Network Analysis and Simulation
Solution of lumped and distributed networks. Time-domain solutions, discretization and integration rules. Frequency-domain solutions, FFT and windowing techniques. Systems of linear equations, reduction and sparsity techniques. Nonlinear elements. Computer-aided simulation.
The course provides the background to understand the principles, capabilities, and limitations of circuit design programs like SPICE for electronic circuits and the EMTP for power systems. Topics include the discretization of differential equations, selection of step size Delta-t, solution bandwidth, numerical oscillations, propagation in transmission lines, frequency dependence, nonlinear elements, and network equivalents. Course evaluation is based on project assignments. Typically eight or nine assignments are given during the term. In the assignments, the students are asked to write their own computer programs to solve cases illustrating the techniques discussed in the lectures. The students are asked to compare the results from their own programs with those obtained running the MicroTran(R) software (EMTP). A limited version of MicroTran will be available to the students.
- Time domain solution of electric transients. The EMTP and SPICE simulators. Component modelling requirements. Integration rules for the discretization of basic R, L, C components. Step size Δt requirements. Representation of switching operations.
- Wave propagation in ideal transmission lines. Simplified line models. Wave propagation in lines with losses and frequency-dependent parameters.
- Time domain equivalents for frequency dependent lumped and distributed parameter systems. Frequency dependent transmission line models.
- Coupled multiconductor transmission line modelling. Eigenvalue/eigenvector analysis. System decoupling through similarity transformations.
- Numerical discretization techniques. Time-step size and frequency bandwidth. Distortion of the circuit parameters. Numerical stability. Numerical oscillations. Elimination of numerical oscillations. Critical damping adjustment (CDA).
- Modelling of nonlinear elements. Piecewise and continuous nonlinearities.
- Large network solutions. Sparsity techniques. Modified nodal analysis (MNA). Partitioning techniques. Diakoptics. Multi-Area Thevenin Equivalents (MATE). Time latency techniques for multirate systems.