Transformer modeling ATP : internal faults & high-frequency discretization

Power transformers are key components of the power grid and are also one of the most subjected to a variety of power system transients. The failure of a large transformer can cause severe monetary losses to a utility, thus adequate protection schemes are of great importance to avoid transformer damage and maximize the continuity of service. Computer modeling can be used as an efficient tool to improve the reliability of a transformer protective relay application. Unfortunately, transformer models presently available in commercial software lack completeness in the representation of several aspects such as internal winding faults, which is a common cause of transformer failure. It is also important to adequately represent the transformer at frequencies higher than the power frequency for a more accurate simulation of switching transients since these are a well known cause for the unwanted tripping of protective relays. This work develops new capabilities for the Hybrid Transformer Model (XFMR) implemented in ATPDraw to allow the representation of internal winding faults and slow-front transients up to 10 kHz. The new model can be developed using any of two sources of information: 1) test report data and 2) design data. When only test-report data is available, a higher-order leakage inductance matrix is created from standard measurements. If design information is available, a Finite Element Model is created to calculate the leakage parameters for the higher-order model. An analytical model is also implemented as an alternative to FEM modeling. Measurements on 15-kVA 240?/208Y V and 500-kVA 11430Y/235Y V distribution transformers were performed to validate the model. A transformer model that is valid for simulations for frequencies above the power frequency was developed after continuing the division of windings into multiple sections and including a higher-order capacitance matrix. Frequency-scan laboratory measurements were used to benchmark the simulations. Finally, a stability analysis of the higher-order model was made by analyzing the trapezoidal rule for numerical integration as used in ATP. Numerical damping was also added to suppress oscillations locally when discontinuities occurred in the solution. A maximum error magnitude of 7.84% was encountered in the simulated currents for different turn-to-ground and turn-to-turn faults. The FEM approach provided the most accurate means to determine the leakage parameters for the ATP model. The higher-order model was found to reproduce the short-circuit impedance acceptably up to about 10 kHz and the behavior at the first anti-resonant frequency was better matched with the measurements.

Two-Phase Flow In Microchannels: Morphology And Interface Phenomena

The existence and morphology, as well as the dynamics of micro-scale gas-liquid interfaces is investigated numerically and experimentally. These studies can be used to assess liquid management issues in microsystems such as PEMFC gas flow channels, and are meant to open new research perspectives in two-phase flow, particularly in film deposition on non-wetting surfaces. For example the critical plug volume data can be used to deliver desired length plugs, or to determine the plug formation frequency. The dynamics of gas-liquid interfaces, of interest for applications involving small passages (e.g. heat exchangers, phase separators and filtration systems), was investigated using high-speed microscopy - a method that also proved useful for the study of film deposition processes. The existence limit for a liquid plug forming in a mixed wetting channel is determined by numerical simulations using Surface Evolver. The plug model simulate actual conditions in the gas flow channels of PEM fuel cells, the wetting of the gas diffusion layer (GDL) side of the channel being different from the wetting of the bipolar plate walls. The minimum plug volume, denoted as critical volume is computed for a series of GDL and bipolar plate wetting properties. Critical volume data is meant to assist in the water management of PEMFC, when corroborated with experimental data. The effect of cross section geometry is assessed by computing the critical volume in square and trapezoidal channels. Droplet simulations show that water can be passively removed from the GDL surface towards the bipolar plate if we take advantage on differing wetting properties between the two surfaces, to possibly avoid the gas transport blockage through the GDL. High speed microscopy was employed in two-phase and film deposition experiments with water in round and square capillary tubes. Periodic interface destabilization was observed and the existence of compression waves in the gas phase is discussed by taking into consideration a naturally occurring convergent-divergent nozzle formed by the flowing liquid phase. The effect of channel geometry and wetting properties was investigated through two-phase water-air flow in square and round microchannels, having three static contact angles of 20, 80 and 105 degrees. Four different flow regimes are observed for a fixed flow rate, this being thought to be caused by the wetting behavior of liquid flowing in the corners as well as the liquid film stability. Film deposition experiments in wetting and non-wetting round microchannels show that a thicker film is deposited for wetting conditions departing from the ideal 0 degrees contact angle. A film thickness dependence with the contact angle theta as well as the Capillary number, in the form h_R ~ Ca^(2/3)/ cos(theta) is inferred from scaling arguments, for contact angles smaller than 36 degrees. Non-wetting film deposition experiments reveal that a film significantly thicker than the wetting Bretherton film is deposited. A hydraulic jump occurs if critical conditions are met, as given by a proposed nondimensional parameter similar to the Froude number. Film thickness correlations are also found by matching the measured and the proposed velocity derived in the shock theory. The surface wetting as well as the presence of the shock cause morphological changes in the Taylor bubble flow.