Circuit for disconnecting an impulse generator during the second half-wave
Abstract Generated abstract
This paper proposes a commutation circuit for disconnecting a single-phase shock generator from an inductive load at the second zero crossing of current. Using the characteristic asymmetry of shock-generator short-circuit current, the scheme carries the large first half-wave through a high-speed mechanical contact device, then transfers the smaller second half-wave through an auxiliary valve by means of saturable reactors so that the contacts can open without arcing. The authors derive simplified current expressions for the first generator period and use them to justify the timing and rating of the mechanical contacts, valves, and reactors. The circuit is presented as a simpler alternative to earlier ion-mechanical switching arrangements, suitable especially for high-energy pulsed magnetic-field applications at generator frequencies up to about 50 Hz.
Full Text
CIRCUIT FOR DISCONNECTING A SHOCK GENERATOR DURING THE SECOND HALF-WAVE OF CURRENT
G. A. Sipailov, V. V. Ivashin
(Presented at a scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)
In generating pulsed powers for obtaining magnetic fields with high energy, used for confining plasma, for creating a controlling field in charged-particle accelerators, and in many other areas of physics and technology, in a number of cases a promising scheme may be one employing a special synchronous machine—a single-phase shock-power generator (shock generator)—as the energy storage device and source.
It is known that in a shock generator the energy is accumulated in the cheapest way—in rotating masses; therefore, an installation for high energies of the order of \(10^6\)—\(10^7\) J and more, using a shock generator, may be the most economical and compact in comparison with generators with capacitive and even inductive energy storage.
Academician P. L. Kapitsa appreciated the merits of the special synchronous machine as early as 1923–25, when he first used a shock generator to obtain strong magnetic fields [1]. The obstacle to the wide use of a shock generator in the practice of physical and electrical-engineering experiments is the difficulty of commutating the generator current. At the powers used by P. L. Kapitsa, it was possible to employ a mechanical high-speed device to connect and disconnect the generator. The generator was connected to the load at an emf phase close to zero and was disconnected in the region of the first passage of the current through zero. The arc arising upon disconnection was extinguished by blowing. The generator voltage was \(\approx 1200\) V.
The arcless ion-mechanical switching devices developed at TPI, and the circuits for their application, in principle make it possible to commutate the current of shock generators of practically any power [2, 3].
The circuit considered makes it possible to commutate energy from the shock generator with its disconnection from the load at the second passage of the current through zero.
The switching device of the circuit considered in this paper is considerably simpler than the switching devices considered in [2, 3].
Principle of Operation of the Circuit
The schematic diagram for switching the current of the shock generator is shown in Fig. 1, where
\(UG\) — shock generator, the energy source;
\(e\) — generator e.m.f.;
\(K\) — a high-speed mechanical contact device; moreover, in order to provide the necessary speed and reliability of operation in the circuit, two devices may be used, one of which switches on and the other switches off;
\(B_1\) — auxiliary valve (ignitron, thyratron) for switching on the generator;
\(B_2\) — auxiliary valve for disconnecting the generator;
\(D_1, D_2\) — saturable reactors;
\(L_{\mathrm{n}}\) — load inductance.
Fig. 1. Schematic diagram for switching the current of a shock generator.
The principle of operation of the circuit follows from the specific nature of the current curve of the shock generator: when it is connected to the load at the instant when the generator e.m.f. passes through zero, the current of the first, positive half-wave, owing to the presence of an aperiodic component, has maximum amplitude and duration, while the current of the second, negative half-wave has minimum amplitude and duration.
Depending on the parameters of the generator, the amplitude and duration of the current of the second half-wave may vary; however, for parameter values characteristic of high-power shock generators, the amplitude of the current of the second half-wave averages about 10%, and its duration about 20%, of the amplitude and duration of the current of the first half-wave. Therefore the mean and effective values of the current of the negative half-wave amount to less than 5% of the corresponding values of the current of the positive half-wave. To verify this, it is sufficient to examine the current curve of the shock generator.
