## Stability of Power Supply Systems

Programme Summary

Major: 13.04.02 Power Industry and Electrical Engineering

Specialisation: Power Supply

Degree: Master

Course units:

Introduction. Origins and developments in research on power system stability.

Unit 1. Static stability analysis methods

Unit 2. Electromagnetic transient equations

Unit 3. Dynamic stability analysis methods

Unit 4. Stability of load nodes

Unit 5. Effect of generator regulators on stability

Unit 6. Asynchronous operation modes of AC machines

Unit 7. Isolated operation of industrial power plants

Unit 8. Analysis of static and dynamic stability of isolated electric power systems

Course contents:

Introduction. Origins and developments in research on power system stability.

A brief overview of the origins and developments in research on power system stability. Evolution of the stability analysis methods in Russia and abroad. Analysis, design and control of transients. Main goals and tasks of the course and its connection to related disciplines. Main forms of stability, their features and impact on the power system. Physical and mathematical modelling principles and techniques in stability studies. Application of computers.

Unit 1. Static stability analysis methods

Sustainability of steady state. General description of static stability analysis methods. Compiling a set of steady state equations. Accurate static stability assessment criteria. Stability of a power system comprising generators equipped with ATS. Small oscillations method in case of operation off an infinite bus or within a multimachine system. Calculation of relative acceleration and synchronizing power. Practical static stability assessment criteria and their application. Looking into possible solutions for the set of steady state equations aimed at analyzing stability. Self-oscillation and its approximate evaluation. Static dead-beat and oscillatory stability. Stability of long-distance power lines.

Unit 2. Electromagnetic transient equations

An approach of dynamic stability analysis. Quality of a transient. An insight into dynamic stability criteria. Basic assumptions. The motion equation of a generator rotor and its solution. The equation of the flux linkage in a synchronous machine. Application of the Park-Gorev equations for a power system. Application of simplified Park-Gorev equations. Numerical integration of differential equation systems. The Runge-Kutt methods.

Unit 3. Dynamic stability analysis methods

General description of dynamic stability analysis methods. Simplified methods of dynamic stability analysis. Dynamic stability assessment criteria. Method of successive intervals. Area rule. Dynamic stability calculation. EMF change behind transient and subtransient inductive reactance. Stability improvement. Quick fault clearing. Synchronous generator parameters and their impact on stability. Impact of the neutral point on dynamic stability. Machine oscillations. High forced oscillations.

Unit 4. Stability of load nodes

Static and dynamic load characteristics of industrial consumers. Static stability of load nodes. Safety factors. Secondary signs of load stability. Dynamic stability of synchronous and induction motors. Stability criteria for synchronous and induction motors. Synchronous motor excitation current control and stability. Stability of a cluster of motors. Effect of static capacitor banks and synchronous capacitors on stability. Self-starting of motors.

Unit 5. Effect of generator regulators on stability

Features of prime movers. Features of speed governors. The purpose of primary and secondary regulation. Emergency turbine control. Synchronous generator excitation and automatic transfer switching. Selection of regulation channel parameters by voltage deviation. Static characteristics of excitation and speed governors. Effect of excitation and speed governors on static and dynamic stability of turbogenerators. The behavior of governors during oscillations. Frequency and voltage control in an electric power system and its impact on stability.

Unit 6. Asynchronous operation modes of AC machines

Asynchronous operation of a synchronous generator. General provisions of asynchronous operation calculation methods. Asynchronous operation of a synchronous motor. The nature of asynchronous power and its impact on the resulting stability of an electric power system. The loss of stability and synchronization. Elimination of asynchronous operation. Re-synchronization.

Unit 7. Isolated operation of industrial power plants

Pre-conditions for isolated operation. In-house power plants. Isolated operation of power supply systems. Calculation of steady state and transient regimes of isolated power supply systems. Operation features of governors in isolated conditions. The change of the regime parameters when shifting for isolated operation. Synchronous and asynchronous power in isolated conditions.

Unit 8. Analysis of static and dynamic stability of isolated electric power systems

Features of the analysis of static and dynamic stability of isolated electric power systems. Transmission limits in isolated operation. Frequency and voltage control in an isolated power supply system. Stability of synchronous and induction motors in isolated conditions. The relative angles of a generator rotor and a synchronous motor. Impact of asynchronous power on synchronization when shifting for isolated operation.

Activities:

1. Teacher-led group activities in a classroom;
2. Extracurricular self-study of the teacher’s assignments and tasks, including the use of educational facilities (obligatory);
3. Office-hours.

Total hours – 144

Total points – 4

Classroom hours (lectures, laboratory and practical classes) – 52

Unsupervised hours – 56

Midterm assessment – Pass/fail examination