Voltage and Current-Mode Control for a Multi-phase Bi-directional DC-DC Converter

Mitja Truntič, Miran Rodič, Miro Milanovič

University of Maribor FERI, Smetanova 17, 2000-SI Maribor, Slovenia mitja.truntic@uni-mb.si, miran.rodic@uni-mb.si, milanovic@uni-mb.si

Abstract-This paper describes a completely digitally controlled bidirectional multi-phase dc-dc converter capable to operate in buck-and boost mode. All necessary tasks are performed within a FPGA circuitry. The voltage and current mode control is based on a voltage to frequency converter (u/f), also called voltage control oscillator (VCO), performing measurements of input/output-voltages and inductor-currents, respectively. This measurement principle uses digital counters (digital integrators) in order to obtain the average values of the output-voltages and inductor-currents. In analogue current-mode control the instantaneous current-value-measurement is used for the switching action. In case of using VCO measurement principle the digital equivalents of average values of input/output voltages and all measured currents will appear in the counter, which is the part of FPGA unit. All other tasks, like control algorithm and pulse width modulation, were also implemented within the FPGA. This approach enabled programmability and configurability of the control tasks. The proposed approach was verified experimentally.

I. INTRODUCTION

Digitally-controlled pulse-width modulation (PWM) converters have several potential advantages, including programmability, robustness to parameter variations, reduction of external passive components, as well as the potential to apply more advanced algorithms for control and protection. When using microprocessors, their computing capabilities are to slow for calculating the necessary time-critical calculations, required in the control algorithm during the switching-period. Advances in digital technology prompted some research groups to use Field-Programmable Gate Arrays (FPGA's) or Digital Signal Processors (DSP's) [1]-[11]. The Field-Programmable Gate Array's applications are well described in survey [12] where the authors addresses various research fields which can exploit the advantages of FPGA's. Usually the voltage control-loop is superior and it is realized by conventional (P or PI) controller which generates the reference current for the inferior current-control loop. The current-mode control, proposed in [9], suggests that the switch or the inductor current is performed within an inner-loop, and replaces the conventional PI controller and saw-tooth generator which are necessary for the Pulse Width Modulation (PWM) function. Such approaches were used within the continuous time domain with the analogue hardware traditionally, but recently some algorithms have been developed based on an instantaneous current measurement and prediction strategy [13], [14]. According to the digital-control approach, the current must be sampled at

least twice during the switching-period in order to perform the DC-DC converter control function; whereas the actual trajectory of the inductor current is unknown to the controller. Some research work has been done in the digitalization area where the prediction method is used. The inductor current was sampled at least twice, when the current was rising or falling, as is discussed in [14]. By using such an algorithm, the peak or valley current-mode control could be applied.

This paper explores a digital average voltage and current-mode control for a bi-directional dc-dc converter based on the average value of output-voltage and inductor-currents measurements, by using a voltage-controlled oscillator and digital counter for these purposes. Parallel bi-directional DC-DC converters gained popularity in several applications where the currents are relatively high and the required current ripple should be as small as possible. For example, this is the case in the electric and hybrid vehicles, where the battery or super-capacitors provide the source and at the same time storage of electric power. By using the parallel structure, current in each parallel leg is lower (total current divided by the number of legs), and additionally the current ripple is reduced by the phase introduced into the switching command signal of power switches. Thereby the switching frequency is increased without increasing the switching losses, thus enabling the reduced size and weight of inductors used [15], [16]. It is important to note, that the switching command signals of the legs should be synchronized and delayed for the switching period divided by the number of legs in order to assure the uniform frequency. However, this can be easily performed with any kind of digital realization .

An example of bi-directional DC-DC converter and its control, realized by FPGA, is presented in the following text. Section II presents operating principle and theoretical analysis of the average voltage and inductor currents measurements. Section III discusses the FPGA implementation of the whole system, including signal conditioning, voltage and current controllers, and the necessary synchronization procedure. Also, the set-up bench is described there. Some chapters in section III are devoted to the discussion of the experimental results obtained when converter operates in buck or boost mode, respectively. The algorithm was investigated theoretically, and verified by experimentation.

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II. THE CONVERTER OPERATION

The bi-directional multi-phase DC-DC converter is shown in Fig. 1. By using appropriate switching strategy the power flow can be bi-directional. The chosen converter consists of four legs (half-bridge circuits) and four inductors. Power conversion was realized with the control of inductor currents and voltages. Due to demanded digitalization, voltages and currents were measured by using voltage to frequency converters (VCO) instead of the classical A/D converters as suggested in [13]. In order to reach bi-directionality, two voltages (Ubat and Udc) and four inductor currents (iL1, iL2, iL3 and iL4) must be measured and controlled as shown in Fig. 1.

