Network Modelling for Harmonic Studies

Network
Modelling for
Harmonic
Studies

 Introduction
 Study Domain and Modelling Approaches
 Classical Network Element Models
 Power Electronic Based Network Element Models
 General Considerations for Harmonic Studies
 Conclusions
Presentation Outline

Why Bother Performing Harmonic Studies?
 Non-linear equipment introduces distortion in voltage and current waveforms.
 Excessive distortion has detrimental effects on equipment and increases system losses.
 Standardisation is in place to control level of waveform distortion in public grids.
 System owners/operators need to perform harmonics studies to ensure adherence to statutory
limits.
 Customers need to perform harmonic studies to demonstrate compliance withthe allocated
limits and to protect their own equipment.
 Accurate modelling is required in order to define realistic harmonic specifications and to avoid
unnecessary investment in mitigation.
Note:
Standardization & methods for allocation of harmonic limits are outside the scope of this work.

Motivation
 Emerging harmonic voltage distortion issues in power systems driven by
proliferation of power electronic converters (generation & demand),FACTS,
HVDC converters and HVAC cables.
 New focus towards the need to undertake detailed analysis at the planning
stages in order to ensure adherence to statutory limits.
 Accurate modelling: Co-ordinate emission of harmonics onto the system and
specify/design harmonic filters.
 Available information and guidelines are either out-dated, scarce or in scattered
form.
 Harmonic studies are complex.
 Skill gap.
 Need for collating available information and formulating a practical
modelling and study guidance document.

What will you find in the Technical Brochure?
 Comprehensive modelling guidelines for practicing power system engineers
covering most common network components and nonlinear devices.
 Focus on practical aspects of modelling:
 Direct application in the planning process of connecting a new customer
 When introducing a change to the system as part of asset replacement or system expansion.
 Frequency domain modelling
 Range: up to the 50th harmonic (2.5 kHz in 50 Hz systems or 3 kHz in 60 Hz
systems), consistent with typical power quality assessments.
 Guidelines on the general approach to harmonic studies.
Note: DC harmonics, transient phenomena and harmonic stability/control interaction
are outside the scope of this work.

Technical Brochure
Table of Contents:
Executive Summary
1. Introduction
2. StudyDomainand Modelling approaches
3. Classical Network Element Models
4. Power ElectronicBased Network ElementModels
5. General Considerationsfor Harmonic Studies
6. Conclusions
7. Bibliography/References
AppendicesA to G

Study Domain and
Modelling Approaches
Chapter 2

Frequency Domain
Frequency-DomainMethods
Network
Impedance
Calculation
Frequency Scan
Balanced Unbalanced
Calculationof Harmonic
Voltages and Currents
Harmonic
Penetration
Direct
Balanced Unbalanced
Iterative
Balanced Unbalanced
HarmonicLoad
Flow
Balanced Unbalanced

Frequency Scan
• Recalculation of the network admittance matrix at each
frequency step within the frequency range of interest
• A 1 p.u. current injection is applied to obtain the
corresponding bus voltages
𝑌𝑌 𝑉𝑉ℎ ℎ = 𝐼𝐼ℎ
I(f)
2 4 6 8 10 12 14 16 18 20
Harmonic [-]
0
200
400
600
800
1000
1200
1400
1600
1800
Impedance[]
50
40
30
20
10
0
3 3.5
Harmonic [-]
4
• The bus voltage at the current source is known as the ‘driving point impedance’ and theremote
bus voltage is known as the ‘transfer impedance’
• The injected current can be positive-, negative- or zero-sequence and results in the positive-,
negative- or zero-sequence driving point or transfer impedances

Harmonic Penetration
• Often referred to as “harmonic load flow”
• A reformulation of the network admittance matrix is performed at each frequency step within the range of
interest
• Current or voltage sources are applied at relevant buses to obtain the bus voltages
• Direct (non-iterative) solution of the linear system:
𝑌𝑌ℎ 𝑉𝑉ℎ = 𝐼𝐼ℎ
• It is assumed that there is no harmonic interaction between the network and nonlinear devices
• If the stationary assumption is satisfied, the Fourier decomposition can be applied and look-up tables
used to describe a fixed operating point
I(f)
I(f)

