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

1
Admittance (or ABCD) Matrix of a Voltage Source
Converter (VSC)

• Presenter Ryan Lian
• Supervisor Prof. P. W.Lehn
• Energy and Systems Group
• University of Toronto

2
Introduction (1)

• 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

1
R. K. Lian
3
Introduction (2)

• Objective
• To accurately model VSC for harmonics study

• Input-Output Relation

2
R. K. Lian
4
Main Concept

• Linear Relation

• Our Proposed Method
• Solve for piecewise LTI differential equations in
  the time domain
• Apply periodicity constraints

3
R. K. Lian
5
Results (1)

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

4
R. K. Lian
6
Results (2)

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

5
R. K. Lian
7
Results (3)

• 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
6
R. K. Lian
8
Results (4)

• Increase harmonic numbers to 50

Resulting first 4 output currents
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
7
R. K. Lian
9
Results (5)

• The proposed method does not suffer truncation
  errors

Resulting first 4 output currents
Phase A Current Proposed Time Domain (h10) Proposed Time Domain (h50)
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
R. K. Lian
8
10
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_at_ecf.utoronto.ca

9
R. K. Lian