Energy is one of the highest cost items in a plant or facility, and motors often consume the lion’s share of plant power, so making sure motors are operating optimally is vital. Accurate power measurements can help to reduce energy consumption, as measurement is always the first step toward better performance and can also help extend the life of a motor. Small misalignments or other issues are often invisible to the naked eye, and the slightest wobble in a shaft can negatively affect productivity and quality, and even shorten the life of the motor.

In this document, we will discuss the basics of AC, DC, and power measurements, and a four-step process for making precision electrical and mechanical power measurements on variable speed drive motors and variable frequency drive (VFD) systems. We will also show how these measurements are used to calculate the energy efficiency for variable speed motor and mechanical variable speed drive systems.

Electric motors are electromechanical machines that convert electric energy into mechanical energy as shown in figure 1. Despite differences in size and type, all variable speed electric motors work in much the same way: an electric current flowing through a wire coil in a magnetic field creates a force that rotates the coil, thus creating torque.

Understanding power generation, power loss, and the different types of power measured can be intimidating. Below is an overview of basic electric and mechanical power measurements. For more detailed information on basic electrical power measurements, we recommend reading "The Fundamentals of Power Measurements."

Figure 1 - A motor converts electrical energy into mechanical energy.

What is power? In the most basic form, power is work performed over a specific amount of time. In a motor, power is delivered to the load by converting electrical energy per the following laws of science.

In electrical systems, voltage is the force required to move electrons. Current is the rate of the flow of charge per second through a material to which a specific voltage is applied. By taking the voltage and multiplying it by the associated current, the power can be determined.

A watt (W) is a unit of power defined as one Joule per second. Determining the power in watts for an AC source must include the power factor (PF), so W = V x A x PF for AC systems.

The power factor is a unitless ration ranging from -1 to 1 and represents the amount of real power performing work at a load. For power factos less than unity, which is almost always the case, there will be losses in real power. This is because the voltage and current of an AC circuit and sinusoidal in nature, with the amplitude of the current and voltage of an AC circuit constantly shifting and not typically in perfect alignment.

Since power is voltage times current, power is highest when the voltage and current are lined up together so that the peaks and zero points on the voltage and current waveforms occur at the same time. This would be typical of a simple resistive load. In this situation, the two waveforms are "in phase" with one another and the power factor would be 1. This is a rare case, as almost all loads aren't simply perfectly resistive.

Two waveforms are said to be out of phase or phase shifted when the two signals do not correlate from point to point. This can be caused by inductive or non-linear loads. In this situation, the power factor would be less than 1, and less real power would be realized.

Due to the possible fluctuations in the current and the voltage in AC circuits, power is measured in a few different ways. Real or true power is the actual amount of power being used in a circuit and is measured in watts. Digital power analyzers use techniques to digitize the incoming voltage and current waveforms to calculate true power.

In this example the instataneous voltage is multiplied by the instantaneous current (I) then integrated over a specific time period (t). A true power calculation will work on any type of waveform regardless of the power factor.

Harmonics create an additional complication. Even though the power grid nominally operates at a frequency of 60 Hz, there are many other frequencies or harmonics that potentially exist in a circuit, and there can also be a DC or direct current component. Total power is calculated by considering and summing all content, including harmonics.

The calculation methods above are used to provide a true power measurement and true root mean square (rms) measurements on any type of waveform, including all harmonic content, up to the bandwidth of the instrument.

Unlike single-phase systems, the conducting wires in a three-phase power supply system each carry an alternating current of the same frequency and voltage amplitude relative to a common reference, but with a phase difference of one third the period.

Three-phase systems have advantages over single-phase that make it suitable for transporting power and in applications such as induction motors.

- Phase voltage is the voltage measured across the motor windings to a neutral point.
- Phase current is the current through any one component comprising a three-phase source or load.
- In a delta connection, the line voltage is same as the phase voltage. For sine waves, the line current is √3 times the phase current.
- In a star or (wye) connection, the line voltage is √3 times the phase voltage while the currents are the same.
- The magnitude and frequency of the phase currents determine the motors torque and rotational speed.

