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) 1R. K. Lian 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

3. Introduction (2) 2R. K. Lian Objective: To accurately model VSC for harmonics study Input-Output Relation

4. Main Concept 3R. K. Lian Linear Relation: Our Proposed Method: Solve for piecewise LTI differential equations in the time domain Apply periodicity constraints

5. Results (1) ABCD parameters based on proposed method with h= -10..10 included 4R. K. Lian

6. Results (2) 5R. K. Lian ABCD parameters based on harmonic domain method with h=-10..10 included

7. Results (3) 6R. K. Lian Apply an arbitrary set of input stimuli to both ABCD parameters to compare output currents Resulting first 4 output currents Phase A CurrentHarmonic Domain Proposed Time Domain DC-0.0147-0.0127 Fundamental-0.6751 - j0.4428-0.6396 -j 0.4227 2 nd harmonic0.0102 - j0.03240.0081-j0.0126 3 rd harmonic0.1848 + j0.01130.1820 +j 0.0157

8. Results (4) 7R. K. Lian Increase harmonic numbers to 50 Phase A CurrentHarmonic Domain Proposed Time Domain DC-0.0127 Fundamental-0.6395 - j0.4173-0.6396 - j0.4227 2 nd harmonic0.0080-j0.01250.0081-j0.0126 3 rd harmonic0.1817 + j0.01570.1820 +j 0.0157 Resulting first 4 output currents

9. Results (5) 8 R. K. Lian The proposed method does not suffer truncation errors Phase A CurrentProposed Time Domain (h=10) Proposed Time Domain (h=50) DC-0.0127 Fundamental-0.6396 -j 0.4227 2 nd harmonic0.0081-j0.0126 3 rd harmonic0.1820 +j 0.0157 Resulting first 4 output currents

10. 9R. K. Lian 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