458
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 3, MAY/JUNE 1998
Control of Square-Wave Inverters in High-Power
Hybrid Active Filter Systems
Po-Tai Cheng, Subhashish Bhattacharya, and Deepak M. Divan
Abstract— This paper presents a new control scheme for a
hybrid parallel active filter (HPAF) system intended for highpower applications—up to 100-MW nonlinear loads—to meet
IEEE 519 recommended harmonic standards. The active filter
inverter is realized with small-rated (1%–2% of the load rating) square-wave inverters operating at the dominant harmonic
frequencies. The proposed system achieves harmonic isolation
at desired dominant harmonic frequencies, such as the fifth
and seventh, even in the presence of supply voltage harmonic
distortions. A novel method of active filter inverter dc-bus control,
as proposed here, achieves power balancing by exchanging energy
at the fundamental frequency and at the dominant harmonic
frequency (such as the fifth). The proposed square-wave inverterbased HPAF system provides improved filtering characteristics as
compared to the conventional passive filter and is expected to be
cost effective for high-power nonlinear loads compared to the
conventional passive filter or other active filtering solutions. The
concept of harmonic isolation at dominant harmonic frequencies
by square-wave inverters with the proposed control scheme is
validated by simulation results.
Index Terms—Active filter, harmonic filtering, harmonic isolation, square-wave inverter.
NOMENCLATURE
Three-phase fifth harmonic filter
current.
– quantities of
under synchronous reference frame
(SRF) rotating at the fifth harmonic
frequency.
DC components of
and
, respectively, which represent the fifth
harmonic component of
,
.
and
– quantities of
under SRF rotating at the fundamental frequency.
DC components of
and
,
respectively, which represent funPaper IPCSD 97–67, presented at the 1996 Industry Applications Society
Annual Meeting, San Diego, CA, October 6–10, and approved for publication
in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Power
Converter Committee of the IEEE Industry Applications Society. Manuscript
released for publication October 20, 1997.
P.-T. Cheng and S. Bhattacharya are with the Department of Electrical and
Computer Engineering, University of Wisconsin, Madison, WI 53706 USA
(e-mail: po-tai@cae.wisc.edu; bhattach@cae.wisc.edu).
D. M. Divan is with Soft Switching Technologies Corporation, Middleton,
WI 53562 USA, on leave from the Department of Electrical and Computer
Engineering, University of Wisconsin, Madison, WI 53706 USA (e-mail:
divan@engr.wisc.edu).
Publisher Item Identifier S 0093-9994(98)03624-X.
0093–9994/98$10.00  1998 IEEE
damental frequency component of
, and
.
Three-phase seventh harmonic filter
current.
– quantities of
under SRF rotating at the fifth harmonic frequency.
DC components of
and
, respectively, which represent the fifth
,
harmonic component of
.
and
Three-phase load current.
– quantities of
,
,
under SRF rotating at the fifth harmonic frequency.
DC components of
and
, respectively, which represent
the fifth harmonic component of
, and
.
Three-phase supply current.
– quantities of
under
SRF rotating at the fifth harmonic
frequency.
DC components of
and
, respectively, which represent the fifth
,
harmonic component of
.
and
Fifth harmonic SRF – quantities
of the fifth harmonic voltage command.
DC components of fifth harmonic
SRF – quantities of the fifth
harmonic active filter inverter
output voltage, which represent the
fifth harmonic component of the
fifth harmonic active filter inverter
output voltage.
Three-phase quantities obtained by
applying inverse SRF transformaand
at the fifth
tion to
harmonic frequency.
Fundamental frequency SRF –
quantities of fundamental frequency
voltage command.
Three-phase quantities obtained by
applying inverse SRF transformation to
and
at fundamental frequency.
CHENG et al.: CONTROL OF SQUARE-WAVE INVERTERS
Fifth harmonic SRF – quantities
of the seventh harmonic active filter
inverter output voltages.
DC components of
and
, respectively, which represent
the fifth harmonic component
of seventh harmonic active filter
inverter output voltages.
Fifth harmonic SRF – quantities
of feedback voltage command.
Fifth harmonic SRF – quantities
of feedforward voltage command.
Three-phase load/filter terminal
voltages.
– quantities of
, and
under SRF rotating at the fifth
harmonic frequency.
DC components of
, and
, respectively, which represent
the fifth harmonic component of
, and
.
Three-phase supply voltage.
– quantities of
under SRF rotating at the fifth harmonic frequency.
DC components of
and
, respectively, which represent the fifth
harmonic component of
,
and
.
Fifth harmonic SRF – quantities
of active tuning voltage command.
Fifth harmonic SRF – quantities
of supply harmonic voltage tracking
command.
Active impedance commands.
Triangular-wave carriers synchronized to
, and
,
respectively.
Reference of the fifth harmonic active filter inverter dc-bus voltage.
Measurement of the fifth harmonic
active filter inverter dc-bus voltage.
Output of inverter dc-bus proportional integral (PI) regulator.
I. INTRODUCTION
P
ROLIFERATION of nonlinear loads, such as three-phase
rectifiers, adjustable-speed drives (ASD’s), and uninterruptible power supplies (UPS’s) continue at an unprecedented
pace. This equipment improves energy efficiency, but also
injects harmonic current into the utility due to its nonlinear
nature. In the mean time, installation of power factor correction
capacitors by customers for displacement factor improvement and by utilities for voltage support are being increasingly used. Harmonic current causes resonance between utility
and harmonic-producing loads or among multiple harmonicproducing loads. These harmonic-related phenomena result
459
in derating of the system equipment such as transformers,
higher transmission line loss, and reduced system stability
margin. Harmonic standards, such as IEEE 519, are strongly
recommended by the utilities to alleviate harmonic-related
problems. Incentives are often provided in the form of rebates,
because customers do receive direct benefit by conforming to
such standards.
