energies

Article

A Novel Design of Static Electrostatic Generator forHigh Voltage Low Power Applications Based on ElectricField Manipulation by Area Geometric Difference

Hosam Alharbi *,† , Muhammad Khalid † and Mohammad Abido †

Department of Electrical Engineering, King Fahd University of Petroleum and Minerals (KFUPM),Dhahran 31261, Saudi Arabia; mkhalid@kfupm.edu.sa (M.K.); mabido@kfupm.edu.sa (M.A.)* Correspondence: g201701570@kfupm.edu.sa; Tel.: +966-567999976† These authors contributed equally to this work.

Received: 18 January 2019; Accepted: 22 February 2019; Published: 28 February 2019�����������������

Abstract: An electrostatic generator is an electromechanical device that produces static chargesat high voltage and low current. This technology is mature enough, as it has existed for manycenturies. Nevertheless, the working principle of most of the commonly used electrostatic generatorsis still based on typical mechanical methods, which consequently makes them bulky and limits theircontrollability on the generated charges, e.g., Van de Graaff generator that uses the friction betweentwo different materials to generate electrostatic charges. In this paper, a novel design of a staticelectrostatic generator (SEG) is presented based on a completely different idea compared to existingelectrostatic generators, which offers several potential benefits. The idea originates from the studyof a parallel plates capacitor—for instance, if a voltage is applied to two plates of a capacitor, thenaccording to Gauss’s law, both of the plates must have an equal and opposite charge. Suppose one ofthe plates has a different geometry, with a shorter length than the other, then the number of the chargeson both plates will not be equal. Thus, by manipulating the geometrical area of the device, a differentnumber of charges will be generated on both metal conductors. Therefore, a different numberof charges are generated on both conductors; hence, by connecting both conductor plates of thecapacitance, excess charges will remain on the device. The proposed idea was assessed with computersimulations using finite element and finite difference methods for a variety of different scenariosto determine the optimal design of the proposed device. The device offers several advantages overtraditional electrostatic generators, such as that it can generate either positive or negative charges bymerely reversing the polarity of the DC source; additionally, it is very simple, lightweight, and easyto manufacture. In particular, the principal advantage of the proposed device is that it is a static one,and no mechanical movement is required to produce charges. Further, the design is general enoughand scalable. The simulation results demonstrate the performance of the proposed device.

Keywords: electrostatic generator; controllable static charge generator; high voltage; finite differencemethod; static electrostatic generator

1. Introduction

In the early 1900s, physics researchers needed a high-voltage DC source, in millions of volts, withlow current to accelerate electrons and ions to investigate the internal atom construction. However,with the available equipment at that time, it meant installing a costly, huge, and well-insulatedtransformer and a high-voltage rectifier to provide high DC voltage for the particles accelerator [1].In Reference [2], Van de Graff presented a simple and economical solution to produce a high DCvoltage source with low current. Ever since the inception of an electrostatic generator and its impacton nuclear physics research, it has been gaining much attention in research.

Energies 2019, 12, 802; doi:10.3390/en12050802 www.mdpi.com/journal/energies

Energies 2019, 12, 802 2 of 18

In the renewable energy sector, electrostatic generation plays an important role as well. Withthe increasing energy demands worldwide and the effects to the earth ecosystem, such as globalwarming and pollution caused by traditional energy sources, such as oil, coal, and nuclear, the needfor renewable energy sources increases. The increasing demands of renewable energy sources, capitalcost reduction, and efficient renewable energy systems were some of the motivations that help topropel the world to investigate, research, and improve renewable energy to make it a more viableeconomic option. In Reference [3], Matthew presented a variable capacitor—which is an electrostaticgenerator—as a power source for space applications using electrets. More recent work done byO’Donnell, Schofield, Smith, and Cullen in Reference [4] on electrostatic power generation for windturbine showed promising results for power grid generation. Since an offshore wind farm mostly usesHigh Voltage Direct Current (HVDC) to transmit power efficiently, the proposed generator eliminatedthe need for an AC to DC converter, since the electricity generated was DC. In a more recent techniquefrom 2005 [5], Djairam, Hubacz, Morshuis, Marijnissen, Smit, in harvesting the wind energy, used anelectrostatic wind converter (EWICON) instead of the traditional wind generator. EWICON generatesthe electrical power by forcing the charges to move in the opposite direction of the electric field by thewind to increase the energy of the system. In 2014 [6], the authors presented a high-efficiency ballisticelectrostatic generator using microdroplets. The presented electrostatic generator has a conversionefficiency that reaches up to 48% in converting mechanical energy to electrical energy.

In energy harvesting, in 2011, de Queiroz and Domingues used an electrostatic generator knownas a “doubler of electricity” as an energy harvesting device and a battery charger [7].

One of the major applications of electrostatic is bio-MEMS (biological microelectromechanicalsystem). These electrostatic bio-MEMS actuators are designed for aqueous environments and benefitfrom the relativity permittivity factor of water, which is usually greater than 1. In Reference [8],The authors demonstrated a high-speed gap-closing actuator (GCA) with a low voltage level (6 V).The presented actuator was designed to generate up to 4.6mN force. In Reference [9], a curved electrodeelectrostatic actuator’s design, fabrication, and characterization were presented. The presented curvedelectrode actuator works with low voltage (±8 V) in an underwater environment, which resulted inlarge displacement and forces due to the high relative permittivity of water. In Reference [10], anactuator was fabricated without gold/chromium conductive layers to improve adhesion with minimaleffect on the actuator displacement and force.

