Minimization of DC Reactor and Operation Characteristics of
Direct-Power-Controlled Current-Source PWM Rectifier
Toshihiko Noguchi, Akira Sato, and Daisuke Takeuchi
Nagaoka University of Technology
1603-1 Kamitomioka, Nagaoka 940-2188, JAPANtnoguchi@vos.nagaokaut.ac.jp
Abstract – This paper describes a direct-power-controlledcurrent-source PWM rectifier, and presents operation
characteristics by using a 2-kW experimental setup. The key ofthe proposed strategy is a direct selection of switching modes on
the basis of a relay control technique of instantaneous active andreactive power, using an optimum switching table. The mainfeature of the direct power control is high-speed response of thepower control; hence inductance of the DC reactor can be
reduced.
Feasibility of the strategy is verified throughexperimental tests, using the prototype. Experimental results
demonstrate that the inductance of the DC reactor can be
reduced down to 0.7 mH in the prototype, achieving the 92.5-%
maximum efficiency, 99.9-% maximum total input power factor,
and 3.1-% total harmonic distortion of the input current.
Furthermore, operation characteristics are examined under
unbalanced power source condition.

control based current-source PWM rectifier, where theinstantaneous active power P and the instantaneous reactive
power Q are directly controlled in a manner of relay control orbang-bang control.
In the system, power-source voltages vu, vv, vw and line
currents iu, iv, iw are detected, using transformers andHall-effect current transducers. These detected three-phase
quantities are transformed to two-phase quantities according
to (1) and (2).

I. INTRODUCTION
An AC/DC power converter is required to convert electric
power from AC to DC, to obtain a stable voltage fed to a load,
to improve input power factor, and to suppress harmonic
currents at the same time. In order to achieve this goal, a
PWM rectifier is widely used in variety of industry
applications, which can be classified to a current-source PWM
rectifier and a voltage-source PWM rectifier. The latter is adual circuit of the former, and is more popular than the former.
The authors have investigated a direct power control
technique of both types of the rectifiers, which allows
high-speed response of the active and the reactive power
control. The key feature of this technique is as follows:
1) No need to implement current minor loops;
2) No need for rotational coordinate transformation; and
3) Relay (bang-bang) algorithm based direct active andreactive power control.
This paper verified experimental operation characteristicsof the direct power control based current-source PWM
rectifier with a miniaturized DC reactor. In addition,
operation performance under an unbalanced three-phasepower source is discussed in the paper, which shows
feasibility of the proposed strategy.
II. SYSTEM CONFIGURATION AND CONTROLALGORITHM

2 ⎡1
⎢
3 ⎣0

⎡iα ⎤
⎢ ⎥=
⎣⎢i β ⎦⎥

2 ⎡1
⎢
3 ⎣0

⎡ vu ⎤−1 2− 1 2 ⎤⎢ ⎥⎥ v v , and3 2 − 3 2⎦ ⎢ ⎥⎢⎣v w ⎥⎦

(1)

⎡ iu ⎤− 1 2 ⎤⎢ ⎥⎥ iv .
3 2 − 3 2⎦ ⎢ ⎥⎢⎣i w ⎥⎦

(2)

−1 2

The instantaneous active power P and the instantaneous
reactive power Q are calculated from the results of the abovetransformations as follows:⎡ P ⎤ ⎡vα⎢ ⎥ = ⎢v
⎣Q ⎦ ⎢⎣ βv β ⎤ ⎡iα ⎤⎥⎢ ⎥ .
− vα ⎥⎦ ⎢⎣i β ⎥⎦(3)

