6. Power-System Dynamics and Stability

Introduction and Context

An electric power system must remain in a condition from which acceptable operation can be maintained after changes in generation, demand, network configuration, or faults. This requirement is more demanding than the maintenance of a steady-state power-flow solution. A system may satisfy the algebraic power-flow equations before and after a disturbance and yet lose synchronism, experience unacceptable voltage decline, or undergo frequency collapse during the transition. Power-system stability is therefore a dynamic property: it concerns the ability of interconnected machines and controlled devices to respond to disturbances while preserving an acceptable operating state.

The subject connects circuit theory, electromechanical energy conversion, automatic control, numerical simulation, protection, and system operation. Rotor-angle stability is associated primarily with the synchronizing relationship between generators. Voltage stability concerns the ability of the system to maintain acceptable bus voltages following disturbances or gradual changes in loading. Frequency stability concerns the balance between real-power supply and demand and the effectiveness of controls such as turbine governors, automatic generation control, and under-frequency load shedding.

A useful distinction is made between small-disturbance and large-disturbance stability. Small-disturbance analysis examines the behavior produced by infinitesimal or modest changes around an operating point and commonly uses linearization and eigenvalue methods. Large-disturbance, or transient, stability examines severe events such as three-phase faults, generator trips, major line outages, and sudden loss of load. It generally requires nonlinear simulation, direct methods based on energy functions, or carefully justified approximations.

This chapter develops the principal models and analytical methods used to study these forms of stability. It also considers practical controls, digital tools, limitations of simplified models, and an illustrative planning case.

Learning Objectives

After studying this chapter, the reader should be able to:

1. Distinguish rotor-angle, voltage, and frequency stability and explain their interactions.

2. Formulate and interpret the swing equation for a synchronous generator.

3. Use equal-area concepts and transient simulation to assess large-disturbance stability.

4. Linearize a multimachine system and interpret eigenvalues, modes, participation factors, and damping.

5. Explain voltage-collapse mechanisms using reactive-power balance and continuation methods.

6. Assess the influence of excitation systems, governors, power-system stabilizers, FACTS devices, HVDC controls, and protection.

7. Identify modelling assumptions, analytical limitations, operational risks, and good professional practice.

Stability as a Dynamic Property

At an operating point, a power system is represented by differential equations for machines, controls, and dynamic loads together with algebraic network equations. In compact form,

\[

\dot{x}=f(x,y,u), \qquad 0=g(x,y,u),

\]

where \(x\) contains dynamic states, \(y\) contains algebraic variables such as bus voltage magnitudes and angles, and \(u\) represents inputs or disturbances. A stable response means that relevant variables remain within prescribed limits and, where appropriate, return toward an equilibrium or an acceptable post-disturbance trajectory.

Stability is not identical to reliability. Reliability includes adequacy, security, protection performance, and the ability to serve demand over time. Stability is one important component of security: it asks whether the system can withstand a specified disturbance without unacceptable dynamic consequences.

The classical classification is useful but not absolute. Rotor-angle, voltage, and frequency phenomena are physically coupled. For example, a voltage depression can reduce electrical power transfer, accelerate generator rotors, and thereby contribute to angle instability. Conversely, loss of synchronism can cause severe voltage oscillations. The classification identifies the dominant mechanism and the most appropriate analytical tools; it does not imply independent subsystems.

Rotor-Angle Dynamics and the Swing Equation

A synchronous generator converts mechanical input from a turbine into electrical output. If mechanical and electrical powers are unequal, the rotor accelerates or decelerates. Let \(\delta\) denote the electrical angle of the rotor relative to a synchronously rotating reference, and let \(\omega\) denote speed deviation. The fundamental electromechanical relation is

\[

\frac{2H}{\omega_s}\frac{d^2\delta}{dt^2}=P_m-P_e=P_a,

\]

where \(H\) is the inertia constant in seconds, \(\omega_s\) is synchronous electrical angular speed, \(P_m\) is mechanical input power, \(P_e\) is electrical output power, and \(P_a\) is accelerating power. With damping included, a commonly used form is

\[

\frac{2H}{\omega_s}\ddot{\delta}+D\dot{\delta}=P_m-P_e.

\]

The inertia constant represents the kinetic energy stored at rated speed per unit machine rating. Larger inertia slows the initial rate of frequency and angle change, but it does not by itself guarantee long-term stability. Damping represents effects that oppose speed oscillations, including damper windings, turbine effects, and frequency-sensitive loads.

