1 Chapter 1: An Overview of Power System Harmonic Analysis Organized by Task Force on Harmonics Modeling & Simulation Adapted and Presented by Paulo F

1

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

Contributors: W. Xu and S. Ranade

2

• Status and methods of harmonic analysis

• New challenges of harmonic analysis

• Summary

Outline


• Modeling of power system components• Algorithms for harmonic analysis

• Analysis of systems with distributed harmonic sources• Modes of harmonic resonance• Analysis of interharmonics

3

Status and methods of harmonic analysis


Methods: 1) Frequency scan2) Harmonic power flow

Models: 1) Harmonic source: current source model2) Non H-source: linear impedance model

Variations: 1) Single-phase versus multiphase2) Iterative versus non-iterative H power flow

Applications: Systems with limited number of H-sources andthe sources are typically large in size

4

VFD

V I

+

-

V1I1

+

-

P+

jQ

VhIh

+

-

h=2,H

_1

1_

h spch

spc

II I

I _ 1_h h spc spch

VFD load VFD model at60Hz

= +

VFD model atharmonic freq.

spc = given spectrum data

Modeling of harmonic loads as current sources


5

Example of source modeling


100 20( )VFDS P jQ j kVA 1 25 / 3 0 14.43 0( )V kV

1 2.355 11.31 ( )3VFDS

I AV

5 1 5_ % 2.355*18.24% 0.4296spcI I I A 5 5_ 1_5 55.68 5 ( 11.31) 112.23spc spc

Typical Spectrum Harmonic CurrentSource

HarmonicOrder

_ (%)h spcI _ ( )h spc ( )hI A ( )h

1 100 0 2.355 -11.315 18.24 -55.68 0.4296 -112.237 11.9 -84.11 0.2802 -163.2811 5.73 -143.56 0.1349 -267.9713 4.01 -175.58 0.0944 -322.6117 1.93 111.39 0.0455 -80.8819 1.39 68.30 0.0327 -146.5923 0.94 -24.61 0.0221 -284.7425 0.86 -67.64 0.0203 -350.39

6

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

Network

Frequency Scan:Determine the frequency response of a network at a given bus

Z

f

0

..

..

0

1

..

..

..

......

..

.

.

..

....

..

.

.

..

....

..

.

.

..

..

..

..

1

2

1

1

21

11

2

1

NN

N

N

NN Y

Y

Y

Y

Y

Y

V

V

V

1

Frequency scan analysis


8

Objective: compute harmonic distortion levels for a given operating condition

• Fundamental frequency power flow results (I1 and q1).• Typical spectrum of harmonic sources (Ih-spc, qh-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 discussthe most useful algorithm.

• Current source model for harmonic sources• Frequency domain• Non-iterative

Harmonic power flow analysis


• Current source model described earlier

9

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.

Harmonic power flow analysis


10

• Time domain algorithm (e.g. EMTP simulation) or hybrid algorithm

• Iterative algorithms (frequency domain)

F( [V1], [V2],...,[Vn], [I1], [I2], ..., [In],C) =0

1) Newton method2) Harmonic iteration method (see the diagram below)

Linear network(including powerflow constraints)

Harmonic Source(non-linear)

Bus voltages

Current source

Harmonic power flow analysis - other algorithms


11

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

New challenges 1 - distributed harmonic sources


The harmonic-production characteristics of the sources will affect each other. (attenuation and diversity effects)

The harmonic sources may also vary randomly.

0

5

10

15

20

25

30

35

40

45

50

0 20 40 60 80 100 120 140

Bus number

Volt

ag

e T

HD

(%

) Traditional method

Iterative method

Actual results

New harmonic analysis methods need to take into account the characteristics

05

1015

2025

30

1311

97

53

0

20

40

60

80

100Ih

/I1

(%)

VTHD (%)Harmonic Order

New challenges 1 - distributed harmonic sources


Harmonic attenuation effect

· 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?

0

1

2

3

4

0 5 10 15 20 25 30Frequency (pu)

Impe

danc

e (p

u)

Bus 9

Bus 10

Bus 5

Bus 7

New challenges 2 - analysis of harmonic 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.

XL XC IVI

jXjXIYV

CL

11 )11

(

If this term = 0 => Resonance

][][][ 1 IYV



]][[][][ 1 TTY Eigen-decomposition of the Y matrix:

Left eigenvectormatrix

Eigenvaluematrix

Right eigenvectormatrix

][][][ 1 JU ][][][ 1 IYV

[U]=[T][V] -- called modal voltage[J] =[T][I] -- called modal current[L] -- can be called modal Y matrix



nnn J

J

J

U

U

U

JU...

000

0...00

000

000

...][][][ 2

1

1

12

11

2

1

1

• 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)



0

1

2

3

4

0 5 10 15 20 25 30Frequency (pu)

Impe

danc

e (p

u)

Bus 9

Bus 10

Bus 5

Bus 7

0

5

10

15

20

0 5 10 15 20 25 30

Frequency (pu)

Mo

da

l im

ped

an

ce (

pu) Resonance mode

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 thereassurance - based on the eigenvector information





3

G

1

G

2 Converter

SVC C

4 5

6

13

7

8 9

10 11

14

12

Harmonic=5.9

Participation of buses in a resonance

Participation of componentsin a resonance

InverterConverter MotorSource

60Hz 50Hz

DC link reactor

60Hz ripple 50Hz ripple

• Interharmonics produce flicker• Frequency of interharmonic varies with the drive operating condition

New challenges 3 - analysis of interharmonics


An interharmonic-producing drive cannot be modeled as an interharmonic current source

Inverter MotorSource

60Hz 50Hz

VDC2

IDC2

Converter

IAC2

•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



0

100

200

300

400

500

600

700

800

0 10 20 30 40 50 60 70

Drive Output Frequency (Hz)

Inte

rhar

mon

ic F

requ

ency

(H

z)

Positive sequence Negative sequence

A

B

X

Y

Practical operating range

Sequence characteristics of interharmonics



• 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


Documents

1 Chapter 1: An Overview of Power System Harmonic Analysis Organized by Task Force on Harmonics Modeling & Simulation Adapted and Presented by Paulo F