IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

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Voltage Balancing control in 3-Level Neutral-Point

Clamped Inverters Using Triangular Carrier PWM

Modulation for FACTS Applications

Javier Chivite-Zabalza, Pedro Izurza-Moreno, Danel Madariaga, Gorka Calvo,

and Miguel Angel Rodr´ıguez, Member, IEEE

Abstract—In this paper, a novel technique to balance the voltage

of the two split dc capacitors of a 3-Level neutral-point-clamped

inverter using triangular carrier pulse width modulation is presented. This technique, suitable for reactive power compensation

and for inverters operating with a relatively low switching frequency, consists in adding a square wave at six times the output

frequency. Subsequently, this paper presents a comparison with

two already known strategies in which a sinusoidal waveform at

two and six times the output frequency are injected. The current

contribution to the midpoint of the dc bus is then analyzed for

different modulation indexes and operating conditions. Based on

this analysis, a small-signal averaged model, suitable for control

design purposes is presented. Finally, simulation and experimental

results on a 690-Vac, 120-kVA test bench that validate the theory

are shown.

Index Terms—FACTS, insulated gate bipolar transistors

(IGBT), multilevel inverters, SHE, static synchronous series compensator (SSSC), STATCOM, VSC.

I. INTRODUCTION

HE development of FACTS devices, which aim for the

transmission network to operate close to its thermal limit

by providing a fast dynamic control [1]–[3], has been boosted

in recent times by the emergence of new semiconductor devices such as high-voltage insulated-gate bipolar transistors (IGBTs) [4]. The well-known neutral point clamped (NPC) 3-level

(3-L) inverter has been widely used in this type of applications [1], [2], and [4]. These inverters are often based on wellproven solutions, also used in other high-integrity demanding

applications such as steel mill processes, ship propulsion, and

ship dredger pumps [6]. An example of such equipment, are the

Ingedrive MV100 range of Ingeteam, shown in Fig. 1. These

are 3-L NPC IGBT-based inverters, where each has a power in

the range of 3.5 MVA.

One of the main control challenges in 3-L NPC inverters is to keep the voltage across the two dc-split capacitors

T

Manuscript received July 10, 2012; revised November 9, 2012; accepted

December 26, 2012. Date of current version March 15, 2013. Recommended

for publication by Associate Editor F. Wang.

The authors are with Ingeteam Power Technology S.A., Parque tecnol´ogico

de Bizkaia, 48170 Zamudio, Spain (e-mail: [email protected];

[email protected]; [email protected]; [email protected]

ingeteam.com; [email protected]).

Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2012.2237415

Fig. 1. Main power stack characteristics for the MV100-INGECON WIND

converter system.

balanced [5], [7]–[29]. The use of space vector pulse width modulation (SVPWM) techniques, widespread these days, presents

limitations to control the midpoint voltage at very low power

factor operation and high modulation indexes, as is often the

case of FACTS devices [7]–[9]. Moreover, there are applications where the use of traditional triangle carrier modulation is

preferred. For instance when the output waveforms are nonsinusoidal, as is the case of active filters, or when the topology

requires additional balancing loops, for instance antisaturation

control of magnetic devices connected at the inverter output,

i.e., coupling transformers.

The addition of a dc-offset to the reference waveform is a

recurred technique in applications with a power factor close to

unity, but that has no effect on pure reactive compensation [26].

The next section describes three voltage-balancing techniques

suitable for this purpose, two of them have been found in the

literature and the third one is a contribution of this paper.

II. VOLTAGE BALANCING TECHNIQUES FOR REACTIVE

COMPENSATION

This section begins by describing the compensation techniques based on sinusoidal second and sixth harmonic injection,

followed by the newly proposed compensation method. The explanation of the voltage balancing technique is based on the

3-L NPC inverter seen in Fig. 2. The explanation assumes that

0885-8993/$31.00 © 2012 IEEE

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

The effect of this technique in the modulation reference waveforms is seen in Fig. 3(a), where the modulation index for the

reference and injected waveform is 0.6 and 0.1, respectively.

The magnitude of the injected waveform in these figures has

been exaggerated for clarity purposes.

One of the disadvantages of this method is that second harmonic voltage components are heavily penalized in most power

quality legislations. To overcome this problem, the injection of

a sinusoidal waveform at six times the supply frequency can be

used instead, as explained in the next section.

Fig. 2. Three-level NPC inverter configuration with ideal sinusoidal current

sources.

the inverter is supplied by a three phase set of pure sinusoidal

currents (1). However, the experimental results show later on

in this paper that the analysis and proposed techniques are also

valid for an unbalanced supply system.

Also, the output voltage of the inverter is produced by comparing the reference waveform showed in (2), with two levelshifted triangular carrier waveforms to obtain a 3-L output [5].

In addition, the injection of a third harmonic waveform, as seen

in (3), is a well recurred method to increase the magnitude of

the output voltage, about 15% higher where K3 takes a value of

1/6 [5]

iA = Iˆ sin (ωt + φ)

iB = Iˆ sin ωt − 2π/3 + φ

iC = Iˆ sin ωt + 2π/3 + φ

(1)

vA = E/2 m1 sin (ωt)

vB = E/2 m11 sin ωt − 2π/3

vC = E/2 m1 sin ωt + 2π/3

(2)

v3 = E/2 m1 K3 sin (3ωt)

(3)

B. Sinusoidal Sixth Harmonic Injection

It is well known that harmonics multiple of three times the

output frequency are zero sequence, that is, they are in phase

across all three phases and are, therefore, inherently cancelled

out at the output of a three-phase system [5]. Moreover, even

harmonics contribute with a nonzero average value of current

to the midpoint in the same way as explained in the previous

section. This method consists in injecting a sinusoidal waveform

at six times the supply frequency as seen in (5) [29]. The effect

of this method on the output waveform is showed in Fig. 3(b)

for a m1 index of 0.6 and a modulation index of the injected

waveform m6 of 0.1

vA −6 sin = vA + E/2m6−sin sin (6ωt + φ6−sin )

vB −6 sin = vB + E/2m6−sin sin (6ωt + φ6−sin )

vC −6 sin = vC + E/2m6−sin sin (6ωt + φ6−sin )

where m1 is the modulation index and K3 is the amount of third

harmonic injection

(5)

where m6 is the modulation index for the compensation waveform.

One of the potential disadvantages of using this method in

large power inverter systems is the relatively high switching

frequency that is required to materialize the sixth harmonic component. This has a frequency of 300 and 360 Hz, respectively

for supply frequencies of 50 or 60 Hz. Large power inverters

normally operate at relatively low switching frequencies, below

1 kHz. The next section proposes a voltage balancing method

that aims to overcome this problem.

A. Sinusoidal Second Harmonic Injection

C. Squared Sixth Harmonic Injection

This method consists in injecting a negative sequence second

harmonic voltage waveform, superimposed to the fundamental

output waveform defined in (4). Since the second harmonic

components are negative sequence, a negative sequence of those

will be in phase with the positive fundamental sequence [27],

[28]

This technique can be seen as an evolution of that presented in

the previous section and consists in injecting a squared wave at

six times the supply frequency. Since the injection of a squared

wave can be regarded as the addition of a dc offset of a given

magnitude to the reference waveform that changes sign every

30 electrical degrees, its practical implementation is likely to be

simpler, especially in inverters operating with a low switching

frequency. This injected waveform can be expressed as

vA −2 sin = vA + E/2 m2 sin (2ωt + φ2 )

vB −2 sin = vB + E/2 m2 sin 2 ωt + 2π/3 + φ2

vC −2 sin = vC + E/2 m2 sin 2 ωt − 2π/3 + φ2

vA −6sq = vA + v6−sq

(4)

where m2 is the modulation index for the compensation waveform.

vB −6sq = vB + v6−sq

vC −6sq = vA + v6−sq

v6−sq = E/2m6−sq sign [sin (6ωt + φ6−sq )] .

(6)

CHIVITE-ZABALZA et al.: VOLTAGE BALANCING CONTROL IN 3-LEVEL NEUTRAL-POINT CLAMPED INVERTERS

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Fig. 3. Line-to-midpoint output voltage for: (a) sinusoidal second harmonic injection; (b) sinusoidal sixth harmonic injection; (c) squared sixth harmonic

injection. Continuous line: v A ; dashed line: v B ; dotted line: v C , normalized with respect to E/2.

The effect of this technique on the inverter output waveform is

illustrated in Fig. 3(c) for a m1 index of 0.6 and a modulation

index of the injected waveform m6 of 0.1. The next section evaluates the ability of the three compensation approaches described

so far to control de midpoint voltage.

III. ANALYSIS OF THE AVERAGE CURRENT CONTRIBUTION

TO THE MIDPOINT AND AN AVERAGE MODE

This section begins by analyzing the current contribution to

the midpoint for the three voltage balancing techniques explained in the previous section. Subsequently, a sensitivity analysis for different modulation indexes and phase-shift angles is

performed. Next, a small signal averaged model of the midpoint

balance control loop, suitable for control design purposes, is

proposed.

Fig. 4.

Second harmonic compensation for m 1 = 0.6 and m 2 = 0.3.

Fig. 5.

= 0.2.

Sixth harmonic sinusoidal compensation for m 1 = 0.6 and m 6 − sin

A. Analysis of the Current Contribution to the Midpoint

As already explained in [27], [28], the instantaneous duty

ratio d of the portion of the phase input current that flows to the

midpoint is defined as

⎫

⎧

−E/ ≤ vK < 0 ⎬

⎨ 1 + 2vK/E

2

dK =

(7)

⎩

0 ≤ vK ≤ −E/ ⎭

1 − 2vK/E

2

where k = A, B, or C

Consequently, the instantaneous contribution of any phase to

the midpoint current is obtained by multiplying the duty ratio

dK by the phase current (1)

iM −K = dK iK .

(8)

Since the voltage drift of the midpoint is a comparatively slower

varying process than the instantaneous voltage ripple present in

the dc bus, the effectiveness of the midpoint voltage control can

be evaluated by considering the mean dc midpoint current over

an entire line period T . This is calculated in a straightforward

manner as

T

¯iM −K = 1

iM −K dt

(9)

T 0

where the total average current contribution to the midpoint is

¯iM = ¯iM −A + ¯iM −B + ¯iM −C

1 T

=

(iM −A + iM −B + iM −C ) dt.

T 0

(10)

The effect that the injection of a negative sequence second harmonic, sinusoidal sixth harmonic and squared sixth harmonic,

have on the midpoint current can be visually seen by looking at

the waveforms in Figs. 4–6 respectively, corresponding to phase

A.

