# A Review on Distribution System State Estimation Algorithms
## 4 Auxiliary Algorithms
### Meter Placement  
The meter placement in a distribution system constitutes a key decision problem. For this purpose, three main sorts of algorithms are distinguished: (i) rule-based, (ii) metaheuristic, and (iii) optimization with an objective function subjected to a set of constraints [110]. In more detail, rule-based algorithms comprise of a number of rules that lead to the easy and fast solution of a problem at the cost of providing non-optimal solutions. Metaheuristic algorithms are usually bio-inspired and more evolved than rule-based algorithms. Indicative examples are Particle Swarm Optimization (PSO), Tabu Search (TS), etc. [111]. By using these sort of algorithms, sufficiently good solutions can be obtained but global optimality is not guaranteed. However, the most recent trends indicate the use of optimizers, which  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Method** & **Description** & **Advantages and Disadvantages** \\ \hline Model-based & L\({}_{2}\)-norm [84; 85; 86; 87; 88; 89], LNR [90; 91; 92; 93; 94], Chi-square [78; 95; 96; 97], & Robust and simple methods. Not as accurate. \\
[78; 84; 85; 86; 87; 88; 89] & Combination [98] & \\ \hline Data-driven & LR [99], SVM [96; 100; 101; 102; 103], ANN [100; 104], RNN [82; 103], CNN & Very accurate methods. Need large amounts \\
[105; 99; 100; 101; 102; 103], MSA [102], k-NN [106], ENN [106], KMC [107], FC [108; 109] & of data. \\ \hline \hline \end{tabular}
\end{table}
Table 4: Bad data detection methods [78; 82; 84; 85; 86; 87; 88; 89].  
aim to maximize/minimize an objective function, limited by constraints, in order to obtain the optimal solution [112]. The main idea is to model constraints such as energy balances, power flows, voltage limitations, etc., and create a space for possible/feasible decisions. The purpose is to find the optimal set of decisions that maximizes/minimizes the value of the objective function. These problems can be Mixed Integer Linear Programming (MILP), Mixed Integer Nonlinear Programming (MINLP), etc., depending on the nature of the problem [113].  
In literature, all of the aforementioned strategies have been recruited for meter placement, as presented in Table 5. For example, a rule-based meter placement strategy is presented in [21]. The developed methodology is simple (but not optimal) and is applicable only to radial distribution networks. Its purpose is to reduce the overall meter cost. Metaheuristics have been used by the authors of [114; 115; 116; 117]. More specifically, ref. [114] uses a Genetic Algorithm (GA) in order to ensure adequate accuracy at the lowest possible cost. In [115], binary PSO is implemented in order for the maximization of state estimation accuracy, limited by a maximum number of meters. Further, the authors of [116; 117] use the fruit fly and TS metaheuristic algorithms, respectively, for the minimization of measurement units that can sustain observability. Regarding optimization approaches, ref. [19] proposes the use of Mixed Integer Semidefinite Programming (MISDP), which is a subfield of convex optimization, where the objective is the maximization of state estimation accuracy. The same objective is used in [118], approached with an optimization non-relaxed, Boolean convex model. The authors of [25] propose MISDP for the minimization of worst-case estimation errors.  
It is evident that optimization algorithms constitute the most advanced approaches, while rule-based algorithms constitute the simplest and least optimal ones. This is a typical trade-off between more modern and more conventional approaches. Nevertheless, it is at the operator's discretion to choose the one that suits their purposes the best.