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High-Frequency & Shaft Modelling

High-Frequency Transient and Mechanical Shaft Modelling of Synchronous Machines

The detailed dq0 machine model — field, dampers, saturation, equivalent-circuit parameters — is essential for fault, load-rejection, stability and excitation studies, but it does not represent two other things. It does not represent how a steep-front surge distributes inside the winding, between turns and to ground; and it does not, by itself, represent how the turbine-generator shaft twists when electrical torque contains oscillatory components. Those are different physics, answered by a high-frequency winding model and a multimass mechanical shaft model. This guide covers both, and when each is required.

Reading time ≈ 40 min · Winding surge models & torsional shaft models

Two electromagnetic questions must be separated: how does the machine appear from its terminals during a high-frequency surge? and how is the surge voltage distributed inside the winding, between turns, coils and ground insulation? A simple terminal equivalent can answer the first; only a detailed winding model answers the second. A third, mechanical question — how does the shaft respond when electrical torque contains oscillatory or subsynchronous components? — needs a multimass shaft model, not a winding model.

Abbreviations used on this page
EMTP®Electromagnetic Transients Program
EMTElectromagnetic transient
SSRSubsynchronous resonance
dq0Direct / quadrature / zero-sequence model
\(C\)Winding capacitance (turn / ground / slot)
\(J, K, D\)Inertia, shaft stiffness, damping
\(\Delta\omega, \delta\)Speed deviation, angular displacement
\(\sigma_i\)Modal decrement factor
log-decLogarithmic decrement (per-cycle decay)
Key idea
  1. A machine has no single universal model: dq0 for electromechanical behaviour, a high-frequency winding model for surge insulation stress, a multimass shaft model for torsional interaction.
  2. At steep fronts the voltage divides capacitively, not linearly — the line-end turns can take a disproportionate share, so an acceptable terminal voltage does not prove acceptable interturn stress.
  3. A terminal equivalent gives terminal voltage; internal stress needs a segmented (lumped or distributed) winding model with frequency-dependent parameters.
  4. A single-mass model gives centre-of-inertia motion; a multimass model gives shaft torsion — required for SSR, shaft torque and series-compensated networks.
Key terms used on this page
01Interturn voltage
The voltage stress between adjacent turns of a winding during a surge.
02Line-end coil
The first coil seen by an incoming surge; usually the most highly stressed.
03Terminal equivalent
A lumped model giving terminal voltage but not internal distribution.
04Distributed winding model
A multiconductor transmission-line model resolving wave propagation in the winding.
05Slot / overhang section
Coil parts inside the slot (near grounded iron) and in the end-winding region.
06Skin / proximity effect
Frequency-dependent crowding of conductor current toward the surface / toward neighbours.
07Multimass shaft
Turbine, generator and exciter rotors as separate inertias joined by elastic shafts.
08Torsional mode
A natural oscillation of the shaft with a characteristic frequency and mode shape.
09Mode shape
The relative angular displacement of each mass in a given torsional mode.
10Logarithmic decrement
ln of the ratio of successive oscillation peaks; the per-cycle fractional decay.

Section 1

Three modelling questions, three models

The dq0 model answers how the machine behaves as an electromechanical energy-conversion device. A high-frequency winding model answers how surge voltage is distributed through the physical winding insulation system. A multimass shaft model answers how the rotor train twists under oscillatory torque. All three are valid — they answer different questions — and the right one is chosen from the time scale and the physical output required. This guide treats the two specialised models in turn, then gives integrated guidance.

It assumes the low-frequency models built earlier in this series: frequency-range model selection, the per-unit equivalent circuits, the reactances and short-circuit response and magnetic saturation (the previous page). Rather than repeat that theory, this page goes beyond it to the two regimes the dq0 model does not cover.

