John Milias-Argitis

Geometric Algebra: A Powerful Tool for Representing Power Under Nonsinusoidal Conditions

Geometric algebra is used in this paper for a rigorous mathematical treatment of power in single-phase circuits under nonsinusoidal conditions, as complex algebra for sinusoidal conditions. This framework clearly displays the multidimensional nature of power, which is represented by a multivector. The power multivector with its three attributes (magnitude, direction and sense) provides the means to encode all the necessary information in a single entity. This property, in conjunction with the fact that there is a one-to-one correspondence between the terms of this multivector, the instantaneous and the apparent power equation, distinguishes it as a highly efficient mathematical tool. In this way one can successfully describe power phenomena and handle practical problems (e.g., power factor improvement). Two simple examples show some of these features. In short, the power multivector under nonsinusoidal situations can be perceived as the generalization of the complex power under sinusoidal situations

Three-Phase Transformer Model Including Magnetic Hysteresis and Eddy Currents Effects

In this paper, a three-phase transformer model is developed to be suitable for slow transient and power-quality studies. The proposed model takes into account the eddy currents, the magnetic core topology, and the nonlinear characteristics of the core material. In order to model the eddy currents effects in the magnetic core, Bertottis work for the eddy currents is used and nonlinear resistors dependent on the magnetic core topology are proposed. A systematic procedure is developed for the determination of the incremental self and mutual inductances of the windings. The nonlinear characteristics of the core material are represented either by a magnetization curve or by a hysteresis loop. The hysteresis loop is introduced either by the mathematical model proposed by Tellinen or by the macroscopic model presented by Jiles-Atherton. Simulations results are compared to published measurements in order to verify the proposed model.

An incremental transformer model for the study of harmonic overvoltages in weak AC/DC systems

An incremental transformer model suitable for slow transient studies was developed. A typical application is the study of temporary harmonic overvoltages in AC/DC systems caused by transformer saturation. The proposed model represents the nonlinear magnetic circuit of the transformer and is, therefore, more complex that the piecewise-linear models often used to simulate saturation. Despite its complexity, the model formulation is suitable for direct solution at each integration step and this results in reasonable simulation time. The proposed model is particularly suitable for HVDC system studies since only a few elements of the transformer matrix need to be updated at each switching instant to account for the switching action of the converter valves. A study of temporary overvoltages in a weak AC/DC system is presented. Two types of disturbances leading to temporary harmonic overvoltages are simulated using both the piecewise-linear and the proposed incremental transformer model. Comparison of the simulation results indicates that the proposed model can be successfully used for the validation of temporary overvoltage studies conducted with simpler and faster transformer models. >

Modeling and simulation of a single-phase residential photovoltaic system

A grid connected single-phase residential photovoltaic system is modeled and simulated using a detailed transformer model. The transformer model takes into account the non-linearity of the core material, which further affects the harmonic currents injected into the utility grid. Furthermore, suitable models for the photovoltaic array and the inverter have been used to assemble a system model in the field of standard form state equations. Comparison with published results has been made with a prototype installation of the same configuration. Very good agreement is accomplished between the predicted and measured values. Thus, a valid powerful tool is given for studies of such grid connected single-phase photovoltaic systems.

A transformation method for the solution of power switching circuits based on network topological concepts

In this paper, a general and systematic method for the analysis of varying topology power semiconductor circuits is presented. the changes of the conduction state of the semiconductor switching devices are handled by successive modifications of the tree of the circuit graph. These tree modifications are systematically reflected on a square transformation tensor. On the basis of well known network topological concepts, this generalized transformation tensor can be constructed in a relatively simple way. This tensor constitutes a flexible and powerful tool to assemble automatically the necessary on-switch current and off-switch voltage equations required for any conduction pattern. These manipulations are accomplished with a step-by-step modification procedure of the equations describing the circuit in the most previous conduction state. the basic steps of an algorithm suitable for the practical implementation of the analysis of any power switching network on a digital computer are described, and an example is used to demonstrate the effectiveness of the proposed method.

An algorithm for transient simulation of power electronics systems

The development of a general algorithm, which constructs the state equations of switching systems as a function of the state of their switching elements, is presented. Although the algorithm is developed primarily for transient simulation of power electronics systems, it can be applied to any system that can be modeled by an equivalent circuit consisting of linear ERLC elements and ideal switches.

First-order circuits driven by a photovoltaic generator☆

Abstract The study of the dynamic behaviour of circuits containing one or more energy-storing elements is of considerable importance to the engineer. The dynamic response of linear first-order circuits, when subjected to conventional forcing functions, has been well established employing classical techniques. However, up to now, the corresponding response of these circuits, when driven by a photovoltaic (PV) generator, has not received special attention in the literature. Since a PV array constitutes a special power source, due to the extreme non-linear i − v external characteristics, it can be expected that its transient response will be different from that obtained with conventional power sources. Using a linear or piecewise-linear representation of the i − v characteristic one obtains a first approximation to the problem. In this paper, an approach is outlined, based on an incremental model of the PV generator, suitable for description of transient behaviour both quantitatively and qualitatively.

Transformer modeling based on incremental reluctances

This paper is the completion of a previous work, published recently, on transformer modeling where the magnetic core topology is taken into account. A new circuit, that represents the magnetic core, is proposed, more easily handled mathematically in antithesis to the conventional magnetic circuit that is used in the literature. The proposed circuit has the same topology with the nonlinear magnetic circuit of the core and, in each time interval of a dynamic simulation, it is considered as linear circuit. Its excitations and responses are the time derivatives of both the magnetomotive forces and the magnetic fluxes, respectively. This modeling approach helps power engineers to construct easily a nonlinear transformer model. Applying any method of circuit analysis on the proposed circuit, one can directly write linear differential equations, in each time interval Δt, for the magnetic core and the state equations of the electrical part are written in standard form.

Transient phenomena of RLC circuits - The photovoltaic input

Abstract The calculation and study of transient phenomena occurring when a photovoltaic (PV) source is applied to RLC circuits are presented in this paper. The method of approach adopted is based on an incremental model of the photovoltaic generator as opposed to the usual numerical integration algorithm for the solution of the governing non-linear differential equations. Such an approach is of particular advantage in many respects. On the quantitative basis, it ensures both accuracy and numerical stability even if a large time step is used. On the qualitative basis, it gives the ability to have a better insight into the response evolution and visualizes the effects that the various parameters may have on the nature of the transient response. Finally, it reveals some interesting and useful features about the transient behavior of a passive load driven by a PV generator, so that conclusions from the engineering viewpoint can be drawn.

Power components under nonsinusoidal conditions using a power multivector

In this paper, a description of power components in single-phase circuits under nonsinusoidal conditions is provided from a quantitative as well as a qualitative perspective. The representation of power is based on Geometric Algebra, a mathematical tool that provides the means to encode all the necessary information in a single entity. This entity is the power multivector, which is analogous to complex power under sinusoidal conditions. An interpretation of each power component is then derived, based on a generalization of the concept of mutual coupling. It is also verified that this approach is consistent with other well-established methods.