Motor Starting Analysis: Voltage Dip Calculation and Starting Methods

Published: June 2026
Technical Level: Advanced Category: Industrial Power Systems

Abstract

The direct-on-line starting of a large induction motor draws a current several times its rated value, and the resulting voltage dip on the supplying system can disturb other loads, drop out contactors, and in severe cases prevent the motor from accelerating. This paper develops the analysis of motor starting and the voltage dip it produces, deriving the dip from the motor's locked-rotor current and the source impedance, identifying the limits that equipment sensitivity and contactor hold-in impose, and comparing the principal reduced-voltage and electronic starting methods by which the dip is contained. The objective is to give the engineer the basis for predicting the starting dip of a given motor on a given system and for selecting the starting method that holds the dip within acceptable limits while still delivering the torque the load requires.

1. Motor Starting Fundamentals

An induction motor at the instant of starting presents to the supply an impedance close to its locked-rotor value, far lower than its impedance at running speed, and it therefore draws a starting current that is typically five to seven times its full-load current. This inrush persists until the motor accelerates toward its operating speed, a process that may take from a fraction of a second for a lightly loaded small motor to many seconds for a large motor driving a high-inertia load. Throughout the acceleration the motor draws a current well above its rated value, and the supplying system must carry this current while maintaining enough voltage for the motor to develop the torque needed to accelerate.

The voltage dip arises because the large starting current flows through the impedance of the supply system — the source, the transformer, and the cable feeding the motor — and the voltage drop across that impedance reduces the voltage available at the motor terminals and at every other load on the same bus. The magnitude of the dip is governed by the ratio of the motor's starting current to the available fault current at the bus, which is equivalent to the ratio of the source impedance to the motor's locked-rotor impedance. The voltage at the bus during starting is approximated by:

$V_{dip} = \frac{S_{sc}}{S_{sc} + S_{LR}}$

Where:

$V_{dip}$ is the per-unit voltage remaining at the bus during starting.

$S_{sc}$ is the short-circuit apparent power available at the bus in MVA.

$S_{LR}$ is the locked-rotor apparent power drawn by the motor at starting in MVA.

This relationship makes the governing factor explicit: the dip is determined by the strength of the supply relative to the size of the motor. A motor that is small relative to the short-circuit capacity of its bus produces a negligible dip, while a motor whose locked-rotor demand is a significant fraction of the bus fault capacity produces a deep dip. The first step in any motor-starting study is therefore to compare the motor's locked-rotor demand with the short-circuit strength of the bus, because that comparison determines whether a reduced-voltage starting method is necessary at all.

2. Voltage Dip Impact Assessment

The acceptability of a starting dip is judged against the sensitivity of the equipment that shares the affected bus. A voltage dip that the starting motor itself can tolerate may nonetheless be unacceptable because of its effect on other loads. Electromagnetic contactors and relays are particularly vulnerable: a contactor holds its load only while its coil voltage remains above a dropout threshold, and a starting dip that depresses the bus voltage below that threshold will drop out contactors throughout the facility, tripping running motors and processes that have nothing to do with the motor being started. The contactor dropout threshold is therefore frequently the binding constraint on the allowable dip, more restrictive than the starting motor's own torque requirement.

Other consequences of the dip include the perceptible flicker of lighting, which the starting of a large motor can produce if it occurs frequently, and the disturbance of voltage-sensitive electronic loads. The starting motor itself imposes a further constraint: the torque an induction motor develops varies with the square of the terminal voltage, so a deep dip reduces the available starting torque sharply, and if the dip is severe enough the motor may be unable to develop the torque needed to accelerate its load, stalling at low speed while drawing locked-rotor current indefinitely. The voltage dip study must therefore confirm both that the dip does not disturb the rest of the system beyond acceptable limits and that enough voltage remains at the motor terminals for it to accelerate its load.

3. Starting Methods

Where direct-on-line starting produces an unacceptable dip, a reduced-voltage starting method limits the starting current at the cost of reduced starting torque. The classical electromechanical methods reduce the voltage applied to the motor during starting. Wye-delta starting connects the motor windings in wye during starting, applying a reduced voltage to each winding and drawing roughly a third of the direct-on-line current, then reconnects them in delta for running; it is simple and inexpensive but provides correspondingly reduced starting torque and imposes a transient at the transition. Autotransformer starting applies a tapped fraction of the full voltage during starting and offers a choice of taps to trade starting current against starting torque, providing more flexibility than the fixed wye-delta ratio.

The electronic methods provide smoother and more controllable starting. A solid-state soft starter uses thyristors to ramp the voltage applied to the motor gradually from a low value to full voltage, controlling the starting current and acceleration smoothly and avoiding the transition transient of the electromechanical methods. The variable-frequency drive provides the most complete control: by supplying the motor with a voltage and frequency that rise together from a low value, it can accelerate the motor at near-rated torque while drawing little more than rated current, essentially eliminating the starting dip, and it provides speed control during running as well. The cost of the starting methods rises with their capability, from the inexpensive wye-delta and autotransformer methods through the soft starter to the variable-frequency drive, and the selection balances the severity of the dip that must be controlled, the starting torque the load requires, and whether speed control during running is also wanted.

4. Worked Example: Starting a 500 HP Motor on a 2 MVA Source

Consider a 500 HP, 460 V, three-phase induction motor to be started across-the-line on a 480 V bus fed from a 2 MVA, 5.75 percent impedance transformer supplied from a utility source whose contribution is large enough that the transformer impedance dominates the source impedance at the bus. The motor's full-load current is approximately 565 A, its service factor is 1.15, and its nameplate code letter G corresponds to a locked-rotor apparent power of approximately 6.0 to 6.29 kVA per horsepower. The objective is to predict the bus voltage dip at the instant of starting and to compare it against the dropout threshold of the contactors on the bus.

