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# EEEN50100

#### Stability Analysis of Nonlinear Systems (EEEN50100)

Subject:
Electronic & Electrical Eng
College:
Engineering & Architecture
School:
Electrical & Electronic Eng
Level:
5 (Doctoral)
Credits:
5
Module Coordinator:
Professor Federico Milano
Trimester:
Spring
Mode of Delivery:
Online
Internship Module:
No

Curricular information is subject to change.

The objective of this module is to show the students basic concepts of stability of nonlinear dynamical systems and maps. In particular, the main concepts of bifurcation theory and Lyapunov stability criteria will be provided. The approach is both theoretical and practical. Each topic is first formulated in mathematical terms and suitable numerical methods are discussed. Several examples, mostly based on major power systems blackouts, as well as control remedial actions are described. The students will also get familiar with open source software to solve stability analysis of nonlinear dynamical systems.

###### Learning Outcomes:

Concepts of stability analysis of nonlinear dynamical systems. Concepts of bifurcation theory. Lyapunov stability first and second criteria. Numerical techniques for the stability analysis of nonlinear differential equations. Basic concepts of delay differential equations. Basic concepts of chaos. Real-world examples based on power systems blackouts.

###### Indicative Module Content:

Definitions of nonlinear system stability. Basic bifurcation theory concepts. Stability of maps. Small-signal stability analysis (Lyapunov first stability criterion). Transient Stability analysis and transient energy function (Lyapunov second stability criterion). Voltage stability. Frequency stability. Monodromy matrix and Floquet multipliers. Routes to chaos.

###### Student Effort Hours:
Student Effort Type Hours
Lectures

20

Tutorial

5

Laboratories

15

Autonomous Student Learning

60

Total

100

###### Approaches to Teaching and Learning:
Lectures with a blend of theory, numerical examples and practical applications.
Requirements, Exclusions and Recommendations

Not applicable to this module.

Module Requisites and Incompatibles
Pre-requisite:
EEEN40010 - Control Theory

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Individual Project: Report on a specific topic related to the stability analysis of nonlinear dynamical systems (typically, power systems). The topic is to be agreed between the student and the coordinator of the module. Week 15 Standard conversion grade scale 40% Yes

100

Yes

Carry forward of passed components
No

Remediation Type Remediation Timing
In-Module Resit Prior to relevant Programme Exam Board