# Motors, efficiency, and adjustable-speed drives

Adjustable-frequency drives have been billed as an energy efficient way to drive three-phase ac induction motors. Nevertheless, designers should understand that motors fed by inverter power experience additional losses which incrementally degrade their energy efficiency. Inverter current waveforms (such as six-step) generated by older technology had substantial harmonic content. Today's PWM (pulse-width modulated) inverters are capable of producing waveforms with little lower-order harmonic content. In fact, the majority of the “non fundamental” frequency content in modern PWM current waveforms is at the switching frequency. This, of course, is not really a “harmonic” for typical asynchronous carrier modulation schemes.

It is useful to review the impact of inverter waveforms on the component losses and overall losses of induction motors. The effects of various filters which may be applied between the inverter and motor can also have an impact on losses. And there are challenges associated with making accurate efficiency measurements on inverter-fed motors, especially those with extremely high efficiency.

All in all, three-phase ac induction motors demonstrate high efficiency and can maintain it across a substantial range of loading conditions. But when fed by inverter power, these motors experience losses that incrementally degrade their energy efficiency.

Additional losses in motors fed by inverter power can be categorized by their causes into five areas: non-fundamental frequency voltage components; non-fundamental frequency current components; those due to operation above or below base frequency; those due to operation above or below optimal flux level, and; operation with unbalanced voltages or currents. In some cases, these conditions can come into play on line-fed motors as well. Operation with high or low line voltage, or with unbalanced lines, is a reality of life for line-fed motors.

When an inverter is introduced into the system, there's an opportunity to improve these conditions or make them worse than those seen in the line-fed case. For some inverters, the output is filtered to a degree. For many medium-voltage (MV) inverters, the filtering is rather substantial in that the waveforms can approach a pure sinewave. In other low voltage (LV) cases, there may be just a small amount of output inductance to simply slope-off the edges of the PWM wave transitions.

The losses in polyphase induction motors typically divide into five categories: stator I^{2}R losses, rotor I^{2}R losses, iron (core) losses, friction and windage loss, and stray load loss. The stator and rotor I^{2}R losses on sinusoidal power are typically the dominant loss components. They are easy to understand — they are basically resistive losses proportional to the square of the current flow through the respective winding. Because the resistivities of typical motor winding materials (copper and aluminum) are a function of temperature, one must assume a specific temperature at which the I^{2}R losses apply. It is most common to model these losses at the specific temperature seen when operating steady-state at the motor nameplate rating.

The iron loss (or core loss) is associated with the losses in the laminations which make up the stator and rotor cores. The hysteresis component of loss comes from the fact that the relationship between flux density (B) and field intensity (H) in soft magnetic materials exhibits a “memory” effect. The fact that virtually all locations in the motor laminations have time varying magnetic fields means there is a real power loss as field intensity and flux density change. In addition, the laminations in a motor also experience minor loops through BH states as well.

The second component of iron loss is most commonly called eddy current loss and is a key reason why motor core sections are made up of thin laminations. The driving force behind the eddy current loss is the time-varying nature of the motor magnetic fields. The time variation in B causes real current flow in the core section. It is the loss associated with this current flow that is called the eddy current loss component of iron loss. One way to minimize this component of core loss is to reduce the lamination thickness so the eddy currents are resistance-limited.

There is a third component of iron loss that accounts for aspects that are not accurately described by models for hysteresis and eddy currents. This is often referred to as the anomalous loss. It is sometimes attributed to movement of magnetic domain walls.

Both the hysteresis and eddy current components of iron loss are frequency-dependent (more loss with higher frequencies). The fundamental frequency of the magnetic fields in the stator core are at line frequency while in the rotor core, they are at slip frequency. So the iron losses are primarily associated with the stator rather than the rotor. The iron losses are measured via no-load testing, and in that sense may be called no-load iron losses.

The friction and windage losses are typically accounted for by simply subtracting the available shaft torque, and as such may be further categorized as a mechanical loss.

