anki a unified control strategy for three-phase inverter.pdf
TRANSCRIPT
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1176 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 3, MARCH 2014
A Unified Control Strategy for Three-Phase Inverter
in Distributed GenerationZeng Liu, Student Member, IEEE, Jinjun Liu, Senior Member, IEEE, and Yalin Zhao
AbstractThis paper presents a unified control strategy that en-ablesboth islanded and grid-tied operations of three-phase inverterin distributed generation, with no need for switching between twocorresponding controllers or critical islanding detection. The pro-posed control strategy composes of an inner inductor current loop,and a novel voltage loop in the synchronous reference frame. Theinverter is regulated as a current source just by the inner induc-tor current loop in grid-tied operation, and the voltage controlleris automatically activated to regulate the load voltage upon theoccurrence of islanding. Furthermore, the waveforms of the gridcurrent in the grid-tied mode and the load voltage in the islandingmode are distorted under nonlinear local load with the conven-tional strategy. And this issue is addressed by proposing a unified
load current feedforward in this paper. Additionally, this paperpresents the detailed analysis and the parameter design of thecontrol strategy. Finally, the effectiveness of the proposed controlstrategy is validated by the simulation and experimental results.
Index TermsDistributed generation (DG), islanding, load cur-rent, seamless transfer, three-phase inverter, unified control.
I. INTRODUCTION
DISTRIBUTED generation (DG) is emerging as a viable
alternative when renewable or nonconventional energy
resources are available, such as wind turbines, photovoltaic ar-
rays, fuel cells, microturbines [1], [3]. Most of these resourcesare connected to the utility through power electronic interfacing
converters, i.e., three-phase inverter. Moreover, DG is a suitable
form to offer high reliable electrical power supply, as it is able to
operate either in the grid-tied mode or in the islanded mode [2].
In the grid-tied operation, DG deliveries power to the utility
and the local critical load. Upon the occurrence of utility outage,
the islanding is formed. Under this circumstance, the DG must
be tripped and cease to energize the portion of utility as soon as
possible according to IEEE Standard 929-2000 [4]. However,
in order to improve the power reliability of some local critical
Manuscript received December 15, 2012; revised March 4, 2013; acceptedApril 21, 2013. Date of current version September 18, 2013. This work wassupported in part by the National Basic Research Program (973 Program) of
China under Project 2009CB219705, and by the State Key Laboratory of Elec-trical Insulation and Power Equipment under Project EIPE09109. This paperwas presented in part at the 26th IEEE Applied Power Electronics Conferenceand Exposition, Fort Worth, TX, USA, March 611, 2011. Recommended forpublication by Associate Editor D. Xu.
The authors are with the State Key Lab of Electrical Insulation andPower Equipment, School of Electrical Engineering, Xian Jiaotong Univer-sity, Xian 710049, China (e-mail: [email protected]; [email protected];[email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPEL.2013.2262078
load, the DG should disconnect to the utility and continue to
feed the local critical load [5]. The load voltage is key issue of
these two operation modes, because it is fixed by the utility in
the grid-tied operation, and formed by the DG in the islanded
mode, respectively. Therefore, upon the happening of islanding,
DG must take over the load voltage as soon as possible, in order
to reduce the transient in the load voltage. And this issue brings
a challenge for the operation of DG.
Droop-based control is used widely for the power sharing of
parallel inverters [11], [12], which is called as voltage mode
control in this paper, and it can also be applied to DG to real-
ize the power sharing between DG and utility in the grid-tied
mode [13][16], [53]. In this situation, the inverter is always
regulated as a voltage source by the voltage loop, and the qual-
ity of the load voltage can be guaranteed during the transition
of operation modes. However, the limitation of this approach is
that the dynamic performance is poor, because the bandwidth
of the external power loop, realizing droop control, is much
lower than the voltage loop. Moreover, the grid current is not
controlled directly, and the issue of the inrush grid current dur-
ing the transition from the islanded mode to the grid-tied mode
always exists, even though phase-locked loop (PLL) and the
virtual inductance are adopted [15].
The hybrid voltage and current mode control is a popularalternative for DG, in which two distinct sets of controllers
are employed [17][40]. The inverter is controlled as a current
source by one sets of a controller in the grid-tied mode, while
as a voltage source by the other sets of controller in the islanded
mode. As the voltage loop or current loop is just utilized in
this approach, a nice dynamic performance can be achieved.
Besides, the output current is directly controlled in the grid-tied
mode, and the inrush grid current is almost eliminated.
In the hybrid voltage and current mode control, there is a
need to switch the controller when the operation mode of DG
is changed. During the interval from the occurrence of utility
outage and switching the controller to voltage mode, the load
voltage is neither fixed by the utility, nor regulated by the DG,
and the length of the time interval is determined by the islanding
detection process. Therefore, the main issue in this approach is
that it makes the quality of the load voltage heavily reliant on the
speed and accuracy of the islanding detection method [6][10].
Another issue associated with the aforementioned approaches
is the waveform quality of the grid current and the load voltage
under nonlinear local load. In the grid-tied mode, the output
current of DG is generally desired to be pure sinusoidal [18].
When the nonlinear local load is fed, the harmonic component
of the load current will fully flow into the utility. A single-phase
DG,which injects harmonic current into theutility for mitigating
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Fig. 1. Schematic diagram of the DG based on the proposed control strategy.
the harmonic component of the grid current, is presented in [41].
The voltage mode control is enhanced by controlling the DG to
emulate a resistance at the harmonic frequency, and then the
harmonic current flowing into utility can be mitigated [42].
