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Applications of Power Measurement and Whitepapers in the Field of Power Electronics

Field Design Division, PM Department HIOKI E.E. CORPORATION, 81 Koizumi, Ueda, Nagano, Japan

1. Current Measurement Methods that Deliver High Precision PowerAnalysis in the Field of Power Electronics

2. High-precision, Wideband, High Stable Current Sensing Technology

3. High-precision Power Measurement of SiC Inverters

4. Identification of PMSM Motor Parameters with a Power Analyzer

5. Measurement of Loss in High-Frequency Reactors

6. Effectiveness of Phase Correction When Evaluating the Efficiency ofHigh-efficiency Motor Drives

©2018 HIOKI E.E. CORPORATION

Current Measurement Methodsthat Deliver High Precision

Power Analysisin the Field of Power Electronics

By Hajime Yoda, Hiroki Kobayashi, Shinya Takiguchi

1 IntroductionVarious power electronics applications demand high-precision power (current and voltage) measurement ofsuch characteristics as the power conversion efficiencyof power conditioners, the efficiency of inverters andmotors, and reactor losses. This paper narrows the fo-cus of the discussion to current measurement methodsand introduces some of Hioki’s expertise as a long-standing developer of both current sensors and poweranalyzers leveraging proprietary technologies.

2 Current MeasurementMethods

Power analyzers generally measure current by meansof either the direct connection method (Fig.1 [a]) orthe current sensor method (Fig.1 [b]). The followingprovides a detailed description of the characteristics ofeach approach.

2.1 Direct Connection MethodIn the direct connection method, current is measured byrouting wires from the measured object to the poweranalyzer and connecting them to the instrument’s cur-rent input terminals. The measurement principle itselfis extremely simple, with the advantage of enabling apower analyzer to be used to measure current on a stan-dalone basis, making it the de facto method for manyyears. However, since the current wires must be routedover a long distance and the current input portion of the

power analyzer must be inserted into the measured ob-ject’s circuit, the following disadvantages exist:

i) Conditions differ from those that characterize ac-tual operation.

ii) There is increased loss due to the wire resistanceof the long wires.

iii) Capacitance coupling occurs between individualwires and between wires and the ground, causinghigh-frequency leakage current to increase.

For example, concerning the effect described in ii)above, a 5-meter run using No. 6 AWG wire wouldhave a wire resistance of approximately 6.5 mΩ. If thecurrent under measurement were 30 A, the loss result-ing from this wiring resistance would be 5.85 W. Al-though it is impossible to make any judgment concern-ing the magnitude of the loss based solely on this value,it would be too large to ignore for some measured powervalues.

In addition, when using the direct connection method,current usually is measured by means of a shunt resis-tance. This shunt resistance method suffers from thefollowing disadvantages:

i) When current flows into the shunt resistance, Jouleheat proportional to the square of the current oc-curs in the resistance. In addition to instrumentloss attributed to the joule heat, the selfheating willchange the resistance value of the shunt resistanceitself, which will further worsen the measurementaccuracy.

©2018 HIOKI E.E. CORPORATION 2

Power supply

Inverter

Motor

Power analyzer

Measured current

Wire resistance loss

Leak currentJoule heat

Shunt resistor

Measured current

[a] Direct connection method.

Output signal of current sensor

MotorPower supply

Power analyzer

Current Sensor

Inverter

[b] Current sensor method.

Fig. 1: General Current Measurement Methods (Directconnection method[a] and Current sensor method[b])．

ii) To limit this heating, a shunt resistance with a lowresistance value is used. However, when a smallshunt resistance is used to measure a large cur-rent, even slight inductive components cannot beignored, which degrades the frequency character-istics.

iii) Each of these disadvantages significantly worsenscurrent and power measurement precision, dictat-ing caution when measuring large currents.

Fig.2 illustrates the process of self-heating that occurswhen a current of 20 A flows through a 2 mΩ shuntresistance. For comparison purposes, a Hioki CT6862current sensor with a rating of 50 A has been connectedto the circuit. You can see that the temperature of theshunt resistance rises to about 50C due to self-heatingcaused by Joule heat. By contrast, the current sensor

60.058.0 52.0 46.0 40.0 34.0 28.0

Fig. 2: Self-heating of shunt resistance.

is mostly unaffected by Joule heat and associated self-heating, and instrument loss and effects of the sensor’sown temperature characteristics on measurement preci-sion are negligible. As demonstrated by the above dis-cussion, the direct connection about 1 A where the ef-fects of the shunt resistance’s Joule heat are sufficientlysmall, for example measurement of the standby powerof electronic devices or measurement of the power con-sumption of LED lighting.

2.2 Current Sensor Method

The current sensor method is a method for measuringcurrent whereby a current sensor is connected to thewires on the equipment under test, and the output sig-nal (current or voltage) from the sensor is input into thepower analyzer.

The current sensor method can be used to measure a tar-get in its operating state, and the almost complete lackof self-heating when measuring large currents meansthat there is no effect on measurement accuracy. Thecurrent sensor method is better than the direct connec-tion method at measuring large currents of about 5 A orgreater with a high degree of precision, and it is gener-ally used in the power electronics field.

Fig.3 illustrates the approximate range of current val-ues that can be measured with a high degree of pre-cision and the associated general frequency band forboth the direct connection method and the current sen-sor method. Please note that just because a value fallsoutside the range shown in the figure does not necessar-ily mean that it cannot be measured using the method inquestion.


Power supply

Inverter

Motor

Power analyzer

Measured current

Wire resistance loss

Leak currentJoule heat

Shunt resistor

Measured current

[a] Direct connection method.

Output signal of current sensor

MotorPower supply

Power analyzer

Current Sensor

Inverter

[b] Current sensor method.

Fig. 1: General Current Measurement Methods (Directconnection method[a] and Current sensor method[b])．

ii) To limit this heating, a shunt resistance with a lowresistance value is used. However, when a smallshunt resistance is used to measure a large cur-rent, even slight inductive components cannot beignored, which degrades the frequency character-istics.

iii) Each of these disadvantages significantly worsenscurrent and power measurement precision, dictat-ing caution when measuring large currents.

Fig.2 illustrates the process of self-heating that occurswhen a current of 20 A flows through a 2 mΩ shuntresistance. For comparison purposes, a Hioki CT6862current sensor with a rating of 50 A has been connectedto the circuit. You can see that the temperature of theshunt resistance rises to about 50C due to self-heatingcaused by Joule heat. By contrast, the current sensor

60.058.0 52.0 46.0 40.0 34.0 28.0

Fig. 2: Self-heating of shunt resistance.

is mostly unaffected by Joule heat and associated self-heating, and instrument loss and effects of the sensor’sown temperature characteristics on measurement preci-sion are negligible. As demonstrated by the above dis-cussion, the direct connection about 1 A where the ef-fects of the shunt resistance’s Joule heat are sufficientlysmall, for example measurement of the standby powerof electronic devices or measurement of the power con-sumption of LED lighting.

2.2 Current Sensor Method

The current sensor method is a method for measuringcurrent whereby a current sensor is connected to thewires on the equipment under test, and the output sig-nal (current or voltage) from the sensor is input into thepower analyzer.

The current sensor method can be used to measure a tar-get in its operating state, and the almost complete lackof self-heating when measuring large currents meansthat there is no effect on measurement accuracy. Thecurrent sensor method is better than the direct connec-tion method at measuring large currents of about 5 A orgreater with a high degree of precision, and it is gener-ally used in the power electronics field.

Fig.3 illustrates the approximate range of current val-ues that can be measured with a high degree of pre-cision and the associated general frequency band forboth the direct connection method and the current sen-sor method. Please note that just because a value fallsoutside the range shown in the figure does not necessar-ily mean that it cannot be measured using the method inquestion.

2

1

10

100

1000

Current[A]

5

20

2

30

10010 10MFrequency[Hz]

1 1k 10k 100k 1M

Current sensor method

Direct connection method(using shunt resistor)

Fig. 3: Direct connection method and current sensormethod: Approximate ranges of current values and fre-quency bands that can be measured at high precision.*Exclusion from the ranges shown in the figure doesnot necessarily mean a value cannot be measured.

3 High-Precision Power Measure-ment using the Current SensorMethod

As described above, it is typical to use the current sen-sor method when measuring currents in excess of 5A. While the current sensor method does not sufferfrom the same disadvantages as the direct connectionmethod, there are nonetheless a number of precautionsthat must be borne in mind in order to measure currentat a high level of precision. This section outlines thoseprecautions.

3.1 Selecting a Suitable Current SensorHigh-precision, highly reproducible power measure-ment using the current sensor method presumes selec-tion of a suitable current sensor. Specific selection cri-teria include the following two considerations:

i) The current sensor’s rated current value must beappropriate for the magnitude of current to be mea-sured.

ii) All frequency components of the current to bemeasured must fall within the current sensor’smeasurable frequency band.

Furthermore, the following considerations should beborne in mind:

iii) The current sensor must provide a sufficient levelof measurement accuracy that is defined across theentire measurable frequency band.

iv) All error factors, for example output noise, tem-perature characteristics, conductor position effects,external magnetic field effects, magnetization ef-fects, and common-mode voltage effects for thecurrent sensor, must be defined and sufficientlysmall in magnitude.

A sufficient level of caution is required when selectinga current sensor. In particular, concerning considera-tion iii), amplitude and phase accuracy for most currentsensors are only defined for DC and 50/60 Hz frequen-cies, and accuracy for other frequency ranges is pro-vided only for reference purposes only.

It is important to note that high-precision current mea-surement using the current sensor method hinges on theavailability of both current sensors and a power ana-lyzer with an adequate level of performance.

3.2 Overall Optimization of Power Mea-surement Systems Including CurrentSensors

Simply selecting a suitable current sensor as describedabove is not a sufficient condition for high-precisionpower measurement using the current sensor method.In addition, it is necessary to optimize the entirepower measurement system, including the current sen-sor. Even if the current sensor detects the target currentwith an exceptionally high degree of precision, it willbe impossible to measure the current with a similarlyhigh degree of precision if the sensor’s output signal isdegraded before reaching the power analyzer.

Fig.4 illustrates a typical power measurement systemthat includes a current sensor. As described above,some current sensors generate current output, while oth-ers generate voltage output. Since current-output sen-sors are more commonly used than voltage-output sen-sors, this discussion will assume use of a current-outputsensor.

The following conditions must be satisfied in order toensure that the current sensor’s output signal can betransmitted to the power analyzer without degradation.

i) A high-quality power supply must be used for thesensor, and it must be properly grounded.

ii) Coupling capacitance between multiple cables andbetween cables and ground must be low, and thenoise resistance of the cables must be high.


Power Sourcefor Current Sensor

Isolation

Coupling C

Coupling C

Load RPower Analyzer

Shunt R Coupling CNoise

Noise

Current Sensor

Wire R

IsolationCMRR

Ground Loop

Fig. 4: Typical power measurement system.

iii) The power analyzer’s current inputs must offergood frequency characteristics with little heatingand high insulation performance (high CMRR andlow leak current). In addition, the instrument mustprovide high noise resistance, and it must be prop-erly grounded.

In general, power is measured with current sensors, apower supply to drive the sensors, and a power analyzerthat are all from different manufacturers, and the ca-ble type as well as wiring method are dependent on theuser’s discretion. In light of this, it goes without say-ing that it is extremely difficult for current sensor man-ufacturers, power analyzer manufacturers, and sensorpower supply manufacturers to guarantee that all of theconditions listed above will be satisfied for any givensetup, that the current sensor’s output signal will reachthe power analyzer without suffering degradation, andthat the target current will in fact be measured at a highlevel of precision.

On the other hand, Hioki is the only test and measure-ment instrument manufacturer in the world that inde-pendently develops and designs both current sensorsand power analyzers, giving us the ability to deliver allof the components necessary for building a completepower measuring system.

Hioki power measurement systems provide the follow-ing features:

i) We use voltage-output current sensors for whichaccuracy has been defined across the entire mea-

surable frequency band.

ii) Power analyzers’ current inputs are designedspecifically for use with voltage-output currentsensors, and both sensor output voltage levels andinput voltage levels for power analyzers’ currentinputs have been optimized.

iii) Power analyzers have a built-in sensor power sup-ply that drive the sensors with power whose qualityis identical to that used at Hioki when determiningaccuracy. By applying a number of meaningful de-sign features such as using the same ground for thepower analyzer and the sensor power supply andeliminating the causes of ground loops, we havevastly improved measurement precision and repro-ducibility.

iv) In addition to using shielded wires to carry sensoroutput as a way to counteract noise, Hioki has builtin functionality for adjusting sensor output gainto compensate for the minuscule voltage dropoffcaused by the cables.

Furthermore, Hioki subjects current sensors and poweranalyzers together to evaluations of measurement accu-racy and noise testing both in-house and by third-partycertification authorities.

Power Analyzer (PW6001)

Current Sensors(CT686x,CT684x, 9709, 3274)

Noise SourcePC for Data Aquisition

Fig. 5: Immunity testing of a Hioki power measurementsystem by a third-party certification authority.

