CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 1 Modified reference voltages and triangular carriers for a five-level SPWM scheme

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 2 The inverter switching vectors and their switching time durations during sampling interval T S (Reference voltages are within the inner carrier region, M < 0.433)

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 3 Determination of the T a_cross, T b_cross and T c_cross during switching interval T S (When reference voltages are spanning the inner carrier region, M < 0.433)

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 4 Determination of the T a_cross, T b_cross and T c_cross during switching interval T S (When reference voltages are spanning the inner carrier region, M < 0.433)

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 5 Determination of the T a_cross, T b_cross and T c_cross during switching interval T S (When reference voltages are spanning the entire carrier region, 0.433<M < 0.866)

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 6 Determination of the T a_cross, T b_cross and T c_cross during switching interval T S (When reference voltages are spanning the entire carrier region, 0.433<M < 0.866)

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 7 SUMMARY: T a_cross, T b_cross and T c_cross for various carrier regions

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 8 Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages Equivalence to Conventional SVPWM The reference signals in carrier based SVPWM are shifted to one carrier region The outer sub-hexagon in the conventional SVPWM are shifted to central sub-hexagon in conventional SVPWM The reference signal shifting in carrier based SVPWM is equivalent to sub-hexagonal shifting in the conventional SVPWM

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 9, x= a, b, c Algorithm for inverter leg switching time calculation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 10 The traces of T first_cross, T second_cross and T third_cross showing non-centered time duration for middle vectors

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 11 The traces of T g_first_cross, T g_second_cross and T g third_cross showing centered time duration for middle vectors

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 12 T offset1 + T offset2 waveforms for various modulation indices

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 13 T as + T offset2 +T offset2 waveforms

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 14 Generalization for ‘n’ level PWM ( ‘n’ even)

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 15 Generalization for ‘n’ level PWM (‘n’ odd)

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 16 Generalization for ‘n’ level PWM ‘n’ even ‘n’ odd

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 17 Proposed SVPWM signal generation in over-modulation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 18 Proposed SVPWM signal generation in over-modulation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 19 Proposed SVPWM signal generation in over-modulation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 20 Proposed SVPWM signal generation in over-modulation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 21 Proposed SVPWM signal generation in over-modulation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 22 Proposed SVPWM signal generation in over-modulation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 23 Summary: linear range of modulation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 24 Summary: over-modulation condition

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 25 Inverter configuration

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 26 Phase-A voltage and phase-A current waveforms for modulation index 0.15 (Layer 1 operation).

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 27 Plot of T ga and offset time T offset1 + T offset2 for modulation index 0.15 (Layer 1 operation). [DAC output]

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 28 Phase-A voltage and phase-A current waveforms for modulation index 0.3 (Layer 2 operation).

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 29 Plot of T ga and offset time T offset1 + T offset2 for modulation index 0.3 (Layer 2 operation) [DAC output]

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 30 Phase-A voltage and phase-A current waveforms for modulation index 0.6 (Layer 3 operation).

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 31 Plot of T ga and offset time T offset1 + T offset2 for modulation index 0.6 (Layer 3 operation)[DAC output]

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 32 The phase-A voltage and phase-A current waveforms for modulation index 0.85 (Layer 4 operation).

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 33 Plot of T ga and offset time T offset1 + T offset2 for modulation index 0.85 (Layer 4 operation) [DAC output]

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 34 The phase-A voltage and phase-A current waveforms for modulation index 1.15 (over-modulation).

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 35 Phase-A current waveform for speed reversal from 40Hz to -40 Hz [modulation index 0.70]

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 36 Space Phasor Based Self Adaptive Current Hysteresis Controller

37 A Space Phasor Based Self Adaptive Current Hysteresis Controller Using Adjacent Inverter Voltage Vectors with Smooth Transition to Six Step Operation for a Three Phase Voltage Source Inverter

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 38 A self adaptive space phasor based current hysteresis controller is proposed for a voltage source inverter Current error space phasor is held within a hexagonal boundary Current errors are monitored along jA, jB, jC axes Ensures optimum switching Does not require computations, uses simple look up table Uses a self adaptive sector change logic Introduction

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 39 The combine effect of the three current errors can be represented as a space phasor The current error space phasor is kept within a boundary by switching an appropriate voltage vector The nearest vector is selected Current error space phasor

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 40 This equation defines the direction in which current error space phasor moves =

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 41 Directions of current error space phasor in sector -1

42 V1V1 V2V2 VZVZ R1R1 R2R2 R3R3 Vectors to be switched in sector-1 to bring back the error

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 43 Directions of current error space phasor in sector -2

44 V 2 V 3 V Z V 3 V Z V 2 Vectors to be switched in sector-2 to bring back the error V 3

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 45 Vectors to be switched in different sectors

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 46 The combined error boundary

47 Modified regions for odd sectors Modified regions for even sectors Region identification

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 48 Region identification contd.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 49 O P Q P’ Detecting The Sector Change Current error space phasor moves out through a unique axis during sector change

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 50 Sector Change Detected using an outer hysteresis

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 51 Over modulation Switching between the active vectors, V 1 and V 2 Sector 1

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 52 Over modulation Sector change logic for over modulation region

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 53 Simulation Results The error boundary Sectors & Vectors Nearest vectors are selected in every sector

54 Simulation Results …. Over modulation Transition to six step Error space phasorCurrent space phasor

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 55 The error boundary 1 div = 0.3 Amp Phase voltage and current Experimental Results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 56 The machine current space phasor ( no load )1 div = 1 amp The machine current space phasor when loaded ( 1 div = 2 A mp ) Experimental Results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 57 Experimental Results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 58 Experimental Results Over modulationSix step operation Transition to six step mode

