DOCSLIB.ORG

Mechanical Dynamics of a Sensorless Pmsynrel Drive

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Mechanical Dynamics of a Sensorless Pmsynrel Drive Mechanical Dynamics of a Sensorless PMSynRel Drive Yingbei Yu Degree project in Electrical Machines and Drives Stockholm, Sweden 2013 XR-EE-E2C 2013:004 Mechanical dynamics of a sensorless PMSynRel drive by Yingbei Yu Master Thesis Royal Institute of Technology School of Electrical Engineering Dept. Electrical Energy Conversion Stockholm 2013 XR-EE-E2C 2013:004 Mechanical dynamics of a sensorless PMSynRel drive YINGBEI YU c YINGBEI YU, 2013. School of Electrical Engineering Department of Electrical Machines and Power Electronics Kungliga Tekniska H¨ogskolan SE–100 44 Stockholm Sweden To my family iv Abstract Hybrid electric vehicle (HEV) concept has, combining conventional internal combustion engines and electric drives, gained more and more interest due to its environmental friendly features. A PMSynRel based electric drive is considered as a good option due to its high torque density and high efficiency. To reduce the overall cost of HEVs, the position resolvers can be replaced by Hall-sensors or using sensorless control. However, the dynamics of such electric drives may be degraded. The main objective of this MSc project is to develop torque dynamics of such electric drives when operating with/without a position sensor. The developed torque dynamic can be used to analyze the limits of hall senor/sensorless strategy when, e.g. anti-oscillation control is required. The torque dynamic is presented as a matrix based transfer function extracted from the speed responses and torque responses using Identification Tool Box in Matlab. Firstly, the transfer function was derived by means of simulations in both time and frequency domains. Secondly, similar procedures were applied to extract the transfer functions based on the experimental results. Keywords: Bode plot, Hall-effect sensor, Matlab Identification Toolbox, MIMO, PMSynRel, sensorless control, transfer function. Sammanfattning Elektriska hybridfordon, där en konventionell förbränningsmotor kombineras med ett elektriskt drivsystem, uppmärksammas mer och mer på grund av de miljömässiga fördelarna. En eldrift baserad på en permanentmagnetiserad synkron reluktansmaskin (PMSynRel) är ett bra alternativ tack vara den höga momenttätheten och den höga verkningsgraden. För att minska systemkostnaden kan positionsgivarenen (resolver) ersättas med Hall-givare eller att motorn styrs med, så kalla, sensorlös reglering. En nackdel med dessa alternativ är att den mekaniska dynamiken kan försämras. Huvudmålet med detta examensarbete är att studera hur momentdynamiken kan kvantifieras med och utan en positionsgivare. De framtagna modellerna kan användas till att utvärdera huruvida tex svängningar i fordonets drivlina kan dämpas ut med hjälp av det elektriska drivsystemet i de fall då positionen mäts med en Hall-givare eller skattas via den sensorlösa algoritmen. I detta arbete modelleras momentdynamiken med hjälp av en matrisbaserad överföringsmatris var element identifierats i en simuleringsmodell implementerad i Matlab/Simulink. I examensarbetets sista skede jämfördes den modellerade dynamiken med tidiga experimentella försök i en laborativ försöksrigg. Nyckelord: Bodediagram, Hall-givare, MIMO, PMSynRel, sensorlös reglering, överföringsfunktion. V vi Acknowledgements In the first place, I would like to thank Phd student Shuang Zhao and my supervisor and examiner Dr. Oskar Wallmark for providing me with thorough technical explanation and guidance through the whole thesis work. I’ve learned a lot during each discussion and meeting for this thesis work. Especially thanks to Shuang Zhao, he was very patient to help me with any questions I had related to this project. I am also very grateful to Mats Leksell for introducing me to this valuable opportu- nity to work on this project at the Department of Electrical Energy Conversion. I also want to thank the people who work at this department at KTH for assisting me in different questions and problems. In addition, I’d like to appreciate my manager Vidar Grimelind working at FM- CTechnologies AS for the permission on my temporary study leave. Thanks for his kind- ness, generousness and understanding. Finally, I would like to express my deepest gratitude to my parents for all the sup- ports and love, not only during the period I am abroad, but through all my life. They are the greatest parents in the world! Last but not least, I would like to thank my husband Xu Yuan for all the encouragements, understandings and love. Yingbei Yu Stockholm, Sweden April 2013 vii viii Contents Abstract v Acknowledgements vii Contents ix 1 Introduction 1 1.1 BackgroundandObjectives. 