Overhead-line impedance and admittance change with frequency, so a model that serves load flow or short circuit may not be adequate for harmonic analysis. This page covers the choice between lumped, cascaded and distributed-parameter line models; skin effect and frequency-dependent parameters; earth-return and zero-sequence impedance; line shunt capacitance and compensation; transposition and inter-circuit coupling; and when a balanced model is enough versus a full multi-phase representation.
Reading time ≈ 24 min · Part Two of the series
Overhead lines are important components in harmonic studies because their impedance and admittance change with frequency. A line that is electrically short at the fundamental frequency may become electrically long at harmonic frequencies. The modelling approach used for a normal load-flow or short-circuit study may therefore not be sufficient for harmonic analysis.
For harmonic studies, the line model must represent the series impedance, the shunt admittance, the frequency dependency of the parameters, long-line effects, phase imbalance and zero-sequence behaviour — and, where relevant, any line shunt compensation. The correct model depends on the line length, harmonic order, study objective and required accuracy.
Key idea
Line impedance and admittance are frequency dependent, so harmonic results are sensitive to the line model.
Choose between a lumped nominal-π, cascaded sections, or a distributed equivalent-π model based on length and harmonic order.
Skin effect, earth-return/zero-sequence impedance and shunt compensation usually matter most for resonance.
Use a multi-phase model where asymmetry, transposition, coupling or phase-wise limits are relevant.
Key terms used on this page
01Series impedance, \(Z\)
The impedance along the line-conductor path.
02Shunt admittance, \(Y\)
The admittance from the conductor to earth or between conductors, mainly due to capacitance.
03Lumped model
A simplified model where the line impedance and admittance are concentrated into one equivalent section.
04Cascaded model
Several lumped line sections connected together to better represent a long line.
05Distributed-parameter model
A model where impedance and admittance are treated as continuously distributed along the line.
06Zero-sequence impedance, \(Z_0\)
The impedance seen by zero-sequence currents, where the three phase currents are in phase and return through earth, shield wires or neutral paths.
07Earth-return impedance
The part of the impedance influenced by current returning through the earth.
08Transposition
Changing the physical position of conductors along the route to reduce phase imbalance.
09Inter-circuit coupling
Electromagnetic coupling between circuits running close to each other.
Section 1
Why line modelling differs at harmonic frequencies
An overhead line is not just a 50 Hz impedance. At harmonic frequencies its resistance, inductive reactance, shunt capacitance, earth-return path and coupling with other phases or circuits can all change the calculated harmonic impedance. This means the selected line model can shift resonance frequencies, change the height of impedance peaks and alter the calculated harmonic voltage distortion at nearby buses.
At fundamental frequency, an overhead line is often represented using positive-sequence and zero-sequence impedance values. This can be adequate for load flow, short-circuit calculation or protection studies. In harmonic studies it is not always adequate, because the electrical behaviour of the line changes with harmonic order. The line series reactance rises with frequency while the capacitive reactance falls:
As a result, the line can participate in resonance with other network elements — capacitor banks, cables, filters, transformers and shunt reactors. The key practical relationship remains:
\[ V_h=Z_h\,I_h \]
\(V_h\)
harmonic voltage at order \(h\)
\(I_h\)
harmonic current at order \(h\)
\(Z_h\)
harmonic impedance of the network at order \(h\)
If the line model gives an inaccurate value of \(Z_h\), the calculated harmonic voltage distortion will also be inaccurate. The line model is therefore not a background detail — it directly sets the harmonic impedance the study is trying to find.
Section 2
Available line representations
For harmonic analysis, overhead lines can generally be represented using two main approaches: a lumped-parameter model or a distributed-parameter model. The lumped model is normally implemented as a nominal-π section; the distributed model is normally implemented as an equivalent-π derived from travelling-wave (long-line) equations.
