In order to improve the quality of the billet continuous casting, a twophase orthogonal power supply (TPOPS) for electromagnetic stirrer is researched, which is composed of threephase PWM rectifier and threeleg inverter. According to the power analysis of system, the ripple of dclink voltage is analyzed and its analytical expression is derived. In order to improve the performance of electromagnetic stirring, an integrated control method with feedforward control is proposed for PWM rectifier to suppress the fluctuations of dclink voltage and provide a stable dc source for inverter. According to the simplified equivalent model, a composite current control method is proposed for inverter. This proposed method can combine the merits of feedforward control with feedback control to effectively improve the dynamic output performance of TPOPS. Finally, a 300kVA prototype of TPOPS is developed, and the results have verified the analysis and control method.
1. Introduction
Special steel is the key material of major equipment manufacturers, construction projects and defense advanced weapons, and the quality of special steel has a very important influence on the manufacturing level. Currently, the electromagnetic (EM) stirring technology is a key technical way to improve the quality of special billet
[1
,
2]
. By using different forms of magnetic generators to produce a moved magnetic field, a powerful EM stirring force can be induced in the molten steel. The EM stirring force can be used to control the flow and solidification of the molten steel in the continuous casting process, and then it can expand the equiaxed crystal zone and reduce the center porosity to improve the quality of steel products
[3
,
4]
.
Nowadays, the structure of twophase orthogonal power supply (TPOPS) is widely used in the continuous casting process. TPOPS can output twophase orthogonal currents to power two coils, and then form a rotating EM stirring force to excite a rotary motion of molten steel
[5
,
6]
. In terms of the topology of TPOPS, it is always composed of threephase rectifier and twophase inverter. The former rectifier of TPOPS generally adopts threephase uncontrolled rectifier
[7
,
8]
, thus the content of harmonic currents is high. According to the requirements of continuous casting, alternate rotation is needed to make the EM stirring of molten steel more uniformly. As the output currents of TPOPS will change rapidly in the alternate process, the energy of induction coils will vary dramatically. The energy of dclink capacitor cannot be quickly released and absorbed by the uncontrolled rectifier, which can lead to significant fluctuations of dclink voltage and affect the normal control of back inverter. As for the topology of twophase inverter, four legs were adopted to form two singlephase fullbridge inverters
[9]
, so they can be controlled separately. This structure has high utilization rate of dclink voltage, but the number of power switches is 8. Therefore, two legs were proposed to form a twophase inverter in
[10]
, which can be considered as two singlephase halfbridge inverters and they were shared with dclink capacitors. This structure only needs 4 power switches, however, the utilization rate of dclink voltage is low and a voltagebalanced control is needed for two dclink capacitors. Therefore, in order to make up for their defects, a twophase threeleg inverter (TPTLI) was put forward in
[11
,
12]
, in which two legs were independent and the third leg was for public use. According to the analysis above, a TPTLI is adopted for TPOPS in the paper. Meanwhile, in order to improve power quality of system and maintain a stable dc voltage for inverter, a threephase pulse width modulation (PWM) rectifier is adopted.
As for the control of TPOPS, the references were mainly discussed about the control methods of back inverter. In
[11]
, a set of output filters was adopted by TPTLI for EM stirrer, and a deadbeat control method of TPTLI based on the switching model was derived. In
[13

15]
, a proportionalintegral (PI) control or hysteresis control was used by twophase inverter to achieve current closedloop control, and then the control system adopted sinusoidal PWM method to generate switching signals to drive power switches. In
[16]
, a synchronous frame current control scheme was proposed for voltagesource inverter to drive a twophase linear motor. Later, spacevector modulation (SVM) methods were proposed for TPTLI to improve the utilization rate of dclink voltage
[12
,
17
,
18]
, which can enhance the output capacity of TPTLI for twophase motors. However, fast positive and negative alternate rotations are needed to make the EM stirring of molten steel more symmetrically and uniformly, so the output currents of TPOPS have to be changed rapidly in the casting process. According to this requirement, TPOPS is expected to have a fast dynamic tracking performance, while the control method of TPOPS is the key section to meet the satisfactory stirring performance.
