A block-diagonal structured model reduction scheme for power grid networks

We propose a block-diagonal structured model order reduction (BDSM) scheme for fast power grid analysis. Compared with existing power grid model order reduction (MOR) methods, BDSM has several advantages. First, unlike many power grid reductions that are based on terminal reduction and thus error-prone, BDSM utilizes an exact column-by-column moment matching to provide higher numerical accuracy. Second, with similar accuracy and macromodel size, BDSM generates very sparse block-diagonal reduced-order models (ROMs) for massive-port systems at a lower cost, whereas traditional algorithms such as PRIMA produce full dense models inefficient for the subsequent simulation. Third, different from those MOR schemes based on extended Krylov subspace (EKS) technique, BDSM is input-signal independent, so the resulting ROM is reusable under different excitations. Finally, due to its blockdiagonal structure, the obtained ROM can be simulated very fast. The accuracy and efficiency of BDSM are verified by industrial power grid benchmarks. © 2011 EDAA.published_or_final_versionDesign, Automation and Test in Europe Conference and Exhibition (DATE 2011), Grenoble, France, 14-18 March 2011. In Design, Automation, and Test in Europe Conference and Exhibition Proceedings, 2011, p. 44-4

Comparative analysis of model reduction methods applied to building simulation benchmarks

International audienceMany research and development studies use virtual buildings represented by building thermal models at a detailed level. Such models need relatively long computation times for one-year simulations: the use of these tools is then often too time-consuming when it comes to compare technical solutions during the design stage. Model reduction methods allow models with shorter computation times to be synthesized. In this paper, the linear state-space representation of a whole model is extracted and a balanced truncation method is applied to it. The detailed models are built from the SIMBAD library, a Simulink library of building modeling components developed at CSTB. Both linear state-space and reduced order models ensure shorter computation times than the full detailed model. However, the choice of the order of the reduced model has an impact on the final results. The main strengths and weaknesses of using the linear state-space and reduced models built from the same detailed model are investigated. To this end, the physical descriptions of idealized test buildings provided by ASHRAE standard 140 for building simulation tools assessment are used, and the results obtained through the different approaches for computation time reduction are compared

A shifting method for dynamic system Model Order Reduction

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.Includes bibliographical references (p. 83-86).Model Order Reduction (MOR) is becoming increasingly important in computational applications. At the same time, the need for more comprehensive models of systems is generating problems with increasing numbers of outputs and inputs. Classical methods, which were developed for Single-Input Single-Output (SISO) systems, generate reduced models that are too computationally inefficient for large Multiple-Input Multiple-Output (MIMO) systems. Although many approaches exclusively designed for MIMO systems have emerged during the past decade, they cannot satisfy the overall needs for maintaining the characteristics of systems. This research investigates the reasons for the poor performances of the proposed approaches, using specific examples. Inspired by these existing methods, this research develops a novel way to extract information from MIMO systems, by means of system transfer functions. The approach, called Shifting method, iteratively extracts time-constant shifts from the system and splits the transfer function into several simple systems referred to as contour terms that outline the system structure, and a reducible system referred to as remainder system that complement the Contour Terms. This algorithm produces a remainder system that existing approaches can reduce more effectively. This approach works particularly well for systems with either tightly clustered or well separated modes, and all the operations are O(n). The choice of shifts is based on an optimization process, with Chebyshev Polynomial roots as initial guesses. This paper concludes with a demonstration of the procedure as well as related error and stability analysis.by Xu, Song.S.M

Addressing Computational Complexity of High Speed Distributed Circuits Using Model Order Reduction

Advanced in the fabrication technology of integrated circuits (ICs) over the last couple of years has resulted in an unparalleled expansion of the functionality of microelectronic systems. Today’s ICs feature complex deep-submicron mixed-signal designs and have found numerous applications in industry due to their lower manufacturing costs and higher performance levels. The tendency towards smaller feature sizes and increasing clock rates is placing higher demands on signal integrity design by highlighting previously negligible interconnect effects such as distortion, reflection, ringing, delay, and crosstalk. These effects if not predicted in the early stages of the design cycle can severely degrade circuit performance and reliability. The objective of this thesis is to develop new model order reduction (MOR) techniques to minimize the computational complexity of non-linear circuits and electronic systems that have delay elements. MOR techniques provide a mechanism to generate reduced order models from the detailed description of the original modified nodal analysis (MNA) formulation. The following contributions are made in this thesis: 1. The first project presents a methodology for reduction of Partial Element Equivalent Circuit (PEEC) models. PEEC method is widely used in electromagnetic compatibility and signal integrity problems in both the time and frequency domains. The PEEC model with retardation has been applied to 3-D analysis but often result in large and dense matrices, which are computationally expensive to solve. In this thesis, a new moment matching technique based on Multi-order Arnoldi is described to model PEEC networks with retardation. 2. The second project deals with developing an efficient model order reduction algorithm for simulating large interconnect networks with nonlinear elements. The proposed methodology is based on a multidimensional subspace method and uses constraint equations to link the nonlinear elements and biasing sources to the reduced order model. This approach significantly improves the simulation time of distributed nonlinear systems, since additional ports are not required to link the nonlinear elements to the reduced order model, yielding appreciable savings in the size of the reduced order model and computational time. 3. A parameterized reduction technique for nonlinear systems is presented. The proposed method uses multidimensional subspace and variational analysis to capture the variances of design parameters and approximates the weakly nonlinear functions as a Taylor series. An SVD approach is presented to address the efficiency of reduced order model. The proposed methodology significantly improves the simulation time of weakly nonlinear systems since the size of the reduced system is smaller than the original system and a new reduced model is not required each time a design parameter is changed

