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Sagin Alexandr

Urgency

       Automatic control of excitation now, as a rule, is applied on all power stations (generators) attached to electric systems. We shall count the primary goals (that concern to static properties of system and that are considered with the help of a method of small fluctuations), regulations of excitation decided with the help:

       – Increase of border of passing capacity at the expense of management in size Electric driving force .The generator and elimination of the factors, capable to call self-rocking of system near border of stability;

       – Improvement of quality of a mode of system at the expense of support of a voltage in the beginning of transfer and maintenance is possible faster attenuation of small fluctuations which arise in a normal mode and are adversely displayed on quality of researches of system;

       – Improvement of parameters of system, еspecially, change of own frequency of fluctuations and elimination of an opportunity of a resonance of fluctuations.

       That regulators of excitation could solve well the set forth above tasks, it is necessary to pick up definitely parameters of all system of excitation, switching and parameters of the regulators. Decisions of each task imposes on a choice of parameters of system of regulation the requirements which change at change of the circuit and parameters of the regulated system, together with at change of its mode.

       Task of the analysis – check of stability of system and definition of quality of transient at the set parameters of a regulator and system;

       The task of synthesis – when, proceeding from the certain requirements to stability and qualities of transient of the regulated system is determined a kind of a regulator (the block diagram of system of regulation) and its parameters.

       In work the system is considered, which will consist of station, which works through transfer (probably, with intermediate loadings) on trunks of a constant voltage and frequency.

       At the analysis of the regulated system, it is equal as well as at synthesis, it is necessary mathematiks to describe processes that in her occur, so that from the decision of the corresponding differential equations to find all necessary factors which characterize proof job of system at set or that at the set parameters to check up, whether there will be a system steady.

       Drawing up of such equation and the analysis of its properties for system of regulation of excitation of strong action will be the basic purpose and a task of degree work.

       For achievement of the purpose of job there were put and decided following tasks:

       – Development of the software for studying theoretical positions of the analysis of static stability of electric systems with automatic regulator of excitation strong action strong action;

       – Development of the software for performance of calculations concerning definition of conditions of static stability by a method of small fluctuations;

       – Researches of electric system with automatic regulator of excitation strong action strong action;

       – Development of methodical recommendations for creation of laboratory job on studying conditions of static stability of more simple electric system with automatic regulator of excitation strong action strong action.

       Equipment of electric systems by high-speed regulators of excitation, forces to apply this method and to research of stability of electric systems.

       Thus elements of electric system - generators with their systems of excitation, a transmission line and loading - are considered as uniform object which stability as a whole should be provided. As a result of research there are requirements both to an automatic regulator and to the system of excitation, and the question and on change of parameters of the capital equipment can be on occassion put: generators and synchronous equalisers.

       Method of small fluctuations based on research of the equations of transient in the considered system, and the equations, and their linear approximation will be used not. Opportunity of research of static stability on linear the equation the shown A.M. Ljapunovim which has proved, that system steady in small if its linear approximation is steady.

       That linear the nonlinear differential equations of transient, it is necessary:

       – To admit, that deviations of coordinates (independent variables) small;

       – All nonlinear functions which enter at the equation to spread out in Taylor's lines in surburbs of preset values of coordinates (an initial mode):

       – In decomposition to leave only members which contain a deviation in the first degrees (linear members);

       – From the received equations to exclude the equation of balance.

       To judge stability of system it is possible on a sign on the valid part of roots of the characteristic equation with which is the main determinant of the received system of the equations. System steady if all valid roots and the valid parts of complex roots imaginary, that is all roots are located on the left side from an imaginary mark of a complex plane. However to determine roots of the characteristic equation it is rather hard, as the order of the characteristic equation usually high, - the fifth and is higher. For this purpose use methods which allow, not determining roots of the characteristic equation to judge about their arrangement on a complex plane. These are Gurvits's criteria, Raussa, Mihaylova, a method of allocation of areas of stability in a plane of one or two parameters (D-splitting), etc.

       The circuit of the elementary electric system concerning which static stability will be studied, is shown on fig. 1. The system has automatic control of excitation which will consist of three elements which parameters submitted on fig. 1.

       The regulator is executed with the help of electric elements (separate elements are led round by a dotted line).

