cedt_part9

INVESTIGATIONS ON BOUNDARY SELECTION FOR SWITCHING

FREQUENCY VARIATION CONTROL OF CURRENT ERROR SPACE PHASOR BASED

HYSTERESIS CONTROLLERS FOR INVERTER FED IM DRIVES

Rijil Ramchand

Research Supervisor: Prof. K. Gopakumar

PART I

An Improved Space Phasor Based Current Hysteresis Controller with

Reduced Switching Frequency Variations Using Variable Parabolic

Bands

ORGANIZATION

I. IntroductionII. Current Error Space Phasor in VC

– SVPWMIII. Parabolic Boundary for Current

Error Space PhasorIV. Vector Change Detection in

Proposed ControllerV. Sector Change Detection in

Proposed ControllerVI. Simulation Results &

Experimental ResultsVII. Conclusion

3CEDT, Indian Institute of Science,Bangalore

Introduction

PWM Voltage Source Inverter (VSI)

Voltage controlled PWM VSI Current controlled PWM VSI

Current Controlled PWM VSIAdvantages:

Simple, so can be implemented easily Excellent dynamic response

Disadvantages: Large current ripple in steady-state Generation of sub harmonic component

in the current Variation in switching frequency


IntroductionCurrent Controlled PWM VSI

Can be classified into:

Hysteresis Current Controller based VSI

Ramp Comparison Controller based VSI

Predictive Current Controller based VSI

Other controllers On-off controller Neural network controller Fuzzy logic controller


Introduction

Hysteresis Current Controller based VSI

Fixed Tolerance band Hysteresis Current Controller based VSI

Variable Tolerance band Hysteresis Current Controller based VSI


IntroductionFixed Tolerance band Hysteresis

Current Controller based VSI Eliminates first two disadvantages of the

conventional CC – PWM VSI It’s drawback is the variation of switching

frequency in a fundamental cycle and with variation in the motor speed. Increased switching losses in the inverter Non-optimum current ripple Excess harmonic content in the load current

causing overheating of the machine


Introduction

Variable Tolerance band Hysteresis Current Controller

based VSIUses variable hysteresis band to keep the switching frequency constant.

Examples are: Adaptive hysteresis band Sinusoidal hysteresis bandDisadvantages: Complex to implement Stability problems Limitations in transient performance


Proposed Variable Band Hysteresis Current Controller based VSI

Continuously varying Parabolic Boundary for Current Error Space Phasor

A new sector selection logic eliminating the two outer parabolas used in earlier work is proposed in the present work. This method uses the change in direction of

the current error during sector change along any one of the orthogonal axes.


Current Error Space Phasor in VC – SVPWM

(a) Power schematic of a three-phase (b) Voltage space phasorstructure two-level VSI fed IM drive of the two-level VSI


Basic switching vectors and Sectors

Basic switching vectors and sectors.

6 active vectors (V1,V2, V3, V4, V5, V6)

Axes of a hexagonal

DC link voltage is supplied to the load

Each sector (1 to 6): 60 degrees

2 zero vectors (V0, V7)

At origin

No voltage is supplied to the load




0

0

0

sin(60,

sin 60

sin

sin 60

( )

mS

dc

m2 S

dc

0 S 1 2

1V θ)

TV

V θT T and

V

T T T T

T

*i i i

Δi j 2 3 j 4 3A B Ci i e i e



sd

R L ,dt k b

iV i V *where i Δi i

**

k bΔi i

V Δi i Vs sd d

R L R Ldt dt

**

k bΔi i

Δi V i Vs sd d

R L R Ldt dt

*

*k b

Δi iV i Vs

d dL R L

dt dt

sd

R Ldt

**

m bi

where V i V

k kV V

σ

dΔi ΔVdt= dt

dt L

Integrating both the sides

k

k

VV

σ

ΔVΔi = t

L

dL ,

dt k mΔi

V V



1 2 0here can beeither T or T or T depending uponσ

t ,L

t

kk

(V )(V )

k

ΔV Δi

V

1

2

0

T

T and

T

σ

σ

σ

= ,L

= ,L

=L

11

22

00

(V )(V )

(V )(V )

(V )(V )

ΔVΔi

ΔVΔi

ΔVΔi



(c) at end of the Sector-1 ( varies from 54 to 60 approximately)

(a) at start of the Sector-1 ( varies from 0 to 7 approximately)

(b) at middle of the Sector-1 ( varies from 27 to 33 approximately),

Movement of current error space phasor (on - plane) in a few sampling intervals of VC-SVPWM based two-level VSI fed IM drive when the reference voltage space phasor



Current error boundary is approximated as the combination of four parabolas at 20Hz operation



Approximate theoretical boundary of current error space phasor for VC-SVPWM based two-level VSI fed IM drive for position of reference voltage space phasor in Sector-1 for different

operating speeds: (a) 10Hz operation, (b) 20 Hz operation, (c) 30 Hz operation, and (d) 40 Hz operation

(a) (b)

(c) (d)


Parabolic Boundary for Current Error Space Phasor

Four unique Parabolas acts as boundary for current error in sector-I.

This parabolic boundary varies with the frequency.

These parabolas are characterised by the equations

For other sectors the boundary defined by these parabolas will remain the same, but their orientation will change.(i.e., the X axis and Y axis will change)

2x-h =4p y-k

2y-k =4p x-h


Variation of parabola parameters p1, p2, h1, k2 for variation in frequency from 0 to 45 Hz


Parabolic Boundary for Current Error Space Phasor

Vector Change Detection in Proposed Controller

The amplitude of Δi is monitored along A, B, C, jA, jB and jC axes for vector selection

The X axis and Y axis for parabolas for different sectors are shown in table given below


VECTOR SELECTION FOR SECTOR- I (BASED ON INNER PARABOLIC BANDS) FOR FORWARD DIRECTION OF ROTATION OF MACHINE



Sector Change Detection in Proposed Controller

Sector change detection using outer parabolic

boundary

Simulation Results for Sector change detection using outer parabolic boundary (current error along jA axis & sector are the two traces)


Current error during sector-1 to sector-2 change

Simulation Results showing the variation of current error along jA axis during sector change for constant frequency VC SVPWM based two level inverter (sector-3 to sector-4 change)



The property of the current error space phasor that it will change it’s direction along one of the orthogonal axes jA, jB or jC during a sector change is utilized.




Proposed sector change detection logic for forward rotation of machine

Present sector

Presentvector “ON”

Axis along which there will be change in direction of

current error during sector change

Forward Rotation

jA jB jC

1 V2 or V7 or V8 * * 2

2 V3 or V7 or V8 * 3 *

3 V4 or V7 or V8 4 * *

4 V5 or V7 or V8 * * 5

5 V6 or V7 or V8 * 6 *

6 V1 or V7 or V8 1 * *

(‘*’ means continue with the same sector)


Block diagram of the experimental setup


Simulation Results

10Hz operation for VC-SVPWM & Hysteresis Controller with outer parabola


Simulation Results &Experimental Results

Experimental results at 10Hz operation for Proposed Hysteresis Controller with outer parabola

Simulation results at 10Hz operation for Proposed Hysteresis Controller with outer parabola


Simulation Results




Simulation & Experimental results at 10Hz operation for Proposed Hysteresis Controller without outer parabola


Experimental Results

Sector and current error along jA axis for the proposed HC

Sector and current error along jA axis for the HC with outer parabola

10Hz Operation

Output of the sector change detection block with current error along jA axis




Simulation Results


Experimental results at 20Hz operation for Proposed Hysteresis Controller without outer parabola

Simulation results at 20Hz operation for Proposed Hysteresis Controller without outer parabola




Simulation Results






Sector and current error along jA axis for the proposed HC

Sector and current error along jA axis for the HC with outer parabola

20Hz Operation

Output of the sector change detection block with current error along jA axis




Simulation Results






Experimental results for Proposed Hysteresis Controller in over-modulation and six-step mode

Simulation results for Proposed Hysteresis Controller in over-modulation and six-step mode



Experimental results for Proposed Hysteresis Controller in six-step mode

Simulation results for Proposed Hysteresis Controller in six-step mode


Simulation Results

Acceleration of the IM from stand still to 10Hz in 2 sec

Acceleration of the IM from 30Hz to 50Hz (six step) in 2.5 sec.


