3.The practical significance of the results

1. Using the proposed method in the transformation of complex patterns of substitution of equivalent to a form suitable for modeling, will conduct research on various PC transients on the basis of a single universal program.
2. A set of programs in the environment application package MathCAD, which allows for simplification of the complex equivalent circuits of various structures and perform mathematical modeling of electromagnetic transients with differential equations of the Park – Gorev.Obtained in this paper the mathematical model of turbine generators and set up the program for calculation of transient processes should be used in the design and operating organizations for studies of electromagnetic transients during short circuits. Results have been implemented in the educational process GVUZ Donetsk National Technical University . Testing results of master's work. The main findings were presented and discussed: the Day of Science GVUZ Donetsk National Technical University (May, 2010., Donetsk), at the International scientific – practical conference Research and Applications. Current status and development trends, 2010 , (2010г., Odessa).

Picture 1 – Synchronous machine

4. Analysis of existing schemes

The most commonly used equivalent circuit in which it is assumed that the chain winding stator excitation and damping circuits are magnetically communicating only through the main magnetic field, the mutual reactivity. In such schemes, replacing T – shaped like (Picture. 2) winding of the generator (GPB) can be represented by one Multiloop circuit, or an independent chain[1].

In recent papers [2,3] on the construction and use of equivalent circuits of the refined structure (Picture. 3). They are more reliable from a physical point of view, since they the difference is taken into account the mutual inductive magnetic coupling between windings stator excitation equivalent circuits and damper system.

Picture 2 – Equivalent circuit of CM T – shaped like

When used to simulate the equivalent circuits with varying the magnetic coupling between circuits, usually damper system are simply as an equivalent circuit.

Picture 3 – The equivalent circuit taking into account the different magnetic coupling between the circuits

The staff of the Siberian Research Institute of Energy and the proposed obtain more complex structures are equivalent equivalent circuits of turbogenerators, also take into account the relationship between different vzaimoinduktivnuyu circuits located on the rotor. The main distinguishing feature of these equivalent circuits is representation of the damper system of the machine in the longitudinal and transverse axes of the rotor as the main damping circuit, covering the mutual magnetic flux between the stator and rotor, and a number of local loops, covering the magnetic fluxes scattering and excitation windings. In this case the field winding of the generator, damper system and its mutual inductance between them are characterized by complicated dependence on high – order slip (Picture. 4).

Picture 4 – Equivalent circuit of CM – order

In these schemes are not considered current replacement in each wedge, and in individual elements of the array of active zones and the end of the rotor SM. In [4] proposed complex equivalent circuit of turbogenerators with respect to calculation of the steady disturbance associated with large slides (unbalanced load, unbalanced short – circuit nepolnofaznye modes), which takes into account the presence of the rotor actual physical contours.

When using the equivalent circuits shown Pictureures 1 and 2, the procedure of finding the currents in the circuits of the stator and rotor study of transient causes no difficulties. Analysis by complex equivalent circuits of high – order (Picture. 3) and proposed in [4] is the fundamental difficulty in determining these currents. In calculating transients, such as in the operator form, this leads to complex operator calculations are not always giving the opportunity for practical calculations jump into the time domain. So much more convenient to have a scheme substitution with constant parameters of the form shown in Pictureure 1 and 2.

For a general analysis of transient processes terms of identifying the extreme values of the parameters of the differential mode equations are inconvenient. For this purpose, developed a model of EM, based on analytical description of the transients. In [5] proposed to use frequency method considering dynamic modes, which allows us to solve number of tasks on the basis of the general solution in analytical form.

Picture 5 – Equivalent circuit of CM T – shaped type

In the method for calculating the frequency of transients more effective is the analytical description of the frequency characteristics of using the L – shaped patterns with a substitution made at a branch of the source terminals of the magnetization (Picture. 5). It should also be noted that this form of information collection electromagnetic parameters of the SM is the most convenient from the point of view storing it in computer memory and then determine on the basis of its transient features.

The general way to convert the equivalent circuits replacement of one structure to another is in the synthesis of equivalent circuit parameters the necessary structures for the complexes of the frequency characteristics of the input impedance  or conduction the original scheme structures.

In [6] developed a method of determining the parameters n parallel chains of the equivalent circuit of the conductivity in n complexes . On its basis can be a transition from the equivalent circuit of any structure to the equivalent circuit, shown in Pictureure 5. In this case, when the number of units in the scheme of substitution G – shaped type, equal to the number of contours in the original scheme, the difference frequency characteristics of the conductivity or resistivity is less than the specified accuracy iterative calculation procedure. Parallel chains in the schemes shown in Pictureure 4 does not represent a real damper winding or circuit on the rotor, and only characterize their mutual influence, since the current in each of them represents one of the components of the stator current transient, changing one time constant. From this it follows that the use of schemes replacing the clamps with external source branch of the magnetization, the parameters which are calculated only on the basis of the adequacy of the frequency characteristics input impedance , or admittances  with of the stator windings, to solve the problem of determining the currents in the windings, located on the rotor, it is not possible.

Since the current in each of n magnetically windings varies with n time constants, the T – shaped equivalent substitution patterns, each of the actual contours on the rotor must be submitted Self Multiloop circuit. This will increase the contour diagram substitution n times. However, most research problems of transition processes are limited to only the precise definition of the current in the field winding. The currents in the rotor of massive structural elements considered equivalent. In this case, the equivalent circuit showing the effect of n circuits on the rotor will be have 2n parallel chains. Of these n branches will characterize the OECS and the rest represent the equivalent damper system (Picture. 6).

