A New DC-Voltage-Balancing Circuit Including A

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 2, MARCH/APRIL 2011 841

A New DC-Voltage-Balancing Circuit Including aSingle Coupled Inductor for a Five-Level

Diode-Clamped PWM InverterKazunori Hasegawa, Student Member, IEEE, and Hirofumi Akagi, Fellow, IEEE

Abstract—This paper proposes a new dc-voltage-balancing cir-cuit for a five-level diode-clamped inverter intended for a medi-um-voltage motor drive with a three-phase diode rectifier used asthe front end. This circuit consists of two unidirectional choppersand a single coupled inductor with two galvanically isolated wind-ings. The inductor produces no net dc magnetic flux because theindividual dc magnetic fluxes generated by the two windings arecanceled out with each other. This makes the inductor compact bya factor of six, compared with the balancing circuit including twononcoupled inductors. Moreover, introducing phase-shift controlto the new balancing circuit makes it possible to adjust the mid-point voltage. As a result, the dc mean voltages of all the four splitdc capacitors can be balanced, independent of inverter control.Experimental results obtained from a 200-V 5.5-kW downscaledmodel verify the effectiveness of the new balancing circuit.

Index Terms—Coupled inductors, motor drives, multilevel in-verters, voltage balancing.

I. INTRODUCTION

S INCE THE three-level neutral-point-clamped, or diode-clamped, inverter was invented in 1979 [1], it has been

applied to steel-mill drives, unified power flow controllers, theJapanese bullet train (the so-called “Shinkansen”), and so on.Recently, attention has been paid to multilevel (more than threelevels) inverters intended for medium-voltage and high-powerapplications [2]–[10]. A main motivation of research on a five-level diode-clamped pulsewidth-modulated (PWM) inverterusing 3.3-, 4.5-, or 6.5-kV insulated-gate bipolar transistors(IGBTs) is to eliminate bulky line-frequency transformers frommedium-voltage motor drives. However, four split dc-capacitorvoltages tend to be unequal even in an ideal operating conditionas long as active power flows into, or out of, the five-level PWMinverter [2], [4].

The authors of [5] had a theoretical discussion on a space-vector pulsewidth-modulation method capable of balancingthe four dc-capacitor voltages without additional hardwareinstallation. Although this method is based on selecting anappropriate switching state from some redundant switchingstates, it works only in low-modulation indices. The authors of

Manuscript received May 19, 2010; accepted July 25, 2010. Date of pub-lication December 23, 2010; date of current version March 18, 2011. Paper2010-IPCC-154, presented at the 2009 IEEE Energy Conversion Congress andExposition, San Jose, CA, September 20–24, and approved for publication inthe IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the IndustrialPower Converter Committee of the IEEE Industry Applications Society.

The authors are with Tokyo Institute of Technology, Tokyo 152-8550, Japan(e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TIA.2010.2102327

[6] addressed another pulsewidth-modulation method that doesnot suffer from these restrictions, without additional hardwareinstallation, but at the expense of increasing the switchinglosses and output voltage total harmonic distortion. The authorsof [7] proposed a sophisticated pulsewidth-modulation methodfor balancing the dc-capacitor voltages and mitigating line-harmonic currents in a five-level PWM rectifier/inverter systemfor a motor drive.

A three-phase six-pulse diode rectifier is lower in cost, higherin power conversion efficiency, and much more reliable thana five-level PWM rectifier. Therefore, the diode rectifier isapplicable to fans, blowers, pumps, and compressors withoutregenerative braking. As for complying with harmonic guide-lines or regulations, a transformerless hybrid active filter hasbeen proposed to devote itself to the diode rectifier used as thefront end of a medium-voltage motor drive. The hybrid filteris characterized by series connection of a passive filter tunedto the seventh harmonic frequency and an active filter using athree-level diode-clamped PWM converter [11], [12].

This paper proposes a new dc-voltage-balancing circuit in-tegrating a single inductor having two galvanically isolatedwindings into two unidirectional choppers. Canceling out theindividual dc magnetic fluxes produced by the two windingsmakes the coupled inductor significantly compact and light.Note that a fully coupled inductor without air gap acts as anideal transformer and not as an energy-storage magnetic device.Moreover, a small amount of leakage inductance inherent ineach winding plays an important role in achieving a stableoperation of the new balancing circuit.

This paper introduces the following two balancing controlmethods to the new circuit: 1) duty-factor control and 2) phase-shift control. The former is used for voltage balancing betweenthe two dc capacitors at the positive side and between those atthe negative side. The latter achieves voltage balancing betweena set of the two dc capacitors at the positive side and theother set at the negative side. In other words, it can control themidpoint voltage with respect to the positive or negative dc link.As a result, the new circuit can balance all the four split dc-capacitor voltages, independent of the pulsewidth modulationof the inverter.

