Speed increasing scheme by using 3000v dc power supply for lowspeed Maglev
 Authors: Wang X.^{1}, Jin Y.^{1}, Lin Y.^{1}, Lu D.^{1}, Qin F.^{1}

Affiliations:
 National Maglev Engineering Technology Center, Tongji University
 Issue: Vol 4, No 3 (2018)
 Pages: 102116
 Section: Original papers
 URL: https://journals.ecovector.com/transsyst/article/view/10431
 DOI: https://doi.org/10.17816/transsyst201843102116
Cite item
Full Text
Abstract
Background: Lowspeed maglev is usually designed to run at a maximum speed of about 100~110 km/h, the system does not have any advantage to the traditional urban railway transportation system at the aspect of running speed.
Aim: Increase the speed of lowspeed Maglev is an urgent task for future promotion.
Methods: This paper presents a speed increasing scheme by using 3000 V DC power supply instead of original 1500 V DC.
Results: Under this condition, the max output voltage of propulsion inverter could be doubled. For reason that the insulation of linear induction motor has enough margin, only small adjustment of motor is needed to adapt the doubled voltage.
Conclusion: To calculate the performance of lowspeed maglev while using 3000 V DC, a Tmodel circuit of singlesided linear induction motor is built, and the result shows that the maximum running speed could be increased to over 160 km/h. This scheme provides a promising way for speed increasing, and it’s a simple and economical approach to enhance the competitiveness of lowspeed maglev.
Full Text
INTRODUCTION
Lowspeed maglev has made great progress in engineering application. Changsha maglev express, as the longest lowspeed maglev line in the world, came into commercial operation in 2016 [1], and Beijing subway line S1 came into commercial operation at the end of 2017. These projects have verified that lowspeed maglev has some merits when compared with the traditional urban railway, such as low noise, low vibration, excellent adaptability for smaller radius curves and larger slopes. As a result, several cities in China now plan to use lowspeed maglev in urban transportation. But there still has a troublesome problem hard to overcome in the promotion of this technology. The suspending force of electromagnet has a limitation and couldn’t be improved considerably, as a consequence, the passenger capacity of lowspeed maglev is significantly lower than that of the metro and the light railway, which means this technology perhaps is more suitable for suburb transportation, which needs a higher running speed due to the longer distance between stations. Therefore, if lowspeed maglev couldn’t significantly increase the running speed, its future would be pessimistic.
For decades, lowspeed maglev in different countries is usually designed to run at a maximum speed of 100~110 km/h, which is similar to that of the metro. The Lowspeed maglev line located at AICHI, Japan as the first commercial running maglev line in the world, based on the HSST 100L system has a maximum speed of 100 km/h [1]. The UTM02 system of Korea put into service in 2016 at Incheon International Airport, has a maximum speed of 110 km/h [3]. Changsha maglev express’s highest speed is 100 km/h [2]. However, there is still no proper rail transportation form to fill the blank of 140~200 km/h, neither do maglev, nor metro.
As mentioned above, to speed up the lowspeed maglev to the so called ‘mediumspeed maglev’, performance studies of singlesided linear induction motor (SLIM) of lowspeed maglev is necessary. Reference [3] provided one useful function expression $f\left(q\right)$ according to the SLIM secondary eddy current average value. This paper supposed that the airgap flux linkage increased in the exponential function form from the entrance end to the exit end, it is affected by the SLIM running speed, secondary resistance and some other structure parameters. The perphase simplified model can be used to calculate the output thrust force, efficiency conveniently. Reference [4] deduced a twoaxis models to predict the SLIM dynamic performance, which can be applied in vector control of direct torque control. Reference [5] derived an equivalent circuit model from the polebypole method, based on the winding functions of the SLIM primary winds. Reference [6] based on the results of reference [5], divided the SLIM airgap flux density into three components. Then these three components were derived and get the inductance, secondary resistance and other parameters. A field theory analysis is performed to build a combinedparameter SLIM model in Reference [7]. The paper estimated the endeffect, the skin effect, and the backiron saturation. Several different models were built from the electromagnetic relation in the air gap through a Fourierseries approach [8, 9, 10]. However, there are very few researches focused on speed increasing scheme for the SLIM of lowspeed maglev. CRRC Zhuzhou Institute LTD. China is now developing on ‘lowspeed maglev 2.0’ whose maximum speed is designed at 160 km/h. The primary approach used in the project is to redesign the linear induction motor by extending the length and width of iron cores so as to improve the thrust force [13]. Consequently, the motor is getting much heavier, and this kind of design challenges the electromagnetic suspending system, weakens the adaptability of line curve. Furthermore, the vehicle structure has to be redesigned totally. Obviously, there are tremendous works need to be done before finally achieving the goal speed.
