IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 29, NO. 1, JANUARYIFEBRUAKY 1993
136
Control of Parallel Connected Inverters
in Standalone ac Supply Systems
Mukul C. Chandorkar, Student Member, IEEE, Deepakraj M.
Divan, Member, IEEE, and Rambabu Adapa, Senior Member, IEEE
Abstract-A scheme for controlling parallel-connected invertJnvener
ers in a standalone ac supply system is presented in this paper.
This scheme is suitable for control of inverters in distributed
source environments such as in isolated ac systems, large and
distributed uninterruptible power supply (UPS) systems, photovoltaic systems connected to ac grids, and low-voltage dc power
""
transmission meshes. A key feature of the control scheme is that
Fig. 1. Inverter connected to stiff ac system.
it uses feedback of only those variables that can be measured
locally at the inverter and does not need communication of control
signals between the inverters. This is essential for the operation
of large ac systems, where distances between inverters make for power transmission have traditionally been current sourced,
communication impractical. It is also important in high-reliability in recent years, voltage source inverters (VSI) have been
UPS systems where system operation can be maintained in the increasingly used for high-power applications like electric
face of a communication breakdown. Real and reactive power traction and mill drives, photovoltaic power systems, and
sharing between inverters can be achieved by controlling two battery storage systems. Control schemes for VSI's in power
independent quantities-the power angle, and the fundamental
inverter voltage magnitude. Simulation results obtained with the system environments have formed the topic of recent work
[2]. Further, with inverter topologies like the neutral-point
control scheme are also presented.
f
I. INTRODUCTION
A
S DC TO AC power converters feeding power to ac supply systems become more numerous, the issues relating
to their control need to be addressed in greater detail. Inverters
connecting dc power supplies to ac systems occur in numerous
applications. Photovoltaic power plants and battery storage
installations are examples of such applications. In either case,
the inverter interfaces could be connected to a common ac
system. Distributed uninterruptible power supply (UPS) systems feeding power to a common ac system are also possible
examples. In addition, over the past several years, there has
been considerable interest in applying inverter technology to
low voltage dc (LVDC) meshed power transmission systems.
The feasibility from the control viewpoint of an LVDC mesh
has been demonstrated in [l]. The transmission system could
typically consist of inverters connected at several points on
the LVDC mesh, providing power to ac systems that could
be interconnected as well. Multiple inverters connected to a
common ac system essentially operate in parallel and need to
be controlled in a manner that ensures stable operation and
prevents inverter overloads. Although inverter topologies used
Paper IPCSD 92-16, approved by the Industrial Power Converter Committee
of the IEEE Industry Applications Society for presentation at the 1991 Industry
Applications Society Annual Meeting, Dearborn, MI, September 28-October
4. This work was supported by NSF grant 8 818 339 and EPRI Agreement
RP7911-12. Manuscript released for publication April 25, 1992.
M. C. Chandorkar and D. M. Divan are with the Department of Electrical
and Computer Engineering, University of Wisconsin, Madison, WI 53706.
R. Adapa is with the Electric Power Research Institute, Palo Alto, CA
94303.
IEEE Log Number 9204199.
clamped (NPC) inverter [3], it is possible to achieve substantial harmonic reduction at reasonably low PWM switching
frequencies.
A standalone ac system may be described as one in which
the entire ac power is delivered to the system through inverters.
In a standalone ac system, there are no synchronous alternators
present in the system that would provide a reference for the
system frequency and voltage. All inverters in the system need
to be operated to provide a stable frequency and voltage in the
presence of arbitrarily varying loads. This paper first develops
a control method for an inverter feeding real and reactive
power into a stiff ac system with a defined voltage, as shown
in Fig. 1. This forms the basis of a control method suitable for
standalone operation. The inverter is a VSI with gate turn-off
(GTO) thyristor switches, operating from a dc power source,
and feeding into the ac system through a filter inductor. In
a standalone system, a filter capacitor is needed to suppress
the voltage harmonics of the inverter. The requirements for
controlling such an interface are described in the next section.
Later sections describe the development of an effective control
scheme to meet these requirements and present simulation
results obtained from the study of a power distribution system
with parallel-connected inverters.
11. REQUIREMENTS OF THE CONTROL SYSTEM
The control of inverters used to supply power to an ac
system in a distributed environment should be based on
information that is available locally at the inverter. In typical
power systems, large distances between inverters may make
communication of information between inverters impractical.
