Study on a Highly Stabilized Power Supply for Hybrid

Plasma Science and Technology, Vol.16, No.9, Sep. 2014

Study on a Highly Stabilized Power Supply for Hybrid-MagnetSuperconducting Outsert∗

WU Jinglin (吴景林)1, LONG Jiaojiao (龙佼佼)2, LIU Xiaoning (刘小宁)2

1University of Science and Technology of China, Hefei 230026, China2High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China

Abstract The superconducting outsert of the 40 T hybrid-magnet in High Magnetic Field

Laboratory (HMFL) of Chinese Academy of Sciences (CAS) requires a highly stabilized power

supply. In this paper, two kinds of power supply design are briefly presented and both advantages

and disadvantages are analyzed. In order to overcome the drawbacks of switching power supply,

a series regulated active filter is adopted and a new design is proposed which ensures cooperative

relationship between the feedback control loops of the switching converter and the series regulated

active filter. Besides, unlike the traditional switching power supply, which can generate positive

voltage only, this new design can also generate negative voltage which is needed in the quench

protection for the superconducting magnet. In order to demonstrate the effectiveness of the

methodology, a low-power prototype has been accomplished. The simulation and experiment

results show that the power supply achieves high precision under the combined action of two

feedback control loops. The peak-to-peak amplitude of the output ripple voltage of the prototype

is 0.063%, while the peak-to-peak amplitude of the output ripple current is 120 ppm.

Keywords: superconducting magnet, switching power supply, series regulating, feedbackcontrol, quench protection

PACS: 84.70.+p, 52.50.−b

DOI: 10.1088/1009-0630/16/9/15

(Some figures may appear in colour only in the online journal)

1 Introduction

A highly magnetic field is an extreme environmentthat can be widely used for nuclear science, chemistry,biology, etc. Compared with the conventional mag-nets, superconducting magnets have much smaller vol-ume, much better flexibility and much higher efficiency.These features result in superconducting magnets be-ing used in various scientific equipment, especially inmagnetic confinement fusion devices such as Interna-tional Thermonuclear Experimental Reactor (ITER) [1]

and Experimental Advanced Superconducting Toka-mak (EAST) [2−4].

The hybrid-magnet superconducting outsert inHMFL requires an 8 V/14 kA power supply with highcurrent and voltage precision. The power supply isplanned to adopt two kinds of schemes. One is thesilicon-controlled rectifier (SCR) which is similar to thescheme used in EAST [5] and the other is the switchingpower supply.

This paper gives a brief account of both schemes anddescribes an improved scheme based on the switchingpower technology. The experimental results have illus-trated the feasibility of the improved scheme, which canthus provide a simple reference for the power supply

systems of other magnetic confinement fusion devices.

2 Original schemes

2.1 Dual reverse star-shaped SCRscheme

Fig. 1 shows the topology of a dual reverse star-shaped SCR. The secondary side of the transformerconsists of a pair of windings with equivalent turns andopposite polarity for each phase. The windings are con-nected to two three-phase half-wave rectifiers as shownin Fig. 1. SM is the superconducting magnet.

Lp1 and Lp2 in Fig. 1 are balance inductors whichalso function as filters. The balance inductors can en-sure that both the three-phase half-wave rectifiers op-erate at the same time so that this rectifier can outputdouble current, like a three-phase full-bridge rectifier,to meet the demand of high current.

With the help of voltage signals produced by syn-chronous transformer and feedback control loops, thephase shifter and thyristor trigger can produce pulseswith an appropriate delay angle which determines theaverage DC output voltage of the dual reverse star-

∗supported by National Natural Science Foundation of China (No. 50977086)

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WU Jinglin et al.: Study on a Highly Stabilized Power Supply for Hybrid-Magnet Superconducting Outsert

shaped SCR. Therefore, the power supply can respondrapidly to the changes of load currents or realize con-stant output.

The advantages of this solution are matured tech-nique, high reliability and high precision. However, thedisadvantages are low power factor, bulky and heavyequipment, etc.

