Parallel Interleaved Inverters for Reactive Power and Harmonic by dyr60218

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									                                                     Parallel Interleaved Inverters
                                           for Reactive Power and Harmonic Compensation

                 L. Asiminoaei1, E. Aeloiza2, J. H. Kim3, P. Enjeti2, F. Blaabjerg1, L. T. Moran4, S. K. Sul3
     1)                                       2)                                          3)                                             4)
      Institute of Energy                        Department of Electrical                    Engineering and Computer                     Department of Electrical
         Technology,                                 Engineering,                                    Science,                                  Engineering,
     Aalborg University,                        Texas A&M University,                       Seoul National University,                   University of Concepcion,
    DK-9220, Aalborg SE,                        77843 College Station,                            151-742 Seoul,                               Conception,
          Denmark,                                      Texas,                                        Korea,                                       Chile,
       las@iet.aau.dk,                          eaeloiza@ee.tamu.edu,                        ghks95@eepel.snu.ac.kr                          lmoran@udec.cl
       fbl@iet.aau.dk                             enjeti@ee.tamu.edu                          sulsk@plaza.snu.ac.kr

    Abstract − This article investigates the concept of                                    This movement creates a potential market for high power
paralleling power inverters for reactive power and harmonic                                reactive compensation devices, motivating the production of
compensation. The investigation focuses on a topology that                                 efficient reactive power units. Thereby, the research may be
shares the dc-bus capacitor between two parallel interleaved                               leaned in finding new topologies with cheaper passive
inverters. The advantages of the proposed approach are: i)                                 components, higher power integration, higher redundancy
decreased current ripple or use of lower switching frequency                               and lower EMI [9].
due to the interleaving, ii) reduced stress in dc-link capacitor
due to the shared connection, iii) efficient implementation for
                                                                                               The present work analyzes the application of parallel-
high power applications because of paralleling. Different                                  interleaved inverters for reactive and harmonic current
comparisons between the selected topology and regular power                                compensation. The topology consists of a parallel connection
converters are discussed. Practical tests, on a three-phase 5                              of (two) identical three-phase interleaved PWM inverters,
kVA, 400 V prototype, are presented to validate the analysis.                              sharing the same dc-capacitor as depicted in Fig. 1.
                                                                                           Several issues are presented and discussed in the paper; like
                                                                                           reduction of the switching current ripple, the use of smaller
   Keywords – interconnected power systems; pulse width                                    passive components and the implementation of different
modulated inverters; reactive power; power system                                          modulation strategies to reduce the EMI. The design of the
harmonic; active filters.                                                                  selected topology is discussed by comparing it to regular
                                                                                           power inverters.
                             I. INTRODUCTION                                                   The results obtained show that for the proposed topology
     The demand of high power in power electronics is                                      the line inductors are reduced almost to 60% comparing to a
usually limited by the available semiconductor technology,                                 typical there-phase PWM inverter. Furthermore, if the
due to the maximum allowed current, voltage, losses and                                    topology is to be used for reactive power compensation then
switching frequency. One solution to cope with the required                                the dc-capacitor is reduced to 25%, due to the decrease of
power is to build the power converter from multiple lower                                  dc-current ripple.
power units connected in parallel, either connecting multiple                                  As the present technology in IGBT’s allows for
power switches or multiple inverters in parallel [1]−[3].                                  switching frequencies typically of 10 kHz − 20 kHz, it opens
     This paper discusses the connection in parallel of multiple                           the possibility of a reactive power compensator mainly
inverters. Some arguments to support the paralleling concept                               composed of semiconductors with very small passive
are briefly described such as it is easier to extend the total                             components. Hence, the usage of smaller passive
rated power of the application by simply adding a new                                      components and the possibility of building it as a modular
inverter. The design, production, installation and maintenance                             device makes this topology very attractive for high power
of each inverter become much simpler and flexible.                                         industrial applications.
Furthermore, parallel inverters may be physically
implemented as independent controlled modules, which give
the entire power unit an intrinsic redundancy feature,
providing ride-through functions when a module fails (Fig. 1).
     There are many parallel topologies described in the
literature, for different fields especially where a high power
density integration is required, such as power sources, traction
systems, uninterruptible power supplies [4], power factor
correction circuits and active power filters (APF) [5], [6].
     Regarding the compensation of the reactive power,
different considerations [7], [8] are currently discussed,
proposing that the users supplying reactive power should be
paid since they provide voltage regulation and reduction of                                    Fig. 1. Principle diagram of paralleling n multiple power inverters. All
the power losses.                                                                                               inverters share the same capacitor Cdc.




