Advanced Calculator
Impedance Component Graph
Example Data Table
| Case | |Za| Ω | ∠Za | |Zb| Ω | ∠Zb | |Zc| Ω | ∠Zc | Use |
|---|---|---|---|---|---|---|---|
| Transmission line | 5.00 | 12° | 5.30 | -108° | 4.90 | 132° | Balanced component review |
| Feeder study | 2.20 | 18° | 2.45 | -102° | 2.30 | 138° | Protection estimate |
| Motor supply | 0.80 | 25° | 0.83 | -95° | 0.78 | 145° | Sequence network model |
Formula Used
The positive sequence operator is: a = 1∠120° and a² = 1∠240°.
Positive sequence impedance is calculated as: Z₁ = (Za + aZb + a²Zc) / 3.
Base impedance is: Zbase = kV² / MVA.
Per unit impedance is: Z₁ pu = Z₁ / Zbase.
Per kilometer impedance is: Z₁ per km = Z₁ / line length.
How to Use This Calculator
Enter the phase impedance magnitudes in ohms.
Enter each phase angle in degrees.
Use normal symmetrical phase spacing when known.
Add base MVA and base kV for per unit output.
Add line length to get impedance per kilometer.
Press the calculate button to view results above the form.
Use CSV for spreadsheet work.
Use PDF for a quick engineering report.
Positive Sequence Impedance Study Guide
Meaning of Positive Sequence Impedance
Positive sequence impedance is a key value in power system analysis. It represents the impedance seen by balanced three phase currents. These currents have equal magnitude. They are separated by 120 electrical degrees. This condition appears in normal operation. It also appears in many fault calculations.
Why Engineers Calculate It
Engineers use this value to build sequence networks. These networks simplify complex unbalanced systems. They are useful for short circuit studies. They also support relay setting checks. A correct value improves protection coordination. It also helps compare system strength at different buses.
Input Quality Matters
The calculator accepts phase impedance magnitudes and angles. Accurate source data gives better results. Cable data, transformer data, and line data should use the same frequency. Units must also remain consistent. Mixing ohms and per unit values can create large errors.
Per Unit Conversion
Per unit conversion is useful for large networks. It places different voltage levels on one common scale. The calculator uses system base MVA and base kV. It then finds base impedance. The positive sequence value is divided by that base value.
Line Length Interpretation
Long feeders often need impedance per kilometer. This makes comparison easier. It also helps estimate voltage drop and fault current changes. Enter the total modeled length. The tool divides the calculated positive sequence impedance by that length.
Using the Results
Review the rectangular result first. The real part shows resistance. The imaginary part shows reactance. Then check magnitude and angle. Use the graph to compare phase components. Export the data when you need documentation or further analysis.
FAQs
What is positive sequence impedance?
It is the impedance seen by balanced three phase currents. These currents have equal magnitude and 120 degree phase separation.
Why is positive sequence impedance important?
It supports load flow, short circuit, relay, and stability studies. It gives the normal balanced network impedance.
What does the operator a mean?
The operator a is a complex rotation of 120 degrees. It shifts phase quantities during symmetrical component calculation.
Can I use cable impedance values?
Yes. Enter cable phase impedance magnitudes and angles. Make sure all values use ohms and the same frequency base.
What is per unit impedance?
Per unit impedance is normalized impedance. It uses selected base voltage and base power for easier network comparison.
Can this calculator estimate fault current?
It gives a basic fault current estimate from fault MVA and base kV. Detailed studies need full network data.
What happens with balanced inputs?
Balanced inputs usually produce a clean positive sequence value. Negative and zero sequence effects become much smaller.
Can I export the result?
Yes. Use the CSV button for spreadsheet use. Use the PDF button for a simple saved report.