The Frenet Frame as a Generalization of the Park Transform

The paper proposes a generalization of the Park transform based on the Frenet frame, which is a special set of coordinates defined in differential geometry for space curves. The proposed geometric transform is first discussed for three dimensions, which correspond to the common three-phase circuits. Then, the expression of the time derivative of the proposed transform is discussed and the Frenet-Serret formulas and the Darboux vector are introduced. The change of reference frame and its differentiation based on Cartan's moving frames and attitude matrices are also described. Finally, the extension to circuits with more than three phases is presented. The features of the Frenet frame are illustrated through a variety of examples, including a case study based on the IEEE 39-bus system.Comment: 11 pages, 2 figures, accepted for publication on the IEEE Transactions on Circuits and Systems I: Regular Paper

Modeling Hybrid AC/DC Power Systems with the Complex Frequency Concept

The concept of complex frequency has been recently introduced on the IEEE Transactions on Power Systems to study bus voltage variations in magnitude and frequency and their link with complex power injections of a power system. In this paper, the complex frequency is applied to time-varying series connections, namely, RLC dynamic branches, regulating transformers and AC/DC converters. The proposed modeling approach allows deriving an explicit expression for the complex frequency of the voltage of a certain bus as a linear combination of three elements: net current injected by the devices connected to the bus, adjacent voltages, and time-varying series branches. The proposed formulation unifies the link between voltage and frequency dynamics in AC, DC, as well as hybrid AC/DC power systems. A variety of static and dynamic examples are presented to show the potential of the proposed formulation. Relevant applications of the proposed modeling approach are outlined

Multi-Criteria Optimal Planning for Energy Policies in CLP

In the policy making process a number of disparate and diverse issues such as economic development, environmental aspects, as well as the social acceptance of the policy, need to be considered. A single person might not have all the required expertises, and decision support systems featuring optimization components can help to assess policies. Leveraging on previous work on Strategic Environmental Assessment, we developed a fully-fledged system that is able to provide optimal plans with respect to a given objective, to perform multi-objective optimization and provide sets of Pareto optimal plans, and to visually compare them. Each plan is environmentally assessed and its footprint is evaluated. The heart of the system is an application developed in a popular Constraint Logic Programming system on the Reals sort. It has been equipped with a web service module that can be queried through standard interfaces, and an intuitive graphic user interface.Comment: Accepted at ICLP2014 Conference as Technical Communication, due to appear in Theory and Practice of Logic Programming (TPLP

An Efficient Representation Format for Fuzzy Intervals Based on Symmetric Membership Functions

International audienceThis paper proposes a novel implementation of fuzzy arithmetics that exploits both fuzzy intervals and hardware specificities. First, we propose and evaluate the benefit of an alternative representation format to the traditional lower-upper and midpoint-radius representation formats for intervals. Thanks to the proposed formats, we show that it is possible to halve the number of operations and memory requirements compared to conventional methods. Then, we show that operations on fuzzy intervals are sensitive to hardware specificities of accelerators such as GPU. These include static rounding, memory usage, instruction level parallelism (ILP) and thread-level parallelism (TLP). We develop a library of fuzzy arithmetic operations in CUDA and C++ over several formats. The proposed library is evaluated using compute-bound and memory-bound benchmarks on Nvidia GPUs, and shows a performance gain of 2 to 20 over traditional approaches

Instantaneous Frequency Estimation in Unbalanced Systems Using Affine Differential Geometry

The paper discusses the relationships between electrical quantities, namely voltages and frequency, and affine differential geometry ones, namely affine arc length and curvature. Moreover, it establishes a link between frequency and time derivatives of voltage, through the utilization of affine differential geometry invariants. Based on this link, a new instantaneous frequency estimation formula is proposed, which is particularly suited for unbalanced systems. An application of the proposed formula to single-phase systems is also provided. Several numerical examples based on balanced, unbalanced, as well as single-phase systems illustrate the findings of the paper

Enhancing Frequency Control through Rate of Change of Voltage Feedback

This letter proposes a simple and inexpensive technique to improve the frequency control of distributed energy resources. The proposed control consists in modifying the conventional estimated bus frequency signal with an additional feedback signal that utilizes the rate of change of the voltage magnitude measured at the same bus. The case study showcases the benefits of the proposed control and compares its performance with standard frequency control schemes through time-domain simulations

Extraneous Instabilities Arising in Power Systems with Non-Synchronous Distributed Energy Resources

Abstract This short communication describes an extraneous instability that can be observed when solving time domain simulations for power systems with inclusion of non-synchronous distributed energy resources such as those based on voltage source converters and asynchronous generators. The instability object of the paper is caused by the interaction of (i) synchronous machines modeled using a synchronous reference speed and (ii) non-synchronous generators whose controllers depend on a d-q transformation. The paper also provides two simple solutions able to remove such extraneous instabilities. The New England 39-bus benchmark system is used for testing the proposed solutions