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Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
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Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications Jesus E. Valdez-Resendiz a, Victor M. Sanchez b,*, Julio C. Rosas-Caro c, Jonathan C. Mayo-Maldonado a, J.M. Sierra d, Romeli Barbosa c a
Tecnologico de Monterrey, Av. Eugenio Garza Sada 2501 Sur, Tecnologico, Monterrey, 64849, Mexico Universidad de Quintana Roo, Blvd. Bahia, Chetumal, Q. Roo, 77019, Mexico c Universidad Panamericana Guadalajara, Av. Circunvalacion Poniente 49, Zapopan, 45010, Mexico d Universidad Autonoma Del Carmen, Calle 56, 4, Cd. Del Carmen, 24115, Mexico b
article info
abstract
Article history:
This paper proposes a buck-boost converter topology with continuous input-current
Received 2 June 2017
capability for proton exchange fuel cells (PEMFC) systems. The continuous input-current
Received in revised form
feature of the converter contributes to maintain the PEMFC life-time, which is in sharp
12 October 2017
contrast with traditional buck-boost converters whose input currents damage the PEMFC
Accepted 13 October 2017
and reduce the efficiency. Moreover, this converter offers the main advantages found in
Available online xxx
traditional topologies, such as the Cuk or the SEPIC converters, using a reduced number of electronic components. In particular, the topology features buck-boost conversion range
PACS:
capability, low input-current ripple, and a simple low-cost structure. A detailed analysis
71.35.-y
that encompasses steady state analysis, dynamic modelling, stability analysis, control and
71.35.Lk
experimental results are provided.
71.36.þc
© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Keywords: Power conditioning converters Fuel cell systems DC-DC converters Buck-boost converters
Introduction One of the main challenges in the design of power conditioning systems for PEMFCs, consists in achieving a well regulated voltage from a variable one, while draining a nonpulsating current with a small ripple from the voltage sources, e.g. a fuel cell (FC). Traditional technologies of FCs provide DC voltages that vary between 50 and 100% of its nominal
value [1,2], which is usually very low; consequently, boost converters are usually implemented. Recently, nominal voltages provided by FCs over 100 V have become very common and such a current trend aims at achieving even higher nominal voltages in the future [1,2]. Hence, buck-boost topologies are required when the input-to-output voltage characteristics of the converter falls short with respect to the required range of operation of the FC generation devices [2,3].
* Corresponding author. E-mail addresses: [email protected] (J.E. Valdez-Resendiz), [email protected] (V.M. Sanchez), [email protected] (J.C. Rosas-Caro), [email protected] (J.C. Mayo-Maldonado). https://doi.org/10.1016/j.ijhydene.2017.10.077 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Valdez-Resendiz JE, et al., Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.10.077
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Traditional buck-boost converter topologies drain a pulsating current from the input power source [4]. This issue induces an accelerated aging rate of the electrodes [5,6]. Usually, power converter topologies with input inductors are used in order to reduce the PEMFCs current ripple, since in this way the inductor provides a trade-off between input current ripple and the converter dynamic response. According to this situation, Cuk and Sepic converters can be used to induce a nonpulsating current from the FC; however, these converters require a higher number of electronic components witch is detrimental for the cost of the implementation [3]. Other topologies that display plausible performance results have been also reported in the literature, see e.g. Refs. [7e9]; however, such configurations also require an increased number of electronic components. In order to overcome these challenges, we propose the use of a single-inductor continuous input-current buck-boost converter for applications in FCs. It is the only converter found in the literature with a single inductor and capable of either increasing or reducing the input voltage. This converter has been studied in Refs. [10,11], without addressing and specific application. In this work a DC-DC buck-boost converter topology with continuous input current (CICBB) is applied to a FC generation system, even though it is also suitable for implementations involving photovoltaic cells and electric vehicles (see e.g. Refs. [8,12]). The main aims of this paper are: (i) showing the main features of the continuous input-current buck-boost DC-DC converter topology, such as ripple characteristics and overall steady state analysis; (ii) introducing the proposed application in PEMFCs; (iii) showing a detailed compendium of experimental results to validate the theoretical analysis; (iv) studying the dynamics of the converter for control purposes; (v) implementing a current-mode controller for an experimental prototype.
Proposed topology The proposed continuous input current buck-boost converter is shown in Fig. 1 (b) while the traditional buck-boost converter is depicted in Fig. 1(a). Though both topologies in Fig. 1 are similar, the converter in Fig. 1(b) has a special capacitor connection that, instead of being grounded, is connected to the positive terminal of the input voltage. When the switch closes the inductor is charged with a positive current (positive with respect to the sign defined in Fig. 1) and when the switch is open, the inductor
current closes the diode in order to charge the capacitor with a positive voltage (with respect to the specified signs). When the switch is closed, the diode is open because of the capacitor terminals coincide with the those of the diode.
Steady state operation in continuous conduction mode (CCM) Fig. 2 shows the equivalent circuits that correspond to the switching states of the converter, as well as some relevant waveforms in continuous conduction mode (CCM). By defining D as the duty cycle, which corresponds the portion of time when the switch is closed with respect to the switching period Ts , and by using the small ripple approximation [4], the average voltage across the inductor in steady state can be expressed as 〈vL ðtÞ〉 :¼ DVg þ ð1 DÞ Vg Vc ;
(1)
where the (average) DC component of the voltage across the capacitor and the input voltage are denoted by Vc and Vg respectively. During steady state, the average voltage across the inductor is equal zero, then DVg þ ð1 DÞ Vg Vc ¼ 00Vc ¼ Vg
1 : 1D
(2)
Note that the voltage across the capacitor has the same steady state gain as that of the traditional boost converter. However, in this case the output voltage is given by the sum of the capacitor voltage and the input voltage, i.e. the input voltage is in series with the capacitor voltage. Hence, considering the signs defined in Figs. 1 and 2, the output voltage can be expressed as Vo ¼ Vc Vg ¼ Vg
1 D Vg ¼ Vg : 1D 1D
(3)
The continuous input current converter has the same conversion ratio as in the traditional buck-boost converter. The main advantage of the proposed converter can be seen in Figs. 1 and 2, the input voltage is connected to the reference node with the inductor and the load, both the inductor and the load drain a continuous current and then the input current is continuous. We now derive the DC current through the inductor. By using the small ripple approximation, the average current through the capacitor can be expressed as Vc Vg Vc Vg þ ð1 DÞ IL 〈iC ðtÞ〉 :¼ D R R Vc Vg ¼ þ ð1 DÞIL : R
(4)
where IL denotes the current through the inductor. During the steady state, the average current through the capacitor is equal zero, then the current through the inductor can be expressed as IL ¼ Fig. 1 e (a) Traditional buck-boost converter, (b) Continuous input current buck-boost converter.
Vc Vg : ð1 DÞR
(5)
By substituting (2) in (5) the DC current through the inductor is expressed as
Please cite this article in press as: Valdez-Resendiz JE, et al., Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.10.077
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Fig. 2 e Equivalent circuits for the switching states in CCM when (a) the switch is on (b) the switch is off (c) some important waveforms.
Vg 1 1 1 Vg Vg ¼ 1 0IL ð1 DÞR 1D ð1 DÞR 1 D Vg D ¼ R ð1 DÞ2
IL ¼
〈iS ðtÞ〉 ¼ DIL ¼ (6)
The switch and diode voltage and current stress can be calculated with a similar procedure. When the switch is open, it blocks the capacitor voltage given by (2), which is actually the same voltage rating across a switch in the traditional buck-boost- and Cuk-converter. The current through the switch can be computed from the switching states (Fig. 2) and expressed as
2 Vg D : R 1D
(7)
When the diode is open, it blocks the voltage across the capacitor expressed in (2), and its average current can be expressed as 〈iD ðtÞ〉 ¼ ð1 DÞIL ¼ ð1 DÞ
Vg Vg D D : ¼ R ð1 DÞ2 R ð1 DÞ
(8)
The steady state analysis is thus summarized using Eqs. (2), (3) and (6)e(8). Note that even though the features of this converter are improved, it maintains a simple structure with a
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reduced number of components, which is not the case in other topologies such as the Cuk and Sepic converters.
