On the Calculation of Operating Characteristics of Low- and Medium-Power Synchronous Motors with Phase Compounding

A. N. Shchipkov

(Presented by the scientific seminar of the Electromechanical Faculty)

At present the question is being raised of the mass application of synchronous motors in the national economy. This is due to certain advantages of synchronous motors over asynchronous ones [1]. Regulation of the excitation current of synchronous motors makes it possible to reveal these advantages more fully and to use them to improve the techno-economic indices of operation of these machines. For synchronous motors of low and medium power ratings (up to 100–150 kW), the most profitable law of excitation-current regulation is maintenance of a constant power factor (minimum losses), in particular at $\cos \varphi = 1$ [2, 3]. Investigations of phase-compounding circuits for synchronous motors [4, 5, 6, 8] have revealed the possibility of using them to maintain the constancy of the motor power factor over a considerable range of load variation, while at the same time the overload capacity of the motor was also substantially increased. These circuits are the simplest, cheapest, and most reliable [6, 7]. The stabilizing three-winding transformer “TC” in the indicated circuits (Fig. 1) performs the role not only of a step-down transformer, but also of an integrator, in which the output current $I_2$ is determined by the stator current, its voltage, and the angle between them.

Fig. 1.

In [4, 5, 8], methods were proposed for calculating the optimum parameters of a phase-compounding circuit with a three-winding transfor-

motor and of the operating characteristics of the motor with the indicated excitation circuit. The determination of the parameters and the calculation of the characteristics were carried out without taking into account the saliency of the synchronous motor and without allowing for the change in its parameters \(x_{ad}, x_s\) under different operating conditions due to saturation of the magnetic system.

Allowance for saliency and for changes in the motor parameters is possible when using \(U\)-shaped characteristics, which can be constructed from the vector diagram or else obtained experimentally, taking into account all active resistances of the stator circuit (Fig. 2).

Fig. 2.

For low- and medium-power motors, when calculating operating characteristics it is especially necessary to take careful account of the active resistances of the stator, the series winding of the transformer, and the resistances introduced into the stator circuit through the “TC” transformer by the rectifier and the excitation winding. By specifying some value of \(\cos\varphi\), from the characteristic \(\cos\varphi = f(i_v)\) we determine, for some power \(P_k\) (characteristic 1 in Fig. 2), the excitation current \(i_{vk}\), and from the \(U\)-shaped curve we find the stator current \(I_{ck}\) corresponding, at the given power \(P_k\), to the value \(\cos\varphi_k\). In this way one can construct a family of regulating characteristics \(i_v = f(I_c)\) for specified values of \(\cos\varphi\). For the case \(\cos\varphi = 1\), the regulating characteristic will be the curve \(AB\), passing through the vertices of the \(U\)-shaped characteristics. Further, using the regulating characteristic constructed for the required value of \(\cos\varphi\) (in our case \(\cos\varphi = 1\)), it is possible to determine the parameters of the phase-compounding system [4, 5, 8] and to construct the required operating characteristics (Fig. 4). To determine the overload capacity and the stability margin of a motor with phase compounding under slowly varying load, it is necessary to construct the angular characteristic \(\Theta_k = f(P_1)\), where \(\Theta_k\) is the angle between the axes of the stator and rotor poles in operating conditions. The construction of the angular characteristic, taking into account all the special features of the given motor (saliency, the magnitude of the changes in \(x_{ad}, x_s, x_q\), the values of the resistances in the stator circuit, etc.), can be carried out as follows.

1. We construct a family of curves \(\Theta = f(P_1)\) (dash-dotted lines in Fig. 3) for different values of the motor excitation current. The construction is carried out taking into account the active resistances in the circuit.

stator, and the power supplied to the motor \(P_1\) is determined by formula [9]:

\[ P_1=\frac{3U_1E_{10}}{x_{dr}}\sin\Theta+ \frac{3U_1^2}{2}\left(\frac{1}{x_q}-\frac{\beta}{x_{dr}}\right)\sin 2\Theta+ \]

\[ +\frac{3U_1r_1\cos\Theta}{x_{dr}\cdot x_q} \left(E_{10}-U_1\beta\cos\Theta\right); \]

\[ x_{dr}=x_d+\frac{r_1}{x_q};\quad \beta=1+\frac{r_1}{x_q}\operatorname{tg}\Theta;\quad r_1=r_{\mathrm{st}}+r_{\mathrm{e}}, \]

\(r_{\mathrm{e}}\) is the resultant active resistance in the stator circuit introduced by the phase-compounding circuit [5].

1. We construct the static curve \(i_{\mathrm{v}}=f(P_1)\) (Fig. 3) for the phase-compounding system.

2. By assigning different values of the power \(P_1\) according to the characteristic \(i_{\mathrm{v}}=f(P_1)\), we find the corresponding value of \(i_{\mathrm{v}}\). For the specified power \(P_1\) and the obtained value of the excitation current \(i_{\mathrm{v}}\), from the family of curves \(\Theta=f(P_1)\) we determine the required angle \(\Theta\). Thus the dependence of the angle \(\Theta\) on the supplied power \(P_1\) under phase compounding is constructed (Fig. 3, curve \(\Theta_k=f(P_1)\)).

For comparison, Fig. 4 gives the operating characteristics obtained by calculation and experimentally.

The work was carried out on a synchronous machine of type MSA 72-4A:

Fig. 3.

Fig. 4.

\[ P_{\mathrm{n}}=15\ \text{kVA}\ (12\ \text{kW}),\qquad r_{\mathrm{st}}=0.15\ \Omega, \]

\[ I_{\mathrm{n}}=37.6\ \text{A},\qquad r_{\mathrm{e}}=0.0175\ \Omega. \]

\[ U_{\mathrm{n}}=230\ \text{V}, \]

Conclusions

1. Using U-shaped and regulation characteristics, it is possible, in calculating operating characteristics, to take into account certain features of synchronous motors (saliency, change in the degree of saturation).

2. In view of the small change in the motor power factor under substantial changes in load, a phase-compounding circuit may be used to stabilize \(\cos \varphi\).

3. Calculation of the torque-angle characteristic has shown a considerable overload capacity of the synchronous motor with a phase compounding circuit, which makes it possible, in the joint design of synchronous motors and compounding circuits for them, to reduce the weight of the motor.

References

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2. I. A. Syromyatnikov. Operating modes of asynchronous and synchronous electric motors. GEI, 1963.

3. D. P. Petelin. The law of excitation regulation of a synchronous motor for minimum losses. Izvestiya OTN AN SSSR, series “Power Engineering—Automation,” No. 4, 1959.

4. N. M. Tarasov. Investigation of the operation of the excitation circuit of low- and medium-power synchronous motors from semiconductor rectifiers. Izvestiya vuzov, “Electromechanics,” No. 4, 1958.

5. N. S. Siyunov, N. M. Tarasov. Graph-analytical calculation of the characteristics of compounded synchronous motors. Izvestiya vuzov, “Electromechanics,” No. 1, 1959.

6. V. L. Iposov, V. E. Krutikova, V. A. Kameneva. Synchronous Motors with Excitation from Semiconductor Rectifiers. GITL, 1960.

7. S. I. Loginov. Technical-and-economic comparison of synchronous motors with various excitation systems. Izvestiya vuzov, “Electromechanics,” No. 7, 1963.

8. R. B. Goncharenko, Ya. B. Danilevich, S. I. Loginov. Investigation and calculation of the excitation system of a synchronous motor with a three-winding transformer and semiconductor rectifiers. Collection of Works on Electromechanics, No. 8, 1963.

9. G. N. Petrov. Electrical Machines. GEI, 1963.