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 59 The error boundary 1 div = 1 amp The machine current space phasor ( 1 div = 3 A mp ) Experimental Results : Over modulation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 60 Salient Features Space phasor based hysteresis controller with optimum switching is proposed Self adaptive sector change logic Smooth transition to over modulation and to six step mode No computation of machine back emf is required Uses simple look up tables Ensures that only one inverter leg is switched during transition of inverter state

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 61 Current Error Space Phasor Based Hysteresis PWM Controller with Self Adaptive Logic and Adjacent Voltage Vector Selection for The Entire Modulation Range for Three-level Voltage Source Inverter Fed Drive

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 62 Power Schematic of a Dual Two-level Voltage Source Inverter Fed IM Drive

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 63 Combined Voltage Space Phasor Locations and Inverter Switching Vector Combinations for Three-level Inverter 24 Sectors 19 Vectors 64 Switching States

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 64 Directions of Current Error Space Phasor for Tip of V m in Sector -7

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 65 Directions of Current Error Space Phasor for Tip of V m in Sector -8

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 66 Directions of Current Error Space Phasor for Tip of V m in Sector –1 and Sector-2

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 67 Vectors to be Switched in Sector-7 to Keep the Current Error Space Phasor Inside the Boundary

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 68 Vectors to be Switched in Sector-8 to Keep the Current Error Space Phasor inside the Boundary

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 69 Vectors to be Switched in Different Sectors for Different Regions

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 70 Vectors to be Selected in Different Sectors for Different Regions SectorRegion R1R1 R2R2 R3R3 R1R1 R2R2 R3R3 1V0V0 V1V1 V2V V2V2 V3V3 V0V0 3V4V4 V0V0 V3V V0V0 V4V4 V5V5 5V5V5 V6V6 V0V V1V1 V0V0 V6V6 7V1V1 V8V8 V9V9 --- ::::::: 24---V8V8 V1V1 V7V7

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 71 Clamping of Inverters for Adjacent Sectors SectorRegion R1R1 R2R2 R3R3 R1R1 R2R2 R3R3 187’17’27’ ’86’88’ 348’88’38’ ’81’82’ 557’67’77’ ’77’73’ 784’14’24’--- ::::::: ’17’13’

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 72 Comparators Used for Region Detection

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 73 Region Formation from the Segments of the Hexagonal Boundary When comparator along j A is ON and else

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 74 Region Formation from the Segments of the Hexagonal Boundary

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 75 Detecting The Sector Change Using an Outer Hysteresis

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 76 Sector Change Detection for Two-level Operation (Trajectory ‘a’) Current error space phasor moves out through a unique axis during a sector change

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 77 Mapping of Outer Sectors to Inner Sectors

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 78 Sets of Sector Changes Detected Along j A Axis and –j A Axis

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 79 Sector Change Along Corner to Corner Sectors (Trajectory ‘c’) Sector Change from 23 to 8 is Detected Along –j A Direction

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 80 Prevention of JitterPrevention of False Sector Change

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 81 Sector Change During Over Modulation (Trajectory ‘f’)

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 82 Sector Change During Over Modulation (Sector-7 to Sector-9) Trajectory of Current Error Space Phasor

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 83 Sector Change During Over Modulation (Sector-9 to Sector-10) Trajectory of Current Error Space Phasor

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 84 Sector Detection Including Over Modulation (Forward Rotation) Sector Change Detection FromTo Direction along which the outer comparator is in ON state jAjA jBjB jCjC -j A -j B -j C 1*82*** 2***113* 34*14*** 4**** **** 6***1*23 7*989** 8**1191* ::::::: 24***7**

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 85 Simulation Results Two-level operation 1 div. = 0.6 A

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 86 Simulation Results Transition from two-level to three-level Transition from three-level to over modulation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 87 Simulation Results Three-level operation 1 div. = 0.6 A

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 88 Simulation Results Over modulation 1 div.=0.6 A Starting of the machine

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 89 Block Schematic of Experimental Set-up

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 90 1 div = 0.3 Amp Two-level operation Experimental Results 1 div = 0.75Amp

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 91 Transition form two-level to three-level and vice versa Experimental Results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 92 1 div = 0.3 Amp Three-level operation Experimental Results 1 div = 0.75Amp

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 93 1 div = 0.75 Amp Over modulation Experimental Results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 94 Starting of the machine Experimental Results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 95 Speed reversal of the machine Experimental Results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 96 Speed reversals of the machine Experimental Results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 97 Normalized harmonic spectrum of current waveforms Two-level operation Experimental Results Three-level operation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 98 Normalized harmonic spectrum of voltage waveforms Two-level operation Experimental Results Three-level operation

A HARMONIC ELIMINATION SCHEME FOR AN OPEN – END WINDING INDUCTION MOTOR DRIVE FED FROM TWO INVERTERS WITH ASYMMETRICAL DC LINK VOLTAGES

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 100 A low order harmonic elimination technique for an open–end winding induction motor drive is proposed. For the present open–end winding drive, the induction motor is fed from two 2-level inverters with different isolated DC-link voltages of ratio equal to 1: With such a scheme it is found that all the 5 th and 7 th order (6n  1, where n = 1,3,5,7 etc.) harmonics are absent in the motor phase voltage. The third harmonic order currents are eliminated from the motor by using isolated DC-link supply for the two inverters. A smooth transition to the over-modulation region is also achievable from the present open– end winding IM drive. Salient features

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 101  Open end winding circuit schematic  Inverter – 1 DC-link voltage is V DC  Inverter – 2 DC-link voltage is V dc  V DC = V dc INVERTER - 2 O INVERTER - 1 A B C C’C’ B’B’ A’A’ O’ V dc /2 V DC /2 Open-end winding IM drive

