M
odel-based predictive
control (MPC) for power
converters and drives is
a control technique that
has gained attention in
the research communi-
ty. The main reason for
this is that although MPC presents high com-
putational burden, it can easily handle mul-
tivariable case and system constraints and
nonlinearities in a very intuitive way. Taking
advantage of that, MPC has been success-
fully used for different applications such as
an active front end (AFE), power converters
connected to resistor–inductor RL loads,
uninterruptible power supplies, and high-
performance drives for induction machines,
among others. This article provides a review
of the application of MPC in the power elec-
tronics area.
MPC presents a dramatic advance in the
theory of modern automatic control [1]. MPC
was originally studied and applied in the pro-
cess industry, where it has been in use for
decades [2]. Now, predictive control is being
considered in other areas, such as power
electronics and drives [3]–[6]. The reason
for the growing interest in the use of MPC in
this field is the existence of very good mathe-
matical models to predict the behavior of the
Model Predictive Control
A Review of Its Applications in Power Electronics
SERGIO VAZQUEZ, JOSE I. LEON, LEOPOLDO G. FRANQUELO, JOSE RODRÍGUEZ, HECTOR A. YOUNG,
ABRAHAM MARQUEZ, and PERICLE ZANCHETTA
variables under control in electrical
and mechanical systems. In addition,
today’s powerful microprocessors can
perform the large amount of calcula-
tions needed in MPC at a high speed
and reduced cost.
The research works published be-
tween 2007 and 2012 in IEEE Xplore
have been analyzed by performing a
search using the keywords “predic-
tive” and “power converters.” This
search generated more than 200 pa-
pers on MPC applied to pulsewidth
modulation (PWM) power converters
published in conferences and journals
[7]. The applications covered by these
research works can be catego-
rized into four main groups: grid-
connected converters, inverters
with RL output load, inverters
with output inductor-capacitor
(LC) filters, and high-perfor-
mance drives. Figure 1 shows
how these research works are
distributed among these four
groups. It is also interesting to
study how these categories have
attracted the attention of the
research community in recent
years. Figures 2 and 3 present
information about this issue.
Figure 2 shows that grid-con-
nected converters and high-
performance drives are the
application where researchers
have paid more attention, be-
ing a current focus of interest.
Figure 3 shows how research
community attention has not de-
creased in this period and is still
increasing. It should be noted
that, for all categories, the cu-
mulative line trends are positive.
This article presents the use
of MPC for the four main cat-
egories of applications for PWM
power converters that can be
found in the literature. This
includes various applications
such as grid-connected convert-
ers, inverters with RL output
load, inverters with output LC
filters, and high-performance
drives. The basic issues of well-
established MPC algorithms
are presented for these applica-
tions, and new challenges for
MPC control for power converters and
drives are also addressed.
The MPC Control Strategy
Predictive control is understood as a
wide class of controllers—the main char-
acteristic is the use of the model of the
system for the prediction of the future be-
havior of the controlled variables over a
prediction horizon,
N.
This information
is used by the MPC control strategy to
provide the control action sequence for
the system by optimizing a user-defined
cost function [8]. It should be noted that
the algorithm is executed again every
sampling period and only the first value
of the optimal sequence is applied
to the system at instant
k.
The
cost function can have any form,
but it is usually defined as
g x
p
h
2
,
*
=
/
m -
(1)
i
^
xi
i
i
where
x
i
is the reference com-
mand,
x
p
is the predicted value
*
i
for variable
x ,
i
m
i
is a weighting
factor, and index
i
stands for the
number of variables to be con-
trolled. In this simple way, it is
possible to include several control
objectives (multivariable case),
constraints, and nonlinearities.
The predicted values,
x
p
,
are cal-
i
culated by means of the model of
the system to be controlled.
MPC for Power Converters
The application of MPC for
power converters has increased
because of the improvement of
digital microcontrollers [3], [9].
This control technique requires a
nonnegligible amount of calcula-
tions during small sampling times
when applied for controlling pow-
er converters and drives.
