The University of Southampton
Courses

# ELEC2215 Power Circuits

## Module Overview

### Aims and Objectives

#### Module Aims

The module aims to provide a detailed understanding of more advanced topics in circuit theory, in particular developing a good understanding of the fundamental theory of three-phase circuits, power transmission lines, general network solutions and the state space approach.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Concepts of network topology applied to network problems.
• State-space methods applied to network problems.
• Basic synthesis techniques.
• Power in AC circuits, conservation of power.
• Transmission line theory; short, medium and long lines, including full solution.
• Balanced and unbalanced three phase circuits.
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Undertake laboratory experiment as part of a small team.
• Record and report laboratory work.
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Undertake measurements of transmission line parameters.
• Model and analyse circuits with different methods.
• Apply basic synthesis techniques for realising impedances.
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Calculate electrical power in single and three-phase circuits.
• Apply different solution methods to general electrical network problems.
• Model transmission lines of varying length.
• Apply sequence network representation to overhead lines and buried cables.
• Use basic synthesis techniques.
• Perform a range of electrical measurements on three-phase circuits.

### Syllabus

Transmission line theory: Definition of short, medium and long lines and their simulation with discrete elements; solution of T and Pi networks, with appropriate phasor diagrams, ABCD constants. Lossy and lossless line models. Voltage and current loci; rigorous solution for uniformly distributed constants (in both the time and frequency domains); reflected and incident values, propagation constant, attenuation and phase constants, surge/characteristic impedance; algebraic and hyperbolic equations with ABCD comparison of the latter with Pi networks. Impact of transposition. Application of sequence networks. Network Topology: Definitions: trees, links, loops, cuts etc.; conversion of circuits to branches and loops, etc. and the possible variations for any given circuit; expansion of Kirchhoffs laws in cuts and loops; formation of current branch matrices and the relationships I = C.i and V = A.B; determination of admittance and impedance matrices; methods of solutions (including revision of matrix algebra). State Space: Motivation; definitions: state-variable, state-variable, etc.; algorithms for writing state equations for circuits; solution of such equations by Laplace transform methods; solution of simple circuit network problems. Solution of state equations in the time domain (linear-time invariant case): solution of the state differential equation (exponential of a matrix, its computation, forced- and free response in the state-space setting); dynamics of eigenvectors and eigenvalues, and their circuit interpretation; sinusoidal steady-state from the state-space point of view; introduction to observability and controllability from a circuit-theoretic point of view; internal and i/o stability, and their relationship. Synthesis of one-ports: Positive-real functions; Synthesis of two-element circuits; Brune synthesis. Three-phase: Unbalanced mesh and four-wire star circuits; unbalanced three-wire star circuits; solution by Millman's theorem, star-delta transform and graphical methods; symmetrical components and use in solving unbalanced systems; positive, negative and zero sequence networks; use of twowattmeter method on balanced and unbalanced systems for kW and kVAr measurement. Laboratory Coursework: 3-phase Star and Mesh circuit relationships Transmission line.

### Learning and Teaching

TypeHours
Tutorial12
Preparation for scheduled sessions18
Follow-up work18
Lecture36
Revision10
Total study time150

Rogers (1965). Topology and Matrices in Solution of Networks.

Thomas R E and Rosa A J (2000). The Analysis and Design of Linear Circuits.

Dorf and Svoboda (2006). Electric Circuits.

Van Valkenburg M E (1974). Network Analysis.

### Assessment

#### Summative

MethodPercentage contribution
Class Test 10%
Exam  (2 hours) 80%
Laboratory 10%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External