The final loss component is stray load loss. This component covers losses not otherwise accounted for. Some engineers find the concept of stray load loss unsettling because it seems to imply some loss mechanisms in the motor are not well understood. In fact, there are portions of the stray load loss that can be accounted for, but they do not neatly fit into the other four categories. For example, the presence of load current tends to distort the magnetic fields within the laminations. Those distortions add iron loss that would be absent in the no-load testing used to measure the (no-load) iron loss. Thus though these are iron losses, they typically are grouped with the stray load loss because of how they appear in the testing sequence.

Generally speaking the I^{2}R losses dominate the overall breakdown of losses. However, the relative contributions of the core loss and stray load loss rise along with motor ratings. Obviously, higher motor speeds lead to increased friction and windage loss.

Perhaps the most obvious way in which inverters affect the motor losses is at frequencies (and therefore speeds) away from the motor base rating. The good news is that there is less friction and windage loss below base speed. Of course, the converse is that friction and windage loss can be significantly higher when operating above base speed. It is for this reason that motors operating well above base speed often minimize windage loss through use of separately powered cooling.

One might also expect iron losses to drop when the motor operates below base speed. The fundamental frequency component of iron loss is indeed less below base speed, but the inverter waveforms can cause a substantial increase in overall iron loss. It is also a challenge to separate out the iron losses when testing a motor powered by an inverter. It is easy enough to operate a motor across a range of flux levels with an inverter. However, there are eddy-current losses generated in the rotor bars during no-load operation which are not technically iron losses - though they show up in that part of the testing.

For the stator I^{2}R loss, the typical assumption is to just consider the increase in the rms value of the stator current over sinewave conditions. For a relatively clean waveform, this assumption only nominally affects the stator I^{2}R loss. However, the added loss is more substantial when the waveforms have a lot of noise that boosts their rms content.

Another practice during testing is to correct the value of stator resistance to that for the (higher) operating temperature seen on inverter power. In some cases it is challenging to measure and model the added stator I^{2}R losses. It is easy enough to model the skin effect that makes the apparent resistance higher at high frequencies, but more challenging to characterize it by testing on inverter waveforms. Losses caused by effects from adjacent conductors (proximity effects) become more challenging both to model and to measure.

Rotor I^{2}R loss is proportional to slip. Tests quantifying this loss capture its fundamental slip frequency aspect but do not account for the higher frequency eddy currents which may flow within each rotor bar. Depending on the design of the rotor and the qualities of the inverter, eddy current loss in the rotor bar may range from negligible to quite substantial.

To quantify the change in stray load loss while operating on inverter power, one must first look at how other additional losses are accounted for. For example, were the rotor bar eddy current losses lumped into the iron losses? This is possible because they show up when running the (no-load) iron loss tests on inverter power. Or, was the added iron loss that arises because of the field distortions from load current counted as a “load-dependent” iron loss? Alternatively, should it be included as one part of the stray load loss? As long as all the losses caused by inverter operation are accounted for, you get the correct overall efficiency. However, if you are trying to mitigate some aspect of loss, it is more useful to know the exact nature, cause, and location of each part of it.

### Example Measured Efficiencies on Sine and Inverter Power

**HP**

**Power**

**Efficiency, %**

**loss, kw**

**Remarks**60 Sine 96.3 1.74 60 PWM 95.4 2.14 2 kHz carrier

frequency

### System interactions

Inverter operation can also increase motor losses through various “system interaction” issues. One such issue can happen when the inverter output is heavily filtered. In such a case, the filter and motor will likely have at least one natural resonance frequency in common. Operation near that frequency will result in poor current waveforms and thus poor motor efficiency.

There are a wide range of motors that can work from inverter power, with varying degrees of success. If designers know at the outset that a motor will only work from inverter power and will not be “across-the-line-started,” they can use an inverter-optimized design which helps reduce the losses caused by the inverter waveforms. For example, the air gap length, bridge thickness, and rotor slot shape can be optimized to reduce the rotor bar losses. Here, bridge thickness is the height of the lamination section between the rotor slot and the rotor OD.

