(SEM VII) THEORY EXAMINATION 2022-2023 POWER SYSTEM DYNAMICS AND CONTROL

SECTION A – Short Answers (2 Marks Each)

(a) Purpose of damper windings in synchronous machines

Damper windings are used to suppress oscillations (hunting) in synchronous machines. They provide damping torque during transient conditions and help improve system stability.

(b) Difference between transient and steady-state stability

Transient stability refers to the ability of the system to remain in synchronism after large disturbances such as faults.

Steady-state stability deals with small, gradual changes in load or operating conditions.

(c) Quantities transformed using Park’s transformation

Park’s transformation converts stator voltages, currents, and flux linkages from three-phase (abc) coordinates to d-q-0 rotating reference frame.

(d) Benefits of per-unit (PU) system

PU system simplifies calculations, reduces numerical errors, allows easy comparison of equipment with different ratings, and eliminates need for repeated unit conversions.

(e) Critical clearing angle

Critical clearing angle is the maximum rotor angle at which a fault must be cleared so that the system remains stable.

(f) Short circuit ratio (SCR) of alternator

SCR is the ratio of field current required for rated voltage on open circuit to the field current required for rated current under short circuit conditions.

(g) Applications of Routh-Hurwitz criterion

Routh-Hurwitz criterion is used to determine steady-state stability of a power system without solving characteristic equations explicitly.

(h) Damping torque and its production

Damping torque is the torque that opposes rotor oscillations. It is produced by damper windings, excitation control, and power system stabilizers.

(i) Function of washout circuit

Washout circuit acts as a high-pass filter, allowing oscillatory signals to pass while blocking steady-state signals.

(j) Power System Stabilizers (PSS)

PSS are control devices used to improve damping of low-frequency oscillations in power systems by modulating excitation.

SECTION B – Long Answers (10 Marks Each)

(a) States of operation for power system security

Power system security includes:

Normal state: All constraints satisfied

Alert state: Constraints may be violated after disturbance

Emergency state: Constraints violated but system intact

In-extremis state: System breakup occurs

Restorative state: System is restored after blackout

(b) Selection of base quantities in PU system

While selecting base:

Same base MVA should be used throughout

Base voltage must be chosen carefully for stator and rotor

Impedance and current bases are derived from MVA and voltage
Proper base selection ensures consistency and accuracy.

(c) Power transmitted by generator connected to infinite bus

When generator with reactance Xg is connected to infinite bus via two parallel lines each of reactance Xt, power transfer is:

Before fault:

P=EVXeqsin⁡δP = \frac{EV}{X_{eq}} \sin \deltaP=Xeq​EV​sinδ

After one line is removed:

Xeq=Xg+2XtX_{eq} = X_g + 2X_tXeq​=Xg​+2Xt​

Thus, power transfer capability reduces, affecting stability.

(d) Application of Routh-Hurwitz criterion

The criterion determines stability by examining signs and magnitudes of coefficients of characteristic equation.
If all elements of first column of Routh array are positive → system is stable.

(e) Power System Stabilizer (speed input)

PSS block consists of:

Speed deviation input

Gain block

Washout circuit

Phase compensator

Exciter

It improves damping by producing supplementary control signal to AVR.

SECTION C – Long Answers (10 Marks Each)

3(a) Critical clearing time (CCT)

Critical clearing time is the maximum time allowed to clear a fault without losing synchronism.

tc=2M(δc−δ0)Pm−Pet_c = \sqrt{\frac{2M(\delta_c - \delta_0)}{P_m - P_e}}tc​=Pm​−Pe​2M(δc​−δ0​)​​

It depends on system inertia, fault location, and power angle.

3(b) Equal area criterion using swing equation

Swing equation:

Md2δdt2=Pm−PeM \frac{d^2\delta}{dt^2} = P_m - P_eMdt2d2δ​=Pm​−Pe​

According to equal area criterion, area of acceleration must equal area of deceleration for stability.

4(a) Park’s Transformation and voltage equations

Park’s transformation converts abc variables into dq0 frame:

[vdvqv0]=T[vavbvc]\begin{bmatrix} v_d \\ v_q \\ v_0 \end{bmatrix} = T \begin{bmatrix} v_a \\ v_b \\ v_c \end{bmatrix}​vd​vq​v0​​​=T​va​vb​vc​​​

It simplifies analysis by converting AC quantities into DC form.

4(b) d-axis and q-axis equivalent circuits

d-axis: Field winding, damper winding, flux linkage

q-axis: No field winding, includes damper effects

Parameters include reactances, resistances, and mutual inductances.

5(a) Synchronizing power of salient pole generator

Synchronizing power is the rate of change of electrical power with respect to rotor angle.

P=EVXdsin⁡δ+V2(Xd−Xq)2XdXqsin⁡2δP = \frac{EV}{X_d} \sin \delta + \frac{V^2(X_d - X_q)}{2X_d X_q} \sin 2\deltaP=Xd​EV​sinδ+2Xd​Xq​V2(Xd​−Xq​)​sin2δ

Higher synchronizing power improves stability.

5(b) Transient stability with series compensation

With 50% series compensation:                                Reactance reduces

Power transfer increases                                           Stability limit improves

Switch opening further affects post-fault reactance and stability margin.

6(a) Stability improvement using SVC

SVC provides dynamic reactive power support.        Power with SVC at midpoint:

P=EVX−Xsvcsin⁡δP = \frac{EV}{X - X_{svc}} \sin \deltaP=X−Xsvc​EV​sinδ

It improves voltage profile and stability limit.

6(b) Automatic Voltage Regulator (AVR)

AVR maintains terminal voltage of generator.

Functions:                                                                Voltage control

Reactive power control                                            Improves transient stability

Reduces voltage fluctuations

7(a) Washout circuit block diagram

Washout circuit consists of:                                      Input signal

High-pass filter                                                         Time constant
It ensures response only to oscillatory signals.

7(b) Concepts and objectives of PSS

Objectives:                                                                Damping electromechanical oscillations

Improve small signal stability                                   Enhance system reliability

PSS is designed based on system configuration such as SMIB or multimachine systems.