Ripple analysis In order to select an adequate inductor/capacitor pair with respect to current/voltage ripple specifications, we use the following equations that are derived from the small ripple approximation in Ref. [4]. From Fig. 2, when the switch is closed, the inductor current change is expressed as 1 DiL ¼ Vg DTS : L
(9)
Since the input current Ii is the sum of the inductor current IL and the load current Io , the output current is decreasing during the on-time when the input current is increasing, because the capacitor is discharging during this time. Furthermore, the output current ripple DIo cancels out part of the inductor current ripple DIL and then the input current ripple DIi is smaller than that of the inductor current DIL . However, since the load current ripple is expected to be small by selecting an adequate capacitor value, the load current ripple can be neglected for the computation of the input current ripple, i.e. the input current ripple can be approximated using the inductor current ripple. Similarly, when the switch is open, the capacitor voltage ripple (see Fig. 2) can be expressed as DvC ¼
1 Io DTS : C
(10)
and amperes-per-second related to the capacitor can be analyzed. Since the output capacitor has to be calculated in such way that it maintains a constant voltage, the small ripple approach can be considered for the capacitor voltage, but not for the inductor current, this is illustrated in Fig. 3. In the DCM there are three switching states, instead of two, since an extra switching state corresponds to the case when both diode and transistors are open. The equivalent circuits and relevant waveforms during DCM are shown in Fig. 3, where instead of dividing the switching period in two time-periods, we use three time periods, D1 TS , D2 TS and D3 TS , see Fig. 3. The inductor voltage can thus be expressed as L
diL ¼ D1 Vg þ D2 Vg VC þ D3 ð0Þ: dt
(13)
In steady state the voltage across the inductor and the current through the capacitor are equal to zero, this yields D1 Vg þ D2 Vg VC þ D3 ð0Þ ¼ 00D2 ¼ D1
Vg : VC Vg
(14)
As illustrated in Fig. 3, the capacitor is discharged by the load current while is charged via the inductor current during D2 Ts . Consequently, VC Vg 1 D2 DiL ¼ : 2 R
(15)
Hence, the current ripple is still expressed as (9) and then VC Vg 1 1 1 D2 Vg D1 TS ¼ 0 Vg D1 D2 ¼ VC Vg : 2 L K R
(16)
2L . By substituting (14) in (16) we obtain where K ¼ RT S
Discontinuous conduction mode (DCM) The converter can be designed with parameters to ensure that the current through the inductor is continuous. However, in some scenarios, e.g. when the value of R changes, it is of interest to predict the behavior of the converter and how its features are affected during such circumstances. The current ripple during the time interval DTS is still expressed as (9), the current through the inductor would be continuous if the DC component (6) is higher than a half of the current ripple expressed in (9), then IL ¼
Vg D DiL 1 ¼ Vg DTS : > 2L R ð1 DÞ2 2
(11)
From (11) we notice that 2L > ð1 DÞ2 : RTS
(12)
The inequality (12) expresses the relationship between constant parameters and a duty cycle that may change in practice. Traditionally 2L=RTS is defined as K and it is a function of D. When such K is greater than its critical value, denoted by KCRIT , the converter operates in continuous conduction mode CCM and in DCM otherwise. Note that this condition coincides with the operation of the traditional buckboost converter. In order to calculate the boost-factor during the DCM the equations for the volts-per-second associated to the inductor
Vg 1 1 Vg D1 D1 ¼ VC Vg 0VC ¼ pffiffiffiffiVg D1 þ Vg K VC Vg K D1 ¼ Vg pffiffiffiffi þ 1 : K
(17)
Then, the output voltage can be derived as (18) 1 Vo D1 Vo ¼ VC Vg ¼ pffiffiffiffiVg D1 þ Vg Vg 0 ¼ pffiffiffiffi : Vg K K
(18)
This is the same gain as that of the traditional buck-boost converter in DCM. Finally, by substituting (17) in (14) the time-period associated to D2 can be computed from Vg Vg D2 ¼ D1 ¼ D1 ; 1 1 p ffiffiffi ffi Vg D1 pffiffiffiffiVg D1 þ Vg Vg K K pffiffiffiffi D1 Vg pffiffiffiffi ¼ K: D2 ¼ K D1 Vg
(19)
Dynamic modelling In this section, a large signal model for the continuous input current buck-boost converter is presented. The nature of this model is nonlinear from the state space approach. In addition, a small signal model is obtained by employing approximate linearization around an equilibrium point (see Ref. [13]). The provided models are essential for the model-based control of the converter. Other issues such as stability and current mode
Please cite this article in press as: Valdez-Resendiz JE, et al., Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.10.077
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Fig. 3 e Equivalent circuits for the switching states in CCM when (a) the switch is on and the diode is off (b) the switch is off and the diode is on (c) both diode and switch are off (d) important waveforms.
control of this converter are also addressed in the following sections.
A set of dynamic equations that is valid for both switching states can be expressed as
Large signal modelling
8 > > <
Let us consider the equivalent circuits shown in Fig. 1, and define the position of the switch as u ¼ 1 and u ¼ 0 when it is closed and open respectively. When the switch is closed as illustrated in Fig. 1 (a), the following set of dynamic equations are obtained 8 > > <
d i ¼ Vg dt ; > > : C d v ¼ Vg v dt R L
(20)
where i is the inductor current; v the output voltage; C the capacitance; L the inductance; R the resistive load; and Vg the input voltage. Note that the variables represent timedependent instantaneous values. On the other hand, when the switch is open, i.e. u ¼ 0, the following set of dynamic equations are obtained 8 > > <
d i ¼ v þ Vg dt : > > : C d v ¼ i þ Vg v dt R L
(21)
d i ¼ ð1 uÞv þ Vg dt : > > : C d v ¼ ð1 uÞi þ Vg v dt R L
(22)
In some cases, average dynamic models are employed for dynamic analysis and control of power electronics devices. The average model is obtained by substituting the binary input u ¼ f0; 1g by the duty cycle uav ¼ ½0; 1 of the converter, this is 8 > > <
d iav ¼ ð1 uav Þvav þ Vg dt ; > > : C d v ¼ ð1 u Þi þ Vg vav av av av dt R L
(23)
where iav and vav represent the average time-dependent variables of the inductor current and capacitor voltage. Since the input u (or the duty cycle uav ) multiplies the state variables in both dynamic equations, the large signal dynamic model of the converter is clearly nonlinear. On the other hand, small signal models that are valid around of a specific operation range (or equilibrium) are frequently employed for this type of converters.