In order to improve the performance of power supply, the control method of TPOPS is researched in the paper. Firstly the power model of system is analyzed, and the ripple of dclink voltage is derived mathematically according to the power analysis in Scetion.II. Then an integrated control method with feedforward control for PWM rectifier is proposed in Scetion.III, and a ripple elimination method for voltage control is presented. According to the simplified equivalent circuit of EM stirrer, a composite current control method is proposed for TPTLI in Scetion.VI, and its closedloop tracking performance is analyzed. Finally, the prototype of TPOPS is developed, meanwhile, the simulation and experimental results have been carried out to verify the analysis and control method.
2. The Topology of TPOPS and its Power Analysis
The topology of TPOPS for EM stirrer in the billet continuous casting is shown as
Fig. 1
. It is composed of a PWM rectifier and a TPTLI. The PWM rectifier is adopted to eliminate the harmonic currents, improve the power factor (PF) of TPOPS, and maintain dclink voltage stably. The PWM rectifier is connected with the threephase grid by filter inductor
L
_{o}
. The load EM stirrer is twophase induction coils installed in the cooling water. In order to filter higher harmonics and prevent overcurrent when shortcircuit fault happens, a set of output filter
L
is adopted. The operation principle of TPOPS is shown as follows: firstly, the threephase ac voltage sources are converted into a dc voltage source by PWM rectifier, and then it can be converted into twophase ac sources to supply EM stirrer by TPTLI. The operation principle of EM stirrer is similar to the twophase asynchronous induction motor
[19
,
20]
. Shown as
Fig. 1
, the load twophase induction coils, which can be considered as the stator, are installed around the crystallizer of molten steel. And the induction coils can generate a rotating magnetic field and motion in the molten steel which is considered as the rotor. The features of rotary motion are directly related with the amplitude and frequency of output currents of TPTLI. According to the attribute requirements of different kinds of steel, the expected output currents of TPTLI are different.
The topology of TPOPS for EM stirring
 2.1 The input power calculation of TPOPS
In order to study the operation of TPOPS, the output and input power of system is analyzed. Assuming the threephase voltages of power grid are:
Where,
U
is the amplitude of phase voltage,
ω_{o}
is the angular frequency of power grid. PWM rectifier can achieve a unit PF rectification by the closedloop control. Assuming threephase input currents of PWM rectifier are:
Where,
I
_{p}
is the amplitude of active current. Assuming the active power of load EM stirrer is
P
_{d}
. If ignore the power loss of TPOPS, then there is:
As the inductance of input filter inductor is
L
_{o}
, and its resistance is small and ignored here. The threephase voltages of filter inductors can be obtained as:
The total input power of PWM rectifier is:
Where,
P
_{S}
is the power generated by threephase gird, and it is 3
UI
_{p}
/2;
P
_{L}
is the power generated by threephase filter inductors, and it is 0.
 2.2 The output power calculation of TPOPS
The load of TPOPS is the EM stirrer shown as
Fig. 1
. The operation principle of EM stirrer is similar to asynchronous induction motor. Twophase induction coils are considered as the stator of motor, while the rotating molten steel can be considered as the rotor. According to the equivalent model of asynchronous induction motor in
[19
,
20]
, the equivalent circuit of EM stirrer can be established shown as
Fig. 2
. Assuming
L
_{δ1}
,
r
_{δ1}
are the equivalent leakage inductance and resistance of induction coils respectively;
L
_{δ2}
,
r
_{δ2}
are the equivalent inductance and resistance of EM stirrer’s rotor respectively.
