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A Study on Wheel Creep Characteristic for Electric Railway Vehicles Gildong Kim*, Hanmin Lee*, Changmu Lee* which is proportional to slip velocity[6][7]. Re-adhesion is the technology to improve performance by detecting accurately slip and controlling torque according to slip. There are two method: (1) Separate re-adhesion after detecting slip (2) Continuous velocity detection in the creep area and torque control according to it. There are many studies under way, and it is to reduce motor torque
     Abstract  -- Vector control was introduced to the control of induction motors which have a wide range of velocity control liketraction motors, and equivalent test equipment was used to testadhesion control. PWM modulation which is used by powersemiconductor from low modulation rate to 180° was used forinverters. Low switching frequency was used for compensationfor a dead time which has an influence on torque pulsation andcurrent waveform in the low velocity area. And good results wereacquired with a loop to control instantaneous current. In themotor operation tests, we found out regenerative braking ispossible before a stop and checked the effective results of vectorcontrol. As for re-adhesion control, a generally used torquereduction method by 1st delay of slip velocity was applied with avelocity control loop which reduce torque in proportion to slipvelocity. Compared to the torque reduction method, when thevelocity control loop was added, slip velocity dropped, andacceleration rose under the same condition. And test resultsconfirmed that adhesion characteristics could be improved bythis method.  Index Terms --Vector control, rolling stock, traction motor,adhesion control I. I  NTRODUCTION  Invertor application is broadening with vector controlcharacterized by its strong control over torque and thedevelopment of devices with magnetic blow-out [1][2][3] , andfollowings can be acquired when vector control is introducedinto electric railway vehicle control. [5]  (1) Improvement of torque accuracy transferred from axesto rails.(2) Improvement of re-adhesion control when axes arerevolving and gliding by fast torque response.(3) Regenerative brake application until a car stopsSince the accuracy of torque decides car'sacceleration/deceleration, slip, and re-adhesion, the effect of vector control is huge for railway vehicles.The re-adhesion of railway vehicles is important toevaluate car performance. Re-adhesion is known to beacquired by reducing motor torque with the 1st delay filter which is proportional to slip velocity [6][7] . Re-adhesion is thetechnology to improve performance by detecting accuratelyslip and controlling torque according to slip.There are two method:(1) Separate re-adhesion after detecting slip(2) Continuous velocity detection in the creep area andtorque control according to it.There are many studies under way, and it is to reducemotor torque when slip is detected. [8][9][10][11]  In this paper, vector control was introduced to the controlof induction motors which have a wide range of velocitycontrol like traction motors, and equivalent test equipmentwas used to test adhesion control.PWM modulation which is used by power semiconductor from low modulation rate to 180 ° was used for inverters. Lowswitching frequency was used for compensation for a deadtime which has an influence on torque pulsation and currentwaveform in the low velocity area. And good results wereacquired with a loop to control instantaneous current. In themotor operation tests, we found out regenerative braking is possible before a stop and checked the effective results of vector control.As for re-adhesion control, a generally used torquereduction method by 1st delay of slip velocity was appliedwith a velocity control loop which reduce torque in proportionto slip velocity. Compared to the torque reduction method,when the velocity control loop was added, slip velocitydropped, and acceleration rose under the same condition. Andtest results confirmed that adhesion characteristics could beimproved by this method.II. O PERATION OF A T RACTION M OTOR   As for vector control, a slip frequency indirect vector method was used. Inverters for vehicles should be used under over 180 ° conducting overmodulation too. In this case, only avoltage phase and frequency can be changed, voltage controlwas used rather than generally used current control. A tractionmotor was operated by method shown in Fig. 1. As shown inFig. 