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.) [email protected]

Abstract- This paper mainly focuses on supplying low The value of current i, in the circuit is voltage continuous load from an electrostatic generator so i (t)=lo e-tl(R.Ceq) (I) that it can widely be used in the day to day domestic and l industrial applications. Also, it will be discussing limitations where 10 = V HIR. & and drawback of electrostatic generation and important c,=(1/C r+ 1/C 2yl (2) consideration for dealing with this generation. It will be including a novel circuit which is very compatible in order to Also, lICs) =V H/{s(R+lIsCeq)} get the low reduced voltage and finally demonstrating the The value of Capacitor voltage C2 will be performance of proposed circuit using simulation model. VC2(s) = l\(s)1 (sC2) (3) Keywords: continuous load, Electrostatic generator, PI controller VC2(s) = V HI {s(R+ 1/sC eq)}· 1/(sC 2) VC2(s) = V HI Ci {S2 . (R+ lIsC eq)} I. INTRODUCTION = V H' Ce/C2· lI{S (S +1IRC eq)} An electrostatic generator or electrostatic machine is a v clt) = V H' C glC • [1- e-tl(R.Ceq)] (4) mechanical device that produces static electricity or electricity e 2 at high voltage, however, at low power levels. The knowledge of Ifvalue of t « RC eq: VC2(t) = 0 static electricity was discussed in mid sixteenth century but eq: merely as an interesting and mystifying phenomenon and often Ifvalue oft» RC VC2(t)=VH. Ceq/C2

confused with magnetism. By the end of 17th century, The variation of voltage across capacitor C2 is shown researchers had developed practical means of generating in the Fig 2 for the values used for model. From this plot it electricity by friction , but the development of electrostatic 5 is seen that the low voltage (500 V from 10 V source) can machine didn't begin in earnest until the 18th century, when they became fundamental instrument in the studies about the new be obtained by selecting the suitable values of C, and C2 science of electricity. and keeping the time constant ofthe series combination to be small. However the final voltage across the load shall II. MODELLING OF AN ELECTROSTATIC also depend on the rate at which the charge is removed GENERATOR from the capacitor C2 at which low voltage is obtained.

The electrostatic generator can be modelled as high voltage I I I I I I I I I I ------T ------., ------,------r ------T ------source and a switch in series with it. The duty cycle of this switch I I , I I I , I I I shall actually determine the rate at which charge is collected at I I I I I I I I , its electrodes. This means if electrostatic generator is having 450 ------+ ------~ ------,------" ------+ ------I I I I I I I I I I higher capacity it shall have higher voltage and high duty cycle I I I , I I I I I I , I I , • maybeused. J!l ------~------:------:------~------~------, I I I I ~ I I I I • From Fig. 1 we can easily observe that the high voltage VH a , I I I , > I I I I I I I I I I can be divided among two capacitances. We shall keep the value 250 ------T ------i ------,------r ------T ------, , I , I , , , I I of resistance R to be very small to have very small time constant. , , I , I I I I I I I I I , I This will ensure the rapid charging of capacitors and the voltage ------T ------,------,------r ------T ------I I I , I I , , , , across capacitor C2 can be determined as follows. , , ,I ,I ,I , , I , I 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 for converting the high voltage to low voltage of an Fig.l The model showing electrostatic generator voltage electrostatic generator so it can be used as day to day division across two capacitors. purpose.

NIET Journal of Engineering & Technology, Vol. 1, Issue 2, 2013 25 C. Modelling of PI Controller Novel circuit Continuous Mechanical••••• Electrostatic •••••• for reduction of - low·voltage,... In PI controller the actual current I'Clln]is compared with the reference current Ire In]and the resulting error in the mput generator voltage level load r* Performation current, e'ln]is calculated at nth sampling instant as: evaluation (5) Fig (a): Block diagram representation supplying LVCL from electrostatic generator. The magnitude of sign may be positive or negative A. Proposed Circuit depending upon the actual current and its reference value. The output of the PI controller at the nth sampling instant The modification of this basic circuit just described is: has been carried out to achieve quick charging of Tin}= T[n.']+ K, . ( e'[n]- e'[n.l]) + K . e'["] (6) capacitor C2 and its controlled discharging to obtain desired constant power. This circuit is given in Fig.3(a). Where K, and K; are the proportional and integral gains of

82 the speed controller respectively. The output of speed controller must be saturated based on the rating of system as follows:

r;= Tmox ifT[n?Tm,x ~~TCI DI Tin]= -r., ifT[n]< -r., + Ve2 R 8* = T[nlI<, Where, Tin]is the reference duty cycle for nth instant Tln.l]is the reference duty cycle for previous instant Fig.3(a) The proposed circuit to supply low-voltage load at constant current. K, is proportional gain

