current distortion analysis of three-phase pwm rectiﬁer in

IEEJ Journal of Industry ApplicationsVol.10 No.3 pp.384–392 DOI: 10.1541/ieejjia.19011016Translated from IEEJ Transactions on Industry Applications, Vol.140 No.9 pp.633–641

Paper(Translation ofIEEJ Trans. IA)

Current Distortion Analysis of Three-Phase PWM Rectifier inOver-Modulation Region and Application to

Air-Cooled Heat Pump Chiller

Yohei Kubota∗a)Member, Keiichi Ishida∗ Member

Masaki Kanamori∗ Member, Yuki Yanase∗ Member

Takahisa Endo∗ Senior Member, Yasushi Yamanashi∗ Senior Member

Hidetoshi Kanazawa∗ Fellow

J-STAGE Advance published date : Feb. 2, 2021

This paper describes an operating method for a PWM rectifier suitable for air-cooled heat pump chillers. The ef-ficiency of chillers have to be improved in the light to middle load ranges, and the harmonic suppression should bereduced in heavy load ranges. To satisfy this requirement, sinusoidal modulation is adopted in the PWM rectifier byapplying over-modulation and two-step boost voltage control. Although over-modulation can reduce switching loss,current distortion remains. In this study, the input current distortion characteristic is derived in the over-modulation,and it is clearly shown that the distortion has a local minimum around a voltage boost ratio of 1.0. Using this character-istic, the efficiency is improved by the operating voltage boost ratio of 1.0 from light to mid-range load. At heavy loads,harmonic restraint and compressor motor high-speed rotation are made compatible by boosting the DC bus voltage tothe second level. It is confirmed that ac to dc power conversion efficiency is equivalent at the voltage boost ratio of1.0, and the input current harmonic is reduced by 40% at the boost ratio of 1.14, compared with the test results of 120◦discontinuous pulse width modulation.

Keywords: PWM rectifier, sinusoidal-modulation, over-modulation, boost voltage, current distortion, chiller

1. Introduction

Large heat source machines such as absorption chiller-heaters and boilers are used in commercial buildings and fac-tories. In recent years, there has been a growing demandto replace these combustion-type machines with electrically-powered air-cooled heat pump chillers in light of reducingCO2 emissions and saving energy. The use of inverter-drivencompressor in chiller has been increasing, and because dioderectifier circuits are mainly used as AC/DC converters, thesuppression of power supply harmonics has been an issue.The harmonic suppression measures guidelines for specificconsumers must be considered in chillers. Harmonic sup-pression in chiller is typically achieved by connecting an ad-ditional harmonic suppression unit such as the 18-pulse rec-tifier (1) (2) (Fig. 1(a)) and active power filter (3) (Fig. 1(b)). The18-pulse rectifier consists of an 18-pulse transformer and twoauxiliary rectifiers. Because it uses only passive compo-nents, the 18-pulse rectifier causes only low noise and re-quires no control. An issue to address, however, is the vol-ume and weight because these commercial frequency com-ponents are mainly made of iron and copper materials. Theactive power filter detects harmonic components generated

a) Correspondence to: Yohei Kubota. E-mail: [email protected]∗ TOSHIBA CARRIER CORPORATION

336, Tadehara, Fuji-shi, Shizuoka 416-8521, Japan

on the equipment side and generates compensating currentby switching operation. It has a higher harmonic suppressioneffect than 18-pulse rectifier and is also capable of obtain-ing sinusoidal input current within the compensation capa-bility. These additional circuits, however, have no functionother than harmonic suppression, and the efficiency is re-duced when connected. Among other issues are many designconstraints such as additional space needed inside the prod-uct, connection configuration, and cooling structure. For airconditioners that use a similar compressor motor drive sys-tem as the chiller, an open-loop control method for a three-phase voltage-type PWM rectifier has been reported (4). Inthis method, a simple control configuration can achieve unitypower factor but it is difficult to design against disturbancedue to the open-loop control. For example, in operation witha power supply where three-phase AC is unbalanced, eachphase current is also unbalanced. In order to balance the cur-rents, the amplitude and phase of each phase duty commandare required to be adjusted properly, leading to a more com-plex design than current feedback control.