The equivalent circuit of EM stirrer
At the rated operation status, the excitation reactance
X
_{N}
meets: ｜
X
_{N}
｜>10*｜
r
_{δ2}
/
S
_{n}
+
j
ω
L
_{δ2}
｜ (
ω
is output angular frequency;
S
_{n}
is the slip ratio). Therefore, the excitation reactance can be neglected. Meanwhile, the flow speed of molten steel is slow and the slip ratio
S
_{n}
is always high according to the engineering practice. In order to facilitate analysis, assuming the slip ratio is equal to 1, so the equivalent resistance
r
_{δ2}
/
S
_{n}
can be simplified as
r
_{δ2}
. The simplified equivalent circuit of EM stirrer can be shown as
Fig. 2(b)
. According to the rated parameters, the equivalent parameters of EM stirrer can be obtained as follows:
Where,
P
_{M}
and
Q
_{M}
are the rated output active and reactive power of EM stirrer respectively;
I
_{N}
is the rated output current. The
α
 and
β
phase equivalent impedance for threeleg inverter can be obtained as:
where, there are
r
_{1}
=
r
_{2}
=
r
_{δ1}
+
r
_{δ2}
and
L
_{1}
=
L
_{2}
=
L
_{δ1}
+
L
_{δ2}
. According to
Fig. 1
and (7), the output voltages of threeleg inverter can be equivalent as:
where,
L
,
r
are the inductance and resistance of output filters respectively shown as
Fig. 1
. Assuming
i
_{α}
=
I
_{m}
sin
ω
t
,
i
_{β}
=
I
_{m}
cos
ωt
, and then there is:
where,
I
_{m}
is the amplitude of output currents,
ω
is output angular frequency of inverter. Then the output voltages can be expressed as:
where,
L
_{m}
=
L
+
L
_{1}
=
L
+
L
_{2}
and
r
_{m}
=
r
+
r
_{1}
=
r
+
r
_{2}
. So the total output power of TPOPS is:
According to the principle of power balance, ignoring the power loss of TPOPS, the dc active power component of
P
_{o}
should meet the following equation:
Therefore, the dc active power absorbed by PWM rectifier is mainly consumed as the work of the electromagnetic force.
 2.3 The calculation of 2ndripple in dclink voltage
As there is a secondary power
P
_{2}
in output power of TPOPS shown as (11), and there is：
According to the principle of power balance, there would be a secondary ripple in dclink voltage. Assuming the dclink voltage is
u
_{dc}
=
U
_{d}
+
δ
sin(2
ωt
+
ϕ
) ,
U
_{d}
is the dc component, and
δ
sin(2
ωt
+
ϕ
) is the voltage ripple. As the instantaneous power of dclink capacitors is:
where,
C
is the total capacitance of dclink capacitors. If neglect the 4
^{th}
ripple, according to the power balance between dc and aclink of TPOPS, it can be obtained as:
So the 2
^{nd}
ripple in dclink voltage can be derived as:
According to power analysis above, a 2
^{nd}
ripple would exist in dclink voltage, and its frequency is 2times of output frequency. The amplitude of ripple is proportional to the square of output current, and it is inversely proportional to the capacitance and dclink voltage.
3. The Integrated Control Method of PWM Rectifier
According to the power analysis above, an integrated control method is proposed for PWM rectifier shown as
Fig. 3
. It is mainly composed of voltage outerloop and current innerloop. According to the analysis in Section.II, there is a 2
^{nd}
ripple in dclink voltage. If it is not eliminated in voltage outerloop, it will generate some additional harmonic instructions for current innerloop. And then it would produce some harmonic currents in the input of PWM rectifier. The calculation of additional harmonic instruction signals is as follows:
The integrated control diagram of PWM rectifier
The voltage error Δ
u
is processed by a PI controller, and then its output will be multiplied with the synchronous signal sin
ω_{o}t
shown as
Fig. 3
. Assuming the expression of voltage PI controller is
k
+
k
_{i}
/
s
, the additional harmonic instruction signal generated by the 2
^{nd}
voltage ripple is:
Seen from (17), it would generate two kinds of harmonic instruction signals. The frequencies of harmonic signals are 2
ω
±
ω_{o}
, and its amplitude is
k
δ
/ 2 . Therefore, a ripple filter method is proposed for voltage outerloop, which can eliminate the 2
^{nd}
ripple and realize the normal control of dclink voltage. The 2
^{nd}
ripple expressed as (16) can be adopted to subtract from the voltage error Δ
u
, then the pure dc error can be got for voltage controller shown as
Fig. 3
. So the output instruction
I
_{dc}
of voltage controller is dc component without ac ripples. However, in the status of alternate rotation process, the system parameters will be varied. As the α and βphase equivalent impedances of EM stirrer are generally symmetrical, the ripple elimination method also can be used for voltage control at this time.
