Harmonic Studies & Modelling

Load and Harmonic Source Modelling for Harmonic Studies

Loads shape a harmonic study in two ways: linear loads provide the damping that limits resonance peaks, while nonlinear loads inject the harmonic currents that create distortion. This page separates the two — passive impedance models for static, motor and aggregate loads, and harmonic current sources for converters and electronic loads — and covers balanced and unbalanced phase-correct spectra, reference current and phase angles, downstream capacitance and power-factor correction, background distortion, and the load uncertainty that usually dominates a harmonic study.

Reading time ≈ 28 min · Part Five of the series

Load modelling is one of the most important and uncertain parts of harmonic studies. Loads influence the harmonic response of the network in two different ways. First, loads provide damping, which can reduce the amplitude of resonance peaks and significantly reduce harmonic voltage distortion. Second, some loads are harmonic sources: nonlinear equipment such as rectifiers, drives, converters, data centres, EV chargers, PV inverters and battery systems injects harmonic currents into the network.

Load modelling must therefore answer two separate questions — how does the load affect network impedance and damping? and what harmonic current does the load inject? These are different requirements: a passive impedance model represents damping and network response, while a current-source model represents harmonic emission. The practical distinction is that a linear load → an impedance model, and a nonlinear load → a harmonic current source. In many studies, both are required.

Key idea

Loads act on both sides of \(V_h=Z_hI_h\): linear loads change \(Z_h\) (damping), nonlinear loads supply \(I_h\) (emission).
Represent damping with passive impedance models; represent emission with harmonic current sources.
Aggregate loads are reduced distribution networks — include downstream transformer impedance and capacitance, not just MW/Mvar.
Load uncertainty often dominates harmonic-study uncertainty; the minimum-damping case can be worse than peak load.

Key terms used on this page

01Passive load impedance

The part of the load model that absorbs harmonic current and provides damping.

02Harmonic current source

A model that injects specified harmonic currents into the network.

03Linear load

A load that does not significantly create harmonics and is mainly represented by impedance.

04Nonlinear load

A load that draws distorted current and may inject harmonic currents.

05Damping

The loss effect that reduces the height of harmonic resonance peaks.

06Aggregate load

A combined representation of many smaller loads.

07Reference current

The base current used to express harmonic-current percentages.

08Background distortion

Harmonic voltage distortion already present in the network before the new project or load is connected.

09Phase-correct spectrum

A harmonic spectrum that includes both magnitude and phase angle, not magnitude only.

Section 1

The two roles of loads

In harmonic studies a load can have two different roles. First, it can behave as a passive impedance that provides damping and changes the network harmonic impedance. Second, it can behave as a harmonic source that injects distorted current. These two roles should not be mixed without explanation, because the same load may reduce resonance in one part of the study and create harmonic distortion in another.

The harmonic voltage at a bus is governed by the familiar relationship, and loads affect both sides of it:

\[ V_h=Z_h\,I_h \]

\(V_h\): harmonic voltage at harmonic order \(h\)
\(Z_h\): network harmonic impedance seen by the source at order \(h\)
\(I_h\): harmonic current injected at order \(h\)

This equation explains why both the source spectrum and the network impedance are required: a small harmonic current can cause high voltage distortion if the network impedance is high at that harmonic order.

A passive load affects \(Z_h\) because it changes the equivalent network impedance and damping. A nonlinear load affects \(I_h\) because it injects harmonic current. If the passive load is neglected, the study may overestimate resonance peaks and produce pessimistic harmonic voltages; if the harmonic source is neglected, it may underestimate the emission; and if the load is represented incorrectly, the resonance frequency, damping and distortion may all be wrong. Load modelling is not a secondary detail — it can control the difference between a realistic result and a misleading one.

Section 2

Linear and nonlinear loads

A linear load draws a sinusoidal current from a sinusoidal voltage — resistive heating, incandescent lighting, conventional passive loads and motors around a linear operating point. A nonlinear load draws a non-sinusoidal current even from a sinusoidal voltage — rectifiers, variable-speed drives, switch-mode supplies, LED drivers, PV inverters, battery converters and EV chargers. The distinction matters because the modelling approach differs.

Table 1 — Load types and their harmonic modelling role.

