> PEDS’01 CONFERENCE PROCEEDINGS<

1

Performance Improvement ofCurrent-Controlled PWM Inverterby Means of Dithering
Toshihiko Noguchi, Member, IEEE, Hirokazu Kodachi, and Isamu Saito

Abstract — This paper describes a novel current control
strategy of a voltage-source PWM (Pulse Width Modulation)
inverter by means of dithering. There have been two principal
methods to achieve the current control, i.e. a sinusoidal PWM(sub-harmonic) method by using PI regulators and a triangularwave carrier, and a relay (bang-bang) control method by using
hysteresis elements as current regulators. It is inherently
impossible to achieve PWM-pattern optimization, quick response
and current-error minimization with those conventional methods
at the same time. The method proposed in this paper is based on
dithering of the hysteresis bands in the current regulators, where
thresholds of the hysteresis elements are modulated by atriangular wave with minute amplitude and high frequency. The
control characteristics of this system mostly depend on theamplitude of the dither signal and all the drawbacks of theconventional methods can be simultaneously overcome by setting
the amplitude as small as the hysteresis bands. This paper
presents a basic concept of the proposed method and the operating
characteristics compared with the commonly known current
control methods.
Consequently, remarkable performance
improvement by the proposed method has been confirmed throughexperimental tests as well as computer simulations.
Index Terms — Current control, current regulator, dithering,and PWM inverter.

I. INTRODUCTIONT

HIS paper focuses on a current control technique of a

voltage-source PWM inverter and proposes a novel control
strategy to improve its operating characteristics by means ofdithering. There have been two principal approaches to achieve
the current control with the inverter [1], [2]. One is a sinusoidal
PWM (sub-harmonic) technique by using current regulators, e.g.
PI elements and a triangular wave as a carrier and the other is arelay (bang-bang) control technique by using hysteresis
elements. The former surpasses the latter with regard to its
optimized PWM pattern that is generated by the inverter but isinferior to the latter from the viewpoint of a response and acontrol error of the currents. The latter has the merits and the
demerits vice versa. Therefore, it is basically impossible toachieve the PWM-pattern optimization, the quick response andthe current-error minimization at the same time with thoseconventional methods.
On the other hand, a technique of dithering has beenrecognized as one of the solutions that can make nonlinear
phenomenon and systems linear. Since the current-controlled
PWM inverter is regarded as a kind of the nonlinear systems,
dithering is a possible choice of the most effective measures toimprove the performance of the current control. The techniqueproposed in this paper is based on dithering of the hysteresis
bands in the current regulators, where the thresholds of thehysteresis elements are modulated by a triangular wave withminute amplitude and high frequency.
The control
characteristics mostly depend on the amplitude of the dither
signal and the drawbacks of the conventional methods describedabove can simultaneously be overcome by setting the amplitude
as small as the hysteresis bands. This paper presents a basic
concept of the proposed technique and performance evaluationcompared with the commonly known conventional methods.
Consequently, excellent control characteristics of the proposed
method have been confirmed through computer simulations andexperimental tests. Also, this paper clarifies optimal conditions
to obtain the maximum effects of dithering when this method isapplied to the current controller.
II. BASIC CONFIGURATIONS AND OPERATIONS OF
CURRENT-CONTROLLED PWM INVERTERS
A. Conventional Current Controllers
A power conversion system to be investigated in this paper isa three-phase voltage-source PWM inverter that is connected toa three-phase balanced reactive load. Fig. 1 shows a schematic

1

Toshihiko Noguchi is with Nagaoka University of Technology, Nagaoka
940-2188, Japan (phone: +81-258-47-9510, fax: +81-258-47-9500, e-mail:tnoguchi@vos.nagaokaut.ac.jp).
Hirokazu Kodachi is with Nagaoka University of Technology, Nagaoka
940-2188, Japan (phone: +81-258-47-9553, fax: +81-258-47-9500, e-mail:kodachi@stn.nagaokaut.ac.jp).
Isamu Saito was with Nagaoka University of Technology. He is currently
with Toshiba Corporation, Tokyo 105-8001, Japan (phone: +81-3-3457-4681,
fax: +81-3-5444-9227, e-mail: isamu.saito@Toshiba.co.jp).

