A space vector based rectifier regulator for ac dc ac conver
1.
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 8, NO. 1, JANUARY 1993
30
A Space VectorBased Rectifier
Regulator for AC/DC/AC Converters
Thomas G. Habetler, Senior Member, IEEE
Abstruct A voltagesourced rectifier control scheme for use
with ac/dc/ac variable speed drives is presented in this paper. A
control scheme is derived that directly calculates the duration of
time spent on the zero state and on each switching state adjacent
to the reference vector, over a constant switching interval, in
order to drive the line current vector to the reference vector. In
addition, under transient conditions, when deadbeat control is not
possible, a control scheme is presented that ensures that the line
current vector is driven in the direction of the reference current
vector. The current reference for the rectifier controller is derived
from the bus voltage error and a feedforward term based on the
estimated converter output power. The proposed space vectorbased rectifier regulator is shown to exhibit improved harmonic
and transient performance over existing perphase duty cycle
prediction methods, especially at modulation indices near unity.
The deadbeat control of the rectifier input current is accomplished every halfcycle with constant switching frequency while
still symmetrically distributing the zero state within the halfcycle period. In this way, satisfactory performance under various
operating conditions is achieved with relatively low switching
frequencies and high bus voltage ripple.
Fig. 1. Schematic of ac/dc/ac converter with controlled rectifier.
Rectifier
Inverter
I. INTRODUCTION
8
C
ONTROLLED rectifiers offer distinct advantages over
typically used uncontrolled diode, or phasecontrolled
thyristor rectifiers in ac/dc/ac converters for variable speed
drive applications. These advantages include unity input power
factor and greatly reduced input line current harmonic distortion due to the nearly sinusoidal input line current attainable with controlled rectifiers. Reversible power flow is also
possible. Fig. 1 shows a schematic of the transistordiode
implementation of the voltagesourced controlled rectifierinverter drive system that is discussed in this paper.
It has been shown, [l], [2], that in order to control the dc
link voltage U&, the input line currents must be regulated. In
typical rectifier controllers that have been presented to date,
such as those in [3][5], the dc bus voltage error is used
to synthesize a line current reference. Specifically, the line
current reference is derived through multiplication of a term
proportional to the bus voltage error by a template sinusoidal
waveform. The sinusoidal template is directly proportional to
the input voltage, thus resulting in unity input power factor.
The line current is then controlled to track this reference using
a suitable current regulator.
The use of load feedforward [ 121 eliminates the steadystate
error that exists when using only proportional bus voltage
Manuscript received November 5 , 1991; revised August 7, 1992.
The author is with the School of Electrical Engineering, Georgia Institute
of Technology, Atlanta, GA 30332.
IEEE Log Number 9204294.
9
J
Magktude
of ia
Feedforward
Fig. 2. Block diagram of rectifier control including output power estimator
for load feedforward.
feedback. This is accomplished by deriving the line current
magnitude reference from the average load current, found from
an output power estimator, plus the proportionalintegral (PI)
controlled bus voltage error. The PI controller then eliminates
the steadystate error in the bus voltage while still maintaining
proper current regulation. In addition, the dynamic response
of the bus voltage to changes in load is significantly increased
due to the load feedforward. A block diagram of this type of
control scheme is shown in Fig. 2.
The task of current regulation can be accomplished through
the use of any number of existing current control schemes
08858993/93$03.00 0 1993 IEEE
2.
31
HABETLER: A SPACE VECTORBASED RECTIFIER REGULATOR
for use in voltagesourced inverters. These include hysteresis
regulators [ 131 and synchronous reference frame regulators
[ 141, which use a proportionalintegral (PI) controller and
sinetriangle pulsewidth modulator (PWM). The sinetriangle
PWMbased schemes have the advantage of fixed switching
frequency, greatly reducing device stresses in comparison with
the hysteresis regulator.
The problem of current control in ac/dc converters differs
from dc/ac converters, even though the topology is unchanged.
