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Combined voltage space vector locations of a dual five-level inverter fed open-end winding IM drive (a nine-level inverter). 217 Combined Voltage Vectors Triangular Sectors 15,625 Switching State Combinations. Shaded voltage vectors generate zero common-mode

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217 combined voltage vectors triangular sectors 15 625 switching state

Combined voltage space vector locations of a dual five-level inverter fed open-end winding IM drive (a nine-level inverter)

  • 217 Combined Voltage

  • Vectors

  • Triangular Sectors

  • 15,625 Switching State

  • Combinations

  • Shaded voltage

  • vectors generate

  • zero common-mode

  • voltage

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Common-mode voltage of the dual five-level inverter fed open-end winding IM drive

  • Common-mode voltage generated by individual five-level inverters

  • (Inverter-A or Inverter-A’)

Inverter-A

Inverter-A’

  • Common-mode voltage in the phase voltage of induction motor with

  • the proposed dual five-level inverter fed drive

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Groups of common-mode voltage generated by individual five-level inverter

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Voltage vectors and corresponding switching states resulting into zero common-mode voltage in individual five-level inverter (Inv.-A or Inv.-A’)

19 Voltage Vectors

24 Triangular Sectors

19 Switching States

  • All the shaded switching

  • states belong to the

  • Group-7,which generate

  • zero common-mode

  • voltage at the inverter

  • poles


217 combined voltage vectors triangular sectors 15 625 switching state

Combined voltage space phasor locations resulting into zero common-mode voltage (a five-level inverter voltage space phasor structure)

61 Combined Voltage

Vectors

96 Triangular Sectors

361 Switching State

Combinations

  • Achieved when individual

  • five-level inverters (Inv.-A

  • and Inv.-A’) are switched

  • using the switching states

  • belonging to the Group-7

  • only.


217 combined voltage vectors triangular sectors 15 625 switching state

Number of redundant switching states available for each voltage vectors of the five-level inverter with zero common-mode voltage

61 Combined Voltage

Vectors

96 Triangular Sectors

361 Switching Stats

Combinations

  • Achieved when individual

  • five-level inverters (Inv.-A

  • and Inv.-A’) are switched

  • using the switching states

  • belonging to the Group-7

  • only.


217 combined voltage vectors triangular sectors 15 625 switching state

Some of the voltage vectors and their redundant switching states for five-level inverter with zero common-mode voltage

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Amplitude of maximum reference space vector possible in linear range of modulation without boost in the DC-link of the proposed inverter

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Generation of same maximum peak fundamental amplitude of the phase voltage equivalent to that of a conventional SVPWM

based five-level inverter

  • A boost of 15% in the dc-link of the proposed drive is

  • required to generate the maximum peak fundamental

  • amplitude of the phase voltage equivalent to that of a

  • conventional SVPWM based five-level inverter.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Voltage space vector locations for proposed five-level inverter with common-mode voltage elimination (with dc-link boost)

61 Combined Voltage

Vectors

96 Triangular Sectors

361 Switching Stats

Combinations

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Switching state combination selected to generate the voltage space phasors of five-level inverter with zero CMV

61 Combined Voltage

Vectors

96 Triangular Sectors

61 Switching Stats

Combinations

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Power scheme of the proposed five-level inverter with CME space phasors of five-level inverter with zero CMV

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Experimental results space phasors of five-level inverter with zero CMV

Pole voltage (VAO)

Two-level operation

Y-axis: 1 div. = 50 V

X-axis: 1 div. = 10 ms

Phase voltage (VA’A)

Pole voltage (VA’O)

Phase voltage FFT

(two-level operation)

Y-axis: Normalized amplitude

X-axis: Order of harmonic

Pole voltage FFT

(two-level operation)

Y-axis: Normalized amplitude

X-axis: Order of harmonic

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Experimental results (contd…) space phasors of five-level inverter with zero CMV

Pole voltage (VAO)

Three-level operation

Y-axis: 1 div. = 40 V

X-axis: 1 div. = 10 ms

Phase voltage (VA’A)

Pole voltage (VA’O)

Phase voltage FFT

(three-level operation)

Y-axis: Normalized amplitude

X-axis: Order of harmonic

Pole voltage FFT

(three-level operation)

Y-axis: Normalized amplitude

X-axis: Order of harmonic

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Experimental results (contd…) space phasors of five-level inverter with zero CMV

Pole voltage (VAO)

Four-level operation

Y-axis: 1 div. = 70 V

X-axis: 1 div. = 5 ms

Phase voltage (VA’A)

Pole voltage (VA’O)

Phase voltage FFT

(four-level operation)

Y-axis: Normalized amplitude

X-axis: Order of harmonic

Pole voltage FFT

(four-level operation)

Y-axis: Normalized amplitude

X-axis: Order of harmonic

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Experimental results (contd…) space phasors of five-level inverter with zero CMV

Pole voltage (VAO)

Five-level operation

Y-axis: 1 div. = 75 V

X-axis: 1 div. = 5 ms

Phase voltage (VA’A)

Pole voltage (VA’O)

Phase voltage FFT

(five-level operation)

Y-axis: Normalized amplitude

X-axis: Order of harmonic

Pole voltage FFT

(five-level operation)

Y-axis: Normalized amplitude

X-axis: Order of harmonic

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Experimental results (contd…) space phasors of five-level inverter with zero CMV

Pole voltage (VAO)

Over-modulation operation

Y-axis: 1 div. = 80 V

X-axis: 1 div. = 5 ms

Phase voltage (VA’A)

Pole voltage (VA’O)

Phase voltage FFT

(over-modulation operation)

Y-axis: Normalized amplitude

X-axis: Order of harmonic

Pole voltage FFT

(over-modulation operation)

Y-axis: Normalized amplitude

X-axis: Order of harmonic

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Experimental results (contd…) space phasors of five-level inverter with zero CMV

Phase voltage (VA’A)

Y-axis: 1 div. = 50 V

Four-level operation

X-axis: 1 div. = 5 ms

Phase current

Y-axis: 1 div. = 1 A

Phase voltage (VA’A)

Y-axis: 1 div. = 50 V

Five-level operation

X-axis: 1 div. = 5 ms

Phase current

Y-axis: 1 div. = 1 A

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Salient features of the proposed common-mode elimination scheme for multilevel inverter fed drive

  • A dual five-level inverter fed open-end winding induction motor

  • drive with elimination of common-mode voltage in the entire

  • operating range.

