Harmonic Studies & Modelling

Synchronous Generator Modelling for Harmonic Studies

A synchronous generator is a rotating machine, not a static inductor, so its harmonic impedance and damping are frequency dependent and behave closer to subtransient or negative-sequence values than to steady-state synchronous reactance. This page covers the generator harmonic impedance and the all-important frequency-dependent resistance that sets resonance damping; positive, negative and zero-sequence models with neutral grounding; the choice between impedance, Thevenin and ideal-source representations; operational inductance; and why the generator model matters most close to generation and at resonance.

Reading time ≈ 27 min · Part Six of the series

Synchronous generators can have an important influence on harmonic studies, especially when the point of assessment is electrically close to a large generator or when network resonance is shaped by generator impedance. Although generators are normally represented by standard positive-sequence models for load flow and short circuit, harmonic studies need more care because generator impedance and damping are frequency dependent.

The main role of a synchronous generator in harmonic analysis is to provide a harmonic impedance path, which affects the harmonic voltage produced by injections elsewhere in the system. The governing relationship is unchanged, and because the generator contributes to \(Z_h\), an incorrect generator impedance can make the calculated harmonic impedance, resonance damping and voltage distortion inaccurate.

Key idea

A generator's harmonic reactance is closer to subtransient or negative-sequence values — not steady-state synchronous reactance.
The frequency-dependent resistance sets the damping, so it controls the resonance-peak amplitude.
Reactance sets the resonance location; resistance sets its height — a useful diagnostic split.
The generator model matters most close to generation and at resonance; far away, lines, cables and loads dominate.

Key terms used on this page

01Synchronous generator

A rotating electrical machine whose rotor speed is synchronised with system frequency.

02Harmonic impedance

The impedance of the generator at a selected harmonic order.

03Subtransient reactance, \(X''\)

The short-time reactance associated with rapid field changes immediately after a disturbance.

04Negative-sequence reactance, \(X_2\)

The reactance seen by negative-sequence currents.

05Zero-sequence reactance, \(X_0\)

The reactance seen by zero-sequence currents, depending strongly on winding connection and grounding.

06Operational inductance

A frequency-dependent inductance derived from the generator dynamic model and time constants.

07Thevenin model

A source voltage behind an impedance.

08Passive impedance model

A model where the generator is represented only by its impedance, without internal harmonic voltage generation.

09Damping

The loss mechanism that limits the height of a harmonic resonance peak.

Section 1

Why generator modelling differs at harmonic frequencies

A synchronous generator is usually modelled as a frequency-dependent impedance in harmonic studies. Its reactance affects the location of resonance, while its resistance and rotor/damper losses affect resonance damping. So the selected generator model can change both the calculated resonance frequency and the height of harmonic impedance peaks — especially when the study point is electrically close to a power station.

A synchronous generator is a rotating electromagnetic machine, so its response to harmonic currents is not the same as a simple static inductor. When a harmonic current flows in the stator, the magnetic field it produces rotates at a speed different from the rotor. For a disturbance at frequency \(h\omega\), the machine response may involve components at \(h\omega\) and at coupled frequencies related to \((h\pm2)\omega\). A synchronous generator therefore cannot be represented with perfect accuracy by a single impedance at one frequency.

For many practical frequency-domain studies, however, the generator is simplified as a passive harmonic impedance:

\[ Z_{gen,h}=R_{gen,h}+jX_{gen,h} \]

\(Z_{gen,h}\): generator harmonic impedance at order \(h\)
\(R_{gen,h}\): frequency-dependent generator resistance
\(X_{gen,h}\): generator harmonic reactance

This representation is practical and widely used, but its limitations should be understood.