These waveforms have been computed using the MATLAB

software using (1)–(10) for a modulation index of the fundamental waveform of m1 = 0.6. The modulation index for the

compensation waveforms where m2 = 0.3, m6−sin = 0.2, and

m6−sq = 0.2 and the phase angle of the injection waveforms

was set to zero, that is, Φ2 = 0, Φ6−sin = 0, and Φ6−sq = 0. The

first two waveforms on top of every figure show the fundamental and the compensating waveforms in continuous and dotted

lines. The second waveform depicts the instantaneous duty ratio

d of the current to the midpoint. The third waveform shows the

current iA flowing into phase A, 90◦ out of phase with respect

to the output voltage. The fourth waveform shows the current

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

TABLE I

IM /m 2 AND IM /m 6 GAINS IN THE FIRST LINEAR OPERATING REGION

Fig. 6. Sixth harmonic squared injection at six times the supply frequency for

m 1 = 0.6 and m 6 −sq = 0.2.

contribution of phase A to the midpoint, calculated by direct

multiplication of the second and third waveforms, as seen in

(8). Finally, the last set of waveforms show the instantaneous

overall current contribution to the midpoint made by all three

phases, using a continuous trace and its average value over the

entire period, using a dotted trace. The voltages and currents

are normalized with respect to E/2 and the phase peak current,

respectively. It can be seen by visual inspection how the average

current has a negative value, more significant in the case of the

second harmonic injection Fig. 4(a). The usual third harmonic

current ripple, which creates a third harmonic voltage ripple in

the midpoint is also present.

The next section carries out a sensitivity analysis of the key

parameters involved in the midpoint balance mechanism.

B. Sensitivity Analysis of the Current Contribution

to the Midpoint

A phase-shift angle sensitivity analysis using numerical calculation for second harmonic injection was carried out first, by

varying the phase-shift angle Φ2 between the injected and reference waveforms and the phase angle Φ between the voltage

and current. The results for modulation indexes of the reference

and injected waveform of 1 and 0.4, respectively, are showed in

Fig. 7(a) and (b). The continuous and dashed lines in Fig. 7(a)

correspond to a pure capacitive and inductive load, respectively.

Also, the reference and injection waveforms in Fig. 7(b) are in

phase, that is Φ2 = 0. It can be seen that the largest contribution

of current to the midpoint takes place for pure reactive loads

where the reference and compensating waveforms are in phase.

Also, there is no current contribution for active loads. Similar

results are obtained for sixth harmonic injection and for different modulation indexes. For that reason, it is proposed in this

paper to choose an injection waveform that is in-phase with the

reference waveform, that is, with Φ2 = 0, Φ6−sin = 0, and Φ6−sq

= 0, as it has the greater compensating effect on the midpoint.

The results of Fig. 7(b) suggest that the voltage balancing

control can also be achieved by phase shifting the injection

waveform rather than by adjusting its amplitude as proposed

in this paper. However, this method has not been adopted by

the authors as it would entitle using an injection waveform of

a constant, and relatively high magnitude at all times, even

if the midpoint capacitors are balanced. This would cause a

degradation of the steady-state harmonic content in the case of

second harmonic injection and a permanent limitation on the

maximum modulation index in all cases.

An interesting observation that can be drawn by looking at

the top waveforms in Figs. 4–6 is that, since the injection waveforms of the three proposed strategies are even harmonics of the

fundamental, they have zero crossings at π/2 and 3π/2, where

the magnitude of the fundamental has its peaks. It follows that

their contribution to the peak value of the resultant reference

waveform will be the same, whether the injection waveform is

in phase, or 180◦ out of phase with respect to the fundamental,

or whether its amplitude is positive or negative.

The variation of the modulation index m2 , m6−sin , and m6−sq

of the injection waveform, defined in (4)–(6), has also been studied and the results are shown in Fig. 8. The plots on the top and

bottom rows have been obtained without and with third harmonic injection. Also, the first, second, and third columns in the

figure show the results for second harmonic, sinusoidal sixth

harmonic and squared sixth harmonic injection, respectively.

The continuous and dotted lines correspond to capacitive compensation where the modulation indexes for the reference waveform were 0.8 and 0.5, respectively. Also, the dashed–dotted

and dashed lines correspond to inductive compensation where

the modulation indexes for the reference waveform are 0.8 and

0.5, respectively. Moreover, the thicker continuous traces correspond to the range of balancing waveform available without

entering in overmodulation. This limitation will be explained in

greater detail in Section III-C.

Looking at the figure, it can be seen how the second harmonic compensation introduces an average value of current to

the midpoint IM significantly higher than that provided by its

sixth harmonic injection counterparts. It can also be appreciated, how all three compensation techniques present a linear

region for low amplitudes of the injected waveform, where the

current IM is proportional to the modulation index of the injected signal. In the case of the second harmonic compensation,

the slope of the curves takes a lower value at a given m2 value.

However, in the case of sixth harmonic injection, it reaches a

peak and then gradually falls down until it collapses to zero or

even becomes negative. The values of the first linear portion of

the curve, namely KM , defined in (11) for all three modulation techniques, with and without third harmonic injection, are

shown in Table I. This value is used in the next section to obtain

an averaged model of the midpoint voltage balance control loop

KM =

IM

IM

IM

or KM =

or KM =

.

ˆ 2

ˆ 6−sin

ˆ 6−sq

Im

Im

Im

(11)

CHIVITE-ZABALZA et al.: VOLTAGE BALANCING CONTROL IN 3-LEVEL NEUTRAL-POINT CLAMPED INVERTERS

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Fig. 7. Current to midpoint im against phase-shift angle Φ 2 for second harmonic sinusoidal injection. (a) Current contribution IM (p.u.) against Φ 2 for a pure

capacitive (continuous trade) and inductive (dashed trace) load. (b) Current contribution IM (p.u.) against Φ.

Fig. 8. Variation of the average current to the midpoint against modulation index of the injected waveform. (a) Second harmonic compensation. (b) Second

harmonic compensation using third harmonic injection. (c) Sinusoidal sixth harmonic compensation. (d) Sinusoidal sixth harmonic compensation using third

harmonic injection. (e) Squared sixth harmonic compensation. (f) Squared sixth harmonic compensation using third harmonic injection.

Fig. 9. Variation of the p.u. average current to the mid-point against the modulation index of the injected waveform, using third harmonic injection, for

an unbalanced set of currents represented by the addition of a 0.5 p.u. inverse sequence. (a) Second harmonic compensation. (b) Sinusoidal sixth harmonic

compensation. (c) Squared sixth harmonic compensation.

By looking at Fig. 8 and Table I, it can be concluded that the

injection of a second harmonic waveform is more suitable for

control purposes since not only it contributes with a comparatively higher current to the midpoint, but also its linear operating

region extends for a wider range of values of the compensating waveform. Moreover, it does not become negative nor it

collapses to zero. Also, the squared harmonic injection technique provides a slightly higher midpoint current IM than the

sinusoidal one.

The reason for this behavior is the linearity property

of the integral appearing in (9), resembling the calculation

of a Fourier series coefficient, which can be expressed as

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

follows:

¯iM −A =

1

2·π

1

=

2·π

0

0

2·π

As long as this condition is met, the previous assumption will be

valid, and the values of IM will be proportional to m2 or m6−sin .

In our particular case, when the sinusoidal second and/or sixth

harmonic are added to the fundamental, this equation becomes

iM −A (ωt) · dωt

2·π

2 · vA

1−

E

(12)

where the time integral has been multiplied by the angular speed

ω, to get an angle integral. This can be simplified to

ˆ 2·π

¯iM −A = − 1 2 · I

vA · sign(vA ) · cos(ωt) · dωt

2·π E 0

(13)

finally resulting in

ˆ π

¯iM −A = − 2 · I

vA · cos(ωt) · dωt

(14)

E·π 0

where it has been assumed that vA is positive for angles ωt in

the range 0 < ωt ≤ π, and negative for angles π < ωt ≤ 2 π.

This assumption will be justified later, and its range of validity

calculated accordingly.

Note that, due to the waveform symmetry, the upper integration limit has been changed from 2 π to π, and the value of

the resulting integral has been doubled accordingly. Thus, the

sign(vA ) function can be suppressed. Therefore, the expression

in (14) becomes linear in the amplitudes of the different harmonics which may form vA . This is expected as odd voltage

harmonics forming vA do not contribute to the integral of (14),

since only even voltage harmonics are expected to contribute to

the balance of the dc voltage of a 3-L-NPC inverter.

For phase symmetry reasons (phase voltages and currents

are supposed to be direct-sequence or zero-sequence, but not

negative-sequence), the average current entering the midpoint

of the dc-bus provided by phases B and C must be the same

as that provided by phase A. Consequently, the values obtained

previously must by multiplied by three to get the total contributions.

This behavior will persist as long as the voltage harmonics

added to the fundamental signal do not force a sign change in the

total voltage waveform vA at any angle, as previously assumed.

Since all harmonics are set up in sine phase, this is, all cross the

zero level, at the same angle and with positive slope, the limit

for that condition is met when the derivative gets close to zero

at the opposite angle (ωt = π), when the waveform crosses zero

from positive to negative values).

Therefore, an algebraic expression for the validity of the linearity condition is obtained as follows:

mh · sin(h · ωt)

V =

h

dV

=

dωt

h · mh · cos(h · ωt)

h

dV

=

h

·

m

−

h · mh < 0. (15)

h

dωt ω t=P i

h·even

2 · m2 + 6 · m6 < 1 · m1 .

· sign(vA ) · Iˆ · cos(ωt) · dωt

h·o dd

(16)

So, in this linear region, valid for small enough amplitudes of

the injected harmonics, the gains obtained with this method are

therefore

E

E

· m1 · sin(ωt) + · m2 · sin(2 · ωt)

2

2

6 · Iˆ π

= 3 · ¯iM −A = −

vA · cos(ωt) · dωt

E·π 0

6 · Iˆ π E

=−

· m2 · sin(2 · ωt) · cos(ωt) · dωt

E·π 0 2

3 · Iˆ · m2 π

=−

sin(2 · ωt) · cos(ωt) · dωt

π

0

¯iM

4

4

(17)

= · Iˆ · m2 → KM =

=

ˆ

π

π

I · m2

vA =

¯iM

¯iM

for the second harmonic compensation, and

E

E

· m1 · sin(ωt) + · m6 · sin(6 · ωt)

2

2

π

ˆ

6·I

= 3 · ¯iM −A = −

vA · cos(ωt) · dωt

E·π 0

6 · Iˆ π E

=−

· m6 · sin(6 · ωt) · cos(ωt) · dωt

E·π 0 2

3 · Iˆ · m6 π

=−

·sin(6 · ωt) · cos(ωt) · dωt

π

0

¯iM

36

36

· Iˆ · m6 → KM =

(18)

=

=

35 · π

35 · π

Iˆ · m6

vA =

¯iM

¯iM

for the sinusoidal sixth harmonic compensation. This confirms

the values shown in Table I, directly measured from the slopes

in Fig. 8(a)–(d).

The case of the squared sixth harmonic compensation is a

little more complex to calculate, since this waveform is composed of infinite harmonics with weights inversely proportional

to their respective harmonic order. That property makes that,

even when very small amplitudes of the squared sixth harmonic

are added, the voltage waveform changes sign in the vicinity

of ωt = π. Therefore, the integral of (14) no longer holds, and

that of (13) applies instead, which is nonlinear due to the sign

function appearing into its integral. Therefore, the behavior of

that strategy is not strictly linear from the very beginning. However, a tangent slope can be calculated for small amplitudes of

the squared sixth harmonic compensating waveform, as already

seen in Fig. 8(e) and (f) and in Table I.