The equation for the resultant short-circuit current of synchronous machines is usually written in the following form [1]:
\[ i_k = - I_{dm}\cos(\omega t + \psi) - (I'_{dm} - I_{dm}) e^{-\frac{t}{T'_d}}\cos(\omega t + \psi) - \]
\[ -\left(I''_{dm}-I'_{dm}\right)e^{-\frac{t}{T''_{d}}}\cos(\omega t+\psi)+I_{am}e^{-\frac{t}{T_a}}\cos\psi, \tag{1} \]
where \(I_{dm}\), \(I'_{dm}\), \(I''_{dm}\), and \(I_{am}\) are the amplitude values, respectively, of the steady-state, transient, subtransient, and aperiodic components of the current;
\(T'_d\), \(T''_d\), and \(T_a\) are the time constants of decay of the transient, subtransient, and aperiodic components of the current;
\(\psi\) is the switching-on phase.
Since, for a shock generator, it is necessary to know the current values only during the first period of the emf, in calculating the current one may use only the subtransient parameters; therefore equation (1) can be substantially simplified, with practically no effect on the accuracy of the calculation results:
\[ i_k=-i_p+i_a, \tag{2} \]
where \(i_p\) is the periodic component of the short-circuit current
\[ i_p=I''_{dm}\,\frac{1+e^{-\frac{t}{T''_d}}}{2}\cos(\omega t+\psi); \tag{3} \]
\(i_a\) is the aperiodic component of the short-circuit current
\[ i_a=I_{am}e^{-\frac{t}{T_a}}\cos\psi. \tag{4} \]
Taking into account that \(I''_{dm}=I_{am}\), and considering that \(\cos\psi=1\) when the generator is switched on through the valve, equation (2) may be represented in the form
\[ i_k=I''_{dm}\left[e^{-\frac{t}{T_a}}-\frac{1}{2}\left(1+e^{-\frac{t}{T''_d}}\right)\cos\omega t\right], \tag{5} \]
where
\[ I''_{dm}=\frac{E_m}{x_{ud}}; \]
\(x_{ud}\) is the reactance of the shock generator, which, with a degree of accuracy sufficient for practical calculations, may be taken as
\[ x_{ud}=1.15\,x_s, \]
where \(x_s\) is the leakage reactance of the stator winding.
The curves of sudden short-circuit currents for a shock generator, calculated according to equation (5), whose time constants are taken equal to the time constants of decay of the generator of breaking capacity TI-75, \(T''_d=0.105\) sec, \(T_a=0.11\) sec, \(x''_d=0.043\), are presented in Fig. 2.
In accordance with the curve of the resultant short-circuit current \(i_k\) (Fig. 2), the essence of arc-free commutation of the current of a shock generator according to the circuit under consideration is that almost the entire current of the first half-wave is passed through the mechanical contact apparatus, practically without energy losses in it, while the current of the second half-wave is artificially transferred, by means of a saturating reactor, into the valve shunting the contacts. In this case the transfer of current from the circuit with the contacts to the circuit with the valve occurs at the first passage of the current through zero, and the arc-
arc interruption of the circuit occurs during the second passage of the current through zero. During the flow in the valve of the current of the negative half-wave, the de-energized contacts of the mechanical apparatus open without an arc.
Fig. 2. Curves of e.m.f. and currents of a sudden short circuit.
For arc-free connection of the generator to the load \(L_{\mathrm{n}}\), it is necessary to open valve \(B_1\) at a positive voltage (the solid line for \(e\) in Fig. 3) and synchronously begin switching on the contact apparatus \(K\). If the operating time of apparatus \(K\) is less than the time interval \(t_2 - t_0\) (Fig. 3) and is equal to the time \(t_1 - t_0\), then at the instant \(t_1\) the contacts will come into contact. At the instant of initial contac—
Fig. 3. Magnitude of current in the various elements of the circuit:
\(i_{b1}\)—current through valve \(B_1\), \(i_{\mathrm{m}}\)—current through the mechanical contact apparatus, \(i_{b2}\)—current through valve \(B_2\).