A third practical approach is also common: cascaded lumped-parameter sections, where a long line is split into several shorter nominal-π sections. This improves the representation of long-line effects but increases the number of nodes and the computational burden.
Practical length guideline
Distributed parameters should be considered when the line length exceeds roughly \(\dfrac{240}{h}\) km, where \(h\) is the harmonic order of interest. At the 5th harmonic, \(\dfrac{240}{5}=48\) km — so a line longer than about 48 km may need distributed modelling if accurate harmonic impedance is required. At the 25th harmonic, \(\dfrac{240}{25}=9.6\) km. In other words, as the harmonic order rises the threshold falls, so even quite short lines may need a more detailed model when high orders are assessed.
Section 3
Lumped-parameter model
The lumped-parameter model represents the line using a series impedance and a shunt admittance concentrated into a single equivalent section. In matrix form the line is described by a frequency-dependent series impedance matrix \([Z(\omega)]\) and a frequency-dependent shunt admittance matrix \([Y(\omega)]\).
In a three-phase or multi-phase model, \([Z(\omega)]\) and \([Y(\omega)]\) are matrices rather than single numbers. The diagonal terms represent each phase’s own impedance or admittance, while the off-diagonal terms represent the coupling between phases or circuits. This is why an unbalanced or multi-phase model carries more information — and more data — than a single positive-sequence value.
The lumped model is simple and computationally efficient, and can be acceptable for short lines and low harmonic orders. Its important limitation is that it cannot fully represent standing-wave effects or multiple resonance points along a long line.
Table 1 — When a lumped nominal-π model is suitable.
Condition
Suitability
Line is short
Suitable
Harmonic order is low
Suitable
Frequency of interest well below first line resonance
Suitable
Only approximate screening is required
May be acceptable
Long line or high harmonic order
Not recommended
When is a single nominal-π model acceptable?
A single nominal-π model may be acceptable for short overhead lines, low harmonic orders and early screening studies. It becomes less reliable when the line is long, the frequency range is high, the study is focused on resonance, or phase-specific harmonic distortion is important. In those cases, cascaded sections or a distributed-parameter model should be used.
Section 4
Distributed-parameter model
The distributed-parameter model represents the line parameters as continuously distributed along the line length. It is more accurate for harmonic studies, especially when the line is long or when higher harmonic frequencies are being assessed. The distributed model captures long-line effects, standing waves, multiple resonance points, frequency-dependent propagation and phase shift along the line.
This matters because, at harmonic frequencies, a line may exhibit several series and parallel resonance points. A simple lumped model may only approximate the first resonance and miss higher-frequency behaviour. The distributed model should normally be the default for overhead lines in harmonic studies, except for very short lines or simple screening.
Practical recommendation
Use distributed-parameter models for accurate harmonic studies — especially where the line length is significant, the harmonic order is high, resonance is important, filter design depends on network impedance, or the compliance margin is small.
Section 5
Cascaded nominal-π sections
If a distributed-parameter model is not available, a long overhead line may be represented using several cascaded nominal-π sections. The concept is to split a long line into multiple shorter sections; as the number of sections increases, the cascaded lumped model approaches the distributed-parameter model. For example, a 250 km line may be modelled as 5 × 50 km sections, or as 10 × 25 km sections.
Increasing the number of sections improves accuracy over a wider frequency range, but also increases the number of intermediate nodes and may increase calculation time. The trade-off is direct: more sections give a better frequency response, but a larger model. Cascading is particularly useful when the voltage or current profile along the line is required, not only the sending-end or receiving-end harmonic values.
Section 6
Frequency dependency of line parameters
Overhead-line parameters are frequency dependent. The most important effects are conductor skin effect, earth-return path behaviour, zero-sequence impedance variation and mutual coupling variation. The harmonic model should calculate the line impedance and admittance at each harmonic frequency, rather than simply scaling the fundamental-frequency impedance. In the harmonic admittance equation \([Y_h][V_h]=[I_h]\), the line contributes to \([Y_h]\) at each order — so if the frequency dependency is wrong, the admittance matrix is wrong.