A disadvantage of injecting a second harmonic voltage is

that, since it is not a zero sequence harmonic, it appears at

the inverter output. It is well known that second harmonic

currents (created by second harmonic voltages) are restricted

CHIVITE-ZABALZA et al.: VOLTAGE BALANCING CONTROL IN 3-LEVEL NEUTRAL-POINT CLAMPED INVERTERS

in most power quality standards. However, the magnitude of the

compensating waveform is expected to be small, and therefore

negligible at the output. Moreover, it is usually injected during

the short transient periods required to balance the midpoint of

the dc-link, out of the steady state operating regime evaluated

by most power quality standards.

The operation of the three techniques under discussion has

also been tested in the presence of unbalance currents by adding

a negative sequence component to the currents seen in (1)

iA = Iˆ sin (ωt + φ) + IˆINV sin (ωt + φINV )

iB = Iˆ sin ωt − 2π/3 + φ + IˆINV sin ωt + 2π/3 + φINV

iC = Iˆ sin ωt + 2π/3 + φ + IˆINV sin ωt − 2π/3 + φINV .

(19)

Using those, the variation of the modulation index m2 , m6−sin ,

and m6−sq of the injection waveform, defined in (4)–(6) and

represented in Fig. 9 has been repeated. The plots on the first,

second, and third columns in the figure show the results for

second harmonic, sinusoidal sixth harmonic and squared sixth

harmonic injection, respectively, where third harmonic injection

has been used.

These have been obtained for inductive compensation and

using modulation indexes of 1 and 0.5 for the reference and

injection waveforms, respectively. The dashed line corresponds

to a balanced set of line currents, that is, where IˆINV = 0. Also,

the dotted and dashed–dotted lines correspond to a ratio of inverse to direct sequence current ratio IˆINV /Iˆ of 0.5. In the

former, the negative sequence currents are in phase with the

direct sequence currents whereas in the latter the negative sequence currents are 90◦ lagging. These results are mirrored for

capacitive reactive compensation. It is clear by looking in the

figures how the presence of a negative sequence has a negligible

effect on the balancing current that flows to the midpoint of the

dc link, particularly, in the linear region of operation. This is

also justified by looking at the symmetry features of (13), which

is zero for the product of odd voltage and current harmonics.

The next Section looks at the maximum waveform that can

be injected for the proposed techniques

C. Limit of the Injection Waveforms

The sum of the reference and compensating waveform should

not exceed the dc-bus voltage E/2. Consequently the compensating waveform must comply with the following expression at

all times

vCOM P ≤ E/2 − vA ,B ,C

(20)

where vCOM P can be either vA ,B ,C −2sin , vA ,B ,C −6sin , or

vA ,B ,C −6sq as defined in (4)–(6), respectively. Also, vA ,B ,C

is expressed in (2) and (3) if third harmonic injection is used.

The maximum modulation index for the injection waveforms

has been calculated by solving (20) for the angle (ωt)M AX

that achieves the peak value in expressions (4)–(6). This angle has been calculated by solving the equation that equates the

4479

angle derivative expression to zero, following basic mathematic

principles.

Using those, the maximum modulation index for the compensating waveform has been calculated for several values of the

modulation index

√ m1 of the reference waveform, close to the

maximum 2/ 3, where third harmonic injection has been used

and the results are shown in Fig. 10. The second harmonic, sinusoidal sixth harmonic, squared sixth harmonic and SVPWM are

represented using continuous, dashed, dashed–dotted and dotted traces, respectively. Also, in that figure, the resultant average

current that flows to the midpoint IM , normalized with respect to

the peak value of the line current is also shown. These results are

compared with the current that is obtained using the well-known

SVPWM technique for a 3-L-NPC inverter [7]–[10].

In that figure, it can be seen how the maximum compensating

waveform that can be injected is gradually reduced as the modulation index for the reference waveform

√ is increased, until it

reaches its maximum value of m1 = 2/ 3, where no compensating waveform can be introduced. On the contrary, SVPWM

can produce a mid-point balancing current even at the maximum

modulation index. It is also seen in Fig. 10 how second harmonic

injection has a higher balancing effect, whereas sinusoidal and

squared harmonic injection can produce compensating currents

with similar values. This is explained, despite squared sixth

harmonic injection having a higher balancing action than sinusoidal sixth harmonic injection, because the latter allows having

an injection waveform of a magnitude higher than that of the

former.

It is important to mention that the contribution of the proposed techniques to the midpoint balancing current can be easily increased at certain times at the expenses of sacrificing the

magnitude of the reference waveform. That is, the value of

m2 , m6−sin , or m6−sq , depending on whichever technique is

used, can be temporarily increased by subsequently reducing

the value of m1 , to bring the midpoint back into balance, as it

will be seen in the experimental results seen in Section IV. This

feature is not straightforward to implement in SVPWM.

An example of the maximum current contribution to the midpoint for a modulation index of m1 = 0.9 and second harmonic,

sinusoidal sixth harmonic, squared sixth harmonic compensation and SVPWM is shown in Fig. 11. In that figure, the instantaneous current is depicted using a continuous trace and its

average value over a supply line cycle is seen with a dotted trace.

The next Section obtains a small-signal averaged model that

can be used for control design purposes.

D. Small Signal Averaged Model of the Split Capacitors

Midpoint Balance

The averaged model of the split capacitors midpoint balance

loop is obtained by averaging the output capacitor currents and

voltages over a supply cycle, that is, by neglecting the instantaneous ripple. The analysis also assumes that the dc bus voltage

vo is stable and has a constant average value of E. This assumption is justified, even at the low switching frequencies typical

of large converter systems, by the criteria chosen to design

the dc-link capacitors. This, with the purpose of avoiding any

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

Fig. 10. (a) Maximum compensating modulation index and (b) produced compensating IM current (normalized against the peak value of the line current),

for the modulation index of the reference waveform. Continuous line: second harmonic compensation, dashed line: sinusoidal sixth harmonic compensation,

dashed-dotted line: squared sixth harmonic compensation, dotted line: SVPWM.

Fig. 11. Maximum instantaneous (continuous trace) and average (dotted trace) current contribution to the mid-point of the dc-capacitors for m 1 = 0.9.

(a) Second harmonic compensation using third harmonic injection for m 2 = 0.237. (b) Sinusoidal sixth harmonic compensation using third harmonic injection

for m 6 −sin = 0.236. (c) Squared sixth harmonic compensation using third harmonic injection for m 6 −sq = 0.221. (d) SVPWM.

overvoltage across the power devices, aims to reduce the voltage switching ripple to a very low value by including enough

capacitance. For that reason, the voltage unbalance within one

switching cycle for the different modulation methods has not

been considered.

By looking at the diagram of Fig. 1, it can be easily deducted

that voltage balance of the midpoint capacitors is

v¯C 2 − v¯C 1 =

1

C

0

T

1

(¯iC 2 − ¯iC 1 ) dt =

C

T

¯iM dt

(21)

0

Expressing this equation in the S domain, and relating the average midpoint current IM to the peak phase current and the

modulation index of the compensating waveform by means of

the KM ratio (11) seen in Table I, the following transfer function

is obtained:

Iˆ sin (φ) KM

VC 2 − VC 1

=

m2 (or m6 )

CS

Fig. 12. Control loop of the split capacitors mid-point balance for reactive

power compensation.

(22)

Based on this transfer function, a control loop structure valid

for reactive power compensation is proposed in Fig. 12, where a

usual PI controller is employed in combination with a low-pass,

first order filter, to suppress the voltage ripple components (23).

The control output is normalized by dividing it by the peak

reactive component of the phase current, a straightforward operation in usual digital control systems. An optional offset has

been added to the setpoint to allow introducing step changes to

evaluate the performance of the control loop. The cross-over frequency of the first order filter is selected to mitigate the third harmonic ripple components present across the capacitors (150 Hz

CHIVITE-ZABALZA et al.: VOLTAGE BALANCING CONTROL IN 3-LEVEL NEUTRAL-POINT CLAMPED INVERTERS

4481

Fig. 13. Step response of the split capacitors voltage balance loop. (a) positive step response and (b) positive and negative step response. The thick continuous

line: averaged response; the thin continuous line: instantaneous response; the tick dotted line: setpoint.

for a 50 Hz system), for example at 15 Hz or 94.25 rad/s. Subsequently, the PI loop can be tuned using conventional techniques,

for instance, aiming to achieve a reasonable Phase Margin [30].

Although, as explained in the next Section IV, the dynamic response achieved using this control strategy is sufficient for most

large power electronics applications, other suitable strategies

compatible with the proposed compensating techniques could

also be devised

Controller T F =

1

KP

S/ + 1

ωP

(S + iTn )

S

(23)

The next section shows simulation and experimental results that

proof the operation of this modeling and control approach.

IV. SIMULATION AND EXPERIMENTAL EVALUATION

The operation of the control strategy proposed in Fig. 12 has

been validated, first in simulation and then experimentally, on

a 690 Vac, 100 A, 120 kVA, 3-L NPC inverter, based on IGBT

devices switching at 600 Hz. Each of the split capacitors had a

capacitance value of 6.6 mF and the positive and negative dclink terminals of the inverter were supplied by a 950 V external

rectifier unit, with the midpoint left floating. The phase-shift

angle of the injection waveforms with respect to the reference

waveform has been chose to be Φ2 = 0, Φ6−sin = 0, Φ6−sq = 0

for a greater compensation effect, as explained in Section III-B.

The simulation results for a step response when second harmonic compensation is selected, are shown in Fig. 13. The

inverter was supplied by a set of ideal current sources of 90-A

RMS and the RMS phase-to-neutral output voltage was 310 V.

To validate the averaged model described in the previous section, the control loop as shown in Fig. 12 has been made run

in parallel with the complete inverter simulation. In that figure, the left and right-hand plots show the response to a 0 to

50 V and 0 to 50 to 0 V offset step respectively. The continuous

thin and thick lines represent the instantaneous and averaged

vC 2 − vC 1 waveforms, which show close correspondence. The

step setpoint is depicted in the figure using a dotted thin trace.

The control parameters where chosen as ω P = 94.24 rads/s;

KP = 0.0863 and iTN = 2.93. The same results were obtained

for sixth harmonic squared and sinusoidal compensation, but

are not shown in this paper for the shake of briefness. The

control loop achieves an open-loop bandwidth of 2.64 Hz, a

settling time of 0.784 s (for a 1% error criteria) and an overshoot of 12%. Therefore, with the proposed adjustment, it will

take about 40 line cycles to complete a step response. Although

this may seem a long time, in practice, due to the amount of

capacitance present in the dc link, as explained in this Section III-D, the dc-link midpoint voltage balance changes relatively slowly. This is confirmed in the experimental section and

in several industrial applications where this strategy has been

implemented.

