The University of Southampton
Courses

# ELEC2229 Power Circuits and Transmission

## Module Overview

### Aims and Objectives

#### Learning Outcomes

##### Knowledge and Understanding

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

• Three phase systems for power systems
• Transmission line theory for both high and low frequency applications
• Network topology and introductory state-space models for circuits
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Gain experience of analytical and numerical modelling at appropriate detail for application
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Gain practical experience of three phase systems
• Gain practical experience of transmission lines

### Syllabus

- 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 circuit models: Examples of derivation; solution of state equations by Laplace transform methods; solution of simple circuit network problems. Sinusoidal steady-state from the state-space point of view. - 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 two wattmeter method on balanced and unbalanced systems for kW and kVAr measurement. - Two Port Networks: ABCD parameters; Simple transmission networks: series impedance, shunt admittance, half T and half Pi network, T and Pi networks, ideal and actual transformer, pure mutual inductance; ABCD relation for a passive network; Output in terms of input; Evaluation of ABCD parameters from short circuit and open circuit tests; ABCD parameters for symmetrical lattice; Networks in parallel; The loaded two port network; image impedances and matching a resistive load to a generator; Image impedance in terms of Zsc and Zoc; Insertion loss ratio; Propagation coefficient; Per-unit system. - Transmission line theory as applied to power transmission and communications: 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. Telegraphist's equations, relation to the wave equation. Voltage standing waves on a lossless line; Standing waves of current on a lossless line. Voltage surges; Reflection coefficient; Pulses on transmission lines, signal transfer. Impedance, Admittance and Smith Chart. Stub matching and stub filters; Voltage surges; Reflection coefficient; Pulses on transmission lines, signal transfer. Distortion free conditions. Special cases: quarter and half wave length lines, matched impedances, short and open terminations. - Electromagnetic background. Field analysis of transmission lines; Telegraphers Equation derived from Field Analysis for the coaxial line. - 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. Examples: Coaxial cable, stripline, microstrip; balanced lines: twisted pairs.

### Learning and Teaching

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

Pozar (2012). Microwave Engineering, 4th edition.

Dorf and Svoboda (2006). Electric Circuits.

### Assessment

#### Summative

MethodPercentage contribution
Continuous Assessment 35%
Final Assessment  65%

#### Repeat

MethodPercentage contribution