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Small signal modelling We present a small signal model of the continuous input current buck-boost converter that is obtained by employing approximate linearization around an equilibrium point (see Ref. [13]). The equilibrium of the dynamic system is obtained from (23), this is 8 Vg > > > < vav ¼ ð1 uav Þ : > vav Vg > > : iav ¼ Rð1 uav Þ
(24)
Vg d ð1 uav Þ iav ¼ vav þ dt L L : > vav V d ð1 u Þ > g av : F ðxÞ ¼ v ¼ iav þ 2 av dt C RC F1 ðxÞ ¼
(25)
By using the following linear approximation for (25) around the equilibrium in (24), we obtain 2
d Diav dt Dvav
vF1 6 vi jp¼p 6 av ¼6 4 vF2 j viav p¼p
3 2 3 vF1 vF1 jp¼p 7 6 jp¼p 7 vvav 7 6 vuav 7 7þ6 7Duav ; 5 4 vF2 5 vF2 jp¼p jp¼p vvav viav
(26)
where Diav ¼ ðiav iav Þ; Dvav ¼ ðvav vav Þ; are linear incremental variables; Duav ¼ ðuav uav Þ is an incremental input, p is the set of variables that include state variables and inputs and p is their corresponding value at the equilibrium point in (24). Eq. (26) can be thus rewritten as
d Diav dt Dvav
2 0 6 ¼6 4 ð1 u Þ av C
8 >
av
> :
¼1þ
Vg vav Riav :
(29)
vav ð0Þ ¼ 0
By considering conditions in (29) in the dynamic system (28), the following equations are obtained
We can formulate the following state space representation for the discussed converter 8 > > <
initial conditions are equal to zero, i.e. an input uav and an initial condition for the output vav ð0Þ is chosen in such way that vav for all t. This is,
3 2 v 3 ð1 uav Þ av 7 6 L 7 L 7Duav : 7þ6 5 5 4 1 iav RC C
(30)
Since parameters in the state equation of the inductor current are strictly positive, the inductor current is not stabilized with respect to a stable output. Consequently, this converter has the feature present also in the traditional buckboost converter and the nonlinear converters (boost, Cuk, Sepic, and so forth), displaying a non-minimum phase output voltage (cf [13]). In order to fix this issue, we can consider the inductor current as the output of the dynamic system, this is 8 > > > > > <
Vg d ð1 uav Þ iav ¼ vav þ dt L L Vg vav : d ð1 uav Þ > v i av ¼ av þ > > dt C RC > > : y ¼ iav
(31)
By considering the zero dynamics of the system, this time choosing uav ¼ 0 and an initial condition iav ð0Þ, we obtain (27)
Eq. (27) is a small signal state space representation of the continuous input current buck-boost converter.
Stability analysis of the large signal model One of the most important issues regarding the dynamics of this converter is its stability. It is well-known that the most of the nonlinear models of power electronics converters have non-minimum phase variables, which constraints the output voltage control of a converter by requiring prior stabilization of the inductor current (see Ref. [13]). In order to illustrate this issue, we start the analysis by choosing the capacitor voltage as the output of the to-be-controlled system. Consider the following input/state-space/output system 8 > > > > > <
Vg d ð1 uav Þ iav ¼ vav þ dt L L Vg vav : d ð1 u Þ av > vav ¼ i þ > av > > dt C RC > : y ¼ vav
8 Vg d > > > iav ¼ > > L < dt : d > vav ¼ 0; > > > dt > : y ¼ vav
8 > < uav ¼ 1 Vg vav : > : iav ð0Þ ¼ 0
(32)
By considering conditions in (29) in the dynamic system (28), the following equations are obtained 8 > > > > > <
d iav ¼ 0 dt d vav Vg : > vav ¼ þ > > dt RC RC > > : y ¼ iav
(33)
Since parameters in (33) are strictly positive, it is clear that the zero dynamics of the system is stable. In other words, the inductor current is a minimum phase variable. A current control mode is allowed by employing the presented large signal dynamic model. An indirect output voltage control can be also used if required as in traditional power electronics converters (see Ref. [13]).
(28)
Let us consider the zero dynamics of system [14], which correspond to the case when the input is turned-off and the
Current mode control Let us consider the dynamic system in (31) in which the average inductor current is the variable to be controlled. The
Please cite this article in press as: Valdez-Resendiz JE, et al., Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.10.077
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input-output feedback linearization technique [14] employed for this case. Express (31) in the following way 8 < d x ¼ f ðxÞ þ gðxÞu av dt ; : y ¼ hðxÞ
is
" # #" # " # " # " 1 0 1 xI 0 d xI iref ; ¼ þ uL dt iav 0 0 0 iav 1
7
(43)
y ¼ iav ; (34)
where the input uL can be defined by a linear control law based on the pole placement technique (see Ref. [15]), this is
where 3 vav Vg þ 7 6 L L 7 6 f ðxÞ ¼ 6 7; 4 Vg vav 5 iav þ RC C 2 v 3 av 6 L 7 7 6 gðxÞ ¼ 6 7; 4 i 5 av C
uL ¼ k1 x1 k1 iav :
2
(35)
T
y ¼ hðxÞ ¼ iav ; x ¼ ½iav vav : In order to obtain a subsystem that represents the inputoutput dynamics of the system the output is derived, this is d vhðxÞ def ½f ðxÞ þ gðxÞuav ¼ Lf hðxÞ þ Lg hðxÞuav ; y :¼ dt vx
(36)
Lf hðxÞ ¼
(37)
Therefore d vav Vg vav y¼ þ þ uav : dt L L L
(38)
This state equation clearly corresponds to the inductor current state equation because y ¼ hðxÞ ¼ iav . Since the input uav is directly involved in the output derivative, the following expression for the input can be used uav ¼
1
Lf hðxÞ þ uL : Lg hðxÞ
(39)
In this case, uav ¼ 1 þ
Vg LuL þ : vav vav
The stability of the linear subsystem (43) is given by the selection of gains kI ; k1 ; k2 . In other words, the input-output subsystem is stable if the well-known closed loop matrix ðA BKÞ is a Hurwitz matrix. The stability of the full-order system can be demonstrated by analyzing the zero dynamics of the closed loop system. Note that this proof is given by setting uL ¼ 0 and considering the same conditions in (32), thus the zero dynamics are given by (33) for this case as well. Therefore we conclude that the internal dynamics of the closed-loop system is stable.
The family of input-series converters
where Lf hðxÞ and Lg hðxÞ are known as the Lie derivatives of hðxÞ along the vectors f and g (cf [14]). Using the definition in (34) and employing equations in (31), the following expressions is obtained vhðxÞ vav Vg f ðxÞ ¼ ½1 0 f ðxÞ ¼ þ ; vx L L vgðxÞ vav gðxÞ ¼ ½1 0gðxÞ ¼ : Lg hðxÞ ¼ vx L
(44)
(40)
The discussed buck-boost converter provides an output corresponding to a series connection of the input voltage with one capacitor, whose voltage is regulated through a switching device. Then it is called input-series buck-boost converter. This section discusses the family of series-input converters, see Fig. 4. The series-input buck-boost converter can be seen as a capacitor connected as in Fig. 4, where the switching cell can be rotated in the clockwise direction. Similarly, a series-input boost converter can be derived with the advantage of having a capacitor which exhibits lower voltages than those in the traditional boost converter. By rotating the buck-boost converter switching cell in counter-clockwise direction, the series-input buck converter is derived.
Bi-directional converters As in the traditional family of DC-DC converters, the inclusion of an additional diode/transistor in anti-parallel connection with the topology transistor/diode enables bidirectional power flow capability. This is illustrated in Fig. 5 for the case of the input series buck-boost-, boost- and buck-converter. Note that as in the traditional buck and boost converter, by switching the input and output ports, the buck-becomes a boost-converter and vice versa.
By substituting (40) into (38), Eq. (38) can be rewritten as
Interleaving structures d y ¼ uL ; dt
(41)
In order to address system uncertainties, the following integrator can be added d ¼ xI ¼ iav iref dt
(42)
where iref is the reference or the desired inductor current. By employing Eqs. (41) and (42), the following linear subsystem is obtained
Another interesting configuration of the buck-boost inputseries converter is the interleaved technique, which has proved to be useful for increasing the power density in switching converters. The interleaving technique consists in connecting two or more converters in parallel to cancel the input current by shifting the switching function in transistors. This section proposes an interleaving connection for the input-series buck-boost converter as shown in Fig. 6, where the corresponding relevant waveforms are also illustrated. It
Please cite this article in press as: Valdez-Resendiz JE, et al., Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.10.077
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Fig. 4 e The family of series-input converters.
