Transformer Extended
Efficiency, copper loss and voltage regulation
Calculation
Quick Introduction
Real transformer performance is influenced by copper and core losses. Under load, secondary voltage drops, which is quantified by voltage regulation.
This extended page complements the classic transformer calculator with practical quality metrics.
Sizing schema:
1) Estimate losses at operating point
2) Compute efficiency
3) Verify load voltage regulation
Formulas (MathJax)
\[\eta = \frac{P_{out}}{P_{out}+P_{Cu}+P_{Fe}+P_{add}}\cdot100\%\]
\[P_{Cu}=k_{ph}\,I^2R_w,\quad k_{ph}=1\;\text{(1-ph)},\;3\;\text{(3-ph)}\]
\[Reg\,[\%]=\frac{U_0-U_{load}}{U_{load}}\cdot100\]
\[P_{in}=P_{out}+P_{loss}\]
Symbol Legend
- \(P_{out}\): output power [W]
- \(P_{Cu}\): copper loss [W]
- \(P_{Fe}\): core loss [W]
- \(P_{add}\): additional losses [W]
- \(I\): winding current [A]
- \(R_w\): winding resistance [Ω]
- \(U_0\): no-load voltage [V]
- \(U_{load}\): load voltage [V]
Examples
Efficiency: \(P_{out}=1000\,W\), \(P_{Cu}=35\,W\), \(P_{Fe}=20\,W\), \(P_{add}=5\,W\) ⇒ \(\eta\approx94.34\%\).
Copper loss: \(I=8\,A\), \(R_w=0.35\,\Omega\), single-phase ⇒ \(P_{Cu}=22.4\,W\).
Regulation: \(U_0=230\,V\), \(U_{load}=220\,V\) ⇒ \(Reg\approx4.55\%\).
Detailed Description & Summary
This extended calculator supports practical transformer assessment. While the classic transformer page focuses on turns ratio and voltage/current conversion, this page adds efficiency and quality evaluation under load.
Copper losses scale with current squared, while core losses are mainly linked to material and frequency. Lower voltage regulation means better output stability.
Summary
- Efficiency from output power and loss terms
- Copper loss via \(I^2R\) for single/three-phase context
- Voltage regulation from no-load and load voltage
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