Electrostatic has a wide range of applications, such as precipitators, electrostatic air cleaning,inkjet printers, electrostatic painting, xerography, ion thrusters, and ion acceleration in nuclear research.In 2014, Wang, Yan, Hu, and Qian [11] investigated and tested the application of rotational speedmeasurement using electrostatic sensing. With a vast range of applications of an electrostatic generator,a highly efficient and more reliable electrostatic generator is required.

Whether in energy harvesting or renewable energy sources, the working principles of most ofthe electrostatic generators are based on mechanical force—either moving a belt, microdroplets orrotating capacitors plates—to move a medium, liquid or solid, which absorbed the charges to a higherpotential. Thus, they have lower efficiency, they are bulky, and it is difficult to control the quantitiesof charges they produce. In this paper, the presented novel static electrostatic generator (SEG) canconvert electrical energy with a low potential to a high potential. Consequently, the device can operateas a DC to DC voltage converter. Furthermore, the presented SEG can function as an electrostaticgenerator—similar to a Van de Graff generator—but unlike all other electrostatic generators, the deviceinput and output energy is purely electrical energy. The proposed SEG can play a significant role in therenewable power sector as well. In fact, the proposed SEG can function as a high-voltage source, whichis required by the electrostatic wind energy converter (EWICON) as in Reference [5]. For example,instead of connecting EWICON directly to a high-voltage source, it can be connected to a low-voltagesource with SEG, which in turn can generate the high voltage required by the generator. Consequently,this will reduce the insulation required for the high voltage supply, which in turn reduces the cost.

Energies 2019, 12, 802 3 of 18

A DC-to-DC converter is a type of electric power converter which converts a DC source voltagefrom one level to another. The DC-to-DC converter is one of an elemental circuit block in manyelectrical devices. It is an essential part of modern system development to maximize the energyharvest for a photovoltaic system and wind turbines. In the early days, before the development ofpower semiconductors, conversion of a DC voltage from one level to another was carried out throughthe conversion of a DC voltage to AC, then back again to DC. Consequently, these converters wererelatively inefficient and expensive due to the uses of different electric components. The introduction ofpower semiconductors and integrated circuits made it economically viable to use different techniquesto acquire the needed voltage level—for instance, one method which has been used to convert theDC power supply to high-frequency AC through the usage of semiconductors. Since the transformervoltage is a function in the frequency, then by feeding the generated high-frequency AC to a transformer,a high voltage level can be obtained. Since the obtained high voltage is an AC, a rectifier circuit isneeded to convert the voltage back to DC.

Many electronic devices, such as cellular phones and laptop computers, which are powered bybatteries, use DC to DC converters. These electronic devices often have several sub-circuits, eachwith its voltage level, which can be different from the voltage supplied by the battery or an externalsupply. As energy is drained from the battery, the voltage level starts declining. Therefore, DC to DCconverters using high-frequency switching offer a method to increase voltage from a partially loweredbattery voltage, thereby saving space instead of using multiple batteries to accomplish the same thing.

Walker and Sernia [12] showed the advantages of using many small DC–AC converters over theusage of a single DC–AC converter in residential photovoltaic (PV) applications. In Reference [13],the authors discussed the main disadvantage of the PV system, which is its variable voltage. Theyproposed a Matlab-based model for an intermediate DC–DC converter which can increase the efficiencyof the system by providing an impedance match between the PV system and load.

A comprehensive review was presented in Reference [14] to demonstrate various high-voltagegain DC–DC converter topologies, control strategies, and recent trades. The paper covered andclassified into several categories different numbers of topologies which have a high voltage conversionratio, low cost, and high-efficiency performance. To optimize the output power of the photovoltaicsystem, it must operate at the maximum power point (MPP), as suggested in Reference [15].The Maximum power point tracking (MPPT) algorithm allows the increase of the output power,and it commonly works with a DC–DC converter. Additionally, the authors presented the analysis andthe essential features of different topologies of DC–DC converters which were designed and simulatedfor solar photovoltaic (PV) applications. Moreover, two conventional MPPT algorithms were evaluatedby computer simulation to analyze their efficiency in different environmental conditions.

In Reference [16], Deihimi and Mahmoodieh reconfigured a high step-up DC–DC converterand integrated it with conventional DC–DC converters simultaneously with a battery. The proposedreconfiguration of a battery-integrated DC–DC converter, BIC, with the linear quadratic regulator (LQR),was verified through simulations and experimental results. Das and Agarwal [17] presented a newhigh voltage gain and high-efficiency DC–DC converter based on coupled inductors, an intermediatecapacitor, and a leakage energy recovery scheme. It used the mutual coupling between conductors tostore the energy in a magnetic field. The mutually coupled conductors are connected to capacitorsof the output stage in a lossless manner. The high efficiency and high gain converter presented inReference [17] has a high efficiency of 96% for low-output voltage sources.

A high-voltage gain DC–DC converter for PV systems was presented in Reference [18].The proposed converter can set up the voltage up to 311 V with the achievement of maximum power.The converter used coupled conductors and sets of capacitors and semiconductors. The converter issuitable for low-input voltages and low-power applications. In Reference [19], the authors presented anovel multiport high-voltage-gain DC–DC converter with two boost stages at the input. The outputvoltage of the presented model can gain up to 20 times the input voltage. Lin and Dong [20] presenteda novel soft-switching DC–DC converter for renewable energy conversion systems with a solar PV cell

Energies 2019, 12, 802 4 of 18

or fuel cell stack as an input to achieve zero-voltage switching (ZVS), a turn-on for active switches andzero-current switching (ZCS), a turn-off for fast recovery diodes. The proposed converter achievedhigh step-up voltage conversion ratio using a boost converter and a voltage-doubler configurationwith a coupled inductor.