This article presents a different way for speed increasing. As 3000 V DC is another electric tracking voltage in IEC standard, 3000 V DC power supply was adopted instead of original 1500 V DC. Then the output voltage of the vehicular propulsion inverter was doubled. A preliminary analysis was performed to confirm the motor insulation has enough margin to endure the doubled voltage. Therefore, little modification is needed for the linear motor and vehicle structures. The key benefits of this approach is that motor voltage can keep rising with speed for longer time, and appearance of the constant power area is delayed. A mathematical model of SLIM based on Tmodel considering the endeffect was built to calculate the performance of the propulsion system, and the result showed that the maximum running speed exceeded 165 km/h when 3 sections formation adopted. The result can contribute to the exploration of a new feasible scheme for the application of ‘mediumspeed maglev’.
MODELING OF THE SLIM
The SLIM used in Lowspeed maglev is shown in Fig. 1. The SLIM primary can be simply regarded as rotary cutopen stator and then rolled flat. The Secondary, similar with rotary induction motor (RIM) rotor, often consists of a sheet conductor, such as copper or aluminum, with a solid back iron acting as return path for the magnetic flux. The thrust force corresponding to the RIM torque can be produced by the reaction between the airgap flux density and the eddy current in the secondary sheet [15].
Fig. 1. Longitudinal structure view of SLIM
The SLIM special structure means that its performance is a little different from that of an RIM. As we know, in the RIM, an accurate equivalent circuit model can be derived easily by simplifying the geometry per pole. Unfortunately, it is not as straightforward as for RIM to gain the equivalent circuit for a SLIM.
In Fig. 1 ${v}_{2}$ is the primary moving speed, ${j}_{1}$ is the primary equivalent current, and ${j}_{2}$ is the secondary equivalent current. In terms of 1D analysis, we can calculate the phase currents and excitation voltages. The air gap flux linkage can be obtained using Maxwell’s field equations and solved using the complex power method with a conformal transformation which considers the effects of the halffilled slots, magnetic saturation, and backiron resistance. By using the equal complex power relationship between the magnetic field and the electrical circuit, we can obtain several circuit parameters, such as mutual inductance ${L}_{m}$, secondary resistance ${R}_{r}$, primary leakage inductance ${L}_{1s}$, secondary leakage inductance ${L}_{1r}$, longitudinal end effect coefficients ${C}_{r}$ and ${C}_{x}$. The comprehensive derivations of the four coefficients can be referred to [15]. The Tmodel equivalent circuit is shown in Fig. 2, where the secondary equivalent resistance ${R}_{r}$ consists of the secondary conducting sheet resistance ${R}_{2sheet}$ and the secondary back iron ${R}_{2back}$. Some brief conclusions are summarized in the following paragraphs.