Section 2

Generator harmonic impedance

At harmonic frequencies, the rotating field created by stator harmonic currents rotates much faster than the rotor. The generator harmonic reactance is therefore commonly related to the negative-sequence reactance, or to the average of the direct- and quadrature-axis subtransient reactances:

\[ X_{gen,h}=hX_2 \qquad\text{or}\qquad X_{gen,h}=h\,\frac{X_d''+X_q''}{2} \]

\(X_{gen,h}\): generator reactance at harmonic order \(h\)
\(h=\dfrac{f}{f_{nom}}\): harmonic order; \(f\) harmonic frequency, \(f_{nom}\) nominal frequency (normally 50 Hz)
\(X_2\): negative-sequence reactance
\(X_d'',\ X_q''\): direct- and quadrature-axis subtransient reactances

This is an approximation, not a universal generator model: it works because the harmonic rotating field interacts with the machine in a way closer to subtransient or negative-sequence behaviour. Where accuracy near the machine matters, use frequency-dependent or operational-inductance models instead.

Notation: the double-prime means “subtransient”

The double-prime symbol (\(''\)) means subtransient — not a second derivative. So \(X_d''\) and \(X_q''\) are the direct- and quadrature-axis subtransient reactances, and \(L_d''\), \(L_q''\) are the matching subtransient inductances. The average subtransient inductance is often written \(L''=\tfrac{1}{2}(L_d''+L_q'')\). (This page does not use \(I''\); where short-circuit current is meant elsewhere it would be written \(I_k''\), the initial symmetrical short-circuit current.)

The reactance normally increases with frequency (\(h\uparrow \Rightarrow X_{gen,h}\uparrow\)). The resistance also changes with frequency, but is harder to estimate — and it is the resistance that controls harmonic damping. Figure 1 shows how a synchronous machine's inductance and reactance vary across the frequency range: both are roughly constant away from the fundamental, but rise sharply to a pole at the rotor (synchronous) frequency, before settling to subtransient-like values at higher orders.

Synchronous machine inductance (red solid) and reactance (blue dashed) versus frequency from 0 to 100 Hz, both nearly constant away from 50 Hz, rising to a sharp pole at the 50 Hz synchronous frequency; annotations mark the synchronous (l, x), transient (l', x') and subtransient (l'', x'') values. — **Figure 1 —** Synchronous machine inductance (red, solid) and reactance (blue, dashed) versus frequency. The sharp pole at the synchronous frequency separates the steady-state values (*l, x*) from the transient (*l′, x′*) and subtransient (*l″, x″*) values used for harmonic impedance.

Section 3

Frequency-dependent resistance

The generator resistance at harmonic frequencies is not equal to the stator resistance at fundamental frequency. It increases with frequency because of skin effect, damper-winding effects, rotor losses and additional electromagnetic losses. A typical empirical form scales the negative-sequence resistance by an exponent:

\[ R_h=h^{\alpha}\,R_2 \]

\(R_h\): generator resistance at harmonic order \(h\)
\(R_2\): negative-sequence resistance at fundamental (or specified reference) frequency
\(\alpha\): empirical exponent representing frequency-dependent losses
\(h\): harmonic order

The resistance model mainly controls the height of a resonance peak; the reactance model mainly controls the frequency at which the resonance occurs.

The exponent depends on the machine design and available data: a lower value gives less damping, a higher value more (\(\alpha\uparrow \Rightarrow R_h\uparrow \Rightarrow\) more damping). At resonance, this can significantly reduce the harmonic impedance peak — so the generator resistance model controls the resonance-peak amplitude.