A high-efficiency dual-mode resonant converter topology with a detailed theoretical analysis of theconverter operation and its DC gain features was presented in Reference [21]—a converter which canmaintain high efficiency for a wide input range at different output power levels by changing resonantmodes depending on the panel operation conditions. The integration of two technologies, a switchedcapacitor and a switched coupled inductor, into one converter to increase voltage gain was presentedin Reference [22]; the developed DC–DC converter configuration has an efficiency of 93.6% at fullload. Ardi, Ajami, and Sabahi [23] proposed a DC–DC converter with high voltage gain, zero currentswitching of the main switch, and low-voltage stress of the main switches. Even though the presentedconverter shows a high voltage gain, it employed fewer components than a traditional converter.

A high-conversion-ratio bidirectional DC–DC converter with maximum efficiency reaching up to96.41% was presented in Reference [24], using a coupled inductor with a lower turn ratio and highconversion ratio. In Reference [25], Chen, Lu, Hung, and Liang used an interleaved boost converter toachieve a high step-up voltage conversion ratio with a maximum efficiency of 94.5%. A bidirectionalDC–DC converter using only two switches and an inductor–capacitor LC resonant transformer capableof controlling the power flow with a high efficiency of 92% was shown in Reference [26], whilein Reference [27], a converter using the techniques of a switched-capacitor, coupled-inductor, andmultiplier capacitor to achieve high voltage gain was presented. In Reference [28], multilevel DC–DCconverters were presented for interconnecting medium-voltage DC networks. In Reference [29], Ahrabi,Ardi, Elmi, and Ajami presented a multi-input DC–DC converter with a control method for hybridelectric vehicles to enhance the efficiency and performance of the converter, while in Reference [30],a multi-input DC–DC converter was presented as a solution for galvanic isolation for AC–DC using anisolation transformer. In Reference [31], a compact and lightweight design of onboard electric vehicle(EV) charger which uses a bidirectional AC–DC single-stage converter was presented.

In this paper, the proposed electrostatic generator (SEG) is small, lightweight, easy to manufacture,and scalable. SEG can be resized to generate electrostatic charges more efficiently with different voltagelevels. Additionally, SEG is more reliable, since it does not depend on any mechanical movement togenerate static charges. Moreover, SEG can produce charges in controllable quantities. The proposedSEG can work as an electrostatic generator, such as the Van de Graaff generator, with efficiency reachingup to 46.95%. The efficiency of the presented SEG is considered among the highest in electrostaticgeneration. Further, SEG does not require any gas or liquid to be under high pressure to generatecharges with high efficiency. Unfortunately, using the device in a DC–DC converter with an efficiencyof 46.95% is not preferable, even though the device did not require any inductor, which means it is nottemperature-sensitive, nor did it use many capacitors to achieve the same high voltage level requiredby different applications.

The remainder of the paper is organized as follows. Section 2 discusses the working principle ofSEG which will show a different perspective on how static charges can be generated, which may helpin understanding some of the phenomena associated with the static charges generations. Section 3presents the proposed methodology. Results and Discussions are presented in Section 4, and Section 5concludes the paper.

2. Proposed Device Working Principle

Figure 1 shows the basic construction of the proposed device, which is similar to a coaxial cable,with a thin wire, a metal sheet surrounding the thin wire, and a dielectric material between them.Three assumptions should be made at the beginning: (1) There should not be any charges on any ofthe conductors; (2) the dielectric material, initially, should have no dipoles, and; (3) the applied voltage

Energies 2019, 12, 802 5 of 18

should be DC Voltage. These assumptions are necessary to ease understanding but will not affectthe outcomes.

Thin metal wire

Cylindrical metal sheet

+++++

-

-

-

Figure 1. Internal construction of the proposed static electrostatic generator (SEG).

When the cylindrical metal sheet is connected to a positive voltage source and the metal wire isconnected to a negative voltage source, the charges start to accumulate on the surfaces of the conductors.Since the area of the thin metal wire is significantly smaller than the area of the cylindrical metalsheet, more charges will accumulate on the cylindrical metal sheet. After charging both conductorswith different amount of charges due to surface area geometric difference between them, switch S1is opened and switch S2 is closed, see Figure 2. By closing S2, the same number of charges on thethin wire will cancel the same number of charges on the cylindrical metal sheet. Since the electricfield which was binding the remaining extra charges on the cylindrical metal sheet is gone when S2 isconnected, the remaining charges on the cylindrical metal sheet are set free. Thus, the number of freecharges can be calculated by:

QFree = QCylinderical−Metal−Sheet −QWire. (1)

The free charges cannot move to the thin wire, since the static charges are not allowed to be insidea metal. The metal sphere shown in Figure 2 acts as a charge collector, since no static charges areallowed to be inside a conductor. The charges start to accumulate once switches S2 and S3 are closedwhile S1 is opened. The metal sphere prevents any voltage difference across S1 except for the batteryvoltage. Any enclosed metal surface will be sufficient to act as a charge accumulator surface, whetherspherical or cylindrical.

