Copper losses (also known as I²R losses) occur in the windings of a transformer due to the flow of current. They're proportional to the square of the current. Full-load copper losses are the losses that occur when the transformer is operating at its rated capacity.
Given Data:
$$ Z_{eq}=10.4+j 31.3 \Omega $$
Step 1: Compute Full-Load Current on HV Side The full-load current on the high-voltage (HV) side is:
$$ \begin{aligned} I_{FL} & =\frac{S_{rated}}{V_{HV}} \\ I_{FL} & =\frac{10,000}{2200} \\ I_{FL} & =4.545 A \end{aligned} $$
Step 2: Compute Full-Load Copper Loss Copper loss is calculated using:
$$ P_{cu}=I_{FL}^2 \times R_{eq} $$
where $R_{\text {eq }}$ is the real part of $Z_{\text {eq }}$, which is $10.4 \Omega$.
$$ \begin{gathered} P_{cu}=(4.545)^2 \times 10.4 \\ P_{cu}=20.66 \times 10.4 \\ P_{cu}=214.86 W \end{gathered} $$
Step 3: Convert to Per Unit (p.u.) The per unit (p.u.) copper loss is:
$$ \begin{gathered} P_{cu, \text { p.u. }}=\frac{P_{cu}}{S_{base}} \\ P_{cu, \text { p.u. }}=\frac{214.86}{10,000} \\ P_{cu, \text { p.u. }}=0.0215 \text { p.u. } \end{gathered} $$
Final Answer:
The correct full-load copper loss in per unit value is 0.0215 p.u.
Here’s a general Python solution to compute the full-load copper loss in per unit (p.u.) for any given transformer parameters.
https://gist.github.com/viadean/d22040f1ecc811bfebd3ce9ddf4a1871
How It Works: