This paper presents a PQ control strategy for micro grid inverters with axial voltage regulators. The inverter works in the voltagecontrolled mode and can help improve the terminal power quality. The inverter has two axial voltage regulators. The 1st regulator involves the output voltage amplitude and output impedance, while the 2nd regulator controls the output frequency. The inverter system is equivalent to a controllable voltage source with a controllable inner output impedance. The basic PQ control for micro grid inverters is easy to accomplish. The output active and reactive powers can be decoupled well by controlling the two axial voltages. The 1st axial voltage regulator controls the reactive power, while the 2nd regulator controls the active power. The paper analyses the axial voltage regulation mechanism, and evaluates the PQ decoupling effect mathematically. The effectiveness of the proposed control strategy is validated by simulation and experimental results.
I. INTRODUCTION
With the rapid development of smart grid and civil distributed generation, micro grids have become a popular trend for distribution networks
[1]
. A microgrid usually consists of distributed photovoltaic generators, wind turbines, combined heat and power plants, fuel batteries and so on. A microgrid is usually connected to the main grid and the main grid provides frequency and amplitude support for the microgrid. It does not have as many traditional synchronous generators as the main grid. When grid faults occur, a microgrid works in the standalone mode and becomes easy to collapse. Commonly used currentcontrolled inverters (CCI)
[2]

[4]
are current sources which only supply power and cannot help to provide transient support. Voltagecontrolled inverters (VCI) can be regarded as voltage sources which can provide voltage support in urgent circumstances
[5]

[8]
.
Inverterbased distributed generators are the main power suppliers of microgrids. Nowadays the inverters applied in microgrids are often paralleled without control interconnection. Thus, the
Pf
droop control, which roughly mimics output characteristic of traditional synchronous generators, is widely used. However, this does have a lot of problems in terms of power sharing and many other aspects
[9]
. The distributed generators for microgrids are not far away from each other. With the development of communication technology, interconnected inverters will be widely used in microgrids. Thus, inverters will often work in the PQ output mode. The PQ references are from the MPPT control or the upper scheduling centers.
The control strategies referred to as virtual synchronous generators (VSG)
[10]

[12]
are developed for microgrid. Most VSG inverters are voltage sources and can help to maintain the stability of microgrids. By using the VSG control strategy, the mature control strategies developed for the main grid can be applied in microgrids as well. Ref.
10
introduced the idea of the VSG mainly based on the rotor equation. Nowadays, the concept of a ‘synchronverter’
[11]
is well known. It is a converter that mimics both the inertial equation and electromagnetic transient process of synchronous generators. However, the inner output impedance of the inverter is the real filter inductor and it is not controllable. In addition, the paper only discussed the inner output power while the filter impact on the active and reactive power output is neglected.
Reference
[13]
has proposed a singlephase voltage controlled inverter with an inner output impedance. The inverter has many great characteristics. However, further control strategies have not been researched yet. This paper improves the control strategy of Reference
[13]
. The hysteresis PWM is replaced by the commonly used SPWM method, and the inverter side inductor current is adopted as the feedback value of the inner current loop. The SOGI is adopted for quadrature signal generation. The working principle of the axial voltage regulators is further analyzed and a basic
PQ
control strategy for microgrids is proposed and discussed in detail.
Section II will discuss the whole inverter system and the 1st axial voltage regulator control strategy. Frequency regulation improvement and analysis will be presented in Section III. The details of the
PQ
control based on axial voltage regulators will be discussed in Section IV. Simulation and experiment results will be given in Section V. Finally, some conclusions are given in Section VI.
