# Smart Grid Fault Mitigation and Cybersecurity with Wide-Area Measurement Systems: A Review
## 3 WAMS Operation and Dynamic Fault Detection
### Optimal PMU Placement and Fault Detection  
WAMS generally uses PMUs that are synchronized using a GPS clock to provide time-synchronized voltage and current phasors, including frequency measurements with sub-microsecond precision [31; 41]. [PERSON] et al. performed further analysis on WAMS communication infrastructure in different routing protocols when background traffic and link failure are present [22]. [PERSON]'s model design does not focus on the optimal communication infrastructure for PMU placement in a power grid. His team identified this limitation, where the optimal WAMS design was dependent on the optimal placement of the PMUs on the power grid [11]. The identified role played by the Wi-Fi and other wireless systems while guaranteeing the effective operation of the WAMS architecture was still necessitated to include the complexities of the IEEE 14 bus systems; however, the rapid transformation of conventional power system networks with such technologies raises concerns for the eventual cyber-physical power system (CPPS) to be developed. [PERSON] and [PERSON] proposed an analysis of real-time data delivery in WAMS [53]. In their proposed model, the real-time potential of the PMUs in the WAMS architecture was analyzed, and they concluded that for the cost-effective deployment of PMUs to provide the maximum operation of the PMUs, the communication backbone network is required to determine the shortest path using a routing algorithm and channel information through an optical fiber in a ground wire without any delay analysis [53]. [PERSON] et al. presented a model in which PMUs themselves may not effectively disperse the advantages of the WAMS architecture. In their argument, the placement of the PMUs and the communications infrastructure is required to ensure the optimal functioning of WAMS. This becomes necessary if the energy grid is designed to continually become flexible for integrating newer models of protection and communication infrastructure. The communication infrastructure in this context is synchronized with the placement of the PMUs for the optimal delivery of PMU data. These indications expose the study of the PMU placement problem [1]. The authors argued that PMUs are costly devices and, therefore, are to be deployed in a way that maximizes their benefit even with limited numbers. They proposed a deployment that would enable the further integration of technologies with no need for a radical alteration to the PMUs deployed or the energy grid itself. They relate the cost of PMU deployment to its effectiveness in the power grid with the following equation [1]:  
\[min\sum_{i=1}^{n}c_{i}x_{i} \tag{1}\]  
\[\text{s.t.}\,f(X)\geq b_{i}\]  
where  
\(x_{i}\) is a binary decision variable vector with entries defined as  
\[x_{i}=\left\{ \begin{array}{l}1\,\,if\,\,\text{PMU is installed at bus $i$}\\ 0\,\,\text{otherwise}\end{array} \right.\]  
\(c_{i}\) is the cost of the PMU installed at bus \(i\);  
\(b\) is the minimum observability matrix. Fault detection is expressed as follows:  
\[V_{f}=V_{i}-Z_{ij}^{d}I_{i}\]  
where  
\[V_{f}=Voltage\,\,at\,\,the\,\,fault\,\,point\]  
\[V_{i}=Voltage\,\,at\,\,bus\,\,i,\]  
\[Z_{ij}^{d}=\,\,\text{{Impedance}\,\,of\,\,the\,\,line\,\,segment\,\,up\,\,to \,\,the\,\,fault\,\,point,}\]  
\[I_{i}=Current\,\,flowing\,\,from\,\,bus\,\,i.\]  
When a fault occurs across the power system, distance d is nominally calculated using the relationship  
\[d=\frac{\left|V_{i}-V_{j}\right|}{\left|I_{i}\right|\cdot Z_{ij}}\]  
where  
\[Z_{ij}=Total\,\,impedance\,\,of\,\,the\,\,line\,\,i-j,\]  
\[V_{j}=Voltage\,\,at\,\,bus\,\,j\]  
Note that \(d\) is mostly calculated using impedance measurements across the line. The values of \(V_{j}\) and \(V_{i}\) are obtained from PMU data, leveraging their ability to provide time-synchronized phasor measurements with high precision. These data are critical for identifying and localizing faults in real time.