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Fig. 2. Typical active front-end inverter topology         Fig. 3. Diagram of 2 separated parallel inverters             Fig. 4. Diagram of the analyzed topology with 2
                     (Case-A).                                     with split dc-capacitors (Case-B).                   parallel interleaved inverters sharing the same dc-
                                                                                                                                         capacitor (Case-C).

                        II. ANALYSIS AND DESIGN                                                  TABLE I. Input parameters used in design and testing (see Fig. 5).
    This section gives the design of the selected topology.                                            Parameter                       Symbol      Normalized      Test values
                                                                                                                                                      value
The main focus is put on the line inductance and the dc-                                    Inverter power                               Sinv          1 pu        4.8 [kVA]
capacitor, which are designed based on some initial                                         Line voltage                                 VLL           1 pu          400 [V]
considerations. The assumptions are that the design is                                      Line current (peak)                        Iinv (pk)     1.42 pu        10 [Apeak]
carried out initially for sinusoidal output current and then                                Line current (RMS)                           Iinv          1 pu         7 [ARMS]
after the obtained design is extended for active power filters,                             Current ripple (peak)                      ∆imax       20 %Iinv (pk)    2 [Apk-pk]
where the inverters control non-sinusoidal currents. Both                                   Ratio of current ripple               KIf = ∆imax/Iinv   0.28 pu         0.28 pu
                                                                                            Base impedance                       Zb = VLL/ 3 Iinv      1 pu           33 [Ω]
parallel inverters are running with the same switching
                                                                                            Ratio of line inductors               KLf= 2πf1Lf/Zb         -               -
frequency, and the inverters have the same power rating,
                                                                                            Ratio of common mode coils           KLcm= 2πf1Lcm/Zb        -               -
thus the total output power is equally divided between them.                                DC-voltage                                   Vdc          1.8 pu         700 [V]
Three cases are studied:                                                                    Ratio of dc-voltage                   KVdc =Vdc/VLL       1.8 pu          1.8 pu
    • Case-A − single unit inverter (typical three-phase                                    DC-voltage ripple                          ∆vmax       1-2 % ⋅ Vdc       10 [V]
    inverter as shown in Fig. 2),                                                           Line frequency                                f1             1           50 [Hz]
                                                                                            Switching frequency                          fsw           204         10.2 [kHz]
    • Case-B − parallel connection of 2 interleaved inverters
                                                                                            Ratio of switching freq.               Kfsw = f1/fsw       204             204
    with split dc-capacitors (as in Fig. 3),                                                Duration of zero vector                       t0             -               -
    • Case-C − parallel connection of 2 inverters, both                                     Ratio of zero vector                    Kt0= t0/Tsw          -               -
    sharing the same dc-capacitor (as in Fig. 4).
Several criteria are imposed, for having the same base of                                   A. Line Inductor
comparison between the selected topologies (see Fig. 5 and
Table I): line-to line voltage VLL is set to 1 per unit (pu),                                   The design of the inductor is based on the imposed line
total output power Sinv of 1 pu (consequently the total                                     current ripple, which depends on the existing dc-voltage,
current delivered to the source Iinv of 1 pu), line current                                 modulation strategy and switching frequency as used in (1).
                                                                                            There are different methods to calculate the value of the
ripple is limited to ∆imax, voltage ripple across the dc-
                                                                                            switching current ripple as a function of the modulation
capacitor is limited to ∆vmax.
                                                                                            strategy and the desired line inductor [12]. A previous study
The design is carried on along with different practical tests
                                                                                            [13] investigates a simplified method for calculation of the
on a laboratory setup described in §V. The values of the line
                                                                                            line inductor, based on the equivalent model of the inverter
inductors are 5 % (i.e. 5 mH) for Case-A and 3 % (i.e. 3
                                                                                            in each commutation states. The value of the line inductor Xf
mH) for Case-B and -C. The total line current Iinv is 6 Apeak.
                                                                                            for Case-A is finally obtained as in (3).
                                                                                                                                     di f (t )
                                                                                                                     vs (t ) = L f               + vi (t )                 (1)
                                                                                                                                       dt
                                                                                                                             Vdc ⋅ ∆t    K V ⋅ ∆t
                                                                                                                 ∆imax = 2            = 2 Vdc LL                           (2)
                                                                                                                              3L f          3L f
                                                                                                                           4π KVdc VLL      f   4π KVdc Z b
                                                                                               X (f CASE − A) = ω1 L f =           ⋅      ⋅ 1 =         ⋅
                                                                                                                             3K If   3Iinv f sw   3K If K fsw              (3)
                                                                                                                                          Zb        1/ K fsw