A. Principle of operation

Block diagram of a cascade-controlled analogue voltage and current-mode control scheme of the multi-phase bi-directional DC-DC converter, is shown in Fig. 1. The current reference iref is obtained as an output signal of the voltage controller (boost or buck voltage controller). The current-mode control scheme is used instead of controller and PWM (pulse width modulator). Every leg (two transistors) is equipped with comparator (C) and R-S flip-flop. The Q output of flip-flop is set to “high” state when clock pulse cli appears. The comparator compares the inductor current iL with the current reference signal iref. The resulting signal is led to the reset R input of the R-S flip-flop in order to set its output Q to “low” state and generate the triggering pulse for the transistor Tri. Digitalization principle that is considered here enables and/or also provides the current's information during the sampling interval. Voltage-to-frequency converters (VCOs) and digital counters were used instead of classical A/D converters. The counter counts (integrates) inductor current during two time-intervals, first during Toff and second during Ton, as indicated in diagrams in Fig. 3.

B. VCO based current and voltage measurement

Fig. 2 shows the used measurement principles. Inductor currents and capacitor voltages signals are preconditioned

Fig. 1: Multi-phase bi-directional DC-DC converter.

with the use of amplifiers (Ai and Au) in order to obtain appropriate signal measuring range and offsets. Due to bi-directional converter operation the information about inductor current flow (sign) is needed, which is provided by amplifier (zero comparator Asi). Mathematical analysis will be performed for one converter leg. The inductor current has the same waveform in the case of boost or buck conversions. The instantaneous VCO frequency of these pulses (fi), can be calculated from:

0i i Lf kAi t f , (1)

where f0 represents the offset frequency, and k is the VCO constant (for the chosen VCO circuit, f0=23.5MHz and k=44.1MHz/V). Voltage L i Lu Ai appears on the VCO input after the inductor current has been measured by the Hall-principle based sensor and amplified with the constant Ai. On the other hand, the inductor-current can be described as a combination of two linear functions, as follows:

max 1

min 2

; when

; when L

i a t Tr OFFi t

i a t Tr ON

, (2)

Fig. 2: Measurement system

Fig. 3: The typical waveforms: iL-inductor current; VCO signal fi, current reference iref and contain of counter depending on the time IL(dig), clock pulse cl., and transistor triggering pulse (t)

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Fig. 4: The voltage measurement waveforms: udc-(or ubat) voltage; fu - VCO output signal, Udc(dig)-(or Ubat(dig)) contents of counter (average output voltage); cl-flip- flop clock signal.

where the maximum inductor current is indicated by imax, and minimum by imin (Fig. 3). Coefficients a1 and a2 depend on the circuit parameters as follows, in buck case

1 dc bata U U L , and 2 bata U L and in boost case

1 dca U L and 2 dc bata U U L . When (2) is introduced into (1) it follows:

max 1 0 0 1

min 2 0 1 2

when ,

when

;

; ,

i

i

i

kA i a t f t t tf

kA i a t f t t t

. (3)

So the inductor current average value is now evaluated as:

2 1

0 0

2

1

max 1 0

min 2 0

1 1t t

L i it ts s

t

it

I f t dt kA i a t f dtT T

kA i a t f dt

, (4)

which can be rewritten as: s L off on iT I Z Z Z , (5)

where: and

2

1min 2 0

t

on itZ kA i a t f dt .

At the end of the sampling intervals the inductor current average value IL(dig)will appear in the counter. Voltage measurement was performed by using the same principle. Referring to Fig. 4, in the steady-state the voltage control function starts when the clock-pulse cl. appears. The VCO converts the measured voltage into frequency:

0u u dcf A u t f , (6)

where Au is measurement resistor attenuation and amplifier gain, f0 is the VCO offset frequency, and voltage (udc(t) or ubat(t)) is considered to be constant over the interval Ts (RC >> Ts).

2 2

0 00 0

1 1t t

u u dct ts s

U f t dt A u t f dtT T

, (7)

which can be rewritten as:

2

00 0

t

s u u dctT U Z A u t f dt . (8)

It should be emphasized that the results of the currents and voltages measurements will appear when measurement procedure has been finished according to intervals as shown in Fig. 3 and Fig. 4, at the counters as Zi and Zu.

III. EXPERIMENTAL SET-UP BENCH

The bi-directional DC-DC converter was designed with four modules. Every module is equipped with the galvanic isolated drivers (for triggering the transistors) and measurement units where the inductor current and also the input and output voltages are measured. Fig. 5 (a) and (b) shows the half-bridge structure and its experimental PCB. The control unit is designed in order to apply all proposed procedures for measurement control and PWM algorithm. The FPGA based control unit is shown in Fig. 6. The whole system was built

(a) (b) Fig. 5. Single half bridge for multi-phase bi-directional DC-DC converter; (a) block scheme; (b) module of half-bridge.

Fig. 6: FPGA-based control unit for multi-phase bi-directional DC-DC converter.

Fig. 7: FPGA-based control unit for multi-phase bi-directional DC-DC converter.

1

0max 1 0

t

off itZ kA i a t f dt

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Fig.8: Multi-phase bi-directional DC-DC converter in buck mode of operation

and Fig. 7 shows the experimental set-up bench appropriate for experimentation.

