9 Selected Problems of Induction Motor Drives with Voltage Inverter and Inverter Output Filters Drives and Filters Overview. Fast switching of power devices in an inverter causes high dv/dt at the rising and falling edges of the inverter output waveform.. High dv/dt in modern inverters is the source of numerous disadvantageous effects i.e. faster motor bearings degradation, over-voltages on motor terminals, failure or degradation of the motor winding insulation due to partial discharges, increase of motor losses, and a higher electromagnetic interference level.. The prevention or limiting of the negative effects of dv/dt is possible if proper passive or active filters are installed in the drive. Particularly passive filters are preferable for industrial application. Passive filters used in induction motor drives are called inerter output filters or motor filters. Depending on filter structures and their arameters, the following filters are specified. Differential mode filters also known as sinusoidal filters or LC filters, and the motor supply voltage is smoothed to almost a sinusoidal shape contrary to the inverter output voltage (filter s input), which is composed of series of short rectangular pulses.. Common mode filters are used mainly to limit the motor leakage currents, which flow through motor parasitic capacitances.. dv/dt filters are used to eliminate the wave reflection effect in long cables, in order to avoid over-voltages on the motor terminal as well as to secure the motor windings insulation from failure. High Performance Control of AC Drives with MATLAB/Simulink Models, First Edition. Haitham Abu-Rub, Atif Iqbal, and Jaroslaw Guzinski. Ó 2012 John Wiley & Sons, Ltd. Published 2012 by John Wiley & Sons, Ltd.
2 High Performance Control of AC Drives Three Phase to Two-Phase Transformations The transformation matrix for the conversion from a three-phase ABC co-ordinate to a twophase ab0 for constant vector magnitude is 2 1 2 A W ¼ 6 4 0 1 1 1 p ffiffi 1 1 p 1 7 ffiffiffi 5 and the transformation matrix for constant power of the system is 2 1 p ffiffiffi pffiffiffi 2 A P ¼ pffiffiffi 6 4 0 1 p ffiffi p 1 ffiffi 6 1 p ffiffi 2 1 p ffiffiffi p 1 ffiffi 6 p 1 7 ffiffi 5 2 Voltage and Current Common Mode Component Figure 9. Structure of the voltage inverter with output voltages notations
Selected Problems of Induction Motor Drives Table 9.1 Voltage inverter output voltages for possible switching combination Binary notation for transistor switching combination 100 110 010 011 001 101 000 111 u U U d U d 0 0 0 U d 0 U d u V 0 U d U d U d 0 0 0 U d u W 0 0 0 U d U d U d 0 U d 2U d 2U d 2U d u 0 u a U p d ffiffi ffiffi 2 p p Ud ffiffi p ffiffi U d pffiffi 6 U p d ffiffi p Ud ffiffi 6 pffiffi ffiffi 2 p p Ud ffiffi U p d ffiffi p Ud ffiffi 6 pffiffi 0 U d pffiffi 0 0 6 p Ud ffiffi u b 0 U p d ffiffi 2 U p d ffiffi 0 p Ud ffiffi 2 2 p Ud ffiffi 0 0 2 Matlab/Simulink model of induction motor drive with PWM inverter and common mode voltage
4 High Performance Control of AC Drives Figure 9.6 Simulation results for motor start-up
Selected Problems of Induction Motor Drives 5 Figure 9.7 Common mode voltage in PWM inverter Induction Motor Common Mode Circuit The motor has some parasitic capacitances with small values with an order of picofarads. Figure 9.8 Parasitic capacitances in the induction motor In Figure 9.8, the following motor parasitic capacitances are marked: C wf parasitic capacitance between stator windings and stator frame; C wr parasitic capacitance between stator winding and rotor winding;
6 High Performance Control of AC Drives C rf parasitic capacitance between the rotor and frame; C b equivalent capacitance of motor bearings; C ph parasitic capacitance between stator windings. Inverter U V W Motor PE Figure 9.9 Common mode current path flow in electric drives with voltage inverter Feeder Motor R c L c R 0 L 0 C wr u 0 C c C wf C rf 2C b i g u b Sw 1 2 R b Figure 9.10 An equivalent circuit of the motor and feeder cable for CM current Bearing Current Types and Reduction Methods High dv/dt on motor terminals Common mode voltage High frequency grounding current Capacitance bearing current 1 Machine discharging current 2 High frequency shaft voltage Rotor grounding current 4 Circulating bearing current Figure 9.11 Bearing current classes
