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A New Constant Switching Frequency Model
Predictive Control Method for Grid Connected 5-level
ANPC Inverter with Capacitors Sensor-less Voltage
Balancing
Mostafa Abarzadeh
Department of Electrical and
Computer Engineering
Marquette University
Milwaukee, WI, USA
m_abarzadeh@ieee.org
Nathan Weise
Department of Electrical and
Computer Engineering
Marquette University
Milwaukee, WI, USA
nathan.weise@marquette.edu
Liuchen Chang
Department of Electrical and
Computer Engineering
University of New Brunswick
Fredericton, Canada
lchang@unb.ca
Kamal Al-Haddad
Department of Electrical
Engineering
Ecole de technologie superieure
Montreal, Canada
kamal.al-haddad@etsmtl.ca
Abstract— In this paper, a constant switching frequency model
predictive control (MPC) method with capacitors voltages self-
balancing is proposed for the 5-level active-neutral-point-clamped
(5L-ANPC) grid connected inverter. The proposed MPC provides
optimum reference voltage for the 5L-ANPC inverter based on
minimizing the derivative of defined cost function with respect to
the output voltage of the 5L-ANPC inverter. The generated
reference voltage by the proposed MPC is applied to a phase
shifted pulse width modulation (PS-PWM) method to provide
constant switching frequency and sensor-less voltage balancing of
the dc-link and flying capacitors of the 5L-ANPC inverter. Hence,
the proposed MPC only needs to measure grid current; thus, the
complexity of control system and number of required sensors are
notably decreased. The proposed MPC is described and
simulation and experimental results are provided for the grid
connected 5L-ANPC inverter. The provided simulation and
experimental results verify the dynamic and steady state
performance as well as viability of the proposed constant
switching frequency MPC for the grid connected 5L-ANPC
inverter.
Keywords—Active-neutral-point-clamped (ANPC) converter,
constant switching frequency, model predictive control, phase
shifted pulse width modulation, sensor-less control.
I. INTRODUCTION
Providing less distorted and high quality injected current to
the grid by renewable and other distributed generation (DG)
energy sources necessitate utilizing more efficient, enhanced,
and reliable power electronic converters with less emitted
electromagnetic interference (EMI) to meet the electromagnetic
compatibility (EMC), and harmonic limits mandated by the
relevant stringent standards. Hence, to improve the quality of
injected current to the power grid, utilizing multilevel converters
(MLCs) can be chosen as a promising solution for integration of
renewable energy and other DG sources to the power grid [1-7].
Moreover, employing enhanced control techniques and
modulation methods in MLCs are highly demanded to improve
transient and steady state performance of the MLCs by utilizing
less number of required sensors [8-13]. Among various
configurations of multilevel converters (MLCs), the 5L-ANPC
converter and its derived hybrid configurations are widely
utilized in different industrial applications such as static ground
power units (SGPUs) for aircraft, medium-voltage variable
frequency drives, and integration of renewable energy sources
to the power grid [14-17]. It is comprised of eight power
switches, two dc-link capacitors, and one flying capacitor (FC).
Four of the power switches commutate at low frequency (LF)
and the other four power switches operate at high frequency
(HF) [18].
Various modulation and control techniques have been
presented in the literature to proper operation of the 5L-ANPC
converter. The main goals of the presented control methods and
switching patterns are voltage balancing of the dc-link and
flying capacitors, providing modified harmonic spectrum of the
output voltage, and improving the dynamic and steady state
performance of the 5L-ANPC converter. In [10], an improved
finite control set model predictive controller (FCS-MPC) has
been presented for the 5L-ANPC converter. The presented FCS-
MPC only requires measuring load current, neutral point and FC
voltages to select the proper switching state of the 5L-ANPC
converter and voltage balancing of dc-link and flying capacitors.
Hence, the number of required sensors for this FCS-MPC is
reduced. A model predictive pulse pattern control (MP
3
C)
method has been presented in [13] for the 5L-ANPC based
medium-voltage drive to provide faster torque response and
improve the current and stator flux quality. The MP
3
C has been
applied to the 5L-ANPC based ABB ACS 2000 general
proposed medium voltage drive. However, even though the
presented MPC methods provide improved and faster dynamic
response, the switching frequency in the presented MP
3
C and
FCS-MPC methods is not constant. Hence, they have sporadic
harmonic spectrum at the output which compels practical issues
in design of the output filter.