Time Domain
• Representation of system behaviour
using differential equations
• A time-domain simulation is carried out
until the system reaches steady-state
0 0.005 0.01 0.015 0.025 0.03 0.035 0.040.02
Tid [s]
-10
-5
0
5
10
Voltage[kV]
Phase A
Phase B
Phase C
Harmonic spectrum at Anholt Island 015 kV
2 3 5 7 9 11 13 15 17 19 20
Harmonic [-]
0
2
4
6
8
12
10
16
14
18
HarmonicDistortion[%]
Time domain Frequency domain
DFT
• Advantage: Accurate consideration of nonlinear devices and their controllers
• Disadvantage: Difficult to model frequency-dependent parameters and obtain
network impedance envelopes; computational expense

Study Domains
Frequency domain Time domain
Advantages • Time-effective method allowing coverage of
many study cases
• Models frequency dependence well
• Large system studies
• Modelling of nonlinear devices and time-varying
properties
Disadvantages • Limited modelling of nonlinear devices and
feedback functions such as converter
controls or active filters
• Slow initialisation and long execution time
• Requires effort to incorporate all nonlinear models
correctly (e.g. transformer saturation and power
electronic converters)
• Difficult to represent frequency dependent
parameters

• Natural asymmetry in the power system can only be
captured using coupled sequence components or
phase quantities
Phase quantities
𝑈𝑈𝑎𝑎 𝑍𝑍𝑎𝑎𝑎𝑎 𝑍𝑍𝑎𝑎𝑏𝑏 𝑍𝑍𝑎𝑎𝑐𝑐 𝐼𝐼𝑎𝑎
𝑈𝑈𝑏𝑏 = 𝑍𝑍𝑏𝑏𝑎𝑎 𝑍𝑍𝑏𝑏𝑏𝑏 𝑍𝑍𝑏𝑏𝑐𝑐 𝐼𝐼𝑏𝑏
𝑈𝑈𝑐𝑐 𝑍𝑍𝑐𝑐𝑎𝑎 𝑍𝑍𝑐𝑐𝑏𝑏 𝑍𝑍𝑐𝑐𝑐𝑐 𝐼𝐼𝑐𝑐
Sequence
components
𝑈𝑈0 𝑍𝑍00 𝑍𝑍01 𝑍𝑍02 𝐼𝐼0
𝑈𝑈1 = 𝑍𝑍10 𝑍𝑍11 𝑍𝑍12 𝐼𝐼1
𝑈𝑈2 𝑍𝑍20 𝑍𝑍21 𝑍𝑍22 𝐼𝐼2
Decoupled sequence
components
𝑈𝑈0 𝑍𝑍00 0 0 𝐼𝐼0
𝑈𝑈1 = 0 𝑍𝑍11 0 𝐼𝐼1
𝑈𝑈2 0 0 𝑍𝑍22 𝐼𝐼2
Network Representation
• Typically, decoupled sequence components are used
for harmonic studies

Harmonic gain factors and frequency
scan of an asymmetrical cable system
• Receiving end of an unloaded 45 km 220 kV
cross-bonded cable system laid in flat formation
• The cable is energised by a 1 p.u. balanced
harmonic voltage (positive sequence) at all
harmonics from the 2nd to the 20th
• Significant inter-sequence coupling (see
harmonic orders 4, 17 and 20)
Harmonic phaseand sequencevoltages
Apparent harmonic phase impedance

Classical Network
Element Models
Chapter 3

Classical Network Element Models
 Overhead lines
 Cables
 Power transformers
 Loads
 Synchronous generators
 Shunt and series compensation
 Network equivalents

Overhead Lines
 Network harmonic impedance highly dependent upon OHLs and cables
 Aspects considered:
 Single- or multi-phase
 Frequency dependence
 Model (nominal-pi vs. equivalent-pi)
 Skin effect
 Line transposition
 Earth resistivity

Overhead Lines: Skin Effect
 Neglecting skin effect leads to underestimation of circuit damping at resonance:

