Admittance (or ABCD) Matrix of a Voltage Source Converter (VSC)

Presenter: Ryan Lian

Supervisor: Prof. P. W.Lehn

Energy and Systems GroupUniversity of Toronto

Introduction (1)

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• Advances in the voltage and current ratings of IGBTs and GTOs result in wide spread use of VSC

• At generation level, back to back VSCs to interface with energy source such as wind conversion systems.

• At transmission level, VSCs are used to improve system stability and power flow

• However, the side effect of these power electronics is the generation of harmonics

Introduction (2)

2R. K. Lian

• Objective: To accurately model VSC for harmonics study

• Input-Output Relation

VSC

hdcI

hacV

hdcV

hacI

switching times,

(Input)

(Input)

(Output)

(Output)

Main Concept

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• Linear Relation:

ABCD parameter

h hac ach hdc dc

A BI VC DV I

• Our Proposed Method:• Solve for piecewise LTI differential equations

in the time domain• Apply periodicity constraints

Results (1)

• ABCD parameters based on proposed method with h= -10..10 included

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Results (2)

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• ABCD parameters based on harmonic domain method with h=-10..10 included

Results (3)

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• Apply an arbitrary set of input stimuli to both ABCD parameters to compare output currents

Resulting first 4 output currents

Phase A Current Harmonic Domain

Proposed Time Domain

DC -0.0147 -0.0127

Fundamental -0.6751 - j0.4428 -0.6396 -j 0.4227

2nd harmonic 0.0102 - j0.0324 0.0081-j0.0126

3rd harmonic 0.1848 + j0.0113 0.1820 +j 0.0157

Results (4)

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• Increase harmonic numbers to 50

Phase A Current Harmonic Domain

Proposed Time Domain

DC -0.0127 -0.0127

Fundamental -0.6395 - j0.4173 -0.6396 - j0.4227

2nd harmonic 0.0080-j0.0125 0.0081-j0.0126

3rd harmonic 0.1817 + j0.0157 0.1820 +j 0.0157

Resulting first 4 output currents

Results (5)

8R. K. Lian

• The proposed method does not suffer truncation errors

Phase A Current Proposed Time Domain(h=10)

Proposed Time Domain(h=50)

DC -0.0127 -0.0127

Fundamental -0.6396 -j 0.4227 -0.6396 -j 0.4227

2nd harmonic 0.0081-j0.0126 0.0081-j0.0126

3rd harmonic 0.1820 +j 0.0157 0.1820 +j 0.0157

Resulting first 4 output currents

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Conclusions

• Admittance matrix derived from the proposed method does not suffer from harmonic truncation error.

• The admittance matrix derived from the proposed time domain method can be used to improve the accuracies of harmonic power flow programs

• Email: liank@ecf.utoronto.ca