Fig. 2. The Tmodel circuit for SLIM
The longitudinal end effect coefficients ${K}_{r}$ and ${K}_{x}$ are denoted by
${K}_{r}=\frac{sG}{2{p}_{e}\tau \sqrt{1+(sG{)}^{2}}}\frac{{C}_{1}^{2}+{C}_{2}^{2}}{{C}_{1}}$ (1)
${K}_{x}=\frac{1}{\left(2{p}_{e}\tau \sqrt{1+{\left(sG\right)}^{2}}\right)}\frac{{C}_{1}^{2}+{C}_{2}^{2}}{{C}_{1}}$ (2)
where $\tau $ is the primary pole pitch, and ${p}_{e}$ is the number of pole pairs. ${C}_{1}$ and ${C}_{2}$ are functions of the slip and machine structure parameters, described as follows,
${C}_{1}=p\tau \mathrm{cos}{\delta}_{s}{N}_{L}\times \left[{\alpha}_{1}^{1}{e}^{p\tau /{\alpha}_{1}}\mathrm{sin}\left({\delta}_{s}\beta +{S}_{L}p\tau \right)\right.+{S}_{L}{e}^{p\tau /{\alpha}_{1}}\mathrm{cos}\left({\delta}_{s}\beta +{S}_{L}p\tau \right)\left.{\alpha}_{1}^{1}\mathrm{sin}\left({\delta}_{s}\beta \right){S}_{L}\mathrm{cos}\left({\delta}_{s}\beta \right)\right]$ (3)
${C}_{2}=p\tau sin{\delta}_{s}{N}_{L}\times \left[{\alpha}_{1}^{1}{e}^{p\tau /{\alpha}_{1}}cos\left({\delta}_{s}\beta +{S}_{L}p\tau \right)\right.+{S}_{L}{e}^{p\tau /{\alpha}_{1}}sin\left({\delta}_{s}\beta +{S}_{L}p\tau \right)\left.+{\alpha}_{1}^{1}cos\left({\delta}_{s}\beta \right){S}_{L}sin\left({\delta}_{s}\beta \right)\right]$ (4)
Parameters in (1) and (2) are calculated as below,
$\begin{array}{l}{\alpha}_{1}=\frac{\tau {g}_{e}}{{g}_{e}X{\mu}_{0}{\sigma}_{e}{v}_{2}}\\ {S}_{L}=k\frac{\pi}{{\tau}_{e}},{M}_{L}={\left({\alpha}_{1}^{1}\right)}^{2}+{S}_{L}^{2}\\ {N}_{L}=\frac{{\alpha}_{1}\pi {\tau}_{e}}{{M}_{L}\tau \sqrt{{\tau}_{e}^{2}+{\left(\pi {\alpha}_{1}\right)}^{2}}}\\ {\delta}_{s}={\mathrm{tan}}^{1}\left(\frac{1}{{S}_{L}G}\right),\beta ={\mathrm{tan}}^{1}\left(\frac{\pi {\alpha}_{1}}{{\tau}_{e}}\right)\end{array}$ (5)
For the existence of halffilled slots in the primary ends, the expression of the primary equivalent sheet current ${J}_{1}$ can be divided into three regions, i.e., entrance halffilled, fullfilled, and exit halffilled slots. Then, the expressions of the airgap flux density can be gained. According to the electric machinery theory and complex power conversion algorithm, the airgap effective electromotive force ${E}_{m}$, airgap reactive power ${Q}_{3}$, secondary active power ${P}_{2}$, mutual inductance and secondary resistance can be deduced by taking the halffilled slots into consideration. By the comparison of these expressions without halffilled slots, the number of equivalent pole pairs ${p}_{e}$ is expressed by
${p}_{e}=\frac{{\left(2p1\right)}^{2}}{4p3+\epsilon /\left({m}_{1}q\right)}$ (6)
where $p$ is the actual number of the pole pairs, ${m}_{1}$ is the number of primary phases, $q$ is the number of coil sides per phase per pole, and $\epsilon $ is the length of the short pitch.
The transversaledgeeffect coefficients are calculated by
${C}_{r}=\frac{sG\left[{R}_{e}^{2}\left[T\right]+{I}_{m}^{2}\left[T\right]\right]}{\mathrm{Re}\left[T\right]}$ (7)
${C}_{x}=\frac{\left[{R}_{e}^{2}\left[T\right]+{I}_{m}^{2}\left[T\right]\right]}{{\mathrm{I}}_{m}\left[T\right]}$ (8)
where $T$ is the function of the slip, goodness factor, and motor structure parameters, ${R}_{e}$ and ${I}_{m}$ are the real and imaginary parts of complex $T$ respectively. Here, $T$ is expressed by
$T=j\left[{\gamma}^{2}+\left(1{\gamma}^{2}\right)\frac{\lambda}{0.5{l}_{\delta}\alpha}th\left(0.5{l}_{\delta}\alpha \right)\right]$ (9)
where $\alpha $ is the ratio of $c$ to $\tau $, $\gamma $ and $\lambda $ can be obtained by
$\lambda =\frac{1}{1+\frac{1}{\gamma}th\left(0.5{l}_{\delta}\alpha \right)th\left[0.5K\left({c}_{2}{l}_{\delta}\right)\right]}$ (10)
${R}^{2}=\frac{1}{1+jsG}$ (11)
where $K$ is the function of the slip and motor structure parameters and ${c}_{2}$ is the width of the secondary sheet.