Simulation Results

Speed reversal of the IM from 10Hz to -10Hz in 4 sec.

Acceleration of the IM from stand still to 25Hz in 3.2 sec. and sudden loading of 5Nm at 4 sec.


Simulation Results

Sudden step change in Isq at 4 sec. (a) Motor current (iA) and Reference current (iA*) (b) Motor Phase voltage (VAN), Motor current (iA) and Reference current (iA*)

(a) (b)



Acceleration of the IM from stand still to 20Hz in 4sec

Acceleration of the IM from 10Hz to 20Hz in 2sec



Machine phase voltage (vAN), and machine phase current (iA) during Transition from 30 Hz to 45 Hz operation

Machine phase voltage (vAN), and machine phase current (iA) during Transition from 45 Hz to 50 Hz operation



Speed reversal of the IM from 20Hz to -20Hz in 6 sec.

Sudden step change in Isq -Motor Phase voltage (VAN), Motor current (iA) and Reference current (iA*)


Conclusion

Switching frequency pattern similar to that of VC-SVPWM is obtained.

Proposed new sector change detection logic is self-adaptive and takes the drive to six-step mode.

It keeps all the inherent advantages of space phasor based hysteresis current controllers adjacent voltage vector switching etc.


PART II

Hysteresis Controller based two-level VSI fed IM Drives with Simple Online Current Error Space Phasor Boundary

Estimation

ORGANIZATION

I. IntroductionII. Online Boundary Computation

for Current Error Space PhasorIII. Sector Change Detection in

Proposed ControllerIV. Vector Change Detection in

Proposed ControllerV. Simulation Results &

Experimental ResultsVI. Salient Features of Proposed

Scheme


Introduction

Constant switching frequency hysteresis controller fed IM drive

Computation of Boundary for current error space phasor to obtain phase voltage harmonic spectrum exactly similar to that of VC SVPWM inverter

Current error space phasor boundary is computed from estimated fundamental stator voltages along alpha and beta axes.

This will give an exact estimate of current error space phasor boundary of VC SVPWM inverter making harmonic spectrum of phase voltage same in both cases.


Online Boundary Computation for Current Error Space Phasor

Estimation of stator voltages along and β axes

Space phasor based equivalent circuit of Induction Motor

Vs

is

sddt rdΨ

dt

Rs σLs Rr

m rjω Ψ

ir

im

(1-σ) Ls

The equivalent circuit shown above will be used for estimating stator voltage along and β axes




ss s s

dV i r

dt

��

��

s rs swhere L i a ��

rs ss rs ss s s s

di didV i r L a i r L aV

dt dt dt

��

From the above equivalent circuit the equation for stator voltage vector can be written as

The stator voltage vector equation can be rewritten as




The stator voltage equation can be re written as when the induction motor is supplied from an inverter.