In the islanded mode, the nonlinear load may distort the load
voltage [43], and many control schemes have been proposed toimprove the quality of the load voltage, including a multiloop
control method [43][46], resonant controllers[48], [49], sliding
mode control [47]. However, existing control strategies, dealing
with the nonlinear local load in DG, mainly focus on either the
quality of the grid current in the grid-tied mode or the one of the
load voltage in the islanded mode, and improving both of them
by a unified control strategy is seldom.
This paper proposes a unified control strategy that avoids
the aforementioned shortcomings. First, the traditional induc-
tor current loop is employed to control the three-phase inverter
in DG to act as a current source with a given reference in the
synchronous reference frame (SRF). Second, a novel voltagecontroller is presented to supply reference for the inner induc-
tor current loop, where a proportional-plus-integral (PI) com-
pensator and a proportional (P) compensator are employed in
D-axis andQ-axis, respectively. In the grid-tied operation, the
load voltage is dominated by the utility, and the voltage com-
pensator inD-axis is saturated, while the output of the voltage
compensator inQ-axis is forced to be zero by the PLL. There-
fore, the reference of the inner current loop cannot regulated by
the voltage loop, and the DG is controlled as a current source
just by the inner current loop. Upon the occurrence of the grid
outage, the load voltage is no more determined by the utility,
and the voltage controller is automatically activated to regulate
the load voltage. These happen naturally, and, thus the proposedcontrol strategy does not need a forced switching between two
distinct sets of controllers. Further, there is no need to detect
the islanding quickly and accurately, and the islanding detec-
tion method is no more critical in this approach. Moreover,
the proposed control strategy, benefiting from just utilizing the
current and voltage feedback control, endows a better dynamic
performance, compared to the voltage mode control.
Third, the proposed control strategy is enhanced by introduc-
ing a unified load current feedforward, in order to deal with
the issue caused by the nonlinear local load, and this scheme
is implemented by adding the load current into the reference
of the inner current loop. In the grid-tied mode, the DG injects
harmonic current into the grid for compensating the harmonic
component of the grid current, and thus, the harmonic compo-
nent of the grid current will be mitigated. Moreover, the benefit
of the proposed load current feedforward can be extended into
the islanded operation mode, due to the improved quality of the
load voltage.The rest of this paper is arranged as follows. Section II de-
scribes the proposed unified control strategy for three-phase
inverter in DG, including the power stage of DG, the basic idea,
and the control diagram. The detailed operation principle of DG
with the proposed control strategy is illustrated in Section III.
The parameter design and small signal analysis of the proposed
control system are given in Section IV. Section V investigates
the proposed control strategy by simulation and experimental
results. Finally, the concluding remarks are given in Section VI.
II. PROPOSED CONTROL STRATEGY
A. Power Stage
This paper presents a unified control strategy for a three-
phase inverter in DG to operate in both islanded and grid-tied
modes. The schematic diagram of the DG based on the proposed
control strategy is shown by Fig. 1. The DG is equipped with
a three-phase interface inverter terminated with aLCfilter. The
primary energy is converted to the electrical energy, which is
then converted to dc by the front-end power converter, and the
output dc voltage is regulated by it. Therefore, they can be
represented by the dc voltage source Vdc in Fig. 1. In the ac side
of inverter, the local critical load is connected directly.
It should be noted that there are two switches, denoted by Suand Si , respectively, in Fig. 1, and their functions are different.
The inverter transfer switch Si is controlled by the DG, and the
utility protection switch Su is governed by the utility. When the
utility is normal, both switches Siand Su are ON, and the DG in
the grid-tied mode injects power to the utility. When the utility is
in fault, the switch Su is tripped by the utility instantly, and then
the islanding is formed. After the islanding has been confirmed
by the DG with the islanding detection scheme [6][10], the
switch Si is disconnected, and the DG is transferred from the
grid-tied mode to theislandedmode. When theutility is restored,
the DG should be resynchronized with the utility first, and then
the switch Si is turned ON to connect the DG with the grid.
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Fig. 2. Overall block diagram of the proposed unified control strategy.
B. Basic Idea
With the hybrid voltage and current mode control [17][40],
the inverter is controlled as a current source to generate the
reference power PDG + jQDG in the grid-tied mode. And itsoutput power PDG + jQD G should be the sum of the powerinjected to the grid Pg + jQg and the load demand Pload +
jQload , which can be expressed as follows by assuming that the
load is represented as a parallel RLCcircuit:
Pload = 3
2 V
2m
R (1)
Qload = 3
2V2m
1
LC
. (2)
In (1) and (2), Vm and represent the amplitude and fre-
quency of the load voltage, respectively. When the nonlinear
local load is fed, it can still be equivalent to the parallel RLC
circuit by just taking account of the fundamental component.
During the time interval from the instant of islanding happen-
ing to the moment of switching the control system to voltage
mode control, the load voltage is neither fixed by the utility norregulated by the inverter, so the load voltage may drift from
the normal range [6]. And this phenomenon can be explained
as below by the power relationship. During this time interval,
the inverter is still controlled as a current source, and its output
power is kept almost unchanged. However, the power injected to
utility decreases to zero rapidly, and then the power consumed
by the load will be imposed to the output power of DG. If both
active power Pg and reactive power Qg injected into the grid are
positive in the grid-tied mode, then Ploadand Qload will increase
after the islanding happens, and the amplitude and frequency of
the load voltage will rise and drop, respectively, according to
(1) and (2).
With the previous analysis, if the output power of inverter
PDG +jQD G could be regulated to match the load demand bychanging the current referencebeforethe islanding is confirmed,
the load voltage excursion will be mitigated. And this basic idea
is utilized in this paper. In the proposed control strategy, the
output power of the inverter is always controlled by regulating
the three-phase inductor currentiLabc , while the magnitude and
frequency of the load voltage vC a b c are monitored. When theislanding happens, the magnitude and frequency of the load volt-
agemay drift from thenormal range,and then they arecontrolled
to recover to the normal range automatically by regulating the
output power of the inverter.
