Method for voltage control in charge circuit of electric discharge installations with two capacitors under nonzero initial conditions Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

Theoretical Electrical Engineering and Electrophysics

UDC 621.3.072 doi: 10.20998/2074-272X.2018.5.07

N.I. Suprunovska, M.A. Shcherba

METHOD FOR VOLTAGE CONTROL IN CHARGE CIRCUIT OF ELECTRIC DISCHARGE INSTALLATIONS WITH TWO CAPACITORS UNDER NONZERO INITIAL CONDITIONS

Purpose. To analyze the transient processes in the charge circuit of electric discharge installations with two capacitors, taking into account the change in the initial conditions of such processes (initial voltage on the capacitors and the initial current in the charge circuit) as well as to develop the method for charge voltage control of such installations using purposeful change of these initial conditions. Methodology. We have applied the concepts of theoretical electrical engineering, the principles of theory of electrical circuits, and mathematical simulation in the software package MathCAD 12. Results. We have obtained analytical expressions and graphical dependencies establishing a quantitative relationship between the value of the maximum charge voltage of an electric discharge installation and the values of the initial voltage on its capacitors and the initial current in the circuit. This allows us to propose the method for the charge voltage control of electric discharge installations with two reservoir capacitors, using a purposeful change in their initial voltages and initial current in the charge circuit. Originality. For the first time, we have found that the charge voltage of the installation can be controlled using two influence mechanisms - either changing the initial current in the charge circuit (by interrupting the transient process of the first capacitor charge at a certain time) or using a nonzero initial voltage on the charged second capacitor. In this case the charge voltage can be varied by 2 times. Practical value. The use of this method makes it possible to obtain discharge pulses of complex shape in the technological load, since the maximum charge voltages of the first capacitor and second one can differ by a factor of 1.5. References 10, figures 4.

Keywords: electric discharge installation, capacitor charge, charge voltage, transients, nonzero initial conditions.

Цель. Целью статьи является анализ переходных процессов в зарядной цепи электроразрядных установок с двумя конденсаторами с учетом изменения начальных условий протекания таких процессов (начального напряжения на конденсаторах и начального тока в зарядной цепи), а также разработка метода регулирования зарядного напряжения таких установок, используя целенаправленное изменение указанных начальных условий. Методика. Для проведения исследований использовались положения теоретической электротехники, теория электрических цепей, математическое моделирование в программном пакете MathCAD 12. Результаты. Получены аналитические выражения и графические зависимости, устанавливающие количественную связь между значением максимального зарядного напряжения установок и величинами начального напряжения на ее конденсаторах и начального тока в цепи. Предложен метод регулирования напряжения заряда электроразрядных установок с двумя накопительными конденсаторами, использующий целенаправленное изменение их начальных напряжений и начального тока в зарядной цепи. Научная новизна. Установлено, что напряжение заряда установки можно регулировать, используя два механизма влияния - как изменяя начальный ток в зарядной цепи (прерыванием переходного процесса заряда первого конденсатора в определенный момент времени), так и используя ненулевое начальное напряжение на заряжаемом втором конденсаторе. При этом напряжение заряда можно изменять в 2 раза. Практическое значение. Использование данного метода позволяет получить разрядные импульсы сложной формы в технологической нагрузке, поскольку максимальные напряжения заряда первого и второго конденсаторов могут отличаться в 1,5раза. Библ. 10, рис. 4.

Ключевые слова: электроразрядная установка, заряд конденсатора, зарядное напряжение, переходные процессы, ненулевые начальные условия.

Introduction. Electric discharge installations (EDIs) with capacitive energy storage devices (reservoir capacitors) have found wide application in the development of new technologies for electric pulse treatment of materials and media (in particular, electro-erosion, electro-hydraulic, magneto-pulse treatments, etc.) [1-8].

The use of parallel connection of capacitors with different capacities is one of the most common methods for control of the EDIs dynamic parameters.

