This paper presents a novel closeloop control scheme based on small signal modeling and weighted composite voltage feedback for a threephase input and singlephase output Matrix Converter (31MC). A small nonpolar capacitor is employed as the decoupling unit. The composite voltage weighted by the load voltage and the decoupling unit voltage is used as the feedback value for the voltage controller. Together with the current loop, the dualloop control is implemented in the 31MC. In this paper, the weighted composite voltage expression is derived based on the sinusoidal pulsewidth modulation (SPWM) strategy. The switch functions of the 31MC are deduced, and the average signal model and small signal model are built. Furthermore, the stability and dynamic performance of the 31MC are studied, and simulation and experiment studies are executed. The results show that the control method is effective and feasible. They also show that the design is reasonable and that the operating performance of the 31MC is good.
I. INTRODUCTION
The alternative part of the output power in a threephase to singlephase Matrix Converter (31MC) causes input current distortions and power factor reductions, due to the direct coupling between the input and output
[1]

[3]
. Paper
[4]
proposed a modulation method where the power pulsation in the output side was absorbed by the inertia of the rotor. However, this method increased the mechanical loss of the motor and reduced the efficiency of the power generation system. In
[5]
, most of the power pulsation was stored in the Zsource impedance network. However, some part of the power pulsation still impacted the input side.
A method where the active power decoupling unit is used to compensate the power pulsation has been shown to be more effective and feasible
[6]

[9]
. Makoto Saito proposed the concept of active power decoupling in 2004, where singlephase power pulsations were stored in an inductor by modulation of the power switches. To reduce the bulk of the decoupling unit, the large inductor was replaced by a capacitor, and a novel singlephase to threephase MC topology was developed in
[7]
. Furthermore,
[8]
investigated the design principle of the decoupling capacitor. Then, a simple decoupling method in which a nonpolar capacitor was used as a decoupling unit was introduced in
[9]
, and the corresponding modulation strategy was discussed.
A 31MC, which is in parallel to the grid, was studied and designed as a constantcurrent source in
[10]
. The input current and output current of the converter were controlled independently. The reference value of the input current controller was calculated by the output power in the grid side, and the power loss is not taken into account. Meanwhile, the regulating algorithm was implemented according to the effective value. Consequently, its accuracy and dynamic performance were not good. This paper presents a novel control method where the composite voltage, which is weighted by its load voltage and decoupling unit voltage, is used as the feedback value. With its instantaneous output voltage control, the novel method makes the performance of the 31MC better.
Control system design based on the small signal model has not been studied a lot for 31MCs. Unlike 33MCs, in which the output voltage can be decomposed into d and q components and the small signal model can be established simply based on them, the modeling of 31MCs is much more difficult. Based on the ideas of
[11]
and
[12]
, a solution is presented here where the small signal model of a 31MC is built based on the composite voltage. With this idea, the dualloop controllers are designed, and the prototype is developed. A series of simulation and experimental studies are executed to verify its effectiveness and feasibility.
II. POWER DECOUPLING UNIT
 A. Power Decoupling Principles
The topology and the equivalent circuit of a 31MC are illustrated in
Fig. 1
and
Fig. 2
. The virtual acdc side is a threephase voltage source type rectifier (VSR). Assuming that the input instantaneous power is constant and that the input current and voltage are inphase, the dc link presents the properties of a constant current source
[13]
. The input power of the converter is equal to the dc link power in ideal conditions. Therefore, the dc link voltage must be maintained as a constant.
31MC with a power decoupling unit.
Equivalent circuit of 31MC.
The virtual dcac side is a twophase current source type inverter (CSI).SPWM is adopted in the load phase and in the active power decoupling phase. The modulation functions are assumed as:
According to the superposition theorem, the dc link voltage is the weighted sum of the load voltage and the decoupling capacitor voltage, i.e. the composite voltage
u_{comp}
satisfies:
In (1) and (2),
are the modulation radios of the load phase and the decoupling phase, respectively,
u_{o}
is the load voltage,
u_{c}
is the decoupling capacitor voltage,
ω_{o}
is the output angular velocity,
φ_{c}
is the initial phase angle of the decoupling modulation wave,
φ_{o}
is the load impedance angle,
U_{o}
is the effective value of the load voltage,
i_{dc}
is the dc link current, and
C_{c}
is the capacitance of the decoupling capacitor. When
and
φ_{c}
satisfy formula (13)
[14]
, pulsed voltage components of twice the output frequency are neutralized. Then,
u_{comp}
is maintained as a constant:
Therefore, the singlephase power pulsation is decoupled with a constant input power, and the instantaneous input power is kept at a constant value, which can be expressed as:
 B.Design of the Power Decoupling Unit
The power pulsation is absorbed and released completely by the decoupling capacitor in a pulsed period. Energy stored in the capacitor is equal to the work of the power pulsation. Then, the relationship between the capacitance of
C_{c}
and its maximum voltage
U
_{cmax}
can be expressed as
[14]
:
Where
P_{o}
is the load power, and
f_{o}
is the output frequency.