C. Control Scheme
Fig. 2 describes the overall block diagram for the proposed
unified control strategy, where the inductor current iLabc , the
utility voltage vg ab c , the load voltage vC a b c , and the load current
iL L ab care sensed. And the three-phase inverter is controlled in
the SRF, in which, three phase variable will be represented
by dc quantity. The control diagram is mainly composed bythe inductor current loop, the PLL, and the current reference
generation module.
In the inductor current loop, the PI compensator is employed
in bothD- andQ-axes, and a decoupling of the cross coupling
denoted by 0 Lf/kPW M is implemented in order to mitigate the
couplings due to the inductor. The output of the inner current
loopddq, together with the decoupling of the capacitor voltage
denoted by 1/kPW M , sets the reference for the standard space
vector modulation that controls the switches of the three-phase
inverter. It should be noted thatkPW M denotes the voltage gain
of the inverter, which equals to half of the dc voltage in this
paper.
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Fig. 3. Block diagram of the current reference generation module.
The PLL in the proposed control strategy is based on the
SRF PLL [50], [51], which is widely used in the three-phasepower converter to estimate the utility frequency and phase.
Furthermore, a limiter is inserted between the PI compensator
GPL L and the integrator, in order to hold the frequency of the
load voltage within the normal range in the islanded operation.
In Fig. 2, it can be found that the inductor current is regulated
to follow the current reference iL re fd q , and the phase of the
current is synchronized to the grid voltage vg ab c . If the current
referenceis constant, the inverter is just controlled to be a current
source, which is the same with the traditional grid-tied inverter.
The new part in this paper is the current reference generation
module shown in Fig. 2, which regulates the current reference to
guarantee the power match between the DG and the local loadand enables the DG to operate in the islanded mode. Moreover,
the unified load current feedforward, to deal with the nonlinear
local load, is also implemented in this module.
The block diagram of the proposed current reference gen-
eration module is shown in Fig. 3, which provides the current
referencefor the inner current loop in both grid-tied and islanded
modes. In this module, it can be found that an unsymmetrical
structure is used in D- and Q-axes. The PI compensator is
adopted in D-axes, while the P compensator is employed in
Q-axis. Besides, an extra limiter is added in theD-axis. More-
over, the load current feedforward is implemented by adding the
load current iLLdqto thefinal inductor current reference iL re fd q .
The benefit brought by the unique structure in Fig. 3 can be rep-resented by two parts: 1) seamless transfer capability without
critical islanding detection; and 2) power quality improvement
in both grid-tied and islanded operations. The current reference
iL re d q composes of four parts in D- and Q-axes respectively:
1) the output of voltage controller ir e f d q ; 2) the grid current
referenceIg re fd q ; 3) the load currentiLLdq; and 4) the current
flowing through the filter capacitor Cf.
In the grid-tied mode, the load voltage vC dq is clamped by the
utility. The current reference is irrelevant to the load voltage, due
to the saturation of the PI compensator in D-axis, and the output
of the P compensator being zero in Q-axis, and thus, the inverter
operates as a current source. Upon occurrence of islanding, the
voltage controller takes over automatically to control the load
voltage by regulating the current reference, and the inverter acts
as a voltage source to supply stable voltage to the local load;
this relieves the need for switching between different control
architectures.
Another distinguished function of the current reference gen-
eration module is the load current feedforward. The sensed
load current is added as a part of the inductor current refer-
ence iL re fd q to compensate the harmonic component in the grid
current under nonlinearlocal load. In theislandedmode, theload
current feedforward operates still, and the disturbance from the
load current, caused by the nonlinear load, can be suppressed
by the fast inner inductor current loop, and thus, the quality of
the load voltage is improved.
The inductor current control in Fig. 2 was proposed in pre-
vious publications for grid-tied operation of DG [18], and the
motivation of this paper is to propose a unified control strategy
for DG in both grid-tied and islanded modes, which is repre-
sented by the current reference generation module in Fig. 3.
The contribution of this module can be summarized in two as-pects. First, by introducing PI compensator and P compensator
in D-axis and Q-axis respectively, the voltage controller is inac-
tivated in the grid-tied mode and can be automatically activated
upon occurrence of islanding. Therefore, there is no need for
switching different controllers or critical islanding detection,
and the quality of the load voltage during the transition from
the grid-tied mode to the islanded mode can be improved. The
second contribution of this module is to present the load current
feedforward to deal with the issue caused by the nonlinear local
load, with which, not only the waveform of the grid current in
grid-tied is improved, but also the quality of the load voltage in
the islanded mode is enhanced.Besides, it should be noted that a three-phase unbalanced
local load cannot be fed by the DG with the proposed control
strategy, because there is no flow path for the zero sequence
current of the unbalanced load, and the regulation of the zero
sequence current is beyond the scope of the proposed control
strategy.
III. OPERATIONPRINCIPLE OFDG
The operation principle of DG with the proposed unified
control strategy will be illustrated in detail in this section, and
there are in total four states for the DG, including the grid-tiedmode, transition from the grid-tied mode to the islanded mode,
the islanded mode, and transition from the islanded mode to the
grid-tied mode.
A. Grid-Tied Mode
When the utility is normal, the DG is controlled as a current
source to supply given active and reactive power by the inductor
current loop, and the active and reactive power can be given
by the current reference ofD- andQ-axis independently. First,
the phase angle of the utility voltage is obtained by the PLL,
which consists of a Park transformation expressed by (3), a PI
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compensator, a limiter, and an integrator
xd
xq
=
2
3
cos cos
2
3
cos
+
2
3
sin sin
23
sin
+
2
3
xaxb
xc
. (3)Second, the filter inductor current, which has been trans-
formed into SRF by the Park transformation, is fed back and
compared with the inductor current reference iL re fd q , and the
inductor current is regulated to track the reference iL re fd q by
the PI compensatorGI.
