In this paper we describe a new method for obtaining, in symbolic form, the network functions and their small-and large-change sensitivities. Our method is based on the two-port transimpedance concept and the sequence of expressions approach to calculation of matrix determinant. We show that the network functions as well as their sensitivities can be expressed by appropriate transimpedances. Each transimpedance is given by an algebraic sum of at most four elements of the inverse of the circuit's reduced node admittance matrix. In our method the complexity of the sequence of expressions grows linearly with the circuit size. The extra effort required to obtain sensitivities is minimal and, more importantly, independent of the circuit size.

The major stumbling block in symbolic analysis of large-scale circuits is the exponential growth of expression complexity with the circuit size. Sequential techniques, introduced more than a decade ago, reduced that growth to quasi-linear. The fundamental assumption in all sequential methods developed so far was that the circuit must be decomposed in order to reduce the complexity of the final expression. In this paper we will show conclusively that this is not the case. We describe a new algebraic approach to symbolic analysis of large-scale networks, based on the reduction of the compacted modified node admittance matrix to a two-port matrix. No circuit partitioning is required. Internal variables are suppressed one by one using Gaussian elimination. To minimise the number of symbolic operations we employ a locally optimal pivoting strategy. Formula complexity is estimated to grow quasi-linearly with circuit size. The technique is conceptually very simple and produces sequential formulae of significantly lesser complexity than any exact method published to date.

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The second system of the IEEE second benchmark model of Subsynchronous Resonance (SSR) is considered. The system can be mathematically modeled as a set of first order nonlinear ordinary differential equations with the compensation factor (µ = Xc/X L ) as a bifurcation (control) parameter. So, bifurcation theory can be applied to nonlinear dynamical systems, which can be written as dx/dt = F (x; µ). The effects of machine components, i.e. damper winding, automatic voltage regulator (AVR), and power system stabilizer (PSS) on SSR in power system are studied. The results show that these components affect the locations, number and type of the Hopf bifurcations.

As the number of students increases quite dramatically in almost every subject taught at a university, delivering tutorials to large classes and providing timely assessment and feedback becomes the major challenge. These problems are especially acute in technical field-of-practice subjects that aim to teach specific numeracy and problem solving skills. In this paper we describe a generic framework for delivering and assessing tutorials over the Web that would enable us to create Web tutorials in several technical subjects. A sample implementation in one of the early stage technical subjects (Electronics & Circuits) will be described. The system, implemented in ASP .NET, presents each student with a number of unique sets of problems (generated by software, not randomly chosen from a fixed pool), guides him/her through the solutions and grades the work. A strict deadline is enforced for each set to encourage systematic approach to learning.