Selected Problems of Induction Motor Drives 7. The machine discharging current i bedm, can reach A in peak when the bearing oil film breaks down.. The bearing circulating current i bcir is induced by a motor shaft voltage u sh. The u sh appears due to parasitic motor flux y cir.. The types of bearing currents were correlated with motor mechanical size H, as follows:. if H < 100 mm, then machine discharging current, i bedm, is dominant;. if 100 mm < H < 280 mm both i bedm and circulating bearing currents i bcir are dominant;. if H > 280 mm circulating bearing currents is dominant. To prevent bearing current flow, the methods presented in Table Reduction of electric discharge current i bedm : Reduction of circulating bearing current i bcir : Reduction of rotor grounding current i gr. ceramic bearings. common mode choke. common mode choke. common mode passive filters. Conductive grease in the bearings. active compensation systems of CM voltage. active compensation systems of CM voltage. active compensation ystems of CM voltage. decreasing of inverter switching frequency. decreasing of inverter switching frequency. decreasing of inverter switching frequency. one or two insulated bearings use. motor shaft grounding by brushes use. one or two insulated bearings use. one or two ceramic bearings use Common Mode Choke Among numerous methods for bearing current reduction, the most popular is known from small electronics circuits is a three-phase common mode choke Figure 9.1 Structure of the common mode choke for a three-phase system
8 High Performance Control of AC Drives Figure 9.14 Waveform of the current measured in the motor grounding wire in 1.5 kw industrial drive without CM choke use Figure 9.15 Waveform of the current measured in the motor grounding wire in 1.5 kw industrial drive with CM choke use Common Mode Transformers The value of the CM voltage may be reduced by using a common mode transformer. The difference between the CM choke and the CM transformer is the additional winding shortened the by resistor Figure 9.16 Common mode transformer
Selected Problems of Induction Motor Drives 9. In the CM transformer, an additional fourth winding is wound with the same number of turns as the choke phase windings. ACM transformer makes it possible to reduce the CM current in the motor by up to 25%, while using less core volume than with a CM choke. If a CM transformer is used, then the CM circuit consists of an additional inductance L t and resistance R t. L t I σt I σt R t Figure 9.17 Equivalent circuit of CM transformer (l st leakage inductance of the transformer) Common Mode Voltage Reduction by PWM Modifications The following are the PWM modifications required for CM reduction:. elimination of zero voltage vectors;. the use of the active vectors, which have the same value of zero sequence voltage u 0. For the classical PWM methods: [V] Z - zero vectors A - active vectors 540 Z A Z A Z A Z A Z A Z A Z A Z A Z A Z A Z A Z A 60 u N0 180 0 0 400 800 2T sw 2T sw 1200 1600 [μs] Figure 9.19 Example of u N0 waveform with classical space vector PWM algorithm (the inverter DC input voltage is U d ¼ 540 V)
10 High Performance Control of AC Drives Table 9.4 Zero sequence vectors of inverter output voltage Arrangement of switches states of three-phase voltage inverter Vectors type Active Zero Vectors notation U w4 U w6 U w2 U w U w1 U w5 U w0 U w7 Vector binary notation 100 110 010 011 001 101 000 111 Vector decimal notation 4 6 2 1 5 0 7 Vectors number 1 2 4 5 6 0 7 u N0 1 U d u 0 (Co-ordinate system ab) U d pffiffi 2 U d 2U d pffiffi 1 U d U d pffiffi 2 U d 2U d pffiffi 1 U d U d pffiffiffi 2 U d 0 U d 2U d pffiffi 0 Notation (1) NP P NP P NP P Z Z (1) Vector: NP non-parity, P parity, Z zero pffiffi Ud In the algorithm, only the output voltage was built with parity and non-parity active vectors. The disadvantage of the PWM based only on parity or odd active vectors is that without overmodulation, the inverter output voltage is decreased. The maximum inverter output voltage using NPAV is limited to U d /. U w2 α com uout ρ u β U w4 1 U d U w1 2 Ud Figure 9.20 strategy The output voltage vector for three non-parity active vectors (NPAV) modulation