In order to achieve sensor-less voltage balancing of the dc-
link capacitors and flying capacitor, and to obtain constant
switching frequency at the output voltage of the 5L-ANPC, the
phase shifted PWM (PS-PWM) method, the hybrid level shifted
carrier PS-PWM (LSC-PS-PWM) method, and the logic
equation based switching method have been presented [8, 12,
978-1-7281-5826-6/20/$31.00 ©2020 IEEE 5904
14]. Hence, the voltage sensors and closed-loop voltage
regulators of the dc-link and flying capacitors are eliminated by
employing the presented modulation methods in the 5L-ANPC
MLC.
In this paper, to achieve improved performance and faster
dynamic response, constant switching frequency, and sensor-
less voltage balancing of the dc-link and flying capacitors at the
same time, a constant switching frequency modulator-based
MPC method with sensor-less dc-link capacitors and FC voltage
balancing is proposed for the 5L-ANPC grid connected inverter.
The proposed MPC provides optimum reference voltage for the
5L-ANPC inverter based on minimizing the derivative of
defined cost function with respect to the output voltage of the
5L-ANPC inverter. The generated reference voltage by the
proposed MPC is applied to the PS-PWM method to provide
constant switching frequency and sensor-less voltage balancing
of the dc-link and flying capacitors of the 5L-ANPC inverter.
II. CONSTANT SWITCHING FREQUENCY MODEL PREDICTIVE
CONTROLLER WITH CAPACIT ORS SENSOR-LESS VOLTAGE
BALANCING
A. The 5L-ANPC Converter Configuration
Fig. 1 depicts the single-phase 5L-ANPC grid connected
system. As shown in Fig. 1, the dc-link capacitors are regulated
to
2
E
and the FC is regulated to
4
E
to generate five-level
output voltage. All switching states, charging/discharging state
of the dc-link and flying capacitors, as well as output voltage
levels are presented in Table I.
Low
Frequency
S
3
S
3
'
S
4
S
4
'
E/2
E/2
C
dc1
C
dc2
S
2
S
1
S
1
'S
2
'
C
1
E/4
Vinv
vs
is
E
R
g
L
g
Fig. 1. The single-
p
hase 5
L
-ANPC grid connected inverter.
T
ABLE
I
S
WITCHING STATES OF THE
5L-ANPC
CONVERTER
.
Switching
State
4S
3S
2S
1S
out
V
Cfc
E
Δ
Cdc
E
Δ
1
V
0 0 0 0
2
E
− - ↓
2
V 0 0 0 1 4
E
− ↑ ↓
3
V 0 0 1 0 4
E
− ↓ ↓
4
V 0 0 1 1 0 - -
5
V 1 1 0 0 0 - -
6
V 1 1 0 1 4
E
+ ↓ ↑
7
V 1 1 1 0 4
E
+ ↑ ↑
8
V 1 1 1 1 2
E
+ - ↑
As presented in Table I, in the 5L-ANPC converter, by
utilizing the possible redundant switching states to generate
4
E
±
voltage levels, the FC can be regulated to
4
E
without
using any voltage sensor or closed loop voltage regulator.
B. The Proposed Constant Switching Frequency MPC
Method
The general model of the grid connected 5L-ANPC inverter
can be determined based on the inverter voltage dynamic
equation as follows
s
inv g g s s
di
VL Riv
dt
=++
(1)
where
g
L
and
g
R
are the inductance and series resistance of the
grid link inductor,
s
i
is the injected current to the grid,
s
v
is the
grid voltage, and
inv
V
is the 5L-ANPC output voltage. The
discrete-time model of
s
i
is calculated as follows by using Euler
Forward approximation
(1) ()
ss s
s
di ik ik
dt T
+−
≈
(2)
where
s
T
is the sampling time. Hence, with respect to (1) and
(2), the discrete-time predictive algorithm with one step
prediction horizon for controlling the injected current to the grid
is expressed as
()
ˆ
( 1) 1 () () ()
gs
Ps
ssinvs
gg
RT T
ik ik V k vk
LL
+= − + −
(3)
where (1)
P
s
ik+ is the predicted value of the injected current to
the grid and
ˆ()
s
vk
is the estimated value of the grid voltage.
