1. IEEE PES General Meeting, Tampa FL June 24-28, 2007 1 Chapter 1: An Overview of Power System Harmonic Analysis Tutorial on Harmonics Modeling and Simulation Contributors: W. Xu and S. Ranade

2. IEEE PES General Meeting, Tampa FL June 24-28, 2007 2 Status and methods of harmonic analysis New challenges of harmonic analysis Summary Outline Chapter 1: An Overview of Power System Harmonic Analysis Modeling of power system components Algorithms for harmonic analysis Analysis of systems with distributed harmonic sources Modes of harmonic resonance Analysis of interharmonics

3. IEEE PES General Meeting, Tampa FL June 24-28, 2007 3 Status and methods of harmonic analysis Chapter 1: An Overview of Power System Harmonic Analysis Methods: 1) Frequency scan 2) Harmonic power flow Models: 1) Harmonic source: current source model 2) Non H-source: linear impedance model Variations: 1) Single-phase versus multiphase 2) Iterative versus non-iterative H power flow Applications: Systems with limited number of H-sources and the sources are typically large in size

4. IEEE PES General Meeting, Tampa FL June 24-28, 2007 4 VFD V I + - V1V1 I1I1 + - P+jQ VhVh IhIh + - h=2,  H VFD load VFD model at 60Hz = + VFD model at harmonic freq. spc = given spectrum data Modeling of harmonic loads as current sources Chapter 1: An Overview of Power System Harmonic Analysis

5. IEEE PES General Meeting, Tampa FL June 24-28, 2007 5 Example of source modeling Chapter 1: An Overview of Power System Harmonic Analysis

6. IEEE PES General Meeting, Tampa FL June 24-28, 2007 6 Harmonic analysis methods Chapter 1: An Overview of Power System Harmonic Analysis Objectives Check if resonance exists Check harmonic distortion levels (safe equipment operation) Filter design Compliance with standards Two types of assessments:  Frequency response check resonance (Frequency scan)filter design  Distortion level calculation compliance check (harmonic power flow)equipment operating conditions

7. IEEE PES General Meeting, Tampa FL June 24-28, 2007 7 Network Frequency Scan: Determine the frequency response of a network at a given bus Z f 1 Frequency scan analysis Chapter 1: An Overview of Power System Harmonic Analysis

8. IEEE PES General Meeting, Tampa FL June 24-28, 2007 8 Objective: compute harmonic distortion levels for a given operating condition Fundamental frequency power flow results (I 1 and q 1 ). Typical spectrum of harmonic sources (I h-spc, q h-spc ) System Y(h) matrix, h=harmonic number What is known for solving the problem There are many harmonic power flow algorithms proposed. Here we discuss the most useful algorithm. Current source model for harmonic sources Frequency domain Non-iterative Harmonic power flow analysis Chapter 1: An Overview of Power System Harmonic Analysis Current source model described earlier

9. IEEE PES General Meeting, Tampa FL June 24-28, 2007 9 Solution steps 1) Compute 60Hz power flow 2) Determine drive current (I 1 and q 1 ) 3) Determine drive harmonic current I(h) using the formula and typical drive spectrum 4) With known Y(h) matrix and drive current I(h), compute nodal voltage V(h) and branch current I B (h) 5) Compute harmonic indices (THD, IHD) using the V(h), I B (h) results. Harmonic power flow analysis Chapter 1: An Overview of Power System Harmonic Analysis

10. IEEE PES General Meeting, Tampa FL June 24-28, 2007 10 Time domain algorithm (e.g. EMTP simulation) or hybrid algorithm Iterative algorithms (frequency domain) F( [V 1 ], [V 2 ],...,[V n ], [I 1 ], [I 2 ],..., [I n ],C) =0 1)Newton method 2)Harmonic iteration method (see the diagram below) Linear network (including power flow constraints) Harmonic Source (non-linear) Bus voltages Current source Harmonic power flow analysis - other algorithms Chapter 1: An Overview of Power System Harmonic Analysis

11. IEEE PES General Meeting, Tampa FL June 24-28, 2007 11 New challenges Chapter 1: An Overview of Power System Harmonic Analysis Distributed harmonic sources Fluctuation of harmonic distortions with time Concerns on interharmonics Need to identify system deficiency more efficiently Need to revisit some of the modeling assumptions