A 200-V 5.5-kW downscaled model is developed, con-structed, and tested to confirm the viability and effectivenessof the new balancing circuit. In addition, this paper makes atheoretical comparison in volume between a single coupledinductor and two noncoupled inductors under the same

0093-9994/$26.00 © 2010 IEEE

842 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 2, MARCH/APRIL 2011

Fig. 1. Previous voltage-balancing circuit equipped with two noncoupledinductors, where 4.5-kV IGBTs and diodes are used [9].

operating conditions. This comparison reveals that the newbalancing circuit makes a significant contribution to reducingthe inductor volume, for example, by a factor of six, comparedwith the balancing circuit using two noncoupled inductors.

II. VOLTAGE IMBALANCE PHENOMENON

Fig. 1 shows the circuit configuration of a medium-voltagemotor drive in which a voltage-balancing circuit is installedon the dc link between the three-phase diode rectifier andthe five-level inverter. The voltage-balancing circuit consistsof two unidirectional buck and boost choppers and two non-coupled inductors. When active power flows from the dioderectifier to the induction motor through the inverter with nobalancing circuit, two outer capacitors (Cdc1 and Cdc4) arealways charged to have higher voltages, whereas the two innercapacitors (Cdc2 and Cdc3) are always discharged to have lowervoltages [2]. Finally, the inner capacitor voltages get zero, thusacting as a three-level inverter. Therefore, a voltage-balancingcircuit for charging the inner capacitors and discharging theouter capacitors is indispensable to solve the voltage imbalancephenomenon of the four split dc capacitors.1 The previous bal-ancing circuit shown in Fig. 1 makes the positive-side chopperdischarge Cdc1 and charge Cdc2, while it makes the negative-side chopper discharge Cdc4 and charge Cdc3.

When the five-level inverter is applied to a static synchronouscompensator (STATCOM), the kilovoltampere rating of the bal-ancing circuit is about 1% of that of the five-level inverter [10].However, when it is applied to a motor drive, the kilovoltampererating of the balancing circuit tends to be larger and larger as theactive power flowing into, or out of, the five-level inverter getshigher and higher [2], [9]. As a result, the two inductors in theprevious balancing circuit would get bulky and heavy.

Each of the two inductors operates as an energy-storageelement. From a practical point of view, it is desirable for the

1If the five-level inverter is operated with regenerative braking, the two innercapacitors are charged to have higher voltage and the two outer capacitorsare discharged to have lower voltage. However, this paper does not pay anyattention to this phenomenon because it focuses on fans, blowers, pumps, andcompressors without regenerative braking.

Fig. 2. Proposed voltage-balancing circuit equipped with a single coupledinductor.

inductor to be as compact and light as possible, meeting theother constrains on it. In general, the volume of an induc-tor is proportional to the maximum stored energy. Reducingthe stored energy, i.e., reducing the inductance value, can berealized by high-frequency switching. However, a practicalswitching frequency of 4.5-kV IGBTs is limited to 1 kHz.

III. NEW DC-VOLTAGE-BALANCING CIRCUIT INCLUDING

A SINGLE COUPLED INDUCTOR

A. Circuit Configuration and Basic Operating Principle

The basic idea of a coupled inductor intended for cancella-tion of the dc magnetic flux is not new in a power electroniccircuit. For example, two-channel interleaved boost converterswith a coupled inductor have been proposed for a power-factor-correction rectifier [13], [14].

Fig. 2 shows a new voltage-balancing circuit including asingle coupled inductor LC for a five-level diode-clampedPWM inverter. The previous balancing circuit consists of twounidirectional “independent” choppers and two noncoupledinductors. The new circuit consists of two unidirectional “com-plementary” choppers and a single coupled inductor in whichthe positive- and negative-side windings are magnetically cou-pled through a common core. Thus, the two complementarychoppers, as a whole, can be considered as a “single” chopperwith the “single” coupled inductor.

Fig. 3 shows the basic principle of the new voltage-balancingcircuit and two switching modes where the positive-sideIGBTs (Q1 and Q2) and the negative-side IGBTs (Q3 and Q4)are complementarily turned on or off.2 Note that the coupledinductor LC is divided into the mutual inductance LM andthe two leakage inductances �P and �N, as shown in Fig. 3.The two leakage inductances are much smaller than the mutualinductance LM.

2In an actual system, a short period of time exists in which either D1 or D4

turns on, and the corresponding inductor current circulates through D1 or D4

in Fig. 3. However, this period can be eliminated from this discussion whenattention is paid to the basic operating principle.

HASEGAWA AND AKAGI: NEW DC-VOLTAGE-BALANCING CIRCUIT INCLUDING INDUCTOR FOR PWM INVERTER 843

Fig. 3. Basic operating modes in the new circuit. (a) Mode A. (b) Mode B.

Fig. 4. Designations of the four split dc capacitors and their associatedvoltages.

