Improving and optimizing electric motor performance and efficiency depends on understanding how electric current is measured.

Electric motors are electromechanical machines that convert electric energy into mechanical energy. Despite differences in size and type, all 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, so let's start with an overview of basic electric and mechanical power measurements.

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.

P = V * I where power (P) is in watts, voltage (V) is in volts and current (I) is in amperes

A watt (W) is a unit of power defined as one Joule per second. For a DC source the calculation is simply the voltage times the current: W = V x A. However, 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 ratio ranging from -1 to 1, and represents the amount of real power performing work at a load. For power factors 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 are 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 (P= V*I), 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, following the method in Figure 1.

In this example the instantaneous 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 (Figure 2).

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 in Figure 2 are used to provide a true power measurement and true RMS measurements on any type of waveform, including all harmonic content, up to the bandwidth of the instrument.

We'll next look at how to actually measure watts in a given circuit. A wattmeter is an instrument that uses voltage and current to determine power in watts. The Blondel Theory states that total power is measured with a minimum of one fewer wattmeters than the number of wires. For example, a single-phase two-wire circuit will use one wattmeter with one voltage and one current measurement.

A single-phase three-wire split-phase system is often found in common housing wiring. These systems require two wattmeters for power measurement.

Most industrial motors use three-phase three-wire circuits that are measured using two wattmeters. In the same fashion, three wattmeters would be necessary for a three-phase four-wire circuit, with the fourth wire being the neutral.

Figure 3 shows a three-phase three-wire system with load attached using the two wattmeter method for measurement. Two line-to-line voltages and two associated phase currents are measured (using wattmeters Wa and Wc). The four measurements (line-to-line and phase current and voltage) are utilized to achieve the total measurement.

Since this method requires only monitoring two currents and two voltages instead of three, installation and wiring configuration is simplified. It can also measure power accurately on a balanced or an unbalanced system. Its flexibility and low-cost installation make it a good fit for production testing in which only the power or a few other parameters need measurement.

For engineering and research and development work, the three-phase three-wire with three wattmeter method is best as it provides additional information that can be used to balance loading and determine true power factor. This method uses all three voltages and all three-currents. All three voltages are measured (a to b, b to c, c to a), and all three currents are monitored.

Figure 4: When designing motors and drives, seeing all three voltages and currents is key, making the three wattmeter method in the figure above the best choice.

In determining the power factor for sine waves, the power factor is equal to the cosine of the angle between the voltage and current (Cos Ø). This is defined as the "displacement" power factor, and is correct for sine waves only. For all other waveforms (non-sine waves), the power factor is defined as real power in watts divided by apparent power in voltage-amperes. This is called the "true" power factor and can be used for all waveforms, both sinusoidal and non-sinusoidal.

However, if the load is unbalanced (the phase currents are different), this could introduce an error in calculating the power factor because only two VA measurements are used in the calculation. The two VAs are averaged because it's assumed they're equal; however, if they're not, a faulty result is obtained.

Therefore, it's best to use the three wattmeter method for unbalanced loads because it will provide a correct power factor calculation for either balanced or unbalanced loads.

Power analyzers from Yokogawa and some other companies use the method above, which is called the 3V-3A (three-voltage three-current) wiring method. This is the best method for engineering and design work because it will provide a correct total power factor and VA measurements for a balanced or unbalanced three-wire system.

In an electric motor, the mechanical power is defined as the speed times the torque. Mechanical power is typically defined as kilowatts (kW) or horsepower (hp) with one watt equaling one joule per second or one Newton-Meter per second.

*Figure 9, Converting hp to watts is achieved using this relationship: 1 hp = 745.69987 W. However, the conversion is often simplified by using 746 W per hp.*

Horsepower is the work done per unit of time. One hp equals 33,000 pound feet per minute. Converting hp to watts is achieved using this relationship: 1 hp = 745.69987 W. However, the conversion is often simplified by using 746 W per hp (Figure 9).