According to
I
_{dc}
and active power
P
_{d}
of EM stirrer, the current instruction signals
of PWM rectifier can be obtained as:
According to (18), the expected input currents of PWM rectifier can be obtained. As the active currents are ac signals, the traditional PI controller has a limited tracking performance and there would be a control error in the steadystate. Therefore, the proportional resonant (PR) controller was put forward to improve the control performance for ac signals in
[21
,
22]
. The
s
domain function of PR controller can be expressed as:
where,
k
_{p}
is the proportional coefficient,
k
_{i}
is the integral coefficient. According to the current tracking errors, the control output of current closedloop can be got by PR controller. So a closedloop dynamic adjustment of output current can be achieved in the steady state.
According to the circuit shown as
Fig. 1
, the output voltages of PWM rectifier can be obtained as:
So the modulation signals of PWM rectifier can be obtained as:
The modulation signals are derived from the switching model of PWM converter, and they can be used as the feedforward instruction signals of PWM rectifier. Associate (18) with (21), the expected feedforward instruction signals of PWM rectifier can be obtained as:
So the control system can fast regulate the output of PWM rectifier according to (22), as well as tracking to the change of instruction signals rapidly. By combining the outputs Δ
m
_{f}
of PR controller with the outputs
m
_{f}
of feedforward control shown as
Fig. 3
, the total modulation signals
m
_{f}
^{*}
(
m
_{fa}
^{*}
,
m
_{fb}
^{*}
,
m
_{fc}
^{*}
) of PWM rectifier can be obtained. According to
m
_{f}
^{*}
, the switching signals can be generated by PWM link, and then it can be used to drive power switches and output the desired voltage.
In order to improve the performance of PWM rectifier, a feedforward control method is added in the voltage outerloop and current innerloop respectively. According to the system’s power analysis, the feedforward signal 2
P
_{d}
/(3
U
) for voltage outerloop can be calculated; similarly, in order to improve current innerloop, a feedforward control signal shown as (22) is used to inhibit the output oscillations of PR controller, and reduce the dynamic adjustment process of current control. Meanwhile, PR controller can be used to improve current control accuracy of PWM rectifier in the steadystate. In this way, the integrated control method can effectively improve the dynamic performance of system, and maintain a stable dc source for the back inverter.
4. The Current Control Method of Twophase Inverter
As the former PWM rectifier is mainly used to provide a stable dc voltage source, the back TPTLI can be controlled independently. The current composite control diagram of TPTLI is proposed as
Fig. 4(a)
.
The control diagram of TPTLI and the performance comparison
Firstly, according to the desired amplitude
I
_{m}
^{*}
and frequency
f
^{*}
of output currents which are determined by the continuous casting process of molten steel
[25]
, the desired output currents of TPTLI can be obtained as:
where,
ω
^{*}
= 2
π
f
^{*}
. Since the load EM stirring is inductive, the amplitude of current instructions is given linearly by the ramp function during the process of positive and negative alternate rotation. The desired output currents
subtract the output currents of inverter respectively, then the current errors can be obtained. And then the dynamic modulation signals Δ
u
_{tα}
, Δ
u
_{tβ}
, Δ
u
_{tc}
of TPTLI can be obtained by PR controller shown as
Fig. 4(a)
. These modulation signals are mainly used to carry out the closedloop tracking control according to current errors.
According to simplified equivalent model of EM stirrer and (10), the feedforward modulation signals of TPTLI for each switch leg can be gained as:
If the current instructions change, these feedforward modulation signals would change correspondingly. So it can rapidly regulate the output voltages of inverter according to the instruction currents. Similarly with the current control of PWM rectifier, this current composite control method can combine the merits of feedforward control and feedback control. So it can effectively improve the tracking performance of inverter to meet the requirements of fast alternate rotation of EM stirring.
