Passive Macromodeling: Theory and Applications

Offers an overview of state of the art passive macromodeling techniques with an emphasis on black-box approaches This book offers coverage of developments in linear macromodeling, with a focus on effective, proven methods. After starting with a definition of the fundamental properties that must characterize models of physical systems, the authors discuss several prominent passive macromodeling algorithms for lumped and distributed systems and compare them under accuracy, efficiency, and robustness standpoints. The book includes chapters with standard background material (such as linear time-invariant circuits and systems, basic discretization of field equations, state-space systems), as well as appendices collecting basic facts from linear algebra, optimization templates, and signals and transforms. The text also covers more technical and advanced topics, intended for the specialist, which may be skipped at first reading. Provides coverage of black-box passive macromodeling, an approach developed by the authors. Elaborates on main concepts and results in a mathematically precise way using easy-to-understand language. Illustrates macromodeling concepts through dedicated examples. Includes a comprehensive set of end-of-chapter problems and exercises. Passive Macromodeling: Theory and Applications serves as a reference for senior or graduate level courses in electrical engineering programs, and to engineers in the fields of numerical modeling, simulation, design, and optimization of electrical/electronic systems

Measurements, Models, Systems and Design

531 s.

Wide-Area Measurement-Driven Approaches for Power System Modeling and Analytics

This dissertation presents wide-area measurement-driven approaches for power system modeling and analytics. Accurate power system dynamic models are the very basis of power system analysis, control, and operation. Meanwhile, phasor measurement data provide first-hand knowledge of power system dynamic behaviors. The idea of building out innovative applications with synchrophasor data is promising. Taking advantage of the real-time wide-area measurements, one of phasor measurements’ novel applications is to develop a synchrophasor-based auto-regressive with exogenous inputs (ARX) model that can be updated online to estimate or predict system dynamic responses. Furthermore, since auto-regressive models are in a big family, the ARX model can be modified as other models for various purposes. A multi-input multi-output (MIMO) auto-regressive moving average with exogenous inputs (ARMAX) model is introduced to identify a low-order transfer function model of power systems for adaptive and coordinated damping control. With the increasing availability of wide-area measurements and the rapid development of system identification techniques, it is possible to identify an online measurement-based transfer function model that can be used to tune the oscillation damping controller. A demonstration on hardware testbed may illustrate the effectiveness of the proposed adaptive and coordinated damping controller. In fact, measurement-driven approaches for power system modeling and analytics are also attractive to the power industry since a huge number of monitoring devices are deployed in substations and power plants. However, most current systems for collecting and monitoring data are isolated, thereby obstructing the integration of the various data into a holistic model. To improve the capability of utilizing big data and leverage wide-area measurement-driven approaches in the power industry, this dissertation also describes a comprehensive solution through building out an enterprise-level data platform based on the PI system to support data-driven applications and analytics. One of the applications is to identify transmission-line parameters using PMU data. The identification can obtain more accurate parameters than the current parameters in PSS®E and EMS after verifying the calculation results in EMS state estimation. In addition, based on temperature information from online asset monitoring, the impact of temperature change can be observed by the variance of transmission-line resistance

Investigation on Statistical Model Calibration and Updating of Physics and Data-driven Modeling for Hybrid Digital Twin