V dc

0

Su

iu
1
0

Sv

iv
1
0

Su

Sv

Sw

Current
Regulators

∆ iu
−
∆ iv
∆ iw

R

iw

Sw
−

−

−

+

+

L

R
L
L

*

iu

*

−

+

iv

*

iw

Fig. 1. Current-controlled three-phase PWM inverter.

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2
K (sT + 1)
1  1

= P I
Go (s) = K P 1 +.
(1)
 sTI  sL + R sTI (sL + R )Assuming that the crossover frequency ω c is given as a design

Carrier∆ iu ,v , w



1 



s T I K P  1 +

−


∗

1
S u ,v , w+

vu , v , w

be approximated as0(a) PI regulator.

G o (s) =1∆ iu ,v , w

S u ,v , w

0∆H(b) Fixed hysteresis-band regulator.

*∆ H u , v, w

iu , v , w
1∆ iu ,v , w

specification of the current controller, open-loop gain at ω c canS u ,v , w
0 ∆ H u, v, w(c) Variable hysteresis-band regulator.

K P ω c2 TI2 + 1

ω c TI ω L + R
2
c

2

2

≈

KP
=1.
ωc L

(2)

Therefore, the proportional gain K P of the PI element can be
determined from the above equation. Particularly, if the integral
time constant TI of the PI element is adjusted to be TI = L R ,zero-pole cancellation occurs in (1), which results in thefollowing simple open-loop transfer function:
K(3)
Go (s) = P .
sLSince the closed-loop transfer function, in this case, becomes
first-order as expressed by (4), no overshoot appears in a step
response.
KP.
(4)
Gc (s) =sL + K P
The switching signals are generated by comparing the voltage
commands with the triangular wave tr (t ) as follows:

DitherSu , Sv , S w = 0

1∆ iu ,v , w

S u ,v , w
0∆H(d) Proposed regulator.
Fig. 2. Detailed configurations of various current regulators.

diagram of the system. As shown in this figure, a controller ofthe inverter has a set of current regulators to control thethree-phase load currents iu , iv and iw with current feedback
loops. The feedback currents are detected by two Hall-effectcurrent transducers and are compared with three-phase current
commands iu∗ , iv∗ and i w∗ to generate current errors ∆iu , ∆iv
and ∆i w , respectively. The current commands are basicallysinusoidal waves of which amplitude and operating frequency
are variable. The current regulators receive the current errors
and output switching signals to the inverter legs so that the load
currents follow the current commands.
Fig. 2 shows detailed configurations of several current
regulators. Fig. 2(a) is the most extensively used PI regulator
with PWM. As can be seen in this diagram, the current error ofeach phase is an input of the PI element and its output is a
voltage command to a corresponding phase of the inverter. To
generate PWM patterns, i.e. switching signals S u , S v and S w ,the three-phase voltage commands v u∗ , v v∗ and v w∗ arecompared with a common triangular wave. In this system, an
open-loop transfer function of the current control loop can be
expressed by the following equation:

if vu∗ , v v∗ , v w∗ < tr (t ).
(5)
Su , Sv , S w = 1
if vu∗ , v v∗ , v w∗ ≥ tr (t )On the other hand, the relay control is the simplest algorithm
to achieve current control with the inverter. Fig. 2(b) shows afixed hysteresis-band regulator, which is commonly employed
as the relay control technique. These regulators receive thecurrent errors and directly output the switching signals to thecorresponding inverter legs. The regulator of each phaseindividually operates to restrict its current error within a
specified hysteresis band. The hysteresis bandwidth ∆H isdetermined on the basis of the average switching frequency of
the inverter.
Su , Sv , S w = 0
if ∆iu , ∆iv , ∆i w > ∆H 2.
(6)
Su , Sv , S w = 1
if ∆iu , ∆i v , ∆i w < − ∆H 2
Fig. 2(c) is a modified version of the relay controller thatfeatures a variable hysteresis bandwidth, which can be found in[3] or [4]. The hysteresis bandwidth of the method described in[4] is changed with respect to time according to the fundamental
current amplitude as expressed by (7).
∆H u = k iu∗ , ∆H v = k iv∗ , ∆H w = k i w∗ .