Fig.5 portrays a power measurement system consist-ing of Hioki current sensors (CT6862, CT6863, 9709,CT6841, CT6843, and 3274) and a power analyzer


Power Sourcefor Current Sensor

Isolation

Coupling C

Coupling C

Load RPower Analyzer

Shunt R Coupling CNoise

Noise

Current Sensor

Wire R

IsolationCMRR

Ground Loop

Fig. 4: Typical power measurement system.

iii) The power analyzer’s current inputs must offergood frequency characteristics with little heatingand high insulation performance (high CMRR andlow leak current). In addition, the instrument mustprovide high noise resistance, and it must be prop-erly grounded.

In general, power is measured with current sensors, apower supply to drive the sensors, and a power analyzerthat are all from different manufacturers, and the ca-ble type as well as wiring method are dependent on theuser’s discretion. In light of this, it goes without say-ing that it is extremely difficult for current sensor man-ufacturers, power analyzer manufacturers, and sensorpower supply manufacturers to guarantee that all of theconditions listed above will be satisfied for any givensetup, that the current sensor’s output signal will reachthe power analyzer without suffering degradation, andthat the target current will in fact be measured at a highlevel of precision.

On the other hand, Hioki is the only test and measure-ment instrument manufacturer in the world that inde-pendently develops and designs both current sensorsand power analyzers, giving us the ability to deliver allof the components necessary for building a completepower measuring system.

Hioki power measurement systems provide the follow-ing features:

i) We use voltage-output current sensors for whichaccuracy has been defined across the entire mea-

surable frequency band.

ii) Power analyzers’ current inputs are designedspecifically for use with voltage-output currentsensors, and both sensor output voltage levels andinput voltage levels for power analyzers’ currentinputs have been optimized.

iii) Power analyzers have a built-in sensor power sup-ply that drive the sensors with power whose qualityis identical to that used at Hioki when determiningaccuracy. By applying a number of meaningful de-sign features such as using the same ground for thepower analyzer and the sensor power supply andeliminating the causes of ground loops, we havevastly improved measurement precision and repro-ducibility.

iv) In addition to using shielded wires to carry sensoroutput as a way to counteract noise, Hioki has builtin functionality for adjusting sensor output gainto compensate for the minuscule voltage dropoffcaused by the cables.

Furthermore, Hioki subjects current sensors and poweranalyzers together to evaluations of measurement accu-racy and noise testing both in-house and by third-partycertification authorities.

Power Analyzer (PW6001)

Current Sensors(CT686x,CT684x, 9709, 3274)

Noise SourcePC for Data Aquisition

Fig. 5: Immunity testing of a Hioki power measurementsystem by a third-party certification authority.

Fig.5 portrays a power measurement system consist-ing of Hioki current sensors (CT6862, CT6863, 9709,CT6841, CT6843, and 3274) and a power analyzer

4

(PW6001) undergoing immunity testing by a third-party certification authority. By carefully designingeach individual element and qualifying them in com-bination in order to optimize the system as a completeset, Hioki is poised to deliver a world-class power mea-surement system to our customers.

4 ConclusionIn addressing high-precision power measurement as re-quired in a variety of settings in the power electron-ics field, this paper focused on current measurementmethods and briefly introduced some of Hioki’s exper-tise as a longstanding developer of both current sensorsand power analyzers leveraging proprietary technolo-gies. Due to the constraints of space, it was unable tocover, or was only able to mention in passing, many ofthe more detailed aspects of this subject. Hioki looksforward to providing similar information to readers inthe future.


High-precision, Wideband,High Stable Current Sensing

TechnologyBy Kenta Ikeda, Hidekazu Masuda

1 Introduction

Currently, there is demand for high-precision, widebandcurrent measurement in the power electronics field,where typical products include power conversion sys-tems such as power conditioners and inverters. Sincelaunching the Clamp Tester CT-300 (see Fig.1) in 1971,Hioki has supplied a variety of current sensors (seeFig.2) designed for specific measurement applications.This paper describes the features of Hioki’s current sen-sors along with key considerations in current measure-ment, with a focus on high-precision, wideband currentmeasurement.

Fig. 1: Current Sensor CT-300, launched in 1971.

2 Detection Methods Used inCurrent Sensors

Current sensors utilize a broad range of detection meth-ods. Among them, many detect current using a mag-

Fig. 2: Hioki zero-flux current sensors.

netic conversion element that is inserted into the gap ofthe magnetic core or a winding making up a magneticcore, depending on the current flowing in the conductorunder test. That said, each detection method is charac-terized by its own advantages and disadvantages, mak-ing it difficult to satisfy all measurement requirementswith any one detection method. Hioki provides high-precision, wideband current sensors by using the zero-flux method (also known as the closed-loop or magneticbalance method), which combines two detection tech-niques.

In the zero-flux method, which relies on a negative feed-back circuit that includes a magnetic circuit such asthose shown in Fig.3 and 4, a current is made to flowin a feedback coil so as to cancel the magnetic flux pro-duced in the core by the current under measurement.This method has the advantage of minimizing the ef-


Magneticfluxdependingonmeasuredcurrent

Magneticcore

Measuringcurrentline

FeedbackcoilcancelsMagneticfluxinthecore.

Flux-gatecoil

Feedback coil

Sensoroutputdependingonthecurrentflowingthroughthefeedbackcoil

Output

Shuntresistor

AmplifierSynchronousdetector

Excitationcircuit

Fig. 3: Zero-flux method (flux-gate type).

fects of the magnetic material’s nonlinearity since theoperating magnetic flux can be controlled so that it iskept to a very low level.

Hioki’s high-precision current sensors use the zero-fluxmethod, which combines the flux-gate method and thecurrent transformer (CT) method shown in Fig.3. Theflux-gate method allows detection based on a DC cur-rent. Because this method does not require use of anysemiconductors, it delivers the advantages of low off-set voltage, high temperature stability, and excellentlong-term stability. Hioki provides current sensors with0.02% rdg. accuracy and a band of 3.5 MHz, makingthem some of the best-performing instruments of theirkind in the world. In addition, the company takes ad-vantage of the flux-gate method’s high temperature sta-bility to deliver products with an operating temperaturerange of –40C to 85C.

By contrast, wideband current sensors use a zero-fluxdesign that combines a Hall element and the currenttransformer (CT) method as illustrated in Fig.4, pro-viding a measurement band that extends from DC to amaximum of 120 MHz. Since Hioki produces in-housethe Hall elements that serve as the key magnetic detec-tion devices in this design with high sensitivity and lownoise characteristics, these sensors are ideally suited touse in applications where minuscule current waveformsmust be observed in combination with an oscilloscope.



Output

ShuntresistorFeedbackcoil

Magneticcore

Amplifier

HallElement


Constantcurrent/voltagesource


Fig. 4: Zero-flux method (Hall element type).

3 Differences in Current SensorArchitecture

Current sensors can be categorized as either through-type or clamp-type instruments based on their design.The through-type architecture eliminates any break inthe surface of the magnetic core, which makes it easy toobtain uniform characteristics around the entire circum-ference of the core and allows construction of extremelyhigh-precision current sensors. However, this design re-quires that the wire under test be disconnected so that itcan be passed through the sensor, making it impossibleto connect the sensor to operating equipment.

By contrast, the clamp-type architecture introduces abreak into the magnetic core, allowing it to be clampedaround the wire being measured. Since there is no needto disconnect the wire under test as with the through-type design, it is easy to measure operating equipment.However, the introduction of a break into the magneticcore makes it difficult to obtain uniform characteristicsaround the entire circumference of the core. As a re-sult, clamptype current sensors generally exhibit lowermeasurement accuracy and have a more pronounced ef-fect of conductor position than their through-type coun-terparts. Consequently, they make it more difficult toobtain measurements with good reproducibility. Hiokitakes advantage of expertise gained over many yearsof developing current sensors to offer high-precision,clamp-type current sensors. The characteristics of theseinstruments are described below.



Magneticcore



Flux-gatecoil

Feedback coil


Output

Shuntresistor

AmplifierSynchronousdetector

Excitationcircuit

Fig. 3: Zero-flux method (flux-gate type).

fects of the magnetic material’s nonlinearity since theoperating magnetic flux can be controlled so that it iskept to a very low level.

Hioki’s high-precision current sensors use the zero-fluxmethod, which combines the flux-gate method and thecurrent transformer (CT) method shown in Fig.3. Theflux-gate method allows detection based on a DC cur-rent. Because this method does not require use of anysemiconductors, it delivers the advantages of low off-set voltage, high temperature stability, and excellentlong-term stability. Hioki provides current sensors with0.02% rdg. accuracy and a band of 3.5 MHz, makingthem some of the best-performing instruments of theirkind in the world. In addition, the company takes ad-vantage of the flux-gate method’s high temperature sta-bility to deliver products with an operating temperaturerange of –40C to 85C.

By contrast, wideband current sensors use a zero-fluxdesign that combines a Hall element and the currenttransformer (CT) method as illustrated in Fig.4, pro-viding a measurement band that extends from DC to amaximum of 120 MHz. Since Hioki produces in-housethe Hall elements that serve as the key magnetic detec-tion devices in this design with high sensitivity and lownoise characteristics, these sensors are ideally suited touse in applications where minuscule current waveformsmust be observed in combination with an oscilloscope.



Output

ShuntresistorFeedbackcoil

Magneticcore

Amplifier

HallElement


Constantcurrent/voltagesource


Fig. 4: Zero-flux method (Hall element type).

3 Differences in Current SensorArchitecture

Current sensors can be categorized as either through-type or clamp-type instruments based on their design.The through-type architecture eliminates any break inthe surface of the magnetic core, which makes it easy toobtain uniform characteristics around the entire circum-ference of the core and allows construction of extremelyhigh-precision current sensors. However, this design re-quires that the wire under test be disconnected so that itcan be passed through the sensor, making it impossibleto connect the sensor to operating equipment.

By contrast, the clamp-type architecture introduces abreak into the magnetic core, allowing it to be clampedaround the wire being measured. Since there is no needto disconnect the wire under test as with the through-type design, it is easy to measure operating equipment.However, the introduction of a break into the magneticcore makes it difficult to obtain uniform characteristicsaround the entire circumference of the core. As a re-sult, clamptype current sensors generally exhibit lowermeasurement accuracy and have a more pronounced ef-fect of conductor position than their through-type coun-terparts. Consequently, they make it more difficult toobtain measurements with good reproducibility. Hiokitakes advantage of expertise gained over many yearsof developing current sensors to offer high-precision,clamp-type current sensors. The characteristics of theseinstruments are described below.

2

4 Key Considerations whenChoosing a Current Sensor

The most important aspect of making high-precisionmeasurements with a current sensor is the selection ofa current sensor that is appropriate for the measurementtarget.

Many high-precision current sensors (i.e., those withan accuracy of 0.1% or less) uses the current outputmethod, but Hioki’s high-precision current sensors usesthe voltage output method. While current output isgenerally regarded as providing superior signal trans-mission quality, voltage output delivers numerous ad-vantages as an output format for current sensors. Thefollowing sections describe key considerations whenchoosing a current sensor while exploring the advan-tages of voltage output.

4.1 Suitability of the Current Sensor’sRating and Measurement Band

To measure a given current with a high degree of pre-cision requires a current sensor whose rating is appro-priate for the magnitude of the target current. For ex-ample, if a 5 A current were measured using two cur-rent sensors with the same accuracy specifications, onewith a 10 A rating and one with a 500 A rating, the re-sults would indicate that the sensor with the 10 A rating,which is closer to the magnitude of the measurementtarget, is advantageous in terms of precision and repro-ducibility. Caution is necessary as Hioki defines ratedcurrents for its current sensors as RMS values, whereasmany current sensors do so using peak values.

In addition, it is important to verify that all frequencycomponents of the current to be measured are includedin the current sensor’s measurement band.

4.2 Defined Accuracy for Amplitude andPhase in the Measurement Band

For most high-precision current sensors used in com-bination with power meters, amplitude accuracy is de-fined only for DC current and commercial frequencies(50 Hz/60 Hz), and phase accuracy is rarely defined atall. In fact, it is difficult to define the accuracy of am-plitude and phase in the high-frequency region for thecurrent output that is generally used by high-precision

current sensors. Caution is necessary as many manu-facturers only publish typical characteristic graphs forfrequencies other than commercial frequencies. SinceHioki sensors use voltage output, it is possible to defineamplitude and phase accuracy across the entire mea-surement band. Because both amplitude accuracy andphase accuracy are critical considerations in accuratepower measurement, it is important to verify that phaseaccuracy has been defined when choosing a current sen-sor, particularly one that is to be used in power measure-ment.

4.3 VersatilityCurrent sensors that produce voltage output have the ad-vantage of being suitable for a variety of measurementapplications since it is easy to connect them not only topower meters, but also to instruments such as DMMs,oscilloscopes, and recorders.