There are several approaches
to dealing with the computa-
tional burden problem. In some
cases, it is possible to solve the
optimization problem offline by
multiparametric programming;
thus, the implementation is re-
duced to some calculations and
a look-up table [10]. Another
method involves using predictive
FIGURE 1 – The research works of MPC for
PWM power converters published in IEEE
conferences and journals from 2007 to 2012:
distribution regarding applications.
Grid Connected
Motor Drives
Inverter with Output LC Filter
Inverter with RL Load
FIGURE 2 – The research works of MPC for PWM power convert-
ers published in IEEE conferences and journals from 2007 to
2012: distribution regarding applications and year of publication.
20
18
16
14
12
10
8
6
4
2
0
2007 2008 2009 2010 2011 2012
Grid Connected
Motor Drives
Inverter with Output LC Filter
Inverter with RL Load
FIGURE 3 – The research works of MPC for PWM power convert-
ers published in IEEE conferences and journals from 2007 to
2012: the cumulative analysis for each application category.
90
80
70
60
50
40
30
20
10
0
2007 2008 2009 2010 2011 2012
Grid Connected
Motor Drives
Inverter with Output LC Filter
Inverter with RL Load
techniques as generalized predictive
control (GPC). GPC provides an online
solution to the optimization problem
and can be used for long prediction
horizons without significantly increas-
ing the computational cost [8], [11].
It should be noted that GPC does not
take into account the switching of
power semiconductors when it is ap-
plied for power electronics and drives.
Therefore, GPC only gives an exact
solution to an approximated optimiza-
tion problem. This approach can be
followed when an explicit solution to
the problem can be found. Usually, this
requires an unconstrained problem,
but it calculates the output voltage
reference to the inverter. This volt-
age should be generated by a PWM
or space-vector modulation (SVM)
technique. Thus, the GPC technique
can take advantage of well-established
knowledge about PWM-SVM to opti-
mize some aspects of the power con-
verter systems [12].
Finally, the discrete nature of pow-
er converters can be considered for
implementing MPC control strategies.
In this way, finding the solution to the
optimization problem can be reduced
to evaluate the cost function only for
the prediction of the system behav-
ior for the power converters possible
switching states. As a finite number of
control actions are evaluated, this ap-
proach is called finite-control-set MPC
(FCS-MPC). This technique has been
extensively used for power converters
because of the finite number of switch-
ing states they present [6].
FCS-MPC Control Principle
Figure 4 shows the block diagram of
FCS-MPC, where a generic converter is
used to feed a generic load. The con-
verter presents
J
different switching
states. The control objective pursuits
that variable
x
has to follow the refer-
ence
.
x
*
The FCS-MPC algorithm has
the following basic steps:
1) Measure and/or estimate the con-
trolled variables.
2) Apply the optimal switching state
(computed in the previous sam-
pling period).
3) For every switching state of the
converter, predict (using the math-
ematical model) the behavior of
variable
x
in the next sampling in-
terval
x
p
.
4) Evaluate the cost function, or error,
for each prediction as, for instance:
*
g | x x
p
|.= -
5) Select the switching state that
minimizes the cost function,
S
opt
,
and store it so that it can be ap-
plied to the converter in the next
sampling period.
As discussed in [13], it is conveni-
ent to perform the prediction two
time steps ahead to reduce the effects
of the delay introduced by the im-
plementation of FCS-MPC in a digital
platform. Another possibility to avoid
the effect of the computation delay
is to use a control strategy that only
requires a small computation time. In
this way, the optimal switching state
is applied to the converter with this
small delay and before the following
sampling instant [14]. A time diagram
of the execution of the FCS-MPC algo-
rithm is presented in Figure 5.
MPC for
Grid-Connected Converters
Several applications use grid-connect-
ed converters as one of their main com-
ponents. This application includes an
AFE for high-performance drives, recti-
fiers, and grid integration of renewable
energies such as wind or photovoltaic
(PV) and energy storage systems. Grid-
connected converters are also used
in flexible ac transmission systems
(FACTS) devices such as static syn-
chronous compensators (STATCOMs),
active power filters (APFs), or as a
part of a unified power flow controller
(UPFC) or a unified power quality con-
ditioner (UPQC) [15]–[17].
