CHAPTER 2 WOUND ROTOR INDUCTION MOTOR WITH PID CONTROLLER

Transcription

1 16 CHAPTER 2 WOUND ROTOR INDUCTION MOTOR WITH PID CONTROLLER 2.1 INTRODUCTION Indutrial application have created a greater demand for the accurate dynamic control of motor. The control of DC machine are found to be more expenive over the rotating machine and expected to have frequent maintenance. Thi i due to the complex contruction of motor. The WRIM ha been ued extenively becaue of high tarting torque and peed control wa etablihed by controlling the lip power through mechanical or electronic concept. The reearcher have developed variou peed control technique in the recent year for WRIM. 2.2 CONTROLLER CONFIGURATION Figure 2.1 how the block diagram of the Wound Rotor Induction Motor with controller. The three phae upply i connected to the tator of Wound Rotor Induction Motor (WRIM) through uncontrolled rectifier and PWM Inverter (Stator ide Inverter). Similarly the rotor terminal are connected to upply line through another PWM Inverter (Rotor ide Inverter), uncontrolled rectifier and three phae tranformer. Thi arrangement i one form of doubly fed wound rotor induction motor. In the developed ytem, the uncontrolled rectifier have a capacitor for filtering and power factor improvement of the overall ytem. Both the Inverter can generate programmable excitation for the machine according to the et peed. The inverter witch can be a Power Tranitor, SCR, GTO, IGBT, power MOSFET or any witching device. In order to get high witching frequency (up to 100 khz) the power MOSFET may be taken a a witching device. Normally on tate drop in the witch i mall and it

2 17 i neglected. When the gate pule i applied, the device i turned on. During the period, the input upply i connected with the repective motor terminal and the motor terminal are diconnected when the device i turned off due to the removal of gate pule. Figure 2.1. Block diagram of the developed ytem The tator ide converter can be controlled by PID baed field oriented controller which utilize the actual peed and the tator current. Similarly the rotor ide converter i controlled by a PID baed field oriented controller which utilize the actual peed and the rotor current. The double ide controller configuration for the double inverter fed wound rotor induction motor i hown in Figure 2.2.

3 18 Figure 2.2 WRIM with Double ide controller The advantage of the ytem include the reduced machine harmonic copper lo and the harmonic current injection. The Inverter can upply input and drive machine for all peed a per the et value. The peed loop will generate the torque component of current o a to balance the developed torque with the load torque. The rotor circuit deliver AC power with variable voltage and frequency when the peed change. The ytem can be atifactorily controlled for tart-up and braking. Stator ide and rotor ide inverter are given excitation a per the command peed and repective current. The machine current i almot inuoidal hence it reduce the harmonic copper lo and improve line ide power factor without harmonic current injection.

4 MATHEMATICAL MODELLING OF WRIM USING 3/2 - TRANSFORMATION The d-q dynamic model of the motor with the reference frame fixed to the tator can be written a given in equation (2.1). d dt i i i i d q q dr q qr 2 L r 0 Lm 0 Vd R Lr L m Rr Lm L rl i m d 2 q 1 0 Lr 0 Lm V q 1 L m R Lr L rlm Rr L i m q (2.1) 2 2 L Lm 0 L 0 Vdr L R Lm L i Lm Rr L L Lm dr q 0 Lm 0 L Vqr L Lm R Lm L Lm Rr L iqr 2 where L L L L r m i d and i q i dr and i qr V d and V q V dr and V qr R and R r L and L r are d- and q- axi tator current are d- and q- axi rotor current are d- and q- axi tator voltage are d- and q- axi rotor voltage are Stator and Rotor Reitance are Stator and Rotor Inductance L m = Mutual Inductance and = Motor Speed The electromagnetic torque T e, can be found from equation (2.2) T e 2 pl 3 L r m i q where, p = Pair of Pole L i L i d r dr m d dr i d qr (2.2)

5 20 qr L r i qr L m i q dr and qr are rotor flux linkage component expreed in the tator reference frame. The field orientation principle i baed on the condition, expreed in the excitation reference frame a e 0, contant e qr dr Hence the field orientation can be expreed a given in equation (2.3) and (2.4) for direct axi. i T (2.3) e 1 r e d dr L m i e d e (2.4) K T T e dr where, T r = L r /R r i the rotor time contant. i d e and i q e are d- and q- axi Stator current reference dr e and qr e are d- and q- axi rotor flux reference Under thee condition, the induction machine behave like a linear current/torque converter which can be repreented a in equation (2.5) T e K i (2.5) T e dr e q where, K T = Torque contant Hence the rotor torque and flux may be controlled eparately through i q and i d repectively. The qd e - qd tranformation can be written a given in equation (2.6) and (2.7). i q i r q co rf i r d in rf (2.6) i d i r q in rf i r d co rf (2.7) Here θ rf repreent the um of lip and rotor angle.