For a simplified lossless, single-machine-infinite-bus system,

\[

P_e=P_{\max}\sin\delta,

\qquad P_{\max}=\frac{E'V}{X},

\]

where \(E'\) is an internal transient voltage, \(V\) is infinite-bus voltage, and \(X\) is the transfer reactance. The equilibrium angle satisfies \(P_m=P_{\max}\sin\delta_0\). The maximum theoretical transfer is reached at \(\delta=90^\circ\), but operation close to this point has poor synchronizing margin and is sensitive to disturbances.

The synchronizing coefficient is the slope of the electrical power-angle curve at the operating point:

\[

K_s=\left.\frac{dP_e}{d\delta}\right|_{\delta_0}=P_{\max}\cos\delta_0.

\]

A positive value provides a restoring synchronizing torque in the linearized model. As the operating angle approaches 90 degrees, \(K_s\) decreases, so small disturbances produce weaker restoring action.

Small-Disturbance Stability and Eigenvalue Interpretation

For a system represented by differential-algebraic equations, linearization about an equilibrium produces, after elimination or reduction of algebraic variables,

\[

\Delta\dot{x}=A\Delta x+B\Delta u.

\]

The eigenvalues of the state matrix \(A\) determine the local modes. An eigenvalue \(\lambda=\sigma\pm j\omega\) corresponds to a mode that behaves approximately as

\[

e^{\sigma t}\left(C_1\cos\omega t+C_2\sin\omega t\right).

\]

A negative real part indicates local decay, a positive real part indicates instability, and a zero or nearly zero real part indicates weak damping or a marginal mode. For an oscillatory mode, the damping ratio is

\[

\zeta=-\frac{\sigma}{\sqrt{\sigma^2+\omega^2}}.

\]

Inter-area modes typically involve coherent groups of generators swinging against other groups and often have lower frequencies and weaker damping than local plant modes. Local modes involve one generator or a small group oscillating against the rest of the system. Control modes may arise from excitation systems, power-system stabilizers, turbine-governor systems, or converter controls.

Eigenvalues alone do not identify which machines or controls are responsible for a mode. Right eigenvectors describe the relative state participation in a mode, while left eigenvectors and participation factors help identify the states that most strongly influence it. This information supports targeted controller tuning rather than indiscriminate increases in gain.

A small-signal study normally involves: selecting a credible operating point; validating the network and dynamic models; solving the power flow; linearizing the complete differential-algebraic model; computing eigenvalues and mode shapes; testing parameter and operating-condition sensitivity; and verifying proposed controls using nonlinear simulation. A system that is stable at one dispatch may have poorly damped modes at another because power transfers, generator commitment, excitation limits, and network topology change.

Large Disturbances: Transient Stability

Transient stability is the ability to retain synchronism after a severe disturbance. During a fault, electrical transfer may fall sharply while mechanical input changes little, producing positive accelerating power. After fault clearing, the network may have a different transfer capability. Stability depends on the energy gained during acceleration and the decelerating capability available after clearing.

The equal-area criterion provides an important physical interpretation for a single-machine-infinite-bus system. In the power-angle plane, the accelerating area is

\[

A_{acc}=\int_{\delta_0}^{\delta_c}(P_m-P_{e,f})d\delta,

\]

where \(\delta_c\) is the rotor angle at clearing and \(P_{e,f}\) is electrical output during the fault. The available decelerating area is

\[

A_{dec}=\int_{\delta_c}^{\delta_{max}}(P_{e,post}-P_m)d\delta.

\]

The system remains stable if the available decelerating area is at least equal to the accelerating area. The critical clearing angle is the largest angle at which the fault can be cleared without loss of synchronism; the corresponding critical clearing time is obtained from the dynamic equation. Faster fault clearing, stronger post-fault transfer, lower pre-fault loading, and higher voltage generally improve the margin.

The equal-area criterion is exact only for the restricted single-machine-infinite-bus model with appropriate assumptions. Multimachine systems require numerical time-domain simulation or specialized direct methods. A typical transient-stability simulation includes generator subtransient or transient models, excitation systems, governors, turbine dynamics, network switching, protection actions, dynamic loads, and converter controls. The simulation must represent the pre-fault state, fault application, clearing sequence, and post-fault topology accurately.