So, for example, several capacitors with different capacities, which are discharged through a load with a time delay, are used in many schemes of electric discharge installations in order to control the shape of the pulse currents in the load [1, 2, 9]. In the installations containing semiconductor DC voltage shapers with filtering capacitors of high-capacity, additional dosing capacitors are used to more accurately control the energy in the load [1, 7, 8, 10]. Additional low-capacity dosing capacitors are also used in the input circuits of semiconductor converters to stabilize

the power consumed by them from the electrical network [2, 3, 5, 10].

It should be noted that in most of considered electric discharge installations, the initial charge voltages and the final discharge voltages of their capacitors were equal to zero [1, 3-6].

At the same time, the reservoir capacitor is not completely discharged in the EDIs for volumetric electro-spark dispersion (VESD) of metal granules in a dielectric liquid. The residual voltage of the capacitor is used as information for changing the voltage of the subsequent charge of the capacitor [7]. In these installations, the dependence of the resistance of the electric spark load on the magnitude and duration of the discharge current is used for parametric stabilization of the dispersion modes [7, 8].

If an oscillatory discharge of the capacitor through the load occurs and the capacitor is partially recharged to a reverse polarity voltage, then the negative feedback

© N.I. Suprunovska, M.A. Shcherba

of the subsequent charge voltage of the capacitor with its previous discharge voltage is realized in the installation. If an aperiodic discharge occurs, then a positive feedback between these voltages is realized. In fact, high-speed control and parametric stabilization of electrical technological modes is implemented in such installations [7, 8].

Thus, the change in the magnitude and sign of the initial voltage of the capacitor can be used to develop methods for high-speed control of energy in the capacitor, discharge pulse parameters, EDIs efficiency, as well as for parametric stabilization of discharge processes in a circuit with a nonlinear load [7, 8].

The solution of the problems of improving the energy characteristics of such EDIs is much more complicated when you change the initial and final conditions of the transients in circuits of reservoir capacitors that are part of such installations.

In addition, the analysis of transient processes with a nonzero initial current in the charging circuit of the EDIs with several reservoir capacitors has not been carried out previously.

Therefore, the purpose of this paper is to analyze the transient processes in the charge circuit of electric discharge installations for the VESD with two reservoir capacitors, taking into account the change in the initial conditions of such processes (initial capacitors voltage and the initial current in the charge circuit), as well as to develop the method for control of the charge voltage of such installations using purposeful change of these initial conditions.

As a typical example of such EDIs, we have considered the installation for electro-spark dispersion of conductive granules in a dielectric liquid, the charge circuit of which includes two reservoir capacitors.

Features of the capacitor charge when the initial current changes. The electric schematic diagram of the charge circuit of the EDI, where the transient processes are analyzed, is shown in Fig. 1.

Fig.1. Electric schematic diagram of the charge circuit of EDI with two reservoir capacitors

The capacitor C (Fig. 1) is charged from a shaper of direct voltage (SDV) with an output voltage USDV through a resistor R, thyristor commutator VT, and inductance coils L and L1. The thyristor VT1 was locked up to a certain time t = t1. There is an oscillatory charge of capacitor C in the charge circuit, since the parameters of the circuit elements (R, C, L, L1) were chosen in such a way as to realize high Q-factor of the circuit (Q > 10).

At time t = t1, when the charge voltage of the capacitor C becomes higher than the SDV voltage UC > USDV, the thyristor commutator VT1 is unlocked.

The capacitor C1 begins to charge from the SDV. We assume that in the general case there is some voltage on the capacitor C1 (U0Ci ^ 0) before starting its charge.

Since UC > USDV, then the capacitor C tries to discharge to the capacitor C1, however, the occurrence of reverse current in the circuit leads to the locking of the thyristor VT. Inductance L is needed to limit the reverse current in the circuit when the thyristor VT is locked.

Thus, there are two transient processes in the charge circuit of an EDI with two capacitors: the first process is the charge of the capacitor C from the SDV in the time interval 0 < t < t1 and the second process is the charge of the capacitor C1 from the SDV at t > t1.