This is because the circuit quantities (input voltage, source
impedance, and dc link voltage) that determine the input line
current are known in ac/dc converters. Therefore, the current
control scheme can be formulated that derive the rectifier
switching function by estimating or predicting the line current
trajectory. One such scheme, Predicted Current Control with
Fixed Switching Frequency (PCFF), was presented in [6] and
[7] for use in rectifier control. This scheme calculates the duty
cycle required for each inverter leg that drives the respective
line current to the reference value in one switching period.
This scheme is based on symmetrical uniformsampled PWM
where the reference voltage is found from a calculation of the
rectifier input (ac side) voltage required to drive the associated
line current to the reference value in a deadbeat fashion.
In this paper a rectifier current regulation scheme is presented that relies on calculation of a duty cycle for each
switching state (space vector) of the rectifier. Calculation of
a space vectorbased duty cycle was shown to be effective
method for inverter voltage regulation [8]. This fundamental
concept is extended to a deadbeat, predictive, rectifier current
regulator in this paper. Direct control of the current space ( d q )
vectors has the advantages of improved harmonic performance,
especially at low dc bus voltages (modulation index near
unity), and improved dynamic response to a transient in the
load power or dc bus voltage at any operating condition in
comparison to perphase PWM techniques.
11. PRELIMINARY CONSIDERATIONS FOR RECTIFIER
CONTROL
where the e superscript denotes a rotating reference frame
quantity. The stationary and rotating reference frame representations of the input line currents are
(4)
and
I" = (Id cos wt
= I;
+ Iq sin wt) + j(ld
sin wt
+ Iq cos wt)
+jI;
(5)
respectively.
B . Formulation of the Current Reference
In order to obtain unity power factor, it is desired that 1
:
be zero since I t is the component of I in quadrature with E.
Therefore,
I,"* = 0
(6)
where the * superscript denotes a reference or command value.
With I: controlled to zero, I: corresponds to the magnitude
of the input line current. As depicted in Fig. 2, the magnitude
of the input current is formulated from a combination of the
bus voltage error and a load feedforward term. The daxis
reference current then, is,
is
where Pout an estimate of the output power delivered to the
motor load and R is a parameter that determines the tradeoff
between steadystate and transient performance. Quantity R
is a userdefinable control parameter, not a circuit resistance.
It can be noted that if R is small, the bus regulation term is
dominant, and steadystate bus voltage ripple is low. If R is
large, the transient performance is improved. The derivation of
the output power is given in [2] and is found from an estimate
of the motor torque and the stator frequency.
A . Reference Frame Transformations
It is assumed that the source is a balanced, sinusoidal threephase voltage supply with frequency w. Because unity input
power factor is desired, it is convenient for this analysis to
take the angle of the aphase input voltage as the reference
angle. That is,
E, = E cos wt
Eb = E cos(wt  2 ~ / 3 )
E, = E cos(wt + 2 ~ / 3 ) .
I* = I: +jI,* = I:* coswt
(1)
The input voltage in a stationary dq reference frame is given by
]E
= Ed+jEq = E,+j
=E
where V I is the dq vector of the stator voltage, A, is the stator
flux, and IT is the component of stator current in quadrature
with A,.
The current reference is then transformed back to the
stationary reference frame by
cos wt+jE sin wt.
/?
+ jId* sinwt.
(9)
The stationary reference frame current I* is then used by the
space vector controller described in the next section.
111. DEADBEAT
STEADYSTATE
SPACE
VECTORCURRENT
REGULATION
AI
The input voltage can then be transformed to a rotating
reference frame dq quantity aligned with E,. This is given by
E"= Edcoswt+jEqsinwt
=E
(3)
The current control method proposed in this paper is accomplished by estimating the appropriate duty cycles for the dq
current vectors adjacent to the reference vector in such a way
that the line current is driven to the reference value at the end
3.
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 8, NO. 1, JANUARY 1993
32
T
s
'a
I
I
'.W
Fig. 3 . Rectifier switching states and input voltage vectors.
Fig. 4. Switching function generation for space vectorbased regulator.
of a constant, known period of time. In the case of steadystate operation, this is equivalent to calculating a reference
voltage vector that accomplishes the deadbeat control and
calculating the duty cycles for the appropriate states using
space vector PWM as described in [8]. In the case where the
voltage vector necessary to drive the current vector to the
reference value cannot be synthesized in half the switching
period (i.e., transient operation), an altemative scheme is used
to ensure the current is driven in the direction of the reference
vector while still maintaining a constant switching frequency.