Time-domain results should be judged using meaningful criteria: bounded rotor-angle separation, acceptable speed deviation, recovery of voltage and frequency, absence of uncontrolled oscillation, and operation within equipment and protection limits. A plot that appears bounded over a short simulation may not demonstrate adequate damping or acceptable recovery.

Voltage Stability and Reactive-Power Phenomena

Voltage stability is the ability of a system to maintain acceptable voltages at all buses under normal conditions and after a disturbance. It is strongly influenced by reactive-power balance, transmission reactance, generator excitation limits, transformer tap changers, load characteristics, and the dynamic response of induction motors and power-electronic devices.

A simple two-bus system illustrates the mechanism. As load increases, voltage decreases and the reactive-power demand of the network may rise. Beyond a nose point on the power-voltage curve, no acceptable high-voltage equilibrium exists. The familiar curve has a stable high-voltage branch and a low-voltage branch, separated by a saddle-node bifurcation under idealized assumptions. The distance to the nose, however, is not a universal measure of operational security because contingencies, controls, load uncertainty, and time-dependent dynamics affect the result.

Voltage instability may be classified as short-term or long-term. Short-term voltage instability develops over fractions of a second to several seconds and may involve induction motors, electronic loads, generator excitation, and fast converter controls. Long-term voltage instability develops over tens of seconds or minutes as transformer tap changers, thermostatic loads, generator reactive limits, and over-excitation limiters act.

Continuation power flow traces equilibrium solutions as a loading parameter changes and is useful for estimating voltage margins and locating voltage-collapse boundaries. Sensitivity measures such as \(dV/dQ\), modal analysis of the reduced Jacobian, and reactive-power reserve indicators help identify weak buses. Yet voltage stability assessment must include dynamic simulation when controls and load recovery are important.

Important mitigation measures include dynamic reactive support from synchronous condensers, static VAR compensators, STATCOMs, switched capacitors, and suitably controlled converters; network reinforcement; transformer-tap and shunt-control coordination; under-voltage load shedding; and operating limits based on contingency analysis. Reactive reserves must be geographically available and dynamically deliverable, not merely present in an accounting sense.

Frequency Stability and System-Wide Power Balance

Frequency stability concerns the ability to maintain system frequency following a significant imbalance between generation and demand. Immediately after generation loss, kinetic energy stored in rotating machines supplies part of the deficit. The initial rate of change of frequency is related to the aggregate inertia and the power imbalance. In simplified form, the centre-of-inertia frequency follows a swing relation in which the sum of accelerating powers is divided by the equivalent inertia.

The frequency response occurs in stages. Inertial response acts immediately but is not sustained. Primary frequency control, supplied by governors and responsive resources, changes mechanical or electrical power within seconds. Secondary control, usually automatic generation control, restores frequency and scheduled interchanges over a longer interval. Tertiary actions include redispatch, reserve deployment, and corrective operator measures. Under-frequency load shedding provides a controlled emergency response when generation and reserves are insufficient.

Low-inertia systems can experience a faster rate of change of frequency and larger frequency nadirs after disturbances. Converter-interfaced generation does not automatically contribute synchronous inertia, although grid-forming and fast-frequency-response controls can provide useful synthetic or emulated response. Such controls must be coordinated with energy availability, current limits, protection, and recovery dynamics.

Frequency and voltage stability interact. A falling frequency may reduce motor speed and alter load demand, while low voltage can reduce or increase real-power consumption depending on the load model. Frequency protection, islanding detection, load shedding, and controlled system separation must therefore be designed using dynamic studies rather than fixed assumptions alone.

Stability-Enhancement Controls

Excitation systems influence both voltage and rotor-angle stability. A fast automatic voltage regulator can increase synchronizing torque and improve transient performance, but high gain may introduce poorly damped modes. Power-system stabilizers add supplementary signals, commonly based on speed, frequency, or electrical power, to produce damping torque over selected frequency ranges. Their phase compensation and washout characteristics must be tuned against the plant, network, and operating conditions.

Turbine governors and fast active-power controls support frequency stability. Their response is limited by ramp rates, dead bands, valve or gate constraints, energy availability, and coordination with secondary control. Automatic generation control should respect participation factors, tie-line schedules, ramp limits, and reserve requirements.