4.4 High S/N ratioHioki’s high-precision current sensors are designed toproduce 2 V of output when measuring the rated cur-rent. For example, when using the Hioki CT6863 (rated200 A), 2 V AC would be input to the power meter whenmeasuring a 200 A AC. Since power meters that acceptcurrent input incorporate shunt resistors into their inputcircuitry, even signals from current sensors that producecurrent output end up being converted to voltage signalsfor processing. If a high-precision current sensor witha conversion ratio of 1500:1 is used to measure a 200 AAC current, the voltage measured by the power meterwill be as follows for the typical shunt resistor resis-tance values of 0.5 Ω and 0.1 Ω :

133.3mA × 0.5Ω = 66.65mV AC133.3mA × 0.1Ω = 13.33mV AC

The signal levels measured by the power meter wouldbe 2 V (with Hioki’s design) versus 13.33 mV to 66.65mV (for a current output-type design), illustrating howthe Hioki design yields a higher S/N ratio than currentsensors that rely on current output.

4.5 Ease of Adjustment and CalibrationSince Hioki’s current sensors generate voltage output,they have the advantage of being easy to adjust and cal-


ibrate. Consequently, their defined accuracy can extendto include the output cable. In addition, Hioki sensorscan be manufactured with custom cable lengths sincethe adjustment process can compensate for the minus-cule voltage drop caused by the cable’s resistance.

Hioki’s high-precision current sensors can be calibratednot only for DC and commercial frequencies, but alsofor the high-frequency region. Following are someexample calibration points for Hioki’s current sensors(traceability is maintained for each frequency point) :

Amplitude : ±DC, 50 Hz, 60 Hz, 1 kHz, 10 kHz,100 kHz, 300 kHz, 700 kHz, 1 MHz

Phase : 50 Hz, 60 Hz, 1 kHz, 10 kHz, 100 kHz,300 kHz, 700 kHz, 1 MHz

5 Precautions for High-precisionMeasurement

This section introduces some precautions that should beobserved when using a current sensor to measure cur-rent with a high degree of precision, based on the ex-perience Hioki has gained over many years of currentsensor development.

5.1 Positioning the Conductor in the Cen-ter of the Sensor

All current sensors are prone to the effects of conductorposition, and the magnitude of those effects increaseswith the measurement frequency. Even through-typecurrent sensors with good characteristics exhibit signif-icant effects at frequencies of 10 kHz and above. Acurrent sensor’s measurement accuracy is always de-fined at the center position of the sensor. When measur-ing a high-frequency current, it is particularly importantto ensure high-precision, highly reproducible measure-ment by positioning the conductor in the center of thesensor.

5.2 Keeping Nearby Conductors awayfrom the Current Sensor

Current sensors function by detecting the magnetic fieldproduced when current flows through the cable beingmeasured. As a result, they are affected in no small partby any currents that may be flowing in nearby conduc-tors. These effects are particularly pronounced for high-

frequency currents. Consequently, it is desirable to keepnearby conductors as far away as possible from the cur-rent sensor so that the target current can be measured ata high level of precision. These effects are particularlysignificant for high-frequency currents, and they shouldbe considered when using all current sensors.

6 Expressing the Accuracy ofHigh-precision Current Sensors

The accuracy of Hioki’s high-precision current sensorsis defined for all frequency bands in the measurementdomain. Current sensor accuracy is typically defined inthe center of the sensor. However, it is no easy feat toposition a conductor in the exact center of the sensorin actual practice. Fig.5 illustrates the frequency char-acteristics and specifications of a Hioki high-precisioncurrent sensor (Model CT6841). Accuracy has beendefined for each region so that the specifications aresatisfied even when the conductor position varies. Inaddition, the accuracy specifications of Hioki’s high-precision current sensors incorporate a sufficient marginof performance. As a result, actual performance tendsto be significantly better than their specifications sug-gest.

Error[%rdg.]

ABCDESpec.

AB D

C

E

Frequency[Hz]

30

20

10

0

-30

-20

-10

10 100 1k 10k 100k 1M

Fig. 5: Gain-frequency characteristics.

7 High-precision Clamp CurrentSensors

As described above, clamp-type current sensors gen-erally exhibit poor accuracy and measurement repro-ducibility due to the break in their magnetic core. This


ibrate. Consequently, their defined accuracy can extendto include the output cable. In addition, Hioki sensorscan be manufactured with custom cable lengths sincethe adjustment process can compensate for the minus-cule voltage drop caused by the cable’s resistance.

Hioki’s high-precision current sensors can be calibratednot only for DC and commercial frequencies, but alsofor the high-frequency region. Following are someexample calibration points for Hioki’s current sensors(traceability is maintained for each frequency point) :

Amplitude : ±DC, 50 Hz, 60 Hz, 1 kHz, 10 kHz,100 kHz, 300 kHz, 700 kHz, 1 MHz

Phase : 50 Hz, 60 Hz, 1 kHz, 10 kHz, 100 kHz,300 kHz, 700 kHz, 1 MHz

5 Precautions for High-precisionMeasurement

This section introduces some precautions that should beobserved when using a current sensor to measure cur-rent with a high degree of precision, based on the ex-perience Hioki has gained over many years of currentsensor development.

5.1 Positioning the Conductor in the Cen-ter of the Sensor

All current sensors are prone to the effects of conductorposition, and the magnitude of those effects increaseswith the measurement frequency. Even through-typecurrent sensors with good characteristics exhibit signif-icant effects at frequencies of 10 kHz and above. Acurrent sensor’s measurement accuracy is always de-fined at the center position of the sensor. When measur-ing a high-frequency current, it is particularly importantto ensure high-precision, highly reproducible measure-ment by positioning the conductor in the center of thesensor.

5.2 Keeping Nearby Conductors awayfrom the Current Sensor

Current sensors function by detecting the magnetic fieldproduced when current flows through the cable beingmeasured. As a result, they are affected in no small partby any currents that may be flowing in nearby conduc-tors. These effects are particularly pronounced for high-

frequency currents. Consequently, it is desirable to keepnearby conductors as far away as possible from the cur-rent sensor so that the target current can be measured ata high level of precision. These effects are particularlysignificant for high-frequency currents, and they shouldbe considered when using all current sensors.

6 Expressing the Accuracy ofHigh-precision Current Sensors

The accuracy of Hioki’s high-precision current sensorsis defined for all frequency bands in the measurementdomain. Current sensor accuracy is typically defined inthe center of the sensor. However, it is no easy feat toposition a conductor in the exact center of the sensorin actual practice. Fig.5 illustrates the frequency char-acteristics and specifications of a Hioki high-precisioncurrent sensor (Model CT6841). Accuracy has beendefined for each region so that the specifications aresatisfied even when the conductor position varies. Inaddition, the accuracy specifications of Hioki’s high-precision current sensors incorporate a sufficient marginof performance. As a result, actual performance tendsto be significantly better than their specifications sug-gest.

Error[%rdg.]

ABCDESpec.

AB D

C

E

Frequency[Hz]

30

20

10

0

-30

-20

-10

10 100 1k 10k 100k 1M

Fig. 5: Gain-frequency characteristics.

7 High-precision Clamp CurrentSensors

As described above, clamp-type current sensors gen-erally exhibit poor accuracy and measurement repro-ducibility due to the break in their magnetic core. This

4

Fig. 6: High-precision clamp sensor.

2

1

0

-2

-1Error[%rdg.]

Inputcurrent[Arms]

DC(Clamp-type)

55Hz(Clamp-type)

DC(Through-type)

55Hz(Through-type)

0.1 1 10 100 1k

Fig. 7: Linearity.

Deviationfromcenter[%]

ABCD E

F

GHI

Conductorposition

A B C D E F G H I

0.04

0.03

0.02

0.01

0

-0.01

-0.02

-0.03

-0.04

DC100Ainput

Clamp-type

Through-type

Fig. 8: Effects of conductor position.

Clamp-type

Through-type

200A/55Hzinput

Error[%rdg.]

Temperature[C]

0.5

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

0.4

-0.5-80 -60 20-40 -20 0 40 60 80 100 120

Fig. 9: Gain-temparature characteristics.

section introduces some of the characteristics of Hioki’sCT6843 high-precision clamp sensor (rated 200 A),shown in Fig.6. Fig.7 through 9 compare those char-acteristics to those of the CT6863, a Hioki through-type current sensor with the same rating (200 A). Thecharacteristics of Hioki ’s clamp-type current sensorsapproach those of through-type current sensors, mak-ing them more than capable enough to be used in high-precision power measurement.These clamp-type current sensors are able to deliver thislevel of performance because they use a uniform struc-ture around the circumference of the magnetic core withthe exception of the break and because the break in thecore is designed to minimize magnetic reluctance. Thisconstruction evokes designs that deliver uniform char-acteristics around the entire circumference of the mag-netic core as in a through-type sensor. Hioki’s clamp-type current sensors are designed to deliver excellentease of use as well as high performance. For example,their jaws can be opened and closed, and their sensorlocked in place, by means of simple, single-handed op-eration. Furthermore, these sensors can operate acrossa broad temperature range of –40C to 85C, allowingtheir use in a variety of environmental tests. As a result,they can be used without issue in harsh environmentssuch as the hot conditions of an automobile’s enginecompartment.In addition, Hioki’s power meters are designed specifi-cally to be used with its current sensors, allowing themto supply power directly to, and automatically detect themodel of, connected sensors. For this reason, Hioki’scurrent sensors are ideal for use in conjunction withpower meters in high-precision, wideband power mea-surement applications.


8 Wideband Clamp-type CurrentSensors

Hioki’s wideband current sensors feature a broadermeasurement band and lower noise levels than the high-precision current sensors described above. Of thoseproducts, the CT6701 (Fig.10), which has the highestcurrent to output voltage conversion rate (“output rate”)and highest frequency band (see Fig.11) of any Hiokiproduct in its class, is ideal for use in the observationof transient response current waveforms, high-speed re-sponse waveforms such as inrush current, and minus-cule current waveforms that include a variety of fre-quency components.

As described above, wideband current sensors use thezero-flux method, which utilizes a thin-film Hall ele-ment. Hioki has developed a thin-film low-noise Hallelement, which is a key device in current sensors, to ac-commodate market demand for improved low-currentmeasurement capabilities. For example, the HiokiCT6701 is able to deliver an output rate of 1 V/A (10times the rate of its predecessor) as well as low-noiseperformance. Fig.12 provides a measured waveformcomparison with the previous model, illustrating howthe waveform of a control current flowing to an electri-cal part in an automobile, for example a small motor,can be more precisely observed on the order of mil-liamperes. Using them in combination with an oscil-loscope is ideal for fully optimizing the performance ofthe 120 MHz (–3dB) wideband characteristics. For ex-ample, it can be used to observe the control current orload current in a switching circuit used in power conver-sion or motor control, the turn-on/turn-off current wave-form of a semiconductor device performing high-speedswitching, or ripple waveforms.

Fig. 10: Wideband current sensor CT6701.

10

0

-10

-20

-30

-40

1 100 10k 1M 100M

Frequency[Hz]

Voltage-currentconversionrate[dB]

Fig. 11: CT6701 amplitude-frequency charactreristics(typical).

Oscilloscopeusagerange:10mV/div

Oscilloscopeusagerange:1mV/div

CT6700

Previousmodels

Fig. 12: 20 mAp-p waveform (comparison with previ-ous Hioki model).

9 Conclusion

This paper has introduced the detection principle usedby the zero-flux method, key considerations whenchoosing a current sensor, precautions when using theseinstruments, and some current sensor characteristics,with a focus on current sensors that have been devel-oped by Hioki for more than 40 years. The authorshope that it will prove useful to anyone measuring cur-rent in the power electronics field, which demands high-precision, wideband current measurement.


High-precision PowerMeasurement of SiC Inverters

Facilitating high-precision measurement of power, efficiency,and loss in SiC inverters and motor drive systems

By Kazunobu Hayashi

Introduction

Development of higher-efficiency, more compact mo-tor drive systems is a key priority for manufacturers ofEVs and HEVs as well as the rail industry, among othersectors of the economy, where companies have startedusing SiC power semiconductors in order to boost theefficiency and shrink the size of the inverters that areprincipal components of motor drive systems1, 2, 3). Ex-pected advantages of SiC power semiconductors in-clude smaller passive component dimensions thanksto higher switching frequencies and lower-loss perfor-mance thanks to low on-resistance values. Accuratepower measurement is a critical precondition for eval-uating motor drive systems, but power measurementof SiC inverters requires high-precision measurementacross a broader band of frequencies than in the past.This paper introduces a range of topics including exper-tise related to power, efficiency, and loss measurementof SiC inverters and motor drive systems, along withactual measurement results.

Measuring the Efficiency of Invert-ers and Motors

During evaluation of motor drive systems that incorpo-rate inverters and motors, it is possible to measure ef-ficiency and loss by measuring the inverter’s input andoutput power and the motor’s power and then calculat-ing the ratio or differential between the input and outputvalues. Fig.1 provides a measurement block diagram il-lustrating the measurement of the efficiency of a stan-dard motor drive system.