Section 4

Sequence representation

For harmonic studies the generator may be represented in positive, negative and zero sequence. The positive- and negative-sequence impedances are frequency-dependent series R-L branches; the zero-sequence impedance also includes the neutral grounding path. In harmonic-order notation:

\[ Z_1(h)=R_{str}(h)+jhL_1(h) \qquad Z_2(h)=R_2(h)+jhL_2(h) \] \[ Z_0(h)=R_0(h)+3R_e+jhL_0(h)+jh\,3L_e \]

\(Z_1(h),\ Z_2(h),\ Z_0(h)\): positive-, negative- and zero-sequence generator impedance at order \(h\)
\(R_{str}(h)\): stator (positive-sequence) resistance at order \(h\)
\(R_2(h),\ R_0(h)\): negative- and zero-sequence resistance at order \(h\)
\(L_1(h),\ L_2(h),\ L_0(h)\): positive-, negative- and zero-sequence inductance at order \(h\)
\(R_e,\ L_e\): neutral grounding resistance and inductance
\(3R_e,\ 3L_e\): grounding terms in the zero-sequence path (see below)

Notation: the subscripts 0, 1 and 2 refer to sequence components, not harmonic order — harmonic order is always shown by \(h\). For example, \(Z_0(5)\) means the zero-sequence impedance at the 5th harmonic.

The neutral grounding impedance appears as \(3Z_e\) in the zero-sequence network because the zero-sequence current is the same in all three phases. The neutral current is therefore three times the zero-sequence phase current, so the voltage drop across the grounding impedance is represented as \(3Z_e\) in the per-phase zero-sequence equivalent circuit. The zero-sequence generator impedance therefore depends strongly on neutral grounding — for triplen harmonics or unbalanced studies, the grounding arrangement must be represented correctly. Figure 2 shows the three sequence networks as passive frequency-dependent impedances.

Three sequence-domain impedance circuits for a synchronous generator. Positive sequence: R_str(f) and omega L_1(f) in series. Negative sequence: R_2(f) and omega L_2(f). Zero sequence: R_0(f)+3 R_e and omega L_0(f)+omega 3 L_e, each as a series resistance and inductance between two terminals. — **Figure 2 —** Passive sequence-domain harmonic impedance of a synchronous generator. Each network is a frequency-dependent series resistance (white) and inductance (black); the zero-sequence branch adds the grounding terms `3·R_e` and `ω·3·L_e`.

The positive-sequence model is used for balanced harmonic propagation. The negative-sequence model is important because many harmonic components interact with the machine in a way that resembles negative-sequence behaviour. The zero-sequence model matters for triplen harmonics, neutral current, grounding impedance, unbalanced sources and phase-domain propagation. Where the generator is treated as a source rather than a passive element, the same networks carry an internal harmonic voltage source behind the impedance, as in Figure 3.

The same three sequence circuits for a synchronous generator but each including a harmonic voltage source in series, labelled U_1(f), U_2(f) and U_0(f) for the positive, negative and zero-sequence networks respectively. — **Figure 3 —** Sequence-domain representation with an internal harmonic voltage source `U₁(f)`, `U₂(f)`, `U₀(f)` behind the frequency-dependent impedance — the Thevenin-style form used when the generator is modelled as a harmonic source.

A balanced harmonic penetration study may use only the positive-sequence model; an unbalanced phase-domain study should include positive, negative and zero sequence, or an equivalent phase-domain machine representation.

Section 5

Impedance, Thevenin and ideal-source models

The impedance model represents the generator as a passive impedance \(Z_{gen}(h)=R(h)+jX(h)\) at each harmonic frequency. It answers “what impedance does the generator present at this frequency?” and is normally used for frequency scans, resonance screening, network harmonic impedance calculation and passive damping assessment. It does not represent the generator as an active source — only its passive response.

The Thevenin equivalent adds an internal harmonic voltage source behind the series impedance — conceptually \(E_h\angle\phi_h\) behind \(Z_{gen,h}\) (Figure 3). It is useful when the generator is treated as a source of harmonic voltage, and answers “what harmonic voltage does the generator impose through its internal impedance?” The ideal voltage source represents the generator as a voltage source with negligible internal harmonic impedance — suitable only where the terminal is genuinely stiff or the source behaviour is imposed directly, and unsuitable for resonance and damping studies because it omits the frequency-dependent impedance.

Table 1 — Synchronous generator representations for harmonic studies.