The five parameters in Tmodel circuit, respectively named as the primary resistance ${R}_{s}$, primary leakage inductance ${L}_{1s}$, secondary resistance ${R}_{r}$, secondary leakage inductance ${L}_{1r}$, and exciting inductance ${L}_{m}$, can be calculated as follows.
The primary resistance ${R}_{s}$ is
${R}_{s}={\rho}_{Cu}\times 2{l}_{av}{W}_{1}/{S}_{cu}$ (12)
where $p$ is the resistivity of copper, ${l}_{av}$ is half the average length of the primary winding coil, ${W}_{1}$ is the number of turns in series of the primary per phase, and ${S}_{Cu}$ is the effective crosssectional area of the primary winding conductor.
The primary leakage inductance ${L}_{1s}$ is
${L}_{1s}=0.025{W}_{1}^{2}\frac{{l}_{\delta}}{q}\left(\frac{\lambda}{p}+\frac{{\lambda}_{t}+{\lambda}_{e}+{\lambda}_{d}}{{p}_{e}}\right)$ (13)
where ${\lambda}_{s}$ is the primary slot leakage magnetic conductance, ${\lambda}_{e}$ is the primary winding end leakage magnetic conductance, and ${\lambda}_{d}$ is the primary harmonic leakage magnetic conductance.
The secondary resistance is composed of two parts, which is sheet and back resistance, because the flux can penetrate through the aluminum or copper sheet and enter the back iron. The depth of the flux density into the back iron ${d}_{Fe}$ is
${d}_{Fe}=\sqrt{\frac{2{\rho}_{Fe}}{s{\omega}_{e}{\mu}_{Fe}}}$ (14)
where ${p}_{e}$ is the back iron resistivity, ${\mu}_{Fe}$ is the permeability of the back iron, and ${\omega}_{e}$ is the primary synchronous angular frequency. The resistance of the secondary conducting sheet ${R}_{2sheet}$ is
${R}_{2sheet}=4{m}_{1}{\rho}_{sheet}\frac{{\left({W}_{1}{K}_{W1}\right)}^{2}}{2{p}_{e}}\frac{{l}_{\delta}}{d\tau}$ (15)
where ${p}_{sheet}$ is the resistivity of the secondary conductance sheet and ${K}_{W1}$ is the primary winding coefficient.
The resistance of the secondary back iron ${R}_{2back}$ is
${R}_{2back}=4{m}_{1}{\rho}_{Fe}\frac{{\left({W}_{1}{K}_{W1}\right)}^{2}}{2{p}_{e}}\frac{{l}_{\delta}}{{d}_{Fe}\tau}$ (16)
Therefore, the secondary equivalent resistance ${R}_{r}$ is
${R}_{r}=\frac{{R}_{2sheet}{R}_{2back}}{{R}_{2sheeet}+{R}_{2back}}$ (17)
The secondary leakage reactance is
${L}_{1r}=\frac{{R}_{r}}{2\pi {f}_{s}s}{B}_{1}sh\left(2Kd\right)$ (18)
where ${f}_{s}$ is the primary frequency and ${B}_{1}$ is the function of the slip, primary frequency, and machine structure parameters.
The exciting inductance is
${L}_{m1}=4{m}_{1}{\mu}_{0}{\left({W}_{1}{K}_{W1}\right)}^{2}\frac{{l}_{\delta}{V}_{s}}{4{\pi}^{2}{f}_{s}{g}_{e}{p}_{e}}$ (19)
where ${V}_{s}$ is the synchronous velocity of the primary side and ${g}_{e}$ is the equivalent airgap width.
The iron loss in the SLIM is composed of the primary yoke, primary tooth, and secondary back iron losses. These three parts can be calculated as follows.
