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POWER ELECTRONICS EPE 550 CIRCUITS, DEVICES, AND APPLICATIONS ELECTRICAL DRIVES: An Application of Power Electronics Eng.Mohammed Alsumady CONTENTS Power Electronic Systems Modern Electrical Drive Systems Power Electronic Converters in Electrical Drives :: DC and AC Drives Modeling and Control of Electrical Drives :: Current controlled Converters :: Modeling of Power Converters :: Scalar control of IM Power Electronic Systems What is Power Electronics ? A field of Electrical Engineering that deals with the application of power semiconductor devices for the control and conversion of electric power Input Source - AC - DC - unregulated Reference sensors Power Electronics Converters Load Output - AC - DC Controller POWER ELECTRONIC CONVERTERS – the heart of power in a power electronics system Power Electronic Systems Why Power Electronics ? Power semiconductor devices Power switches isw ON or OFF + vsw − =0 isw = 0 Ploss = vsw× isw = 0 + Losses ideally ZERO ! vsw − Power Electronic Systems Why Power Electronics ? Power semiconductor devices - A K K K ia Power switches - G G Vak Vak Vak + + + A ia A ia Power Electronic Systems Why Power Electronics ? Power semiconductor devices Power switches D iD C ic + + VDS G - G VCE - S E Power Electronic Systems Why Power Electronics ? Passive elements + VL - iL High frequency transformer + + V1 V2 - - Inductor + iC VC - Power Electronic Systems Why Power Electronics ? sensors Input Source - AC - DC - unregulated Reference Power Electronics Converters IDEALLY LOSSLESS Load ! Output - AC - DC Controller Power Electronic Systems Why Power Electronics ? Other factors: • Improvements in power semiconductors fabrication • Power Integrated Module (PIM), Intelligent Power Modules (IPM) • Decline cost in power semiconductor • Advancement in semiconductor fabrication • ASICs • FPGA • DSPs • Faster and cheaper to implement complex algorithm Advancement in semiconductor fabrication • • • A field-programmable gate array (FPGA) is an integrated circuit designed to be configured by the customer or designer after manufacturing—hence "field-programmable". The FPGA configuration is generally specified using a hardware description language (HDL), similar to that used for an application-specific integrated circuit (ASIC) circuit diagrams were previously used to specify the configuration, as they were for ASICs, but this is increasingly rare). FPGAs can be used to implement any logical function that an ASIC could perform. The ability to update the functionality after shipping, partial re-configuration of the portion of the design and the low non-recurring engineering costs relative to an ASIC design (notwithstanding the generally higher unit cost), offer advantages for many applications. FPGAs contain programmable logic components called "logic blocks", and a hierarchy of reconfigurable interconnects that allow the blocks to be "wired together"—somewhat like many (changeable) logic gates that can be inter-wired in (many) different configurations. Logic blocks can be configured to perform complex combinational functions, or merely simple logic gates like AND and XOR. In most FPGAs, the logic blocks also include memory elements, which may be simple flip-flops or more complete blocks of memory. In addition to digital functions, some FPGAs have analog features. The most common analog feature is programmable slew rate and drive strength on each output pin, allowing the engineer to set slow rates on lightly loaded pins that would otherwise ring unacceptably, and to set stronger, faster rates on heavily loaded pins on high-speed channels that would otherwise run too slow. Another relatively common analog feature is differential comparators on input pins designed to be connected to differential signaling channels. A field-programmable gate array (FPGA) • The FPGA industry sprouted from programmable read-only memory (PROM) and programmable logic devices (PLDs). PROMs and PLDs both had the option of being programmed in batches in a factory or in the field (field programmable), however programmable logic was hard-wired between logic gates. • A recent trend has been to take the