On the other hand, the instantaneous active powercommand P* is provided from a DC bus current control block,while the instantaneous reactive power command Q* is given
from outside of the system as shown in Fig. 1. If a unity total
power factor operation is desired, zero command value of Q*
is given to the system, which is the most common operating
condition of a grid-connected rectifier. Control errors ∆P =
P*−P and ∆Q = Q*−Q are used to generate quantized signals Sp
and Sq with hysteresis comparators. As described later on, adither signal, which is a high-frequency triangular waveformwith as minute amplitude as hysteresis bandwidth, issuperposed onto the control errors to improve the operation
performances.
Furthermore, a phase angle of thepower-source voltage vector is also quantized to 6 sectors Θn
as shown in Fig. 2, where α-axis and β-axis denote real andimaginary parts of the vector, respectively. The quantized
sectors Θn is mathematically expressed asπ
6

A. System Configuration
Fig. 1 depicts a system configuration of the direct power

1-4244-0136-4/06/$20.00 '2006 IEEE

⎡vα ⎤
⎢ ⎥=
⎣⎢v β ⎦⎥

2787

(2n − 3) ≤ Θ n <π
6( 2n − 1) Q n = 1, 2, L , 6 .

(4)

By using the quantized signals Sp, Sq and Θn, an appropriate

L
Sy

Sw

Θ1

Sx

Θ2

Θ3

Θ4

Θ5

Θ6

NPO

NOP

ONP

PNO

Su

3φ
AC200V-50 (Hz)

Su

Sv

Sp Sq

Sw

Lf
Load
Cf

Sx

Sy

vβ

0

PON

OPN

1

1

PNO

PON

OPN

NPO

NOP

ONP

0

0

SOO

OOS

OSO

SOO

OOS

OSO

0

1

ONP

PNO

PON

OPN

NPO

NOP

Sp

Sz
1

iα

iβ

Su

(3)
P

Q

Sv

P

Switching Table
s

kd

s

kd

∆Q

vs

1

1 α

ΔQ

6
5

0
P*

Q

AC Power Source
Including Lf
is

Θn
P*

ΔP

2
3β
4

Q*

vs

Fig. 3. Optimum switching state table and comparators for quantization.

PI

∆P

Θn

Sq

0

IDC *

Sw

Sz

1

(1)，(2)vα

Sv

Q*

Irms, ωCf

Fig. 1. System configuration of direct-power-controlled current-source
PWM rectifier.

α

PWM Rectirier
is'icFig. 4. Current-source PWM rectifier model.

vsΘ1

B. Switching State Table

Θ6

Θ2
β

Θ5

Θ3
Θ4

Fig. 2. Quantized phase of power-source voltage vector.

switching state of the PWM rectifier is uniquely determined torestrict the control errors ∆P and ∆Q within the hysteresis
bandwidth. In other words, ascent or descent of theinstantaneous power is controlled to make the actual power
follow its command value within a minute tolerance. If eachof Sp and Sq in a certain Θn is “1”, one of the switching states toincrease the power is selected, and vice versa in the case that
Sp and Sq are “0”. In order to achieve this relay control
operation, an optimum switching state table is employed to
select unique appropriate switching state of the PWM rectifier,according to the quantized signals Sp, Sq and Θn. Fig. 3 depicts
the optimum switching state table, which generates ON or
OFF control signals for each switching semiconductor device
in the PWM rectifier. In the table, a switching state “P”
indicates that high side devices are turned on and that low side
devices are turned off, and “N” indicates vice versa. Anotherswitching state “O” corresponds to a state that both of the highand the low side devices are simultaneously turned off.
Moreover, the other switching state “S” means short circuit
situation by turning on the high- and the low-side devices in
one of the three legs at the same time.