Meanwhile, in addition to power supply harmonic counter-measures, there are increasing demands for the improvementof COP (Coefficient Of Performance) and IPLVc (IntegratedPart Load Value, Cooling) as energy-saving performance in-dexes for chiller. COP is calculated by dividing the cool-ing or heating capacity by power consumption which indi-cates the energy-saving performance of a chiller. IPLVc is an

c© 2021 The Institute of Electrical Engineers of Japan. 384

Current Distortion Analysis of Three-Phase PWM Rectifier（Yohei Kubota et al.）

(a) Diode rectifier with 18-pulse transformer and auxiliary diode rectifiers(18-pulse rectifier)

(b) Diode rectifier with active power filter

Fig. 1. Conventional compressor motor drive system forchillers with current harmonic suppression function

energy-saving performance index close to the actual usagewhich is calculated as a weight average of COP at each partload with the occurrence rate being weighted.

IPLVc = 0.01 × COP100% + 0.47 × COP75%

+ 0.37×COP50%+0.15×COP25% · · · · · · (1)

The coefficients in Eq. (1) are occurrence rates of each loadcondition. Light and middle load ranges, in which the loadis 75% or less, are more weighted in the equation. Amongmethods for improving the efficiency in the light to middleload ranges is the application of a high induced voltage mo-tor to the compressor. Compared to the system with a con-ventional low induced voltage motor, the same load torquecan be obtained with less current, improving the system effi-ciency. However, in the high-speed rotation and heavy loadrange, the induced voltage becomes higher than the conven-tional system, narrowing the motor operating range. For im-proving the inverter output voltage, it is necessary to use incombination with DC voltage boosting technology (5)–(7).

Against this background, this study focused on a chillerinverter using a three-phase voltage-type PWM rectifier foran AC/DC converter and examined an operating method toachieve both power supply harmonic suppression and im-provement of energy-saving performance. There are variousmodulation methods for a PWM rectifier such as (a) sinu-soidal pulse width modulation (SPWM) that compares sinu-soidal command values with triangular carrier wave, (b) dis-continuous pulse width modulation (DPWM) that turns offthe switching of the maximum or minimum voltage phase for120◦, and (c) third harmonic injection pulse width modula-tion (THIPWM) that superimposes the third harmonic com-ponent onto the command value to improve the voltage uti-lization in SPWM. In this study, SPWM has been chosen as

the suitable modulation method for chiller. In SPWM, over-modulation occurs in the region where the DC voltage boostratio is less than 1.15, and thereby the number of switchingcycles can be reduced to suppress the loss. On the otherhand, input current distortion remains due to the overmod-ulation, reducing the harmonic suppression effect. While thecurrent distortion characteristics of voltage-type converters inthe overmodulation region have been reported in referencessuch as (8) and (9), there is no detailed study of waveformdistortion in a three-phase PWM rectifier reported.

In this study, the current distortion characteristics of aPWM rectifier in the overmodulation region is analyzed.First, the characteristics in the overmodulation region wherea local minimum of current distortion appears around a volt-age boost ratio of 1 are mathematically clarified. Further-more, a simulation of current feedback control, consideringthe actual device implementation, is performed to show thatthe current distortion is reduced by increasing the controlbandwidth. Then, the result of comparison of current distor-tion characteristics between SPWM and DPWM is presented.THIPWM was not examined in the study because it has a dis-advantage of worsening switching loss at low voltage boostratios. DPWM causes lower distortion than SPWM in prin-ciple because no overmodulation occurs at a voltage boostratio of 1 or higher in DPWM. When dead time is added,however, SPWM can generate lower-distortion waveforms athigh voltage boost ratios. The experimental results demon-strate that the efficiency and current distortion are comparablewith DPWM at the voltage boost ratio of 1, and the currentdistortion is improved by 40% at the ratio of 1.14. Lastly,product development is discussed. A comparison test is con-ducted for a PWM rectifier-equipped inverter with a two-stepvoltage booster based on the current distortion characteristicsof SPWM and the conventional 18-pulse rectifier. The resultsshow that the AC/AC conversion efficiency can be improvedby 1.2 pt at a mid-range load of 6.3 kW and the input currentharmonics are also substantially reduced.