Load Type	Harmonic Modelling Role	Typical Representation
Static linear load	Provides damping	Resistance or admittance
Motor load	Frequency-dependent damping and inductive behaviour	R-L motor equivalent
Distribution load aggregate	Downstream network damping and resonance	Composite equivalent
Power electronic load	Injects harmonic current; may add nonlinear damping	Harmonic current source or detailed model
Active front-end converter	Behaviour depends on controls	Current source, Norton equivalent or time-domain model

A realistic harmonic study must separate the passive behaviour of the load from its emission behaviour.

Section 3

Passive impedance load models

Passive impedance models represent how loads affect harmonic impedance, and are normally derived from the fundamental-frequency load-flow result. At fundamental frequency, the load is known from its active power \(P\) and reactive power \(Q\). The equivalent resistance and parallel reactance may be estimated as:

\[ R=\frac{U^2}{P} \qquad\qquad X=\frac{U^2}{Q} \]

\(U\): nominal or operating voltage
\(P,\ Q\): active and reactive power of the load

Don't model loads as sources only

Do not model all loads only as harmonic current sources. If passive load impedance is omitted, network damping may be underestimated and resonance peaks may become unrealistically high. Conversely, do not model nonlinear loads only as passive impedance if their harmonic emission is relevant. A good model may need both components: an impedance branch for damping and a current-source spectrum for emission.

These provide a starting point but do not fully capture real load behaviour at harmonic frequencies, because damping changes with frequency and different load components behave differently. In short, \(P,Q\) at fundamental frequency is not a complete harmonic load model.

Inductive, capacitive and mixed representation

In software, a passive load may be represented as inductive (\(R+jhX_L\)), capacitive (\(G+jhB_C\)) or mixed. A mixed load is useful when the equivalent includes downstream cables, power-factor-correction capacitors, motors and static demand. The reactive parts scale with order, \(X_L(h)=hX_{L1}\) and \(B_C(h)=hB_{C1}\) (equivalently \(X_C(h)=X_{C1}/h\)). This frequency dependency matters because inductive and capacitive components can form resonance, so a mixed load may behave as a damping element + resonant element, not just a constant impedance.

Static load modelling

Static loads are often represented as resistive or R-L equivalents. The simplest model is a pure resistance \(R=U^2/P\), which provides damping and is often used where the motor fraction is small. A more general model uses series form \(Z=R+jhX\) or parallel form \(Y=G+jhB\); the parallel form is often more natural when the load is derived from \(P\) and \(Q\). Static models suit domestic, commercial and general distribution demand, but they are not universal — a distribution load may include lighting, heating, motors, electronic devices, cables and power-factor-correction equipment. They are useful approximations, not physical descriptions of every device.

Section 4

Motor load modelling

Motors matter because they provide damping and inductive behaviour, and their harmonic impedance is not the same as a simple static resistance. Induction motors are often represented using an equivalent resistance and reactance related to the locked-rotor or negative-sequence impedance:

\[ Z_m(h)=R_m(h)+jh\,X_m \]

\(Z_m(h)\): motor harmonic impedance at order \(h\)
\(R_m(h)\): frequency-dependent motor damping
\(X_m\): motor leakage reactance

Rotating machines can strongly affect resonance damping, especially near harmonic-emitting installations: more motor damping → lower harmonic resonance peak. A network with significant motor load may show much lower resonance peaks than the same network with loads neglected. However, motor modelling is uncertain because the actual number of motors, their loading, size distribution and operating condition are often unknown.

Section 5

Aggregate load modelling

In transmission-level studies it is usually impractical to model every downstream LV and MV load individually. Instead, the downstream network and its loads are represented as an aggregate harmonic load model that may include static load, motor load, power-factor-correction capacitors, distribution transformers, downstream cables and overhead lines, and an electronic-load component. The aggregate load is therefore not only a load — it is a reduced equivalent of a distribution network, which can introduce its own parallel and series resonance. If these downstream components are ignored, the transmission harmonic impedance may be calculated incorrectly. An aggregate model should capture the main downstream network characteristics, not just the active and reactive power demand.

Component-based and measurement-based models

There are two main ways to develop an aggregate model. A component-based (bottom-up) model is built from known or assumed load composition — the engineer estimates the proportion of static, motor, electronic load, capacitors and downstream impedance. A measurement-based (top-down) model is derived from measured frequency response, measured harmonics or system identification.