Regarding the fact that the variation of the grid voltage is
negligible in comparison to the sampling frequency, thus
ˆˆ
() ( 1)
ss
vk vk=−
. With respect to (1),
ˆ(1)
s
vk−
is calculated as
ˆ(1) (1) () (1)
gg
sinv sgs
ss
LL
vk V k ik R ik
TT
−= −− − − −
(4)
The aim of the proposed MPC is regulating the value of the
injected current to the grid (
s
i
). Hence, the cost function of the
proposed MPC is defined as
*2
()
P
ss
g
ii
λ
=−
(5)
where
*
s
i is the reference value of the injected current to the grid.
It is worth mentioning that since the cost function of the
proposed MPC consists of only
s
i
term, the weighting factor of
the cost function is considered as
1
λ
=
. In contrast to the
presented FCS-MPC in [10] in which the cost function is
comprised of the reference current, neutral point voltage, and FC
voltage, in the proposed MPC, the cost function only consists of
the reference current. Hence, the proposed MPC algorithm only
needs to measure the injected current to the grid. Moreover, by
employing the PS-PWM method in the proposed constant
switching frequency MPC, not only is the constant switching
frequency obtained, also sensor-less voltage balancing of the dc-
link capacitors and FC are achieved. With regards to (3) and (5),
5905
()
2
*
ˆ
( 1) 1 () () ()
gs s
ssinvs
gg
g
RT T
ik ik V k vk
LL
λ
=
+− − − −
(6)
where
ˆ()
s
vk
is calculated by (4). In contrast to the FCS-MPC
method in which all of the possible switching states and their
corresponding voltage vectors are calculated to find the
minimum value of the cost function, the proposed MPC
algorithm exploits derivative of the defined cost function with
respect to the 5L-ANPC inverter output voltage to generate the
minimum
()
inv
Vk
to apply it to the proposed modulation method
for the 5L-ANPC. Hence, the main aim of the proposed MPC is
find the minimum value of the
()
inv
g
V
,
()
*
2
ˆ
( 1) 1 () () ()
s
inv g
gs s
ssinvs
gg
T
g
VL
RT T
ik ik V k vk
LL
λ
∂=− ⋅
∂
+− − − −
(7)
Hence, the minimum value of
()
inv
Vk
is calculated by
0
inv
g
V
∂=
∂
. Thus,
*
min
0
ˆ
(1) 1 () (1) ()
inv
ggs s
inv s s s
sg g
g
V
LRT T
Vk ikik vk
TL L
−
∂=
∂
+=− − − +−
(8)
Accordingly, the proposed MPC algorithm is obtained by
(3), (4), and (8). The flowchart of the proposed MPC algorithm
is presented in Fig. 2. The calculated value of
min
(1)
inv
Vk
−
+
is
given to the suggested PS-PWM method to generate
corresponding switching signals for
()
11
,SS
,
()
22
,SS
,
()
33
,SS
, and
()
44
,SS
. Voltage balancing of the dc-link and flying
capacitors without using any closed-loop voltage regulator, and
constant switching frequency operation of the 5L-ANPC
inverter are obtained by applying the suggested PS-PWM
modulation method. Furthermore, by utilizing the suggested PS-
PWM modulation method, odd multiples of the switching
harmonic clusters are eliminated from the output voltage
harmonic spectrum. Hence, the first switching harmonic cluster
frequency of the output voltage is doubled which leads to
halving the value of the grid link inductor.
III.
S
IMULATION
R
ESULTS
The grid connected 5L-ANPC inverter controlled by the
proposed constant switching frequency MPC with sensor-less
modulation method has been simulated in MATLAB/Simulink
platform. The performance of the proposed constant switching
frequency MPC has been evaluated for both cases of injecting
the active power to the grid and exchanging the reactive power
with the grid. The main parameters of the simulated grid
connected 5L-ANPC converter is illustrated in Table II. In
addition, the sampling time of the proposed MPC is set to
4
s
Ts
μ
=
. The schematic diagram of the simulated grid
connected 5L-ANPC inverter controlled by the proposed
constant switching frequency MPC with sensor-less modulation
method is shown in Fig. 3.