In practice these effects can be applied through frequency characteristics. Because resistance and inductance vary with frequency — through skin effect and variations in internal inductance — we can associate a frequency characteristic with these quantities and let the software scale them per harmonic. In DIgSILENT PowerFactory, two types are available: a Frequency Polynomial Characteristic (ChaPol) or a user-defined frequency table (TriFreq / ChaVec). The characteristic is assigned on the Power Quality/Harmonics page of the element dialog — for a line type, against the resistance and inductance fields shown in Figure 1.
Figure 1 — The Power Quality/Harmonics page of a line type (TypLne). Each resistance and inductance has a frequency field — R1'(AC)(f), L1'(f), R0'(AC)(f), L0'(f) — where a frequency characteristic can be attached.
A characteristic is attached from the drop-down beside the relevant field by choosing Select… and pointing to a frequency-characteristic object in the library, as in Figure 2. The same mechanism is available for several line-related objects: the line type (TypLne), series reactor, resistor and capacitor elements (ElmSind, ElmScap) and the series RLC filter (ElmSfilt). Frequency-dependent impedances are also handled automatically for lines represented by a tower type (TypTow, TypGeo) or a cable system type (TypCabsys).
Figure 2 — Assigning a frequency characteristic to a line-type parameter. Here a Frequency Polynomial Characteristic is already attached to R1'(AC)(f); the Select… menu attaches one to L1'(f).
For the Frequency Polynomial Characteristic of Figure 3, the scaling factor is a simple polynomial of frequency:
scaling factor at harmonic frequency \(f_h\) (usually a per-unit / percentage of the input parameter)
\(f_h,\ f_1\)
harmonic frequency and fundamental (nominal) frequency
\(a,\ b\)
polynomial coefficients set in the characteristic dialog
The factor is then applied to the corresponding input parameter. For the line resistance, for example:
\[ R(f_h)=R\cdot y(f_h) \]
\(R(f_h)\)
resistance at harmonic frequency \(f_h\)
\(R\)
input (fundamental-frequency) resistance
\(y(f_h)\)
frequency scaling factor from the characteristic
Figure 3 — The Frequency Polynomial Characteristic (ChaPol). The coefficients a and b define how the parameter scales with frequency; a vectorial characteristic (ChaVec) can be used instead where a measured table is preferred.
Skin effect
Skin effect causes current to concentrate near the conductor surface as frequency increases. This reduces the effective cross-section carrying the current and increases the effective AC resistance, so that \(R(h)>R_1\), where \(R(h)\) is the resistance at order \(h\) and \(R_1\) the fundamental value.
Skin effect matters because resistance provides damping, and at resonance the amplitude of the harmonic impedance peak is strongly affected by damping. If skin effect is neglected, the model may underestimate damping and overestimate resonance peaks. At resonance, \(Z_h\) may be dominated by the resistive part of the network, so even a moderate error in resistance can significantly change the calculated harmonic voltage. A frequency characteristic on the AC-resistance field (Figure 1) is the practical way to include this.
Practical message
Skin effect must be included for harmonic studies, especially where resonance is being assessed.
Earth return and zero-sequence impedance
Earth resistivity has a major influence on zero-sequence impedance, because zero-sequence current returns through the earth and/or earth wires. For positive-sequence studies, earth resistivity often has only a limited effect; for zero-sequence and unbalanced harmonic studies it can be very important. The zero-sequence impedance depends on earth resistivity, frequency, conductor height, earth-wire arrangement, mutual coupling and the return path, and both its real and imaginary parts can vary significantly with frequency:
\[ Z_0(h)=R_0(h)+j\,X_0(h) \]
\(Z_0(h)\)
zero-sequence impedance at harmonic order \(h\)
\(R_0(h)\)
zero-sequence resistance at harmonic order \(h\)
\(X_0(h)\)
zero-sequence reactance at harmonic order \(h\)
\(h\)
harmonic order, equal to \(f/f_1\)
\(f,\ f_1\)
harmonic frequency and fundamental frequency (normally 50 Hz in the UK and Ireland)
\(j\)
imaginary operator
Table 2 — Where accurate zero-sequence / earth-return modelling matters.
