A Model Reduction Perspective on Thermal Models for Induction Machine Overload Relays

Analytical Thermal Model for Fast Stator Winding Temperature Prediction

“…where the elements of the constant matrices at the right side of (16) are the coefficients of the polynomials introduced in (14,15), as summarized in (17) …”

“…Thermal models can be used not only at the design stage, but also for the online prediction of the motor temperature distribution [13]. Although LPTNs can provide good temperature estimation [14], their computational cost could still be excessive for online implementation and a trade-off between accuracy and computational speed is necessary [15]. First order LPTNs require less computational effort but are shown to be accurate only for short transients [16].…”

A thermal modeling methodology for power semiconductor modules

“…Based on this realization obtained via M the system can be truncated such that the states whose SVs are small and which therefore do not contribute much to the system's energy transfer are abandoned, according to Eq. (14). A more formal and mathematical derivation of this system truncation process can be found in [19] and [20].…”

“…This model truncation approach has been successfully used for many applications e.g. for obtaining a reduced thermal model of an electric machine [14]. For this work the balanced truncation algorithms provided by MATLAB have been used to reduce the thermal model.…”

“…The FDM is shaped such that it can be represented by a linear state space model. This allows applying state space algebraic concepts for simulation and model reduction: The concept of balanced truncation [14] is used resulting in a significant reduction of the system states and thus the simulation complexity. This results in a compact transient model.…”