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 102 Vector diagram inverter – 1 Vector magnitude = V DC V DC 4 (-++) 4’(-++) 1’(+--) 6’(+-+) 5’(--+) 2’(++-) 3’(-+-) 5 (--+)6 (+-+) 1 (+--) 2 (++-) 3 (-+-) Vector diagram inverter – 2 Vector magnitude = V dc Voltage space phasor diagrams of individual inverters V DC

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA  6’ 1,1’  (+--) 2,2’  (++-) 3,3’  (-+-) 4,4’  (-++) 5,5’  (--+) 6,6’  (+-+) 7,7’  (+++) 8,8’  (---) `5` 6 3’ 5’ 4’1’ 6’ 2’ 1’ 3’2’ 4’ 5’ V DC V DC V DC sin15 0 = k V DC sin45 0 So k = sin15 0 / sin45 0 = k V DC  Selected combinations of the vector positions from inverter – 1 and inverter – 2 and calculation of DC – link voltage ratio (k) for both the inverters.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 104 (a) - Fundamental II 2 1 II 1 1 -II 2 1 -II 1 1 I11I11 I21I21 Ref. point (b) – 5 th Harmonics -II 1 5 -II 2 5 II 1 5 II 2 5 I15I15 I25I25 Ref. point (c) – 7 th Harmonics -II 1 7 -II 2 7 I27I27 I17I17 II 1 7 II 2 7 Ref. point (d) – 11 th Harmonics -II II 1 11 I 1 11 I 2 11 II 2 11 II 1 11 Ref. point (e) – 13 th Harmonics -II II 2 13 I 1 13 I 2 13 II 2 13 II 1 13 Relative position of different harmonics (1 st to 13 th ) of the motor phase from both inverter – 1 and inverter – 2

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 105 Relative position of different harmonics (17 th to 25 th ) of the motor phase from both inverter – 1 and inverter – 2 (f) – 17 th Harmonics (g) – 19 th Harmonics II 2 23 II II 1 23 I 2 23 I II 2 23 (h) – 23rd Harmonics (i) – 25 th Harmonics II 1 17 II 2 17 I 2 17 I II II 1 17 Ref. point -II II 1 19 II 2 19 II 1 19 I 1 19 I 2 19 Ref. point II 1 25 II II II 2 25 I 1 25 I 2 25 Ref. point

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA V CO  t  t V AO V BO  Switching vectors and pole voltage (V AO, V BO, V CO ) of inverter I V A’O V B’O V C’O  t  t II  Switching vectors and pole voltage (V A’O, V B’O, V C’O ) of inverter - 2

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 107 EXPERIMENTAL RESULTS OVER MODULATION Phase voltage Harmonic spectrum Phase current Phase current and Fourier spectrum show absence of all 6n±1 (n = 1,3,5.. etc) harmonics Y-axis : 75v/div Y-axis : 1 amp/div

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 108 EXPERIMENTAL RESULTS MODULATING WAVE,TRIANGLE CARRIER WAVE AND CORRESPONDING GATE SIGNAL a – Modulating wave and triangle carrier wave (inverter-1). b – Inverter-1 pole voltage. c – Modulating wave and triangle carrier wave (inverter-2). d – Inverter-2 pole voltage (fc = 6f) Phase-A and A’ Phase-B and B’ Phase-C and C’ abcdabcd abcdabcd abcdabcd

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 109 EXPERIMENTAL RESULTS MODULATION INDEX LESS THAN ONE (fc = 6f) PHASE VOLTAGE FOURIER SPECTRUM PHASE CURRENT The Fourier spectrum shows increase in harmonic contents compared to that of over-modulation case. Y axis : 100v/div Y-axis : 1 amp/div

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 110 EXPERIMENTAL RESULTS MODULATION INDEX = 0.45 (fc = 12f) PHASE VOLTAGE FOURIER SPECTRUM PHASE CURRENT The Fourier spectrum shows increase in 23 rd and 25 th harmonic contents. Y-axis : 100v/div Y-axis : 1 amp/div

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 111 Fundamental 11 th 25 th 23 rd 13 th THE RELATIVE RATIO OF DIFFERENT HARMONICS GENERATED BY TRIANGULAR CARRIER AT DIFFERENT MODULATION INDICES fc = 6f

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 112 THE RELATIVE RATIO OF DIFFERENT HARMONICS GENERATED BY TRIANGULAR CARRIER AT DIFFERENT MODULATION INDICES fc = 12f Fundamental 23 rd  11 th,  13 th 25 th

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 113 THE RELATIVE RATIO OF DIFFERENT HARMONICS GENERATED BY TRIANGULAR CARRIER AT DIFFERENT MODULATION INDICES fc = 24f fundamental ***: 11 th, +++ : 13 th ooo: 23 rd, xxx : 25 th

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 114 THE RELATIVE RATIO OF DIFFERENT HARMONICS GENERATED BY TRIANGULAR CARRIER AT DIFFERENT MODULATION INDEX fc = 24f fundamental 47th ***: 37 th, +++ : 39 th 49 th

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 115  All the 6n  1, n = 1, 3, 5 etc,. order harmonics are eliminated from the motor phase voltage in the entire speed range.  A linear transition to the maximum modulation is possible.  By properly choosing the frequency modulation ratio (6, 12, 24, 48) at different speed ranges, the switching frequency of both inverters can be controlled within 500hz.   In the extreme speed range the lower voltage inverter is switched more frequently than the higher voltage inverter.  The 11 th and 13 th order harmonic voltage amplitudes in the motor phase voltage can be suppressed by introducing notches in the modulating wave.  The resultant fundamental is reduced to 99.57%.  The resultant 11 th order harmonic is reduced to 50%. And the 13 th order harmonic is reduced to 31.86%. CONCLUSION & SALIENT FEATURES