In the experimental validation, the inverter output terminals

were connected to an 18 mH inductive load and it was operated in current control mode. To verify the ability to control

the midpoint, an offset step of 50 V was introduced when the

output current was controlled to be 70-A RMS and the results

are shown in Fig. 14(a)–(c), for second harmonic, sinusoidal

sixth harmonic, and squared sixth harmonic compensation, respectively.

The first two waveforms show the capacitor voltages vC 1 and

vC 2 , the third waveform the inverter output voltage with respect

to the midpoint of the dc-link capacitors vAG and the bottom

waveform shows the output current iA . The proportional gain

KP for second and sixth harmonic was chosen to be 0.3 and

0.85, respectively, whereas the integral term iTn and the filter

crossover frequency were 2.93 and 94.24 rad/s, respectively, in

all three cases (23). These waveforms show how the midpoint

voltage balance can be successfully controlled for all the proposed strategies. A similar response was obtained for a falling

50 V to 0 V step response. By looking at the results, it is very hard

to appreciate substantial differences between response obtained

using sinusoidal and squared sixth harmonic injection. Therefore, the main difference between these two techniques lies in the

easier implementation offered by the squared harmonic injection at low switching frequencies. In the waveforms of Fig. 14,

a dip in the output current during the midpoint transient can be

observed, which highlights a limitation of the proposed compensation techniques. This is due to the output voltage required

to control the output current, already operating close to its limit

in this experiment, diminishing to accommodate the midpoint

compensating waveforms. This effect is significantly greater in

the case of the sixth harmonic injection strategies as their compensation power is about three or four times smaller than that of

the second harmonic strategy. This limitation is only likely to

appear when operating at very high modulation indexes and is

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

Fig. 14. Instantaneous response for a mid-point imbalance step of 0 to 50 V, 70 A RMS. (a) sinusoidal second harmonic injection; (b) sinusoidal sixth harmonic

injection; (c) squared sixth harmonic injection. First waveform: v c 1 (100 V/div), second waveform: v c 2 (100 V/div), third waveform v A G (500 V/div), fourth

waveform: iA (100 A/div). Time scaling: 40 ms/div.

Fig. 15. Instantaneous response for a mid-point imbalance step of 0– 50 V, 35 A RMS, unbalanced load: (a) sinusoidal second harmonic injection; (b) sinusoidal

sixth harmonic injection; (c) squared sixth harmonic injection. First waveform: v c 1 (100 V/div), second waveform: v c 2 (100 V/div, third waveform iA (50 V/div),

fourth waveform: iB (50 A/div). Time scaling: 40 ms/div.

Fig. 16. Instantaneous response for a step change on the phase current, second harmonic compensation K P = 0.3, iTn = 2.93, ωP = 94.24 rad/s. (a) 10 to

75 A RMS, K P = 0 (controller disabled); (b) 10 to 75 A RMS (c) 75 to 10 A RMS. First waveform: v c 1 (100 V/div), second waveform: v c 2 (100 V/div), third

waveform: v A G (500 V/div), fourth waveform: iA (100 A/div); Time scaling: (a): 40 ms/div. (b) and (c): 100 ms/div.

related to the nature of the transient, the control loop adjustment

and the dc-bus capacitance.

In addition, to verify the level of second harmonic introduced

by the second harmonic injection strategy, the harmonic content of the voltage and current waveforms shown in Fig. 14(a)

has been measured using a high-bandwidth Yokogawa PM3000

power quality analyzer. These measurements, carried out at

steady-state operating conditions, show that the second harmonic voltage and current content, expressed as a percentage of

the fundamental is 1% and 0.4% respectively. These are residual values, not necessarily related to the midpoint balancing

strategy but to the asymmetries introduced by the low switching

frequency that is used [1].

The next test consisted in evaluating the performance midpoint balance control loop for a sudden step change of the output

current. The waveforms seen in Fig. 16(a) show that, for a rising step from 10 to 75 A, under no midpoint control (KP =

0), there was a drift of the midpoint voltage balance, eventually causing a inverter trip. The order of the waveforms is the

same as that explained for Fig. 14. However, when the midpoint voltage balance control is activated, in this case for second harmonic compensation, the midpoint remained balanced

for both a rising current step (10 to 75 A), Fig. 16(b), and a

falling step (75 to 10 A), Fig. 16(c). Similar results were obtained when sinusoidal or squared sixth harmonic injection was

used.

CHIVITE-ZABALZA et al.: VOLTAGE BALANCING CONTROL IN 3-LEVEL NEUTRAL-POINT CLAMPED INVERTERS

To evaluate the performance when supplying an unbalanced

load, the midpoint response was tested by connecting an unbalanced inductive load at the secondary of a star-delta transformer.

This particular test setup was chosen due to availability reasons.

The RMS value of the A, B, and C phases was 30, 34, and 34 A,

respectively, which created the circulation of 32.7 A of positive

sequence, 2.6 a of negative sequence and 0.3 A of zero sequence,

as measured by a Yokogawa WT3000 precision power analyzer.

The results are showed on Fig. 15 where the top two waveforms

represent the dc-link capacitor voltages vC 1 and vC 2 and the

top two waveforms represent the two output currents iA and iB .

It can be seen in that figure how the midpoint voltage can be

controlled for second harmonic (a) sinusoidal sixth harmonic,

(b) squared sixth harmonic injection and (c) under an unbalanced load situation, validating the analysis shown in Section

III-D. Again, similar results were obtained for sixth harmonic

injection.

V. CONCLUSION

This paper has presented a novel technique to balance the voltage of the two split dc capacitors of a 3-L neutral-point clamped

inverter, suitable for reactive power compensation, when triangular carrier PWM modulation is employed. It consists in

injecting a squared waveform at six times the supply frequency.

Subsequently, it has been compared with two already known

strategies based on the injection of a negative-sequence second

harmonic and a sinusoidal sixth harmonic waveform. The contribution of current to the inverter midpoint of these techniques has

been analyzed as a performance measure. Subsequently a smallsignal averaged model, suitable for control design purposes has

been presented and a control strategy has been proposed. Finally, these techniques have been evaluated both in simulation

and in a 690-V ac, 120 kVA experimental setup when supplying

both a balanced and an unbalanced inductive load. The results

conclude that, although the three techniques are valid, second

harmonic injection has a major effect in balancing the inverter

midpoint and the even harmonics that it introduces are negligible and only present during transients. However, out of the two

sixth harmonic injection methods that do not produce even harmonics at the inverter output, the proposed squared waveform

technique is preferred, as it has a slightly greater compensation

effect on the dc midpoint and is easier to implement, particularly,

in systems employing a low modulation index.

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Prentice Hall, Sep. 2009.

Javier Chivite-Zabalza received the B.Sc. Eng. degree in electrical and electronic engineering from

Mondragon University, Mondragon, Spain, in 1993,

the M.Sc. degree in power electronics and drives

from the Universities of Birmingham and Nottingham (joint degree), Birmingham, U.K., in 2003, and

the Ph.D. degree from the University of Manchester,

Manchester, U.K., in 2006.

He was a Project Engineer in the field of industrial

automation and drives from 1994 to 1999 in Spain,

and from 1999 to 2003 in the U.K. From 2003 to

2006, he was with Goodrich ESTC, Birmingham, U.K. where he was involved

in the development of high power-factor rectifiers for aerospace applications.

From 2006 to 2008, he was with the Rolls-Royce University Technology Centre,

University of Manchester, where he was involved in research on more electric

concepts for autonomous aerospace power systems. In 2008, he joined Ingeteam

Technology S.A., in Spain, developing power electronic converters for FACTS

devices and motor drives applications, where he is currently In-Charge of the

voltage source converter development for the 47 MVAR SSSC demonstrator.

Dr. Chivite-Zabalza is a Registered Chartered Engineer in the U.K. and a

member of the Institution of Engineering and Technology.

Pedro Izurza-Moreno was born in Bilbao, Spain, in

1982. He received the M.Sc. degree in automation

and industrial electronics from Mondragon University, Mondragon, Spain, in 2007.

In 2007, he joined the Industrial and Marine

Drives Department, Ingeteam Technology, S.A., Zamudio, Spain, where he was involved in research

on high-power inverters, especially on vector control, firmware design and programming, pulse width

modulation (PWM), space-vector PWM, selective

harmonic elimination modulation, and three-level

neutral-point-clamped inverters.

Danel Madariaga was born in Bilbao, Spain, in

1973. He received the M.Sc. degree in industrial engineering from the University of the Basque Country

(EHU-UPV), Bilbao, Spain, in 1998, and the M.Sc.

degree in physics from the Universidad Nacional de

Educaci´on a Distancia, Madrid, Spain, in 2008.

In 1998, he joined R&D Department, Ingeteam

Technology, S.A., Zamudio, Spain, where he was

mainly involved in research on high-power inverters, especially on vector control, firmware design

and programming, mathematical modeling, spacevector pulsewidth modulation (PWM), and three-level neutral-point-clamped

(3-L NPC) inverters. He was a part-time Science Teacher for four years. His

current research interests include solving the polynomial equation systems appearing in selective harmonic elimination PWM techniques, and modulation

techniques for balancing the dc bus of 3-L NPC inverters.

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

Gorka Calvo received the B.Sc. degree in electronics

engineering from the Escuela de Ingenier´ıa T´ecnica

Industrial de Bilbao, Bilbao, Spain, in 2005, and the

M.Sc. degree in automatics and industrial electronics

from the Escuela T´ecnica Superior de Ingenier´ıa de

Bilbao, Bilbao, in 2009.

Since 2009, he has been with the Ingeteam Power

Technology S.A., Zamudio, Spain, where he is engaged in high-voltage and high-power converters,

for industrial and FACTs applications. From 2007

to 2009, he was with Supsonik S.L, Sondika, Spain,

as RDi Engineer of power electronics, designing and testing hardware and control of rectifiers, UPS, voltage-frecuency converters, and PV inverters of power

converters. His research interests include power electronics, control of power

converters, and modeling.

Miguel Angel Rodr´ıguez (M’06) was born in San

Sebastian, Spain, in August, 1966. He received the

B.Sc. (Eng.) degree in electronic engineering from

Mondragon University, Mondragon, Spain, in 1989,

the M. Sc degree in electrical engineering from the

Swiss Federal Institute of Technology Lausanne,

Lausanne, Switzerland, in 1992, and the Ph.D. degree in industrial engineering from the University of

Zaragoza, Zaragoza, Spain, in 2000.

From 1992 to 2008, he was an Associate Professor in the Department of Electronics, University of

Mondragon and participated in different research projects in the field of wind

energy systems, lift drives, and railway traction. In September 2008, he joined

Ingeteam Power Technology S.A., Zamudio, Spain. He is currently the Power

Electronics Systems Manager at the Power Grid Automation Business Unit of

Ingeteam Power Technology, responsible for developing new power electronics solutions for transmission and distribution grid applications. His research

interest includes modeling and control of voltage source converters for FACTS

applications such as SSSC, STATCOM and energy storage systems, and the grid

integration studies for those systems.