In order to further analyze the tracking characteristic of current composite control method for inverter, the closedloop control diagram is established shown as
Fig. 4(b)
. In
Fig. 4(b)
,
k
_{g}
is the normalized parameter, equal to 2 /
u
_{dc}
;
e
^{−Ts}
is the output delay link, which means that the output delays a control cycle
T
, and it can be simplified as (1−0.5
T
s
) / (1+0.5
Ts
) by 1
^{st}
order pade approximation
[23]
;
H
(
s
) is the detection feedback link, which can be considered as 1 / (
τs
+1) ;
k_{PWM}
is the gain of PWM link, and it is equal to
u
_{dc}
/ 2 ;
Z
_{d}
(
s
) is the equivalent impedance of load, and it is equal to
L
_{m}
s
+
r
_{m}
.
Seen from
Fig. 4(b)
, assuming:
Then the openloop transfer function of inverter can be expressed as:
The errortracking transfer function of inverter can be expressed as:
In
Fig. 4(c)
, it can be seen that when using the composite control method, the gain of openloop control characteristic is basically 1 at the highfrequency range. It means that the composite control method can realize a quick response to highfrequency input signal and improve the dynamic performance of inverter. At the same time, when only using the traditional feedback control method, the gain of openloop control of system is attenuated at the highfrequency range. So the dynamic response of system with the proposed control method will be better than the one with the traditional control method.
Seen from
Fig. 4(d)
, when using the composite control method, the errortracking characteristic of system at the lowfrequency working range is attenuated more seriously than traditional control method. The control error at the lowfrequency working range with proposed control method would be smaller, so the control precision can be improved.
5. Simulation and Experimental Results
 5.1 Simulation results
To verify the analysis and control method of TPOPS proposed in the paper, the simulation of TPOPS shown as
Fig. 1
is built by using software PSIM.9. The threephase source is 380V/50Hz. This design of TPOPS is used for a production line of 200*200mm billet continuous casting. According to the theory and practice of EM stirring
[25]
, the rated output current is set as 400A and the rated output frequency is set as 10Hz. In the steadystate, the output capacity of TPOPS is 300kVA, and the rated output active power and reactive power are 90kW, 286kVar, respectively. The design of main circuit and control parameters of TPOPS are presented in the appendix. The parameter values of system are shown as
Table 1
.
Parameters of TPOPS
Before put into the EM stirring load, the dclink voltage is stable at 750V by PWM rectification. At 0.4s, the EM stirring load is put into system. In
Fig. 5
, I1, I2, I3 are the output currents of TPOPS respectively. Since the EM stirring load is inductive, the amplitude of output current instructions is given linearly. From 0.4s to 0.6s, the amplitude of current instructions is increased from 0 to 566A. Seen from
Fig. 5(a)
, the output currents of inverter increase linearly from 0 at 0.4s, and almost reach a stable state at 0.6s. Meanwhile, the active power of load almost increases as the square of output currents. With the proposed control method, PWM rectifier can fast track to the change of output active power. Shown as
Fig. 5(b)
, the input currents of PWM rectifier approximate to increase quadratically, and it almost gets into the steady state at 0.6s. The change of input currents is nearly synchronous with the variation of output currents, so the proposed control method can effectively improve the tracking performance of PWM rectifier to maintain dclink voltage stably shown as
Fig. 5(c)
. According to the analysis in Section. II, there is a 2
^{nd}
ripple in dclink voltage shown as
Fig. 5(c)
, and the amplitude of ripple is almost increasing with the rise of output currents.
The dynamical waveforms when switching into the EM stirring load
In order to verify the ripple filter method, a simulation comparison is carried out. In
Fig. 6(a)
, ‘Udc’ is the detected dclink voltage; ‘Vripple’ is the value calculated by (16). In the steadystate the detected ripple in dclink voltage is almost the same as the calculated ripple. In
Fig. 6(a)
, the amplitude of the ripple is about 14V and its frequency is 20Hz.
