18 High Voltage Engineering:Fundamentals equal amounts g to C....C2.C and g to the load during T.Therefore, C can only be charged up to a maximum voltage of (VC)max =(VC)max- ng Cn As the capacitor C will be charged up to this voltage minus (n-1)q/c1 etc.,one can easily form the general rules for the total voltage drop at the smoothing stack C1...Cn If all the capacitors within the cascade circuit are equal or C1=C=C2=C.=...Cn=Cr=C, then the voltage drops across the individual stages are △Vm=(q/c)n; △Vn-1=(q/c)[2n+(m-1小： △V1=(q/c)2n+2(n-1)+2(n-2)+..+2×2+1]. (2.8) By summation,and with g=1/f,we find (2.9) Thus the lowest capacitors are most responsible for the total A Vo as is the case of the ripple,egn (2.7).However,only a doubling of C is convenient,since this capacitor has to withstand only half the voltage of the other capacitors; namely Vmax.Therefore,AVn decreases by an amount of 0.5 ng/c,which reduces AV of every stage by the same amount,thus n times.Hence, 2n3 (2.10) For this case and n>4 we may neglect the linear term and therefore approx- imate the maximum output voltage by Vom兰2nVmx-f元× 2n3 (2.11) For a given number of stages,this maximum voltage or also the mean value Vo =(Vomax-8V)will decrease linearly with the load current I at constant
18 High Voltage Engineering: Fundamentals equal amounts q to C0 n2,...C0 2, C0 1 and q to the load during T. Therefore, C0 n 1 can only be charged up to a maximum voltage of VC0 n 1 max D 2Vmax nq C0 n nq Cn D VCn max nq Cn . As the capacitor C0 n 1 will be charged up to this voltage minus n 1q/c0 n 1, etc., one can easily form the general rules for the total voltage drop at the smoothing stack C1 ...Cn If all the capacitors within the cascade circuit are equal or C1 D C0 1 D C2 D C0 2 D ...Cn D C0 n D C, then the voltage drops across the individual stages are Vn D q/cn; Vn 1 D q/c[2n C n 1]; . . . V1 D q/c[2n C 2n 1 C 2n 2 C ... C 2 ð 2 C 1]. 2.8 By summation, and with q D I/f, we find V0 D 1 fC 2n3 3 C n2 2 n 6 . 2.9 Thus the lowest capacitors are most responsible for the total V0 as is the case of the ripple, eqn (2.7). However, only a doubling of C0 n is convenient, since this capacitor has to withstand only half the voltage of the other capacitors; namely Vmax. Therefore, Vn decreases by an amount of 0.5 nq/c, which reduces V of every stage by the same amount, thus n times. Hence, V0 D 1 fC 2n3 3 n 6 . 2.10 For this case and n ½ 4 we may neglect the linear term and therefore approximate the maximum output voltage by V0 max ¾D 2nVmax I fC ð 2n3 3 . 2.11 For a given number of stages, this maximum voltage or also the mean value V0 D V0 max υV will decrease linearly with the load current I at constant
Generation of high voltages 19 frequency,which is obvious.For a given load,however,Vo may rise initially with the number of stages n,but reaches an optimum value and even decreases if n is too large.Thus-with respect to constant values of I Vmax,f and C-the highest value can be reached with the 'optimum'number of stages, obtained by differentiating eqn(2.11)with respect to n.Then max.fC (2.12) For a generator with Vmax 100kV,f =500 Hz,C=7uF and I =500 mA, nop=10.It is,however,not desirable to use the optimum number of stages, as then Vomax is reduced to 2/3 of its maximum value (2nVmax).Also the voltage variations for varying loads will increase too much. The application of this circuit to high power output,which means high prod- ucts of IVo is also limited by egns (2.9)and (2.11),in which again the large influence of the product fC can be seen.An increase of supply frequency is in general more economical than an increase of the capacitance values; small values of C also provide a d.c.supply with limited stored energy,which might be an essential design factor,i.e.for breakdown investigations on insu- lating materials.A further advantage is related to regulation systems,which are always necessary if a stable and constant output voltage Vo is required. Regulation can be achieved by a measurement of Vo with suitable voltage dividers (see Chapter 3,section 3.6.4)within a closed-loop regulation system, which controls the a.c.supply voltage V(t).For fast