II. SYSTEM DESCRIPTION AND 1STAXIAL VOLTAGE REGULATOR CONTROL STRATEGY
The main circuit and control strategy are shown in
Fig. 1
. Here the voltage of the DC bus is regarded as a constant. A LCL filter is used for the single phase inverter. The current through inductor
L_{1}
is measured for the PWM generation. A small
L_{2}
is chosen so that
v_{o}
is nearly the same as
v_{g}
. Since the inverter is designed mainly for microgrids and civil distributed generation, the nominal power rate is small. Thus, a resister cascaded with the capacitor will not cause a large power loss but will greatly help simplify the inverter design. The output voltage
v_{o}
and output current
i_{o}
are measured. The output P & Q are calculated and compared with the reference values. Then they are sent into the main control strategy through 2 PI controllers. As described in reference
[8]
, here in
Fig. 1
,
V_{1}
^{*}
and
V_{2}
^{*}
are the input values of the axial voltage regulators.
V_{1}
^{*}
controls the amplitude of the equivalent voltage, while
V_{2}
^{*}
regulates the output frequency. The whole control strategy of the
V_{1}
^{*}
regulator is shown in
Fig. 2
while details of the
V_{2}
^{*}
regulator will be discussed in the next section.
The system and the whole control strategy.
Details of V_{1}^{*} regulator.
The detailed control strategy of the
V_{1}
^{*}
regulator is shown in
Fig. 2
. Here in
Fig 2
,
V_{1}
^{*}
and
E_{N}
have been multiplied by the phase information from the
V_{2}
^{*}
regulator, which will be discussed in the next section. The reference of
V_{1}
^{*}
came from the output power loop.
K_{mu1}
is the
V_{1}
^{*}
regulation coefficient. It can help regulate the effect of the output voltage
v_{o}
more flexibly. α is the PI gain, and
T_{i}
is the integral time constant. These two are the main parameters for the inner impedance design. β and γ are the feedback coefficients of the output current and the filter capacitor current. They will help simplify the output expression.
V_{1}
^{*}
contains information from the outer power loop. It is multiplied with the output voltage
v_{o}
to form a voltage reference signal, and the voltage reference signal is sent to the PI controller after adding the nominal voltage. The output of the PI controller with feedback from the capacitor current and output current forms the reference current of the inner current loop.
By this control strategy, equation (1) is satisfied.
Multiply the inner loop gain
k
and
G_{PWM}
together to from a new
G_{PWM}
. The inner current loop satisfies equation (2).
If
G_{PWM}
is much larger than 1, from equation (2), the reference current
I_{1}
^{*}
is equal to
I_{1}
. Suppose
γ
=
G_{PWM}
/(1+
G_{PWM}
). Then, equations 12 will be simplified and equation 3 is satisfied.
From equation (3), the system is equivalent to
Fig. 3
. The output characteristic is equivalent to a voltage source with an inner output impedance. Equations (4)(6) are expressions of the components in
Fig. 3
.
As shown in equations (4)(6), all of the components of the equivalent circuit in
Fig. 3
can be controlled accurately via setting certain control parameters.
Equivalent circuit of the system.
From the analysis above, the
V_{1}
^{*}
regulator keeps the system equivalent to a voltage source with an inner output impedance. The voltage source and the output impedance both can be controlled accurately by setting certain control parameters. Here in the distributed generations for microgrids, a small
T_{i}
will be chosen to make the output impedance inductive for output power decoupling. This will be further discussed in Section IV.
III. 2NDAXIAL VOLTAGE REGULATOR IN THE GRIDCONNECTED MODE
Details of the
V_{2}
^{*}
regulator are shown in
Fig 4
. This regulator is responsible for the frequency regulation of the inverter. The phase information is sent to the voltage references in the
V_{1}
^{*}
regulator. Here in this paper, the 1/4 period time delay quadrature signal generator is replaced by the second order generalized integrator (SOGI) method
[14]
,
[15]
. Details of the SOGI are shown in
Fig 5
. It is a widely used quadrature signal generation method. It can help filter higher harmonic waves and has better performance when the grid frequency fluctuates. The dynamic response of the SOGI is faster as well.
Control block of V_{2}^{*} regulator.
Control block of SOGI.
The adoption of the SOGI improves the performance of the whole inverter. The improvement is shown in
Fig 6
. Parameters are chosen that are the same as those in Section V. The output power is
P
=800W and
Q
=600Var (at full load).