Where , is the instantaneous space phasor output from inverter

sk rs s s

diV i r L aV

dt

��

kV��

** s s

k rs s s sd(i i )

V (i i )r L aVdt

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

** s s

k rs ss s s sdi d i

V (i r L ) ( i r L ) aVdt dt





The expression for the fundamental rotor voltage vector in terms of applied inverter voltage vector, reference current vector, and current error space phasor

The fundamental stator voltage vector is given by

** s s

r k s ss s s s1 di d i

V V (i r L ) ( i r L )a dt dt


** s

s r s s sdi

V aV (i r L )dt

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

The fundamental stator voltage vector can be rewritten as s

s k s s sd i

V V ( i r L )dt

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA




The fundamental stator voltage vector along and β axes can be rewritten as

During zero vector, fundamental stator voltage vector along and β axes can be rewritten as

ss s s s

d iV i r L

dt

ss s s s

d iV i r L

dt

ss k s s s

d iV V ( i r L )

dt

ss k s s s

d iV V ( i r L )

dt



From estimated Vs and Vsβ , compute instantaneous phase voltages va, vb & vc

Using the computed values of va, vb & vc, individual vector timings T1, T2 & T0 are calculated. T1 is switching time for vector , T2 is switching time for vector , and T0 is switching time for zero vectors in space vector PWM.

The instantaneous voltage error vectors , and are computed

The instantaneous current error vectors , and are computed

Compute the current error boundary along orthogonal axes jA, jB & jC

1VAAAAAAAAAAAAAA

2VAAAAAAAAAAAAAA

0VAAAAAAAAAAAAAA

1iAAAAAAAAAAAAAA

2iAAAAAAAAAAAAAA

0iAAAAAAAAAAAAAA



Instantaneous stator phase voltages

The instantaneous stator phase voltages can be calculated as

as

bs

c

1 0v

V2 1 3v * *

V3 2 2v

1 32 2



Switching times computation

The instantaneous stator phase voltages can be calculated as

aas s

dc

vT * T

V

bbs s

dc

vT * T

V

ccs s

dc

vT * T

V

active max minT T T

0 s activeT T T

1 max mi dT T T

2 mid minT T T



Switching times computation

The table below gives how T1, T2 and T0 for different sectors can be computed from Tas, Tbs & Tcs

Sector Tmax Tmid Tmin T1 T2

1 Tas Tbs Tcs Tas - Tbs Tbs - Tcs

2 Tbs Tas Tcs Tas - Tcs Tbs - Tas

3 Tbs Tcs Tas Tbs - Tcs Tcs - Tas

4 Tcs Tbs Tas Tbs - Tas Tcs - Tbs

5 Tcs Tas Tbs Tcs - Tas Tas - Tbs

6 Tas Tcs Tbs Tcs - Tbs Tas - Tcs



Instantaneous voltage errors

The instantaneous voltage errors are computed using equation given below

AAAAAAAAAAAAAA

2 21 dc s 1 sV V V 2V V cos

AAAAAAAAAAAAAA

2 2 0 02 dc s 2 sΔV = V +V - 2V V cos(60 - )

ssΔV =VAAAAAAAAAAAAAA

Vs

V1

ΔV1

α0

V1 = Vdc

Vs

V2

ΔV2

60 -α0

V2=Vdc



Instantaneous current errors

The instantaneous current error magnitudes are computed using equation given below

11 1

σ

VΔi = T

L

22 2

σ

VΔi = T

L

00 0

σ

VΔi = T

L

The instantaneous current error magnitudes are then converted into components along jA, jB & jC axes for voltage vector change detection



