Most of the work on behavior prediction on the field of Qualitative Reasoning has focused on transient behavior and responses to perturbations; very little has been done about systems in steady state. A large class of systems, especially in the area of power systems, are designed for sinusoidal steady-state operation. Thus, an understanding of the steady state of electrical circuits is very important.

This dissertation presents a framework for reasoning about linear electrical cir­cuits in sinusoidal steady state. The reasoning process relies on a constraint-based model of the circuit, derived from electro-magnetic theory and generated automati­cally from the structure of the circuit. In a linear circuit operating in steady state, all quantities are sinusoidals of the same frequency as the source. Since any sinusoidal can be expressed as the real part of a complex exponential, we use the complex form,which simplifies computations; this complex form, characterized by magnitude and angle, is called a phasor. In order to capture magnitude and phase angle information in the model, all constraints operate on phasor variables.

Constraint propagation (CP) is the main inference mechanism. The CP module reasons with as much information and precision as the user provides, ranging from qualitative to quantitative. Intervals provide a general representation mechanism.

The framework presented in this dissertation has been implemented in a pro­gram called Qualitative Phasor Analysis (QPA), which performs the following rea­soning tasks: analysis, parameter design, diagnosis, control design, and structure simplification. Circuits with multiple sources are solved using the superposition prin­iple.

Power systems can be modeled as linear circuits and normally operate in steady state. A power system problem is translated to a circuit problem and solved by QPA; the results are then translated back to the original power system.

By extending the circuit ontology to include phasor information, this disserta­tion extends the range of problems that can be solved by qualitative reasoning.