1 1.2 MotivationofHybridElectricVehicles . ..... 1 1.3 ConfigurationsofHEVs .......................... 2 1.3.1 SeriesHEVConfiguration . 2 1.3.2 ParallelHEVConfiguration . 2 1.4 PMSynRelmachineinHEVapplications. .. 2 1.5 ControlofPMSynRelinHEVapplications. ... 4 1.6 OutlineofThesis .............................. 4 2 PMSynRel Control 5 2.1 FieldOrientedControl ........................... 5 2.2 ResolverandHall-effectsensor. ... 6 2.2.1 Resolver .............................. 6 2.2.2 TheHall-Effectsensor . 6 2.3 TheSensorlessControl ........................... 8 3 Simulation Models 13 3.1 Matlab/Simulink .............................. 13 3.1.1 BasicSimulinkModel . 13 3.1.2 AdvancedSimulinkModel/Fluxmapmodel . 14 4 Implementation of rotor position detection in Simulink 15 4.1 Modelingofrotatorypositionsensors . .... 15 4.1.1 Resolvermodeling . .. .. .. .. .. .. .. 15 4.1.2 Hall-effectsensormodeling . 15 ix Contents 4.2 Modelingofsensorlesscontrol . .. 17 4.2.1 SignalInjection........................... 17 4.3 Result of the Hall-effect sensor and sensorless control ........... 18 5 Transfer Function 23 5.1 Setinputandoutput ............................ 23 5.2 Identificationandevaluationprocess . ..... 24 5.2.1 Transfer functions identification and evaluation process in time domain 24 5.2.2 Transfer functions identification and evaluation process in frequency domain 26 6 Experimental Result 43 6.1 Experiment ................................. 43 7 Conclusion and future work 47 7.1 Summary .................................. 47 7.2 Futurework................................. 48 7.2.1 SensorlesscontrolandHall-effectsensors . ..... 48 7.2.2 Torque dynamics in frequency domain from the experiment ... 48 A Laboratory Setup 49 References 51 x Chapter 1 Introduction This chapter briefly introduces the background and the outline of this thesis. The moti- vation, configuration and principle of hybrid electric vehicles is also presented in this chapter. 1.1 Background and Objectives HEV applications have gained more and more interest due to its environmental friendly features. A PMSynRel based electric drive is considered as good option due to its high torque density and high efficiency. The main objectives of this thesis work is to develop torque dynamics of such electric drives when operating without a position sensor. The developed torque dynamic can be used to analyze the limits of sensorless strategy when, e.g. anti oscillation control is required. 1.2 Motivation of Hybrid Electric Vehicles As the concerns of environmental degradation are growing, many countries have made na- tional plans to significantly reduce the oil consumption. More and more strict regulations are pronounced by governments, which force manufactures to find alternatives to replace conventional vehicles. Besides the environmental feature, relatively low operational costs is another main motivation of the HEV technology. HEV has the great potential to fulfill the emission requirement while still being able to meet the power demand. The HEV consists of an internal combustion engine (ICE) and at least one electrical machine in the power train. With the help of the ICE, HEVs have larger driving ranges in comparison to the pure electric vehicles (EVs) [8]. 1 Chapter 1. Introduction 1.3 Configurations of HEVs HEVs are typically classified into two basic configurations, series or parallel. 1.3.1 Series HEV Configuration A series HEV configuration is shown in Figure 1.1 where there is no physical connection between the ICE and transmission. The generator converts the mechanical power (deliv- ered from ICE) to electrical power which can be used either for charging the battery or for propelling the vehicle. The advantages of this configuration is listed as follows: 1. Since the ICE is only used to charge the battery, the operating point can be optimized to achieve a high efficiency. 