coarse-grained architectural approach a step further by combining the logic blocks and interconnects of traditional FPGAs with embedded microprocessors and related peripherals to form a complete "system on a programmable chip“. A field-programmable gate array (FPGA) Power Electronic Systems Some Applications of Power Electronics : Typically used in systems requiring efficient control and conversion of electric energy: Domestic and Commercial Applications Industrial Applications Telecommunications Transportation Generation, Transmission and Distribution of electrical energy Power rating of < 1 W (portable equipment) Tens or hundreds Watts (Power supplies for computers /office equipment) kW to MW : drives Hundreds of MW in DC transmission system (HVDC) Modern Electrical Drive Systems • About 50% of electrical energy used for drives • Can be either used for fixed speed or variable speed • • 75% - constant speed, 25% variable speed (expanding) Variable speed drives typically used PEC to supply the motors DC motors (brushed) SRM • • • • IM: Induction Motor PMSM: Permanent Magnet Synchronous Motor SRM: Switched Reluctance Motor BLDC: Brushless DC Motor BLDC AC motors - IM - PMSM Permanent Magnet Synchronous Motor The Permanent Magnet Synchronous motor is a rotating electric machine where the stator is a classic three phase stator like that of an induction motor and the rotor has permanent magnets. In this respect, the PM Synchronous motor is equivalent to an induction motor, except the rotor magnetic field in case of PMSM is produced by permanent magnets. The use of a permanent magnet to generate a substantial air gap magnetic flux makes it possible to design highly efficient PM motors. Medium construction complexity, multiple fields, delicate magnets • High reliability (no brush wear), even at very high achievable speeds • High efficiency • Low EMI • Driven by multi-phase Inverter controllers • Sensorless speed control possible • Higher total system cost than for DC motors • Smooth rotation - without torque ripple • Appropriate for position control Permanent Magnet Synchronous Motor Switched Reluctance (SR) Motor Switched reluctance (SR) motor is a brushless AC motor. It has simple mechanical construction and does not require permanent magnet for its operation. The stator and rotor in a SR motor have salient poles. The number of poles presence on the stator depends on the number of phases the motor is designed to operate in. Normally, two stator poles at opposite ends are configured to form one phase. In this configuration, a 3-phase SR motor has 6 stator poles. The number of rotor poles are chosen to be different to the number of stator poles. A 3-phase SR motor with 6 stator poles and 4 rotor poles is also known as a 6/4 3-Phase SR motor. SR motor has the phase winding on its stator only. Concentrated windings are used. The windings are inserted onto the stator poles and connected in series to form one phase of the motor. In a 3-Phase SR motor, there are 3 pairs of concentrated windings and each pair of the winding is connected in series to form each phase respectively. Future Electric Motors Build will be SR Motors • The small-size SR motor was developed by Akira Chiba, professor at the Department of Electrical Engineering, Faculty of Science & Technology, Tokyo University of Science. • The prototyped SR motor has the same size as the 50kW synchronous motor equipped in the second-generation Toyota Prius. Currently all produced Electric cars are equipped with a synchronous motor whose rotor is embedded with a permanent magnet. • But as the permanent magnets are getting more and more pricey (the price has doubled or tripled) because of higher demand, the future of SR Motors is now imminent. • A four-phase 8/6 switched-reluctance motor is shown in cross section. In order to produce continuous shaft rotation, each of the four stator phases is energized and then de-energized in succession at specific positions of the rotor as illustrated. Future electric motors build will be SR Motors. Brushless DC Motor • A BLDC motor has permanent magnets which rotate, and a fixed armature, eliminating the problems of connecting current to the moving