The primary yoke iron loss ${P}_{Fe}$ is
${P}_{Fe}={P}_{\text{10/}50}{B}_{y}^{2}{\left(\frac{{f}_{s}}{50}\right)}^{1.3}{W}_{y}$ (20)
The primary tooth iron loss ${P}_{Fe}$ is
${P}_{Feb}={P}_{10/50}{B}_{b}^{2}{\left(\frac{sf}{50}\right)}^{1.3}{W}_{b}$ (21)
Hence, the total iron loss ${P}_{Fe}$ is
${P}_{Fe}={P}_{Fet}+{P}_{Fey}+{P}_{Feb}$ (22)
In (20)(21), ${P}_{\raisebox{1ex}{$10$}\!\left/ \!\raisebox{1ex}{$50$}\right.}$ is the iron loss value under 1.0 T and 50 Hz; ${B}_{y}$, ${B}_{t}$ and ${B}_{b}$ are the primary yoke, primary tooth and secondary back iron flux densities respectively; ${W}_{y}$, ${W}_{t}$ and ${W}_{b}$ are the primary yoke, primary tooth and secondary back iron weights respectively; and is the slip frequency in the secondary. According to the electromagnetic design methods in [11], ${B}_{y}$, ${B}_{t}$ and ${B}_{b}$ can be calculated as follows,
${B}_{y}=\sqrt{2}{\varphi}_{y}/\left(2l\delta {K}_{lam}{h}_{y}\right)$ (23)
${B}_{t}={B}_{g}{t}_{1}/\left({K}_{lam}{t}_{2}\right)$ (24)
${B}_{b}={\varphi}_{g}/\left({c}_{2}{K}_{lam}{h}_{b}\right)$ (25)
where ${\varphi}_{g}$ is the flux rootmeansquare value per pole pair, ${K}_{lam}$ is the silicon steel stacking factor, ${h}_{y}$ is the primary height, ${B}_{g}$ is the leakage airgap flux density, ${t}_{1}$ is the pitch of the primary teeth, ${t}_{2}$ is the width of the primary teeth, and ${h}_{y}$ is the height of the secondary back iron.
The iron loss resistance ${R}_{Fe}$ in series with the excitation branch can be calculated by
${R}_{Fe}={P}_{Fe}/{I}_{e}^{2}$ (26)
where ${I}_{e}$ is the field current.
Besides the edgeeffect, the skineffect, big airgap and thick secondary conductor are also very influential to SLIM’s performance when running at a relative high speed. In order to get more accurate circuits, a skineffect coefficient is calculated to adjust the secondary leakage inductance by using 2D electromagnetic field theory in [15]. The skineffect coefficient is
${k}_{f}=\frac{1+{\left(B\mathrm{sinh}2k\delta \right)}^{2}}{A\left[1+{\left(B\mathrm{sinh}2kd\right)}^{2}\right]}$ (27)
where $d$ is the thickness of secondary conductor sheet. Coefficients $A$ and $B$ are calculated as follows
$A={\mathrm{cosh}}^{2}k{\delta}^{\text{'}}+{\left(\frac{k{\rho}_{sheet}shnhk{\delta}^{\text{'}}}{s{\omega}_{e}{\mu}_{0}d}\right)}^{2}$ (28)
$B=\frac{s{\omega}_{e}{\mu}_{0}d}{2k{\rho}_{sheet}}\left[1+{\left(\frac{k{\rho}_{sheet}}{s{\omega}_{e}{\mu}_{0}d}\right)}^{2}\right]$ (29)
where $s$ is the slip of SLIM, ${\mu}_{0}$ is the air relative permeability, $\delta \text{'}$ is the equivalent airgap.
PERFORMANCE CALCULATION
After approximate analysis of the four coefficients and parameter calculations, the SLIM Tmodel equivalent circuit indicated in Fig. 2 is got. The model is similar to that of RIM. The influence of longitudinal and transversal endeffect and halffilled slots can be estimated by corresponding coefficients. Therefore, it is very convenient to analyze the performance of the SLIM in a similar way to RIM. Main performance index calculation is showed as follows.