12. IEEE PES General Meeting, Tampa FL June 24-28, 2007 New challenges 1 - distributed harmonic sources Chapter 1: An Overview of Power System Harmonic Analysis The harmonic-production characteristics of the sources will affect each other. (attenuation and diversity effects) The harmonic sources may also vary randomly. Actual results

13. IEEE PES General Meeting, Tampa FL June 24-28, 2007 New harmonic analysis methods need to take into account the characteristics New challenges 1 - distributed harmonic sources Chapter 1: An Overview of Power System Harmonic Analysis Harmonic attenuation effect

14. IEEE PES General Meeting, Tampa FL June 24-28, 2007 · Which bus can excite a particular resonance more easily? · Where the resonance can be observed more easily? · What are the components involved in the resonance? · How far the resonance can propagate in a system? New challenges 2 - analysis of harmonic resonance Chapter 1: An Overview of Power System Harmonic Analysis

15. IEEE PES General Meeting, Tampa FL June 24-28, 2007 Some elements of [Y] -1 are large (the extreme case is [Y] -1 =  ) Implies that [Y] approaches singularity (something like [Y]=0) The singularity of [Y] can only be caused by one or more eigenvalues of the [Y] matrix = 0. XLXL XCXC I V If this term = 0 => Resonance New challenges 2 - analysis of harmonic resonance Chapter 1: An Overview of Power System Harmonic Analysis

16. IEEE PES General Meeting, Tampa FL June 24-28, 2007 Eigen-decomposition of the Y matrix: Left eigenvector matrix Eigenvalue matrix Right eigenvector matrix [U]=[T][V] -- called modal voltage [J] =[T][I] -- called modal current [L] -- can be called modal Y matrix New challenges 2 - analysis of harmonic resonance Chapter 1: An Overview of Power System Harmonic Analysis

17. IEEE PES General Meeting, Tampa FL June 24-28, 2007 Assume l 1 is the eigenvalue approaching zero modal current J 1 will lead to a large modal voltage U 1 Other modal voltages are not affected (since they are decoupled from l 1 ) New challenges 2 - analysis of harmonic resonance Chapter 1: An Overview of Power System Harmonic Analysis

18. IEEE PES General Meeting, Tampa FL June 24-28, 2007 Physical domain Modal domain Summary: In the modal domain, it is much easier to find the ‘locations’ or ‘buses’ (i.e. the modes) that are related to a resonance Once we know the resonance mode, we can find the buses most affected by the reassurance - based on the eigenvector information New challenges 2 - analysis of harmonic resonance Chapter 1: An Overview of Power System Harmonic Analysis

19. IEEE PES General Meeting, Tampa FL June 24-28, 2007 New challenges 2 - analysis of harmonic resonance Chapter 1: An Overview of Power System Harmonic Analysis Participation of buses in a resonance Participation of components in a resonance

20. IEEE PES General Meeting, Tampa FL June 24-28, 2007 Interharmonics produce flicker Frequency of interharmonic varies with the drive operating condition New challenges 3 - analysis of interharmonics Chapter 1: An Overview of Power System Harmonic Analysis

21. IEEE PES General Meeting, Tampa FL June 24-28, 2007 An interharmonic-producing drive cannot be modeled as an interharmonic current source Inverter MotorSource 60Hz 50Hz V DC2 I DC2 Converter I AC2 V DC2 has ripples associated with the motor frequency V DC2 produces I DC2 through some impedances (including supply system Z) I DC2 is rectified (or penetrate) into the AC side to produce I AC2 Therefore, interharmonic current of I AC2 is affected by some impedances New challenges 3 - analysis of interharmonics Chapter 1: An Overview of Power System Harmonic Analysis

22. IEEE PES General Meeting, Tampa FL June 24-28, 2007 Sequence characteristics of interharmonics New challenges 3 - analysis of interharmonics Chapter 1: An Overview of Power System Harmonic Analysis

23. IEEE PES General Meeting, Tampa FL June 24-28, 2007 Harmonic analysis has become a relatively mature area. This tutorial will focus on the well-established methods It is important to note that there are still many subjects remaining to be explored. Three examples have been used to demonstrate the possible developments in the area Summary Chapter 1: An Overview of Power System Harmonic Analysis