2. Since electrical machine is used to propel the wheels, which can operate in a wide speed range, the multi-gear transmission can be removed from the power train. However, this configuration requires several energy conversions which lead to a low over- all efficiency. Furthermore, this HEV configuration requires a large electrical machine, therefore, all drivetrain components have to be designed to match the peak power of the electrical machine. 1.3.2 Parallel HEV Configuration A parallel HEV configuration is shown in Figure 1.2, where the propulsion power is pro- vided by the ICE and/or electrical machine. The major advantage of the parallel HEV configuration compared to the series HEV configuration is that the electrical machine can be used to convert the mechanical power to the electrical power. Thus, the generator can be eliminated. Since the vehicle is propelled by electric-machine and ICE(provided the battery is never be depleted), both of them can be downsized. 1.4 PMSynRel machine in HEV applications In HEV applications, together with the ICE, the electrical machine is a key
Load more

Recommended publications
  • Input and Output Directions and Hankel Singular Values CEE 629
    Principal Input and Output Directions and Hankel Singular Values CEE 629. System Identification Duke University, Fall 2017 1 Continuous-time systems in the frequency domain In the frequency domain, the input-output relationship of a LTI system (with r inputs, m outputs, and n internal states) is represented by the m-by-r rational frequency response function matrix equation y(ω) = H(ω)u(ω) . At a frequency ω a set of inputs with amplitudes u(ω) generate steady-state outputs with amplitudes y(ω). (These amplitude vectors are, in general, complex-valued, indicating mag- nitude and phase.) The singular value decomposition of the transfer function matrix is H(ω) = Y (ω) Σ(ω) U ∗(ω) (1) where: U(ω) is the r by r orthonormal matrix of input amplitude vectors, U ∗U = I, and Y (ω) is the m by m orthonormal matrix of output amplitude vectors, Y ∗Y = I Σ(ω) is the m by r diagonal matrix of singular values, Σ(ω) = diag(σ1(ω), σ2(ω), ··· σn(ω)) At any frequency ω, the singular values are ordered as: σ1(ω) ≥ σ2(ω) ≥ · · · ≥ σn(ω) ≥ 0 Re-arranging the singular value decomposition of H(s), H(ω)U(ω) = Y (ω) Σ(ω) or H(ω) ui(ω) = σi(ω) yi(ω) where ui(ω) and yi(ω) are the i-th columns of U(ω) and Y (ω). Since ||ui(ω)||2 = 1 and ||yi(ω)||2 = 1, the singular value σi(ω) represents the scaling from inputs with complex am- plitudes ui(ω) to outputs with amplitudes yi(ω).
    [Show full text]
  • Lecture 3: Transfer Function and Dynamic Response Analysis
    Transfer function approach Dynamic response Summary Basics of Automation and Control I Lecture 3: Transfer function and dynamic response analysis Paweł Malczyk Division of Theory of Machines and Robots Institute of Aeronautics and Applied Mechanics Faculty of Power and Aeronautical Engineering Warsaw University of Technology October 17, 2019 © Paweł Malczyk. Basics of Automation and Control I Lecture 3: Transfer function and dynamic response analysis 1 / 31 Transfer function approach Dynamic response Summary Outline 1 Transfer function approach 2 Dynamic response 3 Summary © Paweł Malczyk. Basics of Automation and Control I Lecture 3: Transfer function and dynamic response analysis 2 / 31 Transfer function approach Dynamic response Summary Transfer function approach 1 Transfer function approach SISO system Definition Poles and zeros Transfer function for multivariable system Properties 2 Dynamic response 3 Summary © Paweł Malczyk. Basics of Automation and Control I Lecture 3: Transfer function and dynamic response analysis 3 / 31 Transfer function approach Dynamic response Summary SISO system Fig. 1: Block diagram of a single input single output (SISO) system Consider the continuous, linear time-invariant (LTI) system defined by linear constant coefficient ordinary differential equation (LCCODE): dny dn−1y + − + ··· + _ + = an n an 1 n−1 a1y a0y dt dt (1) dmu dm−1u = b + b − + ··· + b u_ + b u m dtm m 1 dtm−1 1 0 initial conditions y(0), y_(0),..., y(n−1)(0), and u(0),..., u(m−1)(0) given, u(t) – input signal, y(t) – output signal, ai – real constants for i = 1, ··· , n, and bj – real constants for j = 1, ··· , m. How do I find the LCCODE (1)? .
