STUDY OF TRANSIENT PROCESSES IN A VALVE PULSE GENERATOR

A. V. LOOS, Yu. I. RYABCHIKOV, G. A. SIPAILOV

(Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)

For generating powerful energy pulses of millisecond duration, a number of systems use a synchronous generator operating in the mode of sudden switching-on through an uncontrolled semiconductor rectifier to an active load (Fig. 1, a). Valve pulse generators have found wide application in pulse welding, electro-erosion machining of metals, and for supplying many other pulse consumers. They offer broad possibilities with respect to regulating the pulse parameters and their repetition frequency, and have good overall size-and-weight characteristics.

However, at present a whole series of theoretical questions that hinder the design and application of valve pulse generators has not been studied. Such questions include: the determination of the matched load resistance and the influence of its value on the energy characteristics of the system; the influence of the degree of salient-pole construction and of the switching angle on the load; the absence of calculation relationships for the current and power in the load; and many others.

Analysis of these questions, taking into account the full complex of factors, leads to the necessity of solving the complete system of differential equations written for the synchronous generator, the rectifier, and the load. We shall present some results of studies of a valve pulse generator carried out on the MN14 computer [1].

In the case of a sudden short circuit at the terminals of a valve pulse generator, significant oscillations follow a large current surge. Under short-circuit conditions the voltage at the rectifier terminals is zero, and with ideal valves the voltage drops across any of them are also equal to zero. The phase voltages $U_a$, $U_b$, $U_c$ are related to the voltage drops across the valves by the relations:

\[ U_a = \frac{1}{3}(2U_1 - U_3 - U_5), \]

\[ U_b = \frac{1}{3}(2U_3 - U_1 - U_5), \]

\[ U_c = \frac{1}{3}(2U_5 - U_1 - U_3). \tag{1} \]

Consequently, for $R_{\mathrm{н}} = 0$, the phase voltages $U_a = U_b = U_c = 0$, i.e., the synchronous generator operates in the mode of a symmetrical short circuit.

closing, the transient process in it can be calculated from known relations [2].

Taking into account the impossibility of simultaneous operation of two valves of one phase, we find that the currents in the open valves are equal to the phase currents of the generator. The presence of aperiodic components in the phase currents disturbs the angle between them, which also causes current pulsations at the generator output. The duration of these oscillations depends on the value of the time constant of the armature circuit. The duration of the transient process depends on the values of the time constants \(T_a\), \(T''_d\), \(T'_d\). The peak value of the current may exceed the rated current of the generator, depending on the parameters, by a factor of 5–20. After the first surge, the load current initially decreases relatively rapidly, the rate of decay depending mainly on the values of the time constants \(T''_d\) and \(T_a\); then it slowly decreases to the steady-state value with the time constant \(T'_d\).

The load resistance reduces the surge of the current \(i_{\mathrm{n}}\) and smooths its oscillations; moreover, the larger \(R_{\mathrm{n}}\) is in comparison with the subtransient resistance \(x''_d\), the more substantially the current oscillations decrease. The matched load resistance was determined by plotting the dependence \(i_{\mathrm{n}}^2 R_{\mathrm{n}} = f(R_{\mathrm{n}})\) for various values of the generator subtransient resistance.

The maximum impact power corresponds to the load resistance \(R_{\mathrm{n}} = 1.5 x''_d\); however, the maximum amount of energy transferred to the load, depending on the required pulse duration, is provided at resistances \(R_{\mathrm{n}} = (1.5 \div 2)x''_d\). This is explained by the fact that, with time, the subtransient processes decay, the internal resistance of the generator increases and, consequently, the condition for matching the generator and the load changes. As the pulse duration is increased, the resistance \(R_{\mathrm{n}}\) must be selected from the condition of obtaining maximum energy in the load and, consequently, will shift toward larger values. If the load resistance lies within the limits \((1.5 \div 2)x''_d\), then the three-phase, two-half-period rectification circuit operates in the mode in which valves conduct in groups of three. With a further increase in \(R_{\mathrm{n}}\), two- and three-valve modes alternate in the circuit.

Analyzing the oscillograms of the transient processes of the valve pulse generator (Fig. 2), it is easy to establish that, owing to the nonlinearity of the volt-ampere characteristics of the valves, the synchronous generator experiences an asymmetrical load by phases. Indeed, as a result of valve commutation, the load is continuously redistributed among the phases with a periodicity of 180 electrical degrees. For this reason the periodic components of the phase currents are shifted relative to one another by 120 electrical degrees and, if damping is not taken into account, have the same shape and amplitude, i.e., they possess the features characteristic of the symmetrical operating mode of a synchronous generator. This circumstance suggests the possibility of replacing the rectifier with a load on the rectified-current side by such a symmetrical load, for which the transient processes in the synchronous generator will be close to one another.