Passive filters have long been used to absorb harmonic
current of nonlinear loads. Their advantages are low cost and
high efficiency. However, they are susceptible to supply and
load (series and parallel) resonance. Further, their compensation characteristics are affected by the passive component
tolerances and utility system impedance variations due to
line switchings, feeder expansion, and load expansion. A
stiff utility system poses greater difficulties for the design of
passive filters because sharp tuning and high quality factor are
required to sink harmonic current.
Pure series and shunt active filters provide effective solution
[1]–[4] for a small-rating nonlinear load, but are not feasible
and cost effective for a large-rating nonlinear load due to their
high rating requirement. Hybrid series and shunt active filters,
characterized by a combination of passive filters and active
filers, offer a cost-effective and practical solution for harmonic
filtering and harmonic isolation for a large-rated nonlinear
load and especially for a group of nonlinear loads. However,
implementation of a hybrid series or hybrid shunt active
filter system typically requires a high-bandwidth pulsewidth
modulation (PWM) inverter [5]–[10]. Hence, applications of
the existing hybrid series and hybrid shunt active filter systems
are limited to a medium power range of nonlinear loads,
typically between 500 kW–10 MW. For nonlinear loads rated
higher than 10 MW, the existing hybrid active filter systems
are not cost effective, due to the high bandwidth requirement,
high rating requirement, and low efficiency. Consequently,
passive filter solutions are typically used for harmonic filtering
of high-power nonlinear loads. As stated previously, passive
filter solutions have several drawbacks and may not meet the
IEEE 519 harmonic standard. In this paper, a cost-effective
active filtering solution for high-power nonlinear loads to meet
IEEE 519 harmonic standard is proposed.
Among several active filter topologies, the hybrid active
filter topologies are preferred for harmonic filtering of highpower nonlinear loads, due to the small rating of the active
filter inverter and inherent reactive power compensation capability [11], [12]. Further, the hybrid shunt topology is suitable
for higher power applications compared to hybrid series topology, due to easier protection and switchgear requirement. The
hybrid shunt topology also lends itself to retrofit applications
with existing passive filters in the system. Therefore, the
hybrid shunt topology is chosen for the proposed system. To
replace the high-bandwidth PWM inverter connected to the
passive filter bank in the conventional hybrid shunt active filter
system, individual small-rated square-wave inverter switching
at dominant harmonic frequency is transformer coupled to
each – tuned branch of the passive filter to form the
hybrid parallel active filter (HPAF) system, as shown in
Fig. 1. The HPAF system employs low-rating low-switchingfrequency square-wave inverters to achieve harmonic isolation
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 3, MAY/JUNE 1998
Fig. 2. Fifth harmonic equivalent circuit of the proposed HPAF system.
Fig. 1. Proposed HPAF system.
at dominant harmonic frequencies, as proposed by the authors
in [13]. Therefore, it is viable and cost effective for high-power
application, as suggested by the authors. Implementation of
the HPAF system based on square-wave inverters has been
proposed in [14] and [15].
A new control scheme based on SRF transformation [16] for
the proposed HPAF system employing square-wave inverters
is designed for harmonic compensation of large-rated nonlinear loads (above 10 MW) to meet the IEEE 519 harmonic
standard. The proposed controller achieves harmonic isolation
at dominant fifth and seventh harmonic frequencies with
square-wave inverter implementation in the presence of supply
voltage distortion and ambient nonlinear load. The proposed
control scheme also includes inverter dc-bus voltage controller
for power balancing purposes. Therefore, the proposed HPAF
system can operate in a self-sufficient manner without any
additional energy storage devices.
It is expected that the proposed HPAF system with smallrated (1%–2% of nonlinear load rating) square-wave inverters
will provide a viable and cost-effective solution for a highpower nonlinear load to meet the IEEE 519 standard. The main
features of the proposed HPAF system and control strategy
include the following.
• It provides harmonic isolation at selected dominant harmonic frequencies.
• Operation is self sufficient, with no additional energy storage device or inverter dc-bus regulating circuit needed.
• It prevents resonance associated with – tuned passive
filters at the fifth and seventh harmonic frequencies.
• It requires significantly less system study and system
engineering cost.
• It allows retrofit applications with existing tuned passive
filters at load sites.
II. HPAF SYSTEM IMPLEMENTATION
Fig. 1 shows the HPAF system. It consists of fifth and
, , and
seventh – tuned filter branches given by ,
, respectively. An optional high-pass filter, as shown in
Fig. 1, can be used to attenuate higher order harmonic current.
The nonlinear load is a typical six-pulse thyristor or diode
rectifier front end with dominant fifth and seventh harmonic
load current. Note that the nonlinear load can also be a 12pulse diode/thyristor rectifier with corresponding eleventh and
thirteenth tuned passive filters.
The fifth and seventh square-wave active filter inverters are
connected in series with the fifth and seventh – filters by
coupling transformers, respectively. Transformer coupling is
required to reduce dc-bus ripple and to match the current rating
and voltage rating of the inverter semiconductor devices for
better device utilization. Cost optimization among transformers, dc capacitor, and power electronics devices can be done
depending on the manufacturer’s cost structure and emphasis.