4473

Voltage Balancing control in 3-Level Neutral-Point

Clamped Inverters Using Triangular Carrier PWM

Modulation for FACTS Applications

Javier Chivite-Zabalza, Pedro Izurza-Moreno, Danel Madariaga, Gorka Calvo,

and Miguel Angel Rodr´ıguez, Member, IEEE

Abstract—In this paper, a novel technique to balance the voltage

of the two split dc capacitors of a 3-Level neutral-point-clamped

inverter using triangular carrier pulse width modulation is presented. This technique, suitable for reactive power compensation

and for inverters operating with a relatively low switching frequency, consists in adding a square wave at six times the output

frequency. Subsequently, this paper presents a comparison with

two already known strategies in which a sinusoidal waveform at

two and six times the output frequency are injected. The current

contribution to the midpoint of the dc bus is then analyzed for

different modulation indexes and operating conditions. Based on

this analysis, a small-signal averaged model, suitable for control

design purposes is presented. Finally, simulation and experimental

results on a 690-Vac, 120-kVA test bench that validate the theory

are shown.

Index Terms—FACTS, insulated gate bipolar transistors

(IGBT), multilevel inverters, SHE, static synchronous series compensator (SSSC), STATCOM, VSC.

I. INTRODUCTION

HE development of FACTS devices, which aim for the

transmission network to operate close to its thermal limit

by providing a fast dynamic control [1]–[3], has been boosted

in recent times by the emergence of new semiconductor devices such as high-voltage insulated-gate bipolar transistors (IGBTs) [4]. The well-known neutral point clamped (NPC) 3-level

(3-L) inverter has been widely used in this type of applications [1], [2], and [4]. These inverters are often based on wellproven solutions, also used in other high-integrity demanding

applications such as steel mill processes, ship propulsion, and

ship dredger pumps [6]. An example of such equipment, are the

Ingedrive MV100 range of Ingeteam, shown in Fig. 1. These

are 3-L NPC IGBT-based inverters, where each has a power in

the range of 3.5 MVA.

One of the main control challenges in 3-L NPC inverters is to keep the voltage across the two dc-split capacitors

T

Manuscript received July 10, 2012; revised November 9, 2012; accepted

December 26, 2012. Date of current version March 15, 2013. Recommended

for publication by Associate Editor F. Wang.

The authors are with Ingeteam Power Technology S.A., Parque tecnol´ogico

de Bizkaia, 48170 Zamudio, Spain (e-mail: [email protected];

[email protected]; [email protected]; [email protected]

ingeteam.com; [email protected]).

Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2012.2237415

Fig. 1. Main power stack characteristics for the MV100-INGECON WIND

converter system.

balanced [5], [7]–[29]. The use of space vector pulse width modulation (SVPWM) techniques, widespread these days, presents

limitations to control the midpoint voltage at very low power

factor operation and high modulation indexes, as is often the

case of FACTS devices [7]–[9]. Moreover, there are applications where the use of traditional triangle carrier modulation is

preferred. For instance when the output waveforms are nonsinusoidal, as is the case of active filters, or when the topology

requires additional balancing loops, for instance antisaturation

control of magnetic devices connected at the inverter output,

i.e., coupling transformers.

The addition of a dc-offset to the reference waveform is a

recurred technique in applications with a power factor close to

unity, but that has no effect on pure reactive compensation [26].

The next section describes three voltage-balancing techniques

suitable for this purpose, two of them have been found in the

literature and the third one is a contribution of this paper.

II. VOLTAGE BALANCING TECHNIQUES FOR REACTIVE

COMPENSATION

This section begins by describing the compensation techniques based on sinusoidal second and sixth harmonic injection,

followed by the newly proposed compensation method. The explanation of the voltage balancing technique is based on the

3-L NPC inverter seen in Fig. 2. The explanation assumes that

0885-8993/$31.00 © 2012 IEEE

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

The effect of this technique in the modulation reference waveforms is seen in Fig. 3(a), where the modulation index for the

reference and injected waveform is 0.6 and 0.1, respectively.

The magnitude of the injected waveform in these figures has

been exaggerated for clarity purposes.

One of the disadvantages of this method is that second harmonic voltage components are heavily penalized in most power

quality legislations. To overcome this problem, the injection of

a sinusoidal waveform at six times the supply frequency can be

used instead, as explained in the next section.

Fig. 2. Three-level NPC inverter configuration with ideal sinusoidal current

sources.

the inverter is supplied by a three phase set of pure sinusoidal

currents (1). However, the experimental results show later on

in this paper that the analysis and proposed techniques are also

valid for an unbalanced supply system.

Also, the output voltage of the inverter is produced by comparing the reference waveform showed in (2), with two levelshifted triangular carrier waveforms to obtain a 3-L output [5].

In addition, the injection of a third harmonic waveform, as seen

in (3), is a well recurred method to increase the magnitude of

the output voltage, about 15% higher where K3 takes a value of

1/6 [5]

iA = Iˆ sin (ωt + φ)

iB = Iˆ sin ωt − 2π/3 + φ

iC = Iˆ sin ωt + 2π/3 + φ

(1)

vA = E/2 m1 sin (ωt)

vB = E/2 m11 sin ωt − 2π/3

vC = E/2 m1 sin ωt + 2π/3

(2)

v3 = E/2 m1 K3 sin (3ωt)

(3)

B. Sinusoidal Sixth Harmonic Injection

It is well known that harmonics multiple of three times the

output frequency are zero sequence, that is, they are in phase

across all three phases and are, therefore, inherently cancelled

out at the output of a three-phase system [5]. Moreover, even

harmonics contribute with a nonzero average value of current

to the midpoint in the same way as explained in the previous

section. This method consists in injecting a sinusoidal waveform

at six times the supply frequency as seen in (5) [29]. The effect

of this method on the output waveform is showed in Fig. 3(b)

for a m1 index of 0.6 and a modulation index of the injected

waveform m6 of 0.1

vA −6 sin = vA + E/2m6−sin sin (6ωt + φ6−sin )

vB −6 sin = vB + E/2m6−sin sin (6ωt + φ6−sin )

vC −6 sin = vC + E/2m6−sin sin (6ωt + φ6−sin )

where m1 is the modulation index and K3 is the amount of third

harmonic injection

(5)

where m6 is the modulation index for the compensation waveform.

One of the potential disadvantages of using this method in

large power inverter systems is the relatively high switching

frequency that is required to materialize the sixth harmonic component. This has a frequency of 300 and 360 Hz, respectively

for supply frequencies of 50 or 60 Hz. Large power inverters

normally operate at relatively low switching frequencies, below

1 kHz. The next section proposes a voltage balancing method

that aims to overcome this problem.

A. Sinusoidal Second Harmonic Injection

C. Squared Sixth Harmonic Injection

This method consists in injecting a negative sequence second

harmonic voltage waveform, superimposed to the fundamental

output waveform defined in (4). Since the second harmonic

components are negative sequence, a negative sequence of those

will be in phase with the positive fundamental sequence [27],

[28]

This technique can be seen as an evolution of that presented in

the previous section and consists in injecting a squared wave at

six times the supply frequency. Since the injection of a squared

wave can be regarded as the addition of a dc offset of a given

magnitude to the reference waveform that changes sign every

30 electrical degrees, its practical implementation is likely to be

simpler, especially in inverters operating with a low switching

frequency. This injected waveform can be expressed as

vA −2 sin = vA + E/2 m2 sin (2ωt + φ2 )

vB −2 sin = vB + E/2 m2 sin 2 ωt + 2π/3 + φ2

vC −2 sin = vC + E/2 m2 sin 2 ωt − 2π/3 + φ2

vA −6sq = vA + v6−sq

(4)

where m2 is the modulation index for the compensation waveform.

vB −6sq = vB + v6−sq

vC −6sq = vA + v6−sq

v6−sq = E/2m6−sq sign [sin (6ωt + φ6−sq )] .

(6)

CHIVITE-ZABALZA et al.: VOLTAGE BALANCING CONTROL IN 3-LEVEL NEUTRAL-POINT CLAMPED INVERTERS

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Fig. 3. Line-to-midpoint output voltage for: (a) sinusoidal second harmonic injection; (b) sinusoidal sixth harmonic injection; (c) squared sixth harmonic

injection. Continuous line: v A ; dashed line: v B ; dotted line: v C , normalized with respect to E/2.

The effect of this technique on the inverter output waveform is

illustrated in Fig. 3(c) for a m1 index of 0.6 and a modulation

index of the injected waveform m6 of 0.1. The next section evaluates the ability of the three compensation approaches described

so far to control de midpoint voltage.

III. ANALYSIS OF THE AVERAGE CURRENT CONTRIBUTION

TO THE MIDPOINT AND AN AVERAGE MODE

This section begins by analyzing the current contribution to

the midpoint for the three voltage balancing techniques explained in the previous section. Subsequently, a sensitivity analysis for different modulation indexes and phase-shift angles is

performed. Next, a small signal averaged model of the midpoint

balance control loop, suitable for control design purposes, is

proposed.

Fig. 4.

Second harmonic compensation for m 1 = 0.6 and m 2 = 0.3.

Fig. 5.

= 0.2.

Sixth harmonic sinusoidal compensation for m 1 = 0.6 and m 6 − sin

A. Analysis of the Current Contribution to the Midpoint

As already explained in [27], [28], the instantaneous duty

ratio d of the portion of the phase input current that flows to the

midpoint is defined as

⎫

⎧

−E/ ≤ vK < 0 ⎬

⎨ 1 + 2vK/E

2

dK =

(7)

⎩

0 ≤ vK ≤ −E/ ⎭

1 − 2vK/E

2

where k = A, B, or C

Consequently, the instantaneous contribution of any phase to

the midpoint current is obtained by multiplying the duty ratio

dK by the phase current (1)

iM −K = dK iK .

(8)

Since the voltage drift of the midpoint is a comparatively slower

varying process than the instantaneous voltage ripple present in

the dc bus, the effectiveness of the midpoint voltage control can

be evaluated by considering the mean dc midpoint current over

an entire line period T . This is calculated in a straightforward

manner as

T

¯iM −K = 1

iM −K dt

(9)

T 0

where the total average current contribution to the midpoint is

¯iM = ¯iM −A + ¯iM −B + ¯iM −C

1 T

=

(iM −A + iM −B + iM −C ) dt.

T 0

(10)

The effect that the injection of a negative sequence second harmonic, sinusoidal sixth harmonic and squared sixth harmonic,

have on the midpoint current can be visually seen by looking at

the waveforms in Figs. 4–6 respectively, corresponding to phase

A.