2. Current Distortion Characteristics of PWMRectifier

2.1 Control Configuration of PWM RectifierFigure 2 shows the diagram of a compressor motor drive

system with a PWM rectifier for chiller. The area surroundedby the dashed line is an operation block in the microcon-troller. By controlling the PWM rectifier and compressormotor drive inverter at the same time, it is possible to op-erate the PWM rectifier according to the rotation speed of thecompressor. For the purpose of removing PWM square wavecomponent, a filter circuit consisting of a reactor Lf and acapacitor Cf is connected to the input port. The control ofthe PWM rectifier consists of a voltage control system thatcontrols the DC voltage vDC and a current control system thatcontrols the input currents ir, is, and it in the rotational co-ordinates. The power supply phase angle θ used in the coor-dinate transformation is calculated by performing PLL basedon the zero-crossing information of the power supply volt-age. Equation (2) is used for the coordinate transformation.The d-axis is treated as the active part, and the q-axis as thereactive part.

385 IEEJ Journal IA, Vol.10, No.3, 2021


Fig. 2. Control block diagram of compressor motor drive system with PWM rectifier

[idiq

]=

23

[cos θ sin θ− sin θ cos θ

] [1 −1/2 −1/20√

3/2 −√3/2

] ⎡⎢⎢⎢⎢⎢⎢⎢⎣irisit

⎤⎥⎥⎥⎥⎥⎥⎥⎦· · · · · · · · · · · · · · · · · · · · (2)

In the voltage control system, the deviation of the DC voltagecommand value V∗DC and the vDC is input to the PI controllerto generate the d-axis current command value i∗d. Two set-tings are given to V∗DC according to the rotation speed of thecompressor motor. In the current control system, the q-axiscurrent command value i∗q is set to 0 in order to have theinput power factor of 1. The deviations of dq-axis currentsid and iq, which are obtained by coordinate transformationof i∗d and i∗q with ir, is, and it, are input to the PI controllerfor follow-up control. Inverse coordinate transformation isperformed for the obtained dq-axis voltage command valuesv∗d and v∗q to generate PWM rectifier voltage command val-ues v∗rc, v∗sc, and v∗tc, which are used as duty command forcarrier comparison.2.2 Sinusoidal Modulation and OvermodulationAn equivalent circuit where the PWM rectifier is replaced

with a voltage source is shown in Fig. 3. The input filter isremoved for simplicity. Each vectors and parameters are de-fined as the following; the power supply voltage vector as Vs,the input current vector as Is, the output voltage vector of thePWM rectifier as Vc, the inductance of the boosting reactoras Lb, and the resistance of the reactor as Rb. Denoting theeffective value of line voltage (root-mean-square voltage) byV rms, Vs can be expressed as follows:

Vs =

√23

Vrmsejθ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (3)

Base on the relationship in Fig. 3, Vc is expressed as

Vc = Vs − (Rb + jωLb)Is · · · · · · · · · · · · · · · · · · · · · · · · · (4)

Voltage and current vectors of the PWM rectifier at unitypower factor are illustrated in Fig. 4. Since the voltage dropdue to the reactor is sufficiently small and the second term onthe right side of Equation (4) can be ignored, the followingapproximation can be accepted.

Vc � Vs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (5)

Here, denoting the DC voltage of PWM rectifier by VDC, the

Fig. 3. Equivalent circuit of PWM rectifier input

Fig. 4. Voltage and current vectors at unity power factor

limit voltage that can generate a pure sine wave in SPWMcan be expressed as follows:

Vc =VDC

2ejθ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (6)

Based on Equations (3), (5), and (6), the minimum DC volt-age that does not cause overmodulation in SPWM is givenby

VDC = 2

√23

Vrms =2√3

VDC(st)

VDC(st) =√

2Vrms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (7)

VDC(st) is the DC voltage at no load when the PWM rectifieris not operating. The voltage boost ratio of the PWM rectifierα is defined as follows:

α =VDC

VDC(st)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (8)

According to Equation (7), a sine wave can be generatedwithout overmodulation when α is set to 1.15 or greater. Onthe other hand, in DPWM, voltage utilization improves and itcan be expressed as follows:

Vc =1√3

VDCejθ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (9)

Here, no overmodulation occurs even when α = 1.Figure 5 shows the spatial vectors of PWM rectifier when

SPWM is applied. From Equation (5), Vc is nearly equal toVs, and therefore they are represented as fixed-length vectorsaccording to the power supply voltage. On the other hand,



Fig. 5. Output voltage vectors of PWM rectifier appliedSPWM

(a) D > 1

(b) D � 1

Fig. 6. Relationship between duty command and DCbus voltage in SPWM

each voltage vector output by the PWM rectifier varies withα. The vector length of the rectifier output is 2/3 · VDC.The shaded part represents the overmodulation region of1 � α < 2/

√3.