Control of an Active Front End
The power circuit of a grid-connect-
ed converter through a smoothing
inductor,
L,
is presented in Figure 6.
As shown, the main system variables
are the grid current,
i
L,abc
,
grid volt-
age,
v
S,abc
,
and the output capacitor
dc-link voltage,
v
dc
.
The load con-
nected to the dc link represents any
generic load connected to an AFE.
Thus, it can be a resistor for a rec-
tifier, a PV panel, or a converter to
control the torque and/or speed of a
FIGURE 4 – An FCS-MPC block diagram.
Converter Load
x
Predictive
Model
Optimization
Measurement
and
Estimation
J
x
∗
x
p
S
opt
FIGURE 5 – The time diagram of the execution
of the FS-MPC algorithm.
Optimize
Measure
x(k), x
∗
(k)
Apply
S (k)
opt
Store
S (k + 1)
opt
Predict
p p
. .
x , x
2
.
x
p
1
J
Evaluate
g x , g x
.
g x
p
p p
. .
1 2 J
k – 1
k
k + 1
wind turbine for grid integration of
renewable energies.
The main objective of the control
strategy is to calculate the output in-
verter voltage,
v
I,abc
,
to regulate the
output dc-link capacitor voltage to a
*
reference,
v ,
dc
for any connected load
and inject into the grid any reactive
power command reference,
.
q
*
There are several alternatives for
designing the control algorithm for
an AFE. In general, a cascade control
structure is used. An external control
loop is employed to regulate the dc-
link voltage. On the other hand, an in-
ternal control loop is adopted to track
the grid currents or the instantaneous
active and reactive power references
regarding the states variables used to
develop this controller [18], [19].
MPC has mainly been used as a con-
trol strategy for the inner control loop.
Although some works developing grid
current controllers can be found in the
literature, the main approach has been
the direct power control (DPC) for
tracking the commands for the instan-
taneous active and reactive powers,
P
and
Q.
The application of FCS-MPC-
DPC and predictive DPC (P-DPC) with
SVM modulation strategy is well estab-
lished [14], [20]–[22].
The block diagram of the FCS-
MPC-DPC strategy is presented in
Figure 7. In this case, the model of
the system is used to predict values
of the instantaneous active and re-
active power over a prediction ho-
p
rizon
N = 1, P (k 2),
+ Q
p
(k 2).+
In [14] and [20], a three-phase, two-
level AFE was controlled adopting
this strategy. The algorithm was
developed in the
ab
frame. There-
fore, only the seven possible output
vectors were considered to perform
the prediction; thus, the number of
switching states is
J = 7.
Once the
seven output voltage predictions are
calculated, the cost function
( ) )
h
( ) )
h
2 2
is minimized to find the inverter out-
put vector that should be applied in
the next sampling period.
Figure 8 presents the experimental
results obtained using this strategy
[14]. It should be noted that predic-
tions in instants
(k + 2)
are used to
compensate for the control action
^
g P k P
p
(k
^
(2)
+ + - +Q k Q
p
(k
2 2
*
*
2
2
= + - +
delay of the digital implementation of
the control strategy.
Another way to perform predic-
tive control for the AFE is by using
the P-DPC strategy. The block diagram
of the P-DPC strategy is presented in
Figure 9. Like GPC, the P-DPC strat-
egy does not take into account the
switching of power semiconductors;
therefore, it provides an exact solu-
tion to an approximated optimization
problem. In addition, P-DPC consid-
ers an unconstrained MPC problem.
FIGURE 6 – The power circuit of the AFE.
v
dc
Load
i
La
v
Sa
i
Lb
i
Lc
v
Sb
v
Sc
L
L
L
n
FIGURE 7 – A block diagram of the FCS-MPC control strategy for the AFE.
Predictive
Model
Minimization
of
Cost Function
J
v
dc
v
dc
Load
i L
La
v
Sa
L
i
Lb
v
Sb
i
Lc
v
Sc
S
opt
v
S
(k )
i
L
(k )
L
n
v
∗
dc
+
–
PI
P
∗
(k + 2)
Q
∗
(k + 2)
Q
p
(k + 2)
J
P
p
(k + 2)
FIGURE 8 – The experimental results of the FCS-MPC-DPC for a three-phase, two-level AFE.
