MASTER S THESIS HYBRID DU/DT-FILTER IN FREQUENCY CONVERTER APPLICATIONS

Transcription

1 FACULTY OF TECHNOLOGY LUT ENERGY ELECTRICAL ENGINEERING MASTER S THESIS HYBRID DU/DT-FILTER IN FREQUENCY CONVERTER APPLICATIONS Examiners: Proessor Pertti Silventoinen Proessor Victor Vtorov Supervisors: Proessor Pertti Silventoinen D.Sc. Valentin Dzhankhotov D.Sc. Mikko Kuisma Lappeenranta, May 20, 2009 Elena Rubtsova Punkkerikatu 5A Lappeenranta helena.rubtsova@gmail.com

2 ABSTRACT Lappeenranta University o Technology Faculty o Technology Department o Electrical Engineering Elena Rubtsova HYBRID DU/DT-FILTER IN FREQUENCY CONVERTER APPLICATIONS MASTER S THESIS pages, 47 igures, 8 tables and 1 appendix Examiners: Proessor Pertti Silventoinen Proessor Victor Vtorov Keywords: Inverter output ilter, pulse-width modulation, permanent magnet synchronous motor, current vector control The aim o the thesis is to investigate the hybrid LC ilter behavior in modern power drives; to analyze the inluence o such a du/dt ilter on the control system stability. With the implementation o the inverter output RLC ilter the motor control becomes more complicated. And during the design process the inluence o the ilter on the motor should be considered and the ilter RLC parameters should be constrained.

3 Acknowledgments This master s thesis was done at the Department o Electrical Engineering at Lappeenranta University o Technology during the winter and spring period A lot o people helped me to realize this work and without them this experience abroad would deinitely not have been as special and great as it was. First o all, I kindly thank my supervisors, Proessor Pertti Silventoinen, D.Sc. Valentin Dzhankhotov, D.Sc. Mikko Kuisma or their guidance, new knowledge and support. It was a great opportunity to work with you and I have learned a lot rom you. I thank Samuli Kallio and Mr. Martti Lindh or their help in the laboratory. I am also very grateul to Proessor Victor Vtorov and Proessor Alexander Mikerov rom Saint-Petersburg State Electrotechnical University or their help and participation during my study. I express my appreciation to Yulia Vauterin and Juha Purhönen or giving me opportunity to study at LUT. I want to thank my riends whom I have met here Dmitry, Polina, Sergei, Marina, Mitya, Yulia, Kattaden, Maria, Pavel. I thank the best tutor Alexander Smirnov! My special thanks to my best riend Lyudmila Popova! Lie is not the days that have passed, but those that remembered. Thank you or a lot o vivid and unorgettable moments in my lie during this year! Finally, I would like express my deepest gratitude to my amily. This work is dedicated to my parents Lyubov and Alexander as well as to my brother Ivan. Thank you or believing in me, you are my all. Lappeenranta, May 2010 Elena Rubtsova

4 TABLE OF CONTENTS List o Symbols and Abbreviations Introduction PWM adverse eects and their mitigation Electrical circuit o the drive AC drives control Measurements in electrical drives with respect to electrical ilters Inverter output du/dt ilters Conventional du/dt ilter Hybrid LC ilter Filter parameters selection Objectives and outline o the thesis Drive system simulation in matlab/simulink Basics o the permanent magnet synchronous motor vector control Pulse-width modulation method Speed Control Permanent magnet synchronous motor model Mathematical model Equivalent electrical circuit Hybrid LC in requency domain Hybrid LC ilter electrical characteristics measurements HLCF model Simulation and experimental results The system without and with an HLCF The estimation o the inluence o the ilter parameters on the output perormance o the drive Inductance oversizing

5 4.2.2 Capacitance oversizing Conclusions Reerences Appendix

6 List o Symbols and Abbreviations Symbols B C b, C b1 C e C i C i1 C i2 C C m D out h h D J i a, i b, i c i d, i q i dre, i qre I ph I nom k 1 k p k u L d, L q L cab L L m L main M N p Q peak lux density main capacitance (capacitance between main and auxiliary oil) end-to-end capacitance o one winding intra capacitance o the winding intra capacitance o the main oil intra capacitance o the auxiliary oil capacitance o a ilter capacitance o a motor ilter outer diameter requency height o the hybrid LC ilter aspect ratio o the hybrid LC ilter rotor moment o inertia currents in the phases a, b, c direct-axis and quadrature-axis currents direct-axis and quadrature-axis current reerences phase current nominal current constant or the core material proportional gain back RMF direct- and quadrature-axis inductances cable inductance inductance o a ilter inductance o a motor main inductance (inductance o the main oil) mutual inductance number o oscillations number o poles quality actor o the ilter 6

7 R R ESR R R in R inv R out T e U a, U b, U c U d, U q, U m U out U DC U s V ω m ω r x y z c z Lm resistance equivalent series resistance resistance o a ilter inner input resistance o the impedance analyzer inverter resistance inner output resistance o the impedance analyzer electromagnetic torque voltages in the phases a, b, c direct-axis and quadrature-axis voltages voltage at motor terminals output voltage o the hybrid LC ilter DC link voltage stator voltage eective core volume rotor mechanical speed rotor electrical speed requency exponent lux density exponent capacitive ilter impedance inductive motor impedance Greek symbols Ψ PM Ψ d, Ψ q ξ θ r θ p permanent magnet lux linkage direct-axis and quadrature-axis magnetic lux damping actor rotor angle phase delay Abbreviaations A/D analog/digital AC alternating current AE gain-phase analyzer earth-connected terminal o the auxiliary oil DC direct current 7

8 EMI HLCF IGBT MAI MAO PI PMSM PWM electromagnetic emissions hybrid LC ilter insulated gate bipolar transistors gain-phase analyzer input-connected terminal o the main oil gain-phase analyzer output-connected terminal o the main oil proportional-integral permanent magnet synchronous motor pulse-width modulation 8