Selected Problems of Induction Motor Drives 11 In the three active vectors (AVM) method, the position of the voltage vector is divided into six sectors and displaced by 0 degrees from the original sectors in the classical space vector modulation SVPWM Sector 2 (U w6, U w, U w5 ) U w6 β Sector (U w2, U w1, U w4 ) U w4 Sector 1 (U w4, Uw2, Uw1) U w2 com u out α Sector 4 (U w, U w5, U w6 ) U w 2 9 U d U w5 Sector 6 (U w5, U w6, U w4 ) U w1 Sector 5 (U w1, U w4, U w2 ) Figure 9.21 Output voltage vector for AVM modulation strategy Another modulation method that reduces the common mode current is the active zero vector control(azvc) method, in which the zero voltage vectors are replaced by two opposite active vectors (AZVC-2) Figure 9.22, or one active vector (AZVC-1) Figure 9.2. Figure 9.22 AZVC-2 modulation: (a) vectors; (b) timings
12 High Performance Control of AC Drives Figure 9.2 AZVC-1 modulation: (a) vectors; (b) timings Selected Structures of Inverter Output Filters. The improvement of the AC motor operation in inverter fed drives is possible if the shape of the stator voltage becomes as close as possible to the sinusoidal.. Motor side filters may be categorized into three basic types:. Sine filter LC filter;. Common mode filter;. du/dt filter.. The mentioned types of filters could be used separately or combined in different combinations, e.g. connecting a sine filter with a CM one. Figure 9.24 Inverter output filter Structure 1
Selected Problems of Induction Motor Drives 1 It is a combination of two filters: a sinusoidal filter and common mode filter. Connection of such filters makes it possible to obtain sinusoidal voltage and current at the filter output, and also limits common mode current. Figure 9.2 Voltage and current waveforms in inverter fed drives with filter from Figure 9.24 Inverter Output Filters Design When selecting filter parameters, it is convenient to use a transformation from a three-phase system to a rectangular one, while maintaining the power of the system during transformation. Figure 9. Equivalent circuits of the filter from Figure 9.24 for orthogonal coordinate components ab0: (a) a; (b) b; (c) 0
14 High Performance Control of AC Drives Selection of Differential Mode (Normal Mode) Filter Elements. Selection of filter elements requires a specific compromise between total harmonic distortion (THD) in the voltage waveform, weight, dimension, price of the filter, and current parameters of the inverter.. The selection of sinusoidal filter decides:. Assumed acceptable level of output voltage distortion;. Maximum allowed voltage drop in the filter;. Switching frequency of the power switches. Figure 9.4 Equivalent circuit of the inverter and sinusoidal filter For the chosen elements of the sinusoidal filter, it is possible to find its frequency characteristic based on the known filter transfer function presented as a two-port network Figure 9.6 Equivalent circuit of the filter for a component
Selected Problems of Induction Motor Drives 15 Figure 9.8 Phase and magnitude plots of a sinusoidal filter (filter chosen for a 1.5 kw motor; Lf ¼ 4 mh, Cf ¼ mf, Rf ¼ 1 W) Figure 9.9 Voltage waveforms on input and output of the sinusoidal filter for 40 Hz inverter output voltage frequency
16 High Performance Control of AC Drives Figure 9.40 Current waveforms before (ch 1) and after (ch 2) the sinusoidal filter for 40 Hz inverter output voltage frequency. Matlab/Simulink model of induction motor drive with PWM inverter and differential mode (normal mode) LC filter
Selected Problems of Induction Motor Drives 17 Figure 9.49 Simulation of the drive start-up and speed variations Estimation Problems in the Drive with Filters. In case of motor filter use, the estimation process is more complicated. Some of the solutions propose the installation of voltage and current sensors outside the converter, for direct motor current and voltage measurement.. To prevent noise, all sensors should be installed inside the converter box. A drive with such limited sensors is known as a sensorless drive.. The more useful solution is to implement the filter model in the estimation algorithm. In that case, the sensor structure can be the same as in the drives without filter use. Then the general structure of the sensorless drive with the LC filter is as presented in Figure 9.51. Figure 9.51 General structure of the sensorless AC drive with motor LC filter use