Fig.1 Dual reverse star-shaped SCR topology

2.2 Switching power supply scheme

Fig. 2 shows the topology of switching power sup-ply. In this figure, Vgrid is the three-phase grid inputvoltage, D1-D6 are rectifier diodes, Lin is the input fil-ter inductance, Cin is the input filter capacitor, QA-QF

are power MOSFETs, Ls is the freewheel inductance,Lf is the input filter inductance, Cf is the input filtercapacitor.

Fig.2 Switching power supply topology

The input portion of the power supply is a three-phase full-bridge uncontrolled rectifier. Then there isa soft switching inverter. A saturated inductor is con-nected to the transformer primary coils in series. Mean-while, synchronous rectifiers are connected to trans-former secondary coils. In order to obtain high-poweroutput performance, the output portion of the powersupply adopts multiple rectifying circuits.

The high-frequency switch technology makes thepower supply smaller and more efficient, which alsoconforms to the development trend of magnetic con-finement fusion devices. However, because of the highripple in its output current/voltage, the original switch-ing power supply scheme cannot be directly used for thesuperconducting magnet.

3 Improved scheme based onswitching power technology

In order to reduce the output ripple, the passive fil-ter, if used alone, requires much larger output induc-

tance and capacitance, which will increase the cost andvolume of the device and exacerbate dynamic charac-teristics. Moreover, the low-frequency output ripplecannot be depressed effectively. Accordingly, an activefilter is usually added to the output of the switchingpower supply.

The improved scheme adopts a series regulator,which takes advantage of the on-resistance variabilityof adjusting transistors to depress the input voltage rip-ple and obtain extremely low output ripple voltage. Atpresent, the HMFL power supplies in USA, Holland andJapan have adopted this kind of active filter.

3.1 Selection of adjusting transistor ofseries regulator

In this paper, the output voltage of the power supplyis 8 V. If the voltage across adjusting transistor is high,the power loss of the series regulator will definitely im-pair the supply’s efficiency.

With the development of the power MOSFET, theminimum on-resistance (Rds) is measured to be of theorder of mΩ, which makes the drain-to-source voltage(Vds) remain low when the through-current of powerMOSFET is high.

Because of the positive temperature coefficient(PTC) characteristic of the MOSFET in steady con-ducting state, a rise in the temperature of one of theshunt MOSFETs will result in an increase in the re-sistance, which leads to the decrease of the currentand temperature of the MOSFET. Thereby, it is easyto implement automatic current-sharing control andachieve current equilibrium when the adjusting tran-sistor adopts MOSFETs in parallel connection.

3.2 Control solution in the improvedscheme

Fig. 3 shows a functional block diagram of the rou-tine series regulated switching power supply.

Fig.3 Routine series regulated switching power supply

Because the two feedback control loops in the figureare mutually independent, only the voltage across theadjusting transistor (Vds) can be regulated when theload changes suddenly. However, if the load change isgreat, Vds will change dramatically, which may damagethe adjusting transistor.

To solve the problem mentioned above, the improvedscheme designates Vds as a feedback parameter to con-trol the output of switching converter as shown in

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Fig.4 Improved feedback control system

Fig. 4. The feedback loop 1 adopts the single-loop volt-age control strategy while the feedback loop 2 adoptsthe double closed-loop control strategy, which consistsof an outer current loop and an inner voltage loop.

When the output current increases, the feedbackloop 2 will motivate VGS to decrease, which leads toan increase in Rds and Vds.

On one hand, the last output voltage can be acquiredas Fig. 4

Vo = V ′o − Vds. (1)

Therefore, an increase in Vds can result in a decreasein Vo.

On the other hand, the feedback loop 2, as Vds in-creases, will narrow the PWM pulse width, which leadsto a decrease in V ′

o and Vo as shown in Eq. (1).As Vo decreases, the output current will decrease too,

which makes the power supply approach to a steadystate.

The above analysis results show that the feedbackloop 1 and loop 2 act synergistically to stabilize theoutput.

4 The effect of improved schemein quench protection

During a quench, the tremendous energy stored inthe superconducting magnet can be converted into heat.If there are no discharge circuits, the thermal stresscaused by the local over-heating may damage the mag-net. Moreover, the high voltage rise caused by thequench may lead to dielectric breakdown. Therefore,it is extremely important to introduce a quench protec-tion circuit [6].