  • Each five-level inverter of the proposed drive is formed by

  • cascading two conventional two-level inverters and a conventional

  • three-level NPC inverter. Hence, the proposed drive offers simple

  • power-bus structure compared to the five-level NPC inverter fed

  • drive.

  • There is no alternating common-mode voltage in the inverter

  • poles as well as at the phase windings of the induction machine.

CEDT, Indian Institute of Science CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Salient features of proposed common-mode elimination scheme for multilevel inverter fed drive (contd…)

  • A common DC-link is used at both the ends of the open-end

  • winding induction machine, for both the five-level inverters.

  • The DC-link voltage requirement of proposed open-end winding

  • IM drive is nearly half as compared to that of a single five-level

  • inverter fed conventional IM drive.

  • Hence, the voltage stress on the devices is reduced and devices

  • with lower voltage blocking capability can be used, which makes

  • the proposed drive scheme suitable for high power applications.

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


Conclusion

In the implemented scheme, the rotor flux position is estimated from the motor phase current ripples

During the low speed region of operation, the current ripple during the zero vector periods are used for rotor flux position estimation

During the high speed region of operation, the current ripple during the active vector periods are used for rotor flux position estimation

The scheme is implemented for a three phase motor, but the scheme can be extended to any multi phase motor and also with open-end winding structure

CONCLUSION

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Linearization of the Multi-level SVPWM in Over-modulation Region

By

R. S. Kanchan, P. N. Tekwani, and K. Gopakumar

Centre for Electronic Design and Technology,

Indian Institute of Science

Bangalore, INDIA

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

v Region

v

v

AN

BN

CN

0.5

Reference signals

Vt

and carrier

V

/2

dc

-0.5

a0

V

-V

/2

dc

V

/2

dc

b0

V

-V

/2

dc

V

/2

dc

c0

2 π

3 π/2

(wt)

π/2

π

V

-V

/2

dc

Linearization of the Multi-level SVPWM in the Over-Modulation Region

Conventional two-level Sine-Triangle PWM

The fundamental component in the output PWM waveform is equal to

k = (peak amplitude of the sinusoidal reference) / (height of the triangular carrier signal)

  • Three sinusoidal (1200 phase shifted) reference signals are compared with triangular carrier

  • The PWM signals are generated for three phases

  • The pole voltage is clamped to +ve DC link bus if Vref >Vt else to –ve DC link bus

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

V Region

V

V

CN

AN

BN

V

/2

dc

-V

/2

dc

V

/2

dc

a0

V

-V

/2

dc

V

/2

dc

b0

V

-V

/2

dc

V

/2

dc

c0

V

-V

/2

dc

(wt)

3 π/2

π

2 π

π/2

Linearization of the Multi-level SVPWM in the Over-Modulation Region

Conventional Sine-Triangle PWM: Over-Modulation Range

  • When ref signal is greater than carrier, the pole voltages are clamped to the DC link bus voltage

  • The fundamental component in output PWM waveform is not given by

  • But there is reduction in the fundamental component in the output voltage

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

0.5 Region

0

π/2

π

00

wt

Linearization of the Multi-level SVPWM in the Over-Modulation Region

Conventional Sine-Triangle PWM: Over-Modulation Range

  • Reduction in the output fundamental is proportional to the shaded area

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

0.637 Region

0.50

Non-linear characteristic

k

Linear range

Over-modulation

0.7854

MI

Linearization of the Multi-level SVPWM in the Over-Modulation Region

Conventional Sine-Triangle PWM

  • The voltage transfer characteristics i.e the ratio between the output fundamental and the reference signal amplitude is non-linear in the over-modulation region

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

v* RegionBN

v*CN

v*AN

0.5

and carrier

Reference signals

-0.5

200

400

600

800

1000

1200

1400

1600

1800

V

/2

dc

a0

V

-V

/2

dc

200

400

600

800

1000

1200

1400

1600

1800

V

/2

dc

b0

V

-V

/2

dc

200

400

600

800

1000

1200

1400

1600

1800

V

/2

1

dc

c0

V

-V

/2

dc

2 π

3 π/2

π/2

π

(wt)

Linearization of the Multi-level SVPWM in the Over-Modulation Region

Carrier based Space-Vector PWM (SVPWM)

  • The reference signals are added with an offset voffset1

  • The resultant PWM is a Space Vector PWM

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

0.5 Region

0

π/2

00

wt

π/6

π/3

2π/3

π

Linearization of the Multi-level SVPWM in the Over-Modulation Region

Carrier based Space-Vector PWM (SVPWM)

  • Again when ref signal is greater than carrier, the pole voltages are clamped to the DC link bus voltage

  • There is reduction in the fundamental component in the output voltage

  • Reduction in the output fundamental is proportional to the shaded area

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

0.637 Region

0.577

0.5

SPWM

SVPWM

Non-linear characteristic

Output voltage (per unit w.r.t Vdc )

