Power Sharing in a Double-Input Buck Converter Using Dead-Time ...

Power Sharing in a Double-Input Buck Converter Using Dead-Time Control Venkata Anand K. Prabhala

Deepak Somayajula

Mehdi Ferdowsi

Student Member, IEEE Missouri S&T 301 W. 16th Street Rolla, MO 65409, USA [email protected]

Student Member, IEEE Missouri S&T 301 W. 16th Street Rolla, MO 65409, USA [email protected]

Member, IEEE Missouri S&T 301 W. 16th Street Rolla, MO 65409, USA [email protected]

Abstract—Multi-input converters are becoming important in various renewable energy applications like wind energy, fuel cell systems, photovoltaic systems, and hybrid electric vehicles. In this paper, it is shown that in a double-input buck converter the dead-time of the switch commands along with the two duty ratios will have a direct impact on the amount of current drawn from the sources/inputs. This dead-time is used as an additional control variable apart from the switch commands to meet the control objective of meeting a constant load demand when the source currents are varying which is very common in hybrid energy systems. Theoretical derivations agree well with the simulation results. The new control method has good dynamic response and improves the speed of the system. Index Terms—Dead-time control, Multi-input converter, Multi-port converter

I. INTRODUCTION Multi-input converters can provide great advantages in hybrid energy systems including wind, solar, fuel cells, and electric-drive vehicles which have multiple energy sources. Renewable energy sources tend to be intermittent and therefore they need to be combined or hybridized with more reliable sources of energy to cater to a common load. The sources in hybrid energy systems are interfaced with the load through a dc-dc power electronic converter. However, hybridizing energy sources is more efficient utilizing a single dc-dc multi-input converter supplying a common load. As it has been reported in the literature [1-12], hybridizing energy sources with a single multi-input dc-dc converter reduces the cost and component count. It is also easier to regulate the output voltage of a dc-dc multi-input converter when compared to several separate single-input dc-dc converters operating in parallel [1]. Various methods of developing and synthesizing multiinput converter topologies as well as their advantages are presented in [2-5]. Different kinds of multi-input topologies for various renewable applications are developed in [6-13] and a comparison between them is presented in [14] to help in choosing the appropriate topology based on the application. In [15], various multi-input converters are compared based on their cost, modularity potential, and reliability. In [16], a control strategy is proposed to minimize the inductor current ripple in a double-input (DI) buck

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converter. It is shown that having a delay between the switch commands would reduce the inductor current ripple and the delay is optimized for minimum inductor current ripple. In [17, 18], two different topologies of the DI buck converter are proposed which have the same output voltage equation but differ slightly in terms of the modes of operation. In [19], a DI buck converter is used for power factor correction. The concept of controlling the input currents of the DI buck converter is yet to be explored and this is really important in hybrid energy systems like the hybrid electric vehicles and photovoltaic systems which may have a battery/ultra-capacitor combination or grid/solar combination in the energy storage system [18]. In such a system the control objective generally is to increase the battery current reference when the ultra-capacitor state of charge decreases for a constant power load such that the load demand is met. Also in a grid/solar hybrid energy system when there is a decrease in the solar radiation the amount of power supplied by the PV array decreases and the amount of power supplied from grid or the reference current of the grid needs to increase to meet the required load demand. In this paper, it is shown that in a DI buck converter the dead-time between the two switching commands directly affects the input currents. Therefore, this dead-time can be used as the third control input in addition to the two duty ratios. Using this additional control input improves the dynamic performance of the system. The newly devised control method hereinafter is called dead-time control. Offset-time control, a simpler version of the proposed control method, has been discussed and applied to a DI buckboost converter in [20]. Unlike the DI buckboost converter, the DI buck converter does not have a mode restriction and therefore the control method presented here is more general which can easily be extended to other DI topologies. In section II, the DI buck converter topology is briefly introduced and the control equations for dead-time control in various modes of operation are presented in sub-sections II (A) and II (B), respectively. In sub-section II (C) the implementation of the dead-time control scheme is explained; simulation results and analysis is presented in section III and section IV includes the concluding remarks.

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Fig. 1. Circuit diagram of the restricted DI buck converter [3, 4].

Fig. 2. Circuit diagram of the non-restricted DI buck converter [3, 5].