1, after setting current and slip by torque and flux,voltage vectors were calculated with detected motor velocity.Calculated voltage in coordinates were transformed intovectors for PWM modulation, and there was a currentfeedback loop to prevent current vibration and waveformcompensation. Also, voltage vectors were transformed intovectors by coordinates to undergo PWM overmodulation. A Study on Wheel Creep Characteristicfor Electric Railway Vehicles Gildong Kim*, Hanmin Lee*, Changmu Lee* Gildong Kim is with Advanced EMU Research Team, Korea RailroadResearch Institute, Korea.(e-mail:gdkim@krri.re.kr)Hanmin Lee is with Advanced EMU Research Team, Korea RailroadResearch Institute, Korea.(e-mail:hanmin@krri.re.kr)Changmu Lee is with Advanced EMU Research Team, Korea RailroadResearch Institute, Korea.(e-mail:cmlee@krri.re.kr)    Flux was decided by the size of vector.Since inverter modulation should be used to control a widerange of velocity within the range of overmodulation, power semiconductors should be modulated to the range wherecurrent flows continuously at 180 ° . This condition was setwith modulation rate, r  =1. And this was realized as shown inFig. 1 in which a modulation rate was limited by fluxcontroller. Fig. 1. Vector control for traction motors As for vectors, they were transformed into voltage vectorsin polar coordinates which slip at equivalent velocity, amodulator was designed of which output voltage is proportional to r  , in the domain r  <1. Since the size of voltagevectors transformed into polar coordinates is relatedto modulation rates, there should be the minimum vector inwhich power semiconductors continuously flow currentaround 180°. This case is r  =1. A proportional integralcontroller which uses the minimum voltage vector as astandard was used as a flux controller. When a modulationrate is r  <1, regarding the voltage vector of a motor, fluxcontrol and feedback described in Fig. 1 was designed to berating flux and be saturated in the linear operation domain of ainverter. As for vector calculation, based on a flux vector axis,the 1st voltage was calculated; and flux current, torque current,and slip by error which were necessary for vector calculationwere set with motor torque and flux. Also, slip control wasapplied to compensate errors by slip. When the contractionmotor ran backwards, the inverter was on. and if thecontraction motor ran forwards, the inverter was off. Andthe inverter ran backwards and stopped repeatedly. At thistime, soft driving is necessary. And this was acquired bydemodulation rate change. Induction motor torque is in proportion to terminal voltage square under constant slipfrequency. Therefore, dropping terminal voltage duringoperation led torque square to drop at square rate, which inturn made current drop proportional to voltage. This principalwas applied to realize soft driving by demodulation rate. SincePWM modulators cannot control voltage vectors when itshould flow 180° continuously, phase control should beapplied. Under this condition, carrier waves and modulationwaves are synchro-modulated, frequency should be controlledto match the phases of calculated voltage vectors and inverters.III. A DHESION S YSTEM  Document [6] was referred for the adhesion system.Theoretical backgrouns are as follows.  A. Adhesion Constant  For adhesion constants in slip, following assumptions wereused. ․ Highest before slip. ( v µ  ) ․ Drops after slip. ( µ  ∆ ) ․ Drops in proportion to slip rates. (  s v ⋅−  ρ  )Based on this, following equation(1) and Fig. 2 wereapplied.  