Figure 6 represents the relationship between r-phase dutycommand and drive signal as well as DC voltage in SPWM.D is the amplitude of duty command. Figure 6(a) shows thecase of the overmodulation with D > 1, and the DC voltageVDC(a) is lower than 2/

√3 · VDC(st). In the region where the

duty command exceeds the triangular wave carrier, switch-ing is off, thus reducing the loss. Figure 6(b) illustrates thecase when D � 1 and the DC voltage VDC(b) is no less than2/√

3 · VDC(st).2.3 Current Distortion in Overmodulation RegionIn the overmodulation region, since the PWM rectifier out-

put voltage is not a sinusoidal wave, distortion remains inthe input current. Here, the relationship between the voltageboost ratio α and current distortion in the overmodulation re-gion is derived. The r-phase component vrc of Vc excludingthe PWM square wave component in the overmodulation isshown in Fig. 7.

Fig. 7. Fourier series expansion analysis model ofPWM rectifier voltage waveform

vrc(θ) =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(−π ≤ θ < −π + γ),VDC

2D · sin θ (−γ ≤ θ < γ),

(π − γ ≤ θ < π)+

VDC

2(γ ≤ θ < π − γ)

−VDC

2(−π + γ ≤ θ < −γ)

θ = ωt

γ = sin−1

(1D

)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (10)

The harmonic components can be derived by the Fourierseries expansion of vrc(θ). Because vrc(θ) is an odd function,it can be expressed as follows:

vrc(θ) =√

2∞∑

n=1

Vn sin(nθ)

Vn =

√2π

∫ π

0vrc(θ) · sin(nθ)dθ

n = 1, 2, 3 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (11)

The voltage harmonic effective value Vn is given by the fol-lowing.⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

V1 =VDC√

2π

{2 cos γ − D

(sin 2γ

2− γ

)}

Vn =VDC√

2π

[2n

cos(nγ) − D

{sin(n + 1)γ

n + 1− sin(n − 1)γ

n − 1

}]n = 2m + 1 (m = 1, 2, 3 · · · ) · · · · · · · · · · · · · · · · · · · · · (12)

Assuming that the carrier amplitude is the DC voltage and theduty command amplitude is the maximum value of the PWMrectifier output voltage, the relationship between α and D canbe expressed in Equation (13) below.

α =2√3· 1

D· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13)

It should be noted that Equation (13) is valid only in theregion with no overmodulation. In the overmodulation re-gion, V1 in Equation (12) is the effective value of fundamen-tal wave in consideration of the contribution of fundamentalwave amplitude of duty command. Therefore, the followingis given.

α =1√3· π{

2 cos γ − D

(sin 2γ

2− γ

)} · · · · · · · · · · · (14)



Fig. 8. Relation between current distortion and boost ratio

The current distortion δ is generated from the harmonic com-ponent of the voltage according to the relationship betweenEquations (4) and (11) and given as follows.

In =Vn√

Rb2 + (nωLb)2

δ =

√∑n

In2

n = 2m + 1 (m = 1, 2, 3 · · · ) · · · · · · · · · · · · · · · · · · (15)

Here, because the system in this study is three-phase system,when they are balanced, multiples of the third harmonic arecancelled out each other. Therefore, only n-th componentsbelow are included.

n = 6m ± 1 (m = 1, 2, 3 · · · ) · · · · · · · · · · · · · · · · · · · (16)

Figure 8 is the relationship between δ and α, where δ is cal-culated for each voltage boost ratio α based on Equations (14)to (16) using D as a parameter. Calculation is performed upto the 40th harmonic for δ. When the PWM rectifier operationis stopped, the voltage of the DC capacitor decreases with in-crease in the load and thereby the region of α < 1 is alsoshown. In the case where the multiples of the third harmonicare included, δ decreases monotonically as α increases. Onthe other hand, for the balanced three-phase system, whilethe distortion mostly decreases as the voltage boost ratio in-creases, a local minimum is found around α = 1.

