Power Systems

Chapter 8
Power-System Stability and Dynamic Performance

Bachelors Program in Electrical Engineering
Power Systems • Bachelor

Power-System Stability and Dynamic Performance

Introduction

A power system must remain in an acceptable operating state after disturbances such as faults, generator outages, transmission-line trips, abrupt load changes, and converter-control interactions. Stability is not a single phenomenon: rotor angles, system frequency, and bus voltages involve different physical mechanisms and time scales.

Stability assessment determines whether synchronism is preserved, frequency remains within operational limits, voltages recover, and oscillations are adequately damped. It therefore connects machine dynamics, network analysis, protection, control, and operational planning.

Learning Objectives

After studying this chapter, students should be able to:

Distinguish rotor-angle, frequency, and voltage stability.
Derive and apply the synchronous-machine swing equation.
Use the power-angle relation and equal-area criterion for first-swing assessment.
Formulate multimachine dynamics on a common MVA base correctly.
Analyze small-signal oscillations using linearized models.
Estimate initial rate of change of frequency following a power imbalance.
Explain voltage instability using reactive-power limitations and power-flow Jacobians.
Evaluate emergency controls and stability-improvement measures.
Select appropriate dynamic simulation methods for engineering studies.

1. Classification of Power-System Stability

Power-system stability is the ability of an initially operating electric power system to regain an acceptable equilibrium after a physical disturbance, with most system variables bounded and the interconnected system remaining substantially intact.

Category	Principal variable	Typical causes	Approximate time scale
Rotor-angle stability	Generator rotor angles	Faults, line trips, weak synchronizing torque	Fractions of a second to tens of seconds
Frequency stability	System frequency	Major generation–load imbalance, islanding	Seconds to minutes
Voltage stability	Bus voltage magnitudes	Reactive-power deficiency, heavy transfer, load recovery	Seconds to tens of minutes

Rotor-angle stability is subdivided into:

Transient stability: response to severe disturbances for which nonlinear dynamics are important.
Small-signal stability: response to sufficiently small disturbances that linearization around an operating point is valid.

Voltage stability may be short-term or long-term. Frequency stability may involve short-term arrest of a frequency decline and longer-term restoration by governors, automatic generation control, and operator action.

These categories interact. A fault can simultaneously accelerate generators, depress voltage, and reduce electrical load. Likewise, low voltage can trigger motor stalling and deepen a frequency disturbance.

2. Rotor Dynamics and the Swing Equation

2.1 Mechanical foundation

For a synchronous generator rotor,

J\frac{dω_m}{dt}=T_m-T_e-T_d

where J is rotor moment of inertia in kg·m², ω_m is mechanical angular speed in rad/s, T_m is mechanical torque, T_e is electromagnetic torque, and T_d represents damping torque.

The inertia constant is

H=\frac{\tfrac{1}{2}Jω_m,s²}{S_r}

where ω_m,s is rated mechanical speed and S_r is machine rating. When stored kinetic energy is expressed in MJ and rating in MVA, H is measured in seconds.

Let δ be the rotor electrical angle relative to a synchronously rotating reference, and let ω_s=2πf₀ be synchronous electrical angular frequency. Assuming speed remains close enough to synchronous speed to replace torque by power divided by synchronous speed, the per-unit swing equation is

\frac{2H}{ω_s}\frac{d²δ}{dt²}=P_m-P_e-D\frac{dδ}{dt}

Here P_m and P_e are mechanical and electrical powers in per unit on the machine base. The coefficient D is a damping coefficient expressed as per-unit power per electrical rad/s. Electrical radians are dimensionless, so 2H/ω_s has dimensions of seconds squared.

Without damping,

\frac{d²δ}{dt²}=\frac{ω_s}{2H}P_a, \qquad P_a=P_m-P_e

A positive accelerating power P_a increases rotor speed relative to the synchronous reference.

Worked Example 1: Initial rotor acceleration

A 50 Hz generator has H=5\ s. Immediately after a disturbance, its accelerating power is 0.20 pu. Neglect damping.

\frac{d²δ}{dt²}=\frac{2π(50)}{2(5)}(0.20)=6.283\ \text{rad/s}²

If this acceleration remains constant for 0.10 s,

Δ\dot{δ}=6.283(0.10)=0.6283\ \text{rad/s}

Δδ=\frac{1}{2}(6.283)(0.10)²=0.03142\ \text{rad}=1.80°

The corresponding electrical frequency deviation is Δf=Δ\dot{δ}/(2π)=0.10\ Hz. The constant-acceleration assumption is suitable only for a short interval over which powers do not change appreciably.