9 1. Introduction 1.1 PWM adverse eects and their mitigation Electrical Speed Drives have ound wide applications in the modern industry. The Electrical Drives contain the power electronics, an electrical motor, a controller, and the measuring equipment. Mostly used type o electrical motors is a three-phase induction motor, because it is simple in design, inexpensive and reliable. However, in contrast with the DC motors, the induction motor is diicult to control. The development o high-quality permanent magnet materials or commercial production brought various types o permanent magnet synchronous machines (PMSM) available in today s market. These motors are more simple in the control than induction AC motors, they have good eiciency due to the magnets on the rotor, but more expensive because o the complicated rotor construction. In many motor drive applications, a precise speed or torque control is needed. A requency converter is used to control the speed and the torque o the AC motors. In this application, the typical requency converter is a three-phase two-level voltage source inverter containing power semiconductor switches (IGBTs). The phase voltages are usually generated by a controller with the help o a Pulse Width Modulation (PWM) method. The output voltage o a pulse-width modulated (PWM) inverter consists o sharpedged voltage pulses, which cause unwanted eects in the motor drive. Sudden alterations o the voltage produce high voltage stresses in the motor insulations, especially i a long cable is used, and may cause bearing currents (Salomäki 2007). In addition, high du/dt in PWM wave may cause EMI problems. The method, which is able to reduce these problems, is the inverter output LCR ilter, installed at the output o the inverter. Resistive elements in these ilters generate large losses, heat very much and can require additional cooling system, lead to other components electrical and mechanical oversizing, increase the attenuation, especially at high requencies, and, thereore, are undesirable. This results in essential additional expenses. Depending on the application, resistors price can vary rom 15% to 70% 9

10 o other ilter components cost. However, resistors provide voltage oscillations damping and are unavoidable or many cases. I the inverter output LCR ilter is implemented, the motor control becomes more complicated. For the drive with LC ilter additional control algorithms are required compared to a drive without a ilter. The stator and the measured inverter output currents are dierent. Thus, the inluence o the ilter should be taken into account, because the system dynamics with ilter is changed. The LC ilter implementation is expected to decelerate the dynamics o the stator current control. Also the stability o the system can be lost. During the design process the inluence o the ilter on the motor should be considered and the ilter RLC parameters can be constrained. The structure o the inverter output ilter is shown in Figure 1.1. L Rectiier Inverter L L Cable R C C C R R Motor Figure 1.1 Circuit diagram o electric drive equipped with three phase inverter output RLC ilter. There are two types o inverter output ilters: du/dt ilters and sinusoidal ilters depending on the cut o requency. The cut o requency o the du/dt ilters is above the switching requency o the inverter. As ollows rom their name, du/dt ilters are used to reduce the rise rates o the inverter output voltage pulses. 1.2 Electrical circuit o the drive A Figure 1.2 shows the electrical circuit diagram o a three-phase voltage-source converter. It consists o a sinusoidal three-phase network power supply, a diode 10

11 bridge (rectiier) or voltage rectiication, a DC link or smoothing the rectiied voltage, a PWM inverter that ampliies digital control signals, a cabling system and the motor. 3-phase supply Diode Bridge DC link PWM inverter Cabling L dc+ +U DC-link L s D 1 D 2 D 3 C dc+ T A+ T B+ D A+ T C+ D B+ D C+ L cab L s L s 0 L cab L cab Motor T A- T B- T C- D 4 D 5 D 6 L C dc- dc- D A- D B- D C- -U DC-link Figure 1.2 Main circuit o a voltage source electric drive. The diode bridge consists o positive and negative commutating groups. The DC link contains DC chokes and a large capacitor. The PWM inverter contains six IGBT transistors with diodes. Each o the inverter output voltages (u A, u B, u C can be connected either to the upper or lower potential o the DC link (Dzhankhotov 2009). The diode bridge consists o the positive and negative commutating groups. The DC link contains DC chokes and a large capacitor. The PWM inverter contains six IGBT transistors with diodes. Each o the inverter output voltages (u a, u b, u c can be connected either to the upper or lower potential o the DC link. A three - phase power supply can be described by its internal inductance L s as shown in Figure 1.2. The diode bridge rectiies the AC grid voltage to a DC voltage. To smooth a considerable ripple in the rectiied voltage ater the diode bridge a DC link is used. DC link usually contains two or three capacitors in series. When the DC link contains two capacitors C dc+ and C dc the system has a midpoint O. I voltages are smoothed well, the potential in this point approaches zero. In other words, the midpoint may be considered as a natural neutral point o the drive (which, however, may loat against, or example, the earth potential) (Dzhankhotov 2009). A two-level inverter converts the DC voltage to the controlled AC voltage 11

12 or the motor. The base requency is usually 50Hz (Europe) and 60 Hz (USA). Switching requency depends on the transistors implemented or the energy conversion. For the power applications this requency lies within 1.5 khz to 5 khz range. The inverter consists o power electronic switches, which are usually insulated gate bipolar transistors (IGBTs). As a rule, the voltage control is perormed by pulse width modulation method. The cable between the inverter and the motor can be described with the help o a inite RLC structures. Roughly, every additional meter o motor cable contributes to the model a new RLC inite element. Manuactures o power cables usually provide inormation about these inite element values. The theoretical background o the drive with the long cable is given by the theory o transmission lines. This theory describes energy low in cable with the help o relected waves between motor phases (which have essential impedance at high requencies in question). Finite RLC structure slow down the voltage rise rates but, as resistances are very small, lead to signiicant voltage oscillations at motor terminals, with doubled irst overshoot (theoretically). Oscillations at appear every time switching on or o takes place and this lead to the accelerated phases insulation wear-out. 1.3 AC drives control When considering close loop drive systems it is necessary to know the motor speed which is compared with a reerence value. In many cases the speed measurement is perormed by the rotating speed sensor. This sensor is installed on the motor or load shat and requires a transormation block which converts the mechanical speed value to an analog or discrete electrical signal proportional to the measured value. These sensors give precise inormation about the rotor speed and angle. However, their price is quite high and they also decrease the system reliability. The tendency over the last decades has been to remove any expensive systems rom the drive and obtain all the required inormation about motor rotation rom current sensors installed at the output o the converter. 12

