PEDS 2007

Specific Harmonic Power Suppression of DirectPower-Controlled Current-Source PWM Rectifier
Toshihiko Noguchi *, IEEE Senior Member, and Kohji Sano **Nagaoka University of Technology
Address: 1603-1 Kamitomioka, Nagaoka, Niigata 940-2188, Japan
Phone: +81-258-47-9510, Fax: +81-258-47-9500
e-mail: tnoguchi@vos.nagaokaut.ac.jp
Abstract— This paper focuses on specific harmonic active
power suppression of a direct-power-controlled (DPC)PWM current-source rectifier (CSR) in order to achieve low
distortion of the input line currents. Total input power
factor of the DPC-based PWMCSR becomes worse as theload gets lower due to the low-order harmonics in the line
currents, especially the fifth and the seventh. Since thedominant low-order harmonic currents cause an oscillationin the active power at frequency of sixth, suppression of thesixth-order harmonic active power is essential to improve
the total power factor particularly in the low-load range.
The paper describes a theoretical aspect and a suppression
technique of the harmonic active power, followed by basic
configuration and operation of the DPC-based PWMCSR.
Effectiveness of the proposed technique is confirmed
through computer simulations and experimental tests, using
a 2-kW prototype. As a result, the total harmonic distortionof the line currents is effectively reduced by 10 %, which
results in approximately 20-% improvement of the total
input power factor at a 350-W load condition
Index Terms— current-source PWM rectifier, direct
power control, relay control, instantaneous power, andharmonic power suppression.

I. INTRODUCTION
In general, PWM rectifiers are extensively used as an
AC/DC power converter in order to improve the total
input power factor. There are two classes of the PWM
rectifiers, i.e., a voltage-source rectifier and a currentsource rectifier. The two rectifiers are dual with eachother from the viewpoint of the circuit topology, and theformer has been intensively investigated and widely been
applied to various industry applications, compared withthe latter. In both cases, conventional control strategiesof the PWM rectifiers achieve a unity power factor
operation by forcing the input line currents in phase withthe power-source voltages. Therefore, most of theconventional systems have a current minor control loopwith a rotational coordinate transformation like AC motor
drive systems.
However, this approach has somedrawbacks as pointed out below.
(1) It inherently suffers from a slow response due to thecurrent minor loop, especially due to PI regulators.
(2) It is difficult to reduce its capacitive or inductive
value in the DC-bus energy buffering devices.
(3) Its control algorithm is inherently complicated due tothe rotational coordinate transformation.
(4) It requires a pulse width modulator to generateswitching signals for the power devices.

1-4244-0645-5/07/$20.00©2007 IEEE

(5) In order to make the unity power factor operation
possible, high-resolution in detecting relative phaseof the power-source voltage is indispensable.
(6) Under some conditions where waveform distortion
and/or unbalance in the power-source occur, it
requires additional circuits to cope with such cases.
The authors have been investigating a direct power
control (DPC) strategy of various power converters to
overcome the drawbacks mentioned above. The key ofthis strategy is a direct selection of optimum switchingstates to perform high-speed relay (bang-bang) control of
the instantaneous active and reactive power of theconverters. This eliminates the pulse width modulator
and the PI regulators in the current minor loop, whichleads to extremely quick response and high controllabilityof the power. By controlling the active power at aconstant value and the reactive power to be zero,sinusoidal line currents in phase with the power-source
voltages are resultantly obtained with neither the current
minor loop nor the rotational coordinate transformation.
Furthermore, the DPC system does not need any auxiliarycompensator against the waveform distortion and/or theunbalance of the power-source, which is a unique featureof this approach.
However, the DPC still has some problems as follows:(1) Switching frequency of the converter varies as theload and/or operating condition change, which makes
input filter design difficult.
(2) Waveform distortion of the line currents apt to beworse in the low-load range.
(3) The system performance is rather sensitive to delay
time in the power feedback paths.
This paper discusses a compensation technique for the
waveform distortion of the line currents in order toimprove the total power factor in the low-load range,
focusing on the DPC based PWM current-source rectifier(CSR). Through several computer simulations andexperimental tests, the proposed technique is found to beeffective to reduce the low-order harmonic currents andto improve the total input power factor without
sacrificing inherent advantages of the DPC strategy.
II. BASIC CONFIGURATION AND OPERATION
A. System Configuration
Fig. 1 shows a schematic diagram of the DPC-based
PWMCSR. As shown in the figure, relay (bang-bang)
control of the instantaneous active power P and the1436

instantaneous reactive power Q is performed with use of
their feedback values. Both of P and Q are calculated as
expressed in the following equations:
⎡vα ⎤
⎢ ⎥=
⎣⎢v β ⎦⎥