Communication of information may be used to enhance system
0093-9994/93$03.00 0 1993 IEEE
CHANDORKAR er al.: CONTROL OF PARALLEL-CONNECTED INVERTERS
137
I
I
3
2
I
P = X!L sin6
Q=
w
Lf
w
Lf
*
- =cos6
w Lf
Fig. 2. Real and reactive power flows.
performance but must not be critical for system operation. This
essentially implies that inverter control should be based on
terminal quantities.
It is well known that stable operation of a power system
needs good control of the real power flow P and the reactive
power flow Q. The P and Q flows in an ac system are
decoupled to a good extent [4]. P depends predominantly on
the power angle, and Q depends predominantly on the voltage
magnitude. This is illustrated in Fig. 2. It is essential to have
good control of the power angle and the voltage level by means
of the inverter. Control of frequency dynamically controls
the power angle and, thus, the real power flow. To avoid
overloading the inverters, it is important to ensure that changes
in load are taken up by the inverters in a predetermined manner
without communication. This is achieved in conventional
power systems with multiple generators by introducing a droop
in the frequency of each generator with the real power P
delivered by the generator [4]. This permits each generator to
take up changes in total load in a manner determined by its
frequency droop characteristicsand essentially utilizes the system frequency as a communication link between the generator
control systems. In this paper, the same philosophy is used to
ensure reasonable distribution of total power between parallelconnected inverters in a standalone ac system. Similarly, a
droop in the voltage with reactive power is used to ensure
reactive power sharing.
An important aspect of the control methodology developed
here is that it is highly modular in nature. Thus, the basic
control scheme can be very easily adapted to meet variations in
the configuration of the power system, as shown in Sections 111
and IV. This modularity is achieved by choosing the controlled
quantities of the slow, outer control loops to meet the dictates
of the power system configuration while maintaining the same
fast, inner inverter control structure. The controller for an
inverter connected to a stiff ac system, which is detailed
in Section 111, is easily modified for the control of parallelconnected inverters feeding a standalone ac system, which is
detailed in Section IV.
111. CONTROL OF SINGLE INVERTER
FEEDINGINTO A STIFF SYSTEM
The power schematic of Fig. 1 shows a single inverter
connected to a stiff ac system through a filter inductor.
The inverter is assumed to be a six-pulse GTO VSI. This
section details the control of the inverter based on feedback
of quantities measured locally at the inverter. The real and
reactive power fed into the ac system are the two variables that
are controlled by the inverter. Given set points for the real and
I
V
d
1 :Inverter Voltage Vwtor 1
0:
S e ” I For Choice of Inverter Voltage Vector
(a)
1
2
3
4
(b)
Fig. 3. (a) Inverter output voltage vectors; (b) inverter switch positions.
reactive power P* and Q*, the real and reactive power P and
Q fed by the inverter into the ac system can be controlled by
a method that controls the time integral of the inverter output
voltage space vector. This concept has previously been applied
extensively to ac motor drives [ 5 ] , [6]. The entire control of
the inverter is performed in the stationary d-q reference frame
and is essentially vector control. The transformation from the
physical a-b-c reference frame to the stationary d-q-n reference
frame is described by the following equations [7].
In these equations, the quantity f generically denotes a
physical quantity, such as a voltage or a current. In the absence
of a neutral connection, the quantity fn is of no interest. For
a six-pulse VSI, the inverter output voltage space vector can
take any of seven positions in the plane specified by the d-q
coordinates. These are shown in Fig. 3 as the vectors 0-6.
The time integral of the inverter output voltage space vector
is called the “inverter flux vector” for short. The flux vector
does not have the same significance as in motor applications.
Rather, it is a fictitious quantity related to the volt-seconds in
the filter inductor. The d and q axis components of the inverter
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 29, NO. 1, JANUARY/FEBRUARY 1993
138
PI
L o w Pass
Filter
Regulator
P' & Q* : Set Points for Real & Reactive Power
Fig. 4. Inverter control scheme-stiff
flux vector
are defined as
1
t
=
$du
Vddr
(4)
ac system.
In (9), e, and e d are the q- and d-axis components, respectively, of the ac system voltage vector E. In addition, i, and i d
are the components of the current vector 7. When i , and i d are
expressed in terms of the fluxes, the equation is expressed as
--CO
/
t
$,U
=
(5)
--CO
The magnitude of
& is
Taking into account the spatial relationships between the
two flux vectors and assuming the ac system voltage to be
sinusoidal, (10) can be expressed as
3
p = - w$,$, sin 6,.