This is described in detail in Section IV.
Let T, denote half the switching period. That is, T, =
1/(2fsw), where f s w is the rectifier switching frequency. If
T,, is assumed to be small in comparison with the frequency
of E,
then IE can be assumed constant over the period T,. Let
t, denote the time at the beginning of one T, period. Then the
change in line current over one period (neglecting the source
resistance) is
where Tk and Tk+l are the time durations spent on states k
and k 1, respectively. The remainder of the period is spent
on the zero state. That is,
A I = I(t,
+ T,)  I(t,) =
L
i

T,
(10)
where V is the average value of the ac side rectifier voltage
over T,. In order to control the line current in a deadbeat
manner, A I must be
AI = I*  I(t,).
(1 1)
The value of average rectifier input voltage V *, which satisfies
(ll), is
The rectifier ac side voltage dq vector that corresponds to
the kth rectifier switching state ( k = 0 , . . . ,7) is given by
The seven rectifier switching states and the v k vectors are
shown in Fig. 3. If VI, and v k + l are the two voltage vectors
adjacent to V * ,then V * can be synthesized using the space
vector PWM by
1
v* = (VkT
T,
k f
Vk+lTk+l)
(14)
+
To = T ,  Tk  Tk+1.
(15)
In order to minimize the ripple content of the line current,
the time spent on the zero state is equally distributed at the
beginning and the end of the T, period. The rectifier leg
switching functions and the definitions of To,Tk, and Tk+1,
are illustrated in Fig. 4.
With space vector current regulation, the line currents are
controlled to the reference value over the period T,, and each
of the three inverter legs has been exercised once. Therefore,
it is clear that with this scheme the current is controlled on
a twiceperswitching cycle basis. This is not the case with
perphase duty cycle control as in [6]. In the PCFF scheme,
the voltage is updated only once per switching period. The
ability of the space vector current regulator to control the line
current twice per switching cycle is important several reasons.
The first is, clearly, that the ripple current is reduced since
the current (and voltage) references are updated twice as fast
with the space vector control. This is particularly important
at lower switching frequencies where error is introduced by
assuming that IE is constant over the switching period. Another
important reason is that in most current regulator applications,
including the one described here, the current reference I*
typically cannot be predicted at the end of the switching cycle.
The reference current is known only in real time. Therefore,
replacing I* with I*(t,) in (12), results in the line current
following the reference current with one period of delay.
Therefore, the steadystate line current error is significantly
reduced with the space vector current regulation.
PWM PREDICTIVE
CONTROL
IV. ASYMMETRICAL
The harmonic current distortion of the PCFF duty cycle
control scheme presented in [6] can be improved, especially
at lower switching frequencies (4 kHz), by updating the
duty cycle twice per switching period, as is the case with
space vector current regulation and conventional asymmetrical
uniform sampled PWM [ 151. This is accomplished by updating
the duty cycle and the control voltage U* for each phase, at
the beginning of each straight line segment of the triangle
carrier. This is illustrated in Fig. 5. The control voltage that
4.
HABETLER: A SPACE VECTORBASED RECTIFIER REGULATOR
,4TS
L

I
V

Fig. 7. Diagram illustrating the change in line current associated with each
rectifier switching state.
 +.
I
r.
1
1
AI.
I
vc
f
4 Ts + I
I
va
33
s
Rectifier
Inverter
Harmonic Distortion Comparison
Fig. 8. Block schematic of ac/dc/ac converter
V. HARMONIC
PERFORMANCE
COMPARISON
0
0.2
0.4
0.6
0.8
1
1.2
Modulation Index
Fig. 6. Line current harmonic distortion as a function of modulation index.
accomplishes the deadbeat current regulation is
The total harmonic distortion in steadystate operation can
be compared for the three control schemes discussed above.