Sector VectorsOrthogonal axes for vector change

detection

1

1 jC

2 jA

7jB

8

Present

Sector

Present

Vector

Previous

Vector

Next Vector

1

17 - - 2

2 - - 7

28 1 - -

1 8 - -

7 - - 1 -

8 - - 2 -

2 jA*A A

iji ( ji ) 0

2

0 jB*B B

iji ( ji ) 0

2

1jC*

C C

iji ( ji ) 0

2

2 jA*

A A

iji ( ji ) 0

2



Sector Identification using estimated Vs and Vsβ

The magnitude of fundamental stator voltage vector can be calculated as

cos α and sin α can be computed as

2 2s s sV V V

AAAAAAAAAAAAAA

s

s

Vcos

V AAAAAAAAAAAAAA

s

s

Vsin

V AAAAAAAAAAAAAA

α - axis

β - axis

α0

Vs

Vsα

Vsβ



Sector Identification using estimated Vs and Vsβ

Present

Sector

Next

Sector

Present vector Cos α Sin α

12

V2 or V7 or V8 < 0.5 > 0.866

23

V3 or V7 or V8 < -0.5 < 0.866

34

V4 or V7 or V8 = -1 <= 0

45

V5 or V7 or V8 > -0.5 < -0.866

56

V6 or V7 or V8 > 0.5 > -0.866

61

V1 or V7 or V8 = 1 >= 0

Present

Sector

Next

SectorPresent

vectorCos α Sin α

1 6 V6 or V7 or V8 = 1 <= 0

2 1 V1 or V7 or V8 > 0.5 < 0.866

3 2 V2 or V7 or V8 > -0.5 > 0.866

4 3 V3 or V7 or V8 = -1 >= 0

54

V4 or V7 or V8 < -0.5> -

0.866

65

V5 or V7 or V8 < 0.5< -

0.866

Conditions to be satisfied for sector change during forward rotation of the

motor

Conditions to be satisfied for sector change during reverse rotation of the

motor


START

Read Vkα,Vkβ,

Δisα and Δisβ

ComputeVsα and Vsβ

(6) & (7)

IM ParametersLσ and rs

ComputeVa ,Vb and Vc

(11)

ComputeT1 ,T2 and T0

(12)

ComputeΔV1 ,ΔV2 and ΔV0

(13), (14) & (15)

ComputeΔi1 ,Δi2 and Δi0

(16)

Compute orthogonal components of Δi1 ,Δi2 and

Δi0

(Δi1jA ,Δi1jB ,Δi1jC ,Δi2jA ,Δi2jB ,Δi2jC, Δi0jA ,,Δi0jB

and Δi0jC)

Check for Sector change

1

1

Update the sector value

YES

Check for Vector change

NO

StoresVsα , Vsβ,

Present sectorand

Present vector

Stores1. orthogonal components

of Δi1 ,Δi2 and Δi0

2. Actual current errors along orthogonal axes

ΔijA ,ΔijB and ΔijC

3. Previous vector

Actual current errors along

orthogonal axesΔijA ,ΔijB and ΔijC

Update the vector value

YES

END

NO

Previous Vector

Flow Chart for proposed hysteresis controller



Step 1:Estimate Vs and Vsβ and using zero and active vectors.

Step 2:From Vs and Vsβ , the instantaneous stator phase voltages va, vb & vc are computed.

Step 3:Using the computed values of va, vb & vc, individual vector timings T1, T2 & T0 are calculated.

Step 4:Compute instantaneous voltage error vectors , & are computed.


1VAAAAAAAAAAAAAA

2VAAAAAAAAAAAAAA

0VAAAAAAAAAAAAAA


Step 5:Compute instantaneous current error vectors , & are computed.Step 6:This current error boundary values Δi1, Δi2 & Δi0 into components along the orthogonal axes jA, jB & jC.Step 7:Check for sector change using estimated Vs and Vsβ.

Step 8:Check whether the current error along the particular orthogonal axis (axis for the present vector along which current error has to be monitored) has crossed the hysteresis boundary computed for Vector change detection.


1iAAAAAAAAAAAAAA

2iAAAAAAAAAAAAAA

0iAAAAAAAAAAAAAA

Block diagram of proposed hysteresis controller based Inverter fed IM drive

Online computation of current error

boundary

iα and iβ iα* and iβ*

RS, σLS & TS


Simulation Results

10Hz steady state operation – phase voltage, phase current

10Hz steady state operation – FFT of phase voltage




10Hz steady state operation – reference current & phase current


Simulation Results

10Hz steady state operation – Current error space phasor trajectory in sectors 1, 2, 3, one cycle and current space phasor for one cycle



10Hz steady state operation – Current error space phasor

trajectory in sectors 1, 2, 3 and one cycle72CEDT, Indian Institute of Science,Bangalore

