IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004
1205
A Wireless Controller to Enhance Dynamic
Performance of Parallel Inverters in
Distributed Generation Systems
Josep M. Guerrero, Member, IEEE, Luis García de Vicuña, José Matas, Miguel Castilla, and
Jaume Miret, Member, IEEE
Abstract—This paper presents a novel control strategy for parallel inverters of distributed generation units in an ac distribution
system. The proposed control technique, based on the droop control method, uses only locally measurable feedback signals. This
method is usually applied to achieve good active and reactive power
sharing when communication between the inverters is difficult due
to its physical location. However, the conventional voltage and frequency droop methods of achieving load sharing have a slow and
oscillating transient response. Moreover, there is no possibility to
modify the transient response without the loss of power sharing
precision or output-voltage and frequency accuracy. In this work, a
great improvement in transient response is achieved by introducing
power derivative-integral terms into a conventional droop scheme.
Hence, better controllability of the system is obtained and, consequently, proper transient performance can be achieved. In addition, an instantaneous current control loop is also included in the
novel controller to ensure proper sharing of harmonic components
when supplying nonlinear loads. Simulation and experimental results are presented to prove the validity of this approach, which
shows excellent performance as opposed to the conventional one.
Index Terms—Distributed generation (DG), droop control
method, nonlinear loads.
I. INTRODUCTION
D
ISTRIBUTED generation (DG) systems are presented as a
suitable form to offer high reliable electrical power supply
[1]. The concept is particularly interesting when different kinds
of energy resources are available, such as photovoltaic panels,
fuel cells, or speed wind turbines [2], [3]. Most part of these
resources need power electronic interfaces to make up local ac
grids [4], [5]. This way, inverters or ac-to-ac converters are connected to an ac common bus with the aim to share properly the
disperse loads connected to the local grid [6]. In addition, every
unit must be able to operate independently when communication is too difficult due to the long distance between its connection points [7]. In this sense, several control techniques have
been proposed without control wire interconnections based on
Manuscript received July 16, 2003; revised June 3, 2004. This paper was presented in part at PESC’03, Acapulco, México, June 15–19, 2003. This work was
supported by the Spanish Ministry of Science and Technology under CICYT
DPI 2003-06508-C02-01. Recommended by Associate Editor I. Gadoura.
The authors are with the Departament d’Enginyeria de Sistemes, Automàtica
i Informàtica Industrial, Departament d’Enginyeria Electrònica, Universidad
Politécnica de Cataluña, Barcelona, Spain (e-mail: josep.m.guerrero@upc.es).
Digital Object Identifier 10.1109/TPEL.2004.833451
the droop method [8]–[11]. To achieve good power sharing, the
control loop makes tight adjustments over the output voltage frequency and amplitude of the inverter, in order to compensate the
active and reactive power unbalances [12]. This concept steams
from the power system theory, in which a generator connected
to the utility mains drops its frequency when the power required
increases [13].
In the literature, there are many control schemes based on the
droop method to share linear loads [14]. Nevertheless, nowadays
the proliferation of nonlinear loads has become a problem, because the units must both share harmonic current and to balance
active and reactive power. In [15], a controller was proposed
to share nonlinear loads by adjusting the output voltage bandwidth with the delivered harmonic power. However, this technique has two main limitations: the controller uses an algorithm
which is too complicated to calculate the harmonic current content, and the harmonic current sharing is achieved at the expense
of reducing the stability of the system. Recently, novel control
loops that adjust the output impedance of the units by adding
virtual resistors [16] or reactors [17] have been included in the
droop method, with the purpose to share the harmonic current
content properly. In another approach [18], every single term of
the harmonic current is used to produce a proportional droop in
the corresponding harmonic voltage term, which is added to the
output-voltage reference. Nevertheless, the control approaches
mentioned above have an inherent tradeoff between voltage regulation and power sharing. Besides, the droop method exhibits
slow dynamic response, since it requires low-pass filters with a
reduced bandwidth to calculate the average value of the active
and reactive power [19]. Then, the stability and the dynamics of
the whole system are strongly influenced by the characteristics
of these filters and by the value of the droop coefficients, which
are bounded by the maximum allowed deviations of the output
voltage amplitude and frequency.