6 21 Similarly the qd - abc tranformation can be written a in equation (2.8), (2.9) and (2.10). i (2.8) a i q i b 1 3 iq id (2.9) 2 2 i c 1 3 iq id (2.10) 2 2 A inuoidal current ource of variable magnitude and frequency i ued to repreent the fundamental component of the actual PWM inverter waveform. Thi reduce the imulation time caued by the PWM witching. The rotor-ide current do not have any fluctuation when rotor flux magnitude i kept contant. But when the tator-ide current i controlled, the rotor-ide current i generated automatically. Thu, the rotor-ide inverter voltage reference i generated jut to keep r contant at it rated value for all rotor upply frequencie. And for a particular rotor peed, the fuzzy controller directly control the rotor flux angular velocity with repect to the rotor. 2.4 PID CONTROLLER PID controller improve the teady tate and tranient repone. It i the combination of proportional control action, integral action and derivative action. A proportional integral derivative controller (PID Controller) i widely ued in indutrial application. The PID meaurement depend upon three parameter which i called the proportional (P), integral (I) and derivative (D) part. P determine the reaction to preent error, I determine the reaction to the um of recently appeared error D determine the reaction according to the rate off error changing. It i general control loop feedback mechanim and ued a a feedback

7 22 controller. PID working principle i that it calculate an error value from proceed meaured value and the deired reference point. The controller i ued to minimize the error by changing the input of the ytem. In a cloed loop ytem the controller ued to provide the motor peed at any deired et-point under change in ource voltage and changing load condition. Thi controller can alo be ued to keep the peed at the et-point value when, the et-point i ramping up or down at a defined rate. PID controller provide almot the bet reult if it i tuned properly by keeping parameter of the ytem according to the nature of ytem. In thi cloed loop peed controller, the motor peed i fed back to the input where the peed i ubtracted from the et-point peed to produce an error ignal. Then the error i fed to the controller to work out what the magnitude of controller output will be to make the motor run at the deired et-point peed. For example, if the error i poitive, thi mean the motor i running low o that the controller output hould be increaed and vice-vera. The um of all three part of PID contribute the control mechanim uch a peed control of a motor in which P value depend upon current error, I on the accumulation of previou error and D predict future error baed on the newet rate of change. The control action can be imagined at firt ight a omething imple like if the error i negative, then multiply it by ome cale factor generally known a gain and et the output drive to the deired level. But thi approach i only partially ucceful due to the following reaon: if the motor i at the et-point under no load there i no error o the motor free run. If a load i applied, the motor low down and a poitive error i oberved. Then the output increae by a proportional amount to try and retore the deired peed. However, when the motor peed recover, the error reduce dratically and o doe the drive level. The reult i that the motor peed will tabilize at a peed below the et-point peed at which the load i balanced by the product of error and the gain. Thi

8 23 baic technique dicued above i known a "proportional control" and it ha limited ue a it can never force the motor to run exactly at the et-point. From the above dicuion an improvement i required for the correction to the output which will keep on adding or ubtracting a mall amount to the output until the motor reache the et-point. Thi effect can be done by keeping a total of the error oberved for intant at regular interval and multiplying thi by another gain before adding the reult to the proportional correction found earlier. Thi approach i baically baed on what i effectively the integration of the error. Till now we have two mechanim working imultaneouly trying to correct the motor peed which contitute a PI (Proportional-Integral) controller. The proportional term doe the job of fat-acting correction which will produce a change in the output a quickly a the error arie. The integral action take a finite time to act but ha the capability to make the teady-tate peed error zero. A further refinement ue the rate of change of error to apply an additional correction to the output drive. Thi i known a Derivative approach. It can be ued to give a very fat repone to udden change in motor peed Deign of PID Controller PID controller are commonly ued to regulate the time-domain behavior of many different type of dynamic plant. The plant i a wound rotor induction motor whoe peed mut be controlled. Different characteritic of the motor repone (Rie time, ettling time, Maximum over hoot and teady-tate error etc.) are controlled by election of the three gain that modify the PID controller dynamic.

