A Low-Inertia Control Device for Power Regulators of Electric Arc Steelmaking Furnaces

V. A. Beinarovich, N. G. Volkov

(Presented by the scientific and technical seminar of the Research Institute of Electric-Machine Automation at TPI)

At present, most domestic electric arc steelmaking furnaces are equipped with arc-power regulators that contain an electric-machine (or magnetic) amplifier, a DC actuator motor, and a control device called the arc-power setpoint unit, a simplified circuit of which is shown in Fig. 1.

A disadvantage of such regulators is the high inertia of the actuator motor and amplifier, which leads to a significant overconsumption of electric energy during the melting process, especially during the melting-down period, when short-circuit modes (during collapse of the charge) alternate with no-load modes (during arc breaks).

Increasing the speed of response of power regulators makes it possible to raise furnace productivity, reduce the cost of processing one tonne of steel, and improve its quality.

In developing fast-response arc-power regulators, problems arise in reducing the inertia of the actuator drive for electrode movement, minimizing the inertia of the amplifier and of the control device. Means for implementing fast-response electromechanical systems are known: the use of smooth-armature motors, the use of inertialess thyristor amplifiers, and the creation of control systems optimal in speed of response. A necessary condition for normal operation of a fast-response regulator is evidently also the inertialessness of the device that sets the arc power.

Let us consider the operation of the circuit in Fig. 1. Two signals are applied to the input of the arc-power setpoint unit (Fig. 2): an AC voltage \(U_2\), proportional to the arc voltage \(U_d\), and an AC voltage \(U_2\), proportional to the arc current \(I_d\). The voltage \(U_1\) lags in phase behind \(U_2\) by an angle \(\varphi\), determined by the phase shift of the arc current relative to the voltage. The angle \(\varphi\) varies depending on the operating mode of the furnace. The form of the voltages \(U_1\) and \(U_2\) for the real operating mode (one of the melting periods) is shown by a solid curve; the averaged form, by a dashed curve. As a result of full-wave rectification and algebraic summation of the voltages \(U_1\) and \(U_2\), the voltage \(U_y\) is obtained at the output of the arc-power setpoint unit. When the arc power is equal to the prescribed value, the voltage \(U_y\) has a sawtooth form (Fig. 2), but the average value of the voltage \(U_y\) is zero. The amplitude of the voltage \(U_y\) in this mode is about 50% of the amplitude of the input voltages \(U_1\) and \(U_2\) (at \(\varphi \cong 30^\circ\)).

Fig. 1. Arc-power setter.

Fig. 2. Voltage waveforms of the arc-power setter.

The use of a voltage \(U_y\) of this shape to control electric drives with an electric-machine or magnetic amplifier and a motor of conventional design does not lead to the occurrence of current pulsations and pulsating displacements, owing to the considerable inertia of such electric drives.

When fast-acting electric drives are used, the pulsations of the voltage \(U_y\) are already perceived by the system as a useful signal, which leads to the appearance of alternating current in the armature of the actuator motor and may cause pulsating displacements. In addition, in inertia-free thyristor amplifiers the use of a pulsating voltage \(U_y\) (Fig. 2) is altogether inadmissible, since it causes false turn-off of the thyristors. The use of smoothing filters, however, leads to an increase in the inertia of the arc-power setter and, consequently, to a reduction in the speed of response of the regulator.

To reduce the voltage pulsations at the output of the power setter—

...of the arc power without a substantial increase in its inertia, it is possible to use an artificial increase in the number of rectification phases of the voltages \(U_1\) and \(U_2\) on the basis of parametric phase-shifting circuits. Figure 3 shows the circuit of such an arc-power sensor.

Studies [2] have shown that, when the number of rectification phases is increased from two to six, the speed of response in tracking changes in the average value of the input signal increases by approximately a factor of 30, provided that the ripple of the rectified voltage is the same. As the number of rectification phases increases, the ripple decreases to an ever greater extent and the speed of response of the power sensor increases for a specified ripple level, which makes it possible to increase substantially the pass frequency of the control system as a whole.

Fig. 3. Arc-power sensor with the number of rectification phases increased to six

Let us determine the basic relationships for selecting the parameters of the circuit in Fig. 3.

Consider, in the general case, one bridge of the phase shifter, containing the secondary winding of a transformer with a midpoint and with the voltage of each arm \(U\), an arm with a reactive element \(Z\) (capacitive or inductive), an arm with a resistor \(R\), and a load resistor \(R_{\mathrm{н}}\) connected in the diagonal of the bridge. On the basis of Kirchhoff’s laws, the following equations can be written for the phase-shifter bridge:

\[ \left. \begin{aligned} \dot I_R R - \dot I_{\mathrm{н}} R_{\mathrm{н}} &= \dot U,\\ \dot I_{\mathrm{н}} R_{\mathrm{н}} + \dot I_Z Z &= \dot U,\\ \dot I_R + \dot I_{\mathrm{н}} - \dot I_Z &= 0 \end{aligned} \right\}, \tag{1} \]

where \(\dot I_R\), \(\dot I_Z\), and \(\dot I_{\mathrm{н}}\) are, respectively, the currents of the bridge arms and of the load. From (1), the expression for the load voltage will have the form