Since the proposed DPC system is in principle based on arelay control technique, it is significant to investigate
relationship between the switching state of the PWM rectifierand polarities of time derivatives of the active and reactive
power dP/dt and dQ/dt. According to the time derivatives
dP/dt and dQ/dt mathematically solved in terms of theswitching state of the PWM rectifier, one of the switchingstates of the PWM rectifier must uniquely be determined torestrict the control errors ∆P and ∆Q within the hysteresis
bandwidth. In the following discussion, therefore, the time
derivatives dP/dt and dQ/dt in an exceedingly short-time
duration, which corresponds to a moment of switching
operation in the PWM rectifier, are theoretically investigated.
Fig. 4 illustrates a grid-connected PWM rectifier model,
where the power source including an inductance Lf of the input
LC filter is regarded as a current source. From this model, thefollowing circuit equation is given:
i s + ic = i s + C f

dv c= i s′ .
dt(5)

In the above equation, a current vector of the PWM rectifier is’
is a function of the switching state as indicated in (6), where
IDC is an output DC bus current.
i s′ =

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

(6)

Each of S u , S v , and S w in (6) takes one of the three values“1”, “-1” and “0”, which corresponds to the switching state2788

dP dQ
,
dt dt

α

P N O

P O N

，

，

O N P

O O O

，

，

Fig. 7. Compensation by means of dithering.
TABLE I ELECTRIC PARAMETERS OF POWER CIRCUIT.

βInput filter inductance Lf
Input filter capacitance Cf
DC bus inductance L
Power source voltage
DC bus current command
Hysteresis bandwidth
Dithering signal

O P N

，

，
N P O

Fig. 5. Symbolized time derivatives of instantaneous active and reactive
power in case of sector Θ 1 .
kd

P, Q

P', Q'

Sv S w⎧
dP I rms ⎡=−) cos θ⎢− 3I rms + 2 I dc ⎨( S u −
Cf ⎣
dt
2
2
⎩

“P”, “N”, and “O or S”, respectively. On the other hand, thepower source current vector is is defined by the following
equation:
2π
4π ⎞
⎛
j
j
2⎜
3 +i e 3 ⎟ ,
i
i
e
+
u
v
w
⎟
3 ⎜⎜
⎟
⎠
⎝

3
⎪⎫⎤
+
( S v − S w ) sin θ ⎬⎥
2
⎪⎭⎥⎦

(7)

dQ
=
dt

i v = 2 I rms cos(ωt − 2π / 3) .

(8)

i w = 2 I rms cos(ωt − 4π / 3)

Substituting (8) into (7), The power source current vector iscan be expressed as a rotating vector with an amplitude of
3 I rms and a frequency of ω.
i s = 3 I rms e jωt .

(9)

As assumed early in this discussion, since a variation of is isnegligibly small due to the input filter inductance Lf in as
short-time duration as a PWM pulse period, the filter
capacitance voltage vc can nearly be regarded as thepower-source voltage vs. Therefore, the time derivatives of
the active and reactive power dP/dt and dQ/dt derived from
(3) can be approximated as follows:
dv
di
dv
dP
= i s • s + s • v s ≈ i s • c , and
dt
dt
dt
dt

(10)

2 I rms I DC ⎧⎪ 3
( S s − S t ) cos θ
⎨−
Cf
⎪⎩ 2
S
S
⎫
+ ( S r − s − t ) sin θ ⎬22⎭

iu = 2 I rms cos ωt∵

2.7 mH40 µF
0.7 mH200 V, 50 Hz
12.5 A
100 W and 100 var
150 W and 150 var, 34 KHz

respectively. Substituting (5), (6) and (9) into the above
equations, dP/dt and dQ/dt are solved as follows:

Fig. 6. Resonance suppression block.

i s = iα + ji β =S p, S q

0
Dither signal
34 kHz

，

N O P

s

1

∆P, ∆Q

vs

,

, and

(12)

(13)

where θ is an argument of the power-source voltage vector vsshown in Fig. 2. Since both of dP/dt and dQ/dt are calculated
from (12) and (13), ascent or descent of the instantaneous
active and reactive power can be found in connection with theswitching state of the PWM rectifier as illustrated in Fig. 5.
Therefore, the contents of the optimum switching state table istheoretically determined on the basis of the above discussion.
C. LC Filter Resonance Suppression

