1. DESE, Indian Institute of Science Bangalore1 Induction Motor Drives Based on Multilevel Dodecagonal and Octadecagonal Voltage Space Vectors Mathew K. Research Advisors: Prof. K Gopakumar and Prof. L Umanand Department of Electronic Systems Engineering, Indian Institute of Science, Bangalore-560012, INDIA

2. DESE, Indian Institute of Science Bangalore2 Overview of the presentation Evolution of multilevel space vector structures Comparison of Hexagonal, Dodecagonal and Octadecagonal Space-vector Switching Multilevel Dodecagonal Voltage Space-vector Generation using Cascaded H-bridges Multilevel Dodecagonal Voltage Space-vector Generation using 2-level and 3-level Inverters Multilevel Octadecagonal Voltage Space-vector Generation for Induction Motor Drives Conclusion

3. DESE, Indian Institute of Science Bangalore Evolution of space vector structures (Hexagonal,12-sided and 18-sided) 2-level 3

4. DESE, Indian Institute of Science Bangalore Evolution of space vector structures (Hexagonal,12-sided and 18-sided) Hexagonal space vectors. 2-level 3-level 4

5. DESE, Indian Institute of Science Bangalore Evolution of space vector structures (Hexagonal,12-sided and 18-sided) Hexagonal space vectors. 2-level 3-level 5-level 5

6. DESE, Indian Institute of Science Bangalore Evolution of spce vector structures (Hexagonal,12-sided and 18-sided) Hexagonal space vectors. 12-sided polygonal space vectors. 2-level 3-level 5-level 6

7. DESE, Indian Institute of Science Bangalore Evolution of space vector structures (Hexagonal,12-sided and 18-sided) Hexagonal space vectors. 12-sided polygonal space vectors. 3-level 5-level 2-level 7

8. DESE, Indian Institute of Science Bangalore Evolution of space vector structures (Hexagonal,12-sided and 18-sided) Hexagonal space vectors. 12-sided polygonal space vectors. 18-sided polygonal space vectors. 2-level 3-level 5-level 8

9. DESE, Indian Institute of Science Bangalore Evolution of space vector structures (Hexagonal,12-sided and 18-sided) Hexagonal space vectors. 12-sided polygonal space vectors. 18-sided polygonal space vectors. 2-level 3-level 5-level 9

10. Advantages of multilevel inverter Output wave shape is more closer to sine wave in the entire modulation range Size of the filters are reduced Low voltage ratings are sufficient for the switching devices Low electromagnetic interference due to lower dv/dt in the output waveform It is possible to eliminate common mode voltage DESE, Indian Institute of Science Bangalore10

11. DESE, Indian Institute of Science Bangalore11 Harmonics for hexagonal switching Harmonic order harmonic amplitude Normalized harmonic spectrum of phase voltage Harmonics present present for hexagonal switching are 5,7,11,13,17,19,... Hexagonal switching points Phase voltage waveform

12. DESE, Indian Institute of Science Bangalore12 Harmonics for dodecagonal switching harmonics are completely absent Harmonics present present for dodecagonal switching are 11,13,23,25,... Waveform has less dv/dt and less Harmonic distortion compared to hexagonal switching Harmonic order Normalized harmonic spectrum of phase voltage Dodecagonal switching points Phase voltage waveform harmonic amplitude

13. Determination of pole voltages for dodecagonal switching DESE, Indian Institute of Science Bangalore13

14. DESE, Indian Institute of Science Bangalore14 Harmonics for Octadecagonal switching Harmonic order Dodecagonal switching points Phase voltage waveform 5th, 7th, 11th, 13th harmonics are completely absent Harmonics present present for dodecagonal switching are 17,19,35,37... Waveform has less dv/dt and less Harmonic distortion compared with dodecagonal switching Normalized harmonic spectrum of phase voltage harmonic amplitude

15. DESE, Indian Institute of Science Bangalore Determination of pole voltages for Octadecagonal switching 15

16. Multilevel Dodecagonal Voltage Space-vector Generation Using Cascaded H-bridges DESE, Indian Institute of Science Bangalore16

17. Schematic DESE, Indian Institute of Science Bangalore17 Each phase voltage is the sum of the output voltages of two H bridges Six isolated sources are required to power the H-bridges The output of CELL-1 can be +kVdc, 0, -kVdc The output of CELL-2 can be +0.366kVdc, 0, -0.366kVdc 24 IGBTs are required for the construction The series connection of H bridges results in a 9-level inverter

