This project will develop a holistic approach to the modelling and performance optimisation of energy harvester (EH) through the use of hardware description languages (HDLs). Energy harvesters which convert ambient environment energy into electrical energy consist mainly of mechanical and electrical domains, i.e. mixed technology. The proposed approach uses an HDL to model the EH (micro-generator, booster, etc). The salient feature of an integrated model is that it allows optimisation based on system performance, and in our approach an HDL is used not only for the modelling and simulation of the whole EH system but also for the implementation of optimisation algorithms. This has resulted in an integrated performance optimisation system wholly implemented in HDL. Several case studies of various vibration-based EHs will be presented. Mixed-technology HDL itself is not new, but what is new is to maximize the performance of EH through the use of HDL-based modelling and optimisation. Several HDLs that support multiple domain system modelling and simulation have been available, such as VHDL-AMS, Verilog-AMS and SystemC-A, and we investigate these tools for developing integrated models to enable optimisation of various parts of an EH to maximize its efficiency. In this paper VHDL-AMS has been chosen as the modelling language. (Back to top)

2 State of the art

Energy harvesting is the process by which ambient energy from the environment is captured and stored. Various devices have been reported to scavenge energy from different sources, such as light, heat, RF and vibrations. Great research interests have been attracted to the development of energy harvesters because it addresses the energy issue of the recent growth in mobile electronics and several emerging applications including wireless sensor networks. Most mobile devices and wireless sensor nodes are now powered by batteries, which need charging or replacement after a period of time (Figure 1). If these devices could be self-powered by energy harvesters (Figure 2), great amount of cost in maintenance will be saved. In addition some applications with limited accessibility such as biomedical implants and structure embedded micro-sensors will also benefit from energy harvesters.

Figure 1. Charging of a mobile phone

Figure 2. Mobile phone without a charger

Among all the available sources, kinetic based EH seems to be the most popular since mechanical vibrations are widely present. There are three main transduction mechanisms in vibration-based energy harvesting: electromagnetic, piezoelectric and electrostatic, each of which has various examples reported in literature. Because the ambient vibrations in environment are usually of a quite small amplitude, the generated voltage from a micro-generator may not be able to power an electronic device directly. In most cases, external circuits are necessary to boost up the voltage and store the energy into a battery or a super capacitor. Clearly such an EH consists of components from both mechanical and electrical domains as well as external circuits which regulate and store the generated energy. Therefore the performance optimisation should only be based on a model that describes the EH as an integrated system. However, most existing modelling and optimisation methods are concentrating on either the micro-generator or the external circuits separately while the design tools for an integrated system are missing. Finite Element (FE) method is widely used to model the micro-generator and most circuit models employ SPICE-like simulators. Many reported circuit designs treat the micro-generator as an ideal voltage source or use equivalent circuit model because “the current EDA tools do not support direct integration of the electromechanical dynamics of vibration-based energy harvesters into circuit simulations”. (Back to top)

3 Integrated approach of EH modelling and optimisation

An EH normally has three main components: the microgenerator which converts ambient environment energy into electrical energy, the voltage booster which pumps up and regulates the generated voltage, and the storage element such as a super capacitor or a battery (Figure 3). VHDL-AMS describes the micro-generator as a series of differential and algebra equations (DAEs). The voltage booster could be modelled at circuit or behaviour level.

Figure 3. Block diagram of an EH.

Figure 4 shows the proposed approach for EH modelling and optimisation. The original design chooses certain micro-generator structure and booster topology to form an EH. This EH is then modelled and simulated in VHDL-AMS testbench. With the integrated model, a designer will be able to modify an EH with only the system performance in mind. Two back-curves in the figure represent two ways to maximize the system’s efficiency. Firstly, system components could be changed to find a combination that meets the specification. The presented case study below examines two type of voltage booster with the same electromagnetic micro-generator. Similarly, different generator mechanisms, such as piezoelectric or electrostatic, can also be tested with the same voltage booster. Secondly, the parameters of one component could be optimised to achieve better performance. Here we developed a genetic optimisation wholly implemented in VHDL-AMS testbench but other optimisation methodologies can also be investigated based on the integrated model. The traditional trial-and-error process will then be replaced by multiple simulations. (Back to top)

Figure 4. Proposed integrated approach for EH modelling and optimisation.

4 Modelling of a vibration-based EH

4.1 Electromagnetic micro-generator

The case study presented here uses a vibration based electromagnetic micro-generator as example. The design is based on a cantilever structure. The coil is fixed to the base and four magnets, which are located on both sides of the coil, form the proof mass (Figure 5).

Figure 5. Electromagnetic micro-generator.

The VHDL-AMS code of the model is given below:

library IEEE;
use IEEE.ENERGY SYSTEMS.all;
use IEEE.MECHANICAL SYSTEMS.all;
use IEEE.ELECTRICAL SYSTEMS.all;
use IEEE.math real.all;
use work.EnergyHarvester.all;
entity EMH is
port(terminal HOUSE:translational;
terminal LOAD:electrical);
end entity EMH;
architecture Behaviour of EMH is
quantity yt across HOUSE to translational ref;
quantity zt:DISPLACEMENT;
quantity emv:VOLTAGE;
quantity vt across it through LOAD to
electrical ref;
quantity Fem:force;
begin
mp*zt’DOT’DOT+Cp*zt’DOT+Ks*zt+Fem==-mp*yt’DOT’DOT;
Phi*zt’DOT==emv;
emv==vt-Rc*it-Lc*it’DOT;
Fem==-Phi*it;
end architecture Behaviour;