On the other hand, the converter usually works in the linear modulation range. Therefore, the sum of the load phase duty ratio
d_{l}
and the decoupling phase duty ratio
d_{c}
should be less than 1 in real time. Combining (1) with (3), the duty ratios:
By using the Cosine theorem, the amplitude of the sum of the duty ratios satisfies:
To improve the utilization rate of the power switches and the voltage transfer ratio, 
d
_{∑}
 should be designed to be as large as possible. 
d
_{∑}
 = 1 can be assumed here. Substitute (4) into (7). Then, the relationship between the dc link current and the capacitance of
C_{c}
is obtained as:
Taking
U_{o}
= 150
V
as an example, the relationships between
C_{c}
and
I_{dc}
are presented in
Fig. 3
for situations of different output powers and different output frequencies .The dc link current is increased when a larger capacitance is chosen and its value also grows with an increase of the power and frequency.
Relation curves of capacitance and current stress.
Combined with the limitation of (5), in low power appliance like 500W,50
Hz
, if the capacitance of
C_{c}
is chosen between 20
μF
30
μF
, the voltage stress and current stress are well balanced.
In relative high power application, the power pulsation can also be compensated by the decoupling capacitor in the same method, when the parameters of the modulation functions meet equation (3).
Table I
lists the design values of
C_{c}
at different output frequencies of the 5kW matrix converter. The maximum voltage of the decoupling capacitor is designed as about 400V.
CAPACITANCE OFCcIN 5KWMATRIX CONVERTER
CAPACITANCE OF C_{c} IN 5KWMATRIX CONVERTER
III. MODULATION OF THE 31 MC
After increasing the power decoupling unit, a modulation method that synthesizes the modulation of the VSR and the CSI is adopted for the 31 MC.
 A. SVPWM Modulation for VSR
For the VSR, SVPWM is applied
[15]
,
[16]
.
Fig. 4
shows the voltage space of the VSR input side. It is divided into six sectors by six basic vectors, and the amplitude of each basic vector is 2
u_{comp}
/3 .In order to implement the unit power factor, the threephase input voltages need to be symmetrical sinusoidal voltages.
Voltage vector diagram of MC input side.
Namely the space vector
rotates at a constant speed in the
αβ
static coordinate system. Therefore, the rotation vector
in each sector can be composited by the adjacent basic vectors, and the trajectory of its endpoint is an approximate voltage cycle.
According to the voltage vector synthesis relationship and the sine theorem
[17]
, the operating times
T
_{i1}
and
T
_{i2}
of the basic vectors
U
_{i1}
and
U
_{i2}
in each sector can be obtained in
Table II
.
T
_{i0}
is the operating time of the zero vector which can be calculated as:
T
_{i0}
=
T_{s}

T
_{i1}

T
_{i2}
.
OPERATING TIME OF VECTORS IN EACH SECTOR
OPERATING TIME OF VECTORS IN EACH SECTOR
By detecting the sector signal of the vector
, the operating voltage vectors in each sector and their operating times are determined. Then, the VSR is modulated to make the virtual dc link perform as a current source.
 B. Staggered Modulation for CSI
For the CSI, when the load phase and decoupling phase work together, simultaneous conduction of the same pole side switches (
S_{ps}
,
S_{pr}
) and (
S_{ns}
,
S_{nr}
) must be avoided. Otherwise two capacitors with different voltages connect in parallel, and the short circuit current will breakdown the power switches (as shown in
Fig. 5
). Thus, staggered modulation is carried out for the CSI.
Short circuit fault.