To estimate the device efficiency, firstly, the total energy stored (TES) within the device after itis fully charged must be calculated. Then, by forcing the number of charges on the cylindrical metalsheet to equal the number of charges on the thin wire, the energy lost (EL) can be calculated. Thus,the efficiency can be calculated by:

η =TES− EL

TES× 100 (2)

The novel SEG presented in this paper has many advantages over existing ones. It is capable offast charge generation using fast switching transistors. Additionally, it can generate either positiveor negative charges by merely reversing the battery polarity. Moreover, it can control the number ofcharges generated by controlling the voltage and the switching time of the transistors. Furthermore,it does not require any mechanical method to generate electrostatic charges, as it is a static device.The efficiency of the presented device cannot reach a higher level than 46.95%, as will be shown in

Energies 2019, 12, 802 6 of 18

the Results section, where many different scenarios were tested to optimize the device output andefficiency. The simulation of the device was carried out in MATLAB (R2017a, MathWorks, Inc, Natick,MA, USA)using the finite difference method (FDM), and FEMM ( version 4.2, David Meeker, QinetiQNorth America, MA, USA) [32] using the finite element method (FEM) to ensure the obtained resultsare in a good agreement.

Thin metal wire

Cylindrical metal sheet

++++

-

--

Metal sphere

+

BatteryS1

S2

S3

Figure 2. Field interaction of the proposed SEG.

3. Finite Difference Method

One of the numerical solutions used in simulating the proposed device was FDM. FDM is oneof the numerical solution methods to solve complex problems that are difficult to solve analyticallyor by linearizing differential equations [33]. It is a numerical approximation solution that convertsdifferential equations to finite-difference equations, and through iterations of algebraic equations,a solution of a complex differential equation can be obtained [34].

Laplace’s equation and Poisson’s equation are powerful tools to represent an electrostatic system.Solving these differential equations for complex geometry in order to represent the behavior of theelectrostatic model must be carried out through a numerical solution. There are many methods offinite difference that can be applied to solve Laplace’s and Poisson’s equations; the method used inthis paper of finite difference is the five-point star (leapfrog) [35].

3.1. Laplace’s Equation

To solve the differential equation of the proposed device, we must convert the differential equationto a finite difference equation:

5 ·D = 0, (3)

since:D = ε0εr E, (4)

then:5 ·

[ε0εr E

]= 0, (5)

52 V = 0, (6)

since:

52 =∂2

∂x2 +∂2

∂y2 +∂2

∂z2 . (7)

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Under the assumption that there are no changes in the z-components, we only solve for x andy, thus:

52 V =∂2V∂x2 +

∂2V∂y2 . (8)

To solve the Laplace differential equation, firstly, the area of interest to study and simulate thebehavior of electrostatic must be divided into a fine mesh using the five-point star configuration asshown in Figure 3.

V(i,j+1)

ᵋ(i-1,j) ᵋ(i,j)

ᵋ(i-1,j-1) ᵋ(i,j-1)

X

Y

Xi Xi+1Xi-1

Yi

Yi+1

Yi-1

V(i+1,j+1)V(i-1,j+1)

V(i,j) V(i+1,j)V(i-1,j)

V(i,j-1) V(i+1,j-1)V(i-1,j-1)

Figure 3. The potential interaction of the proposed SEG.

∂2V∂x2∼=

V(i+1,j) − 2V(i,j) + V(i−1,j)

h2 (9)

∂2V∂y2∼=

V(i,j+1) − 2V(i,j) + V(i,j−1)

h2 (10)

Uniform grid case:

52 V =V(i+1,j) + V(i−1,j) + V(i,j+1) + V(i,j−1) − 4V(i,j)

h2 = 0 (11)

V(i,j) =14

[V(i+1,j) + V(i−1,j) + V(i,j+1) + V(i,j−1)

](12)

Varying dielectrics case:

a0 = ε(i, j) + ε(i− 1, j) + ε(i, j− 1) + ε(i− 1, j− 1) (13)

a1 =12[ε(i, j) + ε(i, j− 1)] (14)

a2 =12[ε(i− 1, j) + ε(i, j)] (15)

a3 =12[ε(i− 1, j− 1) + ε(i− 1, j)] (16)

a4 =12[ε(i, j− 1) + ε(i− 1, j− 1)] (17)

−a0V(i, j) + a1V(i + 1, j) + a2V(i, j− 1) + a3V(i− 1, j)

+a4V(i, j + 1) = 0(18)

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V(i, j) =1a0[a1V(i + 1, j) + a2V(i, j− 1)

+a3V(i− 1, j) + a4V(i, j + 1)](19)

3.2. Poisson’s Equation

Using Poisson’s equation, the charges on each plate can be calculated. Since:

5 ·D = ρc (20)

−a0V(i, j) + a1V(i + 1, j) + a2V(i, j− 1) + a3V(i− 1, j)

+a4V(i, j + 1) = −Q(i, j)ε0

(21)

3.3. Electric Field

The electric field is calculated as shown in Figure 4.V

(i,j+1

)

X

Y

Xi Xi+1Xi-1

Yi

Yi+1

Yi-1

V(i+

1,j+

1)

V(i-1

,j+1

)

V(i,j)V(i+1,j)V(i-1,j)

V(i,j-1

)

V(i+

1,j-1

)

V(i-1

,j-1)

Ex(i-1

,j+1

)

Ex(i,j+

1)

Ey(i-1,j) Ey(i+1,j)

Ey(i-1,j-1) Ey(i+1,j-1)

Ex(i-1

,j-1)

Ex(i,j-1

)

Ey(i,j)

Ey(i,j-1)

Ex(i-1

,j)

Ex(i,j)

Figure 4. The electric field interaction of the proposed SEG.