(7)

The hysteresis bandwidth of each phase becomes wider aroundcurrent peaks and does narrower around zero-crossing points.
Therefore, it is difficult to avoid violent increase of the inverter
switching frequency around the zero-current.
B. Proposed Current Control with Dithering
An objective of the proposed technique is to fuse every
advantage of the conventional methods without sacrificing
simplicity of its configuration and control algorithm, i.e. to

> PEDS’01 CONFERENCE PROCEEDINGS<i

H ysteresis Band

Superposed Dither Signals

PW M PatternFig. 3. Operation of proposed method.

achieve the optimized PWM patterns, a quick response of theload currents and the minimized current error at the same time[5]. Fig. 2(d) depicts a schematic diagram of the proposedcurrent regulator and Fig. 3 illustrates the operation of theregulator with hysteresis-band dithering. As shown in Fig. 2(d),the skeletal configuration of the regulator is not changed fromthat of the original relay current regulator. The only difference
from the conventional regulator is time-varying thresholds ofthe hysteresis elements. The hysteresis bands are dithered bysuperposing a minute and high-frequency triangular wave onto
both the upper and the lower thresholds. The amplitude of thetriangular wave is the most important factor to determine theoperating characteristics of the proposed control, which isnormally chosen to be as small as the hysteresis bands. The
frequency of the triangular wave is set at a specific value
required by the power devices employed in the inverter.
III. PERFORMANCE EVALUATION OF CURRENT CONTROLLERS
A. Computer Simulation Results
Computer simulations and experimental tests have been
conducted to examine the operating characteristics of the four
methods, i.e. the PI regulator, the fixed hysteresis-band
regulator, the variable hysteresis-band regulator and the
proposed regulator. Fig. 4 shows computer simulation results ofthe four methods, where the PWM pattern, the current
waveforms, the current vector and the current-error vector loci,and the frequency spectra of the current are depicted for eachmethod.
As shown in Fig. 4(a), the PI regulator demonstrates an
excellent PWM pattern in the line-to-line inverter output
voltage waveform. However, phase and amplitude errors areobserved between the current command and the feedback
current although the current ripple is effectively suppressed. As
can be seen in the current-error vector locus, the current-error
vector distributes in a hexagonal shape with a center hall. The
current controllability can be evaluated from the viewpoint of
the locus area. Also, it is found that the frequency spectra of thismethod have conspicuous multiple harmonic components of thecarrier frequency.
Fig. 4(b) shows the characteristics of the fixed3
hysteresis-band regulator. In contrast with those of the PI
regulator, less phase and amplitude errors are observed between
the current command and the feedback current, which can also
be confirmed in the current-error vector locus. As known well,
the current-error vector locus of this method indicates a shape ofhexagonal star because of independent three-phase relay actions
with the fixed hysteresis band. The frequency characteristic of
the current is so called spread spectra with no conspicuouscomponents. However, the PWM pattern of the inverter is not
optimized and several inappropriate switching operations areobserved in the voltage waveform. These merits and demerits
are undertaken to the variable hysteresis-band regulator as
shown in Fig. 4(c). Even though the hysteresis bandwidth is
dynamically changed with current amplitude, the PWM pattern
optimization cannot be achieved and current-error vector locus
is not reduced. However, this method is scarcely effective to
reduce the lower-order harmonic components of the current.
On the other hand, the proposed method demonstrates
excellent performance with regard to both current and voltage
waveforms. As shown in Fig. 4(d), it is possible to reduce thecurrent-error vector less than that of the fixed hysteresis-band
regulator and to optimize the PWM pattern as well as the PI
regulator. It is found that the locus shape of the current error isalmost circle, which contributes to reduce the rms value of theerror. The frequency spectra of the proposed method show amixed characteristic of the two conventional methods.
B. Experimental Results
An experimental system was setup to verify feasibility of thesimulation results and actual control performance. In the system,
the current regulators are composed with digital-and-analog
hybrid hardware and one of the four methods can be digitally
selected on the unified circuit. Also, exactly identical electriccomponents, for example main power circuits, current sensors
and so forth, are employed to make performance evaluations
fair. The 50-Hz sinusoidal current commands are given to thecontrol circuits by a synthesized function generator. The DC
bus voltage is kept constant at 280 (V) and the inverter
switching frequency is set at 2 (kHz) for every method. Also, alockout circuit of which dead time is 2 (µs) is implemented on
every controller to prevent short-circuit across the DC bus.
Fig. 5(a)-(d) depict experimental results of the four methods,
where the test conditions are identical to those of thesimulations. All of the experimental data were measured with adigital oscilloscope that can store the data on a floppy disk in
ASCII format. As shown in these results, every operating
characteristic agrees with that of the simulations very well. It
can be seen that the proposed method is capable to optimize thePWM pattern, to minimize the current ripple and to reduce thecurrent error at the same time.
IV. OPERATING CHARACTERISTICS OF DITHER BASEDCURRENT CONTROLLER UNDER VARIOUS CONDITIONS
The operating characteristics of the proposed methodstrongly depend on the dither signal superposed onto thehysteresis thresholds; hence dependency of the amplitude has

