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  • 1.
    Cottet, Didier
    et al.
    ABB Corporate Research.
    Stevanovic, Ivica
    ABB Corporate Research.
    Wunsch, Bernhard
    ABB Corporate Research.
    Daroui, Danesh
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Ekman, Jonas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Antonini, Giulio
    University of L’Aquila.
    EM simulation of planar bus bars in multi-level power converters2012In: EMC Europe 2012: International Symposium on Electromagnetic Compatibillity, September 15-21, Rome, Italy, 2012Conference paper (Refereed)
    Abstract [en]

    This paper presents recent progress in the acceleration of PEEC based electromagnetic simulations and its impact on the design of complex bus bar structures as used in multi-level power converters. The approach presented consists of providing different dedicated acceleration methods for the different design tasks. The first acceleration technique applied is the so called reluctance matrix method for full 3D field results, reducing memory consumption by orders of magnitude and computing time by a factor 3 to 5. The second acceleration method applied is based on model order reduction techniques for port-to-port impedance extraction, reducing the computation time by several orders of magnitude and allowing wideband macro modeling for system level simulations. The paper focuses on the application of these methods showing the impact on practical bus bar design tasks

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  • 2.
    Daroui, Danesh
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Efficient PEEC-based solver for complex electromagnetic problems in power electronics2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The research presented in this thesis discusses an electromagnetic (EM) analysis tool which is based on the partial element equivalent circuit (PEEC) method and is appropriate for combined EM and circuit simulations especially power electronics applications. EM analysis is important to ensure that a system will not affect the correct operation of other devices nor cause interference between various electrical systems. In power electronic applications, the increased switching speed can cause voltage overshoots, unbalanced current share between semiconductor modules, and unwanted resonances. Therefore, EM analysis should be carried out to perform design optimizations in order to minimize unwanted effects of high frequencies. The solver developed in this work is an appropriate solution to address the needs of EM analysis in general and power electronics in particular. The conducted research consists of performance acceleration and implementation of the solver, and verification of the simulation results by means of measurements. This work was done in two major phases.In the first phase, the solver was accelerated to optimize its performance when quasi-static (R,Lp,C)PEEC as well as full-wave (R,Lp,C,tau)PEEC simulations were carried out. The main optimizations were based on exploiting parallelism and high performance computing to solve very large problems and non-uniform mesh, which was helpful in simulating skin- and proximity effects while keeping the problem size to a minimum. The presented results and comparisons with the measurements confirmed that non-uniform mesh helped in accurately simulating large bus bar models and correctly predicting system resonances when the size of the problem was minimized. On-the-fly calculation was also developed to reduce memory usage, while increasing solution time.The second phase consists of methods to increase the performance of the solver while including some levels of approximations. In this phase sparsification techniques were used to convert a dense PEEC system into a sparse system. The sparsification was done by calculating the reluctance matrix, which can be sparsified by maintaining the accuracy at the desired level, because of the locality and the shielding effect of the reluctance matrix. Efficient algorithms were developed to perform sparse matrix-matrix multiplication and assemble the sparse coefficient matrix in a row-by-row manner to reduce the peak memory usage. The sparse system was then solved using both sparse direct and iterative solvers with proper preconditioning. The acquired results from the sparse direct solution confirmed that the memory consumption and solution time were reduced by orders of magnitude and by a factor 3 to 5. Moreover, the Schur complement was used together with the iterative approach, making it possible to solve large problems within a few iterations by preconditioning the system, and using less memory and lower computational complexity. Bus bars used in two types of power frequency converters manufactured by ABB were modelled and analysed with the developed PEEC-based solver in this research, and the simulations and measurements agreed very well. Results of simulations also led to improvement in the physical design of the bars, which reduced the inductance of the layout.With the accelerated solver, it is now possible to solve very large and complex problems on conventional computer systems, which was not possible before. This provides new possibilities to study real-world problems which are typically large in size and have complex structures.