13 This has led to the sensorless speed estimation methods development at which the measured value is determined indirectly through the easily measurable electrical variables. Primarily, these values are inverter voltage, which eeds the motor and the stator current. In the context o a circuit design, this approach means the devolution to the electronic part unctions previously perormed by a rotating sensor. This leads to the complexity, but with using modern microcontrollers such a complexity does not lead to the drive cost increasing. There is one more positive thing - no need or wires connection between the sensor and the control system which can be at a considerable distance rom the motor and sensor. The sensorless speed determination can be obtained by dierent methods, the complexity o which is determined by required accuracy o speed. These methods can be classiied into ive groups. The irst group includes non-adaptive methods in which the speed is determined directly rom the measured stator voltage and current. The second group includes adaptive techniques. They are oriented to the closed loop systems o electric drive control, in which adaptation is applied to improve the accuracy o the measuring system. The third group includes methods based on the design eatures o the motor which use the inormation o the magnetization curve o the machine. The ourth group includes a non-linear method based on the theory o neural circuits. And the ith group is the group o methods which are used to improve the accuracy due to additional high-requency signals or other additional inormation (Sokolovskiy 2006). 1.4 Measurements in electrical drives with respect to electrical ilters An AC drive without output ilter requires just an inverter output current measurement, DC-link voltage and the rotor speed measurements, because i ilter is not used the inverter output current equals to the stator current (i not take into account a long cable between inverter and motor). 13

14 I the output ilter is implemented between the inverter and the motor as presented in Figure 1.3, then the problem o the current sensor locating occurs. There are two possibilities: the current sensor is placed beore the ilter and the current sensor is placed between the ilter and motor. In many cases, or example, in water pumps, the distance between the requency converter and the motor is more than tens o meters. It is diicult, at least expensive, to attach any sensors to the motor. However, a long cable speciicity requires to protect the motor rom voltage oscillations with the help o the electrical ilter. Filter parameters depend on the concrete application eatures (e.g., the length o the cable and the parameters o the cable), so that a mass-production converter manuacturer cannot predict them. Thus, as a rule, current sensors are installed inside the converter box. In an ideal case the drive measurements rom the DC-link voltage u dc, the inverter output current i A, inverter output voltage u A, the stator current i s, the stator voltage u s, and the rotor speed ω m are required. Such a large number o measurements require great number o sensors, A/D converters, and signal wires or connection with the requency converter. In practice, the number o measurements should be minimized. Control u dc i A u A i s u s ω m Diode Bridge Inverter Output ilter Figure 1.3 Possible measurements in drive when inverter output ilter is used. Double lines indicate complex quantities (space vectors) whereas single lines indicate real quantities (scalars) (Salomäki 2009). 14

15 The speed - sensorless control method or an IM has been proposed by (Salomäki 2007). Figure 1.4 shows a simpliied block diagram o the control system (the estimated quantities being marked by the symbol ^). The cascade control and the speed-adaptive ull-order observer are implemented in the estimated rotor lux reerence rame. u A,re Estimated rotor lux, reerence rame Stator reerence rame ω m,re Voltage control Speed control i s,re Stator current control u s,re Stator voltage control i A,re Inverter current control u A,re ^ j s e θ u dc PWM ^ ω m i^ s u^ s Adaptive ull-order observer j s e θ^ i A M Figure 1.4 Simpliied block diagram o cascade control system. Double lines indicate complex quantities (space vectors) whereas single lines indicate real quantities (scalars) (Salomäki 2007). In this case the only measured parameters are the inverter output current i A and the dc-link voltage u dc, while the stator voltage u s, the stator current i s and the electrical angular speed o the rotor ω m can be estimated by an observer. So the current sensor is advisably to place between the inverter and ilter. 1.5 Inverter output du/dt ilters The relection rom the motor and motor cable interace can cause surpassing o the motor impulse voltage rating, which is adverse to the insulation o the motor. The over voltages and adverse eects caused by voltage relections in long cables are reduced by applying dierent iltering solutions: output reactors as well as ilters at 15

16 converter or motor terminals. For many cases, the most eicient solution is converter output du/dt ilters (Moreira) Conventional du/dt ilter The typical du/dt ilter consists o a series inductance and a parallel capacitance, and the losses in the circuit are tuned in order to obtain the desired transient output response or the drive. This kind o a system consisting o inductance, capacitance, and resistance is generally a second order system. However, since a second order system itsel is a resonance circuit, it easily becomes a source o overvoltage and oscillation instead o the inverter-power cable electric motor resonator, i not suiciently damped (Ström 2009). du/dt ilters reduce the du/dt o the output voltage at motor terminals. Insulation motor ailure is oten caused by the ast voltage and current increasing. du/dt ilter designed so that it reduce ast voltage increasing and thus prevent the breakdowns. du/dt ilters impact positive inluence or the electromagnetic noise emission in motor cable. In comparison with the sinusoidal ilters du/dt ilters cut o requencies higher than switching requency. du/dt ilters are less expansive because they have smaller inductance and capacitance. They typically also have lower losses. The du/dt is reduced in accordance with the LC constant value. An acceptable transient response is obtained with a damping, which means losses. In the passive du/dt design process design parameters like the resonance requency ω r and the damping actor ξ should be taken into account. At the cable oscillation requencies the ilter is designed or and the ilter attenuation should be maximized. The compromise between these eatures should be ound when du/dt ilter is designed. 16

17 1.5.2 Hybrid LC ilter In our days the oil-wound choke which is characterized by low DC and AC resistances is widely used in industry. To avoid short-circuit using oil-wound the suraces between coil turns have to be separated by insulation layer. The insulation causes a high capacitance between the turns which is called intra capacitance, but it weakens a heat transer. A new hybrid LC ilter (HLCF) is presented in Figure 1.5. Detailed description o a hybrid LC ilter was proposed (Dzhankhotov 2009). plastic tube main oil insulator auxiliary oil insulator Figure 1.5 Principal coniguration o a single phase o a novel air-core hybrid LC ilter (Dzhankhotov 2009). One phase o a hybrid LC represents two or more oils isolated rom each other and coiled on an air core. The irst layer is called main oil and other ones are auxiliary oils. Between the main and auxiliary oil the signiicant capacitance is occurred. The eective inductance o the main coil is called main inductance and the eective capacitance between the main and auxiliary oils is main capacitance. Such a ilter 17

