Weiwei LIU, Hongfa DING 1, Xianzhong DUAN 1, Liang LI 1, Fritz HERLACH 2 Huazhong University of Science and Technology (1), Katholieke Universiteit, Leuven (2) A Novel Control Strategy for the Power Supply to Achieve the 45 T / 6 s Flat-Top Field Abstract. In order to achieve the 45 T / 6 s flat-top field, one type of high-field quasi-continuous agnets (HFQCM) and a power supply syste related are now under construction at the Wuhan National High Magnetic Field Center (WHMFC). Considering the teperature rise of the agnet and ripple iniization, the topology and the novel repetitive control ethod of the power supply syste is detailed. Siulated results are provided to validate the proposed ethod. Streszczenie. Aby wytworzyć pole agnetyczne 45 T/6 s opracowano specjalny typ układu zasilającego. Uwzględniono ryzyko wzrostu teperatury i potrzebę inializacji zafalowań. (Nowa etod sterowania układe zasilania elektroagnesu uożliwiająca otrzyanie pola agnetycznego 45 T) Keywords: high-field quasi-continuous agnets, phase-controlled rectifier, dc passive filter, repetitive control. Słowa kluczowe: pole agnetyczne, układ zasilania, elektroagnes. Introduction A wide variety of high-field agnet systes will be developed and operated at the Wuhan National High Magnetic Field Center (WHMFC) at Wuhan, China, with support fro the National Developent and Reforation Coittee. Basic scientific research such as biology, cheistry, geology, aterial science engineering, edicine and solid-state physics, can then be carried out in this extree physical environent. Research under high agnetic field conditions soeties requires the agnetic field to be as constant as possible [1, 2, 3]. To eet the low -ripple requireent, one nitrogen-cooled, 45 T / 6 s high-field quasi-continuous agnet (HFQCM) was specified to obtain the best perforance available at the required high power level to be provided by industrial power supplies. In order to energize the HFQCM, a hybrid power supply, consisting of a 12-pulse phase-controlled rectifier (PCR) in parallel with a dc passive filter (DCPF), is proposed. The pulsed power and energy for the PCR is provided by a 1 MVA / 1 MJ flywheel pulse generator (FPG), which has been installed and coissioned at the WHMFC [4]. Two three-winding step-down 6.9 kv /.66 kv transforers, connecting the FPG and the PCR, are now under construction. The dc ripple during the flat-top period is reduced by the DCPF. With this schee, the large power handling capability of the PCR and the good filtering ability of the DCPF are fully utilized in a copleentary way. A novel control ethod that ipleents the desired agnetic field wavefor for the PCR is proposed. Due to the high current flowing through the agnet, the teperature rises due to the increase of the resistance, which ay have a negative influence on the control of the agnetic field wavefor. Using the current reference profile, the agnet resistance odel is utilized to predict the required output voltage wavefor. The operating principles of the power circuit and the control schee are discussed in the paper. A design exaple is given and siulated results are provided to validate the proposed structure and control schee. Power supply configuration The design of the power supply syste for the 45 T / 6 s agnet is ainly driven by the constraints governing the agnet design and only to a lesser degree by liitations of power supply coponents and schees, and liitations given by the power source [5,6, 7]. The identical odules use a thyristorized preregulator, which is a 12- pulse PCR. Fig. 1 shows the scheatic of the proposed power supply odule. In this hybrid structure, the FPG (Part 1) has been assebled and installed already at the WHMFC. The PCR (Part 2) is now under construction, while the DCPF (Part 3) is under design. The PCR is designed to handle the bulk of the output power, as the DCPF is only used for haronic cancellation under transient conditions. FPG M Part 1 PCR 6.9kV/.66kV Part 2 i dc i pf u 1kV Doubly-fed Control G 1MW/ 1MJ Voltage Exciter Control Load Breaker T 1 T 2 6.9kV/.66kV RE 1 RE 2 L 2 L 3 R 1 L 1 C 1 C 3 R 2 C 2 DCPF Part 3 Magnet R L Fig. 1 Circuit diagra of the power supply syste. 