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  • 3.
    Daroui, Danesh
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Implementation and optimization of partial element equivalent circuit-based solver2010Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    The Partial Element Equivalent Circuit (PEEC) method is an integral equation based full-wave approach to solve combined circuit and electromagnetic problems in the time and frequency domain. Using PEEC, an electromagnetic problem is transferred to the circuit domain and then solved using circuit theory which gives PEEC a high flexibility to be used in combined electromagnetic and circuit modeling problems. Thus, the method can be applied to different classes of problems, for example power electronics systems and antenna simulation to ensure the functionality of the system and also comply with electromagnetic compatibility (EMC) regulations. Other methods, like Finite Element Method or Finite Difference Time Domain Methods, are also used for electromagnetic analysis and an optimal computer implementation is needed to be able to handle such problems within a reasonable time and at certain accuracy.This work presents the development and optimization of a PEEC-based software on different computing platforms. The aim of the acceleration is to be able to solve problems using the PEEC method as fast as possible with optimum memory usage on a regular computer system. The PEEC-based solver has been developed for desktop machines using the GMM++ linear algebra package. This implementation was optimized by improving the code, to use more efficient libraries and adapt the program to run on powerful machines. Another part of this optimization process was to implement smart algorithms like non-uniform meshing and on-the-fly calculations for the partial elements. Though, the code has been recently enhanced to take advantage of the multicore hardware by replacing old library with Intel Math Kernel Library (MKL) in order to take advantage of several processors which exist on typical computer system.To be able to solve very large problems which for example needs several hundred gigabytes of memory, the code was also ported into parallel computer systems. The parallel PEEC solver is compatible with the distributed memory architecture and thus, is scalable by using a set of computing units which collaborate to solve a problem. Hence, by allocating enough number of processors and amount of memory, the load of the solution will be distributed over different elements. Consequently, one of the challenging parts of these kinds of distributed computations is to distribute data, using a balanced manner to minimize data movement between nodes which will slow down the running process. The balanced distribution of data was ensured, by using Basic Linear Algebra Subprograms (BLAS) and Scalable Linear Algebra Package (ScaLAPACK) libraries to handle linear algebraic calculations in the parallel solver. Using these tools, the matrix elements are dispensed according to the block-cyclic decomposition scheme which guarantees that data is uniformly assigned to each computing node. Several test cases have been run, in order to benchmark the computer implementation. On account of the applied optimization techniques, the sequential solver needs less memory and performs the solution remarkably faster than before. As an example, high frequency simulations can now be run now with the optimized code, within shorter time and with less memory usage, by having very light mesh, using non-uniform meshing. According to the benchmarking results of the parallel solver, the results of these tests did agree very well with the physical measurements and also showed an acceptable speed-up factor as number of processors as well as size of the problems grew in the parallel version of the solver. The robustness of the parallel solver was verified by stressing the code with the largest test case which was a problem with more than 250 000 unknowns. Further steps of the acceleration would be focusing on the smarter algorithms as well as numerical methods like Fast Multipole Method (FMM), using iterative solvers instead of direct solvers and QR Decomposition. An important issue which needs to be considered is the approximations which will appear in the results as a consequence of usage of such techniques like numerical instabilities and loss of accuracy.

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  • 4.
    Daroui, Danesh
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Ekman, Jonas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Combined circuit and electromagnetic modelling on multi-core platforms2011Conference paper (Refereed)
    Abstract [en]