FACTS devices can regulate voltage, series impedance, or power flow. A STATCOM supplies dynamic reactive current and is particularly useful during depressed-voltage conditions. A series compensator can increase transfer capability but may create subsynchronous-resonance or control-interaction risks. HVDC links can rapidly modulate active power to support frequency, damp inter-area oscillations, or control power exchange between asynchronous areas.

Protection is itself a stability control. High-speed fault clearing is often decisive for transient stability. Out-of-step protection, remedial action schemes, controlled islanding, under-frequency load shedding, and under-voltage load shedding can prevent widespread collapse. These schemes require dependable communications, validated logic, fail-safe behavior, and clear coordination with conventional protection.

An Illustrative Planning Case

Background

Consider an illustrative 400-kV interconnected corridor transferring 2,400 MW from a generation area to a load centre. The corridor consists of two parallel transmission circuits. Several large synchronous generators use fast excitation systems, while a growing fraction of new generation is converter-interfaced.

Situation

Planning studies show that a three-phase fault near a receiving-end substation may lead to instability if one circuit is cleared after 120 ms and the other is subsequently unavailable. Under a high-transfer dispatch, an inter-area oscillation is also weakly damped. A separate contingency involving the loss of a large generator produces a frequency nadir close to the emergency operating threshold.

Analysis

A power-flow study alone does not reveal the problem because a post-contingency equilibrium exists. Transient simulation shows that the fault causes rapid rotor acceleration and that the weakened post-fault corridor cannot provide sufficient decelerating power. Small-signal analysis identifies a 0.6-Hz inter-area mode with low damping, involving coherent motion of the exporting generators against the receiving-area machines. A frequency study indicates that aggregate synchronous inertia has declined and that governor response is insufficient during the first few seconds.

Strategy

The utility evaluates a coordinated package rather than a single corrective action. It reduces the pre-contingency transfer limit under the most severe topology, upgrades selected breakers to reduce fault-clearing time, retunes power-system stabilizers using mode-shape information, installs dynamic reactive support at the receiving end, and enables controlled active-power modulation on an HVDC tie. Fast frequency response from converter-based resources is specified with recovery constraints so that the initial injection does not create a secondary frequency event.

Outcome

Repeated nonlinear simulations across seasonal dispatches show increased critical clearing time, improved damping of the inter-area mode, and a higher frequency nadir after generator loss. The package is accepted only after model validation, protection coordination checks, communication-failure tests, and hardware-in-the-loop verification of the remedial action logic.

Learning Points

The case demonstrates that stability is a system property. Breaker speed, operating limits, excitation control, damping control, reactive support, HVDC modulation, and frequency response must be assessed together. It also illustrates why a single nominal operating point and a single stability index are inadequate for planning decisions.

Modelling, Computation, and Professional Practice

Stability conclusions are only as credible as the models and assumptions behind them. Common errors include using generic generator parameters without validation, neglecting saturation and limiters, representing loads as constant impedance when motor or electronic behavior is important, omitting protection actions, and applying an unrealistic fault-clearing time. Converter models require particular care because control modes, current limits, phase-locked loops, grid strength, and firmware settings influence both small- and large-disturbance behavior.

RMS phasor-domain simulation is efficient for electromechanical transients over seconds or minutes. Electromagnetic-transient simulation is more appropriate for fast converter interactions, switching phenomena, protection transients, and weak-grid behavior. Hybrid and real-time digital simulation support controller and protection testing. Automated contingency screening, eigenvalue computation, continuation methods, and machine-learning-assisted anomaly detection can improve workflow, but data-driven tools should supplement—not replace—physical models, engineering judgment, and validation.

Uncertainty should be treated explicitly. Dispatch, renewable output, load composition, topology, fault resistance, protection delays, and controller parameters vary. Sensitivity studies, probabilistic assessment, and scenario libraries help distinguish robust conclusions from results that depend on one favourable assumption. Cybersecurity and governance are also relevant: stability-control settings, model databases, and remedial-action logic must be protected against unauthorized alteration, and changes must be traceable through formal configuration management.

Challenges, Limitations, and Best Practices

The principal analytical challenge is the simultaneous presence of multiple time scales. Electromagnetic, control, electromechanical, and long-term processes may interact. Simplified models are valuable for insight but may conceal control interactions or limit-induced changes in behavior. Linearization describes local behavior and cannot establish transient stability after a major fault. Conversely, a time-domain simulation demonstrates only the scenarios and time horizon that were actually studied.