The reference of the inductor current loop iL re fd q seems
complex andit is explained as below. It is assumed that theutility
is stiff, and the three-phase utility voltage can be expressed as
vga
=Vgcos
vgb =Vgcos
2
3
vgc =Vgcos
+
2
3
(4)
where Vgis the magnitude of the grid voltage, and is the actual
phase angle. By the Park transformation, the utility voltage is
transformed into the SRF, which is shown asvg d =Vgcos(
)vg q =Vgsin(
).(5)
vgq is regulated to zero by the PLL, sovgd equals the mag-nitude of the utility voltage Vg . As the filter capacitor voltage
equals the utility voltage in the gird-tied mode,vC d equals the
magnitude of the utility voltage Vg , andvC qequals zero, too.
In the D-axis, the inductor current reference iL r e f d can be
expressed by (6) according to Fig. 3
iL r e f d =Ig r e f d + iLL d0 Cf vC q. (6)The first part is the output of the limiter. It is assumed that
the given voltage reference Vma x is larger than the magnitude
of the utility voltagevC d in steady state, so the PI compensator,
denoted by GV D in the following part, will saturate, and the
limiter outputs its upper value Ig r e f d . The second part is the
load current ofD-axisiLL d , which is determined by the charac-teristic of the local load. The third part is the proportional part
0 Cf vC q, where 0 is the rated angle frequency, and Cfis the capacitance of the filter capacitor. It is fixed as vC q de-
pends on the utility voltage. Consequently, the current reference
iL r e f d is imposed by the given reference Ig r e f d and the load
currentiLL d , and is independent of the load voltage.
In theQ-axis, the inductor current reference iL r e f q consists
of four parts as
iL r e f q =vC qkGv q+Ig r e f q + iLL q+0 Cf vC d (7)wherekGv q is the parameter of the P compensator, denoted by
GV Q in the following part. The first part is the output ofGV Q ,
Fig. 4. Simplified block diagram of the unified control strategy when DGoperates in the grid-tied mode.
which is zero as thevC qhas been regulated to zero by the PLL.
The second part is the given current reference Ig r e f q , and the
third part represents the load current in Q-axis. The final part
is the proportional part0 Cf vC d , which is fixed since vC ddepends on the utility voltage. Therefore, the current reference
iL r e f q cannot be influenced by the external voltage loop and is
determined by the given reference Ig r e f q and the load current
iLL q.With the previous analysis, the control diagram of the inverter
can be simplified as Fig. 4 in the grid-tied mode, and the inverter
is controlled as a current source by the inductor current loop
with the inductor current reference being determined by the
current reference Ig r e f d q and the load current iLLdq. In other
words, the inductor current tracks the current reference and the
load current. If the steady state error is zero, Ig re fd q represents
the grid current actually, and this will be analyzed in the next
section.
B. Transition From the Grid-Tied Mode to the Islanded Mode
When the utility switch Su opens, the islanding happens, andthe amplitude and frequency of the load voltage will drift due
to the active and reactive power mismatch between the DG and
the load demand. The transition, shown in Fig. 5, can be divided
into two time interval. The first time intervals is from the instant
of turning off Su to the instant of turning off Si when islanding
is confirmed. The second time interval begins from the instant
of turning off inverter switch Si .
During the first time interval, the utility voltage vg ab c is still
the same with the load voltage vC a b c as the switch Si is in ON
state. As thedynamic of theinductor current loop andthe voltage
loop is much faster than the PLL [52], while the load voltage
and current are varying dramatically, the angle frequency of the
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Fig. 5. Operation sequence during the transition from the grid-tied mode to
the islanded mode.
Fig. 6. Transient process of the voltage and current when the islandinghappens.
load voltage can be considered to be not varied. The dynamicprocess in this time interval can be described by Fig. 6, and it is
illustrated later.
In the grid-tied mode, it is assumed that the DG injects ac-
tive and reactive power into the utility, which can be expressed
by (8) and (9), and that the local critical load, shown in (10),
represented by a series connected RLCcircuit with the lagging
power factor
Pg = 3
2(vC d igd + vC qigq) =
3
2vC d ig d (8)
Qg = 3
2(vC qigdvC d igq) =
3
2vC d igq (9)
Zsload =Rs+ j Ls+ 1
j Cs
=Rs+ j
Ls
1
Cs
=Rs+ jXs . (10)
When islanding happens, igd will decrease from positive to
zero, and ig qwill increase from negative to zero. At the same
time, the load current will vary in the opposite direction. The
load voltage in D- andQ-axes is shown by (11) and (12), and
each of them consists of two terms. It can be found that the
load voltage inD-axisvC d will increase as both terms increase.However, the trend of the load voltage in Q-axis vC q is uncertain
because the first term decreases and the second term increases,
and it is not concerned for a while
vC d =iLL dRsiLL qXs (11)vC q =iLL qRs+ iLL dXs . (12)
With the increase of the load voltage in D-axis vC d , when
it reaches and exceeds Vma x , the input of the PI compensator
GV D will become negative, so its output will decrease. Then,
the output of limiter will not imposed toIg r e f d any longer, and
the current reference iL r e f d will drop. With the regulation of
the inductor current loop, the load current in D-axisiLL d will
decrease. As a result, the load voltage in D-axisvC d will drop
and recover toVm ax . AfteriLL d has almost fallen to the normal
value, the load voltage in Q-axis vC q will drop according to
(12). AsvC q is decreased from zero to negative, then the input
of the PI compensator GPL Lwill be negative, and its output will
drop. In other words, the angle frequency will be reduced.