Table 2 — Component-based versus measurement-based aggregate models.

Approach	Main Advantage	Main Limitation
Component-based	Can be built before measurements exist	Requires assumptions on load composition
Measurement-based	Captures actual behaviour at the measured point	Valid only for the measured condition and location
Hybrid approach	Combines engineering knowledge and measurement	Requires both data and interpretation

In planning studies, component-based models are common because measurements may not exist; in existing systems, measurement-based models can give better confidence. CIGRE and IEEE load-model practice generally recognises that no single equivalent suits all studies — the correct model depends on load composition, voltage level, network topology, motor and electronic-load fractions, distribution capacitance, power-factor correction and the study objective. Use simple R or R-L models only when their limitations are acceptable, and composite models where downstream damping and resonance matter.

Section 6

Electronic loads and harmonic sources

Power electronic loads are difficult to represent with passive impedance alone: their behaviour depends on converter topology, control system, operating point, firing angle, switching frequency, DC-link behaviour and AC-system impedance.

Table 3 — Electronic loads and their harmonic behaviour.

Equipment	Harmonic Behaviour
Six-pulse diode rectifier	Characteristic harmonics \(6n\pm1\)
Twelve-pulse rectifier	Characteristic harmonics \(12n\pm1\)
Variable-speed drive	Spectrum depends on rectifier and DC link
Active front-end converter	Harmonics depend on PWM and control
EV charger	Depends on charger topology and operating point
PV inverter	Spectrum depends on control and grid impedance
Data-centre power supplies	Aggregated nonlinear current injection

For frequency-domain studies these nonlinear loads are usually represented as harmonic current sources injecting a defined spectrum \(I_5,\ I_7,\ I_{11},\ I_{13},\ \ldots\), which the network converts into harmonic voltages through \(V_h=Z_hI_h\).

Section 7

Harmonic current source modelling

A harmonic current source represents the emission from a nonlinear load, usually defined by magnitude and phase angle at each harmonic order:

\[ i(t)=I_1\sin(\omega t+\phi_1)+\sum_{h=2}^{H}I_h\sin(h\omega t+\phi_h) \qquad\Longrightarrow\qquad I_h=|I_h|\angle\phi_h \]

\(I_1\): fundamental current
\(I_h,\ |I_h|\): harmonic current phasor and its RMS magnitude at order \(h\)
\(\phi_h\): phase angle of the harmonic current at order \(h\)
\(h\): harmonic order

A harmonic source should ideally be defined using both magnitude and phase angle, because phase angles determine whether harmonic contributions from different sources add or cancel.

In a frequency-domain model the waveform itself is not simulated — the harmonic current phasors \(I_h\angle\phi_h\) are injected into the network at each order. The practical input is therefore a table of \(h\), \(|I_h|\) and \(\phi_h\).

Current notation used on this page

\(I_h\) is the RMS harmonic current at order \(h\); \(|I_h|\) its magnitude; \(\phi_h\) its phase angle. \(I_1\) is the RMS fundamental current and \(I_{rated}\) the rated current of the equipment. Note that \(I_1\) (and \(I_0,\ I_2\)) can also mean the positive- (zero-, negative-) sequence current in sequence-component notation. To avoid confusion, this page uses \(I_1\) for fundamental current; where a sequence current at a harmonic order is meant, it is written \(I_{1,h}\) (positive-sequence current at order \(h\)).

Section 8

Balanced phase-correct harmonic sources

A balanced phase-correct source is used when the harmonic source is assumed balanced across the three phases and the phase relationship of harmonic currents is correctly represented — commonly for ideal or symmetrical three-phase converters. For a six-pulse converter the characteristic harmonics are \(h=6n\pm1\), giving 5, 7, 11, 13, 17, 19, …, with an idealised magnitude that decreases with order:

\[ I_h \approx \frac{I_1}{h} \]

\(I_h\): characteristic harmonic current at order \(h\)
\(I_1\): fundamental current

This is why a six-pulse spectrum table has large 5th and 7th components and progressively smaller higher orders. Figure 1 shows such a spectrum defined in software for a 6-pulse bridge: each row gives the harmonic current as a percentage of the fundamental (\(I_h/I_1\)) and the phase angle (\(\varphi_h-h\varphi_1\)). In practice the actual spectrum depends on commutation overlap, DC-link smoothing, converter loading and supply impedance.

