SYMBOLIC MODELING OF VIBRATION ENERGY HARVESTING BY POWER PZT STACK LOADED ON LI-ION BATTERY

Transcription

1 SYMBOLIC MODELING OF VIBRATION ENERGY HARVESTING BY POWER PZT STACK LOADED ON LI-ION BATTERY Rostov on Don, Russia Kaohsiung, Taiwan, R.O.C. S. Shevtsov, S.-H. Chang, 1

2 These oscillations arise freely, and I have determined various conditions, and have performed a great many beautiful experiments on the position of the knot points and the pitch of the tone, which agree beautifully with the theory. Daniel Bernoulli (from a letter to Leonhard Euler) Motivation 1. Renevable Energy and Power PZT Harvesting Systems 2. Most Important and Difficult Problems at the Conversion from Mechanical to Electric Energy 3. Why we Study the Battery as Electric Load for PZT Harvesting Circuit 4. Assumed Application and Assumptions 5. From the Physical and FE models to the Lumped Model of PZT Stack Circuit 6. Battery Model and its Properties as the Electric Load 7. Transient Analysis of the Battery Charge Process and Some Optimization Results 8. Conclusions We have found a new method for the development of polar electricity in these same crystals, consisting in subjecting them to variations in pressure along their hemihedral axes. Pierre and Paul-Jacques Curie (from the paper announcing their discovery) 2

3 Renevable Energy and Power PZT Harvesting Systems. Sources of Mechanical Energy, which can be Captured by PZT Stacks Mechanical vibrations of the road and bridges due to cars motion Oscillations of noise protective walls Oscillation of floor at the walking people 3

4 Most Important and Difficult Problems at the Conversion from Mechanical to Electric Energy and to Store it The principle of piezoelectric energies transformation Leakage. Need cyclic loading! Output electric power depends on the excitation frequency and load resistance! 4

5 Most Important and Difficult Problems at the Conversion from Mechanical to Electric Energy and to Store it Equivalent scheme of PZT transducer at low frequency approximation (beyond eigenfrequency band) Load Output voltage and electric power strongly depend on the load resistance, capacitance and inductance. Hence, PZT output and load input impedances matching is necessary! 5

6 Why we Study the Battery as Electric Load for PZT Harvesting Circuit? Random mechanical excitation Alternating voltage Electric circuit DC charge DC discharge Action of the wheels on the roadway Transform from mechanical strain to AC Rectifier, filter, matching of impedances Battery LED 1. Transformation the mechanical energy to the heat (resistive load) or to the electromagnetic field (capacitive and/or inductive load) is senselessly! 2. The use of electric energy immediately after its transformation cannot be realized in practice! 3. Harvested energy should be stored for the following or currently use 4. Alternating voltage should be rectified to charge a battery 5. DC voltage from PZT transducer should match to the battery and LED nominal voltage 6

7 Assumed Application and Assumptions Lighting tunnels and crossroads, remote from electric power grids These requirements need to be considered to obtain an efficient electric energy harvesting 1. Frequency spectrum of excitaton forces is enough wide, but it locate below 1 st eigenfrequency of PZT stack. Hence, low frequency approximation is well grounded 2. Forces from the moving transport, which act on the highway s cover are intensive, with random amplitude and frequency that depends on the cars weight, speed, and daily traffic intensity 3. PZT stack s cross-section depends on the perceived forces and strength of piezoelectric ceramics, whereas number of PZT layers depends on the nominal voltage of lighting devices and battery 4. Impedances of battery and PZT electric energy harvester should be matched. 5. The PZT electric energy harvester must provide a battery charge, which is enough to work in the dark 7

8 From the Physical and FE models to the Lumped Model of PZT Stack Circuit - 1 Two PZT stacks with different number and thickness of PZT layers were studied experimentally at the harmonic and impulse mechanical excitation. These results were then used for the models validation. 8

9 From the Physical and FE models to the Lumped Model of PZT Stack Circuit - 2 The set of stacks FE 3D and axially symmetric 2D models was built with the different number of parallel connected PZT layers, and these models were studied at harmonic and impulse excitations. Prestress force 9

10 From the Physical and FE models to the Lumped Model of PZT Stack Circuit - 3 Some FE simulation results, which have been used to tune the lumped model. (PZT stack consists of 16 layers of 1 mm thickness and experience the stress amplitude 1.35 Mpa) 10