Fig. 4 shows the dc-link voltage vP2−N2, which is the voltageof node P2 with respect to node N2, and the four dc-capacitorvoltages, along with the five nodes P2, P1, M, N1, and N2. Inmode A, the voltage across the positive-side winding vMP isnearly equal to vP2−P1 because the positive-side IGBTs remainturned on. The negative-side winding voltage vMN is also nearlyequal to vP2−P1 because the negative-side winding voltage isthe same as the positive-side one. In this case, Cdc3 is beingcharged by vMN through D3. As a result, the energy stored inCdc1 is transferring to Cdc3. On the other hand, the energystored in Cdc4 is transferring to Cdc2 in mode B. The twoswitching modes repeat alternately so as to discharge Cdc1 andCdc4 and to charge Cdc2 and Cdc3. Finally, the dc mean voltagesof the four split dc capacitors are balanced completely.

B. Why Are the Leakage Inductances Necessary?

Fig. 5(a) shows an equivalent circuit focusing on the voltagesacross the positive- and negative-side windings in mode A,where VQsum is the sum of the saturation voltages of Q1 andQ2 and VDsum is a forward voltage of D3. The voltage acrossthe positive-side winding is slightly lower than that across thedc capacitor Cdc1, while the voltage across the negative-sidewinding is a little bit higher than that across the dc capacitorCdc3. If the coupled inductor is ideal under a condition ofiLP = iLN, Fig. 5(a) results in such a simple equivalent circuit

Fig. 5. Equivalent circuit to the voltages across the positive- and negative-sidewindings.

as shown in Fig. 5(b). In addition, if the two dc-capacitorvoltages are equal, i.e., vP2−P1 = vM−N1

|v�P + v�N| = VQsum + VDsum. (1)

Thus, the sum of the saturation and forward voltages of thetwo IGBTs and the two diodes is applied to the two leakageinductances. Unless leakage inductance existed, the sum ofVQsum and VDsum would cause an overcurrent. The leakageinductance value produces a significant effect on current ripplesof iLP and iLN. A voltage across a noncoupled inductor inthe previous balancing circuit is equal to the voltage acrossa split dc capacitor. On the other hand, a voltage across aleakage inductance in the new circuit is equal to the sum ofthe saturation and forward voltages, which is much lower thanthe voltage across a split dc capacitor. Therefore, this makes theleakage inductance much smaller in inductance value than thenoncoupled inductor. Current ripples of iLP and iLN, i.e., ΔILP

and ΔILN, are given by

ΔILP = ΔILN =|VQsum + VDsum|

�P + �N· τ (2)

where τ is a time interval of mode A or B. Equation (2) makesit possible to determine the required values of �P and �N.Note that the current ripples tend to increase when the twodc-capacitor voltages are unequal, because a voltage differencevP2−P1 − vM−N1 or vP1−M − vN1−N2 is applied to the corre-sponding leakage inductance.

Moreover, the leakage inductances play an important role inboth duty-factor and phase-shift controls as described in thefollowing sections.

C. Comparison to the Previous Balancing Circuit

Each of two noncoupled inductors acts as an energy-storageelement in the previous circuit, whereas the coupled inductoroperates as a non-energy-storage element in the new circuit.

Fig. 6(a) shows a magnetic flux in one noncoupled inductor,and Fig. 6(b) shows that in the coupled inductor. The magneticflux in the noncoupled inductor has a dc component becauseit carries a dc current, whereas the magnetic flux in the cou-pled inductor has no dc component because the individual dcmagnetic fluxes caused by iLP and iLN are canceled out with


Fig. 6. Magnetic flux in an inductor. (a) Noncoupled inductor. (b) Coupledinductor.

Fig. 7. Switching sequence of the voltage-balancing circuit.

each other3 [14], [15]. Hence, the maximum magnetic flux inthe coupled inductor is much lower than that of the noncoupledinductor. As a result, the coupled inductor has a smaller cross-sectional area when the noncoupled and coupled inductors aredesigned as long as both inductors have the same magnetic fluxdensity and the same turns of windings.

IV. DUTY-FACTOR CONTROL

In theory, the new circuit including a single coupled inductorcan balance the four split dc-capacitor voltages as long asthe positive- and the negative-side IGBTs are complementarilyturned on or off. In practice, however, small voltage differenceswould remain among the four split dc capacitors because satura-tion and forward voltage drops occur in the IGBTs and diodes.4

The following sections have an intensive discussion on voltagefeedback control for mitigating the effect of the voltage dropson voltage-balancing performance.

A. Switching Sequence

Fig. 7 shows the switching sequence consisting of eightoperating periods numbered 1–8. The negative-side IGBTs (Q3

and Q4) are phase-shifted by π (in radians) from the positive-side IGBTs (Q1 and Q2).