Figure 9 presents the result of simulation to examine thevalidity of current distortion characteristics obtained mathe-matically. The circuit parameters used for the simulation aregiven in Table 1. The input filter is removed for simplicity.The simulation was performed for (a) the case where a sine-wave duty command is given in an open-loop and (b) the casewhere the feedback control shown in Fig. 2 is applied. As aresult, δ of the obtained current waveforms was plotted. Inthe feedback control, the bandwidth of the input current con-trol system is set to about 1 kHz. The current distortion char-acteristics are presented in Fig. 9(a), where (I) indicates α thatgives the local minimum of δ in the case of feedback con-trol, (II) indicates α that gives the local maximum, and (III)indicates α at the end of overmodulation. The current dis-tortion characteristics in the case of open-loop are very wellmatched with the mathematical derivation, confirming its va-lidity. In contrast, in the case of feedback control, although

(a) Current distortion

(b) Duty command at α = 1.03

(c) Current waveforms (feedback control)

Fig. 9. Simulation result of current distortion at differ-ent boost ratio

Table 1. Circuit parameters

the general features are consistent, the current distortion isreduced throughout the overmodulation region. Figure 9(b)is the duty command at the voltage boost ratio (II), where aslight deformation can be found for feedback control. In thisway, when feedback control is applied, the duty command isdeformed by the effect of current control system, resulting inthe reduction of distortion. On the other hand, in the regionwith the voltage boost ratio greater than (III), where it is nolonger overmodulated, similar duty command waveforms areobtained for both cases and thus they resulted in similar cur-rent distortions. Figure 9(c) is the input current waveformat each voltage boost ratio. The waveforms also confirm thecurrent distortion that is characteristic to SPWM.

Figure 10 presents the simulation results where the controlbandwidth was varied from 0.1 kHz to 1.5 kHz in order toexamine the relationship between the current control band-width and the current distortion. As the control bandwidthincreases, the tracking to current command value improves,and consequently the current distortion was reduced as a re-sult. However, when the input filter is connected, an LCL



Fig. 10. Relation between current control bandwidthand current distortion (simulation result)

Fig. 11. Load characteristics of current distortion (sim-ulation result)

Fig. 12. Current distortion of SPWM and DPWM (sim-ulation result)

resonance circuit is formed. Therefore, the current controlbandwidth must be designed to be sufficiently below the res-onant frequency.

Figure 11 shows the simulation results where the inputpower was varied from 2 kW to 12 kW in order to examinethe load characteristics of current distortion. The current con-trol bandwidth is set to 1 kHz and the voltage boost ratio isset to (I) to (III) given in Fig. 9. The current distortion at eachvoltage boost ratio is load independent and mostly constant.This is because the current harmonic component In shown inEquation (15) takes a load-independent value.

Figure 12 presents the simulation results where the currentdistortion was compared between SPWM and DPWM at aninput power of 10 kW. The current control bandwidth is setto 0.1 kHz, close to open-loop control. At an ideal state whendead time td is set to 0, DPWM does not cause overmodu-

Fig. 13. Two-step boost voltage

lation when α � 1, thereby giving a lower distortion thanSPWM. In the case when td = 2 μs in consideration of actualdevice mounting, on the other hand, the current distortionin SPWM was improved in the overmodulation region up toaround α = 1.13, while it was worsened in DPWM. As pre-viously reported (10), the converter output voltage is affectedby dead time. During power running of a PWM rectifier, thevoltage is added when the input current is positive and sub-tracted when it is negative. For this reason, the PWM rectifieroutput voltage component that is averaged from the squarewave is affected positively. However, because the PWM rec-tifier output voltage becomes nearly equivalent to the inputvoltage as shown in Equation (5), the DC voltage is reducedto maintain this relationship. When the DC voltage is re-duced, the peak duty command is reduced by the voltagecontrol system, restoring the DC voltage. As a result, theregion where the duty command is kept at maximum or min-imum becomes smaller in the overmodulation region, con-tributing to the reduction in current distortion. On the otherhand, in the region beyond overmodulation, dead time onlyacts as a disturbance, worsening the current distortion. Con-sequently, the reduction in current distortion was obtained ina wide range of overmodulation α < 1.15 in SPWM, whileit is worsened extensively in DPWM with no overmodula-tion in the range of α � 1. Furthermore, the reason for theworse current distortion of DPWM than SPWM at high volt-age boost ratios is because the duty command is asymmet-rical in DPWM and thereby more susceptible the effect ofnon-linear property due to dead time.