    Computer simulation techniques are widely used in various fields to design and verify the functionality, performance, quality, or safety of a product. In electrical systems, with increasing operational frequencies, capacitive and inductive couplings between parts in an embedded system might have to be taken into account. Therefore, traditional circuit analysis are not sufficient for such problems. Hence, other simulation approaches such as Partial Element Equivalent Circuit (PEEC), Method of Moments, and Finite Element Methods, and other have been developed to fulfill this need. By using the PEEC method, the simulation of the functionality of an electrical device can be combined with an electromagnetic analysis. Thus, the method has been widely used in combined circuit and electromagnetic modeling on problems in different classes in power electronic industry and antenna design. The main aim of this paper is to demonstrate how multi-core systems can contribute to improve the performance of a PEEC-based electromagnetic simulation tool and to show that the improvements make it possible to solve larger and more complex problems in a reasonable time.A PEEC-based solver has been developed at Luleå University of Technology. The kernel of the solver has been implemented in C++ and is designed to run on different desktop platforms and operating systems. It is known that in the PEEC formulations there are large, dense, and in many cases non-symmetric matrices which increase the computational costs. Hence, using an efficient and robust library as well as support for the recently advanced hardware, is vital and will highly affect the performance of the solver.

  • 5.
    Daroui, Danesh
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Ekman, Jonas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Efficient PEEC-based simulations using reluctance method for power electronic applications2012In: Applied Computational Electromagnetics Society Journal, ISSN 1054-4887, Vol. 27, no 10, p. 830-841Article in journal (Refereed)
    Abstract [en]

    This paper presents a partial element equivalent circuit (PEEC)-based solver that has been accelerated to exploit the massively parallel structure of graphics processing unit (GPU) technology, in order to employ a reluctance-based method in an efficient way. A grouping algorithm is also presented which makes reluctance calculation efficient, suitable for GPUs, and feasible even for very large problems. It has been shown that by using the reluctance method, the coefficient matrix in the system equation can be safely sparsified whilst the required accuracy is maintained. Because the calculation of the reluctance matrix includes matrix inversion, which is a task with high computational complexity, GPUs as cooperative units are utilized to reduce computational costs by taking advantage of parallelism. Two test models have been simulated and analyzed to benchmark the solver, and the results have been compared with the previously developed solver. Furthermore, analyzing the results reveals that the reluctance method makes it possible to use a considerably sparser system and thereby solve large problems by decreasing the memory demands and the solution time. It is also proven that the solution is reliable and accurate, whereas the problem has become noticeably smaller.

  • 6.
    Daroui, Danesh
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Ekman, Jonas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Iterative PEEC-based power electronic systems simulations using reluctance and regularization techniques2012In: EMC Europe 2012: International Symposium on Electromagnetic Compatibillity, September 15-21, Rome, Italy, 2012Conference paper (Refereed)
    Abstract [en]

    This paper presents a method to deal with the ill-posed and rank-deficient linear systems arising from sparsified partial element equivalent circuit-based electromagnetic simulations via a reluctance method. Since conventional, direct methods, cannot be used to solve these kind of problems, regularization techniques need to be employed. Among various regularization techniques, a least square-based method entitled LSQR is utilized to solve the rank-deficient problems. The proposed method is specially proper for the models where capacitive couplings can be neglected, since magnetic field is the dominating factor, like problems within power electronics. The correctness of the presented PEEC-based solver is ensured by studying bus bar models which are a part of frequency converters with application in power electronics.

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    FULLTEXT01
  • 7. Daroui, Danesh
    et al.
    Ekman, Jonas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Parallel implementations of the PEEC method2010In: Applied Computational Electromagnetics Society Journal, ISSN 1054-4887, Vol. 25, no 5, p. 410-422Article in journal (Refereed)
    Abstract [en]

    This paper presents the first parallel implementation of a partial element equivalent circuit (PEEC) based electromagnetic modelling code suitable for solving general electromagnetic problems. The parallelization is based on the GMM++ and ScaLAPACK packages which are cross-platform libraries available for major operating systems. The parallel PEEC solver has been tested on several high performance computer systems. Large structures containing over 250 000 unknown current and voltage basis functions were successfully analyzed for the first time with a general PEEC-solver. The numerical examples are of orthogonal type, studied both in the time and frequency domain, for which memory, performance, and speed-up results are presented.

