2010
IEEE International Conference of Electron Devices and Solid-State Circuits (EDSSC)
Voltage Mode Control of Coupled Inductor Bidirectional DC to DC Converter Narasimharaju.B.L
S. P. Dub ey
S. P. S i n gh
Department of Electrical Engineering
Department of Electrical Engineering
Department of Electrical Engineering
Indian Institute of Technology
Indian Institute of Technology
Indian Institute of Technology
Roorkee-247 667, India
Roorkee-247 667, India
E-mail:
[email protected]
E-mail:
[email protected]
Abstract-In this paper, authors propose a coupled inductor bidirectional converter, and design of classical PI controllers in voltage mode control. The proposed converter has the high
voltage diversity which enables battery module of low voltage to be interfaced with the high-voltage dc bus or the micro grid for and PI based voltage controller design of the proposed converter
subsequent utilization. The working principles, design guidelines, is discussed in detail.
converter
with
Theoretical principles of
voltage
controller
are
battery fed
validated
through
simulation in the Matlab/Simulink environment. Also, prototype
coupled inductor DOC converter is developed and performances are evaluated.
KeywordsBidirectional Simulation; Control;
I.
converter;
Coupled
inductor;
Roorkee-247 667, India
Email:
[email protected]
isolated converters, and third one is use of coupling inductors in non-isolated. Unfortunately, switches of four and beyond in isolated and cascading non-isolated topologies increase production costs, suffer from high voltage/current stress, and also, reduce conversion efficiency. In order to eliminate some of these shortcomings unidirectional converter topologies with coupled inductor is reported in [10]-[14]. The coupled inductor has the benefits that the duty ratio of the converter at the operating point can be adjusted to a value at which its device utilization is improved and hence the efficiency. Therefore, authors propose a coupled inductor bidirectional converter (CIBDC) topology which could be more attractive for micro/mini power grid in renewable energy conversion systems.
INTRODUCTION
The characteristics of small energy storage systems using storage batteries include the ability to install them in proximity to users, the promise of cost reduction through mass production, the ease of securing installation space, and the ability to combine UPS functions [5]. For this reason they are considered prime candidates for peaking power, standby reserve and load-balancing systems when used in conjunction with traditional sources of energy [5]. It is more economical for storage batteries to use a few large-capacity cells than many small-capacity cells, and for that reason the number of cells used in small/micro power grid is limited. Usually, inverters used in DC-UPS (DUPS) systems require comparatively high input DC voltages of about 240V; which necessitates voltage step up when discharging batteries, and step down when charging them. Thus, batteries need high voltage diversity ratio in discharging, and charging modes. In some applications [4]-[9], the battery-bank is directly connected to a dc bus without a bidirectional converter. This configuration requires more battery stacks and reduces the system efficiency. The above shortcomings can be fulfilled by using bidirectional DC-DC (BDC) converters between the storage devices and grid supply or load. However, conventional based BDC topologies [1]-[4] are well reported in the literature. But, in the applications where the voltage diversity requirement is higher, not possible to realize with single converter, then there are three possible solutions, first one is isolated-based converters, second one is cascading non-
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IEEE
The control strategy is the heart of DC-DC converters as concern to the output regulation irrespective of the source and the load disturbances. In contrast, quite commonly used control techniques for DC-DC converters are voltage mode control, and current mode control. However, each controller has its own merits and demerits. In this paper, the voltage mode control is used due to its simplicity, and good load regulation characteristics. In voltage controllers, usually output voltage is used as a feedback parameter. It is fortunate that, we have the well known Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) controller for any control process. However, the proper way tuning of the controller parameter is very essential otherwise badly tuned controller leads to deterioration in system performances and hence, reduction in overall competitiveness. In this work PI controller is tuned in frequency domain, bode plots are used throughout the design process. In this paper the design guidelines, operation, and voltage controller design of the proposed CIBDC topology is discussed and then validated through simulation. The paper organized in four sections. Starting with Section I, the others sections cover the design analysis and the controller design in Section-II, simulation performance analysis in section-III, and conclusive observations in Section-IV.