In this paper, we propose a novel control scheme that is able
to improve the transient response of parallel-connected inverters
without using communication signals. A wireless controller was
developed, by adding a supplemental transient droop characteristic to the conventional static droop approach, which improves
the paralleled-system dynamics. The novel droop function ensures both steady-state objectives and a good transient performance. Simulation and experimental results are reported, confirming the validity of this control technique.
0885-8993/04$20.00 © 2004 IEEE
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004
Fig. 3. Static droop characteristics P
Fig. 1.
0 ! and Q 0 E .
Distributed generation units connected in parallel to a common ac bus.
Fig. 2. Equivalent circuit of an inverter connected to a bus.
II. REVIEW OF THE CONVENTIONAL DROOP METHOD
Fig. 1 shows a DG system made up of different kind of resources, such as solar panels, fuel cells, and speed wind turbines. As mentioned previously, every resource needs an electric
power interface to transfer energy to the common bus. We can
model every unit as an inverter connected to the common bus
through a decoupling impedance, as shown in Fig. 2. Usually the
inverter output impedance is highly inductive,
and, hence, the active and reactive powers drawn to the bus can
be expressed as [13]
(1)
(2)
is the output reactance of an inverter, is the phase
where
angle between the output voltage of the inverter and the voltage
of the common bus, and and are the amplitude of the output
voltage of the inverter and the load voltage, respectively.
From the above equations, it can be derived that the
is predominately dependent on the power
active power
mostly depends on
angle , while the reactive power
the output-voltage amplitude. Consequently, most of the
wireless-control of paralleled-inverters uses the conventional
droop method, which introduces the following droops in the
amplitude and the frequency of the inverter output voltage
(3)
(4)
being
and
the output voltage angular frequency and amand are the droop coefficients for
plitude at no load, and
the frequency and amplitude, respectively.
It is well known that if droop coefficients are increased, then
good power sharing is achieved at the expense of degrading the
Fig. 4. Tradeoff between frequency deviation and active power sharing (droop
coefficient m > m).
voltage regulation [15], which can be acceptable if, for instance,
the frequency and amplitude deviations are mostly at 2% and
5%, respectively (see Figs. 3 and 4). The inherent tradeoff of
this scheme restricts the mentioned coefficients, which can be a
serious limitation in terms of transient response, power sharing
accuracy, and system stability [19].
On the other hand, to carry out the droop functions expressed
by (3) and (4), it is necessary to calculate the average value over
one line-cycle of the output active and reactive instantaneous
power. This can be implemented by means of low-pass filters
with a smaller bandwidth than that of the closed-loop inverter.
Consequently, the power calculation filters and droop coefficients determine, to a large extent, the dynamics and the stability
of the paralleled-inverters [19]. Damping and oscillatory phenomena of phase shift difference could cause instabilities and a
large transient circulating current that can overload and damage
the units.
In conclusion, the conventional droop method has several
intrinsic problems related to its limited transient response,
since the system dynamics depends on the power-calculation
filter characteristics, the droop coefficients, and the output
impedance. These parameters are determined by the line-frequency, the maximum allowed frequency and amplitude
deviations, and the nominal output power. Thus, by using the
conventional droop method, the inverter dynamics cannot be
independently controlled.
III. PROPOSED CONTROL TECHNIQUE
In this paper, we will try to overcome the above limitations
and to synthesize a novel control strategy without communication wires that could be appropriate for a high-performance
GUERRERO et al.: WIRELESS CONTROLLER
1207
voltage proportionally to the time-derivative of the fundamental
output-current. On the other hand, in order to share harmonic
current content, without increasing output-voltage THD too
much, the resistive-impedance should be achieved. Hence, a
high pass filter can easily carry out both behaviors. Note that
the gain and the pole value of this filter must be carefully
chosen. The proper design of this output impedance can reduce,
to a large extent, the line-impedance impact over the power
sharing accuracy.
V. SMALL-SIGNAL MODELING
Fig. 5. Block diagram of the proposed controller.
DG electrical ac interface system. To improve the dynamics of
the system, the following novel droop-based control scheme is
proposed:
(5)
To analyze the stability and the transient response, a smallsignal model of the parallel-inverter system is proposed. An objective of the above controllers is to avoid the existence of a
circulating current among the inverters. Hence, this current can
be an interesting variable to investigate; however, it is a fast
and oscillating variable, which can complicate the analysis of
the system. To facilitate this analysis, from Fig. 2, the envelope
signal of the current drawn to the bus can be found
(7)
(6)
where
is the derivative coefficient of the reactive power ;
,
, and
are the integral, proportional, and derivative coefficients of the active power . Note that if we take into account
, the steady-state voltage and the frequency
that
droops coincide exactly with those obtained with the conventional method, expressed by (3) and (4).