Powersource Inverter Motor Load

Voltage,Current

Voltage,Current

Torque, Speed

Power analyzer

Pin Pout Pm

Loss, Ploss = Pin - Pout

Efficiency, η = Pout / Pin

Fig. 1: Measuring the efficiency of a motor drive sys-tem.

The output of inverters and motors fluctuates over time.Consequently, accurate measurement is made difficultby imperfect synchronization of measurement timingand by differences in calculation methods when calcu-lating efficiency and loss by measuring the respectivepoints with separate instruments. Accordingly, it is nec-essary to take all measurements simultaneously, eitherby using a single instrument for all of them or throughthe synchronized control of multiple instruments. Thisrequirement can be met by using a power analyzer.Standard power analyzers provide four to six channelsof power measurement along with motor analysis func-tionality, allowing them to measure efficiency and losswith a high degree of precision.

Looking more closely at the measurement process, re-


sults vary depending on how the time period acrosswhich power calculations are performed is defined.Power analyzers determine the periods across whichcalculations are performed by detecting zero-crossevents in input waveforms. Generally speaking, thechannel corresponding to the signal for which zero-cross events will be detected can be set as desired asthe synchronization source. Setting the optimal syn-chronization source enables stable power measurement,making it possible to measure efficiency and loss with ahigh degree of precision. For example, if the inverter isfed DC input, the calculation periods can be synchro-nized by setting the same synchronization source forthe input and output channels. In this way, it is pos-sible to measure efficiency and loss in a stable manner.In the example shown in Fig.1, power at two points andmotor power at one point are being measured in a sta-ble manner by setting the synchronization source for allchannels to the inverter’s output current.

Measuring an Inverter’s InputPowerTo measure efficiency and loss, it is necessary to mea-sure the power being input to the inverter. This inputpower will serve as the basis for measuring efficiencyand loss. Generally speaking, either DC or AC com-mercial power is used as inverter input. If the valuesyielded by measurement of the input and output powercontain an error component, it will have a significant ef-fect on the efficiency and loss values. Consequently, itis necessary to measure the inverter’s input power witha high degree of precision. For example, an error of0.5% in the input power measured value for an inverterwith an efficiency of 99% will result in an error of 50%for the loss. Although it is possible to calculate powerusing a general-purpose waveform recorder, one mustexercise caution to ensure that a sufficient level of ac-curacy has been defined for the band that you wish tomeasure.

Caution is especially warranted during DC power mea-surement, which should be preceded by adjusting thepower analyzer and current sensors’ DC offsets. If thepower analyzer provides a zero-adjustment function,perform zero-adjustment after zeroing out input to thepower analyzer and current sensors. In this way, it ispossible to enable accurate DC measurement by can-celing out the instrument’s DC offset.

L R

Inverter output Back electromotive

force

Fig. 2: Equivalent circuit for a motor (1 phase).

Measuring an Inverter’s OutputPower

Inverters generate PWM-modulated output that in-cludes the switching frequency and its harmonic com-ponents. Consequently, power measurement must beperformed over a wider band than when measuring DCor commercial frequency power.

Let’s study the band that is needed in order to mea-sure power at the switching frequency and its harmon-ics. Fig.2 provides an equivalent circuit for a motor thatis driven by an inverter. Since the motor’s windingshave an inductance component, high-frequency currentis less likely to flow to the motor. Since the voltage isa PWM waveform, it can be approximated as a rectan-gular wave. At this time, the current will take the shapeof a triangular waveform. When calculating RMS val-ues for the triangular waveform over the frequency do-main, measurement can yield RMS values with an errorof 0.1% or less if harmonics can be measured to the5th order. Here the active power Pf can be expressedas a function of the voltage U f , the current I f , and thevoltage-current phase difference θ f as follows:

Pf = U f · I f · cos θ f . (1)

Consequently, if either the voltage or current is 0, theactive power for that frequency component will be 0.Assuming measurement at a precision of 0.1%, currentat 7th order and higher harmonic components can beignored, as noted above. Therefore, the ability to mea-sure voltage, current, and phase difference accuratelywithin the band of 5 times to 7 times the switching fre-quency is sufficient in order to measure power at theswitching frequency and its harmonics with an error of0.1% or less. However, loss in an actual motor includesthe magnetic material’s core loss as well as losses fromfactors such as wire skin effects in addition to the re-


sults vary depending on how the time period acrosswhich power calculations are performed is defined.Power analyzers determine the periods across whichcalculations are performed by detecting zero-crossevents in input waveforms. Generally speaking, thechannel corresponding to the signal for which zero-cross events will be detected can be set as desired asthe synchronization source. Setting the optimal syn-chronization source enables stable power measurement,making it possible to measure efficiency and loss with ahigh degree of precision. For example, if the inverter isfed DC input, the calculation periods can be synchro-nized by setting the same synchronization source forthe input and output channels. In this way, it is pos-sible to measure efficiency and loss in a stable manner.In the example shown in Fig.1, power at two points andmotor power at one point are being measured in a sta-ble manner by setting the synchronization source for allchannels to the inverter’s output current.

Measuring an Inverter’s InputPowerTo measure efficiency and loss, it is necessary to mea-sure the power being input to the inverter. This inputpower will serve as the basis for measuring efficiencyand loss. Generally speaking, either DC or AC com-mercial power is used as inverter input. If the valuesyielded by measurement of the input and output powercontain an error component, it will have a significant ef-fect on the efficiency and loss values. Consequently, itis necessary to measure the inverter’s input power witha high degree of precision. For example, an error of0.5% in the input power measured value for an inverterwith an efficiency of 99% will result in an error of 50%for the loss. Although it is possible to calculate powerusing a general-purpose waveform recorder, one mustexercise caution to ensure that a sufficient level of ac-curacy has been defined for the band that you wish tomeasure.

Caution is especially warranted during DC power mea-surement, which should be preceded by adjusting thepower analyzer and current sensors’ DC offsets. If thepower analyzer provides a zero-adjustment function,perform zero-adjustment after zeroing out input to thepower analyzer and current sensors. In this way, it ispossible to enable accurate DC measurement by can-celing out the instrument’s DC offset.

L R

Inverter output Backelectromotive

force

Fig. 2: Equivalent circuit for a motor (1 phase).

Measuring an Inverter’s OutputPower

Inverters generate PWM-modulated output that in-cludes the switching frequency and its harmonic com-ponents. Consequently, power measurement must beperformed over a wider band than when measuring DCor commercial frequency power.

Let’s study the band that is needed in order to mea-sure power at the switching frequency and its harmon-ics. Fig.2 provides an equivalent circuit for a motor thatis driven by an inverter. Since the motor’s windingshave an inductance component, high-frequency currentis less likely to flow to the motor. Since the voltage isa PWM waveform, it can be approximated as a rectan-gular wave. At this time, the current will take the shapeof a triangular waveform. When calculating RMS val-ues for the triangular waveform over the frequency do-main, measurement can yield RMS values with an errorof 0.1% or less if harmonics can be measured to the5th order. Here the active power Pf can be expressedas a function of the voltage U f , the current I f , and thevoltage-current phase difference θ f as follows:

Pf = U f · I f · cos θ f . (1)

Consequently, if either the voltage or current is 0, theactive power for that frequency component will be 0.Assuming measurement at a precision of 0.1%, currentat 7th order and higher harmonic components can beignored, as noted above. Therefore, the ability to mea-sure voltage, current, and phase difference accuratelywithin the band of 5 times to 7 times the switching fre-quency is sufficient in order to measure power at theswitching frequency and its harmonics with an error of0.1% or less. However, loss in an actual motor includesthe magnetic material’s core loss as well as losses fromfactors such as wire skin effects in addition to the re-

2

Voltagewaveform

Currentwaveform

FFTSpectrum

Voltage

Current

100

10

1

0.1

10m

1m

%f.s.

0 400k 800k 1.2M 2M1.6M

Fig. 3: Waveforms and FFT results for an actualinverter-driven motor (measured with the Power Ana-lyzer PW6001).

sistance portion shown in Fig.2. Consequently, a some-what wider frequency band is needed in order to moreaccurately measure power at the switching frequencyand its harmonics. The band that is actually needed isaffected by factors such as the frequency characteristicsof the respective losses.

Fig.3 shows the actual voltage and current waveformsof a motor driven by an SiC inverter, as well as associ-ated FFT results. Table 1 provides detailed informationabout the measurement targets. Since the voltage is aPWM waveform, an examination of the FFT results re-veals frequency components in excess of 1 MHz. Stan-dard power analyzers do not provide a sufficient mea-surement band to measure voltage waveforms with therequired degree of accuracy. Looking at the current,it is apparent that the current components do not ex-ceed about 200 kHz. In addition, the waveform closelyresembles a sine wave. This shape derives from thefact that the motor’s inductance component makes itless likely that high-frequency current will flow, as de-scribed above.

In this way, it is desirable to use a power analyzerwith favorable characteristics for voltage, current, andphase difference characteristics in the frequency bandof at least 5 to 7 times the switching frequency in orderto allow accurate measurement of the inverter’s outputpower. Use of increasingly high switching frequenciesfor SiC inverters has the effect of requiring a higher-frequency band in this regard.

Table 1: Specifications of measured SiC inverter andmotor.

Inverter MotorSwitching Switching

Inductance Resistanceelement frequency

SiC-MOSFETSCH2080KE 20 kHz 3.6 mH 0.9Ω

(ROHM)

Phase

Corrected

Frequency [Hz]

Ph

ase [

deg

.]

2

0

-2

-4

-8

-6

-101M100k10k1k

Fig. 4: Compensating a current sensor’s phase error.

Generally speaking, current sensors are used when mea-suring current in a motor drive system. In such appli-cations, the current sensors’ phase error becomes prob-lematic. All current sensors exhibit a tendency towardincreased phase error at higher frequencies, and thistendency becomes a source of error when measuringhigh-frequency power. As shown in Fig.2, the motorwindings’ inductance component is dominant at highfrequencies. As a result, power at the switching fre-quency and its harmonics is characterized by a lowerpower factor. Based on Eq.(1), phase error has anextremely large impact on power measurement errorat low power factor values (θ values of approximately90). Consequently, it is not possible to measure powerat a high degree of precision unless the current sen-sors’ phase error can be corrected. Hioki’s Power Ana-lyzer PW6001 provides functionality for compensationfor current sensor phase error, as shown in Fig.4. Thisphase compensation function makes it possible to mea-sure inverter output power more accurately.


Measuring a Motor’s PowerIn order to measure the overall efficiency and loss of amotor or motor drive system, it is necessary to measurethe motor’s power. To calculate motor power Pm[W]using Eq.(2), we all need to measure torque T [N·m] andMotor rpm n[rpm].

Pm = T · 2 · π · n/60. (2)

The motor’s rpm is measured using a tachometer orpulse encoder, while torque is measured using a torquemeter. In order to measure efficiency and loss, it is nec-essary to measure power and motor power at the sametime. Consequently, we need to use a power analyzerthat can accept signals from a tachometer, pulse en-coder, and torque meter as input.

Example Measurement of the Effi-ciency of an Inverter with SiC PowerSemiconducutorsFig.5 illustrates the results of measuring the efficiencyof an SiC inverter that is driving a motor. The setupuses a Hioki Power Analyzer PW6001 and CurrentBox PW9100, and the figure illustrates the results ofmeasurement while varying the cutoff frequency of thePW6001’s LPF from 1 kHz to 2 MHz. The measure-ment targets are the same as those described in Table1. The measured efficiency values change dramaticallyaround a cutoff frequency of 10 kHz to 50 kHz. Thischange reflects the difference in whether power at theswitching frequency and its harmonic components arebeing measured. In short, efficiency values at and below10 kHz derive from measurement of only the power atthe fundamental frequency, which is synchronized withthe motor’s rpm, and its harmonic components. On theother hand, efficiency values at and above 50 kHz de-rive from also the measurement of power at the switch-ing frequency and its harmonic components. At andabove 50 kHz, efficiency values increase as the cutofffrequency increases. This change is a result of the abil-ity to measure the higher-order harmonic componentsof the switching frequency.

In this way, the PW6001 Power Analyzer is capableof high-precision, high-stability measurement of motordrive system efficiency and loss up to the 2 MHz band,

fsw = 20kHz

Cutoff frequency of LPF[Hz]

Invert

er

effi

cie

ncy[%

]

99.0

98.5

97.5

97.0

96.5

98.0

95.5

95.0

96.0

1M100k10k1k 10M

Fig. 5: Efficiency measurement results of an SiC in-verter while varying the Power Analyzer PW6001’sLPF cutoff frequency.

indicating that the instrument can measure efficiencyand loss based on accurate measurement of power atthe switching frequency and its harmonic components.