SPWM is adopted for both phases and their modulation functions are given by (1). In order to implement staggered modulation, the duty ratios of the load phase and decoupling phase should be reasonably allocated to assure that the conducting time of the bridge arms(
S_{pr}
,
S_{nr}
)and(
S_{ps}
,
S_{ns}
) do not overlap.
Where
U
_{i1}
lag
U
_{i2}
,
T_{s}
is PWM period ,
u_{rα}
,
u_{rβ}
are the value of
in
αβ
static coordinate system.
Therefore, the carrier contains a couple of opposite triangular waves. The bridge arm (
S_{pr}
,
S_{nr}
) is modulated by the decreasingcount triangle wave, while the bridge arm (
S_{ps}
,
S_{ns}
) is modulated by the increasingcount triangle wave. Then, the operating time of the two phases is allotted from two ends of a PWM period, as shown in
Fig. 6
.
Staggered modulation for CSI.
In addition, the sum of the duty ratios of the two phases should be less than 1.The amplitude of the sum of the duty ratios 
d
_{∑}
 meets equation (7):
The modulation ratio
is a constant. Therefore, 
d
_{∑}
 has a positive correlation relationship with
C_{c}
when the load
Z_{o}
remains unchanged. Only when
C_{c}
is less than the limit value given by (8), can the requirement of 
d
_{∑}
 ≤ 1can be guaranteed. In this case, the zero current state is always existent.
Table III
shows the time distribution in a PWM period for the CSI.
TIME DISTRIBUTION FOR CSI
TIME DISTRIBUTION FOR CSI
As for the current type inverter, when only the load phase operates, the CSI’s input voltage component is
f_{l}u_{o}
:
There is a low frequency pulsed component. If this pulsed component directly reflects the input side, it will cause input current distortion.
When only the decoupling phase operates, the CSI’s input voltage component
f_{c}u_{c}
happens to be a pulsed component of twice the output frequency.
However, actual operation of the CSI should combine the load phase and the decoupling phase, so that the input voltage of the CSI is a composite voltage
u_{comp}
.When the modulation function satisfies (3),
u_{comp}
is simplified as:
In (11), the low frequency pulsed component is eliminated and the composite voltage maintains constant.
Using the described modulation method, the current and voltage vector diagram of the CSI output side is obtained as shown in
Fig. 7
. The current space is divided into 4 sectors according to the direction of the current. The
γ
axis and
ψ
axis are perpendicular to the load phase current vector and the decoupling phase current vector, respectively. The
ψ
axis lags the
γ
axis by
φ_{c}
. Combined with the VSR voltage space vector diagram, a 31MC with active power decoupling capacitor has a total of 6×4=24 kinds of sector combinations.
Output current and voltage vectors of CSI.
 C. Switch Modes of the MC
After modulation synthesis, the operating time of each sector is reduced. When the operating vector of the VSR is
U
_{i1}
, the conduction time of the load phase and decoupling phase are expressed as:
When the operating vector of the VSR turns into
U
_{i2}
,the conduction time of the two phases change as:
Therefore, the operating time of the zero vector can be calculated:
Combining
Table II
and formula (6), 5 slices of the time signal of the 31 MC in all of the sectors are obtained.
To investigate working states of the 31 MC in different sectors, it is assumed that the input frequency is 50Hz and that the output frequency is 400Hz. Then, each voltage sector contains all of the current sectors.
Table IV
shows the power switch state of the 31 MC.
SWITCH STATES IN DIFFERENT KIND OF SECTOR COMBINATIONS
SWITCH STATES IN DIFFERENT KIND OF SECTOR COMBINATIONS
The 31MC has 5 kinds of switch modes in every sector combination. Take the VI—Z4 sector as an example to analyze the switch modes under the 5 timeslice signals (as illustrated in
Fig. 8
). Suppose time variables:
Switching modes of 31MC in a PWM period.
In mode (a), the inductor current of phase A and phase C discharge the load phase, while the decoupling capacitor energy remains unchanged. In mode (b), the inductors discharge the decoupling phase, whose charge current is the sum of the inductor currents of phase A and phase C, and filter capacitor discharges the load. In mode (c), the inductor current turns to discharge the load phase, but the charge current is the inductor current of phase A. In mode (d), the inductor current of phase A discharges the decoupling phase and the filter capacitor discharges the load. Mode (e) is the working state of the zero vector, in which the three phase inductors store energy.