학위논문(박사) -- 서울대학교대학원 : 공과대학 기계항공공학부, 2022.2. 윤병동.실제 운행중인 공학 시스템의 가상 디지털 객체를 구축하여 시스템의 관측 데이터를 기반으로 실제 시스템의 다양한 상황을 모사할 수 있는 디지털 트윈 기술은 설계, 제조 및 시스템 상태 관리와 같은 공학적 의사 결정을 지원할 수 있는 솔루션을 제공합니다. 디지털 트윈 접근 방식은 1) 데이터 기반 접근 방식, 2) 물리 기반 접근 방식, 3) 융합형 접근 방식의 세 가지 범주로 나눌 수 있습니다. 융합형 디지털 트윈은 데이터 기반 모델과 물리 기반 모델을 모두 활용하여 이 두 가지 접근 방식의 단점을 극복하기 때문에 관찰된 데이터를 바탕으로 신뢰할 수 있는 공학적 의사 결정을 가능하게 합니다. 그러나 이를 적용하기 위해 필요한 시스템에 대한 사전 정보들은 대부분의 공학 시스템에서 제한적으로 이용 가능합니다. 이러한 사전 정보에는 모델 입력 변수의 통계적 정보, 데이터 기반 혹은 물리 기반 모델링에 필요한 모델링 정보, 시스템 이상 상태에 대한 물리적 사전 지식이 포함됩니다. 많은 경우, 주어진 사전 정보가 충분하지 않은 상황에서 디지털 트윈을 활용한 의사 결정의 신뢰성 문제가 발생합니다. 통계적 모델 보정 및 갱신 방법은 불충분한 사전 정보 하에서 디지털 트윈 분석을 검증 및 고도화하는 데 사용할 수 있습니다. 본 박사 학위 논문은 사전 정보가 부족한 상황에서 융합형 디지털 트윈을 구축하기 위해 모델 보정 및 갱신에서 세 가지 필수 및 관련 연구 분야를 발전시키는 것을 목표로 합니다. 유효한 디지털 트윈 모델을 구축하기 위해서는 다양한 운행 조건에서 충분한 관측 데이터와 시스템 형상, 재료 속성, 작동 조건과 같은 사전 지식이 필요합니다. 그러나 복잡한 엔지니어링 시스템에서는 모델 구축을 위한 사전 정보를 얻기가 어렵습니다. 첫번째 연구에서는 모델 구축에 필요한 사전 지식 부족 시에도 활용 가능한 데이터 기반 동적 모델 갱신 방법을 제안합니다. 제안된 신호 전 처리를 사용하여 관측된 신호에서 시스템 이상 감지를 위한 시간-주파수 영역 특성을 추출합니다. 다양한 작동 조건에서의 시스템 구동 상태를 예측하기 위해 부분 공간 상태 공간 시스템 식별 방법을 이용하여 상태 공간 모델을 구축합니다. 시스템 작동 조건은 시스템 모델의 매개변수화된 입력 신호로 정의됩니다. 다음으로, 신호 관측 시점에서의 시스템 작동 조건과 이상 상태를 추정하기 위해 입력 신호 매개변수는 기준 신호와 관측 신호의 오차를 최소화하도록 갱신됩니다. 모델 입력 변수의 통계적 정보 부족할 경우 최적화 기반 통계 모델 보정을 통해 미지 입력 변수를 추정하여 모델의 예측 능력을 향상시킬 수 있습니다. 최적화 기반 통계 모델 보정은 가상 모델의 예측 응답과 실제 시스템의 관측 응답 간의 통계적 유사성을 최대화하여 모델에 존재하는 미지 입력 변수의 통계적 모수를 추정하는 최적화 문제로 공식화 됩니다. 이때 보정 척도는 통계적 유사성을 정량화하는 목적 함수로 정의됩니다. 두 번째 연구에서는 모델 보정의 정확도와 효율성을 높이기 위해 통계적 상관관계를 고려한 새로운 보정 메트릭인 Marginal Probability and Correlation Residual (MPCR)을 제안합니다. MPCR의 기본 아이디어는 출력 응답 간의 통계적 상관 관계를 고려하면서 다 변량 결합 확률 분포를 수치적 계산 비용이 낮은 다중 주변 확률 분포로 분해하는 것입니다. 디지털 트윈을 이용하여 고장 상태에 대한 사전 지식 부재한 공학 시스템의 고장 상태를 예측하기 위해, 제조 및 실험 조건의 불확실성들이 고려되어야 합니다. 세 번째 연구 방향은 고장 상태에 대한 사전 지식이 부재한 시스템의 피로 균열 시작 및 성장을 추정하기 위한 융합형 디지털 트윈 접근 방식을 제안하였습니다. 본 연구에서는 피로 균열의 시작과 성장을 추정하기 위해 두 가지 기술: (i) 통계적 모델 보정과 (ii) 확률적 요소 갱신을 제안합니다. 통계 모델 보정에서는 균열 시작 조건과 관련된 관찰된 응답을 기반으로 제조 및 실험 조건의 불확실성을 나타내는 입력 변수의 통계적 매개변수를 추정합니다. 통계적 보정을 통해 불확실성을 고려한 확률론적 물리 기반 해석을 통해 균열 시작 및 성장을 나타내는 주요 취약 요소를 예측할 수 있습니다. 확률적 요소 갱신에서는 시스템의 피로 균열 시작 및 성장을 추정하기 위해 균열 성장 조건에서 관찰된 응답을 이용한 최대 우도 법을 갱신 기준으로 모델을 갱신합니다.Digital Twin technology, a virtual representation of the physical entity, has been explored toward providing a solution that could support engineering decisions, such as design, manufacturing, and system health management. Digital twin approaches can be divided into three categories: 1) data-driven, 2) physics-based, and 3) hybrid approaches. The hybrid digital twin is recognized as a promising solution for reliable engineering decisions based on the observed data because it utilizes both the data-driven and physics-based models to overcome the disadvantages of these two approaches. However, the applicability of the digital twin approach has been limited by a lack of prior information. The prior information includes the statistics of model input parameters, required information for (data-driven, physics-based, and hybrid) modeling, and prior knowledge about system failure. Now, a question of fundamental importance arises how to help decision-making using a digital twin under a given insufficient prior information. Statistical model calibration and updating can be used to validate the digital twin analysis under insufficient prior information. In order to build a hybrid digital twin under insufficient prior information, this doctoral dissertation aims the investigation on three co-related research areas in model calibration and updating: Research Thrust 1 – Data-driven dynamic model updating for anomaly detection with an insufficient prior information Research Thrust 2 – A new calibration metric formulation considering the statistical correlation Research Thrust 3 – Hybrid model calibration and updating considering system failure A sufficient prior knowledge such as observed data in various conditions, geometry, material properties, and operating conditions for data-driven / physics-based modeling are required to build a valid digital twin model. However, the prior information for modeling is hard to obtain for complex engineering system. Research Thrust 1 proposes Data-driven dynamic model updating for anomaly detection with insufficient prior knowledge. The time-frequency domain features are extracted from the observed signal using signal pre-processing. The state-space model is driven by a numerical algorithm for subspace state-space system identification (N4SID) to predict the extracted features under different operating conditions. In the model, the operating condition is defined as a parameterized input signal of a system model. Next, the input signal parameters are updated to minimize the prediction error that quantify the discrepancy between the target observed signal and reference model