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Static converters generate current harmonics in power grids. For numerous studies, analytical frequency modeling is preferred to carry out their harmonic modeling in the context of sizing by optimization. However, a design by optimization has to consider other constraints, e.g. modeling constraints and operating constraints. In this way, this paper aims to focus on applying an analytical frequency modeling on the sizing by optimization of an aircraft electrical power channel.

The paper aims to size a multiphysical system by optimization. In this way, the sizing of an aircraft electrical power channel by optimization has been carried out. The models of all the channel components are analytical. Specifically, the frequency model of the power electronics is based on Tran et al. (2016) and is made of equalities and inequalities. Due to this modeling choice, the optimization satisfies hundreds of constraints, such as modeling constraints and static converter operating constraints. Furthermore, transient constraints are only verified after optimization.

The difficulty is the modeling of the system by taking into account nonlinear implicit equations having several solutions. A solution is the addition of inequality constraints to the model to guide the implicit solving. Furthermore, this greatly helps the optimization algorithm to find the good operating mode of the static converter, at steady state. This aspect is indispensable to validate the sizing model.

The number of the configurations per operating period of the static converters is defined a priori and limited.

The analytical model for the sizing is formulated as a constrained optimization problem. Its solving and the sizing by optimization are carried out by the same optimization algorithm.

This paper aims to describe a modelling and solving methodology of a (static converter–electric motor–control) system for its sizing by optimization, considering the dynamic thermal heating of the machine.

The electrical drive sizing model is composed of two simulators (electrical and thermal) that are co-simulated with a master−slave relationship for the time step management. The computation is stopped according to simulation criteria.

This paper details a methodology to represent and size an electrical drive using a multiphysics and multidynamics approach. The thermal simulator is the master and calls the electrical system simulator at a fixed exchange time step. The two simulators use a dedicated dynamic time solver with adaptive time step and event management. The simulation automatically stops on pre-established criteria, avoiding useless simulations.

This paper aims to present a generic methodology for the sizing by optimization of electrical drives with a multiphysics approach, so the precision and computation time highly depend on the modelling method of each components. A genetic multiobjective optimization algorithm is used.

The methodology can be applied to size electrical drives operating in a thermally limited zone. The power electronics converter and electrical machine can be easily adapted by modifying their sub-model, without impacting the global model and simulation principle.

The approach enables to compute a maximum operating duration before reaching thermal limits and to use it as an optimization constraint. These system considerations allow to over constrain the electrical machine, enabling to size a smaller machine while guaranteeing the same output performances.

With the increasing number of onboard controlled static converters in aeronautics, methods to design lighter configurations are required. This study aims to help the designer sizing optimal electromagnetic compatibility (EMC) filters and, moreover, finding optimal voltage levels and switching frequency, which have a great impact on the design and global mass of such converters.

Analytical models for capacitors, inductors and heatsink are settled. Using frequency modeling, EMC can be studied analytically. To deal with frequency and voltages variations, models of perturbations sources are developed. Concerning the problem of surveilling thousands of harmonics to check the whole frequency range of EMC standards in optimization, a strategy that drastically reduces the number of computations and has a good convergence is proposed.

The methods settled in the paper allow to optimize a controlled static converter with its EMC filters along with finding optimal switching frequency and voltage levels. A study on a three-phase rectifier reveals the importance of the switching frequency on converter design with EMC filters. A 28 per cent mass reduction is predicted by increasing the switching frequency from 10 to 30 kHz. The designed converters are verified by simulations.

Investigating the voltage levels along with the switching frequency has not been achieved yet for static controlled converters with EMC constraints. The approach lacks experimental validations, but it is currently ongoing.

Dealing analytically with the changes of frequency or voltages in an EMC study is a new feature. The possibility to use deterministic algorithm is essential for dealing with the important number of constraints and the numerous interactions between all the parts of the problem, especially EMC.

This study aims to optimize electrical systems represented by ordinary differential equations and events, using their frequency spectrum is an important purpose for designers, especially to calculate harmonics.

