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Chapter 8: Procedure of Time-Domain Harmonics Modeling and Simulation

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

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Chapter 8: Procedure of Time-Domain Harmonics Modeling and Simulation

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

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

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

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

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

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

  13. Summary of The Time Domain Procedure

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

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

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

  18. 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: Inject positive, negative, or zero sequence current separately at unit amplitude; Arrive at steady state Obtain bus voltage Apply FFT Driving point impedance Transfer Impedance Impedance Scans Using Rigid Harmonic Sources

  19. 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 Define network as a subsystem; Define the controlling signals of the current sources as the inputs; Define the voltages at the buses of interest as the outputs; Use the LTI tool box to obtain the driving and transfer impedances. Impedance Scan: Transfer Function Method

  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. 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. 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: • Drive the block input by the interface bus voltage; • Connect the block output to the input of a signal driven current source; • Connect the current source to the interface bus;

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

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

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