# Communication Performance Assessment for Advanced Metering Infrastructure
## 3 Communication Performance Index  
Through the proposed CPI of a smart meter, the CPI for the communication path between the meters can also be calculated. Using Figure 6 as an example, it can be obviously seen that the CPIs for communication paths between smart meters \(M_{i}\) and \(M_{k}\) and smart meters \(M_{j}\) and \(M_{k}\) are equal to the CPIs of \(M_{i}\) and \(M_{j}\), respectively. Therefore, the CPIs for communication paths between smart meters \(M_{i}\) and \(M_{k}\) and smart meters \(M_{j}\) and \(M_{k}\) can be expressed as  
\[\text{CPI}(M_{i},M_{k})=\text{CPI}(M_{i}) \tag{4a}\] \[\text{CPI}(M_{j},M_{k})=\text{CPI}(M_{j}) \tag{4b}\]  
where \(\text{CPI}(M_{x})\) is the calculated CPI for smart meter \(M_{x}\). \(\text{CPI}(M_{x},M_{y})\) is the CPI for the communication path between smart meters \(M_{x}\) and \(M_{y}\).  
A smart meter needs to send its own meter data to DCU; therefore, smart meter \(M_{k}\) will act like a router and transmit the meter data received from smart meters \(M_{i}\) and \(M_{j}\) to DCU. The CPI for the communication path between DCU and smart meter \(M_{k}\) can be calculated by the geometric average and is expressed as  
\[\text{CPI}(M_{k},DCU)=\frac{N_{i}\times\text{CPI}(M_{i})+N_{j}\times\text{CPI }(M_{j})+N_{k}\times\text{CPI}(M_{k})}{N_{i}+N_{j}+N_{k}} \tag{5}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(RSR\)} & \multicolumn{5}{c}{**\(RT\)**} \\ \cline{2-7}  & **NB** & **NS** & **ZE** & **PS** & **PB** \\ \hline \multirow{2}{*}{**NB**} & Rule1 & Rule2 & Rule3 & Rule4 & Rule5 \\  & NB & NB & NB & NB & NB \\  & Rule6 & Rule7 & Rule8 & Rule9 & Rule10 \\  & NS & NS & NB & NB & NB \\
**ZE** & Rule11 & Rule12 & Rule13 & Rule14 & Rule15 \\  & ZE & ZE & NS & NS & NB \\  & Rule16 & Rule17 & Rule18 & Rule19 & Rule20 \\  & PS & PS & PS = min(0.25,0.80) & ZE = min(0.25,0.20) & NS & NS \\  & Rule21 & Rule22 & Rule23 & Rule24 & Rule25 \\  & PB & PB = min(0.85,0.80) & PS = min(0.85,0.20) & ZE & ZE \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results of Activated Fuzzy Rules.  
Figure 5: Results of Fuzzy Rules and Minimum Inference Engine.  
where \(N_{x}\) is the number of data transmission from meter \(M_{x}\).  
Obviously, \(\text{CPI}(M_{k},DCU)\) in Figure 6 can be determined as the CPI of this DCU.  
The above-mentioned procedure can be easily extended to assess the communication performance of an actual AMI. Figure 7 shows an actual small-scale PLC-based AMI acquired from the Institute for Information Industry of Taiwan, the CPI of each communication path can be calculated by  
\[\text{CPI}(M_{x},M_{y})=\frac{\sum\limits_{m\in\phi_{xy}}N_{m}\times\text{CPI} (M_{m})}{\sum\limits_{m\in\phi_{xy}}N_{m}} \tag{6}\]  
where \(\phi_{xy}\) indicates the meter set using the communication path between smart meter \(M_{x}\) and \(M_{y}\) to transmit data to DCU. \(N_{m}\) is the number of data transmission for smart meter \(M_{m}\) belonging to \(\phi_{xy}\) and using the communication path between smart meters \(M_{x}\) and \(M_{y}\).  
The CPI of each smart meter can be assessed first and then the CPIs for the communication paths, DCUs and whole AMI can be calculated accordingly based on the CPIs of smart meters. With the proposed communication performance assessment, the communication performance and stability for an AMI can be effectively supervised.  
Figure 6: Part of Communication Network under DCU.