Part One · High-Frequency Winding Models

Section 2

Why the low-frequency model is not enough

The conventional model — stator in dq0 form, field, dampers, saturation, rotor dynamics — is very effective for faults, voltage recovery, load rejection, synchronisation and subsynchronous resonance, where the internal electromagnetic and mechanical state matters. But fast-front and very-fast-front transients need a different representation: lightning surges reaching machine terminals, very steep switching surges, vacuum-breaker switching, current chopping, high-frequency reignition or restrike, motor-cable switching, surges travelling along connected cables, and steep-front stress on line-end coils. In these the first part of the transient is controlled by electromagnetic wave propagation and capacitive voltage distribution inside the winding — not by the dq0 equations. A dq0 model may correctly represent subtransient reactance, field response and damper effects yet say nothing about the voltage across the first few turns during a steep front.

Section 3

Sources of steep-front voltages

Lightning can send high-amplitude travelling waves into a plant that reach the machine through transformers, cables, busbars or connected equipment; direct terminal exposure is usually limited in well-protected generator installations but cannot be ignored in every layout. Switching can also produce steep fronts — vacuum breakers can interrupt high-frequency currents and reignite repeatedly or impose steep recovery voltages, and current chopping creates overvoltage when switching inductive loads. Cable-fed machines are particularly sensitive, because reflection between the cable and the machine terminal can magnify the terminal voltage. (Many practical steep-front winding-stress problems occur in large cable-fed AC motors; the same modelling principles apply to synchronous-machine windings.) The severity depends on the breaker technology, chopping level, reignition behaviour, cable length and surge impedance, machine terminal impedance, arresters and terminal capacitors, the winding and line-end-coil design, the earthing/shielding arrangement, and the operating condition at the switching instant.

Section 4

Voltage distribution along the winding

At low frequency the voltage divides smoothly and almost linearly along the winding, in proportion to position. At high frequency it does not: during a steep front the distribution is controlled mainly by capacitances rather than inductive division, and the first few turns — especially at the line end — can take a disproportionate share of the applied surge. So a terminal voltage that looks acceptable can still produce severe interturn stress inside the winding. The critical stresses include turn-to-turn, coil-to-coil and line-end-coil voltage, turn-to-ground voltage, slot-section and overhang-section stress, stress at coil entrance and exit, and stress between the first turn and the adjacent grounded core or slot wall.

Why it matters

A model that only shows terminal voltage cannot prove that internal winding stress is acceptable — the distinction is central to machine insulation coordination.

Section 5

Two modelling objectives

High-frequency machine models split by objective. For terminal behaviour — the voltage and current at the machine terminals — a relatively simple lumped representation can suffice, useful for system-level surge studies where the machine is one component among cables, transformers, arresters and breakers. For internal winding stress — how the surge distributes inside the winding — a detailed representation of geometry, capacitances, series impedances, losses and turn/coil coupling is required. The modeller must decide which applies: “What is the surge voltage at the terminal?” → terminal equivalent; “What is the voltage across the first turn or line-end coil?” → detailed winding model. This is one of the most important practical decisions in high-frequency machine modelling.

Section 6

Physical elements and core flux penetration

Any high-frequency winding model must represent three effects. Capacitance — turn-to-turn, turn-to-ground, coil-to-coil and section-to-slot-wall — strongly controls voltage distribution at steep-front time scales. Series impedance — conductor resistance and inductance — is not constant at high frequency, because skin and proximity effects change the current distribution. Loss — in conductors, core, insulation and dielectric — affects attenuation, damping and the distribution shape. A model that ignores any of these can mislead.

For very short times after surge arrival, the flux may not penetrate deeply into the iron core, which can then behave as a flux barrier and change the apparent winding inductance. But this is not always valid: the degree of penetration depends on frequency, core material, lamination, slot structure and geometry — a solid path behaves differently from a laminated core, and assuming slot walls are always perfect flux barriers can be wrong, especially beyond the first microseconds or across multiple switching events (second- and third-pole closure). For the earliest part of a very fast surge the core may be treated as a flux barrier; for longer high-frequency transients or laminated-core effects, flux penetration may need more careful representation.

