TOPIC-02 · Engineering guide
Lagging Load Power Factor Correction
The required capacitive vars are P times the drop in tan(acos pf). For 10000 W from 0.8 to 1.0, that is 7500 var. Leading loads are rejected.
Formula, variables and conditions
tan(pf) = sqrt(1 − pf²) / pf Qc = 0 when the power factors are equal; otherwise Qc = P × (tan(pf_before) − tan(pf_target)) Delta branch: C = Qc / (6 × π × f × Vll²) Star branch: C = Qc / (2 × π × f × Vll²) Single-phase: C = Qc / (2 × π × f × V²)
Variables and units
- P: active power in W, greater than 0.
- pf_before and pf_target: greater than 0 and at most 1. The target must not be below the initial value.
- V: system voltage in V. For delta and star it is line-to-line.
- f: frequency in Hz.
- C: capacitance per branch in farads. Multiply by 1e6 for microfarads.
Conditions
- Load direction must be lagging. A leading load returns LEADING_LOAD and no capacitance.
- Resonance, harmonics, switching steps, protection and code compliance are marked not-evaluated.
- SRC-004 stores the Schneider compensation URL. accessedAt on that record is null.
Worked example
Locked TC-006 input: delta connection, 50 Hz, lagging.
- Active power
- 10000 W
- Power factor
- 0.8 to 1.0
- Voltage / frequency
- 400 V line-to-line / 50 Hz
- Connection
- delta
- Required vars
- 7500 var
- Capacitance per delta branch
- 49.735919716217 µF
tan(acos(0.8)) = 0.75 and tan(acos(1)) = 0, so Qc = 10000 × 0.75 = 7500 var. The unit test locks the delta branch farads times 1e6 at 49.735919716217. The same inputs in star use divisor 2 instead of 6, so that branch capacitance is three times the delta value.
Boundaries and common mistakes
Boundaries
- An unchanged target of 0.8 returns exactly 0 var and 0 F.
- A target below 0.8 is rejected.
- This is not a capacitor-bank specification. Discharge, switching and harmonic duty are outside the model.
Common mistakes
- Correcting a leading load with the lagging formula. The calculator rejects that direction.
- Using the single-phase divisor on a line-to-line delta voltage.
- Treating 7500 var as a kilovar equipment rating without checking voltage and steps.