The contrast waveforms for the ripple filter
Fig. 6(b)
represents the current waveforms and spectrums without using the ripple filter method respectively. As the dclink voltage contains a 2
^{nd}
ripple, after the adjustment of PI controller, the ripple would be multiplied with the synchronous signal. Then it would generate two kinds of additional harmonic instruction signals for current innerloop, of which the frequencies are 30Hz and 70Hz respectively shown as (17). By the closedloop control of current controller, the input currents of PWM rectifier would contain these two kinds of harmonic currents shown as
Fig. 6(b)
. The amplitude of these two harmonics are both about 15A shown as the spectrums in
Fig. 6(b)
, so it is basically consistent with the analysis in Section.III.
Fig. 6(c)
represents the current waveforms and spectrums with using the ripple filter method. The ripple can be calculated as (16), then it can be eliminated from the voltage error and the pure dc error can be obtained for voltage PI controller. So the voltage controller would not produce additional harmonic instructions for current controller, and there is little harmonic current in input currents shown as the spectrums in
Fig. 6(c)
. Therefore, the voltage controller of PWM rectifier can operate normally without adding a lower pass filter to attenuate the ac ripples.
As shown in
Fig. 6(c)
, the amplitude of input currents in the steadystate is 153A. The PF of PWM rectifier is 0.99, and the total harmonic distortion (THD) of current is 3.1%. Therefore, PWM rectifier can effectively improve power quality of TPOPS.
In order to verify the current control method of inverter, the EM stirrer would reversely rotate at 2.0s. The amplitude of α and βphase current instructions of TPTLI changes linearly at 1.6s from +566A to 0 within 0.2s, then the inverter would stop working for 0.2s. Finally, the amplitude of αphase current instruction would increase linearly at 2.0s from 0 to +566A within 0.2s, while the amplitude of βphase current instruction would increase linearly at 2.0s from 0 to 566A within 0.2s shown as
Fig. 7(a)
. So the reverse rotation of EM stirrer can be achieved.
The current and voltage waveforms during the period of alternate rotation
In
Fig. 7(b)
and
(c)
, I1, I2, I3 are the output currents of TPTLI respectively, and ie2 represents the tracking error of αphase output current of inverter.
Fig. 7(b)
shows the waveforms when only using PR current controller. Since the output current instructions of inverter are changing, the modulation signals of inverter are completely from the output of PR controller. The PR controller is a current feedback control, which has a relatively lag to response, so there is a piece of vibration process in the tracking error. The maximum peak of tracking error is almost 20A shown as
Fig. 7(b)
. When using the proposed current control method, the dynamical waveforms are shown as
Fig. 7(c)
. Since the feedforward signals shown as (24) are obtained from the model of EM stirrer, it can fast control TPTLI to output the corresponding voltages according to the instruction currents. When the current instructions change, the feedforward signals would be varied at the same time. So the current tracking error is almost without vibrations shown as
Fig. 7(c)
. Meanwhile, by using PR feedback control, it can achieve a closedloop tracking to the current instruction signals and improve the control precision. Therefore, the proposed composite control method can effectively improve the tracking performance of inverter, so as to meet the requirements of fast alternate rotation of EM stirrer.
Fig. 7(d)
shows the input currents and dclink voltage of PWM rectifier with the proposed control method during the period of alternate rotation. The input currents of PWM rectifier almost follow the change of output currents, therefore, PWM rectifier can fast track the change of load power. And with the change of output currents, the 2
^{nd}
ripple of dclink voltage is varied correspondingly.
 5.2 Experimental results
In order to further verify the analysis and control method, a 300kVA380V lowfrequency TPOPS for EM stirrer is developed, and the physical layout diagram of TPOPS is shown as
Fig. 8(a)
. PWM rectifier and threeleg inverter adopt a TMS320F2812 separately as the digital signal processor (DSP), which is used to sample signals, execute algorithm and generate PWM drive signals for IGBTs. The Aphase voltage is processed by zerocrossing comparison circuit, which is used to generate an interrupt for DSP to initialize the phase angle. The temperature of cooling water in EM stirrer is sampled for protection and two DSPs are communicated with each other by RS232. The system parameters of device for experiments are shown in
Table. 1
. The control frequency of power switches is 10kHz.