Fig. 8 shows the balancing circuit in which ON-state semi-conductor devices and the corresponding current loop pathsare shown in each period. Period 1 is the same as mode A inFig. 3, in which Cdc1 is discharged whereas Cdc3 is charged.On the other hand, Cdc4 is discharged whereas Cdc2 is chargedin period 5, which is the same as mode B. However, using onlyperiods 1 and 5 makes the outer capacitor voltages higher than

3The dc components of iLP and iLN are determined by those of the currentflowing out of node P1 into the inverter, i.e., iP1, and the current flowing intonode N1 out of the inverter, i.e., iN1, respectively. These currents have the samedc component in principle. Therefore, the dc components of iLP and iLN arethe same.

4The voltage drops have an adverse function of decreasing the active powerwhich is transferred from the outer capacitor Cdc1 or Cdc4 to the innercapacitor Cdc2 or Cdc3. Therefore, the inner capacitor voltages tend to getlower than the outer capacitor voltages.

the inner capacitor voltages because a small amount of voltagedifference remains in the four split dc-capacitor voltages. Thus,additional operating periods 2, 4, 6, and 8 are introduced tocharge the inner capacitors and to discharge the outer capac-itors. During periods 2 and 8, Cdc1 is discharged because ashort circuit is formed by Cdc1 and the two series-connectedleakage inductances (�P + �N). During periods 4 and 6, Cdc4 isdischarged. The voltage balancing of the four split dc capacitorscan be achieved by appropriately adjusting these periods withthe help of voltage feedback control of the four dc capacitors.Note that neither charge nor discharge occurs during periods 3and 7.

B. Control Diagram

Fig. 9 shows the control diagram of the voltage-balancingcircuit. The negative-side control diagram is independent of thepositive-side one. Note that the negative-side carrier signal vtriN

is phase-shifted by 180◦ from the positive-side one vtriP. Aproportional-plus-integral controller for voltage regulation hasa proportional gain of 0.5 A/V and an integral time constantof 50 ms. A proportional controller for current control hasa proportional gain of 0.15 V/A. The circulating period TR

corresponds to periods 3 and 4 or 6 and 7 in the positive-sidesequence (Q1 and Q2) in Fig. 7, or to periods 2 and 3 or 7 and8 in the negative-side sequence (Q3 and Q4). It is defined as atime interval in which the inductor current iLP or iLN circulatesthrough D1 or D4 and Q2 or Q3 on the ON state, respectively.The ratio of the circulating period TR with respect to the carrier-wave period TCB is defined as ΔD

ΔD ≡ 2TR

TCB. (3)

The following experiment has a parameter of ΔD = 0.1 atTCB = 800 μs.

V. PHASE-SHIFT CONTROL FOR

MIDPOINT-VOLTAGE BALANCING

In practice, a small amount of dc current would flow into orout of the midpoint (node M), which is produced by unequalconducting and switching losses, as well as signal imbalanceinherent in the control circuit including voltage/current sensors.This makes the midpoint voltage imbalanced. The midpointvoltage can be balanced by means of the so-called “zero-sequence voltage injection” [9], [16]. However, it may pose alimitation on the degree-of-freedom of pulsewidth modulationand may cause a saturated ac voltage of the inverter when amodulation index of the inverter is near 1.0.

The following sections discuss the modeling of the balanc-ing circuit and reveal that the balancing circuit operates as abidirectional half-bridge dc–dc converter between the positiveand the negative side. As a result, the balancing circuit canbe used for voltage regulation between the two positive-sidecapacitors and the negative-side ones. In other words, it cancontrol the midpoint voltage. Moreover, theoretical analysis ofthe balancing circuit confirms that a power flow between the


Fig. 8. Eight operating periods in the voltage-balancing circuit. (a) Period 1. (b) Period 2. (c) Period 3. (d) Period 4. (e) Period 5. (f) Period 6. (g) Period 7.(h) Period 8.

Fig. 9. Control diagram of the voltage-balancing circuit. (a) Positive side.(b) Negative side.

positive and the negative side is in proportion to a phase-shiftangle between them.

A. Modeling of the DC-Voltage-Balancing Circuit

Fig. 10 shows the equivalent circuit of the dc-voltage-balancing circuit where the positive-side circuit is shown in theleft and the negative-side circuit is shown in the right. Let the dccomponent of the current flowing out of node P1 be a currentsource IP1 and the dc component of the current flowing intonode N1 be a current source IN1. Currents flowing out of or intonode P2 or N2 practically exist. However, these currents canbe discarded because they are independent of the dc-voltage-balancing circuit. If clamping diodes D1 and D4 are eliminated

Fig. 10. DC-voltage-balancing circuit behaving like a bidirectional half-bridge dc–dc converter.

and free-wheeling diodes D2 and D3 are regarded as activeswitches, the circuit looks like a bidirectional half-bridge dc–dcconverter [17], [18]. Since the positive-side IGBTs (Q1 and Q2)and the negative-side IGBTs (Q3 and Q4) are complementarilyturned on or off, a set of positive-side IGBTs and D3 and theother set of negative-side IGBTs and D2 are alternately turnedon or off. Thus, it seems that the bidirectional dc–dc converteroperates with no phase shift. Phase-shift control can adjust anamount of power flow between the positive and the negativeside, which can be used for midpoint-voltage balancing.