As can be seen from the 5 kinds of switch modes, the current of the two phases with the largest amplitude charge the load and the power decoupling capacitor. This conforms to the law of voltage space vector modulation. The working state of the inductors and capacitors in the other sector combinations can be analyzed in the same way.
IV. MODELING OF THE 31MC
A set of power switches and a decoupling capacitor are introduced into a 31MC, which increases the timevarying and nonlinear factors in the 31 MC mathematical model. In order to investigate the closedloop control strategy, the average signal model of the 31MC is built in the dq coordinate system. Then, disturbances are separated to obtain a small signal model with the feedforward decoupling control.
 A. Average Signal Model
Combined with the equivalent circuit of the 31 MC power decoupling topology, the mathematical model of the VSR is derived by using the switch average model:
Where
S
* = (
S_{a}
+
S_{b}
+
S_{c}
) / 3 and
S_{i}
(
i
=
a,b,c
)are switching functions.
KCL is applied for the CSI, and then the mathematical model can be expressed as:
Using formula (2), the state equation of the 31 MC power decoupling topology in static coordinates is deduced:
In the static coordinates system, the average signal model of the 31MC is very intuitive and each variable has a clear physical meaning. However, the input current and voltage are ac variables, which is not conducive to control system designing and causes steadystate errors
[18]
. Therefore, the equivalent transformation matrix of the rotating coordinate system is employed:
Assuming that the threephase input power is symmetrical, i.e.
i_{a}
+
i_{b}
+
i_{c}
= 0 ,
u_{a}
+
u_{b}
+
u_{c}
= 0 , the state equation of the 31 MC power decoupling topology in the rotating coordinate system is derived as:
Where
ω_{i}
is the input angular velocity,
d_{d},d_{q}
,
i_{d},i_{q}
and
u_{d},u_{q}
are the switching functions, input current and voltage in rotating coordinate system.
According to state equation (15), the average signal model of the 31MC in the dq coordinate system is illustrated in
Fig. 9
. To eliminate the timevarying factors caused by switches, the nonlinear switching elements are replaced by controlled sources which use the average components as control variables.
Average signal model of 31MC.
The voltage controlled sources of the input side:
The current controlled sources of the output side:
Although the ac variables of the 31MC input side are turned into average dc components in the dq coordinate system,
u_{o}
and
u_{c}
in the output side are still ac variables. Therefore, it is necessary to use the composite voltage
u_{comp}
to express
u_{o}
and
u_{c}
, and to separate the disturbances to obtain a linearized small signal model.
 B. Small Signal Model
In order to eliminate timevarying variables, the disturbances of the references and high order small signal components are ignored, while only the disturbances from the input source and load are considered. The average signal variables in the average signal model are assumed as:
,
x
= {
i_{d}
,
i_{q}
,
d_{d}
,
d_{q}
,
u_{d}
,
u_{q}
,
u_{comp}
,
i_{dc}
,
u_{o}
,
u_{c}
}. Insert
x
into (2). Then:
The small signal components of the load voltage and decoupling capacitor voltage are:
Combined with (16)(18), the small signal component of the weighted composite voltage
ũ_{comp}
is obtained as:
Formula (19) shows the linear relationship between
ũ_{comp}
and
. The weighted composite voltage indirectly reflects the load voltage and decoupling capacitor voltage. As a result,
ũ_{comp}
can be substituted for the ac variables
u_{o}
and
u_{c}
in the state equation of the 31 MC. Then, all of the ac components in the model are eliminated.
In the average signal model, the input d axis current and the q axis current are coupling. Thus, feedforward decoupling control is employed to make the control circuits of the d axis and q axis mutually independent. According to the relationship between the input power references and the current references as Equation (20), the input unity power factor can be achieved if the reactive current reference is set to 0.
After the feedforward decoupling control, all of the small signal components in (15) are separated. The differential equations of the d and q axis are deduced as follows:
Based on differential equations, the small signal circuit model of the 31MC with feedforward decoupling control is built in
Fig.10
, where:
Small signal circuit model of 31MC with feedforward decoupling control.
The small signal circuit model is very simple and clear. The input sides of the model are two independent Boost type switch networks in parallel. This greatly simplifies the timevarying, complex mathematical model of the 31MC. In addition, regulation without steadystate errors can be achieved. This contributes to the research and design of the closedloop system.
