Low-order Thermal Model Research Articles

Automated Extraction of Low-Order Thermal Model With Controllable Error Bounds for SiC MOSFET Power Modules

Automated Extraction of Low-Order Thermal Model With Controllable Error Bounds for SiC MOSFET Power Modules

Improved Low-Order Thermal Model for Critical Temperature Estimation of PMSM

The low-order lumped parameter thermal models (LPTMs) are one of the most competitive online approaches to estimate the critical temperatures in electrical machines. Firstly, this paper explores the correlation between the conventional high-order and low-order LPTMs and then presents some critical modelling guidelines of low-order LPTM together with an improved four-order LPTM. Secondly, a simple dynamic quasi-linear model (DQM) is proposed to define convection thermal resistances, which can be used in both conventional high-order and low-order LPTMs. The application of DQM can improve the estimation accuracy by indirectly introducing more degrees of freedom, which is especially beneficial for the magnet temperature estimation in the low-order LPTM due to its highly abstract rotor thermal modelling. Finally, a prototype permanent magnet synchronous machine is used for experimental validation under different operation profiles.

AN EXPERIMENTALLY VALIDATED LOW ORDER MODEL OF THE THERMAL RESPONSE OF DOUBLE-WALL EFFUSION COOLING SYSTEMS FOR HP TURBINE BLADES

Abstract Transpiration cooling represents the pinnacle of turbine cooling and is characterised by an intrinsic porosity achieving high internal convective cooling, and full coverage film cooling. The quasi-transpiration, double-wall effusion system attempts to replicate the cooling effect of transpiration cooling. The system is characterised by a large wetted area providing high internal convective cooling performance, with a highly porous external wall allowing the formation of a protective cooling film. This paper presents a low-order thermal model of a double-wall system designed to rapidly ascertain cooling performance based solely on the geometry, thermal conductivity, and approximate surface heat transfer coefficients. Initially validation uses experimental data with heat transfer coefficients for the low order model obtained from fully conjugate CFD simulations. A more controlled CFD study is then undertaken with both fully conjugate and fluid only simulations performed on several double-wall geometries to ascertain both overall and film effectiveness data. Data from these simulations are used as inputs to the low order thermal model and the results compared. The low order model successfully captures both the trends and absolute cooling effectiveness achieved by the various double-wall geometries. The model therefore provides a powerful tool whereby the cooling performance of double-wall geometries can be near instantaneously predicted during the initial design stage, potentially allowing geometry optimisation to rapidly occur prior to more in-depth, costly and time-consuming analyses. This benefit is demonstrated via the implementation of the model with input boundary conditions obtained using empirical correlations.

A global Curie depth model utilising the equivalent source magnetic dipole method

The depth to the Curie isotherm provides a snapshot into the deep thermal conditions of the crust, which helps constrain models of thermally controlled physical properties and processes. In this study, we present an updated global Curie depth model by employing the equivalent source dipole method to fit the lithospheric magnetic field model LCS-1 from spherical harmonic degree 16 to 100. In addition to the new field mode, we utilise all three vector components and include a laterally variable magnetic susceptibility model. We also employ an improved thermal model, TC1, to supplement the degree 1 to 15 components that are otherwise contaminated by the core field. Our new Curie depth model differs by as much as ±20 km relative to previous models, with the largest differences arising from the low order thermal model and variable susceptibility. Key differences are found in central Africa due to application of a variable susceptibility model, and shield regions, but continents with poor constraints such as Antarctica require additional improvement. This new Curie depth model shows good agreement with continental heat flow observations, and provides further evidence that Curie depth estimates may be used to constrain evaluations of the thermal state of the continental lithosphere, especially in regions with sparse or surface contaminated heat flow observations.

Enhanced Power Capability of Generator Units for Increased Operational Security Using NMPC

The ever-increasing penetration of intermittent energy sources introduces new demanding operating regimes for the bulk power generation in the power grid. During a worst-case power system disturbance scenario, the generator needs to operate beyond its limits to maintain stable operation. Therefore, a new online low-order thermal model of a hydrogenerator has been recently proposed, where the periodic extension of the long-forgotten capability diagram of the machine was in-depth investigated. An increased performance can be obtained if the total thermal capacity of the generator is exploited by applying optimal control theory in the Automatic Voltage Regulator (AVR). This paper proposes a Non-linear Model Predictive Controller (NMPC) combined with an Unscented Kalman Filter (UKF) with a modeling framework geared for use in a supervisory control structure for the conventional control system. The method provides maximum utilization of the machine's thermal capacity by providing the controller with an Enhanced Capability Diagram (ECD). Case studies on a single-machine system and a 16-bus multi-machine system were investigated. The results show that a satisfying controller action during different long-term voltage instability scenarios is realized.

Thermal Homogenization of Electrical Machine Windings Applying the Multiple-Scales Method

Low-order thermal models of electrical machines are fundamental for the design and management of electric powertrains since they allow evaluation of multiple drive cycles in a very short simulation time and implementation of model-based control schemes. A common technique to obtain these models involves homogenization of the electrical winding geometry and thermal properties. However, incorrect estimation of homogenized parameters has a significant impact on the accuracy of the model. Since the experimental estimation of these parameters is both costly and time-consuming, authors usually prefer to rely either on simple analytical formulae or complex numerical calculations. In this paper, we derive a low-order homogenized model using the method of multiple-scales (MS) and show that this gives an accurate steady-state and transient prediction of hot-spot temperature within the windings. The accuracy of the proposed method is shown by comparing the results with both high-order numerical simulations and experimental measurements from the literature.

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

Full-order thermal models are often used by machine designers to analyze the induction machine thermal behavior. The real-time implementation of such models for the purpose of motor thermal protection is difficult because an extensive knowledge on motors and sufficient computational resource are required. This paper demonstrates that full-order thermal models can be systematically reduced via pole-zero cancellation or Hankel singular-values-based model reduction techniques without additional physical assumptions. As a result, a system of a substantially lower dimension, which has nearly the same response characteristics in the frequency band of interest, is obtained. Both the estimated rotor cage temperature, which is extracted from the voltage and current measurements by a sensorless rotor temperature estimator, and the measured stator winding temperature are used to evaluate the performance of low-order thermal models. Given a certain tolerance for the modeling error, a reduced low-order thermal model can be used to characterize the thermal dynamics of a small- to medium-sized line-connected induction machine and to provide proper protection against motor overheating.

A Low-Order Thermal Model with a Flow Pattern Similar to Hill's Spherical Vortex

A thermal model containing time-variable parameters is constructed from an assumed velocity field and density disturbance. The fluid field is similar to Hill's spherical vortex, and the density disturbance is represented by a low-order Hermitian function series. The time variation of the model parameters is estimated by an optimal approximation method for the inviscid and non-diffusive Boussinesq equations. Initially, there is no motion but there is a low-density disturbance in the environment of neutral stratification. The time variation of the model parameters is studied with the aid of numerical integration. The time evolution of this model within a short period seems to be qualitatively comparable with some computer simulation results.