# A Self-Adaptive and Self-Sufficient Energy Harvesting System

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. System Setup

#### 2.1. Overview

#### 2.2. Adaptivity and Bandwidth

_{r,M}= 36.4 Hz (Figure 4, filled diamonds and solid line). The magnetic forces now no longer caused step losses, so all further tests were carried out with this setting.

#### 2.3. Stepper Motor

#### 2.4. Vibration Frequency Measurement

^{11}= 2048 values are required because of the limitation of the library function to powers of two). In the case of clearly defined vibration frequencies, the measurement duration can be reduced. A total of 1024 measured values are recorded in $T=2.56\text{}\mathrm{s}$, so that the sensor only runs half of the time compared to the longer measurement. After zero-padding the measurement data to 2048 measurement points [35] (p. 31), the spectrum provides a graphic resolution of $\Delta {f}_{\mathrm{S}}=0.2\text{}\mathrm{Hz}$. However, an FFT with 2048 measuring points is still required.

#### 2.5. Loop Algorithm

## 3. Results

#### 3.1. Experimental Setup

#### 3.2. Periodic Adaptation

#### 3.3. Interpretation

#### 3.4. Generalization

## 4. Summary and Outlook

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Sketch of the self-adaptive energy harvester on the test bench. Dashed lines indicate data exchange, solid lines indicate energy flow. Coupling magnet (CM), tuning magnet (TM), acceleration sensor (S), energy management (EM), microcontroller (MCU).

**Figure 2.**Self-adaptive energy harvesting system with electromagnetic tuning. (

**a**) Harvester prototype on the test bench. d

_{CT}is the magnet gap. (

**b**) The angle α is defined by the position of the south (S) and north (N) poles between the coupling magnet (top) and tuning magnet (bottom).

**Figure 3.**Resonance curves of the open circuit voltage for different rotation angles α between α = 0° (red) and α = 180° (blue). The magnet distance was d

_{CT}= 13 mm.

**Figure 4.**Relationship between the magnet angle α and the resonance frequency f

_{r}. The unfilled and filled diamonds, respectively, represent the measured resonance frequencies f

_{r}for d

_{CT}= 13 mm (see Figure 3) and d

_{CT}= 14 mm. The solid and dotted lines are the results of fitting the trigonometric function (4) to the measurement data.

**Figure 5.**Evaluation of the vibration frequency f

_{a}from a discrete spectrum involving the leakage effect: (

**a**) The amplitude spectrum |A

_{s}(f)| (solid line) and discrete spectrum |A

_{sf}(f)| (crosses) of a harmonic signal with the frequency f

_{a}measured over a time T, which is not an integer multiple of 1/f

_{a}. (

**b**) The ratio of the two largest values in the discrete spectrum according to Equation (6). A discrete version of the function involving 21 data points was saved in a lookup table. The pole at $\Delta {f}_{{f}_{\mathrm{a}}}=0$ was arbitrarily replaced by a finite value of 100.

**Figure 6.**Vibration frequencies f

_{a,meas}measured by our system when excited with different frequencies f

_{a}. Each point is the average of five individual measurements (95% confidence level). The dark and light gray bands represent respective tolerance bands of ±0.05 Hz and ±0.1 Hz around the true value (dotted line).

**Figure 8.**Harvested power P

_{0}of a sequence with A = 1 m/s² and τ = 5 min. The numbers in circles mark the time intervals i during which the vibration frequency was constant at f

_{a,i}. The interval boundaries are marked by gray dashed lines. (

**a**) The complete sequence. (

**b**) Detail of (

**a**) in the vicinity of the first adaptation step.

**Figure 9.**Net harvested energy W

_{net}at a stationarity duration of τ = 5 min for different acceleration amplitudes A. The red circles mark calculation points for the net power P

_{net}.

**Figure 10.**Net energy W

_{net}at A = 1.0 m/s² for different stationarity durations τ. The red circles mark calculation points for the net power P

_{net}. The sequence duration was t = 6τ.

**Figure 11.**Net power P

_{net}depending on the stationarity duration (length of the time interval between two subsequent ambient vibration frequency changes) τ. The dots mark the values from Table 1, the dashed lines are fit functions according to Equation (7). The value of the harvested power P

_{0}for A = 1.0 m/s² is the fit function result. It can also be interpreted as the limit value of P

_{net}for τ → ∞.

**Table 1.**Average net power P

_{net}of a sequence for different acceleration amplitudes A and stationarity durations τ.

P_{net}/µW | τ = 2 min | τ = 5 min | τ = 10 min |

A = 0.8 m/s² | — ^{1} | −13 | 127 |

A = 1.0 m/s² | −359 | 154 | 225 |

A = 1.2 m/s² | −47 | 424 | — ^{1} |

^{1}No reliable average values.

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**MDPI and ACS Style**

Mösch, M.; Fischerauer, G.; Hoffmann, D.
A Self-Adaptive and Self-Sufficient Energy Harvesting System. *Sensors* **2020**, *20*, 2519.
https://doi.org/10.3390/s20092519

**AMA Style**

Mösch M, Fischerauer G, Hoffmann D.
A Self-Adaptive and Self-Sufficient Energy Harvesting System. *Sensors*. 2020; 20(9):2519.
https://doi.org/10.3390/s20092519

**Chicago/Turabian Style**

Mösch, Mario, Gerhard Fischerauer, and Daniel Hoffmann.
2020. "A Self-Adaptive and Self-Sufficient Energy Harvesting System" *Sensors* 20, no. 9: 2519.
https://doi.org/10.3390/s20092519