When discussing power measurements with wattmeters, Blondel’s Theorem is often referenced when determining the number of wattmeters required to multi-phase power. The Theorem states that the power provided to a system of N conductors is equal to the algebraic sum of the power measured by N wattmeters. Additionally, if a common point is located on one of the conductors, that conductor’s meter can be removed, and only N-1 meters are required.

Measurement is relatively simple if the measurement object is a three-phase 4-wire system. As shown in Figure 2, three-phase 4-wire involves connecting wattmeters to each phase winding based on a neutral conductor. Obtain power for each phase winding by measuring voltage (phase voltage) and current (phase current) for each phase with different wattmeters. Totaling this will give the three-phase power value. Measuring three-phase 4-wire power requires three wattmeters.

Figure 2 - Three-phase Star Connection (3P4W)

Most motors do not have a neutral connection and therefore require voltmeters to be connected in the delta configuration (3V3A). This means phase voltage cannot be directly measured and voltmeters instead connected line-to-line (delta). This wiring method results in a 3-wire measurement and the three voltages are measured (R to T, S to T, R to S). A connection diagram for the delta connection method and a vector map are shown in Figure 3.

Figure 3 - Three-phase Delta Connection (3V3A)

By applying Blondel's Theorem, only 2 wattmeters are used in the total power computation. Despite only 2 wattmeters being needed, using three-wattmeter’s is desirable as it provides additional information that can be used to balance loading and determine true power factor.

In an electric motor, the mechanical power is defined as the speed times the torque. Mechanical power is typically defined as kilowatt or horsepower, with one W equaling 1 Joule/sec or 1 Nm/sec.

Horsepower is the work done per unit of time. One hp equals 33,000-pound feet per minute. Converting hp to watt is achieved using this relationship: 1 hp = 746 W. However, the conversion is often simplified by using 746W per hp. Mechanical power is measured as the motor speed times the motor torque. There are many different types of speed and torque sensors on the market that can be integrated into a dynamometer. These sensors can be used to provide the speed and torque measurements needed for mechanical measurement information in order to calculate the mechanical power measurements in the power analyzer.

Calculations of motor and speed can be made directly on a power analyzer. The wiring for this measurement depends on the signal type for speed and torque, output as either a pulse or analog signal, or a three-phase encoder pulse represented by phases A, B, Z.

Figure 4 - Torque and speed wiring for analog or pulse waveform

Figure 5 - Torque and motor wiring for three-phase encoder

How do I test a Variabe Speed Drive and Motor System?

Complete testing of a motor and drive system is a four-step process.

Step 1 is accurate measurement of three-phase input power to the variable frequency drive (VFD).

Step 2 is accurate DC Bus voltage measurement.

Step 3 is accurate measurement of motor input power / PWM variable frequency drives (VFD) output power.

Step 4 is accurate measurement of motor mechanical power.

In this section, we will discuss how to achieve the most accurate power and efficiency measurements, power measurements for three-phase AC motors and drive systems by stepping through the measurement points listed below, and how to achieve the most accurate power and efficiency measurements. When using a PWM VFD to operate a motor, it is often necessary to measure both the input and output of the VFD, as well as the AD to DC conversion section to get a total picture of AC drive design and operational efficiency.

Figure 6 - Measurements and measurement points of an AC motor and drive system

Measurement of input power is not only important to understand how clean the power is that enters the AC drive, it is also important to measure any harmonics that the drive may generate that are put back onto this grid. The architecture of the AC Drive consists of a rectifier section that chops the AC waveforms and filters the AC line voltage into DC, and an inverter section that converts the DC into pulse waveform modulated (PWM) signals that drive the motor. The voltage and current signals at the rectification and inverter output stages (points 2 & 3) will have distortion related due to the technologies employed. These technologies often use pulsed power electronics that produce high-frequency waveforms, resulting harmonic content at the input power mains (point 1). A total harmonic distortion measurement (THD) at the input will reflect the impact that the technologies employed by the motor and drive system have on mains power quality.

