Mathematical Problems in Engineering

Volume 2015, Article ID 350148, 9 pages

http://dx.doi.org/10.1155/2015/350148

## Forecasting Models for Hydropower Unit Stability Using LS-SVM

College of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China

Received 14 January 2015; Revised 30 April 2015; Accepted 7 May 2015

Academic Editor: Michael Small

Copyright © 2015 Liangliang Qiao and Qijuan Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper discusses a least square support vector machine (LS-SVM) approach for forecasting stability parameters of Francis turbine unit. To achieve training and testing data for the models, four field tests were presented, especially for the vibration in -direction of lower generator bearing (LGB) and pressure in draft tube (DT). A heuristic method such as a neural network using Backpropagation (NNBP) is introduced as a comparison model to examine the feasibility of forecasting performance. In the experimental results, LS-SVM showed superior forecasting accuracies and performances to the NNBP, which is of significant importance to better monitor the unit safety and potential faults diagnosis.

#### 1. Introduction

Hydroelectric power’s low cost, near-zero pollution emissions, and ability to quickly respond to peak loads make it a valuable renewable energy source [1]. According to statistics, hydropower provides 22.45% of the electricity used in China and almost 30% of the nation’s electricity from all renewable sources in 2013 [2]. By the end of 2013, about 273,000 MW of hydropower generation capacity exists in China [3]. More than half of China hydroelectric capacity is in the western provinces of Yunnan, Tibet, and Sichuan, with approximately 57% of the national total capacity [4, 5].

Hydropower generation varies greatly between years with varying inflows, as well as competing water uses, such as flood control, water supply, recreation, and in-stream flow requirements [1]. Given hydropower’s economic value and its role in complex water systems, it is reasonable to monitor and protect the hydropower unit from harmful operation modes. A unit is often operated through rough zone which will cause the unit vibration and the stability performance will decline. The accident occurred at 8:13 a.m. on August 17, 2009, at turbine number 2 of the Sayano-Shushenskaya Dam, Russia’s largest hydropower plant, which caused heavy casualties and property losses [6]. As [7] states, the main technological causes are that hydraulic unit number 2 often entered the nonrecommended band during startup and shutdown operations and load regulation; what is worse, the unit was under long-term service with inadmissible vibration, particularly during the operation with the temporary turbine wheel, to ensure the stability is ultimately connected with the safety and significant economic efficiency of using hydropower plants as a source of renewable energy.

There are some parameters to describe the unit stability, such as vibration, pressure, and noise. When the parameters exceed a certain value, the unit would run in an instability condition. The serious vibration of rotating parts will cause the shaft misalignment. Excessive vibration of generator rotor will increase the abrasion between slip ring and brush, and the brush would spark. What is worse, the whole plant house and equipment would be damaged when the resonance occurs. The fluctuating pressure in DT will make the flow system oscillate and the pipe wall crack and even the steel plate will be lost. Abnormal noise generated by unit unstable operation will be harmful to the workers’ physical and mental health. Existing recommendations in Chinese National Standards regarding stability parameters of hydropower units, GB/T 11348.5-2008 [8] and GB/T 17189-2007 [9], have alarm levels based on statistical data and are often used as an aid to determine and decide if a unit is to be stopped for maintenance. For example, the standards GB/T11348.5-2008 and GB/T17189-2007 divide vibration levels into classes with increasing levels from Class A to Class D, where Class A is a good machine that does not need attention while Class D is a machine that should be stopped for immediate corrective action. The permitted levels for each class vary with the unit’s rotational speed; a low speed permits higher values of vibration levels in each class, compared to high speed. The standards are not sufficient as vibration monitoring standards since they do not consider the physical properties of bearings and brackets, as well as specific characteristics of a plant [10].

It is an effective way to understand the stability characteristics of a unit by field test under different working conditions. To determine a machine’s mechanical condition, Nässelqvist et al. [10, 11] used strained gauges installed inside pivot pin to measure the bearing load in a hydropower unit. Talas and Toom [12] studied the accurate measurement and analysis of the dynamic air gap behavior of large hydroelectric generators using a new fibre-optics instrumentation system and the air gap tests were performed on four 184 MV·A, 15.6 m stator bore diameter generators with 16 radial stator support rods. Sun et al. [13] made stability tests for the ALSTOM units on the left bank of the Three Gorge hydropower station under low head and gave suggestions for the operation. Fendin et al. [14] gave a black start test of the Swedish power system, which is focused on voltage control and governor control as well as on the capability of the individual power units. Khodabakhchian et al. [15] performed a more thorough EMTP investigation in which the models and data were adjusted to reproduce recordings from a field test and proposed a test procedure to determine the parameters of a hydraulic turbine model.