Fig. 6
(a), (c) are the inverter performances using the SOGI, while
Fig. 6
(b), (d) are the inverter performances using the 1/4 period time delay.
Fig. 6
(a), (b) show the situation of the frequency fluctuation. The grid frequency varies from 52Hz to 48Hz. The two figures show that the SOGI can output the grid frequency accurately, while the frequency of the 1/4 period time delay has a large 100Hz sinusoid fluctuation.
Fig. 6
(c), (d) show the performances with harmonic waves inside. 3
^{th}
, 5
^{th}
and 7
^{th}
harmonic waves with the same amplitude of 11√2V are added into the grid voltage at t=2s. The THD of the voltage is up to 8.10%. The output frequency of the SOGI is accurate, and the output fluctuation is much smaller than that of the 1/4 period time delay.
Frequency response of SOGI and 1/4 period time delay.
Because of the adoption of the SOGI, the dynamic expressions of the output frequency and phase are changed in comparison with Reference
8
. A small
L_{2}
is chosen in
Fig 1
so that
v_{o}
≈
v_{g}
is satisfied. Thus,
v_{o}
(=
V_{o}
sin
φ_{o}
) can be replaced by
v_{g}
(=
V_{g}
sin
φ_{g}
) from here on. Here in
Fig. 4
, Equation (7) is deduced by the SOGI and
dq
transformation.
Given
φ_{i}

φ_{g}
≈0 and some simplification for
Fig. 4
, the following equation will be satisfied.
Simplify Equation (8) with Equation (7). Then, Equation (9) can be achieved.
Thus, equation (10) is satisfied for steady state.
Hence, the inverter frequency will finally be the same as the grid if connected to the grid. The selfsynchronous ability remains.
Usually, the power angle
δ
determines the output power. The steady state value of
δ
is calculated as follows.
The expressions of the frequency and phase are greatly simplified when compared to reference (8). Given a certain
V_{2}
^{*}
and no closed loop control, some conclusion can be made from equation 8 in the gridconnected mode.

1) IfωN>ωg, thenδhas an escalating trend and active power tends to flow from the inverter to the grid. IfωN<ωg, the power trend is opposite.

2) IfV2*>0, thenδhas a rising trend and active power tends to flow from the inverter to the grid. IfV2*<0, the trend is opposite.
IV. AXIAL VOLTAGE REGULATION FORPQCONTROL
As mentioned in Section II, a small
T_{i}
is chosen to make the output impedance inductive. The line impedance and equivalent impedance of the grid is variable in microgrids. Different impedance characteristics have different output power characteristics. Thus a large enough α is necessary to offset the small transmission line impedance and the grid equivalent impedance. The resistive component of the whole impedance can be regarded as 0 by the choice of these control parameters. The expressions of the output power are as follows by
Fig. 3
.
X
is the total impedance between
e_{i}
and
v_{g}
in
Fig. 3
. It is mainly determined by the inner output impedance of the inverter.
E_{i}
and
δ
are the main control parameters that determine the output power. When in the grid connected mode, the output frequency
ω_{i}
will finally be the same as the grid frequency
ω_{g}
as shown in Section III. The steady state of the
E_{i}
and
δ
expressions are as follows.
E_{i}
and
δ
are controlled separately by different axial voltage regulators. Partial derivatives for P & Q are figured out from equations (12) and (13) to evaluate the control impact of the regulators.
Since
δ
is very small, equations (16) and (17) show that
V_{1}
^{*}
can control the output reactive power, while
V_{2}
^{*}
controls the output active power. The relationship is linear. To evaluate the 2 axial voltage regulators’ impact on power regulation more accurately, 3dimensional
P/Q
VS.
V_{1}
^{*}
&
V_{2}
^{*}
figures are drawn. The main control parameters adopted are the same as those in Section V.
