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Model Predictive Control of Bidirectional Isolated DC-DC Converter for Energy Conversion SystemParvez Aktera, Nadia Mei Lin Tanb, Saad Mekhilefc & Hirofumi Akagida Power Electronics and Renewable Energy Research Laboratory (PEARL), Department ofElectrical Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysiab Member, IEEE, Department of Electrical Power Engineering, Universiti Tenaga Nasional,Kajang 43000, Malaysiac Senior Member, IEEE, Power Electronics and Renewable Energy Research Laboratory(PEARL), Department of Electrical Engineering, University of Malaya, 50603 KualaLumpur, Malaysiad Fellow, IEEE, Department of Electrical and Electronic Engineering, Tokyo Institute ofTechnology, Tokyo 152-8552, JapanAccepted author version posted online: 12 Mar 2015.
To cite this article: Parvez Akter, Nadia Mei Lin Tan, Saad Mekhilef & Hirofumi Akagi (2015): Model Predictive Controlof Bidirectional Isolated DC-DC Converter for Energy Conversion System, International Journal of Electronics, DOI:10.1080/00207217.2015.1028479
To link to this article: http://dx.doi.org/10.1080/00207217.2015.1028479
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Publisher: Taylor & Francis
Journal: International Journal of Electronics
DOI: 10.1080/00207217.2015.1028479
Model Predictive Control of Bidirectional Isolated DC-DC Converter
for Energy Conversion System
Corresponding author:
Parvez Akter
Power Electronics and Renewable Energy Research Laboratory (PEARL), Department
of Electrical Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia
E-mail: [email protected]
Contact No: +60169067036
Co-authors:
Nadia Mei Lin Tan
Member, IEEE, Department of Electrical Power Engineering, Universiti Tenaga
Nasional, Kajang 43000, Malaysia
Saad Mekhilef
Senior Member, IEEE, Power Electronics and Renewable Energy Research Laboratory
(PEARL), Department of Electrical Engineering, University of Malaya, 50603 Kuala
Lumpur, Malaysia
Hirofumi Akagi
Fellow, IEEE, Department of Electrical and Electronic Engineering, Tokyo Institute of
Technology, Tokyo 152-8552, Japan
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Model Predictive Control of Bidirectional Isolated DC-DC Converter
for Energy Conversion System
Model Predictive control (MPC) is a powerful and emerging control algorithm in
the field of power converters and energy conversion systems. This paper
proposes a model predictive algorithm to control the power flow between the
high voltage and low voltage DC buses of a bidirectional isolated full-bridge DC-
DC converter. The predictive control algorithm utilizes the discrete nature of the
power converters and predicts the future nature of the system, which are
compared with the references to calculate the cost function. The switching state
that minimizes the cost function is selected for firing the converter in the next
sampling time period. The proposed MPC controlled bidirectional DC-DC
converter is simulated with Matlab/Simulink and further verified with a 2.5 kW
experimental configuration. Both the simulation and experimental results confirm
that the proposed MPC algorithm of the DC-DC converter reduces reactive
power by avoiding the phase-shift between primary and secondary sides of the
high frequency transformer and allow power transfer with unity-power-factor.
Finally, an efficiency comparison is performed between the MPC and dual-
phase-shift based PWM controlled DC-DC converter which ensures the
effectiveness of the MPC controller.
Keywords: Predictive control; bidirectional DC-DC converter; unity power
factor; reactive power; power conversion system.
1. Introduction
An efficient bidirectional DC-DC converter is indispensable to manage the power flow
by switching action to provide high performance and efficiency of an energy conversion
system. Hence, the control algorithm of this DC-DC converter needs to be immensely
effective, as it consist of two conversion stages (single phase inverter and rectifier)
along with an isolated high frequency transformer (Zhao, Song, Liu, & Sun, 2014).
Several improved control techniques, such as fuzzy-neural control (Cheng, Hsu, Lin,
Lee, & Li, 2007), hysteresis control (Leung & Chung, 2005), sliding-mode control
(Cheng et al., 2007; Tsai & Chen, 2007), have been investigated in power electronic
systems to control power converters. The practical applications of these control methods
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are confined to simple configured boost, buck, half-bridge, and full-bridge
unidirectional converters topologies till today. Nevertheless, these controls are aimed to
control more complex-configured converters topologies (Bai & Mi, 2008a; Rivetta,
Emadi, Williamson, Jayabalan, & Fahimi, 2006).