Passive filters are often mistuned due to typical 10%
component tolerances, component variation resulting from
aging, temperature rise, and out-of-specification inductors.
Hence, field retuning is often required. The var consumption of
the load determines the total capacitance of the passive filter.
Due to nonlinearities in the utility system and neighboring
nonlinear loads, supply voltage usually contains harmonic
distortion. At 480 V, 1%–3% of voltage harmonic distortion is
typical. IEEE 519 allows maximum voltage distortion at 5%,
with no individual harmonic component exceeding 3%.
III. HARMONIC ISOLATION WITH
SQUARE-WAVE-INVERTER-BASED HPAF SYSTEM
The equivalent circuit of the HPAF system shown in Fig. 1
at the fifth harmonic frequency is shown in Fig. 2.
If harmonic isolation at the fifth harmonic frequency is
achieved between the supply and the load, i.e., under the assumption that the fifth harmonic component of supply current
is equal to zero, the fifth harmonic filter current can be
expressed as
(1)
where
(2)
(3)
where
represents the fundamenNotice that
tal frequency. This is because the fifth harmonic current generated by the six-pulse rectifier load is in negative sequence.
CHENG et al.: CONTROL OF SQUARE-WAVE INVERTERS
461
represents the fifth harmonic voltage component of the
represents the fifth
fifth harmonic active filter inverter.
harmonic sideband voltage generated by the seventh harmonic
active filter inverter.
To prevent the fifth harmonic current from flowing into the
supply, the fifth harmonic voltage at the load terminal
has to “track” the fifth harmonic component of supply voltage
:
(4)
Hence, the required fifth harmonic voltage component of the
active filter inverter is given as
(5)
Based on (1), (4), and (5), the active filter inverter (connected in series with the fifth – tuned filter) can achieve
harmonic isolation at fifth harmonic frequency by generating
the following fifth harmonic voltage:
(6)
Equation (6) shows the feasibility of achieving harmonic
isolation with the proposed HPAF system. Note that, for the
is small (ideally zero) and is
fifth – tuned filter,
determined by the quality factor
of the filter. The first term
has
of (6) implies that the active filter inverter voltage
to achieve harmonic isolation at the fifth harmonic
to track
frequency. Tuned passive filters also reduce the required rating
of the active filter inverter, since both the second and third
term of (6) will approach zero. It also indicates that the fifth
harmonic sideband voltage of the seventh harmonic active
filter inverter
does not have a significant effect on the
is
harmonic isolation at the fifth harmonic frequency if
small.
IV. CONTROL STRATEGY
A new control strategy, as shown in Fig. 3, is proposed
for the HPAF system implemented with square-wave inverters
to achieve harmonic isolation at dominant fifth and seventh
harmonic frequencies, even in the presence of supply voltage
harmonic distortion. The proposed controller is based on the
SRF transformation and can be divided into the following three
parts, as shown in the controller block diagram in Fig. 3:
• feedforward;
• feedback;
• dc-bus control.
These three subcontrollers are described in the following
subsections, respectively, for the fifth harmonic square-waveinverter-based active filter. A similar controller is employed to
achieve harmonic isolation at the seventh harmonic frequency
by another square-wave active filter inverter connected in
series with the seventh harmonic – filter.
A. Feedforward Control
Feedforward control is to provide active tuning to correct
mistuning of the passive filter, if any, and to provide tracking
of the supply voltage harmonic distortion to achieve harmonic
isolation at the fifth harmonic frequency, as given in (6).
Active tuning is required because passive filter component
values change due to temperature change or partial failure
of capacitor cans. Supply voltage harmonic distortion also
varies dynamically due to a change of ambient nonlinear load
and a change of utility circuit configuration; thus, tracking is
required.
1) Active Tuning: The first component of the feedforward
controller is to provide active tuning of the passive filter. The
and
are based on
tuning voltage commands
the active impedance proposed in [17] and [18] as shown in
the Feedforward block of Fig. 3. Three-phase fifth harmonic
– filter currents
, and
are measured and
transformed into fifth harmonic frequency SRF quantities
and
. DC components of
and
, indicated by
and
, respectively, represent the fifth harmonic component
and are extracted by low-pass filters. The process of
of
SRF transformation and low-pass filtering is applied to load
and
to obtain
terminal voltage
and
, which represent the fifth harmonic component
of the three-phase load terminal voltages
, and
. The active impedance command
and
are
calculated from
and
:
(7)
(8)
and
are calculated according to (7) and (8)
before the active filter inverters are started.
is calculated
The active tuning voltage command
as follows and shown in Fig. 3:
(9)
and
, the mistuning of the pasBy injecting
sive filter will be corrected. Consequently, the fifth harmonic
component of the load current will be constrained in the fifth
harmonic filter branch. In addition, the fifth harmonic sideband
voltage of the seventh harmonic active filter inverter will not
interfere with the harmonic isolation at the fifth harmonic
frequency and also will not result in an increased voltage
rating of the fifth harmonic active filter inverter, as discussed
in Section III.
2) Tracking of Supply Harmonic Voltage Distortion: Active
tuning of mistuned passive filters by active filter inverter
voltage is not sufficient to guarantee harmonic isolation in
the presence of supply voltage harmonics, as shown by (6).
For example, the presence of fifth harmonic supply voltage
will result in overloading of the fifth harmonic – filter.