The secondary current is
${I}_{r}={I}_{s}\times \frac{{R}_{Fe}+j{\omega}_{e}{L}_{m}}{{R}_{Fe}+j{\omega}_{e}{L}_{m}+{R}_{r}+j{\omega}_{e}{L}_{2r}}$ (30)
The output mechanical power is
${P}_{m}={I}_{r}^{2}\left(\frac{1s}{s}{K}_{r}{C}_{r}{R}_{r}\right)$ (31)
The power factor is
$\mathrm{cos}\phi =\mathrm{cos}\left(\mathrm{atan}\left(\frac{\mathrm{Im}\left({R}_{s}+j{\omega}_{e}{L}_{1s}+\frac{\left({R}_{Fe}+j{\omega}_{e}{L}_{m}\right)\left({R}_{r}+j{\omega}_{e}{L}_{2r}\right)}{{R}_{Fe}+j{\omega}_{e}{L}_{m}+{R}_{r}+j{\omega}_{e}{L}_{2r}}\right)}{\mathrm{Re}\left({R}_{s}+j{\omega}_{e}{L}_{1s}+\frac{\left({R}_{Fe}+j{\omega}_{e}{L}_{m}\right)\left({R}_{r}+j{\omega}_{e}{L}_{2r}\right)}{{R}_{Fe}+j{\omega}_{e}{L}_{m}+{R}_{r}+j{\omega}_{e}{L}_{2r}}\right)}\right)\right)$ (32)
The input voltage of the SLIM is
${U}_{s}={I}_{s}\times \left({R}_{s}+j{\omega}_{e}{L}_{1s}+\frac{\left({R}_{Fe}+j{\omega}_{e}{L}_{m}\right)\left({R}_{r}+j{\omega}_{e}{L}_{2r}\right)}{{R}_{Fe}+j{\omega}_{e}{L}_{m}+{R}_{r}+j{\omega}_{e}{L}_{2r}}\right)$ (33)
The efficiency of the SLIM is
$\eta ={P}_{m}/\left({U}_{s}{I}_{s}\mathrm{cos}\phi \right)$ (34)
The output thrust force of single SLIM is
${F}_{x}={P}_{m}/{v}_{2}$ (35)
INSULATION ANALYSIS
When 3000 V DC is adopted as input voltage from the power rail, the maximum output voltage of the vehicular propulsion inverter doubles to 2200 V AC, each SLIM’s maximum input voltage rises to 440 V AC, and the maximum phase voltage is 254 V. Through the control of the inverter, the maximum input current is still limited to 300 A, therefore main size of SLIM wouldn’t change a lot, the mechanical interface could keep unchanged.
From the design experience, we know that usually the weakest part of machine insulation system is the turntoturn insulation. At this point, the test line in Shanghai and the commercial line in Changsha all use polyimide film (PI) as the main turntoturn insulation. 2 layers of PI using 1/2 lapping method wrapped up around the primary aluminum winding coil, each layer’s thickness is 0.06mm and the total turntoturn insulation thickness is 0.12 mm. The insulation strength of the common industrial PI reaches 200 kV/mm [16], the coronaresistance reaches about 2 kV/mm. On condition of using PI thickness of 0.12 mm, the insulation strength of the primary coil is no less than 20 kV and coronaresistance is no less than 2 kV. The insulation capability is significantly higher than the doubled input voltage of SLIM. Even when the voltage of the first turn of motor could reach nearly 80 % of terminal voltage in a PWM control system [17], there is still enough voltage margin to the insulation limitation.
SLIP FREQUENCY AND MOTOR PARAMETERS
Because the SLIM of lowspeed maglev has quite different structure with that of RIM [12],the control strategy is also quite different. Considering the unique phenomenon of normal force, constant slip frequency control strategy is chosen to minimize the influence on suspending control [17]. But the reference slip frequency must be confirmed before using constant slip frequency control.
Set slip frequency as the independent variable and normal force as the dependent variable, the relation curve is show in Fig. 3. The figure shows that the normal force is very close to zero when slip frequency equals to 12 Hz. Hence, 12 Hz is selected as the reference slip frequency in performance calculation.
Fig. 3. Normal force curve at different slip frequency
After confirming the slip frequency, all parameter could finally be substituted into Tmodel equations. The main parameters of the SLIM in this paper are listed in Table 1, and the vehicle configurations are listed in Table 2.
Table 1. Main parameter of the SLIM
Items  Unit  Value 
Width of primary iron core  mm  190 
Pole pairs 
 9/2 
Silicon steel sheet length  mm  1783 
Gap flux  T  0.1467 
Rated frequency  Hz  42.5 
Pole pitch  mm  202.5 
Secondary sheet thickness  mm  4 
Width of secondary sheet  mm  200 
Mechanical air gap  mm  10 
Primary slots number 
 79 
Slot width  mm  16.1 
Tooth width  mm  6.4 
Series turns per phase 
 96 
Table 2. Vehicle configuration
Motor number per section  10 
Section number  3 
Full loaded mass per section(kg)  30000 
Motors in series  5 
Paralleling motor branches  2 
Maximum inverter current(A)  300 
RESULTS AND DISCUSSION
This paper focus on speed increasing of lowspeed maglev, so the most important performance index is maximum running speed. Tmodel circuit is used to calculate the propulsion thrust force at each ${v}_{2}$ of primary side, which is the running speed of maglev vehicle too. It’s easy to find that the cross point of thrust force curve and resistance force curve is the ultimate running speed.