The bidirectional isolated DC-DC converter has many advantages over
traditional converters, such as bidirectional energy flow, soft switching, galvanic
isolation, high power density and low system parasitic sensitivity as has been
investigated in (Bai & Mi, 2008b), (N. M. Tan, T. Abe, & H. Akagi, 2012) and
(Naayagi, Forsyth, & Shuttleworth, 2012). A traditional PI-based phase-shift control has
been used previously to control the bidirectional isolated DC-DC converter in
(DeDoncker, Kheraluwala, & Divan, 1991). This method of control has a simple
structure and is very easy to implement. Moreover, a phase-shift modulation control has
been applied for high power transfer in (Kheraluwala, Gascoigne, Divan, & Baumann,
1992) and (Tan, Inoue, Kobayashi, & Akagi, 2008). The major drawbacks of this phase-
shift modulation control are reactive power losses and existence of dead-time effect.
Subsequently, various control algorithms have been introduced to improve the
performance of the system. In order to achieve a higher converter efficiency and expand
the zero-voltage switching region, a phase-shift plus pulse-width modulation (PWM)
algorithm has been applied in (Xu, Zhao, & Fan, 2004) and the effectiveness is verified
for soft-switching in (Lee, Ko, & Chi, 2010) and (Xiao & Xie, 2008). On the other
hand, in literature a dual-phase-shift (DPS) control method is proposed to eliminate the
reactive power in isolated bidirectional full-bridge DC-DC converter (Bai & Mi,
2008b), which is being extended as a model-based phase-shift control and applied in
(Bai, Nie, & Mi, 2010) to improve dynamic performance of the converter. Furthermore,
two PI controller based adaptive control algorithm is presented in (De Breucker,
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Engelen, Tant, & Driesen, 2010) to operate and verify the changes of current in small
and large extent, separately. There is a trade-off between transient response and
robustness in parameter selection of a PI controller, which is very empirical. Therefore,
computer aided optimization of DC-DC converter have been carried out by using two
PWM controller integrated circuits (ICs) in (Neugebauer & Perreault, 2003) and
(Garcia, Zumel, de Castro, & Cobos, 2006).
The principle feature of MPC scheme is to predict the future behavior of control
variables. This control algorithm has become the most attractive mode of technique to
control the bidirectional DC-DC converter comparing with all the classical control
techniques discussed above due to its simple and intuitive concept with fast dynamic
responses (Cortes, Kazmierkowski, Kennel, Quevedo, & Rodríguez, 2008; Rodriguez et
al., 2013). Moreover model predictive control algorithm is easy to configure with
constraints and non-linearity and also very easy for practical implementation. The fast
and powerful microprocessors are available today to implement the predictive control
algorithm very easily as it requires higher number of calculations compared with all the
classical controls stated in (Cortes et al., 2008; Muslem Uddin, Mekhilef, Rivera, &
Rodriguez, 2013). So, the application of model predictive control algorithm in power
converter is increasing day by day. Till to date, this algorithm is proposed for a DC-DC
buck converter (Bibian & Jin, 2002), (Geyer, Papafotiou, & Morari, 2008), boost
converter (Bibian & Jin, 2001) and buck-boost converter (Chen, Prodic, Erickson, &
Maksimovic, 2003). The authors of (Xie, Ghaemi, Sun, & Freudenberg, 2012) proposed
model predictive control for full bridge DC-DC converter. However, this model is
limited only for unidirectional power flow. Although model predictive algorithm is an
efficient and attractive alternative for controlling the power converters, it has not been
used to control power flow of a bidirectional isolated DC-DC converter yet.
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200 V50 Hz
PWM Converter
4 kHzTransformer
6 : 1
Cdc1V1 V2
Vdc1
Idc1
Bidirectional Isolated DC-DC Converter
Bridge 1 Bridge 2
i1 i2
idc2
Cdc2 Vdc2
S1 S3
S2 S4
S5 S7
S6 S8
a
b
c
d
Lah Lal
High Voltage DC Bus Low Voltage DC Bus
Power Flow
Figure 1. Energy conversion system based on the bidirectional isolated DC-DC
converter (N. M. L. Tan, T. Abe, & H. Akagi, 2012).