Practical mistakes include interpreting a positive damping ratio as proof of transient security, ignoring unstable low-voltage equilibria, treating reactive reserve as uniformly effective, assuming converter controls behave like synchronous-machine inertia, and using critical clearing time without verifying protection sequence and topology. Another mistake is tuning a controller for one operating condition without checking seasonal and contingency variations.

Good practice includes the following:

• define stability criteria before conducting simulations;
• validate steady-state and dynamic models against field or manufacturer data;
• represent protection, limiters, saturation, load recovery, and converter controls where relevant;
• examine credible operating states and contingencies rather than a single base case;
• combine eigenvalue analysis, nonlinear simulation, sensitivity studies, and direct methods where appropriate;
• report assumptions, uncertainty, numerical tolerances, and model versions;
• coordinate planning, operations, protection, and control engineering decisions;
• verify remedial schemes under communication failures and abnormal conditions.

Professional decisions must balance security, cost, environmental constraints, equipment capability, and the consequences of unnecessary control action. Emergency schemes should be selective and dependable: excessive load shedding or unnecessary islanding can itself create operational and social harm. Regulatory criteria and interconnection requirements provide minimum obligations, but responsible engineering also considers cascading risk and public-service continuity.

Current Developments

Power systems are moving toward lower synchronous inertia, greater dependence on inverter-based resources, increasingly active distribution networks, and more variable operating conditions. Grid-forming converters, distributed fast frequency response, synthetic inertia, wide-area measurement systems, and adaptive protection are therefore receiving substantial attention. Phasor measurement units enable synchronized observation of oscillations and support online damping assessment, event location, and model validation.

Digital twins and high-performance computing allow more operating scenarios to be screened. Probabilistic and risk-based stability assessment is becoming more important than deterministic evaluation of a small number of cases. Nevertheless, emerging controls introduce new questions concerning interoperability, cyber resilience, black-start behavior, fault ride-through, and interactions between transmission and distribution systems. The central engineering principle remains unchanged: new technology must be assessed through validated dynamic models and demonstrated performance under credible disturbances.

Chapter Summary

Power-system stability is the ability of an interconnected system to preserve acceptable operation after disturbances. Rotor-angle stability is governed by synchronizing and damping torque and is analysed using the swing equation, equal-area concepts, eigenvalues, and nonlinear simulation. Small-disturbance studies identify oscillatory modes, damping, and influential states, while transient studies examine severe faults and switching events. Voltage stability depends strongly on reactive-power balance, network strength, load behavior, and control limits; continuation power flow and dynamic simulation are complementary tools. Frequency stability depends on inertia, primary and secondary controls, reserves, load shedding, and the interaction of synchronous and converter-based resources. Stability enhancement requires coordinated excitation, damping, governor, reactive-power, HVDC, protection, and remedial-action controls. Reliable conclusions require validated models, realistic contingencies, uncertainty assessment, and disciplined professional governance.

Key Terms

Rotor-angle stability: Ability of synchronous machines to remain in synchronism after a disturbance.

Voltage stability: Ability to maintain acceptable bus voltages under normal and disturbed conditions.

Frequency stability: Ability to maintain and recover system frequency after a real-power imbalance.

Swing equation: Differential equation relating rotor acceleration to the difference between mechanical and electrical power.

Inertia constant: Kinetic energy stored in a rotating machine at rated speed per unit machine rating.

Synchronizing power coefficient: Slope of the electrical power-angle curve at an operating point.

Damping torque: Torque opposing speed or rotor-angle oscillations.

Transient stability: Large-disturbance rotor-angle stability following severe events.

Small-disturbance stability: Local stability assessed after linearization about an equilibrium.

Equal-area criterion: Energy-based graphical test for transient stability in a single-machine-infinite-bus system.

Critical clearing angle: Maximum rotor angle at which a fault may be cleared without losing synchronism.

Critical clearing time: Maximum permissible fault duration for transient stability.

Eigenvalue: Root of the characteristic equation defining a linearized system mode.

Participation factor: Measure indicating the association of a state with a dynamic mode.

Inter-area mode: Oscillation involving coherent groups of generators in different areas.

Continuation power flow: Numerical method for tracing equilibrium voltage solutions as loading changes.

Reactive-power reserve: Available capability to supply or absorb reactive power at relevant locations.

