Motor Starting Voltage Dip

The constant-impedance method for the bus dip and the motor terminal voltage while a motor starts.

1. What this check does

Builds the source and transformer impedance to the motor bus, adds the existing load as a fixed impedance and the starting motor as its locked-rotor impedance behind the feeder, and solves the voltage divider. It reports the bus voltage before and during the start, the dip other loads see, and — for across-the-line starting — the motor terminal voltage and the share of locked-rotor torque it leaves.

2. Inputs used

Motor bus voltage; utility short-circuit MVA and X/R, or an infinite bus; optional transformer kVA, %Z and X/R.
Optional load already on the bus (kVA and power factor) and the feeder to the motor (length, R and X per conductor, parallel sets).
Motor output (hp or kW), efficiency, running power factor, starting method with its locked-rotor multiple, autotransformer tap or current limit, and starting power factor.
Criteria: maximum bus dip and minimum motor voltage while starting.

3. Formulas and assumptions

Impedances on the motor bus voltage

Source, transformer

Z_Q = \dfrac{V^2}{S_{sc}} \qquad Z_T = \dfrac{z\%}{100}\,\dfrac{V^2}{S_T} \qquad Z_s = Z_Q + Z_T

R = |Z|/√(1 + (X/R)²), X = R·X/R. Feeder Z_c = (R + jX)·length / parallel sets.

Starting motor

Z_M = \dfrac{V^2}{S_{\text{start}}}\angle\arccos \mathrm{PF}_s, \qquad S_{\text{start}} = k_{\text{start}}\,\dfrac{P}{\eta\,\mathrm{PF}}

k_start = LR (DOL), LR/3 (star-delta), LR·tap² (autotransformer), current limit (soft starter, VFD).

Existing load

Z_L = \dfrac{V^2}{S_{\text{pre}}}\angle\arccos \mathrm{PF}_{\text{pre}}

Voltages

Before

V_0 = \left|\dfrac{Z_L}{Z_s + Z_L}\right|

During

V_b = \left|\dfrac{Z_p}{Z_s + Z_p}\right|, \qquad Z_p = Z_L \parallel (Z_c + Z_M)

Motor

V_m = V_b\left|\dfrac{Z_M}{Z_c + Z_M}\right| \qquad T \approx V_m^2\,T_{LR}

Dip

\Delta V\% = \dfrac{V_0 - V_b}{V_0}\times 100

Compared with the maximum bus dip; Vm with the minimum motor voltage.

Symbols

$V$	Motor bus line-to-line voltage	V
$S_{sc},\ S_T,\ z\%$	Utility short-circuit power; transformer rating and impedance	MVA, kVA, %
$Z_s,\ Z_c$	Source-plus-transformer impedance; feeder impedance	Ω
$Z_M,\ Z_L$	Starting motor impedance; existing load impedance	Ω
$P,\ \eta,\ \mathrm{PF}$	Motor rated output, efficiency, running power factor	kW, —, —
$S_{\text{start}},\ \mathrm{PF}_s,\ k_{\text{start}}$	Line-side starting kVA, starting power factor, starting multiple	kVA, —, —
$V_0,\ V_b,\ V_m$	Bus voltage before and during the start; motor terminal voltage	per unit
$T,\ T_{LR}$	Available starting torque; locked-rotor torque at rated voltage	%

The starting motor is a constant impedance drawing its starting kVA at rated voltage and the starting power factor; at lower voltage its current falls in proportion, which is how a locked rotor behaves.
Line-side starting kVA multiples: across-the-line = locked-rotor multiple, star-delta = one third of it, autotransformer = multiple × tap², soft starter and VFD = the current limit. With a reduced-voltage starter only the line side is assessed.
Available starting torque scales with the square of the motor voltage (V² × locked-rotor torque).
The existing load is a constant impedance, and the dip is measured against the bus voltage just before the start.
Default criteria are RokBench assumptions: 10 % bus dip and 80 % motor voltage while starting. Use your project, utility and equipment criteria.

4. What is NOT checked

Acceleration time and the motor and load torque curves (a dynamic motor-starting study).
Transformer tap changers, voltage regulators and capacitor switching during the start.
Generator sources — the transient reactance and voltage regulator govern there (see Emergency Generator Sizing).
Flicker limits for repeated starts and utility point-of-common-coupling requirements.

5. Reference standards

Pointers only; consult the edition adopted by your authority having jurisdiction.

IEEE Std 399 (Brown Book) and IEEE Std 3002.7 — motor-starting studies
NEMA MG 1 — motor performance at reduced voltage, locked-rotor code letters
IEEE Std 1453 / IEC 61000-3-3 — voltage fluctuation and flicker
NEC 2023 Article 430 — motor circuits (context)

6. Validation cases

These worked examples run through the engine on every change; the expected values come from the cited source. All cases: Validation.

150 kW motor started across the line on a 1500 kVA, 5.75 % Z transformer motor/starting · Hand calculation

Pass

Source: Hand calculation from the constant-impedance equations on the Methods page — Zt = 0.0575 · 480² / 1.5 MVA = 8.832 mΩ at X/R 6 (R 1.452, X 8.712 mΩ). Running 150/(0.95·0.88) = 179.4 kVA, starting 6 × = 1076.6 kVA → Zm = 480²/1076.6 kVA = 0.21401 Ω at PF 0.3 (R 64.20, X 204.15 mΩ). V = |Zm|/|Zt + Zm| = 0.21401/0.22276 = 0.9607 → dip 3.93 %; torque ≈ 0.9607² = 92.3 % of locked-rotor.

Quantity	Expected	RokBench	Error	Result
startingKva	1076.6	1076.6	0%	Pass
busDuringPercent	96.07	96.07	0%	Pass
busDipPercent	3.93	3.93	0%	Pass
torquePercentOfLocked	92.3	92.3	0%	Pass

7. Known issues and changes

See the Changelog. Try the tool: Motor Starting Voltage Dip.