PowerFactory Harmonic Sources dialog for a 6-pulse bridge (B6) harmonic current spectrum, set to Balanced, Phase Correct, listing I_h/I_1 percentage and phase angle for harmonic orders 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35 and 37. — **Figure 1 —** A balanced phase-correct harmonic current spectrum for a six-pulse bridge, defined as a type object. The 5th harmonic is 20% of fundamental, the 7th 14.3%, the 11th 9.1%, and so on — the characteristic \(6n\pm1\) orders decreasing roughly as \(1/h\), each with its phase angle.

A balanced phase-correct source therefore represents a symmetrical three-phase harmonic injection — appropriate when the converter is balanced and the purpose is normal harmonic penetration analysis.

Section 9

Unbalanced and IEC harmonic sources

An unbalanced phase-correct source is used when the magnitude and phase angle of harmonic current differ between phases — required when the source is not symmetrical, as with single-phase nonlinear loads, unequal phase loading, unbalanced converter operation, single-phase traction or asymmetric feeders. Harmonic injection is then defined separately for each phase:

\[ I_{a,h}\angle\phi_{a,h}\,,\qquad I_{b,h}\angle\phi_{b,h}\,,\qquad I_{c,h}\angle\phi_{c,h} \]

This allows positive-, negative- and zero-sequence harmonic components to be represented — an unbalanced source needs a phase-domain model, which is more detailed but requires more input data. Triplen harmonics — multiples of three such as the 3rd, 9th and 15th — are particularly relevant here: in a balanced three-phase system they are zero-sequence quantities and can add in the neutral conductor instead of cancelling between phases, which is another reason unbalanced or phase-domain modelling may be required.

IEC 61000 representation

Some source models follow an IEC-style harmonic emission input, allowing odd, even and non-integer harmonics. This is useful where the spectrum is not limited to characteristic integer harmonics — non-integer components may arise from interharmonics, converter-control interaction, frequency conversion, modulation, arc-furnace behaviour or variable-speed-drive operation. An IEC-style source therefore represents a more general harmonic and interharmonic spectrum, useful when a measured or specified emission spectrum contains components outside the normal characteristic sequence.

Section 10

Reference current and phase angles

Harmonic current magnitudes may be defined relative to either the fundamental current or the rated current, and the distinction matters. Referred to the fundamental, \(|I_h|=k_h|I_1|\), the injection is load-dependent — if the load current falls, the harmonic current falls. Referred to rated current, \(|I_h|=k_h|I_{rated}|\), the injection is based on equipment rating, which can be more conservative or more appropriate when an emission limit is specified against rated current.

\[ |I_h|=k_h\,|I_1| \qquad\qquad |I_h|=k_h\,|I_{rated}| \]

\(k_h\): harmonic current magnitude (per unit or percent of the reference)
\(I_1,\ I_{rated}\): fundamental and rated reference currents

Equivalently, a harmonic spectrum is often given as a percentage of a reference current:

\[ I_h(\%)=\frac{|I_h|}{I_{ref}}\times 100 \]

\(I_h(\%)\): harmonic current at order \(h\), as a percentage
\(|I_h|\): RMS harmonic current magnitude at order \(h\)
\(I_{ref}\): reference current, normally \(I_1\) or \(I_{rated}\)

The report must state whether \(I_{ref}\) is the actual fundamental current, rated current, maximum-demand current or a manufacturer-defined reference. Otherwise the same harmonic percentage can represent very different absolute current values.

The report should always state which reference is used: referred to \(I_1\) gives a load-dependent harmonic current; referred to \(I_{rated}\) gives a rating-based harmonic current. A spectrum given as “20% 5th harmonic” is incomplete unless the reference is stated. If it is 20% of rated current, the absolute harmonic injection stays high even at low loading; if it is 20% of actual fundamental current, the injection falls as the load falls. This difference can significantly change minimum-load harmonic-distortion results.

