Gandu, K R

Green, T C

Mitcheson, P D

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SIMULATION TOOLKIT FOR ENERGY SCAVENGING INERTIAL MICROPOWER GENERATORSG. Kondala Rao, P. D. Mitcheson, T. C. GreenImperial College London, Department of Electrical EngineeringExhibition Road, South Kensington, London, SW7 2AZ, UK.Abstract: A critical issue to the optimization of a micro generator is the electromechanical link betweenthe transducer and power processing circuitry because the performance of each subsystem depends onthe behavior of the other. In order to accurately simulate and optimize a micro generator system, acombined electromechanical simulation is required. In this paper, a PSpice based electromechanicalsimulation tool kit for energy harvesting inertial micro generators has been developed. The tool kitconsists of a generic Mass-Spring-Damper (MSD) model coupled to models of Electromagnetic (EM),Electrostatic (ES) and Piezoelectric (PZ) transduction mechanisms. Additional features of the physicalsystems that affect the overall performance such as end stop dynamics and parasitic damping are alsoincluded. The realisation of these models in PSpice is explained and case study simulation results ofthese models are also presented.keywords: Energy scavenging, PSpice modeling, inertial micro generator1. INTRODUCTIONMotion and vibration are attractive sources formicroengineered energy scavenging generators [1].The most universal motion scavengers are of theinertial type, i.e. having a proof mass suspendedwithin a frame, and energy extracted by a trans-ducer that damps the motion of the proof masswithin the frame. These devices have the ad-vantage that they can function simply by beingattached to a source of motion at a single point,rather than relying on the relative motion of dif-ferent parts of the host structure. Thus they arealso well suited to miniaturisation. However in[2], it has been shown that the reported inertialmicro generators are operating well below theirmaximum power limit. Improving the performanceof micro generators is important either to increasethe power output for a given size or to reducethe size of the micro generator for the requiredpower. In [3] and [4] methods for optimizationof an electromagnetic micro generator are given.These methods are theoretical and only part of thesystem was modeled before making a practicaldevice. Complete physics based models of themicro generator systems have not been reportedin the literature. In this paper, a PSpice basedsimulation tool kit for inertial micro generators hasbeen developed. This simulation tool kit, free fordownload from our research group website, can beused to simulate or to optimize the micro generatorsystem or to develop suitable power conversioncircuits as per load requirements. The developmentof this toolkit is discussed in the rest of the paperand usage examples are presented.2. COMBINED ELECTRO-MECHANICALSIMULATION MODELA critical issue for the optimization of a microgenerator is the electromechanical link betweenthe transducer and power processing circuitry be-cause the performance each subsystem depends onthe behavior of the other. Therefore, In order toaccurately simulate and optimize a micro generatorsystem, a combined electromechanical simulationis required. An equivalent circuit approach iscommonly used for combined electromechanicalsimulation by representing the mechanical andelectrical parts in electrical circuit elements [5].Fig. 1. shows an equivalent circuit representationof a piezoelectric bimorph [1] and this can besimulated using any standard circuit simulator.However, the representation of mechanical partsby electrical elements is often not intuitive andin the case of inertial micro generators modelingof non-linear effects such as the proof mass hit-ting an end stop and loosing some momentum is137very difficult. A PSpice based simulation modelwhich considers the non-linear effects and electro-mechanical interactions has been developed in [6]for the electrostatic parametric generator. Here,we have modularised this model and developeda complete toolkit for inertial micro generatorsincludes Electromagnetic, Electrostatic and Piezo-electric transducer technologies.Fig. 1. Equivalent circuit representation of piezoelectric bimorph[1]A block diagram of the generic inertial microgenerator for modeling it’s electromechanical be-havior is shown in Fig. 2. It consists of genericmass spring damper (MSD) model with end stopdynamics, the electrical and parasitic dampingdirectly arising from the transduction mechanismis also present.Parasitic viscous Z(t)Z(t)Mass − Spring − Damper ModelMechanicalVibrationsParasitic non lineardampingElectrical Damping Force(Dz,F)Transducer ModeldampingY(t).VelocityPower Processing CircuitLoadAC VoltageDisplacementFig. 2. Block diagram of the generic electromechanical behaviormodel of the inertial micro generatorThe generic MSD model gives accurate positionof the proof mass with reference to end stop limitsand it has been realised by solving the differentialequ. 1 using the PSpice Analog Behavioral Model(ABM) library.mz̈(t) = mÿ(t) Dmż(t) Deż(t) Ksz(t) FESD(1)The terms in equ. 1 represent the force due tothe linear mass, spring and damper elements ex-cept FESD which represents the non-linear end stopdynamics. The end stop dynamics are modeledin such way that whenever the proof mass hitseither of end limits (i.e. +Zl or Zl) some of itskinetic energy will be dissipated as heat. The FESDforce is modeled as a damped spring system and isgiven in equ. 2. Zl is the end stop limit which canbe varied according to desired specification andKESD and DESD are the end stop impact springand damping coefficients respectively, which canbe altered depends on the material used in thefabrication.FESD =( z(t) zl) KESD+ ż(t) DESD if Z(t) Zl0 Otherwise(2)The electrical damping force De and the para-sitic damping force Dm in equ. 1 depend on thetransduction mechanism (Electromagnetic, Elec-trostatic and Piezoelectric) and so the MSD modelmust be combined with suitable transducer blockto build up a full simulation. Modeling of electricaldamping forces associated with EM and ES trans-duction mechanisms is discussed in the followingsection. Details of modeling of Piezoelectric elec-trical damping force and parasitic damping forcesassociated with each transduction mechanism arenot provided in this paper.3. MODELING OF EM AND ES DAMPINGFORCESElectromagnetic:The voltage developed by an electromagnetictransducer is described by faraday’s law of induc-tion. In a micro generator, this corresponds to avelocity dependent voltage source. The magnitudeof the voltage source is given byVcoil(t) = (Nc Bm Lc)V (t) (3)where Lc is active length of the coil in the mag-netic flux cutting region, Nc is no of the coil turns,Bm is change in flux density and V (t) is velocity ofthe proof mass. The inductance and resistance ofthe coil are then added in series with the voltagesource.The PSpice model of the electromagnetic trans-duction mechanism is shown in Fig. 3. The relativemass velocity is multiplied with the factor NcBm Lc to represent the rate of change of fluxlinkage using a gain block and a voltage dependentvoltage source (E) is used to represent velocity138dependent voltage source. The electrical dampingforce (BIL force) is calculated by multiplying thecurrent through the coil Lm with Nc Bm Lc. Thisforce can be used as electrical damping inputto the generic MSD model. The two terminalsLoad pos and Load neg are then used to connectthe electrical load.Fig. 3. EM transduction PSpice simulation modelThe case study simulation results of electromag-netic transduction mechanism are given in section4.Electrostatic:A capacitor can be thought of as a chargecontrolled voltage source. A time varying capac-itor is a charge controlled voltage source withvariable gain. To represent this kind of variablegain voltage sources, a generic variable capacitoris realised using a fixed capacitor and a multiplieras shown in Fig. 4.C_fixedMULTIPLIERX(Z(t)) C_var+C_var−Fig. 4. Generic Variable Capacitor realisationThe fixed capacitor voltage is multiplied witha position dependent factor X(z(t)), therefore thevariable capacitor voltage is given by:VCvar = (1+X(z(t)))VCfixed (4)where VCvar and VCfixed are voltages across thevariable capacitor and the fixed capacitor respec-tively, which are referenced to C var , so that thevariable capacitor can be realised as a fully floatingcomponent (i.e. it is not ground referenced). TheX(z(t))value is derived based on the principle thatthe current flowing through the variable capacitorand fixed capacitor is the same and is given byI =CfixedddtVCfixed (5)from voltage relation equ. 4, substituting theVf ixed valueI =Cfixed(1+X(z(t)))ddtVCvar (6)Any time varying capacitance can be simulatedusing this generic variable capacitor model shownin Fig. 4, if its capacitance can be written of theformCfixed1+X(z(t)) . Different types of variable capaci-tor’s Cfixed and X(z(t)) values are given in Table. I.Variable ca-pacitor typeCfixed X (z(t)) ES ForceInplane