18. Switching states and Pole voltage levels DESE, Indian Institute of Science Bangalore Nine pole voltage levels are possible at the output The levels are numbered from 4 to -4 18

19. Space vector diagram DESE, Indian Institute of Science Bangalore Point Va Vb Vc 61 1.366 -0.634 -1.366 62 1.366 0.634 -1.366 63 0.634 1.366 -1.366 The total number of combinations for a 3- phase, 9-level inverter is 9 x 9 x 9 = 729 Some switching points are on the vertices of 12-sided polygons Out of the 7 available 12 sided polygons, 6 are used for switching Three polygons have vertex on the ABC-axis Other three polygons are rotated by 15 degrees Other than zero vector, there are 72 switching points 19

20. Space-vector locations and switching states DESE, Indian Institute of Science Bangalore20

21. Triangular regions in the space-vector diagram DESE, Indian Institute of Science Bangalore21 Vertices of adjacent 12 sided polygons can be joined to form triangles There are 120 isosceles triangular regions in the vector diagram The legs of all the triangles are same but there are 6 different base lengths There are two types of triangles: Type 1 triangles are within angles n*30 to (n+1)*30 degrees, Type 2 triangles are within angles (n+0.5)*30 to (n+1.5)*30 degrees Where n = 0,1,2,3,... If the tip of a reference vector is inside a triangle, the reference vector can be realized by switching between the vertices of the triangle keeping volt- second balancing

22. Calculation of switching times DESE, Indian Institute of Science Bangalore Tip of reference vector is inside the triangle region formed by P1, P2, P3 Volt-second balancing is done to realize the reference vector Switching triangle should be identified Timings T1,T2,T3 should be calculated Proper devices should be activated to generate the vectors P1, P2, P3 for the calculated time 22

23. Timing calculation procedure DESE, Indian Institute of Science Bangalore Find timings for the outermost hexagon from the sampled references of Va,Vb,Vc Convert these timings to outermost dodecagon Again convert these timings to outermost dodecagon, which is rotated by 15 degrees Identify the sector (1 to 24) in which the reference vector lies Calculate the timings of the switching triangle from the dodecagon timings 23

24. Switching times for the hexagon DESE, Indian Institute of Science Bangalore For odd numbered sectors For even numbered sectors Sector identification logic 24

25. Switching times for dodecagon - case 1 DESE, Indian Institute of Science Bangalore25 The basis vectors for hexagonal switching are V1,V2 The new basis vectors are V1' & V2' Need to find the matrix for the change of basis The standard basis in two dimension The basis for the hexagonal vectors V1,V2 The basis for the dodecagonal vectors V1',V2' The new timings are

26. Switching times for dodecagon - case 2 DESE, Indian Institute of Science Bangalore The basis for the hexagonal vectors V1,V2 The basis for the dodecagonal vectors V1',V2‘ The new timings are 26

27. Switching times for the triangular region DESE, Indian Institute of Science Bangalore The previous timing calculations are for the outermost dodecagons with zero pivot vector The system requires nonzero pivot vectors and smaller active vectors Switching times of the internal triangular region can be found by volt second balancing The calculated timings for the inner triangle are 27

28. Finding the exact triangular region DESE, Indian Institute of Science Bangalore To find the exact triangle of operation a searching algorithm may be used There are 10 triangles in which searching should be performed The searching can be stopped when the calculated values of timings are all positive If Ts/2 >T0, the given order of searching will be efficient For larger values of T0, reverse order may be used 28

29. DESE, Indian Institute of Science Bangalore Finding the exact triangular region 29

30. DESE, Indian Institute of Science Bangalore Finding the exact triangular region 30

31. DESE, Indian Institute of Science Bangalore Finding the exact triangular region 31

32. DESE, Indian Institute of Science Bangalore Finding the exact triangular region 32

33. DESE, Indian Institute of Science Bangalore Finding the exact triangular region 33

34. DESE, Indian Institute of Science Bangalore Finding the exact triangular region 34

35. DESE, Indian Institute of Science Bangalore Finding the exact triangular region 35

36. DESE, Indian Institute of Science Bangalore Finding the exact triangular region 36

37. DESE, Indian Institute of Science Bangalore Finding the exact triangular region 37

38. DESE, Indian Institute of Science Bangalore Alternate timing computation method Each hexagonal sector is divided into 4 sub-sectors Each sub-sector spans 15 degrees The reference vector can be brought to sub-sector 1 of sector 1, using linear transformation 38