0.866

Linear range

Over-modulation

0.785

MI

Linearization of the Multi-level SVPWM in the Over-Modulation Region

  • The extended linear region in SVPWM as compared to SPWM

  • The voltage transfer characteristics is again non-linear in the over-modulation region similar to SPWM

Ideal requirement for the PWM modulator : Linear voltage transfer characteristics

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


217 combined voltage vectors triangular sectors 15 625 switching state

Linearization of the Multi-level SVPWM in the Over-Modulation Region

In the Proposed Work

  • An over-modulation scheme with the linear voltage transfer characteristics for a general n-level SVPWM signal generation

  • Reference signal to the PWM modulator is pre-scaled in over-modulation region such that

    • The fundamental component of the original and the modified reference signal is same

    • The modified reference signal is always within carrier region

  • Thus voltage transfer characteristic is a linear function of the modulation index both in the linear-modulation as well as in the over-modulation region

  • The inverter leg switching times are directly obtained with a simple algorithm using only the sampled amplitudes of the reference phase voltages

  • CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    Principle of linearization: when k=0.637 i.e. six step mode

    k=0.637

    • F1, the original reference signal in six step mode ( f1 (pk)=0.637) goes above the carrier (0.5)

    • The output voltage will be less, if f1 is used for PWM generation

    • f2 is a rectangular signal such that fundamental component of f2 is equal to f1, the original reference signal in six step mode i.e. F2 (1)=0.637

    • Therefore, f2 can be used for PWM generation instead of f1

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    0.5 Over-Modulation Region

    0

    signal

    Reference

    -0.5

    1

    1

    f

    0

    -1

    1

    2

    f

    0

    -1

    0.5

    signal

    0

    modified ref.

    -0.5

    3 π/2

    2 π

    π/2

    π

    θ

    π-θ

    2π-θ

    π+θ

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    Principle of linearization: when 0.5 < k < 0.637

    • A part of original reference signal is clamped

    • The fundamental component of the modified reference signal is same as original reference signal

    • This requires that the fundamental component of rectangular pulse f2 is equal to fundamental component of part of the original reference signal f1

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    0.5 Over-Modulation Region

    0

    signal

    Reference

    -0.5

    1

    1

    f

    0

    -1

    1

    2

    f

    0

    -1

    0.5

    signal

    modified ref.

    0

    -0.5

    3 π/2

    2 π

    π/2

    π

    θ

    π-θ

    2π-θ

    π+θ

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    • Fundamental component of part of the original reference signal f1 =

    • Fundamental component of rectangular pulse f2 =

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    1 Over-Modulation Region

    0.9739

    0.9524

    0.9111

    MI

    0.8796

    0.8482

    0.8168

    0.7854

    0

    10

    20

    30

    40

    50

    60

    70

    80

    90

    q

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    • The relationship between modulation index MI and clamping angle q

    • Thus if MI is known, the clamping angle q can be determined

    • The modified reference signal is clamped for the angle q to π-θand π+θ to 2π-θ

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    0.5 Over-Modulation Region

    0

    00

    π

    π/3

    π/2

    π/6

    2π/3

    wt

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    Principle of the proposed SVPWM in the over-modulation region

    • Modified reference signal

    • Reference signal goes out of the carrier two times in the positive half cycle

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    0.5 Over-Modulation Region

    θ0

    (2π/3-θ)0

    0

    π/3

    π

    π/2

    π/6

    2π/3

    wt

    00

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    Principle of the proposed SVPWM in the over-modulation region

    • The reference signal is clamped to 0.5 twice in +ve half cycle

    • Again the fundamental component of the modified reference signal is same as original reference signal

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    Principle of the proposed SVPWM in the over-modulation

    • The fundamental component of the original reference signal f1 between q to 2π/3-θ

    0.5

    θ0

    (2π/3-θ)0

    • The fundamental component of rectangular pulse f2 between q to 2π/3-θ

    0

    0.5

    • For the fundamental component of the modified reference signal to be same as original signal,

    θ0

    (2π/3-θ)0

    0

    π/3

    π/2

    wt

    π/6

    00

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    Principle of the proposed SVPWM in the over-modulation

    • The relationship between modulation index MI and clamping angle q

    • Thus if MI is known, the clamping angle θ can be determined

    • Clamping of the modulating signal starts when

    0.5

    and clamping angle θ is equal to π/3

    • When clamping angle = π/6, k =0.60337

    • Thus the clamping scheme can be used only in the range 0.577<k <0.60337 as the clamping starts at an angle less than π/6, where modulating wave is (3/2)ksin(wt) instead of

    θ0

    This is referred as over-modulation Mode-I (0.577<k <0.60337)

    (2π/3-θ)0

    0

    π/3

    π/2

    π/6

    wt

    00

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    Principle of the proposed SVPWM in the over-modulation MODE-II

    • The reference signal is clamped to 0.5 for θ < wt < π- θ

    • Again the fundamental component of the modified reference signal is same as original reference signal (dotted line)

    • The MI range greater than 0.60337, angle θ at which clamping starts is less than π/3

    .