These waveforms have been computed using the MATLAB

software using (1)–(10) for a modulation index of the fundamental waveform of m1 = 0.6. The modulation index for the

compensation waveforms where m2 = 0.3, m6−sin = 0.2, and

m6−sq = 0.2 and the phase angle of the injection waveforms

was set to zero, that is, Φ2 = 0, Φ6−sin = 0, and Φ6−sq = 0. The

first two waveforms on top of every figure show the fundamental and the compensating waveforms in continuous and dotted

lines. The second waveform depicts the instantaneous duty ratio

d of the current to the midpoint. The third waveform shows the

current iA flowing into phase A, 90◦ out of phase with respect

to the output voltage. The fourth waveform shows the current

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

TABLE I

IM /m 2 AND IM /m 6 GAINS IN THE FIRST LINEAR OPERATING REGION

Fig. 6. Sixth harmonic squared injection at six times the supply frequency for

m 1 = 0.6 and m 6 −sq = 0.2.

contribution of phase A to the midpoint, calculated by direct

multiplication of the second and third waveforms, as seen in

(8). Finally, the last set of waveforms show the instantaneous

overall current contribution to the midpoint made by all three

phases, using a continuous trace and its average value over the

entire period, using a dotted trace. The voltages and currents

are normalized with respect to E/2 and the phase peak current,

respectively. It can be seen by visual inspection how the average

current has a negative value, more significant in the case of the

second harmonic injection Fig. 4(a). The usual third harmonic

current ripple, which creates a third harmonic voltage ripple in

the midpoint is also present.

The next section carries out a sensitivity analysis of the key

parameters involved in the midpoint balance mechanism.

B. Sensitivity Analysis of the Current Contribution

to the Midpoint

A phase-shift angle sensitivity analysis using numerical calculation for second harmonic injection was carried out first, by

varying the phase-shift angle Φ2 between the injected and reference waveforms and the phase angle Φ between the voltage

and current. The results for modulation indexes of the reference

and injected waveform of 1 and 0.4, respectively, are showed in

Fig. 7(a) and (b). The continuous and dashed lines in Fig. 7(a)

correspond to a pure capacitive and inductive load, respectively.

Also, the reference and injection waveforms in Fig. 7(b) are in

phase, that is Φ2 = 0. It can be seen that the largest contribution

of current to the midpoint takes place for pure reactive loads

where the reference and compensating waveforms are in phase.

Also, there is no current contribution for active loads. Similar

results are obtained for sixth harmonic injection and for different modulation indexes. For that reason, it is proposed in this

paper to choose an injection waveform that is in-phase with the

reference waveform, that is, with Φ2 = 0, Φ6−sin = 0, and Φ6−sq

= 0, as it has the greater compensating effect on the midpoint.

The results of Fig. 7(b) suggest that the voltage balancing

control can also be achieved by phase shifting the injection

waveform rather than by adjusting its amplitude as proposed

in this paper. However, this method has not been adopted by

the authors as it would entitle using an injection waveform of

a constant, and relatively high magnitude at all times, even

if the midpoint capacitors are balanced. This would cause a

degradation of the steady-state harmonic content in the case of

second harmonic injection and a permanent limitation on the

maximum modulation index in all cases.

An interesting observation that can be drawn by looking at

the top waveforms in Figs. 4–6 is that, since the injection waveforms of the three proposed strategies are even harmonics of the

fundamental, they have zero crossings at π/2 and 3π/2, where

the magnitude of the fundamental has its peaks. It follows that

their contribution to the peak value of the resultant reference

waveform will be the same, whether the injection waveform is

in phase, or 180◦ out of phase with respect to the fundamental,

or whether its amplitude is positive or negative.

The variation of the modulation index m2 , m6−sin , and m6−sq

of the injection waveform, defined in (4)–(6), has also been studied and the results are shown in Fig. 8. The plots on the top and

bottom rows have been obtained without and with third harmonic injection. Also, the first, second, and third columns in the

figure show the results for second harmonic, sinusoidal sixth

harmonic and squared sixth harmonic injection, respectively.

The continuous and dotted lines correspond to capacitive compensation where the modulation indexes for the reference waveform were 0.8 and 0.5, respectively. Also, the dashed–dotted

and dashed lines correspond to inductive compensation where

the modulation indexes for the reference waveform are 0.8 and

0.5, respectively. Moreover, the thicker continuous traces correspond to the range of balancing waveform available without

entering in overmodulation. This limitation will be explained in

greater detail in Section III-C.

Looking at the figure, it can be seen how the second harmonic compensation introduces an average value of current to

the midpoint IM significantly higher than that provided by its

sixth harmonic injection counterparts. It can also be appreciated, how all three compensation techniques present a linear

region for low amplitudes of the injected waveform, where the

current IM is proportional to the modulation index of the injected signal. In the case of the second harmonic compensation,

the slope of the curves takes a lower value at a given m2 value.

However, in the case of sixth harmonic injection, it reaches a

peak and then gradually falls down until it collapses to zero or

even becomes negative. The values of the first linear portion of

the curve, namely KM , defined in (11) for all three modulation techniques, with and without third harmonic injection, are

shown in Table I. This value is used in the next section to obtain

an averaged model of the midpoint voltage balance control loop

KM =

IM

IM

IM

or KM =

or KM =

.

ˆ 2

ˆ 6−sin

ˆ 6−sq

Im

Im

Im

(11)

CHIVITE-ZABALZA et al.: VOLTAGE BALANCING CONTROL IN 3-LEVEL NEUTRAL-POINT CLAMPED INVERTERS

4477

Fig. 7. Current to midpoint im against phase-shift angle Φ 2 for second harmonic sinusoidal injection. (a) Current contribution IM (p.u.) against Φ 2 for a pure

capacitive (continuous trade) and inductive (dashed trace) load. (b) Current contribution IM (p.u.) against Φ.

Fig. 8. Variation of the average current to the midpoint against modulation index of the injected waveform. (a) Second harmonic compensation. (b) Second

harmonic compensation using third harmonic injection. (c) Sinusoidal sixth harmonic compensation. (d) Sinusoidal sixth harmonic compensation using third

harmonic injection. (e) Squared sixth harmonic compensation. (f) Squared sixth harmonic compensation using third harmonic injection.

Fig. 9. Variation of the p.u. average current to the mid-point against the modulation index of the injected waveform, using third harmonic injection, for

an unbalanced set of currents represented by the addition of a 0.5 p.u. inverse sequence. (a) Second harmonic compensation. (b) Sinusoidal sixth harmonic

compensation. (c) Squared sixth harmonic compensation.

By looking at Fig. 8 and Table I, it can be concluded that the

injection of a second harmonic waveform is more suitable for

control purposes since not only it contributes with a comparatively higher current to the midpoint, but also its linear operating

region extends for a wider range of values of the compensating waveform. Moreover, it does not become negative nor it

collapses to zero. Also, the squared harmonic injection technique provides a slightly higher midpoint current IM than the

sinusoidal one.

The reason for this behavior is the linearity property

of the integral appearing in (9), resembling the calculation

of a Fourier series coefficient, which can be expressed as

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

follows:

¯iM −A =

1

2·π

1

=

2·π

0

0

2·π

As long as this condition is met, the previous assumption will be

valid, and the values of IM will be proportional to m2 or m6−sin .

In our particular case, when the sinusoidal second and/or sixth

harmonic are added to the fundamental, this equation becomes

iM −A (ωt) · dωt

2·π

2 · vA

1−

E

(12)

where the time integral has been multiplied by the angular speed

ω, to get an angle integral. This can be simplified to

ˆ 2·π

¯iM −A = − 1 2 · I

vA · sign(vA ) · cos(ωt) · dωt

2·π E 0

(13)

finally resulting in

ˆ π

¯iM −A = − 2 · I

vA · cos(ωt) · dωt

(14)

E·π 0

where it has been assumed that vA is positive for angles ωt in

the range 0 < ωt ≤ π, and negative for angles π < ωt ≤ 2 π.

This assumption will be justified later, and its range of validity

calculated accordingly.

Note that, due to the waveform symmetry, the upper integration limit has been changed from 2 π to π, and the value of

the resulting integral has been doubled accordingly. Thus, the

sign(vA ) function can be suppressed. Therefore, the expression

in (14) becomes linear in the amplitudes of the different harmonics which may form vA . This is expected as odd voltage

harmonics forming vA do not contribute to the integral of (14),

since only even voltage harmonics are expected to contribute to

the balance of the dc voltage of a 3-L-NPC inverter.

For phase symmetry reasons (phase voltages and currents

are supposed to be direct-sequence or zero-sequence, but not

negative-sequence), the average current entering the midpoint

of the dc-bus provided by phases B and C must be the same

as that provided by phase A. Consequently, the values obtained

previously must by multiplied by three to get the total contributions.

This behavior will persist as long as the voltage harmonics

added to the fundamental signal do not force a sign change in the

total voltage waveform vA at any angle, as previously assumed.

Since all harmonics are set up in sine phase, this is, all cross the

zero level, at the same angle and with positive slope, the limit

for that condition is met when the derivative gets close to zero

at the opposite angle (ωt = π), when the waveform crosses zero

from positive to negative values).

Therefore, an algebraic expression for the validity of the linearity condition is obtained as follows:

mh · sin(h · ωt)

V =

h

dV

=

dωt

h · mh · cos(h · ωt)

h

dV

=

h

·

m

−

h · mh < 0. (15)

h

dωt ω t=P i

h·even

2 · m2 + 6 · m6 < 1 · m1 .

· sign(vA ) · Iˆ · cos(ωt) · dωt

h·o dd

(16)

So, in this linear region, valid for small enough amplitudes of

the injected harmonics, the gains obtained with this method are

therefore

E

E

· m1 · sin(ωt) + · m2 · sin(2 · ωt)

2

2

6 · Iˆ π

= 3 · ¯iM −A = −

vA · cos(ωt) · dωt

E·π 0

6 · Iˆ π E

=−

· m2 · sin(2 · ωt) · cos(ωt) · dωt

E·π 0 2

3 · Iˆ · m2 π

=−

sin(2 · ωt) · cos(ωt) · dωt

π

0

¯iM

4

4

(17)

= · Iˆ · m2 → KM =

=

ˆ

π

π

I · m2

vA =

¯iM

¯iM

for the second harmonic compensation, and

E

E

· m1 · sin(ωt) + · m6 · sin(6 · ωt)

2

2

π

ˆ

6·I

= 3 · ¯iM −A = −

vA · cos(ωt) · dωt

E·π 0

6 · Iˆ π E

=−

· m6 · sin(6 · ωt) · cos(ωt) · dωt

E·π 0 2

3 · Iˆ · m6 π

=−

·sin(6 · ωt) · cos(ωt) · dωt

π

0

¯iM

36

36

· Iˆ · m6 → KM =

(18)

=

=

35 · π

35 · π

Iˆ · m6

vA =

¯iM

¯iM

for the sinusoidal sixth harmonic compensation. This confirms

the values shown in Table I, directly measured from the slopes

in Fig. 8(a)–(d).

The case of the squared sixth harmonic compensation is a

little more complex to calculate, since this waveform is composed of infinite harmonics with weights inversely proportional

to their respective harmonic order. That property makes that,

even when very small amplitudes of the squared sixth harmonic

are added, the voltage waveform changes sign in the vicinity

of ωt = π. Therefore, the integral of (14) no longer holds, and

that of (13) applies instead, which is nonlinear due to the sign

function appearing into its integral. Therefore, the behavior of

that strategy is not strictly linear from the very beginning. However, a tangent slope can be calculated for small amplitudes of

the squared sixth harmonic compensating waveform, as already

seen in Fig. 8(e) and (f) and in Table I.

