When Ms. [ Name]'s travel companion, Mr. M, received a call from a client, his beaming joy almost surpassed the bright spring sunshine. He readily agreed to cover the entire cost of the pre-arranged lunch (split the bill). It turned out that the client had significantly reduced their electricity bills after purchasing high-efficiency motors supplied by Mr. M, and the practical application of these motors was beginning to yield substantial returns.
High-efficiency motors, as the name suggests, must be highly efficient and meet specified energy consumption standards. To achieve this, controlling and reducing motor losses is crucial, and it is essential to understand the mechanisms underlying these losses.
The Importance of Motor Losses
The consideration of motor losses is important for the following three reasons:
(1) Losses determine motor efficiency and greatly affect motor operating costs.
(2) Losses cause the motor to heat up, and the corresponding temperature rise level determines the maximum power output that can be obtained.
(3) The voltage drop or current factors associated with these losses must be reasonably considered in the motor design scheme.
Motor efficiency calculation
The efficiency of the motor is given by the following formula:
Efficiency = Output / Input ……………(1)
Or it can be expressed as equation (2) and equation (3).
Efficiency = (Input - Loss) / Input = 1 - Loss / Input ……………(2)
Efficiency = Output / (Output + Loss) ……………(3)
Types of Losses and Their Generation Mechanisms
Directly measuring the input and output power under load and using equation (1) to determine motor efficiency is limited or constrained by many factors. Usually, motor efficiency is calculated by measuring losses and using equations (2) and (3). If the exact same measurement and calculation methods are used, the efficiency determined by measuring losses can be used to compare competing motor products.
Several types of losses that typically need to be considered include ohmic losses, mechanical losses, open-circuit or no-load core losses, and load stray losses.
● Ohmic loss
Ohmic losses, also known as I²R losses, exist in all windings of the motor. Although calculations are typically corrected by measuring the winding temperature at each specific operating point, the DC resistance of the winding at 75°C is conventionally used when calculating these losses. Furthermore, the winding I²R losses under AC conditions depend on the effective (AC) resistance of the winding, which is related to the operating frequency and the motor's magnetic flux. The loss deviation caused by the difference between the DC resistance and the effective resistance is included in the load stray losses.
For the excitation system of synchronous motors and DC motors, only the losses in the excitation winding are included in the motor efficiency calculation; the losses in the external power supply that provides excitation are included in the power plant efficiency as part of the motor.
Closely related to I²R losses are the contact losses of the slip rings and commutators. Conventionally, this loss is usually ignored in induction and synchronous motors. In industrial DC motors, when leaded (lobe-shaped) carbon and graphite brushes are used, the total brush contact voltage drop is considered to be a constant value of 2V.
●Mechanical loss
Mechanical losses include frictional losses on brushes and bearings, and losses caused by air resistance. If there is a ventilation system, whether it is a built-in fan or an external fan, the power required to circulate air between the motor and the ventilation system should also be included (in the case of duct ventilation, excluding the power required to force airflow through long or narrow ducts outside the motor). Friction and air resistance losses can be determined by measuring the motor's input power, at which point the motor is running at an appropriate speed but without load and without excitation. Typically, friction and air resistance losses are combined with core losses and determined simultaneously.
●Loss of the core under open circuit or no-load conditions
Open-circuit or no-load core losses, including hysteresis and eddy current losses, are losses caused by the time-varying magnetic flux density in the motor core only when the main excitation winding is excited.
In DC and synchronous motors, although the change in magnetic flux caused by slotting will also cause losses in the pole core, especially in the pole shoes and pole faces of the pole core, the core loss is mainly limited to the armature core, or in other words, only the armature core loss is calculated.
In induction motors, core losses are primarily confined to the stator core. Rotor core losses are generally negligible due to the very low slip frequency of the alternating magnetic field. The open-circuit core loss can be obtained by operating the motor unloaded at its rated speed or frequency and under appropriate magnetic flux or voltage conditions, subtracting friction and wind resistance losses, and, if the motor is self-driven, adding the no-load armature I²R loss (the no-load stator I²R loss of the induction motor).
Typically, near the rated voltage, the no-load core loss as a function of armature voltage is measured. It can be assumed that the rated voltage is corrected using the armature resistance voltage drop under load (for AC motors, phasor correction is used), and the core loss under load is the loss value measured when the voltage equals the correction value. However, for induction motors, this correction is usually omitted, and the core loss under rated voltage is generally used. If the sole purpose is to determine efficiency, it is unnecessary to separate the open-circuit core loss from friction and wind resistance losses; the sum of these two is collectively referred to as no-load rotational loss.
● Load stray losses
Stray load losses include losses caused by uneven current distribution in the copper conductor, additional core losses caused by magnetic field distortion due to load current, and so on. These types of losses are difficult to determine precisely. By convention, 1.0 % of the output power is generally taken for DC motors. For synchronous and induction motors, stray load losses are generally determined through multiple standard tests.
Calculation of eddy currents and hysteresis losses
Eddy current loss varies with the square of magnetic flux density, frequency, and lamination thickness. Under normal operating conditions, eddy current loss can be approximated sufficiently accurately as follows:
Pe=Ke(Bmaxfδ)2…………(4)
In the formula, is the lamination thickness; Bmax is the maximum magnetic flux density; f is the frequency; and Ke is the proportionality coefficient. The coefficient Ke depends on the unit used, the core volume, and the core resistivity.
The variation law of hysteresis loss can only be expressed by empirical formulas. The most commonly used relationship is shown in equation (5).
In equation (5): Ks is the proportionality coefficient, which depends on the characteristics and volume of the iron core and the unit used; the exponent n is between 1.5 and 2.5 , and the value often taken in motor estimation is 2.0 . In equations (4) and (5), the frequency can be replaced by the speed, and the magnetic flux density can be replaced by the voltage, but the proportionality coefficient needs to be changed accordingly.
When a motor is under load, the magnetomotive force generated by the load current significantly affects the spatial distribution of magnetic flux density, potentially increasing actual core losses. For example, harmonic magnetomotive forces can generate considerable losses in the core near the air gap. The increased total core loss is typically attributed to load stray losses.
