# Grid Nodes Selection Strategies for Power Quality Monitoring
## 2 Literature Review
### Scientific Papers and Practical Reports
Despite being the first found example of a large-scale test system (2998 busbars), it remains unclear whether different scenarios were investigated and mentioned extensions were applied during IEEE 123 and EPRI Ckt5 2998 tests (as it was performed in the case of CIGRE when, for example, generator connection states were comprehensively investigated). Hence, the impact of large-scale (real) system topological changes (due to commutations, new lines installation, power plants construction, etc.) on final solution (monitors quantity and locations) has not been examined and remains unclear. The authors of [18] also focus on short-circuit voltage sag monitoring, since voltage sags cause big damage to sensitive equipment and interrupt industrial processes. To begin with, the paper proposes a new method for illustration of voltage sag propagation, which significantly simplifies the analysis and highly contributes to the efficient solving of PQ allocation problems. A table-matrix (called voltage sag matrix) is created for that purpose--the example for a 6-node grid is given in Figure 4. Positions of busbars and faults are numbered in rows and columns of the matrix and cells are filled with residual voltage value. Obviously, in the general case, diagonal values are equal to 0. The algorithm is tested on IEEE 13 and IEEE 123 test systems, and the authors conclude that their paper gives \"an innovative method\" for different types of faults analysis. However, residual voltage calculation requires a bus impedance matrix (all three sequences) which will be very complicated in the case of massive application in large power systems. Node priority (for  
Figure 3: Multiple fault estimation problem—the symmetry issue: if impedances between monitor (**a**) M1 and faults F1 and F2 are equal, fault differentiation is impossible. Alternative monitor position should be determined, for example, (**b**) M2. PQ monitoring) is determined estimating the highest voltage sag observability in solution array (similar to [16; 17]--kindred papers to [18]). In [19] (2020), a new allocation method flowchart consists of four stages, and the authors specify that all PQ phenomena are considered: RMS voltage, THD, unbalance, flickers, etc. The following tasks must be accomplished in order to find optimal placement strategy:  
1. The estimation of a minimum number of monitors is based on sample size estimation theory. Existing monitoring system data are required for input. Statistical precision of non-repeating random sample is measured as a percentage of deviation of the sample mean from the true population mean, and is calculated as follows: \[r=\frac{\sigma}{\mu}\cdot\frac{Z}{\sqrt{n}}\cdot\sqrt{\frac{N-n}{N-1}},\] (3) where \(r\)--simple random sampling precision; \(\sigma\)--standard deviation; \(\mu\)--mean; \(Z\)--\(z\)-test critical value for required (chosen) confidence level; \(n\)--sample size; \(N\)--population size. 2. Establishment of an optimization targets quantization system is based on the issues, for example, of grid planning and grid operation, but the paper mainly focuses on disturbance source management, PQ maintenance management, and user marketing services. Considering the task, four targets with their own aim functions are established: 1. High-importance (model parameters: coverage of interference source (i.e., pollution propagation mechanism), coverage of important sensitive users, total short-circuit capacity); 2. Weak-area coverage (model parameters: average line loss rate, power outages rate, complaints rate, number of damaged pieces of equipment); 3. Coverage of monitoring scope (requires states of as many power grid nodes as possible, nodes states without monitoring can be estimated with PQ propagation mechanism); 4. Excellent economic benefit (which should be achieved with minimum monitors). 3. Multi-targets optimization is defined as follows: \[\left\{ \begin{array}{l}\max f_{1},\max f_{2},\max f_{3},\min f_{4}\\ \
i X\in\mathbf{R}\\ \mathbf{R}\subseteq\mathbf{U}\end{array}