# Long-Lifetime Event-Driven Wireless Monitoring System for Pole-Mounted Transformers
## 2 Conventional Monitoring Systems
### Conventional Battery-Powered Wireless Monitoring  
Figure 3a shows a basic battery-powered wireless monitoring system in a noisy environment, with a band-pass filter (BPF) as a signal conditioner [19; 20; 21; 22; 25]. The BPF input \(v_{\text{SN}}\) is defined as  
\[v_{\text{SN}}(t)=v_{\text{S}}(t)+v_{\text{N}}(t), \tag{1}\]  
where \(v_{\text{S}}\) and \(v_{\text{N}}\) are the sensor output and noise, respectively. Assuming that \(v_{\text{N}}\) is white noise, the output signal of the BPF, \(v_{\text{IN}}\), can be expressed as  
\[v_{\text{IN}}(t)=v_{\text{S}}(t)+v_{\text{NF}}(t), \tag{2}\]  
where \(v_{\text{NF}}\) is the filtered noise. This \(v_{\text{IN}}\) is fed to an analog-to-digital converter (ADC) with high sampling frequency \(f_{\text{H}}\). Assume the abnormal input is an intermittent continuous signal with \(i\)th lower and upper time bounds \(t_{\text{Li}}\) and \(t_{\text{Ui}}\), respectively, as depicted in Figure 3b.  
Figure 2: Block diagrams of conventional monitoring systems: (**a**) wired monitoring for large-scale transformers, (**b**) remote and (**c**) wireless monitoring for distribution transformers.  
A monitoring system requires a large number of samples; in fact, the sampling frequency \(f_{\rm H}\) must be higher than the Nyquist rate of \(v_{\rm IN}\). The energy required for monitoring the \(i\)th intermittent abnormal input sampled at \(f_{\rm H}\), \(E_{\rm Bi}(f_{\rm H})\), can be calculated as  
\[E_{\rm Bi}(f_{\rm H})=\big{[}P({\rm BPF})+P({\rm ADC}(f_{H}))+P({\rm TX}(f_{\rm H }))\big{]}\cdot\Big{(}t_{L(i+1)}-t_{Li}\Big{)}, \tag{3}\]  
where \(P(X)\) is the average power consumption of block \(X\). The power consumption in an ADC and TX can be functions of \(f_{\rm H}\). As the minimum sampling speed is limited by the Nyquist rate, \(f_{\rm H}\) cannot be decreased to reduce energy consumption. Therefore, to lower energy consumption, it is critical to have a signal conditioner that converts an input to another form that allows for a reduced sampling rate without degrading the physical significance of the input. The RMS value is one of the most important criteria for evaluating the signal acquired by various sensors, including PD and acoustic emission [26; 27; 28]. Adding an RMS converter to the signal conditioner, as depicted in Figure 4a, the output of the RMS converter, \(v_{\rm RMS}\), can be expressed as  
\[v_{\rm RMS}(t)=RMS(v_{\rm IN}(t))=\sqrt{\frac{1}{t-t_{\rm L}}\int_{t_{\rm L}} ^{t}v_{\rm IN}^{2}(\tau)d\tau}, \tag{4}\]  
where \(RMS(x(t))\) is the RMS value of \(x\) from the lower time bound \(t_{\rm L}\) to \(t\).  
The frequency of \(v_{\rm RMS}\) can be lower than that of \(v_{\rm IN}\) by the integration, which means the sampling frequency of the RMS output,\(f_{L}\), can be much lower than \(f_{\rm H}\) (\(f_{\rm H}>2f_{\rm VIN}>f_{\rm L}>2f_{\rm VRMS}\)), as shown in Figure 4b. Note that \(f_{\rm VIN}\) and \(f_{\rm V  
Figure 4: Conventional low-speed monitoring system with RMS converter. (**a**) Block and (**b**) timing diagrams.  
Figure 3: Conventional high-speed monitoring system with a band-pass filter (BPF) as a signal conditioner. (**a**) Block and (**b**) timing diagrams with noise.  
signals \(v_{\text{IN}}\) and \(v_{\text{RMS}}\), respectively. Thus, the energy consumption for the \(i\)th intermittent abnormal input using an RMS converter sampled at \(f_{\text{L}}\), \(E_{\text{RMSi}}(f_{\text{L}})\), can be expressed as  
\[E_{\text{RMSi}}(f_{\text{L}})=[P(\text{BPF})+P(\text{RMS})+P(\text{ADC}(f_{L} ))+P(\text{TX}(f_{\text{L}}))]\cdot\Big{(}t_{\text{L}(i+1)}-t_{\text{L}i}\Big{)} \tag{5}\]  
As the provided condition \(P(\text{RMS})+P(\text{ADC}(f_{\text{L}}))+P(\text{TX}(f_{\text{L}}))<P(\text{ADC }(f_{\text{FI}}))+P(\text{TX}(f_{\text{FI}}))\) is satisfied, from (3) and (5), \(E_{\text{RMSi}}\) can be lower than \(E_{\text{Bi}}\).