Fig. 5 shows a basic quench protection circuit. Inthis figure, DS represents the fast DC circuit breaker,Re the dump resistor, Rp the grounding resistor for themagnet, and SM the superconducting magnet.

Fig.5 Quench protection circuit

If the current passing through the coils of the super-conducting magnet (Ism) is very high when the magnetquenches, no matter what is the design of the powersupply, the DS contact must be interrupted, and theenergy stored in the superconducting magnet shouldbe consumed on the dump resistor.

If a dual reverse star-shaped SCR is adopted, a neg-ative voltage (−Uo) can be generated by the inverter.Meanwhile, −Uo can be expressed as:

−Uo = Lsmdi

dt, (2)

where Lsm represents magnet inductance.The period of time that Ism drops from I to 0 A

during a quench is:

t = I/(−di

dt). (3)

In case of a quench, I2t must be smaller than M toprotect the magnet from damage. Therefore:

∫ t

0

(I +di

dtt)2dt =

∫ I LsmUo

0

(I − U

Lsmt)2dt < M. (4)

We obtain:

I < 3

√3UoM

Lsm. (5)

Thus, if Ism accords with formula (5) when the magnetquenches, the negative voltage −Uo can force Ism to

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decrease linearly to realize a quench protection withoutthe operation of protective switches.

However, if the original switching power supply,which cannot generate a negative voltage, is adopted, itis impossible for Ism to decrease safely and controllablywithout the operation of protective switches even if Ism

accords with formula (5).In the improved scheme, if Ism is very low when the

magnet quenches, we can set the feedback control loop2 as Fig. 6 shows. The feedback voltage is the voltageacross the adjusting transistor and the reference voltagecan be calculated according to the demand of quenchprotection.

Fig.6 Another form of feedback loop 2

The two transistors on the secondary of transformerare turned on synchronously, then Vds can be oppositelyplaced across the magnet as Fig. 7 shows to realize acontrollable decrease of Ism.

Fig.7 Vds oppositely placed across the magnet

5 Development of prototype

Table 1 shows the circuit parameters’ values of thelow-power experimental prototype.

5.1 Design of feedback control loop 1

It is assumed that the feedback control loop 2 func-tions perfectly when feedback control loop 1 is takeninto account. Thus, the adjusting transistor could bemodelled as a fixed resistor Rds.

Ref. [7] introduced a small-signal model of a con-ventional full-bridge phase-shifted soft switching powersupply. Compared with the conventional scheme, a sat-urated inductor was connected to the transformer pri-mary coils in series and the load consisted of a resistorin series with an inductor. Through a similar analysisas performed in Ref. [7], some results can be concludedthat: ∧

deff =∧d +

∧di +

∧dv, (6)

∧di = −K ·Rd

Vin

∧ILf , (7)

Table 1. Circuit parameters’ values

Circuit parameters Values

Input voltage (three phase AC), Vin 380 VOutput voltage (DC), Vo 8 VOutput current (DC), Io 50 ASwitching frequency, fs 200 kHzPeak value of sawtooth wave, VM 2.8 VTransformer winding turns ratio, K 38Transformer leakage inductance, Llk 7.5 µHSaturated inductance, Ls 150 µHOutput filtering inductance, Lf 2 µHOutput filtering capacitance, Cf 7.5 mFEquivalent series resistance of Cf , ESR 1 mΩLoad inductance, Lo 10 µHDC load resistance, Ro 0.15 ΩReference voltage across adjusting 1 V

transistor, Vref

The ratio of sampling of voltage 1:1across adjusting transistor

The ratio of output voltage sampling 1:4The ratio of output current sampling 1:4

Rd =4Llkfs

K2, (8)

∧dv = [

Llk

K(2ILf − D′VoTs

2Lf) + 2LsIs]

fs

V 2in

∧Vin, (9)

where∧

deff is the modulation of effective duty cycle,∧d is

the modulation of duty cycle of the primary voltage,∧di

is the duty cycle modulation due to the change of the

filter inductor current (∧

ILf),∧dv is the duty cycle mod-

ulation due to the change of the input voltage (∧

Vin),D is the duty cycle of the primary voltage set by thecontrol, D′ = 1−D, and Is is the saturated current ofthe saturated inductor.