armature. An electronic controller replaces the brush commutator assembly of the brushed DC motor, which continually switches the phase to the windings to keep the motor turning. The controller performs similar timed power distribution by using a solid-state circuit rather than the brush commutator system. • BLDC motors offer several advantages over brushed DC motors, including more torque per weight, more torque per watt (increased efficiency), increased reliability, reduced noise, longer lifetime (no brush and commutator erosion), elimination of ionizing sparks from the commutator, and overall reduction of electromagnetic interference (EMI). With no windings on the rotor, they are not subjected to centrifugal forces, and because the windings are supported by the housing, they can be cooled by conduction, requiring no airflow inside the motor for cooling. This in turn means that the motor's internals can be entirely enclosed and protected from dirt or other foreign matter. BLDC: Brushless DC Motor Modern Electrical Drive Systems Classic Electrical Drive for Variable Speed Application : • Bulky • Inefficient • inflexible Modern Electrical Drive Systems Typical Modern Electric Drive Systems Electric Motor Power Electronic Converters Electric Energy - Unregulated - POWER IN Electric Energy - Regulated - Power Electronic Converters Moto r feedback Reference Controller Electric Energy Mechanical Energy Load Modern Electrical Drive Systems Example on Variable Speed Drives (VSD) application Variable Speed Drives Constant speed valve Supply motor pump Power out Power In Power loss Mainly in valve Modern Electrical Drive Systems Example on Variable Speed Drives (VSD) application Variable Speed Drives Constant speed valve Supply motor Supply pump PEC Power out Power In motor pump Power out Power In Power loss Mainly in valve Power loss Modern Electrical Drive Systems Example on VSD application Variable Speed Drives Constant speed valve Supply motor Supply pump PEC Power out Power In motor pump Power out Power In Power loss Mainly in valve Power loss Modern Electrical Drive Systems Example on VSD application Electric motor consumes more than half of electrical energy in the US Fixed speed Variable speed Improvements in energy utilization in electric motors give large impact to the overall energy consumption HOW ? Replacing fixed speed drives with variable speed drives Using the high efficiency motors Improves the existing power converter–based drive systems Modern Electrical Drive Systems Overview of AC and DC drives DC drives: Electrical drives that use DC motors as the prime mover Regular maintenance, heavy, expensive, speed limit Easy control, decouple control of torque and flux AC drives: Electrical drives that use AC motors as the prime mover Less maintenance, light, less expensive, high speed Coupling between torque and flux – variable spatial angle between rotor and stator flux Modern Electrical Drive Systems Overview of AC and DC drives Before semiconductor devices were introduced (<1950) • AC motors for fixed speed applications • DC motors for variable speed applications After semiconductor devices were introduced (1960s) • Variable frequency sources available – AC motors in variable speed applications • Coupling between flux and torque control • Application limited to medium performance applications – fans, blowers, compressors – scalar control • High performance applications dominated by DC motors – tractions, elevators, servos, etc Modern Electrical Drive Systems Overview of AC and DC drives After vector control drives were introduced (1980s) • AC motors used in high performance applications – elevators, tractions, servos • AC motors favorable than DC motors – however control is complex hence expensive • Cost of microprocessor/semiconductors decreasing –predicted 30 years ago AC motors would take over DC motors Modern Electrical Drive Systems Overview of AC and DC drives Extracted from Boldea & Nasar Power Electronic Converters in Electrical Drive Systems Converters for Motor Drives (some possible configurations) DC Drives DC Source AC Source DC-AC-DC AC-DC AC Drives AC-DC-DC DC Source AC Source DC-DC AC-DC-AC Const. DC Variable DC AC-AC