Journal of Power Electronics, to be published
1
The Control Strategy Design of Grid-Connected and
Stand-Alone Single-Phase Inverter for Distributed
Generation
Fenghuang Cai†***, Dexiang Lu*, Qiongbin Lin*,**, and Wu Wang*,**
†*
School of Electrical Engineering and Automation, Fuzhou University, Fuzhou, China
Research Center for Advanced Process Control, Fuzhou University, Fuzhou, China.
***
Fujian Key Laboratory of New Energy Generation and Power Conversion, Fuzhou University, Fuzhou, China
**
Abstract
A dual-mode photovoltaic power system should be able to operate in grid-connected (GC) and stand-alone (SA) modes for
distributed generation. In different working modes, the optimal parameters of the inverter output filter are different. Since the
inverter operates more time in the GC mode, a smaller capacitance is beneficial to the GC topology for reasonable compromise.
In the GC mode, a predictive current control scheme is proposed to control the grid current to obtain a high-performance power
quality. Notice that the filter is not optimal in the SA mode. Then, a compound control strategy, consisting of predictive current
control, instantaneous voltage control and repetitive control (RC), is proposed to achieve low total harmonic distortion and thus
improve the output voltage spectrum. The detailed process of the seamless transfer between GC and SA is illustrated. Finally,
simulation and experimental results of a 4kVA prototype demonstrate the effectiveness of the proposed control strategy.
Key words: Distributed generation (DG), Grid-connected, Predictive current control, Repetitive control, Single-phase inverter,
Stand-alone power supply
I.
INTRODUCTION
During the two past decades, some renewable energy
technologies have been proposed to relieve the environmental
pollution problems and to achieve social sustainable
development [1], [2]. Renewable energies, including
photovoltaic power energy, wind energy, etc., have been
widely applied to distributed generation (DG) installations [3].
However, the DG units often cannot directly support the
electrical appliances with the same power qualities of the grid
in terms of frequency and amplitude. So, DG systems are
connected to the utility grid (UG) through power electronic
inverters. Due to unexpected power disruption, the
grid-connected (GC) inverter should be able to operate in GC
and stand-alone (SA) modes in order to provide power to the
emergency load during outages. A high-performance inverter
with the abilities of both stand-alone operation and utility-grid
connection is necessary to ensure efficient utilization of DG
units [4].
Grid-connected inverter can be achieved by various circuit
topologies [5], but new designed circuit topologies cannot be
popularly adopted in commercial products [4]. A single phase
inverter with low cost and high efficiency shown in Fig. 1 has a
simple circuit topology and low component counts. As the
grid-interactive inverter should operate in SA mode, the filter
capacitor is necessary [6]. Nevertheless, the filter capacitor can
affect the quality of the grid current in the GC mode, especially
at low output power. Since the inverter operates more time in
the GC mode, a smaller capacitor is beneficial to the GC
topology for reasonable compromise. A low-pass filter with the
values of Lf = 1.3 mH and Cf = 4.4 μF is selected by
considering the switching frequency and the output
fundamental frequency in Fig. 1[7]. The value of capacitor is
smaller than the capacitor which is designed in [8] (Cf = 14.25
μF) , [9] (Cf = 20 μF ) and [10] (Cf = 75 μF). The control
objective of the DG system in this paper is: (1) to supply a
2 Journal of Power Electronics, to be published
sinusoidal output voltage at load terminal (vinv) in the SA mode;
(2) to transfer a sinusoidal grid current (ig) to the utility grid in
GC mode; (3) to obtain smooth transition between the two
modes. Up to now, many control approaches have been
proposed to control the DC/AC inverter, such as, PI control,
sliding-mode control, optimal multi-loop linear resonant
control, linear control, backstepping control, and
passivity-based control etc. However, some of these control
methods are only suitable for SA mode or GC mode, while
some control methods are very complex and are difficult to
realize and apply to industry. In order to solve these problems,
a novel control method is proposed in this paper. In the GC
mode, a predictive current control scheme is proposed to
control the grid current to obtain a high-performance power
quality. Notice that the filter is not optimal in the SA mode. So
a compound control strategy, consisting of predictive current
control, instantaneous voltage control and repetitive control, is
proposed to achieve low total harmonic distortion and thus
improve the output voltage spectrum.
