Voltage Change and Flicker Formulas

Voltage change formulas: step change from a load, the dip as the ratio of load to short-circuit level, and the short-circuit level from the fault current.

The formulas

V is the line-to-line voltage in volts, R and X the resistance and reactance of the supply in ohms per phase, ΔP and ΔQ the step in real and reactive power (three-phase, in W and VAR), ΔS the step in apparent power and Ssc the short-circuit level at the same point in the same units as ΔS. The formulas are first-order estimates for a small step. A load that starts often or varies quickly causes flicker, and the limit on the voltage change depends on how often it repeats and on the utility or the standard that applies (for example IEC 61000-3-3 and IEC 61000-3-11), so use your own limit.

Worked example: a load step on an 11 kV supply

A step of 200 kW and 100 kVAR on a supply with R = 0.5 Ω and X = 2 Ω.

1. ΔV/V = (0.5 × 200,000 + 2 × 100,000) / 11,000² = 0.002479
2. That is a voltage change of 0.2479%

Worked example: the ratio of the step to the short-circuit level

A 0.5 MVA step on a point with a short-circuit level of 50 MVA.

1. ΔV/V ≈ 0.5 / 50 = 1%

Worked example: short-circuit level from the fault current

A fault current of 10 kA at 11 kV.

1. Ssc = √3 × 11,000 × 10,000 = 190.5 MVA

Voltage change for steps on a 50 MVA supply

Frequently asked questions

What is the difference between a voltage dip and flicker?

A dip is one drop in voltage, such as during a motor start. Flicker is the effect of repeated small changes on the light from a lamp, and the limit depends on how often the changes occur.

Why does a stiff supply help?

A higher short-circuit level means a lower supply impedance, so the same step in load causes a smaller change in voltage.

When is the ratio ΔS / Ssc accurate?

When the supply reactance is much larger than its resistance, which is typical for a transformer or a high-voltage network. Use the full formula with R and X for a cable or a small supply.

Does this cover a motor start?

Yes, as a first estimate: use the starting kVA as ΔS. The motor starting article gives the dip for a motor on a given supply.

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