This paper proposes a MPC algorithm and its application for a bidirectional
isolated full-bridge DC-DC converter and is organized in the following manner. The
system configuration and working principle of energy conversion system topology are
elaborately described in section 2. The formulation of MPC method with discrete time
model, the cost function used for selection of switching state and a detailed explanation
of control scheme and algorithm are mentioned in section 3. The efficiency and
performance of the proposed MPC controlled bidirectional isolated DC-DC converter is
tested with Matlab/Simulink and the simulation results are analyzed in section 4.
Therefore, the DC-DC converter is further verified with a 2.50 kW experimental set-up,
which is depicted in section 5. Finally the conclusions are drawn in section 6.
2. Description of energy conversion system topology
2.1. System configuration
Figure 1 shows the energy conversion system topology, which bi-directionally converts
the AC power from three-phase AC-grid to low voltage DC bus and is configured with a
three phase bidirectional PWM controlled AC-DC converter and a bidirectional full-
bridge isolated DC-DC converter. The energy conversion system in Figure 1 is similar
to that in (N. M. Tan et al., 2012) because this paper intends to improve the efficiency
and performance of the bidirectional isolated DC-DC converter using MPC algorithm.
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AC-DC
IDC2
Vdc2DC-ACVdc1 Cdc2Cdc1V2V1
i1 i2
LeqReq
IDC1
Bridge 1 Bridge 2
Power flow
Figure 2. Simplified bidirectional isolated high frequency transformer linked DC-DC converter scheme.
The bidirectional DC-DC converter consist of two symmetrical structured
converters denoted as bridge 1 and bridge 2, which are isolated with a high frequency
(4-kHz) transformer. Bridge 1 consists of four IGBT-Diode switches (S1-S4). Each leg
of the converter contains two IGBTs in series. A snubber capacitor is connected with
each of the IGBTs for minimizing the turn-off overvoltage and also achieves zero-
voltage switching. Again, bridge 2 is configured with four MOSFET switches (S5-S8),
as it is operated in low voltage (60 V) condition. To minimize the switching loss, small
snubber capacitor is connected with each MOSFET switches.
2.2 Working principle
Model predictive control (MPC) algorithm is applied to control the power flow of
bidirectional isolated DC-DC converter. The working principle of MPC method is based
on a finite number of possible switching states, which utilizes the discrete behaviour of
a static power converter. In the case of bidirectional isolated DC-DC converter, MPC
algorithm utilizes the discrete nature of equivalent inductances (Leq) to control the
power flow by appropriate switching action. The equivalent inductance (Leq) is defined
with the simplified diagram of bidirectional DC-DC converter presented in Figure 2, as
the equivalent inductance value of the transformer high side auxiliary inductance (Lah),
low side auxiliary inductance (Lal) and leakage inductance (Lleak). For the selection of
the appropriate switching state to be applied to the converter, a selection criterion must
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be defined with a cost function which measures the error between references and
predicted values. Finally, the state that minimizes the cost function is selected for the
next sampling interval.
The gating signals Sa, Sb, Sc and Sd determine the switching states of the
Bidirectional DC-DC converter as follows:
=on is and off is ,0off is andon is ,1
21
21
SSSS
Sa (1)
=on is and off is ,0off is andon is ,1
43
43
SSSS
Sb (2)
=on is and off is ,0off is andon is ,1
65
65
SSSS
Sc (3)
=on is and off is ,0off is andon is ,1
87
87
SSSS
Sd (4)
Hence, the switching function (S) for the bridges 1 and 2 of the DC-DC converter can
be expressed as:
babridge SSS −=1 (5)
and
dcbridge SSS −=2 (6)
The bidirectional DC-DC converter operates in two modes. First one is buck
mode, which allows power transfer from high voltage DC bus to low voltage DC bus.
During this buck mode of operation, bridge 1 of the bidirectional isolated DC-DC
converter (Figure 3) is working as a DC-AC inverter, supplying power to high-
frequency transformer while bridge 2 working as AC-DC rectifier. On the other hand, in
case of boost mode, power flows in opposite direction and bridge 2 of the DC-DC
converter (Figure 4) acts as DC-AC inverter and bridge 1 as AC-DC rectifier.
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4 kHzTransformer
6 : 1
V1 V2Vdc1
Idc1 Buck Mode of DC-DC Converter
Bridge 1 Bridge 2
i1 i2
Idc2
Cdc1
Vdc2
S1 S3
S2 S4
S5 S7
S6 S8
Cdc2
iC2
a
b
c
d
Power flow
Lah Lal
Figure 3. Buck mode operation of DC-DC converter.