Start
(), ()
sinv
M
easure i k V k
11 22 33 44
(S ,S ),(S ,S ), (S ,S ),(S , S ) PWM Signals
′′′ ′
ˆ() ( 1) () ( 1)
gg
sinv s g s
ss
LL
vk V k ik R ik
TT
=−− −− −
*
min
ˆ
(1) 1 () (1) ()
ggs s
inv s s s
sg g
LRT T
Vk ikik vk
TL L
−
+=− − − +−
The 5L-ANPC Sensor-less
PS-PWM Modulation Method
*
PLL& ( 1)
s
Generate i k +
Fig. 2. Flowchart of the proposed constant switching frequency MPC with
sensor-less modulation method.
S
3
S
3
'
S
4
S
4
'
E/2
E/2
C
dc1
C
dc2
S
2
S
1
S
1
'S
2
'
C
1
E/4
V
inv
v
s
i
s
E
R
g
L
g
PLLsin
∑
Q
Controller
Ref.
Current
×
The 5L-ANPC
Sensor-less PS-PWM
Modulation Method
ref
θ
M
I
offset
θ
0
θ
ref
i
Eq. (4)
i
s
Eq. (8)
V
inv
i
s
Proposed Constant Switching Freq. MPC
11 22 33 44
(S ,S ),(S ,S ),(S , S ),(S ,S )
′′′′
ˆ
s
v
ˆ
s
v
Fig. 3. The grid connected 5
L
-ANPC inverte
r
controlled by the proposed
constant switching frequency MPC with sensor-less modulation method.
5906
T
ABLE
II
P
ARAMETERS OF THE
S
IMULATED AND
I
MPLEMENTED
G
RID
C
ONNECTED
5L-
ANPC
C
ONVERTER
.
Parameters Value
DC-link voltage
600
E
V=
Power Switches IRFP460 MOSFET
DC-link capacitors
12
2400
dc dc
CC F
μ
==
Flying capacitor (FC) 680
FC
CF
μ
=
Grid frequency
0
50
fHz=
Grid peak voltage 270
grid peak
VV
−
=
Grid-link inductor 2
g
L
mH=
Grid-link inductor series
resistance 0.1
g
R=Ω
Switching frequency 10
SW
fkHz=
Fig. 4 presents the grid voltage, the injected current to the
grid multiplied by 20, the 5L-ANPC inverter output voltage, and
the voltage of FC during the converter start-up and steady state
for the reference injected current of 10A. As shown in Fig. 4, the
injected current to the grid is almost sinusoidal and the FC
voltage is regulated to its desired value without utilizing any
closed-loop voltage regulator. Hence, the five-level output
voltage of the 5L-ANPC inverter is obtained.
Fig. 5 shows the grid voltage, the injected current to the grid
multiplied by 20, and the 5L-ANPC inverter output voltage
during step change in the reference injected current from 5A to
10A with unity PF. Moreover, Fig. 6 depicts the grid voltage,
the injected current to the grid multiplied by 20, and the 5L-
ANPC inverter output voltage during step change in the PF from
0.86 to 1 with the reference injected current of 10A. As
presented in Figs. 5 and 6, the proposed constant switching
frequency MPC provides improved performance and fast
dynamic response for both cases of injecting the active power to
the grid and exchanging the reactive power with the grid.
Fig. 4. The grid voltage, the injected current to the grid multiplied by 20, the
5L-ANPC inverter output voltage, and the voltage of FC during the c onverter
start-up and steady state for the reference injected current of 10A.
Fig. 5. The grid voltage, the injected current to the grid multiplied by 20, and
the 5L-ANPC inverter output voltage during step change in the reference
injected current from 5A to 10A with unity PF.
Fig. 6. The grid voltage, the injected current to the grid multiplied by 20, and
the 5L-ANPC inverter output voltage during step change in the PF from 0.86
to 1 with the reference injected current of 10A.
Fig. 7. The FFT analysis of the injected current to the grid and the FFT
analysis of the 5L-ANPC output voltage.
Fig. 7 depicts the FFT analysis of the injected current to the
grid and the FFT analysis of the 5L-ANPC output voltage. As
shown in Fig. 7, constant switching frequency operation of the
5L-ANPC inverter is obtained by employing the proposed MPC
5907
method. Moreover, the first switching harmonic cluster of the
output voltage is shifted to
1
20
st Harmonic
f
kHz
−
=
whereas the
switching frequency is set to
10
SW
f
kHz=
. Hence, the utilized
PS-PWM method cancels out the odd multiples of the switching
frequency from the output voltage of the 5L-ANPC inverter, and
the output voltage frequency spectrum is improved.