B. Power Flow Between the Positive and the Negative Side

Fig. 11 shows the simplified equivalent circuit of the dc-voltage-balancing circuit with focus on saturation voltages ofIGBTs and forward voltages of diodes. Let the saturationvoltage of an IGBT be VQ, the forward voltage of a diode beVD, and the capacitor voltage be Vdc. The positive-side leg canbe considered as the three-pole switch clamping nodes P2, P1,or M. The negative-side leg is also shown as the three-pole


Fig. 11. Simplified equivalent circuit with focus on saturation and forwardvoltages of IGBTs and diodes, where � = �P + �N.

switch clamping nodes M, N1, or N2. The coupled inductor isreplaced with the sum of the positive-side leakage inductance�P and the negative-side leakage �N, where the mutual induc-tance is neglected because it is assumed to be much larger thanleakage inductances. Note that v� is the voltage across leakageinductance � and i� is the current flowing into the negative sidethrough the leakage inductance. Furthermore, IP1 and IN1 areneglected because they do not produce any effect on the powerflow between the positive and the negative side.

Fig. 12 shows the switching sequence and the analyzedwaveforms, in which α is the pulsewidth of Q1 or Q4, βis that of Q2 or Q3, and θn (n = 1, 2, . . . , 8) is the phaseangle of the corresponding period. What is most importantin Fig. 12 is that the waveforms of iPM and iNM have no dccomponents when no phase-shift angle occurs between thepositive and the negative side.5 Hence, no power flow existsbetween the positive and the negative side. On the other hand,as shown in Fig. 12(b), the waveforms of iPM and iNM containdc components when a phase-shift angle φ is introduced.Therefore, a small amount of power flow occurs from thepositive to the negative side when the negative-side switchingsequence lags the positive-side one. The dc components of iPM

and iNM are given by (see the Appendix)

INM = IPM =Vdc − 2VQ

ω�

(1 − β

2π

)φ (4)

where ω = 2πf and f is the switching frequency. Thus, thepower flow between the positive and the negative side, namely,PPN, is given by

PPN =2V 2

dc − 4VQVdc

ω�

(1 − β

2π

)φ. (5)

Equation (5) suggests that PPN is in inverse proportion tothe leakage inductance � and in proportion to the phase-shiftangle φ.

This power flow brings a slight increase in the power rating ofthe coupled inductor LC. However, it is negligible in an actualsystem because an amount of power to control the midpointvoltage is so small that the phase-shift angle is close to zero.

5The phase-shift angle is defined as zero in case the negative-side IGBTs arephase-shifted by exactly π (in radians) from the positive-side ones.

C. How to Implement the Phase-Shift Control

The phase-shift control should produce no effect on the duty-factor control. In other words, the phase-shift angle between thepositive side and the negative side should give no disturbanceto duty factors of Q1, Q2, Q3, and Q4.

Fig. 13 shows the implementation of the phase-shift control,where vref is a reference signal of an IGBT, vtri is a carriersignal which has an amplitude of unity, and δ is a period duringwhich the IGBT remains turned on. The waveform denoted byv′ref results from superimposing a square wave on vref . The

superimposed square wave has a positive value when the slopeof vtri has a positive value, whereas it has a negative valuewhen the slope has a negative value. Thus, an intersection ofvtri and v′

ref always lags with respect to that of vtri and vref . Nochange occurs in δ even if the phase-shift angle is controlled. Alagging phase-shift angle φ is in proportion to an amplitude ofthe square wave Δvref as

φ = π · Δvref . (6)

In addition, in case of Δvref < 0, a leading phase-shift angle isobtained.

Fig. 14 shows the control diagram in which φ∗ is a laggingphase-shift angle reference of the negative-side leg, vP2−M isthe voltage of node P2 with respect to node M, and vM−N2 isthe voltage of node M with respect to node N2. This consists ofa low-pass filter with a cutoff frequency of 5 Hz (T = 32 ms)and a proportional gain of 0.05 rad/V. The low-pass filter is usedfor the filtering of ripple components from the two detecteddc-capacitor voltages.

VI. EXPERIMENTAL RESULTS

A. Experimental System Configuration

Fig. 15 shows the experimental motor drive system that con-sists of a front-end diode rectifier, a new dc-voltage-balancingcircuit, a five-level diode-clamped PWM inverter, and a three-phase four-pole induction motor. Table I summarizes the ratingsand circuit parameters of the experimental system. The front-end diode rectifier is connected to the ac mains through an acinductor. A permanent-magnet synchronous generator is me-chanically coupled with the induction motor, and a three-phasestar-connected resistive load is connected to the synchronousgenerator. The resistive load is adjusted to make the dissipatedpower proportional to a cubic of the rotating speed of the motor.As a result, the combination of the synchronous generator andthe resistive load acts as a fan or a blower.

