Aalborg Universitet
DAVIC
A New Distributed Adaptive Virtual Impedance Control for Parallel-Connected Voltage Source
Inverters in Modular UPS System
Wei, Baoze; Marzabal, Albert; Ruiz, Ruben; Guerrero, Josep M.; Vasquez, Juan C.
Published in:
I E E E Transactions on Power Electronics
DOI (link to publication from Publisher):
10.1109/TPEL.2018.2869870
Publication date:
2019
Document Version
Accepted author manuscript, peer reviewed version
Link to publication from Aalborg University
Citation for published version (APA):
Wei, B., Marzabal, A., Ruiz, R., Guerrero, J. M., & Vasquez, J. C. (2019). DAVIC: A New Distributed Adaptive
Virtual Impedance Control for Parallel-Connected Voltage Source Inverters in Modular UPS System. I E E E
Transactions on Power Electronics, 34(6), 5953 - 5968. [8463524]. https://doi.org/10.1109/TPEL.2018.2869870
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2018.2869870, IEEE
Transactions on Power Electronics
1
Abstract— In this paper, an average active power
sharing control strategy based on distributed concept for
the parallel operation of voltage source inverters (VSIs)
is proposed to be applied to the modular uninterruptible
power supply (UPS) systems. The presented method is
named distributed adaptive virtual impedance control
(DAVIC), which is coordinated with the droop control
method. Low bandwidth CAN-based communication is
used for the requirement of data sharing of the proposed
method in the real modular UPS system. Unlike the
conventional virtual impedance control techniques, the
virtual impedance of a converter module is adjusted
automatically by using global information when DAVIC
is applied, further to tune the output impedance of the
power modules. The adaptive virtual impedance is
calculated by using the difference between the active
power of a local module and the average active power of
all the modules in a modular UPS. The DAVIC
overcomes the drawback of conventional virtual
impedance control since an accurate value of the real
output impedances of different converter modules is not
required. Simulations using PLECS and experiments on
a real commercial modular UPS are developed to verify
the effectiveness of the proposed control methodology.
These results shown a superior power sharing
performance is obtained when using the proposed
method.
Index Terms— droop control; adaptive virtual
impedance; modular uninterruptible power supply
system; power sharing; circulating current.
I. INTRODUCTION
The microgrid concept has been proposed several years
ago to meet the requirement of the increasing penetration of
renewable energy resources into the grid [1]. In the past few
years, the study of microgrids has attracted more attention for
its reliability and flexibility due to the use of cooperative
control of different distributed generators (DGs), energy
storage systems, and local loads [2]-[5]. Typically, DGs use
inverters for interfacing renewables and power systems [6-
9]. Thus, the power converter control of DGs in a microgrid
is about the control of several parallel-connected inverters.
Alternatively, the uninterruptible power supply (UPS)
systems are often based on voltage source inverters (VSI) to
provide power to the critical loads, such as data centers,
telecom systems, and so on [10], [11]. In order to obtain a
higher reliability, the modular UPS concept appears in the
1990s [10]. Similar to the microgrid, it contains several
converters that are connected in parallel forming a modular
UPS architecture. The modular concept has some
advantages, such as increasing the power capacity regardless
of the limited power rate of switching devices, increasing the
flexibility, reliability and maintainability of power supply
systems to meet the requirements of customers. Further,
some redundant power modules will be equipped in the
modular UPS to ensure high availability, which is called N+X
configuration (N parallel + X redundant modules) applied by
some UPS design and manufacture companies like ABB,
Delta, AEG power solutions, STATRON, among others [10],
[11]. Fig. 1 shows a typical configuration of a modular UPS.
Each module can be controlled independently since it
contains all the components needed for operation, like the
AC/DC and DC/AC converters, static bypass switch and a
full functional control unit.
Fig. 1. Typical configuration of a modular UPS.
The control method applied to the control of DGs in the
microgrid can be transferred to the modular UPS system [12-
15]. In recent years, the most common method that used for
the control of parallel-connected converters within a
microgrid is based on decentralized droop characteristics,
which have been identified as effective approaches [16-18].
The droop control is widespread due to its attractive features,
such as expandability, modularity, redundancy, and
flexibility [19], [20]. It performs the wireless control of
multi-parallel inverters and is more convenient to implement
the decentralized control of DGs in a power plant. However,
the performance of the droop control is greatly influenced by
the unbalanced output impedances of the converters [2], [9].