    [Show full text]
  • An Approximate Transfer Function Model for a Double-Pipe Counter-Flow Heat Exchanger
    energies Article An Approximate Transfer Function Model for a Double-Pipe Counter-Flow Heat Exchanger Krzysztof Bartecki Division of Control Science and Engineering, Opole University of Technology, ul. Prószkowska 76, 45-758 Opole, Poland; [email protected] Abstract: The transfer functions G(s) for different types of heat exchangers obtained from their par- tial differential equations usually contain some irrational components which reflect quite well their spatio-temporal dynamic properties. However, such a relatively complex mathematical representa- tion is often not suitable for various practical applications, and some kind of approximation of the original model would be more preferable. In this paper we discuss approximate rational transfer func- tions Gˆ(s) for a typical thick-walled double-pipe heat exchanger operating in the counter-flow mode. Using the semi-analytical method of lines, we transform the original partial differential equations into a set of ordinary differential equations representing N spatial sections of the exchanger, where each nth section can be described by a simple rational transfer function matrix Gn(s), n = 1, 2, ... , N. Their proper interconnection results in the overall approximation model expressed by a rational transfer function matrix Gˆ(s) of high order. As compared to the previously analyzed approximation model for the double-pipe parallel-flow heat exchanger which took the form of a simple, cascade interconnection of the sections, here we obtain a different connection structure which requires the use of the so-called linear fractional transformation with the Redheffer star product. Based on the resulting rational transfer function matrix Gˆ(s), the frequency and the steady-state responses of the approximate model are compared here with those obtained from the original irrational transfer Citation: Bartecki, K.
    [Show full text]
  • A Passive Synthesis for Time-Invariant Transfer Functions
    IEEE TRANSACTIONS ON CIRCUIT THEORY, VOL. CT-17, NO. 3, AUGUST 1970 333 A Passive Synthesis for Time-Invariant Transfer Functions PATRICK DEWILDE, STUDENT MEMBER, IEEE, LEONARD hiI. SILVERRJAN, MEMBER, IEEE, AND R. W. NEW-COMB, MEMBER, IEEE Absfroct-A passive transfer-function synthesis based upon state- [6], p. 307), in which a minimal-reactance scalar transfer- space techniques is presented. The method rests upon the formation function synthesis can be obtained; it provides a circuit of a coupling admittance that, when synthesized by. resistors and consideration of such concepts as stability, conkol- gyrators, is to be loaded by capacitors whose voltages form the state. By the use of a Lyapunov transformation, the coupling admittance lability, and observability. Background and the general is made positive real, while further transformations allow internal theory and position of state-space techniques in net- dissipation to be moved to the source or the load. A general class work theory can be found in [7]. of configurations applicable to integrated circuits and using only grounded gyrators, resistors, and a minimal number of capacitors II. PRELIMINARIES is obtained. The minimum number of resistors for the structure is also obtained. The technique illustrates how state-variable We first recall several facts pertinent to the intended theory can be used to obtain results not yet available through synthesis. other methods. Given a transfer function n X m matrix T(p) that is rational wit.h real coefficients (called real-rational) and I. INTRODUCTION that has T(m) = D, a finite constant matrix, there exist, real constant matrices A, B, C, such that (lk is the N ill, a procedure for time-v:$able minimum-re- k X lc identity, ,C[ ] is the Laplace transform) actance passive synthesis of a “stable” impulse response matrix was given based on a new-state- T(p) = D + C[pl, - A]-‘B, JXYI = T(~)=Wl equation technique for imbedding the impulse-response (14 matrix in a passive driving-point impulse-response matrix.
    [Show full text]
  • State Space Models
    State Space Models MUS420 Equations of motion for any physical system may be Introduction to Linear State Space Models conveniently formulated in terms of its state x(t): Julius O. Smith III ([email protected]) Center for Computer Research in Music and Acoustics (CCRMA) Input Forces u(t) Department of Music, Stanford University Stanford, California 94305 ft Model State x(t) x˙(t) February 5, 2019 Outline R State Space Models x˙(t)= ft[x(t),u(t)] • where Linear State Space Formulation • x(t) = state of the system at time t Markov Parameters (Impulse Response) • u(t) = vector of external inputs (typically driving forces) Transfer Function • ft = general function mapping the current state x(t) and Difference Equations to State Space Models inputs u(t) to the state time-derivative x˙(t) • Similarity Transformations The function f may be time-varying, in general • • t Modal Representation (Diagonalization) This potentially nonlinear time-varying model is • • Matlab Examples extremely general (but causal) • Even the human brain can be modeled in this form • 1 2 State-Space History Key Property of State Vector The key property of the state vector x(t) in the state 1. Classic phase-space in physics (Gibbs 1901) space formulation is that it completely determines the System state = point in position-momentum space system at time t 2. Digital computer (1950s) 3. Finite State Machines (Mealy and Moore, 1960s) Future states depend only on the current state x(t) • and on any inputs u(t) at time t and beyond 4. Finite Automata All past states and the entire input history are 5.
