Engineering Sciences Reports, Kyushu University
Vol. 33, No. 1, pp. 7-10, JUN, 2011

九州大学大学院総合理工学報告第33巻 第1号 7-10頁 平成23年6月

Simulation on Toroidal Field Power Supply of HL-2A
Tokamak: Application of Dual DQ0 Transformation forSix-Phase Synchronous Generator Model
Xiaolong LIU*1,† Kazuo NAKAMURA*2 Kazutoshi TOKUNAGA*2
Makoto HASEGAWA*2 Kuniaki ARAKI*2 Yi JIANG*1 Tatsuya YOSHISUE*1Hideki ZUSHI*2 Kazuaki HANADA*2 Akihide FUJISAWA*2 Hiroshi IDEI*2Shoji KAWASAKI*2 Hisatoshi NAKASHIMA*2 Aki HIGASHIJIMA*2E-mail of corresponding author: liuxl@triam.kyushu-u.ac.jp†(Received April 28, 2011)
The toroidal field power supply of HL-2A Tokamak operated in pulse mode is fed by two sets ofmotor generators with corresponding diode rectifiers. Each six-phase generator has two star statorwindings with a phase difference of 30o between them. In this paper, the model of six-phase generator with rectifier load is built and toroidal field discharge operated in pulse mode is simulated basedon dual DQ0 transformation.
Key words: toroidal field, HL-2A, six-phase generator, dual DQ0 transformation

1.

Introduction

HL-2A tokamak is a magnetic confinement
fusion device which is operating at SWIP
(Southwestern Institute of Physics), Chengdu,
China, has approached its operational rated
parameters with Ip = 480 kA and Bt = 2.8 T;
based on the parameter Bt, the current of toroidal field coil (It) must reach 45 kA at the flat
top with voltage 3,510 V during pulse discharge1). There are two types of power supplies
for magnetic field of HL-2A tokamak: poloidal
field power supplies and toroidal field power
supply2,3). The poloidal field power supplies
include ohmic heating, radial field, multi-polefield and auxiliary heating power supplies; thetoroidal field power supply must generate astable, low-corrugation longitudinal magnetic
field in the center of plasma during discharge.
Three sets of flywheel motor generators with
their corresponding transformers and rectifiers are equipped for the requirement of toroidal and poloidal field power supplies. The
power of poloidal field coils (PFC) is suppliedby one set of pulse motor generator; the powerof toroidal field coil is supplied by two sets offlywheel motor generators through two groups*1 Department of Advanced Energy Engineering Science,
Graduate Student*2 Research Institute for Applied Mechanics

of diode rectifiers, the AC input sides of rectifiers are connected with the stator windings
independently; DC output sides of rectifiers
are connected with toroidal field coil in parallel
directly4).
Three sets of motor generators are operated
in the same way which is called “pulse mode”:
The low power from the grid is accumulated in
the flywheels by driving the motors for a longtime, and then part of the energy from gridstored in the flywheels is released rapidly witha high power by the main synchronous generators connected to the magnetic field power
supply units. The current of toroidal field coilis adjusted by controlling the exciter on thegenerator directly. According to the requireIt

Utflat top

Uf
forced exciting
sudden drop

de-excitingt [s]Fig.1 A typical adjustment process of excitation system
during discharge.

8Simulation on Toroidal Field Power Supply of HL-2A Tokamak

B1

sistance is 161 mΩ, the inductance of toroidal
field coils is 230 mH and the resistance of toroidal field coils is 60 mΩ, so Tf is 3.727 s, Tt is
3.833 s, the toroidal coil current is difficult tobe controlled quickly because of the long time
constants, a control mode including feedback
gain and stability can be analyzed from thecontrol diagram and verified by simulation.

UfIf
A1

A2
B2 C2

C1
L2i2

L1i1
Lt
it

2.