Study Condition
Reason
Unbalanced harmonic studies
Negative and zero sequence may be present
Triplen harmonic propagation
Zero-sequence path is important
Telephone interference
Zero-sequence and earth-return effects matter
Parallel lines
Mutual coupling may involve the earth return
Long lines over varying geology
Earth resistivity may vary along the route
If accurate zero-sequence behaviour is required, the line route may need to be divided into sections with representative earth-resistivity values.
Soil-resistivity caution
Soil resistivity is often uncertain. Where earth-return impedance is important, the assumed soil resistivity should be stated in the report. If the line route crosses areas with significantly different soil conditions, sensitivity studies — or route sections modelled with different earth-resistivity values — may be required.
Zero-sequence mutual impedance
Where zero-sequence mutual impedance is defined between lines or circuits, it should be included if zero-sequence or unbalanced propagation is relevant. In simplified implementations the zero-sequence mutual reactance may be scaled by harmonic order, reflecting its inductive nature:
For more accurate studies, especially at higher harmonic orders, zero-sequence mutual impedance should ideally be calculated from frequency-dependent line geometry and earth-return models rather than simple scaling. Simple scaling may be acceptable for screening, but frequency-dependent zero-sequence modelling is preferred for detailed studies.
Section 7
Shunt admittance and compensation
The shunt admittance of an overhead line is mainly capacitive, and the capacitive susceptance increases with frequency. For a shunt capacitance \(Y_C=j\omega C\), at harmonic order \(h\) the admittance becomes \(Y_C(h)=jh\omega_1 C\), so the susceptance scales with order:
\[ B_C(h)=h\,B_{C1} \]
\(B_C(h)\)
capacitive susceptance at order \(h\)
\(B_{C1}\)
fundamental-frequency capacitive susceptance
This is important because shunt capacitance contributes to resonance and long-line effects, and becomes more influential at higher harmonic frequencies. A line that appears mainly inductive at fundamental frequency may become part of a resonant circuit at harmonic frequencies through its distributed capacitance.
Line shunt compensation must also be represented correctly. Compensation may be installed as shunt reactors or shunt capacitors, and the harmonic behaviour differs: a reactor is inductive and its reactance increases with frequency, while a capacitor is capacitive and its susceptance increases (its reactance decreases) with frequency. Compensation must therefore be scaled according to its physical nature.
Shunt reactor compensation
For a shunt reactor the impedance is inductive, \(Z_L=j\omega L\), so at order \(h\) it is \(Z_L(h)=jh\omega_1 L\). The imaginary part of the reactor impedance scales with harmonic order:
This is critical because shunt capacitors can create parallel resonance with the system inductance. For this reason, capacitor banks must be included accurately in harmonic studies.
Section 8
Balanced and unbalanced line models
An overhead line can be modelled using either a balanced or an unbalanced representation. A balanced representation assumes the three phases are symmetrical and is normally based on positive-sequence data. It may be acceptable when the line is transposed, the phase geometry is symmetrical, only positive-sequence harmonic propagation is required, or the study is preliminary.
However, most overhead-line geometries are not perfectly symmetrical: phase conductors sit at different physical positions and mutual coupling between phases may be unequal. An unbalanced or multi-phase model should be used in the following cases.
Table 3 — When to use an unbalanced / multi-phase line model.