    0.5

    θ0

    (π-θ)0

    0

    π

    π/3

    π/2

    π/6

    2π/3

    wt

    00

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    . Over-Modulation Region

    0.5

    θ0

    (π-θ)0

    0

    wt

    π/3

    2π/3

    5π/6

    π

    π/2

    π/6

    00

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    Principle of the proposed SVPWM in the over-modulation MODE-II

    • The relationship between θ and k can be derived similarly

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    Principle of the proposed SVPWM in the over-modulation MODE-II

    Summary: The relationship between θ and k

    • Over-modulation Mode-I (0.577<k <0.60337) & clamping angle π/3<θ< π/6

    • Over-modulation Mode-II (0.60337<k <0.637) & clamping angle 0<θ< π/3

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Mode-II Over-Modulation Region

    Mode-I

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    The relationship between θ and k (MI)for SPWM and SVPWM

    • Steps

    • Read Modulation Index MI

    • Determine clamping angle θ

    • Clamp the reference signal to 0.5 appropriately

    • The implementation needs instantaneous angle information

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    Modified reference voltages and triangular carriers for a five-level SVPWM scheme

    • n-level SPWM scheme uses n-1 level shifted carrier waves

    • Sinusoidal reference signals are added with offset which centers them within carrier region

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    Determination of the Ta_cross , Tb_cross and Tc_cross during switching interval TS (When reference voltages are spanning the inner carrier region, MI < 0.433)

    Ta_cross , Tb_cross and Tc_cross : the time duration from the start of switching interval when the reference phase - A, B and C cross the carrier

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    Determination of the Ta_cross , Tb_cross and Tc_cross during switching interval TS (When reference voltages are spanning the inner carrier region, MI < 0.433)

    Carrier- C1

    Carrier- C2

    Carrier- C2

    T*as , T*bs and T*cs : Time equivalents of the modified reference signal amplitudes

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    Determination of the Ta_cross , Tb_cross and Tc_cross during switching interval TS (When reference voltages are spanning the entire carrier region, 0.433<MI < 0.866)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    SUMMARY: Ta_cross , Tb_cross and Tc_cross for various carrier regions to bring the reference within a carrier region

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    3600

    00

    900

    1800

    2700

    wt

    Determination of the Ta_cross:

    Represent the carriers and ref. signals in terms of time equivalents using relationship

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    3600

    00

    900

    1800

    2700

    wt

    Determination of the Ta_cross:

    Shift the ref. signal into one carrier region (first +ve carrier) by adding proper offset

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    3600

    00

    900

    1800

    2700

    wt

    Determination of the Ta_cross

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    3600

    00

    900

    1800

    2700

    wt

    Determination of the Ta_cross

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    00

    900

    1800

    00

    900

    1800

    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


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    Algorithm for inverter leg switching time calculation: Tfirst_cross , Tsecond_cross and Tthird_cross : the time duration from the start of switching interval when the reference phases cross the carrier for first, second and third time respectively.

    , x= a, b, c

    Inverter leg switching times

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    Tgfirst_cross , Tgsecond_cross and Tgthird_cross : the inverter leg switching time for the reference phases which cross the carrier for first, second and third time respectively.

    The traces of Tgfirst_cross , Tgsecond_cross and Tgthird_cross showing centered time duration for middle vectors

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

    Schematic representation of the Multi-level SVPWM

    Inverter

    Gating Signals

    PWM

    Compa-

    rators

    Gating

    Signals

    Tgx

    Ta_cross,

    Tb_cross

    Tc_cross

    VAN

    Time

    Equivalents

    Txs

    +

    VBN

    +

    VCN

    Toffset1

    Toffset2

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Implementation of the Multi-level SVPWM with Linear Transfer Characteristics in Over-Modulation

    In overmodulation, clamps the reference signals appropriately

    MI

    Vs

    Inverter

    Gating Signals

    PWM

    Compa-

    rators

    Gating

    Signals

    Tgx

    Ta_cross,

    Tb_cross

    Tc_cross

    Pre-

    scaler

    VAN

    +

    Time

    Equivalents

    Txs

    VBN

    Toffset2

    +

    VCN

    Toffset1

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    0.5 Characteristics in Over-Modulation

    0.5

    A

    A

    SVPWM MODE-II, (θ< π/6)

    SVPWM MODE-I, (θ> π/6)

    0

    0

    π

    00

    π/2

    π

    π/2

    wt

    wt

    00

    Implementation of the Multi-level SVPWM with Linear Transfer Characteristics in Over-Modulation

    • Pre-scaler:

    • Read Modulation Index MI

    • Determine clamping angle θand then Clamping level ‘A’

    • Clamp the reference signal if it is greater than ‘A’

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    0.5 Characteristics in Over-Modulation

    60

    50

    0.4

    40

    0.3

    A

    Clamping level 'A'

    q

    30

    0.2

    θ

    20

    0.1

    10

    0

    0

    0.9

    0.92

    0.94

    0.96

    0.98

    1

    Modulation Index 'MI'

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    • The clamping angle information is converted into a level signal ‘A’

    • Prescaler: A simple look-up table of MI vs A

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    MI Characteristics in Over-Modulation

    Vs

    PWM

    Compa-

    rators

    Gating

    Signals

    Tgx

    Ta_cross,

    Tb_cross

    Tc_cross

    Pre-

    scaler

    VAN

    Time

    Equivalents

    Txs

    +

    VBN

    Toffset2

    +

    VCN

    Toffset1

    Simulation Results: Linear-Modulation Region

    • No clamping of Tas in linear range of modulation

    • Pre-scaler is inactive in linear modulation range

    (wt)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    (wt) Characteristics in Over-Modulation

    Simulation Results: Over-Modulation Region (MI: 0.92)

    • Clamping of Tas in over-modulation (Mode-I)

    • Pre-scaler is active in over-modulation range

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    (wt) Characteristics in Over-Modulation

    Simulation Results: Over-Modulation Region (MI: 0.94)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    (wt) Characteristics in Over-Modulation

    Simulation Results: Over-Modulation Region (MI: 0.95)

    • Clamping of Tas in over-modulation (Mode-II)