In the analysis of transient processes we have assumed that the thyristors VT and VT1 are ideal switches (without energy losses and with instantaneous commutation), and the inductance value L is less by two orders of the inductance L1, therefore, value L can be ignored in the analysis of the first transient process.

Since the first transient is the ordinary oscillating charge of the capacitor C from the SDV under zero initial conditions, then we have analyzed in detail only the second transient process - the charge of the capacitor C1 from the SDV, which occurs under a nonzero initial conditions in voltage Uoc1 and in current I1 (due to the

first transient process and the presence of inductance in the circuit) after switching thyristor VT1.

The initial current I1 is determined by the known formulas for the oscillatory charge of the capacitor from a direct voltage source. The parameters of the charge circuit of the capacitor C1 (R, C1, L1) are also chosen so there was an oscillatory transient process.

Transient analysis of the capacitor charge under nonzero initial voltage and current conditions. The

initial time of the second transient process is t = t1 and we

*

denote it as t0 . The current time of this transient process,

denoted by t*, is defined as t* = t -11 = t -1* .

According to the second Kirchhoffs law the current in the SDV-R-VT1-C1-L1-SDV circuit (Fig. 1) is given by formula

i(t ) = \Usdv - «C1(f ) - %(f ))/R

(1)

here uCi (t ) and uL (t ) are the voltage drop across the

capacitor C1 and the inductance L1, respectively.

* * / * Since i(t ) = Ci duc1(t ) dt , and

* * / * 2 * / *2 uLi (t ) = Li di(t )/ dt = LCi d uc (t ) dt , then

equation (1) can be reduced to the form:

d uci (t ) R duci (t ) duci (t ) = USDV

■1 ~ i ~ = ~ . (2)

*2

dt* L1 dt L1C1 L1C1 Taking into account that in the general case there are the certain voltage Uoc1 ^ 0 on the capacitor C1 before

start of its charge and nonzero current of value I1 in the circuit (determined in the first transient process of charging the capacitor C), then we can write the solution of such a non-uniform equation in the form:

L1C1

L1C1

uc1 (t*) = USDV + [{P2 (t/QCj - USDV )(P2 - Pi)-

- V q Kif* + {/ C - p2 ( - Usdv )* * * / * Since /(t ) = Q duCi (t ) / dt , the expression for the

current in the charge circuit can be written as:

/(t*) = ( - Usdv)(ePlt* - ep2t* )/l (P2 - Pi)+ (4)

+ Ii(P2t* - PiePlt*)(P2 - Pi)• '

Since charge circuit parameters are selected so that the circuit has a high 0-factor, then there is an oscillatory transient process, and consequently the roots of the characteristic equation are conjugate complexes:

Pi = -R/2Li + jj1/LiCi - R2/4Li2 = -b + jm , P2 = -R/2Li - jj1/LiCi - R2/4Li2 = -b - jm ,

here m = ^1/LiCi - R2/4Li2 , b = R/2Li.

After substituting the values of p1 and p2 in (3) and

(4) and performing the transformations, we obtain

* *

expressions for uq (t ) and /(t ):

Uc1 (t*) = Usdv - bt* ((b/m -1J m • * • Q )sinmt* + *)

+ cos mt J

^ _hf^ 1/ i i \ • ^

/(t ) = e ((Ljm -/ib/m)sinmt + /jcosmi

(5)

. - (6)

here 7 = usdv - UQC1 •

The value of the current I1, which is the initial current for second transient (charge transient of the capacitor C1), we determine by the formula for the oscillatory charge of the capacitor C (in general having some initial voltage UQC) from the SDV:

Il = i(t = ti) = (Usdv - Uqc)e-btl • sinaitjLipi , (7)

1 =VVLiC-R2/4L2 •

of the initial current Ii: (Q, Iimax/2, 2Iimax/3, Ilmax) and the initial voltage U qC = 0.

