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Neural networks applied in control loops and safety-critical domains have to meet more requirements than just the overall best function approximation. On the one hand, a small approximation error is required; on the other hand, the smoothness and the monotonicity of selected input–output relations have to be guaranteed. Otherwise, the stability of most of the control laws is lost. In this article we compare two neural network-based approaches incorporating partial monotonicity by structure, namely the Monotonic Multi-Layer Perceptron (MONMLP) network and the Monotonic MIN–MAX (MONMM) network. We show the universal approximation capabilities of both types of network for partially monotone functions. On a number of datasets, we investigate the advantages and disadvantages of these approaches related to approximation performance, training of the model and convergence.

Accurate simulation of a power grid requires use of detailed power equipment models in order to reflect maximum of complex dynamics occurs in the grid. Conventional approaches are not always sufficient to fulfill necessity of meticulous description of processes in power devices. Existence of physical difference even between devices of exactly the same type pulls the accuracy of the whole grid simulation using one model for each type of equipment down. A completely new approach of power equipment modeling – modeling based on Complex-Valued Neural Networks (CVNN) – gives an opportunity to build a high-quality models which are able to track dynamics of grid devices. The nature of the approach makes it relatively easy to build models of all electric network devices even individually taking into account the uniqueness of each one. Power transformer, being quite common and, generally, complicated nonlinear element of power grid, has been chosen for demonstration of CVNN method. Results obtained from this work show that application of CVNN in power engineering modeling appears as quite promising method.