response,high supply frequencies and small stored energy are prerequisites. For tall constructions in the MV range,the circuit of Fig.2.3(a)does not comprise all circuit elements which are influencing the real working condi- tions.There are not only the impedances of the diodes and the supply trans- former which have to be taken into consideration;stray capacitances between the two capacitor columns and capacitor elements to ground form a much more complex network.There are also improved circuits available by adding one or two additional 'oscillating'columns which charge the same smoothing stack.This additional column can be fed by phase-shifted a.c.voltages,by which the ripple and voltage drop can further be reduced.For more details see reference 8. Cascade generators of Cockcroft-Walton type are used and manufactured today worldwide.More information about possible constructions can be found in the literature(.10)or in company brochures.The d.c.voltages produced with this circuit may range from some 10kV up to more than 2 MV,with current ratings from some 10uA up to some 100 mA.Supply frequencies of 50/60 Hz are heavily limiting the efficiency,and therefore higher frequencies up to about 1000 Hz(produced by single-phase alternators)or some 10kHz(produced by electronic circuits)are dominating
Generation of high voltages 19 frequency, which is obvious. For a given load, however, V0 may rise initially with the number of stages n, but reaches an optimum value and even decreases if n is too large. Thus – with respect to constant values of I Vmax, f and C – the highest value can be reached with the ‘optimum’ number of stages, obtained by differentiating eqn (2.11) with respect to n. Then nopt D VmaxfC I 2.12 For a generator with Vmax D 100 kV, f D 500 Hz, C D 7 µF and I D 500 mA, nopt D 10. It is, however, not desirable to use the optimum number of stages, as then V0 max is reduced to 2/3 of its maximum value 2nVmax. Also the voltage variations for varying loads will increase too much. The application of this circuit to high power output, which means high products of IV0 is also limited by eqns (2.9) and (2.11), in which again the large influence of the product fC can be seen. An increase of supply frequency is in general more economical than an increase of the capacitance values; small values of C also provide a d.c. supply with limited stored energy, which might be an essential design factor, i.e. for breakdown investigations on insulating materials. A further advantage is related to regulation systems, which are always necessary if a stable and constant output voltage V0 is required. Regulation can be achieved by a measurement of V0 with suitable voltage dividers (see Chapter 3, section 3.6.4) within a closed-loop regulation system, which controls the a.c. supply voltage Vt. For fast response, high supply frequencies and small stored energy are prerequisites. For tall constructions in the MV range, the circuit of Fig. 2.3(a) does not comprise all circuit elements which are influencing the real working conditions. There are not only the impedances of the diodes and the supply transformer which have to be taken into consideration; stray capacitances between the two capacitor columns and capacitor elements to ground form a much more complex network. There are also improved circuits available by adding one or two additional ‘oscillating’ columns which charge the same smoothing stack. This additional column can be fed by phase-shifted a.c. voltages, by which the ripple and voltage drop can further be reduced. For more details see reference 8. Cascade generators of Cockcroft–Walton type are used and manufactured today worldwide. More information about possible constructions can be found in the literature9,10 or in company brochures. The d.c. voltages produced with this circuit may range from some 10 kV up to more than 2 MV, with current ratings from some 10 µA up to some 100 mA. Supply frequencies of 50/60 Hz are heavily limiting the efficiency, and therefore higher frequencies up to about 1000 Hz (produced by single-phase alternators) or some 10 kHz (produced by electronic circuits) are dominating.