II. A.
CONVERTER OPERATIONS AND CONTROLLER DESIGN
Converter Operation and Design Analysis
the VLv and the VHv can be attained with volt-second balance principle. It can be expressed by
(I)
The BDC converter operation can be identified in two modes. One is discharge mode during which the BDC is used to boost the battery voltage to a suitable high level DC bus voltage. Second is the charging mode during which the BDC is used to buck the DC bus voltage to a suitable low level battery voltage. The converter operation in continuous conduction mode ( CCM ) is a suitable choice to get a better dynamic response and also a tight regulation of output voltage for the entire load variation. The proposed bidirectional DC-DC converter topology is depicted as in fig. I (a). The converter operation is categorized into four modes. In mode-l and mode2 converter operates in forward boost mode, the power flow is from battery to DC bus. In mode-3 and mode-4 the converter operates in reverse buck mode, the power flow will reverses and is now from the DC bus to battery. The ideal waveforms of both boost and buck modes are depicted in Fig. 2. The major symbol representations are summarized as follows. VLV and VHV, respectively, denote the voltages at the low-voltage (LV) and high-voltage (HV), L I and L2 represent individual inductors in the primary and secondary sides of the coupled inductor respectively, where the primary side is connect to a battery module. The symbols S I and S2 are the low-voltage step-up switch and high-voltage step-down switch respectively. The following assumptions are made to simplifY the converter analyses: 1) All MOSFETs (including their body diodes) are assumed to be ideal switching elements. 2) The conductive voltage drops of the switch and diode are neglected. 3) Delay time (td) is assumed to be negligible 4) Negligible battery internal resistance voltage drop. The operation in mode l and mode-2 is equally valid for mode-4 and mode-3 respectively. Thus, only operation in mode-l and mode-2 is described as follows:
Mode-l/Fig. l(b)f: In this mode, the LV side switch (Sl) is conducting for TON time. Because the inductor is charged by the battery, the magnetizing current increases gradually in an approximately linear way. The secondary current is zero since diode 02 is reverse biased. Mode-2/Fig. lc)f: In this mode, the LV side switch (S I) is turned off for TOFF time. Thus reverses the polarities of the coupled inductors. The diode 02 gets forward biased and the mode begins when the primary current equals the secondary current. The battery and the coupled inductor are connecting in series to discharge into the HV DC bus through the diode 02 by way of a low current type. Because the inductor is supplied to the DC bus, the magnetizing current decreases gradually in an approximately linear way. Mode- 3 and mode-4 are similar to the mode-2 and mode-l respectively. Hence, the converter operation is now considered to be in reverse buck mode during which switch (S2) is pulse modulated and the diode Dl is the freewheeling device. The secondary current (Id is from the DC bus by way of the two series windings (LJand L2) of the coupled inductor to charge the battery in the LV side. As the converter operation is chosen for continuous current mode (CCM), the relationship between
(a) l'roposcd Coupled Inductor Bidirectional DC-DC Converter
1..,(0,) .--
. t ILl() i�L(t)
rL
+
VL1 -
------------
. (t) -. - 'L' -V
ov I·do,)
•••
�
+
L2 -
I
t ii i
V,L(t)
It
_-----------'Y
(b) When
SION& D20FF (Discharge mode) or D.ON& Szon (Charge mode)
iLl(t)
(e) When
•
LI(n.)
____
:J2(nz)
iL2(t)
DZON& SlOFF(Dischargc mode) or SZON& Dl0�Chargc mode)
Figure I. Proposed bidirectional DC-DC converter, and its equivalent circuits in operating modes
O
V PI/be _ /Joos/
��S� , 7� · ����----t--T�T � m� i C� ns� i T VPIiISC B"Ck
_ O�-�-�-�---r--+-��
o
I----+---i----!---. i L2 (/)
O�---+--1_---�--+-�� o
i,.,(I)
O�'::"":""--+-----i--.
}
noost Mode
) J
nUCk Mode
o �---+--1_---�--T-�� t--�- (VII" + NV I. •' ) (I + N) o �---�-�---�--+-�� Figure 2.
