# A Review on Distribution System State Estimation Algorithms
## 3 DSSE Fundamentals and Main Algorithms
### DSSE Algorithms
#### 3.2.3 Data-Driven Algorithms  
Due to the ascending amalgamation of Information Technologies (IT) in the energy sector, data-driven algorithms have gained popularity in the field of state estimation over the past few years [54]. A major advantage of data-driven algorithms is that they assist in overcoming the issues that are encountered in other DSSE algorithms, which depend on parameters and models of distribution networks, are complicated, time-consuming, and very sensitive to initial conditions. Nevertheless, it should be highlighted that for this purpose a significant amount of data are required [55, 56].  
In literature, there is a variety of Artificial Intelligence (AI) and Machine Learning (ML) approaches including: (i) supervised, (ii) unsupervised, and (iii) reinforcement learning [57] that are also utilized in several fields of study [58, 59]. In supervised learning, a labeled dataset, including input data and their corresponding output, is required. In the training phase of the algorithm, the relation between the provided inputs and outputs is defined as a function. Artificial Neural Networks (ANN), the popularity of which is increased, fall in this sort of learning. In addition, it should be highlighted that a well-known subcategory of ANN are the Deep Neural Networks (DNN), which in contrast to simple ANN have more than one hidden layer. On the other hand, in unsupervised learning, there are no complete and clean-labeled datasets. This is a sort of learning that finds previously unknown patterns in datasets and discovers the output. Finally, reinforcement learning is based on the interaction with the environment. In this case, an agent interacts with the environment by performing actions and learns either from errors or rewards [60].  
In literature, the most common data-driven DSSE algorithms are based on ANN. For example, the authors of [61, 62] use ANN algorithms to perform DSSE in MV and LV levels. Studies and experimental tests show that once the ANN is trained, it is characterized by low computational complexity. Since the estimation process is computationally simple, a main advantage is that it can be executed on a low-cost hardware. Of course, the accuracy depends on the number and quality of the available measurements. Other developers choose to add more than one hidden layer to their ANN-based solutions, i.e., DNN. For example, the authors of [63] have developed a DNN framework to perform DSSE, which relies on a deep Recurrent Neural Network (RNN) postulating module. Additionally, following a more complex approach, in [64, 65, 66] physics-aware neural networks are proposed. In this case, the underlying physical model, meaning the structure of the distribution network, is exploited, unlike the previous learning models, where the physics of the underlying distribution network are overlooked. By pruning the unneeded neural network connections, the overfitting behavior of the algorithm is prohibited. Furthermore, according to the respective research, physics-aware neural networks are often compared to WLS in order to highlight the superiority of their performance.  
Of course, there are also developers who prefer to combine data-driven and model-based approaches, resulting in hybrid DSSE algorithms [67, 68]. Indicatively, the authors of [67] have developed a hybrid algorithm that combines a DNN state estimator and a WLAV state estimator in order to ensure robust results at a low time scale. In this case, except from the DNN, the methodology includes a random forest topology identification, which is also a data-driven approach.