A. Converter operation in Buck mode

Bi-directional converter was first investigated under the buck mode of operation as shown Fig. 8. In the system of DC-DC converter the current mode controller is implemented instead of the PI current controller and PWM unit.

An undesirable limit-cycle oscillation can occur as presented in [17], [18] if resolution of "PWM" is not high enough. In particular, if none of the achievable output voltages falls within the range of ubat around the reference, in steady-state the duty ratio must oscillate through a range of two or more values. A necessary condition for avoiding limit-cycle oscillation is that the output-voltage increment that corresponds to the least-significant bit of the duty-ratio command must be smaller than ubat. A high-resolution digital PWM can be constructed in different ways. In [11] and [20], authors propose a hybrid digital pulse-width modulator based on the delay-cell in the ring-oscillator. This principle enables the lower clock-frequency, as follows from [17]. It also requires more gates from FPGA in order to perform the PWM. The principle described in [18] has been applied due to this reason and due to the available member of gate arrays. Usually, the components of PWM are the fast clock-counter and digital comparator. In order to achieve n-bit resolution at the frequency of fs, the required clock-frequency must be 2nxfs. The selected current-controller scheme is shown in Fig. 9. An experimental set-up of multi-phase bi-directional DC-DC converter and appropriate FPGA interface card was built based on the proposed principle. The current-mode control in buck operation mode was verified by experiments. The converter was designed with following parameters: switching frequency fs = 25 kHz, inductors L1-4 = 1.2 mH, battery capacitors Cbat = 110 F, dc-bus capacitors Cdc = 880 F. For the calculation of current reference the cascade-control structure was used, which was calculated by the voltage controller.

Fig.9: (a) Digital implementation of current-mode controller; (b) Synchronization signals for voltage control: cl.- flip-flop clock signal; Q- flip-flop output signal.

Fig. 10: Measured output voltage Ubat, current Ib and inductor currents IL1 to IL4 during the start-up of multi-phase bi-directional DC-DC converter, Udc=90V, R=30

Fig. 10 shows the start-up response of bi-directional DC-DC converter output voltage, inductor currents and output current in the buck mode operation of the converter. The voltage reference was set to Ubat = 40V at the input voltage of Udc = 90V.

Fig. 11 shows close-ups of the battery voltage and inductor currents during the steady state operation. The currents between legs are shifted by 90°, whereby the current ripple is reduced at the output and operational frequency of the multi-phase converter is raised by four times compared with the switching frequency of one leg. The transient response to load resistance change from R = 30Ω to14Ω is shown in Fig.12. The voltage dynamic error was ± 5.5%.

B. Converter operation in Boost Mode

Further bi-directional DC-DC converter was also investigated in boost mode of operation as shown Fig. 13. Fig. 14 shows the response of bi-directional DC-DC when the voltage reference was changed from 60V to 90V. The voltage dynamic error was ± 4.5%. The operation of the bi-directional converter in steady- state is shown in Fig. 15 where the output current and voltage along with four inductor currents transient responses are presented.

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Transient response of the converter when the load resistance was changed from R = 30Ω to14Ω is shown in Fig. 16, where the inductor currents, output voltage and current are measured. The dynamic error was ± 5.5% and a static error is present.

Fig. 11: Measured output voltage Ubat, and inductor current IL1 to IL4 during the steady-state of multi-phase bi-directional DC-DC converter, Udc=90V, R=14

Fig. 12: Measured output voltage Ubat, and inductor current IL1 to IL4 during the transient when load was changed from R=30 to R=14and input voltage was Udc=90V.

Fig. 13: Multi-phase bi-directional DC-DC converter operated in boost mode.

Fig. 14: Measured output voltage Udc, load current Idc and inductor current IL1 to IL4 during the transient when reference voltage was changed from Udc=60V to Udc=90V load was R=14and the input voltage was Ubat=40V.

Fig. 15: Measured steady-state operation of the converter during the steady-state operation where the input voltage was Ubat=40V, output voltage vas Udc=90V with the load R=14connected to the converter.

Fig. 16: Measured output voltage Udc, load current Idc and inductor current IL1 to IL4 during the load transient form R=30to R=15Input voltage was Ubat=40V and the output voltage was set to Udc=90V.

CONCLUSION

A current-mode control algorithm for continuous current mode (CCM) operation was presented for multi-phase bi-directional DC-DC converter. This current-mode control algorithm is suitable for digital realization. The average current control technique was designed based on the sampled values of inductor currents. Signals are measured by using the VCOs. The analytical form of the digital-integration processes required in order to achieve the average voltage and current values has been derived. Such an approach is suitable

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for the implementation of all algorithms within the FPGA circuit. The proposed digital control technique can be used for the range of DC-DC converters, including buck, boost and buck-boost. It is, therefore, adequate for many industrial applications such as high-power multi-phase DC-DC converters.

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