Table i

The results of calculation of currents and charge voltages of capacitor C in the time interval from t ~ Tcharge/2 to t = Tcharge

tiiQ"6, s i(ti), A u(ti) = UCmax, V

2i7.9 Ii = -^imax = 335 469

337.9 Ii = 2Iimaxl3 = 223 824

366.9 Ii = Iimx/2 = i68 88i

444.4 Ii = 0 947

i(t), A for UQCi=0 450r

375

3QQ

225

i5Q

75

Ii Iimax

« f Ii = y 2Iimax/3

« • • • • fo •>\ •n r Ii =Iima x/2

• • • • ¡TV „for Ii = Q

*<•

\ i" V • • k'. \ •

here a>i =

Calculations and data processing for the charge circuit (Fig. i) with parameters Usdv = 500 V, L = 2-iQ"6 H, Li = 2-iQ"4 H, C = iQ"4 F, Ci = 4-iQ"5 F, R = 0.i Ohm we have performed using the software package MathCAD i2. As mentioned above, the inductance L is two orders of magnitude smaller than Li, so we did not take it into account when performing calculations.

Table i shows the results of the calculation of the first transient process (the currents in the charge circuit and the charge voltage of capacitor C in the time interval from t ~ Tchargel2 (when the current is Ii = Iimax) to t = Tcharge (when current Ii = 0). Here Tcharge is the charge duration of capacitor C. These results are required for further analysis.

Analysis of the results of Table i shows that interrupting the charging process of capacitor C, when the charge circuit current reaches values in the range Iimax - 0, we can change the control conditions of the charge voltage of the capacitor C, i.e. we can adjust the charge voltage (to perform so-called a tune-up) in the range of 7 - 50 %.

Fig. 2 represents the time dependence of the current

*

in the charge circuit of the EDI i(t ) for various values

—5 —4 -4 —4 —4 —4

0 5-10 5 1 -10 4 1.5-10 4 2-10 4 2.5-10 4 3-10 4

*

t , s

Fig. 2. The time variation in the charging current of capacitor C1 with initial voltage U0C1 = 0 at different initial circuit current values

As can be seen from Fig. 2, with a decrease in the value of the initial current /i the amplitude value of the current in the charge transient process of the capacitor C1 decreases, and the duration of current flow increases. In other words, the earlier the first transient is interrupted, the faster and with the higher currents the second one proceeds.

Fig. 3,a-c shows the time dependence of the voltage

*

uc1 (t ), and Table 2 represents the values of the

maximum charge voltage of the capacitor C1 for different initial current /1 (0, /imax/2, 2/1max/3, /1max) and initial voltage U0C1 (0, Udv/2, 2Usdv/3).

Analyzing dependences shown in Fig. 3 and the data in Table 2, we can conclude that with a decrease in the initial current /i, the maximum charging voltage of the capacitor Ci in the second transient process also decreases.

So if the initial current decreases from /imax to zero, the voltage value UCimax decreases by 30 % at U0C1 = 0

and by 47 % at U0C1 = 2Usdv/3 . Thus, the magnitude of

the initial voltage U0Ci also affects the value of UCimax ,

and with increasing U0Ci the voltage UCi max also

decreases.

For example, if the initial voltage U0q of the

capacitor C1 increases from zero to 2USDVI3 when the value of the current in the SDV-R-VT-C-L-L1-SDV circuit I1 = I1max, the value of the maximum charge voltage Uq max of the capacitor C1 decreases by 9 %, and at

current value I1 = 0 this voltage decreases by 32 %. In other words, the later the first charge transient of capacitor C is interrupted, and the higher initial voltage on capacitor C1, the lower its maximum charge voltage after

second transient.

