ТЕХНИЧЕСКИЕ НАУКИ/ 5. Энергетика

Shishka N.V., Candidate of Physico-mathematical Sciences Kuleshova E.O.

National Research Tomsk Polytechnic University

The description of the one-machine power supply system by means of transfer function

Simulation of the linearized equations of the system of regulation of power supply systems in MatLab Simulink through transfer functions does not require reception of the characteristic equation the conclusion of which, as a rule, is not made in polynomial form for complex power supply systems, as a rule, because of excessive complexity of mathematical transformations. It provides the way to investigate complete transient phenomena in power supply systems more detailed.

Introduction

Nowadays all manufacture, the basic part of distribution and consumption electricity in power supply systems are carried out on an alternating current. Therefore, the frequency, size and the voltage form of pressure have got values of the parameters describing the quality of the electric power. It is necessary to calculate the static stability of power supply system to form a system of differential equations of transients and linearization of these equations hold in order. Altogether these equations make mathematical model of a power supply system.

Mathematical model of a power supply system

For the description of a power supply system by means of transfer functions let us consider an one-machine power supply system (fig. 1) the synchronous generator of which is equipped by an automatic regulator of excitation strong action (ARE SA). [1].

Fig. 1. The diagram of an one-machine power supply system.

The basic linearized equations of transients an one-machine power supply system with ARE SA look like [1, 2]:

, , ,

, .

In the process of linearization of the regulatory system, all variables are expressed in deviations from steady-state values assigned to the nominal values. So we take as parameters to control the error voltage vector generator voltage Ug, and the rotation frequency f of the generator rotor.

The simulation of an one-machine power supply system through transfer functions [3] (fig. 2), describing the given object, will be executed in the environment of Matlab Simulink [4].

The coefficients of transfer functions were calculated for the following types of electrical equipment and parameters with the help of the software package MathCad [5]:

The generator G is the equivalent of two turbo-generators such as DVT-200-2UZ. The transformer T1 is the equivalent of two types of transformers TDTS-250000/220. Transformer T2 is the equivalent of two groups of single-phase transformer type ATDTSTN-250000/220/110. Line VL - double circuit, the wire is made with the cable ASO-300 which has a length of 200 km. System C: Uc = 115 kV. The turbine of an equivalent generator is: the regime of P_m(1) = 0.5P_max. Gate factors ARV: K_0U = 100 unit. exc. x * s / unit. voltage. K_1U = 10 unit. exc. x * s / unit. voltage., K_0f, K_1f.

The generator exciter: Te = 2. The excitation controller: Tp = 0.1 s.

Fig. 2. The diagram of an one-machine power supply system in MatLab

Charts of transient are resulted on fig. 3.

Fig. 3. Charts of errors 1 - the voltage and 2 – the frequency

From Fig. 3 you can see that the deviation of the voltage and frequency from the set of values tends to zero, consequently, the system is stable. The time constant of the transient phenomena is an average of 10-14 s.

Conclusion

A block scheme of the one-machine power supply system with ARE SA is obtained. The simulation of the system in MatLab Simulink is produced. The quality of electricity can be judged by the process of changing the frequency in the power system. At the initial stage of the transition the frequency ranges 49,5-50,5 Hz, which is valid for a short-term operation. In a normal mode, the frequency must be maintained with an accuracy Hz. As can be seen from the graphs, the model fulfills this condition completely.

References

1. Хрущев Ю.В. Методы расчета устойчивости энергосистем. Учебное пособие. – Томск: Изд-во ТПУ, 2005. – 176 с.

2. Электромеханические переходные процессы в электроэнергетических системах: учебное пособие/ Ю. В. Хрущев, К. И. Заподовников, А. Ю. Ушков; Томский политехнический университет. – Томск: Изд-во Томского политехнического университета, 2010. –160 с.

3. Коновалов Б.И., Лебедев Ю.М. Теория автоматического управления: Учебное методическое пособие. — Томск: Факультет дистанционного обучения, ТУСУР, 2010. — 162 с.

4. Лазарев Ю. Моделирование процессов и систем в MATLAB. Учебный курс. – СПб.: Питер, Киев: Издательская группа BHV, 2005 – 512 с.: ил.

5. Ивановский Р. И. Компьютерные технологии в науки и образовании. Практика применения системы MathCAD Pro: Учеб. пособие/Р. И. Ивановский. – М.: Высш. шк., 2003. – 431с.: ил.