2.1.1. Buck Mode Operation
Buck mode operation of DC-DC converter with MPC method is illustrated in Figure 3,
where bridge 1 of the DC-DC converter acts as an inverter and the equivalent
inductance Leq, resistance Req and rest of the part of the circuit act as an equivalent load
for the inverter. By applying Kirchhoff’s voltage law at the AC side of inverter (bridge
1), the model current equation of the inverter becomes,
2111 nVVS
dtdiL dcbridgeeq −= (7)
Where, Leq is the sum of transformer leakage inductance (Lleak), Lah and n2Lal
mentioned in Fig. 3. Vdc1 is the DC voltage at high voltage DC bus acting as supply
voltage for bridge 1.
On the other hand, bridge 2 of the converter is working as a single phase voltage
mode controlled rectifier. The transformer secondary winding voltage (V2) and current
(i2) act as a source voltage and current for this rectifier. Therefore, the model voltage
equation of the rectifier can be obtained by using the Kirchhoff’s current law at the low
voltage DC bus side,
2222
2 dcbridgedc
dc ISidt
dVC −= (8)
Where, Cdc2 is the capacitance connected in parallel with low voltage DC bus; Vdc2 and
Idc2 are the DC voltage and DC current respectively at the low voltage DC bus.
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4 kHzTransformer
6 : 1
V1V2VDC1
IDC1 Boost Mode of DC-DC Converter
Bridge 1 Bridge 2
i1 i2
IDC2
CDC1
Vdc2
S1 S3
S2 S4
S5 S7
S6 S8
CDC2
iC2
a
b
c
d
Power flow
Lah Lal
Figure 4. Boost mode operation of DC-DC converter.
2.1.2. Boost Mode Operation
Figure 4 describes the boost mode operation of the DC-DC converter, in which the
energy is transferred from low voltage DC bus to high voltage DC bus. In this case,
bridge 2 of the DC-DC converter acts as inverter and bridge 1 as rectifier. Hence,
similar to the equations (7) and (8), model of the inverter and rectifier in boost mode
can be obtained and presented in equations (9) and (10) as below:
nVVS
dtdiL dcbridgeeq
122
2 −= (9)
where, Vdc2 is the DC voltage at low voltage DC bus acting as supply voltage for the
bridge 2.
1111
1 dcbridgedc
dc ISidt
dVC −= (10)
where, Cdc1 is the capacitance connected in parallel with high voltage DC bus; Vdc1 and
Idc1 are the DC voltage and DC current respectively at the high voltage DC bus.
3. Formulation of MPC method for DC-DC converter
The formulation of model predictive control (MPC) algorithm for bidirectional isolated
DC-DC converter is described in the following section. It is necessary to transform the
dynamic system of DC-DC converter for both buck and boost mode of operation
represented in equation (7)–(10) into discrete time model at a specific sampling time Ts.
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3.1 Discrete Time Model for Prediction Horizon
The discrete time model is used to predict the future values of currents and voltages in
the next sampling interval (k+1), from the measured currents and voltages at the kth
sampling instant. The system model derivative dtdx from Euler approximation can be
expressed as:
sTkxkx
dtdx )()1( −+
≈ (11)
Using the above approximation, the discrete time model of predictive currents and
voltages for the next (k+1) sampling instant of the bidirectional full-bridge DC-DC
converter in buck and boost mode can be derived.
