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Chapter 3Harmonic Modeling of Networks

Chapter 3Harmonic Modeling of Networks

Contributors: T. Ortmyer, C. Hatziadoniu, and P. Ribeiro

Organized by

Task Force on Harmonics Modeling & Simulation

Adapted and Presented by Paulo F Ribeiro

AMSC

May 28-29, 2008

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Distribution System Modeling 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 thestudy constrain these decisions.

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A Typical Primary Distribution SystemA Typical Primary Distribution System

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Things to noteThings 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

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:

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

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

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 based on measurements and load distribution

Validate with measurements taken as harmonic sources/capacitor banks are switched in and out

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Representative secondary distribution systemRepresentative secondary distribution system

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Characteristics of secondary studiesCharacteristics 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 transformersModeling 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 ModelsLine 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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CapacitorsCapacitors

• 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 ModelsLoad Models

• Linear Loads

• Induction and Synchronous Machines

• Non-linear Loads

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Linear Passive LoadsLinear 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

Line Connected MOTOR/GENERATOR LOADS

Induction Motor Fundamental Frequency Per Phase Equivalent Circuit

synch

rotorsynch

n

nns

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IM Per Phase Harmonic ModelIM Per Phase Harmonic Model

0.1

synch

rotorsynchh hn

nhns

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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 LoadsNonlinear Loads

• Adjustable speed drives

• fluorescent lamps, computers and other electronic loads

• arc furnaces and welders

• These loads generate harmonic currents, and are modeled as sources at the harmonic frequencies

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Load Model 1: Series Passive LoadLoad Model 1: Series Passive Load

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2 2

2

2 2

VR P

P Q

VX Q

P Q

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Load Model 2: Parallel Passive LoadLoad Model 2: Parallel Passive Load

2

2

VR

P

VX

Q

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Load Model 3. Skin Effect Parallel Load Model

Load Model 3. Skin Effect Parallel Load Model

2

2

( )( )

( )( )

( ) 0.1 0.9

VR h

m h P

VX h

m h Q

m h h

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Load Model 4. Induction Motor plus Resistive

Load Model 4. Induction Motor plus Resistive

2

1

2

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1

(1 )

Install Factor ( 1.2)

Severity Factor ( 8)

fraction of motor load

m

m

VR

K P

VX

K K K P

K

K

K

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Load Model 5. CIGRE/EDFLoad Model 5. CIGRE/EDF

2

2

2 22

1

(1 )

0.073

(6.7 tan 0.74)

tan

fraction of motor load

VR

K P

X R

VX

K P

QP

K

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Load Model 6. Inclusion of Load Transformer and Motor DampingLoad Model 6. Inclusion of Load Transformer and Motor Damping

1 1

2 2

11

3

3

X and as in Model 4

X 0.1

is the effective quality factor

of the motor circuit.

R

R

XR K

K

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I. Case Study 1: Load Impedance Frequency Study

I. Case Study 1: Load Impedance Frequency Study

0.001

0.0107H

11 kVSystemSource

HarmonicSource

Load

PFC

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Case Study 1 ParametersCase Study 1 Parameters

• Linear Load=743 kW.

• PF Cap.=741kVAr, (C=5.4F).

• 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

Case Study 1: Load Model 1, 2, and 3 results

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Case Study 1: Load Model 4, 5, and 6 Results

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)

Sensitivity of Impedance to Motor Penetration Level (Load Model 6, fixed PFC)

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Sensitivity of Impedance to IM Penetration– w/changing PFCSensitivity of Impedance to IM Penetration– w/changing PFC

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SummarySummary

• Define study needs

• Determine the modeling needs

• Get the data

• Validate the data

• Produce good results!!