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 116 a – Modulating wave (11 th and 13 th harmonics suppressed) and triangle carrier wave (inverter-1) b – Inverter-1 pole voltage c – Modulating wave (11 th and 13 th harmonics suppressed) and triangle carrier wave (inverter-2) d – Inverter-2 pole voltage EXPERIMENTAL RESULTS: 11 th and 13 th suppression Pole voltage of inverter-2 ( Over modulation) Pole voltage of inverter-1 ( Over modulation) Modulating wave and triangular carrier wave (over modulation ) fc/f = 12

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 117 EXPERIMENTAL RESULTS PHASE VOLTAGE,FOURIER SPECTRUM,PHASE CURRENTS(m > 1) Modulation index = 1.0 Over-modulation. Phase voltage with 11 th and 13 th suppressed. Y-axis : 75v/div; X-axis : 5ms/div Modulation index = 1.0 Over-modulation Fourier spectrum With 11 th and 13 th suppressed. Modulation index = 1.0 Phase current during overmodulation.(No load operation with 11 th and 13 th suppressed) Y-axis : 1A/div; X-axis : 5ms/div

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 118 EXPERIMENTAL RESULTS PHASE VOLTAGE,FOURIER SPECTRUM,PHASE CURRENTS(m > 0.9) Y-axis : 1A/div Y-axis : 75v/div Modulation index = 0.9. Phase voltage. fc = 12f, With 11 th and 13 th suppressed. Y-axis : 75v/div; X-axis : 5ms/div Modulation index = 0.9. fourier spectrum. fc = 12f. With 11 th and 13 th suppressed Modulation index = 0.9. Phase current waveform. fc = 12f ( no load operation with 11 th and 13 th suppressed). Y-axis : 1A/div; X-axis : 5ms/div

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 119 EXPERIMENTAL RESULTS PHASE VOLTAGE,FOURIER SPECTRUM,PHASE CURRENTS(m > 0.45) Y-axis : 1A/div Y-axis : 75v/div Modulation index = Phase voltage. fc = 12f. With 11 th and 13 th suppressed. Y-axis : 75v/div; X-axis : 5ms/div Modulation index = Phase current waveform. fc = 12f ( no load operation with 11 th and 13 th suppressed). Y-axis : 1A/div; X-axis : 10ms/div Modulation index = Fourier spectrum. fc = 12f. With 11 th and 13 th suppressed

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 120 Fundamental 25 th 23 rd  11 th,  13 th fundamental ***: 11 th, +++ : 13 th ooo: 23 rd, xxx : 25 th fc = 12f fc = 24f fundamental ***: 11 th, +++ : 13 th ooo: 23 rd, xxx : 25 th fc = 48f HARMONIC ANALYSIS RATIO OF DIFFERENT HARMONICS VERSES MODULATION INDEX

A Novel Modulation Scheme for a Six Phase Induction Motor with Open-End Windings

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 122 Six phase (split phase)motor configuration is achieved by splitting the phase belt of a conventional 3-phase induction motor into two halves namely abc and a’b’c’. The phase separation between a and a’, b and b’ and c and c’ is 30° Winding disposition of a six-phase machine

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 123 For a six phase induction motor drive harmonics of the order 6n  1( n=1,3,5 etc.,) will not contribute to the air gap flux. All these 6n  1 ( n=1,3,5 etc.,) order harmonic currents are limited by the stator impedance only and hence contribute to large harmonic currents. Inverter fed six-phase IM drive

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 124 The phase voltages and currents in a six phase motor can be represented by a six dimensional vector. By proper transformation three different sub-spaces can be generated which correspond to three different set of harmonic orders. The generalised vector used for the transformation matrix is S k (a) = [cos k(a) cos k(a-θ) · · · · cos k(a-9θ)]. Winding disposition of a six-phase machine

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 125 By putting a = 0 and π/2, and θ equals to multiples of 30º in the generalised vector a transformation matrix is obtained. θ = angular space separation between the two sets of 3- phase windings.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 126 The harmonics of order 6n  1 ( n = 0, 2,4 etc.,) span a 2- dimesional subspace ‘s 1 ’. The harmonics of order 6n  1 ( n = 1, 3,5 etc.,) span a 2- dimesional subspace ‘s 2 ’. The triplen order harmonics span a 2-dimesional subspace ‘s 3 ’. They are orthogonal to each other.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 127 All switching vectors projected on subspace‘S 1 ’ generates 6n  1 ( n = 0, 2,4 etc.,) harmonics. Switching vectors in sub-space ‘S1’

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 128 All switching vectors projected on subspace‘S 2 ’ generates 6n  1 ( n = 1, 3,5 etc.,) harmonics Switching vectors in sub-space ‘S2’

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 129 In the proposed scheme a modulation technique is used to eliminate all the 6n  1 ( n = 1,3,5 etc.,) harmonics from the stator phases. An open-end winding drive configuration with DC-link voltages chosen in a ratio of 1:0.366 will eliminate 6n  1 ( n = 1,3,5 etc.,) harmonics. Power schematic to suppress the 6n1 ( n = 1,3,5 etc.,) harmonics

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 130 From one side of open-end winding (inverter-1 and inverter-4) 11’,21’, 22’, 32’,33’,43’,44’,54,,55’,65’,66’ and 16’ vectors are switched. From the opposite side (inverter-2 and inverter-3) vectors 53’, 45’, 64’, 56’, 15’, 61’, 26’, 12’, 31’, 23’, 42’, and 34’ are switched. Inverter vector selection to suppress the 6n  1 ( n = 1,3,5 etc.,) harmonics