20 High Voltage Engineering:Fundamentals Also for this kind of generators,voltage reversal can be performed by a reversal of all diodes.For some special tests on components as used for HVDC transmission,a fast reversal of the d.c.voltages is necessary.This can be done with special mechanical arrangements of the diodes,as published by W.Hauschild et al.(50.51)Figure 2.5 shows such a unit for a d.c.voltage up to Figure 2.5 A Cockroft-Walton d.c.generator for voltages up to 900 kV/10 mA with fast polarity reversal at ETH Zurich(courtesy HIGH VOLT,Dresden,Germany)
20 High Voltage Engineering: Fundamentals Also for this kind of generators, voltage reversal can be performed by a reversal of all diodes. For some special tests on components as used for HVDC transmission, a fast reversal of the d.c. voltages is necessary. This can be done with special mechanical arrangements of the diodes, as published by W. Hauschild et al. 50,51 Figure 2.5 shows such a unit for a d.c. voltage up to Figure 2.5 A Cockroft–Walton d.c. generator for voltages up to 900 kV/10 mA with fast polarity reversal at ETH Zurich (courtesy HIGH VOLT, Dresden, Germany)
Generation of high voltages 21 900kV.Here,also the general structure of the Cockroft-Walton circuit can be identified. Voltage multiplier with cascaded transformers The multiple charge transfer within the cascade circuit of the Cock- croft-Walton type demonstrated the limitations in d.c.power output.This disadvantage can be reduced if single-or full-wave rectifier systems,each having its own a.c.power source,are connected in series at the d.c.output only.Then the a.c.potentials remain more or less at d.c.potentials.Although there are many modifications possible,the principle that will be demonstrated here is based upon a very common circuit,which is shown in Fig.2.6.Every transformer per stage consists of an I.v.primary (1),h.v.secondary(2),and Lv. tertiary winding(3),the last of which excites the primary winding of the next upper stage.As none of the h.v.secondary windings is on ground potential, a d.c.voltage insulation within each transformer (T1,T2,etc.)is necessary, which can be subdivided within the transformers.Every h.v.winding feeds two half-wave rectifiers,which have been explained before.Although there Further states (up to n) 3 风人风 Stage 2 n.2V 3 人人人 Stage 1 Figure 2.6 D.C.cascade circuit with cascaded transformers
Generation of high voltages 21 900 kV. Here, also the general structure of the Cockroft–Walton circuit can be identified. Voltage multiplier with cascaded transformers The multiple charge transfer within the cascade circuit of the Cockcroft–Walton type demonstrated the limitations in d.c. power output. This disadvantage can be reduced if single- or full-wave rectifier systems, each having its own a.c. power source, are connected in series at the d.c. output only. Then the a.c. potentials remain more or less at d.c. potentials. Although there are many modifications possible, the principle that will be demonstrated here is based upon a very common circuit, which is shown in Fig. 2.6. Every transformer per stage consists of an l.v. primary (1), h.v. secondary (2), and l.v. tertiary winding (3), the last of which excites the primary winding of the next upper stage. As none of the h.v. secondary windings is on ground potential, a d.c. voltage insulation within each transformer (T1, T2, etc.) is necessary, which can be subdivided within the transformers. Every h.v. winding feeds two half-wave rectifiers, which have been explained before. Although there Further states (up to n) Stage 2 Stage 1 3 2 1 n.2V 1 ∼ 3 2 T1 T2 V Figure 2.6 D.C. cascade circuit with cascaded transformers
22 High Voltage Engineering:Fundamentals are limitations as far as the number of stages is concerned,as the lower trans- formers have to supply the energy for the upper ones,this circuit,excited with power frequency,provides an economical d.c.power supply for h.v.testing purposes with moderate ripple factors and high power capabilities. The 'Engetron'circuit(Deltatron) A very sophisticated cascade transformer HVDC generator circuit was described by Enge in a US Patent.Although such generators might be limited in the power output up to about 1 MV and some milliamperes,the very small ripple factors,high stability,fast regulation and small stored energies are essential capabilities of this circuit. The circuit is shown in Fig.2.7.It consists primarily of a series connection of transformers,which do not have any iron core.These transformers are coupled by series capacitors C,which compensate most of the stray inductance Termination HV d.c.-output Further stages Module Stage 2 Cockcroft-Walton multipliers Stage 1 Oscillator (50...100kc/s) Figure 2.7 The 'Engetron'or Deltatron principle
22 High Voltage Engineering: Fundamentals are limitations as far as the number of stages is concerned, as the lower transformers have to supply the energy for the upper ones, this circuit, excited with power frequency, provides an economical d.c. power supply for h.v. testing purposes with moderate ripple factors and high power capabilities. The ‘Engetron’ circuit (Deltatron) A very sophisticated cascade transformer HVDC generator circuit was described by Enge in a US Patent.11 Although such generators might be limited in the power output up to about 1 MV and some milliamperes, the very small ripple factors, high stability, fast regulation and small stored energies are essential capabilities of this circuit. The circuit is shown in Fig. 2.7. It consists primarily of a series connection of transformers, which do not have any iron core. These transformers are coupled by series capacitors Cs which compensate most of the stray inductance Termination HV d.c. − output Further stages Module Stage 2 Stage 1 Cockcroft−Walton multipliers Cs Cp ∼ Oscillator (50 . . . 100 kc/s) Figure 2.7 The ‘Engetron’ or Deltatron principle