If it falls to the lower value of the limiter mi n , then the angle
frequency will be fixed at m in .
Consequently, at the end of the first time interval, the load
voltage in D -axis vC d will be increased to and fixed at Vm ax ,
and the angle frequency of the load voltage will drop. If it is
higher than the lower value of the limiter m in , the PLL can still
operate normally, and the load voltage in Q-axis vC q will be
zero. Otherwise, if it is fixed atm in , the load voltage inQ-axis
vC qwill be negative. As the absolute values ofvC d and vC q,
at least the one ofvC d , are raised, the magnitude of the load
voltage will increase finally.
The variation of the amplitude and frequency in the load volt-
age can also be explained by the power relationship mentioned
before. When the islanding happens, the local load must ab-sorb the extra power injected to the grid, as the output power
of inverter is not changed instantaneously. According to (1), the
magnitude of the load voltageVm will rise with the increase of
Pload . At the same time, the angle frequency should drop, in
order to consume more reactive power with (2). Therefore, the
result through the power relationship coincides with the previ-
ous analysis.
The second time interval of the transition begins from the
instant when the switch Si is open after the islanding has been
confirmed by the islanding detection method. If the switch S iopens, the load voltage vC a b c is independent with the grid volt-
age vgabc . At the same time, vg ab c will reduce to zero theo-retically as the switch Su has opened. Then, the input of the
compensator GPL L becomes zero and the angle frequency is
invariable and fixed to the value at the end of the first interval.
Under this circumstance,vC dqis regulated by the voltage loop,
and the inverter is controlled to be a voltage source.
With the previous analysis, it can be concluded that the drift
of the amplitude and frequency in the load voltage is restricted
in the given range when islanding happens. And the inverter
is transferred from the current source operation mode to the
voltage source operation mode autonomously. In the hybrid
voltage and current mode control [17][40], the time delay of
islanding detection is critical to the drift of the frequency and
magnitude in the load voltage, because the drift is worse withthe increase of the delay time. However, this phenomenon is
avoided in the proposed control strategy.
C. Islanded Mode
In the islanded mode, switching Si and Su are both in OFF
state. The PLL cannot track the utility voltage normally, and the
angle frequency is fixed. In this situation, the DG is controlled as
a voltage source, because voltage compensatorGV D andGV Qcan regulate the load voltage vC dq. The voltage references in D-
andQ-axis areVma x and zero, respectively. And the magnitude
of the load voltage equals to Vm ax approximately, which will
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Fig. 7. Simplified block diagram of the unified control strategy when DG
operates in the islanded mode.
be analyzed in Section IV. Consequently, the control diagram of
the three-phase inverter in the islanded mode can be simplified
as shown in Fig. 7.
In Fig. 7, the load current iLLdq is partial reference of the
inductor current loop. So, if there is disturbance in the load
current, it will be suppressed quickly by the inductor current
loop, and a stiff load voltage can be achieved.
D. Transition From the Islanded Mode to the Grid-Tied Mode
If the utility is restored and the utility switch Su is ON, the
DG should be connected with utility by turning on switch S i .
However, several preparation steps should be performed before
turning on switch Si .
First, as soon as utility voltage is restored, the PLL will track
the phase of the utility voltage. As a result, the phase angle of
the load voltagevC a b c will follow the grid voltagevg ab c . If the
load voltagevC a b c is in phase with the utility voltage,vg d will
equal the magnitude of the utility voltage according to (5).
Second, as the magnitude of the load voltage Vm ax is larger
than the utility voltage magnitudeVg , the voltage referenceVre f
will be changed to Vg by toggling the selector S from terminals 1to 2. As a result, the load voltage will equal to the utility voltage
in both phase and magnitude.
Third, the switch Si is turned on, and the selector S is reset
to terminal 1. In this situation, the load voltage will be held by
the utility. As the voltage reference Vre f equals Vm ax , which
is larger than the magnitude of the utility voltage Vg , so the
PI compensator GV D will saturate, and the limiter outputs its
upper value Ig r e f d . At the same time,vC qis regulated to zero
by the PLL according to (5), so the output of GV Q will be
zero. Consequently, the voltage regulators GV D andGV Q are
inactivated, and the DG is controlled as a current source just by
the inductor current loop.
IV. ANALYSIS ANDDESIGN
In this section, the three-phase inverter with the proposed
control strategy is analyzed and designed in both steady state
and transient state. In the steady state, the operation points of
DG in both grid-tied and islanded modes are analyzed, and
the limiters and references are selected. In the transient state,
compensators in both inductor current loop and the externalvoltage loop are designed based on the small-signal model, and
the impact of the load current feedforward is analyzed as well.
A. Steady State
1) Analysis of Operation Points: As analyzed previously, in
the grid-tied mode, the inverter is controlled as a current source,
and the current reference for the inductor current loop iL re fd q is
expressed by (6) and (7). The steady-state error will be zero with
the PI compensator in the inductor current loop, so the inductor
current in steady state can be expressed as follows:
iLd =Ig r e f d0 Cf vC q+iLL diLq =vC qkGv q+ 0 Cf vC d+ Ig r e f q +iLL q. (13)
In the SRF, the relationship between the voltage and the cur-
rent of the filter capacitor in steady state can be expressed byiC d =vC qCfiC q =vC dCf
(14)
where represents the angle frequency of the DG and Cfdenotes capacitance of the filter capacitor. As a result, the output
current of the inverter iod qcan be gained
iod =iLdiC d =Ig r e f d(0)Cf vC q+iLL d
ioq =iLqiC q =vC qkGv q+Ig r e f q + (0)Cf vC q+iLL q.