    [Show full text]
  • MUS420 Introduction to Linear State Space Models
    State Space Models MUS420 Equations of motion for any physical system may be Introduction to Linear State Space Models conveniently formulated in terms of its state x(t): Julius O. Smith III ([email protected]) Center for Computer Research in Music and Acoustics (CCRMA) Input Forces u(t) Department of Music, Stanford University Stanford, California 94305 ft Model State x(t) x˙(t) February 5, 2019 Outline R State Space Models x˙(t)= ft[x(t),u(t)] • where Linear State Space Formulation • x(t) = state of the system at time t Markov Parameters (Impulse Response) • u(t) = vector of external inputs (typically driving forces) Transfer Function • ft = general function mapping the current state x(t) and Difference Equations to State Space Models inputs u(t) to the state time-derivative x˙(t) • Similarity Transformations The function f may be time-varying, in general • • t Modal Representation (Diagonalization) This potentially nonlinear time-varying model is • • Matlab Examples extremely general (but causal) • Even the human brain can be modeled in this form • 1 2 State-Space History Key Property of State Vector The key property of the state vector x(t) in the state 1. Classic phase-space in physics (Gibbs 1901) space formulation is that it completely determines the System state = point in position-momentum space system at time t 2. Digital computer (1950s) 3. Finite State Machines (Mealy and Moore, 1960s) Future states depend only on the current state x(t) • and on any inputs u(t) at time t and beyond 4. Finite Automata All past states and the entire input history are 5.
    [Show full text]
  • ECE504: Lecture 2
    ECE504: Lecture 2 ECE504: Lecture 2 D. Richard Brown III Worcester Polytechnic Institute 15-Sep-2009 Worcester Polytechnic Institute D. Richard Brown III 15-Sep-2009 1 / 46 ECE504: Lecture 2 Lecture 2 Major Topics We are still in Part I of ECE504: Mathematical description of systems model mathematical description → You should be reading Chen chapters 2-3 now. 1. Advantages and disadvantages of different mathematical descriptions 2. CT and DT transfer functions review 3. Relationships between mathematical descriptions Worcester Polytechnic Institute D. Richard Brown III 15-Sep-2009 2 / 46 ECE504: Lecture 2 Preliminary Definition: Relaxed Systems Definition A system is said to be “relaxed” at time t = t0 if the output y(t) for all t t is excited exclusively by the ≥ 0 input u(t) for t t . ≥ 0 Worcester Polytechnic Institute D. Richard Brown III 15-Sep-2009 3 / 46 ECE504: Lecture 2 Input-Output DE Description: Capabilities and Limitations Example: by˙(t) ay(t)+ = du(t)+ eu˙(t) cy¨(t) + Can describe memoryless, lumped, or distributed systems. + Can describe causal or non-causal systems. + Can describe linear or non-linear systems. + Can describe time-invariant or time-varying systems. + Can describe relaxed or non-relaxed systems (non-zero initial conditions). — No explicit access to internal behavior of systems, e.g. doesn’t directly to apply to systems like “sharks and sardines”. — Difficult to analyze directly (differential equations). Worcester Polytechnic Institute D. Richard Brown III 15-Sep-2009 4 / 46 ECE504: Lecture 2 State-Space Description: Capabilities and Limitations Example: x˙ (t) = Ax(t)+ Bu(t) y(t) = Cx(t)+ Du(t) — Can’t describe distributed systems.