Fig. 16 is a photograph of the coupled inductor designedand constructed by the authors. It uses silicon-steel cut cores.Table II shows the circuit parameters of the inductor. Optimaldesign would bring a further reduction in volume to the coupledinductor.

B. Performance of the Phase-Shift Control

Fig. 17 shows the voltage difference between the positive andthe negative side, VDif = |VP2−M − VM−N2|, in a modulation


Fig. 12. Waveforms and the switching sequence. (a) With no phase shift. (b) With a phase shift of φ.

Fig. 13. Implementation of the phase-shift control.

Fig. 14. Control diagram of the phase-shift angle reference φ∗, in which T =32 ms and K = 0.05 rad/V.

index range from 0.4 to 1.15. Table III summarizes the outputpower of the inverter. When no phase-shift control was applied,the voltage difference VDif increased as the modulation indexdecreased. It was 1.4 V (1% of 135 V) at MI = 0.4 with nocontrol, whereas it was less than 0.2 V (0.2%) with it.

Fig. 18 shows special experimental results where a resistorof 500 Ω (0.7% of the rated power) was intentionally con-nected between nodes M and N2. The voltage difference VDif

increased to 10.4 V (7.6% of 135 V) at MI = 0.4 with nocontrol, whereas it decreased to 3 V (2.2%) with control.

C. Experimental Waveforms

Fig. 19 shows experimental waveforms when the five-levelinverter was operated at the following conditions: a modulationindex of MI = 1.15 with third harmonic injection, an outputfrequency of f = 57.5 Hz, and an output power of PO =4.7 kW. The u-phase voltage with respect to the midpoint M,i.e., vuM, was a five-level PWM waveform, and the line-to-linevoltage between the u phase and the v phase, namely, vuv, wasa nine-level PWM waveform. The four dc-capacitor voltageswere well balanced as expected.

Fig. 20 shows experimental waveforms when the five-levelinverter was operated at the following conditions: a modulationindex of MI = 0.8, an output frequency of f = 40 Hz, andan output power of PO = 1.6 kW. In this case, the inductorcurrents iLP and iLN take the same maximum value as 7 A(40%) when a fan or a blower is loaded on the motor [9].The four dc-capacitor voltages were also well balanced, andboth inductor currents were well controlled without magneticsaturation. This means that the leakage inductance inherent inthe coupled inductor plays an important role in controlling theinductor current.

Table IV summarizes dc mean voltages of the four split dccapacitors in the experimental results, as shown in Figs. 19 and20. The dc mean voltages are balanced well.


Fig. 15. Three-phase 200-V 5.5-kW laboratory motor drive system.

TABLE IRATINGS AND CIRCUIT PARAMETERS

Fig. 16. Coupled inductor used for experiment, along with a ballpoint pen.

VII. COMPARISON IN INDUCTOR VOLUME

This section makes a theoretical comparison in volume be-tween two noncoupled inductors in the previous circuit and asingle coupled inductor in the new circuit. This comparison isbased on the so-called “area product” [20], [21].

TABLE IICIRCUIT PARAMETERS OF THE COUPLED INDUCTOR

TABLE IIIOUTPUT POWER OF THE INVERTER

A. Area Product

The area product is useful for evaluating the volume of aninductor or a transformer, which was introduced in [20]. It isdefined by the following equation as the product of a core cross-sectional area Acore and a core window area Awindow, as shownin Fig. 21:

Ap = AcoreAwindow. (7)

Since the core window is perpendicular to the core cross sec-tion, the volume of an inductor or a transformer can be specifiedwhen the two areas are specified. The volume V is related to thearea product Ap as follows:

V = KVA3/4p (8)

where KV is a constant parameter depending on the coregeometry.


Fig. 17. Voltage differences between the positive and the negative side.

Fig. 18. Voltage difference when a resistor of 500 Ω is connected betweennodes M and N2.

Fig. 19. Experimental waveforms at MI = 1.15, f = 57.5 Hz, and PO =4.7 kW.

The area product of an inductor is given by

ApL =2W

KuBmJw(9)

where W is the maximum stored energy, Ku is a utilizationfactor of the window, Bm is the maximum magnetic flux densityof the core, and Jw is the maximum current density of thewinding lead wire. Thus, the area product of an inductor isproportional to the maximum stored energy.

Fig. 20. Experimental waveforms at MI = 0.8, f = 40 Hz, and PO =1.6 kW.

TABLE IVSPLIT DC-CAPACITOR VOLTAGES IN FIGS. 19 AND 20

Fig. 21. Definition of area product.

The area product of a transformer is given by

ApT =2P

4KufSBmJw(10)

where P is the rated power capacity of the transformer and fS

is a switching or operating frequency. After all, the area productof a transformer is proportional to the rated power capacity.