For ac induction motors, the actual or rotor speed is the speed at which the shaft (rotor) rotates, typically measured using a tachometer. The synchronous speed is the speed of the stator's magnetic field rotation, calculated as 120 times the line frequency divided by the number of poles in the motor. Synchronous speed is motor's theoretical maximum speed, but the rotor will always turn at a slightly slower rate than the synchronous speed due to losses, and this speed difference is defined as slip.

Slip is the difference in the speed of the rotor and the synchronous speed. To determine the percentage of slip a simple percentage calculation of the synchronous speed minus the rotor speed divided by the synchronous speed is used.

Efficiency can be expressed in 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.

Different associations have developed testing standards that define the accuracy of instrumentation required to conform to their standard: IEEE 112 2004, NVLAP 160, and CSA C390. All three include standards for the measurement of input power, voltage and current, torque sensors, motor speed, and more. Current transformers (CTs) and potential transformers (PTs) are some of the primary instrumentation devices used to make these measurements.

The corresponding standards are very similar with a few exceptions. The allowable instrumentation errors for IEEE 112 2004 and NVLAP 150 standards are identical; however, CSA C390 2006 has some difference in terms of temperatures and readings.

For example, the input power requirement for CSA C390 2006 is ±0.5% of the reading and must include the CT and PT errors, whereas those for IEEE 112 2004 and NVLAP 150 both only require ±0.5% of FS (full scale).

Current sensors are usually required for testing because high current cannot be brought directly into the measuring equipment. There is a variety of sensors available to match specific applications. Clamp-on sensors can be used with power analyzers. Scope probes can also be used, but caution must be applied when using these probes to make sure the instrument is not exposed to high currents.

For CTs, the feed wire can be connected through the window (CTs are typically donut shaped or oblong, with the hole or inner portion referred to as the window), or low current connections can be made to the terminals on the top of the device. Shunts are typically used for dc applications but not ac or distorted frequencies, although they can be used for synchronous motors up to a few hundred Hz. Specialized current transformers are available that work well for high frequencies, more commonly found in lighting applications as opposed to motors and drives.

Yokogawa along with LEM Instruments designed a unique current transformer system that delivers high accuracy from dc to the kHz range. It's an active type transformer that uses a power supply conditioning unit and provides accuracies of approximately 0.05 to 0.02% of the reading. This type of current transformer system provides very high accuracy measurements, especially for VFDs, which can go from 0 Hz up to the operating speed of the connected motor.

Voltage transformers simply transform a voltage from one level to another. In measurement applications, step-down transformers are sometimes required to reduce the voltage delivered to the measuring instrument, although many instruments can accommodate relatively high voltages and don't require a step-down transformer.

Instrument transformers are usually a combination of a current transformer and a voltage transformer, and can reduce the number of required transducers in certain measurement applications.

When deciding which device to use, the first question is the frequency range of the parameters to be measured. Dc-to-line frequency sine waves can use dc shunts, which offer high accuracy and simple installation. For ac and dc applications, the Hall Effect or active type instrument transformer can be used. Hall Effect technology has a lower accuracy rate, while the active type provides more precision. Various instrument transformers can operate at high frequencies of 30 Hz or more, but they can't be used for dc.

The next consideration is the level of accuracy required. For an instrument transformer, it's typically specified as the turns ratio accuracy. Phase shift is another important factor, and it's very important because many transformers are designed for current measurement only and aren't compensated for phase shift.

Phase shift is basically an effect of power factor for power measurement, and it will thus have an influence on the power calculation. For example, a current transformer that has a 2° maximum phase shift as part of its specification would introduce an error of cosine (2°), or 0.06% error. The user must decide if that percentage of error is acceptable for the application.

A current transformer is a current source. According to Ohm's law, voltage (E) equals the current through the conductor (I) multiplied by the resistance (R) of the conductor in units of ohms. Opening the secondary of a CT effectively drives the resistance to infinity. This means the internal current will saturate the coil, the voltage will go to infinity as well, and the unit will damage or destroy itself. Worse yet, a current transformer with an accidentally opened secondary could seriously injure workers.