Condition
Reason
Line is untransposed
Phase impedances are not equal
Double circuits share right of way
Inter-circuit coupling may be important
Telephone interference is assessed
Zero sequence and mutual coupling matter
Triplen harmonics are relevant
Zero-sequence path matters
Resonance occurs near a harmonic order of interest
Phase differences can be amplified
Phase-wise harmonic limits are required
Individual phase results are needed
Circuit geometry changes along the route
Sectional modelling is needed
The practical recommendation is to use multi-phase line models as the default where data and software allow, because modern software can usually handle the additional matrix size without excessive computational burden.
Line transposition
Transposition reduces phase imbalance at fundamental frequency, but its effectiveness decreases at harmonic frequencies. At higher frequencies the electrical length of each transposition section becomes more significant, so transposition can create different resonance behaviour in each phase. To model it correctly, the line should be divided into homogeneous sections, each with its own phase arrangement — for example Section 1 as A-B-C, Section 2 as B-C-A and Section 3 as C-A-B — each modelled separately and connected in cascade.
Practical rule
Do not average out transposition effects when harmonic resonance is important — a single averaged transposed-line model may hide phase-specific resonance or inter-sequence coupling.
What is inter-sequence coupling?
Inter-sequence coupling means that the positive-, negative- and zero-sequence components are not completely independent. In an unbalanced or asymmetrical line model, a disturbance in one sequence can influence another. This is one reason a balanced positive-sequence model may miss some harmonic-propagation effects that an unbalanced model would capture.
Inter-circuit coupling
Where two or more circuits run in parallel or share a right of way, mutual coupling should be considered. Inter-circuit coupling can affect positive-, negative- and zero-sequence impedance, harmonic transfer between circuits, telephone interference and phase-wise voltage distortion. A coupled double-circuit line may require a \(6\times 6\) impedance and admittance matrix, and more complex rights of way may require even larger matrices. If coupling is ignored, the model may underestimate harmonic transfer between circuits or misrepresent resonance frequencies.
Average conductor height
The average conductor height above ground affects line capacitance and earth-return impedance. A common approximation is:
vertical difference between the support-point height and the midspan conductor height
This approximation is used because the conductor is not at a constant height along the span, and the effective height influences both the line capacitance and the earth-return impedance.
Table 4 — Factors that affect average conductor height.
Factor
Effect
Terrain
Changes clearance and average height
Span length
Changes sag profile
Temperature
Changes conductor sag
Loading
Heating changes sag
River or road crossings
Changes local height
Tower type
Changes conductor geometry
For many harmonic studies, small variations in average height have a relatively minor effect compared with the model type, skin effect and earth resistivity — but the value should still be chosen realistically. Small height errors give a minor harmonic-impedance error, whereas an incorrect model type or missing skin effect gives a major one.
Section 9
Lumped vs distributed — comparison
The difference between lumped and distributed modelling grows as frequency and line length increase. A lumped nominal-π model may represent the first resonance approximately, but cannot represent the full series of resonances caused by long-line effects. A distributed model can represent multiple resonance points and propagation effects.
Table 5 — Lumped, cascaded and distributed line models compared.
Aspect
Lumped nominal-π
Cascaded nominal-π
Distributed equivalent-π
Simplicity
High
Medium
Medium
Long-line effects
Poor
Improved
Good
Multiple resonance points
Poor
Improved
Good
Accuracy at high harmonic orders
Low
Depends on section length
High
Model size
Small
Larger
Moderate
Use case
Short lines, screening
Intermediate solution
Detailed studies
The practical recommendation: for short lines and low harmonics, a lumped model may be acceptable; for long lines or resonance studies, use a distributed model.
Section 10
Practical modelling workflow
A practical overhead-line modelling workflow for harmonic studies can be structured as a sequence of decisions and data collection:
Define the study objective — screening, compliance, filter design, resonance, unbalance or telephone interference.
Identify the harmonic frequency range — e.g. \(h=2\) to \(50\), or another range as required.
Collect the required line data (see Table 6).
Select the model type — lumped, cascaded lumped, or distributed.
Decide whether the model should be balanced or unbalanced.