2.1 FPG The FPG syste is coposed of an induction otor and a synchronous generator [8]. A doubly fed control syste is utilized to raise the rotating speed of the FPG to the original axiu speed 713 rp. At this speed, the axiu rotating speed of the generator, about 185 MJ are stored in the shaft train. The upper speed liit for pulse operation is 713 rp (95 Hz) and the lower liit is 495 rp (66 Hz), PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 33-297, R. 87 NR 11/211 285
allowing up to about 1 MJ to be extracted with a duration of 4 seconds every 2 inutes. In the present configuration of the FPG syste, pulses are usually started at 594 rp to liit fatigue of the rotor aterials. The exciter and the voltage control syste collaborate to stabilize the generator output voltage to be constant over the energizing period of the pulse. 2.2 PCR Two independent 6-pulse rectifiers, connected in parallel through a soothing reactor, resulting in a 12-pulse PCR, are identical and are fed fro the FPG. The power of the 12-pulse PCR is provided by two 9.66 MVA transforer stations, whose priary windings are connected to the 6.9 kv transission syste, while the secondary voltages are.66 kv. A ±1% tap changer allows slow voltage adjustents to satisfy varied needs of agnets. One of the transforers is a - unit and the other a -Y unit, producing the two 3º phase shifted three phase systes needed for the 12-pulse PCR prototype. One set of underground cables, which connects the FPG to the WHFMC laboratory, is connected to a load breaker. 2.3 DCPF The PCR will produce even-nubered ripple (1.14 khz to.79 khz ainly) of the ac syste frequency in the dc circuit. For the HFQCM, the ripple should be filtered out. One DCPF is connected at the output of the PCR. It consists of a single tuned filter branch, a capacitor branch and an R-C daping branch. At the output of the FPG, the voltage wavefor can be soothed [9, 1]. The DCPF structure in reference [1] is utilized to build the filtering syste. The DCPF paraeters are given in the Appendix. The transfer function for the DCPF of Fig. 1 can be calculated as follows, (1) Zpf 1 1 Z1 1 Z2 1 Z3 (2) Z1 R1sL1 1 sc1 Z2 R2 1 sc2 Z3 1 sc3 resistance and specific heat of the agnet. The resistance variation of the agnet is affected by three factors: the current, the resistivity and the specific heat. A resistance circuit odel of the pulsed agnet with the concept of an iterative algorith is utilized [11]: 2 i t R t dt c t MadT (3) R t R T ct ct t is the tie, (t) is the coil current of the agnet, R (t) is the agnet resistance proportional to the teperature, α is a coefficient, the initial resistance of the agnet is R, c(t) is the specific heat as function of tie, c(t) is the specific heat function of the teperature, M a is the ass of the agnet, ΔT is the increent of the teperature, the initial teperature T is 77 K. Fig. 3 shows the curves of the agnet resistance R coinciding with the agnet teperature versus tie during a pulse. R (t) changes fro 3.5 Ω to 11.67 Ω as the teperature drifts fro 77 K to 155 K. All the agnet paraeters are given in the Appendix. R Fig. 3 Magnet resistance and teperature during a long pulse. 3.2 Control of PCR The ai of the control schee adopted in this paper is to aintain the HFQCM flat-top field constant and reduce the dc current ripple to an extreely sall value. This is achieved by controlling the firing angle α during the pulse period. Under continuous-current operating conditions, the PCR output voltage u dc ay be represented by (4) udc udc u dc Z pf (5) Where u dc U t d t 2 u dc Cn cosnt n nk 2 2 cos Fig. 2 Frequency response of the DCPF. According to the DCPF paraeters detailed in the Appendix, the frequency response of Z pf is shown in Fig. 2. The DCPF, which acts like a high pass filter, provides a low ipedance path to frequencies higher than 1 Hz and can substantially decrease the flat-top ripple of the agnet. Power supply control strategy 3.1 Magnet resistance When a high current flows through the agnet, the teperature increases, resulting in increasing the (6) a n U t n t d t b n U t n t d t 2 2 Cn an bn and n=k, =6, k=1, 2, 3... 2 2 cos sin 2 2 cos cos 286 PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 33-297, R. 87 NR 11/211