(15)
As angle frequency is very close to the rated angle fre-
quency0 , the output currentiod qcan be simplified asiod =Ig r e f d + iLL d
ioq =vC qkGv q+Ig r e f q +iLL q.(16)
It can be found that the output current follows Ig r e f d q and the
load current iLLdq, as vC qequals zero in the grid-tied mode. The
active and reactive power injected into utility can be obtained
as follows. Consequently, the active power and reactive power
flowing from the inverter to utility can be given by Ig r e f d andIg r e f q , respectively
Pg =3
2[vC d(iodiLL d ) +vC q(ioqiLL q)]
=3
2vC d Ig re f d
Qg = 3
2[vC q(iodiLL d )vcC d(ioqiLL q)]
=32vC d Ig r e f q .
(17)
In the islanded mode, the inverter is controlled as a volt-
age source by the external voltage loop. In the D-axis,vC d is
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regulated by the PI compensatorGV D , so the steady state error
will be zero andvC d can be expressed as follows:
vC d =Vre f (18)
whereVre fis the voltage reference inD-axis.
In the Q-axis, the regulator GV Q is P compensator, so the
steady state error may not be zero. As the load current is added
to the inductor reference, the condition shown as below can be
achieved
vC qkGv q+Ig r e f q = 0. (19)And then, the load voltage in Q-axis can be expressed by
(20). It should be noted that the absolute value ofvC qrises with
the increase of the current reference Ig r e f q which is related to
the reactive power injected into the utility
vC q =Ig r e f q
kGv q. (20)
The magnitude of the load voltage Vm can be represented as
follows. It equals toVre fapproximately, becausevC qshould bemuch lower thanVre fwith proper current reference Ig r e f q
Vm =
V2re f+
Ig r e f q
kGv q
2Vre f. (21)
When the islanding happens, the angle frequency is restricted
in the given range by the limiter. As analyzed previously, the an-
gle frequency in the islanded mode is determined in the first time
interval of the transition from the grid-tied made to the islanded
mode. According to (20), if the current reference Ig r e f q is set
to zero, vC q is zero. Then, it means that the angle frequency
does not vary in the first time interval of the transition, and
it should equal g 0 , which denotes the angle frequency of theutility before islanding happens. Consequently, the angle fre-
quency of the load voltage in the islanded mode is determined
by the current referenceIg r e f q , and it can be expressed by (22),
wherem in andm ax represent the upper and lower values of
the limiter shown in Fig. 2, respectively
=
m in , Ig r e f q >0
g 0 , Ig r e f q = 0
m ax , Ig r e f q
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TABLE IPARAMETERS OF THEPOWERSTAGE
Fig. 8. Bode plot of the control-to-current transfer function in grid-tied andislanded modes.
0 Cfin Fig. 3 [12]. Therefore, the small-signal model can be
simplified into two identical SISO systems, which is representedby (28) and the subscriptd andqare ignored
Vdc
2 d= Lf
d
dtiL+Rl iL + vC
iL =Cfd
dtvC + iLL + ig .
(28)
2) Design and Analysis of the Current Loop: The inductor
current loop should operate normally to regulate the inductor
current loop in both islanded andgrid-tiedmodes. In the islanded
mode, the small-signal model of the control-to-current can be
obtained according to (28), which is shown as
Gid 1 (s) =iL (s)
d(s)=
Vdc
2 sCf
s2 LfCf +sRl Cf + 1. (29)
However, in the grid-tied mode, the dynamic of the capacitor
Cfis ignored due to the stiff utility [34], and the small-signal
model of the control-to-current is described by
Gid 2 (s) =iL (s)
d(s)=
Vdc
2 1
sLf +Rl. (30)
The parameters of the power stage in this paper are shown
in Table I, and the Bode plot of the control-to-current transfer
function in both of operation modes is shown in Fig. 8. It can
be found that huge difference appears in the low and medium
Fig. 9. Bode plot of the loop gain of the inner current loop.
Fig. 10. Block diagram of the simplified voltage loop.
frequency range, and it is difficult to design the compensator GIto achieve good performance in both of operation modes.
The reason for this difference between the islanded mode
and the grid-tied mode is that the inductor current is coupled
with the capacitor voltage in the islanded mode. To mitigate
this difference, the capacitor voltage is fed forward with the
coefficient 1/kPW M in Fig. 2, and then the inductor current
can be decoupled with the capacitor voltage. Consequently, thetransfer function of control to current in the islanded mode
is changed to be close to the one in the grid-tied mode, and
the current compensator GIcan be designed based on unified
transfer function shown by (30).
The PI compensatorGI in (31) is designed, and the digital
delay caused by the pulse width modulation (PWM) and sample
is considered as well. The loop gain of the current loop is shown
in Fig. 9, with the crossover frequency of 1100 Hz, and the phase
margin of 65
Gi (s) =kGi1 + s
G i
s . (31)
3) Design and Analysis of the Voltage Loop: The voltage
loop just operates in the islanded mode to regulate the load
voltage, and the simplified block diagram is shown in Fig. 10,
where Gic (s) and Gv i (s) denote the closed-looptransfer function
of an inductor loop and the impedance of the filter capacitor Cf,
respectively.
In theD-axis,GV D is a PI compensator shown in (32), while
a P compensator GV Q expressed by (33) is used in Q-axis.