E = −5V (22)

E = −x∂V∂x− y

∂V∂x

(23)

E = Ex(i, j) + Ey(i, j) (24)

Ex(i, j) = −V(i + 1, j)−V(i, j)h

(25)

Ey(i, j) = −V(i, j + 1)−V(i, j)h

(26)

After obtaining the potential for each point on the unified mesh, the electric field can be calculatedusing a gradient function in MATLAB. The magnitude of the net electric field can be calculated as:

E =√

E2x + E2

y. (27)

After obtaining the electric field of the unified mesh, the energy for each cell in the mesh can becalculated using:

Energy =12

ε0E2 Vcell . (28)

Energies 2019, 12, 802 9 of 18

4. Simulation Results

The simulation of the device was carried out in MATLAB using FDM and FEMM software [32]using FEM. The proposed device and its dimensions are shown in Figure 5 and Table 1. The proposeddimensions are based on the applied DC voltage and the breakdown voltage of the dielectric materialbetween the thin wire and the metal sheet. The applied DC voltage must as high as possible and belowthe breakdown voltage of the dielectric material between the thin wire and the metal sheet. Differentscenarios were studied to find the optimum design, maximum output charges, and maximum efficiency.

Wire

Dielectric Material, εr

Cylindrical Metal sheet

r1

r2

r3

V1

V2

Q2

Q1

Figure 5. Cross-section of the inner and outer conductors of the proposed device.

Table 1. System parameters.

Dimension of the Simulated Volume

X (mm) Y (mm) Z (mm)

20 20 100

Device Parameters

r1 (mm) r2 (mm) r3 (mm) εr VDC (Volt)

0.04 1 1.1 1 1000

To determine the number of charges freed from the outer metal sheet, first, a voltage must beapplied between the wire and the metal sheet (see Table 2, Case 0). Then, the difference in the numberof charges between the wire and the metal sheet, which is due to the area geometric difference betweenboth of the conductors, is the number of free charges. Figure 6 shows the electric potential distributionof the proposed device. Figure 7 shows the electric field distribution of the proposed device.

To estimate the efficiency of the proposed device, first, an equal amount of the charges are forcedon both the wire and the metallic sheet, which is the number of charges on the thin wire since thosecharges will be canceled out with an equal number of charges on the metallic sheet. Then, by comparingthe total amount of energy stored within the device with the amount of energy associated with anequal number of charges, the efficiency of the device can be calculated. Thus, by forcing:

Q2 = −Q1, (29)

and by calculating the energy associated with the charges, efficiency can be calculated.

Energies 2019, 12, 802 10 of 18

Electric Potential Distribution, V(x,y)in Volts

Y-ax

is in

mill

imet

er

X-axis in millimeter

Figure 6. The electric potential distribution of the proposed device.

Electric Field Distribution, E(x,y)in V/m

Y-ax

is in

mill

imet

er

X-axis in millimeter

Figure 7. The electric field distribution of the proposed device.

4.1. CASE I: Effects of the Dielectric Material

In this case, the dielectric material between the conductors is replaced with a material which hasεr = 10, to study the effects on charge production and the efficiency of the device, see Table 2, Case I.Figure 8 shows the electric potential distribution of the proposed device. Figure 9 shows the electricfield distribution of the proposed device.

Table 2, Case I shows that the number of freed charges is slightly lower, and the efficiency of thedevice is dropped dramatically. This is due to the loss of the energy stored within the dielectric material.

Energies 2019, 12, 802 11 of 18

Electric Potential Distribution, V(x,y)in Volts

Y-ax

is in

mill

imet

er

X-axis in millimeter

Figure 8. The electric potential distribution of the proposed device when εr = 10.

Electric Field Distribution, E(x,y)in V/m

Y-ax

is in

mill

imet

er

X-axis in millimeter

Figure 9. Tlectric field distribution of the proposed device when εr = 10.

4.2. CASE II: Effects of the Applied Voltage

In this case, the applied voltage between the conductors is reduced by half of the original value(500V) to study the effects on charge production and the efficiency of the device, see Table 2, Case II.Figure 10 shows the electric potential distribution of the proposed device. Figure 11 shows the electricfield distribution of the proposed device.

Table 2, Case II shows that the number of freed charges and the efficiency dropped about half thevalues of Case 0, see Table 2. Thus, increasing the potential will help in improving both the efficiency ofthe device and the number of generated charges. The breakdown voltage and the maximum switchingvoltage must be considered in the design.

Energies 2019, 12, 802 12 of 18

Electric Potential Distribution, V(x,y)in Volts

Y-ax

is in

mill

imet

er

X-axis in millimeter

Figure 10. The electric potential distribution of the proposed device when the voltage is halved.

Electric Field Distribution, E(x,y)in V/m

Y-ax

is in

mill

imet

er

X-axis in millimeter

Figure 11. The electric field distribution of the proposed device when the voltage is halved.

4.3. CASE III: Effects of the Thin Wire Diameter

In this case, the diameter of the thin wire is doubled to study the effects on charge production andthe efficiency of the device, see Table 2, Case III. Figure 12 shows the electric potential distribution ofthe proposed device. Figure 13 shows the electric field distribution of the proposed device.

Table 2, Case III shows that the number of freed charges is slightly higher due to the slight decrementsof distance between the conductors, while the efficiency of the device is dropped dramatically.

