1-s2.0-S0019057820305425-main

ISA Transactions 114 (2021) 485–498
Contents lists available at ScienceDirect
ISA Transactions
journal homepage: www.elsevier.com/locate/isatrans
Practice article
Design, implementation and model predictive based control of a
mode-changeable DC/DC converter for hybrid renewable energy
systems
Naki Güler a , Erdal Irmak b ,
a
b
∗
Technical Sciences Vocational School, Gazi University, Ankara, Turkey
Electrical and Electronics Eng. Department, Fac. of Technology, Gazi University, Ankara, Turkey
article
info
Article history:
Received 1 February 2020
Received in revised form 7 November 2020
Accepted 10 December 2020
Available online 13 December 2020
Keywords:
Hybrid renewable energy system
Mode-changeable converter
Model predictive control
Multi-input multi-output system
a b s t r a c t
Since renewable energy sources such as PV and wind provide intermittent energy generation, this
paper presents an advanced DC/DC converter that is able to set its operational mode automatically
to either multi-input multi-output (MIMO) or single-input multi-output (SIMO) depending on the
input source conditions. Power flow is controlled through the auxiliary relays added to a double-layer
boost converter. Considering the transient events require fast dynamic response, model predictive
control (MPC) is used to achieve the current control processes for both layers. Furthermore, the MPC is
modified to adapt itself to changes in the topology. The proposed system is verified by simulations and
experimentally. Results show that the proposed mode-changeable converter successfully determines
the optimum power route after deciding the best operational mode in accordance with the input source
conditions. Furthermore, the control method achieves a powerful and effective control process in both
MIMO and SIMO modes.
© 2020 ISA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Over the past decades, DC–DC power converters have been
adopted for a wide variety of applications ranging from power
supplies, renewable energy systems, motor drives and LED lighting. Although the main role of DC–DC conversion is specified as
control the voltage gain, it has gained another importance with
the multi-port operation ability in the last decade [1–4]. The
integration of multiple sources and feeding of multiple loads can
be highlighted as the major advantage of the multi-port power
converters.
Multi-input multi-output (MIMO) DC/DC topologies are used
to control the power flow from multiple sources to multiple
loads. Thanks to the power control capability, MIMO converters
have widespread usage in such applications as battery charging
systems [5], energy transferring operations between multiple
sources [6,7], electrical vehicles [8] and the power systems those
have loads requiring different voltage levels [9]. In order to reduce the number of circuit components, single-inductor MIMO
(SI-MIMO) types are especially preferred, where the inductor is
charged by switching the input sources sequentially while the
output power is controlled by using different switches. In these
∗ Corresponding author.
E-mail addresses: [email protected] (N. Güler), [email protected]
(E. Irmak).
https://doi.org/10.1016/j.isatra.2020.12.023
0019-0578/© 2020 ISA. Published by Elsevier Ltd. All rights reserved.
structures, each layer requires two switches at least [1,9–11],
which makes the control harder. Due to the inductor current
is the sum of all layer currents, the cross-regulation problem
is inevitable, and the control of inductor current is very complicated. Besides, SI-MIMO converters have limited voltage gain
because they usually cannot provide the symmetrical output voltage. Although the SI-MIMO topology presents a simple multi-port
structure, its complicated control strategy and cross-regulation
problem are the main challenges for implementation.
Single-input multi-output (SIMO) converters are another type
of multi-port converters. Similar to other types, these structures
have independent power layers too. In general, SIMO models
include additional control switches attached to the output of a
main converter [12]. Thus, each switch controls the power and
voltage level of its own layer. Since the unsymmetrical currents of
the layers, the control of input current is complicated. Besides, the
voltage gain band is limited especially in buck type SIMOs [12–
14]. Similar to SI-MIMO, the cross-regulation problem is the key
challenge in control of single inductor SIMO models.
The power control of converters is as important as their circuit
topology and a great deal of studies in recent literature deal with
this subject [8,15]. In this context, increased speed and measurement capabilities of microcontrollers have made it possible to use
of model-based control systems widespread. As compared with
the conventional techniques [16–18], model predictive control
(MPC) method stands out with its some features such as fast
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
Fig. 1. Block diagram of the proposed mode-changeable converter and MPC scheme.
dynamic response and easy implementation [19–22]. Therefore,
MPC is widely used for controlling the input and the output
power in multi-port converters. Usage of MPC method offers
better solutions to provide the power sharing between the input
sources in MIMO converters [9] and to achieve the control of
output voltages both in MIMO and SIMO converters [12].
Considering such issues summarized above, this paper
presents an advanced converter that can automatically switches
its topology to either MIMO or SIMO depending on the voltage
level of the input sources. The idea behind this topology is to
maintain the power flow by changing the operational mode
against the interruptions in the sources. Besides the fundamental
difference between the existing topologies, the total cost is reduced by using simple relays instead of power diodes to turn on
or off the sources. As mentioned earlier, the voltage gain is limited
in SI-MIMO structures because of their non-symmetrical outputs.
In order to overcome this problem, the proposed converter uses
a double layer boost converter structure with separate inductors.
During the SIMO operation, the positive layer operates in buckboost mode while the negative one operates in boost mode. Thus,
the voltage gain band is expanded to be use with different type
and size of loads. Since each layer of the proposed converter
is structured with independent inductors, the cross-regulation
problem is eliminated and the control strategy is considerably
simplified. Moreover, comprising fewer components than some
similar types in [9–11] is another simplification in terms of the
model-based control strategy. On the other hand, a fast dynamic
response requirement is essential due to the mode transition
feature of the proposed topology. Besides the fundamental requirement, the control method should have a good match with
the changes from boost to buck-boost in SIMO modes. Therefore,
the control algorithm should be able to adapt itself to changes in
the topology. MPC method is preferred to control the input currents of the proposed mode-changeable converter, by considering
control requirements [9,23]. Thanks to model based structure of
the MPC method, the operational changes in the topology are
defined into the control algorithm.
The current control operation of converters in discontinuous conduction mode (DCM) needs mean value calculation of
input currents [24] and this decreases the dynamic capability
of the control process. Therefore, some control methods have
been proposed to perform the control process in DCM and CCM
separately [25,26]. Similarly, the current control operation developed in this study is achieved in only CCM. MPC based average
current control of DC/DC converters was presented by using
average calculation [24,27], Kalman filter [28], observer [29], and
RMS calculation [24]. However, the design process of these techniques complicates the implementation of the control method.