2L.f
The angle of
5with respect to the y axis is
In this expression,
and
are the magnitudes of the ac
system and the inverter flux vectors, respectively, and 6, is the
6, = tan-' (7) spatial angle between the two flux vectors. w is the frequency
of rotation of the two flux vectors. The expression for reactive
The d and y axis components of the ac system voltage flux power transfer for Fig. 1 can be derived in a similar manner.
vector
its magnitude, and angle are defined in a similar This is
and
is defined as
manner. The angle between
3 w
(12)
Q = - -[$U$, COS - 7 / 5 3 .
6, = 6, - Se.
2 L.f
(8)
.I::(
5,
6
Control of the flux vector has been shown to have good
dynamic and steady-state performance [5],[6]. It also provides
a convenient means to define the power angle since the inverter
voltage vector switches position in the d - y plane, whereas
there is no discontinuity in the inverter flux vector. It is useful
to develop the power transfer relationships in terms of the
flux vectors. The basic real power transfer relationship for the
system of Fig. 1 in the d-q reference frame is
3
P = -(eqi,
2
+edid).
(9)
Equations (11) and (12) indicate that P can be controlled
by controlling S,, which can be defined as the power angle,
and Q can be controlled by controlling &,. The cross coupling
between the control of P and Q is also apparent from these
equations.
The control system for the inverter is given in Fig. 4. The
two variables that are controlled directly by the inverter are
is controlled to have a specified
and 6,. The vector
magnitude and a specified position relative to the ac system
This control forms the innermost control loop
flux vector
and is very fast. It is noted that both the inverter and the
6.
CHANDORKAR et al.: CONTROL OF PARALLEL-CONNECTED INVERTERS
139
"
TABLEI
CHOICEOF SWITCHINGVECTOR
Sector No. (Location of
I
z)
I I m r v v v 1
Increase
2
3
4
5
6
1
Decrease &
3
4
5
6
1
2
(The zero vector is chosen to decrease 4,)
.ii
33
N
ac system voltage space vectors ,are obtained by measuring
instantaneous voltage values that are available locally. The set
points for the controller are P* and Q*, and the set points for
the innermost control loop $: and 6; are derived from these.
The actual values of P and Q calculated from the feedback are
compared with the set values. The error drives a proportionalintegral (P-I) regulator, which generates the set points $; and
6; for the innermost control loop. The control of the inverter
to generate the specified $, and 6, is detailed in the next
subsection.
0
10
c>
LIU 0
- 6 00
-2.011
2 00
h v
In
6 00
11
VS
Fig. 5. Inverter flux vector.
0
A. Control of $, and 6,
The control of 4, and 6, forms the first level of control
and directly controls the inverter switching. The choice of
the inverter switching vector is made on the basis of the
deviations of $,, and 6, from the set values $: and 6;
and the position of the inverter flux vector in the d-q plane
given by 6,. If the deviation of 6, from 6; is more than
a specified limit, a zero switching vector is chosen. If this
deviation is less than a specified limit or if $, deviates from
$: by more than a specified amount, a switching vector that
increases 6, and changes $, in the correct direction is chosen.
This is essentially accomplished by hysteresis comparators for
the set values and then using a look-up table to choose the
correct inverter output voltage vector. The considerations for
developing the look-up table are dealt with in [ 5 ] . The choice
' 1.694
1l.727
1l.760
1'.794
1l.827
s 1'.860
T *10-1
of inverter switching vector is dictated by the value of 6,.
Fig. 6. Inverter voltage and current waveforms.
The d-q plane is divided into six sectors for 6, as shown in
Fig. 3(a), which also shows the inverter switching vectors.