Hence, a second component of the feedforward controller is
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 3, MAY/JUNE 1998
Fig. 3. Controller block diagram.
required to provide “tracking” of the supply voltage harmonic
distortion. This “tracking” voltage achieves zero fifth harmonic
current in the supply and also prevents overloading of the
tuned fifth harmonic – filter in the presence of supply
voltage harmonic distortion.
The fifth harmonic current in the supply can be eliminated
if the following condition is met:
(10)
and
are dc quantities of – components of
, and
under SRF rotating at
.
and
represent the fifth harmonic component of supply voltages
,
, and
.
and
represent the fifth harmonic
component of
, and
.
where
Since the voltage drop across the fifth harmonic – filter
at the fifth harmonic frequency is canceled by the active tuning
voltage command
, superimposing
given in
(11) onto
will meet the criterion of (10):
(11)
Active tuning voltage command
and active tracking voltage command
are added together to form
the feedforward voltage command
, as shown in Fig. 3.
The feedforward voltage command will eliminate the fifth harmonic component in the supply current and achieve harmonic
isolation at the fifth harmonic frequency. The feedforward
command improves the dynamic performance of the HPAF
system.
CHENG et al.: CONTROL OF SQUARE-WAVE INVERTERS
B. Feedback Control
Feedback control is to improve the robustness of the active filter system, so that its performance is insensitive to
system parameter variations and any error in the feedforward
command. The Feedback block of Fig. 3 shows the feedback
controller of the HPAF system. The feedback controller employs PI regulators to drive the fifth harmonic component of
, and
to zero to achieve harmonic
supply currents
isolation at the fifth harmonic frequency.
, and
are measured and transSupply currents
. Under the SRF, the fifth
formed into SRF rotating at
harmonic current component is transformed into dc values,
while all the other harmonic components are transformed into
ac values. Low-pass filters are used to extract the dc values,
,
which represent the fifth harmonic component of
and
, without any phase delay [2], [5], [17]. This is an
advantage, since most other controllers, such as notch-filterbased implementations, will introduce significant phase delay
to the extracted information. The low-pass filtered values
and
are compared with the reference values
and
, which are both zero, in order to achieve harmonic
isolation between the supply and load. PI regulators generate
and
from the
the feedback voltage command
resulting current error to achieve harmonic isolation at the
fifth harmonic frequency.
,
and feedback
Feedforward voltage command
,
are added to form the fifth
voltage command
and
for the fifth
harmonic voltage reference
harmonic active filter inverter.
An inverse SRF transformation at the same rotation frequency as the previous forward transformation is applied
and
to generate corresponding three-phase
to
, and
, which
inverter voltage commands
are then used to generate square-wave inverter gate signals, as
explained in Section IV-D.
C. Square-Wave Inverter DC-Bus Control
A dc-bus control scheme shown in the DC bus control block
of Fig. 3 is to achieve the following:
• dynamically generate the inverter dc-bus voltage reference
in response to the fifth harmonic voltage
references
and
of the fifth harmonic active
filter inverter;
• regulation of the inverter dc-bus voltage during transient;
• achieve power balancing of the inverter dc bus between
the fifth harmonic and fundamental frequency at steady
state.
Inverter dc-bus voltage reference
is derived from the
magnitude of the fifth harmonic voltage reference of the
active filter inverter
and
. The gain factor
is for normalization. The measured inverter dc-bus voltage
and inverter dc-bus voltage reference
are fed into
a PI regulator for dc-bus regulation. The measured dc-bus
voltage is low-pass filtered to attenuate the 360-Hz ripple due
to the fundamental component of the filter current. This avoids
possible harmonic interaction among the active filter inverter,
the utility, and the nonlinear load.
463
The required power flow to regulate inverter dc-bus voltage
is established at fundamental frequency. The active filter inverter is controlled to generate fundamental frequency voltages
(
and
, as shown in Fig. 3) in phase (or out of
phase) with the fundamental frequency current
and
in the fifth harmonic filter branch to establish the required
power flow for inverter dc-bus regulation.
As shown in Fig. 3, the fifth harmonic filter current
, and
are measured and transformed into
and
under the SRF rotating at . The dc values
and
extracted by low-pass filters represent the fundamental
,
, and
.
and
are multiplied
component of
by the output of the dc-bus controller PI regulator to generate
the inverter fundamental voltage command
and
.
and
An inverse SRF transformation is applied to
to form the three-phase fundamental inverter voltage
,
, and
. Inverter gating signals
commands
are derived from the comparison of the inverter fundamental
, and
with the fifth
voltage commands
, and
. The
harmonic carrier waveforms
carrier signals are synchronized to
, and
,
respectively, but out of phase, in order to accommodate the
minus sign in the comparison process with the fundamental
reference signals. The above modulation process will generate
desired fifth harmonic voltage for harmonic isolation and
desired fundamental voltage for inverter dc-bus voltage
control, as given in Section IV-D.
During transient, inverter dc-bus voltage reference
varies according to
and
. The dc-bus controller
will regulate the inverter dc-bus voltage by charging or discharging the inverter dc-bus voltage through the fundamental
remains
frequency component. At steady state, although
constant, a steady power flow at the fifth harmonic frequency
still exists. Assuming that harmonic isolation at the fifth
harmonic frequency is achieved, the fifth harmonic voltages
generated by the fifth harmonic square-wave active filter
and
are equal to
and
,
inverter
respectively. The fifth harmonic component of the load current
will be forced into the fifth harmonic filter branch because
the fifth harmonic – filter is actively tuned, and harmonic
isolation at the fifth harmonic frequency is achieved. Real
power flow of the active filter inverter at the fifth harmonic
frequency can be expressed as
(12)
At steady state, the inverter dc-bus controller will provide power balancing by exchanging real power between
the fifth harmonic frequency component and the fundamental
frequency component.