This paper presents a methodology to achieve this, by using a gradient-based optimization algorithm. The paper proposes to use a time simulation of the electrical system, and then to compute its frequency spectrum in the optimization loop.

The paper shows how to proceed efficiently to compute the frequency spectrum of an electrical system to include it in an optimization loop. Derivatives of the frequency spectrum such as the optimization inputs can also be calculated. This is possible even if the sized system behavior cannot be defined a priori, e.g. when there are static converters or electrical devices with natural switching.

Using an efficient sequential quadratic programming optimizer, automatic differentiation is used to compute the model gradients. Frequency spectrum derivatives with respect to the optimization inputs are calculated by an analytical formula. The methodology uses a “white-box” approach so that automatic differentiation and the differential equations simulator can be used, unlike most state-of-the-art simulators.

The thermal modelling of an electrical machine is difficult because the thermal behavior depends on its geometry, the used materials and its manufacturing process. In the paper, such a thermal model is used during the sizing process by optimization of a hybrid electric vehicle (HEV). This paper aims to deal with the sensitivities of thermal parameters on temperatures inside the electrical machine to allow the assessment of the influence of thermal parameters that are hard to assess.

A sensitivity analysis by Sobol indices is used to assess the sensitivities of the thermal parameters on electrical machine temperatures. As the optimization process needs fast computations, a lumped parameter thermal network (LPTN) is proposed for the thermal modelling of the machine, because of its fastness. This is also useful for the Sobol method that needs too many calls to this thermal model. This model is also used in a global model of a hybrid vehicle.

The difficulty is the thermal modelling of the machine on the validity domain of the sizing problem. The Sobol indices allow to find where a modelling effort has to be carried out.

The Sobol indices have a significant value according to the number of calls of the model and their type (first-order, total, etc.). Therefore, the quality of the thermal sensitivity analysis is a compromise between computation times and modelling accuracy.

Thermal modelling of an electrical machine in a sizing process by optimization.

The use of Sobol indices for the sensitivity analysis of the thermal parameters of an electrical machine.

The paper aims to deal with the exact computation of the Jacobian of a time criteria from a numerical simulation of power electronics structures, for the sizing by gradient-based optimization algorithm.

Runge Kutta 44 is used to solve the state equations. The generic approach combines numerical and symbolic approaches. The modelling of the static converter is based on ideal switches.

The paper extends the state equations to derivate any state variable according a sizing parameter. The integral expressions used for some sizing performances (e.g. average or RMS values) mix symbolic and numerical approaches. Choices are made for the derivatives of the extrema of which the search is not a continuous process. The use of an object-oriented implementation allows to have generic formulation of some design performances.

The paper aims to propose and to test formulations of sizing criteria and their gradients; so, the modelling of the study case is carried out manually. Due to generic modelling approach used for the power electronics, the model is not completely continuous. So, the derivatives according some parameters (e.g. switch controls) must be carried out by finite differences. However, as the global behaviour is continuous, it is not critical.

The proposed formulations can be easily applied on simple static converter applications. For applications with large state equations, it should be possible to use the basic model of switches used in simulation tools of power electronics. The solving process and the sizing criteria formulation (with their derivatives) are generic and can be instantiate for any study.

The approach proposes formulations giving a numerical sizing dynamic model with a Jacobian computed, if possible, by an exact derivation useful for optimization studies. The approach gives fast simulation and fast computation of the derivatives by combining numerical and analytical approaches.

The purpose of this paper is to deal with the design of passive filter for power electronics voltage inverters used in aircraft electrical drives (a permanent magnet synchronous machine fed by a six-phase voltage inverter with PMW control), using optimization for both sizing and sensibility analyses.

The approach is generic. An aid allows to modify easily the frequency model and so to check various study cases, and to carry out the filter optimization for different topologies or control strategies.

The approach is generic. An aid allows to modify easily the frequency model and so to check various study cases, and to carry out the filter optimization for different topologies or control strategies.

The power electronics load is supposed to be a set of predefined harmonic sources, obtained by experiment or time simulation plus fast fourier transformation before the optimization process.

The problem has numerous constraints on the components, mainly technological constraints. The volume is minimized, respecting electromagnetic standards and an electro magnetic interference filter prototype has been made.