The inverter switch positions for the vectors are shown in Fig. the power system of Fig. 1 are presented in Figs. 5-7. The dc
3(b). The value of 6, determines the choice of two possible bus voltage is taken to be 10 kV, and the line-to-line voltage
inverter switching vectors apart from the zero vector. One of the ac system is taken to be 3.3 kV rms. The inductor L
vector increases the magnitude $,, and the other decreases is 17 mH. Fig. 5 gives the plot of the locus of the inverter
it, whereas both tend to increase 6,. Thus, to decrease 6,, the flux vector
The locus is seen to be close to a circle since
zero switching vector is chosen. To correct the value of $,,, the magnitude $, is very tightly controlled. Fig. 6 shows the
one of the two active switching vectors is chosen, depending inverter line-to-line voltage ?& and the inverter line current iu
on the sign of the correction required. Table I gives the choice for P* = 1MW and Q* = 500 kvar. Fig. 7 shows the response
of active vectors for given positions of the inverter flux vector, of the inverter to step changes in Q* and P*, successively. It
which is specified by 6,. In this manner, $, and 6, are tightly is noted that there is a disturbance in P when Q* is changed
controlled to lie within specified hysteresis bands by means and a disturbance in Q when P* is changed. In each case, the
of inverter switching. The tip of the inverter flux vector is P-I regulators modify the set values of :
6 and 4,: to main
guided along an almost circular path. Control of $, and 6, the P and the Q at the set values. In addition, the tight contro
in this manner results in a PWM voltage waveform at the of P and Q within limits is apparent from Fig. 7.
inverter output.
I v . CONTROL OF INVERTERS IN A STANDALONE SYSTEM
B. Simulation Results
The control of a single inverter feeding a stiff ac system
-
I
6.
Simulation results of the control scheme of Fig. 4 applied to
based only on instantaneous measurement of terminal quanti-
140
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 29, NO. 1, JANUARYFEBRUARY 1993
0
I
I
I
I
I
0
frequency of
are obtained from the outermost loop, which
implements specified droop characteristics for the frequency
with P and magnitude with Q, as mentioned in Section 11. The
entire control is, thus, a three-level structure. The innermost
control level controls
and 6, and is the same as that
described in the previous section. The second level controls
the ac side frequency and the voltage at each inverter and
6 and $: for the innermost level. The
provides set points :
third level computes the set points for frequency and voltage
for each inverter. The two outer control levels are described
below.
A. Control of Frequency and Voltage
ol
0.02
I
0.06
0.11
T
0.15
0.20
I
S
0.25
Fig. 7. Inverter real and reactive power.
The frequency controller determines the setpoint 6; that is
needed to attain the specified frequency. The structure of the
frequency controller is given in Fig. 10. The frequency setting
w* is integrated to obtain a reference for the position 6:c of
the ac system voltage vector across the filter capacitor. This
is compared with the actual position Sa, of E. The error is
used to drive a P-I regulator, which produces the setpoint
a,: which is given to the innermost control loop described
previously. This scheme achieves a very tight control of the
output frequency since the regulator attempts to control the
output voltage vector angle at every instant.
The voltage controller determines the setpoint $: that is
needed to attain the specified ac system voltage magnitude.
The voltage controller needs to take care of the filter dynamics
to determine the exact value of $:. The structure of the voltage
controller is given in Fig. 11. The controller command input
is E*, which is the specified value of the magnitude of F.
The controller consists of a command feedforward term and a
voltage magnitude feedback term. The command feedforward
term is given by
Fig. 8. Standalone ac system.
ties now forms the basis of the control scheme for multiple
inverters in standalone system environments. The essential
difference in the control scheme is that in the standalone
system, there is no ac side voltage available for reference. The
inverters themselves produce the ac system voltage, which is
fed back to control the inverters. There is thus a possibility
of controlling the voltage and the frequency of the ac system
by inverter control. Fig. 8 shows two inverters feeding into
a standalone ac system. The inverters are interfaced to the ac
system through LC filters. The two inverters are connected by
a tie line, and each inverter has a local load. The dc power
source represents a 10-kV dc power transmission mesh. The
nominal voltage on the ac system is 3.6 kV rms line to line, and
the nominal frequency is 60 Hz. Each inverter is a six-pulse
VSI made up of GTO switches.
Fig. 9 shows the block diagram of the control of inverters
in a standalone system. As in the single inverter case, the two
and 6, for each
variables that are directly controlled are
inverter. Middle control loops are then used to control the
magnitude and angular frequency of the ac system voltage
vector E. The set points f o r the magnitude and angular
The command feedforward gives the value of $: needed to
achieve the specified E* with an unloaded filter and is intended
to speed up the voltage control loop. The voltage magnitude
feedback term is used to generate an error signal that actuates
a P-I controller. The resultant value of $: is used as a setpoint
for the innermost control loop described previously.