If a load resistance is connected to the microgenerator, it has been proved that maximum power will be delivered to the load when the system’s parasitic damping equals to the electromagnetic damping. When excited by a 50Hz sine wave vibration of 8.4μm amplitude, this device can generate a maximum power of 45.7μW under the optimal load condition. The output voltage is around 600mV. (Back to top)

4.2 Voltage booster

4.2.1 Voltage multiplier (VM)

Because the output voltage from a micro-generator is often not large enough to power any electronic device directly, external circuits are necessary to boost up the voltage and AC-DC rectification is normally required. A voltage multiplier, which uses cascaded diodes and capacitors to achieve higher DC voltage from an AC input, seems to meet the requirements and has been investigated here. There are two types of voltage multiplier based on different configurations,
Villard (Figure 6(a)) and Dickson (Figure 6(b)). To evaluate their performances, circuit simulations have been carried out. The input voltage is from an ideal voltage source. The frequency is 50Hz and the amplitude is 640mV, which are the same as the optimal output from the micro-generator. Both of the voltage multipliers are configured as 6-stage and the output is connected to a 0.22F super capacitor. Simulation results show that the Villard multiplier can charge the super capacitor to 2V in 8 minutes and 46 seconds and the Dickson type can reach that voltage in only 3 minutes and 13 seconds. (Back to top)

(a) Villard VM (b) Dickson VM

Figure 6. Voltage multiplier configurations.

4.2.2 Voltage transformer (VT)

A voltage transformer together with a rectifier can also act as the voltage booster for an EH. The advantage of a voltage transformer is that due to the electromagnetic coupling, the affect of the capacitive load is reduced and the microgenerator may work under optimal conditions. Two types of rectifier configuration have been tested. Simulation results show that comparing to a common full-bridge rectifier, the configuration in Figure 7 gives better performance since it uses less diodes and thus loses less energy. The number of turns and the resistance value of primary (N1,R1) and secondary winding (N2,R2) are the four main parameters that determine the voltage transformer’s performance. (Back to top)

Figure 7. Voltage transformer configuration.

4.3 Performance of the integrated EH

An integrated VHDL-AMS model of the EH has been built to evaluate its overall performance. The VHDL-AMS model incorporates both the electromagnetic microgenerator and the VM booster. Here the ideal voltage source has been replaced by the mixed technology model of the micro-generator. Simulation results are shown in Figure 8.

Figure 8. Simulation waveforms of EH models with VM booster.

As can be seen from the waveforms, the integrated model behaves massively different from the independent model. The EH with Villard voltage multiplier takes more than 10 hours to charge up the super capacitor to 2V while the Dickson configuration, which shows better performance in the independent circuit simulation, has even not reached the required value. (Back to top)

5 Optimisation of EH with voltage transformer

Simulation results above indicate that the voltage booster can greatly affect the output from the micro-generator. Thus the performance optimisation of an EH should only be based on an integrated model. Here we uses VHDL-AMS to implement a genetic algorithm (GA) to optimise the EH model with voltage transformer as the booster. A GA is an optimisation method based on natural selection, which usually has the following elements: populations of chromosomes, selection according to fitness, crossover to produce new offspring, and random mutation of new offspring.

5.1 Parallel GA in VHDL-AMS testbench

In the VHDL-AMS implementation, the chromosome is modelled as a component with 4 genes as input parameters (N1,R1,N2,R2), the base vibration y(t) as the excitation and the charging speed of the super capacitor v′dot as the output fitness. A flow chart of how the parallel GA is implemented and executed in the VHDL-AMS testbench is shown in Figure 9. Unlike most existing computer implementations of GA that evaluate one chromosome iteratively to form a population, in the VHDL-AMS based optimisation here, the chromosomes of a population are implemented in parallel. The genes are initialized by uniformly distributed random numbers. The same stimulus is applied to the population and all the chromosomes are evaluated simultaneously to get a vector of fitness values. The tournament selection is chosen as the parent selection method, because it prevents premature convergence with efficient computations. The selection method uses fitness values in which parents with higher fitness (i.e. higher v′dot) are more likely to be selected to produce offspring. Elitism is also used to improve GA’s efficiency by artificially inserting the best solution into each new generation. Since the genes are real numbers, arithmetic crossover is used to generate the offspring. Finally, gene mutation is employed to introduce new solutions into the new population. The evaluation-selectioncrossover-mutation process is repeated until all the chromosomes converge to the same fitness. In VHDL-AMS, this loop is controlled by a finite state machine. (Back to top)

Figure 9. Genetic optimisation in a VHDL-AMS testbench using concurrently running chromosomes.

5.2 Simulation results

In the genetic optimisation, the population size is 100 chromosomes. The crossover and mutation rate are 0.8 and 0.02 respectively. The chromosome’s fitness is updated every 50ms. After simulating the testbench for 30 seconds, which corresponds to 600 generations in the GA optimisation, the gene values converge to an optimum. The values of the genes are listed in Table 1.

Table 1. Parameters of optimal VT configuration.

Then, the GA-optimised EH model is simulated and the waveform of the super capacitor charging is shown in Figure 10. For comparison, the EH models with VM boosters are also presented. As can be seen from the simulation results, the optimised EH can charge up the 0.22F super capacitor to 2V in 6 hours, which is 40% improvement comparing to the Villard voltage multiplier. (Back to top)

Figure 10. Simulation waveforms of super capacitor charging by different EH models.