                                                                                                For Case-B and Case–C, the inductor is designed using
                                                                                            the same equation as in (1) separately applied for each
                                                                                            inverter. The total line current is the summation the
                                                                                            individual inverter currents.
       Fig. 5. Imposed criteria used for designing the power inverter.




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                          (A)                                                          (B)                                                              (C)




                          (D)                                                          (E)                                                              (F)
Fig. 6. Measured line currents for a reference current of 6 Apeak reactive current and sinusoidal PWM modulation: A) Case-A, B) Case-B, C) Case-C; D), E),
                                F) harmonic current spectrum for each measured current focused at the switching frequencies.

     It is proven in [13] that the total line current ripple (Ifsum                          effect, since its frequency is given by the switching
in Fig. 3) is reduced due to the interleaving, to a fraction of                              frequency. The amplitude of the cross-currents can be
0.6 times individual inverter’s ripple. Or vice versa, if the                                calculated as in (5).
line current ripple is maintained as imposed in Table I, then                                    Fig. 6 shows the time- respective the frequency domain
the inductors can be reduced by the same amount, as given                                    waveforms of the measured currents for all three cases. The
in (4).                                                                                      line current ripple in Case-B and -C is near the same as the
               X (f
                    Case − C )
                               = X (f
                                      Case − B )
                                                 = 0.6 ⋅ X (f
                                                              Case − A)                      ripple in Case-A, even though the line inductors are
                                                                        (4)
                                                                                             decreased to 60 % in Case-B and -C. The cross-current Icc
     When connecting the inverters in parallel, cross-currents
                                                                                             can also be seen in Case-C.
circulate from one inverter to the other, depending on the
                                                                                                 Different solutions can be found to reduce or eliminate
inverters’ switching states. If the power source is stiff, (i.e.
                                                                                             the cross-currents as like: galvanic isolation transformer [6],
low short-circuit impedance), then the cross-currents in
                                                                                             separate dc-capacitors [15], inter-phase coils on the dc-bus,
Case-B are negligible, because the current ripple generated
                                                                                             higher switching frequency PWM strategies [16].
by each inverter sinks into the grid.
                                                                                             Most of these solutions have different drawbacks, for instance
     However, for Case-C, because there is no galvanic
                                                                                             the galvanic isolation transformer must be designed for higher
isolation between inverters and they share the dc-capacitor
                                                                                             frequency and rated at the total nominal current; the inter-
Cdc, there is a circulation current (referred to as cross-current
                                                                                             phase coils must carry a dc-current which is difficult to design
Icc in Fig. 6C) that occurs due to the opposite zero vectors v7
                                                                                             in respect the core saturation limits; the increase in the
and v0 [13]. The cross-current Icc is the natural consequence
                                                                                             switching frequency may also be limited in practice.
of interleaving the carriers by 180°.                                                            The solution applied here is the use of common mode
     There are 2 important effects of the cross-current. The                                 coils (Lcm in Fig. 4) to provide a high impedance path for
first effect is the increase of the current peak value in each                               circulating cross-currents.
inverter as it will described next. The second effect is the                                                                                            ∆icc (t )
risk that may appear in the case of a small unbalance                                                          Vdc = ( L f 1 + L f 2 + Lcm1 + Lcm 2 )                    (5)
                                                                                                                                                         t0 (t )
between inverters (e.g. different line inductances, different
                                                                                             where: Vdc is the voltage on the dc-capacitor, the Lf1, and Lf2 are the values
duty cycles), which determines a lower frequency current                                     of the line inductors, ∆icc is the amplitude of the cross-current developed
circulating between inverters as a zero-sequence current                                     during the interval t0 which depends on the duration of the zero vectors.
[14]. Since the zero-sequence current is of a low frequency,                                                2 3π KVdc Kt 0 VLL f1             3π KVdc K t 0
a proper controller designed for the zero-axes can remove it.                                      I cc =                              =                       I inv
                                                                                                            2( K Lf + K Lcm ) 3Z b f sw ( K Lf + K Lcm ) K fsw           (6)
However, a current controller cannot mitigate the first                                                                         I inv   1/ K fsw