Simulation Results

10Hz steady state operation – Sector and Vector for one fundamental cycle and zoomed version showing sector-2 and it’s vector switching


Simulation Results








Simulation Results




20Hz steady state operation – Current error space phasor trajectory in sectors 1, 2, 3 and one cycle


Simulation Results

20Hz steady state operation – Sector and Vector for one fundamental cycle and zoomed version showing sector-2 and it’s vector switching


Simulation Results








Simulation Results




40Hz steady state operation – Current error space phasor trajectory in sectors 1, 2, 3 and

one cycle


Simulation Results


50Hz steady state operation (six step mode) –phase voltage & phase current



50Hz steady state operation (six step mode) –

phase voltage & phase current


Simulation Results

Acceleration of the IM from standstill to 10Hz in 1 sec.

Speed reversal of the IM from 10Hz to -10Hz



Deceleration of the IM from standstill to -10Hz in 1 sec.



Simulation & Experimental Results

Sudden change in Isq at 10Hz – Simulation Results

Sudden change in Isq at 10Hz – Experimental Results


Simulation Results


Sudden change in Isq at 20Hz – Simulation Results






Simulation Results


Sudden change in Isq at 40Hz –

Simulation Results90CEDT, Indian Institute of Science,Bangalore





Salient Features of proposed schemes

PART I Hysteresis controller with parabolic boundary for

vector selection with new sector change detection logic is proposed.

This eliminates outer parabolas used previously for sector change detection.

Proposed scheme gives phase voltage harmonic spectrum similar to that of constant switching frequency SVPWM inverter fed drive.

The proposed controller is taking the drive into over-modulation and six-step mode of operation if demanded by the load.


Salient Features of proposed schemes

PART II Hysteresis controller with online computation

current error space phasor boundary is proposed for two-level inverter.

It eliminates the look-up table used for implementing the parabolic boundary.

This scheme gives phase voltage harmonic spectrum which is exactly similar to that of constant switching frequency SVPWM inverter.

Boundary is computed using estimated stator voltages along alpha and beta axes during zero and active vectors .

The scheme is modular and can be extended to any n-level multilevel inverter


Overall Experimental Setup


Publications1. Rijil Ramchand, P. N. Tekwani, M. R. Baiju and K. Gopakumar,

“An Improved Space Phasor Based Current Hysteresis Controller with Reduced Switching Frequency Variations Using Variable Parabolic Bands”, NPEC-2007, IISc, Bangalore, December 16-19, 2007.

2. Rijil Ramchand, K. Sivakumar, Anandarup Das, Chintan Patel and K. Gopakumar, “A Hysteresis PWM Controller with Constant Switching Frequency for Two-level VSI fed Drives with Operation Extending to the Six-Step Mode”, PCIM Europe-2009 at Nuremberg, May 12-14, 2009.

3. Rijil Ramchand, K. Sivakumar, Anandarup Das, Chintan Patel and K. Gopakumar, “Improved Switching Frequency Variation Control of Hysteresis Controlled VSI Fed IM Drives Using Current Error Space Vector”, IET Power Electronics, vol. 3, no. 2, pp. 219-231, March 2010.


Publications4. Rijil Ramchand, Chintan Patel, K. Sivakumar, Anandarup Das

and K. Gopakumar, “Online Computation of Hysteresis Boundary from Estimated Stator Voltages during Zero and Active Vector Periods for Constant Switching Frequency Current Error Space Vector Based Hysteresis Controller for VSI fed IM Drives”, Communicated to IEEE Trans. on Power Electronics

5. Rijil Ramchand, Chintan Patel, Anandarup Das, K. Sivakumar, and K.Gopakumar, “A Current Error Space Vector Based Hysteresis Controller with Constant Switching Frequencyand Simple Online boundary Computation for VSI fed IM Drive”, Communicated to IEEE IECON 2010, 7-10 November 2010 at Glendale, AZ, USA.



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