**5. Results and Discussion**

*5.1. Performance Analysis of the Harvester*

On obtaining the voltage time-history data through wind tunnel experiments, the root mean square (RMS) value of voltage *VRMS* can be calculated:

$$V\_{RMS} = \sqrt{\frac{1}{T\_2 - T\_1} \int\_{T\_1}^{T\_2} u(t)dt} \tag{12}$$

Accordingly, the mean power *P* can be obtained as:

$$P = \frac{1}{T\_2 - T\_1} \int\_{T\_1}^{T\_2} \frac{u(t)^2}{R\_L} dt \tag{13}$$

in which *T2* and *T1* are the start and end time during the acquisition period, respectively, *RL* is the external load resistance, and *u*(*t*) is the instantaneous voltage.

Figure 6 displays the results of the RMS voltage and mean power output by connecting various load resistances from 10 kΩ to 1 MΩ in the PVDF film in the wind speed range of 3–10 m/s. It can be seen in Figure 6a that under the same load resistance, the wind speed continues to increase, and the output RMS voltage has an obvious upward trend. The minimum RMS voltage recorded under a load resistance of 10 kΩ is 350 mV. In addition, the output RMS voltage of this resistance model is relatively small. In the wind speed range of 3–10 m/s, the output RMS voltage steadily increased from 350 mv to 0.14 V. The highest RMS voltage recorded under the load resistance of 1 MΩ was 2.96 V. It can be found from Figure 6b that in the wind speed range of 3–10 m/s, the rising trend of output power was similar to the rising trend of RMS output voltage. When the wind speed was 10 m/s, the maximum load resistance of 200 kΩ in this experiment was 12.1 μW. The results indicate that when the load resistance is constant, as the input air speed increases, the voltage and power between the load resistances increase almost in advance.

**Figure 6.** (**a**) Output voltage and (**b**) power with different wind speed.

According to the RMS voltage and output power calculated by Formulas (12) and (13), the power density and voltage density per scanning volume, which are defined as the power value and RMS voltage value divided by the volume of piezoelectric film, were calculated. In the analysis that followed, the load resistance first had to be matched to evaluate the harvesting performance. Figure 7 displays the change of output voltage density and power density with load resistance under different wind speeds. Figure 7a shows that the overall output trend of the measured voltage density increases with the increase of resistance within a certain wind speed range, and the maximum voltage density is 29.1 V/mm3. Figure 7b shows that within a certain range, the overall output power trend of the measured power density at all wind speeds increases as the resistance increases. The optimal value of the load resistance for different wind speeds is between 100 kΩ and 430 kΩ. Outside this load resistance range, the average power generated is significantly reduced. After intensive testing, it was found that when the load resistance is about 200 kΩ, it provides the highest output average power. Therefore, *R0* = *RL* = 200 kΩ is the optimal electrical load resistance, and this result will be used for the efficiency of the energy harvester in the subsequent experimental discussion when the load resistance is 200 KΩ, and the power density is 119.7 μW/mm3. Previous studies have pointed out that there is an optimal resistance *R0* for the best collection efficiency. Neglecting the effects of damping and dielectric loss, the optimization resistance can be determined as [36]:

$$R\_0 = \frac{1}{2\pi fC} \tag{14}$$

where *C* is the harvester capacitance and *f* is the vibration frequency.

**Figure 7.** (**a**) Output voltage density and (**b**) power density with different load resistance.

To further explore the working performance of the harvester, it was necessary to analyze the piezoelectric film dynamics characteristics. Figure 8 displays the time history of the output voltage with a load resistance of 300 kΩ at a wind speed of 3–7 m/s. As demonstrated, the voltage signal fluctuates periodically for each case associated with a fixed wind speed, and the amplitude of the voltage increases distinctly as the wind speed increases (from 0.14 V to 1.12 V). Apparently, the periodic variation of output voltage is attributed to the periodic evolution of the strain around the fix end of the cantilever beam. Because the galloping amplitude increases consistently with the increase of wind speed, the strain becomes larger for the cases with stronger incoming wind, which further leads to higher output voltage.

**Figure 8.** Diagram of Voltage time history (*RL* = 100 kΩ).