TABLE I MODES OF OPERATION OF A DI RESTRICTED BUCK CONVERTER Mode S1 S2 VD VL

TABLE II MODES OF OPERATION OF A DI BUCK CONVERTER VD1 S1 S2 VL

I

On

Off

V1-Vo

-V1

Mode I

On

Off

V1-Vo

VD2

-V1

0

II

Off

On

V2-Vo

-V2

II

Off

On

V2-Vo

0

-V2

III

Off

Off

-Vo

0

III

Off

Off

-Vo

0

0

IV

On

On

IV

On

On

V1+V2-Vo

-V1

-V2

Not allowed

II. DOUBLE-INPUT BUCK CONVERTER Two different topologies for the DI buck converter are discussed in [3-5, 16-18]. The circuit diagram of a restricted DI buck converter is shown in Fig. 1 [4, 17]. This topology has a mode restriction and the inductor cannot be energized by both of the sources at the same time. In other words, both switches S1 and S2 cannot be ON at the same time [17]. The modes of operation of the restricted DI buck converter are shown in Table I. In Fig. 2, the circuit diagram of the nonrestricted DI buck converter topology is presented [5, 18]. The modes of operation of this topology are shown in Table II and it can be seen that both of the switches can be ON at the same time [18]. In this paper, the non-restricted DI buck converter is considered for the development of the dead-time control scheme. The results can easily be extended to the restricted topology as a special case. For both topologies, the steady-state input-output voltage relationship is Vout = D1V1 + D2V2 (1) where D1 and D2 are the on-time duty ratios of switches S1 and S2, respectively. Average inductor current IL for a resistive load R is equal to iL = I L = Vout R . (2) The ratio between average switch current is1 and is2 is defined as α. Or i α = s1 (3) is 2

A. Dead-Time Control Scheme Considering Modes I, II, and III Modes I, II and III are common in both topologies. The equations in this sub-section are developed based on the assumption that the operation of the converters is restricted to these three modes. The steady-state inductor current waveform in this case is shown in Fig. 3. It is clear that D1+D12+D2+D21=1. Using this figure and Table I one can write i max 1 = i min 1 +

(V 1 − V out ) D 1T L

imax 2 = imin1 +

Vout D21T L

(4) (5)

(V2 − Vout ) D2T L (6) (V − Vout ) V = imin1 + out D21T − 2 D 2T L L Equations (4), (5), and (6) describe imax1, imax2, and imin2 as functions of imin1 which is the inductor current at the beginning of the switching cycle. If one tries to find the average inductor current in Fig. 3, they should find the area of the four trapezoids. Using (4), (5), and (6) in this procedure leads to T imin1 = iL − [(V1 − Vout )( D12 + D1 D12 ) 2L (7) +(V2 − Vout )(− D2 2 − D2 D12 )

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imin 2 = imax 2 −

+Vout ( D12 D21 + 2 D2 D21 + D212 )]

iL imax1 imax2 imin2 imin1

imin1

D1T

D12T

D2T

D21T

I

III

II

III

T

Fig. 3. Steady-state inductor current waveform for modes I, II, and III.

Fig. 4. Steady-state inductor current waveform when mode IV is also included.

Equations (4), (5), (6), (7) indicate that imax1, imax2, imin1, and imin2 all depend D21T which is named as the dead-time. Now, the average current equations for sources V1 and V2 can be derived. Average switch currents and can be described by the following equations

Similar to the previous sub-section, one can find imin1 by attempting to find the average inductor current using (10), (11), and (12). V (1 − D1 ) imin1 = iL − out T 2L (13) V D (2 − D1 − D2 ) VDD + 2 2 T − 2 2 21 T 2L L Also, the average current supplied by each voltage source can be described as

is1 = ( imax 1 + imin1 )

D1 2

(8)

is 2 = (imax 2 + imin 2 )

D2 2

(9)