B. Comparison Between the Previous and New Circuits

First of all, let us calculate the total volume of the twononcoupled inductors in the previous circuit for the 200-V5.5-kW downscaled model with the following parameters:

1) rated dc mean inductor current: IL (in amperes);2) switching frequency: fS (in hertz);3) dc-capacitor voltage: Vdc (in volts);4) ripple width of inductor current: ΔIL (in amperes, peak

to peak);5) maximum magnetic flux density: Bm (in teslas);6) rated current density of winding lead wire: Jw (in am-

peres per square meter);7) utilization factor of window: Ku.


The inductance value of the noncoupled inductor LNC isgiven by

LNC =Vdc

2ΔILfS(in henry). (11)

Here, the ripple ratio of the inductor current is given by

r =ΔIL/2

IL(12)

where the ripple ratio has a range of 0 < r ≤ 1 if the inductorcurrent keeps a continuous current mode. The maximum storedenergy in the noncoupled inductor WNC is calculated by thefollowing equation:

WNC =12LNC

(IL +

ΔIL

2

)2

=12· Vdc

4rILfS· I2

L · (1 + r)2

=VdcIL

2fS· (1 + r)2

4r(in joules). (13)

The maximum stored energy WNC gets a minimum value at theripple ratio of r = 1 that is the maximum to keep a continuouscurrent mode. Equation (13) gives the area product of thenoncoupled inductor ApNC as follows:

ApNC =2

BmJwKu· VdcIL

2fS· (1 + r)2

4r

=(1 + r)2

4r· VdcIL

BmJwKufS(in m4). (14)

Next, let us calculate the area product of the coupled inductorin the new circuit under the same conditions as those in theprevious circuit. The area product of the coupled inductor canuse that of a transformer because the coupled inductor is thesame as a transformer in terms of operating principle. Whenthe leakage inductance is assumed to produce no effect on thevolume of the coupled inductor, the area product of the coupledinductor ApC is given as follows:

ApC =12· VdcIL

BmJwKufS(in m4). (15)

Note that the area product of the noncoupled inductor dependson the ripple ratio, whereas that of the coupled inductor doesnot. Equations (14) and (15) yield the area product ratio of thecoupled inductor with respect to the two noncoupled inductorsas follows:

ApC

ApNC=

2r

(1 + r)2. (16)

Equations (8) and (16) give the volume ratio of the coupled in-ductor with respect to the two noncoupled inductors as follows:

VC

2VNC=

12

{2r

(1 + r)2

}3/4

. (17)

Equation (17) is a monotonically increasing function whenthe ripple ratio has a range of 0 < r ≤ 1. The volume of thecoupled inductor is about 30% with respect to that of the

two noncoupled inductors when the ripple ratio is maximum(r = 1). The ripple factor in the experimental result shown inFig. 20 is r = 0.14 because the ripple current width is 2 A andthe rated inductor current is 7 A. In this case, the volume of thecoupled inductor is about 16% of the total volume of the twononcoupled inductors.

VIII. CONCLUSION

This paper has proposed a new dc-voltage-balancing circuitfor a five-level diode-clamped PWM inverter intended for amedium-voltage motor drive without regenerative braking. Thenew circuit is characterized by replacing two noncoupled in-ductors with a single coupled inductor. Theoretical comparisonbased on the so-called area product has revealed that the volumeof the single coupled inductor can be reduced by a factor of six,compared with the total volume of the two noncoupled induc-tors. Experimental results obtained from the 200-V downscaledmodel have confirmed the viability and effectiveness of the newbalancing circuit, verifying that the dc mean voltages of the foursplit dc capacitors are well balanced as expected.

APPENDIX

The phases in the eight operating periods θ1−θ8 in Fig. 12are given by

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

θ1

θ2

θ3

θ4

θ5

θ6

θ7

θ8

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

=

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

2π − β−π + α+β

2 − φπ − α + φ

−π + α+β2 − φ

2π − β−π + α+β

2 + φπ − α − φ

−π + α+β2 + φ

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(18)

where φ is the phase-shift angle. In addition, V�L and V�H aregiven by (

V�H

V�L

)=

(Vdc − 3VQ − VD

−2VQ − 2VD

). (19)

From the waveform of i�, the relations between I�n andI�n−1, where n equals 1, 2, 3, 4, 5, 6, 7, or 8, are given bythe following:

I�1 =1ω�

V�H · θ8 + I�8 (20)

I�2 =1ω�

V�L · θ1 + I�1 (21)

I�3 =1ω�

V�H · θ2 + I�2 (22)

I�4 =1ω�

V�L · θ3 + I�3 (23)

I�5 =1ω�

V�H · θ4 + I�4 (24)

I�6 =1ω�

V�L · θ5 + I�5 (25)

I�7 =1ω�

V�H · θ6 + I�6 (26)

I�8 =1ω�

V�L · θ7 + I�7. (27)


