Danyelle M. M. SANTANA 1 , Niraldo R. FERREIRA 2 , Fabiano F. COSTA 2 , Antonio C. de C. LIMA 2 Federal Institute of Sergipe (1), Federal University of Bahia (2) doi:10.15199/48.2015.01.09 A Novel Prony Approach for Synchronous Generator Parameter Estimation Abstract. In this paper we propose to use a novel Prony’s approach, relying on suitable time-segmentation of current oscillograms and proper model order choice, to estimate transient and sub-transient parameters of synchronous generators associated to sudden three-phase short-circuit tests. Comparison between the proposed approach and a traditional graphical method, described in the IEEE-115 standard, has been performed. The current data used here have been generated from characteristic equations of short-circuit armature current. Based on these results, we conclude that the Prony’s algorithm is a suitable alternative to the graphical method for parameter estimation in synchronous machines, providing more accurate estimates than the later approach. Streszczenie. W artykule zaproponowano system, bazuj ˛ acy na algorytmie Prony, slu˙ z˛ acy do analizy stanów przej´ sciowych w generatorze synchron- icznym poddanym testom trójfazowego zwarcia. Porównano t˛ e metod˛ e z tradycyjn ˛ a metod ˛ a bazuj ˛ ac ˛ a na normie IEEE-115. Algorytm wykorzystuj ˛ acy metod ˛ e Prony byl bardzie dokladny. Nowa metoda bazuj ˛ aca na algorytmie Prony do okre´ slania parametrów generatora synchronicznego Keywords: Prony algorithm; synchronous generators; parameter estimation; short-circuit test Slowa kluczowe: algorytm Prony, generator synchroniczny, testy zwarciowe Introduction Regarding electrical power systems, the usage of nu- merical simulations to probe operational efficiency and safe- ness is a common practice. Particularly, transient simulations are quite informative to forecast the power system behavior under the influence of faults or abrupt changes in its topol- ogy [1, 2, 3, 4]. The information extracted from these simula- tions must include parameter values from different machines placed along the power grid. In this context, and taking ac- count the recent competitiveness and deregulated conditions of the energy market, the estimation of the parameters of syn- chronous machines for distinct stages of a transient system condition is a concern of growing relevancy [5, 6, 7]. This pa- rameters are an essential data for the developing of control schemes for power quality as well the adoption of efficient protection procedures. In literature, one may find out some useful methods to estimate transient parameters for synchronous machines. The standard IEEE-115 [8] suggests the sudden short-circuit test to obtain these parameters through a graphical pro- cedure, based upon the construction of envelopes passing through the phase currents peaks. Unfortunately, this pro- cedure is inaccurate and may lead to unsatisfying results, specially to small rated machines ranging from 30 kVA to 2 MVA with very short time constants [13]. For instance, a sub- transient time constant of one cycle or less and with the first peak located at half cycle afterwards the short-circuit instant the may require few samples and the usage of interpolation techniques. This can result in a large statical dispersion with regards to the parameter values related to a time-consuming process. There have been efforts to overcome the aforemen- tioned limitations. In [14] it was proposed an improved on- line procedure based on a genetic algorithm for synchronous machine parameter estimation. Reference [15] proposed a complete modeling which takes into account the existence of dampers and use the least-squares algorithm to obtain the machine model reactances and time constants. In [16], it was outlined a method weaving the least-squares algorithm, the wavelet transform and the Prony’s method. This last tech- nique was applied only to estimate the sub-transient param- eters. This paper proposes a simple identification procedure totally based on the Prony’s modeling of the current signal and proper trace segmentation. This procedure provide all sub-transient, transient and steady-state parameters. It re- lays on the application of the Prony’s method on three dif- ferent intervals of the short-circuit current signal. For each interval, the model order is convenient selected and a set of parameters is determined. This paper is organized as follows. The second sec- tion describes the model of a short-circuit stator current for synchronous machine. The third section outlines the tradi- tional graphical method, usually applied for determining the transient parameters. The next section formalize the main equations comprising the Prony’s algorithm. The fifth sec- tion explains the implementation of the Prony’s technique for the present problem. The results are presented in the sixth section and the conclusions are drawn in the final section. Sudden three-phase short-circuit test Sudden-short-circuit test is usually applied to verify weather the machine mechanical design is suitable to with- stand the ensuing efforts of short-circuits and abnormal op- eration conditions. These tests, however, are also useful in determining certain machine parameters such as reactances and time constants. The sudden-short-circuit-test is performed by shorting the synchronous machine terminals and keeping the speed at a constant rate throughout the duration of the evaluation [8]. In such conditions the armature current comprises the following: AC fundamental frequency or symmetric compo- nent, including the sub-transient, transient and stead state components; direct-current component, and the second har- monic component, modeled by (1) [15]. I a (t) = E √ 2 2  1 X ′ d + 1 X ′′ q  e − t T a cos λ (1) + E √ 2 2  1 X ′′ d - 1 X ′′ q  e − t T a cos(2ωt + λ) - E √ 2  1 X d +  1 X ′ d - 1 X d  e − t T ′ d +  1 X ′′ d - 1 X ′ d  e − t T ′′ d  cos(ωt + λ) This equation provides the instantaneous value of the arma- ture current, I a , which is a function of the effective value of the open-circuit voltage, E, before shorting the machine ter- 50 PRZEGL ˛ AD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 91 NR 1/2015