POWER ELECTRONICS Eng.Mohammed Alsumady EPE 550 ELECTRICAL DRIVES: 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 sensors Power Electronics Converters Input Source AC DC unregulated Load Output - AC - DC Controller POWER ELECTRONIC CONVERTERS – the heart of power in a power electronics system Reference

Power Electronic Systems Why Power Electronics ? Power semiconductor devices Power switches + vsw − = 0 isw ON or OFF + vsw − isw = 0 Ploss = vsw× isw = 0 Losses ideally ZERO !

Power Electronic Systems Why Power Electronics ? Power semiconductor devices Power switches - Vak + ia K A - Vak + ia G K A - Vak + ia G K A

Power Electronic Systems Why Power Electronics ? Power semiconductor devices Power switches D C iD ic + VDS - + VCE - G G S E

Power Electronic Systems Why Power Electronics ? Passive elements High frequency transformer Inductor + VL - iL + V1 - V2 + VC - iC

Power Electronic Systems Why Power Electronics ? sensors Load Controller Output - AC - DC Input Source AC DC unregulated Reference Power Electronics Converters IDEALLY LOSSLESS !

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 IM: Induction Motor PMSM: Permanent Magnet Synchronous Motor SRM: Switched Reluctance Motor BLDC: Brushless DC Motor DC motors (brushed) AC motors - IM PMSM SRM BLDC

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 Power Electronic Converters Electric Energy - Unregulated - - Regulated - Electric Motor Electric Energy Mechanical Power Electronic Converters POWER IN Motor Load feedback Controller Reference

Modern Electrical Drive Systems Example on Variable Speed Drives (VSD) application Constant speed Variable Speed Drives motor pump valve Supply Power In Power loss Mainly in valve Power out

Modern Electrical Drive Systems Example on Variable Speed Drives (VSD) application Constant speed Variable Speed Drives motor pump valve Supply motor PEC pump Supply Power In Power loss Mainly in valve Power out Power In Power loss Power out

Modern Electrical Drive Systems Example on VSD application Constant speed Variable Speed Drives motor pump valve Supply motor PEC pump Supply Power In Power loss Mainly in valve Power out Power In Power loss Power out

Modern Electrical Drive Systems Example on VSD application Electric motor consumes more than half of electrical energy in the US Variable speed Fixed 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 AC Drives AC Source DC Source DC Source AC Source AC-DC-DC AC-DC DC-DC DC-AC-DC AC-DC-AC AC-AC DC-AC DC-DC-AC Const. DC Variable NCC FCC

Converters for Motor Drives 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 Control Control Uncontrolled Rectifier Single-phase Three-phase Controlled Rectifier Single-phase Three-phase DC-DC Switched mode 1-quadrant, 2-quadrant 4-quadrant

Power Electronic Converters in ED Systems DC DRIVES AC-DC + Vo  50Hz 1-phase Average voltage over 10ms 50Hz 3-phase + Vo  Average voltage over 3.33 ms

Power Electronic Converters in ED Systems DC DRIVES AC-DC + Vo  50Hz 1-phase 90o 180o Average voltage over 10ms 50Hz 3-phase + Vo  90o 180o Average voltage over 3.33 ms

Power Electronic Converters in ED Systems DC DRIVES AC-DC 3-phase supply + Vt  ia Ia Q1 Q2 Q3 Q4 Vt - Operation in quadrant 1 and 4 only

Power Electronic Converters in ED Systems DC DRIVES AC-DC 3-phase supply + Vt  Q1 Q2 Q3 Q4  T

Power Electronic Converters in ED Systems DC DRIVES AC-DC F1 F2 R1 R2 + Va - 3-phase supply Q1 Q2 Q3 Q4  T

Power Electronic Converters in ED Systems DC DRIVES AC-DC Cascade control structure with armature reversal (4-quadrant): iD w wref Speed controller iD,ref + Current Controller Firing Circuit + _ _ iD,ref Armature reversal iD,

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 + Vdc  D1 ia Q2 Q1 Ia + Va - D2 T2 T1 conducts  va = Vdc