The dc-bus voltage regulation and power balancing must be
carried out at the fundamental frequency rather than at any
other harmonic frequencies to avoid harmonic interaction between the active filter inverter and supply/load. The harmonic
isolation function of the system will not be affected by adding
fundamental voltage in the inverter output, because they are
independent of the harmonic voltages generated by the active
filter inverter [19].
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 3, MAY/JUNE 1998
Fig. 4. Conventional sine-triangle PWM.
This control requirement is the key to the operation of the
proposed HPAF system and controller. DC-bus regulation and
the power balancing function of this controller eliminates the
need for any energy storage device or additional power supply
requirement in such systems.
The injection of fundamental voltage has no significant
effect on the reactive power compensation, because it is very
small compared to the fundamental voltage across the passive
.
filter capacitor
D. Synthesis of Inverter Output Voltage with Dominant
Harmonic Frequency Switching
The proposed SRF controller directly generates inverter
voltage references and enables implementation of the active
filter by low switching frequency inverters, including squarewave inverters operating at dominant harmonic frequencies.
Two voltage components are generated by the proposed controller to achieve a harmonic isolation function in a selfsufficient manner:
to achieve harmonic isolation at the
to control the inverter
fifth harmonic frequency and
dc-bus voltage and to balance the power flow of the active
and
will be generated by a
filter inverter.
“modified” sine-triangle modulation.
Fig. 4 shows the waveforms and spectrum of the conventional sine-triangle PWM. All three phase references are
modulated by a common triangular carrier. The line-neutral
output voltage of a three-legged inverter controlled by this conventional sine-triangle PWM will not generate any component
at the triangular carrier frequency
due to its zero-sequence
nature, as shown in Fig. 4. The output has only sideband
, where
components around the carrier frequency at
is the reference signal frequency.
A “modified” sine-triangle PWM is used to synthesize the
and fundamental voltrequired fifth harmonic voltage
for the proposed HPAF system. Three individual
age
, and
are synchronized to the
carriers
three-phase signal
, and
, but out of phase,
as explained in Section IV-C. Hence, the triangular carriers are
phase displaced by 120 at the fifth harmonic frequency. The
reference waveforms are the three-phase signals
,
and
, as shown in the controller block diagram in Fig. 3.
,
The three-phase fundamental voltage references
are compared with the three triangular carriers
and
, and
, respectively, to generate the gating
signals of the fifth harmonic active filter inverter.
Fig. 5(a) shows that modulated line-neutral output voltage
contains the required voltage components at the fundamental
frequency and, also, at the fifth harmonic frequency, due to the
use of three-phase fundamental references and three triangular
carrier phase displaced by 120 . The magnitude and phase
of the fundamental component is controlled by the magnitude
and phase of the fundamental frequency references. The magis
nitude of the component at carrier frequency
. The phase
proportional to the inverter dc-bus voltage
of component at carrier frequency is controlled by the phase
of the triangular carriers. Hence, this modulation strategy
is capable of generating independent fifth harmonic voltage
and the fundamental voltage required to achieve harmonic
isolation at the fifth harmonic frequency, inverter dc-bus
voltage control, and power balancing of the active filter
inverter. This modulation strategy enables harmonic frequency
switching for the active filter inverters.
does not exist because of
The sideband at
its zero-sequence nature. The sideband at
is about 2%–5% of the component at , depending on the
modulation index of the fundamental frequency reference signals based on the derivation of Bessel function approximation
given in [20]. The sideband at the seventh harmonic frequency
is small and does not have significant interference to the
harmonic isolation at the seventh harmonic frequency achieved
by the seventh harmonic active filter inverter.
Fig. 5(b) shows the modulation process of the seventh
harmonic active filter inverter. Three carriers phase displaced
by 120 at the seventh harmonic frequency and three-phase
fundamental references are used. The sideband at
is small and does not interfere with the harmonic isolation
at the fifth harmonic frequency. The sideband at
does not exist, due to its zero-sequence nature.
Both fifth harmonic active filter inverter and seventh harmonic active filter inverter generate sideband components at
CHENG et al.: CONTROL OF SQUARE-WAVE INVERTERS
465
(a)
(b)
Fig. 5. Proposed sine-triangle PWM. (a) Fifth harmonic active filter inverter. (b) Seventh harmonic active filter inverter.
the fundamental frequency. Bessel function approximation
shows the magnitude will be very small and does not have
any significant effect on the fundamental voltage component
of both active filter inverters.
An alternative modulation strategy for square-wave inverters with fixed dc-bus voltage applicable for the HPAF system
has been proposed by the authors in [13]. In this scheme,
notches are introduced to control the inverter output voltage
and can be implemented by phase-shift control of two threephase inverters.
V. ACTIVE FILTER INVERTER VOLTAGE
COMPONENTS OVERVIEW
Fig. 6 shows the various voltage components generated by
the SRF controller for the fifth harmonic active filter inverter
will correct
of the HPAF system shown in Fig. 1.
the mistuning of the fifth harmonic – filter.