The proposed control scheme allows us to modify the transient response, act on the control coefficients, and, at the same
time, keep the static droop characteristic. Also, it minimizes
the transient circulating current among the units and further improves the dynamic performance of the whole system. In fact,
the coefficients
and fix the steady-state droop function
,
, and
are selected to guarantee stability and
while
good transient response.
IV. CONTROLLER IMPLEMENTATION
Fig. 5 depicts the block diagram of the proposed controller.
The average active power can be obtained by multiplying the
inverter output voltage by the inverter output current , and
by filtering the product using a low-pass filter. In a similar way,
the average reactive power is obtained, but in this case the output
voltage must be delayed 90 .
In order to adjust the output voltage phase, (5) is implemented, which corresponds to a PID controller applied over
the average active power signal. The output-voltage amplitude
is regulated by using the conventional droop method with the
inclusion of the reactive power derivative term [see (6)].
Finally, the output impedance of the inverter can be emulated
by means of a high-pass filter to share linear and nonlinear
loads [20]. In this case, an additional faster loop is added to
program the output impedance. On the one hand, inductive
output impedance can be implemented by dropping the output
By taking the usual approximations
, we can derive
,
, and
(8)
where is a small variation of the phase difference. As it can
be seen, the envelope of is proportional to the power angle .
Consequently, a small-signal analysis is proposed to obtain the
dynamics of taking into account the well-known infinite bus
approximation [13], [19].
First, we must take into account the expression of the lowpass filters, shown in Fig. 5, which averages the instantaneous
active and reactive power values. By using (1) and (2), and modeling the low-pass filters as a first-order system, it yields to
(9)
(10)
where denotes perturbed values, capital letters mean equilibrium point values, and
is the cut-off angular frequency of
the low-pass filters, which must be fixed over one decade below
from frequency mains.
Second, by perturbing (5)–(6) and using (9)–(10), we obtain
(11)
(12)
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004
Finally, substituting (12) into (11), it can be found
(13)
where
,
, and
are
Using (13), the stability of the closed-loop system can be evaluated, and a desired transient response can be selected following
a linear three-order dynamics. From the values of , , and
coefficients, it can be seen that the proposed controller endows
superior controllability of the dynamics as opposed to the con,
, and
.
ventional approach, in which
Fig. 6. Root locus diagrams for (a) 0 10
,
= 2 1 10 .
(b) 0 VI. DESIGN METHODOLOGY
In order to properly select the coefficients of the loadsharing controller, we propose a design methodology. First,
the coefficients and can be chosen as in the conventional
droop method to ensure steady state control objectives [15] as
follows:
(14)
(15)
where
and
are the maximum active and reactive
and
powers that can be delivered by the inverter and
are the maximum frequency and amplitude output-voltage deviations allowed (see Fig. 3). Hence, these two parameters can be
fixed by the designer taking into account the tradeoff between
the power sharing accuracy and the frequency and amplitude
deviation.
,
, and
are chosen in order
Second, the coefficients
to adjust the transient response, and ensuring system stability. In
this sense, the analysis of the eigenvalues of (13) through several
root locus plots as a function of these parameters is presented.
Fig. 6(a) and (b) show the root locus plots using the parameters listed in Table I, and considering a variation of the coef-
m
m
m
10
,
m
= 5 1 10
TABLE I
PARAMETERS OF THE WIRELESS LOAD-SHARING CONTROL
and
GUERRERO et al.: WIRELESS CONTROLLER
Fig. 7.
Family of root locus diagrams for
and (b) 0
10 .
m 10
m n
1209
1
= 0, 5 10
, and 10
. (a) 0
Fig. 8.
1
0 1
ficients
and
from zero to
. Notice that this system
has three roots: two conjugated poles ( and ) and a real pole
. The arrows indicate the evolution of the corresponding
pole when the coefficient increases. As Fig. 6(a) shows, with
the increasing of
, the conjugated poles tend to go far away
from the imaginary axis splitting as two real poles, while the
single pole is attracted toward the origin, becoming the dominant root. Thus, the system behavior can be approximated as a
first order system but it turns slower. Fig. 6(b) shows that when
, the complex poles become dominant, resulting
increasing
in a near second order behavior. Since in both cases the poles
remain in the left half -plane, the system is stable in the range
of concern.
over the system
Fig. 7 illustrates the low sensibility of
dynamics, through three superimposed root locus plots considering the same variations as in Fig. 6. Due to the small variation
in the root locus, this parameter can be previously fixed or finally adjusted for fine tuning purposes.