3.1.1. Buck Mode
During the buck mode operation of the system, bridge 1 of the DC-DC converter is
working as inverter and it is controlled in current mode. On the other hand, bridge 2 is
controlled with voltage mode as it is working as a rectifier. Hence the discrete time
model of predictive currents at the next sampling instant (k+1) for the inverter (bridge
1) of the DC-DC converter can be evaluated from equation (7) and (11) as:
( ) )()()(1 21111 knVkVSLTkiki dcbridge
eq
s −+=+ (12)
and the discrete time model of predictive voltage at the next sampling instant (k+1) for
the rectifier (bridge 2) can also be presented from equation (8) and (11) as follows:
( ) )()()(1 2222
22 kIkiSCTkVkV dcbridgedc
sdcdc −+=+ (13)
3.1.2. Boost Mode
In boost mode operation, the DC-DC converter operates in reverse mode corresponding
to buck one. Therefore, bridge 1 of this converter works as rectifier and bridge 2 as
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inverter. Then, discrete time model of predictive voltage and current for the inverter and
rectifier can be written as:
( ) )()()(1 1111
11 kIkiSCTkVkV dcbridge
dc
sdcdc −+=+ (14)
and
( )
−+=+
nkVkVS
LTkiki dcbridge
eq
s )()()(1 12222 (15)
3.2. Cost function:
The main objective of model predictive control algorithm is to minimize the error with
fast dynamic response between the predicted and reference values of the discrete
variables. To achieve this objective, an appropriate cost function is defined with a
measurement of predicted input error. Hence, the cost function for inverter and rectifier
can be expressed with the absolute error between the predictive and reference values for
both the buck and boost mode as below:
)1()1( +−+= kikig prefi (16)
and
)1()1( +−+= kVkVg prefr (17)
where, gi and gr are the cost function for inverter and rectifier respectively. iref(k+1) and
ip(k+1) are the reference and predicted current for the inverter. On the other case,
Vref(k+1)and Vp(k+1)are the reference and predicted voltage for the rectifier.
3.3. Control Scheme
Figure 5 shows the proposed control strategy of model predictive control (MPC)
algorithm. At first, the operating mode is selected depending on the direction of power
flow. During buck mode of operation, the input current i1(k) is measured and the future
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value of this current i1 (k+1) is predicted by using the discrete time equation (12) for
each one of four possible switching vector (Sbridge1) of bridge 1 which is act as a
inverter. Simultaneously, for bridge 2, the present value of output voltage Vdc2(k) is
measured and the prediction of its future voltage Vdc2(k+1) is also generated for four
possible switching vector (Sbridge2) by using the equation (13). These future currents and
voltages are compared with the reference current (bridge 1) and voltage (bridge 2) by
utilizing the cost function equation (16) and (17). Finally, the switching states of bridge
1 and bridge 2, which minimizes the cost functions, are selected for the next interval.
Similarly, in boost mode of operation, the future value of input current i2(k+1)
for bridge 2 and output voltage Vdc1(k+1) for bridge 1 is predicted by using the discrete
time equation (15) and (14). Hence, the optimizing switching sates are selected for
firing the switches by using cost function equation (16) and (17).
The amount of power transfer by the DC-DC converter is controlled with the
reference currents and voltages of the inverter and rectifier bridges respectively for both
buck and boost mode. In buck mode, the power transferred to the low voltage DC bus is
222 dcdcdc IVP ×= (18)
where, Pdc2 is the transferred power by the converter. Vdc2 and Idc2 are the DC voltage
and DC current respectively at the low voltage DC bus.
Low DC bus voltage (Vdc2) is controlled precisely at the giving reference voltage (Vref)
for bridge 2, while an accurate value of current Idc2 is achieved by fixing an optimum
value of reference current (iref) for bridge 1.
Similarly in boost mode, power transfer (Pdc1) is also controlled with the
reference current (iref) of bridge 2 and voltage (Vref) of bridge 1 as:
111 dcdcdc IVP ×= (19)
where, Vdc1 and Idc1 are the DC voltage and DC current respectively at the high DC bus.
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3-PhasePWM
Converter3 DC-AC
Bridge 1AC-DCBridge 2
Optimization of Cost Function
Predictive ModelVdc1(k)
Idc1(k)
i1(k) V1(k) V2(k) i2(k)
Idc2(k)
Vdc2(k)
Vdc1(k+1) i1(k+1) i2(k+1)Vdc2(k+1)
Sa Sb Sc Sd
refirefV
Vdc2(k)Vdc1(k)
AC Supply
Idc2(k)i1(k)
V1(k) V2(k)
i2(k)
4 kHz Transformer
4444
Idc1(k)
Figure 5. Proposed control scheme of MPC algorithm for the bidirectional isolated DC-DC converter.
3.4. Control algorithm
The control algorithm of model predictive control (MPC) is presented in Figure 6. The
whole predictive control process completes the following steps for selecting the
optimized switching state of the converter in the next sampling interval (k+1).
• The control algorithm starts with measuring and sampling the high DC bus
voltage Vdc1(k), current Idc1(k); low DC bus voltage Vdc2(k), current Idc2(k);
transformer high side voltage V1(k), current i1(k) and transformer low side
voltage V2(k) and current i2(k) for the kth sampling period.