In general, a current-source PWM rectifier requires an input
LC filter, which may cause current waveform distortions dueto the LC resonance. Therefore, it is necessary to dump the
LC resonance based oscillation with a feedback compensation
technique of the instantaneous active and reactive power
control loops. Fig. 6 shows a block diagram of the power
feedback compensation, which is constituted by differential
elements kd. This compensation adds a dumping factor to thetransfer function between the AC power source and the DC
bus of the PWM rectifier.
D. Compensation by Means of Dithering

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

(11)

where • and × denote a scalar product and a vector product,

The proposed DPC strategy employs a relay control
technique of the instantaneous active and reactive power toachieve ultimately high-speed response. However, switchingfrequency varies due to the load time constant, hysteresis

2789

(a)

Input voltage, input current, current PWM pattern, and DC bus current
waveforms.

(b)

FFT analysis result of input current.

Fig. 9. DC bus current step response.

(c) FFT analysis result of current PWM pattern.
Fig. 8. Waveforms and FFT analysis results in steady state.

bandwidth, and delay time of the controller, which makes the
input LC filter design rather difficult. This drawback of therelay-control based system can be overcome with acompensation technique, which is called “dithering.”
Fig. 7 depicts a block diagram of the compensator by meansof dithering. As shown in the figure, a high-frequency
triangular signal with minute amplitude is superposed onto thecontrol errors ∆P and ∆Q. Its amplitude is as minute as thehysteresis bandwidth of the power control loops, so thedithering technique effectively makes switching frequency
almost constant in the steady state without sacrificing theinherent high-speed response in the transient.
III. EXPERIMENTAL RESULTS AND PERFORMANCEEVALUATION
A. Operation Waveforms in Steady State

In order to verify the feasibility of the proposed system, a2-kW prototype was set up and various experimental tests
were conducted. Electric parameters of the prototype power
circuit are listed in TABLE I. It should be noted that theFig. 10. Step response to sudden load change.

inductance L of the DC reactor is as low as 0.7 mH. Fig. 8
represents several operation waveforms of the prototype in thesteady state, where the DC bus current command is 12.5 A andthe load is 2 kW. As can be seen in the figure, the input
current from the power source is in phase with the powersource voltage, and has a sinusoidal waveform similarly to thevoltage waveform. The DPC based PWM rectifier makes
unity total power factor operation possible as shown in the
figure with neither current minor loops nor rotational
coordinate transformation that requires a trigonometriccalculation. Furthermore, it can be seen that the DC bus
current is stably regulated regardless of the small DC reactor.
The FFT analysis result of the input current indicates that noconspicuous harmonic components are observed and that thefrequency spectrum widely spreads over the measured range,
which proves low harmonic distortion in the input current
waveform. On the other hand, the current PWM waveform of
the rectifier has a remarkable spectrum at 34 kHz, which is
caused by the superposed triangular signal for dithering. This

2790

Fig. 11. Waveforms under unbalanced power source condition.

characteristic is quite similar to that of the conventional
sub-harmonic modulation technique. However, dithering
does not affect the transient response of the power control
because the superposed triangular signal merely has as minuteamplitude as the hysteresis bandwidth and power control
loops have no linear regulators such as PI elements.
Fig. 9 shows a transient response when the DC bus current
command is changed stepwise between 10.5 and 12.5 A. As
can be seen here, the response time is approximately 2 ms andexcellent transient waveforms are observed without anovershoot.
Fig. 10 is another transient response that shows waveforms
in a load step change between 1.5 and 2 kW. The DC bus
current is kept almost constant at the commanded value eventhough the sudden load change is applied.
B. Operation Characteristics under Unbalanced Power
Source Condition