The ac system frequency w is computed six times in one
cycle. For this purpose, six axes are defined in the d-q plane.
The time taken by the vector E to cross from one axis to
the next consecutive axis is used to compute the frequency.
For parallel operation of multiple inverter units, the setpoints
w* and E* need to be chosen to ensure the correct P and
Q sharing between the inverters in response to arbitrary load
changes. This has to be done without communication of the
setpoints between the two inverter systems. The next subsection describes the outermost control loop, which determines the
setpoints w* and E* for each inverter system independently
without any signal communication. This is done on the basis
of the real andreactive power loading of the inverter systems.
CHANDORKAR
et
al.: CONTROL OF PARALLEL-CONNECTED INVERTERS
Outer hop: Droop Characteristics
---
I - - -
I
---
--
Middle Loop: E and o
--
I
I
I
J
,
Feedback ' PandQ &E*=f(Q)
Voltage
Innerbop:
---
Droops
AC System
141
!
SYStelll
Voltage
Vector
_--
--T--
-
E*
I
E
Inverter
oand
,
+ Flux
Control
,
Calc.
Vector
vvand
_--
Sp
---
WV
vv*
Inverter
-1
I
I
I
Vector
Control
+Inverter
Switches
1-
I
AC System Voltage
Feedback
Inverter Voltage
Feedback
V
E
Fig. 9. Inverter control scheme-standalone
ac system.
slopes m, for different inverters are chosen such that
*
0'
mlPo2 = maPo2 = ... = mnPon
sx
I
From Filter Output
Fig. 10. Frequency controller for standalone system.
(14)
then for a total power P , the load distribution between the
inverters satisfies the relationships
mlP1 = mzP2 = ... = mnPn
(15)
By choosing the slopes according to (14), it can be ensured
that load changes are taken up by the inverters in proportion
to their power ratings. The power-sharing mechanism can
Fig. 11. Voltage controller for standalone system.
be best understood by considering the two-inverter system
shown in Fig. 8. An increase in power drawn by the load
B. Computing w* and E* for Parallel Operation
near Inverter 2 results in increased power from both inverters.
The outermost loop determines the setpoints for w* and If the magnitude of m2 is larger than that of m l , w; would
E* to ensure correct real and reactive power sharing between tend to drop lower than w:. Hence, the vector Fz would lag
the parallel connected inverters. This action is similar to that the vector El, and the power flow in the tieline from Inverter
used in conventional power systems to ensure the correct load 1 to Inverter 2 would increase. Thus, Inverter 1 would take
sharing between generators feeding to a common ac system up a larger proportion of the load. It is possible to define
[4].For the frequency set point, a droop is defined for the P- a composite power-frequency curve for all the inverters in
w* characteristic of each inverter. The frequency set point is the system. The composite load curve is likewise defined.
thus made to decrease with increasing real power supplied by At the steady-state operating point on the composite loadthe inverter. The P-U* droop characteristic can be described frequency curve, the total power delivered by the inverters
matches the power consumed by the loads. Depending on the
by
stiffness of the composite power-frequency curve, the steadywt = W O - m,(Po; - P,) = g,(P).
(13)
state system frequency will change on changing loads. The
frequency may then be restored to its nominal value by a
In this expression, i = 1 for inverter 1, and i = 2 for slower outer loop. To restore the frequency, the value of Po;,
inverter 2 (Fig. 8). W O is the nominal operating frequency of (13) has to be modified for the inverters. This is equivalent to
the ac system and is taken to be 377 rads (60 Hz). Po, is the shifting the power-frequency curve vertically. The restoration
power rating of the ith inverter, and P, is its actual loading. of the frequency may be done in a slow, coordinated manner
The slope of the droop characteristic is m, and is numerically by a master controller, using a slow communication channel
negative. The values of m; for different inverters determine between the inverters.
In a similar manner, the setpoints E,* for the ac system
the relative power sharing between the inverters. In typical
systems, the P-w* characteristics are stiff, and the frequency voltages at the inverter systems can be determined from
change from no load to full load is extremely small. If the drooping reactive power-voltage characteristics (Q-E) for
Regulator
From Filter
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 29, NO. 1, JANUARYIFEBRUARY 1993
142
the inverters. This droop ensures the desired reactive power
sharing between the inverter systems and is described by
Ef = Eo
- n;(Qoi - Q;) = f ; ( P ) .