,
combined will make
approximately zero. Active
and
tuning will force the fifth harmonic component of the load
current into the fifth harmonic filter branch and also prevent
the fifth harmonic sideband voltage of the seventh harmonic
active filter inverter from affecting the harmonic isolation at
the fifth harmonic frequency, as shown in (6).
is
controlled to follow the fifth supply voltage harmonics
to
Fig. 6. Active filter inverter voltage components.
suppress the fifth harmonic current caused by supply voltage
harmonics. Thus, harmonic isolation at the fifth harmonic
frequency is achieved.
and
are combined
to form the feedforward command
of this controller.
is generated by PI closed-loop regulators on the fifth
harmonic component of the supply current. Feedback control is
required to improve the robustness of the HPAF system against
parameter variations and error of the feedforward command.
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 3, MAY/JUNE 1998
TABLE I
DOMINANT HARMONIC COMPONENT OF THE SIX-PULSE FRONT-END CURRENT
PARAMETERS
OF
TABLE II
PASSIVE FILTER COMPONENTS
Fig. 7. Simulation model.
Feedfoward command
and feedback command
are added to form the total fifth harmonic voltage command
of the fifth harmonic active filter inverter.
is
to regulate inverter dc-bus voltage during transient according
derived from
. At
to dc-bus voltage reference
is to create a power flow at fundamental
steady state,
frequency to balance the power flow created by the fifth harand
monic component of the fifth harmonic filter branch
generated by the fifth harmonic
fifth harmonic voltage
active filter inverter, as given in (12).
represents the
sideband voltage components of the fifth harmonic active filter
is generated as a result of the modulation
inverter.
process of the three-phase fundamental frequency references
and three-phase fifth harmonic frequency triangular carriers.
contains small component at the seventh harmonic
frequency, but does not have any significant effect on the
harmonic isolation at the seventh harmonic frequency achieved
by the seventh harmonic active filter inverter.
The fifth harmonic active filter inverter generates the above
fifth harmonic frequency voltage components to achieve harmonic isolation at the fifth harmonic frequency and fundamental frequency voltage component to achieve inverter
dc-bus regulation and power balancing of the active filter
inverter. The output voltage of the seventh harmonic active
filter inverter contains the same voltage components to achieve
harmonic isolation at the seventh harmonic frequency, inverter
dc-bus voltage regulation, and power balancing of the seventh
harmonic active filter inverter.
VI. SIMULATION RESULTS
Fig. 7 shows the simulation model.
The system parameters are as follows.
Supply: 480 V (line to line, rms) with 3% of the fifth
and seventh harmonic distortion. Typically, measured supply
voltage distortion at 480 V is 1%–3%, due to nonlinearities of
the utility system and ambient nonlinear loads. The IEEE 519
harmonic standard allows maximum voltage distortion of 5%,
with no individual harmonic component exceeding 3%.
Load: 300 KVA, 370 A (rms) six-pulse front end, with
dominant harmonic current given in Table I.
Active Filter:
• coupling transformer turn ratio
20 : 1 (inverter side :
passive filter side) for both active filter inverters;
• dc-bus capacitor 5000 F for both active filter inverters.
Passive Filter: The component values of the fifth and seventh harmonic – filters are given in Table II.
The short circuit ratio (SCR) is 19.9. The IEEE 519 standard
requires the THD of the supply current to be within 5% (4%
for the fifth and seventh harmonic components).
A. Simulation Results Under the Presence of Supply Voltage
Harmonics and Mistuned Passive Filters
Fig. 8 shows the simulation results of the system with
supply voltage harmonic distortion (3% of the fifth and seventh
harmonic) and mistuned passive filters. Supply current
shows large distortion, with THD of 17.8% due to the supply
voltage harmonic distortion before the active filters are started.
also shows distortion due to harmonic distortion of
supply current. Both the fifth harmonic active filter inverter and
the seventh harmonic active filter inverter are started at
s. After the system reaches steady state, the distortion of supply
current is reduced (THD 4.77%). The spectra of show
that the fifth and seventh harmonic current components meet
IEEE 519 harmonic current limits (shown by the dashed line)
after the active filter inverters are started. The supply current
still contains higher order harmonic components, as shown
in the time-domain waveform and spectra of . The existing
fifth and seventh harmonic – filters usually provide enough
attenuation for higher order harmonic current to meet IEEE
519 harmonic standard. A high-pass filter can be added if
necessary, as shown in Fig. 1.
Spectra of
show that the fifth and seventh harmonic
are equal to the supply voltage harmonic
components of
distortion at fifth and seventh harmonic frequencies (
V). It shows that harmonic isolation is achieved
at fifth and seventh harmonic frequencies at steady state in the
presence of supply voltage harmonic distortion.
The inverter output voltage waveforms
and
are
very similar to six-step waveforms, except that they both
contain small magnitude of 60-Hz component for dc-bus
voltage control and power balancing.
,
(dashed line),
, and
(dashed line) show the dc-bus voltages and the
dc-bus voltage references of the fifth and seventh harmonic
active filter inverters. The control of the dc-bus voltage is
achieved by injecting the fundamental voltage component
from the inverter to form a power flow with the fundamental
component of the filter current. The simulation results show
CHENG et al.: CONTROL OF SQUARE-WAVE INVERTERS
467
Fig. 8. Simulation results with mistuned passive filter and supply voltage harmonic distortion. Time-domain waveforms: supply current is , load current
iload , filter currents if5 and if7 , load voltage vload , and inverter dc-bus voltages vdc5 and vdc7 ; frequency-domain spectra: supply current is , load
current iload , and load voltage vload .
that the actual dc-bus voltages track their dc-bus voltage
references within 5% error.