It ay be noted that as in the case of the PCR, for which the corresponding expressions are given in equations (4) ~ (6), the ripple voltage u dc is a function of α. In Fig. 4 are shown curves of the noralized ripple aplitude dn Cn 2U2 versus α with n as a paraeter [12]. Considering both the iniization of u dc and the overlap angle liitation, it is strongly suggested to work within the recoended working area for the PCR in the converter ode. For this reason, one goal for the PCR control is to keep α as sall as possible during the flat-top of the agnetic field. However, not only the control ethod, but also the secondary voltage U 2 on the transforer and the agnet paraeters ay affect the control of α. dn.3.2 6 12.1 Recoended working area. 3 6 9 12 15 18 Fig. 4 d n versus α with n as a paraeter. Conventionally, K rt is the steady-state gain of the PCR and the dead-tie delay can be considered as one-twelfth of the ac source angle. The PCR controller is a feedback controller, which provides pole-zero cancellation for the R -L plant. This is a coplex-coefficient PI controller, with cross-coupling decoupling and with the feed-forward control of the reference of the firing angle α ref. Kp is1 (12) GPI is Assuing ω s and R constant, The PI paraeters K p and τ i are selected as τ i = L / R, with K p sall, such that the controller has relatively slow response, which does not interfere with the feed-forward controller. But the current control loop ust be designed faster than the feed-forward controller to get a good perforance. A syste block diagra of the proposed agnet power supply syste, including the controller (12), the PCR odel (1) and the target odel (9), is shown in Fig. 6. ref p i ref + - GPI PI Tier + + set p GPCR u dc Gobj + - u dc R s L s idc R 1 L 1 C 1 i pf C 3 u Fig. 5 The equivalent power circuit. The equivalent power circuit of the whole syste is shown in Fig. 5, R s and L s are the resistance and the inductance of the soothing reactor, R and L represent the agnet load, and R 1, L 1, C 1, R 2, C 2, and C 3 represent the DCPF. Based on Kirchhoff s current law, the functions of the power supply are given by udc u idczs u ipfzpf (7) u iz idc i ipf (8) R 2 C 2 R L Zs = Rs sls Z R sl Substituting (8) in (7), the transfer function of the control object can be expressed as i 1 1 (9) G obj udc Zs 1 Z Zs Z Zpf Under several assuptions, the PCR can be represented as a dead-tie eleent [13]: d (1) GPCR Krte s (11) Krt.9U 2 d 1 12s Fig. 6 The PCR control loop. The control syste contains two parts: one is the firing angle open loop, the other is the current closed loop. α ref (p) is the reference of the firing angle at the pulse nuber p. α set (p) is the output firing angle of the PCR control syste. α PI, the output of the closed loop, is liited ±2 º. As a result of the control strategy, the coil current ay clib to about 4 ka during a pulse. The precise easureent of such high level is a real challenge. The device selected for the PCR control syste ight use the zero-flux-principle DCCT [14][15]. The Bode plot of the PCR closed loop is drawn in Fig. 7. Depending on the value of K p, the attenuation at the frequency 1 khz ay be better or worse. When K p =.5, it is deonstrated that there ight be a agnitude aplification at the frequency 2 Hz. Nevertheless, it is confired in the siulations that oscillations always exist when K p.1. It is suggested that K p is selected to a sall value such that the oscillation could be prevented. But the effect of changing K p ust be also thought of how uch the closed loop working on the whole syste. Magnitude (db) Phase (deg) 5-5 -1-15 -2-25 -9-18 -27-36 -45 K p=.5 K p=.5 K p =.5 K p=.5 K p=5 1 1 1 1 2 1 3 1 4 1 5 Frequency (Hz) Fig. 7 Bode plot of the PCR closed loop. Considering the stability and the iniization of the tracking error by selecting K p, a repetitive control ethod is proposed. Both α ref (p) and α set (p) are eorized at the end of each pulse. A tier is set up to ake sure that the closed loop functions only at the flat-top duration. (13) set p ref p PI PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 33-297, R. 87 NR 11/211 287
