Calculation of the Characteristics of a Synchronous Motor with Automatic Excitation Current Control

CALCULATION OF THE CHARACTERISTICS OF A SYNCHRONOUS MOTOR
UNDER AUTOMATIC REGULATION
OF THE EXCITATION CURRENT

A. N. Shchipkov, D. V. Istratkin

(Presented by the scientific-technical seminar of the Research Institute of AEM)

At present, regulation of the excitation of synchronous motors under sharply varying load as a function of the internal operating angle \(\Theta\) is persistently recommended for practical application, as it ensures better techno-economic operating indices [1, 2]. However, methods and procedures for calculating the operating and angular static characteristics of a synchronous motor, linked with the calculation of the parameters of the ARE circuit and taking into account the nonlinearity of the characteristics and the dependence of certain motor parameters on the operating mode, have not yet been sufficiently developed for such regulation. The present article is devoted to these questions.

Fig. 1.

Before calculating the operating characteristics, the law and parameter of excitation regulation must be selected, and the U-shaped and angular characteristics at various excitation currents of the synchronous motor must also be determined (Fig. 1). When designing the system of automatic excitation regulation (ARE) of synchronous motors, the main

the characteristic is the dependence of the excitation current on the input control parameter (the regulating characteristic), ensuring the selected control law. In contrast to [3], let us consider the construction of the regulating characteristic for the law of regulation to constancy of any specified value of the motor power factor. For this purpose the U-shaped characteristics of the SM are used; depending on the conditions, these are either obtained experimentally or constructed by known methods (Fig. 1, a).

Having specified the control law \(\operatorname{Cos}\varphi_i=\operatorname{Const}\), we draw in Fig. 1,a the line \(\operatorname{Cos}\varphi=\operatorname{Const}\), and at the points of its intersection with the U-shaped characteristics we determine, for the corresponding values of power \(P_i\), the magnitudes of the stator current \(I_i\) and of the excitation current \(i_i\) (the subscript \(i\) denotes the ordinal number). Next, knowing \(i_i\) and \(P_i\), from the curves \(P(\Theta)\) (Fig. 1,b) we find the value of the angle \(\Theta_i\). Relating to one another the corresponding values of \(i_{n_i}\) and \(\Theta_{n_i}\) for one and the same power \(P_i\), we obtain the regulating characteristic \(i=f(\Theta)\), ensuring

Fig. 2

the implementation of the specified law of excitation regulation. Using these characteristics, one can construct regulating characteristics also for other control laws. The next stage of the calculation should be regarded as the determination of the parameters of the AER system that would form the regulating characteristic found. Such a problem is solved in [2] and [3].

For a technical comparison of AER circuits of synchronous motors it is necessary to construct their operating and angular characteristics under the action of the AER. In Fig. 1,b, using the curves \(P(\Theta)\) constructed for various excitation currents \(i\), and the regulating characteristic \(i(\Theta)\), we construct the angular characteristic \(P'(\Theta)\) of the motor under the action of the AER. To construct the operating characteristics of an SM with AER, showing the dependence of the stator current, \(\operatorname{Cos}\varphi\), efficiency, consumed power \(P_1\), etc., on the shaft power \(P_2\), we use the same curves of Fig. 1 in the following sequence. Having specified the power \(P_n\) (Fig. 1,a), from the angular characteristic \(P'(\Theta)\) we find \(\Theta_n\), and from the regulating characteristic \(i(\Theta)\) we find \(i_n\) (Fig. 1,b). Transferring the value \(i_n\) to Fig. 1,a, from the quantities \(P_n\) and \(i_n\) we find the stator current \(I_n\) and \(\operatorname{Cos}\varphi_n\), necessary for constructing the operating characteristics. The power \(P_2\) is determined by the formula \(P_2=P_1-\Delta P_\varepsilon\), where \(\Delta P_\varepsilon\) is the total losses in the motor, consisting of losses in

the stator copper losses \(3I^{2}r_{\mathrm{st}}\), no-load losses \(\Delta P_{0}\), and additional losses \(\Delta P_{\mathrm{add}}\). Thus, all parameters of the operating characteristics shown in Fig. 2 for a synchronous machine of type MSA-72-4A are determined. The overload capacity \(\lambda\) of the motor under ARV with respect to the angle \(\Theta\) was determined from the characteristics found, taking into account the change in the value of the direct-axis reactance from the value \(X_{dh}\) in the rated mode to the value \(X_{dm}\) at the maximum value of the excitation current. Then

\[ \lambda=\frac{P_{\max}}{P_{\mathrm{n}}} =\frac{E_{\max}\cdot X_{dh}}{E_{\mathrm{n}}\cdot X_{dm}\cdot \sin \theta_{\mathrm{n}}}. \]

For our example, the value \(\lambda=4.6\) for

\[ X_{dh}=2.2;\quad X_{dm}=1.2. \]

Thus, it may be concluded that, using the \(U\)-shaped and angular characteristics of a synchronous motor and the regulating characteristic of the ARV unit, one can determine with sufficient accuracy the parameters of the excitation-control system and construct the motor operating characteristics under automatic variation of the excitation current.

LITERATURE

1. Synchronous Drives. Edited by M. G. Chilikin. “Energiya,” 1967.
2. N. R. Ipatenko, M. V. Bokanov, N. U. Kosmachev. On the calculation of the automatic-control circuit for synchronous motors. “Elektrotekhnika,” 1970, No. 9.
3. A. N. Shchipkov. A high-speed automatic-control system for the operating angle of a synchronous motor. Reports to the VI Scientific and Technical Conference on Production Automation, vol. 1, Tomsk, 1969.