As shown above, in consideration of actual device mount-ing, the current distortion in SPWM can be improved inthe overmodulation region and it can realize a less-distortedwaveform than DPWM at high voltage boost ratios.2.4 Two-step Voltage Boosting In this section, the

setting for V∗DC of the PWM rectifier that takes advantageof the current distortion characteristics in the overmodula-tion region is described. Figure 13 is a schematic diagramillustrating the relationship between the compressor motorrotation speed and V∗DC. In general, the load in chiller in-creases in proportion to the rotation speed of compressor mo-tor. Since the efficiency in the light to middle load rangesgreatly influences IPLVc, overmodulation is performed set-ting V∗DC to be near (I) in Fig. 9, which can lead to the reduc-tion in loss. As the current distortion takes a local minimumwhen α < 1, in consideration of stability in the light load re-gion, the operation is performed at α = 1 and setting V∗DC



to be the DC voltage with no load VDC1 (= VDC(st)). On theother hand, under the high-speed, heavy-load conditions, ahigh input current makes harmonic currents an issue, as wellas increasing the induced voltage of the compressor motor. Inthis case, we set V∗DC to be near (III) in Fig. 9 while avoidingnear (II) in order to maintain the operation of the compres-sor motor while increasing the harmonic suppression effect.Switching of V∗DC is carried out with hysteresis of the rota-tion speeds S1 and S2.

In this manner, an operation suitable for a chiller in SPWMcan be achieved only by changing the target DC voltage with-out switching the modulation method during the operation.

3. Experimental Results

A comparison test of current distortion characteristics ofSPWM against DPWM is performed. For the test, in additionto the circuit parameters in Table 1, an input filter with pa-rameters shown in Table 2 has been applied. A semiconduc-tor device, 600 V/150 A IGBT module, is used as the PWMrectifier. The current control bandwidth in the actual deviceis set to about 0.5 kHz. Dead time is set to 2 μs.

Figure 14 shows the operating waveforms at the voltageboost ratio of 1. In order to verify the output voltage pulseof the PWM rectifier, the collector-emitter voltage vce ofthe r-phase lower arm IGBT shown in Fig. 2 was obtained.

Table 2. Parameters of input filter

(a) SPWM.

(b) DPWM.

Fig. 14. Comparison of operating waveforms at α = 1.0(experimental result)

Figure 14(a) is the waveform for SPWM, where switching-offperiods are found confirming the operation in the overmod-ulation region. Figure 14(b) is the waveform for DPWM,where switching-off periods with cycles of 1/3 was con-firmed.

Figure 15 is the results of comparison of input currentdistortion. Compared with the simulation results shown inFig. 12, the difference is that the current distortion in DPWMincreases around the voltage boost ratio of 1. This is be-cause the ideal drive pulse could not be output in the actualdevice due to dead time and various non-linear factors suchas ON/OFF transmission delay. Such non-linear factors arethought to cause the switching-off periods in the waveformshown in Fig. 14(b) although a voltage boost ratio of 1 orhigher normally should not result in overmodulation.

Figure 16 presents the result of comparison of AC/DC con-version efficiency. At the voltage boost ratio of 1, since thenumber of switching is reduced due to overmodulation, theefficiency of SPWM was comparable with DPWM. At thevoltage boost ratio of 1.14, the number of switching increasedmore than DPWM, the efficiency was reduced by 0.2 pt.

As shown above, it is demonstrated that in SPWM, the cur-rent distortion and efficiency equivalent to DPWM can beachieved at around the voltage boost ratio of 1. It is alsoshown that the current distortion can be reduced by 40% inthe region beyond overmodulation at the voltage boost ra-tio of 1.14. From these results, it is verified that performingtwo-step voltage boosting method enables a suitable opera-tion for chillers, which require the improvement of energy-saving performance in the light to middle load ranges andharmonic suppression at high rotation speed and heavy load.

Fig. 15. Comparison of current distortion (experimentalresult)

Fig. 16. Comparison of ac to dc power conversion effi-ciency (experimental result)



Fig. 17. Appearance of developed air-cooled heat pompchiller

Fig. 18. Appearance comparison of reactor

4. Product Development

The appearance of an air-cooled heat pump chiller with thedeveloped PWM rectifiers is shown in Fig. 17. There are fourcompressors in one unit, and each compressor motor drive in-verter has a PWM rectifier. One unit can handle heat sourceup to 70 HP. By applying PWM rectifiers, an input power fac-tor of 99% or higher is achieved for the entire product duringrated operation.