The simulation results are illustrated in Fig. 6, with a switching frequency of 2 kHz. The operating conditions for each
switching scheme are identical. It is very important to note that
the space vector current control provides superior harmonic
performance to perphase duty cycle generation since the space
vector control results in a switching pattern wherein the zero
state is symmetrically distributed at the beginning and end
of each half cycle. This ensures minimum current ripple. The
PCFF scheme also symmetrically distributes the zero state but
only does so over the entire switching period, 2T, = l/fsw.
VI. TRANSIENT
OPERATION
where Vtri is the peak of the triangle carrier as indicated in Fig.
5, and 2,. is the reference current for phase j
a, b, c. This
scheme will be referred to as “asymmetrical PWM predictive
control.” In comparing (12) with (16), it is very important to
note that the actual duty cycle of each pole of the rectifier
is identical for the asymmetrical PWM predictive control and
the space vector current regulator. This is to be expected since
they both accomplish the same deadbeat control. The switching
pattems as a function of time, however, are not the same
since the space vector current regulator distributes the time
spent on the zero state symmetrically within the period and the
asymmetrical PWM predictive control does not. This accounts
for the difference in harmonic performance as discussed in the
next section.
Maximizing transient performance is very important in rectifier control in order to minimize the magnitude of transients
in the dc bus voltage and, subsequently, to minimize the
size of the dc bus capacitance required. The semiconductor
switches in the boosttype rectifier discussed in this paper must
block a higher voltage than the devices used in conjunction
with a conventional diode rectifier. Operation at modulation
index near unity is therefore desirable. Therefore, in addition
to considering the response of the current regulator to load
transients, it is also important to consider the performance of
the current regulator at modulation index near unity. These
two topics are addressed in this section.
Transient operation can be defined as an operation condition
where the solution of (14) results in the sum TI, Tk+1 being
+
5.
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 8, NO. 1, JANUARY 1993
34
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(b)
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 2
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(e)
Fig. 9. Converter waveforms under steadystate operating conditions. (a) Input line current. (b) Input line current dq vector. (c) DC bus voltage.
(d) Lineline switching function. (e) Inverter line current.
larger than T,. In other words, the value of V* calculated
in (12), cannot be synthesized, in an average sense, from VI,
and Vk+l over the period T,. Under this condition, deadbeat
control of the current is no longer possible. The best transient
performance that can be achieved is to switch the rectifier such
that the line current is driven in the direction of the reference
value. That is, it is desired that the angle of AI be control
to be equal to the angle of AI*. Controlling the rectifier so
that the actual average voltage at the input to the rectifier is
proportional to V* does not cause the current to be driven in
the correct direction. This can easily be seen from (12). The
angle of AI is equal to the angle of V*  E.
Therefore, an
actual input voltage vector proportional to V* (but not equal
to V*) results in an incorrect angle for AI.
Let AI, be the change in line current associated with
switching state m. That is,
AI, =
EV,
Li
~
T,
m= 1,2,...6
.
(17)
6.
35
HABETLER: A SPACE VECTORBASED RECTIFIER REGULATOR
The two adjacent states, m = k and m = k + l , which drive the
line current in the correct direction, can be found by calculating
AI, for each of the six nonzero switching states. Then k and
k 1 correspond to the two AI, vectors that are adjacent to
AI*. Note that the value of T, is not needed to determine k
and IC 1. Referring to Fig. 7, states 2 and 3 are adjacent to
the reference current vector.
1 are known, then the values of T and
k
Once k and k
Tk+1, which would drive the current to the reference value,
can be found from
+
+
+
LiAI* = E(Tk f Tk+1) VkTk  Vk+1Tk+1
4.5
3.6
a
Y
2.7
%
$
d
1.8
n
4
0.9
(18)
0
0
Equation (18) represents two equations with Tk and Tk+1 as
k Tk+1 will be larger than T, in the
unknowns. The sum T
transient condition. Therefore, in order to maintain a constant
switching frequency, T and Tk+1 can be multiplied by a
k
constant without changing the angle of AI*. That is,
1
2
3
4
5
6
7
wt (rad)
+
(a)
2

1.5
Y
where T and TL+l are the actual switching intervals for states
L
IC and k + 1, respectively. Note from (19) that T +
L
=
T,, and therefore the zero state is not used under transient
i!