Overhead Lines: Key Points
 Model:
 The frequency dependent, distributed parameter model capturing long line effects should be
used by default (for all but the shortest lines)
 Cascading sections:
 Accuracy of the lumped parameter model can be improved
 Skin effect:
 Neglecting this leads to underestimation of circuit damping at resonant frequencies
 Earth resistivity:
 Accurate estimation only required for unbalanced studies
 Average conductor height:
 Small variations have no significant impact

Cables
 Cables are more likely than OHLs to cause resonance at lower frequencies
 Length
 Design characteristics (conductor radius, insulation thickness)
 Layout
 Sheath bonding
 Model (lumped vs. distributed parameters)
 Impedance and admittance formulae
• Skin effect
• Proximity effect

Cables
 Skin and proximity effects should be modelled as accurately as possible:
Figures reproduced from: Ł. H. Kocewiak, B. Gustavsen and Andrzej Hołdyk, "Wind Power Plant Transmission System Modelling for Harmonic Propagation and Small-signal Stability
Analysis", International Workshop on Large-Scale Integration of Wind Power into Power Systems, and Transmission Networks for Offshore Wind Farms, Berlin, 2017.

Power Transformers
 Inductive behaviour:
 Interactions with capacitive
elements should be modelled
 Model comparisons (including
Electra and IEEE)
 Model validation
 Frequency dependent resistance

Power Transformers: Key Points
 Model:
 Insignificant for electrically distant nodes
 Very important at nodes where Zh is dominated by power transformers
 Losses:
 Frequency dependent losses should be represented (manufacturer-
supplied characteristic, if possible)
 Damping:
 Larger differences between models observed for resonances at higher
frequencies
 Some models overestimate damping
 Model validation:
 Input parameters should be as accurate as possible

Loads
 Considerable influence on harmonic characteristics of network
 Location of resonances and level of damping

Loads: Key Points
 Model:
 Difficult due to lack of information (composition, feeder type, location of PF correction capacitors)
 Detailed feeder modelling:
 Captures important damping effects even at light load
 Load models could accurately represent resonant frequency
 Load models could not accurately represent damping
 In conjunction with detailed load models: could accurately represent damping
 Downstream impedance:
 Should be represented as accurately as possible
 Damping:
 Difficult to capture accurately; some cases may require time-domain modelling

Synchronous Generators
 IEEE model: Choice of alpha exponent
 Proximity to generation

Synchronous Generators: Key Points
 Model:
 Choice of model only has a noticeable effect at parallel resonant points and at nodesthat
are electrically close to synchronous generators
 Frequency dependent resistance:
 Requires accurate input data
 IEEE model requires correctly selected exponent
 High-frequency losses:
 Important to model accurately

Shunt and Series Compensation: Key Points
 Accurate modelling
important: Significant
effect on system
harmonic impedance
 Consideration of
resistive losses:
Recommended if data
is available
 Low-order harmonics:
Effects appreciable

Network Equivalent for Harmonic Studies: Key Points
 Extent of network model: Usually limited due to:
 Model data sharing between neighbouring network owners/operators
 Different specialist software packages
 Data confidentiality; simplicity of exchanged data
 Computational efficiency
 Norton or Thévenin equivalent: Reduction of detail
 Background distortion:
 Fixed value based on measurements and/or estimates; or
 Based on certain restrictions, such as compatibility levels, planning levels or otherwise determined
permissible incremental or aggregate values
 Further discussion: Chapter 5 (General Considerations)

Power Electronic Based
Network Element Models
Chapter 4

 Introduction
Generic model structure
 Converter-Based
Generation
Wind and PV generation
 HVDC Converters
VSC and LCC
 FACTS Devices
STATCOMs, SVCs, etc.
 Traction Systems
AC and DC railway systems
 Electric Arc Furnaces
 Variable Speed Drives
with diode rectifier, PWM
converters, etc.
Power Electronic Based
Network Element Models

Introduction
Generic model structure
 Model proposed in IEC TR 61400-21-3: 2019.
 Small-signal linear representation.
 Converter control as well as passive
components included.
 Sequence and frequency couplings are
outside the scope.
 Active filtering can also be integrated
into the model.

