←
Lesson 47 · Sag and fault
The same percent, twice
score 0

The same percent, twice

Every transformer has impedance in its own windings, and the nameplate states it as percent impedance, %Z\%Z. Read the definition carefully, because everything else follows from it: %Z\%Z is the percentage of rated voltage you must apply to the primary, with the secondary shorted, to push RATED current through. A 5% unit needs 5% of rated volts to make 100% of rated amps.

At working loads that impedance costs you a few volts: Vd=%Z100⋅SLSR⋅VRV_d = \dfrac{\%Z}{100}\cdot\dfrac{S_L}{S_R}\cdot V_R, where VdV_d is the drop inside the windings in volts, SLS_L is the actual load and SRS_R the transformer's rating (both kVA, so the ratio is bare), and VRV_R is the rated secondary voltage. The ratio SL/SRS_L/S_R is simply how much of the nameplate you are using — at full load it is 1, and the drop is the full %Z\%Z of rated volts.

Measure that same droop instead of predicting it, and you have voltage regulation: %VR=100(Vnl−Vfl)Vfl\%VR = \dfrac{100(V_{nl} - V_{fl})}{V_{fl}}, where VnlV_{nl} is the terminal voltage with the load off and VflV_{fl} the voltage at rated load, both in volts. The base is the FULL-LOAD reading — the loaded terminal, the one your equipment actually lives on.

Now short the secondary and read the same nameplate the other way. If %Z\%Z of rated voltage drives rated current, then full rated voltage drives 100%Z\dfrac{100}{\%Z} times rated current: ISC=100 IFL%ZI_{SC} = \dfrac{100\, I_{FL}}{\%Z}. A 5% transformer can deliver twenty times its rated current into a bolted fault. That is the number a panel's interrupting rating has to beat, and note the direction it runs — a LOWER impedance means a HIGHER fault current, which is why the stiffest transformers are the ones that need the most expensive gear behind them.

VnlVfl%VR

%VR=100 (Vnl−Vfl)Vfl\%VR = \frac{100 \, (V_{nl} - V_{fl})}{V_{fl}}

  • %VR\%VR= Voltage regulation (concentration)
  • VnlV_{nl}= No-load voltage (voltage)
  • VflV_{fl}= Full-load voltage (voltage)
Voltage Regulation solver →
SL%ZSRVdVR

Vd=%Z100⋅SLSR⋅VRV_{d} = \frac{\%Z}{100} \cdot \frac{S_{L}}{S_{R}} \cdot V_{R}

  • VdV_{d}= Impedance voltage drop (voltage)
  • %Z\%Z= Percent impedance (concentration)
  • SLS_{L}= Actual load (kVA) (power)
  • SRS_{R}= Transformer rating (kVA) (power)
  • VRV_{R}= Rated secondary voltage (voltage)
Transformer Percent-Impedance Voltage Drop solver →
ISCIFL%Z

ISC=100 IFL%ZI_{SC} = \frac{100 \, I_{FL}}{\%Z}

  • ISCI_{SC}= Available short-circuit current (electric current)
  • IFLI_{FL}= Full-load current (electric current)
  • %Z\%Z= Percent impedance (concentration)
Available Short-Circuit Current from Percent Impedance solver →