The short-circuit apparent power available at the bus is governed by the transformer impedance. For a 2 MVA transformer at 5.75 percent impedance, the short-circuit apparent power referred to the secondary, neglecting the smaller source impedance, is:

$S_{sc} = \frac{S_{tx}}{Z_{pu}} = \frac{2.0\ \text{MVA}}{0.0575} = 34.8\ \text{MVA}$

Where:

$S_{tx}$ is the transformer base rating in MVA.

$Z_{pu}$ is the transformer per-unit impedance on its own base.

The locked-rotor apparent power of the motor, taking the midpoint of the code-letter G band at 6.15 kVA per horsepower, is:

$S_{LR} = 500\ \text{HP} \times 6.15\ \frac{\text{kVA}}{\text{HP}} = 3{,}075\ \text{kVA} = 3.08\ \text{MVA}$

Where:

$S_{LR}$ is the locked-rotor apparent power drawn at the instant of starting in MVA.

Applying the bus voltage dip relationship developed in Section 1:

$V_{dip} = \frac{S_{sc}}{S_{sc} + S_{LR}} = \frac{34.8}{34.8 + 3.08} = 0.919\ \text{per unit}$

The bus voltage during starting therefore holds at approximately 91.9 percent of nominal, a dip of roughly 8.1 percent. This result must now be judged against the two binding constraints. The first is contactor hold-in: NEMA-rated motor contactors are required to hold their armature down to 85 percent of rated coil voltage, so a bus voltage of 91.9 percent leaves a comfortable margin above the 85 percent dropout threshold, and the starting event will not drop out other running loads on the bus. The second is the starting torque of the motor itself. Because induction motor torque varies with the square of terminal voltage, the torque developed at 91.9 percent voltage is:

$\frac{T_{start}}{T_{rated\text{-}voltage}} = V_{dip}^{2} = (0.919)^{2} = 0.845$

Where:

$T_{start}$ is the starting torque developed at the depressed terminal voltage.

$T_{rated\text{-}voltage}$ is the starting torque the motor would develop at full rated voltage.

The motor develops approximately 84.5 percent of its rated-voltage starting torque, which is acceptable provided the driven load's breakaway and accelerating torque requirement is met with that margin. For this system the conclusion is that across-the-line starting is acceptable: the 8.1 percent dip neither drops out bus contactors nor depresses the starting torque below a workable level. Had the same motor been applied to a 1 MVA transformer, the short-circuit power would fall to 17.4 MVA, the dip relationship would yield a remaining voltage of $17.4 / (17.4 + 3.08) = 0.850$ per unit — exactly at the contactor dropout threshold — and a reduced-voltage starting method would then be required to restore margin. This sensitivity to source strength is the reason the motor-starting study must always begin with the short-circuit capacity of the specific bus on which the motor is applied.

5. Conclusion

The starting of a large induction motor draws several times its rated current and produces a voltage dip whose depth is set by the ratio of the motor's locked-rotor demand to the short-circuit strength of the supplying bus. The acceptability of the dip is judged not only against the starting motor's own torque requirement but against the sensitivity of the equipment sharing the bus, with contactor dropout frequently the binding constraint, and against the flicker and disturbance the dip imposes on other loads. Where direct-on-line starting produces an unacceptable dip, the engineer selects a reduced-voltage or electronic starting method — wye-delta, autotransformer, soft starter, or variable-frequency drive — trading cost and complexity against the control of starting current and the preservation of starting torque. The motor-starting study, by predicting the dip and confirming it against these limits, determines whether reduced-voltage starting is required and which method delivers the necessary control.

Related Work

The analysis in this paper connects to several companion studies in this library. Readers concerned with the upstream and downstream engineering will find Motor Starting Voltage Dip Mitigation develops a closely related aspect of the same problem, while Industrial Facility Power Distribution extends the treatment into an adjacent domain. For the broader methodological context, Short-Circuit Analysis provides complementary depth.

The dependence of the starting voltage dip on source strength is shown in Figure 1, which plots the retained bus voltage against motor locked-rotor MVA for grids ranging from a weak 2 MVA source to a stiff 20 MVA source.

Bus voltage remaining during motor starting as a function of motor locked-rotor MVA, for four source-strength scenarios. The shaded band marks the region below the 0.85 pu contactor dropout threshold.

Figure 1. Bus voltage remaining during motor starting as a function of motor locked-rotor MVA, for four source-strength scenarios. The shaded band marks the region below the 0.85 pu contactor dropout threshold.

The figure makes the design margin explicit: on the 2 MVA source the bus voltage approaches the 0.85 pu contactor dropout limit as the motor size grows, whereas the 20 MVA source holds the bus above 0.98 pu across the full range. In practice this is why across-the-line starting of a large motor is acceptable on a stiff bus but requires a reduced-voltage starter, soft starter, or variable-frequency drive when the available short-circuit MVA at the motor terminals is low.

References

[1] IEEE Standard 399-1997, IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis (Brown Book), IEEE, 1997.

[2] IEEE Standard 141-1993, IEEE Recommended Practice for Electric Power Distribution for Industrial Plants (Red Book), IEEE, 1993.

[3] NEMA MG 1-2021, Motors and Generators, National Electrical Manufacturers Association, 2021.

[4] IEEE Standard 3002.7-2018, IEEE Recommended Practice for Conducting Motor-Starting Studies and Analysis of Industrial and Commercial Power Systems, IEEE, 2018.

[5] A. E. Fitzgerald, C. Kingsley, and S. D. Umans, Electric Machinery, 6th ed., McGraw-Hill, 2003.

[6] NFPA 70-2023, National Electrical Code, National Fire Protection Association, 2023.