In this paper, the average current control of the proposed modechangeable converter is implemented without neither calculation
method nor observer. CCM operation is provided with the selection of converter parameters in accordance with the methodology
reported in [30] and then model predictive current control structure is applied. Both the simulation and the experimental results
show that the proposed converter and its control algorithm successfully provides fast and stable operation not only in the steady
state conditions but also during the transitional states. Especially
the results of SIMO mode show that the MPC method adapts itself
to change in topology.
The proposed mode-changeable topology can be used in several applications, some of which are as follows:
• Multiple PV strings can be connected to multi inputs of the
converter for hybrid operation.
• Different types of energy sources like renewables and the
grid can be combined on the same bus [25].
• Multiple loads such as industrial loads and batteries can be
fed by the system thanks to its multi output feature [11].
2. Proposed mode-changeable DC/DC converter model
In order to explain and analyze the proposed system, a sample
two-input two-output converter model is designed consisting
of two boost converters as shown in Fig. 1 [31]. Unlike typical
double-layer boost converters, the proposed system includes four
auxiliary relays to route the power from multiple sources to
multiple loads, in different configurations by altering the switch
positions of the relays. Thus, the converter is able to set its mode
to either SIMO or MIMO automatically. Switches of the newly
added relays are numbered from S3 to S8 and their connection
diagrams are illustrated with dashed lines in Fig. 1.
Table 1 shows the relevant switch positions for each mode.
The mode SIMOV1 indicates that only the first input source (V1 )
is active and the system has two outputs. Similarly, the mode
SIMOV2 indicates the case where only the second source (V2 )
is active and the system has still two outputs. All inputs and
all outputs are active in the last mode called MIMO. A mode
detection algorithm is used to select an appropriate operational
mode automatically. Fig. 2 shows the flowchart of the mode
detection algorithm which determines the positions of auxiliary
relays depending on the source voltages [31]. Clearly, the algorithm compares the source voltages with a predefined threshold
voltage and it determines the positions of the auxiliary relays
according to Table 1. Consequently, the mode detection algorithm automatically integrates the active sources to the system
by changing the operational mode between MIMO and SIMOs.
486
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
being charged through the input sources. At the same time, the
capacitors C1 and C2 are discharged through the loads.
Switching State 2: In this case, S1 and S2 are OFF. Since the
inductance L1 is in discharging mode, the diode D1 is forward biased. Therefore, the energy is transferred from the L1 inductor and
the V1 input source to the C1 capacitor. The first layer operates as
a typical boost converter in this mode. Similarly, the energy flows
from the L2 inductance and the V2 input source to the C2 capacitor
on the second layer.
For MIMO operation, the relation between the output voltages
(VOUT 1 and VOUT 2 ) and the inputs is calculated by using the typical
boost converter equations as given in (1) and (2), where d1 and
d2 indicates the duty cycle ratios of the switches S1 and S2 ,
respectively.
VOUT 1 = V1
VOUT 2 = V2
1
(1 − d1 )
1
(1 − d2 )
(1)
(2)
2.2. Analysis of SIMO operation
In order to obtain the SIMO structure, the switches of the
auxiliary relays are set to the relevant positions according to
Table 1. As seen from the table, the switch s7 is OFF in SIMOV 1
mode. Therefore, the source V2 is completely separated from the
system. Similarly, the source V1 is separated from the system
through the auxiliary switches (s5 and s6 ) during the SIMOV 2
operation.
In the model, the first layer associated with the first IGBT (S1 )
controls the first output voltage (VOUT 1 ) while the second layer
controlled by the second IGBT (S2 ) manages the second output
voltage (VOUT 2 ). Thus, both outputs are controlled separately. In
both modes (SIMOV 1 and SIMOV 2 ), while the first layer operates in
buck-boost mode, the second one operates in boost mode. Thus,
SIMOV 1 and SIMOV 2 operations can be analyzed according to the
ON and OFF positions of the IGBTs as following.
Switching State 1: In this case, both the S1 and the S2 are ON.
Each inductor in the circuit is charged from the input source
connected to its own layer. The output energy is supplied through
the capacitors and the power to be transferred can be changed by
controlling the duty cycles of the S1 and the S2 .
Switching State 2: In this case, both the S1 and the S2 are OFF
and the diode D1 is forward biased because the inductance L1 is
in discharge mode. Thus, the energy flows to the loads and to the
capacitor C1 via the inductance L1 . In the second layer, the energy
also flows to the loads and to the capacitor C2 via the inductance
L1 and the active input source.
Eq. (3) gives the continuous mode voltage gain of the SIMO
mode, where Vin specifies the voltage of the active input source,
and d1 and d2 indicate the duty cycle ratios of the S1 and the S2 ,
respectively.
Fig. 2. Flowchart of the mode detection algorithm.
Table 1
Switch positions for operational modes.
Mode
SIMOV1
SIMOV2
MIMO
IGBTs
Switches of the Aux
relays for power routing
moden
S1
S2
s3
s4
s5
s6
s7
s8
1
2
3
Gate1
Gate1
Gate1
Gate2
Gate2
Gate2
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
2.1. Analysis of MIMO operation
VOUT 1 (1 − d1 ) + VOUT 2 (1 − d2 ) = V1,2 (1 + d1 )
According to Fig. 1 and Table 1, if the contacts of auxiliary
relays s4 , s6 and s7 are ON while the others are OFF, the converter
starts to operate in MIMO mode. In this case, V1 and V2 sources
are connected to separate boost converters as seen from Fig. 1.
Duty cycles of the IGBTs (S1 and S2 ) are separately controlled so
that the output voltages can be obtained independently. Thus,
it is possible to feed the loads requiring different voltage levels.
To better analyze the dynamic response of the proposed model
in MIMO mode, ON and OFF states of the IGBTs are studied
separately as following.