The paper is organized as follows. The description of the
inverter, the control methods for the SA and GC mode, and the
detailed process of the seamless transition between the two
modes are developed in Section II. In order to show the
usefulness of the proposed control strategies, simulation results
are presented in Section III. In addition, experimental results
are performed to verify the theoretical analysis in Section IV.
Finally, some conclusions are drawn in Section V.
II.
SYSTEM CONFIGURATION AND
PROPOSED CONTROL STRATEGY
A. Single-Phase Inverter Description
Fig. 1 shows the conventional full-bridge inverter scheme.
The PWM inverter framework includes four power switches
(S1, S2, S3, and S4) and a low-pass filter (L and C). Moreover,
critical-load represents an output load in the SA mode. Vbus, vg,
vinv are the voltages of the DC bus, the utility grid and the
inverter output, respectively. vAB is the voltage between point A
and B. iL, ic, iinv, io, ig are the currents of the filter inductor, the
filter capacitor, the inverter output, the critical-load and the
utility grid, respectively. The grid-connected switch (Tg) is used
to disconnect or reconnect the inverter output to the grid. When
Tg is closed, the inverter is working in the GC mode to transmit
the power of DG units into the utility grid. Under utility
interruption or abnormal grid condition, Tg is open, and then
the inverter provides power to the emergency load and operates
in SA mode.
S1
Vbus
S3
A
C1
iL
vAB
S2
L
B
Tg
iinv
iC
C
S4
io
ig
vg
vinv
Critical-load
Fig.1. Single-Phase Full-Bridge Inverter of Dual-Mode
The dc-ac converter is a nonlinear system by nature due to
the existence of the solid-state switches. A nonlinear system
needs be firstly linearized around its operating point before the
linear controller can be designed. The performance of the
controlled system in the neighborhood of that operating point
can be guaranteed if the designed controller is robust enough.
The wider the bandwidth of the system is, the larger the
neighborhood will be. From Fig. 1, the inverter model is
decided by following differential equation:
diL
dt
 Vbus  D
v AB  vinv  L
v AB
(1)
(2)
where D is the PWM duty cycle during one switching period.
B. System Control Method
The system control block diagram is shown in Fig. 2.
Switching between GC and SA is determined by islanding
detection. Although the current controllers in both GC mode
and SA mode are the same, the current commands are
different. When the inverter is operated in the GC mode, the

current command iLref
is equal to i L  GC , which is decided
by maximum power point tracking (MPPT) control and
digital phase locked loop (PLL) control. Owing to the limited
space in this paper, these two control methods are not
addressed here, please refer to the references [11], [12].

is
When the inverter is operated in the SA mode, the iLref
equal to i L  SA , which is decided by the inverter output
voltage controller. Next, the algorithm will be analyzed in
detail.
GC Mode
vbus
ibus
vg
MPPT
PLL
Islanding
Detection
v*inv
vinv
io
i*L-GC
Output
Voltage
Control
Mode
select
i*L-SA
SA Mode
Fig.2. The system control block diagram
i*Lref
Inductor
Current
Control
iL
Journal of Power Electronics, to be published 3
C. GC mode
In the GC mode, inverter behaves as controllable
current-sources. The closed-loop control method should
manipulate the output current (ig) with a high power factor.