18 implemented to the output o the PWM inverter provides a low impedance path or the harmonics o PWM voltage and suppresses dierential- and common-mode voltages. 1.6 Filter parameters selection Some ilter design guidelines have been suggested in the literature, e.g. (von Jouanne, Lee and Nam, Dzhankhotov). However, the limits o the ilter parameters variation seem not to be analyzed well. The single phase equivalent circuit o a RLC ilter is presented in Figure 1.6. Here the L, C, R are inductance, capacitance and resistance o the ilter, the C cab are the cable inductance and capacitance, the L m and and capacitance o the motor, the L cab and C m are the inductance U DC and U m are the voltages rom the DC link and on the motor terminals. Usually the motor inductance more than the ilter inductance which in turn more than the cable inductance L >> L >> L. The m cab cable is considered as a lossless transmission line and sometimes, i relevant, can be neglected. Let us consider dierent possibilities in order to understand the basic philosophy o the ilter design. L L cab L m U DC + - R C L cab L m + U m - Figure 1.6 Single phase equivalent circuit o drive system with RLC ilter and cable. There are dierent restrictions on the ilter parameters: electrical, mechanical, thermal, drive control limitations, restrictions due to the speciicity o the application (or example, special requirements humidity or saety), etc (Figure 1.7). 18

19 Mechanical Electrical RESTRICTIONS Thermal Control System Others Figure 1.7 The classiication o the ilter parameters limitations. The electrical limitations describe the needed relation between the ilter parameters in order to achieve the required iltration properties with the certain resistance R, inductance L, capacitance C. Some general remarks are presented below. 1. Predominant inductance. I the ilter inductance L is ininite, the inductive impedance is also ininite ( Z L = ω L = ). In this case, the phases represent the open circuits and there is no current lowing to the motor. The equivalent circuit or this case is presented in Figure 1.8(a). 2. Predominant capacitance. I the ilter capacitance C is ininite, but the ilter resistance R and inductance L are zero, all the current lows back to the converter. This case can be represented with Figure 1.8 (b). I the ilter inductance L is comparable with the sum inductance o the cable and the motor (L cab + L m ), some current proportional to the ratio (L cab + L m )/ (L + L cab + L m ) penetrates to the cable and motor. The capacitive impedance approaches zero ( Z 1 c = = 0 ω ). C 19

20 L m L L m + C U DC U U DC m R C m C m U m (a) (b) Figure 1.8 Equivalent circuit o drive system with RLC ilter (a) L (b) C, the phase represents an open circuit. 3. Predominant resistance. I the ilter resistance R is ininite, the RC-chain o the ilter is open-circuited. This means that the only inductor L exists in the ilter. The equivalent circuit is presented in Figure 1.9. This means that we have a irst order ilter instead o the second order ilter so that the attenuation properties o such a ilter become much worse (-20 db/dec instead o -40 db/dec). However, there is no LC resonance in such a ilter. L L m + C + - R C m - U m Figure 1.9 Equivalent circuit o drive system with RLC ilter, R. 4. Q-actor. The inductance, resistance and capacitance relation describes also the oscillations in the output voltage and the output current. This relation can be expressed with the quality actor: Q p = C L 2 R (1.1) Quality actor Qp is proportional to the number o the oscillations N. The smaller ilter inductance L and the larger ilter capacitance C and resistance R, the smaller quality actor Q p and the oscillations N decrease too. 20

21 The drive control restrictions to the ilter parameters describe the output perormance o the application. In other words, the ilter should not signiicantly change the dynamics o the system. 1. DC-link voltage distribution. For the control system designer (as well as or the motor designer) the ilter phase inductance L is a leakage inductance. The less ilter inductance the less voltage is required rom the DC link since the ilter inductor voltage drop is decreased. The equivalent circuit is shown in Figure U L = I Z = I ω L (1. 2) L L L U m U Z DC Lm = (1. 3) L Z + Z Lm L U DC L m U m Figure 1.10 Equivalent circuit o drive system or L m << L. From the motor point the ilter inductance L is equivalent to the leakage inductance and it decreases the eiciency. So the small ilter inductance is good or the motor system. 2. Output speed and torque reduction. Consider a divider which consists o the motor and ilter inductances as shown in Figure 1.11 the phase voltage U out decreases then the ilter inductance L increases according to (1.4). 21

22 L U in Lm U out Figure 1.11 Voltage divider consists o the motor and ilter inductances. U U out in L ω L m m = =, Lm ω + L ω Lm + L (1.4) where U out - phase voltage, U in - voltage equivalent to the DC link voltage. With the increasing o the ilter inductance and the phase current reduction. I U L the impedance Z = ωl increases out ph = decreases which cause the torque and the speed ωl 3. Contribution to the delays. The ilter consists o the reactive component and, thereore contributes to a time delay. This time delay is usually not compensated by the control system. One phase equivalent circuit o the system is o the second order due to the L and C. Phase delay contributed by it depend on L : L + Lm Θp = arctg( ωm ) (1.5) R + R m where R = R + R + R and cab inv ESR, cab R ESR is an equivalent series resistance. R is a cable resistance, R inv is an inverter resistance 22

23 Usually L m >> L L, let us say, i Lm = 3 mh and L = 100µH, m = 30. Thereore, L the ilter contribution to the angle delay is negligible or many o the practical cases. However, i motor inductance attention should be given to the system stability. Lm is closed to ilter inductance L, special The thermal restrictions are related to the dierent kind o losses. Resistive elements in these ilters generate large losses, heat very much and can require additional cooling system. This leads to other components electrical and mechanical over sizing, decrease the attenuation, especially at high requencies, and, thereore, are undesirable. 1. Power losses in the inductor. Power losses P L in the inductor are the unction o the magnetic lux B and dimensions. Accurate estimation o the magnetic core loss is important when designing the magnetic devices used with switching power converters. The core loss o an inductor is deined by the general ormula: x y PL = k1 B V (1.6) where k1 - constant or the core material, - requency, x - requency exponent, B - peak lux density, y - lux density exponent, V - eective core volume. I consider two ilters which have inductances L 1 and L 2, and L 1 < L 2 and volumes V are constant, then magnetic lux B 1 < B 2 so the power losses P L1 > P L2 and thus the higher ilter inductance the ilter inductance should not have very large value. L the more power losses P L that means that 2. Power losses in the resistor. However, i the ilter inductance L is very small, the ilter capacitance C should be excessively large, then big portion o the current lows via the damping circuit so that very large ilter resistance 23 R with very big

