Most power systems' approaches are currently tending towards stochastic and probabilistic methods due to the high variability of renewable sources and the stochastic nature of loads. Conventional power flow (PF) approaches such as forward-backward sweep (FBS) and Newton-Raphson require a high number of iterations to solve non-linear PF equations making them computationally very intensive. PF is the most important study performed by utility, required in all stages of the power system, especially in operations and planning. This paper discusses the applications of deep learning (DL) to predict PF solutions for three-phase unbalanced power distribution grids. Three deep neural networks (DNNs); Radial Basis Function Network (RBFnet), Multi-Layer Perceptron (MLP), and Convolutional Neural Network (CNN), are proposed in this paper to predict PF solutions. The PF problem is formulated as a multi-output regression model where two or more output values are predicted based on the inputs. The training and testing data are generated through the OpenDSS-MATLAB COM interface. These methods are completely data-driven where the training relies on reducing the mismatch at each node without the need for the knowledge of the system. The novelty of the proposed methodology is that the models can accurately predict the PF solutions for the unbalanced distribution grids with mutual coupling and are robust to different R/X ratios, topology changes as well as generation and load variability introduced by the integration of distributed energy resources (DERs) and electric vehicles (EVs). To test the efficacy of the DNN models, they are applied to IEEE 4-node and 123-node test cases, and the American Electric Power (AEP) feeder model. The PF results for RBFnet, MLP, and CNN models are discussed in this paper demonstrating that all three DNN models provide highly accurate results in predicting PF solutions.

In this article, we will talk about one of the algorithms that belong to the deep learning algorithms, RBFNs, as they are a special type of feeder neural network that use radial basis functions as activation functions. It has an input layer, a hidden layer, and an output layer and is mostly used for classification, regression, and time-series prediction. Radial basis function (RBF) networks are a common type of use in artificial neural networks for function approximation problems. Radial-based function networks are distinguished from other neural networks due to their global approximation and fast learning speed. The main advantage of the RBF network is that it has only one hidden layer and uses the radial basis function as the activation function.

This study is focused on the development of the cortex-like visual object recognition system. We propose a general framework, which consists of three hierarchical levels (modules). These modules functionally correspond to the V1, V4 and IT areas. Both bottom-up and top-down connections between the hierarchical levels V4 and IT are employed. The higher the degree of matching between the input and the preferred stimulus, the shorter the response time of the neuron. Therefore information about a single stimulus is distributed in time and is transmitted by the waves of spikes. The reciprocal connections and waves of spikes implement predictive coding: an initial hypothesis is generated on the basis of information delivered by the first wave of spikes and is tested with the information carried by the consecutive waves. The development is considered as extraction and accumulation of features in V4 and objects in IT. Once stored a feature can be disposed, if rarely activated. This cause update of feature repository. Consequently, objects in IT are also updated. This illustrates the growing process and dynamical change of topological structures of V4, IT and connections between these areas.