## 3 Experimental Studies and Discussions
### Voltage and Power Output Performance  
In this section, we evaluate the frequency responses of the voltage and power output of the proposed multiple-cantilever PEH. Noting that a power transformer substation has a primary operational frequency of 100 Hz [8; 9; 10; 11], the performances of the PEH were evaluated close to this frequency value. Base-movement excitations with a constant amplitude of acceleration were provided by an electromagnet shaker and controlled by an acceleration meter, as previously illustrated in Figure 3. It was illustrated experimentally that a Three-Phase Three-Leg Core with a 142 mm ribbon, which was 142 mm wide and had a 60 mm lamination thickness of its core, would yield vibration with amplitudes up to 1.5-4 g [53]. Therefore, the acceleration values of excitations were chosen as 0.373-2.98 g, which are common values in real applications [53]. Figure 4: (a) Diagram and (b) experimental platform of the wireless sensing node and host computer. Figure 5 shows the open circuit voltage output under forward and backward frequency sweeping. The voltage outputs of the piezoelectric transducer on the first layer at the fixed end (PZT1) under excitations with different amplitudes are presented for illustration. The forward frequency responses are shown in Figure 5a, where the frequencies of excitations sweep from low to high. It can be seen that the harvester reached its RMS open circuit voltage output of 14.28 V under 0.745 g amplitude excitation in the forward frequency responses, as shown in Figure 5a. An increase in the amplitudes of excitation can effectively enhance the voltage outputs. For instance, the peak output of the PEH is 29.17 V under an excitation of 2.98 g. Additionally, the proposed PEH exhibits a softening effect under a large amplitude excitation of 2.98 g, i.e., the voltage outputs lean towards the left under a large amplitude excitation with a sudden decrease at 98.88 Hz in the forward frequency sweeping. This phenomenon can be attributed to the nonlinearity of the additional constraints, which led to uneven stress in the three beams, since the three cantilevers are assembled in parallel. In addition, the backward frequency responses are shown in Figure 5b, where the frequencies of excitations sweep from high to low. The frequency responses under forward and backward responses show difference with each other due to the exitances of nonlinearity. The voltage outputs in this scenario are smaller than those under forward frequency sweeping. The high voltage output can be achieved by properly selecting the frequency sweeping direction in a real application. Additionally, an increase in the amplitudes of excitation can effectively enhance the voltage outputs. Nevertheless, the PEH has large amplitude voltage outputs around 100 Hz that could power the wireless sensor node. As the proposed PEH contains six piezoelectric transducers, the open circuit RMS voltages of all the transducers were measured and compared, as shown in Figure 6. The voltage outputs were measured under excitations of 0.745 g. In addition, the voltage outputs of different piezoelectric transducers exhibited minor differences with each other. These stem from the various material properties of the transducers, as well as manual  
Figure 5: (**a**) Forward and (**b**) backward open circuit voltage output of PZT1. assembly errors. In addition, it can be observed that the transducers attached to the same cantilever have similar voltage outputs. In practice, these outputs are influenced by material properties and the adhesive bonding process. Specifically, the piezoelectric transducers sourced from Jiayeda exhibit slight variations in their piezoelectric and dielectric constants, leading to differences in their voltage outputs in this experiment. Nevertheless, all the piezoelectric transducers can effectively output electrical energy. To evaluate the power output capability of the proposed PEH, each of the piezoelectric transducers were connected to individual resistance loads [32; 33; 34; 35].