The frequency model is automatically generated. A complex aircraft application has been studied thanks to the approach. Several sensibility analyses have been carried out. An EMC filter has been sized and an experimental prototype has been made, comforting the sizing by optimization.

An analytical approach is preferred to carry out the harmonic modelling of power electronics converters because it is generally faster than time simulation chained with FFT. However, the difficulty of such an approach is to build the model and to manage the uncontrolled commutations that occur in the studied static converter, and also to deal with large equations. The purpose of this paper is to propose an aid in the frequency modelling of the drive elements, in the frequency domain, including all key parameters for sizing aim i.e. a way to optimize the EMC filter using different algorithms.

The paper aims to propose an aid to create such models, and to assure its good solving, i.e. that the correct operating mode is represented. So, the solving problem is formulated as an optimization problem under constraints, to solve this difficulty.

The difficulty is to be sure to deal with the good operating mode of the static converter when soft or uncontrolled commutations occur. So, the model is formulated as a constrained optimization problem. The paper proposes a symbolic approach, that allows to build automatically the frequency model. It is translated to be solved in Matlab.

The approach does not fit for static converters with a control implying numerous commutations per operating period. However, the approach deals with natural and soft commutations.

The modelling is based on the use of linear components and ideal switches.

Multiphysical models are often useful for the design of electrical devices such as electrical machines. In this way, the modeling of thermal, magnetic and electrical phenomena by using an equivalent circuit approach is often used in sizing problems. The coupling of such models with other models is difficult to take into account, partly because it adds complexity to the process. The paper proposes an automatic modelling of thermal and magnetic aspects from an equivalent circuit approach, with its computation of gradients, using selectivity on the variables. Then, it discusses the coupling of various physical models, for the sizing by optimization algorithms. Sensibility analyses are discussed and the multiphysical approach is applied on a permanent magnet synchronous machine.

The paper allows one to describe thermal and magnetic models by equivalent circuits. Magnetic aspects are represented by reluctance networks and thermal aspects by thermal equivalent circuits. From circuit modelling and analytical equations, models are generated, coupled and translated into computational codes (Java, C), including the computation of their jacobians. To do so, model generators are used: CADES, Reluctool, Thermotool. The paper illustrates the modelling and automatic programming aspects with Thermotool. The generated codes are directly available for optimization algorithms. Then, the formulation of the coupling with other models is studied in the case of a multiphysical sizing by optimization of the Toyota PRIUS electrical motor.

A main specificity of the approach is the ability to easily deal with the selectivity of the inputs and outputs of the generated model according to the problem specifications, thus reducing drastically the size of the jacobian matrix and the computational complexity. Another specificity is the coupling of the models using analytical equations, possibly implicit equations.

At the present time, the multiphysical modeling is considered only for static phenomena. However, this limit is not important for numerous sizing applications.

The analytical approach with the selectivity gives fast models, well-adapted for optimization. The use of model generators allows robust programming of the models and their jacobians. The automatic calculation of the gradients allows the use of determinist algorithms, such as SQP, well adapted to deal with numerous constraints.

Due to the increase of the traffic, issues are appearing on DC electrified railway feeding systems. One candidate solution to solve these issues and to improve their performances is to add storage systems in the railway DC electrical network. The paper presents a method based on an Optimal Power Flow (OPF) for the analysis and design of DC railway feeding systems with storage.

The paper describes a new methodology based on optimization to study DC electrified railways, including storage systems. A load flow model of a DC 1500V railway electrification system is presented, including the mobility of the train sets. Then, an Optimal Power Flow model of the DC network, including energy storage systems and feeding substation rectifiers has been developed. Finally, the OPF model has been tested on a real application case showing its benefits while searching solutions in order to improve the network performances.

An OPF model suitable for analysis of DC networks with storage is presented. It shows its ability to solve large scale problems.

The paper focuses on the physical model of the network. The optimization model will have to be extended with application constraints.

The hypothesis presented in this paper allows to remove the discontinuities of the system in order to use a continuous optimization approach.