Harmonic phase angles

The phase angle of each harmonic current matters because currents from different sources can add or cancel. For two sources at the same order, the combination is a phasor sum, not an arithmetic one:

\[ I_{h,total}=I_{h,1}+I_{h,2} \qquad\text{(phasor addition)} \]

In phase, they reinforce; in anti-phase, they partially cancel. The angle may be defined relative to the fundamental current angle or the bus voltage angle, depending on the software. Magnitude alone is not always sufficient — the phase angle affects total distortion when several sources share a network. Because phase angles are often uncertain in planning studies, sensitivity studies or conservative aggregation rules may be needed.

Characteristic and non-characteristic harmonics

Characteristic harmonics are expected from an ideal converter under balanced conditions. For a \(p\)-pulse converter, \(h=pn\pm1\) — so \(6n\pm1\) for six-pulse and \(12n\pm1\) for twelve-pulse. Non-characteristic harmonics arise from unbalance, control asymmetry, firing-angle error, background distortion, transformer asymmetry, non-ideal operation or unequal phase impedance. A source model should not always include only characteristic harmonics: if measurements or manufacturer data show non-characteristic components, include them. An ideal characteristic spectrum suits screening; a measured or manufacturer spectrum suits detailed assessment.

Section 11

Composite load models

When modelling aggregate loads, the load transformer is important: it represents the impedance between the network bus and the downstream load, and lets the model represent downstream impedance, voltage-level transfer, the zero-sequence path, damping separation and distribution-network resonance. A composite load model may include HV capacitance, load-transformer reactance, LV capacitance, static resistance, a motor equivalent and a harmonic current source — much more realistic than a simple resistance connected directly at the transmission bus. A load should often be connected through a downstream impedance, especially when representing distribution networks from an HV or EHV bus.

Static and dynamic portions

Some models split the load into static and dynamic portions. The static portion (heating, lighting, resistive demand) mainly provides resistive damping; the dynamic portion (motors, rotating equipment) provides inductive behaviour and motor damping. The split varies with season, time of day, industrial process, weather and load level, so harmonic studies often need several load cases — peak load, light load, summer, winter, maximum motor load and minimum-damping conditions. The worst harmonic case is not always peak load: light-load conditions can give higher harmonic impedance because damping is lower.

Power-factor correction and LV capacitance

Power-factor-correction capacitors and downstream cable capacitance are very important in aggregate models because they can introduce resonance into the load equivalent. A composite model may include an LV capacitance \(C_{LV}\) and an HV capacitance \(C_{HV}\) representing power-factor correction, downstream cable capacitance and distribution capacitance. The capacitive admittance grows with order, \(Y_C(h)=jh\omega_1 C\), so its influence increases with harmonic order. If downstream capacitors are ignored, the model may miss an important resonance — where harmonic resonance matters, do not represent distribution load only as MW and Mvar.

Section 12

Background distortion, damping and cases

Background distortion is the harmonic voltage already present in the network before the studied load is connected. It may come from other customers, upstream network distortion, existing converters, capacitor banks or resonance conditions. For compliance studies, the report should state whether the results include only the new customer contribution, only the background distortion, or the combined distortion — grid-code assessments often distinguish the existing distortion from the incremental contribution. The total is a phasor (and statistical) problem rather than a simple sum:

\[ V_{h,total}=V_{h,background}+V_{h,new}\,,\qquad V_{h,new}=Z_h\,I_{h,new} \]

\(V_{h,total}\): combined harmonic voltage at order \(h\)
\(V_{h,background}\): pre-existing harmonic voltage at order \(h\)
\(V_{h,new}\): harmonic voltage contribution caused by the new load or source

This addition should be done as a phasor calculation where phase angles are available. If phase angles are unknown, the study should clearly state the adopted summation method — arithmetic addition, vector addition, a diversity factor, or a standard-specific summation rule.

So a site with moderate new emission may still fail an objective if background distortion is already high.

Damping and resonance

In harmonic studies the worst case is not always maximum demand. Maximum demand may include more connected load and therefore more damping, while a lighter-load condition may have less damping, so the network impedance peak can become higher. This is why minimum-load, maximum-capacitor and low-damping cases are often important in harmonic compliance studies. The resonance peak is, conceptually, inversely proportional to the damping:

\[ Z_{peak}\propto\frac{1}{R_{\text{damping}}} \]

\(Z_{peak}\): approximate impedance magnitude at resonance
\(R_{\text{damping}}\): effective resistance or loss component providing damping
\(\propto\): “is proportional to”

This is a conceptual relationship only. It is included to show that lower damping can produce higher resonance peaks.