prediction. Optimization-based statistical model calibration (OBSMC) can be applied to estimate unknown input parameters of the digital twin. In OBSMC, the unknown statistical parameters of input variables associated with a digital twin model are inferred by maximizing the statistical similarity between predicted and observed output responses. A calibration metric is defined as the objective function to be maximized that quantifies statistical similarity. Research Thrust 2 proposes a new calibration metric: Marginal Probability and Correlation Residual (MPCR), to improve the accuracy and efficiency of model calibration considering statistical correlation. The foundational idea of the MPCR is to decompose a multivariate joint probability distribution into multiple marginal probability distributions while considering the statistical correlation between output responses. In order to diagnose and predict the system failure of a complex engineering system without prior knowledge about system failure using the digital twin, uncertainties in manufacturing and test conditions must be taken into account. Research Thrust 3 proposed a hybrid digital twin approach for estimating fatigue crack initiation and growth considering those uncertainties. The proposed approach for estimating fatigue crack initiation and growth is based on two techniques; (i) statistical model calibration and (ii) probabilistic element updating. In statistical model calibration, statistical parameters of input variables that indicate uncertainties in manufacturing and test conditions are estimated based on the observed response related to the crack initiation condition. Further, probabilistic analysis using estimated statistical parameters can predict possible critical elements that indicate crack initiation and growth. In probabilistic element updating procedures, the possible crack initiation and growth element is updated based on the Bayesian criteria using observed responses related to the crack growth condition.Abstract i List of Tables ix List of Figures xi Nomenclatures xvi Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Research Scope and Overview 4 1.3 Dissertation Layout 7 Chapter 2 Literature Review 9 2.1 Digital Twin Formulation 9 2.1.1 Data-driven Digital Twin 10 2.1.2 Physics-based Digital Twin 13 2.1.3 Hybrid Digital Twin 17 2.2 Digital Twin Calibration & Updating 18 2.2.1 Optimization-based Statistical Model Calibration 19 2.2.2 Parameter Estimation using Kalman/ Particle filter 24 2.2.3 Summary and Discussion 27 Chapter 3 Data-driven Dynamic Model Updating for Anomaly Detection with an Insufficient Prior Information 28 3.1 System Description of On-Load Tap Changer 30 3.2 Data-driven Dynamic Model Updating for Anomaly Detection with an Insufficient Prior Information 34 3.2.1 Preprocessing of Vibration Signal 37 3.2.2 Reference Model Formulation using N4SID 39 3.2.3 Optimization-based Parameter Updating 43 3.3 Case Study 45 3.3.1 Case Study 1: (Numerical) Vibration Analysis using Parameter Varying Cantilever Beam and Multi-DOF model 45 3.3.2 Case Study 2: Vibration Signal of On Load Tap Changer in Power Transformer 54 3.4 Summary and Discussion 59 Chapter 4 A New Calibration Metric that Considers Statistical Correlation : Marginal Probability and Correlation Residuals 61 4.1 Statistical correlation issue in calibration metric formulation 63 4.1.1 What happens if the statistical correlation is neglected in model calibration? 63 4.1.2 Comments on existing calibration metrics in terms of the statistical correlation 66 4.2 Proposed Method: Marginal probability and correlation residuals (MPCR) 69 4.3 Case Studies 73 4.3.1 Mathematical example 1: Bivariate output responses (Statistical correlation issue 73 4.3.2 Mathematical example 2: Multivariate output responses (Curse of dimensionality issue) 78 4.3.3 Engineering example 1: Modal analysis of a beam structure with uncertain rotational stiffness boundary conditions (Scale issue) 87 4.3.4 Engineering example 2: Crashworthiness of vehicle side impact (High dimensional & nonlinear problem) 93 4.4 Summary and Discussion 101 Chapter 5 Hybrid Model Calibration and Updating for Estimating System Failure 103 5.1 Brief Review of Digital Twin Approaches for Estimating Crack Initiation & Growth 105 5.2 Proposed Digital Twin Approach : Hybrid Model Calibration & Updating 109 5.2.1 Statistical Model Calibration using a Data-driven Twin 110 5.2.2 Probabilistic Element Updating with a Physics-based Twin 114 5.3 Case Study: Automotive Sub-Frame Structure 118 5.3.1 Experimental Fatigue Test 118 5.3.2 Statistical Model Calibration using a Data-driven Twin 121 5.3.3 Element Updating with a Physics-based Twin 127 5.4 Summary and Discussion 131 Chapter 6 Conclusions 133 6.1 Contributions and Significance 133 6.2 Suggestions for Future Research 135 References 138 국문 초록 155박