NCC FCC DC-AC DC-DC-AC Power Electronic Converters in ED Systems Converters for Motor Drives Configurations of Power Electronic Converters depend on: Sources available Type of Motors Drive Performance - applications - Braking - Response - Ratings Power Electronic Converters in ED Systems DC DRIVES Available AC source to control DC motor (brushed) AC-DC AC-DC-DC Uncontrolled Rectifier Control Controlled Rectifier Single-phase Three-phase Single-phase Three-phase Control DC-DC Switched mode 1-quadrant, 2-quadrant 4-quadrant Power Electronic Converters in ED Systems DC DRIVES AC-DC 400 200 0 + 50Hz 1-phase Vo Vo 2Vm cos -200 -400 0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44 10 Average voltage over 10ms - 5 0 0.4 500 0 50Hz 3-phase + Vo - -500 Vo 3VL-L,m 0.4 cos 30 20 Average voltage over 3.33 ms 10 0 0.4 Power Electronic Converters in ED Systems DC DRIVES AC-DC 2Vm + 50Hz 1-phase Vo Vo 2Vm cos 90o 180o 90o 180o Average voltage over 10ms - - 2 Vm 3VL-L,m 50Hz 3-phase + Vo - Vo 3VL-L,m cos Average voltage over 3.33 ms - 3VL - L,m Power Electronic Converters in ED Systems DC DRIVES AC-DC ia Vt + 3-phase supply Vt Q2 Q1 - Q3 Q4 - Operation in quadrant 1 and 4 only Ia Power Electronic Converters in ED Systems DC DRIVES AC-DC 3phase supply + 3-phase supply Vt - Q2 Q1 Q3 Q4 T Power Electronic Converters in ED Systems DC DRIVES AC-DC R1 F1 3-phase supply + Va F2 R2 Q2 Q1 Q3 Q4 - T Power Electronic Converters in ED Systems DC DRIVES AC-DC Cascade control structure with armature reversal (4-quadrant): iD ref + Speed controller _ iD,ref + _ iD,ref iD, Current Controller Armature reversal Firing Circuit Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC Uncontrolled rectifier control Switch Mode DC-DC 1-Quadrant 2-Quadrant 4-Quadrant Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC control Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va + T1 D1 ia Vdc - Q2 Ia + T2 Q1 D2 Va - T1 conducts va = Vdc Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va + T1 D1 ia Vdc - Q2 Q1 Ia + T2 D2 Va - D2 conducts va = 0 Va T1 conducts va = Vdc Eb Quadrant 1 The average voltage is made larger than the back emf Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va + T1 D1 ia Vdc - Q2 Ia + T2 Q1 D2 Va - D1 conducts va = Vdc Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va + T1 D1 ia Vdc - Q2 Q1 Ia + T2 D2 Va - T2 conducts va = 0 Va D1 conducts va = Vdc Eb Quadrant 2 The average voltage is made smallerr than the back emf, thus forcing the current to flow in the reverse direction Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter 2vtri + vA vc Vdc - 0 + vc Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A + Q1 leg B D3 D1 + Va - Q3 Vdc - Positive current va = Vdc when Q1 and Q2 are ON Q4 D4 D2 Q2 Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A + Q1 leg B D3 D1 + Va - Q3 Vdc - Q4 D4 Positive current va = Vdc when Q1 and Q2 are ON va = -Vdc when D3 and D4 are ON va = 0 when current freewheels through Q and D D2 Q2 Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A + Q1 leg B D3 D1 + Va - Q3 Vdc - Q4 D4 Positive current va = Vdc when Q1 and Q2 are ON va = -Vdc when D3 and D4 are ON va = 0 when current freewheels through Q and D D2 Q2 Negative current va = Vdc when D1 and D2 are ON Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A + Q1 leg B D3 D1 + Va - Q3 Vdc - Q4 D4 Positive current D2 Q2 Negative current va = Vdc when Q1 and Q2 are ON va = Vdc when D1 and D2 are ON va = -Vdc when D3 and D4 are ON va = -Vdc when Q3 and Q4 are ON va = 0 when current freewheels through Q and D va = 0 when current freewheels through Q and D Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC Bipolar switching scheme – output swings between VDC and -VDC 2vtri Vdc + vA + vB - - vA vc Vdc 0 Vdc vB 0 Vdc vc vAB + _ -Vdc Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC Unipolar switching scheme – output swings between Vdc and -Vdc vc Vtri -vc Vdc + vA + vB - - Vdc vA 0 Vdc vc vB + _ -vc 0 Vdc vAB 0 Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter Armature current 200 150 Vdc Vdc 200 Vdc 100 100 50 50 0 0 -50 -50 -100 -100 -150 -150 -200 -200 0.04 Armature current 150 0.0405 0.041 0.0415 0.042 0.0425 0.043 0.0435 0.044 