In order to indicate the variation trend of running performance when adopting different over voltage mode, we set the highest voltage 2 times to the current rated voltage, that’s 2.0 pu. Then set another 5 uniform distributed voltage grades with 0.2 pu step, from 1.0 to 2.0 pu. Calculation results are illustrated in Fig. 4.
From the results we can draw some preliminary findings,
 Maximum running speed at 1.0 pu condition is about 108 km/h, the turning point of thrust force curve is around 40 km/h and the start acceleration is about 1.15 m/s^{2}, all these results accord with the design index and the actual testing results. The fact proved that the calculation model built in this article is accuracy and could be used to verify the over voltage performance.
 Voltage has great influence on the maximum speed, when the highest input voltage of the SLIM doubled, maximum speed increased over 50 %. Taken 3 sections formation as example, the maximum speed increased from 108 km/h to 166 km/h.
 The appearance of constant power area of the SLIM is significantly delayed with voltage increased, the higher voltage increased, the later SLIM comes into constant power area;
 With voltage doubled, the curve of propulsion force drops slightly, and there is almost no turning point on the curve. From this we can see that the endeffect, especially longitudinal endeffect significantly affects the performance of the SLIM when high speed running.
Fig. 4. Thrust force versus resistance force
Acceleration ability is also an important performance index. To indicate the acceleration ability, we assumed that vehicle running at a straight line without any turning curves and slopes, then record the distances and times when vehicle get the maximum speed, the results are listed in Table 3. When taking the look at 2.0 pu condition column, although the goal speed of 160 km/h is achieved, the acceleration distance is about 2.5 km, it’s too long if the station spacing is less than 5 km. Furthermore, there must be some speed limitations when applied to actual running line with smaller radius curves and slopes, the acceleration distance would surely be much longer than figures in Table 3.
Table 3. Performance of the 3 sections formation vehicle
Index  2.0/pu  1.8/pu  1.6/pu  1.4/pu  1.2/pu  1.0/pu 
Maximum speed (km/h)  166  157  146  135  122  108 
Acceleration time (s)  298  288  272  265  252  245 
Acceleration distance (m)  2520  2337  2058  1879  1623  1404 
Average acceleration (m/s^{2})  0.56  0.54  0.54  0.51  0.48  0.44 
In Fig. 5, the power factor and motor efficiency curve on condition of 2.0 pu are drew. Efficiency rises from 0.4 to near 0.8 with speed increasing, and power factor drops slightly from about 0.6 to under 0.4. Both index is relatively a bit lower than that of RIM, mainly because of characteristic of induction motor. Besides, big airgap and more field excitation loss at over voltage mode deteriorate the power factor.
Fig. 5. Efficiency and PF of the SLIM at 2.0 pu
CONCLUSION
This paper presented a speed increasing scheme for lowspeed maglev by adopting 3000 V DC power supply. After building a Tmodel circuit in consideration of endeffect, analysis of the SLIM performance is made. Results show that increasing the input voltage of the SLIM is an efficient way to increase the maximum speed of lowspeed maglev. Calculation of thrust force curve indicates a 3 sections formation vehicle can get the highest speed over 165 km/h on condition of 2.0 pu voltage.
This voltage increasing way rarely needs adjustment or redesign to the SLIM, the mechanical interface of the SLIM could remain unchanged, so do the structure of vehicle. It’s an economical way to increase running speed largely. However, the SLIM of lowspeed maglev is originally designed to run at the maximum speed of 100~110 km/h, the performance is far from perfect when running at over voltage mode, for example, the acceleration ability is fairly weak when speed exceeds 100 km/h, and acceleration distance is too long to meet the demands of actual line. Therefore, further research is necessary to optimize the performance of the SLIM and take full advantage of the potentiality of increased terminal voltage.
About the authors
Xiaohua Wang
National Maglev Engineering Technology Center, Tongji University
Author for correspondence.