A disadvantage of injecting a second harmonic voltage is

that, since it is not a zero sequence harmonic, it appears at

the inverter output. It is well known that second harmonic

currents (created by second harmonic voltages) are restricted

CHIVITE-ZABALZA et al.: VOLTAGE BALANCING CONTROL IN 3-LEVEL NEUTRAL-POINT CLAMPED INVERTERS

in most power quality standards. However, the magnitude of the

compensating waveform is expected to be small, and therefore

negligible at the output. Moreover, it is usually injected during

the short transient periods required to balance the midpoint of

the dc-link, out of the steady state operating regime evaluated

by most power quality standards.

The operation of the three techniques under discussion has

also been tested in the presence of unbalance currents by adding

a negative sequence component to the currents seen in (1)

iA = Iˆ sin (ωt + φ) + IˆINV sin (ωt + φINV )

iB = Iˆ sin ωt − 2π/3 + φ + IˆINV sin ωt + 2π/3 + φINV

iC = Iˆ sin ωt + 2π/3 + φ + IˆINV sin ωt − 2π/3 + φINV .

(19)

Using those, the variation of the modulation index m2 , m6−sin ,

and m6−sq of the injection waveform, defined in (4)–(6) and

represented in Fig. 9 has been repeated. The plots on the first,

second, and third columns in the figure show the results for

second harmonic, sinusoidal sixth harmonic and squared sixth

harmonic injection, respectively, where third harmonic injection

has been used.

These have been obtained for inductive compensation and

using modulation indexes of 1 and 0.5 for the reference and

injection waveforms, respectively. The dashed line corresponds

to a balanced set of line currents, that is, where IˆINV = 0. Also,

the dotted and dashed–dotted lines correspond to a ratio of inverse to direct sequence current ratio IˆINV /Iˆ of 0.5. In the

former, the negative sequence currents are in phase with the

direct sequence currents whereas in the latter the negative sequence currents are 90◦ lagging. These results are mirrored for

capacitive reactive compensation. It is clear by looking in the

figures how the presence of a negative sequence has a negligible

effect on the balancing current that flows to the midpoint of the

dc link, particularly, in the linear region of operation. This is

also justified by looking at the symmetry features of (13), which

is zero for the product of odd voltage and current harmonics.

The next Section looks at the maximum waveform that can

be injected for the proposed techniques

C. Limit of the Injection Waveforms

The sum of the reference and compensating waveform should

not exceed the dc-bus voltage E/2. Consequently the compensating waveform must comply with the following expression at

all times

vCOM P ≤ E/2 − vA ,B ,C

(20)

where vCOM P can be either vA ,B ,C −2sin , vA ,B ,C −6sin , or

vA ,B ,C −6sq as defined in (4)–(6), respectively. Also, vA ,B ,C

is expressed in (2) and (3) if third harmonic injection is used.

The maximum modulation index for the injection waveforms

has been calculated by solving (20) for the angle (ωt)M AX

that achieves the peak value in expressions (4)–(6). This angle has been calculated by solving the equation that equates the

4479

angle derivative expression to zero, following basic mathematic

principles.

Using those, the maximum modulation index for the compensating waveform has been calculated for several values of the

modulation index

√ m1 of the reference waveform, close to the

maximum 2/ 3, where third harmonic injection has been used

and the results are shown in Fig. 10. The second harmonic, sinusoidal sixth harmonic, squared sixth harmonic and SVPWM are

represented using continuous, dashed, dashed–dotted and dotted traces, respectively. Also, in that figure, the resultant average

current that flows to the midpoint IM , normalized with respect to

the peak value of the line current is also shown. These results are

compared with the current that is obtained using the well-known

SVPWM technique for a 3-L-NPC inverter [7]–[10].

In that figure, it can be seen how the maximum compensating

waveform that can be injected is gradually reduced as the modulation index for the reference waveform

√ is increased, until it

reaches its maximum value of m1 = 2/ 3, where no compensating waveform can be introduced. On the contrary, SVPWM

can produce a mid-point balancing current even at the maximum

modulation index. It is also seen in Fig. 10 how second harmonic

injection has a higher balancing effect, whereas sinusoidal and

squared harmonic injection can produce compensating currents

with similar values. This is explained, despite squared sixth

harmonic injection having a higher balancing action than sinusoidal sixth harmonic injection, because the latter allows having

an injection waveform of a magnitude higher than that of the

former.

It is important to mention that the contribution of the proposed techniques to the midpoint balancing current can be easily increased at certain times at the expenses of sacrificing the

magnitude of the reference waveform. That is, the value of

m2 , m6−sin , or m6−sq , depending on whichever technique is

used, can be temporarily increased by subsequently reducing

the value of m1 , to bring the midpoint back into balance, as it

will be seen in the experimental results seen in Section IV. This

feature is not straightforward to implement in SVPWM.

An example of the maximum current contribution to the midpoint for a modulation index of m1 = 0.9 and second harmonic,

sinusoidal sixth harmonic, squared sixth harmonic compensation and SVPWM is shown in Fig. 11. In that figure, the instantaneous current is depicted using a continuous trace and its

average value over a supply line cycle is seen with a dotted trace.

The next Section obtains a small-signal averaged model that

can be used for control design purposes.

D. Small Signal Averaged Model of the Split Capacitors

Midpoint Balance

The averaged model of the split capacitors midpoint balance

loop is obtained by averaging the output capacitor currents and

voltages over a supply cycle, that is, by neglecting the instantaneous ripple. The analysis also assumes that the dc bus voltage

vo is stable and has a constant average value of E. This assumption is justified, even at the low switching frequencies typical

of large converter systems, by the criteria chosen to design

the dc-link capacitors. This, with the purpose of avoiding any

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

Fig. 10. (a) Maximum compensating modulation index and (b) produced compensating IM current (normalized against the peak value of the line current),

for the modulation index of the reference waveform. Continuous line: second harmonic compensation, dashed line: sinusoidal sixth harmonic compensation,

dashed-dotted line: squared sixth harmonic compensation, dotted line: SVPWM.

Fig. 11. Maximum instantaneous (continuous trace) and average (dotted trace) current contribution to the mid-point of the dc-capacitors for m 1 = 0.9.

(a) Second harmonic compensation using third harmonic injection for m 2 = 0.237. (b) Sinusoidal sixth harmonic compensation using third harmonic injection

for m 6 −sin = 0.236. (c) Squared sixth harmonic compensation using third harmonic injection for m 6 −sq = 0.221. (d) SVPWM.

overvoltage across the power devices, aims to reduce the voltage switching ripple to a very low value by including enough

capacitance. For that reason, the voltage unbalance within one

switching cycle for the different modulation methods has not

been considered.

By looking at the diagram of Fig. 1, it can be easily deducted

that voltage balance of the midpoint capacitors is

v¯C 2 − v¯C 1 =

1

C

0

T

1

(¯iC 2 − ¯iC 1 ) dt =

C

T

¯iM dt

(21)

0

Expressing this equation in the S domain, and relating the average midpoint current IM to the peak phase current and the

modulation index of the compensating waveform by means of

the KM ratio (11) seen in Table I, the following transfer function

is obtained:

Iˆ sin (φ) KM

VC 2 − VC 1

=

m2 (or m6 )

CS

Fig. 12. Control loop of the split capacitors mid-point balance for reactive

power compensation.

(22)

Based on this transfer function, a control loop structure valid

for reactive power compensation is proposed in Fig. 12, where a

usual PI controller is employed in combination with a low-pass,

first order filter, to suppress the voltage ripple components (23).

The control output is normalized by dividing it by the peak

reactive component of the phase current, a straightforward operation in usual digital control systems. An optional offset has

been added to the setpoint to allow introducing step changes to

evaluate the performance of the control loop. The cross-over frequency of the first order filter is selected to mitigate the third harmonic ripple components present across the capacitors (150 Hz

CHIVITE-ZABALZA et al.: VOLTAGE BALANCING CONTROL IN 3-LEVEL NEUTRAL-POINT CLAMPED INVERTERS

4481

Fig. 13. Step response of the split capacitors voltage balance loop. (a) positive step response and (b) positive and negative step response. The thick continuous

line: averaged response; the thin continuous line: instantaneous response; the tick dotted line: setpoint.

for a 50 Hz system), for example at 15 Hz or 94.25 rad/s. Subsequently, the PI loop can be tuned using conventional techniques,

for instance, aiming to achieve a reasonable Phase Margin [30].

Although, as explained in the next Section IV, the dynamic response achieved using this control strategy is sufficient for most

large power electronics applications, other suitable strategies

compatible with the proposed compensating techniques could

also be devised

Controller T F =

1

KP

S/ + 1

ωP

(S + iTn )

S

(23)

The next section shows simulation and experimental results that

proof the operation of this modeling and control approach.

IV. SIMULATION AND EXPERIMENTAL EVALUATION

The operation of the control strategy proposed in Fig. 12 has

been validated, first in simulation and then experimentally, on

a 690 Vac, 100 A, 120 kVA, 3-L NPC inverter, based on IGBT

devices switching at 600 Hz. Each of the split capacitors had a

capacitance value of 6.6 mF and the positive and negative dclink terminals of the inverter were supplied by a 950 V external

rectifier unit, with the midpoint left floating. The phase-shift

angle of the injection waveforms with respect to the reference

waveform has been chose to be Φ2 = 0, Φ6−sin = 0, Φ6−sq = 0

for a greater compensation effect, as explained in Section III-B.

The simulation results for a step response when second harmonic compensation is selected, are shown in Fig. 13. The

inverter was supplied by a set of ideal current sources of 90-A

RMS and the RMS phase-to-neutral output voltage was 310 V.

To validate the averaged model described in the previous section, the control loop as shown in Fig. 12 has been made run

in parallel with the complete inverter simulation. In that figure, the left and right-hand plots show the response to a 0 to

50 V and 0 to 50 to 0 V offset step respectively. The continuous

thin and thick lines represent the instantaneous and averaged

vC 2 − vC 1 waveforms, which show close correspondence. The

step setpoint is depicted in the figure using a dotted thin trace.

The control parameters where chosen as ω P = 94.24 rads/s;

KP = 0.0863 and iTN = 2.93. The same results were obtained

for sixth harmonic squared and sinusoidal compensation, but

are not shown in this paper for the shake of briefness. The

control loop achieves an open-loop bandwidth of 2.64 Hz, a

settling time of 0.784 s (for a 1% error criteria) and an overshoot of 12%. Therefore, with the proposed adjustment, it will

take about 40 line cycles to complete a step response. Although

this may seem a long time, in practice, due to the amount of

capacitance present in the dc link, as explained in this Section III-D, the dc-link midpoint voltage balance changes relatively slowly. This is confirmed in the experimental section and

in several industrial applications where this strategy has been

implemented.