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Electric Potential Distribution, V(x,y)in Volts

Y-ax

is in

mill

imet

er

X-axis in millimeter

Figure 12. The electric potential distribution of the proposed device when the diameter of the thin wireis doubled.

Electric Field Distribution, E(x,y)in V/m

Y-ax

is in

mill

imet

er

X-axis in millimeter

Figure 13. The electric field distribution of the proposed device when the diameter of the thin wireis doubled.

4.4. CASE IV: Effects of the Thin Metal Sheet Diameter

In this case, the diameters of the thin metal sheet are doubled to study the effects on charge productionand the efficiency of the device, see Table 2, Case IV. Figure 14 shows the electric potential distribution ofthe proposed device. Figure 15 shows the electric field distribution of the proposed device.

Table 2, Case IV shows that the number of freed charges increases due to the increase in thesurface area of the thin metal sheet, while the efficiency of the device is slightly decreased.

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Electric Potential Distribution, V(x,y)in Volts

Y-ax

is in

mill

imet

er

X-axis in millimeter

Figure 14. The electric potential distribution of the proposed device when the thin metal sheet diameteris doubled.

Electric Field Distribution, E(x,y)in V/m

Y-ax

is in

mill

imet

er

X-axis in millimeter

Figure 15. The electric field distribution of the proposed device when the thin metal sheet diameteris doubled.

Table 2. The device performance comparisons.

Case 0 Case I Case II Case III Case IV Case V

V1 (Volt) 500 500 250 500 500 500V2 (Volt) −500 −500 −250 −500 −500 −500

εr 1 10 1 1 1 1r1 (µm) 40 40 40 80 40 40r2 (mm) 1 1 1 1 2 1r3 (mm) 1.1 1.1 1.1 1.1 2.1 1.2

Q1 (Coulombs) 1.74644 × 10−9 1.73631 × 10−8 8.7322 × 10−10 2.19035 × 10−9 1.3409 × 10−9 1.77257 × 10−9

Q2 (Coulombs) −3.22398 × 10−9 −1.88247 × 10−8 −1.61199 × 10−9 −3.66845 × 10−9 −3.4159 × 10−9 −3.13439 × 10−9

Q f ree (Coulombs) −1.47754 × 10−9 −1.4616 × 10−9 −7.3877 × 10−10 −1.4781 × 10−9 −2.075 × 10−9 −1.36182 × 10−9

Energy Stored (J) 1.17827 × 10−6 9.03654 × 10−6 2.94569 × 10−7 1.41549 × 10−6 1.14532 × 10−6 1.19127 × 10−6

When Q1 = − Q2

Energy Stored (J) 6.25078 × 10−7 8.63198 × 10−6 2.18325 × 10−7 1.0802 × 10−6 6.2438 × 10−7 8.98687× 10−7

Efficiency 46.950% 4.48% 25.88% 23.69% 45.48% 24.56%

Energies 2019, 12, 802 15 of 18

4.5. CASE V: Effects of the Thin Metal Sheet Thickness

In this case, the thickness of the thin metal sheet is doubled to study the effects on charge productionand the efficiency of the device, see Table 2, Case V. Figure 16 shows the electric potential distribution ofthe proposed device. Figure 17 shows the electric field distribution of the proposed device.

Electric Potential Distribution, V(x,y)in Volts

Y-ax

is in

mill

imet

er

X-axis in millimeter

Figure 16. The electric potential distribution of the proposed device when the thickness of metal sheetis doubled.

Electric Field Distribution, E(x,y)in V/m

Y-ax

is in

mill

imet

er

X-axis in millimeter

Figure 17. The electric field distribution of the proposed device when the thickness of metal sheetis doubled.

Table 2, Case V shows that the number of freed charges is slightly lower than in Case 0; this isbecause the number of charges on the thin wire is slightly higher, while the charges on the metal sheetare slightly lower. This will lead to lower freed charges and lower efficiency. The higher the thicknessof the metal shell, the more charges are allowed to be on the metal, which will lead to higher energystored within the device.

Energies 2019, 12, 802 16 of 18

From the previous results, the optimum design of the proposed device must have a higher metalsheet area for the outer conductor, while the area of the thin metal wire must be as small as possible.In addition, the applied voltage must be as large as possible, taking the breakdown voltage and themaximum withstand voltage of the transistors into account. Furthermore, the thickness of the metalsheet must be as small as possible, so fewer charges are allowed to be on the thin metal sheet andlower energy is stored within the device.

5. Conclusions

In this paper, a novel design of a static electrostatic generator was presented with an overallefficiency reaching up to 46.95%, especially in cases of ideal switching transistors. The device consistsof thin wire and a thin metallic sheet and is enclosed by a metal to act as a charge-collector. The freecharges are delivered to the enclosed metal surface in a chunk, which is actually a set of charges witheach operation. The amplitude of the DC voltage and the geometric design of the device can control thenumber of freed charges. Thus, if a set of desired charges is required to be deposited on the enclosedmetal, these charges must be a multiplication of each chunk generated. Therefore, the proposed devicegives a certain degree of control over how many charges can be enclosed on metal surface. Further,the proposed device can generate negative or positive charges by simply reversing the polarity ofthe DC voltage source. The device is tested intensively using simulations based on standard finiteelement and finite difference methods for a variety of scenarios to obtain the highest efficiency andalso to determine key parameters affecting the device efficiency. It was concluded that the efficiency ofthe proposed device is heavily dependent on the applied voltage and the geometric design, and theclaimed efficiency might not be the highest as presented in literature, but it is rather a relatively simpledesign, static, controllable, lightweight, small, and it does not require any mechanical moving parts,which is a huge advantage over many other electrostatic generators.