After the contacts touch, the circuit with the valve is closed through the saturating closing reactor \(D_1\) and the contacts. During the remagnetization of reactor \(D_1\), under the action of the voltage drop across the conducting valve \(B_1\), the rate of change of the current in the circuit with the contacts is determined by the remagnetization current of the reactor (\(0.5\)—\(1\,a\)). If the contacts begin to touch at \(t=t_1\), then at \(t=t_2\) the remagnetization of the reactor will be completed, and the resistance of the reactor–contacts circuit will become small. During the time \(t_3-t_2\), the current is commutated from valve \(B_1\) into the circuit with the contacts. Thus, in this circuit the contacts switch on a de-energized circuit at low voltage, which ensures arc-free closing.
After the contacts close, the entire current of the half-wave, maximal in amplitude and duration, flows through the contact apparatus. Toward the end of this half-wave, i.e., at the instant \(t_4\), when the current is close to zero, the saturation reactor \(D_2\), made of magnetically soft steel and carrying a small remagnetization current, begins to remagnetize. Its inductance becomes comparable with the total inductance of the circuit (the sum of the generator leakage inductance and the load inductance).
As follows from Fig. 1, the remagnetization voltage of reactor \(D_2\) is applied to valve \(B_2\) in the forward direction. If valve \(B_2\) is opened at this moment, then the negative half-wave of the current, under the action of the remagnetization voltage, will be taken over by the circuit with valve \(B_2\), and the entire current of this half-wave will pass through valve \(B_2\). The contact apparatus, connected in parallel with valve \(B_2\), will remain de-energized for the entire time of the negative half-wave and therefore can be opened without an arc.
When the current in the valve passes through zero at \(t=t_6\), valve \(B_2\) will block the circuit; the generator voltage will be restored on the contacts and on the valve, but the electric strength of the gap between the contacts, which have opened without an arc, is high; therefore the gap cannot be broken down by the restored voltage. Thus, the generator proves to be disconnected from the load.
When current passes through valve \(B_2\), a voltage equal to the voltage drop across the valve, i.e., approximately \(20\,v\), is applied to reactor \(D_2\). The flux linkage of the reactor, equal to the product of this voltage \(U_v\) by the time interval \(\Delta t\) from the beginning of the negative half-wave to the instant the contacts open, is small, which determines the small dimensions of reactor \(D_2\):
\[ SW=\frac{u_v\cdot \Delta t}{\Delta B}=\frac{\psi}{\Delta B}, \]
where
\(S\) — cross section of the reactor magnetic core,
\(W\) — number of turns of its winding,
\(\psi\) — flux linkage of the reactor,
\(\Delta B\) — change in induction during remagnetization of the reactor.
The average, rms, and maximum values of the current of the negative half-wave are considerably less than the corresponding values of the current of the positive half-wave, which determines the comparatively low power of the valve (or group of valves) carrying the current of the negative half-wave and ensuring arc-free disconnection of the contact apparatus. If, for example, one ignitron IVS-200/15 with an average current of \(200\,a\) is used as valve \(B_2\), then with the aid of the circuit considered it is possible to disconnect a current with an amplitude of the first half-wave of about \(200\,ka\) at a voltage amplitude of \(15\,kv\). It should be noted that the valves must be rated for the full generator voltage.
If necessary, for example when using the circuit under consideration to excite controlling magnetic fields in charged-particle accelerators having a steel magnetic core, the negative half-wave of the current can be used to demagnetize the electromagnet.
Taking into account that the operating time of fast-acting contact devices can at present be brought to approximately \((3—3.5)\cdot 10^{-3}\) sec, use of the circuit will be most expedient at a generator emf frequency of no more than 50 cps, since in this case, with the duration of the first half-wave of the current approximately \((16—18)\cdot 10^{-3}\) sec, the duration of the second half-wave is \((4 \div 6)\cdot 10^{-3}\) sec, which is quite sufficient for opening the circuit by means of a contact device.
REFERENCES
- M. P. Kostenko. Electrical Machines. Special Part, GEI, 1949.
- V. V. Ivashin, G. A. Sipailov. Switching the current of an alternating-current high-power generator during the design of electrical machines, Interuniversity Collection of Papers, Issue 3, Novosibirsk, 1963.
- V. V. Ivashin, G. A. Sipailov. Contactless disconnection of large currents. Elektrotekhnika, No. 9, 1964.