V. CLOSEDLOOP CONTROL AND CONTROLLER DESIGN
 A. DualLoop Control System
In the dq coordinate system, the d axis current and q axis current control the active component and reactive component of the input current independently. However, the reference of the d axis current is a dc signal, so the control variable for the voltage loop should also be a dc signal.
The weighted composite voltage can be expressed as:
This is proportional to the load voltage RMS value, and the ratio is kept constant. Thus, it can be taken as the control variable for the voltage loop.
According to the small signal circuit model and (16)(19), the small signal component of the weighted composite voltage
ũ_{comp}
is composited by the small signal components of the load voltage and decoupling capacitor voltage. It also has a linear relationship with the small signal of the dc link current. As for the current source inverter, the dc link current determines the load voltage and decoupling capacitor voltage.
In addition, the weighted composite voltage can be calculated by sampling the instantaneous values of the load voltage and decoupling unit voltage. The integral computation for calculating the voltage RMS value is no longer necessary.
Therefore, taking the weighted composite voltage as the feedback quantity can indirectly control the load voltage and decoupling capacitor voltage. In addition, its characteristic of rapid calculation will improve the dynamic response speed of the control system.
According to (21), the input current feedforward decoupling control is employed. Then, the d axis current and q axis current are used to adjust the threephase active and reactive power. Through the feedback of the weighted composite voltage, the voltageloop control quantities are dc variables. Therefore, the pi regulation has no steadystate error and the control system design is simplified. Finally, a novel dualloop control strategy with the weighted composite voltage feedback is proposed. The complete closedloop control system of the 31 MC power decoupling topology is illustrated in
Fig. 11
.
Control system of 31MC based on the weighted composite voltage feedback.
 B. Controller Design
In the dualloop control, the outer voltage loop varies much slower than the inner current loop. As a result, it is assumed that
to design the current loop controller.
To keep the system symmetric, the d and q axis current control should be the same. Taking the d axis control block diagram as an example (shown in
Fig. 12
), the following presents the analysis and design of the currentloop control parameters.
axis current loop control.
Where
is the inertia link of the virtual rectifier,
is the inertia link of the controltocurrent transfer function,
is the delay of the current sampling feedback channel, and
k_{ip}
+
k_{ii}
/
s
the PI controller of the current loop.
Two littletime inertial links are equivalent to one inertial link. The zero and pole of the large time constant offset each other to improve the regulation speed. Then, its closedloop transfer function is derived as:
Where
T_{is}
= 0.5
T_{s}
+
nT_{s}
.Then, the scale parameter and the integral parameter are obtained:
In this paper, the inductance and parasitic resistance of the ac inductors are
L_{re}
= 2
mH
,
R_{re}
= 0.1Ω, the PWM frequency is
f_{s}
= 10k
Hz
, and the damping ratio
ξ
is usually 0.707. Then, the scale parameter and the integral parameter are calculated:
k_{ip}
= 0.47,
k_{ii}
= 23.5
The further design for the voltage loop control block diagram is shown in
Fig. 13
. 1/(1 +
T_{uc}s
) is the delay of the voltage sampling feedback channel,
transfer function,
K_{pwm}
/(1 +
T_{i}s
) is the simplified closedloop transfer function of the current loop,
Ti
=
L_{re}/k_{ip}
,and
k_{pv}
+
k_{iv}/s
is the outer loop PI controller.
Outer voltage loop control.
The order is reduced by merging littletime inertial links in the same way, and the openloop transfer function is obtained as follow:
Where
T_{vs}
=
T_{i}
+
T_{uc}
. According to (25), the amplitude frequency characteristics and phase frequency characteristic curves of the outer voltage loop transfer function are given in
Fig. 14
. The transfer function is specially designed so that the zero is between two poles, i.e. the outer loop PI parameters satisfy the formula:
Bode diagram of voltage open loop transfer function of 31MC.
The filter capacitor
C_{f}
= 4.4
μF
, and the load resistance
R_{L}
= 50Ω150Ω .By combining (26) with
Fig. 14
, the outer voltage loop PI parameters are designed as
k_{vp}
= 0.1,
k_{vi}
= 60 . Then, the phase angle margin
γ
= 45°70° . As a result, the overshoot and adjusting time of the control system can be well balanced.