Email: wangxiaohua@tongji.edu.cn
ORCID iD: 0000000310616370
Master degree, assistant researcher
China, ShanghaiYu Jin
National Maglev Engineering Technology Center, Tongji University
Email: jinyu@tongji.edu.cn
Master degree, assistant researcher
China, ShanghaiYing Lin
National Maglev Engineering Technology Center, Tongji University
Email: carfieldlin@tongji.edu.cn
ORCID iD: 000000022270272X
Master degree, assistant researcher
China, ShanghaiDiqiang Lu
National Maglev Engineering Technology Center, Tongji University
Email: ludiqiang@tongji.edu.cn
Doctor degree, assistant researcher
China, ShanghaiFeng Qin
National Maglev Engineering Technology Center, Tongji University
Email: qinfeng@tongji.edu.cn
ResearcherId: Qin Feng
Doctor degree, assistant researcher
China, ShanghaiReferences
 Yasuda Y, Fujino M, Tanaka M, et al. The first HSST Maglev Commercial Train in Japan. Proceedings of the 18th international conference on magnetically levitated systems and linear drives; 2004 Oct. 26–28, Shanghai, China.
 Shin BC, Park DY, Han HS. Korea’s First Urban Maglev System. Proceedings of the 22th International conference on magnetically levitated systems and linear drives; 2014 Sep.28–Oct.2, Rio de Janeiro, Brazil.
 Duncan J. Linear Induction Motorequivalentcircuit Model, IEE Proceedings B (Electric Power Applications). 1983;130(1):5157. doi: 10.1049/ipb.1983.0008
 Kang G, Nam K. Fieldoriented Control Scheme for Linear Induction Motor with the End Effect. IEE ProceedingsElectric Power Applications. 2005;152(6):15651572. doi: 10.1049/ipepa:20045185
 Lipa TA, Nondahl TA. Pole by Pole dq Model of a Linear Induction Machine. IEEE Transactions on Power doi: https://doi.org/10.1109/tpas.1979.319448
 Apparatus and Systems. 1979;PAS98(2):629642. doi: 10.1109/tpas.1979.319448
 Lu CA. A New Coupledcircuit Model of a Linear Induction Motor and Its Application to Steadystate Transient Dynamic and Control Studies [dissertation]. Kingston, Ontario: Queen's University; 1993.
 Idir K, Dawson GE, Eastham AR. Modeling and Performance of Linear Induction Motor With Saturable Primary. Conference Record of the 1991 IEEE Industry Applications Society Annual Meeting; 1991 28 Sept. 4 Oct., Dearborn, MI, USA. New York: IEEE, New York, 1993. doi: 10.1109/ias.1991.178147
 Higuchi T, Nonaka S, Ando M. On the Design of High Efficiency Linear Induction Motors for Linear Metro. Electrical Engineering in Japan. 2001;137(2):3643. doi: 10.1002/eej.1086
 Xu W. Research On the Performance of Singlesided Linear Induction Motor. IEEE International Electric Machines and Drives Conference; 2007 3–5 May; Antalya, Turkey. Piscataway: IEEE, 2007.
 Nonaka S. Investigation of equations for calculation of secondary resistance and secondary leakage reactance of single sided linear induction motors. Electrical Engineering in Japan. 1997;117(5):616621.
 Poloujadoff M. The Theory of Linear Induction Machinery. 1st ed. Clarendon: Oxford University Press; 1980, 273 p.
 Wang K, Shi LM, He JW, Li YH. A Decoupling Control of Normalandthrust Forces in Singlesided Linear Induction Motor. Proceedings of the CSEE. 2009;29(06):100104.
 Yan JP, Wang DW. Prospect Analysis of Application the Lowspeed Maglev System in Changsha. Underground Engineering and Tunnels. 2016;4:2931.
 Deng JM, Liu YM, Chen TF. Discussion on Facing Higher Speed Engineering Applications of Shortprimary Linear Induction Motor. Electric Locomotives & Mass Transit Vehicles. 2017;40(4):15.
 Long XL. Theory and Electromagnetic Design Method of Linear Induction Motor. 1st ed. Beijing: Science Press; 2006.
 Rotating electrical machinesPart 181: Functional evaluation of insulation systems – General guidelines. IEC 60034181. Edition 2.0 201003.
 Zhang LL. Study on Premature Fai1ure Mechenism of PWM InverterFed Traction Motor [dissertation]. Chengdu (Sichuan): Sounthwest Transportation University: 2004.
 Deng JM, Chen TF, Tang JX, Tong LS. Optimum Slip Frequency Control of Maglev Singlesided Linear Induction Motors to Maximum Dynamic Thrust. Proceedings of the CSEE. 2013;12:123130.