9 24 Figure 2.3 Block diagram of PID controller Figure 2.3 how the generalized PID controller configuration in time domain. The error ignal i ent to the PID controller. The controller compute the proportional, integral and derivative of thi error ignal. Therefore, the PID controller i defined by the relationhip between the controller input error e and the controller output quadrature current i q that i applied to the PWM inverter to control the motor. i q K e K P I edt K D de dt where, K P = Proportional gain, K I = Integral gain, and K D =Derivative gain. (2.11) The current i q i ent to the PWM inverter fed wound rotor induction motor, and the new peed will be ened and ent back to the comparator again to find the new error ignal. The controller take error and compute the current i q with the proportional, integral and derivative gain. Thi proce will repeat. By adjuting the weighting contant K P, K I, and K D, the PID controller can be et to give the deired performance. Taking the Laplace tranform of Equation (2.11) give the following tranfer function: iq ( S) K E( S) P K S I K D S (2.12)

10 25 i ( S) K E( S) 1 T Ti S q 1 P d S (2.13) Thi tranfer function clearly illutrate the proportional, integral, and derivative gain that make up the PID controller Tuning of PID parameter by Ziegler-Nichol method There are many technique available for tuning the PID controller gain. Each method ha ome advantage and diadvantage which i given in Table 2.1. Table 2.1 Advantage and diadvantage of different tuning method Method Advantage Diadvantage No mathematical calculation Require experienced Manual Tuning required, jut it i an online method peronnel Proven method, it i alo an Ziegler-Nichol online method Conitent tuning, online or offline method. May include Software Tool value and enor analyi. Allow imulation before downloading Cohen-Coon Good proce model Some trial and error, very aggreive tuning Some cot and training involved Some mathematical calculation required, offline method, only good for firt order proce In the developed ytem the Ziegler-Nichol method i ued for tuning the gain value. According to Ziegler-Nichola method, increae the proportional

11 26 gain K P until the ytem repone ocillate with a contant amplitude and record that gain value a K u (ultimate gain), then calculate the ocillation time period T u. Further the PID parameter are tuned uing Table 2.2. Table 2.2 Ziegler-Nichol rule Parameter K P T I T D P K u /2 PI K u /2.2 T u /1.2 PID K u /1.7 T u /2 T u /8 From the table 2.2 the controller gain were determined. The effect of PID controller performance while varying the parameter i given in Table 2.3. Table 2.3 Effect of PID parameter Parameter Rie Settling Overhoot (Increaing) Time Time K P Decreae Increae Small Change K I Decreae Increae Increae K D Minor Minor Minor Decreae Decreae Decreae Stead tate Error Decreae Decreae Significantly No effect in theory 2.5 DESIGN PARAMETERS OF THE WRIM The motor pecification ued for the deign of tator ide / rotor ide PID baed controller i given in Table 2.4.

12 27 Table 2.4 Specification of Wound Rotor Induction Motor Sl.No. Motor Parameter Value 1. Nominal power ( P n ) 3 HP 2. Motor Line Voltage 440V 3. Stator reitance ( R ) Rotor reitance ( R r ) Stator inductance ( L ) H 6. Rotor inductance ( L r ) H 7. Mutual inductance ( L m ) mh 8. Rotor inertia (J) kg.m 2 9. Number of pole pair ( 2p ) 2 Thee value have been obtained from the manufacturer data of the machine. The imulation and implementation are carried out for the pecified wound rotor induction motor. 2.6 SIMULATION OF THE SYSTEM WITH STATOR SIDE PID CONTROLLER The deigned PID controller ha been conidered for the tator ide inverter and the rotor ide inverter i not controlled by any controller. The rotor ide inverter i working with fixed pule. The developed ytem i imulated uing Matlab/Simulink. The imulink model of the wound rotor induction motor with PID controller on tator ide inverter i hown in 2.4. The pecification of the WRIM ued for imulation i given in Table 2.4.