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 131 Vectors 11’ and 53’ get added in ‘S 1 ’ plane With DC-link voltage ratio of |11’| / |53’| = combined vectors on ‘S 2 ’ plane are cancelled implying all 6n  1 ( n = 1,3,5 etc.,) harmonic elimination. Inverter vector selection to suppress the 6n  1 ( n = 1,3,5 etc.,) harmonics contd.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 132 With DC-link voltage ratio of sided polygonal voltage space phasor combinations are achieved for each 3-phase groups independently. A modulation scheme based on 12-sided polygonal voltage space phasors will cancel the 6n  1 ( n = 1,3,5 etc.,) harmonics voltage from all the motor phases.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 133 Phase voltage Harmonic spectrum Phase currents. 6n  1 ( n = 1,3,5 etc.,) harmonics are absent. Experimental results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 134 To suppress the 11 th and 13 th order harmonics in motor phases additional notches of 3.75° are provided in the modulation voltage. This results in a reduction of 11 th harmonic to 50%,13 th harmonic to 31.86% and fundamental to 99.57% in magnitude.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 135 Experimental results(with notch) Phase voltage Harmonic spectrum Reduction in 11 th and 13 th order harmonic magnitude. Phase currents.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 136 Experimental results(with notch) Modulation ratio of 12. Phase voltage Phase currents

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 137 Experimental results(with notch) Modulation ratio of 24 Phase voltage Phase currents I A

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 138 Experimental results(with notch) Modulation ratio of 48 Phase voltage Phase currents

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 139 Conclusion & salient features A modulation technique to eliminate the 6n  1 ( n=1,3,5 etc.,) harmonic currents, without the need for harmonic filters, from the stator phases of a six phase induction motor drive is explained. By appropriately choosing the frequency ratio between 12,24 and 48 for different speed ranges the inverter switching frequency can be limited to 600 hz. The proposed scheme used 4 inverters with a DC-link voltage of 0.41V DC and 0.15V DC, where V DC is the DC-link voltage of a 2- level 3-phase inverter, if the six-phase machine is run as a conventional 3-phase machine.

INDEPENDENT SPEED CONTROL OF TWO SIX PHASE INDUCTION MOTORS USING A SINGLE SIX PHASE INVERTER

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 141 A method of independent speed control of two induction motors from a single six-phase inverter is proposed. The positive sequence component consists of all the 12n  1 (n = 0,1,2, ….etc.) order harmonics. One of the two zero sequence components consists of all the 6n  1 (n = 1,3,5 ….etc.) order harmonics. Introduction

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 142 A six phase induction motor driven from six phase inverter Vas,Vbs,Vcs are the phase voltages of the a,b,c three phase group Va’s,Vb’s,Vc’s are the phase voltages of the a’,b’,c’ three phase group Inverter fed six-phase IM drive

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 143 Vas, Vbs, Vcs for a,b,c group. Va’s, Vb’s, Vc’s for a’,b’,c’ group. Vα, Vβ … Harmonics spanning subspace S1 [12n  1 (n = 0,1,2,3 ….etc.,)] V1, V2 … Harmonics spanning subspace S2 [6n  1 (n = 1,3,5 order ….etc.,)] Vo1, Vo2… Harmonics spanning subspace S3 [triplen harmonic ]

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 144 Stator Voltage equation is input voltage vectors, is input stator current vectors, is stator resistance matrix,is stator self inductance matrix, is stator to rotor mutual inductance matrix.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 145 Applying the orthogonal transformation to the stator voltage equation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 146 are two orthogonal components of stator currents spanning subspace S1, are two orthogonal components of stator currents spanning subspace S2, are the two orthogonal components of rotor currents spanning subspace S1, are two orthogonal components of rotor currents spanning subspace S2.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 147 Rotor voltage equation is stator resistance matrix,is stator self inductance matrix, is rotor to stator mutual inductance matrix.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 148 By applying the orthogonal transformation to the rotor voltage equation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 149 The corresponding voltage equations of stator and rotor spanning subspaces S1 and S2 can be separated out Subspaces S1 …. Subspaces S2 ….

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 150 Only the positive sequence components traversing subspace S1 contribute for the air gap flux and electromagnetic torque production in machine. The zero sequence components do not contribute towards air gap flux production with the existing winding disposition.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 151 A scheme is proposed where the zero sequence components corresponding to the 6n  1 (n = 1,3,5 ….etc.) order harmonics are impressed across a second six phase motor in proper phase sequence. The zero sequence components acts as positive sequence component for the second motor and hence develop air gap flux and electromagnetic torque in the second motor.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 152 B’ 180˚ +30˚ N N’ C ’ C B A’ A Stator schematic of the reconfigured six phase induction machine ( voltage components in the S2 plane create air gap flux and torque) Six-phase IM winding disposition:- S2 subspace components produce torque

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 153 Stator Voltage equation is input voltage vectors, is input stator current vectors, is stator resistance matrix,is stator self inductance matrix, is stator to rotor mutual inductance matrix.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 154 By applying the orthogonal transformation to the stator voltage equation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 155 Rotor Voltage equation is stator resistance matrix,is stator self inductance matrix, is rotor to stator mutual inductance matrix.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 156 By applying the orthogonal transformation to the rotor voltage equation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 157 The corresponding voltage equations of stator and rotor spanning subspaces S1 and S2 can be separated out Subspaces S1 …. Subspaces S2 ….