Picture 6 – G – shaped equivalent circuit representation for GPB Multiloop circuit

In addition to compliance with the adequacy of the frequency characteristics  original and transformed equivalent circuits to carry out the synthesis of the latter being equal integrated distribution coefficient of the stator current in the branch GPB () for all values ??of slip the rotor. 

The basic mathematical equations. Consider conversion algorithm equivalent circuits to G – imaginative mind when submitting GPB Multiloop circuit (Picture. 6).

Determining the frequency response complex coefficient in the original replacement scheme, we expect frequency response of the conductivity of n parallel paths, reflecting effect of winding in the transformed circuit , the ratio

. (1)

Then the frequency response of the conduction contours, reflecting the effect of the damper system of synchronous machine, is as follows:

. (2)

Applying the left – hand sides expressions (1) and (2) the method described in [6], respectively, define outlines the parameters n, taking into account the effect of GPB, and the same – the damper the system. It is clear that active and inductive resistance of some of them may have negative values .

For the equivalent circuit, shown in Pictureure 1, the dependence of the participation  the frequency is determined accordance with the following relation:

, (3)

where  – frequency dependence of the conductivity of GPB; – frequency characteristic conductivity, measured with respect to terminal branches of the resistance of mutual ,

. (4)

For the equivalent circuits, shown in Picture. 2 and 3, we hav

. (5)

In (5), the conductivity  in accordance with structure of the equivalent circuits calculated in accordance with an aspect ratio:

. (6)

Evaluating the effectiveness of the method transformation. Validation of methods proposed in conversion of complex equivalent circuits based on the adequacy of the current distribution carried out in the field winding of synchronous generators for various structures and capacities. Types of study of generators and the parameters of their initial equivalent circuits are shown in Table 1. Considered the generator of type SG – 18.75, having no damper system. Turbogenerator type of DVT – 300 is one equivalent damper circuit for each axis of the rotor. simultaneous Model generator of the type MT – 30 was characterized by three loops for each of the axes symmetry. For the turbo – generator type TVV – 160 – 2 method was tested for the scheme replacement of the refined structure (Picture. 2) only for the longitudinal axis of the rotor. schemes replacement of the transverse axis in all cases converted to the form presented in Picture. 4.

Conclusion. Proposed in the method equivalent converting equivalent circuits based on the adequacy frequency characteristics of the conductivity of the stator winding and complex distribution coefficients of the stator current in the branches of the field winding allows simplify the complex equivalent circuit of a high order to a simple form convenient for simulation of transients on the basis of the analytical description of the electromagnetic transients.

List of sources

1. Сидельников А.В. Синтез схемы замещения синхронной машины при представлении обмотки возбуждения многоконтурной цепью // Электротехника. – 1983. – №7. – С. 25 – 28.

2. Сивокобыленко В.Ф., Лебедев В.К., Гармаш В.С. Идентификация параметров синхронных и асинхронных машин по данным измерений на неподвижной машине // Изв. АН СССР. Энергетика и транспорт. – 1989. – №4. – С.49 – 57.

3. Escarela – Perez R., Campero – Littlewood E., Niewierowicz T., Hernandez – Anaya. Unique Determination of One – Damper D – Axis Circuits of Synchronous Machines Using Finite – Element Simulations // IEEE Transactions on Energy Conversion. – 2005. – Vol. – 16, No 2. – P. 137 – 142.

4. Шапиро А.С. Схема замещения турбогенератора при больших скольжениях с учетом клиньев и торцевого эффекта // Турбо – и гидрогенераторы большой мощности и перспективы их развития. – Л.: Наука, 1969. – С. 153 – 167.

5. Larin A. Lamary A. Computer simulation of the transient in AC machines at short – circuits and connections to a network on the basis of the experimental frequency – response characteristics // 9th International Symposium on Short – circuit currents in power systems, SCC'2000, Cracow, October 11 – 13, 2000. – P. 39 – 45.

6. Рогозин Г.Г., Ларин А.М. Расчет параметров эквивалентных роторных контуров синхронных машин по их экспериментальным частотным характеристикам // Электричество. – 1974. – № 6. – С.10 – 13.

7. Рогозин Г.Г., Ларин А.М. Расчет параметров эквивалентных роторных контуров синхронных машин по их экспериментальным частотным характеристикам // Электричество. – 1974. – № 6. – С.10 – 13.

8. Гуедиди Фаузи Бен Килани ПРЕОБРАЗОВАНИЕ СЛОЖНЫХ ЭКВИВАЛЕНТНЫХ СХЕМ ЗАМЕЩЕНИЯ ТУРБОГЕНЕРАТОРОВ К ВИДУ, УДОБНОМУ ДЛЯ МОДЕЛИРОВАНИЯ ПЕРЕХОДНЫХ ПРОЦЕССОВ// Вісник Східноукраїнського національного університету – 2007. – №11(117), ч. 1. – стор. 108 – 115.

9. Шапиро А.С. Схема замещения турбогенератора при больших скольжения с учетом клиньев и торцевого эффекта / / Турбо – и гидрогенераторы большой мощности и перспективы их развития. – Л.: Наука, 1969. – С. 153 – 167.

10. Переходные электромеханические процессы в электрических системах: Учеб. для электроэнергет. спец. вузов. – 2 – е изд, перераб. и доп. В. А. Венников / М.: Высш. шк, 1970. – 472 с, ил.