## 1 Introduction
Therefore, it is necessary to establish neural network models for curve extension, bad point correction, and encryption processing of opening lines for the complete characteristic curves. According to whether the flow and moment characteristic curves are pre-transformed, the 3D surface fitting technique can be mainly divided into two categories: the first category is based on the original complete curves of the pump turbine. The original complete curves are fitted using the least squares or neural network models directly. The second category is based on the pre-processed curves using Suter transformation. The pre-processed curves are then fitted using the least squares or neural network models. [PERSON] et al. [14] applied a backpropagation (BP) neural network to process the synthetic characteristic curve for the Francis turbine. Actual engineering applications validate that the proposed method can provide not only higher precision data for the transition process but also better investigation on the real hydraulic unit. [PERSON] et al. [21] applied a radial basis function (RBF) to process the synthetic characteristic curve of the Kaplan turbine. The results have demonstrated that the nonlinear model based on RBF networks can reflect the nonlinear operating characteristics of the Kaplan turbine with higher accuracy. [PERSON] et al. [20] first employed a modified Suter transformation to pre-process the complete characteristic curve and then proposed an Adaboost-BP neural network ensemble model optimized by particle swarm optimization to describe the WH and WM characteristicsof the pump turbine. The results show that the proposed model can obtain higher fitting accuracy and better generalization performance than a single BP neural network model. Although the neural network model can fit and extend the complete characteristic curves and facilitate the calculation of the flow and moment characteristic curves for the pump turbine, the convergence speed of the traditional neural network model is slow and it is easy to fall into local minimum. As a novel single hidden layer feedforward neural network, the extreme learning machine (ELM) obtained the input weights and hidden layer biases through random initialization [22]. The output weights are directly obtained by calculating the generalized inverse matrix of the hidden layer output matrix [23; 24]. The convergence rate is far faster than the traditional BP neural network. The ELM has been widely used in pattern recognition, statistical prediction, and classification and regression [25]. However, because of the random initialization strategy of input weights, the common ELM model fails to make full use of the inherent characteristics of the training data. In addition, the Moore-Penrose generalized inverse used in the ELM model may produce pathological solutions. Therefore, there exists multicollinearity in the output matrix, which affects the fitting and generalization performance of the model [26]. Therefore, there still exists much room to improve in describing pump turbine characteristics using ELM. To improve the modeling accuracy of the pump turbine in the simulation of PTGS, an Autoencoder and partial least squares regression based extreme learning machine model (AE-PLS-ELM) is proposed to model the pumped turbine of a PSU. With the strong fitting ability of the AE-PLS-ELM model, the non-linear mapping relationship of the full characteristic curves of pump turbines is represented. The flow and moment characteristic curves of pump turbines are transformed into neural network models, which can be used for a real-time simulation. On the basis of curve pretreatment with improved Suter transformation, two AE-PLS-ELM models are used to model the characteristic curves. The automatic encoder technique (AE) and partial least squares regression algorithm (PLSR) are introduced to improve the performance of the ELM model. The rest of this paper is arranged as follows.