Motor Power: Nominal, Electrical, Mechanical, Efficiency

August 9, 2025

Understanding Motor Power: Nominal, Electrical, Mechanical, and Efficiency

Understanding the various power ratings and concepts associated with electric motors is crucial for selecting the right motor for an application, designing control systems, and ensuring efficient operation. Motors convert electrical power into mechanical power, and along the way, various factors come into play, including different definitions of power and the inevitable losses that affect efficiency.

Let's dive into the key definitions and formulas.

Background: Controllers and Power Flow

Electrical power can be calculated by multiplying the current along a circuit multiplied by the voltage drop in that circuit.

DC Electrical Power: For a simple DC circuit, the power ( $P_{e l ec, D C}$ ) is straightforward: $P_{e l ec, D C} = V \times I$ Where:

$V$ is the voltage (in Volts, V)
$I$ is the current (in Amperes, A)
$P_{e l ec, D C}$ is the electrical power (in Watts, W)

AC Electrical Power: For AC circuits, especially 3-phase systems common in many motors (like BLDC motors internally), the concept is a bit more involved due to the presence of reactive power. We are primarily concerned with the real power (measured in Watts), which is the power actually converted into useful work (like mechanical output) and heat. Apparent power ( $S$ , in Volt-Amperes, VA) and reactive power ( $Q$ , in Volt-Amperes Reactive, VAR) also exist. The relationship is often described by the power factor (PF).

Single-Phase AC Real Power: $P_{e l ec, A C 1 ϕ} = V \times I \times PF$
Three-Phase AC Real Power: $P_{e l ec, A C 3 ϕ} = 3 \times V_{LL} \times I_{L} \times PF$ Where:
- $V$ is RMS voltage (single phase)
- $V_{LL}$ is RMS line-to-line voltage (three phase)
- $I$ is RMS current (single phase)
- $I_{L}$ is RMS line current (three phase)
- $PF$ is the power factor (a value between 0 and 1)

The power factor ( $PF = cos (ϕ)$ ) represents the phase difference ( $ϕ$ ) between voltage and current. For motors, a lagging power factor is typical.

Input Electrical Power vs Output Electrical Power (Controller Context)

Input electrical power: The input electrical power is the input voltage (which for a BLDC controller will be high), multiplied by the input current. For a BLDC controller, this input current will be lower than the output current and is what your power supply or battery sees.

$P_{in p u t} = V_{in p u t} \times I_{in p u t}$

Output electrical power: The output electrical power is the output phase voltage, which for a BLDC controller will be lower than the input voltage, multiplied by the output phase current. Notably, Spectral micro only has a direct measurement of the output current although it can approximate the output voltage by using the PWM ratio and the input voltage. Note that for a 3-phase motor, the total output electrical power is the sum of the power in each phase.

$P_{o u tp u t, e l ec t r i c a l} \approx 3 \times V_{p ha se, RMS} \times I_{p ha se, RMS} \times P F_{m o t or}$ (Using RMS phase voltage and current, and the motor's power factor)

Mechanical Power

Mechanical power is the rate at which mechanical energy is transferred or converted. For a rotating motor shaft, it's related to torque and speed.

The mechanical power applied to a rotating shaft can be found by multiplying the torque by the rotational speed.

Formula (using angular speed): $P_{m ec h} = τ \times ω$ Where:

$τ$ is the torque (in Newton-meters, Nm)
$ω$ is the angular speed (in radians per second, rad/s)
$P_{m ec h}$ is the mechanical power (in Watts, W)

Efficiency

Efficiency is a measure of how well the motor system converts input electrical power into useful output mechanical power.

Definition: The overall efficiency of a motor controller is the output mechanical power divided by the input electrical power. This will always be less than 100%. The difference goes to losses in the BLDC controller electronics, electrical losses in the motor, electrical losses in the wiring, and mechanical losses in the motor.

Losses within the motor and controller include:

Electrical Losses (Copper Losses): $I^{2} R$ losses in the windings and controller components.
Core Losses (Iron Losses): Hysteresis and eddy current losses in the motor's magnetic core.
Mechanical Losses: Friction in bearings and windage (air resistance).
Switching Losses: In the motor controller's electronic switches (like MOSFETs).

Nominal Power / Rated Power

This is perhaps one of the most important values found on a motor's nameplate.

Nominal Power (or Rated Power): This is the output mechanical power that the motor is designed to deliver continuously under specified operating conditions (voltage, frequency, temperature, etc.) without exceeding its thermal limits. Running a motor consistently above its nominal power rating will cause it to overheat and fail prematurely.

The nameplate (nominal) power is almost always the output mechanical power.

Motor Current Definitions

The terms motor rated current, full load current and nominal current, are very likely to confuse electrical engineers. Even though these terms are quite similar, there are slightly different from each other. Here is the clear definition of each one of them.

Definitions:

Motor rated current: The current drawn by a motor at its full load, calculated using formula is known as the rated current. Motor windings are designed to carry the rated current during normal operations and slightly higher than it for shorter duration.

Motor full load current: The full load current of a motor is the current drawn by it while operating at full load and rated voltage. It is a measured value and can also be calculated using formula. The full load current may vary upon the applied voltage. Also, the rated full load current (FLC) is the one specified by the manufacturer while tested at ideal conditions.

Nominal current: Nominal current is the same as the rated current. It is the current drawn by the motor while delivering rated mechanical output at its shaft.

In practice, "Rated Current", "Full Load Current (FLC)", and "Nominal Current" are often used interchangeably to mean the steady-state current the motor draws when delivering its Nominal (Rated) Mechanical Power at its Rated Voltage and Rated Speed. Manufacturers specify this value as a key operating parameter.

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