For electric vehicles or other applications that supply the drive system with a DC source, the measurement changes but the measurement point and the importance of the measurement doesn’t. This system removes the AC to DC conversion stage within the drive.

Figure 7 - Motor and drive system with DC source

The AC Drive uses capacitive filtering to convert the rectified AC mains into DC signals. Measuring these DC levels is important because the AD to DC converter inevitably introduces highly distorted input current, resulting in serious current harmonics and low power factor.

The DC bus voltage in the AC Drive can be measured to check for over- and under-voltage conditions and can be performed inside the drive on the terminals of the capacitor bank, as shown in Figure 6 at test point 2. However, an easier method is to use a power analyzer waveform display with the cursor measurement. When performing the waveform display with the cursor measurement, one must make sure the cursor isn't directly on top of the small spikes in the display. Instead, the cursor must lie across the waveform to make an accurate measurement.

Just as in Step 1, the measurement of power at the output of the VFD and input to the motor is important for a few reasons. It is necessary to measure the output of the drive to get a proper AC drive efficiency measurement. Also, it is important to measure the harmonics that the AC drive creates that are passed onto the motor. Because the motor is an inductive load, it filters much of the high frequency energy. The energy in the high frequency signals is presented as reactive power which does no work in rotating the motor, but can manifest itself as heat, which can slowly degrade the life of the motor.

When measuring the output of a VDF, it is important to understand the use of a line filter (low-pass) will limit the bandwidth of the measurements. However, it is important to turn on the frequency filter which is independent of the line filter. This filter is in parallel with the ADC and is needed in order to detect the zero crossing of the current waveform without limiting the bandwidth of the measurements. This filter helps determine the fundamental frequency which is necessary for harmonic analysis and correlating the rotating magnetic field speed with the actual rotational speed of the motor.

Figure 8 shows a PWM output voltage waveform with a highly distorted voltage, chopped high frequencies, and a lot of noise on the current side, making for a difficult measurement. High-frequency switching on the voltage signal creates a much-distorted waveform and with high harmonic content.

Figure 8 - AC inverter output voltage and current waveforms

For such a noisy signal, special current sensors are needed for measurement. Accurate PWM power measurements also require wide bandwidth power analyzers capable of measuring these complex signals. Figure 9 is an example of the voltage harmonic content from a PWM output. Beat frequencies are present, and voltage harmonic content exceeds 500 orders (approximately 30 kHz). Most of the harmonic content is in the lower frequencies on the current side.

Inverter voltage, current and power are typically measured by one of three methods that includes harmonic content or a measurement that isolates the magnitude of the fundamental frequency.

The first method is to use a simple low-pass filter (Iine filter) to remove high frequencies. If the power analyzer has this filter, simply turn it on. Proper filtering will result in voltage, current and power measurements representative of the inverter fundamental frequency contributions. However, it is important to understand this type of filtering does not offer a full bandwidth measurement, as such the resulting numbers will be absent of all high-frequency content.

The second method pertains only to the voltage measurements. This is called the rectified mean measurement method, which delivers an rms voltage of the fundamental wave without filtering by using mean-value voltage detection scaled to the rms voltage. The algorithm of the rectified mean of a cycle average will provide the equivalent of the fundamental voltage that will be very close to the rms value of the fundamental wave. Using this method, the total power, total current, and fundamental voltage can be measured.

The third and most complete method is use of digital harmonic analysis. This function can be used to isolate the individual spectral components of voltage, current, and power by using a Fast Fourier Transform (FFT) to determine the amplitude of each harmonic component including the fundamental wave. This method works in parallel with the full bandwidth measurements to simultaneously provide the full bandwidth and fundamental frequency voltage current and power measurements.

A drive should maintain a constant V/Hz ratio over the operating speed of the motor. The power analyzer can calculate V/Hz using the rms or the fundamental voltage value. The analyzer's user-defined math function is used to develop an equation for this measurement.