Effects of Common-Mode Voltage

Fig.6 provides a voltage wiring schematic describingmeasurement of the output power of a 3-phase/3-wireinverter. Since the power analyzer will measure linevoltage, a large common-mode voltage will be appliedacross its channels. In addition, this common-modevoltage includes switching frequency and associatedharmonic components. Consequently, it is necessaryto make measurements with a power analyzer that hasa high common-mode rejection ratio (CMRR) for highfrequencies. A CMRR of 80 dB has an effect of 0.01%of the common-mode voltage on the displayed values.In other words, if a common-mode voltage of 100 V isinput, there would be an effect of 0.01 V on display val-ues.

Fig.6 illustrates the results of measuring the line volt-age and common-mode voltage of an SiC inverter. TheFFT results are similar to the results shown in Fig.3,making it clear that the common-mode voltage includesswitching frequency and associated harmonic compo-nents. Consequently, it can be concluded that as thefrequency of the switching frequency increases, so doesthat of the common-mode voltage. Inverters that use


Measuring a Motor’s PowerIn order to measure the overall efficiency and loss of amotor or motor drive system, it is necessary to measurethe motor’s power. To calculate motor power Pm[W]using Eq.(2), we all need to measure torque T [N·m] andMotor rpm n[rpm].

Pm = T · 2 · π · n/60. (2)

The motor’s rpm is measured using a tachometer orpulse encoder, while torque is measured using a torquemeter. In order to measure efficiency and loss, it is nec-essary to measure power and motor power at the sametime. Consequently, we need to use a power analyzerthat can accept signals from a tachometer, pulse en-coder, and torque meter as input.

Example Measurement of the Effi-ciency of an Inverter with SiC PowerSemiconducutorsFig.5 illustrates the results of measuring the efficiencyof an SiC inverter that is driving a motor. The setupuses a Hioki Power Analyzer PW6001 and CurrentBox PW9100, and the figure illustrates the results ofmeasurement while varying the cutoff frequency of thePW6001’s LPF from 1 kHz to 2 MHz. The measure-ment targets are the same as those described in Table1. The measured efficiency values change dramaticallyaround a cutoff frequency of 10 kHz to 50 kHz. Thischange reflects the difference in whether power at theswitching frequency and its harmonic components arebeing measured. In short, efficiency values at and below10 kHz derive from measurement of only the power atthe fundamental frequency, which is synchronized withthe motor’s rpm, and its harmonic components. On theother hand, efficiency values at and above 50 kHz de-rive from also the measurement of power at the switch-ing frequency and its harmonic components. At andabove 50 kHz, efficiency values increase as the cutofffrequency increases. This change is a result of the abil-ity to measure the higher-order harmonic componentsof the switching frequency.

In this way, the PW6001 Power Analyzer is capableof high-precision, high-stability measurement of motordrive system efficiency and loss up to the 2 MHz band,

fsw = 20kHz

Cutoff frequency of LPF[Hz]

Invert

er

effi

cie

ncy[%

]

99.0

98.5

97.5

97.0

96.5

98.0

95.5

95.0

96.0

1M100k10k1k 10M

Fig. 5: Efficiency measurement results of an SiC in-verter while varying the Power Analyzer PW6001’sLPF cutoff frequency.

indicating that the instrument can measure efficiencyand loss based on accurate measurement of power atthe switching frequency and its harmonic components.

Effects of Common-Mode Voltage

Fig.6 provides a voltage wiring schematic describingmeasurement of the output power of a 3-phase/3-wireinverter. Since the power analyzer will measure linevoltage, a large common-mode voltage will be appliedacross its channels. In addition, this common-modevoltage includes switching frequency and associatedharmonic components. Consequently, it is necessaryto make measurements with a power analyzer that hasa high common-mode rejection ratio (CMRR) for highfrequencies. A CMRR of 80 dB has an effect of 0.01%of the common-mode voltage on the displayed values.In other words, if a common-mode voltage of 100 V isinput, there would be an effect of 0.01 V on display val-ues.

Fig.6 illustrates the results of measuring the line volt-age and common-mode voltage of an SiC inverter. TheFFT results are similar to the results shown in Fig.3,making it clear that the common-mode voltage includesswitching frequency and associated harmonic compo-nents. Consequently, it can be concluded that as thefrequency of the switching frequency increases, so doesthat of the common-mode voltage. Inverters that use

4

Motor

~100kHz Switching

U1U3

U2

DC bus

Fig. 6: Wiring connections when measuring inverteroutput power (3P3W3M).

Line - linevoltage

Line - earthvoltage

FFT spectrum of line - earch

100

10

1

0.1

10m

1m

%f.s.

0 400k 800k 1.2M 2M1.6M

Fig. 7: Common-mode voltage of inverter output volt-age.

SiC power semiconductors are being designed with in-creasingly high switching frequencies. As a result, it isdesirable to choose a power analyzer with a high CMRRfor higher frequencies.

Countermeasures for Current Sen-sor Noise

When measuring a motor or inverter with a high ratedcapacity, it is necessary to measure large currents on theorder of several hundred amperes. It is standard prac-tice to use current sensors when measuring large cur-rents. Inverters produce large amounts of noise, and itis essential to implement measures to address the ef-fects of noise on the sensors themselves and on theroute along which the current sensors’ output signalsare transmitted in order to ensure accurate power mea-surement. Hioki offers a line of high-precision current

Analog band

Aliasing

Volta

ge/C

urre

nt

Frequencyfs / 2 fs

Fig. 8: Relationship between analog band and samplingfrequency in a standard power analyzer.

sensors with such features for use with power analyzers.Consequently, it is possible to perform power measure-ment in a manner that is highly resistant to noise simplyby connecting the power analyzer and current sensorswith a dedicated connector4, 5).

Power Analyzer Frequency Bandand Sampling Frequency

Fig.8 illustrates the relationship between sampling fre-quency and analog band in a typical power analyzer.The analog band of most power analyzers’ input cir-cuitry is greater than half the sampling frequency fs

(i.e., fs/2). In such instruments, the voltage and currentcomponents that exist in frequencies higher than ( fs/2)appear in the low-frequency domain as folding noise.This phenomenon is generally known as aliasing.

When measuring targets that include frequency com-ponents across a broad band like a PWM waveform,it becomes impossible to distinguish between the fold-ing noise and the actual signal. The result of this phe-nomenon is additional measurement error and reducedrepeatability in power measurement. Moreover, it be-comes impossible to distinguish between the foldingnoise and actual harmonics in harmonic analysis. Theresult is that accurate analysis becomes impossible, and,for example, detection of false harmonic componentsmore likely.


As shown in Fig.3, inverter output voltage includescomponents in excess of 1 MHz. Standard power an-alyzers have sampling frequencies ranging from 100kHz to about 5 MHz. Consequently, there are volt-age components at frequencies in excess of ( fs/2). Insuch cases, accurate measurement is not possible whenthe analog band and sampling frequency are related asshown in Fig.8. To enable accurate measurement, it isnecessary to limit the analog band to less than ( fs/2). Inother words, the band that can actually be used is lessthan half the sampling frequency.

In this way, when measuring and analyzing inverter out-put power, it is necessary to use a measuring instrumentthat has been designed in accord with sampling princi-ples. Hioki’s power analyzers are designed in this way.For example, the Power Analyzer PW6001 has a sam-pling frequency of 5 MHz, versus an analog band of 2MHz/-3 dB. Consequently, the instrument is capable ofsimultaneous broadband power measurement, accurateharmonic analysis, and accurate FFT analysis.

SummaryThis paper has introduced key considerations that comeinto play when measuring the efficiency and loss of in-verters and motors while offering actual measurementexamples, as well as related topics such as requirementsfor measuring instruments used in such applications. Ithas devoted special attention to considerations that ap-ply when measuring SiC inverters, which have been en-tering into increasingly widespread use in recent years,as compared to conventional inverters. We also pre-sented actual measurement results to demonstrate howthe efficiency and loss of SiC inverters can be mea-sured with a high degree of precision and stability byeliminating various sources of error. It is the author’shope that the discussions will serve as a useful guide inpower, efficiency, and loss measurement of SiC invert-ers and motor drive systems.

References1) Thal, E., K. Masuda, and E. Wiesner : “New

800A/1200V Full SiC Module”, Bodo’s PowerSystems, April 2015, pp.28-31.

2) Fuji Electronic : “Joint Development of Converter-Inverter for The Tokaido Shinkansen Cars Us-

ing SiC Power Semiconductor Modules”, re-trived from http://www.fujielectric.com/company/news/2015/20150625120019879.html

3) Mitsubishi Electric : “Mitsubishi Electric’s RailcarTraction Inverter with All-SiC Power ModulesAchieves 40% Power Savings”, retrived fromhttp://www.mitsubishielectric.com/news/2015/0622-a print.html

4) Yoda, H., H. Kobayashi, and S. Takiguchi : “Cur-rent Measurement Methods that Deliver High Pre-cision Power Analysis in the Field of PowerElectronics”, Bodo’s Power Systems, April 2016,pp.38-42.

5) Ikeda, K., and H. Masuda : “High-Precision, Wide-band, Highly Stable Current Sensing Technology”,Bodo’s Power Systems, July 2016, pp.22-28.


Identification of PMSM Motor Parameterswith a Power Analyzer

By Kunihisa Kubota, Hajime Yoda, Hiroki Kobayashi and Shinya Takiguchi

1 IntroductionRecent years have seen permanent magnet synchronousmotors (PMSMs) and related control technologiesrapidly permeate into the advanced power electron-ics landscape and markets. These developments re-flect the advent of high-performance, high-efficiencydesigns thanks to progress in permanent magnet mate-rials as well as the advantages of PMSMs relative toother motors in terms of quiet operation and simplicityof maintenance1). Recently, PMSMs are being adoptedin hybrid and electric vehicles in addition to house-hold electronics and industrial machinery, and their en-try into widespread use is expected to accelerate in thefuture2).

In general, PMSM analysis and control are based onthe equivalent circuit model for a motor expressed onthe d- and q-axes. A variety of high-performance con-trol methods have been proposed for PMSMs, and thesecontrol algorithms are based on d-q equivalent circuits,making it extremely important to identify the equivalentcircuit constants—in other words, the motor parameters(d-axis and q-axis inductance, Ld and Lq)—with a highdegree of precision.

Of these motor parameters, Lq exhibits a particularlyhigh degree of current dependence due to magneticsaturation3, 4), making it difficult to implement high-performance control while using low-precision motorparameters measured in a simple manner with an LCRmeter or other instrument while the motor is in thestopped state.

This paper introduces a method by which a power an-alyzer can be used to identify motor parameters easilyand with a high degree of precision while the target mo-tor is operating. In addition, it provides results (mo-tor parameters) obtained through the actual use of thismethod.

2 Method for identifying motorparameters

This chapter provides a brief description of the prin-ciples employed to identify PMSM motor parametersusing a power analyzer and of a procedure for doing so.

2.1 PrinciplesIf we assume the following with regard to the voltageequation for a PMSM expressed on the d-q coordinateaxis, we arrive at Eq.(2.1)3).

i) The spatial distribution of magnetic flux in the gapbetween the stator and rotor takes the form of asine wave moving along the gap.

ii) The harmonic components of the voltage and cur-rent can be ignored.

iii) Core loss can be ignored.

[vd

vq

]=

[R + pLd −ωLq

ωLd R + pLq

] [idiq

]+

[0ωϕa

]

(2.1)

In this equation, vd and vq represent the d-axis and q-axis components of the armature voltage for each phase;id and iq, the d-axis and q-axis components of the arma-ture current for each phase; R, the armature resistancefor each phase; p, the differential operator (d/dt); Ld

and Lq, the d-axis and q-axis self-inductance; ω, the ro-tation angle (electrical angle) speed; and ϕa(= Ke), theRMS value of the permanent magnet’s flux linkage withthe armature (i.e., the induced voltage constant).

Fig.2.1 illustrates the result of assuming a stationarystate (so that time-derivative terms can be ignored) and


expressing Eq.(2.1) as a d-axis and q-axis vector dia-gram. In the figure, v1 and i1 represent the fundamentalcomponents of the phase voltage and phase current, andθv and θi represent the fundamental phase angle of thephase voltage and phase current, respectively. Based onFig.2.1, the d-axis and q-axis voltage equations can beformulated as follows :

Keω + Riq = vq − ωLdid (2.2)vd = Rid − ωLqiq. (2.3)

Solving these for Ld and Lq yields the following equa-tions :

Ld =vq − Keω − Riq

ωid(2.4)

Lq =Rid − vd

ωiq. (2.5)

d-axis (Field axis)

q-axis (Torque axis)

Riq

Ke

id

iqi1

v

v1(vd, vq)

Ldid

Rid Lqiq

i

ω

ωω

θ

θ

Fig. 2.1: PMSM vector diagram.

2.2 Identification procedure

This section describes a procedure by means of whicha power analyzer can be used to identify motor param-eters.

Although this specific procedure uses a Hioki PowerAnalyzer PW6001, motor parameters can be identifiedusing a similar procedure with any power analyzer that

provides an electrical angle measurement function thatis equivalent to that offered by the PW6001.