⎡ vu ⎤
2 ⎡ 1 −1 / 2 −1 / 2 ⎤ ⎢ ⎥⎢⎥ vv ,
3 / 2 − 3 / 2⎦ ⎢ ⎥3 ⎣0⎢⎣v w ⎥⎦

⎡iα ⎤
⎢ ⎥=
⎢⎣i β ⎥⎦

⎡ iu ⎤
2 ⎡ 1 −1 / 2 −1 / 2 ⎤⎢ ⎥⎢⎥ iv , and3 / 2 − 3 / 2⎦ ⎢ ⎥3 ⎣0⎢⎣i w ⎥⎦

⎡ P ⎤ ⎡vα⎢ ⎥ = ⎢v
⎣Q ⎦ ⎣⎢ β

π
3

π
3

is

vc

ic

it
Cf

Load

Sx

vα

vβ

iα

iβ

Sy

Sz

s
s

IDC *

S r Sx S s Sy S t Sz

P, Q cal.

Switching-State Table
Pd

kd
kd

Qd

BPF

Sp

Sq

∆P

∆Q

Θn

PI

ks
P*
Q*

vs

Fig. 1. System configuration of direct power control (DPC) based
current-source PWM rectifier with specific harmonic power suppression

Sp
0
0
1
1

Sr

Sx

Ss

Sy

Sq
0
1
0
1
Sp

Θ1

Θ2

Θ3

Θ4

Θ5

Θ6

SOO
ONP
PON
PNO

OOS
PNO
OPN
PON

OSO
PON
NPO
OPN

SOO
OPN
NOP
NPO

OOS
NPO
ONP
NOP

OSO
NOP
PNO
ONP

St

1

1

0

0

Sz

Θn

Sq

1

6
5

α

4

ΔQ

0 ΔP

2β
3

0

(4)

B. Optimum Switching State Selection
Since the proposed DPC system is, in principle, basedon relay control, it is absolutely significant to investigate
relationship between the switching states of the
PWMCSR and polarities of time derivatives of the active
and reactive power dP/dt and dQ/dt. Their polarities
correspond to the quantized signals Sp and Sq; hence, thetime derivatives of dP/dt and dQ/dt need be solved withrespect to the switching states and the phase informationSt

3φ - 2 φ(2)

A combination of these quantized signals Sp, Sq and Θn isused to select uniquely the most appropriate switchingstate of the PWMCSR. In other words, every time the
PWMCSR changes its switching state, Sp, Sq and Θndetermine the next unique and optimum switching state torestrict ∆P and ∆Q within the corresponding hysteresis
bands. In order to achieve this function, a switching statetable is composed as shown in Fig. 2, of which contents
are predefined so that both of the active and the reactive
power follow their commands with small control errors.
The uniquely selected switching state turns on or off
every switching device in the PWMCSR. In theswitching state table shown in Fig. 2, “P” stands for astate of Su, v, w = “ON” and Sx, y, z = “OFF”, “O” is a stateof Su, v, w = “OFF” and Sx, y, z = “OFF”, “N” is a state of Su,v, w = “OFF” and Sx, y, z = “ON”, and “S” is a state of Su, v, w
= “ON” and Sx, y, z = “ON”.

Ss

ir

ib

(3)

Q n = 1, 2, L , 6 .

Lf

vb

Q P

v β ⎤ ⎡iα ⎤⎥⎢ ⎥ .
− vα ⎦⎥ ⎣⎢i β ⎦⎥≤ Θ n < ( n − 1)

I DC
Sr

3φ
AC200V-50 Hz
va
ia

(1)

As expressed in (3), P and Q can simply be calculatedwith an inner product and an outer product between the
power-source voltage vector and the line current vector,
respectively. On the other hand, the instantaneous active
power command P* is provided from a DC bus current
control block, while the instantaneous reactive powercommand Q* is directly given from the outside of thecontroller, according to the desired input total power
factor. Zero command value for Q* is normally given to
the controller to achieve a unity input power factor
operation. Control errors of the active and the reactive
power, i.e., ∆P = P* - P and, ∆Q = Q* - Q are quantizedwith hysteresis comparators, of which outputs are digital
signals Sp and Sq, respectively. In addition, a relative
phase of the power-source voltage vector is quantized tosix sectors Θn by using several comparators as follows:(n - 2)

L

P*

P

Q

Q*

vα v βFig. 2. Switching state table and power regulators.

of the power-source voltage vector in order to compose
the switching state table appropriately.
From a mathematical model of the PWMCSR
connected to the power grid shown in Fig. 3, thefollowing current equation is established:i s + ic = i s + C f

dv c= i s′ ,dt(5)where the power-source current vector is defined by
i s = iα + ji β =

2π
4π ⎞
⎛
j
j
2 ⎜
3 +i e 3 ⎟ .
i
+
i
e
u
v
w
⎟
3 ⎜⎜
⎟
⎝
⎠

(6)

In the case of three-phase balanced power source, theabove current is represented as a rotating vector withconstant amplitude of Irms expressed asi s = 3 I rms e jωt .

