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Base Impedance (Per-Unit System)
Defines the reference impedance used to convert power system quantities into the per-unit system.
Interpretation
Base impedance in the per‑unit system is Z_base = V_base² / S_base.
It provides a reference impedance for normalising system parameters.
Example: V_base=11kV, S_base=100MVA → Z_base = (11,000)² / 100,000,000 = 1.21Ω.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Z_base | Base impedance | Ω |
| V_base | Base voltage (line-to-line RMS) | kV |
| S_base | Base apparent power (three-phase) | MVA |
What it means
In the per‑unit system, quantities are expressed as fractions of base values. Base impedance is defined as Z_base = V_base² / S_base, where V_base is the base voltage and S_base is the base power. This allows normalisation of impedances and simplifies calculations in power systems with multiple voltage levels. The per‑unit system eliminates the need for transformer ratios and makes it easier to compare equipment ratings. It is widely used in power system analysis, fault calculations, and protective relay coordination. The base values are chosen arbitrarily but should reflect the system’s nominal voltage and power. Example: For a system with V_base = 11 kV and S_base = 100 MVA, Z_base = (11,000)² / 100,000,000 = 121,000,000 / 100,000,000 = 1.21 Ω. An actual impedance of 2.42Ω would be 2.42/1.21 = 2.0 per unit.
Worked example
Base Impedance – Practical Example
Real‑World| Parameter | Value |
|---|---|
| Vbase | 11 kV |
| Sbase | 100 MVA |
| Formula | Zbase = Vbase² / Sbase |
Common mistakes
- V_base: The base voltage (line‑to‑line for three‑phase systems).
- S_base: The base apparent power (usually MVA or kVA).
- Units: Ensure V_base and S_base use consistent units (e.g., kV and MVA).
- Per‑unit system: Normalises quantities for easier analysis.
- Transformer: Base impedance changes when crossing transformer boundaries.
Applications
Base impedance in the per‑unit system is Z_base = V_base²/S_base, providing a reference for normalising parameters. The per‑unit system simplifies the analysis of power systems by eliminating transformer ratios and allowing comparison of equipment of different ratings. Engineers use it for load flow, fault analysis, and stability studies. By using per‑unit values, they can avoid mistakes and focus on the relative values. Understanding base impedance is essential for working with the per‑unit system, which is standard in power system analysis. This formula is a key part of system modelling.
- Power system modelling using per‑unit system
- Load flow analysis and fault studies
- Transformer and generator data representation
- Standardised comparison of equipment ratings
- Educational foundation of per‑unit calculations
Frequently Asked Questions
Base impedance is defined as Z_base = V_base² / S_base, where V_base is the base voltage and S_base is the base power. It is used to convert actual impedances to per-unit values.
It simplifies calculations, makes transformers transparent, and allows comparison of equipment of different ratings.
Z_pu = Z_ohm / Z_base, where Z_base = V_base² / S_base (single-phase) or V_base² / S_base (three-phase, with line-to-line voltage).
They are chosen arbitrarily; for a power system, common base values are 100 MVA and the nominal voltage of the system.
The per-unit impedance remains the same on both sides of an ideal transformer, eliminating the turns ratio from calculations.
Subtransient: 0.1-0.2 pu; transient: 0.2-0.3 pu; synchronous: 1.5-2.5 pu (for large generators).
Z_pu_new = Z_pu_old × (V_base_old/V_base_new)² × (S_base_new/S_base_old).
Use line-to-line voltage and three-phase power as bases; the formulas are consistent if all quantities are per-phase or per-phase.
It requires careful selection of bases and is only valid for linear systems; non-linearities must be handled separately.
Common errors include: 1) using the wrong base values, 2) mixing up line and phase quantities, 3) forgetting to convert impedances, 4) applying to non-linear systems, and 5) using the wrong transformer tapping.