In the case of open rotor slots, as are common for fabricated rotors, the “bridge” of lamination material is not continuous, but rather has a slot opening. Inverter waveforms can induce high losses in the rotor bars if the rotor slot shape is inappropriate (examples include some double-cage designs), or if the motor has an air gap that's too small or a bridge that's too thin. These losses not only degrade the efficiency directly, but also tend to heat the rotor bar which worsens the slip - compounding the loss issue on inverter power.

While it is fairly common for the output of a medium-voltage inverter to be heavily filtered, output reactors are frequently offered as an option on-low voltage inverters. However, these reactors are typically sized to be effective only for sloping-off the high frequency edges of the voltage signal or controlling common-mode currents. They wouldn't meaningfully change the fundamental frequency of the current waveshape.

It is common for voltage-source inverters to have a selectable PWM frequency. Choosing a PWM frequency which is too low can produce a higher ripple current. A higher PWM frequency can promote a more sinusoidal waveform. The downside of a higher PWM frequency is that some losses in the inverter are proportional to switching frequency. To get optimal system efficiency, one must consider both the motor and inverter losses. Once a motor current waveform is nearly sinusoidal, there is minimal benefit to further boosting the PWM frequency.

One area where inverters have the opportunity to match up well against sinusoidal power is in minimizing unbalanced currents. An inverter designed with closed-loop control of the current waveform (not to be confused with closed-loop speed control) can regulate the currents into balance - even if doing so requires some voltage unbalance. In contrast, a small voltage unbalance in a line-powered system can lead to a large unbalance in the phase currents. Of course, accurate current sensors are the key to getting well-balanced line currents with closed-loop control. Any dc offset or calibration error in the feedback sensors can lead to unbalanced currents and the opportunity for torque ripple.

### Testing motors for efficiency

The most common standards used worldwide for measuring motor efficiency are IEEE 112 and IEC 60034. Both are based on sinusoidal power rather than inverter switched waveforms. There are also other testing standards such as JEC-37. However, the most universally utilized are the aforementioned IEEE and IEC standards.

Each test standard has a range of possible methods. It is the author's opinion that as long as a dynamometer is available with an in-line shaft torque transducer, IEEE 112, Method B is a “gold standard” of motor efficiency testing.

Many of the overall concepts in IEEE 112 methods B and F can carry over into the case of inverter power. The primary challenges for accurate testing on inverter power include measurement of the fundamental component of voltage; measurement of average power input; control of input voltage, current, and power to steady values; measurement of average output torque (and therefore power) in the presence of torque ripple; common-mode noise interference with signals; and sampling rates and aliasing with digital instrumentation.

The high efficiencies of polyphase induction motors can make it a challenge to accurately measure the efficiency via input-output methods. For that reason, the use of calorimetry is an interesting option. The data in the accompanying table was obtained by testing per IEEE 112, Method B - as used in accommodating inverter power.

Using the 60 hp data from the table as an example, it can be seen that less than a 1% drop in the efficiency can imply a 23% more motor losses in machines with these high efficiencies. Viewed from another perspective, a calorimetry-based measurement of losses that was ±10% accurate would be “better” (at quantifying losses) than input and output measurements accurate to ±0.5%. While calorimetry has some challenges, especially for air-cooled motors, designers must consider several options to accurately assess these extremely high nominal efficiencies.

In some cases, inverters get deployed simply for better process control or to get soft starting. But in the majority of cases, inverters serve as a means of gaining energy efficiency, perhaps most clearly exemplified by fan applications. When efficiency is a key expectation, the impact of the inverter on the motor energy efficiency is also key. Because motor efficiencies are often in the range of 97%, it is important to use all of available means to accurately assess their efficiency. This is all the more the case when the motor is operating across a range of speeds via an adjustable frequency inverter.

### Estimating PWM Inverter-fed Motor Efficiency from Sinewave Data

Users of inverter-fed motors often have data about the single-speed, sinewave-power efficiency of the motor they are using. However, this information says nothing about the efficiencies at different combinations of speed and load, including the impact of inverter waveforms on motor efficiency. Here's one way to make reasonable estimates based on limited data.