Switching State 1: In this state, S1 and S2 are ON. Once their
modes are changed to ON, the inductances L1 and L2 start to
2.3. Mathematical analysis
(3)
Mathematical models are separately created for each operating mode to better analyze the control process of the input
currents in CCM. During the MIMO operation, both layers are in
the boost mode as mentioned previously. Similar to the previous
notations, 1 and 2 indicate the first and second layers, respectively. Also, V1 and V2 indicate the voltages of first and second
input sources, respectively. If both the S1 and the S2 are ON, the
current of both inductors (iL1 , iL2 ) can be calculated using the
same equation as given in Eq. (4). If they are OFF, the total output
power is supplied from input sources and also from the inductor
487
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
that passes to discharging mode as seen from Eq. (5). Instead of
using separate equations for ON and OFF positions, Eqs. (4) and
(5) can be combined in only one statement as given in Eq. (6).
diL1,2
(
=
dt
diL1,2
1
=
diL1,2
=
)
1
)
(4)
(
)
(
(
V1,2 − RL1,2 iL1,2 − VOUT1,2
L1,2
(
dt
)
1
(
V1,2 − RL1,2 iL1,2
L1,2
(
dt
)
S1,2 =
))
(6)
diL1,2
1
for ON position of the sw itch 1 or 2
dt
dt
dVOUT1,2
dt
C1,2 R1,2
iL1,2
=
VOUT1,2
C1,2
(
−
1
dt
diL1
dt
diL1
dt
(
=
)
=
1
)
L1
(
1
(
V1,2 − RL1 iL1
L1
(
=
1
(8)
)
L1
)
(
)
V1,2 (S1 ) − RL1 iL1 − VOUT1 (1 − S1 )
Vin1 =
for mode1 (represents the SIMOV 1 mode)
⎪
V1
⎪
⎪
⎪
⎩
for mode3 (represents the MIMO mode)
0
for mode2 (represents the SIMOV 2 mode)
Vin1,2
]
moden
− RL1,2 iL1,2 − VOUT1,2 (1 − S1,2 )
)
The inductor current and the output voltage of the converter
can be described as independent states for each layer. The exact
representation of state–space model can be written as in Eqs. (15)
and (16).
ẋ = Ax + Bu
(15)
y = Cx + Du
(16)
(10)
The state vector of the proposed converter can be defined as in
Eq. (17).
(11)
x = iL1 VOUT1 iL2 VOUT2
[
]T
(17)
Since the inherent of switched power converters, averaged models are used to analyze the converter in one switching period.
As seen from Eq. (18), the average state equation is created by
combining the state equations of both ON and OFF positions.
Clearly, the source voltage in the differential equations may
change depending on the activated source. Therefore, the SIMO
operation is separated as SIMOV1 and SIMOV2 modes and the differential equations are structured based on the activated source.
Since V1 or V2 can be used as the source in SIMO mode, source
selectivity is essential to define the active source in Eq. (11).
Source selectivity means that substituting the voltage of activated
source (V1 or V2 ) with V1,2 in Eq. (11). In order to define the
active source in a common current equation for all operational
modes, the input voltage arrays depending on the input sources
are created as given in Eqs. (12) and (13). Moreover, the difference
between differential equations of boost and buck-boost is defined
by using switch position (S1 ) in Eq. (12).
⎧
V1 S1
⎪
⎪
⎪
⎪
⎨V2 S1
L1,2
[
2.4. Continuous-time model
(9)
)
(
−RL1 iL1 − VOUT1
)(
As mentioned earlier, operational mode of the converter is
determined by a mode detection algorithm and it is configured to
generate the n value which is used in Eqs. (12) and (13). Thus, the
changes in the operational mode are defined in the system model.
As seen from Eq. (14), the input voltages are determined from
the arrays according to the operational mode of the converter.
Consequently, the input currents can be calculated by using the
same equation even the input sources are changed.
For the SIMO operation, the first layer is in buck-boost mode
while the second one is in boost mode. Since the type of the
second layer is not changed, Eq. (6) given above can also be
used for the second layer in SIMO modes. It is worth noting that
the input source in Eq. (6) may change depending on the active
source in SIMO mode. The differential equations of the first layer
can be expressed with Eqs. (9) and (10). As clearly seen from
Eq. (9), the inductor is charging by the activated power source (V1
or V2 ) for ON position of the S1 . For OFF state of the switch, the
inductor current can be expressed with Eq. (10), where it is seen
that the output power is only supplied via the inductor. According
to the switch position, Eq. (11) can be derived by combining
Eqs. (9) and (10).
diL1
1
n = {1, 2, 3, 4 mode number used in Eqs. (12) and (13)}
(7)
VOUT1,2
(
=
where;
)
C1,2 R1,2
for OFF position
(14)
)
1
for mode4 (both input sources are disabled)
1 for ON position
Finally, Eq. (14) is obtained after the input voltage arrays in
Eqs. (12) and (13) are combined with the current equations in
Eqs. (6), (11).
for OFF position of the sw itch 1 or 2
(
(13)
where; S1 =
0
=−
for mode3 (represents the MIMO mode)
0
(5)
The differential equations of the output voltage can be described with Eqs. (7) and (8) for ON and OFF positions of the
switch, respectively.
dVOUT1,2
⎪
V2
⎪
⎪
⎪
⎩
for mode2 (represents the SIMOV 2 mode)
0
where;
{
for mode1 (represents the SIMOV 1 mode)
{
V1,2 − RL1,2 iL1,2 − VOUT1,2 1 − S1,2
L1,2
Vin2 =
⎧
V1
⎪
⎪
⎪
⎪
⎨ V2
Aavg = dA1 + (1 − d ) A2
(18)
where, d denotes the duty ratio of switching signal and A1 is the
state matrix for S = ON, while A2 represents the state for S = OFF.
Eqs. (19) and (20) describes both layers of the proposed model in
matrix form.
⎡ ( )
RL1
⎢− L1
⎢
⎢
⎢
0
⎢
A1 = ⎢
⎢
⎢
0
⎢
⎢
⎣
(12)
0
for mode4 (both input sources are disabled)
488
⎤
0
(
−
1
0
0
C1 R1
0
0
0
)
(
−
RL2
)
L2
0
−
⎥
⎥
⎥
⎥
0
⎥
⎥
⎥
⎥
0
⎥
(
)⎥
⎦
1
C2 R 2
(19)
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
Fig. 3. Magnitude and phase responses under a: steady-state, b: various input voltage, c: various duty ratio, d: various load conditions.
⎡ ( )
RL1
−
⎢
⎢ ( L1)
⎢
1
⎢
⎢ C
⎢
1
A2 = ⎢
⎢
⎢
0
⎢
⎢
⎣
( )
1
−
L
( 1 )
1
−
0
0
C1 R 1
(
0
0
0
0
RL2
)
−
L
( 2)
1
C2
⎤
⎥
⎥
⎥
⎥
0
⎥
⎥
( ) ⎥
⎥
1
⎥
−
⎥
L
( 2 )⎥
⎦
1
−
load resistance, and the results are presented in Fig. 3(b), (c), and
(d), respectively [31]. Clearly, the converter is stable despite all
variations.