3. Power-Angle Characteristic

For a classical generator represented by internal voltage E behind reactance and connected through a lossless equivalent reactance X to an infinite bus of voltage V,

P_e=P_max\sin δ, \qquad P_max=\frac{EV}{X}

Voltages are in per unit and X is per-unit reactance on the same base. The infinite bus has constant voltage magnitude, phase reference, and frequency.

At equilibrium,

P_m=P_max\sin δ₀

A feasible equilibrium requires P_m≤P_max. For the lossless sinusoidal model, the equilibrium with δ₀<90° has positive synchronizing coefficient and is locally stable if damping is positive.

Power-angle characteristic and equal-area criterion

Figure: Power-angle characteristic and equal-area criterion

Figure: Power-angle curve showing the initial angle, clearing angle, unstable equilibrium, and energy-balancing regions.

4. Equal-Area Criterion

The equal-area criterion provides a graphical and analytical first-swing stability test. It applies directly to a single-machine–infinite-bus system or a valid two-coherent-group equivalent. It assumes known power-angle curves and normally neglects damping during the first swing. It is not a general substitute for multimachine time-domain simulation.

Multiplying the undamped swing equation by dδ/dt and integrating gives an energy relation. Stability requires that the kinetic energy gained during acceleration can be removed during subsequent deceleration:

\int_δ₀^δ_c(P_m-P_e,f)\,dδ
=
\int_{δ_c}^{δ_max}(P_e,p-P_m)\,dδ

Here P_e,f is electrical power during the fault, P_e,p is the post-fault power-angle curve, δ_c is clearing angle, and δ_max is the maximum first-swing angle. At the critical condition, δ_max reaches the post-fault unstable equilibrium.

Worked Example 2: Critical clearing angle and time

Consider a generator with P_m=0.5\ pu and P_max=1.0\ pu. The pre-fault and post-fault transfer characteristics are identical. During a three-phase fault, assume electrical transfer is zero.

The initial stable angle and unstable equilibrium are

δ₀=\sin^-1(0.5)=30°

δ_u=π-δ₀=150°

For the critical trajectory,

P_m(δ_c-δ₀)=\int_{δ_c}^δ_u(P_max\sin δ-P_m)\,dδ

which reduces to

\cos δ_c=\cos δ_u+\frac{P_m}{P_max}(δ_u-δ₀)

Angles in this equation must be in radians. Thus,

\cos δ_c=-0.8660+0.5(2.0944)=0.1812

Therefore,

δ_c=79.6°

If H=5\ s and f₀=50\ Hz, the fault-on acceleration is constant because P_e,f=0. Hence,

t_c=\sqrt{\frac{4H(δ_c-δ₀)}{ω_sP_m}}
=\sqrt{\frac{4(5)(0.865)}{314.16(0.5)}}=0.332\ \text{s}

This clearing-time result is specific to the assumed zero-transfer fault and constant mechanical power. Practical critical clearing times are obtained from detailed dynamic simulation.

5. Multimachine Stability

5.1 Common-base formulation

For machine i, let H_i be its inertia constant in seconds on its own rating S_i. If all mechanical and electrical powers are expressed in per unit on a common system base S_base, the correct swing equation is

\frac{2H_iS_i}{ω_sS_base}\frac{d²δ_i}{dt²}
=P_mi-P_ei-D_i^sys\frac{dδ_i}{dt}

The damping coefficient D_i^sys is expressed on the system power base. If D_i^mach is on the machine base, then D_i^sys=D_i^machS_i/S_base.

Equivalently, define the inertia constant converted to the common base:

H_i^sys=H_i\frac{S_i}{S_base}

Then the inertia coefficient is 2H_i^sys/ω_s. Omitting the rating ratio S_i/S_base while using common-base powers gives an incorrect acceleration.

For a network reduced to generator internal buses,

P_ei=\sum_j=1ⁿ|E_i||E_j|\left[G_ij\cos(δ_i-δ_j)+B_ij\sin(δ_i-δ_j)\right]

where G_ij+jB_ij is an element of the reduced admittance matrix. This general expression permits transfer conductances; lossless-network simplifications depend on the adopted admittance sign convention.