(17)
In (17), EOis the nominal voltage on the ac system, Qo; is
the nominal reactive power supplied by the ith inverter, and
n; is the slope of the droop characteristic.
The control system described above has been applied to the
standalone system of Fig. 8. The results of simulation studies
are presented below.
C. Simulation Results
For the simulation studies, the droops of the two inverter
systems are characterized by the following parameters:
Pol = 0.75 MW
ml = -1.4 x
Po2 = 0.6
(radls)/W
0.28
U. 24
U.32
T
U.4U
U.36
MW
mz = -1.75 x
Qol = 0.2 Mvar
Qo2 = 0.1 MVU
n1 = -1.0 x 10-4 V/VX
n2
= -2.0 x
(radls)/W
V/var.
The nominal voltage is 3.6 kV rms line to line, and the
nominal frequency is 60 Hz. The filter components for the
two inverter systems are identical as are the initial load
components. The component values are typical for a lowpower ac system. With reference to Fig. 8, the component
values are
3
O.ZI1
I
11.24
I
0.28
I
I
0.32
T
I
0.36
s
J
U.40
Fig. 12. Inverter real and reactive power (standalone system).
Fig. 12 shows the response of the inverters when the
resistance RE^ (Fig. 8) is decreased suddenly to half its value.
Fig. 12 shows the real and reactive powers supplied by the two
inverter systems to the load. The figure shows that Inverter 1
carries a larger share of the real power since it has a stiffer
slope. Fig. 13 shows the line-to-line voltage across the filter
capacitor of Inverter 1. The plot for the reactive powers in
Fig. 12 shows oscillations. These oscillations are the result of
filter interactions and occur in the absence of active damping
of the loop formed by the two filter capacitors and the tie-line
inductance. These oscillations are not uncommon in power
systems and can be damped by the inverters, given sufficient
inverter bandwidth. One effective means of damping these
oscillations is the introduction of a series active filter [8]
between the capacitor and the ac system bus. As mentioned in
[8], this method presents a low resistance to the fundamental
and a high resistance to harmonics, thus effectively limiting
the harmonic current injection into the ac system. The series
active filter inverter is not expected to handle real power and
can have a reasonably low rating.
' I - L'
U.2U
U.24
0.28
0.32
0.36 S
0.40
T
Fig. 13. Voltage across Inverter 1 filter capacitor.
V. CONCLUSIONS
This paper has described a method to effectively control
inverters in a standalone ac supply system without any form of
signal communication. The control methodology has a highly
modular structure. This feature enables easy modification of
the controls to meet the requirements of different ac system
structures. The simulation results presented indicate that the
scheme effectively achieves the goals of power sharing in
the presence of arbitrarily changing loads. Active damping in
the loop formed by the filter capacitors and the tieline would
enhance the performance further. The scheme described in this
paper uses P-I regulators to determine the set points for 6;
CHANDORKAR ef al.: CONTROL OF PARALLEL-CONNECTED INVERTERS
and $:. However, the dynamic performance of the system can
be substantially improved if an observer structure is used to
determine the frequency. The position of the ac system voltage
vector can be determined very accurately at any time. This
information can be used to set up a frequency observer, the
output of which would be an estimated frequency. The time
integral of the estimated frequency can be compared with the
actual position of the voltage vector, and the estimated frequency can be modified accordingly. Feedback of the observer
states results in a system with very good dynamic response and
disturbance rejection properties.
In summary, this paper has
discussed control system requirements for inverters interfaced to an ac system, with emphasis on a standalone ac
system
developed a modular control scheme that meets these
requirements without control signal communication between parallel-connected inverters
presented simulations for the control scheme as applied
to an inverter connected to a strong ac system and to two
inverters connected in parallel to a standalone ac system
briefly discussed the issue of filter interaction in the case
of parallel-connected inverters and suggested a method
for minimizing these interactions.
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[3]
[4]
[5]
[6]
[7]
[8]
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source converter in high power applications,” in IEEE PESC Con$ Rec.,
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A. Nabae, I. Takahashi, and H. Akagi, “A neutral-point-clamped PWM
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Sept./Oct. 1981.
A. R. Bergen, Power System Analysis. Englewood Cliffs, NJ: PrenticeHall, 1986.
I. Takahashi and T. Noguchi, “A new quick-response and high-efficiency
control strategy of an induction motor,” IEEE Trans. Industry Applications, vol. IA-22, pp. 820-827, Sept./Oct. 1986.
