Calculates system base quantities (Base Current, Base Impedance, Base Admittance) and normalizes equipment impedance, voltage, current, and apparent power into dimensionless per-unit (pu) values. Eliminates turns ratios across multi-voltage step-up and step-down transformers.
Governing Formulas & Standards
Standards Basis: IEEE Std 399 (Brown Book) / IEC 60909
Z_{\text{base}} = \frac{V_{\text{base, LL}}^2}{S_{\text{base, 3}\phi}}, \quad I_{\text{base}} = \frac{S_{\text{base, 3}\phi} \times 10^3}{\sqrt{3} \times V_{\text{base, LL}}}, \quad Z_{\text{pu}} = \frac{Z_{\text{actual}}}{Z_{\text{base}}}
Calculates base impedance in Ohms from line-to-line voltage and 3-phase MVA base, then normalizes physical impedance into dimensionless per-unit.
Worked Engineering Example: Per-Unit Impedance of 17.424 Ω Transmission Line on 100 MVA, 132 kV Base
- Calculate Base Impedance: Z_base = (132 kV)² / 100 MVA = 17,424 / 100 → 174.24 Ω
- Calculate Base Current: I_base = (100 × 1000) / (√3 × 132) → 437.39 A
- Calculate Per-Unit Impedance: Z_pu = 17.424 Ω / 174.24 Ω → 0.10 pu (10.0%)
Final Solution: Z_base: 174.24 Ω | I_base: 437.39 A | Z_pu: 0.1000 pu
Frequently Asked Questions
- Why use the per-unit system in power system studies?
- It simplifies network analysis by removing ideal transformer turns ratios, normalizes parameters for comparison across different manufacturer ratings, and reduces computational roundoff errors.
Interactive calculation engine and real-time CAD solver available online at https://amithvijayan.in/tools/per-unit-calculator.