Section 7

Frequency dependence of winding parameters

At high frequency the winding parameters are frequency-dependent. The series resistance rises with skin effect as current crowds toward the conductor surface; the series inductance changes as the field distribution around the conductor and in nearby iron changes; the proximity effect modifies the current distribution because adjacent conductors influence each other magnetically; core-related impedance changes because iron flux penetration depends on frequency; and dielectric losses (the conductance representing capacitive loss) can become frequency-dependent at very high frequency. So a high-frequency model should not automatically use a single constant resistance and inductance over the whole range — the required level of frequency dependence depends on the transient front time and the study objective.

Section 8

The simple terminal equivalent

When the objective is the terminal voltage rather than internal distribution, a simple terminal equivalent may be adequate: a terminal capacitance to ground, an equivalent surge impedance, an equivalent high-frequency resistance, a terminal inductance, any surge arrester or protective capacitance, and the connected cable and breaker models. This suits system-level studies where the machine is part of a larger network and internal stress is not required. It cannot, however, determine voltage across individual turns, coils or slot sections, and must not be used to assess interturn insulation stress.

Section 9

Detailed winding models: lumped and distributed

For internal surge distribution, two approaches are common. A lumped-parameter model divides the winding into discrete sections, each with series inductance and resistance, mutual inductance between turns, turn-to-turn and turn-to-ground capacitance and conductance, and end-winding, slot- and overhang-section capacitance. It is easier to implement and useful when the winding is not too long relative to the transient wavelength or when an engineering approximation is acceptable — the line-end turns must be represented in enough detail because they see the highest stress. Its weakness is that it may not fully capture travelling-wave behaviour if the section length is too large or the front extremely steep.

A multiconductor distributed-parameter model represents the winding as a system of coupled conductors — each coil split into slot and overhang sections, each section into smaller uniform segments, and a phase winding built by cascading coil models — with multiconductor transmission-line sections, capacitance to ground and between turns, mutual inductance, and frequency-dependent series impedance and losses. It is more physically complete (and more demanding in data and computation) and is generally preferred when the study must estimate interturn voltage, line-end coil stress or detailed insulation duty.

Section 10

Slot, overhang and frequency-dependent networks

Windings have slot sections (inside the stator slot, close to the grounded iron and slot wall, where turn-to-ground and slot-wall capacitance dominate) and overhang sections (outside the slot, with different geometry and different capacitances to ground and to adjacent conductors). A good model does not treat the whole coil as geometrically uniform: where internal distribution matters, slot and overhang are represented separately, because the surge enters at the line end, travels through the slot section, passes the overhang and reflects at discontinuities — and those reflections and local capacitances set the stress along the winding.

Frequency-dependent effects can be embedded as equivalent networks: a Cauer network to represent flux penetration into the iron core (reproducing how core-related impedance varies with frequency), and a Foster network to represent skin effect in the copper (reproducing how conductor resistance and inductance vary with frequency). These let a time-domain EMTP® model reproduce frequency-dependent behaviour without recomputing parameters at every frequency.

Section 11

Calculating high-frequency winding parameters

The parallel admittance of a slot section is represented by its capacitance to ground, with the slot capacitance approximated by treating the coil walls as parallel plates:

\[ Y = j\omega C \qquad\qquad C = \frac{\varepsilon\, l\, p_c}{d} \]
\(Y\)
parallel admittance
\(\omega\)
angular frequency
\(C\)
capacitance to ground
\(\varepsilon\)
insulation permittivity
\(l\)
total slot length
\(p_c\)
coil perimeter
\(d\)
insulation thickness

Geometry matters: longer slot length, larger perimeter and higher permittivity raise the capacitance, while greater insulation thickness lowers it. This is an approximate geometry-based estimate (a parallel-plate idealisation), not a universal exact formula — real coil, end-winding and overhang capacitances usually need a finer geometric or numerical evaluation.