Converter-Based Generation
 Harmonics in Type 3 wind turbines
1) Grid-side converter: fast switching from the current-
controlled VSC produces high-frequency harmonics and
interharmonics.
2) Rotor-side converter: low- and high-order rotor
harmonic components propagate to the grid.
3) DFIG windings: high frequency harmonics in the
generated voltage due to the non-linear effect in theair-
gap flux and slip.
Wind generation (as well as PV and other types of converter-basedgeneration)
Type 3 DFIG wind turbine Type 4 full-scale converter wind turbine
 Harmonics in Type 4 wind turbines
1) Grid-side converter: fast switching from the current-
controlled VSC produces high-frequency harmonics and
interharmonics.
2) Operating-point-dependent: wind turbine harmonic
emission changes with the change of setpoint.
3) Small-signal instability: converter small-signal instability
can potentially cause harmonic generation at any
frequency.

HVDC Converters
 HVDC LCC
1) Output current is rich in harmonic content. Under idealized
conditions it consists of “characteristic” harmonics of order 11, 13,
23, 25 …that is 12n±1.
2) The magnitude of the generated characteristic harmonics varies
with transmitted power, increasing nonlinearly.
3) Non-characteristic harmonics also generated by non-ideal
converter or supply voltage.
4) 3rd harmonic caused by unbalance in AC voltage and appears as
positive sequence. Can be significant.
5) Harmonic filters are switched in/out to provide adequatereactive
compensation and adequate filtering at each operatingpoint.
6) The harmonic impedance is a function of the converter physical
characteristics, DC side harmonic impedance, operating point, and
control system action.
(Uac= 1 pu,reactance=0.145 pu,controlangle= 17°)
TakeAway
Theworstcasefor harmonicdistortion performance mayoccurat low DCpower
transmissionlevels rather thanat maximumDCpower.

HVDC Converters
 HVDC VSC
1) The converter appears as a harmonic voltage source
rather than as a current source.
2) Harmonics are of much lower magnitude than for HVDC
LCC.
3) Harmonic generation in the high frequency range, above
the 50th harmonicorder.
4) Representation as voltage source behind harmonic
impedance.
5) The harmonic impedance is a combination of physical
passive components and the internal impedance,
dependent on the control characteristics.
6) The internal impedance may vary between inductive and
capacitive appearance with frequency, and can display a
negative resistive characteristic at some frequencies.
TakeAway
Astheharmonicgeneration istypically very low,it isnormally sufficient to calculate a
non-consistentsetof maximumharmonicvoltages over the complete range of operation.

FACTS Devices
STATCOMs, SVCs, etc.
 SVC
1) Harmonic emission is related to the thyristor-based technology and
dependent on operating point. Behaves as a harmonic current source.
2) Significant characteristic harmonics emissions of order6n±1.
3) Possible resonances can be seen between TSCs, TCRs and othernetwork
components.
4) Harmonic filters usually needed.
5) The use of non-consistent set of harmonic emission values in the studywill
lead to a conservative THD assessment
 STATCOM
1) Harmonic emission related to VSC topology. Behaves as a harmonic voltage
source.
2) Harmonics related to frequency converter modulation andcontrols.
3) Converter control determines the harmonic profile in low frequencyrange.
4) Above the active bandwidth of the inner current controller of the VSC, the
passive component dominates the harmonicimpedance.
5) Normally it is sufficient to calculate a non-consistent set of maximum
harmonic voltages over the complete range of operation of the converter.