Fig. 6
and
Fig. 7
show the relationship between the output
PQ
and
V_{1}
^{*}
&
V_{2}
^{*}
.
Fig. 6
shows that the output active power is linearly controlled by
V_{2}
^{*}
, and that
V_{1}
^{*}
does not change
P
.
Fig. 7
shows that the output reactive power is linearly controlled by
V_{1}
^{*}
, ant that
V_{2}
^{*}
does not change
Q
.
Relationship between output P and V_{1}^{*}&V_{2}^{*}.
V. SIMULATION AND EXPERIMENTAL RESULTS
A simulation model based on the control strategy is built in Matlab/Simulink. The simulation step size is 0.01ms. An Ode 45 is chosen as the solver, and the relative tolerance is 1e4. The main simulation parameters are listed in
Tables I
and
II
. The rated power of the inverter is 1kVA. Just like the situation of a microgrid, the inverter is directly connected to the main grid with a breaker. No isolation transformer is adopted here.
PARAMETERS OF THE MAIN CIRCUIT
PARAMETERS OF THE MAIN CIRCUIT
MAIN CONTROL PARAMETERS
By the parameters in
Table I
and
II
, the equivalent circuit impedance of
Fig. 3
is a 10Ω resistor paralleled with a 2Ω inductor. The resistor is much larger than the inductor impedance. Thus, it can be neglected. The grid voltage RMS value is 220V, with a frequency of 50Hz. The circuit satisfies the following equation.
Thus, the RMS values of the output voltage
V_{o}
and current
I_{o}
satisfy the following equation.
To evaluate the output impedance of the inverter, different resistive loads (∞, 48Ω, 48/2Ω, 48/4Ω, 48/8Ω, 48/16Ω, 48/32Ω, 48/64Ω , and 0) are connected to the system.
Fig. 8
shows the relationship between the RMS values of the output voltage and current. The solid blue line is drawn from Equation (19). The simulation results satisfy theoretical analysis well.
Relationship between Output Q and V_{1}^{*}&V_{2}^{*}.
Characteristics of output voltage and current.
To evaluate the control effects of
V_{1}
^{*}
VS.
Q
and
V_{2}
^{*}
VS.
P
, data with different
PQs
are measured and drawn in
Fig. 10
(a) and (b). The relationship between
V_{1}
^{*}
VS.
Q
and
V_{2}
^{*}
VS.
P
matches the theoretical analysis of Section IV from the figures.
Simulation results of relationship between axial voltages and PQ output.
Fig 11
shows the whole changing process of the power output and controller values. The PQ reference values all underwent step changes. The simulation starts at t=0. The system is synchronized and connected to the grid before t=1s. This process is not the paper’s focus and is ignored. The
P
and
Q
references are all 0 in this process. The reference values change 4 times during the whole process. At t= 1.5s,
P_{ref}
is set as 500W, while
Q_{ref}
remains 0. At t= 2s,
Q_{ref}
jumps to 600Var, while
P_{ref}
remains 500W. At t= 2.5s,
Q_{ref}
steps to 800Var, and
P_{ref}
is still 500W. At t=3s,
P_{ref}
is set as 800W, while
Q_{ref}
remains 800Var.
Fig. 11
(a)(f) shows the value changing process.
Fig. 11
(a)(c) show the relationship of
V_{1}
^{*}

E_{i}

Q
, while
Fig. 11
(d)(f) show the relationship of
V_{2}
^{*}

f

P
. The figures show that
V_{1}
^{*}
controls
E_{i}
and
Q
, while
V_{2}
^{*}
controls the frequency and
P
. The simulation results verify the theoretical analysis.
Fig. 12
shows the decouple control of the
PQ
output. The PQ reference values change linearly and follow the ramp signals. The current is multiplied by 30 to match the amplitude of the voltage. The output
P
(
Q
) remains stable when the output
Q
(
P
) changes. The output voltage and current both transit very smoothly when the PQ references change. The
PQ
output decouples well.
System response with step reference change.