5.2 Center of inertia

The center-of-inertia angle is

δ_COI=\frac{\sum_i H_iS_iδ_i}{\sum_i H_iS_i}

Relative angles δ_i-δ_COI reveal whether individual machines or coherent groups separate. Weighting must use stored kinetic energy, proportional to H_iS_i, rather than inertia constants alone.

The aggregate inertia on the system base is

H_sys=\frac{\sum_i H_iS_i}{S_base}

Worked Example 3: Two machines on a common base

On a 1000 MVA, 50 Hz system base, generator 1 has H₁=4\ s and S₁=500\ MVA, while generator 2 has H₂=3\ s and S₂=1000\ MVA.

Their common-base inertia coefficients are

M₁=\frac{2(4)(500)}{314.16(1000)}=0.01273\ \text{s}²

M₂=\frac{2(3)(1000)}{314.16(1000)}=0.01910\ \text{s}²

If accelerating powers are +0.10 pu and −0.10 pu, respectively, and damping is neglected,

\ddot{δ}₁=\frac{0.10}{0.01273}=7.85\ \text{rad/s}²

\ddot{δ}₂=\frac{-0.10}{0.01910}=-5.24\ \text{rad/s}²

The machines have different accelerations because their stored kinetic energies differ, even though the power deviations have equal magnitudes on the system base.

6. Small-Signal Stability and Oscillations

For a single-machine model, small perturbations around δ₀ give

ΔP_e≈K_sΔδ, \qquad K_s=\left.\frac{dP_e}{dδ}\right|_δ₀=P_max\cos δ₀

The linearized equation is

MΔ\ddot{δ}+DΔ\dot{δ}+K_sΔδ=0, \qquad M=\frac{2H}{ω_s}

For K_s>0, the undamped natural frequency and damping ratio are

ω_n=\sqrt{\frac{K_s}{M}}, \qquad
ζ=\frac{D}{2\sqrt{MK_s}}

These expressions apply to the second-order model with constant coefficients. Detailed multimachine systems are represented by differential-algebraic equations:

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

After linearization and elimination of algebraic increments where the algebraic Jacobian is nonsingular,

Δ\dot{x}=AΔx+BΔu

Each eigenvalue λ=σ±jω_d describes a mode. Stability requires all non-reference dynamic modes to have σ<0. The modal frequency and damping ratio are

f_d=\frac{|ω_d|}{2π}, \qquad ζ=\frac{-σ}{\sqrt{σ²+ω_d²}}

Participation factors help identify states and equipment strongly associated with a mode.

Typical electromechanical modes include:

Local modes: one generator oscillates against nearby units, commonly 0.7–2 Hz.
Inter-area modes: coherent generator groups oscillate against one another, commonly 0.1–0.8 Hz.
Control modes: poorly tuned exciters, governors, converters, or stabilizers dominate.
Torsional modes: turbine-generator shaft sections exchange mechanical energy.

A power-system stabilizer adds a suitably phased supplementary excitation signal, often derived from speed, frequency, or power, to increase damping torque. Poor tuning can reduce damping in another operating condition.

7. Frequency Stability and Inertia

For an approximately coherent system during the first moments after a disturbance,

\frac{2H_sys}{f₀}\frac{df}{dt}=ΔP

where ΔP=P_m-P_e is net accelerating power in per unit on S_base. This relation estimates the initial center-of-inertia rate of change of frequency (RoCoF), before significant governor, load, or converter response.

Worked Example 4: Initial RoCoF

A 50 Hz system has H_sys=4\ s. A generation outage creates a deficit of 0.08 pu.

\frac{df}{dt}=\frac{50}{2(4)}(-0.08)=-0.50\ \text{Hz/s}

The result is an initial value; it must not be extrapolated linearly once controls and frequency-sensitive loads respond.

A simplified longer-term frequency-response model is

\frac{2H_sys}{f₀}\frac{dΔf}{dt}=ΔP_m-ΔP_L-D_fΔf

where D_f is load-frequency sensitivity in pu/Hz. For aggregate governor droop represented by ΔP_m=-Δf/R, with R in Hz/pu, the quasi-steady primary-response deviation after a load increase ΔP_L>0 is

Δf_ss=-\frac{ΔP_L}{D_f+1/R}

Primary control arrests frequency but normally leaves an offset. Secondary control restores frequency and scheduled interchange. Tertiary actions replenish reserves and redispatch generation.