2.2.1 Measuring the armature resistance R foreach phase

Measure the armature resistance R for each phase us-ing a resistance meter or other suitable instrument inadvance.

2.2.2 Performing phase zero-adjustment and iden-tifying the induced voltage constant Ke

After placing the motor terminals of the PMSM beingmeasured in the open state (id = iq = 0), connect themotor terminals to the “CH 1”, “CH 2” and “CH 3”voltage inputs of the Power Analyzer PW6001. Addi-tionally, connect the encoder’s A-phase pulse output to“CH B”, its B-phase pulse output to “CH C”, and its Z-phase pulse (origin signal) output to “CH D” (Fig.2.2).

Configure the Power Analyzer PW6001’s settings bysetting the motor analysis operating mode to “Single”,the measurement parameter to “Torque Speed DirectionOrigin”, and “CH B” input to “Pulse”. In addition, setthe wiring connection for “CH 1”, “CH 2” and “CH 3”to “3P3W3M”, the synchronization source to “Ext1”,and ∆ conversion to “ON”. Setting the synchronizationsource to “Ext1” allows the voltage and current phaseangles to be measured using the inputted encoder pulseas the reference, and setting ∆ conversion to “ON” al-lows the line voltage to be converted to, and measuredas, a phase voltage.

In this state, drive the motor from the load side togenerate an induced voltage and perform phase zero-adjustment on the Power Analyzer PW6001. As a re-sult of this step, θv and θi will represent the phase angleexpressed using the phase of the induced voltage gener-ated in the q-axis direction as the reference—that is, theelectrical angle.

At this time, Eq.(2.4) can be rewritten as follows sincethe induced voltage vq is equal to v1, allowing identifi-cation of Ke.

Ke =vq

ω=

v1

2π f1(2.6)

In this equation, f1(= ω/2π) represents the frequencyof the phase voltage’s fundamental wave.


expressing Eq.(2.1) as a d-axis and q-axis vector dia-gram. In the figure, v1 and i1 represent the fundamentalcomponents of the phase voltage and phase current, andθv and θi represent the fundamental phase angle of thephase voltage and phase current, respectively. Based onFig.2.1, the d-axis and q-axis voltage equations can beformulated as follows :

Keω + Riq = vq − ωLdid (2.2)vd = Rid − ωLqiq. (2.3)

Solving these for Ld and Lq yields the following equa-tions :

Ld =vq − Keω − Riq

ωid(2.4)

Lq =Rid − vd

ωiq. (2.5)

d-axis (Field axis)

q-axis (Torque axis)

Riq

Ke

id

iqi1

v

v1(vd, vq)

Ldid

Rid Lqiq

i

ω

ωω

θ

θ

Fig. 2.1: PMSM vector diagram.

2.2 Identification procedure

This section describes a procedure by means of whicha power analyzer can be used to identify motor param-eters.

Although this specific procedure uses a Hioki PowerAnalyzer PW6001, motor parameters can be identifiedusing a similar procedure with any power analyzer that

provides an electrical angle measurement function thatis equivalent to that offered by the PW6001.

2.2.1 Measuring the armature resistance R foreach phase

Measure the armature resistance R for each phase us-ing a resistance meter or other suitable instrument inadvance.

2.2.2 Performing phase zero-adjustment and iden-tifying the induced voltage constant Ke

After placing the motor terminals of the PMSM beingmeasured in the open state (id = iq = 0), connect themotor terminals to the “CH 1”, “CH 2” and “CH 3”voltage inputs of the Power Analyzer PW6001. Addi-tionally, connect the encoder’s A-phase pulse output to“CH B”, its B-phase pulse output to “CH C”, and its Z-phase pulse (origin signal) output to “CH D” (Fig.2.2).

Configure the Power Analyzer PW6001’s settings bysetting the motor analysis operating mode to “Single”,the measurement parameter to “Torque Speed DirectionOrigin”, and “CH B” input to “Pulse”. In addition, setthe wiring connection for “CH 1”, “CH 2” and “CH 3”to “3P3W3M”, the synchronization source to “Ext1”,and ∆ conversion to “ON”. Setting the synchronizationsource to “Ext1” allows the voltage and current phaseangles to be measured using the inputted encoder pulseas the reference, and setting ∆ conversion to “ON” al-lows the line voltage to be converted to, and measuredas, a phase voltage.

In this state, drive the motor from the load side togenerate an induced voltage and perform phase zero-adjustment on the Power Analyzer PW6001. As a re-sult of this step, θv and θi will represent the phase angleexpressed using the phase of the induced voltage gener-ated in the q-axis direction as the reference—that is, theelectrical angle.

At this time, Eq.(2.4) can be rewritten as follows sincethe induced voltage vq is equal to v1, allowing identifi-cation of Ke.

Ke =vq

ω=

v1

2π f1(2.6)

In this equation, f1(= ω/2π) represents the frequencyof the phase voltage’s fundamental wave.

2

Torque A BZ

Power Analyzer PW6001

CH 1 CH 2 CH 3

PWM Inverter

PMSM Torque Sensor

Load PulseEncoder

A BCD

Fig. 2.2: Wiring connections when performing phasezero-adjustment and identifying the induced voltageconstant Ke.

2.2.3 Identifying the motor parameters Ld and Lq

with user-defined functions

The d-axis and q-axis self-inductance Ld and Lq can beidentified using R as measured in Section 2.2.1 and Ke

as identified in Section 2.2.2. First, connect the drive in-verter output to the motor terminals that were left openin Section 2.2.2 and operate the motor (Fig.2.3). Atthis time, the following equations will obtain based onFig.2.1:

vd = −v1 sin θv (2.7)vq = v1 cos θv (2.8)id = −i1 sin θi (2.9)iq = i1 cos θi (2.10)

By configuring the instrument’s user-defined functions(UDFs) with these equations as well as Eqs.(2.4) and(2.5), it is a simple matter to identify Ld and Lq whilemonitoring vd, vq, id, and iq. See reference5) for specificexamples of settings for the Power Analyzer PW6001’suser-defined functions.

3 Measurement example

This section presents the results of using the proceduredescribed in Section 2.2 to actually identify motor pa-rameters.

PWM Inverter

PMSM Torque Sensor

PulseEncoder

Load

Torque A BZ

Power Analyzer PW6001

CH 1 CH 2 CH 3 A BCD

Fig. 2.3: Wiring connections when identifying the Ld

and Lq motor parameters.

3.1 Measurement conditions

Tables 1, 2 and 3 describe the specifications of the in-verter (Fig.3.1), drive-side motor, and load-side motor(Fig.3.2) used in the procedure.Table 4 describes the measuring instruments that wereused. The Resistance Meter RM3544 noted in the tablewas used to measure the armature resistance R of thedrive-side motor listed in Table 2 for each phase (Sec-tion 2.2.1).

Fig. 3.1: Inverter.

3.2 Identifying the induced voltage con-stant Ke

The induced voltage constant Ke was identified usingthe procedure described in Section 2.2.2. For reference,Fig.3.3 illustrates the induced voltage (phase voltage)waveforms for the drive-side motor and A/B/Z phasepulse waveforms for the encoder during the identifica-


Fig. 3.2: Drive-side motor (left) and load-side motor(right).

Table 1: Inverter specifications.Item Specifications

Rated output capacity 10.0 kVARated output voltage AC 400 VrmsRated output current AC 14.5 ArmsRated input voltage DC 700 VRated input current DC 15.1 A

Maximum input current DC 18.6 A

Input voltage range From DC 0 Vto DC 800 V

Switching frequency Up to 200 kHz

Switching element SiC MOSFETSCH2080KE (ROHM)

Manufacturer Myway Plus Corp.

Table 2: Drive-side motor specifications.Item Specifications

RM86A20-2-E8Model DC brushless motor

with encoderRated voltage DC 100 VRated current 2 A

Rated rpm 2500 rpmRated output 120 W

Armature resistance 0.89768 Ωfor each phaseNumber of poles 8Number of pulse 1024per rotation

Table 3: Load-side motor specifications.Item Specifications

Model DC motor SS60E80-6Rated voltage DC 100VRated current 4.8 A


Table 4: Measuring instrumentsInstrument Model Manufacturer

Power Analyzer PW6001 HIOKI E.E. Corp.Current Sensor CT6841 HIOKI E.E. Corp.

Resistance Meter RM3544 HIOKI E.E. Corp.

tion process.

Fig.3.4 illustrates the relationships between the motorrpm n, the RMS value v1 of the fundamental componentof the drive-side motor induced (phase) voltage, and theidentified induced voltage constant Ke. The measuredv1 value varies proportionally with n, while the identi-fied Ke value remains roughly constant, without regardto n. In this way, the relationships between these threevalues can be seen to satisfy the relationships describedin Eq.(2.6).

Ke exhibits a small amount of variability during low-speed operation due to the more pronounced rotatingunbalance of the motor in that operating regime.

Zoom

20 ms/div

Voltage

400 us/div

Pulse

Fig. 3.3: Drive-side motor induced (phase) voltage andencoder’s A/B/Z phase pulse waveforms during identi-fication of the induced voltage constant Ke.

3.3 Identifying the Ld and Lq motor pa-rameters

The d-axis and q-axis self-inductance Ld and Lq wereidentified using the procedure described in Section2.2.3. For reference, Fig.3.5 illustrates the inverter’ssecondary-side phase voltage and phase current as wellas the encoder’s A/B/Z phase pulse waveforms duringidentification.


Fig. 3.2: Drive-side motor (left) and load-side motor(right).

Table 1: Inverter specifications.Item Specifications

Rated output capacity 10.0 kVARated output voltage AC 400 VrmsRated output current AC 14.5 ArmsRated input voltage DC 700 VRated input current DC 15.1 A

Maximum input current DC 18.6 A

Input voltage range From DC 0 Vto DC 800 V

Switching frequency Up to 200 kHz

Switching element SiC MOSFETSCH2080KE (ROHM)

Manufacturer Myway Plus Corp.

Table 2: Drive-side motor specifications.Item Specifications

RM86A20-2-E8Model DC brushless motor

with encoderRated voltage DC 100 VRated current 2 A


Armature resistance 0.89768 Ωfor each phaseNumber of poles 8Number of pulse 1024per rotation

Table 3: Load-side motor specifications.Item Specifications

Model DC motor SS60E80-6Rated voltage DC 100VRated current 4.8 A


Table 4: Measuring instrumentsInstrument Model Manufacturer

Power Analyzer PW6001 HIOKI E.E. Corp.Current Sensor CT6841 HIOKI E.E. Corp.

Resistance Meter RM3544 HIOKI E.E. Corp.

tion process.

Fig.3.4 illustrates the relationships between the motorrpm n, the RMS value v1 of the fundamental componentof the drive-side motor induced (phase) voltage, and theidentified induced voltage constant Ke. The measuredv1 value varies proportionally with n, while the identi-fied Ke value remains roughly constant, without regardto n. In this way, the relationships between these threevalues can be seen to satisfy the relationships describedin Eq.(2.6).

Ke exhibits a small amount of variability during low-speed operation due to the more pronounced rotatingunbalance of the motor in that operating regime.

Zoom

20 ms/div

Voltage

400 us/div

Pulse

Fig. 3.3: Drive-side motor induced (phase) voltage andencoder’s A/B/Z phase pulse waveforms during identi-fication of the induced voltage constant Ke.

3.3 Identifying the Ld and Lq motor pa-rameters

The d-axis and q-axis self-inductance Ld and Lq wereidentified using the procedure described in Section2.2.3. For reference, Fig.3.5 illustrates the inverter’ssecondary-side phase voltage and phase current as wellas the encoder’s A/B/Z phase pulse waveforms duringidentification.

4

0 500 1000 1500 20000

5

10

15

20

25

30.5

31

31.5

32

32.5

33

Ke

[mV

s/ra

d]

v 1[V

]

n[rpm]

Fig. 3.4: Relationships between the motor rpm n, theRMS value v1 of the fundamental component of thedrive-side motor induced (phase) voltage, and the iden-tified induced voltage constant Ke

Fig.3.6 illustrates the relationships between (a) the d-axis current id and the identified d-axis self-inductanceLd and (b) the q-axis current iq and the identified q-axisself-inductance Lq. Ld remains roughly constant, with-out regard to id. By contrast, Lq exhibits a high degreeof current dependency due to magnetic saturation andvaries significantly with iq. These characteristics makeit clear that it is not possible to use an LCR meter orsimilar instrument to identify Ld with a high degree ofprecision while the motor is in the stopped state. In-stead, the value must be identified while the motor isoperating.

The variability in the Ld and Lq values when the id andiq values are small is also likely to be caused by rotatingunbalance of the motor during low-speed operation.

Fig.3.6 illustrates the results of identifying the Ld andLq motor parameters while the motor’s rpm is variedwhile holding the current phase angle constant, show-ing the current dependence of Ld and Lq. The currentphase angle dependence of the motor parameters canalso be verified by applying this identification method.