Rate of change of frequency: Time derivative of frequency following a power imbalance.

Power-system stabilizer: Supplementary excitation control that provides damping to oscillations.

Remedial action scheme: Automatic coordinated response designed to prevent instability or cascading failure.

Review Questions

Short Answer Questions

1. What physical imbalance is represented by the accelerating power in the swing equation?

2. Why does synchronizing torque decline as the operating angle approaches 90 degrees?

3. What information does the real part of an eigenvalue provide?

4. Distinguish inertial response from primary frequency control.

5. Why can a power-flow solution exist even when voltage stability is threatened?

Long Answer Questions

1. Derive and interpret the swing equation for a synchronous generator, including the roles of inertia and damping.

2. Explain the equal-area criterion and discuss its assumptions and limitations in multimachine systems.

3. Describe a complete small-signal stability assessment using eigenvalues, mode shapes, and participation factors.

4. Explain the mechanisms of short-term and long-term voltage instability and the principal mitigation measures.

5. Discuss how excitation systems, power-system stabilizers, governors, FACTS devices, and HVDC controls contribute to stability.

Analytical / Application Questions

1. A generator transfers power through a corridor whose transfer reactance increases after a line outage. Explain how the power-angle curve, synchronizing coefficient, and transient stability margin change, and identify suitable corrective actions.

2. A system with declining synchronous inertia experiences a large generator trip. Develop a staged frequency-response strategy and discuss the interactions among fast frequency response, governors, reserves, and under-frequency load shedding.

3. An eigenvalue study reveals a poorly damped inter-area mode only under high renewable dispatch. Propose an investigation and control-tuning workflow, including model validation, nonlinear verification, and protection or operational considerations.

22. Multiple Choice Questions with Answers

Question 1

In the swing equation, a positive value of P_m − P_e indicates that the generator rotor is

A. decelerating

B. accelerating

C. at the maximum power-angle point

D. operating at zero speed deviation

Correct Answer: B. accelerating

Question 2

For a single-machine-infinite-bus system, the synchronizing power coefficient at the operating point is

A. P_max sin δ_0

B. P_max cos δ_0

C. P_m/P_max

D. Hω_s/2

Correct Answer: B. P_max cos δ_0

Question 3

An eigenvalue with a positive real part indicates that the corresponding linearized mode is

A. stable and heavily damped

B. marginally stable

C. unstable

D. non-oscillatory by definition

Correct Answer: C. unstable

Question 4

The equal-area criterion primarily compares

A. reactive reserve with voltage demand

B. accelerating energy with available decelerating energy

C. inertia with governor droop

D. fault current with breaker rating

Correct Answer: B. accelerating energy with available decelerating energy

Question 5

Which change generally improves transient rotor-angle stability for a given fault?

A. Slower fault clearing

B. Higher pre-fault transfer angle

C. Faster fault clearing

D. Lower post-fault transfer capability

Correct Answer: C. Faster fault clearing

Question 6

A continuation power-flow study is especially useful for

A. tracing voltage solutions as loading changes

B. calculating breaker interrupting current only

C. tuning turbine valve positions without a network model

D. measuring rotor inertia directly

Correct Answer: A. tracing voltage solutions as loading changes

Question 7

Which phenomenon is most directly associated with a large generation loss and insufficient reserves?

A. Frequency instability

B. Only local rotor damping

C. Saddle-node voltage bifurcation in every case

D. Subtransient reactance reduction

Correct Answer: A. Frequency instability

Question 8

The principal purpose of a power-system stabilizer is to

A. replace all primary frequency control

B. provide supplementary damping through excitation control

C. increase transformer tap-changing speed

D. disconnect every faulted line immediately

Correct Answer: B. provide supplementary damping through excitation control

Question 9

Why may a STATCOM be valuable during a voltage depression?

A. It supplies dynamically controllable reactive current

B. It increases generator mechanical input directly

C. It eliminates the need for protection

D. It guarantees rotor-angle stability for every fault

Correct Answer: A. It supplies dynamically controllable reactive current

Question 10

Which statement best describes a limitation of linear eigenvalue analysis?

A. It cannot identify any oscillatory modes

B. It applies only to voltage stability

C. It describes local behavior and does not by itself establish severe-disturbance stability

D. It requires no operating point or dynamic model

Correct Answer: C. It describes local behavior and does not by itself establish severe-disturbance stability