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va T1 + Vdc  D1 ia Q2 Q1 Ia + Va - D2 T2 D2 conducts  va = 0 T1 conducts  va = Vdc Va 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 + Vdc  D1 ia Q2 Q1 Ia + Va - D2 T2 D1 conducts  va = Vdc

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va T1 + Vdc  D1 ia Q2 Q1 Ia + Va - D2 T2 D1 conducts  va = Vdc T2 conducts  va = 0 Eb Va 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 vc + vA - Vdc + vc

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + Vdc  D1 D3 Q1 Q3 + Va  D4 D2 Q4 Q2 Positive current va = Vdc when Q1 and Q2 are ON

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + Vdc  D1 D3 Q1 Q3 + Va  D4 D2 Q4 Q2 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

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + Vdc  D1 D3 Q1 Q3 + Va  D4 D2 Q4 Q2 Positive current 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 = 0 when current freewheels through Q and D

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + Vdc  D1 D3 Q1 Q3 + Va  D4 D2 Q4 Q2 Positive current 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 Bipolar switching scheme – output swings between VDC and -VDC AC-DC-DC vc + _ Vdc vA - vB 2vtri vc vA Vdc Vdc vB vAB Vdc -Vdc

Power Electronic Converters in ED Systems DC DRIVES Unipolar switching scheme – output swings between Vdc and -Vdc AC-DC-DC Vtri vc -vc Vdc + vA - + vB - vA Vdc vB Vdc vc + vAB Vdc _ -vc

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter Armature current Vdc Vdc Armature current Vdc Bipolar switching scheme 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 Motor Example of current control in cascade control structure converter speed controller position  + * 1/s current T* *   kT

Modeling and Control of Electrical Drives Current controlled converters in DC Drives - Hysteresis-based + Vdc − ia + Va  va iref iref + ierr q _ q High bandwidth, simple implementation, insensitive to parameter variations Variable switching frequency – depending on operating conditions ierr

Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based i*a + Converter i*b + i*c + For isolated neutral load, ia + ib + ic = 0 control is not totally independent 3-phase AC Motor Instantaneous error for isolated neutral load can reach double the band

Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based id iq is Dh Dh For isolated neutral load, ia + ib + ic = 0 control is not totally independent Instantaneous error for isolated neutral load can reach double the band

Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based Dh = 0.3 A Vdc = 600V Sinusoidal reference current, 30Hz 10W, 50mH load

Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based Current error Actual and reference currents

Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based Actual current locus Current error 0.6A 0.6A 0.6A

Modeling and Control of Electrical Drives Current controlled converters in DC Drives - PI-based Vdc Pulse width modulator vc iref PI +  q vtri Vdc q vc q Vdc Pulse width modulator vc

Modeling and Control of Electrical Drives Current controlled converters in DC Drives - PI-based i*a + PI PWM PWM Converter i*b + PI PWM PWM i*c + PI PWM PWM Sinusoidal PWM Motor Interactions between phases  only require 2 controllers Tracking error

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 PWM + PI Converter i*b i*c Motor

Modeling and Control of Electrical Drives Current controlled converters in AC Drives - PI-based i*a 3-2 SVM 2-3 PI Converter i*b i*c 3-2 Motor

Modeling and Control of Electrical Drives Current controlled converters in AC Drives - PI-based PI controller dqabc abcdq SVM or SPWM VSI IM va* vb* vc* id iq +  id* iq* Synch speed estimator s

Modeling and Control of Electrical Drives Current controlled converters in AC Drives - PI-based Stationary - ia Stationary - id Rotating - ia Rotating - id

? Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier firing circuit controlled rectifier  + Va – vc 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 Input voltage  2 3 4 vc vs 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 Vscos() = vc Vscos(t) Vm  2 3 4 vc 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 Single phase, 50Hz vc(s) Va(s) T=10ms Three phase, 50Hz 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 + Va – iref current controller vc firing circuit  controlled rectifier 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 Closed loop current control with PI controller Input 3-phase, 240V, 50Hz

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier Closed loop current control with PI controller Input 3-phase, 240V, 50Hz Voltage Current

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 Switching signals obtained by comparing control signal with triangular wave Vdc + Va − vtri q vc We want to establish a relation between vc and Va AVERAGE voltage Va(s) vc(s) DC motor ?