4 ConclusionThis paper has introduced a method for identifyingPMSM motor parameters easily and with a high degreeof precision using a power analyzer. It also presentsthe results of using the introduced method along with a

Zoom

20 ms/divVoltage

Current

1 ms/div

Pulse

Fig. 3.5: Inverter secondary-side phase voltage andphase current and encoder’s A/B/Z phase pulse wave-forms during identification of the Ld and Lq motor pa-rameters (when driving the motor with the inverter)

0.2 0.3 0.4 0.5 0.6 0.7 0.80

2

4

6

8

100.2 0.3 0.4 0.5 0.6 0.7 0.8

0

2

4

6

8

10

i [A]d

i [A]q

L d[mH]

q[mH]

L

Fig. 3.6: Relationships between (a) the d-axis currentid and the identified d-axis self-inductance Ld (shownin red) and (b) the q-axis current iq and the identifiedq-axis self-inductance Lq (shown in blue).


Hioki Power Analyzer PW6001 to identify actual motorparameters. It must be noted that the method introducedin this paper presumes the use of an analytical modelthat posits that core loss can be ignored. That said, bymeasuring mechanical loss and identifying the equiva-lent core loss resistance in advance, it would be pos-sible to further develop the described method in orderto identify motor parameters while taking into accountcore loss.

The identification of PMSM motor parameters intro-duced in this paper is only one example of an appli-cation for power analyzers, which can be used effec-tively in numerous other settings in the power electron-ics field. The authors look forward in the future to ac-tively introducing other applications in which power an-alyzers can be effectively.

References1) Shigeo Morimoto : “Trend of Permanent Magnet

Sychronous Machines”, IEEJ Trans, Vol.2 (2007),pp.101-108.

2) Investigating R&D Committee on industry applica-tions of PM motors : “Trend in the latest technolo-gies and applications of permanent magnet syn-chronous motors”, IEEJ Technical Report (2009),No.1145 (in Japanese).

3) Shigeo Morimoto, Yoji Takeda, and Takao Hi-rasa : “Method for Measuring a PM Motor’s dqEquivalent Circuit Constants”, IEEJ Transactionson Industry Applications, Vol.113-D (1993) No.11,pp.1330-1331 (in Japanese).

4) A. Soualmi, F. Dubas, D. Depernet, A. Randria andC. Espanet : “Inductances estimation in the d-qaxis for an interior permanent-magnet synchronousmachines with distributed windings”, Proc. XXICEM (2012), pp.308-314.

5) HIOKI E. E. Corp. : “Identification ofPMSM Parameters with the Power Ana-lyzer PW6001” (White paper), retrived fromhttps://www.hioki.com/en/products/detail/?product key=5796.


Measurement of Loss inHigh-Frequency Reactors

Method for Measuring and Analyzing Reactors (Inductors)Using a Power Analyzer

By Kazunobu Hayashi

IntroductionHigh-frequency reactors are used in a variety of loca-tions in electric vehicles (EVs) and hybrid electric ve-hicles (HEVs). Examples include step-up DC/DC con-verters between the battery and the inverter and AC/DCconverters in battery charging circuits. To boost over-all system efficiency, it is necessary to improve the effi-ciency in each constituent circuit, and reactors are onecomponent that is responsible for a large amount of lossin these circuits.

Consequently, accurate measurement of reactor lossis an essential task in improving overall system effi-ciency. In general, because most of these reactors areswitched on and off at high frequencies, conventionalwisdom holds that it is difficult to directly measure re-actor loss. In the past, elements such as IGBTs wereused as switching elements, and switching frequencieswere on the order of tens of kilohertz. In recent years,progress in the commercialization of SiC and GaN ele-ments has made possible switching frequencies greaterthan 100 kHz, spurring demand for measuring instru-ments with high-frequency bands. This paper describesa method for measuring reactor loss with a high degreeof precision, with reference to an actual measurementexample.

Reactor lossFig. 1 illustrates an equivalent circuit for a reactor,which can be thought of as a circuit with an inductancecomponent Ls connected in series with the resistanceRs, representing loss. The equivalent circuit’s Ls and Rs

Fig. 1: Equivalent circuit for a reactor.

can be measured using a standard LCR meter. In sucha scenario, the LCR meter will apply a minuscule sine-wave signal to the measurement target and measure theimpedance. By contrast, the characteristics of a reactorin an operating circuit will differ from a measurementmade with an LCR meter for the following reasons:

· A rectangular-wave voltage will be applied to thecomponent as a result of the switching operation.This will cause a triangular-wave current to flow,with the result that neither the voltage waveformnor the current waveform will take the form of asine wave.

· Due to the characteristics of the component’s mag-netic core, each parameter will exhibit level depen-dence. This dependence will cause quantities suchas Ls and Rs during component operation to differfrom the values obtained by measurement with anLCR meter.

· During use of a DC/DC converter, the current ap-plied to a reactor will exhibit DC superposition.


The parameters during such superposition differdue to the magnetic core’s saturation characteris-tics.

In short, high-precision measurement of reactor lossand parameters must be carried out not with an LCRmeter, but rather while the component is in an operat-ing state.

Method for measuring reactor loss

Fig. 2 provides a measurement block diagram duringmeasurement of reactor loss using a boost chopper cir-cuit as an example. In this example, a Power AnalyzerPW6001 and current sensor are used to make the mea-surement, in which the instrument directly measures thevoltage UL and the current IL that are applied to the re-actor and then calculates the loss. Power as measured inthis setup consists of the total of the power consumed inthe winding and in the core. In short, the reactor’s over-all loss is being measured.

Accuracy in this measurement can be increased bykeeping the current wiring route and the connection ofthe voltage cables to the power analyzer as short as pos-sible. In addition, it is necessary to consider the effectsof metallic and magnetic objects in the vicinity of thereactor. Caution is necessary as wires and other nearbymetallic objects may affect the operation of the reactor.Moreover, due to the potential for measurement to beaffected by peripheral noise from the voltage cables, itis desirable to twist the cables before measuring.

When measuring the loss of the core alone (core loss),the reactor voltage is measured after wrapping sec-ondary wiring around the core as shown in Fig. 3. Be-cause core loss is defined as the area of the B–H loop,the core loss Pc per unit of volume can be calculatedas follows, where T represents the duration of one B–Hloop period:

Pc =1T

∫HdB =

1T

∫ T

0H

dBdt

dt

If the core has a flux path length of l and a cross-sectional area of A, the relationships between the pri-mary winding current i and magnetic field H and thatbetween the secondary winding voltage v and magnetic

Fig. 2: Measurement of reactor loss in a boost choppercircuit.

Fig. 3: Measurement of core loss.


flux density B are as follows:

H =N1i

ldBdt=

vN2A

Consequently, the core loss per unit of volume can becalculated as follows, where P represents the power cal-culated from the primary winding current i and the sec-ondary winding voltage v.

Pc =1lA· N1

N2· 1

T

∫ T

0v · idt

=1lA· N1

N2· P

In addition, since the core’s volume is given by lA, thecore’s overall core loss PcALL can be calculated as fol-lows:

PcALL = Pc · lA = N1

N2P

Accordingly, by making a measurement with the setupshown in Fig. 3, it is possible to measure the core lossunder actual operating conditions.

In addition, the Power Analyzer PW6001 can save 16-bit voltage and current waveform data sampled 5 MSa/sas CSV files and transfer data to MATLAB∗, allowingthe instrument to generate higher-precision waveformdata than is possible to obtain with a standard wave-form recorder. This data also can be used for analyticalpurposes, for example to render the B–H loop.

∗MATLAB is a registered trademark of The Mathworks,Inc.

Why is it difficult to measure reactorloss?

Inductance is the principal component in determininga reactor’s impedance. From a power measurementstandpoint, the measurement is characterized by a lowpower factor. In short, the phase difference between thevoltage and current is close to 90. As illustrated inFig. 4, the effect of the phase error between the instru-

Fig. 4: Relationship between phase error and powermeasurement error.

ment’s voltage and current measurement units on mea-sured values is greater than when measurement is car-ried out with a high power factor. Consequently, themeasurement units must exhibit a high degree of phaseprecision.

In addition, reactors are switched at frequencies rang-ing from tens of kilohertz to hundreds of kilohertz. Asdescribed above, commercialization of SiC and GaN el-ements has resulted in a tendency toward rising switch-ing frequencies, and it is necessary to use measuringinstruments with high phase precision at such high fre-quencies. Furthermore, when using current sensors, itis necessary to consider the current sensor’s phase error.

Moreover, a large common-mode voltage will be ap-plied to the voltage and current measurement units dur-ing the type of measurement illustrated in Fig. 2. As aresult, it is necessary to use an instrument with a highcommon mode rejection ratio (CMRR). As describedabove, the components under measurement are beingswitched at frequencies ranging from several tens ofkilohertz to several hundreds of kilohertz, resulting ina measurement environment that is characterized by anextremely large amount of noise. Consequently, it isnecessary to use an instrument that exhibits high noiseresistance.

In this way, the conventional wisdom holds that measur-ing reactor loss is a difficult process because it requiresan instrument that exhibits a high level of performancein numerous areas. These requirements can be met by


Fig. 5: Reactor voltage and current waveforms in aboost chopper circuit.

using the Power Analyzer PW6001, which offers thefollowing features:

· Broad band and high-precision phase character-istics thanks to its current sensor phase shiftfunction1).

· High CMRR (80 dB or greater at 100 kHz).

· High noise resistance thanks to a dedicated currentsensor2, 3).

Instrument characteristics requiredfor reactor loss measurementFig. 5 illustrates the voltage and current waveforms thatare applied to a reactor in a circuit such as that shown inFig. 2. The voltage waveform takes the form of a rectan-gular wave, while the current waveform takes the formof a triangular wave with a superposed DC component.To measure loss at a precision of 0.1% with waveformssuch as these requires a band of about 5 to 7 times theswitching frequency4). For example, with a switchingfrequency of 100 kHz, the measurement would need toprovide a band of 500 kHz to 700 kHz.

It is important to note that high-precision measurementcapability is required not only for amplitude (gain), butalso for the phase difference between voltage and cur-rent. To measure a high-frequency current in excess ofseveral amperes, it is necessary to use a current sensor2).Since the current sensor’s phase error cannot be ig-nored at high frequencies, it is necessary to adopt somesort of correction method. Most other manufacturers’

Fig. 6: Measurement block diagram.

Table 1: Reactor specifications.Item Specifications

Core material Manganese zinc ferriteWinding 5 Turns

RDC 7 mΩ

power analyzers and oscilloscopes perform this correc-tion using a deskew function. Depending on the currentsensor’s characteristics, that approach requires using adifferent delay time for each measurement frequency.Consequently, it results in larger errors when measuringdistorted waveforms such as triangular waveforms thathave frequency components in a broad band. By us-ing the Power Analyzer PW6001 with a high-precisioncurrent sensor along with the instrument’s phase shiftfunction and entering the current sensors’ phase error atjust one point into the PW6001, it is possible to makemeasurements with low phase error across a broad fre-quency band.

Example of Reactor Measurementwith a Power Analyzer

This section describes an example of reactor measure-ment using the Power Analyzer PW6001 and the Cur-rent Box PW9100. Fig. 6 provides a circuit diagram forthe measurement, while Table 1 lists the specificationsof the reactor under measurement. Measurement wasperformed while applying a sine signal with a poweramplifier (4055, NF Corporation). Power analyzers areused to measure parameters such as RMS voltage andcurrent values as well as phase error and power. ThePW6001 allows operators to combine these basic mea-


Table 2: Configuring user-defined calculations.Parameters Formulas

Z Ufnd/IfndX Z · sin(θU − θI)Rs Z · cos(θU − θI)Ls X/2π f

Ufnd, Ifnd : Voltage and current fundamentalwave components.

θU , θI : Voltage and current phase angles(fundamental wave).

f : Frequency (fundamental wave).

Fig. 7: Measurement example illustrating the level de-pendence of inductance and resistance ( f = 10 kHz).

sured values in the form of user-defined calculationsthat can be carried out in real time. Reactor parameterscan be measured by setting up the user-defined calcu-lations listed in Table 2. Fig. 7 illustrates the changein the inductance Ls and the resistance Rs when the cur-rent level applied to the reactor is varied at a frequencyof 10 kHz, while Fig. 8 illustrates the change in the in-ductance Ls and the resistance Rs when the AC currentRMS value is fixed at 0.5 A and the DC bias currentis varied at a frequency of 100 kHz. Ordinarily, LCRmeters can only measure current on the order of severaldozens of milliamperes. In addition, the range of DCbias currents that can be generated by LCR meters’ DCbias units is limited. As a result of these limitations,measured parameters differ from the values that char-acterize actual operating conditions. As this exampledemonstrates, a power analyzer and power source canbe combined to measure a reactor at current levels thatapproach actual operating conditions.

Fig. 8: Measurement example illustrating the DC su-perposition characteristics of inductance and resistance( f = 100 kHz).