• Then the reference currents iref and reference voltages Vref for inverter and
rectifier are calculated and fixed up correspond with the amount of power flow.
• For buck mode of operation, predicted currents i1(k+1), predicted voltages
Vdc2(k+1) and for boost mode of operation predicted currents i2(k+1), predicted
voltages Vdc1(k+1) are determined for each one of four (j = 4, where j denotes
the possible switching states) possible switching states of the converter by
utilizing the discrete model of the system.
• Then the cost functions of inverter (gi) and rectifier (gr) is calculated with the
predicted and reference values of currents and voltages.
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• Finally, the switching state associated with the minimum cost function is finally
selected for firing the converter in the next sampling time period (k+1).
Start
Sampling of Measured Currents and Voltages
Calculation of Reference Currents and Voltages
Initialization of Cost Function, gopt
for j=1:4,
Prediction of Currents and Voltages
Calculation of Cost Functions, gi and gr
Minimization of Cost Functions, gi and gr
j ≥ 4 ?
Apply Selected Switching State
No
Yes
Switching State Selection
Figure 6. Proposed control algorithm of model predictive control (MPC).
4. Simulation Results Analysis
The proposed MPC algorithm is carried out by using MATLAB/Simulink to validate
the feasibility of the proposed control algorithm. To verify the proposed method in
bidirectional isolated high-frequency link DC-DC converter for energy conversion
system, both the buck and boost mode operations have been investigated for 2.34 kW
and 1.91 kW power transfer respectively. The parameters shown in Table I, are used for
simulation in both buck and boost modes. In addition, the high frequency transformer
model parameters are given in Table II. Sampling time for the inverter bridge (Tsi) and
rectifier bridge (Tsr) are taken as 10 µs and 250 µs respectively.
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TABLE I
Simulation parameters
Parameter Symbol Value Sampling time (inverter bridge) Tsi 10 µs
Sampling time (rectifier bridge) Tsr 250 µs
Rated high DC bus voltage Vdc1 360 V
Rated low DC bus voltage Vdc2 60 V
Capacitance across high voltage DC bus Cdc1 7 mF
Capacitance across low voltage DC bus Cdc2 22 mF
Auxiliary inductance at the high side of transformer Lah 5 µH
Auxiliary inductance at the low side of transformer Lal 0.14 µH
IGBT internal resistance Ron 1 mΩ
Snubber capacitor across IGBTs Csh 10 nF
MOSFET on-state resistance RDS(on) 0.5 mΩ
Snubber resistance across MOSFET Rsl 1.67 Ω
Snubber capacitor across MOSFET Csl 141 nF
TABLE II
Simulation parameters of the 4 kHz transformer
Parameter Symbol Value Nominal Power P 6.5 kW
Nominal frequency fn 4 kHz
Turns ratio N 6:1
Winding 1 nominal voltage (RMS) V1 360 V
Winding 1 Resistance R1 34 mΩ
Winding 1 leakage inductance L1 8.1 µH
Winding 2 nominal voltage (RMS) v2 60 V
Winding 2 Resistance R2 0.94 mΩ
Winding 2 leakage inductance L2 0.225 µH
4.1. Buck Mode Operation
In buck mode of operation, bridge1 operates as a voltage source inverter with current
mode control, hence current is precisely controlled during the operation of bridge 1. On
the other hand, bridge 2 works as a current source rectifier with voltage mode control
fed by the power from bridge 1. In this case, voltage is controlled precisely to the low
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side transformer voltage. Due to the current mode and voltage mode control of the
bridge 1 and bridge 2 during the buck operation, some expected behaviours appears in
the system model as explained in this section.
In current mode control, the relations of high frequency transformer primary
winding current (i1) with the secondary winding current (i2) and primary winding
voltage (V1) with the secondary winding voltage (V2) are presented in Figure 7. It
shows the value of primary winding current i1 = 10 A (peak) and secondary winding
current i2 = 60 A (peak), which exactly follow the high frequency transformer turn ratio
of 6:1. Again, in the same mode, the high side primary winding voltage V1 = 360 V and
low side secondary winding voltage is V2 = 59.60 V, where a slight amount of voltage
is dropped across the equivalence inductance (Leq), which is expected due to current
mode control of bridge 1.
