Erasmus LLP Intensive Programme Powering the Future With Zero Emission and Human Powered Vehicles Antoni Garcia Espinosa UPC Erasmus LLP Intensive Programme Direct Torque Control DTC Erasmus LLP Intensive Programme Introduction This Thi technique t h i involves i l the th respective ti control t l off torque t and stator flux within two distinct bands. This means that the torque and flux are constrained to lie respectively within a set of upper and lower limits. Contrary C t t the to th PWM technique, t h i th switching the it hi frequency is not constant, but depends upon the instantaneous values of the torque TM developed by the motor and the flux S of the stator. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 3 Erasmus LLP Intensive Programme Three-phase converter wherein the instantaneous position of the switches is determined by the flux S of the stator and the torque TM developed by the motor. The flux is allowed to have any value between A and B. The torque is allowed to h have any value l b between t TA and d TB. The nominal value of S corresponds to the average value of A and B . Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 4 Erasmus LLP Intensive Programme Controlling the speed Speed S d control t l iis d done via i th the ttorque TM. Thus Th when h th the speed is lower than a desired value, the control circuit raises the levels of both TA and TB. Consequently, Consequently the torque developed by the motor is suddenly below TB and the system y reacts to increase the torque. Therefore the motor accelerates. When the speed has attained the desired value TM fluctuates between the new settings tti TA and d TB. During D i thi this iinterval, t l th the same switches continue to keep the flux within the levels A and B. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 5 Erasmus LLP Intensive Programme Producing a magnetic field in a 2-phase motor We W representt the th stator t t windings i di by b two t phases h X and d Y that are at right angles to each other. Each pole contains 10 turns turns, thus making a total of 20 turns between terminals x1 - x2 and y1 - y2. The windings respectivelyy produces X and Y. Suppose the nominal flux per pole is 25 mWb. Windings are connected to a 200 V dc source by way of a converter that comprises four switches. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 6 Erasmus LLP Intensive Programme Producing a magnetic field in a 2-phase motor Terminals T i l x1 - x2 : (+ ( -)) (( +)) (+ ( +)) (( -)) When Wh the th polarity l it is the same the terminals are short-circuited. So, there are only three distinct ways to make the connections connections. The same remarks apply to terminals y1 - y2 . Therefore there are 9 distinct ways y wherebyy the X and Y windings g can be connected to the (+) (-) terminals of the source. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 7 Erasmus LLP Intensive Programme Producing a magnetic field in a 2-phase motor The four switches offer nine ways of connecting the windings X and Y to the 200 V dc source. At anyy given g instant at least one of the two windings is in shortcircuit. Schematic diagram of a 2-phase 2 phase induction motor. The value and direction of fluxes X and Y depends upon the volt-seconds applied pp to the respective p winding. g Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 8 Erasmus LLP Intensive Programme Rate R t off change h off flux: fl X E X t N In our case EX=E Ed= 200 V and N=20 N 20 turns: X 200 V Wb mWb 10 10 t 20 turns s ms When EX is zero (terminals in short-circuit), the flux does nott change, d h it remains i att th the value l it h had d when h the short-circuit took place. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 9 Erasmus LLP Intensive Programme Step 1: 0<t<2,5 ms; EX= 200 V; EY=0 V Suppose S ppose that the initial flflux in the motor is zero; ero so that X = Y =0. We then close the switches so that EX= 200 V and EY=0 0V V. Flux X will begin to increase to the right at a rate of 10 mWb/ms. It will reach its nominal value of 25 mWb after a interval of 2,5 ms. We do not want to increase the flux beyond this value, and so we short-circuit short circuit terminals x1 and x2 at the end of this step. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 10 Erasmus LLP Intensive Programme After a interval of 2,5 2 5 ms: Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 11 Erasmus LLP Intensive Programme Step 2: 2,5<t<5 2 5<t<5 ms; EX= 0 V; EY=200 V While terminals x1 and x2 are still short-circuited, we close the switches so that EY=200 V. Flux Y is initially zero, but immediately begins to increase, directly upwards The applied voltage is kept unchanged until upwards. Y reaches its nominal value of 25 mWb. The time required q to reach this value is ∆t=25 mWb/(10 ( mWb/ms)= 2,5 ms. Since flux Y must nor exceed 25 mWb mWb, terminals y1 and y2 are short-circuited so that EY=0 V at the end of p this step. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 12 Erasmus LLP Intensive Programme Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 13 Erasmus LLP Intensive Programme Step 3: 5<t<10 ms; EX= -200 200 V; EY=0 V During this step, we apply a negative voltage EX across winding X. Consequently, flux X will tend to be directly to the left. Increasing at a rate of 10 mWb/ms. Since the initial value of X is 25 mWb mWb, it will become to zero after an interval of 2,5 ms. If we keep the switches in the same state, flux X will continue to build up towards to the left. It will reach its nominal value of 25 mWb after a further interval of 2 2,5 5 ms. At this very moment, we short-circuit terminals x1 and x2 so that the flux stops changing. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 14 Erasmus LLP Intensive Programme Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 15 Erasmus LLP Intensive Programme Step 4: 10<t<15 ms; EX= 0V; EY=-200 V We now apply voltage EY=-200 V across coil Y. Consequently, flux Y tends to be oriented downwards, increasing negatively at a rate of 10 mWb/ms. After 5 ms, flux Y= -25 25 mWb and we short-circuited short circuited the terminals y1 and y2. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 16 Erasmus LLP Intensive Programme Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 17 Erasmus LLP Intensive Programme Step 5: 15<t<20 ms; EX= 200 V; EY=0 V Flux X increases, while being directed to the right. When it reaches +25 mWb,, terminals x1 and x2 are still short-circuited so that the flux ceases to increase any more. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 18 Erasmus LLP Intensive Programme Step 6: 20<t<22,5 ms; EX= 0V; EY= 200 V Flux Fl Y is i di directly tl upwards, d iincreasing i positively iti l att a rate of 10 mWb/ms. Since its initial value is -25 mWb, it will reach 0 mWb after an interval of 2 2,5 5 ms ms. We see that the resultant flux S has made a complete turn. We see that the resultant flux S has made a complete turn in 20 ms which corresponds to a speed of 50 turns per second or 3000 rev/min. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 19 Erasmus LLP Intensive Programme Changes in X and Y produced by successively applying +/-200 V to the X and d Y windings. i di This diagram shows the value and position of the flux S at different instants. It also enables us to visualize the components X and Y. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 20 Erasmus LLP Intensive Programme Problems For example at instant t=6 t 6 ms where X = +15 15 mWb and Y = 25 mWb, the resulting flux is: S 2 X Y 2 152 252 29.1 Wb At the four corners the resulting flux is: S 2 X Y 2 252 252 25 2 35 Wb This is 40% greater than the nominal flux and this situation must be corrected. That is the purpose of the tolerant band. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 21 Erasmus LLP Intensive Programme Controlling the magnetic flux We can obtain a more uniform magnetic flux by imposing upper and lower limits to its value. Suppose, for example, that we wish to restrict the values of flux between 25 mWb and 28 mWb (1 pu and 1,12 pu) . To do so we draw two circles having radii corresponding to 25 mWb and 28 mWb, respectively. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 22 Erasmus LLP Intensive Programme Controlling the magnetic flux Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 23 Erasmus LLP Intensive Programme Controlling the magnetic flux Starting from point 1, we keep X constant and apply EY= 200 V to coil Y. As we have already stated, this causes flux Y to increase upwards at the rate of 10 mWb/ms As soon as the resultant flux is equal to 28 mWb/ms. mWb (point 2 of the external circle), we reduce EY to zero byy short-circuiting g y1 and y2. Next we apply EX= -200 V, which diminishes X without affecting Y. Having arrived at point 3 on the internal circle where S= +25 mWb, we reduce EX to zero. Then we eb briefly e y app apply y EY= 200 00 V,, which c raises a ses the e flux u to o point 4, after we set EY= 0 V. Again applying EX= -200 V, the flux is displaced to the left. Arriving at point 5 where S= 25 mWb, we set EX= 0 V. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 24 Erasmus LLP Intensive Programme Controlling the magnetic flux The bang-bang method of control forces the flux S to stay t within ithi th the lilimits it off 25 mWb Wb and d 28 mWb. Wb Th The short vertical and horizontal zig-zag lines show the path followed by the flux during one revolution revolution. The value and position of the flux are indicated at each instant by the position and amplitude of the vector S. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 25 Erasmus LLP Intensive Programme Controlling the magnetic flux Proceeding P di thi this way between b t the th limits li it iimposed db by th the two circles, we obtain the revolving flux S which passes through points 1 1, 2 2, 3 3, …18, 18 19 19, 20 20. The result is 20 commutations per revolution compared tto 4 in i th the previous i case. IIn thi this manner, the th amplitude lit d of the flux is kept at 26,5 mWb+/- 6%. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 26 Erasmus LLP Intensive Programme Controlling g the magnetic g flux The chopped voltage waveshapes look like PWM, but the switching periods are not constant as they would be if the PWM technique were used used. We can reduce the difference between the upper and lower values of flux S by reducing the tolerance band band. For example by choosing S between 25 and 26.5 (1 pu and 1.06 pu) we can attain a precision of +/- 3 % %. However However, this requires 44 commutations per revolution. Since one revolution is made in 20 ms ms, this amounts to 44/20 ms = 2200 commutations per second. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 27 Erasmus LLP Intensive Programme Controlling the speed of rotation It is important to note that the increase of the number of commutations does not affect the time needed to complete one revolution. As long as the minimum flux level S is 25 mWb, mWb the time to complete one revolution will always be 20 ms. Consequently, the average speed of rotation will always be 3000 rev/min. To generalize, the speed of rotation nR, is given by the expression: nR k Ed S nR: speed of rotation of the flux S [rev/min] Ed: dc voltage of the source [V] S: rated flux per pole [Wb] p upon p the construction of the motor; number k: Constant that depends of turns per pole, etc.. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 28 Erasmus LLP Intensive Programme Controlling the speed of rotation To increase the speed speed, we can rise the dc voltage above 200 V for example to 300 V, thus the speed will increase from 3000 rev/min to 4500 rev/min. In practice, however the supply voltage Ed is fixed. Another way is to reduce the flux S, this is equivalent to reduce the diameter of the circles, while keeping the voltage Ed at 200 V. A third method consists of introducing “zeros” during which moments the voltages EX and EY are simultaneously kept at zero (both windings in short-circuit). During this intervals, the flux S remains frozen in the space. This increases the time required to complete one turn turn. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 29 Erasmus LLP Intensive Programme Controlling the speed of rotation If we introduce 40 zeros each of 2 ms duration, the time required to make one turn is 20 ms+40x2 ms= 100 ms ms. This corresponds to an average speed of 600 rev/min. Note that when EX and EY are simultaneously zero, the flux S is momentarily in space. However as soon as the short short-circuit circuit is removed removed, the flux again rotates at a speed of 3000 rev/min. Thus the flux can be made to constantly advance and stop, its speed fluctuating between 3000 rev/min and zero. The windings are short-circuited short circuited when the motor torque TM is greater than torque TA. This means that the “zeros” zeros are generated by the control process itself. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 30 Erasmus LLP Intensive Programme Programming the logic switching procedure Knowing K i th thatt the th flux fl limits li it are 25 mWb Wb tto 28 mWb Wb and d the Torque limits: TA to TB How can we program this switching process to attain these objectives? Suppose: the flux S has the momentary value and p position indicated by y flux vector S1 and that is rotating g at counterclockwise at 3000 rev/min. and the rotor is turning in the same counterclockwise direction, but a constant t t speed d off 600 rev/min. / i Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 31 Erasmus LLP Intensive Programme Programming the logic switching procedure Since S1 is less than 25 mWb mWb, windings X and Y must be activated so as bring the flux within the desired zone. Five options p are then p possible: Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 32 Erasmus LLP Intensive Programme Programming the logic switching procedure 1. Apply pp y a voltage g of 200 V to winding g X. This will move the flux to the right. 2 Apply a voltage of -200 2. 200 V to winding X X. This will move the flux to the left. REJECTED 3. Apply a voltage of 200 V to winding Y. This will move the flux upwards. 