Load damping is one of the main reasons for including loads: at resonance a network may show a high impedance peak, and load damping reduces it — no load damping → high peak; realistic damping → lower peak. But different models give very different damping: a simple resistive model may overestimate it, neglecting loads may underestimate it, and unrealistic capacitive components may introduce artificial resonance. Load-model uncertainty should be treated as study uncertainty and tested with sensitivity studies.

Load proximity, demand level and season

The location of damping relative to the source matters: a load close to the point of injection provides strong damping, while an electrically distant load has much less effect. Studies for wind farms, HVDC stations, SVCs, industrial converters or data centres should therefore include where load is connected relative to the source and resonance path, not just the total system load. Load composition also changes with time — peak load brings more resistive and motor damping, light load less damping (though some capacitors remain connected), winter favours heating and lighting, summer favours air-conditioning and motors. The harmonic impedance should be checked under several realistic cases, and the minimum-damping case may be more severe than the maximum-load case.

Fault contribution and current components

Some software load models include several internal components, such as passive impedance, harmonic-source injection and a short-circuit (fault-contribution) impedance. In harmonic studies it is important to check which components are actually active: otherwise the model may unintentionally include both a damping path and a source injection, or may double-count part of the load response. The exact behaviour depends on the software — the same load element may act as both impedance and source.

Software modelling check

For each load element, confirm whether the harmonic calculation uses:

the load as a constant impedance;
the load as a constant current;
a motor equivalent;
a harmonic source spectrum;
a power-factor-correction capacitor;
a downstream transformer;
a short-circuit impedance component;
background voltage distortion.

Confirming this prevents hidden modelling assumptions.

Section 13

Choosing the model

The choice depends on what the load represents. Use an impedance model to represent passive damping, downstream network impedance, static and motor load, power-factor correction and load-transformer impedance. Use a current-source model to represent harmonic emission, nonlinear load injection, converter current spectrum, or a measured or manufacturer harmonic spectrum. In many cases both are needed — passive load impedance plus a harmonic current source — representing both damping and emission.

Table 4 — Recommended load representation for harmonic studies.

Load Type	Recommended Representation	Main Reason
Static linear load	Passive impedance	Provides damping
Induction motor load	Motor impedance or aggregate motor model	Affects damping and resonance
Electronic load / rectifier	Harmonic current source plus impedance	Injects harmonic currents and may provide some damping
Large converter load	Manufacturer harmonic source model	Spectrum depends on technology and operating point
Power-factor-correction load	Capacitor/reactor model plus load impedance	May create resonance
Mixed distribution load	Aggregate impedance plus source spectrum	Represents both damping and emission

Balanced vs unbalanced models

Balanced models are simpler and suit symmetrical three-phase conditions. As a practical rule, a balanced model is acceptable for early HV or transmission-level screening where the load is reasonably symmetrical and positive-sequence harmonic behaviour is the main concern. An unbalanced or phase-domain model should be used for distribution networks, data centres, commercial buildings, rail or EV-charging loads, significant single-phase loads, neutral-current assessment, or where phase-specific harmonic limits are checked. In short: balanced for screening, unbalanced for phase-specific and zero-sequence studies.

Section 14

Workflow and sensitivity

A practical workflow for load and harmonic source modelling is as follows:

Define the study objective — resonance screening, harmonic compliance, filter design, equipment duty or connection assessment.
Decide whether each load is a passive impedance, a harmonic current source, or a combination.
Define the load composition — static, motor, electronic, capacitive and downstream network.
Include distribution-transformer impedance and downstream capacitance where relevant.
Define harmonic source spectra as \(h\), \(|I_h|\) and \(\phi_h\).
Decide whether harmonic currents are referred to \(I_1\) or \(I_{rated}\).
Define balanced or unbalanced source representation.
Run sensitivity cases for demand level, motor fraction, electronic-load fraction, capacitor connection and source spectrum.