B. System Response to Load Change
Fig. 9 shows the simulation results of the system with a
50% load increase ramping up from
s to
s.
The system parameters remain the same as in the previous
show less
simulation. The time-domain waveforms of
distortion at steady state, and the spectra of
also indicate
that the fifth and seventh harmonic current components are
suppressed within the requirement of the IEEE 519 harmonic
standard at steady state. The harmonic isolation function is not
affected by the load change. The dc-bus voltage references of
the active filter inverters increase, because higher fifth and
seventh harmonic voltages are required to achieve harmonic
isolation at the fifth and seventh harmonic frequencies.
and
track their references
(dashed line) and
(dashed line) closely throughout the time period of the load
change, and the dc-bus controllers maintain the dc-bus voltages
without being disturbed by the load change.
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 3, MAY/JUNE 1998
Fig. 9. Simulation results under load change between t = 2:0 s and 2:5 s. Time-domain waveforms: supply current is , load current iload , filter currents if5
and if7 , load voltage vload , and inverter dc-bus voltages vdc5 and vdc7 ; frequency-domain spectra: supply current is , load current iload , and load voltage vload .
VII. DISCUSSIONS
A. Comparison With Controller Proposed by Takahashi
A controller has been proposed by Takahashi [14] for the
HPAF system implemented by square-wave inverters. The
main objective of this controller is to dynamically cancel
the voltage drop of the passive filter resistance at dominant
harmonic frequencies, such that the quality factor ( ) of
the passive filter becomes infinite. If the passive filter is
tuned, then this controller will eliminate the fifth and seventh
. This will not meet the IEEE
harmonic component in
519 harmonic standard in the presence of the supply voltage
harmonic distortion, because the harmonic component in the
supply current
is defined by the following:
(13)
(14)
The point-of-common-coupling (PCC) transformer usually
has 5% leakage inductance. This is not capable of suppressing
the fifth and seventh harmonic component of the supply
CHENG et al.: CONTROL OF SQUARE-WAVE INVERTERS
Fig. 10.
469
Simulation results of Takahashi’s controller in the presence of supply voltage harmonic distortion.
current within 4% under the presence of 1%–3% of supply
voltage harmonic distortion at the fifth and seventh harmonic
frequencies [13]. This is the major limitation of Takahashi’s
controller in practical application.
The active filter inverter in [14] is controlled to emulate
a negative resistor. This results in real power flow into the
inverter and requires power balancing of the dc bus. The
control of the active filter inverter as a negative resistor to
achieve infinite factor of the tuned passive filter in a hybrid
active filter system has been proposed in [21]. The emulation
of a negative resistor by a parallel active filter inverter to
provide damping is given in [22].
Figs. 10 and 11 show the simulation results of Takahashi’s
controller and the proposed SRF-based controller with tuned
passive filters and 3% of fifth and seventh harmonic distortion
of supply voltage. Before the active filter inverters are started,
has severe harmonic distortion, due to the
supply current
fifth and seventh harmonic distortion of the supply voltage in
both cases. The fifth and seventh component of exceed the
IEEE 519 harmonic standard, as indicated in the spectra. After
the active filter started at
s, Takahashi’s controller
eliminates the voltage drop across the passive filter resistance
at the following dominant harmonic frequencies:
(15)
(16)
The spectrum of
shows that the fifth and seventh harmonic components are cancelled by the active filters, but
still exhibits severe harmonic distortion, as shown in the timedomain waveform, and its spectrum shows that the fifth and
seventh harmonic components still exceed IEEE 519. Note
that, in the simulation results of Takahashi’s case, the inverter
voltages
and
are generated with constant dc bus.
470
Fig. 11.
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 3, MAY/JUNE 1998
Simulation results of the proposed controller in the presence of supply voltage harmonic distortion.
The magnitude of the inverter output voltage is controlled by
introducing notches into the inverter output voltages.
In contrast, the proposed SRF controller successfully
achieves harmonic isolation at the fifth and seventh harmonic
frequencies by eliminating the fifth and seventh harmonic
components in . At steady state,
(17)
(18)
In the absence of supply voltage harmonic distortion, the
proposed SRF controller corrects the mistuning of the passive
filter, as also achieved by Takahashi’s controller [13]. For the
fifth harmonic component, both controllers generate
to correct mistuning of the fifth harmonic – filter. The
tracking voltage command
and feedback voltage
command
of the SRF controller is close to zero, because
of the absence of supply voltage harmonic distortion. The
voltage component of the SRF controller achieves
dc-bus voltage control and power balancing. The seventh
harmonic active filter will operate in the same fashion to
achieve harmonic isolation at the seventh harmonic frequency.
The proposed SRF controller, as shown in Fig. 3, balances
the real power flow at harmonic frequencies by introducing
another real power flow at fundamental frequency, as shown
W is caused by the fifth harmonic
in Fig. 12.
output voltage of the fifth harmonic active filter inverter
and the fifth harmonic filter current. This power flow at
the fifth harmonic frequency is balanced mostly by another
W introduced by the fundamental
power flow
output voltage of the active filter inverter.
also contributes slightly to the power balancing. It is caused
by higher order harmonic current from the load and active
filter inverter switching sideband voltages. It is relatively
and
. The total power flow
small compared to
CHENG et al.: CONTROL OF SQUARE-WAVE INVERTERS
471
•
Fig. 12.
Inverter power flow of the proposed HPAF system and controller.