These two compensators are designed, and the loop gain of the
current loop is shown in Fig. 11. It can be found that there is a
little difference in the low frequency range. The phase margin
is set to 55, and the crossover frequency is around 600 Hz in
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Fig. 11. Bode plot of the loop gain of the voltage loop inD - andQ-axes.
bothD- andQ-axes
Gv d (s) =kGv d 1 + s G v d
s (32)
Gv q(s) =kGv q. (33)
4) Impact of Load Current Feedforward: In Fig. 10, the load
current iLL is a part of the inductor current reference, and thedisturbance from the load current can be suppressed by the
inductor current loop directly. To evaluate the effect of the load
current feedforward in the islanded mode, the transfer function
of the output impedance is derived. The output impedances with
and without load current feedforward are expressed by
Zo1 (s) = vC(s)
iLL (s) =
Gv i (s)
[1
Gic (s)]
1 +Gv (s)Gic (s)Gv i (s) (34)
Zo2 (s) = vC(s)
iLL (s)= Gv i (s)
1 +Gv (s)Gic (s)Gv i (s). (35)
Comparing (34) and (35), it can be found that an extra factor
[1Gic (s)] appears in the output impedance with load currentfeedforward, and the magnitude of the output impedance will
be reduced in the low frequency range because the gain of
the closed-loop transfer function Gic (s) closes to unity in thebandwidth of the current loop. The Bode plot of the output
impedance of these two conditions is shown in Fig. 12, and
it can be seen that the magnitude of the output impedance is
reduced from dc to 600 Hz with the load current feedforward.
Consequently, the quality of the load voltage vC a b c will be
improved with the load current feedforward.
In the grid-tied mode, the inductor current is regulated by the
inductor current loop directly, and the inductor current reference
is mainly composed by the current reference Ig r e f d q , and the
load current iLLdq. If the load current is not fed forward, the
output currentiod qof the inverter will be fixed byIg r e f d q . As a
result, the disturbance of the load current will be fully injected
into the utility, and this can be represented by
ig (s)
iLL (s)
=
1. (36)
Fig. 12. Bode plot of the output impedance with and without the load currentfeedforward, when DG operates in the islanded mode.
Fig. 13. Bode plot of the transfer function from load current to grid current
with andwithout theloadcurrent feedforward, when DGoperates inthe grid-tiedmode.
With the load current feedforward, the disturbance of the
load current can be compensated by the inverter, and the trans-
fer function from the load current to the grid current can be
described by (37). The Bode plots of transfer function [see (36)
and (37)] are shown in Fig. 13, and the gain is mitigated up to
1050 Hz with the load current feedforward and therefore, the
quality of the grid current can be improved
ig (s)
iLL (s)=Gic (s)1. (37)
V. SIMULATION ANDEXPERIMENTAL RESULTS
A. Simulation Results
To investigate the feasible of the proposed control strategy,
the simulation has been done in PSIM. The power rating of a
three-phase inverter is 3 kW in the simulation. The parameters in
the simulation are shown in Tables I and II. The RMS of the rated
phase voltage is 115 V, and the voltage reference Vm ax is set
as 10% higher than the rated value. The rated utility frequency
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Fig. 16. Diagram of the experimental prototype of DG.
Fig. 17. Experimental waveforms when DG is in the islanded mode: CH1,load currentiL L a , 5 A/div; CH3, load voltage vC a , 100 V/div; CH4, inductorcurrentiL a , 5 A/div.
Fig. 18. Experimental waveforms when DG is in the grid-tied mode: CH1,load current iL L a , 5 A/div;CH2, grid voltage vg a , 100 V/div; CH4,grid currentig a , 10 A/div.
Comparing the simulation results above, it can be found that
the voltage quality is improved deeply by the proposed con-
trol strategy in the transition from the grid-tied mode to the
islanded mode, and the speed of the islanding detection is no
more critical.
Fig. 19. Experimental waveforms when DG is transferred from the grid-tied
mode to the islanded mode with (a) conventional hybrid voltage and currentmode control, and (b) proposed unified control strategy: CH2, load voltage
vC a , 100 V/div; CH3, grid current ig a , 10 A/div; CH4, inductor current iL a ,10 A/div.
B. Experimental Results
To verify the proposed control strategy, an experimental pro-
totype of DG has been established, which is shown in Fig. 16.
The utility for the DG is emulated by a three-phase transformer
and a voltage regulator connected with the actual utility. The
rated line voltage of the actual utility is 380 V. The emulated
utility is called as utility in the below. Moreover, the inverter
in the DG is fed by a three-phase diode rectifier, and the
dc-bus voltage is set to 400 V approximately by the voltage
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Fig. 20. Experimental waveforms when DG is transferred from the islanded mode to the grid-tied mode: CH1, grid voltagevg a , 100 V/div; CH2, load voltagevC a , 100 V/div; CH3, grid currentig a , 10 A/div; CH4, inductor currentiL a , 10 A/div.
regulator. Besides, the control system is implemented fully dig-
itally by digital signal processor TMS320F28335 from Texas
Instruments. The parameters in the experimental DG, shown in
Tables I and II, are identical to the ones used in the simulation.Fig. 17 shows the experimental waveforms when DG is in
the islanded mode, and it can be seen that the magnitude of the
load voltage equals 180 V approximately, and the total harmonic
distortion (THD) of the load voltage is 0.9%.
Fig. 18 shows the experimental waveforms when DG is in the
grid-tied mode. The magnitude of the grid current is closed to
9 A, and the THD of the grid current is 3.6% approximately.
When the DG is transferred from the grid-tied mode to the
islanded mode, the experimental results with the traditional hy-
brid voltage and current mode control and the proposed unified
control strategy are given in Fig. 19. Before the islanding hap-
pens, the magnitude of the load voltage is around 163 V. The
current injected into the utility ig a is in phase with the utility
voltage, and the magnitude ofiga is approximately 9 A. When
the switch Su opens, the islanding happens, and the grid current
ig a drops to zero. In the traditional hybrid voltage and current
mode control, it can be found that the load voltage is seriously
distorted upon the occurrence of islanding. And this condition
lasts until the islanding is confirmed by DG and the control
structure is changed to regulate the load voltage. However, with
the proposed unified control strategy, the distortion of the load
voltage is obviously improved, and the magnitude of the load
voltage increases slightly and is close to 180 V.