Ideal waveforms of proposed BDC in boost mode and buck mode
From (1), the DC gains of the boost mode (0 I) and buck mode (02) is developed as
(2)
Where 0 is the duty ratio of the switch S1 for boost mode and 02=(1-0,) is the duty ratio of the switch S2for buck mode, T
is the switching period, and N
=
!!1... is the tum's ratio of the
The coupled inductor in Fig. 1 can be modeled as an ideal transformer including the magnetizing inductors (Lm' and Lm2) and leakage inductors (Lk' and Ld those are not shown in the fig. The coupling coefficients (k, and k2) of ideal transformer are defined as (3)
The coupling coefficients is simply set at one to obtain Lm,=L, and Lm2=L2 via (3). The series windings (L,and L2) and their mutual inductance (M) can be taken as a single inductor, and the equivalent magnetizing inductor (Lm) can be represented as 1 2 2 L", =(I+N) LI =(1+-) L2 =(LI +L2 + 2M) N
inductance M
_(VHv +NVLV) (N+I)
v
DS'-
(8)
=
K .JL:L:
=NL,
(9) In fig. 1 the filter capacitors CL and CH are used on the LV battery side and HV DC-bus side respectively to achieve ripple free voltages. These capacitors can be calculated based on the desired ripple voltages. Substituting N= 1 4 into (2), the curve of the voltage gain (G1) with respect to the duty cycle (0,) is depicted in fig. 3. As can be seen from this figure, the voltage gain of the proposed converter with a boost type is higher than conventional single-inductor-based converter [2], especially for lower value duty cycle. Also, substituting N= 1 4 into (2), the curve of the voltage gain (02) with respect to the duty cycle (02) is depicted in fig. 4. -
-
-'for various Boost voltage ratio(N)---� gain -- turns-3" r-��--�--� � � ---- -�- . · � Solid Lines: Proposed BoC
28 Marker Line: Conventional BoC
(4)
26
24
for
100%
coupling (i.e. K=1) the equivalent inductor (L) is larger than the value of (L, or L2) to limit the ripple and ascendant rates of the charge current. Assuming boundary between CCM and discontinuous current mode (DCM) (i.e. iLl min 0); the peak
=
values of the inductor currents ILlPk and IL2Pk can be expressed as
� d II
Switch and Battery Vottage relation with duty ratio for various turns ratio(N) 0 18
Solid Lines: Battery Vottage Marker Lines: Switch Vottage
G I'dl (S) =
0 16
14
�
�
(1.667 *101\6S +1.496 *101\9) S2 +1002 S+ 7.469 *101\6
(10)
Buck mode transfer function is given by
0
G vd2 (S) =
0 12 00
1
( 2*101\5S+1.013 *101\9)
(11)
S2 +1002 S + 4.223 *101\7
Using converter transfer functions; the PI based voltage controller Gc(S) is designed to achieve the output regulation of the converter.
0
2
�� °0 �� 0� . -0� .1 2
� � � 0. .6--�0.� 6 --�0 � � 7 ---0�.8 �� 0� .4--�0.� 0.3 ->
Buck Du
ratio d2
Figure 5. Relationship of switch voltage (VDS1) and battery voltage (VLv) with respect to duty cycle «),) for different turns ratios
As can be seen from this fig.ure, the voltage gain of the proposed converter is regulated via the conduction rate of the high-voltage switch (S1), and the stable region of the duty cycle (02) is from zero to its maximum point. Hence, according to the manipulation of 8G 2 0 the maximum controllable 80,
=
duty cycle 02max can be obtained. By analyzing fig. 3 and fig. 4, the turns ratio of the coupled inductor is selected as N=2 when the operational conditions are VLv=24V and VHv=200V. Consequently, the corresponding duty cycles can be obtained as 01=0.71 and 02=0.29 from (2). These values are reasonable in practical applications. According to (2) and (8), the relations of the duty cycle, battery voltage (VLv) and switch voltage (VDS1) under different tum's ratios are illustrated in fig. 5. As can be seen from Fig. 5, the maximum voltage stress across the switch (S I) can be obtained when the duty cycle (02) is set at zero. By analyzing (8), the switch voltage is related to the duty cycle if the values of the battery voltage and the tum's ratio are fixed. Thus, the maximum sustainable voltage of the switch is ensured to be constant. As long as the battery voltage is not higher than the voltage rating of the switch (S I), the discharge mode can be applied well to different battery combinations. According to fig.5, and (8), the low-voltage switch with 90V rated-voltage can be used for both buck and boost states with N=2. B.
...