    • Pre-scaler is active in over-modulation range

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    (wt) Characteristics in Over-Modulation

    Simulation Results: Over-Modulation Region (MI: 0.96)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    (wt) Characteristics in Over-Modulation

    Simulation Results: Over-Modulation Region (MI: 0.98 )

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    (wt) Characteristics in Over-Modulation

    Simulation Results: Over-Modulation Region (MI: 1.00)

    • Square-wave switching mode

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental verification: Five-level inverter fed IM drive configuration

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    + configuration

    Inv1

    Inv2

    -

    Five-level inverter fed IM drive configuration

    Inverter-A

    • Each three-level inverter configuration by cascading two two-level inverters

    • The pole voltage can attain three levels:Vdc/2, 0 ,

    • -Vdc/2

    Ref: V. T. Somasekhar, K. Gopakumar, “Three - level inverter configuration cascading two 2-level inverters”, IEE Proc. – EPA, Vol. 150, No. 3, May 2003, pp.245-254

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    + configuration

    +

    Inv3

    Inv1

    -

    -

    Inv4

    +

    Inv2

    +

    Induction

    motor

    -

    -

    Five-level inverter fed IM drive configuration

    Ref: M. R. Baiju, K. K. Mohapatra, V. T. Somasekhar, K. Gopakumar and L. Umanand, “A five-level inverter voltage space phasor generation for an open-end winding induction motor drive”, IEE Proc. EPA, Vol. 150, No. 5, Sept 2003, pp: 531-538

    • Five-level space phasor generation across induction motor windings : Vdc/2,Vdc/4, 0 , -Vdc/4, or -Vdc/2

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces of pre-scaler output configurationT*as and inverter leg switching time Tga

    Linear-Modulation Region (MI: 0.906)

    T*as

    Tga

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces of pre-scaler output configurationT*as and inverter leg switching time Tga

    Over-Modulation Region (MI: 0.92)

    T*as

    Tga

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces of pre-scaler output configurationT*as and inverter leg switching time Tga

    Over-Modulation Region (MI: 0.94)

    T*as

    Tga

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces of pre-scaler output configurationT*as and inverter leg switching time Tga

    Over-Modulation Region (MI: 0.96)

    T*as

    Tga

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces of pre-scaler output configurationT*as and inverter leg switching time Tga

    Over-Modulation Region (MI: 0.98)

    T*as

    Tga

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces of pre-scaler output configurationT*as and inverter leg switching time Tga

    Square wave switching mode (MI: 1.00)

    T*as

    Tga

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces machine phase voltage and inverter leg switching time Tga

    Linear modulation region (MI: 0.906)

    Phase voltage

    Tga

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces machine phase voltage and inverter leg switching time Tga

    Over-Modulation Region (MI: 0.926)

    Phase voltage

    Tga

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces machine phase voltage and inverter leg switching time Tga

    Over-Modulation Region (MI: 0.97)

    Phase voltage

    Tga

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces machine phase voltage and inverter leg switching time Tga

    Square wave switching mode (MI: 1.00)

    Phase voltage

    Tga

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces machine phase voltage and phase current

    Linear-Modulation Region (MI: 0.906)

    Phase voltage

    Phase current

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces machine phase voltage and phase current

    Linear-Modulation Region (MI: 0.93)

    Phase voltage

    Phase current

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces machine phase voltage and phase current

    Linear-Modulation Region (MI: 0.957)

    Phase voltage

    Phase current

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces machine phase voltage and phase current

    Linear-Modulation Region (MI: 0.97)

    Phase voltage

    Phase current

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: The traces machine phase voltage and phase current

    Square wave switching mode (MI: 1.00)

    Phase voltage

    Phase current

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: Transition from Linear to square wave switching mode

    Top Trace: time equivalent of modified reference signalsT*as

    Bottom Trace: Inverter gate switching time Tga

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental Results: Transition from Linear to six-step mode

    Top Trace: Phase voltage, Bottom Trace: Phase current

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    1 mode

    0.9

    0.8

    0.7

    0.6

    (P.U.)

    0.5

    fund

    V

    0.4

    0.3

    0.2

    0.1

    0

    0

    10

    20

    30

    40

    50

    60

    70

    80

    90

    100

    MI (%)

    Fundamental output voltage as a function of modulation index-MI

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Harmonic components in the output waveform in the over-modulation region

    0.25

    5

    7

    11

    0.2

    13

    0.15

    Harmonic (P.U.)

    0.1

    th

    n

    0.05

    0

    90

    92

    94

    96

    98

    100

    MI (%)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Linearization of the Multi-level SVPWM in the Over-Modulation Region

    SUMMARY:

    • A simple n-level PWM signal generation with linear voltage transfer characteristics throughout the modulation range, up to six-step mode of operation

    • Linear voltage transfer characteristics in the over-modulation region is achieved by modifying the reference signal such that

      • the modified reference signal has the same fundamental component as the original reference signal

      • modified reference signals are always within the carrier region

    • Inverter leg switching times are directly obtained from the sampled amplitudes of reference phase voltages signals

    • Does not require any sector identification, sine look-up tables for switching vector identification

    • Does not use sector mapping or complex timing calculations

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA



    217 combined voltage vectors triangular sectors 15 625 switching state

    Topology of a multilevel inverter for generation of 12-side polygonal voltage space vectors for induction motor drives.

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Generation of voltage space vectors polygonal voltage space vectors for induction motor drives.

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA polygonal voltage space vectors for induction motor drives.


    217 combined voltage vectors triangular sectors 15 625 switching state

    ‘Va’ positive ‘Vb-Vc’ positive: 1st quadrant polygonal voltage space vectors for induction motor drives.