  • 8.
    Daroui, Danesh
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Ekman, Jonas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    PEEC-based Simulations Using Iterative Method and Regularization Technique for Power Electronic Applications2014In: IEEE transactions on electromagnetic compatibility (Print), ISSN 0018-9375, E-ISSN 1558-187X, Vol. 56, no 6, p. 1448-1456Article in journal (Refereed)
    Abstract [en]

    The partial element equivalent circuit (PEEC) method has been widely used in different industrial and scientific fields for electromagnetic analysis. PEEC-based solvers have been optimized and accelerated in order to be able to solve larger and more complex problems that arise in industry. In power electronic system simulations, PEEC models are often simplified by neglecting electric field couplings and using quasi-static model. The simplified system can be further accelerated using reluctance technique and then sparsified up to high levels without degrading the accuracy of the solution. In previous work, the sparse system was solved using sparse direct solution, while in this study, an iterative approach is employed which resulted in lower time complexity of the solution. However, since matrices achieved from PEEC equations are severely ill-conditioned, regularization techniques need to be applied to avoid numerical instabilities. The regularization is done mathematically and can be interpreted as adding a frequency-dependent pseudocapacitor to each node in the PEEC model. Because the pseudocapacitors are frequency dependent, hence frequencies close to dc are not covered in this study and have left as future work. The new sparse and regularized system can then be solved using a Schur complement technique together with iterative solvers with a novel preconditioning approach.

  • 9.
    Daroui, Danesh
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Ekman, Jonas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Performance analysis of parallel non-orthogonal PEEC-based solver for EMC applications2012In: Progress in Electromagnetics Research B, ISSN 1937-6472, E-ISSN 1937-6472, Vol. 41, p. 77-100Article in journal (Refereed)
    Abstract [en]

    A parallel implementation of a quasi-static Partial Element Equivalent Circuit (PEEC)-based solver that can handle electromagnetic problems with non-orthogonal structures is presented in this paper. The solver has been written in C++ and employs GMM++ and ScaLAPACK computational libraries to make the solver fast, efficient, and adaptable to current parallel computer systems. The parallel PEEC-based solver has been tested and studied on high performance computing clusters and the correctness of the solver has been verified by doing comparisons between results from orthogonal routines and also another type of electromagnetic solver, namely FEKO. Two non-orthogonal numerical test cases have been analysed in the time and frequency domain. The results are given for solution time and memory consumption while bottlenecks are pointed out and discussed. The benchmarks show a good speedup which gets improved as the problem size is increased. With the capability of the presented solver, the non-orthogonal PEEC formulation is a viable tool for modelling geometrically complex problems.

  • 10. Daroui, Danesh
    et al.
    Ekman, Jonas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Didier, Cottet
    ABB Switzerland, Corporate Research, Schweiz.
    Dierk, Bormann
    ABB Corporate Research, Sverige.
    Engdahl, Göran
    KTH, Sverige.
    Projekt: Kretsbaserad lösare för elektromagnetisk analys av kraftelektroniksystem- Applikation mot IGBTmoduler2007Other (Other (popular science, discussion, etc.))
    Abstract [sv]

    Projektet syftar till att accelerera och adaptera den programvara, MultiPEEC,som ingick i ELEKTRA-projekt 36021 för att möjliggöra studier avelektromagnetiska effekter i avancerade kraftelektroniksystem.Programvaran bygger på en långsiktig forskningssatsning på Luleå tekniskauniversitet med syfte att kombinera lösningen av elektriska kretsar ochelektromagnetiska effekter i samma miljö med hjälp av en ekvivalent-kretsmetod(PEEC).I första delen av projektet verifierades, optimerades och stabiliseradesprogramvaran i ett mycket nära samarbete med ABB CRC. I den föreslagnaandra delen av projektet kommer programvaran att massivt accelereras föratt möjliggöra detaljstudier av elektromagnetiska effekter i bus bars ochIGBT moduler. För bus bars är det främst studier av parasitiska induktanseroch magnetiska fältmönster som är av intresse för att minimeraoscillationer, spänningstoppar och sk termiska hot spots. För IGBTmodulerna är det främst den dynamiska strömfördelningen i modulerna ochöver seriekopplade konfigurationer som studeras för att förbättrakommande produkter. Exakt med vilken metod den egen-utveckladeprogramvara kommer att accelereras utifrån bestäms under hösten 2010med en litteraturstudie som bas. Tänkbara metoder är QR decomposition,Fast multipole methods, wavelets, eller hierarkiska matrismetoder. Detprimära syftet är att accelerera lösningen av system beskrivna i frekvensdomänen under kvasi-statiska antaganden formulerade med hälp av enmodifierad nodanalys (MNA) då det passar för ovan nämnda designstudier.Vidare är det av stor vikt att kunna uppskatta felet som dessaaccelerationsmetoder introducerar i lösningen så verktyget inte blir praktisktoanvändbart.