Include frequency dependency, especially skin effect and earth-return effects.
Include line compensation and terminal elements.
Validate the line model using frequency scans and sensitivity cases.
Table 6 — Line data required and its use.
Data
Use
Conductor type
Resistance, radius, GMR
Earth-wire data
Shielding and zero-sequence path
Phase geometry
Mutual impedance and capacitance
Tower arrangement
Phase spacing and height
Transposition details
Section-by-section phase arrangement
Line length
Long-line effects
Earth resistivity
Zero-sequence and earth-return modelling
Parallel circuits
Mutual coupling
Shunt compensation
Harmonic impedance contribution
Terminal equipment
Reactors, capacitors, filters, transformers
Sensitivity priorities
Not all modelling parameters have the same effect on harmonic results. The most influential are summarised below.
Table 7 — Relative sensitivity of harmonic results to modelling choices.
Parameter
Typical Impact
Comment
Model representation
High
Lumped vs distributed can change resonance behaviour
Skin effect
High near resonance
Affects damping and peak amplitude
Earth resistivity
High for zero sequence
Important for unbalanced studies
Cascading section length
Medium to high
Determines usable frequency range
Transposition modelling
Medium to high
Important for phase imbalance and resonance
Inter-circuit coupling
Medium to high
Important for parallel circuits
Average conductor height
Low to medium
Usually minor within typical variation
Shunt compensation
High
Can shift resonance significantly
The practical message: model type, skin effect, compensation and zero-sequence modelling usually matter most.
Model selection guide
Table 8 — Selecting an overhead-line model for harmonic studies.
Study Case
Recommended Model
Short line, low harmonic order, screening only
Lumped nominal-π may be acceptable
Long line, resonance assessment
Distributed equivalent-π
Filter design
Distributed equivalent-π, frequency dependent
Compliance study with small margin
Distributed equivalent-π, frequency dependent
Unbalanced harmonic propagation
Multi-phase distributed model
Triplen or zero-sequence harmonic study
Multi-phase model with accurate zero sequence
Telephone interference
Multi-phase model with earth return and coupling
Parallel double-circuit line
Coupled multi-phase model
Transposed line at harmonic frequencies
Cascaded homogeneous sections
Harmonic profile along the line
Cascaded sections or distributed model with internal points
Minimum data for a defensible line model
Because overhead-line modelling depends heavily on data quality, a harmonic overhead-line model should state:
line length;
conductor type and conductor resistance;
conductor radius or GMR;
phase spacing and physical geometry;
earth-wire or shield-wire details;
transposition arrangement;
number of circuits and inter-circuit spacing;
shunt compensation connected to the line;
assumed soil resistivity where zero-sequence or earth-return behaviour is relevant;
selected model type — lumped, cascaded or distributed;
whether the model is balanced, unbalanced or fully multi-phase;
the frequency range and highest harmonic order assessed.
Section 11
Implementation in harmonic analysis software
In commercial harmonic analysis software such as DIgSILENT PowerFactory, overhead lines may be represented using available line models based on either lumped or distributed parameters. The software normally applies frequency dependency to line elements and associated compensation based on their physical behaviour, and — as shown in Section 6 — the frequency dependency of resistance and inductance is applied through frequency characteristics on the Power Quality/Harmonics page.
For line shunt compensation, the inductive and capacitive scaling rules are applied directly. For a shunt reactor the imaginary part of the impedance scales with order; for a shunt capacitor the imaginary part of the admittance scales with order:
For zero-sequence mutual reactance, a simplified harmonic scaling may be applied as \(X_{0m}(h)=h\,X_{0m}(1)\). These rules are consistent with the fundamental frequency dependence of inductive and capacitive elements. However, the engineer should still understand the underlying assumptions: software automation does not remove the need to choose the correct model type, frequency range, phase representation and input data.