The proposed mode-changeable converter is based on a twolayer DC/DC boost converter and each layer is a second-order
system. Although the layers are derived using the conventional
topologies, the mode-changeable structure of the proposed model
requires some specifications in terms of designing the controller.
The requirements in the control strategy can be described as
the fast dynamic response and a good match with the changes
in topology. In general, the fast dynamic response is needed to
achieve a good reference tracking under variations in system
inputs and outputs. In addition to this, the dynamic response is
important for mode transitions times in the proposed topology.
Furthermore, the type of the first layer is changing between
boost and buck-boost in the transition from MIMO to SIMO, viceversa. It is clear that the control method should exhibit a good
match with the changes in topology. A model-based reconfigurable controller type is essential and special for the proposed
mode-changeable converter. On the other hand, MPC exhibits an
excellent dynamic performance for power converters. Considering the requirements, model predictive control is used to control
the proposed converter.
The average input currents are controlled with the model
predictive control (MPC) technique, block diagram of which is
C2 R 2
B = [1/L1 0 1/L2 0]
(21)
C = [0 1 0 1]
(22)
T
3. Model predictive control of the proposed system
(20)
The averaged state–space model can be obtained by substituting
Eqs. (18), and (21) into Eq. (15). Since the design of the converter
plays a crucial role in the performance of closed-loop controller,
the open-loop bode diagram is presented to show the stability
of the converter. Fig. 3 shows the bode plots which are obtained
using the system parameters and state–space model for the first
layer. As mentioned before, the proposed model consists of a two
boost converter. Hence, the results of each layer are the same
and the dynamics are investigated for only the first layer. The
bode result of the steady-state condition is shown in Fig. 3(a).
The phase angle and magnitude are negative at the crossover
frequency. Clearly, the selected design parameters are suitable for
steady-state conditions. However, large variations in the system
input and outputs may cause instabilities. Therefore, the bode
analysis is evaluated by variations in input voltage, duty ratio, and
489
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
Table 2
Model parameters.
Switching frequency
Inductors (L1 and L2 )
Output filters (C1 and C2 )
IGBTs (S1 and S2 )
TS
5–10 kHz
1 mH
1000 µF
2MBI100U4A – 120 – 50
10 µs
The key point of the MPC algorithm is the cost function, which
is created by using the estimation results and the reference values
(i∗L and i∗L ). Eq. (25) presents the created cost function for each
1
2
layer of the converter.
[
gidc1,2 (k + 1) = i∗L1,2 − iL1,2 (k + 1)
]2
(25)
By utilizing the cost function, the algorithm decides the ON or
OFF positions of the IGBTs. Since this digital control method does
not use a comparator, the switching frequency is variable. In the
study, the frequency is reduced by benefiting the advantages of
MPC method, as it is able to control multiple system parameters
together. In order to reduce the switching frequency (fsw ), the
cost function given in Eq. (26) is derived [32], where λ indicates
the weighting factor that has been determined as 0.01 by using
the cost function classification technique. A detailed information
about the use of this technique can be found in [19].
gsw1,2 (k + 1) = λ ∗ ⏐S1,2 − S1,2 (k − 1)⏐
⏐
⏐
(26)
After defining an ideal weighting factor, it is used for reducing
the maximum switching frequency. Eq. (27) gives the complete
cost function obtained by combining the Eqs. (25) and (26).
g1,2 (k + 1) = gidc1,2 (k + 1) + gsw1,2 (k + 1)
Fig. 4 illustrates the flowchart of the MPC algorithm that starts
to operation by measuring the input parameters. In addition, n
parameter which is generated by the mode detection algorithm is
integrated with the MPC to define the operational mode changes
in the system model. For each sampling step, the prediction
algorithm is separately run for two different positions (ON and
OFF ) of the related switch. Thus, two cost functions are created
using the values obtained from the prediction result. Then, the
switch positions are determined by minimizing the cost function
value and appropriate control signals are generated for the next
sampling step.
Fig. 4. Flowchart of the control algorithm.
illustrated in Fig. 1. As seen, the MPC consists of two steps as
the predictive model and the cost function optimization. Current
values at the next sampling iteration are estimated by discretetime model. The cost function optimization minimizes the error
between the reference value and the estimated value. The control signals applied to the IGBTs are generated according to the
minimization result. Since the MPC method operates depending
on a specific time step (TS ), it is necessary to discrete the control equation given in Eq. (14) previously. For this purpose, the
forward-difference Euler method is used as given in Eq. (23),
and the expression obtained after the discretization is given in
Eq. (24) that determines the predicted current value and evaluated separately for each layer of the converter. During a sampling
step, discrete-time equations are calculated for all possible switch
positions.
diL1,2
dt
≈
iL1,2 (k + 1) − iL1,2 (k)
iL1,2 (k + 1) =
[(
Ts
)(
[
]
TS
Vin1,2 mode − RL1,2 iL1,2 (k)
n
L1,2
4. Simulation results
In order to test and verify both the proposed converter model
and its control algorithm, some simulation studies are performed
in MATLAB/Simulink. Table 2 presents the parameters used in the
simulation model. In addition to the current control capability
of the MPC algorithm, the transient states occurred in mode
transitions are tested especially. During the simulation studies,
the switching frequency is changed between 5 kHz and 10 kHz.
(23)
4.1. Simulation results for MIMO operation
When the converter operates in MIMO mode, its capability of tracking a fixed reference is tested under variable input
voltages. Each converter layer starts to operate when its input
voltage exceeds 10 V that is the predefined threshold value in
the control algorithm. Fig. 5 shows the results of the first case
where the reference current is set to 2 A. As seen, the input
voltage of the first layer is suddenly increased from 20 V to
35 V after 1 s from the start. In order to see the transient
response of the system against this situation, the precise time of
transition is zoomed and indicated as Z1. As obviously seen, the
]
(
))
−VOUT1,2 (k) 1 − S1,2
+ iL1,2 (k)
(27)
(24)
where;
iL1,2 (k+1) : predicted current values of iL1 or iL2
Ts : Sampling time
moden : Corresponding operational mode as given in Eqs. (12) and
(13).