Reduced-order modeling of power electronics components and systems

This dissertation addresses the seemingly inevitable compromise between modeling fidelity and simulation speed in power electronics. Higher-order effects are considered at the component and system levels. Order-reduction techniques are applied to provide insight into accurate, computationally efficient component-level (via reduced-order physics-based model) and system-level simulations (via multiresolution simulation). Proposed high-order models, verified with hardware measurements, are, in turn, used to verify the accuracy of final reduced-order models for both small- and large-signal excitations. At the component level, dynamic high-fidelity magnetic equivalent circuits are introduced for laminated and solid magnetic cores. Automated linear and nonlinear order-reduction techniques are introduced for linear magnetic systems, saturated systems, systems with relative motion, and multiple-winding systems, to extract the desired essential system dynamics. Finite-element models of magnetic components incorporating relative motion are set forth and then reduced. At the system level, a framework for multiresolution simulation of switching converters is developed. Multiresolution simulation provides an alternative method to analyze power converters by providing an appropriate amount of detail based on the time scale and phenomenon being considered. A detailed full-order converter model is built based upon high-order component models and accurate switching transitions. Efficient order-reduction techniques are used to extract several lower-order models for the desired resolution of the simulation. This simulation framework is extended to higher-order converters, converters with nonlinear elements, and closed-loop systems. The resulting rapid-to-integrate component models and flexible simulation frameworks could form the computational core of future virtual prototyping design and analysis environments for energy processing units