Solutions on an analog model showed that the value of the equivalent load depends both on the value of \(R_{\mathrm{n}}\) and on the operating modes of the rectifier; moreover, for the case in which the rectifier valves operate in groups of three, it proved to be equal to \(\frac{2}{3}R_{\mathrm{n}}\), while in the alternating two- and three-valve modes it was somewhat smaller.

The same result can also be obtained analytically. Comparing the circuits shown in Figs. 1a and 1b, we note that they will be strictly

equivalent to each other only in the case where the dependence of the phase voltages on the phase currents in both circuits is expressed by one and the same relation.

Fig. 1

For the equivalent circuit, this relationship is expressed by the equation

\[ U_a = R_{\mathrm{e}} i_a . \tag{2} \]

For the circuit with the rectifier, a similar dependence can be obtained comparatively easily only for the fundamental harmonics of the currents and voltages.

In Fig. 1c, proceeding from the fundamental harmonics of the phase currents, the load-current curves and one of the phase-voltage curves have been constructed. The phase-voltage curve has been constructed taking into account relation (1) for the case in which the rectifier valves operate in groups of three (in this mode, the voltage drops across the valves are determined by the direction of the current in the corresponding phases and by the voltage across the load; for example: \(U_1=0\) for \(i_a>0\), \(U_1=-U_{\mathrm{н}}\) for \(i_a<0\), similarly for \(U_3\) and \(U_5\)) and can be represented as the sum of several components, of which the principal one is the fundamental harmonic

\[ U_{a1} = \frac{2}{3} R_{\mathrm{н}} i_a . \tag{3} \]

Comparing (3) with (2), we conclude

\[ R_{\mathrm{e}} = \frac{2}{3} R_{\mathrm{н}} . \tag{4} \]

It should be noted that, since in deriving (4) only the fundamental harmonics of the phase voltages and currents were taken into account, the circuits shown in Fig. 1 are not strictly equivalent. Nevertheless, the solutions for the transient processes in them, obtained on a mathematical model, practically coincide in the region of three-valve operating modes of the rectifier. Thus, it becomes possible to calculate the transient processes of a valve pulse generator using the equivalent-circuit sche-

…section (Fig. 1c). The validity of such a representation is confirmed by the practically coincident oscillograms (Fig. 2) of the phase currents, rotor currents, and flux linkages of the valve pulse generator (solid lines) with similar oscillograms obtained when a three-phase synchronous generator is suddenly connected to a symmetrical active load (dashed lines). Replacing the rectifier by an equivalent circuit makes it possible to calculate the current in the load of the valve pulse generator from the envelope curve of the phase currents of the synchronous generator, which considerably simplifies analytical investigations [3].

Fig. 2. Oscillograms of currents and flux linkages: — valve pulse generator at \(R_{\mathrm{n}}=0.1\), – – – synchronous generator with a symmetrical load \(R_{\mathrm{e}}=\dfrac{2}{3}R_{\mathrm{n}}=0.0666\).

Generator parameters: \(X_d=X_q=1.05,\quad X_{Dd}=X_{Dq}=1.05,\quad X_f=1.2,\quad x_a=1,\quad r_f=r_{Dd}=r_{Dq}=r=0.02\).

The main results of studies on an analog computer using the complete system of differential equations were verified in experimental investigations on a number of prototype models. The experimental results agree well with the theoretical conclusions. Figure 3 shows an oscillogram of the phase currents recorded on a physical model of a generator with a rated power of \(3.5\ \text{kW}\), operating according to the circuits of Fig. 1a and Fig. 1b. The oscillograms were obtained by superimposing the negatives during printing. As can be seen from Fig. 3, the phase currents practically coincide.

Fig. 3. Experimental oscillograms of phase currents during operation according to the circuits in Fig. 1a and Fig. 1b

Conclusions

1. The principal operating mode of a three-phase rectifier circuit of a valve pulse generator, at matched load-resistance values, is the mode in which the valves conduct in groups of three. The matched load resistance of the valve pulse generator is \(R_{\mathrm{n}} = (1.5—2)x''_{d}\).

2. The load current of a valve pulse generator can be calculated from the envelope curve of the phase currents obtained when a synchronous generator is suddenly connected to a symmetrical three-phase active load whose magnitude is \(R_{\mathrm{e}} = 1.5 R_{\mathrm{n}}\).

REFERENCES

1. A. V. Loos, Yu. I. Ryabchikov. Mathematical modeling of a synchronous generator under rectifier loading. TPI Publishing House, vol. 242, 1972.

2. I. I. Treshchev. Methods for studying alternating-current machines. “Energiya,” 1969.

3. A. V. Loos. Application of the method of successive differentiation in calculating transient processes of electromechanical pulse sources. TPI Publishing House. Present collection.