HeylandCircle: A Computational Framework for the Geometric Reconstruction of the Heyland Circle Diagram

TL;DR

HeylandCircle introduces a computational method to reconstruct the Heyland circle diagram from standard test data, enabling precise, reproducible analysis of induction machine steady-state behavior.

Contribution

It formalizes the geometric construction of the Heyland diagram into a deterministic computational framework, facilitating analysis and teaching.

Findings

Close agreement with classical results in validation

Provides explicit geometric relationships for key quantities

Enables systematic extension of traditional diagrams

Abstract

The Heyland circle diagram is a classical graphical tool for representing the steady-state behavior of induction machines using no-load and blocked-rotor test data. While widely used in alternating-current machinery texts, the diagram is typically presented as a hand-constructed aid and lacks a standardized computational formulation. This paper presents HeylandCircle, a computational framework that reconstructs the classical Heyland circle diagram directly from standard test parameters. The framework formalizes the traditional geometric construction as a deterministic, reproducible sequence of geometric operations, establishing a clear mapping between measured data, fixed geometric objects, and steady-state operating points. Quantities such as power factor, slip, output power, torque, and efficiency are obtained through explicit geometric relationships on the constructed diagram. Validation using a representative textbook example demonstrates close agreement with classical results. The framework provides a computational realization of the traditional Heyland diagram suitable for instruction, analysis, and systematic extension.