18 High Performance Control of AC Drives Speed Observer with Disturbances Model. The most common way in estimation methods is to add the filter model dependencies into some known observer structures and to change the observer correction parts.. For the system with the sine filter, the observer equations are extended with LC filter model equations: Figure 9.52 Equivalent circuit of the differential inverter output LC filter Simple Observer Based on Motor Stator Models. The observer is based on the voltage model of the induction motor with a combination of rotor and stator fluxes and stator current relationships.. To prevent the problems of the voltage drift and offset errors, instead of pure integrators, low pass filters were used. The limitation of the estimated stator flux was tuned to the stator flux nominal value.. Closed-loop flux observer has high robustness of the ASD with an observer based on the stator model.. The observer is highly insensitive against stator resistance and other motor parameters mismatch. This significantly extends the stable operating region, even without precise parameter tuning.
Selected Problems of Induction Motor Drives 19 Figure 9.5 Close-loop observer structure Motor Control Problems in the Drive with Filters The differential mode motor filter has a considerable influence on the control process. This is because each filer adds a voltage drop and a phase shift between the current and voltages on the filter input and output.
20 High Performance Control of AC Drives Figure 9.54 Drive with LC filter waveforms of: (a) commanded inverter output voltage; (b) real motor supply voltage. As a result, most of the sophisticated sensorless drives cannot work properly when a filter is installed. It is necessary to take into account the filter s existence in the control process also.. The general concept is to extend the corresponding steering algorithm with its subordinated control system for some of the filter state variable controls.. A differential mode LC filter is a two-dimensional linear stationary controlled system. The controlled state variables are: motor supply voltage u s ; and inverter output current i 1 ; whereas the control quantity is an inverter output voltage u 1. Current i 1 is the filter s internal variables. The corresponding system structure is presented in Figure 9.58. Figure 9.58 Structure of the multi-loop LC filter control system with motor voltage estimation
Selected Problems of Induction Motor Drives 21 Field Oriented Control Figure 9.59 Classical field oriented control structure Figure 9.60 Relations between vectors in FOC system Figure 9.61 observers Operation of the classical FOC system in driver without LC filter system without
22 High Performance Control of AC Drives Figure 9.62 Operation of the classical FOC system in driver with LC filter system without observers Non-Linear Field Oriented Control Figure 9.6 Field oriented control structure modified due to LC filter use
Selected Problems of Induction Motor Drives 2 Figure 9.64 Operation of the modified FOC system for driver with LC filter system without observers Figure 9.65 Operation of the modified FOC system for drive with LC filter in sensorless mode system with variables estimation
24 High Performance Control of AC Drives Figure 9.67 Operation of the modified FOC system for drive with LC filter in sensorless mode system with variables estimation experiment
Selected Problems of Induction Motor Drives 25 The most popular industrial induction motor (IM) control is rotor field oriented control (RFOC). In classical RFOC, the coupling between flux and torque exists. Figure 9.68 Base control system for decoupled rotor field oriented method Extended Control System In order to assure controllability of the system with the LC filter, the motor control structure presented in previous section have be extended using additional controllers.