Model	Use When	Main Limitation
Passive impedance model	Generator acts mainly as network impedance and damping source	Does not represent harmonic voltage emission
Thevenin source behind impedance	Generator harmonic-voltage-source behaviour is relevant	Requires source voltage spectrum and phase data
Ideal voltage source	Only for justified stiff-source assumptions	Can unrealistically suppress harmonic voltage distortion
Frequency-dependent sequence model	Generator is close to the assessment point or affects resonance	Requires data or assumptions for \(R(f)\), \(X(f)\), \(Z_1\), \(Z_2\), \(Z_0\)
Operational inductance model	Subsynchronous or near-nominal-frequency behaviour matters	More complex and requires machine dynamic data

For most resonance-screening studies the passive impedance model is the most important representation; use the Thevenin model when harmonic-voltage-source behaviour is required, and the ideal source only when the assumption is justified.

Section 6

Frequency dependency and standard parameters

Machine reactances are defined at fundamental frequency. At harmonic frequency the reactance changes because \(X=\omega L\) and \(\omega=h\omega_{nom}\), so a general impedance form combines automatic frequency scaling with any actual frequency dependency of the parameters:

\[ Z(h)=R(h)+jh\,\omega_{nom}L(h) \qquad\Longleftrightarrow\qquad Z(h)=R(h)+jhX_L(h) \]

\(Z(h)\): generator impedance at harmonic order \(h\)
\(R(h)\): generator resistance at order \(h\)
\(L(h)\): generator inductance at order \(h\) (henries)
\(X_L(h)\): inductive reactance expressed on the nominal-frequency base
\(\omega_{nom}\): nominal angular frequency, \(2\pi f_{nom}\)
\(h\): harmonic order

Writing \(\omega_{nom}L(h)\) (or \(X_L(h)\)) keeps the units explicit and avoids confusion between inductance in henries and reactance in ohms or per unit. If \(L(h)\) is already expressed in reactance units at nominal frequency, the second form applies directly.

There are two separate effects: the frequency scaling of \(\omega L\) (automatic for an inductor) and the actual frequency dependency of \(L(f)\) (which needs a frequency-dependent characteristic or a more detailed model). Using standard parameters, the harmonic inductance is commonly approximated from the average of the direct- and quadrature-axis subtransient inductances, \(L''=\tfrac{1}{2}(L_d''+L_q'')\), giving sequence impedances \(Z_1(h)=R_{str}(h)+jhL''(h)\), \(Z_2(h)=R_2(h)+jhL_2(h)\) and \(Z_0(h)=R_0(h)+jhL_0(h)\), with the grounding impedance \(Z_e(h)=R_e+jhL_e\) appearing as \(3Z_e(h)\) so that \(Z_{0,total}(h)=Z_0(h)+3Z_e(h)\). This is practical and widely used where detailed frequency-response data is unavailable.

Section 7

Operational inductance

Operational inductance is a frequency-dependent representation of the generator derived from its dynamic model. It is useful when the frequency range is close to the fundamental, when subsynchronous behaviour is important, or when the simple subtransient approximation is not adequate. For routine higher-order harmonic screening it is usually not necessary — so a reader who only needs resonance screening can treat the equations below as optional detail.

The more detailed representation uses frequency transfer functions or operational inductances, derived from the machine dynamic parameters — the transient and subtransient time constants. The axis operational inductances are:

\[ L_d(s)=L_d\frac{(1+sT_d')(1+sT_d'')}{(1+sT_{d0}')(1+sT_{d0}'')} \qquad L_q(s)=L_q\frac{(1+sT_q')(1+sT_q'')}{(1+sT_{q0}')(1+sT_{q0}'')} \]

\(L_d(s),\ L_q(s)\): direct- and quadrature-axis operational inductances
\(s=j\omega\): Laplace operator evaluated on the imaginary axis for frequency-domain analysis
\(T',\ T''\): short-circuit and open-circuit transient/subtransient time constants