Figure 18 compares the appearance of reactor, which oc-cupies a large amount of volume and weight in an inverterdevice, between the product with the conventional 18-pulserectifier and the one with the developed PWM rectifier. Theconnectable load for the 18-pulse transformer is 12 kW, andthat for the PWM rectifier is equivalent to 18 kW. Volumesand weights are compared including the heat sink in additionto the reactor shown in Fig. 18. As a result, the use of thePWM rectifier reduced the volume approximately by 40%and the weight by 50%. For the 18-pulse rectifier to applyto an 18-kW device, larger size is necessary and thereby thedifference in volume and weight will be even greater. In otherwords, the application of PWM rectifier enabled the inverterdevice for chiller to support larger capacities.

Figure 19 shows the result of comparison of AC/AC con-version efficiency including the inverter. In the PWM rec-tifier, two-step voltage boosting was performed; the voltageboost ratio was kept at 1 up to 6.3 kW and the ratio was 1.14beyond 8.0 kW to be almost out of overmodulation. More-over, the PWM rectifier used a motor with about 1.3 timesthe induced voltage constant ratio of the 18-pulse rectifier.The efficiency of the PWM rectifier was higher than that ofthe 18-pulse rectifier over the entire range. This is because,in addition to the effect of overmodulation, the use of thehigh induced voltage motor reduced the motor current and

Fig. 19. Comparison of ac to ac power conversion effi-ciency (experimental result)

Fig. 20. Comparison of harmonic currents per kW (ex-perimental result)

improved the DC/AC conversion efficiency. In particular, animprovement by 1.2 pt was observed with a medium load at6.3 kW.

Figure 20 compares the input harmonic currents betweenthe two systems. In the guidelines of harmonic suppres-sion measures for specific customers, the upper limit of theharmonic outflow current is defined by the current value ateach harmonic order per kW of contracted power. Accord-ingly, the measurement results are presented on per-kW basisat 11.8 kW for the 18-pulse rectifier and at 16.8 kW for thePWM rectifier. The upper limit in the guideline for 6.6 kVpower reception was used for comparison in Fig. 20 after ad-justing it to 200 V. This upper limit is the strictest conditionfor calculation, which assumes the contracted power equiv-alent to the capacity of the connected equipment, the 100%equipment occupancy, and no correction factors to mitigatethe conditions. The harmonic current in the PWM rectifierwas satisfactorily below the upper limit for all harmonic or-ders.

5. Conclusions

In this study, a three-phase PWM rectifier with sinusoidalmodulation is operated, and the current distortion charac-teristics in the overmodulation region are analyzed. In theovermodulation region, current distortion remains due to thetrapezoidal wave of PWM rectifier output voltage. It is pre-sented mathematically that this current distortion has a localminimum around the voltage boost ratio of 1 because of thethree-phase system that cancels out its multiples of the thirdharmonic. It is also shown that the current feedback con-trol system reduces the current distortion with increasing thecontrol bandwidth. It is demonstrated from simulations to



compare current distortions that sinusoidal modulation underhigh voltage boost ratio conditions with dead time resultedin distortion lower than 120◦ discontinuous modulation. Ex-perimental results showed that the efficiency and current dis-tortion in sinusoidal modulation at the voltage boost ratio of1 were comparable with 120◦ discontinuous modulation, andthe current distortion was improved by 40% at the voltageboost ratio of 1.14. Finally, a comparison test with the con-ventional 18-pulse rectifier is performed. The AC/AC con-version efficiency was improved by 1.2 pt at a mid-rangeload of 6.3 kW and the input current harmonics were alsosubstantially reduced, demonstrating the effectiveness of theproposed method for chiller.

References

( 1 ) T. Kobayashi, T. Takada, T. Yamashita, M. Uesugi, and H. Mochikawa: “TheReduction Method of Three Phase Power Supply by 18 Pulse Transformers”,2004 National Convention record I.E.E. Japan, No.4-034 (2004) (in Japanese)

( 2 ) H. Mochikawa, J. Tsuda, M. Uesugi, T. Yamashita, and T. Kobayashi: “ANew 18-Pulse Rectifier Circuit with Small Phase-Shifting Transformer”, The2005 International Power Electronics Conference, pp.1838–1842 (2005)

( 3 ) K. Aiba, T. Watanabe, and A. Sumiya: “Development of Large Current Ca-pacity Active Filter with Current Prediction Method for Heat Pump Chiller”,Mitsubishi Heavy Industries, Ltd. Technical Review, Vol.56, No.1, pp.1–6(2019) (in Japanese)

( 4 ) K. Sumito, T. Kanie, and T. Sato: “Development of 3-Phase Active Converterfor Packaged Air Conditioners”, Mitsubishi Heavy Industries, Ltd. TechnicalReview, Vol.33, No.6, pp.416–419 (1996) (in Japanese)