For the task of stability parameters identification of a hydropower turbine, it is possible to define a regression vector from a set of inputs and nonlinear mapping in order to finally estimate a model suitable for prediction. There are some typical methods for regression applied in many areas of engineering research [16–18], such as artificial neural network (ANN) and support vector machine (SVM). ANN usually suffers from the existence of many local minima, choosing the number of hidden neurons and determining the structure of the network, the length of the learning cycle, and the type of the learning process [19]. SVM is a relatively novel powerful machine learning method based on statistical learning theory, which was introduced by Shahlaei et al. [20]. The standard SVM is solved by quadratic programming methods which are time consuming and finding the final SVM model can be very difficult because a set of nonlinear equations must be solved [21]. As a simplification, Rubio et al. [22] proposed a modified version of SVM called least square support vector machine (LS-SVM) which resulted in a set of linear equations instead of a quadratic program. LS-SVM has been applied to prediction and classification with promising results, as can be seen in some works [23–26].

In this paper, a method based on LS-SVM model is presented for prediction and regression of hydropower unit stability parameters. The data are obtained from a field test of a 200 MW Francis unit under different working conditions. The results show good performance of the model, which is of great significance to the unit condition monitoring and fault detection.

The rest of the paper is organized as follows: in Section 2 a brief description of LS-SVM is given and in Section 3 how to obtain the data based on a field test is shown in detail and the model for prediction and regression of hydropower unit stability parameters is presented. The results using the proposed LS-SVM model are discussed in Section 4. Finally, some conclusions are drawn in Section 5 followed by Acknowledgment and relevant references.

#### 2. Methodology

##### 2.1. Review of LS-SVM

LS-SVM is a modification to SVM regression formulation, proposed by Rubio et al. The main idea is to transform the problem from quadratic programs to solving a set of linear equations. The LS-SVM regression framework can be formulated as follows [23]. Given the data set , with input vectors and output values , consider the regression model , where are deterministic points, is an unknown real-valued smooth function, and are uncorrelated random errors with , . LS-SVMs have been used to estimate the nonlinear of the formwhere denotes the potentially infinite () dimensional feature map. The cost function for the data of the LS-SVM model in the primal space is given by

The formulation includes a bias term, as in most standard SVM formulations, which is usually not the case in the other methods. The relative importance between the smoothness of the solution and data fitting is governed by the scalar, , referred to as the regularization constant. The optimization that is performed is known as a ridge regression. In order to solve the constrained optimization problem, a Lagrangian is constructed:where is as the Lagrange multipliers. The conditions for optimality are given by

By applying the kernel trick with a positive definite kernel, , the dual problem is given by the following set of linear equations:where , , , and with .

The resulting LS-SVM model can be evaluated at new point by

In (7), is defined as the kernel function. The value of the kernel is equal to the inner product of two vectors, and , in the feature spaces and ; that is, . This kernel must be positive definite and must satisfy the Mercer condition.

##### 2.2. Feedforward Neural Network Using Backpropagation (NNBP)

The feedforward NNBP is a very popular model in neural networks. It does not have feedback connections, but errors are backpropagated during model training. Least mean squared error is used. Many applications can be formulated when using a feedforward NNBP and the methodology is used as the model for most multilayered neural networks. Errors in the output determine measures of hidden layer output errors, which are used as a basis to adjust the connection weights between the pairs of layers. Recalculating the outputs is an iterative process that is carried out until the errors fall below a certain tolerance level. Learning rate parameters scale the adjustments to weights. A momentum parameter can also be used in scaling the adjustments from a previous iteration and adding to the adjustments in the current iteration [23].

##### 2.3. Overfitting in LS-SVM and NNBP

How well the developing models will make predictions for cases that are not in the training set should be put into consideration. LS-SVM and NNBP, like other nonlinear parametric models, can suffer from overfitting problem. The models that are too complex may fit the noise, not just the signal, leading to overfitting. Overfitting is dangerous because it can lead to predictions that are far beyond the range of the training data with LS-SVM and NNBP. When the training data include enough information, overfitting can be avoided effectively. In the model applications, the data sets applied in LS-SVM and NNBP models are selected from four field tests, ranging from 0 MW to 200 MW of the whole load. So the training data of the vibration and pressure have covered all the information of the unit, which can deal with overfitting problem of LS-SVM and NNBP models.

LS-SVM is based on the structural risk minimization principle, while NNBP is based on the empirical risk minimization principle. LS-SVM includes two structural parts: the error term and the regularization term , seen as (2). This structure can effectively reduce the risk of overfitting. As for NNBP, because the results are based on partially neglecting the regularization term , there is much more danger for overfitting.

In addition, the selection of the kernel function should satisfy the Mercer condition. The radial basis function (RBF) kernel is selected in this paper. LS-SVM with RBF kernel yields a good generalization performance. And using LS-SVM with an RBF kernel does not risk too much overfitting, which can be explained by looking to the optimal values of the kernel parameter [27].

#### 3. Model Applications

##### 3.1. Data Sets Based on a Field Test

The data sets for the LS-SVM models were selected from field tests of a 200 MW Francis turbine unit in China. The test unit located near the load center of China Eastern Power Grid is mainly used to do the peak and frequency regulation. It was put into power generation on August 16, 2008. Table 1 gives the specifications. The rated power is of 204.1 MW and the rated speed of 150 revolutions per minute (rpm). Its range of working head is between 81 m and 127 m.