490
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
control algorithm immediately makes the related switch OFF for
three periods to prevent the current increase when the voltage
increases. Furthermore, since the proposed system is able to
generate variable switching frequencies, the control algorithm
reduces the switching frequency.
As the second case, the input voltage is decreased from 35 V
to 25 V at 1.4 s. The second zoomed part indicated as Z2 on Fig. 5
presents the system response against this transitional situation.
Similar to the previous case, the system successfully tracks the
reference by adjusting the duty ratio of the switching signal to
an appropriate level for new conditions.
The analysis given Fig. 5 is not only achieved for the first
(positive) layer, but also for the second (negative) layer. For the
first case where the input voltage is suddenly increased from
15 V to 35 V, the control algorithm makes the related switch
OFF until the input current decreases to the desired level. This
situation can be seen obviously from the zoomed part indicated
as Z3 on Fig. 5 After the instant increase on the voltage signal,
the system automatically adjusts the PWM ratio to track the reference successfully. As seen from the last zoomed part indicated
as Z4, the system successfully continues to track the reference
by increasing the duty ratio of the switching signal even the
voltage decreases instantly. In addition to the control results of
input currents, output voltage of both layers are higher than input
voltages. Clearly, both layer operates in boost mode during the
MIMO mode.
As the second test for the MIMO mode, the system performance under variable references is examined. Fig. 6 presents
the simulation results for this case, where the reference currents
change instantly while both layers operate at a fixed input voltage. According to the scenario, the reference value of the positive
layer increases from 2 A to 4 A at 0.2 s. As shown from the
zoomed part indicated as Z1 on Fig. 6, the control algorithm
keeps the switch ON for 2 periods in order to increase the input
current to the reference. As a further scenario, the reference is
decreased to 3 A at 0.25 s. The zoomed part indicated as Z2 shows
that the input current is successfully adjusted to desired level
in this case too. Ability of the proposed converter for tracking
the variable current references is also examined for the second
(negative) layer. The zoomed parts indicated as Z3 and Z4 on
Fig. 6 present the results for these analyzes in detail and confirm
that the proposed control algorithm successfully executes the
current control process. As a common result for this section,
all simulation results performed to analyze the current control
operation in MIMO mode verify that the proposed algorithm
serves a fast and effective control for not only in the steady state
conditions but also in the transitional events.
For both SIMO modes, reference value of the layers are changed
several times to analyze the system response against these transient situations. As obviously seen from results in Fig. 7, the
proposed control algorithm successfully achieves to track the
reference in all cases in similar to MIMO mode operations. Although the input voltages are altered, the average value of the
current is not affected from this situation. As mentioned in the
theoretical analysis, the first layer is in buck-boost mode while
the second one is in boost mode for SIMO modes. It is worth
noting that, the output voltage of the first layer is dependent on
the reference current, load resistance and input voltage. As clearly
seen from Fig. 7, the operational mode of the first layer is changed
depending on the reference current and it can be operated in
buck and boost modes. Furthermore, the results show that the
second layer is operated in boost mode in both SIMO modes.
Consequently, the theoretical considerations have been verified
by simulation studies for all operational modes of the proposed
converter.
5. Experimental study
A real prototype of the proposed system, shown in Fig. 8, is
designed and implemented to test the converter experimentally
in real time conditions. As stated in Table 2, the proposed converter is built by using 2MBI100U4A-120-50 IGBTs. The relays
are used to route the power depending on the operation mode
of the converter. LV 25-P voltage sensors are used as transducers
for measuring the input and output voltages. Input and output
currents are sensed using HAS 50-s. The control software is designed using MATLAB/Simulink environments and it is embedded
in dSPACE ds1104. Two separate DC voltage sources are used as
the main energy sources. To better analyze the proposed modechangeable converter and its control algorithm, experimental
results are presented for MIMO and SIMO modes, separately.
5.1. Experimental results for MIMO operation
To test the converter in MIMO mode, its response to instant
reference changes under fixed input voltages is examined. Fig. 9
shows the dynamic responses of input currents and switching
signals for abrupt changes in the references of inductor currents.
As seen from Fig. 9(a), when the reference for the first layer
changes from 2 A to 4 A, the control algorithm increases the
current by keeping the related switch in ON position for two
periods (230 µs). After this transient situation, the converter
continues to its operation with an average current of 4 A. If the
reference decreases from 4 A to 2 A, the MPC algorithm keeps
the switch in OFF position until (200 µs) the current decreases
to 2 A as seen from Fig. 9(b). The same procedure is also realized
for the second layer. Fig. 9(c) verifies that the proposed model
successfully provides the average current tracking process when
the reference current for the second layer increases from 1.5 A
to 3 A. Even though the reference decreases to 1.5 A again, the
system continues to track it successfully as seen from Fig. 9(d).
Considering the results in Fig. 9, if the reference increases, the
switch remains at ON position until the inductor current reaches
to the peak value of the desired level. Similarly, if the reference
decreases, the switch passes to OFF position until the inductor
current reaches to the new peak value. Clearly, the dynamic
responses in the switching signal shows that MPC selects an
optimal control action independent from switching frequency. As
mentioned earlier, the switching signal is generating as the result
of a logic comparison in digital control methods. This is the fact
that behind the superior dynamic behavior of MPC. Furthermore,
the MPC algorithm eliminates the oscillations occurred in the
transient state and shortens the response time as well. On the
4.2. Simulation results for SIMO operation
SIMO operation means that one of the input sources is deactivated due to operational conditions and thereby the system
works with only one input while there are multi outputs at
the load side. Accordingly, while SIMOV1 expresses the situation
where the second input is turned off and only the first one feeds
the system, SIMOV2 describes the opposite of this condition. A
critical threshold voltage level as 10 V is determined in the study.
Thus, if the voltage level of one of the input sources decreases
below this level, the system automatically disables the related
input. Fig. 7 presents the simulation results under the variable
reference values when the system operates in SIMO mode. As
seen, the system starts to operation in SIMOV1 mode as soon as
the first input voltage exceeds 10 V. According to the scenario, the
first layer is suddenly disabled and the second one is activated
simultaneously at 0.5th second. Upon this new condition, the
system automatically switches its mode to SIMOV2 .
491
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
Fig. 5. Results of tracking a fixed reference under variable input voltages in MIMO mode.