Based on the small signal model of the buck con-verter, a small signal model of the actual switchingpower supply, which is the main component of the ex-perimental prototype, is presented in Fig. 8.

Fig.8 Small signal model

Let∧

Vin = 0,∧dv = 0 is calculated from Eq. (9).

According to the law of Kirchhoff:Vin

K

∧d−Vin

K·K ·Rd

Vin

∧ILf −

∧ILf [sLf +

1sCf

||(R0+Rds)] = 0,

(10)where ∧

ILf =∧Vo /[

1sCf

||(Ro + Rds)], (11)

Vds = V ′o

Rds

Rds + Ro. (12)

Thus, the control-to-output transfer function can beexpressed as

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Gvd =

∧Vds

d

∣∣∣∣∣ ∧Vin=0

=Vin ·Rds

K · [s2LfCf + s( LfR0+Rds

+ RdCf) + RdRo+Rds

+ 1] · (Rds + Ro). (13)

Taking the equivalent series resistance (ESR) zero of the output filtering capacitance into account, the open-looptransfer function of the feedback control loop 1 without compensation can be expressed as

Ap0(s) = GvdGMHu =Vin ·Rds(1 + s · ESR · Cf)

K · [s2LfCf + s( LfR0+Rds

+ RdLf) + RdRo+Rds

+ 1] · (Rds + R0) · VM

, (14)

where GM = 1/VM is the pulse width modulation(PWM) transfer function, Hu is transfer function ofthe sampling system for the voltage across adjustingtransistor.

Transform Eqs. (14) into (15):

Ap0(s) =

VinK · Rds

(Rds+Ro)·VM

1Rd

Ro+Rds+1

(1 + s · ESR · Cf)

s2 LfCfRd

Ro+Rds+1

+ s(

LfRo+Rds

+RdCf )

RdRo+Rds

+1+ 1

=V ′

in

VM

(1 + sESR′C ′)( s

ω′0)2 + 1

Q′ (s

ω′0) + 1

, (15)

whereV ′

in =Vin

K· Rds

Rd + Ro + Rds, (16)

ω′0 =1√

L′C ′=

√Rd + Ro + Rds

LfCf(Ro + Rds), (17)

Q′ = Rds

√C ′

L′=

√LfCf(Ro + Rds)(Rd + Ro + Rds)

Lf + RdCf(Ro + Rds),

(18)ESR · Cf = ESR′ × C ′. (19)

By solving Eqs. (16)-(19), we obtain

L′ =[Lf + RdCf(Ro + Rds)]Rds

Rd + Ro + Rds, (20)

C ′ =Lf + Cf(Ro + Rds)

[LfRdCf(Ro + Rds)]Rds, (21)

ESR′ =ESR · [Lf + RdCf(Ro + Rds)]Rds

Lf(Ro + Rds). (22)

According to Eq. (15), the feedback control loop 1 canbe equivalent to the feedback control loop of the buckconvertor shown in Fig. 9, where V ′

in is the input DCvoltage, fs is the switching frequency, L′ is the filteringinductance, C ′ is the filtering capacitance, ESR′ is theequivalent series resistance of C ′, Rds is the load resis-tance. Besides, the ratio of sampling of voltage acrossadjusting transistor is 1:1, the peak value of sawtoothwave is VM. Then we can design a typical 3-order PIDcompensation network for this buck convertor [8].

Fig. 10 presents the Bode plots of the compensatedopen-loop transfer function of the feedback control loop1. According to the Bode plots, the compensated sys-tem has a phase margin of 45.4 degrees, the open-loopgain crosses the 0 dB axis with a −1 slope and thecrossover frequency is 36.3 kHz. These results com-pletely satisfy the stability criterion [8,9].

Fig.9 Equivalent buck converter

Fig.10 Bode plots of the compensated open-loop transfer

function of the feedback control loop 1

5.2 Design of feedback control loop 2

Fig. 11 illustrates the functional block diagram of thedouble closed-loop control strategy of feedback loop 2.