24 power rating is required and du/dt is high. Large ilter resistance R increases the cost o the ilter and provides poor reliability. In other case system cannot provide required characteristics. The mechanical restrictions o the ilter dimensions and geometry are usually coming rom the application design and power rating. However, it is usually preerable to have desired dimensions as small as possible. The dimensions o the ilter depend on drive requirements set. For example, or the hybrid LC ilter they can be described by an aspect ratio (Dzhanhotov 2009): hd o the LC ilter s axial cross-section h D h D = (1.7) out where h is the ilter height, D out is a ilter outer diameter. To the others restrictions the components humidity durability, the lame proo and the ire saety can be reerred. 1.7 Objectives and outline o the thesis The main objective o this thesis is to investigate behavior o the passive du/dt ilter based on the novel hybrid LC ilter in the modern power drives; to analyze the inluence o such a du/dt ilter on the control system stability. To this end, the ollowing tasks should be considered: Filter parameters selection and dierent restrictions on the ilter parameters. Modelling o a hybrid LC ilter and an equivalent conventional passive LC ilter in requency domain. Measurements o the hybrid LC ilter electrical characteristics in requency domain. 24

25 Simulation o the drive with the PMSM. Investigations o a hybrid LC ilter inluence on the control system stability. The rest o the thesis is divided into the ollowing chapters: Chapter 1 gives general inormation about the background and the problems occurs in the drives with a requency converter. The AC control and drive measurements are considered. Filter parameters selection and dierent restrictions on the ilter parameters are discussed. Chapter 2 presents the drive with the permanent magnet synchronous machine simulation. The Matlab/simulink block diagrams are shown in details. Current vector control is discussed. Implementation o the current and speed controllers are shown. Chapter 3 contains the experimental measurements o the hybrid LC ilter electrical characteristics. The hybrid LC ilter simpliied and general models are proposed. Chapter 4 introduces the simulation results o PMSM drive with the ilter implementation and current vector control. The inluence o the ilter or the control system is shown. Chapter 5 concludes the work covered in this thesis and presents the obtained results. The availability o the results is evaluated and the suggestions or the uture work are given. 25

26 2. Drive system simulation in MATLAB/Simulink The chapter deals with the drive with the permanent magnet synchronous motor simulation. The MATLAB/Simulink block diagrams are shown in details. Current vector control is discussed. Implementation o the current and speed controllers are shown. 2.1 Basics o the permanent magnet synchronous motor vector control Current vector control is widely preerable to the control o the permanent magnet synchronous machines. Such a good perormance can be obtained due to the PM machine parameters like inductances which do not depend on the operating situation comparing with other type o electrical machines. The main reason o selecting current as a controlled variable is similar with the DC machines: the stator dynamics that are stator inductance, stator resistance and induced EMF eects are eliminated. Comparing with the AC drives the current controller is more complicated because it must control the amplitude as well as the phase o the stator current. Also the armature reaction o the PMSM is quite small. Current vector control is perormed in the rotor reerence rame. The control is based on the producing or the d and q axis current reerences i dre and i qre which are implemented by suitably adjusting the voltage. Usually the current reerences are directly ormed rom the torque reerence current reerence i sre Tere or by stator rom the rotating speed controller. Reerences i sare, i sbre, i sbre are ormed by two-phase-to-three-phase transormation or the phase current rom the dq reerences i dre and i qre. The block diagram o the current vector control is presented in Figure

27 PMSM sa sb sc i sa i sb i sc current control i sare i sbre i scre i dre i xre T ere torque control i qre j r e θ i yre i q i d θ r j r e θ θ r Figure 2.1 Block diagram o the current vector control o a PMSM (Pyrhönen 2009). Here the sa, sb, sc are inverter control signals, i sare, i sbre, i sbre are reerences ormed by two-phase-to-three-phase transormation, Tere is a torque reerence, i dre and i qre are d and q axis current reerences, i xre and i yre are x and y axis current reerences, θ r is a rotor angle, i d and i q are d and q axis currents. I the direct-axis and quadrature-axis inductances o the machine are approximately equal the i 0 control can be used. When i 0 control is used the torque can be d = simpliied to the equation: d = T e 3 p[ ψpmisq ] (2.1) 2 27

28 The direct-axis current does not contribute on the torque. Neglecting the armature reaction the current reerences can be written as: i qre = T 3 ψ 2 ere PM (2.2) i dre = 0 (2.3) The inormation about the rotor angle θ r is available and this type o control is very easy to realize. The torque is directly proportional to the stator current as in the DC machine. The drawback o such a type control, that it is impossible to use a ield weakening at all. And the rated speed o the motor has to be selected such that it satisies to the needs o the drive. 2.2 Pulse-width modulation method The PWM method is widely used in the modern power drives (Mohan 2003). Usually the switching requency is kept constant. Such a control is based on the principle o comparing the triangular carrier wave o desire switching requency with the error o the controlled signal. The result o comparison is a voltage control signals which are inputs to the gates o inverter. MATLAB/Simulink PWM inverter block diagram is presented in Figure 2.3. The control is based on the comparison o required phase current and triangle waves: i the phase current is greater than the triangle waveorm the inverter leg is switched to the positive polarity (the high state). I the phase current is less than the triangle waveorm the inverter leg is switched to the negative polarity (the low state). The generation o the PWM signals is shown in Figure

29 The error signal is ormed as the dierence o the reerence signal I r_abc generated in the controller and the signal o the actual motor current I abc as shown in Figure 2.4. current error PWM signal Figure 2.2 PWM current controller. The PWM signal is based on the comparison o required phase current and triangle wave. Figure 2.3 Matlab/Simulink PWM inverter block diagram. PWM comparator generates a PWM signals or the inverter. 29