Table 5 — Relative sensitivity of harmonic results to load-modelling choices.

Parameter	Typical Impact	Reason
Load level	High	Controls damping
Load composition	High	Static, motor and electronic loads differ
Motor fraction	High	Affects damping and inductive behaviour
Downstream capacitance	High	Can introduce resonance
Load transformer impedance	High	Controls transfer from downstream network
Harmonic source spectrum	High	Directly affects injected current
Harmonic phase angles	Medium to high	Affects summation between sources
Current reference basis	Medium	Fundamental vs rated changes emission
Balanced / unbalanced	High where phase effects matter	Affects sequence propagation
Load proximity	High	Nearby loads provide more damping

Because load uncertainty can dominate harmonic-study uncertainty, sensitivity studies are normally required.

Recommended sensitivity cases

maximum demand;
minimum demand;
minimum damping;
maximum electronic-load fraction;
maximum motor-load fraction;
power-factor correction in service and out of service;
background distortion high and low cases;
harmonic source spectrum based on \(I_1\) and \(I_{rated}\), where uncertain;
balanced and unbalanced source representation, where relevant.

Section 15

Reporting and summary

A harmonic study report should clearly state how loads and harmonic sources were represented. A weak statement — “loads were included in the model” — tells the reader nothing.

Examples of a clear modelling statement

“Linear loads were represented as passive frequency-dependent impedance models to provide harmonic damping, while nonlinear loads were represented as harmonic current sources with specified magnitude and phase-angle spectra.”

“The downstream distribution network was represented by an equivalent load transformer, static load, motor component and LV capacitance.”

“Harmonic current injections were defined as balanced phase-correct spectra referred to the fundamental current” — or — “as unbalanced phase-wise spectra referred to rated current.”

Common modelling mistakes

Using current-source models without defining the reference current.
Providing harmonic magnitudes without phase angles.
Ignoring passive load damping.
Assuming maximum demand is always the worst case.
Ignoring background distortion.
Adding background and new harmonic voltages arithmetically without stating the assumption.
Treating all loads as balanced in a distribution network.
Confusing \(I_1\) as fundamental current with \(I_1\) as positive-sequence current.
Forgetting to include power-factor-correction capacitors or downstream cable capacitance.
Not checking which components the software load model actually uses.

To summarise: loads affect both harmonic damping and harmonic emission. Linear loads are represented with impedance models that shape \(Z_h\); nonlinear loads with harmonic current sources that define \(I_h\); and the harmonic voltage follows \(V_h=Z_hI_h\). Both the passive model and the source model matter. Simple models may suffice for screening, but detailed studies may need composite aggregate models including static load, motor load, load-transformer impedance, power-factor correction, downstream cable capacitance and electronic-load harmonic sources. For a current source, the engineer must define the harmonic order, current magnitude, phase angle, reference current, balanced or unbalanced representation, and a characteristic or measured spectrum.

In short: load modelling affects harmonic studies in two ways — passive load impedance provides damping, while nonlinear load components inject harmonic currents — and both effects may be needed in the same model. The report should also explain whether the worst case is driven by maximum harmonic injection, minimum damping, resonance conditions or background distortion; and where the load composition is uncertain, sensitivity studies should be used instead of relying on a single assumed load case. A robust study should then state:

the load composition;
the passive impedance model;
the harmonic source spectrum;
the reference current and phase angles;
the background-distortion treatment;
the balanced or unbalanced representation;
the operating cases assessed.

Key message

Use impedance models to represent damping, and current-source models to represent harmonic emission. A robust study should state the load-model type, load composition, static and motor fractions, downstream-network representation, capacitor/PFC representation, harmonic source spectrum, current reference basis, balanced or unbalanced assumption, and the sensitivity cases run. Only then can harmonic resonance, damping, distortion and compliance results be interpreted correctly.

Part Five Reading now

Load and Harmonic Source Modelling for Harmonic Studies

Passive impedance models for damping; static, motor and aggregate loads; harmonic current sources; balanced and unbalanced phase-correct spectra; reference current, phase angles and background distortion.

Series progress 5 of 11

Part Six

Synchronous Generator Modelling

Frequency-dependent generator impedance and damping; positive, negative and zero-sequence models; subtransient reactance; and impedance vs Thevenin source models.