\[ \dot U_{\mathrm{н}}=\dot I_{\mathrm{н}}R_{\mathrm{н}} =\dot U\,\frac{(R-Z)R_{\mathrm{н}}}{RR_{\mathrm{н}}+(R+R_{\mathrm{н}})Z}, \tag{2} \]

whence the phase shift of the voltage on the load \(U_{\mathrm{н}}\) relative to the supply voltage \(U\) at the fundamental frequency is determined by

\[ \varphi = \operatorname{arc\,tg}\frac{2R\,(R+2R_{\mathrm{n}})}{R^{2}R_{\mathrm{n}}-Z^{2}(R+R_{\mathrm{n}})}, \tag{3} \]

where \(Z=\omega L\) for an active-inductive phase shifter and \(Z=\dfrac{1}{\omega C}\) for an active-capacitive phase shifter.

From expression (3) we determine the value \(R\) that ensures the specified phase shift \(\varphi\) for the known parameters \(Z\) and \(R_{\mathrm{n}}\):

\[ R = \frac{(Z^{2}\operatorname{tg}\varphi+2ZR_{\mathrm{n}}) \pm \sqrt{(Z^{2}\operatorname{tg}\varphi+2ZR_{\mathrm{n}})^{2} +4(R_{\mathrm{n}}\operatorname{tg}\varphi-Z)Z^{2}R_{\mathrm{n}}\operatorname{tg}\varphi}} {2(R_{\mathrm{n}}\operatorname{tg}\varphi-Z)} . \tag{4} \]

The relative value of the voltage modulus at the load is determined by

\[ \frac{|U_{\mathrm{n}}|}{|U|} = \sqrt{ \frac{[K^{2}-R_{\mathrm{n}}(R+R_{\mathrm{n}})]^{2} +K^{2}(R+2R_{\mathrm{n}})^{2}} {[K^{2}+(R+R_{\mathrm{n}})^{2}]^{2}} }, \tag{5} \]

where \(K=\dfrac{RR_{\mathrm{n}}}{\omega L}\) for an active-inductive phase shifter and \(K=RR_{\mathrm{n}}\omega C\) for an active-capacitive phase shifter.

Expressions (3–5) make it possible to investigate the influence of the choice of circuit parameters on the voltage at the load for a specified phase shift.

The best operating mode of the entire device will obviously be one in which the voltage modulus at the specified load remains constant for any phase shift. However, investigations show that fulfillment of this condition requires a considerable increase in the power of the power supply, owing to the need to increase the currents in the arms of the phase-shifter bridges. In addition, this leads to an increase in the dimensions of the reactive elements.

The optimum values of the parameters of the power supply can be found from expressions (3–5) for a specified value of the load resistance \(R_{\mathrm{n}}\) and the required ratio of the load voltage \(U_{\mathrm{n}}\) to the voltage of the transformer half-winding \(U\). As a result of the investigations carried out, the optimum dependences shown in Fig. 4 were obtained for the capacitance \(C\) of the reactive arm of the phase shifter as a function of the load \(R_{\mathrm{n}}\), with the ratio of the voltage \(U_{\mathrm{n}}\) to the voltage \(U_{1}\), ensured at any phase shift, held constant.

Fig. 4. Dependence of the capacitance \(C\) on the load resistance \(R_{\mathrm{n}}\) in the bridge diagonal for ratios of the voltage \(U_{\mathrm{n}}\) at the load to the voltage \(U\) of the transformer half-winding equal to: 1 — 98%, 2 — 95%, 3 — 90%, 4 — 75%.

In an analogous manner one can also obtain the optimal values of the inductance of the reactive arm of the phase shifter.

For a low-inertia rectifying device with capacitive phase shifters, the following calculation procedure may be recommended:

1) from the dependencies in Fig. 4 or from expressions (3—5), the value of the capacitance \(C\) is determined for given values of the load resistance \(K_{\text{н}}\) and the ratio \(U_{\text{н}}\) to \(U\);

2) from the conditions of the permissible voltage ripple at the load, the number of rectification phases \(m\) is selected and the phase shift is determined

\[ \varphi = \frac{2\pi}{m}, \]

3) from expression (4), the resistance of the arm of each \(n\)-th phase shifter is determined from the conditions for obtaining the phase shift \(\Phi = n\varphi_0\) (where \(n = 1, 2, \ldots, m\)).

The considered circuit of the arc-power sensor makes it possible to significantly reduce the inertia in the control circuit of the automatic control system and to reduce the ripple of the rectified voltage, which will substantially increase the response speed of the arc-power regulators. The recommended calculation method makes it possible to determine the necessary circuit parameters for any rectification phase number and, consequently, to obtain ripples of the desired magnitude.

REFERENCES

1. A. A. Bulgakov. Electronic Devices for Automatic Control. Gosenergoizdat, 1958.

2. V. V. Tormasov. A new method for smoothing the voltage of a single-phase rectifier. Proceedings of the Norilsk Evening Industrial Institute, Physico-Electrotechnical issue, collection No. 2, 1964.

3. G. N. Atabekov. Theoretical Foundations of Electrical Engineering, Part 1. “Energiya,” 1966.