In this study, the number of neurons and activation function in layers, back propagation algorithm variables' effects on artificial neural network design were investigated by Box-Behnken experimental design method. The aim of the study is to find the optimal levels by testing the number of neurons, functions and algorithm structures for the dependent variables that form the neural network for power quality disturbances. Different artificial neural network architectures have been designed and tested during the training phase. The performance of the network trained with purelin as the output layer transfer function, logsig as input layer transfer function, trainlm as training algorithm and one hidden layer with neuron number eight on the hidden layer has a more successful result compared to other designed structures. At the end of the study, variance analysis, regression coefficients, graphical results and optimal level results were calculated and shown for each dependent variable. At the end of the study, it has been shown that the parameters which maximize the predictive ability of the artificial neural network are chosen correctly in a shorter time compared to the trial and error method.