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   Fig. 7. Cross-current Icc as a function of both           Fig. 8. Currents and inductances in Case-C as      Fig. 9. Evaluation of the weight and volume of 2
  inductances: inverter inductance Lf respective           functions of the inverter power a) Line current and inductors of 3 % (Case-C) and an inductor of 5 %
           common mode inductance Lcm.                        cross-current. b) Line inductance (3 %) and      (Case-A) for different values of the inverter current
                                                                       common mode inductance.                                          If.

    As indicated in (6), the cross-current depends on the size                             However, as Case-C has supplementary common mode
of both, line inductor (Lf) and the installed common-mode                                  inductors, their weight and volume must also be considered.
inductor (Lcm). Fig. 7 presents how the cross-current                                      It is expected that the common-mode inductors may not be
develops along with the line inductance. It can be seen that a                             very large since their core must be designed mainly for
larger common-mode inductor can effectively reduce the                                     common-mode signals and not the nominal inverter current.
cross-current. For instance, for a value of 3 % line                                       On the other hand the use of common-mode coils is a
inductance alone, the cross current is about 0.3 pu, while                                 common practice in industry for protecting the inverters
installing an additional common-mode inductance of 3 %                                     against common mode noise signals from the grid, thus such
reduces the cross-current to near 0.1 pu.                                                  inductors are used anyway.
    Another calculation example of the common-mode
inductor is given in Fig. 8. Here the size of the common-                                  B. DC-link Capacitor
mode inductor is selected based on the desired value of the
cross-current. For a cross-current Icc of 15 % out of the total                                When the inverter provides only reactive current the
inverter current, the common mode inductor has almost the                                  capacitor may be sized based on the dc-voltage ripple
same absolute value as the line inductor. If one designs the                               caused by the switching frequency. As a general approach
application for lower cross-current, then the value of the                                 the minimum required dc-capacitor is determined as:
common-mode inductor should be highly increased. For an                                                 t2


allowed cross-current value of only 5 %, the common-mode                                                ∫i   dc   (t ) dt
                                                                                                                            , idc (t ) = sa (t ) ⋅ ia (t ) + sb (t ) ⋅ ib (t ) + sc (t ) ⋅ ic (t ) ,
                                                                                           Cdc ,min =   t1
inductor is almost 3 times higher.                                                                       ∆vmax (t )                                                                                    (7)
    As previously calculated, the line inductors are reduced                               where idc(t) and vmax(t) are the capacitor current and voltage ripple; sa,
to 60 % by interleaving the carriers, in order to keep the                                 sb, sc are the switching functions, and ia(t), ib(t), ic(t) are the line
same amplitude for the line current ripple. However, as                                    currents.
Case-A uses a single three-phase inductor, while Case-B and                                    If some simplified assumptions are considered such that
-C use two pairs, the design demands more analysis if this is                              the integration time interval (t1, t2) is half of the switching
economically feasible. In practice, the weight, size, and cost                             period Tsw and the dc-current (Idc) is half of the peak value of
of the inductors are of a major concern. They all depend on                                the nominal line current [12], then the minimum required
many parameters, like the magnetic core, type of windings,                                 dc-capacitor for Case-A is:
manufacturing technology, desired tolerance and required                                                             1 2 I inv          Tsw
                                                                                                 ( Case − A)                                           1              1
operating conditions. These are difficult to analyze from a                                     Cdc ,min           =
                                                                                                                     2 ∆v               2 = 2 6f K
                                                                                                                                        ⋅                                                             (8)
simple approach, but it is assumed that the relation between                                                             max                    1 dc max KVdc K fsw Z b
inductors maintains the same.
An evaluation is given in Fig. 9 for two types of inductors,                                   For Case-B, the dc-current in each capacitor is half of
one of 5 % (as in Case-A) and the other of 3 % (as in Case-                                the total line current, because of the power sharing, which
B or -C). The inductors are calculated as in [17] using                                    makes the ripple of the dc-voltage half as calculated in
laminated iron core, sinusoidal line current and an operating                              Case-A. Or vice-versa, if the dc-voltage ripple is kept
                                                                                           constant, then the capacitor can be reduced to half.
temperature of 25 °C. The calculations did not consider the
                                                                                               In Case-C, since the capacitor is shared between two
required increase of the inductor size in order to cope with
                                                                                           interleaved inverters, the instantaneous dc-current is half of
the heat caused by the power losses in core and windings,
                                                                                           Case-A and its frequency is doubled. This makes the
thus the inductor size increases almost linear with the
                                                                                           capacitor 4 times lower than in Case-A.
current [17].
Fig. 9 shows that the weight of a 5 % inductor rated for 600                                                     C ( Case − A)                C ( Case − A)
                                                                                                   ( Case                        ( Case
                                                                                                  Cdc ,min− B ) = dc ,min , and Cdc ,min−C ) = dc ,min      (9)
Amps is higher than the weight of 2 inductors of 3 % rated                                                            2                            4
for 300 Amps each. Their volume is also in the same ratio.