Section 12
Reporting and summary
A harmonic study report should not simply state that “overhead lines were modelled” — it should state how they were modelled. A clear statement makes the approach transparent and technically defensible.
Examples of a clear modelling statement
“Overhead lines were represented using frequency-dependent distributed-parameter models, including conductor skin effect, shunt capacitance and line compensation.”
“A multi-phase representation was used to capture phase asymmetry, transposition sections, zero-sequence behaviour and inter-circuit coupling where applicable.”
“Short lines were represented using lumped nominal-π models; this approximation is acceptable for the assessed frequency range because the line lengths are short relative to the harmonic wavelengths considered.”
Common modelling mistakes
Using a 50 Hz line model without checking its validity at harmonic frequencies.
Using a single lumped line section for a long line or a high harmonic order.
Ignoring shunt capacitance in resonance studies.
Ignoring earth-return effects when zero-sequence or triplen harmonics are relevant.
Averaging transposed sections when phase-specific resonance is important.
Ignoring inter-circuit coupling on double-circuit or parallel routes.
Not stating the frequency range over which the line model is valid.
To summarise: overhead-line modelling is a critical part of harmonic studies because line impedance and admittance are frequency dependent, and the chosen model can significantly affect calculated resonance frequencies, harmonic impedance peaks, harmonic voltage distortion and filter performance. Lines may be represented using lumped nominal-π models, cascaded nominal-π sections, or distributed equivalent-π models. The lumped model may be acceptable for short lines and low harmonic orders, but cannot accurately represent long-line effects or multiple resonance points; for detailed studies, frequency-dependent distributed-parameter models should normally be used.
The most important modelling aspects are frequency dependency, skin effect, earth-return and zero-sequence impedance, line shunt capacitance, line shunt compensation, transposition, inter-circuit coupling and the balanced or unbalanced representation. For shunt reactors the imaginary part of the impedance increases with order, \(\operatorname{Im}(Z_L(h))=h\operatorname{Im}(Z_L(1))\); for shunt capacitors the imaginary part of the admittance increases with order, \(\operatorname{Im}(Y_C(h))=h\operatorname{Im}(Y_C(1))\); and zero-sequence mutual reactance may use the simplified scaling \(X_{0m}(h)=hX_{0m}(1)\), although detailed frequency-dependent modelling is preferred where zero-sequence or unbalanced behaviour is important.
In short: overhead-line modelling affects resonance frequency, impedance-peak magnitude, harmonic voltage distortion and filter performance. For short lines and low harmonic orders, a lumped nominal-π model may be acceptable. For long lines, high harmonic orders, resonance studies, phase-specific results or inter-circuit coupling, a frequency-dependent distributed multi-phase model is normally preferred. A clear report should then state:
the line model type (lumped, cascaded or distributed);
the frequency-dependency assumptions;
the treatment of skin effect;
earth-return and zero-sequence impedance modelling;
transposition and inter-circuit coupling;
line shunt compensation;
whether the model is balanced or unbalanced.
Key message
Use the simplest line model that is valid for the frequency range and study objective — but for resonance, filter design, compliance studies and unbalanced propagation, use frequency-dependent distributed multi-phase modelling wherever possible. A robust study should clearly state the line model type, frequency dependency, skin-effect treatment, earth-resistivity assumptions, zero-sequence modelling, line compensation, transposition, inter-circuit coupling and the balanced or unbalanced representation. Only then can the harmonic impedance and distortion results be interpreted correctly.
Multi-Part Technical Series
Harmonic Studies in Power Systems
A practical series on how harmonic studies are set up and solved — from choosing the modelling domain, through frequency scan, harmonic penetration and balanced versus unbalanced modelling, to time, hybrid and harmonic-domain methods.
02
02Part TwoReading now
Overhead Line Modelling for Harmonic Studies
Lumped, cascaded and distributed line models; skin effect and frequency-dependent parameters; zero-sequence and earth-return impedance; shunt capacitance, compensation and multi-phase modelling.