The frequency-dependent inductances then give the sequence impedances, e.g. \(Z_1(h)=R_{str}(h)+jh\tfrac{1}{2}(L_{d1}(h)+L_{q1}(h))\), where \(L_{d1}(h)\) and \(L_{q1}(h)\) are the positive-sequence direct- and quadrature-axis operational inductances at order \(h\), and \(R_{str}(h)\) is the stator resistance at order \(h\) (including frequency-dependent effects where applicable). The direct axis and quadrature axis are the two magnetic axes of the synchronous machine; their average is used when a single scalar impedance is required. This approach is useful where the frequency range is close to nominal or where subsynchronous behaviour is important; for conventional higher-order harmonic studies the simpler subtransient or negative-sequence approximation is often adequate.

Section 8

Generator reactance

For many studies the generator reactance is approximated as \(X_{gen,h}=hX_2\) or \(X_{gen,h}=h\tfrac{1}{2}(X_d''+X_q'')\). This is appropriate because the harmonic rotating field interacts with the machine in a way that is closer to subtransient or negative-sequence behaviour than to steady-state synchronous reactance. The synchronous reactance \(X_d\) is normally far too large and not appropriate for harmonic impedance, whereas the subtransient reactance is more relevant because harmonic currents produce rapidly varying fields associated with damper and rotor current effects.

Practical warning

Do not use steady-state synchronous reactance \(X_d\) blindly in harmonic studies. Harmonic currents produce rapidly varying fields, so the generator response is usually closer to negative-sequence or subtransient behaviour. Using \(X_d\) may overestimate the generator reactance and shift the calculated harmonic response — use negative-sequence or subtransient-based values unless manufacturer data indicates otherwise.

Section 9

Resistance, damping and the peak

Generator resistance is more uncertain than reactance, and more important for damping. Different models may use \(R_h=h^{\alpha}R_2\), \(R_h=\sqrt{h}\,R_1\), or more detailed manufacturer-derived functions. Where the generator is electrically close to the assessment point, the selected model can significantly change the resonance peak: \(R_h\uparrow \Rightarrow Z_{peak}\downarrow\). This does not usually shift the resonance frequency much — it mainly changes the peak amplitude.

A useful diagnostic split

The generator resistance model controls the resonance peak magnitude; the generator reactance model controls the resonance location. When sensitivity results change peak height but not frequency, the difference is damping.

Section 10

Model selection and the effect of location

The selected model should depend on the study purpose and the available data. A simple impedance model may be adequate when the generator is electrically distant, resonance is not near the generator, only screening is required, or the study is dominated by lines, cables or loads. A more detailed frequency-dependent model should be used when the study point is close to the generator, parallel resonance is influenced by generator impedance, generator damping affects compliance, the harmonic source is near a power station, accurate resonance-peak magnitude is required, or subsynchronous behaviour matters. In short, model detail should increase when the generator controls the harmonic impedance.

The effect of generator modelling depends strongly on electrical distance. Close to a large generator, the resistance model can significantly change harmonic-impedance peaks; far from generation, the impedance is dominated by lines, cables, transformers and loads, and the generator model may have little impact. Sensitivity studies should therefore be run at representative nodes, especially near large synchronous generation. Differences between models are usually greatest at parallel resonance points, where the network impedance is high and damping is critical; away from resonance the differences are small. This gives the diagnostic rule that a change in peak amplitude but not frequency points to damping, while a change in resonance frequency points to reactance or network topology.

Section 11

Data, generator as source, and flicker

The best generator harmonic model is based on manufacturer data or measurement — \(R(f)\), \(X(f)\), \(L(f)\), \(Z_1(f)\), \(Z_2(f)\), \(Z_0(f)\) and the neutral grounding impedance. Where detailed data is unavailable, standard empirical models may be used, but the uncertainty should be recognised and sensitivity studies performed — especially when the assessment is close to a compliance limit or the mitigation design depends on resonance damping.