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If the application is an active filter, then the capacitor value                                Thus, the comparison between Case-A, -B, -C, resumes
should be calculated to cope with a certain value of dc-                                    to the calculation of the THDHF caused by the switching
voltage drop caused by the load variation.                                                  frequency. The spectrum of the measured dc-current is
                               VLL ∆I inv                                                   calculated for all three cases in Fig. 11.
              Cdc − A ) =
                ( Case

                          2 3 (Vdc , drop − Vdc ) f1
                                 2            2
                                                            (10)
                                                                                                For Case-A the THDHF is double compared to Case-B,
                                                                                            but only one of the capacitors is measured in Case-B, Since
where ∆Iinv is the step increase in the real fundamental line current;
Vdc,drop is the maximum allowed variation of the dc-voltage.                                the capacitor is of a lower capacitance, the equivalent RESR is
                                                                                            almost double, and thus the total power losses for both
     This means that the required capacitance is much larger
                                                                                            capacitors together in Case-B is near the same as the value
than the value in (8) [18]. For Case-B, the dc-capacitor is
                                                                                            calculated in Case-A. In order to reduce the losses the
still half of Case-A because the inverter power is half.
                                                                                            capacitor, its capacitance must be increased but this is not
However, for Case-C the dc-capacitor is the same as in
                                                                                            economically viable.
Case-A, because the same amount of power is required to be
                                                                                            For Case-C the THDHF is half and there is only one dc-
stored in dc-link in order to cope with the load variation.
                                                                                            capacitor. This indicates that the total current stress in Case-C
     Another important issue when designing the capacitor is
                                                                                            is reduced to 25 % compared to Case-A. However, if the
the current stress. Different methods are proposed in
                                                                                            capacitor is 4 times lower (i.e. RESR 4 times higher), the total
literature, either spectral analysis or simulations [12]. The
                                                                                            power losses would be the same. Therefore, the capacitor may
dc-current determines specific power losses in the capacitor
                                                                                            be selected for example only 2 times lower instead of 4 times,
as in (11) and consequently an increase of the capacitor
                                                                                            which is sufficient enough to reduce the losses to half.
temperature as in (12), thus decreasing its lifetime.
      PCdc = ∑ ( PESR (h) ) = ∑ ( RESR (h) ⋅ I C , RMS (h) )
                                               2
                                                             (11)
               h                    h                                                       C. Inverter rating
                         TCdc = Ta + PCdc ⋅ Rth                                 (12)            The rating of the inverter is determined by calculating
where TCdc and Ta are the capacitor respective ambient temperatures,                        the IGBT currents. The cross-current changes the shape of
RESR(h) and IC,RMS(h) are the equivalent series resistance respective the RMS               the IGBT current with a possible increase of the switching
current of the capacitor at different harmonic orders h.                                    and conduction power losses. However, simulation of the
The equivalent series resistance (RESR) decreases whenever                                  inverter for different common mode inductors shows that
one of the following increases: ambient temperature Ta,                                     the RMS value of the IGBT current has insignificant
ripple current, current frequency, capacitor can size, and                                  changes, but only the peak value increases (see Table IV and
capacitance (for the same can size) [19]. Variation of RESR                                 Fig. 12), [13].
with the frequency is only of a small amount, and practically
it can be considered constant for any frequency higher than                                                          III. CONTROL STRUCTURE
2-3 kHz. Its value is averaged to 0.45 times the RESR value
                                                                                                The control algorithm may be developed in different
for 100 Hz at 20°C (see Fig. 10a). On the other hand, the
                                                                                            ways, either in stationary or synchronous frames. Here the
variation of RESR with the capacitance is much larger,
                                                                                            last was selected for implementation [13]. A typical control
reaching a difference of almost 2 times, if one compares the
                                                                                            diagram for Case-A is given in Fig. 13a, which has a current
RESR of a given capacitor to its double value (see Fig. 10b).
                                                                                            controller (Reg Idq) in the inner loop and a voltage controller
If one splits the power losses from (11) into low order
                                                                                            (Reg Vdc) in the outer loop.
harmonics ( PCdc caused mainly by the control) and high
               LF
                                                                                                For active harmonic filtering applications the load
order harmonics ( PCdc caused by the switching frequency),
                    HF
                                                                                            current is also measured and the harmonic currents are
and takes into account that the ESR is almost constant for                                  isolated and imposed as current reference (IHRef) by the
higher frequencies, then it can be proven that high frequency                               harmonic detection block. For Case-B, since there are 2
power losses are directly dependent on the total harmonic                                   independent inverters, the control of each is self-regulating,
distortion (THDHF) calculated as in (13).                                                   which means that the overall implementation of the control
                                                      I                                   is twice as in Fig. 13a.
                                                                 (h)  
                                                                      2