    ‘Va’ negative ‘Vb-Vc’ positive: 2nd quadrant

    ‘Va’ negative ‘Vb-Vc’ negative: 3rd quadrant

    ‘Va’ positive ‘Vb-Vc’ negative: 4th quadrant

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    If in quadrant 1: polygonal voltage space vectors for induction motor drives.

    If |Vb-Vc|<=|Va|.√3.tan150 then sector 1 else

    If |Vb-Vc|<=|Va|.√3.tan450 then sector 2 else

    If |Vb-Vc|<=|Va|.√3.tan750 then sector 3

    else sector 4

    If in quadrant 2:

    If |Vb-Vc|<=|Va|.√3.tan150 then sector 7 else

    If |Vb-Vc|<=|Va|.√3.tan450 then sector 6 else

    If |Vb-Vc|<=|Va|.√3.tan750 then sector 5

    else sector 4

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    If in quadrant 3: polygonal voltage space vectors for induction motor drives.

    If |Vb-Vc|<=|Va|.√3.tan150 then sector 7 else

    If |Vb-Vc|<=|Va|.√3.tan450 then sector 8 else

    If |Vb-Vc|<=|Va|.√3.tan750 then sector 9

    else sector 10

    If in quadrant 4:

    If |Vb-Vc|<=|Va|.√3.tan150 then sector 1 else

    If |Vb-Vc|<=|Va|.√3.tan450 then sector 12 else

    If |Vb-Vc|<=|Va|.√3.tan750 then sector 11

    else sector 10

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    V/f scheme for the drive polygonal voltage space vectors for induction motor drives.

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Comparison to obtain time durations polygonal voltage space vectors for induction motor drives.

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Pole voltage at 30Hz. polygonal voltage space vectors for induction motor drives.

    • Voltage levels at 0.366Vdc, 1.0Vdc and 1.366Vdc are observed.

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Phase voltage at 30Hz. polygonal voltage space vectors for induction motor drives.

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Pole voltage at 50Hz. polygonal voltage space vectors for induction motor drives.

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Phase voltage at 50Hz. polygonal voltage space vectors for induction motor drives.

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Fig. 14a: Phase voltage and motor current at 15Hz. polygonal voltage space vectors for induction motor drives.

    (X-axis: 1div=20ms, Y-axis: 1div=100V)

    Fig. 14b: Pole voltage at 15Hz.

    (X-axis: 1div=20ms, Y-axis:1div=50V)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Fig. 15a: Phase voltage and motor current at 30Hz. polygonal voltage space vectors for induction motor drives.

    (X-axis: 1div=10ms, Y-axis: 1div=50V)

    Fig. 15b: Pole voltage and motor current at 30Hz.

    (X-axis: 1div=5ms, Y-axis: 1div=50V)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Fig. 16a: Phase voltage and motor current at 45Hz. polygonal voltage space vectors for induction motor drives.

    (X-axis: 1div=10ms, Y-axis: 1div=100V)

    Fig. 16b: Pole voltage at 45Hz.

    (X-axis: 1div=10ms, Y-axis: 1div=50V)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Fig. 17b: Pole voltage at 50Hz. polygonal voltage space vectors for induction motor drives.

    (X-axis: 1div=5ms, Y-axis:1div=50V)

    Fig. 17a: Phase voltage and motor current at 50Hz.

    (X-axis: 1div=5ms, Y-axis: 1div=100V)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Fig. 18: Harmonics at 15Hz operation. polygonal voltage space vectors for induction motor drives.

    (X-axis: nth harmonic, Y-axis: Relative amplitude)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Fig. 19: Harmonics in 30Hz operation. . polygonal voltage space vectors for induction motor drives.

    (X-axis: nth harmonic, Y-axis: Relative amplitude)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Fig. 20: Harmonics in 45Hz operation. polygonal voltage space vectors for induction motor drives.

    (X-axis: nth harmonic, Y-axis: Relative amplitude)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Fig. 21: Harmonics in 50Hz operation. polygonal voltage space vectors for induction motor drives.

    . (X-axis: nth harmonic, Y-axis: Relative amplitude)

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Control of Switching Frequency Variation in polygonal voltage space vectors for induction motor drives.

    Hysteresis Controller for IM Drives Using

    Variable Parabolic Bands for Current

    Error Space Phasor

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Problem of Switching Frequency Variation polygonal voltage space vectors for induction motor drives.

    • Common problems associated with the conventional, as well as current error space phasor based hysteresis controllers with fixed bands (boundaries), are the wide variation of switching frequency in a fundamental output cycle and variation of switching frequency with the variation in the speed of the load motor.

    • These problems cause increased switching looses in the inverter, non-optimum current ripple, and excess harmonics in the load current, which leads to additional heating in the motor.

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Two-Level VSI fed IM Drive polygonal voltage space vectors for induction motor drives.

    Voltage Space Phasor Structure

    Power Schematic

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Directions of Current Error Space Phasor When Different Voltage Vectors are Switched for Different Positions of Vm in Sector-1

    Start of the Sector

    Middle of the Sector

    End of the Sector


    217 combined voltage vectors triangular sectors 15 625 switching state

    Factors Influencing the Switching Frequency Variation Voltage Vectors are Switched for Different Positions of

    • Leakage inductance of the machine (L)

    • Machine voltage vector (Vm) (dominated by the back emf vectorVb)

    • DC-link voltage (as amplitude of Vk is decided by dc-link voltage)

    • Current error space phasor ripple ((i))

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Variation of Switching Frequency in Voltage Vectors are Switched for Different Positions of

    Hysteresis Current Controller

    • Over a fundamental period, the position of Vm varies with respect to the inverter voltage vectors of space phasor structure.