(7)

In addition, the input current vector is’ drawn by the
PWMCSR is a function of the switching state as shown
below, where IDC is a DC bus current:i s′ =

24⎛j πj π ⎞⎟
2⎜
I DC ⎜ S u + S v e 3 + S w e 3 ⎟ .
3
⎜
⎟
⎝
⎠

(8)

On the other hand, the time derivatives of dP/dt and1437

dQ/dt are derived from (3) and are approximated asindicated by the following equations because variation of
the power-source current is can be regarded as negligibly
small during switching intervals of the PWMCSR andcapacitor voltage vc is almost equal to the power-source
voltage vs:
dv
di
dv
dP
= i s • s + s • v s ≈ i s • c , and
dt
dt
dt
dt

(9)

dv
di
dv
dQ
= is × s + s × vs ≈ is × c .
dt
dt
dt
dt

(10)

AC Power Source
Including Lf
is

PWM Rectirier
is'Irms, ωic

Cf

Fig. 3. Simplified mathematical model of PWMCSR.
dP dQ
,
dt dt

Substituting (5), (7) and (8) into the above equations,dP dt and dQ dt can be solved as follow:

α

P N O

vs

P O N

，

2

3I
dP
= − rms +dt
Cf

2 I rms I DC ⎧SvS− w ) cos θ⎨( S u −
2
2
Cf
⎩

⎫⎪
3
+
( S v − S w ) sin θ ⎬
2
⎪⎭

，

O N P

, and

O O O

，

，

N O P

(11)

β

，
O P N

，

，
N P O

dQ
=
dt

2 I rms I DC ⎧SvS− w ) sin θ⎨( S u −
Cf
2
2
⎩
⎫⎪
3
−
( S v − S w ) cos θ ⎬
2
⎪⎭

,

(12)

where θ is an argument of the power-source voltage
vector. According to the polarities of dP/dt and dQ/dt
solved as (11) and (12), one of the switching states of the
PWMCSR can uniquely be determined to restrict thecontrol errors ∆P and ∆Q within the hysteresis bands,
which leads to determination of the whole contents of the
optimum switching state table. Fig. 4 is an example ofbehaviors of the active and the reactive power when the
power-source voltage vector is in the sector Θ1, where thetime derivatives dP/dt and dQ/dt are symbolized withtilted arrows.
C. LC filter Resonance Suppression
The PWMCSR requires a LC filter at input terminals,
which possibly causes current oscillation at the resonant
frequency. Therefore, the DPC based PWMCSR has acompensator to damp the oscillation.
A Laplacetransformed circuit equation of the PWMCSR with the
LC filter shown in Fig. 3 can be described on asynchronous rotating reference frame as follows:
V s = sL f I s +1( I s − I s′ ) .
sC fFig. 4. Symbolized time derivatives of instantaneous active and reactive
power in case of sector Θ1.

Is =V s = 3 Vrms , and(14)′ e -jϕ .
I ′ = 3 I rms(15)

L f C f s2 + 1+′ e − jϕ3 I rmss ( L f C f s 2 + 1)≈

′ e − jϕ3 I rmss ( L f C f s 2 + 1).

(16)
Applying an inverse Laplace-transform to (16), thefollowing instantaneous apparent power S is calculated in
the time domain:
S = vs is′ e jϕ − 3Vrms I rms′ e jϕ cos= 3Vrms I rms

1

t

Lf Cf

.

(17)

This equation shows that the first term corresponds to thefundamental frequency components of the active and thereactive power, while the second term is the resonant
frequency components of them. Since the resonant
components have no damping factor as indicated in (17),differential elements are added to the power feedback inorder to damp the oscillation. Applying this feedback
compensation converts the transfer function of the powersource current Is to the following form:(13)

Assuming that the power-source voltage and the input
line current have a relative phase of ϕ, they can be
expressed as

3 Vrms C f

Is ≈′ e − jϕ3 I rmss ( L f C f s 2 + k d s + 1)

.