     PCdc = 0.45 ⋅ RESR (100 Hz ) ⋅ I C , RMS ∑   C , RMS
       HF                             2
                                                                      
                                                       
                                              h > 50   I C , RMS
                                                                       (13)
                                                                     
                                                         2
                                                      THDHF , h>50




                   (a)                                          (b)
Fig. 10. Excerpt from capacitor datasheets showing the dependence of ESR                     Fig. 11. Measured harmonic spectrum of the dc-currents for a) Case-A, b)
                  with the frequency and capacitance [19].                                                Case-B at only one of the inverter, c) Case-C.




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    The control diagram for Case-C is particular because of                                 The common mode inductors in Case-C are set to Lcm1=
the shared dc-capacitor. Thus, there are two additional                                     Lcm2=2 mH. Some of the measurements are already
issues, the zero sequence current and the common dc-                                        presented in §II regarding the generation of the reactive
voltage regulation.                                                                         power (Fig. 6).
In a typical three-phase three-wire stand-alone inverter the                                    Initially the design of the inverter in §II was done for a
zero-sequence current generated by the zero vectors does not                                sinusoidal modulation strategy (SPWM). Other types of
flow, but in the existing topology with parallel inverters there                            modulations are also practically tested as it can be seen in Fig.
is a circulating cross-current as explained in §II. Even if the                             14A: space vector modulation (SVM), discontinuous
average of the cross-current theoretically is zero during one                               modulation with different types of switch clamping (DPWM1
fundamental period, any small difference between the                                        and DPWM3) [12].
inverters determines a lower frequency current circulating                                  Fig. 14B and Fig. 14C show the simulated line current ripple
between them. The zero-sequence current is removed by a                                     as power factor correction (PFC) for Case-A with a line
current controller placed on zero-axis (Reg Iz), which keeps a                              inductor of 5 mH respective for Case-B with a line inductor of
null average of the zero sequence current [14].                                             3 mH each inverter. As it can be seen, the maximum value of
    As both inverters use the same dc-capacitor there is one                                the line current ripple is near the same for SPWM (and also
single voltage control loop. The output of the voltage                                      DPWM3), which validates the design. For the SVM and
controller is equally divided to be the reference for both                                  DPWM1 the ripple increases. For Case-C the line current
inner current controllers. This creates a balance in the power                              ripple is similar for SPWM and SVM. However,
losses dissipation for both inverters and also assures closer                               discontinuous modulations cannot be implemented [16]
symmetry in the voltage references for each inverter, which                                 because cross-currents cannot be regulated, as there are no
is needed in order to have a good cancellation in the current                               alternative zero vectors v0 and v7 during one switching period.
ripple. For the same reason the harmonic current reference is                                   Table II indicates the losses measured of the total
equally divided for each inverter.                                                          inverter in each case for all four modulation strategies.
                                                                                            Case-C has always higher losses because of there are 2
                      V. EXPERIMENTAL RESULTS                                               inverters (thus, involving switching and conduction losses)
                                                                                            but also because of the circulation of the cross-current that
    All three cases are evaluated on an existing laboratory
                                                                                            increases the losses in the line inductors.