Mechanical power is measured as the motor speed times the motor torque. Speed and torque sensors should be fitted to the motor dynomometer and integrated into the test system. These sensors are typically an analog voltage output or a frequency style output. Modern power analyzers can accommodate both types and provide support for rotational position sensors such as encoders.

Efficiency can be expressed in its simplest form as the ratio of the output power to the total input power or efficiency = output power/ input power. For an electrically driven motor, the output power is mechanical while the input power is electrical, so the efficiency equation becomes efficiency = mechanical power/electrical input power.

A more comprehensive method is to use a multiple input power analyzer to measure input and output simultaneously. This results in a more accurate efficiency calculation as it uses a single power analyzer to eliminate potential errors caused by time skew measurements. With the internal math calculations provided by the analyzer, a very simple, menu-driven computation can be set up to calculate the drive loss and drive efficiency.

Figure 9 - Each measurement section of the motor and drive system has specific efficiency measurements.

The AC drive consists of two main sections, AD to DC converter and inverter. The rectification and filtering of the signal to DC often leads to high current harmonics, which leads to losses in power. Understanding the losses and efficiency of this section can help to lead to better AC drive designs and ultimately leads to higher overall efficiency. The equation for AD to DC efficiency is the DC power at measurement point 2 divided by the sum of the three-phase motor power at measurement point 1.

AC drive, drive, or inverter efficiency in its simplest form is calculated as output power divided by input power and represented as a percentage. One method used to measure input and output power is simply to connect power meters on the input and output, with the readings of the two meters used to calculate efficiency as shown in Figure 10.

Because the job of the AC drive is to adjust the speed of the AC output signal to the motor to achieve optimal performance, AC drive efficiency is important when designing the controller algorithms. The equation for drive efficiency is shown as the ratio of the sum of the three-phase motor power at measurement point 3 divided by the sum of the three-phase motor power at the AC input at measurement point 1.

Motor efficiency is the measure of the effectiveness with which electrical energy is converted to mechanical energy. Motor efficiency can be expressed as the power out divided by power in. The measurement of motor efficiency is not as straight forward as the

AC drive measurements because the power out, as designated as the numerator in the equation, is a conversion of mechanical to electrical power, using a torque meter, encoder, or resolver. The equation can be revised to mechanical power divided by the sum of the three-phase motor power at measurement point 3. This measurement is often performed at different speeds under different load, commonly displayed in a speed torque curve.

The motor efficiency measurement is intended to quantify the losses attributed to the design and operation of the motor. The top 5 losses in motors can be categorized as:

- Stator I2R losses
- Rotor I2R losses
- Stray load
- Core losses in the stator and rotor
- Friction and windage

Each of these losses can be minimized through different techniques and is the design goal of motor manufacturers.

The powertrain efficiency measurement can be thought of as an energy conversion chain, considering each sub system including the AD to DC converter, inverter, motor, and mechanical energy device as part of the equation. This measurement takes all losses in the motor and drive system into account and is helpful in new designs where some or all parts of the AC drive are incorporated into the motor design. This measurement is summarized as the mechanical power at measurement point M divided by the sum of three- phase power at measurement point 1.

Many items need to be considered when measuring power in an electric motor and drive system, including input power, inverter efficiency, motor efficiency, harmonics, and power factor. These measurements involve complicated equations, which is why most companies employ a power analyzer to generate results automatically.

When performing the 4-step process on a VFD and motor system, it is necessary to use a 7-phase power analyzer as shown in Figure 10. The simultaneous acquisition of the measurement steps 1-4 in a single instrument is advantageous for phase alignment and deskew between voltage and current measurements, resulting in the most accurate power measurement possible. It also allows for simplified efficiency measurements.

Figure 10 - A motor and drive system connected to a 7-phase power analyzer with mechanical input

Measure characteristics of devices that generate, transform or consume electricity. Also called power meters or wattmeters, these devices measure parameters such as true power (watts), power factor, harmonics, and efficiency.

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