0.0445 0.045 Bipolar switching scheme 0.04 0.0405 0.041 0.0415 0.042 0.0425 0.043 0.0435 0.044 0.0445 0.045 Unipolar switching scheme • Current ripple in unipolar is smaller • Output frequency in unipolar is effectively doubled Power Electronic Converters in ED Systems AC DRIVES AC-DC-AC control The common PWM technique: CB-SPWM with ZSS SVPWM Modeling and Control of Electrical Drives • Control the torque, speed or position • Cascade control structure Example of current control in cascade control structure * + * + - position controller - T* speed controller + - current controller kT 1/s Motor converter Modeling and Control of Electrical Drives Current controlled converters in DC Drives - Hysteresis-based + ia Vdc + iref Va − va iref + _ ierr q • High bandwidth, simple implementation, insensitive to parameter variations • Variable switching frequency – depending on operating conditions q ierr Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based i*a i*b i*c • • + Converter + + For isolated neutral load, ia + ib + ic = 0 control is not totally independent Instantaneous error for isolated neutral load can reach double the band 3-phase AC Motor Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based iq is Dh Dh id • For isolated neutral load, ia + ib + ic = 0 control is not totally independent • Instantaneous error for isolated neutral load can reach double the band Dh Dh Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based Continuous • Dh = 0.3 A • Sinusoidal reference current, 30Hz • Vdc = 600V • 10W,50mH load powergui Scope iaref g To Workspace 1 + A DC Voltage Source c1 p1 c2 p2 c3 p3 ina p4 inb p5 inc p6 Subsystem Sine Wave 2 - Measurement 3 Series RLC Branch Current 3 C Universal Bridge 1 i + - Measurement 1 Series RLC BranchCurrent 1 i + Sine Wave Sine Wave 1 B i + - Series RLC BranchCurrent 2 Measurement 2 Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based Current error Actual and reference currents 0.5 10 0.4 0.3 5 0.2 10 0.1 0 0 9 -0.1 -0.2 8 -5 -0.3 -0.4 7 -10 0.005 -0.5 0.01 0.015 6 0.02 0.025 0.03 -0.5 -0.4 5 4 4 6 8 10 12 14 16 -3 x 10 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based Current error Actual current locus 10 0.5 5 0 0.6A -0.5 0 0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06 -5 0.5 -10 -10 -5 0 5 10 0.6A 0 -0.5 0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06 0.5 0.6A 0 -0.5 0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06 Modeling and Control of Electrical Drives Current controlled converters in DC Drives - PI-based Vdc iref + - PI vc vc vPulse width tri modulator qqq Modeling and Control of Electrical Drives Current controlled converters in DC Drives - PI-based i*a i*b i*c + PI PWM Converter + PI + PWM PI PWM • Sinusoidal PWM • Interactions between phases only require 2 controllers • Tracking error Motor Modeling and Control of Electrical Drives Current controlled converters in DC Drives - PI-based •Perform the 3-phase to 2-phase transformation - only two controllers (instead of 3) are used •Perform the control in synchronous frame - the current will appear as DC •Interactions between phases only require 2 controllers •Tracking error Modeling and Control of Electrical Drives Current controlled converters in AC Drives - PI-based i*a i*b i*c + PI PWM Converter + PI + PWM PI PWM Motor Modeling and Control of Electrical Drives Current controlled converters in AC Drives - PI-based i*a PI i*b SVM 2-3 3-2 Converter PI i*c 3-2 Motor Modeling and Control of Electrical Drives Current controlled converters in AC Drives - PI-based va* id* PI controller + - iq* + - iq id dqabc PI controller vb* SVM or SPWM VSI vc* s Synch speed estimator s abcdq IM Modeling and Control of Electrical Drives Current controlled converters in AC Drives - PI-based Stationary - ia 4 2 3 0 2 -2 1 -4 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 Rotating - ia 4 0 3 0 2 -2 1 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0 0.01 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.01 0.012 0.014 0.016 0.018 0.02 Rotating - id 4 2 -4 Stationary - id 4 0 0.002 0.004 0.006 0.008 Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier + vc firing circuit controlled rectifier Va – vc(s) ? va(s) DC motor The relation between vc and va is determined by the firing circuit It is desirable to have a linear relation between vc and va Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier Cosine-wave crossing control Vm 0 vc 3 2 vs Input voltage 4 Cosine wave compared with vc Results of comparison trigger SCRs Output voltage Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier Cosine-wave crossing control cos(t)= vc Vscos() Vm 0 2 vc 3 v cos-1 c vs 4 vs 2Vm v c -1 v c coscos Va vs vs A linear relation between vc and Va Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier Va is the average voltage over one period of the waveform - sampled data system Delays depending on when the control signal changes – normally taken as half of sampling period Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier Va is the average voltage over one period of the waveform - sampled data system Delays depending on when the control signal changes – normally taken as half of sampling period Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier G H (s) Ke T - s 2 Single phase, 50Hz vc(s) Va(s) K 2Vm Vs T=10ms Three phase, 50Hz K 3VL-L,m Vs T=3.33ms Simplified if control bandwidth is reduced to much lower than the sampling frequency Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier + iref current controller vc firing circuit controlled rectifier Va – • To control the current – current-controlled converter • Torque can be controlled • Only operates in Q1 and Q4 (single converter topology) Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier • • Input 3-phase, 240V, 50Hz Closed loop current control with PI controller Scope 3 + - v Continuous Voltage Measurement4 i + - AC Voltage Source powergui Scope 2 Current Measurement 1 Step AC Voltage Source 1 + g A AC Voltage Source 2 + s v Controlled Voltage Source Series RLC Branch To Workspace B + - v C Universal Bridge Voltage Measurement2 + - v Voltage Measurement - i - + ia Current Measurement To Workspace1 + - v alpha_deg Voltage Measurement3 Mux AB BC + - v Voltage Measurement1 Scope pulses CA Block Synchronized Mux 6-Pulse Generator Scope 1 ir To Workspace2 PID Signal PID Controller Saturation 1 Generator 7 Constant 1 acos -K - Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier • • Input 3-phase, 240V, 50Hz Closed loop current control with PI controller 1000 1000 500 500 Voltage 0 0 -500 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -500 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.25 0.26 0.27 0.28 15 15 10 10 5 Current 5 0 0.22 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.23 0.24 Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Vdc Switching signals obtained by comparing control signal with triangular wave + Va − vtri q vc We want to establish a relation between vc and Va AVERAGE voltage vc(s) ? Va(s) DC motor Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Ttri 1 q 0 vc 1 0 1 d Ttri Vc > Vtri Vc < Vtri t t Ttri q dt t on Ttri ton Vdc 1 dTtri Va Vdc dt dVdc Ttri 0 0 Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters d 0.5 vc -Vtri Vtri vc -Vtri For vc = -Vtri d = 0 Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters d 0.5 vc -Vtri -Vtri Vtri vc Vtri For vc = -Vtri d = 0 For vc = 0 d = 0.5 For vc = Vtri d=1 Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters d 0.5 -Vtri -Vtri vc Vtri Vtri vc 1 d 0.5 vc 2Vtri For vc = -Vtri d = 0 For vc = 0 d = 0.5 For vc = Vtri d=1 Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Thus relation between vc and Va is obtained as: Va 0.5Vdc Vdc vc 2Vtri Introducing perturbation in vc and Va and separating DC and AC components: DC: Vdc Va 0.5Vdc vc 2Vtri AC: Vdc ~ ~ va vc 2Vtri Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Taking Laplace Transform on the AC, the transfer function is obtained as: v a ( s) Vdc v c ( s) 2Vtri vc(s) Vdc 2 Vtri va(s) DC motor Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Bipolar switching scheme Vdc -Vdc q vtri vc 2vtri + Vdc vA Vdc + VAB 0 - − vc Vdc vB 0 q Vdc v d A 0.5 c 2Vtri VA 0.5Vdc Vdc vc 2Vtri v dB 1 - d A 0.5 - c 2Vtri VB 0.5Vdc - Vdc vc 2Vtri vAB -Vdc VA - VB VAB Vdc vc Vtri Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Bipolar