gapClosing2Ng L f hdz(t)d2 Q2z(t)2Ng L f hdInplaneoverlapL f hdz(t)L f+Z(t)Q2d2Ng h1(L f+z(t))2Out of planegap closingAdmin(Zl+z(t) dmin)dminQ22 ATABLE IPARAMETERS OF VARIOUS VARIABLE CAPACITORSDifferent variable capacitors are modeled inPSpice by realising appropriate X(z(t)) in thegeneric variable capacitor equ. 4. For example,the PSpice model for inplane gap closing combdrive structure is shown in Fig. 5. Computationof electrostatic force given in Table I is alsoprovided in the model using ABM library. This canbe used as the electrical damping force input to thegeneric MSD model. Simulation results of inplanegap closing type variable capacitor are discussedin the following section.4. SIMULATION RESULTSComplete micro generator systems are modeledby interfacing various PSpice models such asgeneric MSD model and electrical and parasiticdamping force models according to Fig. 2.The electromagnetic micro generator is simu-lated for given input amplitude Yo= 22 3μm, fre-quency F= 50 Hz, inductance Lm= 2mH, No of139Fig. 5. PSpice model of an inplane gap closing comb drivevariable capacitorturns Nc=1000, active coil length Lc=2 mm, fluxdensity Bm= 0.8T, coil resistance Rc=25 , loadresistance Rl= 2310 , proof mass=1g, parasiticdamping coefficient (assumed) Dm=0.001 and endstop limit being set at 100μm.The simulation results of the proof mass dis-placement and velocity are shown in Fig. 6. It canbe seen that there is a plateau portion at the peak ofthe inertial mass displacement, which occurs whenthe mass hits the end stop limit. Sudden change inthe velocity of the mass on hitting the end stoprepresents the loss of its momentum.Fig. 6. Proof mass relative velocity and displacementIn order to validate the PSpice model of theinplane gap closing variable capacitor, it has beeninterfaced with the generic MSD PSpice modeland also with external circuit elements, which areused to charge and discharge the variable capacitorat specific points of mass travel. The variablecapacitor is charged when it is in the maximumcapacitance position i.e. at z(t) = Zl and z(t) = Zland is discharged when it is in the minimumcapacitance position i.e. at z(t)=0. Fig. 7. showsthe simulation results of the position of the combfingers, the voltage across the variable capacitorand the associated electrostatic force.0.15 0.16 0.17 0.18 0.19 0.2−101x 10−4Displacement[m]0.15 0.16 0.17 0.18 0.19 0.202040VariableCapvoltage[V]0.15 0.16 0.17 0.18 0.19 0.2−4−2024x 10−5Time [s]ESforce[N]Fig. 7. Inplane gap closing comb drive displacement,variablecapacitor voltage and electrostatic force5. CONCLUSIONSA combined electromechanical simulation toolkit has been developed for inertial micro genera-tors. Case study simulation results of Electromag-netic and Electrostatic micro generator systemshave been presented to verify the operation of themodels. In this paper, micro generator systems aresimulated with the load being a simple resistor.However, designing and interfacing of suitablepower conversion circuits needs to be addressed,and the flexibility of our simulation toolkit allowssuch simulations to be achieved by simply drawingthe circuits in PSpice. The toolkit for downloadalong with installation instructions can be foundat http://www.imperial.ac.uk/controlandpower/powermems.REFERENCES[1] S. Roundy, P. K. Wright, and J. M. Rabaey, Energy Scavengingfor Wireless Sensor Networks, 1st ed. Boston, Massachusetts:Kluwer Academic Publishers, 2003.[2] P. D. Mitcheson, E. K. Reilly, T. Toh, P. K. Wright, and E. M.Yeatman, “Transduction mechanisms and power density formems inertial energy scavengers,” in Proceedings of PowerMEMS 06, Berkeley, USA, 2006, pp. 275 – 278.[3] Serre.C, Pe’rez-Rodriguez.A, Fondevilla.N, Martincic.E,Morante.J.R, Montserrat.J, and Esteve.J, “Optimizationkeys for vibrational electromagnetic generators,” in 32ndInternational Conference on Micro and Nano Engineering,Barcelona,Spain, September 2006.[4] C. Saha, T. O’Donnell, H. Loder, S. P. Beeby, and M. J. Tudor,“Optimization of an electromagnetic energy harvesting device,”Magnetics, IEEE Transactions on, vol. 42, no. 10, pp. 3509–3511, 2006.[5] S. D. Senturia, Microsystem Design, 1st ed. Boston, Massa-chussets, USA: Klewer Academic Publishers, 2001.[6] P. D. Mitcheson, “Analysis and optimization of energy harvest-ing micro generator systems,” Ph.D. dissertation, Departmentof Electrical Engineering, Imperial College London, 2005.140

Simulation toolkit for energy scavenging inertial micro power generators

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