Error characterization for the time-domain numerical solution ofMaxwell's equations

The accuracy and stability of transient numerical methods in electromagnetics is an important consideration, for which an analytical measure is necessary. Of the several approaches commonly used to indicate accuracy of numerical methods, the modified equation of Warming and Hyett [1974] is examined, for several finite-difference and finite-element time-domain methods. In the method of Warming and Hyett, a Taylor-series representation of each unknown is substituted into the difference equation and, through a rather lengthy series of algebraic steps, reduced to what is known as a modified equation. From this modified equation, which represents the actual differential equation being solved by the numerical method, the stability, and relative phase and magnitude accuracy, of the method can be ascertained. As a final introductory note, the one-dimensional equations for each of the algorithms are used in the development of the modified equation and the dispersion relations. The extension of each of the one-dimensional results to two and three dimensions is discussed, in the context of each method     

A study of islanding in utility-connected residential photovoltaicsystems. II. Case studies

For pt.I see ibid., vol.4, no.3, p.436-45 (1989). The methods and models developed in pt.I to study the problem of islanding are extended to study systems containing multiple inverters. The key issues addressed are whether multiple power conditioning systems (PCSs) are more prone to islanding and whether the destabilized feedback used in PCSs such as the APCC and Teslaco can prevent islanding even in the presence of other PCSs in the island. It is shown that islanding can be virtually eliminated through the use of destabilized feedback controls such as the ones available on some commercial units     

A study of islanding in utility-connected residential photovoltaicsystems. I. Models and analytical methods

Models and methods for the analysis of the continued operation of a group of utility-connected photovoltaic systems even after loss of the utility source are presented. The methods involve an examination of steady-state power balance under islanded conditions, an examination of large-signal, limit-cycle behavior, and an examination of the effect of specific control systems on the small-signal stability of islanded conditions. In conjunction with each other these methods allow a determination of whether islanding can occur in a specific system. Although all such systems have a natural propensity to island, it is shown that the controls used in many commercially available units make islanding a rather unlikely phenomenon