sv s v ⋅−∆−= ρ µ µ µ  (1) Fig. 2. Adhesion constant Also, the motion equation for slip velocity and torque can be expressed in equation(2). )(1 0 T T  J r vdt dv m sm s −+∆+=  ρτ µ τ  (2)Here,  s v : slip velocity[m/s] (relative velocity of axes and rails)  J  : Compound inertia moment in the axis[Nm·s 2 /rad] m τ  : )/( 2 W  g r  J  ρ  mechanical coefficient of the axis r  : radius of a wheel[m] T  : axis circumference torque[Nm] 0 T  : )( W rgu v torque before slip  B. Re-adhesion characteristics The adhesion of the axis can be acquired by applying 0 =  s v into the axis motion equation. When torque inequation(2) is controlled by slip velocity in order for re-adhesion, it is known that re-adhesion cannot be achieved bycontrolling in proportion to slip velocity  s v to reduce torque.In order to get re-adhesion, the amount of torque reductionwas matched to electronic coefficient, e τ  .Assuming slip velocity could be detected, by controllingmain motor torque into torque with delay e τ  for slip velocity  s v , adhesion characteristics for the system to make 0 =  s v .Response characteristics were changed by 1st delay e τ   for   s v and feedback gain. Based on the existence of re-adhesion, the size was decided.    IV. A DHESION C ONTROL  Torque control with the 1st delay for slip velocity inequation (2) can have various responses according to delayamount, feedback gain and adhesion system conditions, butwe can say whether adhesion takes place or not by checkingwhether there was a point where slip velocity becomes 0 after slip occurred.In this study, two kinds of torque control were used. Toacquire adhesion, torque control with the 1st delay in equation(3) was used. This is a generally method for re-adhesion. The proper selection of proportion constant  K  and time constant e τ  guarantee re-adhesion characteristics.  se  Kvdt dT T  −=+ 11 τ  (3)  s s v K T  −= 2 (4) 210 T T T T  +=− (5)Following control would give improvement in re-adhesioncharacteristics by adding a loop shown in equation(4) tocontrol slip velocity. Basically torque reduction proportionalto slip velocity controls slip velocity. Fig. 3. Torque control Control methods in this study controlled torque accordingto equation (3) and (4) and feedbacked to equation (2) byequation (5). Fig. 3 shows controlling traction motor torque byslip velocity control and the 1st delay.When adhesion control is carried out by proposed method,the adhesion system will be equation (6) by equation(2),(3),(4), and (5). dt dv J r  K dt vd   sem sem sem )( 22 τ τ τ τ τ τ  +−+    ρ µ τ  ∆=−++  sm s v J r  K  K  )1)(( (6)For a response to equation (6) 01)( ≤−+ m s  J r  K  K  τ  (7)Above condition does not have re-adhesion chances andmeans the bigger feedback gain can give more chances for re-adhesion. Since when  K   s   = 0, only the 1st delay was used toachieve re-adhesion, a velocity feedback loop can be said tohave re-adhesion. em sem  J r  K  τ τ τ τ  +− (8)This shows that re-adhesion can be acquired under (+), (-)and 0, but the relations between mechanical coefficients andelectronic coefficients can have a great impact on re-adhesion performance. Compared to (-), (+) has smaller re-adhesiondomain. Since when  K   s   = 0, the selection of  e τ  in equation (8)decides re-adhesion performance, it is very important to selectthe lst delay of torque. However, velocity control loop gain  K   s also are involved in the response of the adhesion system withthe 1st delay. Since the re-adhesion system was designed tocontrol torque based on velocity feedback gain as well as thelst delay of slip velocity, and delay time constants, there can be improved re-adhesion.V. T EST E QUIPMENT  If a vehicle is 5M5T and weighs 540[ton] when it is fullyloaded, and its axis wheel is 860[mm], inertia per tractionmotor is around 100[Nm ․ s 2 /rad][12]. Consideringdeceleration and reduction ratio, the equivalent body for avehicle was designed to have 70[Nm ․ s 2 /rad]. Wheel inertiawas set 30 : 1 to vehicle inertia.The test equipment was designed to be 150:1 equivalentmodel of a traction motor(200kW). An industrial inductionmotor was used for a motor. Wheels and rails had wheels' owninertia, and wheels slides on rails. The test equipmentequivalent to an actual vehicle should have wheel inertia between vehicle inertia body and axes, and slide. The testequipment has the structure shown in Fig. 4. Since anelectronic clutch was available within 500[rpm], 10:1reduction gears were used between wheel inertia and a clutch. Fig. 4. Equivalent equipment In Fig. 4, M is a motor, W W an equivalent wheel inertia body, T a torque transducer, C a clutch, and W J is anequivalent vehicle inertia body. The equivalent body wasdesigned at before presented