**Never open circuit the secondary of a current transformer. Users could be seriously injured, and the CT can be damaged or destroyed.**

To determine instrument compatibility, the output level of the CT needs to be identified. Clamp-on and other CTs will typically have an output specified in millivolts/amp, milliamps/amp, or amps. A typical Instrument CT output can be specified from 0 to 5 amps.

The impedance and load on the CT must be considered, which are factors that are affected by how much wire is used to connect the CT to the instrument. This wiring is the resistance or the burden on the instrument, and thus could have an effect on measurement.

Scope probes can present their own set of problems if not used correctly. Many scope probes are designed to work with the input impedance on an oscilloscope, but the input impedance ranges can be different on a power analyzer, and must be taken into account.

Another item to consider when determining instrument compatibility is the physical requirement of the device. The size needs to be factored along with the type of current transformer, such as a clamp-on or donut type, each of which will work better in a particular situation.

We will now examine a typical three-phase, three-wire motor power measurement using a two-watt meter method. Blondel's theorem states that the number of measurement elements required is one less than the number of current-carrying conductors. This makes it possible to measure the power in a three-phase, three-wire system using two transducers when there is no neutral. However, when there is a neutral, three transducers are used as there are now four conductors.

Three-phase power is used primarily in commercial and industrial environments, especially to power motors and drives, because it's more economical to operate large equipment with three-phase power. In order to calculate three-phase wattage, the voltage of each phase is multiplied by the current of each phase, which is then multiplied by the power factor, and this value is multiplied by the square root of three (the square root of 3 is equal to 1.732).

To measure the three-phase power consumed by a loaded motor, a power analyzer is connected. Figure 1 shows a typical connection with the display showing all three voltages, all three currents, total power and power factor.

Figure 2 shows a three-phase three-wire power measurement accomplished using the two-wattmeter method. All three currents and voltages as well as the total VA and VAR listed. This configuration can display the individual phase power readings, but they should not be used directly, because for this measurement method only the total power is an accurate reading.

Basically, when using the two-wattmeter method on a three-wire three-phase system, individual phase power can't be measured directly, nor can any of the phase parameters be measured, including the phase power factors. However, the total of the phase parameters can be measured.

For a three-phase three-wire delta-connected motor, it's possible to measure line-to-line voltages and individual phase currents. Since there is no neutral, it's not possible to measure phase voltages. This situation results in some readings which must be explained.

Looking at waveform displays in Figure 3, one sees the line-to-line voltages Vab, Vbc, and Vac. The line-to-line voltages seen by the instrument are 60° apart in a balanced system. The currents are phase currents, which are seen by the instruments as 120° apart.

Another representation of this system is depicted in the Phasor Vector diagram shown in Figure 4. The triangle in the upper portion of this figure shows the line-to-line voltage measurements in black, the phase voltage values in red (but these are theoretical because there is no neutral), and the phase currents in blue.

The lower portion of the figure shows the phase differences between the voltages and currents. Again, note that the line-to-line voltages are 60° apart while the phase currents are 120° apart. A further detail is that if the top diagram represented a pure resistive load, then the blue currents would be in sync with the red voltages. However, with an inductive load (like a motor) the blue current vectors are out of phase with the voltages.

In addition, for this measurement method, on the bottom diagram the current vectors will always experience an additional 30° shift from the voltages. The bottom line is that a properly configured power analyzer will account for all of these conditions.

What if the phase power and phase power factor must be accurately measured on a three-phase three-wire system, and not just approximated? Figure 5 shows a technique that enables measurement of the phase parameters on a three-phase three-wire motor by creating a floating neutral.

There are limits to this technique, however. It will work well on the input to an induction motor, a synchronous motor, or a similar motor without a variable speed drive. Caution must be taken when using this technique on a variable speed drive system because the high frequency distorted waveforms and harmonics can cause inconsistent measurements.

Moreover, the floating neutral technique only works for equipment with sine wave-type waveforms. With a pulse-width modulation (PWM) drive, a 500 Hz line filter (low pass filter) can be turned on, which will then enable the readings to be displayed for the fundamental frequency, but not the total.

