Motor Starting Voltage Drop Analysis

Why Motor Starting Matters

An induction motor at standstill looks like a short circuit with a relatively low impedance. The rotor is stationary, slip is 1.0, and the motor draws locked-rotor current (LRA) that is many times greater than full-load amps (FLA). For a typical NEMA Design B motor, the LRA-to-FLA ratio ranges from about 5.5:1 for smaller motors to 7:1 or higher for larger ones. A 200 HP, 460V motor with an FLA of 240A may draw 1,400 to 1,700A during the first few cycles of starting.

This inrush creates a voltage drop across every impedance element between the source (utility transformer or generator) and the motor. The severity depends on the ratio of motor starting kVA to the available short-circuit kVA at the bus. If the starting kVA is 5% of the available fault capacity, the voltage dip will be roughly 5%. If it is 25% of the available capacity, the dip will be around 20%, which is unacceptable in most facilities.

The consequences of excessive voltage dip extend beyond the starting motor. Other motors on the same bus will experience reduced torque (torque is proportional to voltage squared), potentially stalling loads that were running at high torque. Electromagnetic contactors may drop out if the voltage falls below their hold-in threshold (typically 60-70% of rated voltage). Sensitive electronics, PLCs, and VFDs may fault or reset. In facilities with generators rather than utility supply, the stiffer impedance and limited fault capacity make motor starting analysis even more critical.

Code Letter and Locked-Rotor Amps

Every motor nameplate includes a NEMA code letter that indicates the locked-rotor kVA per horsepower. Code letter A means 0-3.15 kVA/HP (low starting current), while code letters J through V indicate progressively higher starting current per HP. Most standard NEMA Design B motors fall in the code letter F to H range, corresponding to roughly 5.0 to 7.1 kVA/HP. A motor with code letter G (5.6-6.3 kVA/HP) at 100 HP draws 560-630 kVA of starting apparent power.

To convert code letter to locked-rotor amps, use: LRA = (code kVA/HP × HP) / (V × √3 / 1000) for three-phase motors. For a 100 HP, 460V motor at the midpoint of code letter G (5.95 kVA/HP): LRA = (5.95 × 100) / (0.460 × 1.732) = 747A. Compare this to the FLA of roughly 124A, giving a starting-to-running ratio of about 6:1.

If the motor nameplate lists LRA directly (common on motors above 100 HP), use that value instead of calculating from the code letter. Some nameplate data is conservative (worst-case), and actual inrush may be 10-15% lower depending on the terminal voltage at the instant of starting. For voltage drop studies, always use the nameplate or calculated LRA at rated voltage as the starting point, then adjust for the actual voltage during starting using an iterative method or the simplified impedance approach.

Impedance Modeling for Voltage Drop

The voltage drop calculation is fundamentally an impedance divider problem. The motor starting impedance (derived from LRA at rated voltage) is in series with the combined impedance of the supply system (utility source, transformer, cables, bus work). The voltage at the motor terminals equals the source voltage multiplied by the ratio of motor impedance to total circuit impedance.

In per-unit terms on the motor's kVA base: V_motor = Z_motor / (Z_source + Z_motor). Convert each element to a common kVA base. The motor starting impedance in per-unit on its own base is approximately 1/LRA_pu, where LRA_pu is the locked-rotor current in per-unit of FLA. For a motor with 6:1 starting ratio, the starting impedance is about 0.167 pu on the motor base. The source impedance includes the transformer percent impedance (converted to the same base) and cable impedance.

For a simplified hand calculation, the voltage dip at the bus can be estimated as: %V_drop ≈ (Motor starting kVA / (Motor starting kVA + Available short-circuit kVA)) × 100. This is a quick screening check. If the result is borderline (10-15% dip), a more detailed impedance study using actual cable lengths, transformer tap positions, and motor acceleration curves is warranted. IEEE 399 (Brown Book) Chapter 9 provides detailed methodology for motor starting studies, and most facilities use software (ETAP, SKM, EasyPower) for the detailed analysis.

Voltage Drop Calculation Step by Step

Step 1: Determine motor starting kVA. Use the code letter or nameplate LRA. For a 200 HP, 460V motor with code letter G (midpoint 5.95 kVA/HP): starting kVA = 5.95 × 200 = 1,190 kVA.

Step 2: Determine the available short-circuit kVA at the motor terminals. This includes the utility source contribution (transformed through the facility transformer), minus the impedance of cables and switchgear between the transformer secondary and the motor. For a 1,500 kVA transformer with 5.75% impedance fed from an infinite bus, the available fault kVA at the secondary is approximately 1,500 / 0.0575 = 26,087 kVA. If the cable run to the motor MCC adds another 1% impedance on the transformer base, the available kVA at the MCC drops accordingly.

Step 3: Apply the voltage dip formula. %V_drop = 1,190 / (1,190 + 26,087) × 100 = 4.4%. This is within typical limits. However, if the transformer were smaller (750 kVA, 5.75% Z), available kVA drops to 13,043 and the dip becomes 1,190 / (1,190 + 13,043) × 100 = 8.4%, which may trigger contactor dropout on adjacent equipment.

Step 4: Check the voltage at the motor terminals against the motor's ability to develop starting torque. Most motors can start successfully down to about 80% of rated voltage (65% of rated torque). Below 80%, the motor may stall during acceleration, particularly if the load has high inertia or high breakaway torque. For critical loads (fire pumps, compressors), many specifications require a minimum of 85% terminal voltage during starting.

Risk Assessment and Mitigation Options

When the calculated voltage dip exceeds facility limits, several mitigation strategies are available. Reduced-voltage starters (autotransformer, wye-delta, part-winding, or solid-state soft starters) reduce the inrush current by 30-70% depending on the type and tap settings. An autotransformer starter at 65% tap reduces starting current to about 42% of across-the-line LRA and starting torque to about 42% of across-the-line torque. Soft starters offer adjustable current limiting (typically settable from 150% to 500% FLA) with smooth acceleration.

Variable frequency drives (VFDs) eliminate the inrush problem entirely by starting the motor at low frequency and voltage, drawing only about 100-150% FLA during acceleration. However, VFDs introduce harmonic currents, require additional panel space, and cost significantly more than across-the-line starters. They are justified when speed control is needed for the process, not just for starting.

Dedicated transformers or feeders can reduce the impedance between the source and the motor, increasing the available fault kVA at the motor bus. Running a dedicated cable from the MCC to a large motor (rather than daisy-chaining through other loads) reduces the cable impedance contribution. In extreme cases, a dedicated transformer for the large motor or motor group isolates the starting dip from the rest of the facility.

Capacitor banks at the motor terminals or bus can provide reactive power during starting, reducing the current drawn from the upstream system. This is less common in modern practice because soft starters and VFDs address the root cause more effectively, but capacitors remain an option where the existing starter configuration cannot be changed.