39. Sub-sector identification DESE, Indian Institute of Science Bangalore The ratio between the active vectors can be used to identify the sub-sector location At sub-sector 1, sub-sector 2 boundary, At sub-sector 2, sub-sector 3 boundary, At sub-sector 3, sub-sector 4 boundary, 39

40. Ten possible locations of the reference vector in sub-sub sector 1 DESE, Indian Institute of Science Bangalore40

41. Calculation of timings for the inner sub- sector 5 DESE, Indian Institute of Science Bangalore For the outer hexagonal vectors For inner sub-sector 5 Equating 41

42. DESE, Indian Institute of Science Bangalore Calculation of timings for the inner sub- sector 5 Resolving along alpha and beta axis The timings for inner subsector 5 is The general equation for the timings 42

43. Block diagram of the experimental setup DESE, Indian Institute of Science Bangalore43 Waveforms are taken for the motor under steady state operation and during acceleration The waveforms taken are 1. Pole voltages of individual H bridges 2. Phase voltage 3. Phase current Rated power: 3.7kW Rated line-to-line voltage: 400V AC Rated frequency: 50Hz Number of poles: 4 stator resistance Rs : 2.08Ω Rotor resistance Rr : 4.19Ω Stator self inductance Ls : 0.28H Rotor self inductance Lr : 0.28H Magnetizing inductance M : 0.272H Moment of inertia J :0.1kg.m2 Motor specifications

44. Experimental results at 10 Hz operation DESE, Indian Institute of Science Bangalore44 Harmonic order harmonic amplitude Normalized harmonic spectrum of voltage Normalized harmonic spectrum of current Time (20 ms/div) Phase voltage (100 V/div) CELL-1 voltage (100 V/div) CELL-2 voltage (100 V/div) Phase current (2 A/div)

45. DESE, Indian Institute of Science Bangalore Experimental results at 24.5 Hz operation 45 Harmonic order harmonic amplitude Normalized harmonic spectrum of voltage Normalized harmonic spectrum of current Time (10 ms/div) Phase voltage (200 V/div) CELL-1 voltage (100 V/div) CELL-2 voltage (100 V/div) Phase current (2 A/div)

46. DESE, Indian Institute of Science Bangalore Experimental results at 40 Hz operation 46 Harmonic order harmonic amplitude Normalized harmonic spectrum of voltage Normalized harmonic spectrum of current Time (5 ms/div) Phase voltage (200 V/div) CELL-1 voltage (100 V/div) CELL-2 voltage (100 V/div) Phase current (2 A/div)

47. DESE, Indian Institute of Science Bangalore Experimental results at 49.9 Hz operation 47 Harmonic order harmonic amplitude Normalized harmonic spectrum of voltage Normalized harmonic spectrum of current Time (5 ms/div) Phase voltage (200 V/div) CELL-1 voltage (100 V/div) CELL-2 voltage (100 V/div) Phase current (2 A/div)

48. DESE, Indian Institute of Science Bangalore Experimental results at 50 Hz operation 48 Harmonic order harmonic amplitude Normalized harmonic spectrum of voltage Normalized harmonic spectrum of current Time (5 ms/div) Phase voltage (200 V/div) CELL-1 voltage (100 V/div) CELL-2 voltage (100 V/div) Phase current (2 A/div)

49. DESE, Indian Institute of Science Bangalore49 Time (1 s/div) Phase voltage (200 V/div) Phase current (2 A/div) Transient performance (10 Hz to 30 Hz)

50. Summary of the work DESE, Indian Institute of Science Bangalore A new inverter power circuit has been proposed that consists of cascaded connection of two H-bridge cells. The circuit is capable of generating six concentric dodecagonal voltage space-vectors and there are 120 triangular regions. Under all operating conditions, switches of the high and low voltage cells have a maximum switching frequency of 500 Hz and 1.5 kHz respectively. Total elimination of harmonics from the phase voltage is possible with increased linear modulation range. Fourier analysis of the phase voltage and phase current shows very low magnitudes for the harmonics. 50