For most network harmonic-propagation studies, the generator should first be treated as an impedance, because its main role is to shape the network harmonic response. Treat it as a harmonic source only when there is evidence or a study requirement to represent generator-produced harmonic voltage — such as slot harmonics, saturation-related distortion or excitation-system effects.

Generators are usually treated as passive impedances, but they can also contribute harmonic voltage distortion through slot harmonics, winding distribution, magnetic saturation, unbalanced operation, or excitation and auxiliary systems. For most network propagation studies these are small compared with converter-based sources, but in special studies they may be represented — with the source voltage defined relative to the machine rated voltage. The distinction is simple: generator as impedance → passive damping and network response; generator as source → harmonic voltage emission. The representation should match the study objective.

Harmonic model ≠ flicker model

In some software the machine is represented differently for flicker than for harmonics — for flicker it may be treated as a constant current source in the positive-sequence system, independent of the harmonic model. Some flicker quantities therefore cannot be back-calculated from the harmonic equivalent circuit, and flicker results should not be interpreted using only the harmonic representation.

Recommended sensitivity cases

Where generator data is uncertain, test at least:

negative-sequence reactance model;
average subtransient reactance model;
low-resistance damping case;
high-resistance damping case;
grounded and ungrounded zero-sequence assumptions, where applicable;
generator in-service and out-of-service cases.

Section 12

Workflow and sensitivity

A practical workflow for synchronous generator modelling in harmonic studies is as follows:

Define the study objective — frequency scan, harmonic load flow, resonance damping, generator harmonic emission, or subsynchronous behaviour.
Choose the model type — impedance model, Thevenin equivalent, or ideal voltage source.
Define the sequence representation — \(Z_1(h)\), \(Z_2(h)\), \(Z_0(h)\).
Include grounding impedance where zero sequence is relevant — \(Z_{0,total}=Z_0+3Z_e\).
Define the frequency dependency of resistance and reactance — \(Z(h)=R(h)+jhL(h)\).
Use manufacturer or measured frequency-dependent data where available.
Perform sensitivity studies for the generator resistance model and damping.
Compare results at nodes close to and far from generation to gauge the importance of the model.

Table 2 — Relative sensitivity of harmonic results to generator modelling choices.

Parameter	Typical Impact	Comment
Frequency-dependent resistance	High near resonance	Controls damping and peak amplitude
Negative-sequence reactance	High	Common basis for harmonic reactance
Subtransient reactance	High	Alternative basis for harmonic reactance
Resistance exponent \(\alpha\)	High	Changes damping significantly
Grounding impedance	High for zero sequence	Affects triplen and unbalanced harmonics
Generator electrical distance	High	Determines whether the model matters at the node
Operational inductance data	Medium to high near nominal	Useful for subsynchronous studies
Harmonic voltage source data	Case-specific	Needed only if generator emission is modelled
Load and transformer proximity	Medium to high	May dominate or mask the generator effect

The practical message: generator model uncertainty matters most near resonance and near generation.

Minimum data for a defensible generator model

A synchronous generator harmonic model should state:

generator rating and voltage level;
rated frequency;
grounding arrangement and neutral grounding impedance;
\(X_d''\), \(X_q''\), \(X_2\) and \(X_0\), where available;
\(R_1\), \(R_2\), \(R_0\), or the assumed resistance model;
the selected frequency-dependent resistance assumption;
the selected reactance model: negative-sequence, subtransient average, operational inductance, or manufacturer-derived;
whether the generator is modelled as passive impedance, Thevenin source or ideal source;
whether harmonic voltage emission is included;
frequency range and highest harmonic order;
sensitivity cases where damping or compliance is important.

Section 13

Reporting and summary

A harmonic study report should clearly state how synchronous generators were represented. A weak statement — “synchronous generators were included” — tells the reader nothing.