30 MATLAB/Simulink PWM comparator block diagram is presented in Figure 2.4. Figure 2.4 MATLAB/Simulink PWM comparator block diagram. The error signal is ormed as the dierence o the reerence signal current I abc and then compared with a triangle wave. I r_abc generated in the controller and the signal o the actual motor 2.3 Speed Control Speed controller calculates the error as a dierence between the reerence speed and the actual speed, which is ed to the PI controller. PI controllers are widely used or the motion control system. They consist o a proportional gain k p and an integration gain s k i. Proportional gain produces an output proportional to the input error and integration gain makes the steady state error zero or a step change in the input. The PI speed controller is shown in Figure 2.5. k p ω re error_speed k i s System ω r ω r Figure 2.5 Speed controller. Speed error calculates as a dierence between the reerence speed and the actual speed. Proportional gain produces an output proportional to the input error and integration gain make the steady state error zero or a step change in the input. 30

31 The speed control o the machine usually consists o two loops: the current loop is an inner loop and the speed loop as outer loop. The current loop should be at least 10 times aster than the speed loop, because the order o the loops is due to their response, shows how ast loops can be changed. 2.4 Permanent magnet synchronous motor model Nowadays, the Permanent Magnet Synchronous motor can be presented in a twoaxis model. Space vector theory is applied or the model derivation. The equivalent circuit o Permanent Magnet Synchronous motor is presented in the rotor reerence rame and separately given or the direct and quadrature axis directions Mathematical model For the PMSM the two-axis model is employed as shown in Figure 2.6 The a, b and c axes shows the direction o the three-phase stator windings. In the two-phase xy reerence rame the axes are ixed in the direction o the stator phase winding a. The rotor two-phase dq reerence rame is ixed with the magnetic pole o the rotor. The rotating angle between the rotor and stator reerence rame is equal to the rotor electric angle θ r. 31

32 b y q d x a c Figure 2.6 Frames o reerence related to PMSM: a, b and c indicate the directions o the magnetic axes o the phase windings o a three-phase stator. The xy reerence rame is a two-phase reerence rame, the axes o which are ixed in the direction o the stator phase winding a and perpendicular to it. The dq reerence rame is a two-phase reerence rame ixed on the rotor, the axes being in the direction o the magnetic pole and perpendicular to it (Pyrhönen 2009). Modeling the PMSM without damper winding on the rotor reerence rame the ollowing assumptions can be accepted: 1) Saturation is negligible; 2) Eddy currents and hysteresis losses are negligible; 3) The induced EMF is sinusoidal; 4) There are no ield current dynamics. Voltage equations are given by: U = R i ω ψ + pψ (2.4) d s d r q d 32

33 U = R i + ω ψ + pψ (2.5) q s q r d q The lux linkages can be presented as: ψ d = L i + ψ (2.6) d d ψ = L i (2.7) q q q Substituting equations (2.6), (2.7) to (2.4), (2.5) U d = R i ω L i + p( L i + ψ ) (2.8) s d r q q d d U = R i + ω ( L i + ψ ) + pl i (2.9) q s q r d d q q The motor torque can be written as: T e ( ψ i + ψ i ) 3 p = d q q d (2.10) 2 2 The mechanical torque equation can be written as: T e dωm = TL + Bωm + J (2.11) dt Expressed ω m rom (2.11) and solve: and Te TL Bωm ωm = dt (2.12) J ω m p = ωr 2 (2.13) whereω is a rotor electrical speed and r ωm is a rotor mechanical speed. 33

34 2.4.2 Equivalent electrical circuit The equivalent circuit can be used or study and simulation o the machine. For the PM synchronous machine the equivalent circuit is presented in the rotor reerence rame. The equivalent circuit is separately given or the direct and quadrature directions. The equivalent circuit o the Permanent Magnet Synchronous machine is presented in Figure 2.7. R s ω r ψ q L d - L dm i PM R s ω r ψ d L q - L qm U d ψ d ψ md L md L mq i PM U q Figure 2.7 Equivalent circuit o the Permanent Magnet Synchronous machine without Damper Windings (Pyrhönen 2009). Current vector control is perormed in the rotor reerence rame. The ollowing equations are expressed in the rotor reerence rame (dq rame): d dt i d 1 R L s q = U d id + pωriq (2.14) Ld Ld Ld d dt i q 1 U R i L p i Ψ pω s d PM r = q q ωr q (2.15) Lq Lq Lq Lq T = 1. p[ Ψ i + ( L L )i i ] (2.16) e 5 PM q d q d q where L q, L d are q and d axis inductances, R s is a resistance o the stator windings, i q, i d are q and d axis currents, U q, U d are q and d axis voltages, ω r is an angular velocity o the rotor, Ψ PM is an amplitude o the lux induced by the permanent 34

35 magnets o the rotor in the stator phases, p is a number o pole pairs, T e electromagnetic torque. is an The MATLAB/Simulink block diagrams or q and d axis currents production are presented in Figure 2.8 and 2.9. The block diagram or the electromagnetic torque production T e is presented in Figure Figure 2.8 MATLAB/Simulink q-axis current i q production block diagram. Figure 2.9 MATLAB/Simulink d-axis current i d production block diagram. 35

36 Figure 2.10 MATLAB/Simulink electromagnetic torque T e production block diagram. PMSM drive simulation is based on some steps and one o such step is the dq0_to_abc phase variables transormation and reverse transormation. In the threephase electric machine models the so-called Park transormation is commonly used. Usually it transorms three quantities. They are direct axis, quadratic axis, and zerosequence components expressed in a two-axis reerence rame back to the phase quantities. The ollowing transormation is used: I = I sin( ωt ) + I cos( ωt ) + I (2.17) a d q 0 2π 2π I b = Id sin( ωt ) + Iq cos( ωt ) + I0 3 3 (2.18) 2π 2π I c = I d sin( ωt + ) + I q cos( ωt + ) + I (2.19) This kind o transormation is the same or the three-phase voltage, the I a, I b, I c, I d, I q and I 0 variables simply replace with the U a, U b, U c, U d, U q, and U 0 variables. The MATLAB/Simulink dq0_to_abc transormation block is presented in Figure

