## Leistungen

Compact thermal models for magnetic components used in WPS are developed. These compact models or equivalent resistive-capacitive networks need to be parameterised to geometry, thermal properties of the materials and convection heat transfer from the components as function of the local airflow properties (velocity, viscosity, density). These parameterised models can then be used in the optimisation procedure for the design of magnetic components.
This study consists of a methodology to deduce parameterised compact thermal models based on FE element computations. In combination with a thorough study of the heat transfer on these models, accurate compact models are obtained. They are implemented in the CAE-WPS design tool. Furthermore, the derived models can be used as resistive thermal networks in an electrical network simulator. In this project the network simulator Simplorer was used to implement the models.
Two different equivalent resistance models for thermal modelling of magnetic components are deduced. The first model consists of two temperature nodes and three thermal resistances. The second and more detailed model contains 4 sub-models with two to eight temperature nodes -depending on the component type- and several thermal resistances linking those nodes. The 1-level model supports solenoid, planar and non-linear components. Possible core shapes are EE, ETD, UU, UR and toroidal cores. Concerning the windings, 3 types -namely round, litz and foils- can be used.

During project CAE-WPS, after stating evaluation criteria, a great number of power circuit topologies have been screened for suitability for welding power supplies. Selections of these have been analysed. Design equations were derived and stress quantities were calculated. Results were implemented into the knowledge base and the SIMPLORER templates to be parameterised by the expert system. Thus the SMEWPS were enabled to design the power electronic circuits without detailed knowledge of the underlying formulae very rapidly.
Analysis of power circuit topologies was based on MATHEMATICA programs, i.e. modules implemented in MATHEMATICA notebooks and packages. These programs were developed on the basis of SyMap, a computer based analysis tool developed by a former research assistant at LEA, and modified to be applicable to welding power supplies. SyMap requires a description of the power circuit topology in means of a net list, a definition of input and output variables, a list of the configurations of the switches, and the switching instances. SyMap computes symbolic expressions that fully describe the circuit. Also symbolically, for each of the user-defined switch configurations, the state space representation is computed. From these representations in conjunction with the switching instances, applying the method of state-space averaging, the large signal non-linear state space model is derived. A symbolic representation of the linearised small signal model as well as the small signal transfer functions are also derived by SyMap.

The CAE-WPS-Tool consists of an expert system, an optimisation program for magnetic components, tools for thermal calculations and edit tools for data-files.
Based on the Graphical User Interface (GUI) named TSelect, combined with the Expert-System-Shell CLIPS, the Tool provides the following functions:
- Editing of specifications.
- Suggestion of appropriate topology.%l- Pre-design and optimisation of magnetic components.
- Parameterisation of other components.
- Generation of electric and thermal simulation sheet.
- Calculation of thermal properties of electric components, heat sinks and air-channel.
Two other programs were made to simplify the creation of data-files which are necessary for the expert system and the magnetic optimiser.
The expert system has a Three-Step selection algorithm. In a first step, all topologies, which are known to perform badly for the given specifications or which cannot fulfil the requirements are discarded. Then components for the remaining topologies are taken and are judged in respect to the given optimisation goal.
A similar selection algorithm is taken for the selection of the best semiconductors and capacitors, while a pre-optimisation program performs a rough pre-design based on the area product.
Data for the expert system was derived from parameter studies of data-sheets, design equations and experience from designers.

First, the control tasks arising in welding power supplies were identified. The regulation was constrained to electrical quantities, especially the important regulation of the welding current. Second, according to the project proposal, controller design methods based on linear, time-invariant plant models were implemented as a Mathematica package named ConSeaDest (Controller Selection and Design tool). The plant models were generated using the results of WB 3.1.2. Since the controller design methods must be applicable without any user intervention, one major concern during their investigation was their potential to be fully automated. Considering the limited accuracy of the underlying models, certain trade-offs of these procedures were accepted.
As outlined in the project proposal this WB includes only linear, time-invariant controllers, which are basically of PID- or PID-derived type (e.g. PI). For these controllers well-known design methods have been implemented such as the absolute optimum method and the damping optimum method. Besides, also PID-tuning methods recently presented to literature have been included, which are promising candidates for an automated tuning.

The electrical modelling of magnetic components was intended for use during topology pre-selection performed by the knowledge-base (KB) and at simulation during the pre-design of the finally selected and parameterised topology. It should yield accurate power losses, size and set-up predictions including electrical circuit properties. Due to the fact, that the demands for accuracy and execution time are different at pre-selection, and pre-design stage, two model types of low (level 0) and high accuracy (level 1) were developed.
The level 0 model is dedicated to be applied for a coarse prediction of the relevant properties in order to derive a single step, non-iterative optimisation of the component.
The level 1 model is intended to achieve accuracy as high as possible considering all major parasitic effects by utilisation of analytical methods aided by Finite-Element parameter studies. This model is dedicated for the application in an iterative parameter optimisation (CAO).
It also contains coarse predictions of magnetic components parasitics like short circuit impedances and main inductances of transformers. The turn ratio n of the transformers and the desired inductance L of inductors is also given. But there is no detailed design of all magnetic components available containing all the necessary information to build a device.
The design and optimisation tool CAEOMAG is integrated into the circuit simulator SIMPLORER, via a graphical user interface. All stress quantities are determined and collected in a file and a magnetic component can be designed and optimised with CAEOMAG.
This design and optimisation tool allows a pre-optimisation of the device with respect to simulated stress quantities yielding a core choice and starting values for the parameter model used by a succeeding parameter optimisation utilising state-of-the-art genetic algorithms. The parameter model allows the automated optimisation of e.g. the layer thickness or core dimensions with respect to an objective function, which can be size, costs, etc. and constraints like temperature rise, maximum saturation induction etc. Several hundred core-winding set-ups are evaluated automatically with varying parameters during such an optimisation, so that a component model is used, which is efficient to compute. The model developed uses analytical methods as shown in modelling chapter .Two thermal models are supported, one with 2 temperature nodes and one with 9, predict the temperature rise with a given ambient temperature and air velocity.

A general methodology for the thermal and mechanical modelling of the cooling systems of welding power supplies (WPS) is based on the extraction of compact models, which predict the thermal behaviour of the systems with satisfactory accuracy. In order to reach this goal, numerical simulation and analysis together with experimental data is applied in order to describe the temperature field in the WPS and parameterise the compact models. Thus, the cooling performance of the air channel can be optimised. The method is implemented in the design tool CAE-WPS.
The aim of compact thermal modelling is to simulate the conduction and convection heat transfer by ordinary differential equations. Since the convection heat transfer from the dissipating components result from local airflow properties, also the airflow needs to be modelled. Therefore, an additional set of equations is needed to calculate the air temperature rise. Also, for determination of the mass flow rate, a compact model is deduced. For components like diodes, transistors and capacitors the equivalent resistances are obtained from manufacturers datasheets. For other components like magnetics and heat sinks equivalent schemes are either numerically (CFD / FEM) or experimentally deduced. Parameterised thermal models for magnetic-components are available from a previous part in the project. The deduction of mechanical and thermal models for heat sinks, screens, channels, obstacles like magnetic-components are performed. The thermal and airflow models are partially evaluated by means of measurements on heat sinks, finger guards, magnetic components and a cooling channel.