    • Also, the selected inverter voltage vector Vk (V1, …, V8) keeps on changing in a fundamental cycle during hysteresis PWM current control.

    • Therefore, either the inverter switching frequency or/and the current error space phasor ripple will vary over a fundamental inverter period.

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Variation of Switching Frequency in Hysteresis Voltage Vectors are Switched for Different Positions of

    Current Controller (Contd…)

    • For the given operating speed, if the shape of the fixed boundary of the current error space phasor is not properly selected, the switching frequency of inverter will vary over a fundamental cycle.

    • Further to this, if the same boundary of current error space phasor is maintained at different operating speeds of the machine (for different fundamental values of the machine back emf) then also the inverter switching frequency will vary.

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Investigation of Current Error Space Phasor in Voltage Vectors are Switched for Different Positions of

    VC-SVPWM based VSI fed IM Drives

    Typical SVPWM

    switching pattern

    of the inverter

    voltage vectors

    for two consecutive

    PWM

    switching intervals

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Investigation of Current Error Space Phasor in VC-SVPWM based VSI fed IM Drives (Contd…)

    Switching times for inverter voltage vectors in a switching interval


    217 combined voltage vectors triangular sectors 15 625 switching state

    Investigation of Current Error Space Phasor in VC-SVPWM based VSI fed IM Drives (Contd…)

    Current error space phasor during switching of various voltage vectors

    Specific form for Sector-1


    217 combined voltage vectors triangular sectors 15 625 switching state

    Movement of current error space phasor (on based VSI fed IM Drives (Contd…)- plane) in a few sampling intervals of VC-SVPWM based two-level VSI fed IM drive

    [Y-axis

    And

    X-axis:

    Current

    In

    Amperes]

    Vm at middle of the sector

    ( varies from 27 to 33)

    Vm at start of the sector

    ( varies from 0 to 7)

    Vm at end of the sector

    ( varies from 54 to 60)


    217 combined voltage vectors triangular sectors 15 625 switching state

    Approximate theoretical boundary of based VSI fed IM Drives (Contd…)i for VC-SVPWM based two-level VSI fed IM drive for position of Vm in Sector-1

    [Y-axis

    And

    X-axis:

    Current

    In

    Amperes]

    10 Hz

    20 Hz

    40 Hz

    30 Hz







    217 combined voltage vectors triangular sectors 15 625 switching state

    Comparison of boundary obtained by theoretical calculations and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    Theoretical

    10 Hz

    30 Hz

    40 Hz

    20 Hz

    0.1 A/div.

    0.2 A/div.

    0.2 A/div.

    0.5 A/div.

    Simulation


    217 combined voltage vectors triangular sectors 15 625 switching state

    Establishing variable boundary for proposed hysteresis controller

    The parabola is defined as the locus of a point which moves so that it is always at the same distance from a fixed point (called the focus) and a given line (called the directrix).

    • Formula for a vertical parabola (having Y-axis as axis of symmetry) with the vertex on (h, k), is: (x-h)2=4p(y-k).

    • Formula for a horizontal parabola (having X-axis as axis of symmetry) with the vertex on (h, k), is: (y-k)2=4p(x-h).

    • Here, p is the distance between

    • vertex and focus of the parabola.


    217 combined voltage vectors triangular sectors 15 625 switching state

    Equivalent new X-axis and Y-axis for the parabolas of current error space phasor boundary in different sectors

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Generalized technique to find the parameters of the boundary defining parabolas for given induction motor

    (x, y),

    (h, k),

    p

    For boundary

    defining parabolas

    for operating

    frequency

    from 1 Hz to 45 Hz

    with the resolution

    of 1 Hz

    Vdc,

    Base_freq,

    L,

    TS,

    Generalized Technique

    (Matlab Program)

    Developed in Proposed Work

    input

    output

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA



    217 combined voltage vectors triangular sectors 15 625 switching state

    Parameters of boundary defining parabolas reference axis

    for proposed hysteresis controller

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA



    217 combined voltage vectors triangular sectors 15 625 switching state

    Output of the generalized technique in terms of the current error space phasor boundary for different operating frequencies

    [conventional Y-axis and X-axis: 1div.=0.5 A]


    217 combined voltage vectors triangular sectors 15 625 switching state

    Voltage vector selection in Sector-1 for forward as well as reverse

    direction of rotation of machine

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Sector changed detection using outer parabolic boundary reverse

    [Y-axis: 1div.=0.2 A and X-axis: 1div.=0.5 A]


    217 combined voltage vectors triangular sectors 15 625 switching state

    Sector change detection logic (based on outer parabolic bands)

    for forward rotation of machine

    (‘*’ means continue with the same sector)

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA







    217 combined voltage vectors triangular sectors 15 625 switching state

    Simulation results of proposed hysteresis controller bands)

    30 Hz Operation

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA



    217 combined voltage vectors triangular sectors 15 625 switching state

    Simulation results of proposed hysteresis controller bands)

    35 Hz Operation

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA



    217 combined voltage vectors triangular sectors 15 625 switching state

    Comparison of boundary obtained by theoretical calculations and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    SVPWM Simulation

    10 Hz

    35 Hz

    40 Hz

    30 Hz

    Proposed Hysteresis Controller Simulation


    217 combined voltage vectors triangular sectors 15 625 switching state

    Simulation results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    47 Hz Operation

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Simulation results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    Six-Step Mode of Operation


    217 combined voltage vectors triangular sectors 15 625 switching state

    Block schematic of experimental set-up used for proposed and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    hysteresis controller

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    vAN, 130 V/div.

    i, 0.2 A/div.

    iA, 1.3 A/div.

