This document analyzes two different formulas used to calculate the 3‑phase dynamic braking current of a permanent‑magnet synchronous motor (PMSM / BLDC) during a Dynamic Braking (3‑phase short‑circuit) event.
The motor 3-phase short current needs to be calculated for motor drive-initiated dynamic braking, triggered automatically (i.e. when a limit switch is hit or when a loop error occurs and LEAC (Loop Error Action Condition) is configured to Dynamic Braking) and for Safety Brake Switch (SBS) activation, where the SBS performs a direct 3‑phase short to the motor phases when STO (Safe Torque Off) is triggered to the drive, ensuring the motor brakes immediately rather than coasting freely.
The first formula is speed dependent and can be utilized when the motor operates at speeds lower than its maximum:
 | (1) |
Where:
- Ke: back‑EMF constant (mechanical rad/s form)
- R: phase resistance
- L: phase inductance
- p: pole pairs
- 0.105≈2π/60 converts RPM → mech. rad/s
The second formula is speed independent and represents the asymptotic current limit the motor approaches at high speed and used when the motor is at or near maximum speed.
 | (2) |
Where:
- Kt: Motor's torque constant (Nm/A)
- Ld: D axis inductance (equal to motor inductance for SPM motors)
- p: pole pairs
Figure 1 illustrates the relationship between motor current and motor speed for a motor with predefined parameters, and it highlights which portion of the curve corresponds to each of the two calculation formulas.
Figure 1. Motor 3-phase short current vs Motor Speed
The following paragraphs will explain how each formula derives and give calculation examples.
The Speed‑Dependent Formula
This formula is used when the motor is not near maximum speed, or when accurate braking current prediction is required at a specific operating point (e.g., when a limit switch is hit during motion).
This expression comes from the classical Thevenin model of a spinning PMSM. The spinning rotor generates back‑EMF:
ωe=p⋅ωm = p⋅ (2π/60) RPM = 0.105p
By dividing the back-EMF by the motor impedance we get the Speed‑Dependent motor 3-phase short current formula:
Interpretation
- At low speed, the inductive term is small → current grows linearly with speed (1)
- At high speed, the inductive reactance dominates → current approaches a constant maximum (2)
This formula is used for real motor behavior at a given RPM, e.g., estimating short‑circuit current during a fault at operating speed.
The Speed‑Independent Formula
This formula comes from the high‑speed asymptote of the short‑circuit current and from d‑axis (demagnetizing) physics of PMSMs.
Important identity for PMSMs:
where
- Kt = torque constant
- p = pole pairs
- λm= PM flux linkage
- Ld= d‑axis inductance
If you short the motor at very high speed, the current approaches:
where
- Ld= d‑axis inductance
This is:
- The maximum short‑circuit current the motor can ever produce
- The maximum demagnetizing current the magnets will see
Interpretation
This formula is not predicting actual current at some RPM.
It predicts:
- The upper limit the speed‑dependent formula approaches
- The magnet demagnetization current limit
Thus, it is speed‑independent by design.
Let's consider the following motor parameters:
| Parameter | Value |
|---|---|
| Pole pairs p | 5 |
| Ld (H) | 0.0004 |
| R (Ω) | 0.2 |
| λm(Wb) | 0.03 |
| Kt=1.5 p λm | 0.225 Nm/A |
| Ke=p λm | 0.15 V/(rad/s) |
Speed‑Independent Formula
Speed Dependent Formula Evaluated at Various Speeds
| RPM | Short‑circuit current (A) |
|---|---|
| 0 | 0.00 |
| 500 | 34.79 |
| 1000 | 54.24 |
| 2000 | 67.68 |
| 3000 | 71.47 |
| 6000 | 74.07 |
| 10000 | 74.66 |
Observation
As RPM increases, the current approaches 75 A exactly — matching the hardware formula.