Supplying A Low-Voltage Continuous-Load From An Electrostatic Generator

Himanshu Tiwari', Monika Agarwal' & Ankita Sagar''.3Noida Institute of Engineering & Technology(NIET), Gr. Noida (V.P.)

lhimanshuti123@gmail.com

Abstract- This paper mainly focuses on supplying lowvoltage continuous load from an electrostatic generator sothat it can widely be used in the day to day domestic andindustrial applications. Also, it will be discussing limitationsand drawback of electrostatic generation and importantconsideration for dealing with this generation. It will beincluding a novel circuit which is very compatible in order toget the low reduced voltage and finally demonstrating theperformance of proposed circuit using simulation model.

Keywords: continuous load, Electrostatic generator, PIcontroller

I. INTRODUCTION

An electrostatic generator or electrostatic machine is amechanical device that produces static electricity or electricityat high voltage, however, at low power levels. The knowledge ofstatic electricity was discussed in mid sixteenth century butmerely as an interesting and mystifying phenomenon and oftenconfused with magnetism. By the end of 17th century,researchers had developed practical means of generatingelectricity by friction , but the development of electrostaticmachine didn't begin in earnest until the 18th century, when theybecame fundamental instrument in the studies about the newscience of electricity.

II. MODELLING OF AN ELECTROSTATICGENERATOR

The electrostatic generator can be modelled as high voltagesource and a switch in series with it. The duty cycle of this switchshall actually determine the rate at which charge is collected atits electrodes. This means if electrostatic generator is havinghigher capacity it shall have higher voltage and high duty cyclemaybeused.

From Fig. 1 we can easily observe that the high voltage VHcan be divided among two capacitances. We shall keep the valueof resistance R to be very small to have very small time constant.This will ensure the rapid charging of capacitors and the voltageacross capacitor C2 can be determined as follows.

Fig.l The model showing electrostatic generator voltagedivision across two capacitors.

The value of current i, in the circuit isi

l(t)=lo e-tl(R.Ceq) (I)

where 10 = V HIR. &c,=(1/C r+ 1/C 2yl (2)

Also, lICs) =V H/{s(R+lIsCeq)}

The value of Capacitor voltage C2 will beVC2(s) = l\(s)1 (sC2) (3)

VC2(s) = V HI {s(R+ 1/sC eq)}· 1/(sC 2)VC2(s) = V HI Ci {S2 . (R+ lIsC eq)}

= V H' Ce/C2· lI{S (S +1IRC eq)}vclt) = V H' CeglC2 • [1- e-tl(R.Ceq)] (4)

Ifvalue of t « RC eq: VC2(t) = 0Ifvalue oft» RC eq: VC2(t)=VH. Ceq/C2

The variation of voltage across capacitor C2 is shownin the Fig 2 for the values used for model. From this plot itis seen that the low voltage (500 V from 105 V source) canbe obtained by selecting the suitable values of C, and C2

and keeping the time constant ofthe series combination tobe small. However the final voltage across the load shallalso depend on the rate at which the charge is removedfrom the capacitor C2 at which low voltage is obtained.

I I I I I

I I I I I

- - - - - - - T - - - - - - - ., - - - - - - - -,- - - - - - - - r - - - - - - - T - - - - - - -

I I , I I

I , I I I

I I I I

I I I I ,450 ---- --+ - - - - - - - ~ - - - - - - - -,- - - - - - - - " - - - - - - - + - - - - - - -I I I I I

I I I I I

I I I , I

I I I I I

, I I , •

- - - - - - ~- - - - - - - -: - - - - - - - -:- - - - - - - - ~- - - - - - - ~- - - - - - -, I I I I

I I I I •

, I I I ,

I I I I I

I I I I I

- - - - - - T - - - - - - - i - - - - - - - -,- - - - - - - - r - - - - - - - T - - - - - - -, , I , I

, , , I I

, , I , I

I I I I I

I I I , I

- - - - - - - T - - - - - - - -,- - - - - - - -,- - - - - - - - r - - - - - - - T - - - - - --

I I I , II , , , ,

, , I I I, , , , ,, , I , I

J!l

~a

>250

500L-----~5----~10~----1~5----~0~----~5-----7.10

TIme (micro-seconds)

Fig.2 Variation of voltage across capacitor C2

III. PROBLEM FORMULATION

The aim of this paper is to build a novel circuit forconverting the high voltage to low voltage of anelectrostatic generator so it can be used as day to daypurpose.