Fig.11 Block diagram of feedback loop 2

The design of feedback loop 2 is mainly based onthe frequency domain simulation in PSPICE. The in-ner loop adopts proportion control strategy, while theouter loop adopts single-pole single-zero PI compensa-tion, as shown in Fig. 12.

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Fig.12 Detailed design of feedback loop 2

Fig. 13 shows the Bode plots of the compensatedopen-loop transfer function of the feedback control loop2. According to the Bode plots, the compensated feed-back control loop 2 is stable [9].

Fig.13 Bode plots of the compensated open-loop transfer

function of the feedback control loop 2

6 Results of simulation and ex-perimental verification

Fig. 14 presents the parametric curves of Io, Vo, V ′o

(the output voltage of the switching converter), and Vds

in PSPICE.

Fig.14 Parametric curves in PSPICE

The simulation results show that Vds tracks V ′o per-

fectly, and the active filter is significantly effective.

The experimental results of the prototype are givenin Fig. 15. In order to verify the automatic regulationability during a sudden load change, the load resistanceis set to change from 0.16 Ω to 0.12 Ω at the momentof 10 ms.

As shown in Fig. 15, when the load changes suddenly,Vo decreases from 8 V to 6 V and Io reverts to 50 Arapidly after a small-scope fluctuation. Then it takesabout 0.3 ms for Vds to revert to 1 V. These resultsshow that the two feedback loops act synergistically toensure a good performance of the feedback control sys-tem.

Fig. 16 shows the voltage waveform of the prototypein detail. According to the figure, the peak-to-peak am-plitude of the ripple voltage is about 5 mV, i.e., 0.063%of the output voltage (8 V), which is much smaller thanthe permissible voltage ripple factor (1%).

Fig.15 Experimental waveforms of the prototype

Fig.16 Detailed voltage waveform of the prototype

The current measurement is based on the high preci-sion DCCT. In order to get the maximum of the peak-to-peak amplitude of ripple current, the current is mea-sured successively under the rated load during an hour.According to the measurement result, the maximumvalue is 50.004 A while the minimum value is 49.998 A,so the peak-to-peak amplitude of the ripple current isabout 6 mA, i.e., 0.012% of the output current (50 A),which is also smaller than the permissible current ripplefactor (0.1%).

7 Conclusion

Compared with the traditional SCR power supply,the high-power high-frequency switching power supply

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has smaller volume, lower cost but worse output rip-ple. In addition, it cannot output negative voltage torealize controllable current decrease for the supercon-ducting magnet in some cases.

In this paper, an improved scheme is proposed tosolve the above-mentioned problem. The experimentson the prototype, which has high output precision andgood dynamic response characteristics, have validatedthe effectiveness of the improved scheme. The improvedscheme can be applied to the power supply systems ofother magnetic confinement fusion devices after certainmodifications.

References

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2 Liu Xiaoning, Wang Fusheng. 2004, Proceedings of theCSEE, 11: 34 (in Chinese)

3 Liu Hui, Tang Ke, Gao Ge, et al. 2013, Plasma Scienceand Technology, 15: 950

4 Zhu Zhe, Zhu Yinfeng, Huang Ronglin, et al. 2012,Plasma Science and Technology, 14: 941

5 Liu Xiaoning, Jiang Jiafu, Xu Liuwei, et al. 2006, Nu-clear Fusion, 46: 90

6 Liu Yanqin, Hu Yanlan. 1995, Cryogenics and Super-conductivity, 27: 11

7 Vlatkovic V, Sabate J A, Ridley R B, et al. 1992, IEEETrans. Power Electronics, 7: 128

8 Maniktala S. 2012, Switching Power Supplies A to Z.Elsevier, Amsterdam

9 Erickson R W, Maksimovic D. 2001, Fundamentals of

Power Electronics. Springer, Berlin

(Manuscript received 9 November 2013)(Manuscript accepted 13 February 2014)E-mail address of WU Jinglin: [email protected]

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Study on a Highly Stabilized Power Supply for Hybrid