Motors that are not optimized for inverter power but which operate from a relatively low carrier frequency PWM inverter (1 kHz carrier, for example), can see as much as 50 % more loss compared to how they operate on sinewave power. At the other extreme, motors optimized for PWM waveforms (at, say, 4 kHz) can see PWM loss over and above sinewave power losses by as little as 10%.

The following procedure assumes there is a curve of motor sinewave power efficiency-versus-load at the motor base speed. This procedure should give reasonable order of magnitude efficiency data across a range of speeds and loads, from 25 to 125% load and from 25 to 150% speed. At speeds and loads below 25% of rated, the total power is typically low enough to be of little consequence.

The first step is to correct the sinewave efficiency data to inverter power efficiencies, both at base speed. The accompanying table provides factors to apply to motor losses as an adjustment to efficiency. Losses and efficiency are related by

where η = per unit efficiency, i.e. η = 0.90 implies 90% efficiency; P = motor output power, hp; W_{L} = total motor loss, W. After the losses are bumped up by the appropriate factor from the table, adjustments need to be made based on the operating speed. For speeds above the motor base speed, the efficiency at a given power level is relatively constant, so there's no adjustment needed for that portion of the speed range. For speeds below base speed, output power drops as speeds come down (at constant torque). So the efficiency does need to be adjusted. Those adjustments are best made to the motor losses, allowing recalculation of the efficiency via equation 1.

### Loss Factors for Various Motors/Inverter Combinations

**Loss factor @ 4kHz PWM**

**Loss factor @ 2kHz PWM**Inverter frequency motor 1.1 1.2 General-purpose motor 1.2 1.3

To estimate losses below base speed, one must separate total inverter power losses into “fixed” and “variable” loss components. The accompanying plots are used to compute a new value of loss for speed and load (torque) conditions below base speed.

For example, consider using a 600-hp, 1,200 rpm “inverter-optimized” motor, with efficiency data given in the accompanying table. The efficiency at various points of load and speed on inverter power (4 kHz PWM frequency) can be estimated as follows. First, the base speed efficiencies can be converted to the corresponding values available on inverter power by boosting loss figures 10%. For this purpose, one converts efficiency data into loss data using Equation 2.

### Sinewave Efficiency Data at Base Speed

**LOAD**

**EFFICIENCY, %**100% 96.3 75% 96.6 50% 96.5 25% 95.0

Then for motor efficiencies on PWM power at base speed and above, the loss data can be reconverted by Equation 1 into efficiency points. Note that at base speed and above, “% load” means % power (not torque), as this is a region of constant power operation. Then, for points at speeds below base speed, the loss data from the accompanying table can be modified using the accompanying plot of percent loss vs. percent speed.

For example, at 25% of rated torque and 56% of base speed, the loss is seen to be 60% of the loss that would exist at base speed and 25% torque. The load point would then be 672 rpm and 656.5 lb-ft, or 84 hp. With losses of 60% of 6478 watts, or 3887 watts, the efficiency can be computed as

Similarly, a point at 16% speed and 100% torque would have 50% of the loss at base speed at rated torque as read from the percent loss/percent speed plot. This would amount to a 9,458 W loss. Then at 96 hp, 192 RPM, 2626 lb-ft, the efficiency would be

### Example Measured Efficiencies on Sine and Inverter Power

**LOAD**

**LOSSES, SINEWAVE W**

**LOSSES, PWM, W**

**PWM EFFICIENCY**100% 17,198 18,917 95.9% 75% 11,816 12,997 96.3% 50% 8,117 8,929 96.2% 25% 5,889 6,478 94.5%

### References

M.J. Melfi, “Quantifying the energy efficiency of motors fed by adjustable frequency inverters,” IEEE 56th annual Industrial Applications Society Petroleum and Chemical Industry conference, 2009, ISBN: 978-1-4244-3798-6.

Baldor Electric, Fort Smith, Ark., www.baldor.com

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