Converter-interfaced resources may provide fast frequency response or grid-forming behavior. Such controls are not automatically equivalent to synchronous inertia: response magnitude, delay, energy limits, current limits, and recovery behavior must be modeled explicitly.

8. Voltage Stability

Voltage stability concerns the ability to maintain acceptable bus voltages after a disturbance. The central mechanism is often inadequate reactive-power support relative to network and load requirements.

For a lossless two-bus system,

P=\frac{V_sV_r}{X}\sin δ

Q_r=\frac{V_sV_r}{X}\cos δ-\frac{V_r²}{X}

where Q_r is reactive power delivered into the receiving bus under the stated sign convention. Heavy transfer, large reactance, and low receiving voltage reduce voltage-security margins.

In power-flow analysis,

\begin{bmatrix}ΔP\\ΔQ\end{bmatrix}
=
\begin{bmatrix}J_Pθ&J_PV\\J_Qθ&J_QV\end{bmatrix}
\begin{bmatrix}Δθ\\ΔV\end{bmatrix}

Near a voltage-collapse point, the relevant power-flow Jacobian becomes singular or severely ill-conditioned. Large sensitivities, such as dV/dQ, indicate reduced margin, but a single local sensitivity is not a universal security index.

Important mechanisms include:

generator field-current and armature-current limits;
insufficient shunt or dynamic reactive support;
tap-changing transformers restoring load and increasing network stress;
induction-motor stalling and slow reacceleration;
constant-power loads drawing more current as voltage falls;
converter current limits and control-mode switching.

P–V curves, Q–V curves, continuation power flow, modal analysis, and time-domain simulation are complementary tools. Static methods locate equilibrium limits; they do not fully represent motor, protection, or control dynamics.

9. Stability Improvement and Emergency Control

Objective	Representative measures
Increase transient stability	Faster fault clearing, single-pole tripping, high-speed reclosing, reduced transfer reactance, dynamic braking, generator rejection
Improve oscillation damping	Power-system stabilizers, governor tuning, FACTS modulation, HVDC supplementary control
Arrest frequency decline	Fast reserves, battery response, under-frequency load shedding, controlled islanding
Support voltage	Synchronous condensers, SVCs, STATCOMs, shunt capacitors, generator excitation, load shedding
Reduce disturbance severity	Remedial action schemes, topology control, transfer limits, preventive redispatch

Transient stability can be improved by increasing post-fault transfer capability, reducing fault duration, reducing accelerating power, or increasing effective decelerating energy. Because protection speed directly affects clearing angle, relay coordination and breaker operating time are stability variables, not merely protection details.

Emergency controls must be dependable and secure. A remedial action scheme that fails to operate may permit cascading instability; one that operates unnecessarily may disconnect customers or generation. Designs therefore require redundancy, communication supervision, periodic testing, and analysis of hidden failures.

10. Dynamic Simulation Practice

A defensible study normally follows these steps:

Validate the steady-state operating point and equipment limits.
Select credible contingencies and protection sequences.
Use models appropriate to the study time scale.
Verify parameters, controls, limiters, load composition, and initialization.
Simulate long enough to detect delayed instability.
Examine angles, frequencies, voltages, control outputs, and protection actions.
Perform sensitivity studies for uncertain parameters and operating conditions.

Positive-sequence RMS simulation is widely used for electromechanical and voltage-stability studies. Electromagnetic-transient simulation is needed where switching, unbalance, subcycle converter controls, weak-grid interactions, or protection waveforms materially affect the outcome.

Model limitations are significant. Classical generator models may overestimate or underestimate stability when excitation, saliency, governors, saturation, or limiters matter. Constant-power load models may exaggerate short-term stress, while static impedance models may hide motor-stalling risks. Validation against event records is therefore essential.

11. Illustrative Case: Stability Assessment of a Low-Inertia Grid

Background

This is an illustrative case. A 10 GW, 50 Hz regional system is importing power through two major corridors. Retirement of synchronous generation has reduced aggregate inertia to 3.0 s on a 10 GVA base.

Problem

The credible loss of a 600 MW generator produces a deficit of 0.06 pu. A separate three-phase transmission fault is also studied because it may cause first-swing separation of the importing region and delayed voltage recovery.