4. Apply a voltage of -200 V to winding Y. This will move the flux downwards. REJECTED 5. Apply zero voltage to both windings by short-circuiting them. REJECTED Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 33 Erasmus LLP Intensive Programme Programming the logic switching procedure To determine which one of the two is preferred we must look at the position of the motor torque TM. If we apply 200 V to winding X, the flux S1 while increasing to S1A it will move clockwise, which it is opposite to the direction of the rotation of the rotor. This choice is appropriate if torque TM is, at this moment, greater than the maximum allowable value of TA. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 34 Erasmus LLP Intensive Programme Programming the logic switching procedure To determine which one of the two is preferred we must l k att th look the position iti off the th motor t torque t TM. If we apply 200 V to winding Y, the flux S1 while increasing to S1A it will move in the same direction of the rotor rotor. Since the flux is moving much faster than the rotor, the effect will be to accelerate the rotor. This is the option that should be taken provided that the torque at this moment TM is, at this moment, less than TB. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 35 Erasmus LLP Intensive Programme Programming the logic switching procedure To determine which one of the two is preferred we must look at the position of the motor torque TM. If the torque TM is already within the tolerance band (between TA and TB), we will select to apply 200 V to winding Y because it produces a torque in the same direction as the rotation of the rotor. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 36 Erasmus LLP Intensive Programme Programming the logic switching procedure C Case off fl flux vector t S2. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 37 Erasmus LLP Intensive Programme Programming the logic switching procedure C Case off fl flux vector t S2. Since it is g greater than 28 mWb windings g X and Y must be exited so that it falls inside the tolerance band. 2.2 - Apply a voltage of -200 V to winding X. X 3.- Apply a voltage of 200 V to winding Y. 5.-Apply zero voltage to both windings by shortcircuiting g them,, rejected j because it should freeze the flux in this current position. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 38 Erasmus LLP Intensive Programme Programming the logic switching procedure C Case off fl flux vector t S2. If we select option p 1 ((Apply pp y a voltage g of 200 V to winding X) a braking torque will be developed. If we choose option 4 (Apply a voltage of -200 V to winding Y) this will produce an accelerating torque on the rotor. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 39 Erasmus LLP Intensive Programme Programming the logic switching procedure C Case off fl flux vector t S3. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 40 Erasmus LLP Intensive Programme Programming the logic switching procedure Case of flux vector S3. If the torque TM is less than TB , the torque must be raised using g option 1 ((Applyy a voltage g of 200 V to winding X). If the torque TM is greater than TA, we will choose option 2 (Apply a voltage of -200 V to winding X). A strong braking torque will result because the flux cuts the rotor bars at a speed of 3000+600=3600 rev/min. If we select option p 5 ((both windings g in short-circuit)) the flux will be stationary in the space. Since the motor continues to turn at 600 rev/min a breaking torque will b again be i applied li d to t the th rotor. t Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 41 Erasmus LLP Intensive Programme Instantaneous slip and production of torque The flux continually advances and stops so that its average speed d iis ffar b below l th the iinstantaneous t t speed d off 3000 rev/min. In fact, the average speed is slightly greater than the 600 rev/min of the rotor rotor. a: Voltage and current induced in the rotor bars. b: Torque TM developed by the motor motor, and the upper and lower limits TA and TB. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 42 Erasmus LLP Intensive Programme Control of 3 3-phase phase motors Switching S it hi combinations bi ti ffor th the windings i di off a 3 3-phase h motor and corresponding positions of the stator flux S. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 43 Erasmus LLP Intensive Programme Control of 3 3-phase phase motors Hexagonal H l path th ffollowed ll db by th the flflux S in i a6 6-step, t 33 phase converter. The amplitude and position of the instantaneous flux are indicated by the vector S. The six arrows emanating from the center show the six directions in which the flux can be moved. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 44 Erasmus LLP Intensive Programme Control of 3 3-phase phase motors Hexagonal path followed by the flux S in a 6-step, 3phase converter. The amplitude and position of the instantaneous flux are indicated by the vector S. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 45 Erasmus LLP Intensive Programme Control of 3 3-phase phase motors Hexagonal path followed by the flux S in a 6-step, 3phase converter. The amplitude and position of the instantaneous flux are indicated by the vector S. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 46 Erasmus LLP Intensive Programme Control of 3 3-phase phase motors The ratio of the maximum flux S to the minimum is imposed by the geometry of the hexagon, namely 2/sqrt(3)=1.155 Hexagonal g p path followed by y the flux S in a 6-step, p, 3-phase p converter. The amplitude and position of the instantaneous flux are indicated by the vector S. The six arrows emanating from the center show the six directions in which the flux can be moved moved. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 47 Erasmus LLP Intensive Programme Commutation process The rotor and the flux rotates counterclockwise. The windings i di are connected t d tto a converter t th thatt offers ff 6 combinations wherein the windings are excited and one combination has all three windings in short-circuit short circuit. If TM<TB then C+ When S1 is less than B, the flux can be increased by selecting one of the following options: A (+), B (-), C (+), or C (-). Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 48 Erasmus LLP Intensive Programme Commutation process If TM>T TA then th A A+ When S1 is less than B, the flux can be increased by selecting one of the following options: A (+), B (-), C (+), or C (-). Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 49 Erasmus LLP Intensive Programme Commutation process If TB<T TM<T TA then th B B- When S1 is less than B, the flux can be increased by selecting one of the following options: A (+), (+) B (-), ( ) C (+), (+) or C (-). () Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 50 Erasmus LLP Intensive Programme Block diagram for the Direct Torque Control strategy Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 51 Erasmus LLP Intensive Programme Block diagram for the Direct Torque Control strategy The controlling variables of DTC are flux linkage and torque, and the principle is to directly select voltage vectors according to the difference between reference and actual value of torque and flux linkage. linkage The torque and flux errors are compared in two-level (or three-level for torque) hysteresis comparators. Then depending on the comparators outputs dl and dT and the sector of the angle r a voltage vector is selected from an optimal switching table. Because the selection referees to a hysteresis output, it is of no matter if the errors are large or small -the output will be the same same. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 52 Erasmus LLP Intensive Programme Block diagram for the Direct Torque Control strategy The Th stator t t flux fl controller t ll imposes i the th time ti duration d ti off the active voltage vectors, which move the stator flux along the reference trajectory trajectory, and the torque controller determinates the time duration of the zero voltage vectors, which keep the motor torque in the defined-byy hysteresis tolerance band. At every sampling time the voltage vector selection block chooses the inverter switching state ((Sa,Sb,Sc), ) which reduces the instantaneous flux and torque errors. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 53 Erasmus LLP Intensive Programme Hysteresis comparators flux comparator torque comparator Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 54 Erasmus LLP Intensive Programme Hysteresis comparators The Th flux fl and d torque t errors, Dl and d DT DT, are applied li d tto respective bang-bang controllers. The flux controller's output signal, signal dl dl, can assume the values of 0 and 1 1, and that, dT, of the torque controller can assume the values of -1, 0, and 1. Selection of the inverter state is based on values of dl, dT and the sector of vector plane in which the stator flux vector is currently located (see next switching tables), ) as well as on the direction of rotation of the motor. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 55 Erasmus LLP Intensive Programme Inverter optimal switching table Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 56 Erasmus LLP Intensive Programme S1 switch ON, S3 switch OFF, S5 switch OFF Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 57 Erasmus LLP Intensive Programme Switching State V On-state Switch 000 0 S4, S6, S2 100 1 S1, S6, S2 110 2 S1, S3, S2 010 3 S4, S3, S2 011 4 S4, S3, S5 001 5 S4, S6, S5 101 6 S1, S6, S5 111 7 S1, S3, S5 Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 58 Erasmus LLP Intensive Programme Switching table Counterclockwise C t l k i rotation t ti d 1 0 dT 1 0 -1 1 0 -1 Sector 1 2 7 6 3 0 5 Sector 2 3 0 1 4 7 6 Sector 3 4 7 2 5 0 1 Sector 4 5 0 3 6 7 2 Sector 5 6 7 4 1 0 3 Sector 6 1 0 5 2 7 4 Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 59 Erasmus LLP Intensive Programme Switching table Clockwise Cl k i rotation t ti d 1 0 dT 1 0 -1 1 0 -1 Sector 1 6 7 2 5 0 3 S t 2 Sector 5 0 1 4 7 2 Sector 3 4 7 6 3 0 1 Sector 4 3 0 5 2 7 6 Sector 5 2 7 4 1 0 5 Sector 6 1 0 3 6 7 4 Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 60 Erasmus LLP Intensive Programme EXAMPLE Th The iinverter t ffeeding di a counterclockwise t l k i rotating motor in a DTC control is in (100). The stator flux is too high high, and the developed torque is too low low, both control errors exceeding their tolerance ranges. With the angular g p position of stator flux vector of 130°, what will be the next state of the inverter? Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 61 Erasmus LLP Intensive Programme flux comparator torque comparator The output signals of the flux and torque controllers are d = 0 and dT = 1. The stator flux vector, ls, is in sector 3 of the vector plane. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 62 Erasmus LLP Intensive Programme The Th output t t signals i l off the th flux fl and d torque t controllers t ll are d= 0 and dT= 1. The stator flux vector, s, is in sector 3 of the vector plane. plane Thus Thus, according to the switching table, the inverter will be switched to state 5. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 63 Erasmus LLP Intensive Programme d 1 0 dT 1 0 -1 1 0 -1 Sector 1 2 7 6 3 0 5 Sector 2 3 0 1 4 7 6 Sector 3 4 7 2 5 0 1 Sector 4 5 0 3 6 7 2 Sector 5 6 7 4 1 0 3 Sector 6 1 0 5 2 7 4 The torque is increased (the resultant flux has the same direction of the motion) and the flux will remain within the tolerance bands as depicts the figure. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 64 Erasmus LLP Intensive Programme Example E l 2 2. Th The iinverter t ffeeding di a counterclockwise t l k i rotating motor in a DTC is in state 1. The stator flux is too high, high and the developed torque is tolerable tolerable. With the angular position of stator flux vector of 130°, what will be the next state of the inverter? Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 65 Erasmus LLP Intensive Programme d dT Sector 1 Sector 2 Sector 3 Sector 4 Sector 5 Sector 6 1 1 2 3 4 5 6 1 0 7 0 7 0 7 0 0 -1 6 1 2 3 4 5 1 3 4 5 6 1 2 0 0 7 0 7 0 7 -1 5 6 1 2 3 4 In I this thi second d example, l d = 0 and d dT = 0. 0 Th Thus, according to the switching table, state 0 is imposed which maintains the direction of the flux in the actual position and no torque is added. Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 66 Erasmus LLP Intensive Programme Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 67 Erasmus LLP Intensive Programme Principle of DTC Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 68 Erasmus LLP Intensive Programme Principle of DTC Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 69 Erasmus LLP Intensive Programme DTC Simulation Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 70 Erasmus LLP Intensive Programme Equations of Permanent Magnet Synchronous Motor (PMSM) disd vsd rs isd Ld er Lq isq dt disq vsq rs isq Lq er Ld isd er PM dt sd Ld isd PM sq Lq isq 3 Te p PM isq+Ld Lq isd isq 2 s sd2 sq2 dr 1 Te D r Tload dt J Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 71 Erasmus LLP Intensive Programme Torque in Permanent Magnet Synchronous Motor (PMSM) 3 Te p s i s 2 3P isq 22 : rotor flux in rotor reference frame isq : torque producing stator current component Te sd isd 3 3 Te p s i s p 2 2 sq isq 3 Te p sdd isq sq isdd 2 3 Te p Ld isd PM isq Lq isq isd 2 3 Te p PM isq+Ld Lq isd isq 2 Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 72 Erasmus LLP Intensive Programme IN PMSM WITH SURFACE MOUNTED MAGNETS Ld Lq 3 Te p PM isqq 2 Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 73 Erasmus LLP Intensive Programme M i Maximum Torque T per Ampere, A i*d=0: i*d 0 Te * isq * 3 p PM isq * 2 2 Te * Lq 3 p PM s* 2 sd 2 sq Ld isd * PM 0 2 Te * Lq s * 3 p PM 2 L i *2 q sq PM 2 Lq isq *2 2 PM 2 Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 74 Erasmus LLP Intensive Programme – VDC + s* 2 e * Lq 3 p PM PM 2 m* h=0.05 |Sn| |S|* 2 |s| = f(( ) + e * - |S| h=0.08 n VSI SWITCHING TABLE SPEED + REGULATOR + m + - SECTOR |S| ia ib FLUX, TORQUE and SECTOR ESTIMATORS m va vb ENC S N PULSES Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 75