stand used for compensation of both reactive power and
                                                                                                Fig. 15 shows the mitigation of the harmonic currents and
harmonic current distortion. The setup consists of 2 paralleled
                                                                                            the spectrum of the line current Is (see also Fig. 4), which
inverters of a total power of 5 kVA, working at 10.2 kHz
                                                                                            indicates that the switching frequency is reduced for Case-B
switching frequency. The line inductors are set as Lf=5 mH
                                                                                            and -C. Different other results are collected in Table III.
for Case-A and Lf=Lf1=Lf2=3 mH for Case-B and -C.




   Fig. 12. Representation of the IGBT
 current during one commutation period.
                                                                               (a)                                                     (b)
                                                                     Fig. 13. Diagram of the control in dq-reference frame for a) Case-A, b) Case-C.


                                                                                                                                      TABLE II. Measured power losses of
                                                                                                                                    the total inverter for different modulation
                                                                                                                                      strategies tested on the existing setup.
                                                                                                                                      Losses [%] vs. Case- Case- Case-
                                                                                                                                       modulation      A     B     C
                                                                                                                                           SPWM       3.8   5.1   6.5
                                                                                                                                     Reactive




                                                                                                                                           SVM        4.8   3.7   5.8
                                                                                                                                      power




                                                                                                                                           DPWM1 3.4        5.3   8.2*
                                                                                                                                           DPWM3 3.2        3.5   6.2*
                                                                                                                                           SPWM       2.8   3.4   7.1
                                                                                                                                     Harmonic
                                                                                                                                      filtering




                                                                                                                                           SVM        2.6   3.1   6.6
                                                                                                                                           DPWM1 2.4        3.0   8.0*
                  (A)                                          (B)                                         (C)                             DPWM3 2.2        2.9   6.7*
                                                                                                                                         *
Fig. 14. Simulated line current ripple for different PWM strategies. a) sin-PWM b) space vector modulation SVM,                              practically not viable because of the
 c) and d) discontinuous PWM (DPWM1,3). A) voltage reference, B) line current ripple in Case-A for Lf of 5 %,                                           strong cross-current [16].
                                 B) line current ripple in Case-B for Lf1, Lf2 of 3 %.




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                      (a)                                                (b)                                               (c)
 Fig. 15. Measured waveforms for mitigation of harmonic currents generated by an Adjustable Speed Drive of 2.5 kVA a) Case-A, b) Case-B, c) Case-C.