Fig. 8 depicts two family of root locus considering a wider
and
coefficients, which allow us to identify
variation of
n
1
m = 0, 5 1 10
m = 010 1 10
m 10 .
Family of root locus diagrams ( = 5 10 ): (a)
for 10
10
and (b)
, 10 10 , and 15 10 for 0
1
1
10 10 , and 15 10
5 10 , 0, 5 10
0
1
m 1
,
,
stable and unstable behaviors. Note that, in this case, when
and
have positive values the system is stable. It can be seen
that there is a small range of negative values of
in which the
system remains stable. Out of this range, the system becomes
unstable (see shadowed area).
and
coefficients should be
In a practical design,
chosen to obtain the desired transient response specifications,
taking into account the well-known tradeoff design between an
over-damping fast response or a slower first order dynamics.
VII. SIMULATION AND EXPERIMENTAL RESULTS
The conventional droop method (3)–(4) and the proposed
control scheme (5)–(6) were simulated with the parameters
listed in Table I and the scheme shown in Fig. 9 for a two-inverter paralleled system in order to compare its outstanding
features. Coefficients and were chosen taking into account
the tradeoff between the power sharing accuracy and the
,
, and
were selected to
voltage regulation, while
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Fig. 9.
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004
Parallel operation of two inverters.
Fig. 11. Dynamic response of the phase difference between inverters, at
and (b)
.
variations of (a)
m
Fig. 10. Transient response of circulating current and its approximated
envelope deduced from (8): (a) conventional droop method and (b) proposed
control method.
ensure stability and a good transient response as explained in
the previous section.
Fig. 10 shows the startup circulating current and its approximated envelope deduced from (8), using the conventional droop
method and the proposed control, respectively. These results
confirm that the proposed controller achieves a better dynamic
response than that of the classical droop method approach. Note
that in spite of the initial current peak due to the initial phaseerror between inverters, a faster transient response, better dynamic performance, and less circulating current are achieved
with the proposed control solution.
Fig. 11 shows startup waveforms of the phase difference between the inverters for different values of the coefficients of the
proposed controller, which proves that the transient response
of the system can be easily modified with these parameters.
m
Fig. 11(a) depicts that the transient behavior turns slower and
less damped when increasing
, due to the fact that the real
pole becomes dominant, as shown Fig. 6(a). Fig. 11(b) shows
the tendency to obtain a more oscillatory response when in, since it attracts the conjugated poles toward the
creasing
imaginary axis, as can be seen in Fig. 6(b). Combining these two
degrees of freedom with the tight adjust of , we can obtain
a better dynamic performance than in the conventional droop
method, since using the conventional one the transient response
can not be adjusted without change and values.
Two 1-kVA single-phase inverter units were built and tested
in order to show the validity of the proposed approach. Each
inverter consisted of a single-phase insulated gate bipolar transistor (IGBT) full-bridge with a switching frequency of 20 kHz
and an
output filter, with the following parameters:
mH,
F,
V, and
V
Hz.
The controllers of these inverters were based on three loops: an
inner current-loop, an outer PI controller that ensures voltage
regulation [21], and the load-sharing controller, based on (5)
and (6). The last controller was implemented by means of a
TMS320LF2407A, fixed-point 40-MHz digital signal processor
(DSP) from Texas Instruments (see Fig. 12), using the parameters listed in Table I. The DSP-controller also includes a PLL
block in order to synchronize the inverter with the common bus.
When this occurs, the static bypass switch is turned on, and the
droop-based control is initiated.
GUERRERO et al.: WIRELESS CONTROLLER
Fig. 12.
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Power stage and controller of a single unit.
(a)
(a)
(b)
(b)
Fig. 13. Transient response of the circulating current (X-axis: 5 A/div, Y-axis:
100 ms/div): (a) conventional droop method and (b) proposed control method.
Fig. 14. Transient response of the active power P (X-axis: 500 W/div, Y-axis:
200 ms/div): (a) conventional droop method and (b) proposed control method.
