1. 1 Chapter 8: Procedure of Time-Domain Harmonics Modeling and Simulation Contributors: C. J. Hatziadoniu, W. Xu, and G. W. Chang Organized by Task Force on Harmonics Modeling & Simulation Adapted and Presented by Paulo F Ribeiro AMSC May 28-29, 2008

2. 2 OUTLINE 1. Introduction: Relevance of the Time Solution Procedures 2. The Modeling Approach Harmonic Sources in the Time Domain Apparatus Modeling Formulation of the Network State Equation Harmonic Solution Procedure 3. Software Demonstration of Harmonic Simulation 4. Summary and Conclusion

3. 3 INTRODUCTION Why Time Domain Solution? When is Time Domain Solution Appropriate? How Accurate is Time Domain Solution Compared to Direct Methods? What are the General Characteristics of a Time Domain Solution Procedure?

4. 4 Why Time Domain Solution? “Time Domain Simulation is preferable to direct methods in certain line varying conditions involving power converters and non-linear devices.” –It allows detail modeling, especially of non-linear network elements; –It allows the assessment of non-linear feedback loops onto the harmonic output (e.g. study of harmonic instability in line commutated converters). Example of Direct Methods –PCFLOH; –SuperHarm.

5. 5 When is Time Domain Solution Appropriate? Calculations of non-characteristic harmonics from power converters. Calculation of harmonic instability and harmonic interactions between power converters and the converter control. Harmonic filter design and harmonic mitigation studies. The effect of harmonics on equipment and protection devices. Real time digital simulations-RTDS of harmonics such as hardware-in-loop simulations.

6. 6 Accuracy of Time Domain Simulation v. Direct Methods The time response of the system must arrive at a periodic steady state. –Quasi periodic or aperiodic response possible under non-linear feedback control. Sampling and integration errors. The sampling step is dictated by the highest harmonic order of interest. Modeling errors approximating the non-linear characteristic of certain apparatuses (e.g. transformer magnetization and arrester v-i characteristics)

7. 7 What are the General Characteristics of a Time Domain Solution Procedure? Slow Transient Modeling. May use programs such as EMTP, PSCAD, and SIMULINK. May incorporate local controls of power converters. Describe a limited part of the system around the harmonic source. Run simulation until steady state  Use FFT within the last simulation cycle to compute harmonics.

8. 8 Modeling Approach Harmonic Sources –Power Converters Detail representation including grid control and, possibly, higher level control loops. Equivalency: Represent as rigid source. –Non-Linear Devices Transformer magnetizing and inrush current. Arrester current in over-voltage operation. –Background harmonics: Rigid source representation.

9. 9 Power Converters: Detail Representation Detail Valve model Surge arrester representation in studies of harmonic overvoltages Representation of the grid control

10. 10 Power Converters: Switching Function Voltage-Sourced inverters are more suitable for this representation. Switching function approach: –Voltage: –Current:

11. 11 Non-Linear Devices: Transformer Piece-wise Linear representation of the core inductance. Switching inductance model (flux controlled switches).

12. 12 Formulation of the Network Equations Pre-integrated Components: Algebraic Equations State Equations: Numerical Integration –Piece-wise Linear Equations –Time Varying Equations

13. 13 Summary of The Time Domain Procedure

14. 14 SIMULINK Demonstrations Converter Simulation Using the Switching Function Non-Linear Resistor Rigid Harmonic Source Impedance Measurement Network Equivalency

15. 15 Converter Simulation Through the Switching Function Linear Network. Insert the converter as: –Voltage source on ac side. –Current source on dc side. Incorporate high level converter controls.

16. 16 Example of Non-Linear Resistor Using User-Defined Functions Voltage Controlled Element: Parasitic capacitance C’ User-defined function describing the i(v) function

17. 17 Rigid Harmonic Source Using the s- Function S-Function: Calculation of the harmonic current: Simulation time slows down with increasing order N

18. 18 Impedance Scans Using Rigid Harmonic Sources Basic assumptions: –Linear Network Model. –Single driving point (e.g. location of harmonic source). –The harmonic source is represented by a rigid current source at pre- defined harmonic orders. Driving point impedance Transfer impedance Procedure: 1.Inject positive, negative, or zero sequence current separately at unit amplitude; 2.Arrive at steady state 3.Obtain bus voltage 4.Apply FFT 1. Driving point impedance 2. Transfer Impedance

19. 19 Impedance Scan: Transfer Function Method Basic Assumptions –The impedance is defined as a current-to- voltage network (transfer) function: –Network is driven by a signal-controlled current source. More than one inputs can be used. Procedure 1.Define network as a subsystem; 2.Define the controlling signals of the current sources as the inputs; 3.Define the voltages at the buses of interest as the outputs; 4.Use the LTI tool box to obtain the driving and transfer impedances.

20. 20 Impedance Scan: Transfer Function Method—Example Inputs: Signal node 1 (array input: number of input signals is three). Outputs: Voltage at network nodes 1, 2, and 3 (each is an array of three). Voltage is measured by the voltmeter or the multimeter block

21. 21 Network Equivalency It is often desirable to represent a part of the network (referred to as the external network) by a reduced bus/element equivalent preserving the impedance characteristic at one or more buses (interface or interconnection buses). The part of the network that is of interest can be represented in detail.

22. 22 Network Equivalency Using SIMULINK The procedure replaces the external network by a TF block representing the driving point impedance at the interface bus. The TF block is embedded into the network of interest: 1.Drive the block input by the interface bus voltage; 2.Connect the block output to the input of a signal driven current source; 3.Connect the current source to the interface bus;

23. 23 Network Equivalency: Example Method becomes cumbersome for multiple interface buses. Mutual phase impedances are omitted.

24. 24 Summary 1. Time domain harmonic computation is useful in cases where detail modeling of the harmonic source is required; 2. The modeling approach is the same as the slow transient modeling approach; 3. The size of the network simulated is limited to a few buses around the harmonic source; 4. Software like SIMULINK combine several useful features that can provide insight into a problem, especially for educational purposes.