It's important to recognize that power will read the same regardless if it's measured in a three-phase three-wire or a three-phase four-wire method. However, using a three-phase four-wire connection, the voltage values being measured are phase voltages from line-to-neutral.

Figure 6 is a screen shot from a power analyzer that shows how similar the power and power factor readings are for a PWM drive operating a motor, comparing a three-phase three-wire 500 Hz filtered input against a three-phase four-wire floating neutral input.

An alternative solution uses a delta measurement function that is found in Yokogawa power analyzers. The delta measurement function uses instantaneous line-to-line voltage and phase current measurements to derive a true line-to-neutral voltage, even if the phases are unbalanced. A vector amplitude calculation inside the processor makes this possible. This function also provides the phase power measurements on the three-wire circuit. The delta measurement solution also provides the neutral current.

Complete testing of a PWM (pulse width modulation)-based drive and motor system is a three step process. Step 1 is accurate measurement of PWM variable speed drive input and output power, in order to identify drive efficiency and power losses. Step 2 is accurate measurement of motor input power and step 3 is accurate measurement of motor mechanical power.

The optimum method is to integrate all three steps using a single power analyzer in order to eliminate time skew. This provides excellent efficiency calculations as well, all in a single software/hardware solution.

Figure 7: This screen shot from a power analyzer shows how the delta measurement function can be used to derive true readings, and phase power, even when the phases are unbalanced.

Some power analyzers have a motor option in which the speed and torque signals can be integrated in this manner. These power analyzers can measure electrical power and mechanical power, and send the data to a PC running software from the original analyzer manufacturer or custom software from a system integrator.

When using a PWM VFD to operate a motor, it is often necessary to measure both the input and output of the VFD using a six-phase power analyzer. Not only can this setup measure the three-phase power, it can also measure dc or single-phase power. See Figure 1.

Depending on the analyzer, the setup mode will be performed in the normal or RMS mode. The wiring configuration should be set to match the application, such as three-phase input and three-phase output.

Any line filter or low-pass filter should be off because the filtering will obscure the measurements. However, the zero-cross filter or frequency filter should be on because it will filter the high frequency noise so the fundamental frequency can be measured. This measurement is necessary when tracking the frequency of a drive.

Figure 2 shows a PWM output voltage waveform with a highly distorted voltage, chopped high frequencies, and with 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. The frequency varies from 0 Hz up to the operating speed.

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 3 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 is typically measured in one of two ways. A true RMS measurement that includes total harmonic content can be used. However, since the fundamental waveform is primarily what contributes to the torque of the motor, a simpler measurement can be made and used. Most applications will only require measurement of the fundamental waveform.

There are two main methods for measuring the fundamental amplitude of the voltage wave. The first and simplest is to use a low-pass filter to remove high frequencies. If the power analyzer has this filter, simply turn it on. Proper filtering will give an RMS voltage of the inverter fundamental frequency. However, this type of filtering does not offer a true total power measurement, so filtering isn't the most exacting method.

The second method is 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 harmonic analysis function can be used to find the true fundamental voltage by using a Fast Fourier Transform (FFT) to determine the amplitude of each harmonic component including the fundamental wave. This gives an accurate RMS voltage measurement of the fundamental wave. The latest power analyzers can make simultaneous true RMS measurements along with harmonic measurements.

In Figure 4, the Urms2 (the RMS value on the PWM output) is a very high number, and F2 (the mean value of the fundamental) is somewhat lower. The value Urms3 (filtering the fundamental) provides a similar result. Finally, U2 (1) is obtained from harmonics analysis or FFT calculations of the fundamental. F2, Urms3 and U2 (1) provide results that are very close, but the U2 (1) FFT calculation is considered the most accurate.

Inverter current is usually measured only one way, and that is as a true RMS signal, because all harmonic currents contribute to and are responsible for temperature rise in the motor, so all must be measured.

Another important measurement involves drive V/Hz (Volts-per-Hertz). A PWM 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.