51. Multilevel Dodecagonal Voltage Space- Vector Generation using 2-level and 3-level Inverters DESE, Indian Institute of Science Bangalore51

52. Schematic of the proposed inverter DESE, Indian Institute of Science Bangalore52 Inverter 1 is a three level inverter and Inverter 2 is a two level inverter The output from the three level inverter is +0.5Vdc, 0, -0.5Vdc The output from the two level inverter is 0, 0.366Vdc This topology requires an open end winding induction motor There are three power sources for the operation

53. Front-end rectifier DESE, Indian Institute of Science Bangalore53 The advantage of front-end power supply using the star-delta transformers is that it takes nearly sinusoidal currents from the grid. The DC output voltage from the delta winding is 0.366Vdc, Output from the star connected winding is 0.634Vdc. A series connection of the outputs from a delta winding and a star winding gives 1Vdc. A series connection of the outputs from two delta windings gives 0.732Vdc.

54. Space vector diagram consisting of three dodecagons DESE, Indian Institute of Science Bangalore54 The total number of switching combinations for the inverter is 216 Some switching points are on the vertices of 12-sided polygons There are three polygons, one polygon has its vertex on the a,b,c phase axis, other two polygons are rotated by 15 degrees Other than zero vector, there are 36 switching points

55. Triangular regions created by adjacent space vectors DESE, Indian Institute of Science Bangalore55 Vertices of adjacent 12 sided polygons can be joined to form triangles and there are 60 isosceles triangular regions in the vector diagram The legs of all the triangles are same but there are 3 different base lengths There are two types of triangles: Type 1 triangles are within angles n*30 to (n+1)*30 degrees Type 2 triangles are within angles (n+0.5)*30 to (n+1.5)*30 degrees. Where n = 0,1,2,3,... If the tip of a reference vector is inside a triangle, the reference vector can be realized by switching between the vertices of the triangle keeping volt - second balancing

56. Space-vector locations and switching states DESE, Indian Institute of Science Bangalore56

57. Synchronous PWM DESE, Indian Institute of Science Bangalore57 A constant sampling frequency of 1 KHz was used for frequencies less than 8.5 Hz. For fundamental frequencies greater than 8.5 Hz, synchronous PWM was used. To achieve this, sampling frequency was made an integral multiple of the fundamental frequency.

58. Comparison of multilevel inverter topologies DESE, Indian Institute of Science Bangalore58

59. DESE, Indian Institute of Science Bangalore Experimental results at 15 Hz operation 59 Harmonic order harmonic amplitude Normalized harmonic spectrum of voltage Time (10 ms/div) Phase voltage (50 V/div) Inverter-1 pole voltage (100 V/div) Inverter-2 pole voltage (100 V/div) Phase current (2 A/div)

60. DESE, Indian Institute of Science Bangalore Experimental results at 30 Hz operation 60 Harmonic order harmonic amplitude Normalized harmonic spectrum of voltage Time (10 ms/div) Phase voltage (100 V/div) Inverter-1 pole voltage (100 V/div) Inverter-2 pole voltage (100 V/div) Phase current (2 A/div)

61. DESE, Indian Institute of Science Bangalore Experimental results at 40 Hz operation 61 Harmonic order harmonic amplitude Time (5 ms/div) Phase voltage (100 V/div) Inverter-1 pole voltage (100 V/div) Inverter-2 pole voltage (100 V/div) Phase current (2 A/div)

62. DESE, Indian Institute of Science Bangalore Experimental results at 48 Hz operation 62 Harmonic order harmonic amplitude Normalized harmonic spectrum of voltage Time (5 ms/div) Phase voltage (100 V/div) Inverter-1 pole voltage (100 V/div) Inverter-2 pole voltage (100 V/div) Phase current (2 A/div)

63. DESE, Indian Institute of Science Bangalore Experimental results at 50 Hz operation 63 Harmonic order harmonic amplitude Normalized harmonic spectrum of voltage Time (5 ms/div) Phase voltage (100 V/div) Inverter-1 pole voltage (100 V/div) Inverter-2 pole voltage (100 V/div) Phase current (2 A/div)

64. DESE, Indian Institute of Science Bangalore64 Time (1 s/div) Phase voltage (75 V/div) Phase current (2 A/div) Transient performance (10 Hz to 50 Hz)