26 High Performance Control of AC Drives Figure 9.69 Induction motor and LC filter nonlinear field oriented control system structure Non-Linear Multiscalar Control The control system is divided into two sub-systems: the superior motor control and the subordinate LC filter control.
Selected Problems of Induction Motor Drives 27 Figure 9.70 Speed sensorless control system
28 High Performance Control of AC Drives Motor control subsystem. In the motor control sub-system the non-linear control using non-linear feedback was used. That control is based on the methods of the differential geometry.. The non-linear and decoupled object is converted into a linear one with the use of the new state variables and the non-linear feedbacks. LC filter control sub-system. In the case of the drive without the LC filter, the MMB output variables u com sa and ucom sb are commanded for the pulse width modulation (PWM) block. The PWM controls the inverter transistors to obtain the commanded voltage on the inverter output.. When the LC filter is used, the inverter output voltage differs from motor supply voltage, so the error in the MMB control loop will appear. To solve that problem. the multi-loop controller loop is used. Predictive Current Control in the Drive System with Output Filter Control system The predictive current controller (PCC) is presented in the IM speed sensorless system with a field oriented control method and load angle regulation. Figure 9.71 Base structure of the FOC algorithm with load angle control (^ denotes variables evaluated in estimation block). In transients, some coupling and interactions appear between the controlled variables. This is due to the inherent non-linearities and couplings existing in the induction motor.. To eliminate these negative features appearing in the drive, the non-linear control principles were implemented.
Selected Problems of Induction Motor Drives 29 Figure 9.72 Structure of the non-linear FOC with load angle control Predictive current controller. The integral part of the FOC system is the IM stator current controller.. The controller uses actual values of the induction motor electromagnetic forces e (emf) to obtain proper current regulation.. The current controller principle is based on the dynamic equation that describes the model of the system. An equivalent model of the presented system contains three parts: inductance, resistance, and emf. Because a motor choke is installed in the ASD, it is acceptable to neglect an equivalent resistance of the load. Figure 9.74 Predictive current controller structure for ASD with motor choke
0 High Performance Control of AC Drives EMF estimation technique. In the case of the ASD with motor choke, the disturbance observer is modified.. In the observer, the motor emf is treated as a disturbance with components in the ab coordinates calculated using the exact disturbance model. In the ASD with motor choke, the L 1 inductance is added to the motor model. Figure 9.75 Induction motor drive with voltage inverter and motor choke. Due to the assumption of the small step of the observer calculation, the derivative of estimated speed was neglected. For the PCC, the value of the motor EMF e is equal to j.. Figure 9.76 presents the operation of the drive without the FOC loop; only with PCC. The controller operates correctly with current regulation error less then 5%. At the 100 ms instant, the inductance of the motor choke L 1 was set to zero. Figure 9.76 Current controller operation
Selected Problems of Induction Motor Drives 1. Figure 9.77 presents the operation of the full control system without non-linear feedback.. In steady state, the system controls correctly the commanded speed and flux, but in transients the interaction between both the regulation systems appear. Figure 9.77 The speed sensorless adjustable speed drive (ASD) in the case of the speed variation in the control system without linearization feedback the control structure is as presented in Figure 9.71 Figure 9.78 The speed sensorless induction motor control in the case of the speed variation in the control system with linearization feedback for speed variations the control structure is as presented in Figure 9.72
2 High Performance Control of AC Drives Figure 9.79 Speed variation for the sensorless control system with linearization feedback with flux and load torque variations control structure as in Figure 9.72 Figure 9.80 Speed variation for the sensorless control system with linearization feedback and low speed variations control structure from Figure 9.72
Selected Problems of Induction Motor Drives Figure 9.81 Speed variation in the sensorless control system with linearization feedback for slow speed reverse the control structure is based as in Figure 9.72