Since i� has no dc component in a steady state, I�1 is equal to−I�6. Thus, by combining (20), (26), and (27), I�1 is given by

I�1 =1ω�

(V�H · θ8 + V�L · θ7 + V�H · θ6) + I�6

=1ω�

(V�H · θ8 + V�L · θ7 + V�H · θ6) − I�1. (28)

Equation (28) results in

I�1 =1

2ω�{V�H(θ8 + θ6) + V�L · θ7} . (29)

Substituting (29) into (21) gives

I�2 =1ω�

V�L · θ1 +1

2ω�{V�H(θ8 + θ6) + V�L · θ7} . (30)

The dc component of iNM is given by

INM =I�1 + I�2

2· θ1

2π

=V�H(θ6 + θ8) + V�L(θ1 + θ7)

2ω�· θ1

2π. (31)

Substituting (18) into (31) yields

INM ={

V�H(−2π+α+β+2φ)2ω�

+V�L(3π−α−β−φ)

2ω�

}×

(1− β

2π

). (32)

On the other hand, v� has no dc component over a switchingperiod. This makes the following relation valid:

V�H(θ2 + θ4 + θ6 + θ8) + V�L(θ1 + θ3 + θ5 + θ7) = 0.(33)

Substituting (18) into (33) gives

V�H(−2π + α + β) + V�L(3π − α − β) = 0. (34)

Equation (32) can be changed, along with considering (34), intothe following:

INM =2V�H − V�L

2ω�

(1 − β

2π

)φ. (35)

Finally, substituting (19) into (35) results in

INM = IPM =Vdc − 2VQ

ω�

(1 − β

2π

)φ. (36)

The dc component of iPM can be obtained by means of the sameprocedure, which is equal to INM.

REFERENCES

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[2] F. Z. Peng, J.-S. Lai, J. McKeever, and J. VanCoevering, “A multilevelvoltage-source converter system with balanced DC voltages,” in Conf.Rec. IEEE PESC, Jun. 1995, pp. 1144–1150.

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Kazunori Hasegawa (S’09) was born in Yokohama,Japan, in 1985. He received the B.S. degree in electri-cal engineering from Tokyo Metropolitan University,Tokyo, Japan, in 2007, and the M.S. degree in electri-cal and electronic engineering from Tokyo Instituteof Technology, Tokyo, in 2009, where he is currentlyworking toward the Ph.D. degree.

Since 2010, he has been a Research Fellow ofthe Japan Society for the Promotion of Science. Hisresearch interests include diode-clamped multilevelconverters.

Mr. Hasegawa was the recipient of the IEEE International Power ElectronicsConference—Sapporo Student Paper Award in 2010.


Hirofumi Akagi (M’87–SM’94–F’96) was born inOkayama, Japan, in 1951. He received the B.S. de-gree in electrical engineering from Nagoya Instituteof Technology, Nagoya, Japan, in 1974, and the M.S.and Ph.D. degrees in electrical engineering fromTokyo Institute of Technology, Tokyo, Japan, in 1976and 1979, respectively.

In 1979, he joined Nagaoka University of Technol-ogy, Nagaoka, Japan, as an Assistant Professor, thenbecoming an Associate Professor in the Departmentof Electrical Engineering. In 1987, he was a Visiting

Scientist at the Massachusetts Institute of Technology (MIT), Cambridge, forten months. From 1991 to 1999, he was a Professor in the Department ofElectrical Engineering, Okayama University, Okayama. From March to Augustof 1996, he was a Visiting Professor at the University of Wisconsin, Madison,and then at MIT. Since January 2000, he has been a Professor in the Departmentof Electrical and Electronic Engineering, Tokyo Institute of Technology. Hisresearch interests include power conversion systems, motor drives, active andpassive electromagnetic-interference filters, high-frequency resonant invertersfor induction heating and corona discharge treatment processes, and utilityapplications of power electronics such as active filters, self-commutated back-to-back systems, and flexible ac transmission systems devices. He has authoredor coauthored more than 90 IEEE TRANSACTIONS papers and two invitedpapers published in the PROCEEDINGS OF THE IEEE in 2001 and 2004.The total citation index for all his papers in Google Scholar is more than12000. He has made presentations many times as a keynote or invited speakerinternationally.

Dr. Akagi was elected as a Distinguished Lecturer of the IEEE PowerElectronics and IEEE Industry Applications Societies for 1998–1999. He wasthe recipient of five IEEE TRANSACTIONS Prize Paper Awards and nine IEEEConference Prize Paper Awards. He is the recipient of the 2001 IEEE WilliamE. Newell Power Electronics Award, the 2004 IEEE Industry ApplicationsSociety Outstanding Achievement Award, and the 2008 IEEE Richard H.Kaufmann Technical Field Award. He served as the President of the IEEEPower Electronics Society for 2007–2008.

A New DC-Voltage-Balancing Circuit Including A

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