In the experimental validation, the inverter output terminals

were connected to an 18 mH inductive load and it was operated in current control mode. To verify the ability to control

the midpoint, an offset step of 50 V was introduced when the

output current was controlled to be 70-A RMS and the results

are shown in Fig. 14(a)–(c), for second harmonic, sinusoidal

sixth harmonic, and squared sixth harmonic compensation, respectively.

The first two waveforms show the capacitor voltages vC 1 and

vC 2 , the third waveform the inverter output voltage with respect

to the midpoint of the dc-link capacitors vAG and the bottom

waveform shows the output current iA . The proportional gain

KP for second and sixth harmonic was chosen to be 0.3 and

0.85, respectively, whereas the integral term iTn and the filter

crossover frequency were 2.93 and 94.24 rad/s, respectively, in

all three cases (23). These waveforms show how the midpoint

voltage balance can be successfully controlled for all the proposed strategies. A similar response was obtained for a falling

50 V to 0 V step response. By looking at the results, it is very hard

to appreciate substantial differences between response obtained

using sinusoidal and squared sixth harmonic injection. Therefore, the main difference between these two techniques lies in the

easier implementation offered by the squared harmonic injection at low switching frequencies. In the waveforms of Fig. 14,

a dip in the output current during the midpoint transient can be

observed, which highlights a limitation of the proposed compensation techniques. This is due to the output voltage required

to control the output current, already operating close to its limit

in this experiment, diminishing to accommodate the midpoint

compensating waveforms. This effect is significantly greater in

the case of the sixth harmonic injection strategies as their compensation power is about three or four times smaller than that of

the second harmonic strategy. This limitation is only likely to

appear when operating at very high modulation indexes and is

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

Fig. 14. Instantaneous response for a mid-point imbalance step of 0 to 50 V, 70 A RMS. (a) sinusoidal second harmonic injection; (b) sinusoidal sixth harmonic

injection; (c) squared sixth harmonic injection. First waveform: v c 1 (100 V/div), second waveform: v c 2 (100 V/div), third waveform v A G (500 V/div), fourth

waveform: iA (100 A/div). Time scaling: 40 ms/div.

Fig. 15. Instantaneous response for a mid-point imbalance step of 0– 50 V, 35 A RMS, unbalanced load: (a) sinusoidal second harmonic injection; (b) sinusoidal

sixth harmonic injection; (c) squared sixth harmonic injection. First waveform: v c 1 (100 V/div), second waveform: v c 2 (100 V/div, third waveform iA (50 V/div),

fourth waveform: iB (50 A/div). Time scaling: 40 ms/div.

Fig. 16. Instantaneous response for a step change on the phase current, second harmonic compensation K P = 0.3, iTn = 2.93, ωP = 94.24 rad/s. (a) 10 to

75 A RMS, K P = 0 (controller disabled); (b) 10 to 75 A RMS (c) 75 to 10 A RMS. First waveform: v c 1 (100 V/div), second waveform: v c 2 (100 V/div), third

waveform: v A G (500 V/div), fourth waveform: iA (100 A/div); Time scaling: (a): 40 ms/div. (b) and (c): 100 ms/div.

related to the nature of the transient, the control loop adjustment

and the dc-bus capacitance.

In addition, to verify the level of second harmonic introduced

by the second harmonic injection strategy, the harmonic content of the voltage and current waveforms shown in Fig. 14(a)

has been measured using a high-bandwidth Yokogawa PM3000

power quality analyzer. These measurements, carried out at

steady-state operating conditions, show that the second harmonic voltage and current content, expressed as a percentage of

the fundamental is 1% and 0.4% respectively. These are residual values, not necessarily related to the midpoint balancing

strategy but to the asymmetries introduced by the low switching

frequency that is used [1].

The next test consisted in evaluating the performance midpoint balance control loop for a sudden step change of the output

current. The waveforms seen in Fig. 16(a) show that, for a rising step from 10 to 75 A, under no midpoint control (KP =

0), there was a drift of the midpoint voltage balance, eventually causing a inverter trip. The order of the waveforms is the

same as that explained for Fig. 14. However, when the midpoint voltage balance control is activated, in this case for second harmonic compensation, the midpoint remained balanced

for both a rising current step (10 to 75 A), Fig. 16(b), and a

falling step (75 to 10 A), Fig. 16(c). Similar results were obtained when sinusoidal or squared sixth harmonic injection was

used.

CHIVITE-ZABALZA et al.: VOLTAGE BALANCING CONTROL IN 3-LEVEL NEUTRAL-POINT CLAMPED INVERTERS

To evaluate the performance when supplying an unbalanced

load, the midpoint response was tested by connecting an unbalanced inductive load at the secondary of a star-delta transformer.

This particular test setup was chosen due to availability reasons.

The RMS value of the A, B, and C phases was 30, 34, and 34 A,

respectively, which created the circulation of 32.7 A of positive

sequence, 2.6 a of negative sequence and 0.3 A of zero sequence,

as measured by a Yokogawa WT3000 precision power analyzer.

The results are showed on Fig. 15 where the top two waveforms

represent the dc-link capacitor voltages vC 1 and vC 2 and the

top two waveforms represent the two output currents iA and iB .

It can be seen in that figure how the midpoint voltage can be

controlled for second harmonic (a) sinusoidal sixth harmonic,

(b) squared sixth harmonic injection and (c) under an unbalanced load situation, validating the analysis shown in Section

III-D. Again, similar results were obtained for sixth harmonic

injection.

V. CONCLUSION

This paper has presented a novel technique to balance the voltage of the two split dc capacitors of a 3-L neutral-point clamped

inverter, suitable for reactive power compensation, when triangular carrier PWM modulation is employed. It consists in

injecting a squared waveform at six times the supply frequency.

Subsequently, it has been compared with two already known

strategies based on the injection of a negative-sequence second

harmonic and a sinusoidal sixth harmonic waveform. The contribution of current to the inverter midpoint of these techniques has

been analyzed as a performance measure. Subsequently a smallsignal averaged model, suitable for control design purposes has

been presented and a control strategy has been proposed. Finally, these techniques have been evaluated both in simulation

and in a 690-V ac, 120 kVA experimental setup when supplying

both a balanced and an unbalanced inductive load. The results

conclude that, although the three techniques are valid, second

harmonic injection has a major effect in balancing the inverter

midpoint and the even harmonics that it introduces are negligible and only present during transients. However, out of the two

sixth harmonic injection methods that do not produce even harmonics at the inverter output, the proposed squared waveform

technique is preferred, as it has a slightly greater compensation

effect on the dc midpoint and is easier to implement, particularly,

in systems employing a low modulation index.

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Javier Chivite-Zabalza received the B.Sc. Eng. degree in electrical and electronic engineering from

Mondragon University, Mondragon, Spain, in 1993,

the M.Sc. degree in power electronics and drives

from the Universities of Birmingham and Nottingham (joint degree), Birmingham, U.K., in 2003, and

the Ph.D. degree from the University of Manchester,

Manchester, U.K., in 2006.

He was a Project Engineer in the field of industrial

automation and drives from 1994 to 1999 in Spain,

and from 1999 to 2003 in the U.K. From 2003 to

2006, he was with Goodrich ESTC, Birmingham, U.K. where he was involved

in the development of high power-factor rectifiers for aerospace applications.

From 2006 to 2008, he was with the Rolls-Royce University Technology Centre,

University of Manchester, where he was involved in research on more electric

concepts for autonomous aerospace power systems. In 2008, he joined Ingeteam

Technology S.A., in Spain, developing power electronic converters for FACTS

devices and motor drives applications, where he is currently In-Charge of the

voltage source converter development for the 47 MVAR SSSC demonstrator.

Dr. Chivite-Zabalza is a Registered Chartered Engineer in the U.K. and a

member of the Institution of Engineering and Technology.

Pedro Izurza-Moreno was born in Bilbao, Spain, in

1982. He received the M.Sc. degree in automation

and industrial electronics from Mondragon University, Mondragon, Spain, in 2007.

In 2007, he joined the Industrial and Marine

Drives Department, Ingeteam Technology, S.A., Zamudio, Spain, where he was involved in research

on high-power inverters, especially on vector control, firmware design and programming, pulse width

modulation (PWM), space-vector PWM, selective

harmonic elimination modulation, and three-level

neutral-point-clamped inverters.

Danel Madariaga was born in Bilbao, Spain, in

1973. He received the M.Sc. degree in industrial engineering from the University of the Basque Country

(EHU-UPV), Bilbao, Spain, in 1998, and the M.Sc.

degree in physics from the Universidad Nacional de

Educaci´on a Distancia, Madrid, Spain, in 2008.

In 1998, he joined R&D Department, Ingeteam

Technology, S.A., Zamudio, Spain, where he was

mainly involved in research on high-power inverters, especially on vector control, firmware design

and programming, mathematical modeling, spacevector pulsewidth modulation (PWM), and three-level neutral-point-clamped

(3-L NPC) inverters. He was a part-time Science Teacher for four years. His

current research interests include solving the polynomial equation systems appearing in selective harmonic elimination PWM techniques, and modulation

techniques for balancing the dc bus of 3-L NPC inverters.

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 10, OCTOBER 2013

Gorka Calvo received the B.Sc. degree in electronics

engineering from the Escuela de Ingenier´ıa T´ecnica

Industrial de Bilbao, Bilbao, Spain, in 2005, and the

M.Sc. degree in automatics and industrial electronics

from the Escuela T´ecnica Superior de Ingenier´ıa de

Bilbao, Bilbao, in 2009.

Since 2009, he has been with the Ingeteam Power

Technology S.A., Zamudio, Spain, where he is engaged in high-voltage and high-power converters,

for industrial and FACTs applications. From 2007

to 2009, he was with Supsonik S.L, Sondika, Spain,

as RDi Engineer of power electronics, designing and testing hardware and control of rectifiers, UPS, voltage-frecuency converters, and PV inverters of power

converters. His research interests include power electronics, control of power

converters, and modeling.

Miguel Angel Rodr´ıguez (M’06) was born in San

Sebastian, Spain, in August, 1966. He received the

B.Sc. (Eng.) degree in electronic engineering from

Mondragon University, Mondragon, Spain, in 1989,

the M. Sc degree in electrical engineering from the

Swiss Federal Institute of Technology Lausanne,

Lausanne, Switzerland, in 1992, and the Ph.D. degree in industrial engineering from the University of

Zaragoza, Zaragoza, Spain, in 2000.

From 1992 to 2008, he was an Associate Professor in the Department of Electronics, University of

Mondragon and participated in different research projects in the field of wind

energy systems, lift drives, and railway traction. In September 2008, he joined

Ingeteam Power Technology S.A., Zamudio, Spain. He is currently the Power

Electronics Systems Manager at the Power Grid Automation Business Unit of

Ingeteam Power Technology, responsible for developing new power electronics solutions for transmission and distribution grid applications. His research

interest includes modeling and control of voltage source converters for FACTS

applications such as SSSC, STATCOM and energy storage systems, and the grid

integration studies for those systems.