Then, the virtual impedance is proposed to adjust the output
impedance to decouple the active and reactive powers [2],
[12], [17], [20], [21]. However, it is difficult to design a
DAVIC: A New Distributed Adaptive Virtual
Impedance Control for Parallel-Connected
Voltage Source Inverters in Modular UPS
System
Baoze Wei, Member, IEEE, Albert Marzàbal, Ruben Ruiz, Josep M. Guerrero, Fellow, IEEE, and Juan C.
Vasquez, Senior Member, IEEE
0885-8993 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2018.2869870, IEEE
Transactions on Power Electronics
2
proper virtual impedance in a practical paralleled inverters
system since the control parameters and the working
conditions will influence the output impedance [2], [22].
With poorly designed virtual impedance, the overall
performance cannot be guaranteed, especially the average
power sharing requirement for the modular UPS.
For the purpose of improving the performance of
conventional droop plus virtual impedance loop framework,
the adaptive virtual impedance control has been proposed in
several research works [22-26]. The output impedance is
commonly adjusted to be inductive in accordance to the
conventional droop function, in which the active power can
be controlled by the inverter frequency while the reactive
power can be regulated by the output-voltage amplitude. In
[23] and [26], reactive power sharing methods based on
adaptive virtual impedance were presented; the adaptive
virtual impedance was obtained by the difference of the
reactive power between the parallel DGs. For example in
[22], the adaptive inductance was calculated by detecting the
circulating current between the parallel inverters, while at the
same time, it should monitor the change trend according to
the differential of the circulating current to time.
Different from the applications proposed in the existing
literatures, the control strategy introduced in this paper is to
be applied into a commercial modular UPS based on parallel
inverters terminated with LC filters. Unlike the grid-
connected applications, an LC filter is applied instead of LCL
filter, which can lower the cost and increase the power
density with a smaller volume. In addition, the second target
is to maximize system flexibility, so that it should work as a
three-phase system, but it should be able to operate as a
single-phase or two phases system as well. Thanks to this
flexibility, maintenance becomes easier and single-phase
tests are feasible, which are important features of such a
product. The control under three-phase stationary
coordinates is implemented for this purpose, which can
reduce the overall resource consumption of the digital signal
processor (DSP) since the coordinate transform is not
required.
For the modular UPS project, particular control strategies
should be developed. The basic control diagram is based on
the decentralized droop and the virtual impedance control.
Considering the LC filter and the purpose of simplifying the
control scheme as mentioned above, the reverse droop (P-V
and Q-f scheme) function is adopted instead of the
conventional droop method (P-f and Q-V scheme) [12]. For
the requirement of resistive output impedance, a virtual
resistance loop is adopted. However, with the virtual
impedance only, it is not enough to reach another important
target, which is the average active power sharing between the
power modules. Note that a poor power sharing performance
will lead to serious circulating current problem and may
cause different current stress on the switching devices, then
significantly decrease the system efficiency and lifetime of
modules whose output power are higher. Further, direct
currents flowing from one module to another may cause
active power absorption in some modules, which may
contribute to DC link voltage raises in UPS’ with
unidirectional rectifiers [33]. Hence, average active power
sharing is necessary when considering modular UPS’.
In real applications, like the modular UPS, even though
using the same models, there is an unavoidable mismatch
between output impedances of the converter modules that
may produce differences between them. In addition, offsets
and gain errors may occur in the analog acquisition of the
currents and voltages, while DSP clocks also present
frequency drifts due to imperfection, which result in active
and reactive power inaccuracies. Further, these differences
will cause problems in some cases, such as the preset value
of the virtual impedance and voltage references, which are
considered in this paper, and will influence active and
reactive power sharing between the parallel modules.
In order to solve the above-mentioned issues, this paper
presents a new distributed adaptive virtual impedance control
(DAVIC) strategy. The adaptive virtual impedance is
calculated by the difference between the local active power
of the module and the average active power of all the
modules, then it is added to a preset virtual impedance to tune
the output impedances of the power modules. With the
proposed DAVIC, the total virtual impedance is not a
constant value; it will be adjusted automatically by the
difference of local active power and average active power of
all the modules. It can be sure, at any time, the total active
power can be average shared between the parallel converters,
so there will be no current flowing from one module to
another to keep the safety of the DC links. The active power
information is being shared through the low bandwidth CAN
bus on the real UPS system for the realization of the
distributed control, which can improve the reliability of
droop control and solve the single point failure of the
centralized control fashion [27].