10

2

iαβ

vuv

iu
5

*

iu

10
Time (ms)

15

1

1
∆ iαβ

0
-1

0.1
0.01
1E-3

-2
-2

20

Current (A)

400
200
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-200
-400
2
1
0
-1
-2
0

4

β-Axis Current (A)Current (A)Voltage (V)> PEDS’01 CONFERENCE PROCEEDINGS<-101
α -Axis Current (A)

1E-4
0

2

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Frequency (kHz)

25

5

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Frequency (kHz)

25

5

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Frequency (kHz)

25

2

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vuv

iu
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iαβ

iu

10
Time (ms)

15

∆iαβ

0
-1
-2
-2

20

1

1

Current (A)

400
200
0
-200
-400
2
1
0
-1
-2
0

β-Axis Current (A)Current (A)Voltage (V)(a) PI plus PWM method.

0.1
0.01
1E-3

-1
0
1
α -Axis Current (A)

1E-4
0

2

2

10

vuv

iu
5

*

iαβ

iu

10
Time (ms)

15

∆ iαβ

0
-1
-2
-2

20

1

1

Current (A)

400
200
0
-200
-400
2
1
0
-1
-2
0

β-Axis Current (A)Current (A)Voltage (V)(b) Fixed hysteresis-band method.

0.1
0.01
1E-3

-1
0
1
α-Axis Current (A)

1E-4
0

2

2

10

vuv

*

iu
5

iαβ

iu

10
Time (ms)

15

20

1

1

Current (A)

400
200
0
-200
-400
2
1
0
-1
-2
0

β-Axis Current (A)Current (A)Voltage (V)(c) Variable hysteresis-band method.

∆iαβ

0
-1
-2
-2

0.1
0.01
1E-3

-1
0
1
α-Axis Current (A)

2

1E-4
0

(d) Proposed method.
Fig. 4. Current control characteristics (simulation results).

> PEDS’01 CONFERENCE PROCEEDINGS<

10

2

*

iu
5

iαβ
β-Axis Current (A)Current (A)

vuv

iu

10
Time (ms)

15

1

1

Current (A)Voltage (V)

400
200
0
-200
-400
2
1
0
-1
-2
0

5

∆ iαβ

0
-1

0.01
1E-3

-2
-2

20

0.1

-1
0
1
α-Axis Current (A)

1E-4
0

2

5

10
15
20
Frequency (kHz)

25

5

10
15
20
Frequency (kHz)25(a) PI plus PWM method.

2

10

iαβ

iu
5

*

β-Axis Current (A)Current (A)

vuv

iu

10
Time (ms)

15

∆iαβ

0
-1
-2
-2

20

1

1

Current (A)Voltage (V)

400
200
0
-200
-400
2
1
0
-1
-2
0

0.1
0.01
1E-3

-1
0
1
α -Axis Current (A)

1E-4
0

2

(b) Fixed hysteresis-band method.

10

2

iαβ

iu
5

*

β-Axis Current (A)Current (A)

vuv

iu

10
Time (ms)

15

∆iαβ

0
-1
-2
-2

20

1

1

Current (A)Voltage (V)

400
200
0
-200
-400
2
1
0
-1
-2
0

0.1
0.01
1E-3

-1
0
1
α-Axis Current (A)

1E-4
0

2

5

10

15

20

25

20

25

Frequency (kHz)(c) Variable hysteresis-band method.

10

2

iαβ

iu
5

*

β-Axis Current (A)Current (A)

vuv

iu

10
Time (ms)

15

20

1

1

Current (A)Voltage (V)

400
200
0
-200
-400
2
1
0
-1
-2
0

∆ iαβ

0
-1
-2
-2

0.1
0.01
1E-3

-1
0
1
α-Axis Current (A)

2

1E-4
0

(d) Proposed method.
Fig. 5. Current control characteristics (experimental results).