With the recently developed high-performance digital signal
processor (DSP), realization of digital controllers with higher
sampling rate becomes possible and this makes the sampling
frequency gradually approaches to the switching frequency of a
digital-controlled power converting system. Assume that the
inverter
is operating with a constant switching frequency, the switching
period is a constant value T . During the switching period
[k , k  1] , (1) and (2) can be rewritten in a discrete form as
v AB [k ]  vinv [k ]  (iL [k  1]  iL [k ]) 
v AB k   Vbus k   Dk 
L
T
unavoidable control delay. If the digital control delay is
considered, the input-to-output transfer function of the current
control loop is:
1
I L ( z)

L
I ref ( z )
z ( z  1)  1
Lm
(8)
The root locus of the closed-loop system (8) is obtained as
shown in Fig. 4(b). It can be observed that the system is
unstable when Lm ≥ L. In order to ensure the system stability,
Lm need be less than L, which can result in poor stability
margin and dynamic performance.
(3)
(4)
Substituting (4) into (3), the D[k ] can be expressed as
D[k ] 
vinv [k ]  (iL [k  1]  iL [k ]) 
L
T
Vbus [k ]
(5)
a. (Lm < 2L)
The target of the controller is that the load current at the
sampling point [k+1] is controlled to equal to the reference
current value at the point [k+1]. So the control law (5) turns to
be (6) [13]. This is the predictive current control.
D[k ] 
vinv [k ]  (iref [k  1]  iL [k ]) 
Vbus [k ]
L
T
(6)
Fig. 3 illustrates the employment of an inner current loop.
z is a control delay. The predictive controller requires full
knowledge of the system parameters. If there exists model
mismatch in the control system, the mismatch will influence
the control accuracy. Lm is the parameters of digital controller.
Without considering the digital control delay, the
input-to-output transfer function of the current control loop is:
-1
I L ( z)
1

L
I ref ( z )
( z  1)  1
Lm
b. (Lm < L)
(7)
c. (Lm < 2L)
Fig.4. Root locus plot of Inner Loop
Fig.3. Current control block diagram
The root locus of the closed-loop system (7) is obtained as
shown in Fig. 4(a). It can be observed that the system poles are
in the unit circle if Lm is less then L. When Lm is greater than L,
it allows a deviation of 50%. No control delay is considered in
(7). However, in the actual digital control system, there exists
The goal of predictive current control is to make the error of
next control period to be zero. However, due to the existence of
the sampling error, the model parameter deviation and so on,
the error is difficult to be controlled to be zero. Taking this fact
into consideration, an improved algorithm is proposed. The
current error will converge to 0 automatically, and the stability
margin of the system can be improved greatly. The control law
is:
4 Journal of Power Electronics, to be published
ie [ k ]  iref [ k ]  i L [ k ]
D[k ] 
vinv [k ]  (iref [k  1]  iL [k ]  0.5 * ie [k ]) 
Vbus [k ]
(9)
Lm
T (10)
From (10), we can give the input-to-output transfer function of
the current control loop as follow:
I L ( z)
z  0.5

L 3
I ref ( z )
( z  z 2 )  0.5 z
Lm
(11)
The root locus of the closed-loop system (11) is obtained as
shown in Fig.4.c. It can be observed that the permissible range
Fig.6. Amplitude frequency response of Vinv / Io
In SA mode, the filter capacitor should choose bigger in
order to improve the quality of the voltage. The small filter
capacitor has a bad effect on the output voltage: First, voltage
Fig. 5. Control block diagram of the grid-interactive inverter in off-grid mode
of the model parameters is the same as (7).
D. SA mode
In the SA mode, the output voltage (vinv) should be
controlled with a low THD. The control block diagram in SA
mode is given in Fig. 5. Three controllers are included in the
control loops: a current tracking controller, a voltage tracking
controller and a repetitive controller. The current control loop
is the same as it is used in GC mode. The output voltage
controller is used to regulate the output voltage, where the
reference voltage vr(z) is a sine waveform and is given by the
DSP. The output of voltage control loop is the reference
current of the current control loop. In order to improve the load
disturbance rejection performance, load current is taken as the
feed-forward compensation in the current loop. kcomp is the
compensation coefficient. The input-to-output transfer function
of the voltage control loop becomes:
Vinv
IO
L
( z  1) 2  (1  k comp )( z  1)
KT

LC
C
( z  1) 3  ( z  1) 2  K p ( z  1)  K i z
T
KT 2
(12)
where Ki and Kp are the integral and proportional coefficients
of the output voltage controller, respectively. It can be seen
from (12) that the inverter in SA mode is stable according to
the conventional control theory. The parameters are as follows:
kcomp = 0.96, Kp = 2.5, Ki = 0.03. Fig. 6 is the amplitude
frequency response of Vinv / Io. The control system has strong
anti-load disturbance performance.