0.5
conditions. This is to be expected since the current is to be
driven to the reference value as quickly as possible.
1.5
VII. RESULTS
A block schematic of the complete rectifier control system
including the space vector current regulator is shown in Fig. 8.
Simulation results for the ac/dc/ac converter with the proposed
space vector current regulator is shown in Figs. 9 and 10.
In all the simulation results given, including those in Fig. 6,
E = 1.0 pu, I , = 0.7 PU, fSw = 2.1 kHz, V,., = 3.0
Vl
pu, input frequency = 60 Hz, output frequency = 90 Hz,
1 / ( 2 ~ 6 0 C )= 3 PU, ( 2 ~ 6 0 ) L i= 0.2 PU, ( 2 ~ 6 0 ) L ,= 0.2
pu, R = 0.05 pu, from (7) K = 12. In order to interpret the
rectifier regulator performance in terms of actual units, for a
20kW converter, with a 300Vdc bus, the value of C in the
simulations is 100pF. Given these actual units, from Fig. 9(c),
the peakpeak ripple on the dc bus would be 35 V.
Fig. 9 illustrates steadystate operating conditions. The
inverter is controlled by a conventional synchronous frame
current regulator with a PI controller. Note that the use of
load feedforward eliminates steadystate error in the dc bus
voltage. Also, the steadystate input line current error caused
by the halfcycle delay in current regulation is compensated
by the bus voltage controller. No addition compensation is
required.
Fig. 10 shows the response of the rectifier control system
to a step change in inverter current command. Note the
quick response of the dc bus voltage and the input line
current resulting from the space vector current control scheme
described above. It should by noted that in examining Fig.
10(a), the bus capacitance is very small, as mentioned in the
previous paragraph. Therefore, the peak voltage under the
transient condition could certainly be reduced by increasing
the value of C. The important point here is that the line current
0
1
2
3
4
5
6
7
5
6
7
wt (rad)
(b)
3
2
 1
&
Y
4
8 0
5
1
2
0
1
2
3
4
wt (rad)
(C)
Fig. 10. Converter waveforms illustrating transient response to a step change
in inverter current reference. (a) DC bus voltage. (b) Rectifier line current. (c)
Inverter line current and reference current.
responds very quickly in order to control the bus voltage. Also,
the time constant of the bus voltage response depends of the
value of R in (7). As R becomes smaller (or K becomes
larger) the transient response time is reduced. This, of course,
comes at the expense of steadystate performance.
VIII. CONCLUSIONS
A new method for current regulation in for use in controlled
rectifiers has been presented in this paper. The proposed
control scheme is based on a deadbeat or predictive control
7.
36
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 8, NO. 1, JANUARY 1993
of the input line current. This is accomplished by calculating
the duration of time spent on the appropriate rectifier states in
order to drive the line current to the reference value at the end
of the cycle. The current is controlled on a halfcycle basis
(i.e., the switching times are calculated twice per switching
cycle). This results in superior harmonic performance. The
space vector current regulator was shown to result in lower
harmonic current distortion in comparison to existing predictive schemes, especially at a high modulation index, where
the rectifier is typically operated. This is because space vector
control results in the zero state being symmetrically distributed
each half cycle. In addition, a method of controlling the current
under transient conditions was introduced, wherein the line
current is always driven in the direction of the reference
voltage, reducing the response time of the current regulator.
The space vector current control, when used in conjunction
with load feedforward and proportional integral control of
the dc bus voltage, was shown to provide unity input power
factor, lowbus voltage ripple, and excellent transient response,
even with low values of dc link capacitance.
[8] H. W. van der Broeck, H.Ch. Skudelny, and G. Stanke, “Analysis and
realization of a pulse width modulator based on voltage space vectors,”
IEEE Trans. Industry Applications, vol. IA24, no. 1, pp. 142150, 1988.
[9] K. P. Gokhale, A. Kawamura, and R. G. Hoft, “Dead beat control of
PWM inverter for sinusoidal output waveform synthesis,” IEEE Trans.
Industry Applications, vol. IA23, no. 5, pp. 901910, 1987.