Fig. 5 e Bidirectional input-series converters. can be seen that since the inductor current provides the inputripple current, by shifting an inductor-current, its ripple cancels out the other inductor current-ripple when added. Consequently, smaller inductors can be used to achieve the desired input current-ripple.
Experimental results A converter prototype was built to validate the proposed characteristics. The prototype is shown in Fig. 7 and its parameters are displayed in Table 1. The test bed that includes the proposed converter and the fuel cell stack is shown in Fig. 8. A resistor bank was used as a load and the Texas Instrument microcontroller TMS320F28377S was used as a controller device. The experimental performance of the converter was tested using a 100 W PEMFC stack of Horizon Technologies, whose technical specifications are provided in Table 2. This PEMFC stack is open-cathode and uses forced ventilation for the oxygen supply and temperature control.
Open-loop experiments Experimental results in open loop that show the characteristics of the continuous input-current and the input voltage of the converter are shown in Fig. 9. Note that the input current is in continuous conduction mode with a current ripple
Fig. 6 e Interleaved 2x input-series buck-boost converter.
Fig. 7 e Experimental prototype.
Please cite this article in press as: Valdez-Resendiz JE, et al., Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.10.077
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Table 1 e Parameters of the experimental prototype. Parameter-Component Maximum power Input voltage range Output voltage range Switching frequency MOSFET Diode Capacitor Inductor
Value and information 150 W 11e14 V 8e18 V 50 kHz IRFIZ44N, 55 V, 31 A, RDSON ¼ 24 mU MBR1560CT, 60 V, 20 A, Fv 0.75 V 22 mF, 250 V, ESR 14 mU 150 mH, 5 A, ESR 50 mU
9
approximately equal to 1A. The input power of the converter is equal to 18:8W. In Fig. 10 we show the traces of the output voltage and output current, where the output power, i.e. the power dissipated by the load, is equal to 18W. A duty cycle of 60% was used for the PWM switching signal. Note that the output voltage gain coincides with the theoretical value (3) of 1.5 for a duty cycle of 60%. The efficiency of the converter in this operating condition is h ¼ 94:14%. Fig. 11 depicts the experimental input voltage/current waveforms in a different operation region. The current input in this operating condition is in continuous conduction mode. Moreover, the input-current ripple is nearly 1A despite of the fact that the load has been increased more than twice. Fig. 12 shows the output voltage/current experimental waveforms with 60% of duty cycle. The input power in this operating condition is of 51:95W. The ratio between the input and output voltage is almost the same (i.e. 1.5) with respect to the experiment in Figs. 9 and 10, with a duty cycle of 60%. The output power of the converter is equal to 45W, and the efficiency is h ¼ 86:7%. The output-voltage ripple increased due to
Fig. 8 e Experimental test bed.
Table 2 e Technical specifications for the H-100 PEMFC stack. Parameter
Value and information
Rated power Number of cells Rated voltage Rated current Reactants Max stack temperature H2 pressure Hydrogen purity Humidification Cooling
100 W 20 12 V 8.3 A Hydrogen and air 65 C 0.45 0.55 bar 99.995% dry H2 Self-humidified Air (integrated cooling fan)
Fig. 9 e Input current/voltage characteristics of the proposed converter with output power equal to 18W.
Fig. 10 e Output current/voltage characteristics of the proposed converter with output power equal to 18W.
Fig. 11 e Input current/voltage characteristics of the proposed converter with output power equal to 45W.
Please cite this article in press as: Valdez-Resendiz JE, et al., Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.10.077
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Fig. 12 e Output current/voltage characteristics of the proposed converter with output power equal to 45W.
the increase of the resistive-load power. However, the outputcurrent ripple is negligible. The experimental polarization curve for the H-100 PEMFC stack was obtained and is shown in Fig. 13.
Fig. 15 e Experimental results of the closed-loop capacitor voltage vav with different set-points for the controlled inductor current (iref ¼0.5,1,1.5).
Closed-loop experiments In order to evaluate the performance of the controller in closed-loop operation, the control law given in Eq. (40) was also implemented. Figs. 14 and 15 show the experimental results of the closed-loop system. The experimental setup was carried out by employing RTAI-Lab which is a Linux-based real-time platform. In addition, a data acquisition card PCI6024E was used as interface between the real-time software platform and the converter. The set-point for the inductor current is changed several times during the experiment by employing the real-time user interface.
Conclusions
Fig. 13 e Experimental polarization curve for the PEMFC stack.
Fig. 14 e Experimental results of the closed-loop inductor current ia v with different set-points (iref ¼0.5,1,1.5).
We introduced a novel buck-boost DC-DC converter topology that provides a continuous input current and a simple structure. The discussed topology provides an output that is a series connection of the input and one capacitor whose voltage is regulated through the switching stage by a PWM. We showed how other converters can be derived in the same way such as the buck and boost converter, those converters can be called input-series converters due to the series connection of the input voltage with the voltage-controlled capacitor. Besides the proposed application on fuel cell generation systems, the input-series buck-boost converter that was proposed can be used for voltage regulation in portable devices where the battery is discharging and the voltage regulator needs to operate within a wide voltage range. This paper also proposes an interleaving connection of the series-input buck-boost converter for reducing passive components size and the input current ripple. The usefulness of the proposed average large signal dynamic model is shown with the experimental results of a current mode control. A stability analysis as well as open and closed loop experiments were provided in order to validate the theoretical analysis.
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Acknowledgments This work was supported by Universidad Panamericana Campus Guadalajara, through the program Fomento a la Investigacion UP 2016, project UPCI-2016-FING-02 “Estudio de n de rizo de corriente, convertidores de cd-cd con cancelacio Mexico. J.E Valdez-Resendiz and J.C Mayo-Maldonado want to thank CONACyT and the Mexican Ministry of Energy (SENER) for their funding support under the project #266632, “Laboratorio Binacional para la Gestion Inteligente de la Sustentabilidad Energetica y la Formacion Tecnologica”, fondo sectorial de sustentabilidad energetica.
references
[1] Horizon fuel cells. [Online]. Available: http://www. horizonfuelcell.com/h-series-stacks. [2] Gao D, Jin Z, Liu J, Ouyang M. An interleaved step-up/stepdown converter for fuel cell vehicle applications. Int J Hydrogen Energy 2016;41(47):22422e32. [3] Rosas-Caro JC, Sanchez VM, Vazquez-Bautista RF, MoralesMendoza LJ, Mayo-Maldonado JC, Garcia-Vite PM, et al. A novel dc-dc multilevel sepic converter for pemfc systems. Int J Hydrogen Energy 2016;41(48):23401e8. [4] Erickson R, Maksimovic D. Fundamentals of power electronics, ser. Power electronics. US: Springer; 2001. [5] Fontes G, Turpin C, Astier S, Meynard TA. Interactions between fuel cells and power converters: influence of current harmonics on a fuel cell stack. IEEE Trans Power Electron March 2007;22(2):670e8.
