Christoph Heitz

Modal Vector Fitting: A Tool For Generating Rational Models of High Accuracy With Arbitrary Terminal Conditions

This paper introduces a new approach for rational macromodeling of multiport devices that ensures high accuracy with arbitrary terminal conditions. This is achieved by reformulating the vector fitting (VF) technique to focus on eigenpairs rather than matrix elements. By choosing the least squares (LS) weighting equal to the inverse of the eigenvalue magnitude, the modal components are fitted with a relative accuracy criterion. The resulting modal vector fitting (MVF) method is shown to give a major improvement in accuracy for cases with a high ratio between the largest and smallest eigenvalue, although it is computationally more costly than VF. It is also shown how to utilize the impedance characteristics of the adjacent network in the fitting process. The application of MVF is demonstrated for a two-conductor stripline, a coaxial cable, and a transformer measurement. We also show a simplified procedure which achieves similar results as MVF if the admittance matrix can be diagonalized by a constant transformation matrix. The extracted model is finally subjected to passivity enforcement by the modal perturbation method, which makes use of a similar LS formulation as MVF for the constrained optimization problem.

Fast Realization of the Modal Vector Fitting Method for Rational Modeling With Accurate Representation of Small Eigenvalues

Admittance-based rational modeling of multiport systems is prone to error magnification in applications with high-impedance terminations. This problem is overcome by the modal vector fitting method (MVF) which is formulated in terms of modal components with inverse least-squares weighting by the eigenvalue magnitude. A direct realization of MVF is very demanding in computation time and memory requirements. This paper overcomes the performance deficiency via three steps: 1) the required number of MVF iterations is reduced by precalculating an improved initial pole set via conventional vector fitting with inverse magnitude weighting; 2) the pole identification step is calculated in an efficient manner by solving for only the few essential unknowns while exploiting the sparse matrix structure; and 3) the residue identification step is calculated efficiently by a row-wise solution procedure that takes advantage of symmetry. The approach is demonstrated to give large savings for the modeling of a frequency-dependent network equivalent.

Analysis of phase-resolved partial discharge patterns of voids based on a stochastic process approach

A method is presented for the determination of physical discharge parameters for partial discharges (PDs) of voids in solid insulation. Based on a recently developed stochastic theory of PD processes, a statistical analysis of a measured phase-resolved partial discharge (PRPD) pattern allows the determination of the relevant physical parameters like first electron availability or decay time constants for deployed charge carriers. These parameters can be estimated directly from the measured patterns without the need of performing simulations. Furthermore, error bounds for the parameter values can be given. The parameter estimation algorithm is based on the analysis of a contiguous region of the PRPD pattern where this region can be chosen nearly arbitrarily. Thus, even patterns with several active PD defects or patterns which are corrupted by noise can be analysed. The method is applied to a sequence of patterns of a void in epoxy resin. The change in first electron availability in the course of a day can be determined quantitatively from the data while the other physical parameters remain constant.

Rational modeling of multiport systems by modal vector fitting

This paper introduces a new approach for rational macromodeling of multiport devices that ensures high accuracy with arbitrary terminal conditions. This is achieved by reformulating the vector fitting technique to focus on eigenpairs rather than matrix elements. By choosing the least squares weighting equal to the inverse of the eigenvalue magnitude is achieved that the eigenvalues are fitted with a relative accuracy criterion. The procedure is shown to give a major improvement in accuracy for cases with a large eigenvalue spread. Also is shown how to utilize the impedance characteristics of the adjacent network in the fitting process.

Some Aspects of Compressed Air and Nitrogen Insulation

Air and nitrogen have been suggested as environmentally uncritical insulation media for gas insulated electrical power equipment. a thorough evaluation of such a concept requires the knowledge of the breakdown fields which control the dimensions and other design parameters of such systems. This paper contributes some preliminary discharge physical background information required to derive design fields. It reports experimental breakdown data on compressed air and nitrogen up to 950 kPa in uniform field gaps with particulate contamination. Furthermore, prebreakdown current measurements and time resolved image converter records are used to identify the relevant discharge mechanisms. in the presence of particulate contamination the breakdown of compressed air insulation is controlled by the leader mechanism; breakdown fields are in the range of 5.5 to 8 kV/cmbar for particles in the range of 3 to 5 mm length. in compressed nitrogen streamers always cross the gap at breakdown level (at least up to 500 kPa) and the breakdown mechanism may be of the direct streamer to spark or leader type. the particle induced breakdown fields in nitrogen are in the range of 4 to 4.5 kV/cmbar, i.e. nitrogen performs less well than air.

The concept of shadow price to monetarize the intangible value of expertise

The pricing of knowledge based services should be based on the three following components: the cost structure, the competition and the perceived value by the client. Practically, it is mainly based on the cost structure which does not account for the real value provided to the client. Based on an integrated optimization model combining an aggregate planning model with a share of choice model, we produce implicit values of expertise. Preliminary results will be presented about a travel agency.

Customer lifetime value under complex contract structures

We analyze the problem of calculating the customer lifetime value (CLV) under contract structures that have an impact on customer dynamics. Typical examples are minimum contract durations, or fixed time points for contract cancellation. We show that classical Markov Chain models are not appropriate and may lead to large errors in the CLV. We propose a Semi-Markov formulation which leads to substantially better results.

Internet of Services

As the relentless march towards an Internet of Services (IoS) continues, it is of utmost importance for the telecoms industry to understand what the IoS is and upon what foundations and methodologies the IoS is based and built on. Further, how the telecom industry can leverage IoS research and push IoS capabilities on and beyond through innovation and how those services within the IoS should be designed and implemented need to be understood. Not only are these questions answered but also so as not to remain stationary in the world of IoS, the telecoms industry must comprehend the upcoming challenges and opportunities that the IoS will present. Within this chapter there are two perspectives taken on the more specific aspects of engineering services for the IoS. The first takes a first principles approach whereas the second takes one from the basis of an innovative methodology. This chapter will provide information and insights that seek to answer the former questions, starting with a discussion on what exactly a service is, moving through the innovation, design and implementation of IoS and its services, and finally arriving at a demonstrator of IoS that points towards its own future.

Modelling customer lifetime value in contractual settings

Service provision is often governed by a contract (e.g., newspaper subscriptions, phone contracts, and credit agreements). Typically, such a contract includes rules that influence the dynamics of the customer in the marketplace. Typical examples are minimum contract durations, or fixed time instants for contract termination. The goal of these rules is to increase the future total profit gained from the customer, which is usually denoted with the term customer lifetime value (CLV). We analyse the problem of calculating the CLV under general contract structures. We show that classical Markov models for describing the customer dynamics are not appropriate and may lead to huge errors in the CLV. We propose a semi-Markov formulation which leads to substantially better results. We apply the framework to data of newspaper subscription.

Decision Making in Asset Management: Optimal Allocation of Resources for Maximizing Value Realization

Asset Management is about realizing value from physical assets, but formal methods how to do this are still missing. In this paper, we present a formal model for decision making in asset management, based on the general concepts of ISO 55000, in particular the notion of value realization. With this framework, we can first define what optimal decisions are, and second show how to solve these problems in the context of Asset Management. The model describes both the cost and the value contributions of assets in an asset portfolio. The basic policy decision problem is decomposed into a budget setting step, and an allocation problem, where the latter can be solved with standard optimization algorithms. We apply the model to the case of an electrical supply network and find that the supply quality (value) can be increased by about 20 % without spending more money, or the costs can be decreased by 16 % without sacrificing quality, by optimized asset policy decisions with our model.