Public Power - November/December 2007 - (Page 47)

using negative sequence directional sensing can be applied in situations where the traditional polarization methods will not work. Finally, provision of a CT on the tertiary affords the opportunity to apply an overcurrent relay to this winding, which is otherwise difficult to protect adequately. Calculations of tertiary winding current given various fault scenarios are needed to determine the proper CT ratio and relay settings. Autotransformer calculations are treated in a number of reference books. Unfortunately there is no standardized calculation approach or standardized nomenclature for the transformer windings and about every possible variation appears in print. Various authors call the primary, secondary, and tertiary by various other names including high, medium, and low; H, X and S; H, X, and Y, or H, X, and T. It is also necessary to understand whether the equations in a given reference are system-based or windingbased, as discussed in Anderson’s book. The lack of a consistent analysis technique can cause confusion and caution is needed to avoid mistakes. A good illustration of autotransformer application calculations, including winding currents, can be found in Protective Relaying Principles and Applications by J. Lewis Blackburn, Marcel Dekker, Inc, 1998. The impedance values provided by the manufacturer can usually be entered directly in a short circuit analysis computer program, but must be converted to an equivalent form for manual calculations. Since www.APPAnet.org an unloaded tertiary winding is not connected to ground in the normal sense (it may be corner-grounded for transient voltage control) the conversion is necessary to provide an equivalent tertiary branch impedance with an accessible terminal to enable writing loop equations for fault calculations. In transformers I have analyzed, which were all designed with unloaded 35 percent tertiary windings, the impedance conversions have resulted in a negative impedance value in the “X” or secondary voltage output branch. This has no actual physical significance. There is no actual tertiary winding terminal or physical negative impedance. These are simply a mathematical construct required to allow the sequence networks to be connected in the loop equations for solution. Per-unit calculations may not be the most suitable approach for solving some problems involving autotransformers. The common portion of the primary-secondary winding carries current associated with both the primary and secondary voltage levels. A common base for per-unit calculations is not easily derived. A mixed approach is therefore needed using per-unit calculations for some tasks and winding currents for others and care is needed to keep the various circuit quantities sorted out. The analysis of these problems is another case where the computer has made things considerably easier for the engineer. Since calculations involving autotransformers generally fit a particular pattern of transformer test data, impedance conversions plus inclusion in a simplified network diagram of high-side and low-side system impedances the general format of the calculations once entered and checked can be used for new problems simply by changing the input data. The detailed calculations are automated by the computer program, a primary source of error in manual calculations is eliminated, and time is saved. As an illustration of the calculations, a sample spreadsheet is available for download with the online version of this article. The spreadsheet can be used to calculate the equivalent impedances, provide a simplified fault calculation with winding currents, and indicate the possibility of polarizing current reversal. Suitable for screening purposes, the fault calculation page is based on reactive impedances only for simplification. The error resulting from ignoring resistances at the voltage levels usually involved is small. If calculations using this worksheet reveal any issues, such as reversal of current in the tertiary winding used for polarizing, a more refined analysis is indicated. The reader is encouraged to modify the sample spreadsheet to suit the situation analyzed and, as always, should check results by comparison to manual calculations or a commercial power system analysis computer program. ❚ Mark Feller is communications and substation superintendent for the city of Wadsworth, Ohio. Prevent Transformer Explosion and Fire During a transformer short circuit, the TRANSFORMER PROTECTORTM (TP) is activated within milliseconds by the first dynamic pressure peak of the shock wave, avoiding transformer explosions before static pressure increases. Avoids oil fire to transformer and surrounding equipment; Allows transformer repair after internal fault; Minimizes the possibility of environmental pollution by containing the oil; Eliminates risk to human life Works with all oil-filled transformers up to 1,000 MVA and more. For more information call: 281-358-9900 www.transproco.com / info@transproco.com NOVEMBER-DECEMBER 2007 47 http://www.transproco.com http://www.APPAnet.org

Table of Contents Feed for the Digital Edition of Public Power - November/December 2007

Public Power - November/December 2007 Contents Washington Focus 10 Questions Connecting with the Customer Through Automation AMR or AMI? The High Court’s Antitrust Thunderbolts California’s Push for Demand-Response Plug-In Partners Get Plugged In Wiring Up for Double-Digit Growth For Engineers Safety Community Broadband For Governing Boards DEED Customer Service Hometown Connections Index to Advertisers Parting shot

Public Power - November/December 2007

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