The series impedance must include iron-core effects, conductor skin effect and insulation-region inductance:

\[ Z = (R_{ic} + R_{sk}) + j\omega(L_{ic} + L_{sk} + L_{in}) \]
\(R_{ic},\ L_{ic}\)
resistance and inductance from flux penetration / loss in the iron core
\(R_{sk},\ L_{sk}\)
resistance and inductance from skin effect in the conductors
\(L_{in}\)
inductance from flux in the insulation region

The winding is not a fixed inductor — its impedance has several physical components. The iron contribution is frequency-dependent: lower frequency allows deeper flux penetration, higher frequency confines flux near the surface. Skin effect raises the effective resistance and changes the internal inductance, and proximity effect matters because slot and overhang conductors are close together; the insulation-region inductance depends on slot width and an equivalent conductor radius (a circular-radius approximation is often used for rectangular conductors). These should be represented where the surge front is steep enough for the effects to matter.

Section 12

Practical high-frequency modelling workflow

  1. Define the objective — terminal voltage, or internal winding stress.
  2. Identify the transient source (lightning, vacuum-breaker switching, current chopping, restrike, cable switching).
  3. Determine the front time and frequency range of interest.
  4. Collect winding geometry: turns, coil arrangement, slot dimensions, overhang geometry, conductor dimensions, insulation thickness.
  5. Collect material data: conductor conductivity, insulation permittivity, iron permeability and resistivity, dielectric-loss data where available.
  6. Select the model type: terminal equivalent, lumped-parameter, or multiconductor distributed.
  7. Calculate capacitances, conductances, series impedances and coupling terms.
  8. Represent frequency-dependent effects with suitable network approximations if required.
  9. Connect the winding model to the external system: breaker, cable, transformer, arrester, terminal capacitance, earthing.
  10. Validate against measurements, manufacturer information or published reference cases where possible.

Section 13

When a detailed winding model is justified

Use a detailed winding model when interturn voltage or line-end coil stress is required, when machine insulation coordination is being assessed, for vacuum-breaker switching, where a long cable connects to a motor or generator, when surge reflections matter, when terminal voltage alone is not enough, when winding-failure risk or turn insulation is the limiting factor, or when protective devices are being designed or evaluated. A detailed winding model is usually not necessary for low-frequency fault current, rotor-angle stability, fundamental-frequency load-rejection voltage, shaft-torque-due-to-electromechanical-oscillation studies, cases where the surge does not reach the terminals, or where internal winding stress is outside the study scope.

Section 14

High-frequency winding model — validation checks

Before a high-frequency winding model is used for an insulation-stress conclusion, confirm that its outputs are physically credible:

  • The terminal surge voltage and current are consistent with the connected cable, breaker and arrester models.
  • The dominant resonant frequencies match the winding geometry and any measured or published frequency response.
  • The line-end coil and first-turn stresses are resolved — not hidden inside an over-coarse section.
  • The voltage distribution along the winding behaves sensibly between the line end and the neutral end.
  • The result is checked for sensitivity to the assumed capacitances and to the surge front time, since both strongly shift the distribution.
  • Where available, the response is compared with a measured frequency-response trace or manufacturer winding data.
Part Two · Mechanical Shaft Models

Section 15

Why the mechanical shaft model matters

The second specialist representation is mechanical, not high-frequency electrical. A surge model is needed when the output is internal winding voltage stress; a shaft model is needed when the output is torsional speed, shaft torque, modal damping or subsynchronous interaction. Everything that follows in Part Two concerns the mechanical rotor train, not the winding insulation.

A generator rotor is connected to turbines, exciters and other masses through shafts of finite stiffness; they do not always move as one rigid body. For ordinary system-dynamic studies a single equivalent mass captures the overall acceleration of the rotor relative to the system. For torsional studies it is not enough: the shaft is flexible, rotor sections oscillate relative to each other at torsional natural frequencies. Torsional oscillations matter for subsynchronous resonance, series-compensated networks, shaft-duty assessment, out-of-phase synchronisation, fault clearing near generators, converter–generator interaction, large torque disturbances and mechanical-stress studies. The principle: a single-mass model captures centre-of-inertia motion, a multimass model captures internal shaft torsion — if the study concerns shaft torque or torsional interaction, a multimass model is required.

