(SEM VII) THEORY EXAMINATION 2024-25 POWER SYSTEM DYNAMICS AND CONTROL

SECTION A

(2 × 10 = 20 Marks)

a) Define power system stability and its types

Power system stability is defined as the ability of an electrical power system to maintain a state of equilibrium under normal operating conditions and to regain an acceptable operating state after being subjected to a disturbance. Depending on the nature and magnitude of the disturbance, power system stability is classified into steady-state stability, transient stability, dynamic or small-signal stability, voltage stability, and frequency stability.

b) What are the states of operation in power systems?

The operation of a power system can be classified into different states based on system security and operating limits. In the normal state, all system variables remain within permissible limits. The alert state occurs when the system is still operating normally but is close to its limits. In the emergency state, one or more system constraints are violated. The in-extremis state refers to severe conditions leading to cascading failures or blackouts, while the restorative state represents the recovery process after a major system collapse.

c) What is Park’s Transformation?

Park’s Transformation is a mathematical transformation used to convert three-phase alternating quantities into direct, quadrature, and zero-axis components. This transformation rotates the reference frame with the rotor, thereby converting time-varying AC quantities into DC quantities under steady-state conditions. It greatly simplifies the analysis of synchronous machines and power system dynamics.

d) Define per-unit quantities and their advantages in power system analysis

Per-unit quantities are normalized values expressed as a fraction of selected base quantities such as voltage, current, power, and impedance. The per-unit system simplifies power system calculations by eliminating the need to account for transformer ratios and allows easy comparison of different equipment ratings while improving numerical accuracy.

e) What is the purpose of excitation system modeling?

Excitation system modeling is carried out to study and control the dynamic behavior of synchronous generators. The excitation system regulates the generator terminal voltage and reactive power output while also improving both transient and small-signal stability. Accurate modeling helps in analyzing system response during disturbances and in designing effective control strategies.

f) Draw a block diagram of an excitation system

An excitation system consists of a reference voltage compared with the terminal voltage to produce an error signal. This error signal is amplified and fed to the exciter, which supplies field current to the generator. The generator terminal voltage is continuously fed back to the comparator, forming a closed-loop control system.

g) Define small signal stability in power systems

Small signal stability refers to the ability of a power system to maintain synchronism when subjected to small disturbances such as minor load changes. This type of stability is analyzed using linearized mathematical models and focuses on the system’s ability to damp low-frequency oscillations.

h) What is the significance of the Routh-Hurwitz criterion in system stability analysis?

The Routh-Hurwitz criterion is a mathematical method used to determine the stability of a linear system by examining the coefficients of its characteristic equation. It allows engineers to assess system stability without explicitly calculating the roots of the equation, making it a powerful and efficient stability analysis tool.

i) Define the function of a washout circuit in a PSS

The washout circuit in a Power System Stabilizer acts as a high-pass filter that allows oscillatory signals to pass while blocking steady-state components. Its main function is to ensure that the PSS responds only to dynamic changes and does not interfere with steady-state operating conditions.

j) List the control signals used in PSS

The control signals used in a Power System Stabilizer are derived from system variables such as rotor speed deviation, frequency deviation, electrical power variation, or accelerating power. These signals help the PSS generate a stabilizing signal to improve damping of oscillations.

SECTION B

(10 × 3 = 30 Marks)

2(a) Explain the concept of power system stability and the associated challenges

Power system stability is a critical requirement for reliable operation of electrical networks. It ensures that generators remain in synchronism following disturbances. Modern power systems face challenges such as increased interconnections, long transmission lines, high power transfers, renewable energy integration, and reduced system inertia. These factors increase the complexity of maintaining stability and require advanced control techniques.

2(b) Discuss the steady-state performance analysis of synchronous machines

Steady-state performance analysis of synchronous machines involves evaluating their behavior under constant operating conditions. This includes studying voltage regulation, power factor control, power-angle characteristics, efficiency, and losses. Such analysis is essential for determining operating limits and ensuring reliable machine operation.

2(c) Explain the measurement techniques for high DC voltages

High DC voltages are measured using techniques such as potential dividers, electrostatic voltmeters, and generating voltmeters. Potential dividers reduce the voltage to a measurable level, while electrostatic voltmeters measure voltage based on electrostatic force. Generating voltmeters are non-contact devices suitable for very high voltage measurements.

2(d) Perform a small signal analysis of a single-machine system

Small signal analysis of a single-machine system involves linearizing the system equations around an operating point. The swing equation is used to represent rotor dynamics, and a block diagram is developed to show the interaction between generator, excitation system, and load. Stability is assessed using eigenvalue analysis.

2(e) Explain the basic concepts of applying Power System Stabilizers

Power System Stabilizers are used to enhance damping of low-frequency oscillations in power systems. They operate by providing supplementary control signals to the excitation system, thereby generating damping torque proportional to speed deviations and improving dynamic stability.

SECTION C

(10 Marks Each)

3(a) Discuss the problems related to system dynamics in power systems

Power system dynamics are affected by non-linear behavior, time delays, and interactions between control systems. Poor damping can lead to sustained oscillations, while rapid load changes can cause instability. Increasing system complexity further aggravates these dynamic issues.

3(b) Derive and analyze the steady-state stability limit of a power system

The steady-state stability limit is derived from the power-angle relationship of a synchronous machine. Maximum power transfer occurs when the load angle reaches ninety degrees. Beyond this point, the system becomes unstable, defining the steady-state stability limit.

4(a) Derive the equivalent circuit of a synchronous machine

The equivalent circuit of a synchronous machine represents its electrical behavior using resistive and reactive elements. It includes armature resistance, leakage reactance, and magnetizing reactance, along with field and damper windings, enabling detailed performance and stability analysis.

4(b) Explain the method to determine the parameters of the equivalent circuit

The parameters of a synchronous machine are obtained through experimental tests such as open-circuit and short-circuit tests. These tests help determine reactance, resistance, and saturation effects required for accurate modeling.

5(a) Derive the state equations for a synchronous machine model

State equations of a synchronous machine are derived by selecting appropriate state variables such as rotor angle, speed, and flux linkages. These equations describe the dynamic behavior of the machine under transient conditions.

5(b) Explain the dynamics of a synchronous generator connected to an infinite bus

When connected to an infinite bus, the generator operates at constant voltage and frequency. Its dynamics are governed by the swing equation, which determines rotor motion in response to disturbances and power imbalances.

6(a) Derive the characteristic equation and apply the Routh-Hurwitz criterion

The characteristic equation of a single-machine system is obtained from the linearized dynamic equations. The Routh-Hurwitz criterion is then applied to assess system stability based on the coefficients of this equation.

6(b) Explain the synchronizing and damping torque analysis

Synchronizing torque helps restore the rotor to its equilibrium position after a disturbance, while damping torque suppresses oscillations. Both torques are essential for maintaining system stability.

7(a) Discuss the structure and tuning methods of PSS

A Power System Stabilizer consists of gain, washout, and phase compensation blocks. Proper tuning is essential and is achieved using techniques such as root locus and frequency response methods to ensure adequate damping.

7(b) Analyze the role of a washout circuit in PSS

The washout circuit ensures that the stabilizer responds only to dynamic disturbances by filtering out steady-state signals. This allows effective damping of oscillations without affecting normal system operation.