TABLE III
RATING OF ACTIVE FILTER INVERTERS OF THE PROPOSED HPAF SYSTEM
•
•
into the active filter inverter is zero, which does not cause
charging/discharging of the inverter dc-bus capacitor.
B. Active Filter Inverter Ratings
Table III shows the ratings of the active filter inverters of
the proposed HPAF system. The ratings are affected by the
supply voltage harmonic distortion, because the active filter
inverters have to track supply voltage harmonic distortion in
order to achieve harmonic isolation as shown in (6).
Tuning of passive filters also affects the rating, because the
active filter inverters have to generate active tuning voltage
to correct the mistuning of passive filters, as shown in the
controller block diagram in Fig. 3. If the passive filters are
tuned at dominant harmonic frequencies, then the rating of the
active filter inverters will be reduced significantly.
The small rating and square-wave operation of the active filter inverters increase the practical viability and cost
effectiveness of the proposed HPAF system for high-power
nonlinear loads. For a 100-MW nonlinear load, 1.8- and 1.4MW square-wave inverters are required, based on 10%
mistuned passive filter components and 3% of fifth and seventh
supply voltage harmonic distortions. Considerable reduction in
the active filter inverter rating will be obtained with reduced
supply voltage harmonic distortion.
VIII. CONCLUSIONS
• An HPAF system using square-wave inverters has been
presented to provide supply-load harmonic isolation at
dominant harmonic frequencies and to meet IEEE 519
•
harmonic standards for high-power applications. The proposed strategy is general and applicable to six-pulse
rectifier loads and 12-pulse rectifier loads. Small-rated
active filter inverters, (1%–2%) of the load rating, provide
a practically viable and cost-effective solution for highpower nonlinear loads up to 100 MW.
A new SRF controller for an HPAF system using squarewave inverters was proposed to achieve harmonic isolation between the supply and load at dominant harmonic
frequencies. The proposed controller also achieves power
balancing of the inverter dc bus by exchanging energy
between the fundamental and dominant (fifth or seventh)
harmonic frequencies. This is required due to real power
flow at dominant harmonic frequency caused by the active
filter inverter operation. This controller design allows the
proposed HPAF system to operate in a self-sufficient
manner, without any energy storage devices or power
supplies, which further enhances the viability and cost
effectiveness of the proposed HPAF system.
The proposed controller does not have the usual requirement of high-bandwidth inverters associated with other
active filter systems and enables the use of low-switchingfrequency inverters, including square-wave inverters.
This scheme is applicable to harmonic compensation
of loads connected to stiff supply systems. Stiff supply
systems are particularly difficult for the design of tuned
passive filters for industrial loads, since they require sharp
tuning and high quality factor, so as to divert/sink a
significant portion of the load current harmonics. The
proposed controller dynamically tunes the passive filter
and achieves harmonic isolation at dominant harmonic
frequencies, as well.
Proposed use and control of square-wave inverters for
harmonic isolation between the supply and load at dominant fifth and seventh harmonic frequencies has been
validated by simulation results. The operation under load
changes has also been verified. Square-wave-inverter implementation increases the cost effectiveness and viability
of the HPAF system for high-power nonlinear loads up
to 100 MW. Main features include the following.
— It accomplishes harmonic isolation at dominant harmonic frequencies with small-rating inverters under
mistuned passive filters, supply voltage harmonic
distortion, and load changes.
— Power flow associated with the inverters is balanced
and inverter dc-bus voltage can be supported by
capacitors, hence, no energy storage devices or
power supplies are required.
— There is better efficiency for high-power active
filter inverters, which are devoid of high-frequency
switching losses, as in a PWM inverter.
— Higher order harmonic components (eleventh, thiteenth, etc.) are smaller and sufficiently attenuated
within the limits of IEEE 519 by the passive filter.
A high-pass filter can be added, if necessary.
— The proposed controller can be implemented by
simple and cost-effective analog/digital hardware or
by a digital signal processor.
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 3, MAY/JUNE 1998
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Po-Tai Cheng received the B.S. degree in control
engineering from National Chiao-Tung University,
Hsinchu, Taiwan, R.O.C., in 1990 and the M.S.E.E.
degree in electrical engineering from the University
of Wisconsin, Madison, where he is currently working toward the Ph.D. degree.
His main research interests are active filters,
utility applications of power electronics, and power
quality issues.
Subhashish Bhattacharya received the B.E.
(Hons.) degree in electrical engineering from the
University of Roorkee, Roorkee, India, in 1986
and the M.E. degree in electrical engineering from
the Indian Institute of Science, Bangalore, India,
in 1988. He is currently working toward the Ph.D.
degree at the University of Wisconsin, Madison.
His primary areas of interest are active filters,
resonant link inverters, utility applications of power
electronics, drives, and control techniques.
Deepak D. Divan received the B.Tech. degree from
the Indian Institute of Technology, Kanpur, India,
in 1975 and the M.S. and Ph.D. degrees from
the University of Calgary, Calgary, Alta., Canada,
in 1979 and 1983, respectively, all in electrical
engineering.
He has been a Professor at the University of
Wisconsin, Madison, since 1985 and is an Associate Director of the Wisconsin Electric Machines
and Power Electronics Consortium (WEMPEC). He
is currently on leave from the university and is
President and CEO of Soft Switching Technologies Corporation, Middleton,
WI, a manufacturer of power conversion equipment. He is the holder of 20
issued and pending patents, and has authored over 90 technical publications,
including several prize-winning papers.