Assuming an unbalanced power source condition, operation
characteristics of the proposed system were experimentally
examined. Even in this occasion, a small reactor of 0.7 mH
was used to smooth the DC bus current. The unbalanced
power source voltages were vuv = 200 V, vvw = 200 V, vwu =173 V, while other test conditions were exactly same as thoseof TABLE I. Fig. 11 shows operation waveforms of the PWM
rectifier when the load is 2 kW and the FFT analysis results of
the input currents are indicated in Fig. 12. As can be seen in
Fig. 11, the input current waveforms are distorted, but the DC
bus current is well regulated at a commanded value without
low-frequency large ripples. As described earlier in this paper,
the DPC based PWM rectifier directly regulates theinstantaneous power by selecting unique and the mostappropriate one of possible switching states at every moment.
Therefore, the DPC system carries out to transfer more active

Fig. 12. FFT analysis results of input current under unbalance power source
condition.

power from AC power source to the DC bus when the DC bus
power goes down, and vice versa. In addition, the input
current is distorted due to the third harmonics included, whichis reluctantly necessary to cancel out the second harmonics
caused by the unbalanced power source voltages. However,the DC bus current is smoothly maintained at a constantcommanded value regardless of the small DC reactor, which is
the most significant feature of the DPC system.
Fig. 13 and Fig. 14 show total efficiency and total input
power factor of the DPC based prototype, respectively. Total
harmonic distortion is depicted in Fig. 15 to evaluate qualityof the input current waveform. These experimental data wereacquired in two cases, i.e., a balanced power source condition
and an unbalanced one. When the power source voltages arebalanced, the maximum total efficiency of the system is92.5 %, the maximum total input power factor is 99.9 %, andthe total harmonic distortion of the input current is 3.1 % at
2-kW load. On the other hand, in the case of unbalanced
power source, the maximum total efficiency and the
maximum total input power factor are 92.4 % and 99.6 %,respectively. The total harmonic distortion of the input
current was different among phase to phase, i.e., 7.7 % for thephase u, 7.4 % for the phase v, 8.1 % for the phase w, and Fig.
15 shows an average of these data. As is found in theexperimental results, almost same performance is achieved interms of the total efficiency in both of the balanced and theunbalanced conditions, but the total input power factor and thetotal harmonic distortion become worse as the load is reduced
under unbalanced condition.

2791

strategy, a relationship between the switching state of the
PWM rectifier and the instantaneous active and reactive
power was clarified, which was essential to select uniquely themost appropriate switching state with a switching table. In
addition, feasibility of the system was examined throughvarious experimental tests, using a 2-kW prototype. From theexperimental results in the steady state, it was found that the
proposed strategy makes it possible to obtain unity total input
power factor by setting the reactive power command at zero.
In other words, the input current waveform was automaticallycontrolled to be sinusoidal and to be in phase with the powersource voltage with neither current minor loops nor
trigonometric calculations. Also, the ultimately high-speed
response of the power control allows minimization of the DC
bus reactor and a few-ms time response to the DC bus current
command and to the disturbance load change.
Furthermore, operation characteristics under an unbalanced
power source condition were experimentally investigated witha small DC reactor of 0.7 mH. The proposed direct power
control technique is capable to regulate the DC bus current
sufficiently stable without low-frequency large ripples
although the power source voltages are unbalanced. This is
the significantly unique feature of the proposed direct power
control strategy.

Fig. 13. Characteristics of total efficiency.

V. REFERENCES[l]

Fig. 14. Characteristics of total input power factor.

[2]

[3]

[4]

[5]

Fig. 15. Characteristics of total harmonic distortion of input current.

IV. CONCLUSION
This paper proposed a novel control strategy of a current
source PWM rectifier, which features direct control of theinstantaneous active and reactive power. The key of thisstrategy is a relay (bang-bang) control of the power by meansof optimum selection of the switching state of the PWM
rectifier. Owing to the relay control algorithm, the ultimately
high-speed response of the instantaneous power control isachieved with neither current minor loops nor complicatedsignal processing such as a rotational coordinatetransformation. In the theoretical analysis of the proposed

[6]

[7]

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