37 Figure 2.11 The MATLAB/Simulink dq0_to_abc transormation block. The abc_to_dq0 transormation block presents the direct axis, quadratic axis, and the zero sequence quantities in a two-axis rotating reerence rame or a three-phase sinusoidal signal. The ollowing transormation is used: V V q d 2 2π 2π = (Va sin( ωt ) + Vb sin( ωt ) + Vc sin( ωt + )) (2.20) π 2π = (Va cos( ωt ) + Vb cos( ωt ) + Vc cos( ωt + )) (2.21) V 0 1 = (Va + Vb + Vc ) (2.22) 3 This kind o transormation is the same or the three-phase current, the U a, U b, U c, U d, U q and U 0 variables simply replace with the I a, I b, I c, I d, I q and I 0 variables. The MATLAB/Simulink abc_to_dq0 transormation block is presented in Figure

38 Figure 2.12 MATLAB/Simulink abc_to_dq0 Transormation block. The ull block diagram is presented in Appendix A. 38

39 3. Hybrid LC ilter in requency domain In this chapter the experimental results o the electrical characteristics measurements are presented. The Bode plots are shown. The hybrid LC ilter simpliied and general models are proposed. 3.1 Hybrid LC ilter electrical characteristics measurements For the uture simulation the LC ilter electrical characteristics should be ound and the model o the ilter prototype should be proposed. The ilter prototype was analyzed with an HP 4194A impedance and a gain-phase analyzer (HP 4194A 1996), which allows impedance measurement in the requency range 100 Hz 40 MHz and gain-phase measurement in the range 10 Hz 100 MHz. The oil outputs and inputs are indicated by terminals 1-1, 1-2, 2-1 and 2-2 as shown in Figure Figure 3.1 Terminals o the investigated ilter (Dzhankhotov 2009). 39

40 The equivalent circuit o the hybrid LC ilter is presented in Figure 3.2. There the L main is a main inductance, L a is auxiliary inductance, M is a mutual inductance and C b1 is a main capacitance C b1 L main M 2-1 L a 2-2 Figure 3.2 Equivalent circuit o Hybrid LC ilter (Dzankhotov 2009). 1. Main inductance L main measurement, the measurement between terminals 1-1 and 1-2. The measured results are shown in the Table 3.1. Measurements at a requency o 8 khz. С i1 is an end-to-end capacitance o one winding. Table 3.1 Main inductance measurement. Measured value L main С i1 Value 124 µh 0.15 nf In Figure 3.3 the measured main inductance is presented. From Figure we can see that the resonance requency is about 1.1 MHz and considered requency domain is under 1.1 MHz. The required bandwidth o the controller is about 1-15 khz, thus, the resonance can be neglected rom the analysis. Figure 3.3 Apparent inductance o the main oil o the prototype. 40

41 2. Auxiliary inductance L a measurement, the measurement between terminals 2-1 and 2-2. The measured results are shown in the Table 3.2. Measurements at a requency 40 khz. Table 3.2 Auxiliary inductance measurement. Measured value L a С i1 Value 123 µh 0.15 nf In Figure 3.4 the measured auxiliary inductance is presented. The resonance requency is the same about 1.1 MHz. Figure 3.4 Apparent inductance o auxiliary oil o the prototype. 3. Main capacitance C b1 measurement, the measurement between terminals 1-1 and 2-1. The measured results are shown in the Table 3.3. Measurements at a requency 40 khz. Table 3.3 Main capacitance measurement. Measured value С b1 R Value 152 nf 1 Ω In Figure 3.5 the measured main capacitance is presented. The resonance requency is the about 0.3 MHz. 41

42 Figure 3.5 Apparent capacitance o main oil o the prototype. 4. Mutual inductance measurement, the measurement between terminals 1-1, 1-2, 2-1, 2-2. The equivalent circuit or the mutual inductance measurement is shown in Figure 3.6. Measurements at a requency 35 khz. L m L a Figure 3.6 Equivalent circuit or the mutual inductance measurement. L = L + L 2M (3.1) m a + The measured results are shown in the Table 3.4. Table 3.4 Mutual inductance measurement. Measured value M Value 490 µh The mutual inductance is calculated as: ( ) 10 M = = 122 µh (3.2) 2 42

43 In Figure 3.7 and 3.8 the mutual inductance and impedance are presented. Figure 3.7 Mutual inductance o the prototype. Figure 3.8 Impedance between the terminals 1-1 and 2-2. Figures 3.9, 3.10 show the impedance o the oils and also between the oils. 43

44 Figure 3.9 Impedance between the terminals 1-1 and 1-2 (dashed line) and terminals 2-1 and 2-2 (solid line). Figure 3.10 Impedance between the terminals 1-1 and

45 Figure 3.8 shows the impedance behavior between terminals 1-1 and 2-2 at low requencies below 10 khz the impedance behavior is resistive. From 10 khz to 30 khz the inductance is dominant and ater 30 khz the capacitance is dominates. Figure 3.9 shows the impedance behavior at low requencies below 10 khz the impedance behavior is resistive. From 10 khz to 1 MHz the inductance is dominant and ater 1 MHz the capacitance is dominates. Figure 3.10 shows the coupling between the oils. At low requencies the coupling is capacitive. The impedance below 400 khz between the points 1-1 and 2-1 is capacitive, ater that it changes to inductive. This phenomenon can be explained as the inductance o the connection wires and the internal inductance o the capacitive winding. Next, let us consider the gain-phase requency responses. In order to urther simpliy the presentation o results, let us apply the ollowing terminology: MAI or the gain-phase analyzer input-connected terminal o the main oil, MAO or the gain-phase analyzer output-connected terminal o the main oil, AE or the gainphase analyzer earth-connected terminal o the auxiliary oil. (Dzhankhotov 2009) In Figure 3.12 and 3.13 the Bode plots with a dierent earthing point or the single phase are presented. Two possible cases are considered: 1. The earthed terminal o the auxiliary oil is 2-1(Figure 3.11(a)), 2. The earthed terminal o the auxiliary oil is 2-2 (Figure 3.11(b)). 45

46 (a) (b) Figure 3.11 Dierent alternatives or auxiliary oil earthing. (a) The earthed terminal o the auxiliary oil is 2-1. (b) The earthed terminal o the auxiliary oil is 2-2.(Dzhankhotov 2009) In case (a) the currents low in the dierent directions in the turns o the main and auxiliary oils. The produced magnetic luxes cancel each other and prevent ast current redistribution. The inductance tends to zero between terminals 1-1 and 1-2 and the coupling is predominantly capacitive. In case (b) the current lows in one direction in the turns o the main and auxiliary oils. The produced magnetic lux orces current redistribution. The system can be presented as a connection o two inductors with magnetic coupling. And in this case the mutual inductance has an important inluence. 3.2 Hybrid LC ilter model One phase general and simpliied hybrid LC ilter block diagrams are presented in Figures 3.12 and They are perormed in Matlab/Simulink 7.7. The R in and R out 46