A further important improvement in this investigation is the unity power factor
control compared to the previous study of DC-DC converter with phase-shift
modulation. In Figure 7, it shows the zero displacement angles between the primary
winding voltage (V1) and current (i1) and also appears to same zero phase-shift between
the secondary winding voltage (V2) and current (i2). As a result, reactive power is
minimized and unity power factor is controlled in the power conversion through the
high frequency (4 kHz) transformer.
In the voltage mode control, low DC bus voltage is 60 V and current has a value
of 39.0 A throughout the simulation time except the transient period, which is consistent
to expected values and are depicted in Figure 8.
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Figure 7. Voltages and current waveforms for 2.34 kW power transfer at the buck mode
of operation; transformer (a) primary winding voltage, (b) secondary winding voltage,
(c) primary winding current, and (d) secondary winding current.
Figure 8. Waveforms of (a) high DC bus voltage Vdc1 and current Idc1 and (b) low DC
bus voltage Vdc2 and current Idc2, at buck mode operation for 2.34 kW power transfer.
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4.2. Boost Mode Operation
In boost mode of operation, bridge 2 is working as a voltage source inverter with
current mode of control. Therefore, current is precisely controlled during the operation
of bridge 2. On the other hand, bridge 1 is operating as a current source rectifier with
voltage mode of control linked by the power from bridge 2 and voltage is controlled
precisely to the high side voltage of the transformer. Because of the current mode and
voltage mode control of the bridge 2 and bridge 1 during the boost operation, the
following behaviours appear in the system model described in this section.
In current mode control, the relations of high frequency transformer primary
winding current (i1) with the secondary winding current (i2) and primary winding
voltage (V1) with the secondary winding voltage (V2) are presented in Figure 9. The
Figure 9 shows that the primary winding current i1 = 75 A (peak) and secondary
winding current i2 = 12.5 A (peak), which exactly follows the high frequency
transformer turn ratio of 6:1. Again, in the same mode, the high side voltage V1 = 360 V
and low side voltage is V2 = 60 V.
In voltage mode control, high bus DC voltage follows the transformer secondary
values around the 360 V. Figure 10 shows the DC current at the values of -5.29 A (
negative sign denotes the opposite direction of power flow), in the whole simulation
time except the transient period.
Besides, similar to the buck operation, the boost operation also shows the unity
power factor control. In Figure 9, it shows the unity power factor between the primary
winding voltage (V1) and current (i1). It also maintains the same phenomena of zero
phase-shift between the secondary winding voltage (V2) and current (i2). As a result,
reactive power is minimized and unity power factor is maintained in the power
conversion through the high frequency (4 kHz) transformer.
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Figure 9. Voltages and current waveforms for 2.1 kW power transfer at the buck mode
of operation; transformer (a) secondary winding voltage, (b) primary winding voltage,
(c) secondary winding current and (d) primary winding current.
Figure 10. Waveforms of (a) low DC bus voltage Vdc2 and current Idc2 and (b) high DC
bus voltage Vdc1 and current Idc1, at the boost mode operation for 1.6 kW power transfer.
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cript Figure 11. Experimental system of bidirectional DC-DC converter with MPC control.
5. Experimental Verification and Efficiency Comparison
A 2.5 kW scaled down laboratory prototype of the bidirectional isolated DC-DC
converter has been developed. The schematic layout of the experimental setup is
presented in Fig. 11. The parameters taken for experiment are provided in Table I.
During the experimentation, a portable DC voltage source [TDK-Lamda] was used for
voltage supply. INTERNATIONAL RECTIFIER–IGBT, TO-247AC, 600V, 60A and
STMICROELECTRONICS-MOSFET, TO-264 were used as power devices.
The experimental verification of the proposed model predictive controlled
bidirectional isolated DC-DC converter is carried out by using the rapid prototyping and
real-time interface system dSPACE with DS1104 control card which consist of Texas
Instruments TMS320F240 sub processor and the Power PC 603e/250 MHz main
processor. This dSPACE control desk works together with Mathwork
MATLAB/Simulink R2013a real-time workshop and real-time interface (RTI) control
cards to implement the proposed predictive control algorithm to the bidirectional
isolated DC-DC converter for energy storage system.
5.1. Experimental Results
The voltage is measured with differential probe [PINTEK DP-25] and the current with
current transducer [LEM LA 25-NP]. The following sub-section presents the
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experimental results for both the operating modes of the bidirectional isolated high-
frequency linked DC-DC converter.