This example illustrates use of a power supply to ap-ply sine-wave current and voltage. As described above,rectangular-wave voltage and triangular-wave currentare usually applied to operating reactors, rather thansine-wave signals. A power analyzer allows direct mea-surement of reactors under such conditions. In addition,parameters such as Ls and Rs can be calculated basedon the results of harmonic calculations performed bythe instrument. These instrument characteristics makepossible more accurate analysis.

Conclusion

This paper introduced a method for measuring and an-alyzing high-frequency reactor loss, with reference toan actual measurement example. In order to accuratelymeasure loss and other parameters of high-frequencyreactors, it is necessary to make measurements underconditions that approach actual operating conditions.In addition, this paper described the high level of per-formance that is required for a power analyzer used tomake such measurements. Finally, it offered an exam-ple in which a PW6001 Power Analyzer was used tomeasure and analyze reactor loss.


References1) Yoda, H. : “Power Analyzer PW6001”, HIOKI

Technical Notes, Vol.2, No.1, 2016, pp.43-49.

2) Yoda, H., H. Kobayashi, and S. Takiguchi : “Cur-rent Measurement Methods that Deliver High Pre-cision Power Analysis in the Field of PowerElectronics”, Bodo’s Power Systems, April 2016,pp.38-42.

3) Ikeda, K., and H. Masuda : “High-Precision, Wide-band, Highly Stable Current Sensing Technology”,Bodo’s Power Systems, July 2016, pp.22-28.

4) Hayashi, K. : “High-Precision Power Measure-ment of SiC Inverters”, Bodo’s Power Systems,September 2016, pp.42-47.


Effectiveness of Phase Correction When Evaluating the Efficiency of High-efficiency Motor DrivesBy Hideharu Kondo, Chiaki Yamaura, Yukiya Saito, Hiroki Kobayashi

1. IntroductionAgainst the backdrop of international efforts to prevent global warming, the increasingly efficient motor drive systems used in electric vehicles and industrial appli-cations have been attracting attention in recent years. Essential in evaluating the efficiency and loss of motor drive systems, the ability to measure power accurately demands a range of expertise.This paper focuses on the characteristics of inverter output waveforms in order to outline requirements for the power measuring instruments that are needed to accurately measure inverter output power. It also in-troduces phase correction by a power analyzer with a focus on current sensor phase error in order to satisfy those requirements. Finally, it reports on the authors’ verification of the effectiveness of current sensor phase correction.

2. Characteristics of inverter out-put waveforms

Principal components of inverter output power include a fundamental frequency component (up to 2 kHz), its harmonic components, the switching frequency (5 kHz to 100 kHz), and its harmonic components. Of those, the fundamental frequency component is dominant. Fig. 1 illustrates an inverter output’s line voltage wave-form, line current waveform, and associated FFT re-sults for a typical motor drive system. Table 1 provides detailed information about the measurement target.Looking at the voltage FFT results, it is possible to observe the fundamental wave that is the principal

component of the line voltage PWM waveform and its harmonics, along with the switching frequency and its harmonic components. A spectrum of at least 0.1% f.s. exists up to approximately 2 MHz.

Fig. 1: Waveform and FFT results for an inverter-driv-en motor (measured using the Hioki Power Analyzer PW6001)

Inverter MotorSwitching element

Switching frequency Inductance Resistance Rated

power outputSiC-MOSFETSCH2080KE

(ROHM)20 kHz 3.6 mH 0.9 Ω 120 W

Table 1: Measurement target specifications

The fundamental wave, its harmonics, the switching frequency, and its harmonic components can also be observed for the current waveform. However, the ob-served spectrum at frequencies of 100 kHz and above falls below 0.1% f.s., and the current level falls abrupt-ly as the frequency increases. This phenomenon can be explained by considering the equivalent circuit of a

Voltagewaveform

Currentwaveform

FFTspectrum


motor that is connected to an inverter as a load (Fig. 2). The motor’s winding can be thought of as an R-L load consisting of a resistance and inductance connected in series. Consequently, impedance grows at high fre-quencies, making it harder for current to flow.

Fig. 2: Motor equivalent circuit (for 1 phase)

Similarly, if we look at the power factor (cos θ) for the power of an R-L load, the power factor approaches a value of 1 when the frequency is low, for example for the fundamental wave and its harmonics. However, because inductive reactance becomes dominant at high frequencies such as the switching frequency and its harmonics, current exhibits lagging phase, resulting in a low power factor.The bottom half of Fig. 3 provides an enlarged view of the time axis for the inverter output voltage and cur-rent waveforms up to the switching frequency region. The voltage waveform is rectangular, while the current waveform is triangular. It is apparent that their phase relationship is characterized by the current’s lagging phase, as described above, resulting in a low power factor.

Fig. 3: Enlarged view of inverter output waveforms

L R

Backelectromotive

force

Inverter output

Voltagewaveform

Currentwaveform

Voltagewaveform

Currentwaveform

Fig. 4: Principal components of inverter output active power and their characteristics

3. Performance required for high-precision measurement of in-verter output

This section describes the requirements that a power measuring instrument must satisfy in order to accu-rately measure inverter output power. Based on the characteristics described above, it is important that such an instrument be capable of measuring active power not only for a high-power-factor fundamental wave and its harmonics, but also for a low-power-factor switching frequency and its harmonic components.

Fig. 5: Relationship between phase error and active power error at different power factors

Fig. 5 illustrates the relationship between phase error and active power error at different power factors. Volt-age and current phase error in the measurement circuit has a greater effect on active power at low power fac-tors than at high power factors. Consequently, accurate

High power factor

Active Power [W]

Frequency

Switching Frequencyand harmonics

[Hz]1k 10k 100k 1M

Low power factor

Fundamental Frequency and harmonics

Power factor ≈ 1

Q Q

P P

Power factor ≈ 0

Active power

Phaseerror

Phaseerror

Error ErrorActive power

θθ


measurement of active power at the switching fre-quency and its harmonic components requires both flat amplitude characteristics and flat phase characteristics across a broad frequency band (the latter being par-ticularly important). For power components that con-sist of a rectangular-wave voltage and triangular-wave current as shown in Fig. 3, the frequency band across which the instrument must exhibit flat amplitude and phase characteristics in order to measure efficiency at a precision of 0.1% is likely 5 to 7 times the switching frequency1).Active power frequency characteristics at a power factor of zero provide a yardstick for measuring flat amplitude and phase performance. Fig. 6 provides example active power frequency characteristics at a power factor of zero for several Hioki Power Analyzer models. Please note that these example characteristics describe the instruments’ standalone performance.

Fig. 6: Example active power frequency characteristics at a power factor of zero for Hioki Power Analyzers

The PW6001 delivers flat characteristics up to 1 MHz, reflecting its envisioned use case of measuring invert-ers that use SiC switching elements.The PW3390, which is designed to measure inverters that use IGBT switching elements, provides flat char-acteristics up to 150 kHz. The instrument is designed to surpass the performance of the 3390, the previous-generation model, in order to facilitate high-precision measurement of inverter output.

4. Current sensor phase correctionWhen a power analyzer is used in a high-precision power measurement application, it is typical to utilize

a current sensor to measure currents that exceed 5 A2). Consequently, in order to implement a power measure-ment system whose flat amplitude and phase charac-teristics extend to high frequencies, it is necessary to satisfy the above performance requirements not for the power analyzer on a standalone basis, but rather when the power analyzer and current sensor are used in com-bination.However, current sensors typically exhibit gradually increasing phase error in the high-frequency region due to the characteristics of the sensor’s magnetic core and circuitry. Furthermore, differences in the design of various sensor models cause the magnitude of this er-ror to vary. Fig. 7 illustrates example phase character-istics for several Hioki high-precision current sensors.

Fig. 7: Current sensor phase-frequency characteristics

The current sensor phase correction functionality provided by the Hioki Power Analyzer PW6001 and PW3390 can be used to resolve this issue. Phase cor-rection uses current sensor-specific phase error infor-mation to correct the error, thereby improving phase characteristics in the high-frequency region and reduc-ing power measurement error.

The phase correction function utilizes virtual oversam-pling technology to perform real-time deskew process-ing for sampled waveforms at a high time resolution equivalent to a frequency that is 400 times higher than the actual sampling frequency. By performing delay compensation for waveforms using the concept of time, phase correction benefits can be extended across the full frequency band.Hioki develops high-precision current sensors inhouse, and it has ascertained the phase characteristics of each sensor model by optimizing design and manufacturing


processes and by implementing strict production con-trol. The current sensor-specific phase characteristics information used in phase correction can be found in the user manual of each Hioki power analyzer. Fig. 8 illustrates the result of performing phase correction for the current sensors shown in Fig. 7 using that phase characteristics information. Performed properly, phase correction yields significantly better phase characteris-tics in the high-frequency region.

Fig. 8 Phase-frequency characteristics following phase correction

5. Comparison of actual inverterefficiency measurements

The authors measured the efficiency of the SiC inverter described in Table 1 above using three Hioki Power Analyzer models and compared the results. Table 2 summarizes the measurement conditions. Separate measurements using the PW6001 and PW3390 were performed with phase correction enabled and disabled.

Item ModelPW6001 PW3390 3390

Input (DC)

Wiring 1P2WCurrent Sensor CT6862

Phase Correction OFF/ ON (-10.96deg@300kHz) N/A

Output (PWM)

Wiring 3P3W3MCurrent Sensor CT6862 × 3

Phase Correction OFF/ ON (-10.96deg@300kHz) N/AFundamental

Frequency 100 HzPower Analyzer Frequency band to 2 MHz to 200 kHz to 150 MHz

Table 2: Measurement conditions

Fig. 9 summarizes the measurement results for effi-ciency and loss. Both the PW6001 and PW3390 yielded efficiency values that were 0.1% to 0.15% greater than

the 3390 with phase correction disabled. The differ-ence in values was likely due to the instruments’ supe-rior active power frequency characteristics at a power factor of zero (Fig. 6).Efficiency values with phase correction enabled were another 0.1% to 0.15% greater than those obtained with the function disabled. Fig. 10 illustrates the DC input power P4 and the PWM output power P123 for the measurements shown in Fig. 9. Whereas the P4 values from the PW6001 and PW3390 remained unchanged regardless of whether phase correction was enabled or disabled, P123 values were 0.1% to 0.15% greater when phase correction was enabled compared to when it was disabled. Based on these results, the reduction in the CT6862 current sensor’s lagging phase error (Fig. 7 and Fig. 8) is readily apparent in the P123 measured values.

Fig. 9: Comparison of inverter efficiency and loss by model

Fig. 10 Comparison of inverter input and output power by model


Finally, a comparison of the loss values shown in Fig. 9 reveals that loss values obtained from the PW6001 and PW3390 with phase correction enabled were 0.1 W (equivalent to 12%) lower than values from the 3390. This test measured a small motor as its load, but a 12% difference in loss for a 10 kW, 95% efficient inverter would be equivalent to 60 W of power, a difference large enough to have an impact on thermal design.To accurately evaluate efficiency down to the 0.1% lev-el and loss to the 1 W level in a high-efficiency motor drive system, it is important to ensure that the entire power measurement system has appropriate amplitude and phase characteristics. The authors’ measurement results illustrate the effectiveness of current sensor phase correction.Because the measured inverter used a switching fre-quency of 20 kHz, both the PW6001 and PW3390 had an adequate frequency band, and there were no sig-nificant differences in the measurement results from the two instruments. However, differences between the two models are expected if the switching frequency increased further.

6. ConclusionThis paper focused on inverter output power, outlining the requirements for power measuring instruments in order to facilitate accurate measurement. It identified the importance of current sensor phase correction ex-pertise in fulfilling those requirements and verified the effectiveness of that technique by comparing actual measurements. In the field of power electronics, there are numerous opportunities for measuring power at high frequencies and low power factors3) apart from motor drive systems, and phase correction expertise can be effectively utilized in those applications. We look forward to providing more useful information about this topic to readers in the future.

References1) Hayashi, K, “High-Precision Power Measurementof SiC Inverters,” Bodo’s Power Systems, September 2016, pp.42-47.2) Yoda, H, et al. ”Current Measurement Methods thatDeliver High Precision Power Analysis in the Field of Power Electronics” Bodo’s Power Systems, April 2016,pp.38-42.

3) Hayashi, K, “Measurement of Loss in High-Fre-quency Reactors,” Bodo’s Power Systems, February 2017, pp.18-22.


About Hioki Established in 1935, HIOKI E.E. CORPORATION (TSE: 6866) has grown to become a world leader in providing consistent delivery of test and measuring instruments through advanced design, manufacturing, and sales and services. By offering over 200 main products charac-terized by safety and quality while meeting an expansive range of applications, we aim to contribute to the efficiency and value of our customers’ work in research and development, production and electrical maintenance. HIOKI products and services are available around the world through our extensive network of subsidiaries and distributors. Information about HIOKI is available at www.hioki.com.

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