Compared with the conventional virtual impedance
control and the existing adaptive virtual impedance control,
the contribution of this paper is to propose an adaptive virtual
impedance control for a modular UPS product. With the
proposed method, it can reduce both the cost of the power
plant and the control unit by choosing a cheaper digital
controller. Simulations using PLECS and experiments on a
real modular UPS platform have been developed. In both the
simulation and experiments, unbalanced set of virtual
impedances are intentionally programmed in order to
simulate different output impedance values of different
power modules and to imitate the inner offset of the DSPs.
The rest of this paper is organized as follows. In Section
II, the concept of the traditional droop method and the virtual
impedance loops are briefly introduced. In Section III, the
idea of the proposed DAVIC is introduced, the design
guideline of the adaptive virtual impedance control
parameters and the stability analysis is also provided. In
Section IV, simulation results are presented, which verify the
effectiveness of the proposed approach. Experimental
verification in an industrial modular UPS platform is
presented in Section V. The conclusions are given in Section
VI.
II. REVIEW OF THE CONVENTIONAL DROOP METHOD AND
THE VIRTUAL IMPEDANCE CONTROL
In this Section, the basic concept of the droop and virtual
impedance framework is reviewed. This is one of the most
popular ways of control the paralleling UPS inverters [3], [9],
[12]-[13], [18]-[22]. Each of the inverters operate as a
voltage source. In order to analyze the conventional
approach, a voltage source inverter (VSI) connected to an ac
bus can be simply drawn as in Fig. 2. Thus, the power
injected to the ac bus from the VSI is given by [28], [29]:
2
cos( ) cos
pcc pcc
EV V
P
ZZ
(1)
0885-8993 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2018.2869870, IEEE
Transactions on Power Electronics
3
2
sin( ) sin
pcc pcc
EV V
Q
ZZ
, (2)
where E and V
pcc
are the amplitude of the inverter output
voltage and the ac bus voltage,
is the power angle of the
inverter, Z and
represent the amplitude and the phase of
the output impedance. Conventionally, the output impedance
is considered highly inductive, which is often obtained with
a large filter inductor connected to the ac bus [30]. In this
case and assuming that the output impedance is purely
inductive (
90
), the active and reactive power
expressions can be simplified as:
sin
pcc
EV
P
Z
(3)
2
cos
pcc pcc
EV V
Q
ZZ
. (4)
Fig. 2. Equivalent circuit of a VSI connected to an ac bus.
The output impedance of the closed-loop inverter
determines the droop control strategy [12]. Normally, the
power angle
is very small, (
sin
,
cos 1
), then
the active power P is mainly related with
, and the reactive
power Q is mainly influenced by the voltage error (E-V
pcc
)
[12], [23]. Thus, the conventional droop scheme
P w
and
QV
is often used, so that the voltage and frequency droop
functions are given as [2], [12]:
*
q
E E m Q
(5)
*
p
mPww
, (6)
in which
*
w
and
*
E
represent the frequency and voltage
amplitude references, m
p
and m
q
are the droop coefficients
[2], [8], [12]. Similarly, for a highly resistive output
impedance (
0
), the active and reactive power can be
calculated as:
2
cos
pcc pcc
EV V
P
ZZ
(7)
2
sin
pcc
EV
Q
Z
. (8)
Different from the conventional droop, the droop function
should be modified as [12], [31], [32]:
*
p
E E m P
(9)
*
q
mQww
. (10)
Thus, the active power can be controlled by the inverter
output-voltage amplitude while the reactive power can be
regulated by the inverter frequency, which is the opposite
strategy of the conventional droop, it is also named as reverse
droop [31], [32]. More details about the choice of droop
function and the analysis of output impedance can be found
in [12], [28], [33], [35], and [36].
As the output impedance plays an important role for the
choice of the droop function, and for the conventional droop
control scheme, a highly inductive output impedance is
required to decouple the influence of P and Q to the
frequency and voltage amplitude [12], [28]. Typically, LCL
filter will be connected the inverter to the common ac bus.
As discussed in the introduction, virtual impedance can be
added to adjust the output impedance. The parallel three-
phase inverters considering the output impedances can be
simplified as Fig. 3 because of the similar principle of three-
phase and single-phase inverters.
Fig. 3. Equivalent circuit of two parallel inverters.
Fig. 4. Equivalent circuit of two parallel inverters with virtual impedances.