p = 1, 2, 3... When it is the first pulse, α set (1) is a copletely open loop. When it is at the pulse nuber p(p 2), let (14) ref p set p 1 This eans that α set (p) contains the tracking error inforation fro the last pulse. After several pulses, for exaple, p 6, α PI decreases to alost zero. The PCR is then controlled approxiately, in an open-loop fashion. Moreover, it responds faster to reference change and is not liited by the rap rate of the current reference. Because of the open-loop nature, it does not have the adverse effects of delay, overshoots, or oscillations existing in a feedback syste. Results A nuber of easureents at priary power conditions was ade during the current stability siulations, and the results are as follows. Fig. 8 gives the coil current wavefors which always coincide with the agnetic field curves under the feedforward control and the proposed repetitive control at pulse i(ka) 4 3 2 1 i(ka) 39.99 39.985 39.98 39.975 39.97.8.9 1. 1.1 1.2 1.3 1.4 t/s nuber 1, 2 and 6. With the feed-forward control only, the flat-top of the agnetic field cannot be aintained because of the nonlinear agnet resistance. As expected, the agnetic field wavefor can be iproved by the proposed control. The coil current aounts to 39.98 ka, the agnetic field reaches 45.45 T closely, and the flat-top tie extends to alost 6 s. By including the DCPF, the ripple of the coil current is greatly reduced. This can be seen ore clearly fro the steady state wavefor in the inset in Fig. 8. Furtherore, the peak-to-peak ripple is highly attenuated at the 2 A level, and the ripple factor achieves about 25 pp. Fig. 9 and Fig. 1 show agnet voltages and the referential firing angles related at pulse nuber 1, 2 and 6 respectively. During the 6 th pulse, as a result of the rise of agnet resistance, the agnet voltages also rise during the flat-top period, which keeps the agnetic field nearly constant. Fig. 11 shows the DCPF current at pulse nuber 6. Fig. 12 shows how the FPG shaft speed changes at the pulse nuber 6. The PCR has to be fully operational across the entire pulse operation frequency-range of the FPG, i.e. 713 rp to 665 rp. 45.465 45.46 45.455 45.45..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. Fig. 8 Coil current wavefors and field curves in three odes of operation. (6) Field(T) (1) (2) (6) 5 4 3 2 1 Field(T) u(v) 12 8 4 u (1) u (2) u (6) ipf(a) 6 4 2 ipf(a) 5 25-25 -5 1.112 1.114 1.116 1.118 1.12-4 -8..5 1. 1.5 2. Fig. 9 Magnet voltages at pulse nuber 1, 2 and 6. -2 i pf (6) -4..5 1. 1.5 2. Fig. 11 DCPF current at pulse nuber 6 as a function of tie. ref 12 8 4 start =65. ref ref ref 1 2 6 end =37.1 FPG Shaft Speed(rp) 71 7 69 68 67..5 1. 1.5 2. Fig. 1 Referential firing angles at pulse nuber 1, 2 and 6. 66..5 1. 1.5 2. Fig. 12 FPG shaft speed at pulse nuber 6 as a function of tie. 288 PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 33-297, R. 87 NR 11/211
