Linear AC Current Regulation

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Prof. T. A. Lipo

University of Wisconsin Madison Wisconsin

Linear AC Current Regulation

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Field Oriented Control Principle

i_sT

i_sf

i_s l_r

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F.O.C. Block Diagram

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Transport and sampling delay caused by the PWM process and digital controller sampling/computation

T_s/2 T_s

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Equivalent Block Diagram

e–sTs 2

Sample Delay

E s 

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Amplitude and Phase of Sample Delay Effect

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Effects of Sampling in Bode Domain

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Step Response in Per Unit Showing Effect of Sample Delay, System Pole Moved From –60 s–¹ to –600 s–¹

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Regulate two out of three currents

Current Regulator Block Diagram

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Stationary Frames of Reference

ABC frame : Three non-orthogonal variables with two degrees of freedom

ab : Two orthogonal variables Clarke (alpha-beta) transform:

Inverse Clarke transform:

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 

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c b a

i i i

i i i i T

i

2 3 2

3 0

2 1 2

1 1

3

ab 2

b a

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b a b

ab a

i i i

T i

i i i

T

c b a

2 3 2

1

2 3 2

1

0 1

3 2

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ab Current Regulator

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System Block Diagram

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Effect of Sampling Delay

Magnitude and Phase Bode plot of open loop forward path loop gain for (a) an ideal controller, (b) sampling delay only, (c) transport and sampling delay, ms, a = 0.103, k_p = 116.

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AC Current Regulation – Using PI Gains

of the DC System

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Optimal Gain Determination

-1 -1

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Optimal Gain Determination

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Optimal Gain Determination

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Open Loop Phase Margn at Maximum Inflection Pt. vs. Ti/Td

Ti/Td f_m(deg)

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Open Loop Transfer Function for Two

Controller Designs

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AC Response of the Optimal Value Design ,40 Degree Phase Margin

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AC Current Regulation Response of Simulated

Optimized Stationary Frame PI Current Regulator

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Comparison of Simulated and Experimental Results

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Resonant Current Regulator

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Resonant Current Regulator

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Resonant Current Regulator

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Magnitude and Phase Bode plot of for PI and PR regulators with sampling/transport delay

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Simulation and Test Results for Resonant

Current Regulator

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Conclusions

• Sampling of the current feedback has a significant effect on regulation

• AC current regulation requires substantially more gain than DC current regulation

• With proper attention to achieving maximum

permissible gain, current regulation to 1-2 degree can be achieved

• Regulation to within a fraction of a degree is possible with a resonant regulator

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The Family of Current Regulation Techniques

Current Regulation

“Linear” Non-Linear

Frame

Stator Synchronous

Frame Hysteresis

Deadbeat FANGS Predictive/

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Benefits of Direct AC Current Regulation

• Approach is the straightforward, least confusing means of control design

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Benefits of Direct AC Current Regulation

•Well known traditional means of control design (root locus, Bode) is readily applied

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Benefits of Direct AC Current Regulation

• Since the problem remains linear, stability is well understood and determined

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Benefits of Direct AC Current Regulation

• Since the problem remains linear, stability is well understood and determined

• Friendly Approach - NO FANGS!!