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[6] Gerard M, Poirot-Crouvezier J-P, Hissel Daniel, Pera M-C. Ripple current effects on pemfc aging test by experimental and modeling. ASME J Fuel Cell Sci Technol 2010;8(2). [7] Samavatian V, Radan A. A novel low-ripple interleaved buckboost converter with high efficiency and low oscillation for fuel-cell applications. Int J Electr Power Energy Syst 2014;63:446e54. [8] Kaouane M, Boukhelifa A, Cheriti A. Regulated output voltage double switch buck-boost converter for photovoltaic energy application. Int J Hydrogen Energy 2016;41(45):20847e57. [9] Rosas-Caro JC, Mayo-Maldonado JC, Mancilla-David F, Valderrabano-Gonzalez A, Carbajal FB. “Single-inductor resonant switched capacitor voltage multiplier with safe commutation. IET Power Electron 2015;8(4):507e16. [10] Rosas-Caro J, Mayo-Maldonado J, Valdez-Resendiz J, SalasCabrera R, Cisneros-Villegas H, Castillo-Ibarra R, et al. Design-oriented analysis and modeling of a single-inductor continuous input-current buck-boost dc-dc converter. In: 2011 World Congr. Eng Comput Sci (WCECS); 2011. p. 329e46. [11] Williams BW. Generation and analysis of canonical switching cell dc-to-dc converters. IEEE Trans Ind Electron Jan 2014;61(1):329e46. [12] Gasbaoui B, Nasri A, Abdelkhalek O, Ghouili J, Ghezouani A. “Behavior pem fuel cell for 4WD electric vehicle under different scenario consideration. Int J Hydrogen Energy 2017;42(1):535e43 [Online]. Available, http://www. sciencedirect.com/science/article/pii/S0360319916325058. [13] Sira-Ramrez H, Silva-Ortigoza R. Control design techniques in power electronics devices, ser. Power systems. US: Springer; 2006. [14] Isidori A. Nonlinear control systems, ser. Communications and control engineering. London: Springer-Verlag; 1995. [15] Franklin GF, Powell JD, Workman M. Digital control of dynamic systems. Addison Wesley; 1997.
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Available online at www.sciencedirect.com
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Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications Jesus E. Valdez-Resendiz a, Victor M. Sanchez b,*, Julio C. Rosas-Caro c, Jonathan C. Mayo-Maldonado a, J.M. Sierra d, Romeli Barbosa c a
Tecnologico de Monterrey, Av. Eugenio Garza Sada 2501 Sur, Tecnologico, Monterrey, 64849, Mexico Universidad de Quintana Roo, Blvd. Bahia, Chetumal, Q. Roo, 77019, Mexico c Universidad Panamericana Guadalajara, Av. Circunvalacion Poniente 49, Zapopan, 45010, Mexico d Universidad Autonoma Del Carmen, Calle 56, 4, Cd. Del Carmen, 24115, Mexico b
article info
abstract
Article history:
This paper proposes a buck-boost converter topology with continuous input-current
Received 2 June 2017
capability for proton exchange fuel cells (PEMFC) systems. The continuous input-current
Received in revised form
feature of the converter contributes to maintain the PEMFC life-time, which is in sharp
12 October 2017
contrast with traditional buck-boost converters whose input currents damage the PEMFC
Accepted 13 October 2017
and reduce the efficiency. Moreover, this converter offers the main advantages found in
Available online xxx
traditional topologies, such as the Cuk or the SEPIC converters, using a reduced number of electronic components. In particular, the topology features buck-boost conversion range
PACS:
capability, low input-current ripple, and a simple low-cost structure. A detailed analysis
71.35.-y
that encompasses steady state analysis, dynamic modelling, stability analysis, control and
71.35.Lk
experimental results are provided.
71.36.þc
© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Keywords: Power conditioning converters Fuel cell systems DC-DC converters Buck-boost converters
Introduction One of the main challenges in the design of power conditioning systems for PEMFCs, consists in achieving a well regulated voltage from a variable one, while draining a nonpulsating current with a small ripple from the voltage sources, e.g. a fuel cell (FC). Traditional technologies of FCs provide DC voltages that vary between 50 and 100% of its nominal
value [1,2], which is usually very low; consequently, boost converters are usually implemented. Recently, nominal voltages provided by FCs over 100 V have become very common and such a current trend aims at achieving even higher nominal voltages in the future [1,2]. Hence, buck-boost topologies are required when the input-to-output voltage characteristics of the converter falls short with respect to the required range of operation of the FC generation devices [2,3].
* Corresponding author. E-mail addresses: [email protected] (J.E. Valdez-Resendiz), [email protected] (V.M. Sanchez), [email protected] (J.C. Rosas-Caro), [email protected] (J.C. Mayo-Maldonado). https://doi.org/10.1016/j.ijhydene.2017.10.077 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Valdez-Resendiz JE, et al., Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.10.077
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Traditional buck-boost converter topologies drain a pulsating current from the input power source [4]. This issue induces an accelerated aging rate of the electrodes [5,6]. Usually, power converter topologies with input inductors are used in order to reduce the PEMFCs current ripple, since in this way the inductor provides a trade-off between input current ripple and the converter dynamic response. According to this situation, Cuk and Sepic converters can be used to induce a nonpulsating current from the FC; however, these converters require a higher number of electronic components witch is detrimental for the cost of the implementation [3]. Other topologies that display plausible performance results have been also reported in the literature, see e.g. Refs. [7e9]; however, such configurations also require an increased number of electronic components. In order to overcome these challenges, we propose the use of a single-inductor continuous input-current buck-boost converter for applications in FCs. It is the only converter found in the literature with a single inductor and capable of either increasing or reducing the input voltage. This converter has been studied in Refs. [10,11], without addressing and specific application. In this work a DC-DC buck-boost converter topology with continuous input current (CICBB) is applied to a FC generation system, even though it is also suitable for implementations involving photovoltaic cells and electric vehicles (see e.g. Refs. [8,12]). The main aims of this paper are: (i) showing the main features of the continuous input-current buck-boost DC-DC converter topology, such as ripple characteristics and overall steady state analysis; (ii) introducing the proposed application in PEMFCs; (iii) showing a detailed compendium of experimental results to validate the theoretical analysis; (iv) studying the dynamics of the converter for control purposes; (v) implementing a current-mode controller for an experimental prototype.
Proposed topology The proposed continuous input current buck-boost converter is shown in Fig. 1 (b) while the traditional buck-boost converter is depicted in Fig. 1(a). Though both topologies in Fig. 1 are similar, the converter in Fig. 1(b) has a special capacitor connection that, instead of being grounded, is connected to the positive terminal of the input voltage. When the switch closes the inductor is charged with a positive current (positive with respect to the sign defined in Fig. 1) and when the switch is open, the inductor
current closes the diode in order to charge the capacitor with a positive voltage (with respect to the specified signs). When the switch is closed, the diode is open because of the capacitor terminals coincide with the those of the diode.
Steady state operation in continuous conduction mode (CCM) Fig. 2 shows the equivalent circuits that correspond to the switching states of the converter, as well as some relevant waveforms in continuous conduction mode (CCM). By defining D as the duty cycle, which corresponds the portion of time when the switch is closed with respect to the switching period Ts , and by using the small ripple approximation [4], the average voltage across the inductor in steady state can be expressed as 〈vL ðtÞ〉 :¼ DVg þ ð1 DÞ Vg Vc ;
(1)
where the (average) DC component of the voltage across the capacitor and the input voltage are denoted by Vc and Vg respectively. During steady state, the average voltage across the inductor is equal zero, then DVg þ ð1 DÞ Vg Vc ¼ 00Vc ¼ Vg
1 : 1D
(2)
Note that the voltage across the capacitor has the same steady state gain as that of the traditional boost converter. However, in this case the output voltage is given by the sum of the capacitor voltage and the input voltage, i.e. the input voltage is in series with the capacitor voltage. Hence, considering the signs defined in Figs. 1 and 2, the output voltage can be expressed as Vo ¼ Vc Vg ¼ Vg
1 D Vg ¼ Vg : 1D 1D
(3)
The continuous input current converter has the same conversion ratio as in the traditional buck-boost converter. The main advantage of the proposed converter can be seen in Figs. 1 and 2, the input voltage is connected to the reference node with the inductor and the load, both the inductor and the load drain a continuous current and then the input current is continuous. We now derive the DC current through the inductor. By using the small ripple approximation, the average current through the capacitor can be expressed as Vc Vg Vc Vg þ ð1 DÞ IL 〈iC ðtÞ〉 :¼ D R R Vc Vg ¼ þ ð1 DÞIL : R
(4)
where IL denotes the current through the inductor. During the steady state, the average current through the capacitor is equal zero, then the current through the inductor can be expressed as IL ¼ Fig. 1 e (a) Traditional buck-boost converter, (b) Continuous input current buck-boost converter.