The method of fast charging of capacitor C2 and its I<, is integral gain controlled discharging to obtain desired constant power is e'[n] is current error at this instant achieved by controlling the switch S, and S2. The e'[n-l lis current error of previous instant 0 operation of switch S, and S2is kept 180 out of phase. For I<, is saturation constant of system the first part of cycle, charge is transferred from 8* is the reference duty cycle electrostatic generator V H to capacitor C2. During second part of the cycle, charge from C2is transferred to the load. D. Modeling of Pulse generator An inductor is put in series with load resistance to have In duty cycle obtained from PI controller is compared constant current. The diode D, shall prevent flow ofload with a saw-tooth carrier waveform in such a way that the current in reverse direction while diode D2 is a free- modulation index is always less than or equal to 1. wheeling diode. When S2 is open, D2 provides an The modeling of saw-tooth carrier is an important aspect alternative path for load-current to discharge the stored for Pulse generator. The magnitude, "mag" of triangular energy in inductor. carrier is found at an instant "t" as follows: B. Control Strategy mag=amp_tri * K A current controller is designed to obtain the value of where, amp_tri is the amplitude of triangular carrier wave, desired current I

If (8<=mag_tri) SF=O If (8)mag_tri) SF=l Ref. Current Pulse I,d Pulse to s, Generator 1. Simulation of Circuit {High if +ve, Low rf-vc} A simulation model has been developed using Actual current. MATLAB software employing its SIMULINKI ILOAD SirnPowerSystem Toolboxes. This model is shown in Fig. 3(b) Pulse generation for controlling duty cycle ofS2. FigA. 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 be 20 . seen in Fig.5 EJ 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 , , , ' , , , . , ' ,

Fig. 4. MATLAB model for simulation of developed configuration for ):~lI. getting continuous output power at reduced voltage. 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 output power obtained with time according to command signals (b) Voltage waveform across the resistive load (c)Variation in load current as per command (d) Variation in voltage across output capacitor.

Product VI. CONCLUSIONS It has been observed that the proposed system is capable S\~tch of converting high voltage into low voltage and it supplies Out l

Fig. 5 The controller Model employing MATLAB. (a) The time constant for charging the capacitor C2 should be very small. This shall require capacitors which have very low resistance of their own and its leads. V. RESULTS AND DISCUSSION (b) The mechanism for generating charge at very high Fig.6 shows the simulation results obtained from rates (of the order of few micro-seconds) will depend developed model. The variation in output power obtained on electrostatic generator design, which may actually with time according to command signals along with the be complex and bulky. voltage waveform across the resistive load, variation in (c) The large value voltage will be acting across capacitor load current as per command and variation in voltage C" therefore, more number of larger capacitance across output capacitor can be seen. It can be seen that the variations in waveforms are according to the command capacitors are to be placed in series. Moreover, the signal. high level of insulation requirement will be there in this part. Initially the load current is 50 A which changes to 100A at OAms and at Ims it settles to 20 A, as per the (d) To have high frequency switching MOSFETs must be desired command signal. Also, the power is 5kW, 17kW employed. Protection of MOSFET for S, will be and 2kW at those instants. Moreover, it is observed that the crucial.

voltage across load and capacitor C2 remains less than It is concluded that by meeting the above stated 600V at all instants. This has established the validity of constraints an electrostatic generator can be successfully proposed model and control strategy. employed for low-voltage, continuous loads.

NIET Journal of Engineering & Technology, Vol. 1, Issue 2, 2013 27 REFERENCES Ankita Sagar is pursuing B.Tech in [I] M. E. Valkenberg, Network Analysis, PHI EEE field from Noida Institute of [2] D Roy Choudhury, etworks and Systems, New Age International Engineering & Technology college Publishers New Delhi 2004. which is affiliated to Ll.P Technical [3] James W.Nilsson and Susan A. Riedel, Electric Circuits, Pearson University. At present she is college Prentice Hall, 2008. ambassador of Think Ware Society. She also participated in Cognizance at IIT- Himanshu Tiwari is pursuing B.Tech Roorkee. She received awards, prizes and certificates in EEE field from Noida Institute of from the college for being active in co-curricular Engineering & Technology college activities. which is affiliated to Ll.P, Technical Monika Agarwal is pursuing B.Tech in University. His area of interest is control EEE field from Noida Institute of system and robotics. At present he is Engineering & Technology college continuing his work in this field. At which is affiliated to Ll.P, Technical present he is college ambassador of Think Ware Society. University. Her area of interest is He also participated in Cognizance at IIT- Roorkee. He microcontroller based applications and received number of awards, prizes and certificates from robotics. Now she is focussing her work the college for being active in co-curricular activities. in the field for genetic algorithms.

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