# Long-Lifetime Event-Driven Wireless Monitoring System for Pole-Mounted Transformers
## 4 Simulation Results  
Measuring an abnormal signal from an active and healthy power transformer can be not only time consuming but also potentially dangerous. To assess the effectiveness of the proposed monitoring system for a pole-mounted transformer, a PD signal was chosen as an input for monitoring and was modeled using an experimental jig, as shown in Figure 8[29]. A function generator supplied an AC input to a power amplifier, producing a 22 kV AC input, which was fed to needle electrodes in an oil-filled can to mimic a PD signal. This signal was sensed using a PD sensor attached to the bottom of the can, and its transient waveform was stored using an oscilloscope, as shown in Figure 9a.  
MATLAB was used to generate the Simulation Program with Integrated Circuit Emphasis (SPICE) simulation program with the PD signal as an input, extracting a fitted curve composed of eight single-tone sine waves given by  
\[f(t)=\sum_{n=1}^{8}a_{n}\sin(b_{n}t+c_{n}), \tag{12}\]  
Figure 8: Experimental jig for modeling the PD in a pole-mounted transformer. (**a**) Schematic diagram for the jig and (**b**) experimental setup.  
Figure 9: PD signal from the PD generator. (**a**) Mimicked PD signal and its fitted curve and (**b**) fast Fourier transform of the mimicked PD signal.  
where the coefficients \(a_{\text{n}}\), \(b_{\text{n}}\), and \(c_{\text{n}}\) are listed in Table 1. The fast Fourier transform of the PD input in Figure 9b exhibits dominant frequencies in several MHz bands.  
In this study, the Cadence Spectre with TSMC 0.18 \(\upmu\)m process parameters was used for SPICE simulation. The control circuit timing diagram is shown in Figure 10. The peak voltage of the fitted input was set to 1 V. Other parameters were set as follows: \(V_{\text{REF1}}=0.4\) V, \(V_{\text{REF2}}=0.1\) V, \(C_{1}=10\) pF, and \(C_{2}=10\) pF.  
The basic operation of this circuit is identical to that shown in Figure 7b. The 3 dB pass band for the BPF was set to 100 Hz-50 MHz. Noise \(v_{\text{N}}\) in (1) was assumed to be a white noise source in the Cadence Spectre simulation. Figure 11 shows simulated SNR results for a conventional system with the proposed EC and event-driven monitoring system. As \(t_{\text{D}}\) is an ad hoc parameter that varies according to the input signal, it was set to a Gaussian random variable with a mean of \((t_{\text{LI}}+t_{\text{LI}})/2-t_{\text{LI}}\) and variance of 1 \(\upmu\)s for the \(i\)th intermittent abnormal input. A total of 1,000,000 iterations were used for validating the ranges of the SNRs in the conventional system with EC and using the proposed method, \(SNR_{\text{EC}}\) and \(SNR_{\text{Prop}}\), respectively. \(SNR_{\text{EC}}\) is shown with error bars, the average value indicated by a square. \(SNR_{\text{Prop}}\) is always equal to or greater than \(SNR_{\text{EC}}\) for any noise level. At \(RMS(v_{\text{N}})=27.68\) mV, \(SNR_{\text{Prop}}\) is greater than the average value of \(SNR_{\text{EC}}\) by 12.93 dB, and greater than the minimum value of \(SNR_{\text{EC}}\) by 135.42 dB.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**n** & \(a_{\text{n}}\) **(V)** & \(b_{\text{n}}\) **(MHz)** & \(c_{\text{n}}\) **(Radian)** \\ \hline
1 & 106.7147 & 4.69 & \(-0.7276\) \\
2 & 70.4558 & 5.08 & 1.7639 \\
3 & 54.6218 & 3.13 & \(-2.0701\) \\
4 & 50.9293 & 4.30 & 2.7057 \\
5 & 47.04 & 2.34 & \(-3.1245\) \\
6 & 40.5062 & 3.52 & 1.1196 \\
7 & 40.3764 & 3.91 & \(-1.4116\) \\
8 & 33.9337 & 1.95 & 0.3388 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Coefficients for curve fitting.  
Figure 10: Simulated waveforms in the proposed monitoring system.