Controller Design
The control strategy is the heart of DC-DC converters and normally implemented in two parts. In the first part of control, the essential variables used in control are sensed and scaled to feed to the processors for the use in control algorithm as the feedbacks. The second stage of control is the control technique responsible for the high-level transient and steady-state performance of the DC-DC converters. Thus, the output voltage in respective modes (discharging/charging) is regulated by closing a feedback loop between the output voltage and duty-ratio signal. The control to output transfer functions of the converter in boost and buck mode are obtained respectively, as follows; Boost mode transfer function is given by
Frequency (rad/sec)
Figure 6.
10' Frequency (rad/sec)
10'
Frequency response in boost mode
The controller is chosen to have an integral characteristic at low frequency in order to ensure zero steady-state error. The control parameters are tuned in frequency domain, bode plots are used throughout the design process. The boost mode controller is designed at crossover frequency around 2.2 kHz, and resulting transfer function Gc I (S) is given by Gcl (S)
=
0.009(S + 13333) S
(12)
The one zero is placed at 13.333kradlsec, and one pole is placed at origin, approximately twice the target crossover frequency. Similarly the buck mode controller is designed at crossover frequency around 1.5 kHz, and resulting transfer function Gcl(S) is given by G c2 (S)
=
0.006(S + 9425) S
(13)
The frequency domain performances the converter system for tuned parameters of the controllers both in boost and buck mode are depicted as shown in fig.6. III.
SIMULAnON AND EXPERIMENTAL ANALYSIS
In order to authenticate the proposed BDC converter operation and closed loop control; specifications, and design values obtained are described in table-I. The Simulink model of the BDC converter with voltage mode control has been developed as depicted in fig.7. Thus, the performance analysis in open loop and closed loop has been evaluated extensively. Fig.8 illustrates the open loop transient and steady-state performances of proposed BDC converter. In fig.8, we can also observe that the dynamic mode change from boost to buck
operation, and vice versa. Fig.9 illustrates the open loop waveforms of voltages and currents of proposed SOC in steady state. These critical analyses and observations confirm improvements of the proposed topology in providing high voltage diversity. Also, justifies the improved utilization factor of switches and hence the minimum current and voltage stresses on the power devices. Fig.10 and fig.11 illustrates the closed loop performances of the converter for various load conditions. The voltage controller increases the immunity of the converter output voltage to changes in the input voltage and load current. Here in, the load regulations under wide range of load conditions have been made extensively. DATA FOR THE PROPOSED COUPLED SDC CONVERTER
TABLE I
Boost (L Vto flV) VLv=24±20% VHy-200 V
r::� c,---= -- \T" ��:S;: � , ��� i :[ �r [r �"--�----"J J __--1 � �g r-______=l Closed Loop Results of Boost Mode Coupled BOC
o
0.005
0.025
0.03
o
0.005 0.01 0.015 0.02 0.025 Clos.d Loo� R.sults of B U C k Mod. C,?upled B D C
0.03
:
�_
0.005
0
0
0.02
.
0.01
dlf.--� 0
0.015
-----:..L.-:-- -- -:-l:: ::
11H 0
0.01
REFERENCES
Tlme(t)
Figure 10. Closed loop perfonnances for different step load changes from full load to light load
0.015
0.02
0.025
�
0.02
0.025
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[2]
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[4]
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0.03
=-=�====---=-=--= � -----.;J
-!.
_-:-:':":-_ -:-':":-----: ' 0.005 0.01 0.015
[I]
0.03
Figure 11. Closed loop perfonnances for different step load changes from light load to overload full load
[10] J. Calvente, and L. M. Salamero, et aI., "Using magnetic Coupling to eliminate Right Half-plane Zeros in Boost Converters," IEEE Trans. On power Electronics letters, Vo1.2, No.2, pp.58-62, June 2004. MSJIOJiI ,.,
Figure 12. Steady state experimental perfonnances of BDC converter (a) boost mode at full load; Ch1:20v/div, Ch2:100v/div, C3:IOA/div and Ch4:100V/div, (b) buck mode at full load; Ch1:20v/div, Ch2:100v/div, C3:10A/div and Ch4:20V/div
IV.
CONCLUSIONS
The design analysis of the proposed converter has been made theoretically, and also design considerations are discussed. The newly designed converter circuit offers the following improvement over those reported elsewhere. 1) This topology requires only two switches to achieve the objective of bidirectional power flow. 2) Voltage and current stress on the
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