In Fig. 3, Z
1
and Z
2
are the output impedances of the two
parallel inverters, respectively, Z
L
is the load impedance, E
1
and E
2
are the output voltages of the two inverters, I
1
and I
2
are the output currents, E
o
is the common as bus voltage and
I
o
is the load current. In a practical system, Z
1
and Z
2
will be
unbalanced because of the different values of filters and line
impedances or stray parameters. According to literature [34],
the circulating current can be defined as
12
cir
I - I
I=
2
. (11)
As shown in Fig. 3, the following equations can be written:
1o
1
1
E - E
I=
Z
(12)
2o
2
2
E - E
I=
Z
. (13)
Assuming that the output impedances of the parallel inverters
are equal to each other, Z
1
=Z
2
=Z, then substituting (12)-(13)
into (11) gives us:
12
cir
E - E
I=
2Z
. (14)
Based on the former analysis, if the output voltages and
the output impedances of the parallel inverters are equal to
each other, respectively, the circulating current can be
eliminated to obtain the target of average power sharing. The
equivalent circuit of two parallel-connected inverters with
virtual impedances is shown in Fig. 4, Z
vir1
and Z
vir2
are the
virtual impedances.
virk virk virk
Z = jX R
(15)
Equation (15) depicts the virtual impedance for the k
th
inverter in a system. The virtual impedance can be purely
resistive, inductive or a combination with two of them based
on the output impedance differences between parallel
inverters.
0885-8993 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2018.2869870, IEEE
Transactions on Power Electronics
4
III. THE DISTRIBUTED ADAPTIVE VIRTUAL IMPEDANCE
CONTROL (DAVIC)
A. The proposed DAVIC method
In the UPS project that discussed in this paper, the LC
filter is applied instead of an LCL filter, then the line
impedance is mainly resistive in the low voltage line [35],
[36]. Thus, in coherence with the line impedance, a virtual
resistive impedance is selected, consequently the reverse
droop (9)-(10) is implemented. For the purpose of improving
the active power sharing accuracy between parallel converter
modules, an adaptive virtual impedance control is proposed,
which is realized by using a distributed control concept as
shown in Fig. 5. The adaptive virtual impedance is calculated
by the difference between the active powers between the
power modules in the UPS. In that figure, R
vir_pre
is the preset
virtual impedance; R
vir_adp
is the adaptive virtual impedance,
so that the final virtual impedance per power module will be
__vir pre vir adp
RR
.
Assuming that there are a number of n power modules that
operate in parallel in a modular UPS, the control scheme
considering the adaptive virtual impedance control is shown
in Fig. 5. The calculation of the adaptive virtual impedance
can be expressed as
_ adp
1
1
( )( ),
n
Iadp
vir adp i av P av i
i
K
R P P K P P
sn
, (16)
The local active power P
i
(i=1 to n) will be compared with
the average active power P
av
, of the paralleled modules in the
UPS. Then through the PI controller, the adaptive virtual
impedance R
vir_adpi
(i=1 to n) is obtained. The reason of P
i
in
the position of minuend is that, suppose that P
i
is higher than
the average active power of the parallel-connected modules,
it means the virtual impedance of the i
th
module should
increase to reduce the output power of P
i
. In Fig. 5, R
vir_adpi
will be positive through the calculation using (16), so the
final total virtual impedance of i
th
module will increase,
which demonstrates the correct compensation direction. The
whole control diagram of a modular UPS with the proposed
adaptive virtual impedance control is shown in Fig. 6.
B. The design of the control parameters of the adaptive
virtual impedance loop
In order to give a design guideline of the parameters of the
adaptive virtual impedance control, a simple model
considering two parallel-connected inverters is built, which
is shown in Fig. 7. R
D1
and R
D2
represent the virtual
impedance, which consist the adaptive virtual impedance.
R
line1
and R
line2
represent the line impedances, only resistive
line impedance is considered since it is mainly resistive in
low voltage line [35], [36].
Fig. 7. Equivalent circuit when two inverters connected in parallel.
Based on Fig. 7, when considering both of the adaptive
virtual impedance and the line impedance, (12) and (13) will
be changed as:
1
1o
1
D1 line
EE
I=
RR
(17)
2
2
22
o
D line
EE
I=
RR
. (18)
If I
1
=I
2
, the following is obtained:
2
1 2 2
1 o o
D1 line D line
E E E E
R R R R
(19)
1 1 1
1
2 2 2 2 2 2
( )( / )
( )( / )
av Padp Iadp pre line
1 o D1 line
o D line av Padp Iadp pre line
P P K K s R R
E E R R
E E R R P P K K s R R
. (20)
Fig. 5. Control scheme for a number n modules in a modular UPS system.