Section 16

Single-mass representation

A single-mass model lumps the whole turbine-generator rotor into one equivalent inertia:

\[ J\,\frac{d\omega_m}{dt} = T_m - T_e \]
\(J\)
equivalent moment of inertia
\(\omega_m\)
mechanical angular speed
\(T_m,\ T_e\)
mechanical and electromagnetic torque

Suitable for general rotor-angle stability, basic load rejection, overall acceleration and centre-of-inertia swing where shaft torque is not required. Not suitable for torsional resonance, shaft stress, SSR, modal damping, torque amplification between turbine sections, or out-of-phase-switching shaft duty.

Section 17

Multimass shaft representation

A multimass model divides the shaft train into several rigid masses connected by elastic shafts. For a large steam turbine-generator the masses may represent the high-pressure turbine, the intermediate-pressure turbine, the low-pressure turbine sections, the generator rotor and the exciter rotor. Each mass has its own inertia; each shaft section has torsional stiffness; damping may be associated with each mass and with relative motion between adjacent masses. This lets shaft sections twist relative to each other and reproduces the torsional modes in the frequency range of interest. A lumped multimass model is usually adequate — a full continuum shaft model is more detailed but rarely necessary for power-system torsional studies.

It is a mass-spring-damper system: each mass carries its inertia, angular position, speed and applied torque; each shaft section a torsional stiffness and (optionally) mutual damping; each mass a possible self-damping. The stiffness torque between adjacent masses depends on the difference in angular displacement (one mass ahead of the next twists the shaft and produces a restoring torque); the mutual damping torque depends on the difference in angular speed; the self-damping torque depends on a mass’s speed deviation. This structure yields both the modal oscillations and the actual shaft torques.

Torsional modes and damping torque

Torsional modes are mechanical oscillation modes of the turbine-generator shaft train. They are different from local plant modes or inter-area electromechanical modes because the individual shaft sections twist against each other rather than the whole generator swinging as one rigid body against the network. In these studies, the important output is not only rotor speed or terminal power, but also shaft-section torque, modal frequency, mode shape and damping. If the electrical network or control system supplies negative damping near a torsional natural frequency, the oscillation may grow even when the average rotor angle remains synchronised.

Section 18

Sources of mechanical damping

Mechanical damping comes from several sources. Steam forces on turbine blades give damping torques related to the speed deviation of individual turbine masses, and this varies with generator loading because steam flow and turbine condition change. Bearing friction and windage relate to the absolute angular speed of the rotating components. Shaft-material hysteresis relates to relative motion between adjacent masses and is often represented as mutual damping. Damping is one of the most uncertain parts of torsional modelling — it can decide whether a torsional interaction grows or decays — so damping assumptions should be treated carefully and supported by measurements where possible.

Section 19

Equation of motion for each mass

For each mass, Newton’s second law for rotation, written in a synchronously rotating reference frame, gives the inertia, self-damping, mutual-damping and stiffness contributions on the left and the net torque on the right:

\[ J_i\frac{d\Delta\omega_i}{dt} + D_{si}\Delta\omega_i + D_{m,i,i-1}(\Delta\omega_i - \Delta\omega_{i-1}) + D_{m,i,i+1}(\Delta\omega_i - \Delta\omega_{i+1}) \] \[ \qquad +\, K_{i,i-1}(\delta_i - \delta_{i-1}) + K_{i,i+1}(\delta_i - \delta_{i+1}) = T_{mi} - T_{ei} \] \[ \frac{d\delta_i}{dt} = \Delta\omega_i \]
\(J_i\)
moment of inertia of mass \(i\)
\(\Delta\omega_i\)
speed deviation of mass \(i\) from synchronous speed
\(\delta_i\)
angular displacement relative to the synchronously rotating frame
\(D_{si}\)
self-damping coefficient
\(D_{m,i,i\pm1}\)
mutual-damping coefficients to adjacent masses
\(K_{i,i\pm1}\)
shaft stiffness coefficients to adjacent masses
\(T_{mi},\ T_{ei}\)
mechanical and electrical torque on the mass