Analysis

The estimated initial RoCoF after the generator loss is

\frac{df}{dt}=\frac{50}{2(3.0)}(-0.06)=-0.50\ \text{Hz/s}

Dynamic simulations show that frequency arrest depends strongly on governor deadbands, battery activation delay, and available headroom. For the transmission fault, generator relative angles are evaluated against the center of inertia. Voltage recovery is examined with induction-motor loads and generator excitation limits enabled.

Approach

The engineering team applies four coordinated measures:

A battery provides rapid active-power response subject to energy and current limits.
Synchronous condensers add short-circuit strength, inertia, and dynamic reactive support.
Critical fault-clearing time is increased through faster breakers and improved transfer capability.
Staged under-frequency and under-voltage load shedding provides backup protection.

Power-system stabilizers are retuned using eigenvalue and time-domain studies so that the weakly damped inter-area mode remains adequately damped over several dispatch patterns.

Outcome

The combined design lowers initial frequency risk, improves voltage recovery, and preserves synchronism for the selected credible contingencies. No single measure is treated as sufficient: battery response supports frequency, synchronous condensers improve voltage and strength, and protection improvements reduce rotor-angle excursion.

Learning Points

Stability categories must be assessed together when controls and disturbances interact.
Initial RoCoF is governed primarily by imbalance and inertia, but the nadir depends on dynamic response.
Converter current and energy limits must be represented explicitly.
Security conclusions should be robust across operating conditions and model uncertainty.

12. Governance, Regulation, and Contemporary Developments

Grid codes increasingly specify fault ride-through, reactive-current injection, frequency response, RoCoF withstand capability, and model-validation requirements. Compliance studies should use controlled model versions and auditable assumptions.

Wide-area measurements enable online oscillation detection and dynamic-security assessment. Machine learning can screen contingencies or estimate stability margins rapidly, but it should not replace physics-based validation. Training data may omit rare severe events, and opaque classifications can create operational risk. Human oversight, uncertainty reporting, cybersecurity, and fallback protection remain necessary.

The transition toward converter-dominated systems is changing stability analysis. Grid-following converters depend on a sufficiently strong voltage waveform, whereas grid-forming converters can establish voltage and frequency references. New concerns include control interaction, current-limited fault response, reduced system strength, and fast instability beyond the bandwidth of traditional electromechanical models.

Chapter Summary

Power-system stability includes rotor-angle, frequency, and voltage phenomena. The swing equation relates accelerating power to rotor-angle acceleration through stored kinetic energy. For common-base multimachine analysis, inertia must be converted using H_iS_i/S_base. The equal-area criterion assesses first-swing stability only for systems reducible to an appropriate one-machine or two-group model.

Small-signal stability is evaluated through linearization, eigenvalues, modal frequencies, damping ratios, and participation factors. Frequency response depends initially on aggregate inertia and power imbalance, then on load response, governors, converters, and reserves. Voltage stability is governed by network transfer capability, reactive support, equipment limits, and load dynamics. Reliable stability improvement combines preventive operation, control tuning, protection, emergency schemes, realistic simulation, and validated models.

Key Terms

Accelerating power: Difference between mechanical input and electrical output power.

Center of inertia: Energy-weighted angular reference for a multimachine system.

Critical clearing angle: Largest fault-clearing rotor angle compatible with first-swing stability under stated assumptions.

Critical clearing time: Maximum fault duration compatible with stability for a specified contingency and protection sequence.

Damping ratio: Measure of the rate at which an oscillatory mode decays.

Equal-area criterion: Energy-based first-swing stability test for an appropriate reduced system.

Frequency nadir: Minimum frequency reached after a generation deficit.

Grid-forming converter: Converter controlled to establish a voltage and frequency reference.

Inertia constant: Stored kinetic energy at rated speed divided by machine rating.

Inter-area mode: Oscillation involving coherent generator groups in different regions.

Power-system stabilizer: Supplementary excitation controller used to increase electromechanical damping.

Rate of change of frequency: Time derivative of system frequency following an imbalance.

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

Small-signal stability: Stability under disturbances sufficiently small for linear analysis.

Synchronizing coefficient: Incremental change in electrical power with rotor angle.

Transient stability: Ability to preserve synchronism following a severe disturbance.

Voltage collapse: Progressive voltage decline associated with loss of a viable stable operating condition.

Voltage stability: Ability to maintain acceptable bus voltages after a disturbance.