* „

uCi (t ), V for U0C1 - 0 1500

1250

1000

750

500

250

* ''A ■ ■* ■* a

* * m~ /> // for I1 -

/ « * V X ^fc r I1 - T ^1max

« St i /. for I1 = 2 ^1max

Mor I1 = 0

> ■ J -S ■

15ckl

1250

1000

750

500

(t ), V for U0c - UsdvI2

* *

/ / •*" \

* ¿4 >' * » for 2 r, I1 = I1m

for I1 I1ma 3 1m x

^for I1 - 0 2

—5 —4 —4 —4 —4 —4

5-10 5 1 -10 4 1.5-10 4 2-10 4 2.5-10 4 3-10 4

t*, s

b

1500

1250

1000

750

500

«c1 (t* ), V for U 0c1 = 2Usdv /3

0

/

f * 4 for 2 I h - I1ma

for I1 for I1 --111 3 11 max

for ¡1 - 0 2 1ma

c t, s

Fig. 3. The change with time of the charge voltage uC1(t*) of the capacitor C1 at its various initial voltages and different initial values of the current in the circuit (0, I1maxI2, 2I1maxI3, I1max): a - for U0C1 = 0; b - for Uoa = Usdv/2; c - Uoa = 2Usdv/3

Fig. 4 represents the dependence of maximum voltage Uqmax on the initial current I1 for different

initial voltages U0C1 on the capacitor C1.

Table 2

Maximum charge voltage UCi max for different values I1 and U0q

V I1, 0 USDV/2 2Usdv/3

I1 = I1max 1349 1252 1234

I1 = 2I1maxI3 1163 1029 1001

I1 = I1max|2 1084 925 889

I1 = 0 966 733 655

U C1 max , V

0 50 100 150 200 250 300 350

I1, A

Fig. 4. The change in the maximum charge voltage uc1 max of

the capacitor C1 as a function of the magnitude of the initial current I1, at which the transient of charge C1 begins

As can be seen in Fig. 4, the charge voltage of the capacitor C1 can be controlled by changing the initial current in its charge circuit by means of varying the duration of the charge process of the capacitor C.

The charge voltage of the capacitor C1 can also be adjusted by changing its initial voltage before the start of the charge process. Of course, we can simultaneously use both methods for control of voltage Uq max. In this case,

the control range can be 655^1349 V, that is, the charge voltage can be changed by 2 times.

The charge voltage of the capacitor C1 can be almost 1.5 times higher than the charge voltage of the capacitor C (see Tables 1 and 2). This fact can be used to produce discharge pulses of complex shapes in spark load. Conclusions.

1. We have carried out the transient analysis in the charge circuit of the capacitors of electric discharge installation, taking into account the change in the initial conditions of such transients (initial voltage on the capacitors and the initial current in the charging circuit). As the results we have defined the analytical expressions for determining the current in the circuit and the capacitor voltage during its charge under nonzero initial current and voltage conditions.

2. From the formula for the capacitor charge voltage under nonzero initial conditions in such installations follows that it depends on two factors: the initial voltage of this capacitor and the value of the initial current in this transient process. The numerical experiment of capacitor charge under nonzero initial conditions has shown that the

0

t, s

a

250

0

250

0

5 4 4 4 4 4

0 5-10 5 1 -10 4 1.5 -10 4 2-10 4 2.5 -10 4 3-10 4

maximum capacitor voltage decreases both with increasing its initial voltage and with decreasing initial circuit current.

3. Based on the revealed dependencies, we proposed a method for charge voltage control of such installations by changing the initial current in the charge circuit (by interrupting the first transient at a certain time), and by using a nonzero initial voltage on the second charged capacitor. The difference in capacitors voltage of the installation can be used to produce discharge pulses of complex shape in the technological load.

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Received 22.05.2018

N.I. SuPrunovska1, Doctor of Technical Science, M.A. Shcherba1, Candidate of Technical Science, 1 The Institute of Electrodynamics of the NAS of Ukraine, 56, prospekt Peremogy, Kiev, 03057, Ukraine, phone +380 44 3662493,

e-mail: [email protected], [email protected]

How to cite this article:

Suprunovska N.I., Shcherba M.A. Method for voltage control in charge circuit of electric discharge installations with two capacitors under nonzero initial conditions. Electrical engineering & electromechanics, 20i8, no.5, pp. 39-43. doi: 10.20998/2074-272X.2018.5.07.