Vc Vg : ð1 DÞR
(5)
By substituting (2) in (5) the DC current through the inductor is expressed as
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Fig. 2 e Equivalent circuits for the switching states in CCM when (a) the switch is on (b) the switch is off (c) some important waveforms.
Vg 1 1 1 Vg Vg ¼ 1 0IL ð1 DÞR 1D ð1 DÞR 1 D Vg D ¼ R ð1 DÞ2
IL ¼
〈iS ðtÞ〉 ¼ DIL ¼ (6)
The switch and diode voltage and current stress can be calculated with a similar procedure. When the switch is open, it blocks the capacitor voltage given by (2), which is actually the same voltage rating across a switch in the traditional buck-boost- and Cuk-converter. The current through the switch can be computed from the switching states (Fig. 2) and expressed as
2 Vg D : R 1D
(7)
When the diode is open, it blocks the voltage across the capacitor expressed in (2), and its average current can be expressed as 〈iD ðtÞ〉 ¼ ð1 DÞIL ¼ ð1 DÞ
Vg Vg D D : ¼ R ð1 DÞ2 R ð1 DÞ
(8)
The steady state analysis is thus summarized using Eqs. (2), (3) and (6)e(8). Note that even though the features of this converter are improved, it maintains a simple structure with a
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reduced number of components, which is not the case in other topologies such as the Cuk and Sepic converters.
Ripple analysis In order to select an adequate inductor/capacitor pair with respect to current/voltage ripple specifications, we use the following equations that are derived from the small ripple approximation in Ref. [4]. From Fig. 2, when the switch is closed, the inductor current change is expressed as 1 DiL ¼ Vg DTS : L
(9)
Since the input current Ii is the sum of the inductor current IL and the load current Io , the output current is decreasing during the on-time when the input current is increasing, because the capacitor is discharging during this time. Furthermore, the output current ripple DIo cancels out part of the inductor current ripple DIL and then the input current ripple DIi is smaller than that of the inductor current DIL . However, since the load current ripple is expected to be small by selecting an adequate capacitor value, the load current ripple can be neglected for the computation of the input current ripple, i.e. the input current ripple can be approximated using the inductor current ripple. Similarly, when the switch is open, the capacitor voltage ripple (see Fig. 2) can be expressed as DvC ¼
1 Io DTS : C
(10)
and amperes-per-second related to the capacitor can be analyzed. Since the output capacitor has to be calculated in such way that it maintains a constant voltage, the small ripple approach can be considered for the capacitor voltage, but not for the inductor current, this is illustrated in Fig. 3. In the DCM there are three switching states, instead of two, since an extra switching state corresponds to the case when both diode and transistors are open. The equivalent circuits and relevant waveforms during DCM are shown in Fig. 3, where instead of dividing the switching period in two time-periods, we use three time periods, D1 TS , D2 TS and D3 TS , see Fig. 3. The inductor voltage can thus be expressed as L
diL ¼ D1 Vg þ D2 Vg VC þ D3 ð0Þ: dt
(13)
In steady state the voltage across the inductor and the current through the capacitor are equal to zero, this yields D1 Vg þ D2 Vg VC þ D3 ð0Þ ¼ 00D2 ¼ D1
Vg : VC Vg
(14)
As illustrated in Fig. 3, the capacitor is discharged by the load current while is charged via the inductor current during D2 Ts . Consequently, VC Vg 1 D2 DiL ¼ : 2 R
(15)
Hence, the current ripple is still expressed as (9) and then VC Vg 1 1 1 D2 Vg D1 TS ¼ 0 Vg D1 D2 ¼ VC Vg : 2 L K R
(16)
2L . By substituting (14) in (16) we obtain where K ¼ RT S
Discontinuous conduction mode (DCM) The converter can be designed with parameters to ensure that the current through the inductor is continuous. However, in some scenarios, e.g. when the value of R changes, it is of interest to predict the behavior of the converter and how its features are affected during such circumstances. The current ripple during the time interval DTS is still expressed as (9), the current through the inductor would be continuous if the DC component (6) is higher than a half of the current ripple expressed in (9), then IL ¼
Vg D DiL 1 ¼ Vg DTS : > 2L R ð1 DÞ2 2
(11)
From (11) we notice that 2L > ð1 DÞ2 : RTS
(12)
The inequality (12) expresses the relationship between constant parameters and a duty cycle that may change in practice. Traditionally 2L=RTS is defined as K and it is a function of D. When such K is greater than its critical value, denoted by KCRIT , the converter operates in continuous conduction mode CCM and in DCM otherwise. Note that this condition coincides with the operation of the traditional buckboost converter. In order to calculate the boost-factor during the DCM the equations for the volts-per-second associated to the inductor
Vg 1 1 Vg D1 D1 ¼ VC Vg 0VC ¼ pffiffiffiffiVg D1 þ Vg K VC Vg K D1 ¼ Vg pffiffiffiffi þ 1 : K
(17)
Then, the output voltage can be derived as (18) 1 Vo D1 Vo ¼ VC Vg ¼ pffiffiffiffiVg D1 þ Vg Vg 0 ¼ pffiffiffiffi : Vg K K
(18)
This is the same gain as that of the traditional buck-boost converter in DCM. Finally, by substituting (17) in (14) the time-period associated to D2 can be computed from Vg Vg D2 ¼ D1 ¼ D1 ; 1 1 p ffiffiffi ffi Vg D1 pffiffiffiffiVg D1 þ Vg Vg K K pffiffiffiffi D1 Vg pffiffiffiffi ¼ K: D2 ¼ K D1 Vg
(19)
Dynamic modelling In this section, a large signal model for the continuous input current buck-boost converter is presented. The nature of this model is nonlinear from the state space approach. In addition, a small signal model is obtained by employing approximate linearization around an equilibrium point (see Ref. [13]). The provided models are essential for the model-based control of the converter. Other issues such as stability and current mode
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Fig. 3 e Equivalent circuits for the switching states in CCM when (a) the switch is on and the diode is off (b) the switch is off and the diode is on (c) both diode and switch are off (d) important waveforms.
control of this converter are also addressed in the following sections.
A set of dynamic equations that is valid for both switching states can be expressed as
Large signal modelling
8 > > <
Let us consider the equivalent circuits shown in Fig. 1, and define the position of the switch as u ¼ 1 and u ¼ 0 when it is closed and open respectively. When the switch is closed as illustrated in Fig. 1 (a), the following set of dynamic equations are obtained 8 > > <
d i ¼ Vg dt ; > > : C d v ¼ Vg v dt R L
(20)
where i is the inductor current; v the output voltage; C the capacitance; L the inductance; R the resistive load; and Vg the input voltage. Note that the variables represent timedependent instantaneous values. On the other hand, when the switch is open, i.e. u ¼ 0, the following set of dynamic equations are obtained 8 > > <
d i ¼ v þ Vg dt : > > : C d v ¼ i þ Vg v dt R L
(21)
d i ¼ ð1 uÞv þ Vg dt : > > : C d v ¼ ð1 uÞi þ Vg v dt R L
(22)
In some cases, average dynamic models are employed for dynamic analysis and control of power electronics devices. The average model is obtained by substituting the binary input u ¼ f0; 1g by the duty cycle uav ¼ ½0; 1 of the converter, this is 8 > > <
d iav ¼ ð1 uav Þvav þ Vg dt ; > > : C d v ¼ ð1 u Þi þ Vg vav av av av dt R L
(23)
where iav and vav represent the average time-dependent variables of the inductor current and capacitor voltage. Since the input u (or the duty cycle uav ) multiplies the state variables in both dynamic equations, the large signal dynamic model of the converter is clearly nonlinear. On the other hand, small signal models that are valid around of a specific operation range (or equilibrium) are frequently employed for this type of converters.