Conclusions The repetitive control ethod for the HFQCM power supply provides a eans to reduce the ripple of the coil current and increase the operational flexibility. The operating principle, siplified control design and feasibility siulations have been presented. Steady-state siulation studies adopting the proposed control strategy show that the coil current will be kept constant during the flat-top tie by controlling the firing angle α. It is conclusively deonstrated that the eliination of the current ripple can be accoplished by installing a DCPF at the output of the PCR. Furtherore, a dc active power filter, cooperating with the DCPF at the WHMFC, is already included in the schedule. Related research results will be published in the near future. The tuned filters for the 11 th and 13 th haronics installed at the output of the FPG will be discussed later. Appendix 1) FPG paraeters: Type: Salient pole; synchronous; 3 phase alternator. Nuber of poles: 16. Initial frequency: 95 Hz. Rotating speed ω s : 713 rp ~ 495 rp. Rate of power: 1 MVA. Energy storage: 185 MJ. WR 2 (set): 1.6 1 6 lbft 2. 2) PCR paraeters: 6.9 kv/.66 kv transforers. R s = 1. Ω, L s = 2.2 H. K p =.8. Sapling tie: 1 s. 3) DCPF paraeters: R 1 = 1. Ω, L 1 = 2.2 H, C 1 = 6 μf, R 2 = 4. Ω, C 2 = 1 μf, C 3 = 2 μf. 4) Magnet paraeters: L 1.56 H,.173, R 3.5 Ω, T 77.K, M a 5. kg. REFERENCES [1] H. Jin, Y. Wang and G. Joos, A Hybrid Structure Using Phase- Controlled Rectifiers and High-Frequency Converters for Magnet-Load Power Supplies, IEEE Trans. Ind. Electron., 43 (1996), No. 1, 126-131. [2] Y. Wang, G. Joos and H. Jin, DC-Side Shunt-Active Power Filter for Phase-Controlled Magnet-Load Power Supplies, IEEE Trans. Power Electron., 12 (1997), No. 5, 765-771. [3] H. Jin and S. B. Dewan, A Cobined Feed-Forward and Feedback Control Schee for Low-Ripple Fast-Response Switch Mode Magnet Power Supplies, IEEE Trans. Magn., 3 (1994), No. 4, 181-184. [4] L. Li, H. F. Ding, T. Peng, et. al., The Pulsed High Magnetic Field Facility at HUST, Wuhan, China and Associated Magnets, IEEE Trans. Appl. Supercond., 18(28), No. 2, 596 599. [5] J. B. Schillig, H. J. Boenig, M. Gordon, et. al., Operating Experience of the United States National High Magnetic Field Laboratory 6T Long Pulse Magnet, IEEE Trans. Appl. Supercond.,1 (2), No. 1, 526-529. [6] J. B. Schillig, H. J. Boenig, J. D. Rogers, et. al., Design of a 4MW Power Supply for a 6T Pulsed Magnet, IEEE Trans. Magn., 3 (1994), No. 4, 177-1773. [7] L. J. Capbell, H. J. Boenig, D. G. Rickel, et. al., Status of the NHMFL 6 Tesla Quasi-Continuous Magnet, IEEE Trans. Magn., 32 (1996), No. 4, 2454-2457. [8] G. Zhuang, Y. H. Ding, M. Zhang, et. al., Reconstruction of the TEXT-U Tokaak in China, Plasa Science and Technology, 11 (29), No. 4, 439-442. [9] W. F. Praeg, A High-Current Low-Pass Filter for Magnet Power Supplies, IEEE Trans. Ind. Elec. and Control Instru., IECI-17 (197), No. 1, 16-22. [1] K. Li, J. J. Liu, G. C. Xiao, et. al., Novel Load Ripple Voltage- Controlled Parallel DC Active Power Filters for High Perforance Magnet Power Supplies, IEEE Trans. Nucl. Sci., 53 (26), No. 3, 153-1539. [11] F. Herlach and N. Miura, High Magnetic Fields Science and Technology, Singapore: World Scientific Publishing, 23. [12] S. B. Dewan and A. Straughen, Power Seiconductor Circuits, New York: John Wiley & Sons, 1975. [13] R. Liang and S. B. Dewan, Modeling and Control of Magnet Power Supply Syste with Switch-Mode Ripple Regulator, IEEE Trans. Ind. Appl., 31 (1995), No. 2, 264-272. [14] H. J. Boenig, F. Bogdan, G. C. Mos, et. al., Design and Preliinary Test Results of the 4 MW Power Supply at the National High Magnetic Field Laboratory, IEEE Trans. Magn., 3 (1994), No. 4, 1774-1777. [15] H. J. Boenig, J. A. Ferner, F. Bogdan, et. al., Design and Operation of a 4-MW, Highly Stabilized Power Supply, IEEE Trans. Ind. Appl., 32 (1996), No. 5, 1146-1157. Authors: dr. Weiwei Liu, Huazhong University of Science and Technology Luoyu str. 137, Wuhan, China, E-ail: loudi_liuvv@foxail.co. prof. Hongfa Ding, Huazhong University of Science and Technology Luoyu str. 137, Wuhan, China, E-ail: dinghongfa@sina.co.cn. prof. Xianzhong Duan, Huazhong University of Science and Technology Luoyu str. 137, Wuhan, China, E-ail: xzduan@hust.edu.cn. prof. Liang Li, Huazhong University of Science and Technology Luoyu str. 137, Wuhan, China, E-ail: liangli44@ail.hust.edu.cn. prof. Fritz Herlach, E- ail: fritz.herlach@fys.kuleuven.be. The correspondence address is: e-ail: loudi_liuvv@foxail.co PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 33-297, R. 87 NR 11/211 289