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 158 Only the harmonic components traversing subspace S2 contribute for the air gap flux and electromagnetic torque production in machine. The the harmonic components traversing subspace S1 do not contribute towards air gap flux production with the existing winding disposition.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 159 The 5 th harmonic voltage, which spans the subspace S2 is represented by The 7 th harmonic voltage, which spans the subspace S2 is represented by The phase relationship among the elements of the vector represented by 5 th harmonic and 7 th harmonic are similar except that the frequencies are different. Hence if the frequency and in the equations are replaced by, then a vector corresponding to the fundamental frequency spanning the subspace can be obtained.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 160 This orthogonal property is made use of for controlling two split-phase induction motors independently by connecting them in series and controlling with a single six-phase inverter. The reference modulating signals for the whole drive system are generated by superimposing the reference signals belonging to the subspace S1 and the reference signals belonging to the subspace S2.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA ˚ N2N2 N2N2 N2N2 A2A2 B2’B2’ C2’C2’ C2C2 B2B2 A2’A2’ C1’C1’ C1C1 B1’B1’ B1B1 A1’A1’ A1A1 MACHINE-1 ( 2-pole 2kw) MACHINE-2 ( 4-pole 1kw) 180˚ +30˚ N’ Schematic of the stator phase windings of the two series connected six phase induction motors

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 162 Motor-1 phase voltage generation Motor-1 and motor-2 combined phase voltage generation Motor-2 phase voltage generation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 163 Control blocks for series connected six phase motor drive

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 164 Voltage waveform of phase-a and phase-a’ of motor-2 (Motor-1 is running at 1000rpm(18hz) and motor-2 is running at 250rpm(9hz). The motors are running in opposite direction).No - load operation. X- axis 20ms/div. Y- axis 20v/div. Voltage waveform of phase-a and phase-a’ of motor-1 (Motor-1is running at 1000rpm(18Hz) and motor-2 is running at 250rpm(9Hz).The motors are running in opposite direction). No - load operation. X- axis 10ms/div. Y- axis 50v/div Reference voltage of phase-a’ of motor-1 and motor- 2 and the their combined voltage for PWM generation (Motor-1 is running at 1000rpm(18Hz) and motor-2 is running at 250rpm(9hz). The motors are running in opposite direction). No - load operation. X- axis 50ms/div. Y- axis 200mv/div. Reference voltage of phase-a of motor-1 and motor- 2 and the their combined voltage for PWM generation (Motor-1 is running at 1000rpm(18 Hz) and motor-2 is running at 250rpm(9 Hz). The motors are running in opposite direction). No - load operation. X- axis 50ms/div. Y- axis 200mv/div. Experimental results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 165 Harmonic spectrum of current waveform in phase- a’ (Motor-1 is running at 1000rpm(18hz) and motor-2 is running at 250rpm(9hz). The motors are running in opposite direction). Along normalised frequency axis 9hz = 1unit. Current waveform of phase-a and phase-a’ (Motor-1 is running at 1000rpm(18hz ) and motor-2 is running at 250rpm(9hz). The motors are running in opposite direction).No - load operation. X- axis 50ms/div. Y- axis 1A/div. Combined phase-a’ voltage waveform (Motor-1is running at 1000rpm(18hz) and motor-2 is running at 250rpm(9hz).The motors are running in opposite direction). X- axis 10ms/div. Y- axis 50v/div. Combined phase-a voltage waveform (Motor-1 is running at 1000rpm(18hz) and motor-2 is running at 250rpm(9hz).The motors are running in opposite direction). X- axis 10ms/div. Y- axis 50v/div. Experimental results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 166 Combined phase-a’ voltage waveform [V A1’N2’ of Fig.4b] (Motor-1is running at 1000rpm(18hz) and motor-2 is running at 500rpm(18hz).The motors are running in same direction). X- axis 10ms/div. Y- axis 50v/div. Combined phase-a voltage waveform [V A1A2 of Fig.4b] (Motor-1is running at 1000rpm(18hz) and motor-2 is running at 500rpm(18hz).The motors are running in same direction). X- axis 10ms/div. Y- axis 50v/div. Voltage waveform of phase-a and phase-a’ of motor-2 (Motor-1 is running at 1000rpm(18hz) and motor-2 is running at 500rpm(18hz).The motors are running in same direction). X- axis 10ms/div. Y- axis 20v/div. Voltage waveform of phase-a and phase-a’ of motor-1 (Motor-1is running at 1000rpm(18hz) and motor-2 is running at 500rpm(18hz).The motors are running in same direction). X- axis 10ms/div. Y- axis 50v/div. Experimental results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 167 Voltage waveform of phase-a and phase-a’ of motor1 (Motor-1 is running at 1000rpm(18hz) and motor-2 is stalled ). X- axis 10ms/div. Y- axis 50v/div. Voltage waveform of phase-a and phase-a’ of motor2 (Motor-1is running at 1000rpm(18hz) and motor-2 is stalled ). X- axis 10ms/div. Y- axis 50v/div. Current waveform of phase-a and phase-a’ (Motor-1 is running at 1000rpm(18hz) and motor-2 is running at 500rpm(18hz).The motors are running in same direction). X- axis 50ms/div. Y- axis 1A/div. No-load operation. Experimental results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 168 Current waveform of phase-a and phase-a’ (Motor-1 is running at 1000rpm(18hz) and motor-2 is stalled ). X- axis 10ms/div. Y- axis 2mv/div. No-load operation. Combined phase-a voltage waveform [V A1A2 of Fig.4b] (Motor-1 is running at 1000rpm(18hz) and motor-2 is stalled). X- axis 10ms/div. Y- axis 50v/div. Combined phase-a’ voltage waveform [V A1’N2’ of Fig.4b] (Motor-1 is running at 1000rpm(18hz) and motor-2 is stalled). X- axis 10ms/div. Y- axis 50v/div. Experimental results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 169 Current waveform of phase-a’ and speed of motor-2 (Motor-1 is making speed reversal from -1000rpm to 1000rpm and motor-2 is running at constant speed at 250rpm ). X- axis 5s/div. Y- axis 1A/div (current), 125rpm/div (speed) Current waveform of phase-a’ and speed of motor-1 (Motor-1 is making speed reversal from -1000rpm to 1000rpm and motor-2 is running at constant speed at 250rpm ). X- axis 5s/div. Y- axis 1A/div (current), 500rpm/div (speed) Current waveform of phase-a’ and speed of motor-2 (Motor-1 is making speed reversal from 1000rpm to –1000rpm and motor-2 making speed reversal from -250rpm to 250rpm ). X- axis 5s/div. Y- axis 4A/div (current), 125rpm/div (speed) Current waveform of phase-a’ and speed of motor-1 (Motor-1 is making speed reversal from 1000rpm to –1000rpm and motor-2 making speed reversal from -250rpm to 250rpm ). X- axis 5s/div. Y- axis 4A/div (current), 500rpm/div (speed) Experimental results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 170 Current waveform of phase-a’ and speed of motor-2 (Motor-1 is running at constant speed of 1000rpm and motor-2 is making speed reversal from -250rpm to 250rpm ). X- axis 5s/div. Y- axis 1A/div (current), 250rpm/div (speed) Current waveform of phase-a’ and speed of motor-2 (Motor-1 is running at constant speed of 1000rpm and motor-2 is making speed reversal from -250rpm to 250rpm ). X- axis 5s/div. Y- axis 1A/div (current), 125rpm/div (speed) Current waveform of phase-a and phase-a’ (Motor-1 running at six step mode and motor-2 is stalled ). X- axis 20ms/div. Y- axis 1A/div Voltage waveform of phase-a’ of motor-1 and motor-2 (Motor-1 running at six step mode and motor-2 is stalled ). X- axis 10ms/div. Y- axis 100v/div. Experimental results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 171 Harmonic spectrum of voltage waveform in phase-a’ of motor-1 (Motor-1 is running in over modulation (12 step) and motor-2 is stalled). Harmonic spectrum of voltage waveform in phase-a’ of motor-2 (Motor-1 is running in over modulation (12 step) and motor-2 is stalled). Current waveform of phase-a and phase-a’ (Motor-1 is stalled and motor-2 is running at six step mode). X- axis 20ms/div. Y- axis 1A/div Voltage waveform of phase-a’ of motor-1 and motor-2 (Motor-1 is stalled and motor-2 is running at six step mode). X- axis 10ms/div. Y- axis 100v/div. Experimental results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 172 Conclusion & salient features A de-coupled speed control of two split phase (six phase) induction motor, from a single six phase inverter system is presented. In normal six phase motor the phase voltages corresponding to the 6n  1 (n = 1,3,5 ….etc.,) harmonic orders do not create torque and air gap flux. But the phase voltages corresponding to the 6n  1(n = 1,3,5 ….etc.,) harmonic orders when applied to another six phase motor in proper phase sequence, torque and air gap flux are created. Thus by the proper series connections of phases of the two six phase motors, the two motors can be run independently from a single six phase inverter. Independent speed control of the two motors are possible without the need for costly and bulky harmonic filters to suppress the high amplitude 6n  1 (n = 1,3,5 ….etc.,) order zero sequence harmonic current components.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 173 Independent Field Oriented Control Of Two Split-phase Induction Motors From A Single Six-phase Inverter