harmonics can not be filtered out effectively; Secondly, the
dead-time in PWM based inverter will result in output
waveform distortion and fundamental voltage loss, especially
when the output voltage is low. When the current reaches zero
during the deadtime and stays at zero level during the rest of
the deadtime, there is no means of controlling the output
voltage, the phenomena of zero crossing is difficult to avoid,
especially when the filter capacitor is small. Since all repetitive
disturbance is repeated for every switching operation, so it can
be solve by the techniques of repetitive control (RC). RC,
which originates from the internal model principle, provides a
solution to eliminate periodic errors.
A plug-in type modified repetitive controller is shown in Fig.
5. The result of the integration, denoted as e[k ] , is then
processed by the following units to generate Dr [14].
1) z  N : time delay unit. It postpones the control action by
one fundamental period so that time advance z k unit as well
as the noncausal zero-phase-shift notch filter included in S (z )
can be realized. Let N = fs / f with f =50Hz be the fundamental
frequency of the reference signal vr(z) , and let fs=16k be the
sampling rate, so N=320 is the order of the RC.
2) S (z ) : compensator. It modifies magnitude characteristic
of the open-loop system for better harmonic rejection.
3) z k : time advance unit. It advances the control action by
Journal of Power Electronics, to be published 5
sample periods in the next fundamental period, so as to
compensate the delay of compensator S (z ) as well as the
inverter.
4) k r : gain. It controls the magnitude of Dr.
Steady-state analysis shows that if the band-limit filter
Q(z ) is unit, no steady-state error occurs. Unfortunately, the
capacitor can help to reduce zero-crossing distortion, but the
large filter capacitor can affect the grid current control in GC
mode and increase the cost of hardware.
Fig. 7(d) shows the simulation of the load step of rated
power, there is a large and relatively transient drop in voltage,
but the drop of RMS value is less than 2V. As can be seen, the
proposed control method in the SA mode is less sensitive to
load variations.
Nyquist criterion reveals that it is not possible to establish a
stable system when Q( z )  1 .With this constraint, set
Q( z )  0.96 . According to [14], the designed parameters are
as follows a=0.2, b=0.8, k r =1, k=5.
E. Seamless Transfer
The detailed process of the seamless transfer between the SA
and GC modes are summarized as follows.
1) SA mode to GC mode:
a) Detect that the grid is operating in nominal condition.
b) Adjust the reference voltage (vr(z)) to match the frequency
and phase of the grid voltage by digital PLL.
c) After the load voltage is equal to the grid voltage, Tg is
turned on at zero crossing of the grid voltage. Then the control
model switches to GC mode.
d) Increase the reference grid current slowly from load
current to the desired value (decided by MPPT).
(a) Double loop control (Cf=4.4μF)
(b) Double loop control (Cf=40μF)
2) GC mode to SA mode:
a) Detect a fault on the utility.
b) Change the reference current to load current.
c) Tg is turned off at zero crossing of the load voltage. Then
the control model switches to SA mode.
III. SIMULATION RESULTS
(c) Compound control with RC (Cf=4.4μF)
To verify the effectiveness of the proposed control strategy,
a simulation model is built in power electronic simulation
software (PSIM) with the system parameters given in Table I.
