The University of Southampton

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.
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.
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.


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

Follow-up work18
Completion of assessment task6
Wider reading or practice50
Preparation for scheduled sessions18
Total study time150

Resources & Reading list

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

Van Valkenburg M E (1974). Network Analysis. 

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

Dorf and Svoboda (2006). Electric Circuits. 



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


MethodPercentage contribution
Examination 100%

Repeat Information

Repeat type: Internal & External

Linked modules

Pre-requisites: ELEC1200 AND MATH1055

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