65. DESE, Indian Institute of Science Bangalore Simulation results at 45 Hz operation 65 Harmonic order harmonic amplitude Time (10 ms/div) Mains voltage (200 V/div) Phase current (1 A/div) Mains current (0.1 A/div)

66. Summary of the work DESE, Indian Institute of Science Bangalore A new multilevel inverter topology that produces three dodecagonal voltage space-vectors has been proposed. The proposed topology utilizes less number of switches and power sources compared to other multilevel dodecagonal strategies. A front-end rectifier circuit using the standard star-delta transformer connection was also suggested for the inverter, resulting in nearly sinusoidal currents form the grid for the full modulation range. Experimental results show complete suppression of the 5 th and 7 th harmonics for the entire modulation range and an improved THD. For the entire modulation range, the dominant harmonics in the phase currents were the 11 th and 13 th. 66

67. Multilevel Octadecagonal Voltage Space-vector Generation for Induction Motor Drives DESE, Indian Institute of Science Bangalore67

68. DESE, Indian Institute of Science Bangalore68 Power circuit of the proposed inverter Inverter 1 and Inverter 2 are three level inverters This topology requires an open end winding induction motor There are four power sources for the operation 12 IGBT Half Bridge modules are required for the construction

69. DESE, Indian Institute of Science Bangalore69 Space vector diagram The total number of combinations of voltage space vectors is Some switching points are on the vertices of 18 sided polygons Three 18 sided polygons are obtained with radii Other than zero vector, there are 54 switching points

70. DESE, Indian Institute of Science Bangalore70 Triangular regions created by adjacent space vectors Adjacent 18 sided polygons can be joined to form triangles There are 90 isosceles triangular regions in the vector diagram The legs of all the triangles are same but there are 3 different base lengths If the tip of a reference vector is inside a triangle, the reference vector can be realized by switching between the vertices of the triangle keeping volt - second balancing

71. DESE, Indian Institute of Science Bangalore71 Space vector locations and the selected switching states For these space vectors, there is no is no redundant switching states

72. DESE, Indian Institute of Science Bangalore72 Timing computation for switching triangles S1 S2 S3 S4 S5 S6 Vs If The reference vector Vs is as shown in Fig, the vertices of triangle 74 should be switched to realize the vector To find the timings for the inner triangle, initially the timings for the outermost hexagon is found out and these timings are mapped to the inner triangles

73. DESE, Indian Institute of Science Bangalore73 Switching times for the hexagon from sampled values of references For odd numbered sectors For even numbered sectors

74. DESE, Indian Institute of Science Bangalore74 Conversion from hexagonal to octadecagonal vectors using change of basis transformation Basis for hexagonal vectors Basis for octadecagonal vectors Octadecagonal switching times

75. DESE, Indian Institute of Science Bangalore75 Mapping of switching times to the triangular region The previous timing calculations is based on octadecagons with 1Vdc as magnitude and zero pivot vector Multilevel operation requires nonzero pivot vectors and smaller active vectors The timings for the inner triangle can be calculated as Magnitude = 1Vdc

76. DESE, Indian Institute of Science Bangalore76 Searching for the exact triangular region There are three different types of triangular regions to which the timings can be mapped The correct triangle can be identified by Selecting the triangle with positive values of the there timings The above equation will be satisfied only for the correct triangle with positive values for the timing

77. DESE, Indian Institute of Science Bangalore77 Conversion from hexagonal to 10 degree rotated octadecagonal vectors Basis for hexagonal vectors Basis for octadecagonal vectors Octadecagonal switching times Magnitude = 1Vdc There are two different types of triangular regions to which the timings can be mapped

78. DESE, Indian Institute of Science Bangalore78 Mapping of switching times to the triangular region The timings for the inner triangle can be calculated as Magnitude = 1Vdc The above equation will be satisfied only for the correct triangle with positive values for the timing

79. DESE, Indian Institute of Science Bangalore79 Algorithm 1) Sample Vα and Vβ and convert to Va, Vb and Vc. 2) Calculate hexagonal switching times from Va, Vb and Vc. 3) Convert the hexagonal switching times to octadecagonal switching times by a change of basis transformation. 4) Map the timings to five different triangles. 5) Find the exact triangle in which the reference vector lies. 6) Find the three space vectors corresponding to the switching triangle. 7) Apply the space vectors for T0, T1 and T2 duration sequentially.