47 are an input and output resistances, which present the drive application impedances per one phase near the resonance requency. Figure 3.12 One phase general hybrid LC ilter block diagram in Matlab/Simulink. The general model has a complex representation and requires a long calculation time, but it is more accurate. This model takes into account the main and auxiliary inductances L main and L a, the mutual inductance M, the AC resistance o the oils R ac, the main capacitances C b1, the intra and auxiliary capacitances C i1 and C i2. The simpliied hybrid LC ilter model presented in Figure This simpliied model takes into account only the main inductance and the main capacitance. Figure 3.13 One phase simpliied hybrid LC ilter block diagram in Matlab/Simulink. 47

48 In the HP analyzer, the input impedance in Bode measurements is always 50 Ω, and the output can selected 50 Ω or 1 MΩ. At Figure 3.14, 3.15 the Bode plot o general and simpliied models are presented. Figure 3.14 Bode plots o the simpliied hybrid LC ilter model (red curve) and general hybrid LC ilter model (blue curve), R in =50 Ω, R out =50 Ω Figure 3.15 Bode plots o the simpliied hybrid LC ilter model (red curve) and general hybrid LC ilter model (blue curve), R in =50 Ω, R out =1 MΩ 48

49 We can see that at low requencies till to the irst corner requency the behavior o the Bode plots is the same. For the control system the considered requency domain is below the irst corner requency. Thus, it is possible in the ollowing simulations to use the simpliied model o the hybrid LC ilter. Figures 3.16 and 3.17 show the simulated requency response and requency responses with dierent earthed points. Figure 3.16 Bode plots with earthed auxiliary oil or R int = 50 Ω, R out = 50 Ω. MAI 1-1 MAO 1-2 AE 2-2 (red curve); MAI 1-1 MAO 1-2 AE 2-1(green curve) and simulated (blue curve) 49

50 Figure 3.17 Bode plots with earthed auxiliary oil or R int = 50 Ω, R out = 1 MΩ. MAI 1-1 MAO 1-2 AE 2-2 (red curve); MAI 1-1 MAO 1-2 AE 2-1(green curve) and simulated (blue curve) In Figure 3.18 the requency response or chosen input and output resistances R in =0.5 Ω, R out =1.3 kω is shown. 50

51 Figure 3.18 Simulated requency responses at R in =0.5 Ω, R out =1.3 kω, MAI 1-1 MAO 1-2 AE 2-2. The response has a resonance, because the input resistance R in is not suicient to damp it as it is with the 50 Ω resistor. 51

52 4. Simulation and experimental results In this chapter the simulation results o PMSM drive with current vector control are presented. The inluence o the ilter or the control system is shown. The estimation o the inluence o the ilter parameters on the output perormance o the drive is considered. 4.1 The system without and with an HLCF I the inverter output LCR ilter is implemented, the motor control becomes more complicated. For the drive with LC ilter additional control algorithms are required compared to a drive without a ilter. The stator and the measured inverter output currents are dierent. Thus, the inluence o the ilter should be taken into account, because the system dynamics with ilter is changed. The LC ilter implementation is expected to decelerate the dynamics o the stator current control. Also the stability o the system can be lost. During the design process the inluence o the ilter on motor should be considered and the ilter RLC parameters can be constrained. The simpliied ilter model is used which was presented in Chapter 3. The system created in Matlab/Simulink has been tested with inverter output ilter and without it. The motor parameters used in simulation are given in the Table 4.1. The PM synchronous motor is operated with constant torque up to its rated speed. 52

53 Table 4.1. Parameters o the motor model. Symbol Value Parameter R s 1.78 Ω stator resistance L d 48.7 mh d-axis inductance L q 75.8 mh q-axis inductance p 10 number o pole pairs J 0.33 kgm 2 rotor moment o inertia I nom 8 A nominal current 50 Hz requency k u 425 V back RMF (no load) The nominal ilter parameters which were ound in chapter 3 are used in simulation and given in the Table 4.2 Table 4.2. Nominal ilter parameters. Symbol Value Parameter L 123 µh ilter inductance C 152 nf ilter capacitance R 100 Ω ilter resistance In Figures 4.1 and 4.2 the transer unctions o speed and torque simulated with ilter and without it are presented. 53

54 Figure 4.1 Transer unction o speed without and with a HLCF. Figure 4.2 Transer unction o torque without and with a HLCF. As we can see rom Figures 4.1 and 4.2 the ilter at nominal values does not inluence to the system dynamics. The error is even less than 1 %. That can be explained that ilter time constant excessively less than motor time constant. 54

55 4.2 The estimation o the inluence o the ilter parameters on the output perormance o the drive As it was discussed previously the ilter parameters should be constrained. The oversizing values o the ilter inductance and capacitance or the speciic case were obtained Inductance oversizing The transer unctions o speed and torque are presented in Figure 4.3 and 4.4. In this speciic case when the ilter capacitance and ilter resistance are about zero the ilter inductance o 500 µh is become excessive or the system stability and the error is about 3-5%. For the inductance o 3 mh we can see that the system stability is lost. Figure 4.3 Transer unction o speed or various ilter inductances. 55

56 Figure 4.4 Transer unction o torque or various ilter inductances. From the simulation we can see that the critical value or the ilter inductance is about 500 µh, ater that value the system becomes unstable Capacitance oversizing The transer unctions o speed and torque are presented in Figure 4.5 and 4.6. For the case when the ilter inductance and ilter resistance are constant and the ilter capacitance o 152 µf is become excessive or the system stability the error is about 3-5%. For the capacitance o 500 mf we can see that the system stability is lost. 56

57 Figure 4.5 Transer unction o speed or various ilter capacitances. Figure 4.6 Transer unction o torque or various ilter capacitances. From the simulation we can see that the critical value or the ilter capacitance is about 10 µh, ater that value the system becomes unstable. 57