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Small signal modelling We present a small signal model of the continuous input current buck-boost converter that is obtained by employing approximate linearization around an equilibrium point (see Ref. [13]). The equilibrium of the dynamic system is obtained from (23), this is 8 Vg > > > < vav ¼ ð1 uav Þ : > vav Vg > > : iav ¼ Rð1 uav Þ
(24)
Vg d ð1 uav Þ iav ¼ vav þ dt L L : > vav V d ð1 u Þ > g av : F ðxÞ ¼ v ¼ iav þ 2 av dt C RC F1 ðxÞ ¼
(25)
By using the following linear approximation for (25) around the equilibrium in (24), we obtain 2
d Diav dt Dvav
vF1 6 vi jp¼p 6 av ¼6 4 vF2 j viav p¼p
3 2 3 vF1 vF1 jp¼p 7 6 jp¼p 7 vvav 7 6 vuav 7 7þ6 7Duav ; 5 4 vF2 5 vF2 jp¼p jp¼p vvav viav
(26)
where Diav ¼ ðiav iav Þ; Dvav ¼ ðvav vav Þ; are linear incremental variables; Duav ¼ ðuav uav Þ is an incremental input, p is the set of variables that include state variables and inputs and p is their corresponding value at the equilibrium point in (24). Eq. (26) can be thus rewritten as
d Diav dt Dvav
2 0 6 ¼6 4 ð1 u Þ av C
8 >
av
> :
¼1þ
Vg vav Riav :
(29)
vav ð0Þ ¼ 0
By considering conditions in (29) in the dynamic system (28), the following equations are obtained
We can formulate the following state space representation for the discussed converter 8 > > <
initial conditions are equal to zero, i.e. an input uav and an initial condition for the output vav ð0Þ is chosen in such way that vav for all t. This is,
3 2 v 3 ð1 uav Þ av 7 6 L 7 L 7Duav : 7þ6 5 5 4 1 iav RC C
(30)
Since parameters in the state equation of the inductor current are strictly positive, the inductor current is not stabilized with respect to a stable output. Consequently, this converter has the feature present also in the traditional buckboost converter and the nonlinear converters (boost, Cuk, Sepic, and so forth), displaying a non-minimum phase output voltage (cf [13]). In order to fix this issue, we can consider the inductor current as the output of the dynamic system, this is 8 > > > > > <
Vg d ð1 uav Þ iav ¼ vav þ dt L L Vg vav : d ð1 uav Þ > v i av ¼ av þ > > dt C RC > > : y ¼ iav
(31)
By considering the zero dynamics of the system, this time choosing uav ¼ 0 and an initial condition iav ð0Þ, we obtain (27)
Eq. (27) is a small signal state space representation of the continuous input current buck-boost converter.
Stability analysis of the large signal model One of the most important issues regarding the dynamics of this converter is its stability. It is well-known that the most of the nonlinear models of power electronics converters have non-minimum phase variables, which constraints the output voltage control of a converter by requiring prior stabilization of the inductor current (see Ref. [13]). In order to illustrate this issue, we start the analysis by choosing the capacitor voltage as the output of the to-be-controlled system. Consider the following input/state-space/output system 8 > > > > > <
Vg d ð1 uav Þ iav ¼ vav þ dt L L Vg vav : d ð1 u Þ av > vav ¼ i þ > av > > dt C RC > : y ¼ vav
8 Vg d > > > iav ¼ > > L < dt : d > vav ¼ 0; > > > dt > : y ¼ vav
8 > < uav ¼ 1 Vg vav : > : iav ð0Þ ¼ 0
(32)
By considering conditions in (29) in the dynamic system (28), the following equations are obtained 8 > > > > > <
d iav ¼ 0 dt d vav Vg : > vav ¼ þ > > dt RC RC > > : y ¼ iav
(33)
Since parameters in (33) are strictly positive, it is clear that the zero dynamics of the system is stable. In other words, the inductor current is a minimum phase variable. A current control mode is allowed by employing the presented large signal dynamic model. An indirect output voltage control can be also used if required as in traditional power electronics converters (see Ref. [13]).
(28)
Let us consider the zero dynamics of system [14], which correspond to the case when the input is turned-off and the
Current mode control Let us consider the dynamic system in (31) in which the average inductor current is the variable to be controlled. The
Please cite this article in press as: Valdez-Resendiz JE, et al., Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.10.077
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input-output feedback linearization technique [14] employed for this case. Express (31) in the following way 8 < d x ¼ f ðxÞ þ gðxÞu av dt ; : y ¼ hðxÞ
is
" # #" # " # " # " 1 0 1 xI 0 d xI iref ; ¼ þ uL dt iav 0 0 0 iav 1
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(43)
y ¼ iav ; (34)
where the input uL can be defined by a linear control law based on the pole placement technique (see Ref. [15]), this is
where 3 vav Vg þ 7 6 L L 7 6 f ðxÞ ¼ 6 7; 4 Vg vav 5 iav þ RC C 2 v 3 av 6 L 7 7 6 gðxÞ ¼ 6 7; 4 i 5 av C
uL ¼ k1 x1 k1 iav :
2
(35)
T
y ¼ hðxÞ ¼ iav ; x ¼ ½iav vav : In order to obtain a subsystem that represents the inputoutput dynamics of the system the output is derived, this is d vhðxÞ def ½f ðxÞ þ gðxÞuav ¼ Lf hðxÞ þ Lg hðxÞuav ; y :¼ dt vx
(36)
Lf hðxÞ ¼
(37)
Therefore d vav Vg vav y¼ þ þ uav : dt L L L
(38)
This state equation clearly corresponds to the inductor current state equation because y ¼ hðxÞ ¼ iav . Since the input uav is directly involved in the output derivative, the following expression for the input can be used uav ¼
1
Lf hðxÞ þ uL : Lg hðxÞ
(39)
In this case, uav ¼ 1 þ
Vg LuL þ : vav vav
The stability of the linear subsystem (43) is given by the selection of gains kI ; k1 ; k2 . In other words, the input-output subsystem is stable if the well-known closed loop matrix ðA BKÞ is a Hurwitz matrix. The stability of the full-order system can be demonstrated by analyzing the zero dynamics of the closed loop system. Note that this proof is given by setting uL ¼ 0 and considering the same conditions in (32), thus the zero dynamics are given by (33) for this case as well. Therefore we conclude that the internal dynamics of the closed-loop system is stable.
The family of input-series converters
where Lf hðxÞ and Lg hðxÞ are known as the Lie derivatives of hðxÞ along the vectors f and g (cf [14]). Using the definition in (34) and employing equations in (31), the following expressions is obtained vhðxÞ vav Vg f ðxÞ ¼ ½1 0 f ðxÞ ¼ þ ; vx L L vgðxÞ vav gðxÞ ¼ ½1 0gðxÞ ¼ : Lg hðxÞ ¼ vx L
(44)
(40)
The discussed buck-boost converter provides an output corresponding to a series connection of the input voltage with one capacitor, whose voltage is regulated through a switching device. Then it is called input-series buck-boost converter. This section discusses the family of series-input converters, see Fig. 4. The series-input buck-boost converter can be seen as a capacitor connected as in Fig. 4, where the switching cell can be rotated in the clockwise direction. Similarly, a series-input boost converter can be derived with the advantage of having a capacitor which exhibits lower voltages than those in the traditional boost converter. By rotating the buck-boost converter switching cell in counter-clockwise direction, the series-input buck converter is derived.