    [Show full text]
  • Chapter 1 Introduction
    Kenneth Pedersen Critical Voltage Distributions in the Dry Type Transformers of Large Wind Turbines when Exposed to Transients PhD thesis, February 2007 Copyright © Ørsted • DTU, Electric Power Engineering Technical University of Denmark Voltage to terminal at node 130 (outlet 7) 1 10 0 10 -1 10 Model .u.] Measurement -2 e [p 10 Voltag -3 10 U V W -4 10 Disc 1 Disc 1 Disc 1 Disc 2 Disc 2 Disc 2 Vout Disc 3 Disc 3 Disc 3 -5 Disc 14 Disc 14 Disc 14 10 1 2 3 D4isc 5 5 Dis6c 5 7 Disc 5 10 10 10 10Disc 6 10 Dis10c 6 10 Disc 6 V1 FrequencDiscy [Hz 7 ] Disc 7 Disc 7 Disc 8 Disc 8 Disc 8 Disc 39 Disc 39 Disc 39 DiDscisc 10314 DisDiscc 10314 DiscDisc 10314 DiDscisc 11145 DisDiscc 11145 DiscDisc 11145 DiDscisc 1256 DisDiscc 1256 DiscDisc 1256 DiDscisc 136 DisDiscc 136 DiscDisc 136 V14 I Preface The present PhD thesis is part of the requirements for obtaining a PhD degree. The work was carried out the at Ørsted•DTU, Power Engineering, Technical University of Denmark. The project ran from 1st of February 2004 until 14th of February 2007 and was financed by Energinet.dk. In addition DONG Energy and ABB Denmark has been part of the steering committee. I would like to thank my supervisors at Ørsted•DTU, Associate Professors Dr. Joachim Holbøll and Dr. Mogens Henriksen for guidance and encouragement. Thanks must also go to the remaining part of the steering committee constituted by Carsten Ras- mussen, Energinet.dk, Erik Koldby, ABB A/S, Denmark and Asger Jensen, DONG Energy as well as Preben Jørgensen, formerly with Energinet.dk, who participated in the steering committee at an early stage.
    [Show full text]
  • Stabilization Theory for Active Multi-Port Networks Mayuresh Bakshi† Member, IEEE,, Virendra R Sule∗ and Maryam Shoejai Baghini‡, Senior Member, IEEE
    1 Stabilization Theory For Active Multi-port Networks Mayuresh Bakshiy Member, IEEE,, Virendra R Sule∗ and Maryam Shoejai Baghiniz, Senior Member, IEEE, Abstract This paper proposes a theory for designing stable interconnection of linear active multi-port networks at the ports. Such interconnections can lead to unstable networks even if the original networks are stable with respect to bounded port excitations. Hence such a theory is necessary for realising interconnections of active multiport networks. Stabilization theory of linear feedback systems using stable coprime factorizations of transfer functions has been well known. This theory witnessed glorious developments in recent past culminating into the H1 approach to design of feedback systems. However these important developments have seldom been utilized for network interconnections due to the difficulty of realizing feedback signal flow graph for multi-port networks with inputs and outputs as port sources and responses. This paper resolves this problem by developing the stabilization theory directly in terms of port connection description without formulation in terms of signal flow graph of the implicit feedback connection. The stable port interconnection results into an affine parametrized network function in which the free parameter is itself a stable network function and describes all stabilizing port compensations of a given network. Index Terms Active networks, Coprime factorization, Feedback stabilization, Multiport network connections. I. INTRODUCTION CTIVE electrical networks, which require energizing sources for their operation, are most widely A used components in engineering. However operating points of such networks are inherently very sensitive to noise, temperature and source variations. Often there are considerable variations in parameters of active circuits from their original design values during manufacturing and cannot be used in applications without external compensation.
