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In this paper, a novel combination of deep learning recurrent neural network and Lyapunov time is proposed to forecast the consumption of electricity load, in Greece, in normal/abrupt change value areas. Our method verifies the chaotic behavior of load time series through chaos time series analysis and with the application of deep learning recurrent neural networks produces predictions for 10 and 20 days ahead. Specifically, four different neural network models constructed (a) feed forward neural network, (b) gated recurrent unit (GRU) neural network, (c) long short-term memory (LSTM) recurrent and (d) bidirectional LSTM neural network to implement the prediction in a prediction horizon, produced through the extraction of maximum Lyapunov exponent. We constructed sequences of algorithms to feed the neural networks, creating three scenarios (a) 1-step, (b) 10-step and (c) 20-step sequences. For each neural network model, we used its predictions as inputs to predict steps forward, iteratively, to examine the accuracy of the proposed models, for horizons that are both inside and outside to that defined by Lyapunov time. The results show that the deep learning GRU neural network produces iterative predictions of high accuracy and stability, following the trend evolution of actual values, even outside the safe horizon for 1-step and 10-step cases. [ABSTRACT FROM AUTHOR]