NIET Journal of Engineering & Technology, Vol. 1, Issue 2, 2013 25

Novel circuit ContinuousMechanical ••••• Electrostatic •••••• for reduction of - low·voltage,...mput generator voltage level load Performation

evaluation

Fig (a): Block diagram representation supplyingLVCL from electrostatic generator.

A. Proposed Circuit

The modification of this basic circuit just describedhas been carried out to achieve quick charging ofcapacitor C2 and its controlled discharging to obtaindesired constant power. This circuit is given in Fig.3(a).

82~~TDICI

+ Ve2

R

Fig.3(a) The proposed circuit to supplylow-voltage load at constant current.

The method of fast charging of capacitor C2 and itscontrolled discharging to obtain desired constant power isachieved by controlling the switch S, and S2. Theoperation of switch S, and S2is kept 1800 out of phase. Forthe first part of cycle, charge is transferred fromelectrostatic generator VH to capacitor C2. During secondpart of the cycle, charge from C2is transferred to the load.An inductor is put in series with load resistance to haveconstant current. The diode D, shall prevent flow ofloadcurrent in reverse direction while diode D2 is a free-wheeling diode. When S2 is open, D2 provides analternative path for load-current to discharge the storedenergy in inductor.

B. Control Strategy

A current controller is designed to obtain the value ofdesired current I<erThe actual load current ILoad shall bemeasured and shall be fed back to the current controllerfor comparison and generation of command signal pulse.The control strategy is shown in Fig. 3(b)

Ref. CurrentI,d Pulse to s,Pulse

Generator{High if +ve,Low rf-vc}

Actual current.ILOAD

Fig. 3(b) Pulse generation for controlling duty cycle ofS2.

C. Modelling of PI Controller

In PI controller the actual current I'Clln]is compared withthe reference current Irer*In]and the resulting error in thecurrent, e'ln] is calculated at nth sampling instant as:

(5)

The magnitude of sign may be positive or negativedepending upon the actual current and its reference value.The output of the PI controller at the nth sampling instantis:

Tin}= T[n.']+ K, . ( e'[n]- e'[n.l]) + K . e'["] (6)

Where K, and K; are the proportional and integral gains ofthe speed controller respectively. The output of speedcontroller must be saturated based on the rating of systemas follows:

r;= Tmox

Tin]= -r.,ifT[n?Tm,x

ifT[n]< -r.,8* = T[nlI<,

Where, Tin]is the reference duty cycle for nth instant

Tln.l]is the reference duty cycle for previous instant

K, is proportional gain

I<, is integral gain

e'[n] is current error at this instante'[n-l lis current error of previous instantI<, is saturation constant of system

8* is the reference duty cycle

D. Modeling of Pulse generator

In duty cycle obtained from PI controller is comparedwith a saw-tooth carrier waveform in such a way that themodulation index is always less than or equal to 1.

The modeling of saw-tooth carrier is an important aspectfor Pulse generator. The magnitude, "mag" of triangularcarrier is found at an instant "t" as follows:

mag=amp_tri * K

where, amp_tri is the amplitude of triangular carrier wave,

K= modulus( t, T)I T for t between 0 & T

Where, T is time-period of triangular carrier wave

The switching function is generated from the duty cycle 8and saw-tooth carrier magnitude at any instant as follows:

If (8<=mag_tri)

If (8)mag_tri)

SF=O

SF=l

1. Simulation of Circuit

A simulation model has been developed usingMATLAB software employing its SIMULINKISirnPowerSystem Toolboxes. This model is shown inFigA. The analysis has been carried out using ODE23tb

26 NIET Journal of Engineering & Technology, Vol. 1, Issue 2, 2013

continuous solver. The details of controller model can beseen in Fig.5

EJ

Fig. 4. MATLAB model for simulation of developed configuration forgetting continuous output power at reduced voltage.