VI. SIMULATION OF THE CLOSED LOOP SYSTEM
To verify the effectiveness of the presented dualloop control scheme, simulations of the dynamic process are performed for a 31MC with the decoupling unit in Matlab Simulink. The major parameters of the numerical simulation are given as:
Where
U_{lin}
is the effective value of the line voltage in the threephase side, and
f_{in}
is the input frequency.
Consider that disturbances are mainly from the source and load in actual operation. The following part analyzes the dynamic regulation features of the 31MC in both disturbance cases.
Load disturbances include sudden load increases and decreases. Simulation waveforms of the input current and voltage, the output load voltage and the decoupling voltage are illustrated in
Fig. 15
(a) when the load suddenly increases. Since the load resistance decreases from
R_{L}
= 100Ω to
R_{L}
= 50Ω, the input current increases twice to maintain the power balance. The load current jumps one time, and consequently the power pulsation absorbed by the decoupling capacitor jumps one time. Then, the maximum voltage of the decoupling capacitor jumps
times, increasing from 226V to 320V. When the load changes, the output voltage presents a little distortion due to a delay of the closedloop controllers. As a result, the voltage has a tiny drop. However, it soon settles down to 150V and its THD remains at 4.5%.In the process of adjustment, the input current and decoupling capacitor voltage both transit to the steady state rapidly and smoothly. The input current is still keep in phase with the input voltage and its THD is only 2.7%.
Simulation waveforms in load disturbance.
Simulation results when load suddenly decreases are illustrated in
Fig. 15
(b). When the load resistance increases from
R_{L}
= 50Ω to
R_{L}
= 100Ω, the regulating process of the input current and decoupling capacitor voltage is exactly opposite to the load increase. Due to the increase of the load resistance and the delay of the closedloop controllers, the output voltage has an overshoot. However, it soon returns to the 150V steady state. The THD of the output voltage and input current are 3.7% and 3.2%.
The input voltages may sharply increase or decrease.
Fig. 16
(a) shows the simulation waveforms of the 31MC when the input voltage suddenly decreases by 36%. The input current continuously increases to keep the power balance. The output voltage has a little distortion in the changing moment. However, it returns to the steady state in a cycle. The output impedance remains unchanged. Therefore, the output power and the power pulsation are the same, and the decoupling capacitor voltage basically remains invariant.
Simulation waveforms in input voltage disturbance.
Fig. 16
(b) shows the simulation waveforms of the 31MC when the input voltage suddenly increases by 36%. Regulating the process of the input current is opposite to the input voltage increase. The maximum voltage of the decoupling capacitor voltage remains the same in the changing moment. The output voltage has a slight distortion. However, it quickly regains stability.
It is seen from the above simulation analysis that whether the disturbance is from the load or input source, the closedloop control system can effectively control the 31MC and adjust the input current and output voltage to the steady state in a cycle. In addition, the steadystate output voltage is not affected by disturbances. These results demonstrate that the proposed control scheme performs well at regulating properties. In addition, the changed power pulsation is absorbed completely by the decoupling capacitor throughout the experiment. This proves that the 31MC system can implement power decoupling in the closedloop regulating process.
VII. EXPERIMENT VERIFICATION
The proposed control strategy and the design of the controllers are verified on a 500W prototype of a 31 MC with a power decoupling unit, as shown in
Fig. 17
. The prototype takes a TMS320F28335+CPLD as the core controller. Fourstep communication is employed for safe communication.
31MC prototype.
The hardware circuit is developed with the same parameters as those in the simulations.
A dynamic experimental study is carried out in four aspects: sudden load increase, sudden load decrease, sudden input voltage increase, sudden input voltage decrease. This is done to analyze the regulating capacity and response speed of the 31 MC with a power decoupling unit.
In
Fig. 18
(a), since the load resistance suddenly drops from
R_{L}
= 100Ω to
R_{L}
= 50Ω, it takes 2 cycles for the input current
i_{a}
to reach the steady state. The current RMS value increases from 3.89 A to 7.5 A, the input current and voltage are still in phase, and the PF value is between 0.996 ~ 0.998. Due to the sudden load increase, the output voltage
u_{o}
has a slight drop in the changing moment. However, it also returns to 150V in 2 cycles. The input current THD is 3.3% and the output voltage THD is 4.7%. The larger load current leads to a larger power pulsation. Thus, the energy stored in decoupling capacitor is greater and the maximum voltage of the capacitor is increased from 225V to 319V.