Author Contributions: The authors’s contributions are given as follows: “conceptualization, H.A. and M.K.;methodology, H.A.; software, H.A.; validation, H.A., M.K., and M.A.; formal analysis, H.A., M.K. and M.A.;investigation, H.A., M.K. and M.A.; resources, M.K.; data curation, H.A.; writing—original draft preparation, H.A.,M.K. and M.A.; writing—review and editing, H.A. and M.K.; visualization, H.A., M.K. and M.A.; supervision,M.K. and M.A.; project administration, H.A. and M.K.; funding acquisition, M.K.”.

Funding: The authors would like to acknowledge the support provided by the Deanship of Research (DSR) atKing Fahd University of Petroleum and Minerals (KFUPM) for funding this work through Project No. RG171009.

Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations

The following abbreviations are used in this manuscript:

W Energy [J]w Energy density [ J

m3 ]D Electric filed density [ C

m ]E Electric filed [ V

m ]εr Relative permittivityε0 Permittivity of Vacuum [ F

m ]V Voltage [V]ρc Charge density [ C

m2 ]e electron charge [C]Q Total charge [C]Vcell Volume of cubic cell [m3]DC Direct currentAC Alternating currentSEG Static electrostatic generator

Energies 2019, 12, 802 17 of 18

EWICON Electrostatic wind converterMPP Maximum power pointMPPT Maximum power point trackingPV Solar photovoltaicDC−−DC DC to DC converterLQR Linear quadratic regulatorZVS Zero-voltage switchesZCS Zero-current switchesEV electric vehiclesS1, S2, S3 SwitchesTES Total energy storedEL Energy lostFDM Finite difference methodFEM Finite element methodη Efficiency

References

1. Fortescue, R.L.; Hall, P.D. The High-Voltage Electrostatic Generator at the Atomic Energy ResearchEstablishment. Proc. IEE—Part I Gen. 1949, 96, 77–85. [CrossRef]

2. van de Graaff, R.J.; Compton, K.T.; van Atta, L.C. The Electrostatic Production of High Voltage for NuclearInvestigations. Phys. Rev. 1933, 43, 149–157. [CrossRef]

3. Matthew, R.E. The use of electrets in electrostatic generators for space. Electr. Eng. 1962, 81, 850–854.[CrossRef]

4. O’Donnell, R.; Schofield, N.; Smith, A.C.; Cullen, J. Design Concepts for High-Voltage Variable-CapacitanceDC Generators. IEEE Trans. Ind. Appl. 2009, 45, 1778–1784. [CrossRef]

5. Djairam, D.; Morshuis, P.H.F.; Smit, J.J. A novel method of wind energy generation-the electrostatic windenergy converter. IEEE Electr. Insul. Mag. 2014, 30, 8–20. [CrossRef]

6. Xie, Y.; Bos, D.; de Vreede, L.J.; de Boer, H.L.; van der Meulen, M.J.; Versluis, M.; Sprenkels, A.J.;van den Berg, A.; Eijkel, J.C.T. High-efficiency ballistic electrostatic generator using microdroplets.Nat. Commun. 2014, 5, 3575. [CrossRef] [PubMed]

7. de Queiroz, A.C.M.; Domingues, M. The Doubler of Electricity Used as Battery Charger. IEEE Trans.Transp. Electrif. 2011, 58, 797–801. [CrossRef]

8. Shih, R.M.; Contreras, D.S.; Massey, T.L.; Greenspun, J.T.; Pister, K.S.J. Characterization of electrostaticgap-closing actuator arrays in aqueous conditions. In Proceedings of the 2018 IEEE Micro Electro MechanicalSystems (MEMS), Belfast, UK, 21–25 January 2018; pp. 596–599. [CrossRef]

9. Preetham, B.S.; Lake, M.A.; Hoelzle, D.J. A curved electrode electrostatic actuator designed for largedisplacement and force in an underwater environment. J. Micromech. Microeng. 2017, 27, 095009. [CrossRef]

10. Burugupally, S.P.; Mangels, J.A. Performance evaluation of a curved electrode actuator fabricated withoutgold/chromium conductive layers. Microsyst. Technol. 2018, 24, 3479–3485. [CrossRef]

11. Wang, L.; Yan, Y.; Hu, Y.; Qian, X. Rotational Speed Measurement Through Electrostatic Sensing andCorrelation Signal Processing. IEEE Trans. Instrum. Meas. 2014, 63, 1190–1199. [CrossRef]

12. Walker, G.R.; Sernia, P.C. Cascaded DC-DC converter connection of photovoltaic modules. IEEE Trans.Power Electron. 2004, 19, 1130–1139. [CrossRef]

13. Marodkar, M.; Adhau, S.; Sabley, M.; Adhau, P. Design and simulation of DC-DC converters for Photovoltaicsystem based on MATLAB. In Proceedings of the 2015 International Conference on Industrial Instrumentationand Control (ICIC), Pune, India, 28–30 May 2015; pp. 1478–1483. [CrossRef]

14. Savakhande, V.B.; Bhattar, C.L.; Bhattar, P.L. Voltage-lift DC-DC converters for photovoltaic application-areview. In Proceedings of the 2017 International Conference on Data Management, Analytics and Innovation(ICDMAI), Pune, India, 24–26 February 2017; pp. 172–176. [CrossRef]