(18)

Therefore, S can be damped by the derivativecompensation elements, which are inserted in the
feedback paths of the active and the reactive power.
When the derivative gain is set at k d = 2 L f C f , acritically damped response of S is achieved as′ e jϕS = 3V rms I rms

Substituting the above equations into (13), the powersource current Is can be derived in an approximatedexpression as follows:′ e− 3V rms I rms

1438

⎛

jϕ ⎜

⎜1 +
⎜
⎝

1
Lf Cf

⎞ −
⎟
t ⎟e
⎟
⎠

1
Lf C ft .

(19)

(a) Waveforms of power-source line-to-neutral voltage, input line
current, PWM current, DC bus current, and active and reactive power.

(a) Waveforms of power-source line-to-neutral voltage, input line
current, PWM current, DC bus current, and active and reactive power.

(b) Frequency spectra of input line current.
Fig. 5. Operating waveforms without compensation at low loadcondition (simulation result).

(b) Frequency spectra of input line current.
Fig. 6. Operating waveforms with sixth-order harmonic active power
suppression at low load condition (simulation result).

Table 1. Electric parameters of power circuit and test conditions.

load range as the hysteresis bandwidths ∆P and ∆Q. If
the hysteresis bandwidths can be narrowed, this problem
may be avoided. Due to the delay time in detection andcalculation of the instantaneous active and reactive power,
however, it is not impossible to restrict ∆P and ∆Q within
the specified hysteresis bandwidths even though the
bandwidths are reduced to nearly zero.

Power source
Input filter
DC bus reactor
DC bus current command
Load power
Hysteresis bandwidth
Central frequency of BPF
Quality factor of BPF

AC 3φ 200 V, 50 Hz
Lf = 2.7 mH, Cf = 40 µF
L = 40 mH
IDC* = 12.5 A
220 W
300 W for P, 300 var for Q
300 Hz (six times of 50 Hz)
20

III. SPECIFIC HARMONIC POWER SUPPRESSION
A. Requirements of Harmonic Power Suppression
As described earlier in this paper, although the control
errors ∆P and ∆Q as well as the relative phase of thepower source voltage vector θ are quite roughly
quantized, sinusoidal waveforms can resultantly beobtained in the input line currents without using a current
minor loop, which is one of the significant features of the
DPC based system. However, when the load power is ina relatively low range, low-order harmonics appear in the
input line currents and detrimentally affects not only the
total harmonic distortion (THD) level of the currents but
also the total input power factor and the total efficiency.
This phenomenon is particularly remarkable in as low-

B. Theoretical Analysis of Harmonic Power
Assuming that the power-source supplies ideallybalanced sinusoidal three-phase voltages to the DPC
based PWMCSR, the power-source voltage vector can be
expressed asωv s = 3 Vrms e

jωt

,

(20)

where a superscript of the root-mean-square value
denotes an angular frequency ω of the voltage vector. As
described previously, the input line current vector has
low-order harmonics; hence, its mathematical expression
can be as follows:ω

is = 3 I rms eωj(ωt −ϕ )5ω - j(5ωt −ϕ+ 3 I rms e5ω

)7ω j(7ωt −ϕ+ 3 I rms e

7ω

)

.

(21)

+L

In this expression, the input line current vector iscomposed of a fundamental component and the harmonic1439

(a) Waveforms of power-source line-to-neutral voltage, input line
current, PWM current, and DC bus current.

(a) Waveforms of power-source line-to-neutral voltage, input line
current, PWM current, and DC bus current.

(b) Frequency spectra of input line current.
Fig. 7. Operating waveforms without compensation at low loadcondition (experimental result).

(b) Frequency spectra of input line current.
Fig. 8. Operating waveforms with sixth-order harmonic active power
suppression at low load condition (experimental result).

components except for multiples of the third-orderharmonics because of a three-phase and three-line system.
As can be seen in the second term of the above equation,
the fifth-order harmonic component causes a negative
sequence, whereas the fundamental and the seventh-ordercomponents constitute a positive sequence. Using theseequations, the apparent power S is derived asorder harmonic component with a band-pass filter (BPF)
as shown in Fig 1. The central frequency of the BPF isadjusted at a frequency of the sixth, and the quality factor
is tuned to have an appropriate damping characteristic.
The proposed technique can effectively diminish the fifth
and the seventh harmonic currents at the same time
without sacrificing inherent simple configuration of the
DPC based PWMCSR.