The inertia term resists acceleration, the damping terms remove energy, the stiffness terms are the shaft-twist torque, and the right side is the accelerating torque (mechanical minus electrical). With this sign convention a positive net torque accelerates the mass in the direction of rotation; for the generator mass the electrical torque is a braking (load) torque, so it is subtracted. A sudden change in electrical torque on the generator mass travels through the shaft and excites the torsional modes; if the electrical system contains a component near a torsional natural frequency, the oscillation can be amplified — the physical basis of subsynchronous resonance.

Section 20

Per-unit mechanical system

For EMTP® studies the electrical and mechanical systems are usually put on a common per-unit base, with the base mechanical power equal to the electrical base power:

\[ S_{mB} = S_B \qquad \omega_{mB} = \frac{2}{p}\,\omega_B \qquad T_{mB} = \frac{S_{mB}}{\omega_{mB}} \] \[ J_B = \frac{T_{mB}}{\omega_{mB}} \qquad D_B = \frac{T_{mB}}{\omega_{mB}} \qquad K_B = \frac{T_{mB}}{\theta_{mB}} \]
\(S_{mB},\ S_B\)
base mechanical and electrical power
\(\omega_{mB},\ \omega_B\)
base mechanical and electrical angular speed (\(p\) = poles)
\(T_{mB},\ J_B,\ D_B,\ K_B\)
base torque, inertia, damping and stiffness
\(\theta_{mB}\)
base mechanical angle (normally \(1\) rad)

A consistent per-unit base lets the shaft model, the electromagnetic torque and the electrical machine model interact correctly. Shaft data may arrive in SI units, in per unit, in modal form (modal inertias, frequencies and damping), or in a manufacturer-specific convention — and an inertia constant \(H_i\) (stored kinetic energy at rated speed divided by rated power) is sometimes given instead of \(J_i\). The base used for each quantity must be confirmed and converted before the data is entered, because a base or convention mismatch silently corrupts the torsional frequencies.

Section 22

Why damping is difficult, and synchronised behaviour

Stiffness and inertia can be estimated from geometry with reasonable accuracy, but damping is much harder — it depends on steam flow, turbine loading, bearing friction, windage, shaft hysteresis, generator electrical damping, network impedance, machine loading and control interaction. Crucially, damping measured while the generator is synchronised includes both mechanical and electrical damping; using that value directly in a study that also models electrical damping through the generator and network double-counts the electrical damping — a serious error. A report should clearly distinguish mechanical damping, electrical damping, the measured combined damping, and the damping actually used in the shaft model.

The synchronised condition also shifts the modes. Unsynchronised, the shaft has a rigid-body Mode 0 at zero frequency (all masses rotate together). Synchronised, the electrical system adds a synchronising torque — an electrical “spring” between the generator rotor and the network — which moves Mode 0 from zero to a low frequency in the electromechanical swing range. The higher torsional modes change far less, because mechanical shaft stiffness greatly exceeds the electrical synchronising stiffness, but their damping can change substantially because the electrical system can add positive or negative damping. So a shaft test under one operating condition does not directly represent another — an important point in SSR studies.

Identify what controls the oscillation

For torsional and SSR studies, always check whether the oscillation is controlled by synchronising torque, damping torque, or a mechanical shaft mode. A single-mass model can show overall rotor acceleration, but it cannot show shaft twist, shaft-section torque or torsional fatigue.