General Considerations
for Harmonic Studies
Chapter 5

General Considerations for Harmonic
Studies
Chapter Contents
 Types of Harmonic Studies
 Considerations for Power System Representation
 Use of Power Frequency Short-Circuit Thevening Equivalent
 Harmonic Impedance Envelopes
 Representation of Customer Installation
 Aggregation of Harmonic Sources
 Background Harmonic Voltage Distortion

Considerations for Power System Representation
Power System Configuration – Key Recommendations
 Scenarios for system peak, valley and intermediate demand levels.
 The range of credible generation dispatches capturing differenttechnologies.
 Status of reactive compensation equipment.
 FACTS and HVDC installations electrically close (various operating points and
harmonic filter status).
 Number and type of contingencies needs to align with operational security standards.
 Include contingencies at least up to three nodes away from the point ofinterest.
 Avoid extreme scenarios/contingencies that do not converge in load flow or result in
breaches to security standards.
 Increasing level of uncertainty in long term scenarios  balance risk and costs

Power Frequency Short Circuit Impedance
Theuseof short-circuitimpedanceasa network equivalent at thePoCmustbe
discouraged for all applications in meshedpower systems
Network equivalent for harmonic studies
 It has been common practice in the past to provide
max. and min. fault levels as a network equivalent
proxy for harmonic studies.
 Assumption: linearity between impedance and
frequency.
 Cannot account for system resonances.
 Large errors introduced in harmonic assessments
based on short-circuit equivalents.
TakeAway

Harmonic Impedance Envelopes
Introduction
 The harmonic impedance of a power system is constantly
changing  Large volume of data
 Data can be exchanged between parties as envelopes in R-X
plane capturing all credible operating points.
 The network harmonic impedance can present any value within
the envelope(s).
 The data can be subdivided and presented as a family of
envelopes each comprising a smaller frequency band.
 Benefits of harmonic impedance envelopes:
 System Operator: Simple format for data provision.
 Customer / Vendor: Simple assessment as only boundary points need
to be studied.

Harmonic Impedance Envelopes
Some Recommendations
 Selection of frequency step resolution to capture all resonances  typically (fn/10) is
adequate, although smaller values may be required in special cases.
 In cases of high asymmetry, the envelopes must contain impedance data of all three
phases.
 The use of a single envelope encompassing impedance for all harmonic orders should
be avoided. Instead the harmonic spectrum should be divided into individual harmonic
orders or into frequency bands, with some overlapping.
 The shape of the envelopes should be selected to minimise “empty” areas without
realistic impedance points.
 Additional margins can be included in the envelopes to future-proof installations.

Background Harmonic Distortion
Why does it matter?
 Background distortion is the existing harmonic content in the power system
caused by the aggregated emissions of non-linear devices at all voltage
levels.
 Interactions between the customer installation and the grid impedance can
cause amplification of the existing background.
 New harmonic distortion introduced by non-linear connection can increase
the level of background distortion at the point of connection and at remote
locations.
 Accurate estimation of pre-connection background is needed to guarantee
adherence to statutory limits and to avoid imposing over-pessimistic
requirements to new customer connections.

Background Harmonic Distortion
Duration of Measurement Campaigns
 Levels of harmonic distortion change over time (daily
and seasonal variations).
 For some harmonics, the levels can be quite constant is
relation to time and season where others measured at
the same location can vary significantly.
 Statistical variations reduce as the period of
measurement increases.
Recommendationfor a “representative measuringperiod” issystemdependent, but
in general it canbe stated that measurementsshouldbe conductedfor aslong as
possible,ideally fornotless than threemonths,including measurementsof all
three phases.
TakeAway
0 2 4 6 12 14 16 18 20
0
0.5
1
1.5
HD[%]
Phase A
Phase B
Phase C
0 2 4 6 8 12 14 16 18 2010
Week[-]
0
0.8
0.6
0.4
0.2
1
HD[%]
8 10
Week [-]
13
th
harmonic:Min=0.40Max=0.59
Weekly 95thpercentile values
11
th
harmonic:Min=0.31Max=0.91

Summary and Conclusions
 Emerging harmonic voltage distortion issues observed in power systems driven by
proliferation of power electronic converters (generation & demand), FACTS, HVDC
converters and HVAC cables  New focus towards the need to undertake detailed
analysis at the planning stages in order to ensure adherence to statutorylimits.
 Performing harmonic studies  new set of skills for many utilities.
 Practical guidelines have been provided in Technical Brochure
 Accurate representation of most network components for typical harmonic studies

Network Modelling for Harmonic Studies

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