5

10
15
Frequency (Hz)

0.20

4

0.15

3

0.10

2

0.05

L/R = 1.8 (ms) 1
L/R = 3.5 (ms)

0.00
0.05

0.10

0.15 0.20 0.25 0.30
Hysteresis Bandwidth (A)Switching Frequency (kHz)6

Switching Frequency (kHz)Dither Signal Amplitude (A)> PEDS’01 CONFERENCE PROCEEDINGS<

0
0.35

4
3
2

0
0

(a) Transition boundaries and average switching frequency withrespect to hysteresis bandwidth.

PI regulator
Fixed hysteresis-band regulator
Variable hysteresis-band regulator
Proposed regulator

1

10
20
30
40
50
60
Fundamental Operating Frequency (Hz)(b) Average switching frequency with respect to operating frequency.

4

0.15

3

0.10

2
L/R = 1.8 (ms) 1
L/R = 3.5 (ms)

0.05
0.00
0.05

0.10

0.15 0.20 0.25 0.30
Hysteresis Bandwidth (A)Switching Frequency (kHz)0.20

Switching Frequency (kHz)Dither Signal Amplitude (A)Fig. 6. Operating characteristics of proposed method (simulation results).

0

4
3
2
PI regulator
Fixed hysteresis-band regulator
Variable hysteresis-band regulator
Proposed regulator

1
0

0

0.35

(a) Transition boundaries and average switching frequency withrespect to hysteresis bandwidth.

10
20
30
40
50
60
Fundamental Operating Frequency (Hz)(b) Average switching frequency with respect to operating frequency.

Fig. 7. Operating characteristics of proposed method (experimental results).

been examined for various values of the hysteresis bandwidth
and the amplitude. Fig. 6(a) and Fig. 7(a) are the simulation andexperimental results, respectively, which show the transitionalboundaries between the two control characteristics of the PI
regulator and the fixed hysteresis-band regulator. Also, average
inverter switching frequencies at the transitional boundaries are
depicted in these figures. The operating characteristics change
from one of the two conventional methods to the other as thedither signal amplitude is consecutively changed. As verified in
the previous section, such optimum operating characteristics as
Fig 4(d) and Fig. 5(d) can be obtained if the dither signal
amplitude is set around these transitional boundaries. Fig. 6(b)and Fig. 7(b) show the average switching frequencies of theinverter. As can be seen in the figures, the switchingfrequencies of the PI regulator and the proposed regulator are
kept at a constant value, which is determined by the carrier orthe dither signal. However, the switching frequencies of thehysteresis regulators vary widely depending on the fundamental
operating frequency, which is another drawback of thehysteresis regulators.

current-controlled PWM inverter by means of dithering.
Dithering is a powerful and effective means to solve thedrawbacks of the conventional current regulators without
sacrificing inherent simplicity of their configurations.
Feasibility of the proposed technique has been examinedthrough the experimental tests as well as the computer
simulations and every result obtained in this investigation
proved advantages of the dither based approach.
REFERENCES
[1]
[2]

[3]

[4]

[5]

V. CONCLUSION
This paper proposed a novel control strategy of theJ. Holtz, “Pulsewidth Modulation for Electronic Power Conversion,”
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Transactions on Industrial Electronics, vol. 45, No. 5, pp. 691-703,
1998.
B. K. Bose, “An Adaptive Hysteresis-Band Current Control Technique ofa Voltage-Fed PWM Inverter for Machine Drive System,” IEEE
Transactions on Industrial Electronics, vol. 37, no. 5, pp. 402-408, 1990.
M. A. Rahman, T. S. Radwan, A. M. Osheiba, and Azza E. Lashine,“Analysis of Current Controllers for Voltage-Source Inverter,” IEEE
Transactions on Industrial Electronics, vol. 44, No. 4, pp. 477-485,
1997.
T. Noguchi, M. Yamamoto, S. Kondo, and I. Takahashi, “Enlarging
Switching Frequency in Direct Torque-Controlled Inverter by Means ofDithering,” IEEE Transactions on Industry Applications Society, vol. 35,
No. 6, pp. 1358-1366, 1999.