Fig. 6. Step change analysis of the currents in MIMO mode.
other hand, the results show that the input current of each layer
is independent of each other. This feature allows the independent
power flow from the input sources. Also, it can be worth noting
that the cross-regulation problem has not occurred.
Depending on the input voltage and the reference signal, the
switching frequency is changed between 5 kHz to 10 kHz during
the experimental tests. This is the reason why the oscillation level
on the inductor current changes as seen in the current graphs.
As reported in [20], even though this issue can be alleviated
by increasing the switching frequency, this is not the case for
high power applications where a low switching frequency is
required. For this reason, controller design for high-power DC–DC
converters working at relatively low frequency (<20 kHz) has an
increasing practical value.
In addition to test the system response against the reference
changes, the fixed current control analysis under variable input
voltages is also tested experimentally and the maximum error
for the average current is measured as 4%. For instance, Fig. 10(a)
492
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
Fig. 7. Simulation results under the variable reference currents in SIMO mode.
Fig. 8. The real prototype of the model for experimental study.
the inductor current in the desired reference against the changes
in the input voltage.
Consequently, all the experimental results described above
separately for each layer verify that the proposed control algorithm successfully achieves the current control process in MIMO
mode even the input voltages are changed.
presents a sample experimental result where the input voltage of
the first layer decreases from 25 V to 15 V. As seen, the average
input current is fixed to the reference value with an error of 2.5%
while the input voltage is 25 V. After the voltage decreases to
15 V, the control algorithm again sets the input current to the
reference with an error of 0.5%.
In similar to the first layer, the second one serves satisfactory
results for the average current control process. Fig. 10(b) presents
an experimental result where the input voltage of the second
layer (VIN2 ) increases from 20 V to 30 V. Once the voltage increase
is occurred, the control method fixes the average current value
to the reference value with an error of 1%. Actually, these error
rates given for both layers mainly cause from the measurement
accuracy of the sensors and ADC resolution of the controller. The
dynamic responses of input and output variables show that the
proposed converter and its control method are able to maintain
5.2. Experimental results for mode transitions and SIMO operation
As mentioned in the theoretical considerations, the mode transition capability is the main advantage of the proposed converter. Experimental results of mode transitions and SIMO operational modes are investigated in this section. As clearly seen from
Fig. 11, the second input source (V2 ) is suddenly disconnected
while the system is being operated in MIMO mode. In this case,
the control algorithm changes the positions of the auxiliary relays
493
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
Fig. 9. Experimental results for tracking the variable references in MIMO mode (a, b) the first layer (c, d) the second layer.
Fig. 10. Current control analysis in MIMO mode (a) the first layer (b) the second layer.
according to Table 1 thereby the system passes to SIMOV 1 mode.
During the transition, the first layer remains at disabled for 5
ms while the relay switches are being repositioned. However, the
duration of this temporary time depends on the processing speed
of the controller and the specifications of hardware devices used
in the system such as relays.
As seen from the detailed current graphs shown in Fig. 11,
while the average current is not changed after the mode transition from MIMO to SIMO, the oscillation on the current signal
increases. This is due to the positive layer operating in the buckboost mode. On the other hand, even if the input source of the
second layer is disabled, its inductor current is maintained at 2
A. The result verifies that the proposed converter and its control
algorithm successfully route the power flow.
As a different experimental scenario, the second input source
is again enabled while the system operates in SIMOV1 mode. In
this case, the system returns back to MIMO mode as seen from
Fig. 11. It is experimentally observed that the average current
494
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
Fig. 11. Experimental results of the mode transitions.
Fig. 12. System responses in SIMO mode a: Reference change in SIMOV 1 mode (IL1 ), b: Voltage change in SIMOV 2 mode (VIN2 ).
values have not changed in this operational condition too. In
order to test the system in SIMOV2 mode, the first input source
(VIN1 ) is disabled. After that, it has been took 32ms for cutting
off the energy of positive layer and changing the converter’s
mode from boost to buck-boost. After the mode change process,
the positive layer operates as buck-boost while the negative one
operates in boost mode. In this case, the MPC algorithm fixes the
average current of both layers to 2 A as seen from the detailed
current graphs in Fig. 11. Similar to the results of the mode
transition from MIMO to SIMOV1 , the results verify that the power
flow is continuing in both layers.
After analyzing the system response in SIMOV1 and SIMOV2
modes, the first input source is re-activated to switch the converter to MIMO mode as seen from the last part of Fig. 11. Similar
to all other cases, the control algorithm successfully continues
to achieve the average current tracking process. Thus, all the
experimental tests conducted for analyzing the system response
during the input source transitions verify that the proposed converter automatically determines its operational mode according
to the input conditions. Moreover, the developed MPC algorithm
successfully provides the current controlling process under all
operational situations.
Another experimental test is conducted by changing the reference value of the input current in SIMOV1 mode. Fig. 12(a)
Fig. 13. The efficiency analysis for both MIMO and SIMO modes.
shows the dynamic responses of input variables for a step change
in the reference current from 1 A to 2 A. As clearly seen, the
control algorithm keeps the related switch in ON state until the
current of positive layer increases to 2 A, and then continues to
operate with the new reference. Fig. 12(b) illustrates a sample
system response against the input voltage changes in SIMOV2
mode. While the VIN2 input voltage is 15 V in this experimental
scenario, the average currents of the first and the second layers
are 1 A and 2 A, respectively. As seen from the figure, these
495
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
is to control the inductor current, the robustness of the control
method is investigated under variations in inductance. The proposed topology consists of two boost converters with the same
component parameters. Since the type and parameters of both
layers are the same as each other, the influence of parameter
variations is analyzed with the first layer by changing L1 . The
inductance value in the control software (L1,control ) is changed
in the range ±50%. The variation in the inductance value is
calculated by Eq. (31). The current error between the reference
and measured current is calculated with Eq. (32).
∆L1 (%) =
∆iL1 (%) =
average current values are not changed even the input voltage
increases to 25 V. However, the ripple on the current signals
increases when the input voltage is increased due to the change
of the switching frequency and input voltage. When the input
voltage reduced from 25 V to 15 V, the ripples on input currents
return back to the initial condition.