The dynamic performance of the parallel system is
experimentally evaluated in case of connecting inverter #2
when the inverter #1 is supplying all the power required by
using
the load. Fig. 13 shows the circulating-current
the (a) conventional droop method and (b) the one proposed.
Fig. 14 depicts the active power transient behavior for both control schemes. These results show an overall improvement in the
dynamic response of the proposed control solution.
The second experimental test consists in supplying a nonlinear load by means of the two parallel inverter systems. Fig. 15
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004
(a)
(b)
Fig. 15. Steady-state waveforms supplying a nonlinear load: (a) load voltage
and current (X-axis: 5 ms/div, Y-axis: 150 V/div, 10 A/div) and (b) output
current of the two units (X-axis: 10 ms/div, Y-axis: 10 A/div).
shows the load voltage and current, and the output current of the
two units. As it can be seen, the load sharing capability is very
good, even when supplying nonlinear loads.
VIII. CONCLUSION
In this paper, a novel load-sharing controller for parallel inverters has been proposed. Based on the droop method, the controller avoids the use of control wire interconnections. In a sharp
contrast with the conventional droop method, the presented controller is able to modify the dynamic response of the paralleled
system by correctly tuning control gain parameters.
Simulation and experimental results show that the dynamic
response is significantly improved, highlighting the possibilities of the proposed approach for inverters in DG systems, when
several units must be connected to a common ac bus with a
proper transient response. Linear and nonlinear loads can be correctly supplied by the parallel system using the proposed control
solution.
ACKNOWLEDGMENT
The authors would like to thank J. Barri, R. Ciurans, D. Montesinos, and A. Sabé, Salicrú Electronics, for their help with the
experimental verification.
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Josep M. Guerrero (S’01–M’03) received the
B.S. degree in telecommunication engineering,
the M.S. degree in electronic engineering, and
the Ph.D. degree from Polytechnic University of
Catalunya, Barcelona, Spain, in 1997, 2000, and
2003, respectively.
Since 1998, he has been an Assistant Professor
in the Department of Automatic Control Systems
and Computer Engineering, Polytechnic University
of Catalunya, where he teaches digital signal
processing, control theory, and microprocessors. His
research interests include DSP-based control, uninterruptible power supplies,
and distributed power systems.
Dr. Guerrero is an Associate Editor with the IEEE TRANSACTIONS ON
INDUSTRIAL ELECTRONICS and is listed in the International Who’s Who in the
World and Who’s Who in Science and Engineering.
GUERRERO et al.: WIRELESS CONTROLLER
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Luis García de Vicuña received the Ingeniero de
Telecomunicación and Dr.Ing. degrees from the Polytechnic University of Catalunya, Barcelona, Spain, in
1980 and 1990, respectively, and the Dr.Sci. degree
from the Université Paul Sabatier, Toulouse, France,
in 1992.
From 1980 to 1982, he was an Engineer with Control Applications Company. He is currently an Associate Professor in the Department of Electronic Engineering, Polytechnic University of Catalunya, where
he teaches power electronics. His research interests
include power electronics modeling, simulation and control, active power filtering, and high-power-factor ac/dc conversion.
Miguel Castilla received the M.S. and Ph.D.
degrees in telecommunication engineering from the
Polytechnic University of Catalunya, Barcelona,
Spain, in 1995 and 1998, respectively.
Since 2002, he has been an Associate Professor
in the Department of Electronic Engineering,
Polytechnic University of Catalunya, where he
teaches analog circuits and power electronics. His
research interests are in the areas of modeling,
simulation, and control of dc-to-dc power converters
and high-power-factor rectifiers.
José Matas received the B.S., M.S., and Ph.D.
degrees in telecommunication engineering from the
Polytechnic University of Catalunya, Barcelona,
Spain, in 1988, 1996, and 2003, respectively.
Since 1997, he has been an Associate Professor
in the Department of Electronic Engineering,
Polytechnic University of Catalunya. His research
interests include power-factor-correction circuits,
distributed power systems, and nonlinear control.
Jaume Miret (M’98) received the B.S. degree
in telecommunications and the M.S. degree in
electronics from the Polytechnic University of
Catalunya, Barcelona, Spain, in 1992 and 1999,
respectively, where he is currently pursuing the
Ph.D. degree.
Since 1993, he has been an Assistant Professor at
the Polytechnic University of Catalunya. His research
interests include dc-to-ac converters, active power filters, and digital control.