Fig. 20 shows the process when DG is transferred from the is-
landed mode to the grid-tied mode. From 0 ms to around 300 ms,the phase of the load voltage is regulated to resynchronize with
the utility voltage, and the phase difference is reduced gradually.
Then, the magnitude of the load voltage is regulated to equal
the utility voltage. At the moment of 350 ms, the switch Si is
turned on, and the current injected into the grid ig a increases
smoothly without huge inrush current, and the load voltage is
stable during the transition.
Fig. 21 shows the experimental waveforms when DG feeds
nonlinear load in the islanded mode. It can be seen that the
distortion of the load voltage is improved by the load current
feedforward, and the THD of the load voltage is reduced from
4.7% to 3.2%.
Fig. 21. Experimental waveform when DG feeds nonlinear load in islandedmode (a) with load current feedforward and (b) without load current feedfor-ward: CH1, load current i L L a , 5 A/div; CH3, load voltage v C a , 100 V/div;CH4, inductor currentiL a , 5 A/div.
When the power of the nonlinear load is varied, the THD of
the load voltage is also changed, and the experimental results are
shown in Fig. 22. It can be seen that with the load current feed-
forward, the THD of the load voltage can always be mitigated
under different power of the nonlinear load.
Fig. 23 shows the experimental waveforms when DG feeds
nonlinear load in the grid-tied mode. It can be seen that with the
load current feedforward, there is harmonic component in the
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Fig. 22. Variation of the THD of the load voltage with the power of thenonlinear load when DG is in the islanded mode.
Fig. 23. Experimental waveforms when DG feeds nonlinear load in the grid-tied mode (a) with load current feedforward and (b) without load current feed-
forward: CH1, inductor current iL a , 10 A/div; CH2,load current iL L a , 5 A/div;CH3, grid voltagevg a , 100 V/div; CH4, grid currentig a , 10 A/div.
inductor currentiLa , and the harmonics component in the grid
current is reduced.
The THD of the grid current under different power of the
nonlinear load and different amplitude of the grid fundamental
Fig. 24. Variation of the THD of the grid current when DG is in the grid-tiedmode with (a) the power of the nonlinear load, and (b) the amplitude of the gridcurrent.
current is investigated, and the experimental results are shown
in Fig. 24. In Fig. 24(a), the amplitude of the grid fundamental
current is set at 7 A, and the power of nonlinear load is varied. It
can be found that with the increaseof the load power, the THD of
the grid current rises, and the THD of the grid current is reduced
with the load current feedforward. In Fig. 24(b), the power ofthe nonlinear load is set at around 600 W, and the amplitude of
the grid fundamental current is changed. It can be seen that the
THD of the grid current can be mitigated at different magnitude
of the grid fundamental current.
VI. CONCLUSION
A unified control strategy was proposed for three-phase in-
verter in DG to operate in both islanded and grid-tied modes,
with no need for switching between two different control ar-
chitectures or critical islanding detection. A novel voltage con-
troller was presented. It is inactivated in the grid-tied mode,
and the DG operates as a current source with fast dynamic
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1190 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 3, MARCH 2014
performance. Upon the utility outage, the voltage controller can
automatically be activated to regulate the load voltage. More-
over, a novel load current feedforward was proposed, and it can
improve the waveform quality of both the grid current in the
grid-tied mode and the load voltage in the islanded mode. The
proposed unified control strategy was verified by the simulation
and experimental results.
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Zeng Liu (S09) received the B.S. degree in electri-cal engineering from Hunan University, Changsha,China, in 2006, and the M.S. degree in electricalengineering from Xian Jiaotong University, Xian,
China, in 2009, where he is currently working towardthe Ph.D. degree.
His research interests include control of single-phase and multiphase power converters for uninter-
rupted power supply and utility application, model-ing, and analysis and control of distributed powersystem based on three-phase ac bus.
Jinjun Liu (M97SM10) received the B.S. andPh.D. degrees in electrical engineering from Xian
Jiaotong University (XJTU), Xian, China, in 1992and 1997, respectively.
He then joined the XJTU Electrical EngineeringSchool as a teaching faculty. In 1998, he led thefounding of XJTU/Rockwell Automation Laboratoryand served as the Lab Director. From 1999 until early2002, he was with the Center for Power Electron-
ics Systems, Virginia Polytechnic Institute and StateUniversity, USA, as a Visiting Scholar. He then came
back to XJTU and in late 2002 was promoted to a Full Professor and the Headof the Power Electronics and Renewable Energy Center, XJTU. During 2005to early 2010, he served as the Associate Dean with the School of ElectricalEngineering, XJTU. He currently also servesas the Dean for Undergraduate Ed-
ucation, XJTU. He coauthored three books, published more than 100 technicalpapers, holds 13 patents. His research interests include power quality control,renewable energy generation and utility applications of power electronics, andmodeling and control of power electronic systems.
Dr. Liu is an AdCom member of the IEEE Power Electronics Society andserves as Region 10 Liaison. He received several national, provincial, or minis-terial awards for scientific or career achievements, and the 2006 Delta ScholarAward. He also serves as an Associate Editor for the IEEE T RANSACTIONS ON
POWER ELECTRONICS. He is an AdCom member and the Chair of Student Ac-tivities Committee for IEEE Xian Section. He is on the Executive Board and
serving as a Deputy Secretary-General for the China Power Electronics Society,and also on the Executive Board and serving as a Deputy Secretary-General forthe China Power Supply Society.
Yalin Zhao received the B.S. degree in electricalengineering from Xian Jiaotong University, Xian,China, in 2011, where he is currently working towardthe M.S. degree.
His research interests include dead-time compen-sation, stability analysis, and control of inverters.