Affiliations: Universidad Michoacana, Morelia 58030, Mexico E‐mail: [email protected] | University of Oregon, Eugene, OR 97403, USA E‐mail: [email protected]
Note: [] Corresponding author.
Abstract: Most of the work on behavior prediction in the field of Qualitative Reasoning has focused on transient behavior and responses to perturbations; very little has been done regarding 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 behavior of electrical circuits is very important. This article 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 article has been implemented in a program called Qualitative Phasor Analysis (QPA), which performs circuit analysis, parameter design, diagnosis, control design, and structure simplification. Circuits with multiple sources are solved using the superposition principle.
