ISSN 1068-3712, Russian Electrical Engineering, 2015, Vol. 86, No. 2, pp. 66–71. © Allerton Press, Inc., 2015. Original Russian Text © Yu.Ya. Lyamets, A.A. Belyanin, P.I. Voronov, 2015, published in Elektrotekhnika, 2015, No. 2, pp. 22–28. 66 The notion of fault components of electric values is inseparably linked with the objectives of relay protec- tion [1]. Fault components arise at point t 0 , at which the previous regime of the electric network shifts over to a current regime. Typically, this is a short circuit regime. Let υ(t) be the observed electrical magnitude: υ pm (t), t < t 0 during the previous regime and υ cm (t), t ≥ t 0 in the current regime. If the previous regime is periodic, the function υ pm has periodically continua- tion with t ≥ 0. The fault component is then defined as the difference of two functions: If the previous regime is not periodic, then the algorithm for determining the fault component involves synthesis: where , t ≥ t 0 is the extrapolation of the func- tions υ pm , t < t 0 to the time after the change of the regime. υ fm t () υ cm t () υ pm t () t t 0 . ≥ , – = υ fm t () υ cm t () υ ˆ pm t () t t 0 , ≥ , – = υ ˆ pm t () The electrical network in which the fault compo- nents of electric values act does not yet have a gener- ally accepted name in the Russian literature, while in the foreign literature it is called a “pure fault regime” [2]. This is enough to distinguish it from a typical fault regime, for example, the short circuit. An example of an object model in which the cur- rents and the voltages are observed in the places marked with indices r and s and a purely fault regime is created by one current source i f acting in place f of a short to earth is shown in Fig. 1, where A ss and A rr are parts of the object model that. in general, are active: A sr is the active model of the rest of the system; Π ff is the passive model simulating the fault;Π ss , Π rr , and Π sr are the passive models provided after the exclusion of sources from A ss , A rr , and A sr , respectively. Doubled indices ss, rr, and ff mark parts of the model that are connected only to one place s, r, or f, and the mixed index marks the part connected with two places at once. The purpose of the article is to show that, as opposed to an unobserved object, a purely fault regime may be subjected to further analysis in an observed object. According to the compensation theorem, the Modifications of Fault Components of Currents and Voltages Yu. Ya. Lyamets, A. A. Belyanin, and P. I. Voronov Chuvash State University, Cheboksary, Chuvashia, 428015 Russia, Research Center Besler, Cheboksary, Chuvashia, 428015 Russia e-mail: journal-elektrotechnika@mail.ru Received January 20, 2015 Abstract—The development is given of ideas regarding the fault components of electrical quantities and about the corresponding pure fault process. The specificity is shown of fault components of currents and volt- ages monitored in different places of the controlled object. Each fault component can be separated into two parts. There are several variants of separation, because the first components are created by half of the observed values: from every point of observation of current and voltage, one is selected. In accordance with the princi- ple of compensation, selected values are introduced as known sources of voltage or current to the model of the passive undamaged object. The first components are determined as the reaction to the action of these sources. The second components are created by unknown sources of a pure fault process occurring operates in the location of a fault of an unknown object. The corresponding active model of a damaged object is open or closed in the places of observation. It is short circuited where a voltage source has previously acted and open wired where a current source was. The theory of fault components is applied to solution of the problem of locating a feeder fault on both observed sides. The objective function is the standard deviation of the second component of fault components of the two voltages, which are determined in an arbitrary position of the feeder as a result of its observations on different sides. Feeder sections that are to the left and right of the deter- mined fault location are described by long line difference equations. Samples of the second component of each of the two voltages in the determined fault point are calculated from lagging and leading samples of the second component of the current in the corresponding place of observation. Different line equations consider losses as lumped resistances. In the considered example, the required accuracy is provided by two resistances at the ends of each feeder section. Keywords: power facility model, monitoring of electrical quantities, fault locating, fault components DOI: 10.3103/S1068371215020078