Fig. 8(b)
and
(c)
are the physical photos of TPOPS, while
Fig. 9
and
Fig. 10
are the experimental waveforms.
The physical implementation pictures of TPOPS
Experimental waveforms during the period of alternate rotation
Experimental waveforms in the steadystate
Seen from
Fig. 9
, it shows the dynamic waveforms when the EM stirrer is in the status of positive and negative alternate rotation. With the proposed control method for TPOPS, the output currents of inverter can change rapidly, and the aphase input current of PWM rectifier can follow the change correspondingly shown as
Fig. 9(b)
. Seen from
Fig. 9(c)
, there is a 20Hz ripple in dclink voltage and it is varied with the change of output currents. When the output currents are 0, the ripple is almost 0 and the dclink voltage is stable at 750V.
Fig. 10
is experimental waveforms in the steadystate. The input currents of PWM rectifier are about 155A. The PF of PWM rectifier is 0.98, and the THD of current is 4.3% shown as
Fig. 10(a)
. While the output currents of TPOPS are about 401A, and the THD of current is 3.4% shown as
Fig. 10(b)
.
The TPOPS with the proposed control method has been installed successfully on production line of the billet continuous casting. With the proposed control method, the period of alternate rotation of EM stirring is reduced. So it can enhance the effective work time of EM stirring and it can make the stirring of molten steel more symmetrically and uniformly. The equiaxed crystal rate of special steel billet is increased from 30% to 53%. Finally, the rate of finished products increases by 5%.
6. Conclusion
In order to improve the quality of billet continuous casting, a kind of TPOPS is researched which is composed of PWM rectifier and threeleg inverter. According to the circuit structure of TPOPS, the power model of system is analyzed. According to the power analysis, an integrated control method with feedforward control for PWM rectifier is proposed, while a current composite control method is proposed for inverter to improve the output tracking performance. The closedloop control diagram in sdomain is established, and the design of control parameters is presented. With the work of proposed control system, the dynamic performance of TPOPS is effectively improved which can meet the requirements of fast and frequent alternate rotation of EM stirring.
Acknowledgements
The financial support of Hunan Provincial Innovation Foundation For Postgraduate (Project No. CX2012A006) and The National Basic Research Program of China (973 Program) (Project No. 2009CB219706) are highly acknowledged.
BIO
Fujun Ma received B.S. degree from college of electrical and information engineering, Hunan University, Changsha, China, in 2008. He is pursuing his Ph.D. degree from college of electrical and information engineering, Hunan University. He is currently an Associate Professor in Hunan University, Changsha, China. His research interests are power quality management, active power filtering and industrial power converter and power electronic system.
An Luo received the B.S. and M.S. degrees from Hunan University, Changsha, in 1982 and 1986, respectively, and the Ph.D. degree from Zhejiang University, Zhejiang, China, in 1993.
Between 1996 and 2002, he was a Professor with the Central South University. In 2003, he became a Professor at Hunan University, where he is currently involved in research on power conversion system, harmonics suppression and reactive power compensation, and electric power saving. He has published more than 300 journal and conference articles. He also serves as the Chief of Hunan Electric Science and Application Laboratory.
Dr. Luo is a recipient of the 2006 National Scientific and Technological Awards of China, and the 2010 National Scientific and Technological Awards of China. He currently serves as the Associate Board Chairperson of the Hunan Society for Electrical Engineering.
Qiaopo Xiong received B.S. degree from school of information science and engineering, Central South University, Changsha, China, in 2009. He received Ph.D. degree from college of electrical and information engineering, Hunan University, Changsha, China, in 2014. He is currently an Associate Research Engineer in 722^{th} Research Institute of CSIC, Wuhan, Hubei Province, China. His research interests are VSC highvoltage direct current system, static var compensator and modular multilevel system design.
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