13 28 Figure 2.4 Simulink Model of the WRIM with PID controller on Stator ide Reult and Dicuion Figure 2.5 how the peed Variation of wound rotor induction motor with repect to time when the PID controller acting on tator ide alone for 50% load. When the reference peed i maintained at 100 rad/, the motor peed i increae linearly and reache the reference value of 100 rad/ at It i etimated that the rie time i 0.09 and the ettling time i 0.22 for 50% of load

14 29 Figure 2.5 Speed variation with repect to time repone for et peed of 100 rad/ with 50% load Figure 2.6 Deflecting Torque variation with repect to time repone for et peed of 100 rad/ with 50% load

15 30 torque. The teady tate error i 3.02% for 50% of load torque when the et peed i 100rad/. It i alo een that there i a overhoot with the action of PID controller on tator ide inverter. The tranient and teady tate performance with repect to peed repone for 50% load torque are given in Table 2.5. The correponding deflecting torque variation are preented in Figure 2.6. The torque increae to 41 Nm then come down and ha contant pulation at It i een from the reult that the torque i pulating in nature even in the teady tate region. Thi pulation i due to the continuou action of controller. Table 2.5 Tranient and teady tate Performance with repect to peed repone Parameter Value Rie time 0.09 Settling time 0.22 Peak over hoot 3.00 % Steady tate Error 3.02 %

16 31 Figure 2.7 Three phae tator current with repect to time repone for et peed of 100 rad/ with 50% load The three phae tator current for WRIM with repect to time repone for the reference peed of 100 rad/ i hown in Figure 2.7. When the peed ettle the correponding current goe and ettle at contant magnitude. It can be een from the graph that the three phae tator current i inuoidal form. The correponding tator d-q current wave form i hown in Figure 2.8.

17 32 Figure 2.8 Stator d-q current with repect to time repone for et peed of 100 rad/ with 50% load

18 33 Figure 2.9 Stator voltage with repect to time repone for et peed of 100 rad/ with 50% load Figure 2.10 Stator d-q voltage with repect to time repone for et peed of 100 rad/ with 50% load

19 34 Figure 2.11 Three phae rotor current with repect to time repone for et peed of 100 rad/ with 50% load Figure 2.12 Rotor d-q current with repect to time repone for et peed of 100 rad/ with 50% load

20 35 Figure 2.13 Rotor d-q voltage with repect to time repone for et peed of 100 rad/ with 50% load The tator voltage and tator d-q voltage are hown in Figure 2.9 and 2.10 repectively. Figure 2.11 how the three phae rotor current for the reference peed of 100 rad/ and the correponding rotor d-q current and voltage are hown in Figure 2.12 and 2.13 repectively. The expanded portion from 0.2 to 0.5 of three phae tator current and three phae rotor current i hown in figure From the graph, it i oberved that the tator current complete 8cycle within a period of rotor current complete it one cycle.

21 36 Figure 2.14 Expanded view of three phae tator current and three phae rotor current Reult and Dicuion for Load Change The imulation i tarted with 50% of full load at the beginning for the reference peed of 100 rad/, and then the load i changed to 75% at 0.4. The peed repone of the imulated reult i hown in Figure It can be een that the peed repone with PID controller on tator ide induce a overhoot. The rie time i 0.09 and the ettling time i 0.22 for the reference peed of 100 rad/ with 50% of full load torque. The teady tate error i 3.02% for 50% of full load torque i.e before load change. When the load i raied to 75% of full load at 0.4, it i oberved that there i a dip in peed from it reference peed of 100rad/. Due to the action of PID controller, the peed reume it reference peed after 0.38 with the teady tate error of 3.70%.

22 37 Figure 2.15 Speed repone for tep change in load from 50% to 75% of full load at 0.4 It i found that the peed control with PID controller on tator ide give poor teady tate repone and ha more teady tate error. It can be een that the peed repone are reduced accuracy when the PID controller acting on tator ide. 2.7 SIMULATION OF THE SYSTEM WITH ROTOR SIDE PID CONTROLLER In thi ection the deigned PID controller ha been conidered for rotor ide inverter and the tator ide inverter i not controller by any controller. The tator ide inverter i working with fixed pule. Figure 2.16 how the imulink model of the wound rotor induction motor with PID controller on rotor ide inverter. The pecification of the WRIM ued for imulation i given in Table 2.4.