IV.
E
XPERIMENTAL
R
ESULTS
The grid connected 5L-ANPC inverter controlled by the
proposed constant switching frequency MPC method has been
implemented. The proposed controller has been implemented in
Texas Instruments TMS320f28335 digital signal controller
(DSC) and the injected grid current is measured by LEM LA55-
P current sensor. The parameters of the implemented grid
connected 5L-ANPC inverter is presented in Table II.
Fig. 8 presents the output voltage of the 5L-ANPC inverter
and the injected current to the grid for the reference injected
current of 10A. As shown in Fig. 8, the output voltage of the 5L-
ANPC inverter has five levels and the injected current to the grid
is approximately sinusoidal. The five-level symmetrical output
voltage of the 5L-ANPC converter verifies sensor-less voltage
balancing of the dc-link capacitors and FC by applying the PS-
PWM modulation method. Moreover, Fig. 9 depicts the output
voltage of the 5L-ANPC inverter and its FFT analysis. As shown
in Fig. 9, the 5L-ANPC inverter operates at constant switching
frequency, and though the switching frequency of the 5L-ANPC
inverter is
10
SW
f
kHz=
, the first switching harmonic cluster
frequency is shifted to around
1
20
st Harmonic
f
kHz
−
=
. Hence, the
odd multiples of the switching frequency are canceled out at the
output voltage of the 5L-ANPC inverter. Fig. 10 depicts the FC
voltage of the grid-connected 5L-ANPC inverter during the
converter start-up. As shown in Fig. 10, the FC voltage is
automatically regulated to its desired value which is
4150
E
V=
in about
300 ms
. To evaluate the dynamic
performance of the proposed constant switching frequency MPC
method, the 5L-ANPC inverter output voltage and the injected
current to the grid during step change in the reference injected
current from 10A to 5A is presented in Fig. 11. As illustrated in
Fig. 11, the proposed constant switching frequency MPC
provides very fast response and improved dynamic performance
for the grid connected 5L-ANPC inverter.
The match and similarity between the experimental and
simulation results verify the feasibility and viability, as well as
the dynamic and steady state performance of the proposed
constant switching frequency MPC method with sensor-less
voltage balancing of the dc-link and flying capacitors.
Fig. 8. The 5
L
-ANPC output voltage (Ch1: 200 volt/div), and the injected
current to the grid (Ch2: 10 amp/div; current sensor: 100 mv/amp).
Fig. 9. The 5
L
-ANPC output voltage (Ch1: 200 volt/div), and its FFT
analysis (Math: vertical: 20 volt/div; horizontal: 5 kHz/div).
Fig. 10. The FC voltage of the 5
L
-ANPC during inverter start-up (Ch1: 40
volt/div).
5908
Fig. 11. The 5
L
-ANPC output voltage (Ch1: 200 volt/div), and the injected
current to the grid (Ch2: 10 amp/div; current sensor: 100 mv/amp) during
step change in the reference injected current from 10A to 5A.
V.
C
ONCLUSION
In this paper, the constant switching frequency MPC
method with sensor-less dc-link capacitors and FC voltages
balancing was proposed for the grid connected 5L-ANPC
inverter. Only measuring the injected current to the grid is
required in the proposed MPC method. The proposed MPC
provides optimum reference voltage for the 5L-ANPC inverter
based on minimizing the derivative of defined cost function
with respect to the output voltage of the 5L-ANPC inverter. The
generated reference voltage by the proposed MPC is given to
the PS-PWM modulation method to provide constant switching
frequency and sensor-less voltage balancing of the dc-link and
flying capacitors of the 5L-ANPC inverter. Thus, the
complexity of control system and number of required sensors
were notably reduced. The proposed MPC was described and
simulation and experimental results were provided for the grid
connected 5L-ANPC inverter. The simulation and experimental
results verified the dynamic and steady state performance as
well as the viability of the proposed sensor-less constant
frequency MPC for the grid connected 5L-ANPC inverter.
A
CKNOWLEDGMENT
The information, data, or work presented herein was funded
in part by the Advanced Research Projects Agency-Energy
(ARPA-E), U.S. Department of Energy, under Award Number
DE-AR0000898 in the CIRCUITS program monitored by Dr.
Isik Kizilyalli. The views and opinions of authors expressed
herein do not necessarily state or reflect those of the United
States Government or any agency thereof.
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