[IO] J. Holtz and S. Stadtfeld, “A PWM inverter drive system with on line
optimized pulse pattems,” European Conf. Power Electron. Applications,
Brussels, Belgium, 1985, pp. 321325.
[ l I] M. P. Kazmierkowski, M. A. Dzieniakowski, W. Sulkowski, “Novel
space vector based current controllers for PWM inverters,” IEEE Trans.
Power Electron., vol. 6, no. 1, pp. 158166, 1991.
[I21 S. K. SUI and T. A. Lipo, “Design and performance of a high frequency
link induction motor drive operating at unity power factor,” IEEE Trans.
Industry Applications, vol. 26, no. 3, pp. 4344L0, 1990.
1131 D. M. Brod and D. W. Novotny, “Current control of VSIPWM
inverters,” IEEE Trans. Industry Applications, vol. IA21, no. 4, pp.
769775, 1984.
[I41 T. M. Rowan and R. J. Kerkman, “A new synchronous current regulator
and an analysis of current regulated PWM inverters,” IEEE Trans.
Industry Applications, vol. IA22, no. 4, pp. 678490, July/Aug. 1986.
[I51 G. Franzo, M. Mazzucchelli, L. Puglisi, and G. Sciutto, “Analysis of
PWM techniques using uniform sampling in variablespeed electrical
drives with large speed range,” in IEEEIAS Annual Meeting Conf. Rec.,
1984, pp. 568575.
REFERENCES
[ I ] R. Mahadevan, “Problems in analysis, control, and design of switching inverters and rectifiers,” Ph.D. dissertation, Califomia Institute of
Technology, Pasadena, CA, 1986.
[2] T. G. Habetler and D. M. Divan, “Angle controlled current regulated
rectifier for ac/ac converters,” IEEE Trans. Power Electron., vol. 6, no.
3, pp. 463469, July 1991.
[3] J. W. Dixon, A. B. Kulkami, M. Nishimoto, and B. T. Ooi, “Characteristics of a controlled current PWM rectifierinverter link,” IEEE Trans.
Industry Applications, vol. IA23, no. 6, pp. 10221028, 1987.
[4] M. Nishimoto, J. W. Dixon, A. B. Kulkami, and B. T. Ooi, “An
integrated controlledcurrent PWM rectifierchopper link for sliding
mode position control,” in IEEEIAS Annual Meeting Conf. Rec., 1986,
pp. 685691.
[5] B. T. Ooi, J. W. Dixon, A. B. Kulkami, and M. Nishimoto, “An
integrated ac drive system using a controlledcurrent PWM rectifier
inverter link,” IEEE Trans. Power Electron., vol. PE3, no. 1, pp. 6471,
1988.
[6] R. Wu, S. B. Dewan, and G. R. Slemon, “A PWM ac to dc converter with
fixed switching frequency,” IEEE Trans. Industry Applications, vol. 26,
no. 5, pp. 88G885, 1990.
[7] R. Wu, S. B. Dewan, and G. R. Slemon, “Analysis of a PWM ac to
dc voltage source converter under predicted current control with fixed
switching frequency,” IEEE Trans. Industry Applications, vol. 27, no.
4,pp. 756764, 1991.
Thomas G. Habetler (S’82M’83S’SSM’89)
received the B.S.E.E. and M.S. degrees in electncal
engineering from Marquette University, Milwaukee,
WI, and the Ph.D. degree from the University of
WisconsinMadison, in 1981, 1984, and 1989, respectively.
From 1983 to 1985 he was employed by the
ElectroMotive Division of General Motors as a
Project Engineer He was involved in the design of
switching power supplies and voltage regulators for
locomotive applications. In 1985 he was awarded
the General Motors Fellowship to attend the University of WisconsinMadison. He is currently an Assistant Professor of Electncal Engmeenng
at the Georgia Institute of Technology, Atlanta. His research interests are in
switching converter technology and electnc machine dnves.
Dr. Habetler was corecipient of the 1989 first and the 1991 secondpnze paper awards of the Industnal Dnves Committee of the IEEE Industry
Applications Society. He is chair of the Membership and Publicity Committee
of the IEEE Power Electronics Society and is a member of the IEEEIAS
Industnal Power Converter Committee and Industnal Drives Committee.
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