Section 23

Determination of mechanical parameters

Mechanical parameters come from two broad test groups. Standstill mechanical tests (harmonic torque excitation, turning-gear engagement) probe the mass-spring system, but applying sufficient excitation to a large shaft can be difficult. Synchronised electrical-torque tests (out-of-phase synchronisation, sinusoidal excitation-power variation, system-switching disturbances) excite the torsional modes through the generator electromagnetic torque; the advantage is easy excitation through the electrical system, the disadvantage is that the measured damping includes electrical effects and needs careful interpretation.

Because models need physical self- and mutual-damping coefficients while tests give modal damping, an iterative method is used: from no-load and full-load decrement data, assume self-damping is negligible at no load (steam-force damping small), guess the mutual-damping coefficients, compute the system eigenvalues, and adjust mutual damping until the no-load modal damping is matched; then guess self-damping coefficients, recompute the eigenvalues, and adjust self-damping until the full-load modal damping is matched. This converts measured modal damping into physical mass-spring-damper coefficients.

Section 24

Practical shaft-modelling workflow

  1. Decide whether the study needs shaft torque or only overall rotor motion.
  2. Use a single-mass model if only overall acceleration is required.
  3. Use a multimass model if torsional modes or shaft torques are relevant.
  4. Obtain inertia values for each major rotor section.
  5. Obtain shaft stiffness values between adjacent masses.
  6. Obtain or estimate damping values.
  7. Calculate torsional natural frequencies and mode shapes.
  8. Compare calculated frequencies with manufacturer or measured values.
  9. Connect the generator electromagnetic torque to the generator mass.
  10. Apply turbine torques to the appropriate turbine masses.
  11. Validate the shaft response against available decrement or disturbance data.
  12. Perform damping sensitivity checks — damping is often uncertain.

Validation checks

Before a shaft model is trusted for a torsional conclusion, confirm:

  • The sum of the mass inertias matches the total machine inertia from the data sheet.
  • The calculated modal frequencies match the manufacturer torsional data or measured values.
  • The mode shapes make physical sense — the right number of polarity reversals, generator participation present.
  • The damping assumptions are stated, with no double-counting of electrical damping.
  • The shaft-torque response to a representative disturbance is of a credible magnitude.
  • The model is stable with no disturbance applied (no spurious growth from the integration or damping settings).
  • The conclusion is checked for sensitivity to the uncertain damping and stiffness values.
  • The multimass model is validated as a set against the available torsional natural frequencies, mode shapes and shaft-inertia distribution — and, because damping decides whether a torsional oscillation decays, persists or grows, uncertain damping is treated as a decisive sensitivity, not a detail.

A multimass shaft model is needed for SSR, series compensation, possible converter–shaft interaction, shaft-torque outputs, out-of-phase switching, generator mechanical-duty and torsional-mode-damping studies, large electrical-torque steps, shaft-stress assessment, or when the manufacturer requires a torsional assessment. A single-mass model may be acceptable when only rotor-angle swing is needed, shaft torque is out of scope, the disturbance does not excite torsional modes, the time range is too short or too slow for torsional detail, or for preliminary screening.

Section 25

Common modelling mistakes

The recurring errors span both specialist models. The first group concerns high-frequency winding stress, the second concerns the mechanical shaft.

Avoid these
  • Using a standard dq0 machine model to assess internal turn-to-turn winding stress — it is not a winding-insulation model.
  • Treating the winding as one lumped inductance for steep-front surge studies.
  • Ignoring line-end coil stress and the local capacitances that set it.
  • Using terminal voltage only when internal insulation stress is the study objective.
  • Applying high-frequency parameters outside the frequency range for which they were derived.
  • Using a single-mass shaft model for subsynchronous-resonance or shaft-torque studies.
  • Ignoring damping uncertainty in torsional studies — or double-counting electrical damping by using synchronised-test damping while also modelling the electrical network.
  • Using shaft data without checking its base units, per-unit convention and mass order.
  • Comparing modal frequencies without checking whether they are mechanical or electrical frequencies.
  • Accepting EMTP® convergence without checking the physical voltage distribution or torsional response.