15. Soriano, L.A.; Ponce, P.; Molina, A. Analysis of DC-DC converters for photovoltaic applications based onconventional MPPT algorithms. In Proceedings of the 2017 14th International Conference on ElectricalEngineering, Computing Science and Automatic Control (CCE), Mexico City, Mexico, 20–22 October 2017;pp. 1–6. [CrossRef]

Energies 2019, 12, 802 18 of 18

16. Deihimi, A.; Mahmoodieh, M.E.S. Analysis and control of battery-integrated dc/dc converters for renewableenergy applications. IET Power Electron. 2017, 10, 1819–1831. [CrossRef]

17. Das, M.; Agarwal, V. Design and Analysis of a High-Efficiency DC DC Converter With Soft SwitchingCapability for Renewable Energy Applications Requiring High Voltage Gain. IEEE Trans. Ind. Electron.2016, 63, 2936–2944. [CrossRef]

18. Freitas, A.A.A.; Tofoli, F.L.; Júnior, E.M.S.; Daher, S.; Antunes, F.L.M. High-voltage gain DC–DC boostconverter with coupled inductors for photovoltaic systems. IET Power Electron. 2015, 8, 1885–1892. [CrossRef]

19. Prabhala, V.A.K.; Fajri, P.; Gouribhatla, V.S.P.; Baddipadiga, B.P.; Ferdowsi, M. A DC DC Converter WithHigh Voltage Gain and Two Input Boost Stages. IEEE Trans. Power Electron. 2016, 31, 4206–4215. [CrossRef]

20. Lin, B.R.; Dong, J.Y. New zero-voltage switching DC-DC converter for renewable energy conversion systems.IET Power Electron. 2012, 5, 393–400. [CrossRef]

21. Liang, Z.; Guo, R.; Li, J.; Huang, A.Q. A High-Efficiency PV Module-Integrated DC/DC Converter for PVEnergy Harvest in FREEDM Systems. IEEE Trans. Power Electron. 2011, 26, 897–909. [CrossRef]

22. Chen, S.M.; Lao, M.L.; Hsieh, Y.H.; Liang, T.J.; Chen, K.H. A Novel Switched-Coupled-Inductor DC DC Step-UpConverter and Its Derivatives. IEEE Trans. Ind. Appl. 2015, 51, 309–314. [CrossRef]

23. Ardi, H.; Ajami, A.; Sabahi, M. A Novel High Step-Up DC–DC Converter With Continuous InputCurrent Integrating Coupled Inductor for Renewable Energy Applications. IEEE Trans. Ind. Electron.2018, 65, 1306–1315. [CrossRef]

24. Liu, H.; Wang, L.; Ji, Y.; Li, F. A Novel Reversal Coupled Inductor High-Conversion-Ratio Bidirectional DCDC Converter. IEEE Trans. Power Electron. 2018, 33, 4968–4979. [CrossRef]

25. Chen, Y.T.; Lu, Z.X.; Liang, R.H.; Hung, C.W. Analysis and implementation of a novel high step-up DCDC converter with low switch voltage stress and reduced diode voltage stress. IET Power Electron. 2016, 9,2003–2012. [CrossRef]

26. Ishigaki, M.; Shin, J.; Dede, E.M. A Novel Soft Switching Bidirectional DC DC Converter Using Magneticand Capacitive Hybrid Power Transfer. IEEE Trans. Power Electron. 2017, 32, 6961–6970. [CrossRef]

27. Chen, Y.T.; Lu, Z.X.; Liang, R.H. Analysis and Design of a Novel High-Step-Up DC DC Converter WithCoupled Inductors. IEEE Trans. Power Electron. 2018, 33, 425–436. [CrossRef]

28. Du, S.; Wu, B.; Tian, K.; Xu, D.; Zargari, N.R. A Novel Medium-Voltage Modular Multilevel DC DC Converter.IEEE Trans. Ind. Electron. 2016, 63, 7939–7949. [CrossRef]

29. Ahrabi, R.R.; Ardi, H.; Elmi, M.; Ajami, A. A Novel Step-Up Multiinput DC DC Converter for HybridElectric Vehicles Application. IEEE Trans. Power Electron. 2017, 32, 3549–3561. [CrossRef]

30. Jou, H.L.; Huang, J.J.; Wu, J.C.; Wu, K.D. Novel Isolated Multilevel DC DC Power Converter. IEEE Trans.Power Electron. 2016, 31, 2690–2694. [CrossRef]

31. Prasanna, U.R.; Singh, A.K.; Rajashekara, K. Novel Bidirectional Single-phase Single-Stage Isolated ACDC Converter With PFC for Charging of Electric Vehicles. IEEE Trans. Transp. Electrif. 2017, 3, 536–544.[CrossRef]

32. Meeker, D.C. Finite Element Method Magnetics, Version 4.2. Finite Element Method Magnetics.Available online: http://www.femm.info/wiki/HomePage (accessed on 27 February 2019).

33. Sadiku, M.N. Numerical Techniques in Electromagnetics with MATLAB; CRC Press: Boca Raton, FL, USA, 2009.34. Kraus, J.D. Electromagnetics; McGraw-Hill Companies: New York, NY, USA, 1992.35. Nagel, J.R. Numerical Solutions to Poisson Equations Using the Finite-Difference Method [Education

Column]. IEEE Antennas Propag. Mag. 2014, 56, 209–224. [CrossRef]

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