Reduced-order electro-thermal models for computationally efficient thermal analysis of power electronics modules

Silicon and Silicon Carbide-based power module are common in power electronic systems used in a wide range of applications, including renewable energy, industrial drives and transportation. Reliability of power electronics converters is very important in many applications. It is well known that reliability and ultimately the lifetime of power modules is affected by the running temperature during power cycles. Although accurate thermal models of power electronics assemblies are widely available, based e.g. on computational fluid dynamics (CFD) solvers, their computational complexity hinders the application in real-time temperature monitoring applications. In the thesis, geometry-based numerical thermal models and compact thermal models will be developed to address the fast thermal simulation in the electronic design process and real-time temperature monitoring, respectively. Accurate geometry-based mathematical models for dynamic thermal analyses can be established with the help of finite difference methods (FDM). However, the computational complexity result from the fine mesh and large dimension of ordinary differential equations (ODE) system matrix makes a drawback on the analysis in parametric studies. In this thesis, a novel multi-parameter order reduction technique is proposed, which can significantly improve the simulation efficiency without having a significant impact on the prediction accuracy. Based on the block Arnoldi method, this method is illustrated by referring to the multi-chip power module connected with air-force cooling system including plate-fin heatsink. In real-time temperature monitoring, more compact tools might be preferable, especially if operating and boundary conditions such as losses and cooling are now known accurately, as it’s often the case in practical applications. Compared with geometry-based model which is more suitable in the design of power modules, lumped parameter thermal compact model is simpler and can be applied in real-time temperature prediction during the power cycles of power modules. This thesis proposes a reduced order state space observer to minimize the error caused by air temperature and air flow rate. Additionally, a novel feedback mechanism for disturbance estimation is introduced to compensate the effect result from the error of input power loss, air flow and changes of other nonlinearities

Efficient Long-Term Simulation of the Heat Equation with Application in Geothermal Energy Storage

Long-term evolutions of parabolic partial differential equations, such as the heat equation, are the subject of interest in many applications. There are several numerical solvers marking the state-of-the-art in diverse scientific fields that may be used with benefit for the numerical simulation of such long-term scenarios. We show how to adapt some of the currently most efficient numerical approaches for solving the fundamental problem of long-term linear heat evolution with internal and external boundary conditions as well as source terms. Such long-term simulations are required for the optimal dimensioning of geothermal energy storages and their profitability assessment, for which we provide a comprehensive analytical and numerical model. Implicit methods are usually considered the best choice for resolving long-term simulations of linear parabolic problems; however, in practice the efficiency of such schemes in terms of the combination of computational load and obtained accuracy may be a delicate issue, as it depends very much on the properties of the underlying model. For example, one of the challenges in long-term simulation may arise by the presence of time-dependent boundary conditions, as in our application. In order to provide both a computationally efficient and accurate enough simulation, we give a thorough discussion of the various numerical solvers along with many technical details and own adaptations. By our investigation, we focus on two largely competitive approaches for our application, namely the fast explicit diffusion method originating in image processing and an adaptation of the Krylov subspace model order reduction method. We validate our numerical findings via several experiments using synthetic and real-world data. We show that we can obtain fast and accurate long-term simulations of typical geothermal energy storage facilities. We conjecture that our techniques can be highly useful for tackling long-term heat evolution in many applications

Modeling and Analysis of Noise and Interconnects for On-Chip Communication Link Design

This thesis considers modeling and analysis of noise and interconnects in onchip communication. Besides transistor count and speed, the capabilities of a modern design are often limited by on-chip communication links. These links typically consist of multiple interconnects that run parallel to each other for long distances between functional or memory blocks. Due to the scaling of technology, the interconnects have considerable electrical parasitics that affect their performance, power dissipation and signal integrity. Furthermore, because of electromagnetic coupling, the interconnects in the link need to be considered as an interacting group instead of as isolated signal paths. There is a need for accurate and computationally effective models in the early stages of the chip design process to assess or optimize issues affecting these interconnects. For this purpose, a set of analytical models is developed for on-chip data links in this thesis. First, a model is proposed for modeling crosstalk and intersymbol interference. The model takes into account the effects of inductance, initial states and bit sequences. Intersymbol interference is shown to affect crosstalk voltage and propagation delay depending on bus throughput and the amount of inductance. Next, a model is proposed for the switching current of a coupled bus. The model is combined with an existing model to evaluate power supply noise. The model is then applied to reduce both functional crosstalk and power supply noise caused by a bus as a trade-off with time. The proposed reduction method is shown to be effective in reducing long-range crosstalk noise. The effects of process variation on encoded signaling are then modeled. In encoded signaling, the input signals to a bus are encoded using additional signaling circuitry. The proposed model includes variation in both the signaling circuitry and in the wires to calculate the total delay variation of a bus. The model is applied to study level-encoded dual-rail and 1-of-4 signaling. In addition to regular voltage-mode and encoded voltage-mode signaling, current-mode signaling is a promising technique for global communication. A model for energy dissipation in RLC current-mode signaling is proposed in the thesis. The energy is derived separately for the driver, wire and receiver termination.Siirretty Doriast