180
170
160
150
140
130
120
v
∗
110
100
90
400
300
200
100
P
s
0
–100
Q
∗
–200
–300
–400
80
60
40
i (×5)
20
0
–20
–40
–60
–80
0 0.02 0.04 0.06 0.08
Time (s)
Time (s)
Time (s)
v
dc
dc
v
sa
sa
P
∗
s
s
Q
s
Q (VAR), P (W)
Voltage (V), Current (A) Voltage (V)s s
Thus, an explicit solution can be ob-
tained provided the control action
is applied once the cost function (2)
is minimized. Therefore, an optimal
switching vector sequence can be cal-
culated. The control strategy provides
the switching vectors and the switch-
ing times; thus, a PWM-SVM modula-
tion strategy is necessary to generate
the firing pulses.
Compared with FCS-MPC, the P-DPC
algorithm uses an external modulator;
thus, a constant switching frequency
is obtained. This can be considered
an advantage, especially in the AFE ap-
plication, because for grid-connected
converters exist highly demanding
codes that impose strict limits to the
low-order harmonics that can be in-
jected into the grid. FCS-MPC presents
variable switching frequency; thus, the
grid current has a widespread harmon-
ic spectrum. On the other hand, P-DPC
provides constant switching frequen-
cy; thus, the grid current harmonic
spectrum is concentrated around the
switching frequency, which decreases
the cost of the output L filter. Figure 10
shows the experimental results ob-
tained using the P-DPC strategy for a
STATCOM application when an instan-
taneous reactive power command
step is imposed [22].
It should be noted that the outer
control loop to regulate the dc-link ca-
pacitor voltage is usually solved using
a conventional proportional-integral
(PI) controller. However, there are
some solutions that replace the PI con-
trol for an MPC strategy [14].
Control of an Active Filter
In its classical configuration, an APF
basically consists of a voltage-source
inverter (VSI) whose dc side is connect-
ed to a capacitor’s bank and whose ac
side is connected to the mains through
a suited filter, usually formed by a set
of series inductors, as shown in Fig-
ure 11 (referring to the most common
three-wire configuration without neu-
tral). In such a configuration, ideally,
the APF is able to operate as a control-
lable current generator, drawing from
the mains any set of current wave-
forms having a null sum. Therefore, an
APF is ideally able to compensate the
unbalanced, reactive, and harmonic
components of the currents drawn by
any load in such a way that the global
equivalent load, as seen from the grid,
resembles a resistive balanced load
drawing about the same active power.
In fact, under steady-state conditions,
the voltage of the dc bus is intended to
remain about constant and close to the
design level to permit an indefinitely
long operation. Therefore, in practice,
the currents drawn by the APF must
FIGURE 9 – A block diagram of the P-DPC strategy for the AFE.
Predictive
Model
P-DPC
J
v
dc
v
dc
Load
i
La
v
Sa
L
i
Lb
v
Sb
i
Lc
v
Sc
v
I, abc
S
abc
v
S
(k )
i
L
(k )
L
L
n
v
∗
P
∗
(k + 2)
dc
+
–
PI
Q
∗
(k + 2)
Q
p
(k + 2)
P
p
(k + 2)
J
PWM-SVM
FIGURE 10 – The experimental results of the P-DPC for a three-phase, two-level AFE for a reactive
power command step from 10 to –10 kVAr. (a) The dc-link voltage. (b) The instantaneous active
and reactive power. (c) The grid voltage and output current for phase
a.
0 0.2 0.4 0.5 0.6 0.8 1
Time (s)
(a)
0
100
800
700
600
500
400
300
200
v (V), i × 10 (A) v (V)
q (kVAr), p (kW)Sa La dc
Time (s)
(b)
0.45 0.47 0.49 0.51 0.53 0.55
Time (s)
(c)
0.45 0.47 0.49 0.51 0.53 0.55
5
0
−5
−10
10
300
200
100
0
−100
−200
−300
−400
400
v i × 10
Sa La
q p
q
∗
v
dc
v
∗
dc