The dc bus voltage in the PWM can be measured to check for over- and under-voltage conditions. This measurement can be performed inside the drive on the terminals of the capacitor bank. 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. Figure 5 shows a PWM voltage measurement with high speed switching. The cursor is placed to read a value, such as 302.81 V in this measurement.

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 work with a variety of motors. Although Yokogawa analyzers can interface with most speed and torque sensors, it's still wise to confirm compatibility in each case. These sensors can be used to provide the mechanical measurement information in order to calculate the mechanical power measurements in the power analyzer.

Many sensors come with interface electronics to condition the signal properly to work with power analyzers or other equipment. The conditioned signal can be an analog output, or a serial communication output that goes to a PC and its application system software.

One option to implement mechanical power measurements is to use both a sensor and a corresponding measurement instrument from a given manufacturer. This approach has advantages since the sensors will be exactly matched to the instrument. Readouts for torque, speed, and power will be available, and there will likely be options for PC connectivity along with associated application software.

A more integrated approach is depicted in Figure 6. With this configuration, the speed and torque signal outputs from the sensor instrumentation are connected directly to power analyzer speed and torque inputs. This offers the big advantage of enabling electrical and mechanical power measurements to be evaluated simultaneously, and efficiency calculations to be performed continuously.

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.

A more comprehensive method is to use a multiple input power analyzer to measure input and output simultaneously as shown in Figure 1. 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 take calculate the drive loss and drive efficiency.

IEEE 112 is the U.S. industry standard for motor testing, and it outlines several methods. Figure 7 shows a power analyzer display supporting "Method A" from the IEEE 112 standard in which all mechanical power is divided by the total input to the motor. The standard defines many parameters beyond the current and motor voltage measurements, and it provides instructions for conducting and reporting generally accepted tests for polyphase and induction motors and generators. Additionally, the standard contains 11 test methods to define how to make efficiency measurements in motors.

Test Method A—input-output defined by IEEE 112: The efficiency is calculated as the ratio of the measurement output power to the measured input power after temperature and dynamometer corrections, if applicable. Tests are done at the rated load by the means of a mechanical brake or dynamometer. This motor power rating should be limited to motors with full load ratings of 1 KW or less.

Test Method B—input-output with loss segregation: In Method B, both input and output power measurements are made, but various losses are separated out. Most of these losses merely produce heat that must be dissipated by the motor assembly and represent energy that's not available to perform work. This method is the recognized testing standard for the U.S. motor industry for motors with full load ratings of 1 to 300 KW.

While both Methods A and B work, Method B requires a lot of instrumentation and is usually only performed by motor manufacturers. Since most manufacturers use Method B and most users prefer Method A, the efficiency calculations between the two may differ. The motor and drive manufacturers' performance data may use different motor speeds, test loads or other test conditions.

Many items need to be considered when measuring power in an electric motor, such as total and true power factor. These measurements involve complicated equations, which is why most companies employ a power analyzer to generate results automatically.

Once the decision is made to use a power analyzer, decisions on the frequency range and accuracy level must be made. Instrument compatibility is another important aspect in obtaining accurate readings safely, particularly with current transformers, and this is an area where the input/options on the analyzer must be considered. Given correct sensor inputs, mechanical power measurements can also be made using a power analyzer. Selecting the right speed and torque sensors is the first step in determining mechanical power.

Certain power analyzers also enable PWM measurements to be made. However, setting up the analyzer for PWM measurements also requires knowledge about how currents and voltages will affect the power measurements.

A precision high-frequency power analyzer is an important tool for measuring both mechanical and electrical power. Its analysis features and readings can help improve operations and even extend the life of a motor. Selecting the right analyzer and implementing it correctly does require knowledge; however, if employed correctly the power analyzer data will provide accurate and highly valuable data.

功率计或称瓦特计，可以测量产生、转换或消耗电能的设备各项特征，包括设备的各项参数，如：功率（瓦特）、功率因数、谐波和效率等等。

YOKOGAWA数字功率分析仪，性能优越、测量可靠，支持各种应用，非常值得拥有。尤其是YOKOGAWA WT300E功率计，在全球功率计市场上口碑与地位日益跃升。

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