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Ttri ton 1 Vc > Vtri Vc < Vtri vc Vdc

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters d 0.5 vc -Vtri Vtri -Vtri vc For vc = -Vtri  d = 0

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters d -Vtri 0.5 vc -Vtri Vtri vc 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 -Vtri 0.5 vc -Vtri Vtri vc 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: Introducing perturbation in vc and Va and separating DC and AC components: DC: AC:

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: va(s) vc(s) DC motor

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Bipolar switching scheme vc vtri + Vdc − q -Vdc + VAB  2vtri vc vA Vdc vB Vdc vAB Vdc -Vdc

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Bipolar switching scheme va(s) vc(s) DC motor

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters + Vdc − vc vtri qa -vc qb Leg a Leg b Unipolar switching scheme Vtri vc -vc vA vB vAB The same average value we’ve seen for bipolar !

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Unipolar switching scheme vc(s) 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 Te = kt ia ee = kt  Extract the dc and ac components by introducing small perturbations in Vt, ia, ea, Te, TL and m ac components dc components

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 Vt(s) = Ia(s)Ra + LasIa + Ea(s) Te(s) = kEIa(s) Ea(s) = kE(s) 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 + -

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Tc vtri + Vdc − q – kt Torque controller + - Torque controller Converter DC motor

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) Zero steady state error – very large DC gain BODE PLOTS Obtain linear small signal model METHOD 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  La = 5.2 mH J = 152 x 10–6 kg.m2 B = 1 x10–4 kg.m2/sec kt = 0.1 Nm/A ke = 0.1 V/(rad/s) 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 kpT= 90 kiT= 18000 compensated compensated

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Speed controller design Torque loop 1 Speed controller * T* T  – +

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Speed controller design Open-loop gain kps= 0.2 kis= 0.14 compensated compensated

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Large Signal Simulation results Speed Torque

Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives INDUCTION MOTOR DRIVES Scalar Control Vector Control Const. V/Hz is=f(wr) FOC DTC Rotor Flux Stator Flux 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): Rr’/s + Vs – Rs Lls Llr’ Eag Is Ir’ Im Lm

Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Te Pull out Torque (Tmax) rotor TL Te Intersection point (Te=TL) determines the steady –state speed sm rated Trated s r s

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: Variable voltage (amplitude), variable frequency (Constant V/Hz) Using power electronics converter Operated at low slip frequency Pole changing Synchronous speed change with no. of poles Discrete step change in speed 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 V = 460 V Rs= 0.25  Rr=0.2  Lr = Ls = 0.5/(2*pi*50) Lm=30/(2*pi*50) f = 50Hz p = 4 Lower speed  slip higher Low efficiency at low speed

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 Eag = k f ag = constant 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

Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant V/Hz Vrated frated Vs 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 Pulse Width Modulator s* + V

Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant V/Hz Simulink blocks for Constant V/Hz Control

Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant V/Hz Speed Torque Stator phase current

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 A low speed, flux falls below the rated value

Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives With compensation (Is,ratedRs) Torque deteriorate at low frequency – hence compensation commonly performed at low frequency In order to truly compensate need to measure stator current – seldom performed

Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives With voltage boost at low frequency Vrated frated Linear offset Non-linear offset – varies with Is Boost

2 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 VSI Rectifier 3-phase supply IM Pulse Width Modulator Vboost Slip speed calculator s* + V Vdc Idc Ramp f C Constant V/f – open-loop with slip compensation and voltage boost

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) Controlled to maintain Im at rated Rr’/s + Vs – Rs Lls Llr’ Eag Is Ir’ Im Lm maintain at rated

Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant air-gap flux

Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Constant air-gap flux Current is controlled using current-controlled 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 VSI Rectifier 3-phase supply IM * + |Is| slip C Current controller s PI r -

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