Decoupling Effect of PQ Output.
To verify the idea, an experiment based on a TMS320F28335 is carried out. The main control parameters are the same as those applied in the simulation. The rated power of the inverter is also 1kVA. The inverter is connected to the grid via an isolation transformer.
Fig. 13
(a)(c) are the different working status of the inverter.
Fig. 13
(a) shows the beginning of the work. The inverter is connected to the grid smoothly with a new seamless transfer strategy. This strategy will be the focus of another paper. The PQ references are both 0. The output voltage is almost the same as the grid voltage, and output current is fluctuating in a small scale around 0. The output P and Q are both close to 0. The inverter outputs active power only in
Fig. 13
(b). The output P is around 910W, and the fluctuation of output Q is 55Var. The current THD is around 4%. Power coefficient is 0.998. The inverter outputs reactive power only in
Fig. 13
(c). The output P fluctuation is 30W, and the output Q is around 880Var. The THD of the output current rises a little to around 5%. This still satisfies the general standard. The terminal voltage rises to around 220V (nominal value), and is much higher than that in
Fig. 13
(b). The power quality is remarkably improved. The inverter outputs almost the same power as the reference values. The transient process when
P_{ref}
is changing is shown in
Fig. 13
(d). Output current and voltage remain high quality.
PQ output of the experiment.
VI. CONCLUSION
A PQ control strategy for a microgrid inverter with axial voltage regulators is raised in the paper. The inverter is voltage controlled and has 2 axial voltage regulators. The 1
^{st}
regulator controls the output voltage and the 2
^{nd}
controls the output frequency. The output
P
is controlled by the 2
^{nd}
axial voltage regulator, and the output
Q
is controlled by the 1
^{st}
axial voltage regulator.
P
and
Q
are decoupled well with proper control parameters. The control strategy is discussed in detail and verified by simulation and experimental results. The inverter has good characteristics for application in microgrid development.
Acknowledgements
The authors would like to thank for the financial support of the Shanghai Talent Development Fund (Grant No. 2012024), the Innovation Program of Shanghai Municipal Education Commission (Grant No. 13ZZ132) and Shanghai Engineering Research Center of Green Energy GridConnected Technology (Grant No. 13DZ2251900).
BIO
Yang Chen was born in China, in 1990. He received his B.S. degree in Electrical Engineering from Zhejiang University, Zhejiang, China, in 2012. He is presently working towards his M.S. degree at the Shanghai University of Electric Power, Shanghai, China. He worked as an Engineer for the NariRelays Corporation, Nanjing, China, from 2012 to 2013. His current research interests include the modeling and control of inverters, and distributed power generation in microgrids.
Jinbin Zhao (M’06) was born in China, in 1972. He received his M.S. and Ph.D. degrees in Electrical Engineering from Oita University, Oita, Japan, in 2002 and 2005, respectively. He worked as a Researcher at the R&D Headquarters of Origin Electric Co., Ltd, Japan, from 2005 to 2011. He is presently working as a Professor at the Shanghai University of Electric Power, Shanghai, China. His current research interests include the control of power converters, softswitching power converters, inverters, distributed power systems, powerfactor correction, and electric drive systems. Dr. Zhao is a Member of the IEEJ and IEICE of Japan as well as a Senior Member of the CPSS.
Keqing Qu was born in China, in 1970. He received his Ph.D. degree in Electrical Engineering from Shanghai University, Shanghai, China, in 2004. He is presently working as an Associate Professor at the Shanghai University of Electric Power, Shanghai, China. He is also a Master Instructor. He studied in Germany as a Visiting Scholar with full funding by the national foundation, from 2009 to 2010. His current research interests include power electronic conversion, and new energy generation and its application to power systems.