Experiment waveforms of load disturbance.
Fig. 18
(b) shows the experimental waveforms of
i_{a}
,
u_{o}
, and
u_{cc}
when the load resistance suddenly increases from
R_{L}
= 50Ω to
R_{L}
= 100Ω.
i_{a},u_{o}
, and
u_{c}
return to the steady state in one cycle after the changing moment. At the beginning of the load decreasing,
u_{o}
has an overshoot of σ% 12% ~ 15% , while the steady output voltage is still 150V.
i_{a}
and
u_{c}
both transit to the steady state smoothly. The adjusting process is exactly the opposite case of the load current sudden increase. After the dynamic process, the THDs of the output voltage and input current remain at 4.0% and 4.1%, respectively.
The experimental waveforms when the input voltage suddenly increases by 33% and decreases by 33% are shown in
Fig. 19
(a)(b).When keeping 100
R_{L}
= 100Ω to
u_{o}
= 150
V
, the input current decreases to 75% and increases to 150% compared with the original value. After the input voltage suddenly changes,
i_{a}
is slightly distorted. However, it restores stability in a half cycle.
Experiment waves of input voltage disturbance.
Load voltage
u_{o}
has a little distortion due to the effect of the
i_{a}
distortion. However, it reaches the steady state quickly. In addition, the THD of
u_{o}
is below 5% in the resteady state. As the power pulsation stays unchanged,
u_{c}
is almost not affected by input voltage disturbances, which is consistent with the simulation results.
The experiment indicates that when a load disturbance or input voltage disturbance occurs, the closedloop control system has a good dynamic regulating capability and a high response speed. Control objects such as the input current, output voltage, and decoupling capacitor voltage are adjusted to the steady state in one half to two cycles after the disturbance occurs. In addition, the PF value of the input current is close to 1 and the output voltage THD<5% in the resteady state. These results confirm that the proposed control strategy is feasible for the 31MC with a power decoupling capacitor.
VIII. CONCLUSION
Based on an analysis of the relationship between the 31MC output load voltage and the decoupling capacitor voltage, this article proposes a novel control strategy that takes the output weighted composite voltage as the outer loop control variable, and realizes the output weighted control of the 31MC. Then, using the d and q axis current with feedforward decoupling control as the current loop control variable, it obtains a unity power factor and a sinusoidal input current. The effectiveness of this strategy has been verified through experiment.
The transfer function expressions and controller design method are deduced through developing and studying the small signal model of a 31MC. By using this method to design a 31MC closedloop control system, the control objects such as the input current and output voltage can be adjusted to the steady state in one half to two cycles after disturbances occur. This demonstrates the rapid dynamic response and the strong stability of the system.
Simulation and experimental results confirm that the closedloop design method based on the proposed strategy is feasible. The system effectively accomplishes power decoupling with a high quality input current and a sinusoidal output voltage. It also demonstrates a fast dynamic adjustment ability.
Acknowledgements
This paper is supported by foundation of Graduate Innovation Center in NUAA, No. kjff 201470, Fundamental Research Funds for the central Universities, and the Joint Funds of the National Natural Science Foundation of China (Grant No. U1233127)
BIO
Si Chen was born in Yiyang, China, in 1991. He received his B.S. degree in Electrical Engineering and Automation from the Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 2013. Since 2013, he has been working toward his M.S. in Civil Aviation Electrical Engineering at NUAA. His current research interests include matrix converter control, and multi pulse rectification technology.
Hongjuan Ge was born in Jiangsu, China, in 1966. She received her B.S. and M.S. degrees in Electrical Engineering from Southeast University, Nanjing, China, in 1985 and 1988, respectively; and her Ph.D. degree in Electric Machines and Electric Apparatus from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2006. Her current research interests include spacevector control of PMMs, ACAC converters, and airworthiness technology.
Wenbin Zhang was born in Suzhou, China, in 1988. He received his B.S. and M.S. degrees in Electrical Engineering and Automation from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2011 and 2014, respectively. His current research interests include ACAC power converters, and renewable energy.
Song Lu was born in Nantong, China, in 1990. He received his B.S. degree in Electrical Engineering from Jiangnan University, Wuxi, China, in 2012; and his M.S. degree in Electric Machines and Electric Apparatus from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2015. His current research interests include power electronics and control, and gridconnected matrix converters.
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