TABLE I
SYSTEM PARAMETERS
Parameters
Rated output power
Grid voltage
Grid frequency(fs)
DC-link voltage(Vbus)
Switching/Sampling frequency(fsample)
Output filter inductance(L)
Output filter capacitance(C)
Values
4kVA
220(rms)
50Hz
370V
16kHz
1.3mH
4.4μF
Fig. 7 shows the simulation results of SA mode. Fig. 7(a)
and Fig.7(c) show the simulation results of the double
controlled and RC + double controlled PWM inverter under
rated output power. It is obviously shown that RC can reduce
zero-crossing distortion. It can be seen from Fig. 7(b), a larger
(d) Output power changes from o to 4kVA
Fig. 7. Simulation waveforms of SA mode
Fig. 8(a) presents the simulation results for a transfer from
GC mode to SA mode. Due to the randomness of the grid fault
and the mismatch of the inverter output power and the load
power, the load voltage and current have some inrush spikes
during the transition period. This process is short and the
waveform will resume normal when the system switches to the
SA control mode.
6 Journal of Power Electronics, to be published
Fig. 8(b) presents the simulation results for a transfer from
SA mode to GC mode. There is not any sudden voltage change
across the emergency load. The load voltage and the load
current, which do not have any inrush spikes during the entire
transition period, reveal a smooth transition from SA mode to
GC mode.
the condition of regular operation or load variations.
(a) Without RC
(a) GC mode to SA mode
(b) With RC
(b) SA mode to GC mode
Fig. 8. Simulation waveforms of transfer control
IV. EXPERIMENTAL RESULTS
To further verify the theoretical analysis and simulated
results, an experimental system is built in the laboratory. The
system parameters used in the experiment are the same as those
in the simulation model given in Table I. The proposed control
scheme is implemented by using a digital-signal-processor
(DSP) TMS320F2808 from Texas Instruments. The 16 kHz
PWM modulated driving signals for the full-bridge inverter are
generated by the DSP and peripheral logic circuits. The
TMS320F2808 is essentially a 32-bit microcontroller with DSP
architecture, most of its instructions can be executed in one
instruction cycle of 10 ns.
Fig. 9(a) and Fig. 9(b) shows the experimental results at
4kW load. With RC compensation, the voltage distortion near
the zero-crossing is reduced and the THD of the voltage
decreases from 2.9% to 0.7%. Fig. 9(c) shows the experimental
results for a rectifier load (2500VA) with power factor (PF) of
0.7. The THD of the voltage is about 2.2%. Fig. 9(d) shows the
step response of the load changes from 0 to 4kVA, the settling
time of the system is about 600μs. As can be seen from Fig. 9,
the performance indexes show that the experimental results
agree with the numerical simulations, and the proposed control
method can provide favorable control performance either under
(c) Rectifying load
(d) 4kVA load
Fig. 9. Experimental Waveforms of SA mode
Fig. 10 presents the experimental results in the GC mode.
The THD of the grid voltage is about 3.1%, but the THD of the
grid current is just 1.8% (4kVA grid-connected power) and
2.5%(2kVA grid-connected power). The PF of the grid current
is 1 (4kVA grid-connected power) and 0.998(2kVA
grid-connected power). The waveform quality of the grid
current is good with the control method even in polluted
Journal of Power Electronics, to be published 7
voltage.
(b)SA mode to GC mode
Fig. 11. Experimental Waveforms of Transfer Control with 2kVA
Load
(a) 2kVA load
(b) 4kVA load
Fig. 10. Experimental voltage and current responses of GC mode
Fig. 11(b) shows the experimental results from SA mode to
GC mode. When the grid is normal, the voltage of inverter
synchronizes with the grid voltage. Tg is turned on at
zero-crossing of the grid voltage and then the control system
switches to current control mode. The reference current
increases from current value. The load voltage and the load
current, which do not have any inrush spikes during the entire
transition period, reveal a smooth transition from SA mode to
GC mode
Fig. 11 presents the experimental results of transfer control
with 2kVA load. Fig. 11(a) shows the experimental results
from GC mode to SA mode. The output power of inverter is
4kVA, iinv is the inverter output current, composed of load
current and grid current. The grid is broken off at t1. Because
the output power of the inverter is greater than the load power
consumption, so the inverter output voltage has inrush spike.