    10 Hz Operation

    i, Sector-2

    i, Sector-3

    i, Sector-1


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    iA*, 1.3 A/div.

    iA, 1.3 A/div.

    i, 1 A/div.

    10 Hz Operation

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    vAN, 130 V/div.

    iA, 1.3 A/div.

    i, 0.35 A/div.

    20 Hz Operation

    i, Sector-1

    i, Sector-2

    i, Sector-3


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    iA*, 1.3 A/div.

    iA, 1.3 A/div.

    i, 1 A/div.

    20 Hz Operation

    iA, 1.3 A/div.

    iA*, 1.3 A/div.


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    vAN, 135 V/div.

    iA, 1.3 A/div.

    i, 0.45 A/div.

    30 Hz Operation

    i, Sector-3

    i, Sector-2

    i, Sector-1


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    iA*, 1.3 A/div.

    iA, 1.3 A/div.

    i, Sector-3, 0.45 A/div.

    30 Hz Operation

    iA, 1.3 A/div.

    iA*, 1.3 A/div.

    i, 1 A/div.


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    vAN, 130 V/div.

    iA, 1.3 A/div.

    i, 0.55 A/div.

    35 Hz Operation

    i, Sector-3-4, 0.55 A/div.

    i, Sector-2, 0.55 A/div.

    i, Sector-3, 0.55 A/div.


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    iA*, 1.3 A/div.

    iA, 1.3 A/div.

    iA*, 1.3 A/div.

    iA, 1.3 A/div.

    35 Hz Operation

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    vAN, 130 V/div.

    i, 0.6 A/div.

    iA, 1.3 A/div.

    40 Hz Operation

    i, Sector-2, 0.6 A/div.

    i, Sector-3, 0.6 A/div.

    i, Sector-1, 0.6 A/div.


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    iA*, 1.3 A/div.

    i, Sector-4-5, 0.6 A/div.

    iA, 1.3 A/div.

    40 Hz Operation

    iA, 1.3 A/div.

    iA*, 1.3 A/div.


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    vAN, 130 V/div.

    iA, 1.3 A/div.

    i, 0.6 A/div.

    45 Hz Operation

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    vAN, 130 V/div.

    i, 0.5 A/div.

    iA, 1.3 A/div.

    47 Hz Operation

    CEDT, Indian Institute of Science, Bangalore, INDIA CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    vAN, 130 V/div.

    50 Hz Operation

    (Six-Step Mode)

    iA, 1.3 A/div.

    i, 1.4 A/div.

    i, 0.65 A/div.


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    vAN, 130 V/div.

    Acceleration Transients

    iA, 1.3 A/div.


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    speed, 910 rpm//div.

    Starting Operation

    iA, 1.3 A/div.

    vAN, 160 V/div.

    iA*, 1.5 A/div.

    iA, 1.5 A/div.

    iA, 1.7 A/div.


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    speed, 910 rpm//div.

    Starting Operation

    iA, 1.3 A/div.

    iA*, 1.5 A/div.

    vAN, 160 V/div.

    iA, 1.5 A/div.

    iA, 1.7 A/div.


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    speed, 910 rpm//div.

    Speed Reversal

    iA, 1.1 A/div.

    iA*, 1.35 A/div.

    vAN, 130 V/div.

    iA, 1.5 A/div.

    iA, 1.35 A/div.


    217 combined voltage vectors triangular sectors 15 625 switching state

    Experimental results of proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    speed, 910 rpm//div.

    Speed Reversal

    iA, 1.1 A/div.

    iA*, 1.5 A/div.

    vAN, 130 V/div.

    iA, 1.65 A/div.

    iA, 1.5 A/div.


    217 combined voltage vectors triangular sectors 15 625 switching state

    Salient features of the proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    • Current error space phasor based simple hysteresis controller

    • Controls the switching frequency variation in a two-level VSI fed IM drive

    • Based on the novel concept of on-line variation of hysteresis band, depending upon the speed of the machine

    • Uses parabolic boundary for the current error space phasor

    • Obtains switching frequency spectrum in the output voltage similar to that of the constant switching frequency VC-SVPWM based VSI fed IM drive.

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Salient features of the proposed hysteresis controller and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    (Contd…)

    • Performance of the proposed controller is independent of the load machine parameters

    • The unique parabolic boundary for different operating speeds for any given induction motor is determined using generalized technique (Matlab program) developed in proposed work

    • Calculation of machine back emf vector is not needed

    • Sector change logic is self-adaptive and is capable of taking the drive up to six-step mode of operation, if needed

    • Controller always selects the adjacent inverter voltage vectors, forming a sector, in which the tip of the machine voltage vector lies

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Multimotor drive setup and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Multimotor drive setup and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA and simulation studies for VC-SVPWM based two-level VSI fed IM drive


    217 combined voltage vectors triangular sectors 15 625 switching state

    Inverter setup for multilevel structure and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    Inverter setup for multilevel structure and simulation studies for VC-SVPWM based two-level VSI fed IM drive

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


    217 combined voltage vectors triangular sectors 15 625 switching state

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA and simulation studies for VC-SVPWM based two-level VSI fed IM drive


    217 combined voltage vectors triangular sectors 15 625 switching state

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA and simulation studies for VC-SVPWM based two-level VSI fed IM drive


    217 combined voltage vectors triangular sectors 15 625 switching state

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA and simulation studies for VC-SVPWM based two-level VSI fed IM drive


    217 combined voltage vectors triangular sectors 15 625 switching state

    CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA and simulation studies for VC-SVPWM based two-level VSI fed IM drive