Chapter 1: An Overview of Power System Harmonic Analysis

1. Contributors: W. Xu and S. Ranade Chapter 1: An Overview of Power System Harmonic Analysis Organized by Task Force on Harmonics Modeling & Simulation Adapted and Presented by Paulo F Ribeiro AMSC May 28-29, 2008

2. Chapter 1: An Overview of Power System Harmonic Analysis Outline • Status and methods of harmonic analysis • New challenges of harmonic analysis • Summary • Modeling of power system components • Algorithms for harmonic analysis • Analysis of systems with distributed harmonic sources • Modes of harmonic resonance • Analysis of interharmonics

3. Chapter 1: An Overview of Power System Harmonic Analysis Status and methods of 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. h=2,H Ih I1 Vh I V1 V + + + P+jQ VFD - - - Chapter 1: An Overview of Power System Harmonic Analysis Modeling of harmonic loads as current sources = + VFD model at harmonic freq. VFD model at 60Hz VFD load spc = given spectrum data

5. Chapter 1: An Overview of Power System Harmonic Analysis Example of source modeling

6. Chapter 1: An Overview of Power System Harmonic Analysis Harmonic analysis methods • 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. Chapter 1: An Overview of Power System Harmonic Analysis Frequency scan analysis 1 Frequency Scan: Determine the frequency response of a network at a given bus Network Z f

8. Chapter 1: An Overview of Power System Harmonic Analysis Harmonic power flow analysis Objective: compute harmonic distortion levels for a given operating condition 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 What is known for solving the problem • Fundamental frequency power flow results (I1 and q1). • Typical spectrum of harmonic sources (Ih-spc, qh-spc) • System Y(h) matrix, h=harmonic number • Current source model described earlier

9. Chapter 1: An Overview of Power System Harmonic Analysis Harmonic power flow analysis Solution steps 1) Compute 60Hz power flow 2) Determine drive current (I1 and q1) 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 IB(h) 5) Compute harmonic indices (THD, IHD) using the V(h), IB(h) results.

10. Chapter 1: An Overview of Power System Harmonic Analysis Harmonic power flow analysis - other algorithms • Time domain algorithm (e.g. EMTP simulation) or hybrid algorithm • Iterative algorithms (frequency domain) F( [V1], [V2],...,[Vn], [I1], [I2], ..., [In],C) =0 • Newton method • Harmonic iteration method (see the diagram below) Bus voltages Harmonic Source (non-linear) Linear network (including power flow constraints) Current source

11. Chapter 1: An Overview of Power System Harmonic Analysis New challenges 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. Chapter 1: An Overview of Power System Harmonic Analysis New challenges 1 - distributed harmonic sources The harmonic-production characteristics of the sources will affect each other. (attenuation and diversity effects) Actual results The harmonic sources may also vary randomly.

13. Chapter 1: An Overview of Power System Harmonic Analysis New challenges 1 - distributed harmonic sources Harmonic attenuation effect New harmonic analysis methods need to take into account the characteristics

14. Chapter 1: An Overview of Power System Harmonic Analysis New challenges 2 - analysis of harmonic resonance · 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?

15. Chapter 1: An Overview of Power System Harmonic Analysis New challenges 2 - analysis of harmonic resonance XL XC I V If this term = 0 => Resonance • 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.

16. Chapter 1: An Overview of Power System Harmonic Analysis New challenges 2 - analysis of harmonic resonance Eigen-decomposition of the Y matrix: Right eigenvector matrix Left eigenvector matrix Eigenvalue matrix [U]=[T][V] -- called modal voltage [J] =[T][I] -- called modal current [L] -- can be called modal Y matrix

17. Chapter 1: An Overview of Power System Harmonic Analysis New challenges 2 - analysis of harmonic resonance • Assume l1 is the eigenvalue approaching zero • modal current J1 will lead to a large modal voltage U1 • Other modal voltages are not affected (since they are decoupled from l1)

18. Chapter 1: An Overview of Power System Harmonic Analysis New challenges 2 - analysis of harmonic resonance Modal domain Physical 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

19. Chapter 1: An Overview of Power System Harmonic Analysis New challenges 2 - analysis of harmonic resonance Participation of components in a resonance Participation of buses in a resonance

20. Chapter 1: An Overview of Power System Harmonic Analysis New challenges 3 - analysis of interharmonics • Interharmonics produce flicker • Frequency of interharmonic varies with the drive operating condition

21. Motor Source Chapter 1: An Overview of Power System Harmonic Analysis New challenges 3 - analysis of interharmonics An interharmonic-producing drive cannot be modeled as an interharmonic current source IDC2 VDC2 Inverter Converter IAC2 50Hz 60Hz • VDC2 has ripples associated with the motor frequency • VDC2 produces IDC2 through some impedances (including supply system Z) • IDC2 is rectified (or penetrate) into the AC side to produce IAC2 • Therefore, interharmonic current of IAC2 is affected by some impedances

22. Chapter 1: An Overview of Power System Harmonic Analysis New challenges 3 - analysis of interharmonics Sequence characteristics of interharmonics

23. Chapter 1: An Overview of Power System Harmonic Analysis Summary • 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