Examples of a clear modelling statement

“Synchronous generators were represented as passive frequency-dependent harmonic impedances based on negative-sequence or subtransient reactance; generator resistance was modelled as frequency dependent to represent harmonic damping.”

“Zero-sequence generator impedance and neutral grounding impedance were included in the model.”

“The generator was represented using a Thevenin equivalent where harmonic-voltage-source behaviour was required, and alternative resistance–frequency characteristics were tested to assess the effect of damping on resonance-peak magnitude.”

Common modelling mistakes

Using synchronous reactance \(X_d\) instead of subtransient or negative-sequence reactance.
Using 50 Hz stator resistance without frequency-dependent correction.
Ignoring generator damping when the study point is close to a power station.
Ignoring neutral grounding impedance in zero-sequence studies.
Confusing sequence subscripts 0, 1 and 2 with harmonic order.
Treating the generator as an ideal voltage source without justification.
Ignoring generator harmonic voltage emission where slot harmonics, saturation or excitation effects are relevant.
Not performing sensitivity studies when manufacturer frequency-response data is unavailable.

To summarise: synchronous generators influence harmonic studies through frequency-dependent impedance and damping, most importantly at parallel resonance and at nodes close to large generation. A generator may be represented as \(Z_{gen,h}=R_{gen,h}+jX_{gen,h}\), with reactance based on negative-sequence or subtransient values (\(X_{gen,h}=hX_2\) or \(h\tfrac{1}{2}(X_d''+X_q'')\)) and a frequency-dependent resistance (\(R_h=h^{\alpha}R_2\)) that controls damping. For sequence studies, \(Z_1(h)=R_{str}(h)+jhL_1(h)\), \(Z_2(h)=R_2(h)+jhL_2(h)\) and \(Z_{0,total}(h)=R_0(h)+3R_e+jhL_0(h)+jh\,3L_e\), with the neutral grounding included where relevant. Use the impedance model for frequency scans, and a Thevenin or ideal-source model for harmonic load flow depending on whether the generator is a source.

In short: synchronous generator modelling affects harmonic resonance, damping and the propagation of harmonic distortion. For most steady-state harmonic studies the generator can be represented as a passive frequency-dependent impedance using negative-sequence or subtransient-based reactance; the resistance model is important because it controls resonance damping and therefore the height of impedance peaks. When the study point is close to a generator, or when compliance margins are small, the assumptions for \(R(f)\), \(X(f)\), \(Z_1(f)\), \(Z_2(f)\), \(Z_0(f)\) and neutral grounding should be stated clearly and tested through sensitivity studies. A Thevenin or harmonic-voltage-source representation should be used only when generator harmonic emission is part of the study objective. A clear report should then state:

the generator model type (passive impedance, Thevenin or ideal source);
the sequence representation;
the reactance basis (negative-sequence, subtransient or operational);
the resistance–frequency characteristic;
the neutral grounding impedance;
the harmonic-source assumption;
the sensitivity cases assessed.

Key message

Use a passive impedance model for resonance and damping studies, a Thevenin model when harmonic-voltage-source behaviour is required, and include frequency-dependent resistance wherever generator damping affects results. A robust study should state the generator model type, sequence representation, reactance basis, resistance–frequency characteristic, grounding impedance, harmonic-source assumption and sensitivity cases — only then can the effect of synchronous generators on harmonic impedance, resonance damping and propagation be interpreted correctly.

Part Six Reading now

Synchronous Generator Modelling for Harmonic Studies

Frequency-dependent generator harmonic impedance and damping; positive, negative and zero-sequence models with neutral grounding; subtransient reactance; impedance, Thevenin and ideal-source representations.

Series progress 6 of 11

Part Seven

Shunt, Series & Passive Filter Modelling

Lumped RLC modelling of shunt and series capacitors and reactors and passive filters; parallel resonance; detuning; filter tuning, damping and component duty.