Considering (8) and (9), it can be concluded that dead-time D21T can be used to control the average value of input currents and . Consequently, α can be controlled as well. Therefore, it can be concluded that D21 can be used as a control variable when the ratio between the input currents is desired to be controlled. B. Dead-Time Control Scheme Considering Modes I, II, III, and IV The inductor current waveform when mode IV is also included is depicted in Fig. 4. Mode IV only takes place in the non-restricted DI buck converter when the conduction of the switches overlaps. In this mode both of the switches are ON for the overlap time D12T. The average current equations are derived from the inductor current waveform. It is clear that D1-D12+D2+D21=1. Using Fig. 4 and Table II one can write (V − V ) imin 2 = imin1 + 1 out (1 − D21 − D2 )T (10) L (V1 + V2 − Vout ) D12T L (V − V ) = imin1 + 1 out (1 − D21 − D2 )T L (V1 + V2 − Vout ) D12T + L

imax1 = imin 2 +

(11)

Vout D21T (12) L Equations (10), (11), and (12) describe imin2, imax1, and imax2 as functions of imin1 which is the inductor current at the beginning of the switching cycle. imax 2 = imin1 +

is1 = imin1 D1 +

(V1 − Vout ) D12 T 2L

V + 2 ( D1 + D2 + D21 − 1)2 T 2L

(14)

(V2 − Vout ) D2 2 (V − V ) D D T + 1 out 1 2 T 2L L Vout D2 ( D1 + D2 + D21 − 1) + T (15) L V ( D + D2 + D21 − 1) 2 − 1 1 T 2L From (13), (14), and (15), it can be observed that average switch currents and are related to imin1 which in turn is related to dead-time D21T. Thus, it can be concluded that average switch currents are dependent on the dead-time D21T even in Mode IV. is 2 = imin1 D2 +

C.

Implementation of Dead-Time Control The dead-time control scheme for the non-restricted DI buck converter is implemented by using D21 as an extra control variable. The control objective of regulating output voltage Vout while average source currents and are controlled can be achieved with the help of a voltage compensator, a current compensator, and a dead-time compensator which will regulate the dead-time D21T. The block diagram of the system is shown in Fig. 5. Switch currents is1 and is2 are sensed and fed to the current compensator and the dead-time compensator. In the deadtime compensator, the measured current values are converted into average values and . Alpha (α) is calculated for each cycle as / and compared with the αref value

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which is Iref1/. The current compensator is used to regulate the average current to the reference value of Iref1 through the control of duty ratio D1 and the value of Iref1 is varied by a system level controller when the power supplied by the second source varies. The voltage compensator is used to regulate output voltage Vout to a constant value through the control of duty ratio D2. The control signals for D2 and D21 are passed through PWM2 block in which a negative-slope ramp is used to generate the pulses S2 and S21. However, PWM1 block is a conventional PWM block with a positive-slope ramp being compared with the control voltage of D1 to generate the switch command S1. III. SIMULATION RESULTS

6000 G c1 ( s ) = s

s ⎛ ⎜ 1+ 6 π * 500 ⎜ s ⎜ ⎜1+ 6 π * 8000 ⎝

⎞ ⎟ ⎟ ⎟ ⎟ ⎠

s s ⎞ ⎛ ⎞⎛ ⎟ ⎜ 1+ ⎟⎜ 1 + 400 ⎜ π π 2 * 1000 2 * 1000 ⎟ ⎟⎜ Gc 2 ( s) = s s ⎟ ⎟⎜ s ⎜ ⎟ ⎜1+ ⎟⎜ 1 + ⎝ 2π * 50000 ⎠⎝ 2π * 50000 ⎠

First, the converter is simulated with only dead-time control loop closed and V1=75, V2=60, f=50 kHz, D1=0.4, D2=0.4, Vout=54 V, L=100 µH, C=50 µF, and R=15 Ω remain constant. For a step change in αref from points A2 (αref =0.9) to point A1 (αref =1.3) as shown in Fig. 6, the response of α is depicted in Fig. 7. The system is then simulated with only

Fig. 5. Block diagram of the overall system. 3

D 1 =0.4, D 2 =0.4 in Overlap region

2.75

D 1 =0.4, D 2 =0.4, Vout=54V D 1 =0.45, D 2 =0.3375 in Overlap region

2.5

D 1 =0.45, D 2 =0.3375, Vout=54V

2.25

D 1 =0.4, D 2 =0.4 in Overlap region

2

Alpha (α)