M. Depenbrock, “Direct self-control (DSC) of inverter-fed induction
machine,” IEEE Trans. Power Electron., vol. 3, pp. 420-429, Oct 1988.
T. A. Lipo, “Analysis of synchronous machines,” course notes, Univ.
of Wisconsin-Madison, 1990.
S. Bhattacharya, D. M. Divan, and B. Banerjee, “Synchronous frame
harmonic isolator using active series filter,” in Proc. 4th Euro. Con5
Power Electron. Applications (Florence, Italy), 1991, vol. 3, pp. 30-35.
Mukul C. Chandorkar (S’90) received the B.Tech.
degree in electrical engineering from the Indian
Institute of Technology, Bombay, India, in 1984 and
the M. Tech. degree in electrical engineering from
the Indian Institute of Technology, Madras, India, in
1987. Since 1989, he has been working on the Ph.
D. program in Electrical and Computer Engineering
at the University of Wisconsin, Madison
From 1984 to 1986, he was with Larsen and
Toubro Limited, Bombay, India, working on the
engineering of cement and chemical plants. He
worked as a design engineer in the power electronics industry in India
during 1988-1989. His primary technical interests are in power electronics
applications to electric machines and to power systems.
143
Deepakraj M. Divan (M83) received the B. Tech
degree in electrical engineering from the Indian
Institute of Technology, Kanpur, India, in 1975. He
also received the M.Sc and Ph.D degrees in electrical engineering from the University of Calgary,
Canada.
He has worked for two years as a Development
Engineer with Philips India Ltd. After finishing his
Masters program in 1979, he started his own concem in Pune, India, providing product development
and manufacturing services in the power electronics
and instrumentation areas. In 1983, he joined the Depa&ent of Electrical
Engineering at the University of Alberta as an Assistant Professor. Since 1985,
he has been with the Department of Electrical and Computer Engineering at
the University of Wisconsin, Madison, where he is presently an Associate
Professor. He is also an Associate Director of the Wisconsin Electric Machines
and Power Electronics Consortium (WEMPEC). His primary areas of interest
are in power electronic converter circuits and control techniques. He has over
30 papers in the area as well as many patents. He is also a consultant for
various industrial concems.
Dr. Divan was a recepient of the Killam Scholarship while in the Ph.D
program and has won various prize papers including the IEEE-US Best Paper
Award for 1988-89, first prize paper for the Industrial Drives and Static Power
Converter Committee in 1989, third prize paper in the Power Semiconductor
Committee and the 1983 third prize paper award of the Static Power Converter
Committee of the IEEE Industry Applications Society. He has been the
Program Chairman for the 1988 and 1989 Static Power Converter Committee
of the IEEE-IAS, Program Chairman for PESC ’91, and a Treasurer for PESC
’89. He is also a Chairman of the Education Committee in the IEEE Power
Electronics Society.
Rambabu Adapa (S’81-M786-SM’90) was bom
in Andhra Pradesh, India, on Sept. 2, 1956. He
received the B.S. degree in electrical engineering
from Jawaharlal Nehru Technological University,
Kakinada, India, in 1979. He received the M.S.
degree in electrical engineering from the Indian
Institute of Technology, Kanpur, India, in 1981. He
received the Ph.D. degree in electrical engineering
from the University of Waterloo, Canada, in 1986.
He joined the Power System Planning and Operations urogram of the Electrical Svstems Division
of the Electric Power Research I n & & (EPRI), Palo Ako, CA, in June
1989. Prior to joining EPRI, he was Staff Engineer in the Systems Engineering department of McGraw-Edison Power Systems, Franksville, WI. At
McGraw-Edison, he was involved in several digital and analog studies, which
included transient, harmonic, and insulation coordination studies performed
for electric utilities. At EPRI, he manages the Electro-Magnetic Transients
Program (EMTP) development and maintenance project, commercialization
of the Harmonic Analysis Software (HARMFLO) endeavor, and several
other EPRUNSF-funded projects. His interests include EMTP, power system
planning and operations, HVDC transmission, harmonics, and expert systems.
Dr. Adapa is a Senior Member of the IEEE Power Engineering Society,
a member of the DC Transmission subcommittee of the Transmission and
Distribution Committee, a member of CIGRE and of the local IEEE Santa
Clara chapter. He is a Registered Professional Engineer in the State of
Wisconsin.