Rt

Fig.2 Simplified toroidal field power supply.

ment that current of toroidal field coil mustreach 45 kA at the flat top and last for about 3s, the control process of exciter is divided into
four stages in time: forced exciting, sudden
drop, flat top and de-exciting to generate toroidal field current during a pulse discharge.
Figure 1 shows a typical adjustment process ofexcitation system during discharge, where Ut
is the voltage of toroidal field coil, It is the toroidal field current, and Uf is the voltage ofexciter.
The parameters of two sets of motor generators with their corresponding rectifiers
equipped for toroidal field power supply arerecognized the same. The unbalance between
the outputs of the two groups of rectifiers issolved by the series connection of exciter coils,
so the toroidal field power supply can be simplified for simulation as one generator with its
corresponding rectifiers because of the same
operational mode. Figure 2 shows that thepower of toroidal field coil is supplied by only
one generator with rectifiers.
Ref +PID
-Uf

1

1

1

Tf s +1

T gs +1

T ts +1

ItFig.3 Control block diagram of toroidal field power supply.

The feedback control diagram of toroidal
field power supply is shown in Fig. 3, where Tf
is the time constant of excitation system, Tg isthe time constant of generator, Tt is the time
constant of toroidal field coil. Based on theparameters of the whole system where the excitation inductance is 600 mH, excitation re-Mathematical Model of Six-Phase
Generator with Rectifier LoadThe stator windings of each six-phasenon-salientsynchronous
generator
aregrouped into two sets of Y-connected windingsthat are geometrically displaced from eachother by 30°. Compared with three-phase generator, higher harmonic of magneto motiveforce in air gap is weakened; the pulsation coefficient of the DC outputs of rectifiers issmaller than that in three-phase condition also.
The inductance coefficients in generator differential equations under ABC coordinate
system are time-variant and changing withrotator position angle (θ). Three-phase generator has 3×3 time-variant inductance coefficients in stator, but for six-phase generator,

B1
B2d

qA230

C1A1C2Fig.4 Dual DQ0 transformation.

there are 6×6 time-variant inductance coefficients for stator windings, the dimension ofdifferential equations significantly increases.
The rotational speed is declining irregular inpulse operational mode; the load of generator
is rectifier with RL circuit, the six-phase stator
windings are running alternately in theasymmetric mode. Based on the previous reasons, dual DQ0 transformation is introduced tobuild the upgraded model of generator, thecoordinate system is built on the rotator, theeddy effect, harmonic distortion and magnetic
saturation are taken for granted, so that the九州大学大学院総合理工学報告

平成 23 年度

time-varying coefficients of generator differential equations are transferred into constant. By
inverting dual DQ0 transformation, the components under dual DQ0 coordinate system aretransformed to components of ABC coordinate
system, the work condition of rectifiers can beanalyzed, and Fig. 4 shows the geometrical
relationship between dual DQ0 and ABC coordinate system.
Similar to DQ0 transformation in threephase condition, dual DQ0 transformation
matrix is built from Fig. 4, it is shown as follows:P

第 33 巻 第 1 号

9Input initial value and parameters

DQ0->ABC transformation on voltage

Solve the conductive status of rectifiers

Solve load differential equation based on the work
status of rectifier
Solve stator winding current based on the work
status of rectifier

2  P1 0 
3  0 P2ABC->DQ0 transformation on current

Solve generator model under DQ0 coordinate

The sub matrix P1 and P2 describe the situation that the ABC components on the twogroups of stator windings are projected on rotator winding, and P1 and P2 are shown in thefollowing matrix, n is sequence number ofstator windings.
(n  1)
(n  1) 2
(n  1) 2 ) cos( ) cos( )
cos( 663
63 
(n  1)
(n  1) 2
(n  1) 2 ) sin( ) sin( )
P n  cos( 66363 
111
222

Based on the dual DQ0 transformation, themodel of six-phase generator under DQ0 coordinate system is shown in the following matrix
equation:dI DQ0f
 BI DQ0f
U DQ0f  Adt(1)

Where A and B are the constant coefficientmatrices and𝑈DQ0f = [𝑢D1

𝑢Q1

𝑢01

𝑢D2

𝑢Q2

𝑢02

𝐼DQ0f = [𝑖D1

𝑖Q1

𝑖01

𝑖D2

𝑖Q2

𝑖02

𝑢f ]T𝑖f ]TWhere the superscript “T” means transposeof matrix.
The load circuit is described by the followingequations:L1d i1d (i  i ) u1  L t 1 2  R t (i1  i 2)
dt
dt

(2)

L2d i2d (i  i ) u 2  L t 1 2  R t (i1  i 2)
dt
dt

(3)

Last step?

