_1}=\frac{240}{2400} \\ {v}_1=2300V \end{gathered}$$

Determine the load impedance.

(b)

Determine the load impedance

Substitute $110kVA$for S and $230Vfor{V}_2$in equation (2).

$$\begin{gathered} 110\times {10}^3=230\times \left(\frac{230}{Z_2}\right) \\ {Z}_2=\frac{230\times 230}{110\times {10}^3} \\ {Z}_2=0.48\Omega \end{gathered}$$

Determine the secondary load impedance referred to the primary.

(c)

Determine the load impedance referred to primary.

Substitute $0.48\Omega$for $Z_2$, 2400 for $N_1$and 240 for $N_2$ in equation (3).

$$\begin{gathered} Z_2\text{'}=0.48\Omega \times {\left(\frac{2400}{240}\right)}^2 \\ {Z}_2\text{'}=48\Omega \end{gathered}$$

Determine the real and reactive power.

(d)

As the ideal transformer is considered, the real and reactive powers of primary and secondary windings will be same.

Determine the active power at primary side.

Substitute $110kVA$for S and 0.8 for $p·f$in equation (4).

$$\begin{gathered} P=110\times 0.8 \\ =88kW \end{gathered}$$

Determine the reactive power at primary side.

Substitute $110kVA$for S and 0.8 for $p·f$in equation (5).

$$\begin{gathered} Q=110\times \sin \left({\cos }^{-1}0.8\right) \\ =110\times 0.6 \\ =66kVAR \end{gathered}$$

By the given data, the power factor is leading, hence $Q=-66kVAR$.