The relationship between α and dead-time D21 is depicted in Fig. 6. In this figure, the duty ratios are selected in a way that the output voltage remains constant. As it can be observed, there are two regions of operation which are 1) the restricted (non-overlap) region which is represented by the thin curve and 2) the non-restricted (overlap) region which is represented by the thick curve. In the non-overlap region, the system operates in modes I, II, and III and the relation between α and D21 are based on the equations derived in subsection II(A). In the overlap region, the system operates in modes I, II, III, and IV and the relation between α and D21 derived in sub-section II(B). It must be noted that when the dead-time control scheme is used for the non-restricted DI buck converter, shown in Fig. 2, the system can operate in both overlap and non-overlap regions. Therefore, the deadtime control benefits from an extended range. Only the negative slope regions of the curves in Fig. 6 are used in control implementation. This negative slope is the reason that a negative-ramp PWM scheme is chosen for PWM2 block. The following compensators are used to control the system: dead-time compensator (10,000/s), a current compensator Gc1(s) and a voltage compensator Gc2(s) are used whose transfer functions are:

D 1 =0.4, D 2 =0.4, Vout=54V

Non-overlap Region

1.75 Overlap Region

1.5 1.25 1

A 1=1.3

0.75 0.5

A2 =0.9 Amin

0.25 0

0.1

0.2

0.3

D

0.4

0.5

0.6

0.7

21

Fig. 6. α vs. D21 for the non-restricted DI buck topology.

two of the three control variables D1 and D2 being controlled for a constant load of 25 Ω, Vref=54 V and for a partial shading or decrease in state of charge situation where the Iref1 decreases from 1 A to 0.5 A. The same test is carried out with all the three control variables controlled, i.e., D1, D2 and D21 and in this case also Vref=54 V and Iref1 decreases from 1 A to 0.5 A. The average switch currents Is1, Is2 and the output voltage Vout waveforms for the system with and without dead-time control are compared in the Figs. 8, 9, and 10, respectively. It can be clearly seen from Figs. 8 and 9 that the Is1 is settling at the commanded currents of 1 A and 0.5 A and the other current Is2 is changing accordingly to meet the load demand. It can also be observed from Figs. 9 and 10 that the Is2 and Vout are settling much faster when dead-time control scheme is included in the system. And it can also be observed from Fig. 10 that the output voltage Vout has a lower overshoot for the case with dead-time control when compared to the case without dead-time control which clearly indicates that the dynamic performance of the system is improved when dead-time D21 is also controlled along with the switch commands D1 and D2. Therefore, though the control objective is achieved in both the cases including the

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dead-time control scheme speeds up the system and gives an extra degree of freedom in controlling the input currents of the system.

Alpha (α)

1.3

IV. CONCLUSIONS

1.1 1 0.9 0.8

0.01

0.012

0.014

0.016

0.018

Time (s)

0.02

0.022

Fig. 7. Dead-time D21 control for step change in αref from 0.9 to 1.3. 1.5

1

without D

S1

21

I

S1

with D

control

21

control

S1

(A)

I

I

In a DI buck converter the dead-time between the switch commands along with the two duty ratios is shown to have a direct impact on the amount of current drawn from the sources. The dead-time control gives an additional control variable apart from the switch commands to meet the control objective of regulating the output voltage and adjusting the amount of power supplied by the source when the power from the other source increases/decreases. The dead-time control scheme is effective in systems which have input current dynamics since the ratio of the switch currents is proportional to the dead-time and therefore, any variations in one input current would also vary the other input current and this would directly affect the ratio and the dead-time. The new control method also has good dynamic response and improves the speed of the system.

1.2

0.5

0

0.0145

0.015

0.0155

0.016

Time (s)

0.0165

0.017

Fig. 8. Average current of switch 1 Is1 waveform with and without Dead-time D21 control.

REFERENCES

1.5

1

I

S2

I 0.5

0

I 0.0145

0.015

S2

S2

0.0155

with D

21

without D

21

0.016

Time (s)

control control

0.0165

0.017

Fig. 9. Average current of switch 1 Is1 waveform with and without dead-time D21 control. 60

V

with D V

out

55

21

control

without D

21

control

out

(V)

out

V

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(A)

[1]

50

45

0.0145

0.015

0.0155

0.016

Time (s)

0.0165

0.017

0.0175

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