ωωS = 3Vrms I rms e
ω

jϕ

ω

5ω j(6ωt −ϕ+ 3Vrms I rmse

5ω

)

ω

7ω − j(6ωt −ϕ+ 3Vrms I rmse

7ω

)

.
+L

(22)
As indicated in (22), the apparent power S has a static DC
component brought by the fundamental components ofthe voltage and the current and the multiples of the sixthorder harmonic components, which result in the dominant
oscillations of the active and the reactive power.
Particularly, the real part of S, i.e., the active power, is amajor component of the sixth-order frequency. Therefore,
suppression of the sixth-order harmonic active power iseffective and essential to reduce the input line current
distortion, especially low-order harmonic components
such as the fifth and the seventh.
C. Specific Harmonic Power Suppression
The fifth and the seventh harmonic distortion of the
input line currents can simultaneously be suppressed by
restricting specifically the sixth-order harmonic active
power; thus minimization of the hysteresis bandwidth
only for the sixth-order harmonic active power is requiredin the DPC system. In order to achieve this goal, afeedback signal of only the sixth-order harmonic active
power is selectively magnified by extracting the sixth-

IV. COMPUTER SIMULATION RESULTS
In order to examine basic operation characteristics ofthe proposed technique, some computer simulations wereconducted with PSIM, where electric parameters of thepower circuit and test conditions are listed in Table 1.
Fig. 5 shows operating waveforms and frequency
spectra of the input line current at as low load as 220 W
with no compensation. As shown in Fig. 5 (a), a large
waveform distortion can be seen in the line current due tothe low-order harmonics caused by active power
deviation out of the specified hysteresis band. The
ripples of the active power appear six times per cycle, i.e.,
300 Hz, whereas the reactive power is properly restrictedwithin the predetermined hysteresis band. This sixthorder harmonic active power brings the fifth and theseventh harmonic currents as indicated by a downward
arrow in Fig. 5 (b), which are more than 10 % of thefundamental component. On the other hand, Fig. 6
depicts operating characteristics at 220-W load power
where the proposed compensation technique is applied tothe system. As shown in the line current waveform,
undesirable large ripples are effectively reduced aroundpeaks of the current, resulting in the sinusoidal waveform.
This effect can be confirmed in the frequency spectra of1440

Fig. 9. Total efficiency characteristics with/without sixth-orderharmonic active power suppression (experimental result).

Fig. 11. Total harmonic distortion characteristics with/without sixthorder harmonic active power suppression (experimental result).

throughout the experimental tests that the averageswitching frequency of the PWMCSR is almost constantat 2 kHz over the full load range regardless of
implementation of the compensation.
VI. CONCLUSIONS

Fig. 10. Total input power factor characteristics with/without sixth-orderharmonic active power suppression (experimental result).

the line currents shown in Fig. 6 (b), where the fifth andthe seventh harmonics are diminished down toapproximately 1 %.
V. EXPERIMENTAL RESULTS
The proposed compensation technique was examinedwith a 2-kW prototype that is composed of analog anddigital mixed signal hardware. The prototype has thesimilar specifications and parameters as used in thecomputer simulations.
Fig. 7 shows an experimental result at low-loadcondition in the case of no compensation. It is found thatthe input line current includes acute ripples around its
peaks, of which main components are the fifth and theseventh as indicated in the FFT analysis result of Fig. 7(b). A relative amount of these current harmonics withrespect to the fundamental component is almost same asthat of the simulation result. Fig. 8 demonstrates anexperimental result with the proposed sixth-orderharmonic active power suppression. As can be seen in
the figure, the current ripples caused by the low-orderharmonics are dramatically rejected and an appropriate
sinusoidal current waveform is drawn by the PWMCSR.
Figs. 9 and 10 depict the total efficiency and the total
input power factor, respectively. Striking difference inthe total efficiency is not seen between with and without
proposed technique, and the maximum efficiency is
88.5 % in both cases. However, the total input power
factor is remarkably improved owing to the sixth-orderharmonic active power suppression, especially in thelower-load range. This improvement is made mainly by
the low-order harmonics rejection in the input line
currents, which can be confirmed by the THD
characteristics shown in Fig. 11. It is confirmed

This paper described a technique to suppress a specificharmonic power in the DPC based PWMCSR. The
proposed technique selectively reduces the specified
order of the harmonic active power, which resultantly
improves not only the input line current waveforms but
also the total input power factor, especially in a low-load
range. The performance of the proposed compensation
technique was examined through computer simulations
and experimental tests, and overall effectiveness wasconsequently confirmed by the operating waveforms, thetotal input power factor and the THD characteristics.
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