11 Batery Model and its Properties as the Electric Load - 1 This model should correctly describe the voltage and current through a battery at the charge / discharge at the different State Of Charge (SOC) We used here the discharge model developed in [*] for the Li-Ion batteries Q it E bat = E0 K + Aexp( B it) R i it 0.1Q where E 0 is battery constant voltage (V), Q is the battery capacity (A*h), i - battery current (A), K - polarization constant (V/(A*h)), A - exponential zone amplitude (V), B - exponential zone time constant inverse (A*h)-1, R is internal resistance of battery (Ohm), and it is the actual battery charge (A*h) it = idt We suggest a simple model for battery charge, which takes into account the actual state of charge SOC in of the battery and added charge Q add expressed in terms of SOC SOC Q (, SOC ) = 1 ( 1 SOC ) add in in exp Q These two models are obtained at the following assumptions: ( 1 SOC ) in 1. The internal resistance is supposed constant during the charge and discharge cycles and does not vary with the amplitude of the current. 2. The model s parameters are deduced from the discharge characteristics and assumed to be the same for charging. 3. The capacity of the battery does not change with the amplitude of the current. The Self-Discharge of the battery is not represented. 4. The battery has no memory effect. * Tremblay, O., Dessaint, L.-A., Experimental Validation of a Battery Dynamic Model for EV Applications, World Electric Vehicle Journal, 3, Q add

12 Batery Model and its Properties as the Electric Load - 2 For the studied battery with nominal capacity 0.25 A*h, rated voltage 12 V, and nominal current 12 ma the dependencies of voltage at discharge, change of the battery SOC at its charge, and corresponded voltage are presented below. At the charge / discharge the model s parameters depend on the state of charge and are changed non-linearly. Hence, the battery cannot be described by system with constant properties, but by nonlinear equations 12

13 Battery Model and its Properties as the Electric Load - 3 We can vary the values of capacitance and inductance to optimize the battery charge process The Simscape - Simulink workflow diagram for PZT harvester's electric load models the battery according Eqs. 13

14 Transient Analysis of the Battery Charge Process and Some Optimization Results - 1 The force, which acts on the stack is the sum of sin waves with random amplitudes and phases plus the prestressing force that eliminate the tensile of PZT material Input forces spectrum 14

15 Transient Analysis of the Battery Charge Process and Some Optimization Results - 2 Initial conditions for battery Main modules: PZT stack Full bridge rectifier Force generation Battery model We can vary the number and thickness of PZT stack with constrained dimensions to optimize the battery charge process 15

16 Tuning the Leakage Resistance and Electric Capacitance Analysis of Stack with a number of PZT Layers 16

17 Transient Analysis of the Battery Charge Process and Some Optimization Results - 3 Dynamics of the battery charge at the varied initial state and stack s structure. For each stack the value of the filter capacitance and inductance are optimal, but rate of charge is weak sensitive to their magnitudes. For each stack s structure there are some state of charge when matching between input resistance of the battery and output resisitance of PZT stack is better. There is most efficient structure of PZT stack for the given excitation and load conditions 17

18 Conclusions We present the equivalent circuit model for the power PZT stack harvesters and some results of their optimization. Such harvesters can be installed under a surface of highways for the random vibration energy harvesting and charging the batteries, which are intended to supply the lighting (by LED e.g.) at the dark. The input data for the problem statement are the mechanical vibrations spectrum, their intensity and also required charge capacity and nominal voltage of the batteries. Taking into account the fatigue strength of piezoelectric ceramics, its elastic, electromechanical and electric properties, these input data constraint the dimensions of PZT stack. Our suggested modeling approach is based on the capabilities of Simscape / Simulink toolboxes, which include full set of electric elements and, particularly, built-in "Piezo Stack" block. This block present a simplified description of the piezoelectric stacks neglecting the effects of hysteresis, non-linearity, leakage, mechanical energy dissipation, but these effects can be easily included using other Simscape and Simulink blocks. In order to correctly describe the dynamic of the battery charge / discharge we proposed the lumped model that allows to express the evolution of the battery state (state of charge and voltage) at its charging by a current, which is generated by PZT stack and rectified by full bridge with the additional resistance, electric capacitance and inductance. By using the built lumped model of the harvesting system, which can work in the batch mode, we obtained the optimized values of the electric scheme for the different structures of PZT stack, and we found the expected values of the harvested power that can be stored in the battery during a given time. 18

19 Thank you VM for your attention 19