Fen Li received her B.S. and Ph.D. degrees in Electrical Engineering from the Huazhong University of Science and Technology, Wuhan, China, in 2005 and 2010, respectively. She has been an Engineer in the Hubei Meteorological Bureau, Wuhan, China, since 2010. She is presently working as a Lecturer at the Shanghai University of Electric Power, Shanghai, China. Her current research interests include high power factor converters, the gridconnected control of renewable energy power generation, solar resource evaluation and forecast, the relationship between photovoltaic power and meteorological factors, and PV power prediction.
Li X. Q.
,
Wu X. J.
,
Geng Y. W.
,
Zhang Q.
2013
“Stability analysis of gridconnected inverters with an LCL filter considering grid impedance,”
Journal of Power Electronics
13
(5)
896 
908
DOI : 10.6113/JPE.2013.13.5.896
Bao C.
,
Ruan X.
,
Wang X.
,
Pan D.
,
Li W.
,
Weng K.
“Design of gridconnected inverters with LCL filter based on PI regulator and capacitor current feedback active damping.”
in Proc. of the CSEE
2012
Vol. 32. No. 25
Wu Y.
,
Kan J.
,
Xie S.
2011
“Control strategy for gridconnected inverter based on double dq coordinates,”
Transactions of CES
26
(8)
106 
112
Yan R.
,
Tapan K. S.
2012
“Investigation of voltage stability for residential customers due to high photovoltaic penetrations,”
IEEE Trans. Power Syst.
27
(2)
651 
662
DOI : 10.1109/TPWRS.2011.2180741
Kim H.
,
Yu T.
,
Choi S.
2008
“Indirect current control algorithm for utility interactive inverters in distributed generation systems,”
IEEE Trans. Power Electron.
23
(3)
1342 
1347
DOI : 10.1109/TPEL.2008.920879
Wu Y.
,
Kan J.
,
Xie S.
2011
“An indirect current control scheme for gridconnected inverter with regulation of active power to phase and reactive power to voltage amplitude,”
Automation of Electric Power Systems
35
(11)
93 
97
Im J. H.
,
Song S. H.
,
Kang S.
2013
“Analysis and compensation of PCC voltage variations caused by wind turbine power fluctuations,”
Journal of Power Electronics
13
(5)
854 
860
DOI : 10.6113/JPE.2013.13.5.854
Li Y. W.
,
Kao C. N.
2009
“An accurate power control strategy for powerelectronicsinterfaced distributed generation units operating in a lowvoltage multibus microgrid,”
IEEE Trans. Power Electronics
24
(12)
2977 
2988
DOI : 10.1109/TPEL.2009.2022828
Gao F.
,
Iravani M. R.
2008
“A control strategy for a distributed generation unit in gridconnected and autonomous modes of operation,”
IEEE Trans. Power Del.
23
(2)
850 
859
DOI : 10.1109/TPWRD.2007.915950
Zhong Q. C.
,
Weiss G.
2011
“Synchronverters: Inverters that mimic synchronous generators,”
IEEE Trans. Ind. Electron.
58
(4)
1259 
1267
DOI : 10.1109/TIE.2010.2048839
Hu J.
,
Zhu J.
,
Dorrell D. G.
2014
“Virtual flux droop method – A new control strategy of inverters in microgrids,”
IEEE Trans. Power Electron.
29
(9)
4704 
4711
DOI : 10.1109/TPEL.2013.2286159
Zhao J. B.
,
Ushiki S.
,
Ohshima M.
“Gridconnected inverter with inner output impedance and governorfree characteristics,”
in Proc. Energy Conversion Congress and Exposition
2010
Park J. S.
,
Nguyen T. H.
,
Lee D. C.
2014
“Advanced SOGIFLL scheme based on fuzzy logic for singlephase gridconnected converters,”
Journal of Power Electronics
14
(3)
598 
607
DOI : 10.6113/JPE.2014.14.3.598
Carugati I.
,
Donato P.
,
Maestri S.
,
Carrica D.
,
Benedetti M.
2012
“Frequency adaptive PLL for polluted singlephase grids,”
IEEE Trans. Power Electron.
27
(5)
2396 
2404
DOI : 10.1109/TPEL.2011.2172000