NoYes
End

Fig.5 Flow chart of simulation.

The toroidal field current It is considered assum of the output current of the rectifiers
during simulation.

3.

Simulation on Toroidal Field
Power Supply on the Basis of Dual
DQ0 Transformation

There are super-transient processes during
discharge, such as short-circuit of generator
during commutation process; the rectifiers areoperated in sundry states, generator terminal
voltage waveform is seriously distorted; therotational speed and frequency of AC output
are changing during discharge. In order to design and verify reasonable operational mode of
toroidal field power supply of HL-2A devices,simulation is necessary.
The basic parameters (per unit) of six-phase
generator under DQ0 coordinate system isshown in the following: Xad is 1.158, Xdm andXqm (the mutual inductance between the twostator windings) are 1.2138, Xd1, Xd2, Xq1 andXq2 are 1.3958, where the basic value of voltage is 5,660 V, the basic value of current is
14,100 A, basic value of rotational speed is1,320 rpm. L1 and L2 are the inductance forkeeping balance between the DC outputs ofrectifiers, which is 10 mH. In order to get thenumerical value of toroidal field current di-10Simulation on Toroidal Field Power Supply of HL-2A Tokamak

rectly, all the parameters in per unit aretransferred to actual value during simulation.
The conductive status of the diodes in thetwo rectifiers is decided by the six-phase AC
voltage of generator; commutation is operated
not only among the different diodes in thesame rectifier, but also could be operated between the different rectifiers. The phase of AC
output voltage is calculated from the rotator
position angle, so that the commutation point
is determined by the rotator position angle,
there are totally 12 commutation points in aperiod, the load circuit can be solved from thedifferent commutation situations. The tworectifiers are set to be operated in 4-5-4 (4 diodes conduction – 5 diodes conduction – 4 diodes conduction) mode during discharge during simulation, that means that the two rectifiers are operate in 2-3-2 (2 diodes conduction –3 diodes conduction – 2 diodes conduction)mode and alternately. The simulation step is
set to be 0.01 ms, the whole simulation time is
7.5 s and de-exciting operation is not simulated.
In order to approach the actual experimental
status of toroidal field discharge, the exciting
voltage and rotational speed of generator are
set to be the same as the actual experimentalcondition; the initial position angle of rotator isset to be 0. Simulation is carried out from themodel of generator under DQ0 coordinate system, work status of rectifiers and load equations; Figure 5 shows the flow chart of simulation, in which dual DQ0 transformation is operated twice in one simulation period.
The simulation result is presented in Fig. 6,
where w is the rotational speed, If is exciting
current, UAB1 is the line voltage between phase
A and phase B and iA1 is the current in phase
A winding of the first stator. The simulationresult shows that the DC output current i1 andi2 are balanced; the adjustment to exciting
voltage is effective for the toroidal field currentcontrol. The result is under the condition that
only one motor generator set for toroidal fieldpower supply, it is about 20 kA at flat top andlast for about 2.5 s.

4.

Summary and Conclusion

According to the requirements of plasma
discharge, the motor generator sets on toroidal
field power supply of HL-2A tokamak must beoperated in pulse mode. The outputs of the twogroups of rectifiers is balanced by the same
exciting coil; the model of six-phase generator

Fig.6 Simulation result of toroidal field discharge.

with rectifiers and RL load circuit is built on
dual DQ0 transformation, the procedure ofpulse discharge is simulated. The simulation
result shows that dual DQ0 transformation iseffective for the six-phase generator model;
verifying discharge process and designing new
operational order; and the model can be applied to the PFC system simulation because of
their similar structure. The simulation could
be upgraded and applied to real- time simulation for whole discharge in future. The powerof toroidal field supplied by two motor generators can also be simulated based on different
rotator position angle.
References
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2) W.M. Xuan, L.Y. Yao, M.N. Bu, et al., The world ofpower supply 10 (2008) 56–58.
3) W.M. Xuan, L.Y. Yao, Y.H. Chen, et al., Power Electronics 3 (2007) 60–63.
4) L.Y. Yao, W.M. Xuan, H.J. Li, et al., Fusion Engineering and Design 75 (2005) 163–167.