23 38 Figure 2.16 Simulink Model of the WRIM with PID controller rotor ide Reult and Dicuion for Step Change in Speed Figure 2.17 how the peed Variation of wound rotor induction motor with repect to time, conidering the PID controller on rotor ide alone. The correponding deflecting torque variation are hown in Figure It i een from the graph that the torque i pulating in nature even in the teady tate region. Thi pulation i due to the continuou action of PID controller.

24 39 Figure 2.17 Speed variation with repect to time repone for et peed of 100 rad/ with 50% load Table 2.6 Tranient and teady tate Performance with repect to peed repone Parameter Value Rie time 0.06 Settling time Peak over hoot 11% Steady tate Error 2.95%

25 40 Figure 2.18 Deflecting Torque variation with repect to time repone for et peed of 100 rad/ with 50% load Figure 2.19 Three phae tator current with repect to time repone for et peed of 100 rad/ with 50% load

26 41 The three phae tator current for WRIM with repect to time repone for the reference peed of 100 rad/ i hown in Figure When the peed ettle the correponding current goe and ettle at contant magnitude. It can be een from the graph that the three phae tator current i inuoidal form. The correponding tator d-q current and voltage wave form are hown in Figure 2.20 and Figure 2.21 repectively. Figure 2.20 Stator d-q current with repect to time repone for et peed of 100 rad/ with 50% load Figure 2.22 how the three phae rotor current for the reference peed of 100 rad/ and the correponding rotor d-q current and voltage are hown in Figure 2.23 and 2.24 repectively.

27 42 Figure 2.21 Stator d-q voltage with repect to time repone for et peed of 100 rad/ with 50% load Figure 2.22 Three phae rotor current with repect to time repone for et peed of 100 rad/ with 50% load

28 43 Figure 2.23 Rotor d-q current with repect to time repone for et peed of 100 rad/ with 50% load Figure 2.24 Rotor d-q voltage with repect to time repone for et peed of 100 rad/ with 50% load

29 Reult and Dicuion for Load Change The imulation i tarted with 50% of full load at the beginning for the reference peed of 100 rad/, and then the load i changed to 75% at 0.4. The peed repone of the imulated reult i hown in Figure It can be een that the peed repone with PID controller on rotor ide alo induce ome overhoot. The rie time i 0.06 and the ettling time i for the reference peed of 100 rad/ with 50% of full load torque. The teady tate error i 2.95% for 50% of full load torque i.e before load change. When the load i raied to 75% of full load at 0.4, it i oberved that there i a dip in peed from it reference peed of 100rad/. Due to the action of PID controller on rotor ide, the peed reume it reference peed after 0.4 with the teady tate error of 3.85%. Figure 2.25 Speed repone for tep change in load from 50% to 75% of full load at 0.4 The tranient and teady tate performance of the WRIM with PID controller acting on rotor ide alone are given in Table 2.7. It i een that the

30 45 ettling time i low when PID controller i ued on rotor ide. Similarly the teady tate error and the percentage over hoot alo reduced with PID controller on rotor ide. Table 2.7 Comparative analyi of peed repone to variou combination of controller for peed change at contant load operation Stator ide Controller Rotor ide Rie time () Settling time () % Over hoot Steady tate error (%) PID No controller No controller PID Table 2.8 Comparative analyi of peed repone to variou combination of controller for load change at contant peed operation Controller Speed Speed Steady tate error (%) drop Recovery Stator ide Rotor ide (%) time () Before Load After Load change change No PID controller No controller PID It can be een that the peed repone are reduced accuracy. It ha been concluded that the PID controller wa ineffective in eliminating the overhoot, rie time and teady tate error.

31 CONCLUSION In thi chapter the block diagram of the propoed double inverter fed wound rotor induction motor ha been preented. The controller configuration for the Wound Rotor Induction Motor wa alo preented for both tator and rotor ide. The direct axi and quadrature axi mathematical modeling of Wound Rotor Induction Motor have been developed and preented. The performance reult for rotor ide control and tator ide control acting independently wa provided. It i een from the above analyi, the rie time, ettling time, percentage overhoot and teady tate error are high for PID controller ued in tator ide and alo ued in rotor ide. It i concluded that the double ide controller are neceary to accomplih the tranient and teady tate performance of the Wound Rotor Induction Motor.