( 5 ) Y. Kubota, K. Ishida, H. Nukushina, and T. Endo: “Control Method of PWMConverter for Heat Pump Chilling Unit”, 2016 National Convention recordI.E.E. Japan, No.4-225 (2016) (in Japanese)

( 6 ) Y. Yanase, H. Morimoto, T. Konakahara, and H. Unno: “Development ofHeat Pump Chilling Unit with Harmonic Suppression Function Using PWMConverter”, 2016 National Convention record I.E.E. Japan, No.4-226 (2016)(in Japanese)

( 7 ) M. Yoshimura, M. Kanamori, K. Ishida, and H. Mochikawa: “Developmentand Practical Application of High Efficiency Inverter System for Air Condi-tioner”, 2017 National Convention record I.E.E. Japan, No.4-117 (2017) (inJapanese)

( 8 ) V. Kaura and V. Blasko: “A New Method to Extend Linearity of a Si-nusoidal PWM in the Overmodulation Region”, IEEE Transaction, Vol.32,No.5, pp.1115–1121 (1996)

( 9 ) D. Stojan and M. Milanovic: “Over-modulation phenomena and its influ-ence on the pulse width modulated single-phase inverter output voltage”, Au-tomatika, Vol.51, No.2, pp.174–180 (2010)

(10) J. Itoh, T. Fujii, T. Hoshino, A. Okada, I. Sato, and D. Tanaka: “Analysis ofDead-Time Compensation Method Using Disturbance Observer for VectorControl”, IEEJ Trans. IA, Vol.128, No.8, pp.1005–1012 (2008) (in Japanese)

Yohei Kubota (Member) received the M.E. degrees in electrical en-gineering from Shizuoka University, Japan, in 2012.He is with Toshiba Carrier Corporation, Japan, andhas been working on the development of the inverterfor air conditioner.

Keiichi Ishida (Member) received the M.E. degrees in electrical en-gineering from Nagaoka University of Technology,Japan, in 2004. He is with Toshiba Carrier Corpo-ration, Japan, and has been working on the develop-ment of the inverter for air conditioners. He receivedthe 64th Electrical Science and Engineering Promo-tion Award. He also received the IEEJ Technical De-velopment Award in 2019. He is a member of theIEEE.

Masaki Kanamori (Member) received the M.E. degrees in electri-cal engineering from Shizuoka University, Japan, in2009. He is with Toshiba Carrier Corporation, Japan,and has been working on the development of the in-verter for air conditioner.

Yuki Yanase (Member) received the M.E. degrees in systems engi-neering from Osaka University, Japan, in 2006. Heis with Toshiba Carrier Corporation, Japan, and hasbeen working on the development of the inverter forair conditioner. He received the 64th Electrical Sci-ence and Engineering Promotion Awards.

Takahisa Endo (Senior Member) received the B.E. degrees in electri-cal engineering from Daiichi Institute of Technology,Japan, in 1991. In April of the same year, he joinedToshiba AVE Corporation, Japan. In 2009, he is withToshiba Carrier Corporation. Since 2019, he has beena Technology Executive of Toshiba Carrier Corpora-tion, Japan. He received the 52nd Electrical Scienceand Engineering Promotion Award. He also receivedthe IEEJ Technical Development Award in 2008 and2019. He is a member of the IEEE.

Yasushi Yamanashi (Senior Member) received the M.E. degreesin electrical engineering from Shizuoka University,Japan, in 1991. In April of the same year, he joinedToshiba Corporation, Japan. Since 2019, he has beena Chief Quality Executive of Toshiba Carrier Corpo-ration, Japan. He received the 57th Electrical Scienceand Engineering Promotion Awards. He also receivedthe IEEJ Technical Development Award in 2019. Heis a member of the Japanese Society for Quality Con-trol (JSQC) and a member of the IEEE.

Hidetoshi Kanazawa (Fellow) received the M.E. degrees in electricalengineering from Nagaoka University of Technology,Japan, in 1983. In April of the same year, he joinedToshiba Corporation, Japan. He was a TechnologyExecutive and Corporate Vice President of ToshibaCarrier Corporation, Japan, in 2008, and 2017, re-spectively. Since 2018, he has been an Advisor. Hereceived the IEEJ Technical Development Award in2000 and 2005. He is a member of IEEE.


current distortion analysis of three-phase pwm rectiﬁer in

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