The grid fault is detected at t2, and the control system switches
the reference current value to the load current. Tg (Bidirectional
triode thyristor) is turned off at t3 (zero-crossing of the inverter
voltage) and then the control system switches to voltage
control mode.
(a) GC mode to SA mode
(b) SA mode to GC mode
Fig. 12. Experimental Waveforms of Transfer Control with 4kVA
Load
(a) GC mode to SA mode
.
Fig. 12 presents the experimental results of transfer control
with 4kVA load. The output power of inverter is 2kVA in GC
mode. Grid and inverter supply power to load at the same time.
Because the load power is greater than the output power of the
inverter, so the inverter output voltage has inrush spike when
the grid is break off at t1. As the same as the analysis of Fig. 11,
the value of reference current switches to the value of load
current and then the control system switches to voltage control
8 Journal of Power Electronics, to be published
mode at zero-crossing of the inverter voltage. As can be seen
from Fig. 12(b), the load voltage and the load current do not
have any inrush spikes during the entire transition period from
SA mode to GC mode.
V. CONCLUSIONS
This study has successfully developed a single-phase
full-bridge inverter with a small filter capacitor. Predictive
current control has been applied well to both the SA and GC
power-supply modes. A compound control strategy is applied
to SA mode. A novel seamless transfer between SA mode and
GC mode is proposed. The proposed control method has salient
features, including fast response characteristics in transient
states, robust control performance, high power-supply quality,
and automatic transformation between the SA mode and the
GC mode. The proposed control schemes also can be extended
easily to other power conversion systems for satisfying high
power quality demands.
ACKNOWLEDGMENT
This work was supported in part by the National Natural
Science Foundation of China under Grant No. 51537001.
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Fenghuang Cai was born in Fujian, China in
1976. He received his B.S in Industrial
Automation, M.S in Control Theory and
Engineering, Ph.D. in Electrical Engineering
from the Fuzhou University, PR China, in
1998, 2002 and 2007, respectively. In 1998,
he joined Fuzhou University, as an teaching
assistant in the Department of Electrical Engineering, and where
he has been an Associate Professor in Control Engineering since
2010. His current research interests include power electronics
and control, which include modeling and control of power
electronic system, digital-signal-processing-based control
applications, distributed generation, and renewable energy.
[8]
Dexiang Lu was born in Fujian, China, in
1990. He received his B.S. degree in
electrical engineering and automation from
the Jimei University, Xiamen, China, in 2013.
He is currently working toward the M.S.
degree in electrical engineering at the School
of electrical engineering and automation,
Fuzhou University, Fuzhou, China. His current research interests
include control techniques of power converter, renewable energy
generation system and high-frequency power conversion. Qiongbin Lin was born in Fujian, China in
1976. He received his B.S in Industrial
Automation, M.S in Control Theory and
Engineering, Ph.D. in Electrical Engineering
from the Fuzhou University, PR China, in
2000, 2003and 2010, respectively. In 2000,
Journal of Power Electronics, to be published 9
he joined Fuzhou University, as an teaching assistant in the
Department of Electrical Engineering, and where he has been an
Associate Professor in Control Engineering since 2012. His
current research interests include power electronics and control,
nonlinear system and fuzzy control, which include modeling and
control
of
power
electronic
system,
digital-signal-processing-based control applications, and DC
microgrids..
Wu Wang was born in Fujian, China, in
1973. He received his B.S in Mechanical
Design and Manufacturing and M.S in
Agricultural Mechanization Engineering
from the Fujian Agriculture and Forestry
University, PR China, in 1996 and 1999,
respectively. He received his PhD in
Electrical Engineering from the Fuzhou
University, PR China, in 2004. He joined Fuzhou University
after obtaining his PhD Degree, where he currently is a Professor
in Control Engineering. His research interests include modeling
and control of power electronic systems, H-infinity control and
filtering, and networked control.