Review Questions

Short Answer Questions

Distinguish transient rotor-angle stability from small-signal stability.
Define the inertia constant and state its physical unit.
Why must machine inertia be converted when powers use a common system MVA base?
What does a negative real part of an eigenvalue indicate?
Why does primary frequency control normally leave a steady-state frequency offset?

Long Answer Questions

Derive the per-unit swing equation from the mechanical torque equation and state its assumptions.
Explain the equal-area criterion, including its applicability conditions and limitations.
Describe the mechanisms of short-term and long-term voltage instability.
Explain how eigenvalues, damping ratios, and participation factors are used in small-signal analysis.
Compare synchronous inertia, fast frequency response, and grid-forming converter behavior.

Analytical / Application Questions

A 60 Hz generator has H=4.5\ s and experiences an accelerating power of 0.15 pu. Neglecting damping, calculate its initial angular acceleration and angle change after 0.08 s.
Two generators rated 300 MVA and 700 MVA have inertia constants of 5 s and 3 s. Form their swing-equation inertia coefficients on a 1000 MVA, 50 Hz base.
Develop a coordinated mitigation plan for a weak area experiencing poor inter-area damping, low post-fault voltage, and excessive RoCoF. Justify each proposed measure.

Multiple Choice Questions with Answers

Question 1

Which statement best defines transient rotor-angle stability?

A. The ability to maintain constant voltage during normal load variation

B. The ability of synchronous machines to remain in synchronism after a severe disturbance

C. The ability of governors to restore scheduled interchange

D. The ability of a power-flow algorithm to converge

Correct Answer: B. The ability of synchronous machines to remain in synchronism after a severe disturbance

Question 2

A 50 Hz generator has H=5\ s and accelerating power of 0.20 pu. Neglecting damping, what is its initial angular acceleration?

A. 3.14 rad/s²

B. 6.28 rad/s²

C. 12.57 rad/s²

D. 31.42 rad/s²

Correct Answer: B. 6.28 rad/s²

Question 3

A generator has H=5\ s and rating 400 MVA. On a 1000 MVA, 50 Hz common base, what is the coefficient multiplying d²δ/dt² in its swing equation?

A. 0.00637 s²

B. 0.01273 s²

C. 0.03183 s²

D. 0.07958 s²

Correct Answer: B. 0.01273 s²

Question 4

The equal-area criterion is directly applicable to which system?

A. Any nonlinear multimachine system without reduction

B. Only a purely resistive distribution feeder

C. A single-machine–infinite-bus system or valid two-coherent-group equivalent

D. Only a system operating at zero mechanical input

Correct Answer: C. A single-machine–infinite-bus system or valid two-coherent-group equivalent

Question 5

For P_m=0.5\ pu and P_max=1.0\ pu, with zero transfer during the fault and identical pre-fault and post-fault curves, what is the critical clearing angle?

A. 30.0°

B. 60.0°

C. 79.6°

D. 150.0°

Correct Answer: C. 79.6°

Question 6

A 50 Hz system with H_sys=4\ s suffers a generation deficit of 0.08 pu. What is the initial RoCoF?

A. −0.25 Hz/s

B. −0.50 Hz/s

C. −1.00 Hz/s

D. −2.00 Hz/s

Correct Answer: B. −0.50 Hz/s

Question 7

For the classical power-angle relation P_e=P_max\sin δ, when is the synchronizing coefficient positive?

A. When \cos δ>0

B. When \sin δ<0

C. Only when δ=90°

D. Whenever mechanical power is zero

Correct Answer: A. When \cos δ>0

Question 8

Which condition most directly indicates proximity to a static voltage-collapse point in power-flow analysis?

A. The rotor inertia becomes infinite

B. The relevant power-flow Jacobian approaches singularity

C. System frequency becomes exactly nominal

D. Transmission resistance becomes zero

Correct Answer: B. The relevant power-flow Jacobian approaches singularity

Question 9

What is the principal purpose of a power-system stabilizer?

A. To increase damping of electromechanical oscillations

B. To calculate economic dispatch

C. To replace generator overcurrent protection

D. To eliminate all reactive-power demand

Correct Answer: A. To increase damping of electromechanical oscillations

Question 10

Which weighting is correct for calculating the multimachine center-of-inertia angle?

A. Machine terminal voltage

B. Machine reactive-power output

C. The product H_iS_i

D. The reciprocal of machine rating

Correct Answer: C. The product H_iS_i

Power Systems
Chapter 8 of 15

Chapter 8 Power-System Stability and Dynamic Performance