 TABLE III. Comparison of the selected topologies for an inverter power                        [4] L. Woo-Cheol, L. Taeck-Ki, L. Sang-Hoon, K. Kyung-Hwan, H.
         Sinv=3 kVA and a switching frequency of 10.2 kHz.                                         Dong-Seok, S. In-Young "A master and slave control strategy for
                                                                                     *
                                                                                                   parallel operation of three-phase UPS systems with different
                Parameter                           Case-A       Case-B Case-C                     ratings", Proc. of APEC '04, Vol. 1, 2004, pp. 456-462.
Front line inductor value (Lf)                      0.05 pu      0.03 pu 0.03 pu
                                                                                               [5] G. Ledwich, P. Doulai, "Multiple converter performance and active
DC-link capacitor value (Cdc)                       0.62 pu      0.31 pu 0.15 pu                   filtering", IEEE Trans. on Power Electronics, Vol. 10, No. 3, pp. 273-
Total power flow in each inverter (Sinv)            1.00 pu      0.50 pu 0.50 pu                   279, 1995.
Total line current distortion (THDi)                 6.5 %        8.4 %       8.9 %            [6] H. Akagi, A. Nabae, S. Atoh, "Control strategies of active power
                                                                                                   filters using multiple voltage-source converters", IEEE Trans. on Ind.
1st switching frequency harmonic of Ifsum            5.6 %        2.0 %       2.1 %                App., Vol. 22, No. 3, pp. 460-465, 1986.
1st switching frequency harmonic of If1              5.6 %        7.2 %      18.2 %
                                                                                               [7] Federal Energy Regulatory Commission web resource,
Current rating for one IGBT [Arms]                  0.53 pu      0.28 pu     0.29 pu                “http://www.ferc.gov”, 2005.
Maximum current for one IGBT [Apk]                  1.15 pu      0.75 pu     0.90 pu           [8] National Energy Marketers Association, web resource,
 *
     tested for a common mode inductor Lcm of 2 mH.                                               “http://www.energymarketers.com/Documents/02-04-05-reactive-
                                                                                                  power.pdf”, 2005.
                                                                                              [9] A.M. Kamel, T.H. Ortmeyer, "Harmonic reduction in single-phase
                               VI. CONCLUSION                                                     inverter using a parallel operation technique", Proc. of APEC' 89,
                                                                                                  1989, pp. 101-108.
        This paper discusses a parallel topology of 2 three-                                 [10] F. Blaabjerg, Z. Chen, S.B. Kjaer, "Power electronics as efficient
phase power inverters connected in parallel and sharing the                                       interface in dispersed power generation systems", IEEE Trans. on
same dc-capacitor. A comparison of the selected topology                                          Power Electronics, Vol. 19, No. 5, pp. 1184-1194, 2004.
with a regular three-phase inverter for application is                                       [11] F.V.P. Robinson, V. Chunkag, "Parallel connection of single-switch
                                                                                                  there-phase power factor correction converters for interleaved
presented for reactive power and harmonic compensation.                                           switching", IEE Proc. of. of Electr. Power Application, Vol. 144, No.
The paper gives different design specifications, which prove                                      6, 1997, pp. 423-433.
that for the selected topology the passive components are                                    [12] J.W. Kolar, H. Ertl, F.C. Zach, “Influence of the modulation method
significantly reduced. Simulation and experimental results                                        on the conduction and switching losses of a PWM converter system”,
for a 400V/5kVA unit validates the presented analysis.                                            IEEE Trans. on Ind. App., Vol. 27, No. 6, pp. 1063-1075, 1991.
                                                                                             [13] L. Asiminoaei, E. Aeloiza, J.H. Kim, P. Enjeti, F. Blaabjerg, L. T.
                  ACKNOWLEDGMENTS                                                                 Moran, S.K. Sul, “An interleaved active power filter with reduced size
                                                                                                  of passive components”, Proc. of APEC’06, Vol. 1, 2006, 969 − 976.
    The authors want to acknowledge the financial support
from Aalborg University, Aalborg, Denmark project 562/06-                                    [14] Y. Zhihong, D. Boroyevich, C. Jae-Young, F.C. Lee, "Control of
                                                                                                    circulating current in two parallel three-phase boost rectifiers", IEEE
14-23632 and the help received from Hitachi Metals Europe,                                          Trans. on Power Electronics, Vol. 17, No. 5, pp. 609-615, 2002.
Duesseldorf, Germany regarding the magnetic materials for                                    [15] S. Ogasawara, J. Takagaki, H. Akagi, A. Nabae, “A novel control
the common mode coils.                                                                            scheme of a parallel current-controlled PWM inverter”, IEEE Trans.
                                                                                                  on Ind. Appl., Vol. 28, No. 5, pp. 1023-1030, 1992.
                                                                                             [16] K. Xing, F.C. Lee, D. Borojevic, Z. Ye, S. Mazumder, “Interleaved
                                                                                                  PWM with discontinuous space-vector modulation”, IEEE Trans. on
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