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A 667 MVA transformer has an efficiency of 99.3 percent when it delivers full power to a load having a power factor of ____.

Answer :

a) Losses in the transformer under the conditions of delivering full power to a load with a power factor of 100%:

Losses ≈ 0.519 MVA

b) Losses and efficiency when the transformer delivers 66.7 MVA to a load with a power factor of 80%:

Losses ≈ 0.395 MVA

Efficiency ≈ 99.246%

Let's break down the problem step by step.

a) To calculate the losses in the transformer under the given conditions:

Given:

Transformer rating (S) = 66.7 MVA

Efficiency (η) = 99.3% = 0.993 (in decimal)

Efficiency is given by the formula:

[tex]\eta=\frac{outpupower}{inpupower}[/tex]

Since the transformer is delivering full power to a load with a power factor of 100%, the apparent power (S) is equal to the real power (P).

So, the output power (P) = 66.7 MVA

Now, let's rearrange the efficiency formula to find the input power (P_in):

[tex]$\begin{aligned} & P_{i n}=\frac{P}{\eta} \\ & P_{\text {in }}=\frac{66.7 \mathrm{MVA}}{0.993} \\ & P_{\text {in }} \approx 67.219 \mathrm{MVA}\end{aligned}$[/tex]

The losses in the transformer can be calculated as the difference between the input power and the output power:

[tex]$\begin{aligned} & \text { Losses }=P_{i n}-P \\ & \text { Losses }=67.219 \mathrm{MVA}-66.7 \mathrm{MVA} \\ & \text { Losses } \approx 0.519 \mathrm{MVA}\end{aligned}$[/tex]

b) Now, let's calculate the losses and efficiency when the transformer delivers 66.7 MVA to a load having a power factor of 80 percent.

Given:

Power factor (pf) = 0.80

First, we need to find the real power (P) delivered to the load:

[tex]$P=S \times$ Power factor$$\begin{aligned}& P=66.7 \mathrm{MVA} \times 0.80 \\& P=53.36 \mathrm{MW}\end{aligned}$$[/tex]

Now, we can find the input power (P_in) using the efficiency formula:

[tex]$\begin{aligned} & P_{\text {in }}=\frac{P}{\eta} \\ & P_{\text {in }}=\frac{53.36 \mathrm{MW}}{0.993} \\ & P_{\text {in }} \approx 53.755 \mathrm{MW}\end{aligned}$[/tex]

The losses in the transformer can be calculated as before:

[tex]Losses $=P_{\text {in }}-P$\\Losses $=53.755 \mathrm{MW}-53.36 \mathrm{MW}$\\Losses $\approx 0.395 \mathrm{MW}$\\[/tex]

Finally, we can calculate the efficiency:

[tex]$\begin{aligned} \eta & =\frac{P}{P_{i n}} \\ \eta & =\frac{53.36 \mathrm{MW}}{53.755 \mathrm{MW}} \\ \eta & \approx 99.246 \%\end{aligned}$[/tex]

Complete question is here:

A 66.7 MVA transformer has an efficiency of 99.3 percent when it delivers full power to a load having a power factor of 100 percent. a. Calculate the losses in the transformer un- 10-25 der these conditions. b. Calculate the losses and efficiency when 10-30 the transformer delivers 66.7 MVA to a load having a power factor of 80 percent.

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Rewritten by : Barada