5.1.1. Buck Mode
Figure 12 and 13 shows the waveforms of the transformer primary and
secondary winding voltages and currents at the buck mode of operation. It shows the
value of primary winding voltage V1 = 360 V and low side secondary winding voltage
is V2 = 60V. Again, the transformer primary winding current i1 = 10 A (peak) and
secondary winding current i2 = 60 A (peak), maintained the zero displacement angles
which ensures the minimization of reactive power.
In the voltage mode control, low DC bus output voltage is 60 V and current has
a value of 37.0 A throughout the experimental time except the transient period, which
ensures the stability of the proposed MPC method of bidirectional isolated DC-DC
converter and are depicted in Figure 14.
Figure 12. Waveforms of the transformer primary and secondary winding voltages.
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Figure 13. Waveforms of the transformer primary and secondary winding currents at the
buck mode of operation.
Figure 14. Waveforms of low DC bus voltage (Vdc2) and current (Idc2), at buck mode.
5.1.1. Boost Mode
Figure 15 and 16 shows the waveforms of the transformer primary and
secondary winding voltages and currents at the boost mode of operation. It shows the
value of primary winding voltage V1 = 360 V and low side secondary winding voltage
is V2 = 60V. Again, the transformer primary winding current i1 = 12 A (peak) and
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secondary winding current i2 = 72 A (peak), maintained the zero displacement angles
which ensures the minimization of reactive power.
Figure 15. Waveforms of transformer primary & secondary side voltages at boost mode.
Figure 16. Waveforms of the transformer primary and secondary winding currents at the
boost mode of operation.
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Figure 17. Output waveforms of high DC bus voltage (Vdc1) and current (Idc1), at the
boost mode of operation.
In the voltage mode control, the high DC bus output voltage is 360 V and
current has a value of 5.0 A throughout the experimental time except the transient
period, which ensures the stability of the proposed MPC method of bidirectional
isolated DC-DC converter and are depicted in Figure 17.
Figure 18. Efficiency comparison between MPC and dual-phase-shift control method.
86
87
88
89
90
91
92
93
0 0.5 1 1.5 2 2.5
Con
verte
r Effi
cien
cy η
[%]
Power transfer [kW]
MPC Algorithm
Dual-Phase-ShiftControl
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5.2. Efficiency Comparison
The efficiency of MPC controlled bidirectional isolated DC-DC converter is measured
with FLUKE 1735 Power Logger. The accuracy of this power logger is ±0.2% of its full
scale. The efficiencies of the bidirectional DC-DC converter are measured in MPC
method against the power transfer ranges from 0.5 kW to 2.0 kW. In order to confirm
the effectiveness of MPC algorithm, the efficiencies of MPC controlled DC-DC
converter are compared with dual-phase-shift controlled DC-DC converter (Bai & Mi,
2008a), presented in Fig. 18. The dual-phase-shift PWM control method is applied in
the 2.0 kW bidirectional isolated high frequency linked DC-DC converter topology with
employing the same parameters and measurement techniques as in MPC algorithm.
Although, MPC algorithm has variable switching frequency problem, the efficiencies
associated with the MPC control are higher compared to the dual-phase-shift based
PWM control method due to the elimination of reactive power and minimized DC
voltage ripple. From Fig. 18, it is clear that the maximum efficiency is achieved at 1.60
kW power transfer for both control methods, where the converter efficiency using MPC
method is 92.52 %, while the efficiency is 89.56% using dual-phase-shift based PWM
control method.
6. Conclusions
Predictive control is a powerful control algorithm in the DC-DC power converters for
energy conversion system, which utilizes the discrete behaviour of the DC-DC
converter. The efficiency and performance of the proposed MPC controlled
bidirectional isolated DC-DC converter is simulated in Matlab/Simulink and further
validated with a 2.5 kW experimental configurations. The most important outcomes of
the proposed MPC algorithm in this investigation are zero phase shift between the
primary and secondary voltage of the transformer and unity power factor between the
primary voltage and primary current, also secondary voltage and secondary current,
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hence minimizing the reactive power in the DC-DC converter. As a result, the
efficiency of the power improved up to 92.52%. The results associated with the
predictive algorithm in this investigation are very much encouraging and will continue
to play a strategic role in the improvement of modern high performance DC-DC power
converters in energy conversion system and will open a new prospect in the power
electronics research.
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