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 174 Terminal connection of the two series connected split-phase (six-phase) induction motors.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 175 Speed reversal of motor-1( Bottom Trace) and motor-2 at different instants (Motor-1 500rpm to –500rpm and motor-2 between-300rpm to 300rpm).

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 176 Torque currents of motors

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 177 simultaneous speed reversal of motors [( motor-1( Bottom trace) 500rpm to –500rpm and motor-2 ( Top Trace) -300rpm to 300rpm]

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 178 Torque currents of motor-1 ( Bottom Trace) and motor-2 (Top Trace)

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 179 Motor-1 is accelerating and motor-2 is running at constant speed

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 180 Motor-1 is doing speed reversal and Motor-2 is at constant speed operation

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 181

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 182 Independent speed control of the two motors are possible without the need for costly and bulky harmonic filters to suppress the high amplitude 6n  1 (n = 1,3,5 ….etc.,) order zero sequence harmonic current components.

A SENSORLESS SPEED CONTROL FOR INDUCTION MOTORS USING RIPPLE CURRENTS IN SPACE PHASOR BASED PWM CONTROL

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 184 A new method to estimate speed of induction motor without shaft transducer is proposed. The motor phase current ripple is used for estimation of rotor flux position. Two different schemes are used for flux position estimation in two different regions, one in low speed region and the other in high speed region. The proposed method uses space vector modulation with constant switching frequency. Introduction

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 185 Steady state equivalent circuit of induction motor in rotor reference frame. The back emf vector lags the rotor flux vector by 90˚ r R  L s R rr jW  k V L)1(  dt d s  d V r m   W synchronous dt id s m V axis   r  m -V

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 186 The stator equation is

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 187 During the effective period Teff (T 1 & T 2 ) both back emf vector and active vectors cause the ripple current to flow. During the zero vector period T 0 only the back emf vector causes the ripple current to flow. 2 0 T 2 T 2 T sk i 2 0 T 2 0 T 1 T 1 V 2 0 T 0 V 0 V 0 V 0 V )1(  ks i eff T 2 V 1 T 1 V 2 V 2 T s i  T T T

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 188 Two samples of current vectors are taken in T/2 time period difference during the zero vector period. When the modulating frequency is less than 50% of the base frequency the zero vector period T 0 is more than the the effective period Teff i.e. T 0 is more than half of the switching period T/2 and hence there is sufficient deviation in current vector during zero period T 0. Flux position estimation in low speed region