Section 26

Integrated EMTP® modelling guidance

The high-frequency winding model and the mechanical shaft model sit at opposite ends of the machine-modelling problem, with the conventional dq0 model between them for low-frequency electrical and electromechanical transients. Choose by the physical question:

  • Fault current and voltage recovery → the dq0 electrical model with suitable subtransient, transient, saturation and excitation representation.
  • Internal winding surge stress → a high-frequency winding model.
  • Shaft torque and torsional interaction → a multimass mechanical shaft model.
  • Terminal surge voltage only → a simplified terminal equivalent may be enough.
  • Very-fast-front insulation stress → do not rely on a low-frequency dq0 model.
  • Subsynchronous resonance → do not rely on a single-mass mechanical model.

The model must always be selected according to the phenomenon being studied.

Section 27

Suggested report wording

Model statement — for a study report

“For high-frequency surge studies the synchronous machine was represented according to the required level of insulation-stress detail. Where only terminal voltage was required, a simplified terminal equivalent was used; where internal winding stress was required, the winding was represented by a segmented high-frequency model including series impedance, capacitance to ground, turn-to-turn capacitance and frequency-dependent loss effects, with slot and overhang sections considered separately where the geometry supported it. For torsional studies the turbine-generator rotor was represented by a lumped multimass shaft model: each major rotor section as a rigid inertia, with adjacent masses connected by shaft stiffness and damping; the generator electromagnetic torque was applied to the generator mass and the turbine torques to the relevant turbine masses. Modal frequencies, mode shapes and damping assumptions were checked against available manufacturer or test data, and sensitivity checks were performed where damping was uncertain.”

Section 28

Main takeaway

The machine model must follow the physics of the study

A synchronous machine has no single universal model. For low-frequency electrical and electromechanical transients, use the dq0 model with field, damper, saturation and mechanical dynamics. For fast-front and very-fast-front surge studies, represent the winding by capacitance, high-frequency impedance, losses and distributed effects if internal insulation stress is required. For torsional and subsynchronous studies, represent the rotor by a multimass shaft model so internal shaft modes and torques can be calculated. The message: use dq0 modelling for electromechanical behaviour, high-frequency winding modelling for surge insulation stress, and multimass shaft modelling for torsional interaction.

References

References

The reference text for both topics, the classic machine-surge and subsynchronous-oscillation references, and the standard stability/modelling works.

  1. J. A. Martínez-Velasco, Ed., Power System Transients: Parameter Determination, Ch. 5 (Synchronous Machines). Boca Raton, FL, USA: CRC Press, 2010.
  2. A. Heller and V. Veverka, Surge Phenomena in Electrical Machines. London, UK: Iliffe Books, 1968.
  3. IEEE Subsynchronous Resonance Working Group, “Terms, definitions and symbols for subsynchronous oscillations,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-104, no. 6, pp. 1326–1334, Jun. 1985.
  4. P. Kundur, Power System Stability and Control. New York, NY, USA: McGraw-Hill, 1994.
  5. IEEE Std 1110-2002, IEEE Guide for Synchronous Generator Modeling Practices and Applications in Power System Stability Analyses. New York, NY, USA: IEEE.

Nine-Part Technical Series

Synchronous Machine Modelling in EMTP®

A nine-part guide to representing the synchronous machine in EMTP® — from the modelling overview and EMT representation, through the dq0 transformation, per-unit equivalent circuits, parameters, data conversion and tests, to magnetic saturation and high-frequency/shaft modelling.

Part Nine Reading now

High-Frequency and Shaft Modelling

Beyond dq0: high-frequency winding models for steep-front surge stress, and multimass mechanical shaft models for torsional and subsynchronous-resonance studies.

Series progress 9 of 9
Part Eight

Magnetic Saturation

The open-circuit characteristic and air-gap line, saturated and unsaturated reactance, and the saturation factor applied to the mutual air-gap inductance.

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