A dip is a time event
Short voltage sags can affect contactors and drive ride-through as well as motor torque. Event duration and recovery matter, not just minimum voltage.
Electrical Engineering
Motor Sensitivity Calculator
Compare induction-motor torque margin under simultaneous voltage and load-torque changes using a transparent voltage-squared screening relation.
MOTOR VOLTAGE SENSITIVITY
See how a voltage dip and a process-torque increase can collapse motor margin together
This two-state induction-motor screen adjusts available torque approximately with the square of terminal-voltage ratio and changes process torque independently. It is useful for identifying adverse scenarios that need a full speed-torque, voltage-drop, VFD, or acceleration study.
Scenario torque factor—
Baseline torque factor—
Torque-factor change—
Scenario available torque (N·m)—
Scenario load torque (N·m)—
Scenario voltage ratio—
MOTOR VOLTAGE SENSITIVITY
Motor voltage-and-load sensitivity ledger
Use a low scenario factor as a trigger for terminal-voltage measurement, feeder voltage-drop analysis, full motor/load torque-speed curves, contactor ride-through, VFD current-limit review, or process mitigation.
| State | Terminal voltage | Load torque | Available torque | Torque factor | Interpretation |
|---|
CURRENT CALCULATION PROCESS
Formula, current substitution, intermediate values, and reconciliation
T_available,scenario ≈ T_available,base(V_scenario/V_base)²; F = T_available/T_load
The base available torque is derived from rated power, speed, service factor, and constant temperature allowance. Scenario voltage changes available induction-motor torque by an approximate squared ratio, while process change alters load torque.
| Symbol | Engineering meaning | Unit | Default |
|---|---|---|---|
| P_rated | Rated shaft output | kW | 45 |
| n | Compared operating speed | rpm | 1480 |
| SF | Applicable service factor | ratio | 1.1 |
| V_base | Baseline motor-terminal voltage | V | 400 |
| V_scenario | Scenario motor-terminal voltage | V | 360 |
| T_load,base | Baseline process torque | N*m | 250 |
| delta_load | Scenario load-torque change | % | 10 |
Intermediate values remain unrounded until display formatting.
HOW TO USE THIS MODEL
Build a credible adverse operating state
- Use motor-terminal voltage rather than upstream bus voltage when cable drop is material.
- Enter base process torque at the reviewed speed and boundary.
- Choose scenario voltage from a measured event or power-system study, not a guessed percentage.
- Change process torque separately to represent buildup, pressure, throughput, or friction.
- If scenario margin is small, replace this screen with complete motor and load torque-speed curves plus acceleration and thermal checks.
MOTOR VOLTAGE SENSITIVITY FUNDAMENTALS
Sensitivity concepts for induction motors
- Voltage-squared relation
- At fixed frequency and within a screening range, induction-motor torque capability is often approximated as proportional to voltage squared.
- Terminal voltage
- The motor sees voltage after transformer, feeder, starter, and cable drops.
- Load-torque curve
- Driven-equipment torque may be constant, speed-dependent, or process-dependent.
- Torque factor
- Available motor torque divided by process torque at the same shaft speed.
- Combined scenario
- Lower voltage reduces available torque while higher process load raises required torque.
- Frequency boundary
- The voltage-squared approximation does not describe arbitrary V/Hz or field-weakening control.
MODEL AND FORMULA
Two independent levers in one torque ratio
T_available,scenario ≈ T_available,base(V_scenario/V_base)²; F = T_available/T_load
The base available torque is derived from rated power, speed, service factor, and constant temperature allowance. Scenario voltage changes available induction-motor torque by an approximate squared ratio, while process change alters load torque.
DEEPER ENGINEERING ANALYSIS
Interpreting voltage sensitivity responsibly
Acceleration can be the critical state
Lower accelerating torque lengthens acceleration, increasing rotor heating and feeder voltage drop. A stable running point can still fail during restart.
VFD motors need a drive model
Current limits, torque control, DC-bus voltage, V/Hz, low-speed cooling, and field weakening can dominate; use drive-specific capability curves.
WORKED DECISION CASES
Adverse scenarios worth screening
Weak-feeder restart
A large motor restarts while neighboring loads remain online. The scenario uses motor-terminal voltage from a study and increased breakaway process torque to flag acceleration risk.
Process buildup at low voltage
A mixer accumulates material as site voltage drifts low. The combined case shows a much larger loss of torque factor than either input change alone.
TECHNICAL LANGUAGE
Motor sensitivity vocabulary
- Voltage sag
- Temporary reduction in RMS voltage over a defined duration.
- Accelerating torque
- Motor torque minus load torque available to increase speed.
- Torque-speed curve
- Relationship between developed torque and rotor speed.
- Terminal voltage
- Voltage measured at motor terminals during the event.
- Ride-through
- Ability of equipment to remain operating through a disturbance.
- Field weakening
- Control region where flux is reduced above base speed, limiting torque.
EVIDENCE AND DATA LINEAGE
Records for an adverse-voltage study
Retain motor and drive identification, nameplate, torque-speed curve, base and event terminal-voltage traces, event duration, feeder model, process torque source, speed, service-factor conditions, temperature allowance, contactor/VFD behavior, and scenario timestamps.
LIMITS AND EXCLUSIONS
Scope of the voltage-squared screen
- The relation is approximate and intended for induction-motor screening at fixed frequency.
- It does not model starting current, acceleration time, inertia, transient sag recovery, contactor dropout, protective trips, VFD control, or thermal accumulation.
- Service factor and temperature allowance are held constant across states; event-specific thermal or cooling changes are excluded.
RELIABLE SOURCES
References for this page's method and boundaries
FREQUENTLY ASKED QUESTIONS
Voltage-and-torque scenario questions
Is torque always exactly proportional to voltage squared?
No. It is a screening approximation for induction motors at fixed frequency and a comparable operating region. Detailed equivalent-circuit or manufacturer curves are more authoritative.
Can I use upstream switchboard voltage?
Only if feeder drop is negligible or modeled. Motor-terminal voltage is the relevant value for developed torque.
Does the page calculate starting time?
No. Starting time requires motor/load torque-speed curves, combined inertia, voltage during acceleration, and thermal limits.
How should a VFD-driven motor be treated?
Use drive and motor capability data. VFD current limit, control mode, V/Hz, DC bus, speed, and cooling can invalidate this simple relation.
Why change load torque separately from voltage?
Process conditions can change at the same time as an electrical event. Keeping them separate shows which assumption creates the margin loss.
Can a negative load change improve the factor?
Yes mathematically, but the scenario must represent a real process state and remain above the minimum allowed demand.
RELATED CALCULATORS
Continue the electrical engineering review
Use the next model to test a separate operating boundary without hiding it inside this result.
IMPORTANT ENGINEERING NOTE
Use full curves before authorizing operation through a sag
A qualified engineer should evaluate the power system, motor, starter or VFD, driven-load curve, acceleration, protection, controls, thermal limits, and event duration. This scenario ratio alone cannot establish ride-through or safe operation.