Bi-directional converters As in the traditional family of DC-DC converters, the inclusion of an additional diode/transistor in anti-parallel connection with the topology transistor/diode enables bidirectional power flow capability. This is illustrated in Fig. 5 for the case of the input series buck-boost-, boost- and buck-converter. Note that as in the traditional buck and boost converter, by switching the input and output ports, the buck-becomes a boost-converter and vice versa.
By substituting (40) into (38), Eq. (38) can be rewritten as
Interleaving structures d y ¼ uL ; dt
(41)
In order to address system uncertainties, the following integrator can be added d ¼ xI ¼ iav iref dt
(42)
where iref is the reference or the desired inductor current. By employing Eqs. (41) and (42), the following linear subsystem is obtained
Another interesting configuration of the buck-boost inputseries converter is the interleaved technique, which has proved to be useful for increasing the power density in switching converters. The interleaving technique consists in connecting two or more converters in parallel to cancel the input current by shifting the switching function in transistors. This section proposes an interleaving connection for the input-series buck-boost converter as shown in Fig. 6, where the corresponding relevant waveforms are also illustrated. It
Please cite this article in press as: Valdez-Resendiz JE, et al., Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.10.077
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Fig. 4 e The family of series-input converters.
Fig. 5 e Bidirectional input-series converters. can be seen that since the inductor current provides the inputripple current, by shifting an inductor-current, its ripple cancels out the other inductor current-ripple when added. Consequently, smaller inductors can be used to achieve the desired input current-ripple.
Experimental results A converter prototype was built to validate the proposed characteristics. The prototype is shown in Fig. 7 and its parameters are displayed in Table 1. The test bed that includes the proposed converter and the fuel cell stack is shown in Fig. 8. A resistor bank was used as a load and the Texas Instrument microcontroller TMS320F28377S was used as a controller device. The experimental performance of the converter was tested using a 100 W PEMFC stack of Horizon Technologies, whose technical specifications are provided in Table 2. This PEMFC stack is open-cathode and uses forced ventilation for the oxygen supply and temperature control.
Open-loop experiments Experimental results in open loop that show the characteristics of the continuous input-current and the input voltage of the converter are shown in Fig. 9. Note that the input current is in continuous conduction mode with a current ripple
Fig. 6 e Interleaved 2x input-series buck-boost converter.
Fig. 7 e Experimental prototype.
Please cite this article in press as: Valdez-Resendiz JE, et al., Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.10.077
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Table 1 e Parameters of the experimental prototype. Parameter-Component Maximum power Input voltage range Output voltage range Switching frequency MOSFET Diode Capacitor Inductor
Value and information 150 W 11e14 V 8e18 V 50 kHz IRFIZ44N, 55 V, 31 A, RDSON ¼ 24 mU MBR1560CT, 60 V, 20 A, Fv 0.75 V 22 mF, 250 V, ESR 14 mU 150 mH, 5 A, ESR 50 mU
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approximately equal to 1A. The input power of the converter is equal to 18:8W. In Fig. 10 we show the traces of the output voltage and output current, where the output power, i.e. the power dissipated by the load, is equal to 18W. A duty cycle of 60% was used for the PWM switching signal. Note that the output voltage gain coincides with the theoretical value (3) of 1.5 for a duty cycle of 60%. The efficiency of the converter in this operating condition is h ¼ 94:14%. Fig. 11 depicts the experimental input voltage/current waveforms in a different operation region. The current input in this operating condition is in continuous conduction mode. Moreover, the input-current ripple is nearly 1A despite of the fact that the load has been increased more than twice. Fig. 12 shows the output voltage/current experimental waveforms with 60% of duty cycle. The input power in this operating condition is of 51:95W. The ratio between the input and output voltage is almost the same (i.e. 1.5) with respect to the experiment in Figs. 9 and 10, with a duty cycle of 60%. The output power of the converter is equal to 45W, and the efficiency is h ¼ 86:7%. The output-voltage ripple increased due to
Fig. 8 e Experimental test bed.
Table 2 e Technical specifications for the H-100 PEMFC stack. Parameter
Value and information
Rated power Number of cells Rated voltage Rated current Reactants Max stack temperature H2 pressure Hydrogen purity Humidification Cooling
100 W 20 12 V 8.3 A Hydrogen and air 65 C 0.45 0.55 bar 99.995% dry H2 Self-humidified Air (integrated cooling fan)
Fig. 9 e Input current/voltage characteristics of the proposed converter with output power equal to 18W.
Fig. 10 e Output current/voltage characteristics of the proposed converter with output power equal to 18W.
Fig. 11 e Input current/voltage characteristics of the proposed converter with output power equal to 45W.
Please cite this article in press as: Valdez-Resendiz JE, et al., Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.10.077
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Fig. 12 e Output current/voltage characteristics of the proposed converter with output power equal to 45W.
the increase of the resistive-load power. However, the outputcurrent ripple is negligible. The experimental polarization curve for the H-100 PEMFC stack was obtained and is shown in Fig. 13.
Fig. 15 e Experimental results of the closed-loop capacitor voltage vav with different set-points for the controlled inductor current (iref ¼0.5,1,1.5).
Closed-loop experiments In order to evaluate the performance of the controller in closed-loop operation, the control law given in Eq. (40) was also implemented. Figs. 14 and 15 show the experimental results of the closed-loop system. The experimental setup was carried out by employing RTAI-Lab which is a Linux-based real-time platform. In addition, a data acquisition card PCI6024E was used as interface between the real-time software platform and the converter. The set-point for the inductor current is changed several times during the experiment by employing the real-time user interface.
Conclusions
Fig. 13 e Experimental polarization curve for the PEMFC stack.
Fig. 14 e Experimental results of the closed-loop inductor current ia v with different set-points (iref ¼0.5,1,1.5).
We introduced a novel buck-boost DC-DC converter topology that provides a continuous input current and a simple structure. The discussed topology provides an output that is a series connection of the input and one capacitor whose voltage is regulated through the switching stage by a PWM. We showed how other converters can be derived in the same way such as the buck and boost converter, those converters can be called input-series converters due to the series connection of the input voltage with the voltage-controlled capacitor. Besides the proposed application on fuel cell generation systems, the input-series buck-boost converter that was proposed can be used for voltage regulation in portable devices where the battery is discharging and the voltage regulator needs to operate within a wide voltage range. This paper also proposes an interleaving connection of the series-input buck-boost converter for reducing passive components size and the input current ripple. The usefulness of the proposed average large signal dynamic model is shown with the experimental results of a current mode control. A stability analysis as well as open and closed loop experiments were provided in order to validate the theoretical analysis.
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Acknowledgments This work was supported by Universidad Panamericana Campus Guadalajara, through the program Fomento a la Investigacion UP 2016, project UPCI-2016-FING-02 “Estudio de n de rizo de corriente, convertidores de cd-cd con cancelacio Mexico. J.E Valdez-Resendiz and J.C Mayo-Maldonado want to thank CONACyT and the Mexican Ministry of Energy (SENER) for their funding support under the project #266632, “Laboratorio Binacional para la Gestion Inteligente de la Sustentabilidad Energetica y la Formacion Tecnologica”, fondo sectorial de sustentabilidad energetica.
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