Product

S\~tchOut l<lrv

PICootroler

Fig. 5 The controller Model employing MATLAB.

V. RESULTS AND DISCUSSION

Fig.6 shows the simulation results obtained fromdeveloped model. The variation in output power obtainedwith time according to command signals along with thevoltage waveform across the resistive load, variation inload current as per command and variation in voltageacross output capacitor can be seen. It can be seen that thevariations in waveforms are according to the commandsignal.

Initially the load current is 50 A which changes to100A at OAms and at Ims it settles to 20 A, as per thedesired command signal. Also, the power is 5kW, 17kWand 2kW at those instants. Moreover, it is observed that thevoltage across load and capacitor C2 remains less than600V at all instants. This has established the validity ofproposed model and control strategy.

20 .

600r wj j......,www;www,.www:mm'::::nl~>:3 400 ··········1···········r···········f···········1-···--------r···········r··· ~

200 j ~ ~ j ~ ~ j .o 'ii . , ; ,

:r~+=f·ltt'T.() .

250, , . , ' ,, , . , ' ,

):~lI.50 ··--···---1········----!---- --f----·-·····r···········1····\:.·;:;···~··+····:.:.,;.;.;c;:,;.;.;.·+-!.;;..;··4'

°O~---2~---7----7---~8----~--~1.~2--~1.~4~Time (ms)

Fig.6. Figure showing simulation results -(a) variation in outputpower obtained with time according to command signals (b) Voltagewaveform across the resistive load (c)Variation in load current as per

command (d) Variation in voltage across output capacitor.

VI. CONCLUSIONS

It has been observed that the proposed system is capableof converting high voltage into low voltage and it suppliescontinuous constant current to load. Such a system is verysuitable for controlled heating applications supplied fromelectrostatic generator.

We must ensure following conditions in the system:

(a) The time constant for charging the capacitor C2 shouldbe very small. This shall require capacitors whichhave very low resistance of their own and its leads.

(b) The mechanism for generating charge at very highrates (of the order of few micro-seconds) will dependon electrostatic generator design, which may actuallybe complex and bulky.

(c) The large value voltage will be acting across capacitorC" therefore, more number of larger capacitancecapacitors are to be placed in series. Moreover, thehigh level of insulation requirement will be there inthis part.

(d) To have high frequency switching MOSFETs must beemployed. Protection of MOSFET for S, will becrucial.

It is concluded that by meeting the above statedconstraints an electrostatic generator can be successfullyemployed for low-voltage, continuous loads.

NIET Journal of Engineering & Technology, Vol. 1, Issue 2, 2013 27

REFERENCES[I] M. E. Valkenberg, Network Analysis, PHI

[2] D Roy Choudhury, etworks and Systems, New Age InternationalPublishers New Delhi 2004.

[3] James W.Nilsson and Susan A. Riedel, Electric Circuits, PearsonPrentice Hall, 2008.

Himanshu Tiwari is pursuing B.Techin EEE field from Noida Institute ofEngineering & Technology collegewhich is affiliated to Ll.P, TechnicalUniversity. His area of interest is controlsystem and robotics. At present he iscontinuing his work in this field. At

present he is college ambassador of Think Ware Society.He also participated in Cognizance at IIT- Roorkee. Hereceived number of awards, prizes and certificates fromthe college for being active in co-curricular activities.

Ankita Sagar is pursuing B.Tech inEEE field from Noida Institute ofEngineering & Technology collegewhich is affiliated to Ll.P TechnicalUniversity. At present she is collegeambassador of Think Ware Society. Shealso participated in Cognizance at IIT-

Roorkee. She received awards, prizes and certificatesfrom the college for being active in co-curricularactivities.

Monika Agarwal is pursuing B.Tech inEEE field from Noida Institute ofEngineering & Technology collegewhich is affiliated to Ll.P, TechnicalUniversity. Her area of interest ismicrocontroller based applications androbotics. Now she is focussing her work

in the field for genetic algorithms.

28 NIET Journal of Engineering & Technology, Vol. 1, Issue 2, 2013