    [Show full text]
  • Parameterized Modeling of Multiport Passive Circuit Blocks
    Parameterized Modeling of Multiport Passive Circuit Blocks by Zohaib Mahmood Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science MASCHU -E ThiJ7T at the OF TC~CL MASSACHUSETTS INSTITUTE OF TECHNOLOGY OCT 735 210 September 2010 L ISRA R I E3 @ Massachusetts Institute of Technology 2010. All rights reserved. ARCHivES Author ........... Depart-.ent of ectrical Engineering and Computer Science August 22, 2010 by. .. .. .. .. k . .. .. Certified .. .. .. .. .. Luca Daniel Associate Professor Thesis Supervisor A. -. Accepted by............. 7 . ......... ............................ Terry Orlando Chairman, Department Committee on Graduate Theses Parameterized Modeling of Multiport Passive Circuit Blocks by Zohaib Mahmood Submitted to the Department of Electrical Engineering and Computer Science on August 22, 2010, in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science Abstract System level design optimization has recently started drawing the attention of circuit de- signers. A system level optimizer would search over the entire design space, adjusting the parameters of interest, for optimal performance metrics. These optimizers demand for the availability of parameterized compact dynamical models of all individual modules. The parameters may include geometrical parameters, such as width and spacing for an induc- tor or design parameters such as center frequency or characteristic impedance in case of distributed transmission line structures. The parameterized models of individual blocks need to be compact and passive since the optimizer would be solving differential equations (time domain integration or periodic steady state methods) to compute the performance metrics.
    [Show full text]
  • Application of Vector Fitting to State Equation Representation of Transformers for Simulation Of
    834 IEEE Transactions on Power Delivery, Vol. 13, No. 3, July 1998 APPLICATION OF VECTOR FITTING TO STATE EQUATION REPRESENTATION OF T FOR SIMULATION OF ELECTROMAGNETIC TRANSIE Bjsrn Gustavsen" Adam Semlyen Department of Electrical and Computer Engineering University of Toronto Toronto, Onta.rio, Canada M5S 3G4 * On leave from the Norwegian Electric Power Research Institute (EFI), Trondheim, Norway. Abstract - This paper presents an efficient methodology for transient model can give unstable simulation results, depending on the modeling of power transformers based on measured or calculated connected network. frequency responses. The responses are approximated with rational In this paper we show that the recently developed method of functions using the method of vector fitting. The resulting model is vector fitting [3] is well suited for finding the needed rational dynamically stable since only negative poles are used, and inputatput function approximations. This method produces a state equation stability is assured by a novel adjusting procedure. The methodology is realization (SER) by solving an overdetermined set of equations as used to formulate two different transformer models: I)a full phase a least squares problem. There is no need for predefining partial domain model realized column-by-column, and 2) a model utilizing fractions, and there are inherent limitations only if a fit of very modal diagonalization. The application of the models is demonstrated order is desired for frequency responses with many peaks. for a 41 0 MVA generator step up transformer. high We use vector fitting to formulate two transformer models based 1 INTRODUCTION on the short circuit admittance matrix Y : The transient behavior of power transformers is very difficult 1.
    [Show full text]
  • Approximate State–Space and Transfer Function Models for 2×2 Linear Hyperbolic Systems with Collocated Boundary Inputs
    Int. J. Appl. Math. Comput. Sci., 2020, Vol. 30, No. 3, 475–491 DOI: 10.34768/amcs-2020-0035 APPROXIMATE STATE–SPACE AND TRANSFER FUNCTION MODELS FOR 2×2 LINEAR HYPERBOLIC SYSTEMS WITH COLLOCATED BOUNDARY INPUTS a KRZYSZTOF BARTECKI aInstitute of Control Engineering Opole University of Technology ul. Prószkowska 76, 45-758 Opole, Poland e-mail: [email protected] Two approximate representations are proposed for distributed parameter systems described by two linear hyperbolic PDEs with two time- and space-dependent state variables and two collocated boundary inputs. Using the method of lines with the backward difference scheme, the original PDEs are transformed into a set of ODEs and expressed in the form of a finite number of dynamical subsystems (sections). Each section of the approximation model is described by state-space equations with matrix-valued state, input and output operators, or, equivalently, by a rational transfer function matrix. The cascade interconnection of a number of sections results in the overall approximation model expressed in finite-dimensional state-space or rational transfer function domains, respectively. The discussion is illustrated with a practical example of a parallel-flow double-pipe heat exchanger. Its steady-state, frequency and impulse responses obtained from the original infinite-dimensional representation are compared with those resulting from its approximate models of different orders. The results show better approximation quality for the “crossover” input–output channels where the in-domain effects prevail as compared with the “straightforward” channels, where the time-delay phenomena are dominating. Keywords: distributed parameter system, hyperbolic equations, approximation model, state space, transfer function.
    [Show full text]