       – On an output of a regulator proportionally to a deviation of a voltage which is measured on a measuring element. The measuring element has the bridge circuit with a nonlinear element in the left top shoulder. Nonlinearity is picked up so, that at

Figure 1 – the circuit of the elementary electric system which has a regulator of excitation of the strong action, submitted three elements (1, 2, 3): - - - a feedback, as a result of which action.

       Any regulator submitted as the block diagram, will consist of four basic elements shown on fig. 2.

Figure 2 – the function chart of a regulator and its action: a – structure of a regulator; b – change of initial parameterat strong regulation without a zone of insensibility (1) and with a zone of insensibility(2).

       The block diagram of a regulator with which help it is possible to consider processes which occur at regulation by a regulator of excitation of strong action it is shown on fig. 3.

Figure 3 – the block diagram of the regulated system shown on fig. 1.

       The initial differential equations

       At research of stability of electric systems electromechanical and electromagnetic transients in electric system are usually considered. The transients connected to relative moving of rotors of synchronous machines first of all concern to them - electromechanical processes and transients in a winding of excitation of the generator and to the activator - electromagnetic processes. These transients are as a first approximation described by the following differential equations:

       The equations of relative movement of a rotor of the generator

(1)

  Where  – a constant of inertia of the generator it (is glad);

             – The corner between a longitudinal axis of a rotor of the generator and a vector which turns around with synchronous in the speed accepted for an axis of readout (is glad);

            t – time it (is glad);

             – Mechanical capacity of the turbine (in relative units);

             – Electric capacity of the generator (in relative units);

       Let's specify, that at the decision of practical tasks convenient other forms of record of this equation, namely:

(2)

       Where – a constant of inertiaand time t expressed in sek, and a corner – in degrees, and

(3)

       Where – a constant of inertiaand time t expressed in sek, and the corner – in is glad. These equations can be received from the equation (1) by corresponding substitutions. The equations of transient in a winding of excitation of the generator

(4)

       Where  – a constant of time of a winding of excitation of the generator at разомкнутой to a winding статора (it is glad. or sek);

                  – Longitudinal electric driving force Accordingly for transitive and synchronous jet resistance;

                  – Electric driving force a constant mode which is equaled in relative units to a voltage of the activator;

                 t – Time (it is glad. or sek);

       The equations of transient in the activator

(5)

       Where  – a constant of time of a winding of excitation of the activator (it is glad. or sek);

                  – Constant value of a voltage of the activator which is equaled in relative units to a voltage on an output of a regulator.

       This equation can be received by below resulted way.

       For the activator (see fig. 1) communication betweenin its winding of excitation (without taking into account saturation) can be submitted in the following kind:

(6)

       For a winding of excitation of the activator it is possible to write down

       Or in the operational form

(7)

       remove from (1.6) and (1.7) current of excitation also we shall designate

       Let's receive

       Acceptingequal to a voltage on an output of a regulator of excitationand passing to system of relative units, we shall receive

       That in the usual form also answers the equation (5).

       The equations of an ideal automatic regulator of a voltage of strong action which instantly changes a voltage on winding of excitation, it is proportional to a deviation of a voltage on clips of the generator:

(8)

       Where – factor of amplification (regulation) of a regulator.

       The system of the resulted equations contains six variables:.

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       5. Переходные электромеханические процессы в электрических системах: Учеб. для электроэнергет. спец. вузов. – 4-е изд., перераб. и доп. / В. А. Венников / М.: Высш. шк., 1985. – 536 с., ил.

       6. Жданов П. С. Статическая устойчивость сложных электрических систем. – М.: 1940,

       7. Ульянов С. А. Электромагнитные переходные процессы. – М.: Энергия, 1970, 518с.

       8. Кафедра ЭСИС- разработка автоматизированной системы управления электрическими системами http://etf.donntu.ru

       9. Методы расчетов предельных по статической устойчивости режимов энергосистем http://referats.allbest.ru/programming/103021.html

      10. РД 34.20.577 Методические указания по определению устойчивости энергосистем. Литкенс И.В., Васин В.П. Работа электрических систем с АРВ сильного действия вблизи границы области устойчивости. "Электричество", 1968, № 7. 57. Автоматические регуляторы возбуждения. Под ред. Г.Р.Герценберга. http://docyment.ru/doc/5933.htm

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