Chapter 3
Harmonic Modeling of Networks
Tutorial on Harmonics Modeling and Simulation
Contributors: T. Ortmyer, C. Hatziadoniu, and P. Ribeiro
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Distribution System Modeling
The initial decisions:
- Three phase or single phase modeling
- The extent of the primary model
- Secondary distribution modeling
The NATURE of the issue and the GOAL of the
study constrain these decisions.
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A Typical Primary Distribution System
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Things to note
•
•
•
•
Any large or unique loads
Capacitor banks/ cables(?)
Transmission supply
Any unusual operating conditions?
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Decision 1: Per phase versus Three Phase
Modeling

The three phase model is required when:
Single phase or unbalanced capacitors are present
 Ground or residual currents are important in the
study

Significant unbalanced loading is present
 A
combination of wye-wye and/or delta-wye
transformers leads to harmonic cancellation*

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The typical instances where a single
phase model may be sufficient are:

A single large three phase harmonic source is
the cause of the study

The remaining system is well balanced

Ground currents are not an issue
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Decision 2: The extent of the system
model

Model the entire primary system

Transmission source can be modeled by the 60 Hertz
short circuit impedance if no significant transmission
capacitance is nearby– but check that the transmission
system is not a source of harmonics

Power factor capacitors and any distributed generation
should be modeled in detail
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Decision 3: Load and harmonic source
modeling

Identify and model all significant harmonic sources

Determine present levels through measurements- also
determine if harmonic levels peak at full or light load
conditions

Develop aggregate load models
measurements and load distribution

Validate with measurements taken as harmonic
sources/capacitor banks are switched in and out
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based
on
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Representative secondary distribution system
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Characteristics of secondary studies

Different voltage levels

Fewer capacitors, and more with tuning coils

Load data is more accessible- and more important

Measurements can be more economical
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Modeling transformers
•
•
•
•
•
Model the transformer connection
Neglect the transformer magnetizing branch (usually
ignore the transformer magnetizing harmonics)
Model the harmonic reactance as the product of short
circuit leakage reactance and harmonic number
Model the harmonic resistance as the short circuit
resistance. Correct for skin effect if data or model
available.
Include stray capacitance for frequencies above the
low khertz range.
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Line Models
•
•
Distribution lines and cables should be
represented by an equivalent pi. An estimated
correction factor for skin effect can be included
Model ground path for zero sequence
harmonics
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Capacitors
•
•
•
Capacitors– model as capacitive reactance– 60
hertz reactance divided by the harmonic number.
Be sure to note those single phase capacitors,
and model as such.
Model the capacitor as either grounded wye, or
ungrounded wye or delta.
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Load Models
•
•
•
Linear Loads
Induction and Synchronous Machines
Non-linear Loads
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Linear Passive Loads
•
TYPES: Incandescent lamps,
resistive heater, electric range,
water heater, space heater,
etc.
•
CHARACTERISTICS: RL type
loads
with
RL
values
independent of frequency.
R
jwhL
=jhXL
Per Phase Model
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Line Connected
MOTOR/GENERATOR LOADS
s
nsynch  nrotor
nsynch
Induction Motor Fundamental Frequency Per
Phase Equivalent Circuit
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IM Per Phase Harmonic Model
sh 
hnsynch  nrotor
hnsynch
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 1.0
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•
For synchronous generators, the per phase model of
the synchronous generator is similar– use a series
combination of stator resistance and substransient
reactance in the model.
•
On all direct connected machines, make sure and
account for the ground connection (or lack of one) in
studies with zero sequence harmonics.
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Nonlinear Loads
•
•
•
•
Adjustable speed drives
fluorescent lamps,
computers and other
electronic loads
arc furnaces and
welders
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These
loads
generate
harmonic currents, and are
modeled as sources at the
harmonic frequencies
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Load Model 1: Series Passive Load
2
V
RP 2
P  Q2
2
V
X Q 2
P  Q2
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Load Model 2: Parallel Passive Load
2
V
R
P
2
V
X
Q
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Load Model 3. Skin Effect Parallel
Load Model
2
V
R ( h) 
m( h )  P
2
V
X ( h) 
m( h )  Q
m(h)  0.1  h  0.9
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Load Model 4. Induction Motor plus
Resistive
V2
R1 
(1  K )  P
V2
X1 
K m K1K  P
K m Install Factor (  1.2)
K1  Severity Factor (  8)
K  fraction of motor load
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Load Model 5. CIGRE/EDF
2
V
R2 
(1  K )  P
X 2  0.073  R2
V2
X1 
K  P  (6.7 tan   0.74)
Q
tan  
P
K  fraction of motor load
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Load Model 6. Inclusion of Load
Transformer and Motor Damping
X1 and R1 as in Model 4
X 2  0.1  R2
R1 
X1
K3
K3 is the effective quality factor
of the motor circuit.
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I. Case Study 1: Load Impedance
Frequency Study
System
Source
11 kV
0.0107H
0.001
Harmonic
Source
PFC
Load
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Case Study 1 Parameters
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•
•
•
•
Linear Load=743 kW.
PF Cap.=741kVAr, (C=5.4mF).
Injected Harmonic Currents (A):
I5 = 0.840 I7 = 0.601
I11=0.382 I13=0.323
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Case Study 1: Load Model 1, 2, and 3
results
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Case Study 1: Load Model 4, 5, and
6 Results
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Sensitivity of Impedance to Motor Penetration
Level (Load Model 6, fixed PFC)
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Sensitivity of Impedance to IM
Penetration– w/changing PFC
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Summary
•
•
•
•
•
Define study needs
Determine the modeling needs
Get the data
Validate the data
Produce good results!!
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