  • 11. Daroui, Danesh
    et al.
    Stevanovic, Ivica
    ABB.
    Cottet, Didier
    ABB.
    Ekman, Jonas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Bus bar simulations using the PEEC method2010In: 26th International Review of Progress in Applied Computational Electromagnetics ACES 2010: Tampere, Finland, April 25-29, 2010, 2010, p. 1-6Conference paper (Refereed)
    Abstract [en]

    The Partial Element Equivalent Circuit (PEEC) is an integral equation based full-wave approach for the solution of combined circuit and electromagnetic problems in the time and the frequency domain. The method is fast and efficient and can be applied to different classes of problems in power electronics system design, antennas modeling, and printed circuit board simulation. This paper presents PEEC usage in simulating a system of parallel bus bars used in distributing the DC-link power in a medium voltage frequency converter. Using PEEC simulations with non-uniform meshing, the impedance of a complete bus bar structure has been simulated. The results of PEEC simulations compare very well with measured values.

  • 12.
    Romano, Daniele
    et al.
    University of L’Aquila.
    Antonini, Giulio
    University of L’Aquila.
    Daroui, Danesh
    Ekman, Jonas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    A Fast Sparse Reluctance- and Capacitance-Based Solver for the Partial Element Equivalent Circuit Method2014In: IEEE transactions on electromagnetic compatibility (Print), ISSN 0018-9375, E-ISSN 1558-187X, Vol. 56, no 5, p. 1077-1085Article in journal (Refereed)
    Abstract [en]

    A new technique for the reluctance method applied to the Partial Element Equivalent Circuit (PEEC) method for the time domain analysis is presented which is well suited tobe combined with acceleration techniques. In particular, taking advantage of the rank-deficiency of the magnetic and electric field couplings, a new technique for the sparsification of reluctance and capacitance matrices is adopted. Furthermore, the multiscale block decomposition technique has been applied to fast fill these matrices. Finally, the the sparse multifrontal LU factorization has been adopted to efficiently compute the global solution. Numerical results demonstrate the validity of the proposed approach.

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  • 13.
    Stevanović, Ivica
    et al.
    ABB Switzerland Ltd., Corporate Research, CH-5405 Baden-Dättwil.
    Cottet, Didier
    ABB Switzerland Ltd., Corporate Research, CH-5405 Baden-Dättwil.
    Wider, Björn
    ABB Switzerland Ltd., ATPT3, CH-5300, Turgi.
    Daroui, Danesh
    Ekman, Jonas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Modeling of large bus bars using PEEC method and circuit level simulators2010In: 2010 IEEE 12th Workshop on Control and Modeling for Power Electronics, COMPEL 2010, Piscataway, NJ: IEEE Communications Society, 2010, p. 1-6Conference paper (Refereed)
    Abstract [en]

    This paper presents an efficient modeling approach for large bus bar systems in power electronic frequency converters using partial element equivalent circuit (PEEC) method and circuit-level simulations. Several acceleration methods have been applied to improve the computational speed and memory efficiency. The approach is verified against measurements, and used to analyze the impact of the stray impedance of bus bars on the electromagnetic and circuit behavior of a static frequency converter system

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