80. DESE, Indian Institute of Science Bangalore80 V/f control - Block diagram Motor specifications: Rated power: 3.7kW Rated line-to-line voltage: 400V AC Rated frequency: 50Hz Number of poles: 4 Stator resistance Rs : 2.08Ω Rotor resistance Rr : 4.19Ω Stator self inductance Ls : 0.28H Rotor self inductance Lr : 0.28H Magnetizing inductance M : 0.272H Moment of inertia J :0.1kg.m2

81. DESE, Indian Institute of Science Bangalore Experimental results at 15 Hz operation 81 Harmonic order harmonic amplitude Normalized harmonic spectrum of voltage Normalized harmonic spectrum of current Time (10 ms/div) Inverter-1 Pole voltage (100 V/div) Inverter-2 Pole voltage (250 V/div) Phase voltage (100 V/div) Phase current (2 A/div)

82. DESE, Indian Institute of Science Bangalore Experimental results at 30 Hz operation 82 Harmonic order harmonic amplitude harmonic amplitude0 Normalized harmonic spectrum of voltage Normalized harmonic spectrum of current Time (5 ms/div) Inverter-11 Pole voltage (100 V/div) Inverter-2 Pole voltage (250 V/div) Phase voltage (200 V/div) Phase current (2 A/div)

83. DESE, Indian Institute of Science Bangalore Experimental results at 40 Hz operation 83 Harmonic order harmonic amplitude Normalized harmonic spectrum of voltage Normalized harmonic spectrum of current Time (5 ms/div) Inverter-1 Pole voltage (100 V/div) Inverter-2 Pole voltage (250 V/div) Phase voltage (200 V/div) Phase current (2 A/div)

84. DESE, Indian Institute of Science Bangalore Experimental results at 50 Hz operation 84 Harmonic order harmonic amplitude Normalized harmonic spectrum of voltage Normalized harmonic spectrum of current Time (5 ms/div) Inverter-1 Pole voltage (100 V/div) Inverter-2 Pole voltage (250 V/div) Phase voltage (200 V/div) Phase current (2 A/div)

85. Vector control – Block diagram DESE, Indian Institute of Science Bangalore85

86. Transient performance (0 Hz to 30Hz) DESE, Indian Institute of Science Bangalore86 Time (0.5 s/div) Rotor magnetizing Current (1 A/div) Phase voltage (200 V/div) Mechanical Speed (35 rad/s/div) Phase current (2 A/div)

87. DESE, Indian Institute of Science Bangalore87 Time (0.5 s/div) Transient performance (-30 Hz to 30Hz) Rotor magnetizing Current (0.5 A/div) Phase voltage (200 V/div) Mechanical Speed (70 rad/s/div) Phase current (2 A/div)

88. Mains voltage and current waves at 45 Hz operation DESE, Indian Institute of Science Bangalore88 Time (0.5 s/div) Rectifier Input voltage (200 V/div) Rectifier Input current (2 A/div) Motor current (2 A/div)

89. Summary of the work DESE, Indian Institute of Science Bangalore89 A new circuit topology has been proposed which can produce three octadecagonal voltage space-vectors. The proposed timing calculation method uses only sampled values of phase voltages references. The calculation method can be easily extended to any multilevel octadecagonal voltage space-vector diagram and be easily implemented using micro controller or DSP. Due to the octadecagonal voltage space-vector based switching pattern, the 5 th, 7 th, 11 th and 13 th harmonics are completely absent in the phase voltages and the linear modulation range is improved.

90. Conclusion DESE, Indian Institute of Science Bangalore Inverter topologies which can generate multilevel dodecagonal and octadecagonal polygonal voltage space-vectors are proposed. The 5 th and 7 th harmonics are dominant for hexagonal voltage space-vector based low frequency switching and it is possible to completely eliminate these harmonics by dodecagonal switching. With octadecagonal switching, the 11 th and 13 th harmonics are also completely suppressed. One sample per sector can also guarantee the mentioned harmonic performance and it is possible to reduce the number of switching of the power devices. These topologies can be used for medium and high-power induction motor drives and the concepts presented are also applicable for synchronous motor drives, grid connected inverters etc.

91. DESE, Indian Institute of Science Bangalore91 Thank you