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 189 Flux position estimation in high speed region Three samples of current are taken at t = 0, t = T/2 and t = T. Effective period Teff is more than T/2(half of the switching period). Ripple current dependent on the two consecutive active vectors and the back emf vector. The flux position is estimated by creation of a virtual short circuit i.e. by eliminating the effect of active vectors from the ripple current.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 190 When the reference vector position θ is within 30˚ from the first active vector in any sector, i.e. 0 < θ <= 30˚, the time period T 1 for the first active vector, is greater than the time period T 2 for the second active vector Three samples of current are taken at t = 0, t = T/2 and t = T 2 0 T 2 0 T eff T 1 T 2 T 0 V 1 V 2 V 0 V 1err I 2 I sk i )1(  ks i )2(  ks i 2 T 2 T

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA T 2 T 2 0 T 2 0 T eff T 1 T 2 T 0 V 1 V 2 V 0 V 1err I 2 I sk i )1(  ks i )2(  ks i When the reference vector position θ is more than 30˚ from the first active vector in a sector i.e. 30˚ < θ <= 60˚,the time period T 1 for the first active vector is less than the time period T 2 for the second active vector Three samples of current are taken at t = 0, t = T/2 and t = T

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 192 Considering one case when reference vector is in sector-1 When  < 30° in sector-1 i.e. when 1 T period is more than 2 T period )2/2/( 1 11 TVTV l i mefferr   }2/)2/({ TVTVTTV l i mefferr   When  > 30° in sector-1i.e. when 2 T period is more than 1 T period }2/)2/({ TVTTVTV l i mefferr   )2/2/( 1 22 TVTV l i mefferr  

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 193 By plotting the current deviation vector due to active vectors in the first half of sampling period for all the sectors we get a hexagon distorted clockwise. By plotting the current deviation vector due to active vectors in the second half of sampling period for all the sectors we get a hexagon distorted anticlockwise. 0 0  0 30   0 90  b -c -a a c-b        axis  0 60  axis  0 0  0 30   0 90  b -c -a a c -b       axis  0 60  1_actveer I 2_actveer I axis    

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 194 By extracting the fundamental components we get that, the fundamental component of lags by Φ from, the fundamental component of reference vector and, the fundamental component of leads by Φ from. Φ = 16.15˚.  f V 1_actveerf I 2_actveerf I  t  t  t 

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 195 Hence 1_actveerf i = _ j actveerf ei  ferr i 1 the fundamental components of 1err i can be written as mfactveerfferr Vii  1_1 mf V =The fundamental components of the current deviation phasor contributed by back emf. Similarly ferr i 2 the fundamental componentsof 2err i can be written as mfactveerfferr Vii  2_2 A high resolution band pass filter whose center frequency is dynamically tuned to the fundamental frequency, is used for extraction of these fundamental components from the sampled ripple currents.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 196 From the three equations the back emf position is found as The rotor flux position leads by 90˚ from the back emf position, hence it can be obtained by adding 90˚ to the position of back emf vector. A speed control scheme is implemented based on the estimated rotor flux position. )1(      j j ferrf mf e eii V

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 197 Block diagram of sensorless speed control scheme

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 198 Flux position at frequency equal to 10 hertz. Flux position at frequency equal to 30 hertz. Experimental Results

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 199 Flux position at frequency equal to 40 hertz. Reference speed and estimated speed for speed reversal application. Speed scaling = 800rpm/div

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 200 Phase current and estimated speed for speed reversal application. Current scaling = 5A/div, Speed scaling = 800rpm/div. Speed reversal (zoomed).

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 201 Torque current and estimated speed during acceleration. Current scaling = 5A/div, Speed scaling = 600rpm/div Phase current and estimated speed during acceleration. Current scaling = 5A/div, Speed scaling = 600rpm/div

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 202 A Five-level Inverter Topology With Common-mode Voltage Elimination for Induction Motor Drives

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 203 A five-level inverter topology and the switching state selection strategy for the PWM control, is proposed. The proposed scheme completely eliminates the common-mode voltages in the entire modulation range of the induction motor drive. The proposed scheme is based on a dual five-level inverter fed open-end winding induction motor configuration. With the absence of common-mode voltage, associated problems, such as, shaft voltages, bearing currents, etc., are also eliminated in the proposed drive. Introduction

A five-level inverter topology is proposed. It is formed by cascading two conventional two-level inverters and a conventional three-level NPC inverter. It offers simple power-bus structure compared to the five-level NPC inverter. It needs only two power diodes per leg (pole). One leg of the proposed five-level inverter topology

CEDT, Indian Institute of Science CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 205 *[“1”  ON, “0”  OFF] **S 11 -S 14, S 21 -S 34, S 24 -S 31, and S 41 -S 44 are complementary pairs of switches Realization of the five different voltage levels Voltag e Level Pole Voltag e State of the switch** S 11 S 21 S 24 S 41 2V dc / V dc / V dc / V dc /40010 IGBT Gating Logic*

Requirement of blocking voltage capability of devices The requirement of blocking voltage capability of individual device goes to as low as V dc /8 for S 11, S 14, S 41, and S 44 while, it is V dc /5.33 (3xV dc /2x8) for S 21, S 34, S 24, and S 31 in the proposed open-end winding IM drive.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 207 Power schematic of the dual-five level inverter fed IM drive

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 208 The nine-level voltage space phasor generation using the dual five-level inverter fed open-end winding IM Voltage space phasor of individual five-level inverters Machine phase voltage in terms of inverter pole voltages Inverter-A Inverter-A’ Combined voltage space phasor

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 209 Switching states and voltage space vector locations of the individual five-level inverter (Inv.-A or Inv.-A’) 61 Voltage Vectors 96 Triangular Sectors 125 Switching States Shaded vectors and states generate zero common-mode voltage