ηSIMO (%) =
POUT
× 100 =
(VOUT 1 iOUT 1 ) + (VOUT 2 iOUT 2 )
× 100
V1 iL1av g + V2 iL2av g
(28)
Pin
× 100 =
(VOUT 1 iOUT 1 ) + (VOUT 2 iOUT 2 )
V1,2 iinav g
× 100
(29)
∫
iinav g = d1
t +T1
iL1 (t ) dt + iL2av g
iL1av g
× 100
(31)
(32)
The comparison of the proposed mode-changeable topology
with four existing multi-port DC/DC topologies is presented in
Table 3. The comparison includes topology, control method, number of switching devices, drivers, switching signal generation
method, switching frequency, efficiency, maximum power and
mode-changeability feature between SIMO and MIMO operational
modes. Among the existing topologies, the proposed topology exists the mode-changeability feature which is able to automatically
change the operational modes between SIMO and MIMO. Furthermore, the maximum efficiency in the SIMO mode can be specified
as a remarkable advantage of the proposed topology. Since the
proposed topology is built by two separate inductors, the crosscoupling effect has not occurred. Hence, the efficiency of the
proposed topology higher than the single-inductor SIMO converter in [12]. The auxiliary switch requirement can be pointed as
a disadvantage of the proposed topology. However, the switches
are only contacts of relays and it does not require special driving
devices. Therefore, the usage of such switches is a cheap and
practical solution for routing the power. On the other hand, while
the proposed topology and SIMO-buck [1] can be implemented
with two switching devices, the other topologies are needed more
switches such as IGBT and MOSFET.
In order to analyze the system efficiency, Eqs. (28) and (29)
are derived for MIMO and SIMO modes, respectively. The average
current values of the inductors are used for calculating the input
power. Unlike MIMO operation, cross-coupling effects disturb the
total input current in SIMO operation because the first layer
operates in buck-boost mode. Therefore, the average value of the
total input current can be calculated by using Eq. (30), where T1
indicates the period time of the first switching signal (d1 ).
Pin
1
× 100
5.5. Comparison with existing control methods
5.3. Efficiency
POUT
i∗L
L1
− iL1avg
Since the cost function has two objectives as control of inductor current and reducing the switching frequency, the influence of
the variations is investigated on the current and average switching frequency as given in Fig. 14. Clearly, the average current error
increases depending on the parameter variation. It is evident
from the figure, the maximum average control error is 2.13%
despite −50% variation in the inductance. On the other hand, the
influence of the variations is also seen in the average switching
frequency.
Fig. 14. Current error and average switching frequency results under parameter
variations in L1 .
ηMIMO (%) =
L1,control − L1
(30)
t
After analyzing the efficiency, a graph is created according to
the output power as presented in Fig. 13. While the output power
increases, the efficiency decreases in both operational modes.
In MIMO mode, the maximum efficiency is about 97% and the
minimum efficiency is about 85%. These values for SIMO mode
are 87% and 83%, respectively. Efficiency of the similar systems in
recent literature is between 80% and 98% depending on the rated
power [1,33]. Considering them, the proposed converter offers
the similar efficiency.
6. Conclusion
In this article, a mode-changeable DC/DC converter with the
capability of automatically set its operational mode to either
MIMO or SIMO is proposed for hybrid operated energy sources.
In case of any interruption in one of the input sources, the modechangeable structure maintains the power flow from the other
source. Auxiliary relays are used in the circuit to route power
from multiple sources to multiple loads, and their positions are
determined by a mode detection algorithm. MPC algorithm is
used to control the currents of the input sources and it is modified to adapt the algorithm with the changes in topology. The
theoretical considerations are verified by both simulation and
experimental studies. The main purpose of this study is to design
a mode-changeable converter to be used in intermittent energy
sources. The results reveal that the proposed converter is able
5.4. Influence of parameter mismatch
The MPC method is a model-based control strategy and it
predicts the next value of the control variable depending on
the system parameters. Therefore, the accuracy of the controller
highly depends on system parameters which are defined in the
control software. The parameters of the system components such
as inductance and capacitance may vary depending on their tolerances and ages. Since the objective of the MPC in this paper
496
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
Table 3
Comparison of four existing multi-port DC/DC topologies with proposed mode-changeable topology.
Description
[1]
[6]
[10]
[12]
Proposed
Topology
mode-changeability
Control approach
Number of switching device
Number of auxiliary relay
Number of driver circuit
Switching signal generation
method
Switching frequency
Maximum power
Maximum efficiency
SIMO-buck
Does not exist
Robust decentralized
2
Does not exist
2
PWM
MIMO-buck-boost
Does not exist
PI
4
Does not exist
4
PWM
SIMO-buck
Does not exist
MPC
3
Does not exist
3
Digital
Multi-mode (SIMO and MIMO)
Exists
MPC
2
4
2
Digital
1 kHz
Not reported
Not reported
20 kHz
240W
Not reported
MIMO
Does not exist
MPPT based PWM controller
5
Does not exist
5
Requires a special PWM
generation strategy
Not reported
2.5 mW
87.6%
Not reported
100 W
83.1%
5 kHz–10 kHz
195 W
97% (MIMO)
87% (SIMO)
to set operational mode according to the voltage level of input
sources. Moreover, the modified MPC exhibits excellent performance under all operating conditions. It reveals that the modified
MPC is adapt itself to changes in the operational modes. On the
other hand, the results showed that the MPC offers very good
current tracking performance for both steady-state and reference
variation conditions.
Besides its advantageous features, the proposed system has
some disadvantages too. Since the variable switching frequency
directly affects the size of passive components in DC/DC converters, it can be stated as a disadvantage for the MPC. On the
other hand, a voltage control method can be applied to the
proposed mode-changeable converter. Considering both lacks in
the controller, developing a controller with the capability of fixed
switching frequency and voltage based control are the subjects of
future works.
[9] Wang B, Xian L, Kanamarlapudi VRK, et al. A digital method
of power-sharing and cross-regulation suppression for single-inductor
multiple-input multiple-output DC–DC converter. IEEE Trans Ind Electron
2017;64(4):2836–47.
[10] Shao H, Li X, Tsui CY, et al. A novel single-inductor dual-input dual-output
DC–DC converter with PWM control for solar energy harvesting system.
IEEE Trans VLSI Syst 2014;22(8):1693–704.
[11] Behjati H, Davoudi A. Single-stage multi-port DC-DC converter topology.
IET Power Electron 2013;6(2):392–403.
[12] Wang B, Kanamarlapudi VRK, Xian L, et al. Model predictive voltage control
for single-inductor multiple-output dc–dc converter with reduced cross
regulation. IEEE Trans Ind Electron 2016;63(7):4187–97.