switching scheme v a ( s) Vdc v c ( s) Vtri vc(s) Vdc Vtri va(s) DC motor Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Vdc Unipolar switching scheme vc Leg b Vtri -vc + vtri Vdc qa vc − vA Leg a vtri d A 0.5 vB qb -vc vc 2Vtri VA 0.5Vdc Vdc vc 2Vtri dB 0.5 VB 0.5Vdc - - vc 2Vtri Vdc vc 2Vtri vAB VA - VB VAB The same average value we’ve seen for bipolar ! Vdc vc Vtri Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Unipolar switching scheme v a ( s) Vdc v c ( s) Vtri vc(s) Vdc Vtri va(s) DC motor Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters DC motor – separately excited or permanent magnet v t ia R a L a di a ea dt Te = kt ia d m Te Tl J dt e e = kt Extract the dc and ac components by introducing small perturbations in Vt, ia, ea, Te, TL and m ac components ~ d i ~ ~ v t ia R a L a a ~ ea dt ~ ~ Te k E ( ia ) dc components Vt Ia R a Ea Te k E Ia ~ ~) ee k E ( Ee k E ~) d( ~ ~ ~ Te TL B J dt Te TL B() Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters DC motor – separately excited or permanent magnet Perform Laplace Transformation on ac components ~ d i ~ ~ v t ia R a L a a ~ ea dt Vt(s) = Ia(s)Ra + LasIa + Ea(s) ~ ~ Te k E ( ia ) Te(s) = kEIa(s) ~ ~) ee k E ( Ea(s) = kE(s) ~) d( ~ ~ ~ Te TL B J dt Te(s) = TL(s) + B(s) + sJ(s) Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters DC motor – separately excited or permanent magnet Tl (s ) Va (s ) + - 1 R a sL a Ia (s ) kT - Te (s ) 1 B sJ + kE (s ) Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters q vtri Torque controller Tc + + Vdc – − q kt DC motor Tl (s ) Converter Te (s ) Torque controller + - Vdc Vtri,pe ak Ia (s ) 1 R a sL a Va (s ) + kT - Te (s ) + - kE 1 B sJ (s ) Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Closed-loop speed control – an example Design procedure in cascade control structure • Inner loop (current or torque loop) the fastest – largest bandwidth • The outer most loop (position loop) the slowest – smallest bandwidth • Design starts from torque loop proceed towards outer loops Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Closed-loop speed control – an example OBJECTIVES: • Fast response – large bandwidth • • Minimum overshoot good phase margin (>65o) BODE PLOTS Zero steady state error – very large DC gain METHOD • Obtain linear small signal model • Design controllers based on linear small signal model • Perform large signal simulation for controllers verification Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Closed-loop speed control – an example Ra = 2 W La = 5.2 mH B = 1 x10–4 kg.m2/sec J = 152 x 10–6 kg.m2 ke = 0.1 V/(rad/s) kt = 0.1 Nm/A Vd = 60 V Vtri = 5 V fs = 33 kHz • PI controllers • Switching signals from comparison of vc and triangular waveform Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Torque controller design Open-loop gain Bode Diagram From: Input Point To: Output Point 150 kpT= 90 Magnitude (dB) 100 compensated kiT= 18000 50 0 -50 90 Phase (deg) 45 0 compensated -45 -90 -2 10 -1 10 0 10 1 10 2 10 Frequency (rad/sec) 3 10 4 10 5 10 Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Speed controller design * + – T* Speed controller Torque loop 1 T 1 B sJ Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Speed controller design Open-loop gain Bode Diagram From: Input Point To: Output Point 150 kps= 0.2 Magnitude (dB) 100 kis= 0.14 50 compensated 0 -50 0 Phase (deg) -45 -90 -135 compensated -180 -2 10 -1 10 0 10 1 10 Frequency (Hz) 2 10 3 10 4 10 Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Large Signal Simulation results 40 20 Speed 0 -20 -40 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 2 1 0 -1 -2 Torque Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives INDUCTION MOTOR DRIVES Scalar Control Const. V/Hz Vector Control is=f(r) FOC Rotor Flux Stator Flux DTC Circular Flux Hexagon Flux DTC SVM Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Control of induction machine based on steady-state model (per phase SS equivalent circuit): Rs Is Llr’ Lls + Vs – Lm + Eag Im Ir ’ – Rr’/s Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Te Pull out Torque (Tmax) Te TL Trated s Intersection point (Te=TL) determines the steady –state speed sm rated rotors r Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Given a load T– characteristic, the steady-state speed can be changed by altering the T– of the motor: Pole changing Synchronous speed change with no. of poles Discrete step change in speed Variable voltage (amplitude), variable frequency (Constant V/Hz) Using power electronics converter Operated at low slip frequency Variable voltage (amplitude), frequency fixed E.g. using transformer or triac Slip becomes high as voltage reduced – low efficiency Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Variable voltage, fixed frequency e.g. 3–phase squirrel cage IM 600 Torque V = 460 V Rs= 0.25 W 500 Rr=0.2 W Lr = Ls = 0.5/(2*pi*50) 400 Lm=30/(2*pi*50) f = 50Hz 300 Lower speed slip higher Low efficiency at low speed 200 100 0 p=4 0 20 40 60 80 w (rad/s) 100 120 140 160 Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant V/Hz To maintain V/Hz constant Approximates constant air-gap flux when Eag is large + V + Eag _ _ ag = constant Eag = k f ag E ag f V f Speed is adjusted by varying f - maintaining V/f constant to avoid flux saturation Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant V/Hz 900 800 50Hz 700 30Hz Torque 600 500 10Hz 400 300 200 100 0 0 20 40 60 80 100 120 140 160 Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant V/Hz Vs Vrated frated f Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant V/Hz Rectifier 3-phase supply VSI IM C f Ramp s* + V Pulse Width Modulator Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant V/Hz In1 Out 1 Subsystem isd Va isq Out1 ird speed 0.41147 Step Slider Gain 1 In 1 Rate Limiter Out2 Vb Vd Scope irq Out3 Constant V /Hz Vq Vc Te speed Induction Machine To Workspace 1 torque To Workspace Simulink blocks for Constant V/Hz Control Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant V/Hz 200 100 Speed 0 -100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 400 200 Torque 0 -200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 200 100 Stator phase current 0 -100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Problems with open-loop constant V/f At low speed, voltage drop across stator impedance is significant compared to airgap voltage - poor torque capability at low speed Solution: 1. Boost voltage at low speed 2. Maintain Im constant – constant ag Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives 700 600 50Hz A low speed, flux falls below the rated value Torque 500 400 30Hz 300 10Hz 200 100 0 0 20 40 60 80 100 120 140 160 Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives With compensation (Is,ratedRs) 700 • Torque deteriorate at low frequency – hence compensation commonly performed at low frequency 600 Torque 500 • In order to truly compensate need to measure stator current – seldom performed 400 300 200 100 0 0 20 40 60 80 100 120 140 160 Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives With voltage boost at low frequency Vrated Linear offset Boost Non-linear offset – varies with Is frated Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Problems with open-loop constant V/f Poor speed regulation Solution: 1. Compesate slip 2. Closed-loop control Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Rectifier 3-phase supply VSI IM C f Ramp s* + + + Slip speed calculator Vdc Idc V + Vboost Pulse Width Modulator Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives A better solution : maintain ag constant. How? ag, constant → Eag/f , constant → Im, constant (rated) Rs Is Controlled to maintain Im at rated Lls Llr’ Ir ’ + + Vs – Lm maintain at rated Im Eag – Rr’/s Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant air-gap flux 900 800 50Hz 700 30Hz Torque 600 500 10Hz 400 300 200 100 0 0 20 40 60 80 100 120 140 160 Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant air-gap flux Im Im Im j L lr Rr s Is R j (L lr L m ) r s j L r Rr s R j r L r r s 1 r jslipTr 1 jslip r Tr 1 1 r Is Is , jslip r Tr 1 1 r Is Im , jslipTr 1 • Current is controlled using currentcontrolled VSI • Dependent on rotor parameters – sensitive to parameter variation Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant air-gap flux 3-phase supply VSI Rectifier IM C Current controller * + PI - slip + r + |Is| s THANK YOU