reduction ratio. When slipvelocity is detected by inertia body and motor velocity, andadhesion control is done by this velocity, the transfer torque of the clutch is controlled to be like Fig. 2.For the test equipment, the motion equation of an inertia body transformed into an axis and slip velocity are equation(9) when equation (1) is applied. )(  sl vW  sl   K T dt d  J  ρω µ µ ω  −∆−−= (9)In equation (9),  sl  ω    is clutch slip velocity transformed intoan axis, the second term in the right side of equation (9) becomes the torque transfer for inertia load with proportionalcoefficient W   K  . Torque transferred right before slip to aninertia body, and mechanical time constant for the equivalentequipment give equation (12), the same type equation (2). vW   K T  µ  = 0 (10)  ρ τ  W m  K  J  = (11)    )(11 0 T T  J dt d  m sl m sl  −+∆+= τ µ ω τ ω  (12)As for the test equipment, torque generated by slide at aclutch was estimated 8[Nm]. When the adhesion constant wasexpressed in percentage( 1 = v µ  [pu]), mechanical timeconstants can be calculated from equation (10) and (11) bydeciding the adhesion constant equivalent to the testequipment.In the test, the clutch was controlled to have adhesionconstant effects shown in Fig. 2. Since the test equipment wasexpressed by slip velocity as in equation(12), by setting slipvelocity as slip velocity [rad/sec] in Fig. 2, the arbitrarycoefficient was decided. In this study, considering thereduction ratio and the mechanical time constant, when  ρ   was 0.143, and u ∆   was 0.2, m τ    of the test equipment wascalculated 0.2[sec]. This was used as the base of the test.VI. T ESTS  Vector control in Fig. 1 should decide coefficients for themotor. In this study, voltage drop ratio was calculated basedon voltage. And flux, induced electromotive force, current,slip, wire wound resistance, and current feedback ratio weredecided by tests. The control program was allowed to changethese values. In the test for the decision of coefficients, ratio between flux and induced electromotive force were decided to be as large as required voltage; then relationship betweencurrent and slip and torque were decided. At low velocity,resistance drop rate and current feedback gain were decided.By observing current, wave and torque, ratio for motor coefficients were decided.  A. Motor Tests The electronic clutch was set to deliver the maximumtorque. Fig. 5 shows results when powerrunning and coastingwere repeated. And Fig. 6 shows the results of breaking.Vector control can be applied to use regenerative brakinguntil complete stop as well as effective torque control. As for slip control, electronic breaking had to stop around 8[Hz] because regenerative braking was not possible at low velocity.However, Fig. 6 shows vector control can be used for complete stop. Fig. 5 shows the test results of powerrunningand coasting frequently used in driving a motor vehicle. Fig. 6describes motor current and breaking torque in breaking.Since the transfer torque of the electronic clutch was operatednear its limits, operating torque should be lowered for tests. Fig. 5. Power and coasting drivingFig. 6. Breaking    B. Adhesion Control  Tests were carried out with 1st delay filters to observe slipvelocity feedback effects, and responses shown in Fig. 7 wereacquired. Delay filter's time constant, e τ  was set to be 2[sec],and by controlling filter gain,  K   , tests were conducted. Asthe filter gain increased, slip velocity declined and torquereduction rated rose. With regard to adhesion control slipvelocity is also one of important factors to access control performance, but torque reduction was proved to be influentialon acceleration performance. Fig. 7 shows results when  K    was 0.3. At this time, motor torque dropped to almost 0 andtorque vibration took place. Fig. 7. K=0.3 In this study, to lower slip velocity, the proposed slipfeedback loop was added.Fig. 8, and 9 show results when slip velocity wasfeedbacked under Fig. 7 conditions. Feedback gains arerespectively 0.02 and 0.03. Low amount of feedback reducedslip velocity and improved drastically torque reduction. Fig. 8had the most outstanding response with the highestacceleration. Fig. 8. Ks=0.02
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