[13] Huang W, Qahouq JAA, Dang Z. CCM–DCM power-multiplexed control
scheme for single-inductor multiple-output dc–dc power converter with
no cross regulation. IEEE Trans Ind Appl 2017;53(2):1219–31.
[14] Wang B, Xian L, Ukil A, et al. Charge Equalization for Series-Connected
Battery Cells using SIMO DC-DC Converter. Chicago, USA: IEEE Power &
Energy Society General Meet; 2017, p. 1–5.
[15] Zhang Q, Zhuang X, Liu Y, Wang C, Guo H. A novel control strategy for
mode seamless switching of PV converter in DC microgrid based on double
integral sliding mode control. ISA Trans 2019.
[16] Ramya G, Ganapathy V, Suresh P. Comprehensive analysis of interleaved
boost converter with simplified H-bridge multilevel inverter based static
synchronous compensator system. Electr Power Syst Res 2019;176:105936.
[17] Naik BB, Mehta AJ. Sliding mode controller with modified sliding function
for DC-DC Buck converter. ISA Trans 2017;70:279–87.
[18] Genc N, Uzmus H, Iskender I. Dynamic behavior of dc-dc boost converter
controlled with cascade PI-ASC. In: 2016 8th international conference on
electronics, computers and artificial intelligence (ECAI), Ploiesti, 2016. p.
1-4.
[19] Rodriguez J, Cortes P. Predictive Control of Power Converters and Electrical
Drives. Wiley; 2012.
[20] Po L, Ruiyu L, Tianying S, et al. Composite adaptive model predictive control for DC–DC boost converters. IET Power Electron
2018;11(10):1706–17.
[21] Khan O, Mustafa G, Khan AQ, Abid M. Robust observer-based model
predictive control of non-uniformly sampled systems. ISA Trans 2019.
[22] Altan A, Hacioglu R. Model predictive control of three-axis gimbal system
mounted on UAV for real-time target tracking under external disturbances.
Mech Syst Signal Process 2020;138:1–23.
[23] Cheng L, Acuna P, Aguilera RP, et al. Model predictive control for DC-DC
boost converters with reduced-prediction horizon and constant switching
frequency. IEEE Trans Power Electron 2018;33(10):9064–75.
[24] Karamanakos P, Geyer T, Manias S. Direct model predictive current control
strategy of DC–DC boost converters. IEEE J Emerg Sel Top Power Electron
2013;1(4):337–46.
[25] Gunasekaran D, Umanand L. Integrated magnetics based multi-port bidirectional DC-DC converter topology for discontinuous-mode operation. IET
Power Electron 2012;5(7):935–44.
[26] Kondrath N, Kazimierczuk MK. Unified model to derive control-to-output
transfer function of peak current-mode-controlled pulse-width modulated
dc-dc converters in continuous conduction mode. IET Power Electron
2012;5(9):1706–13.
[27] Zhou G, Mao G, Zhao H, Zhang W, Xu S. Digital average voltage/digital
average current predictive control for switching DC–DC converters. IEEE J
Emerg Sel Top Power Electron 2018;6(4):1819–30.
[28] Karamanakos P, Geyer T, Manias S. Direct voltage control of DC–DC boost
converters using enumeration-based model predictive control. IEEE Trans
Power Electron 2014;29(2):968–78.
[29] Cheng L, Acuna P, Aguilera RP, Jiang J, Wei S, Fletcher JE, Lu DDC. Model
predictive control for DC–DC boost converters with reduced-prediction
horizon and constant switching frequency. IEEE Trans Power Electron
2018;33(10):9064–75.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared
to influence the work reported in this paper.
Acknowledgments
This work is supported by the Gazi University, Turkey Scientific Research Projects Unit (Project Numbers: 07/2016-19 and
07/2017-08).
References
[1] Medeiros RLP, Barra W, Bessa IV, Filho JEC, Ayres FAC, Neves CC. Robust
decentralized controller for minimizing coupling effect in single inductor
multiple output DC-DC converter operating in continuous conduction
mode. ISA Trans 2018;73:112–29.
[2] Jafari M, Malekjamshidi Z, Zhu J. A magnetically coupled multi-port, multioperation-mode micro-grid with a predictive dynamic programming-based
energy management for residential applications. Int J Electr Power Energy
Syst 2019;104:784–96.
[3] Irmak E, Güler N. Application of a boost based multi-input single-output
DC/DC converter. In: IEEE int. conf. on renewable energy research and appl.
(ICRERA), San Diego, CA: 2017. p. 955-961.
[4] Pires VF, Foito D, Silva JF. A single switch hybrid DC/DC converter with
extended static gain for photovoltaic applications. Electr Power Syst Res
2017;146:228–35.
[5] Nilangekar AA, Kale RG. Design and development of electric vehicle battery
charging using MIMO boost converter. In: Int. conf. on green eng. and tech.
coimbatore, India: 2016. p. 1-6.
[6] Filsoof K, Lehn PW. A bidirectional multiple-input multiple-output modular
multilevel DC–DC converter and its control design. IEEE Trans Power
Electron 2016;31(4):2767–79.
[7] Babaei E, Abbasi O. Structure for multi-input multi-output dc–dc boost
converter. IET Power Electron. 2016;9(1):9–19.
[8] Nahavandi A, Hagh MT, Sharifian MBB, et al. A nonisolated multiinput
multioutput DC–DC boost converter for electric vehicle applications. IEEE
Trans Power Electron 2015;30(4):1818–35.
497
N. Güler and E. Irmak
ISA Transactions 114 (2021) 485–498
[32] Irmak E, Güler N. A model predictive control-based hybrid MPPT method
for boost converters. Int J Electron 2020;107(1):1–16.
[33] Reddi NK, Ramteke MR, Suryawanshi HM, et al. An isolated multi-input ZCS
DC–DC front-end-converter based multilevel inverter for the integration of
renewable energy sources. IEEE Trans Ind Appl 2018;54(1):494–504.
[30] Nozadian MHB, Babaei E, Ranjbarizad V, et al. Analysis and design of
switched-boost inverter in CCM, DCM and BCM operations. In: 43rd annual
conference of the IEEE industrial electronics society (IECON), Beijing, 2017.
p. 8015-8020.
[31] Guler N. Design and Implementation of a Novel DC/DC Converter
using Model Predictive Control Method for Distributed Generation
Sources (Doctoral dissertation), Gazi University; 2019.
498