摘要
在现代大型电力系统中,电压崩溃已经成为威胁电力系统安全运行的重要问题之一。为了预防电压崩溃,需要评估系统运行状态到电压稳定临界点的距离。
临界点的计算可以提供电压稳定裕度的重要信息,但是,在电压稳定临界点处,潮流方程雅可比矩阵奇异,常规潮流方程难以求解。为克服这个困难,采用了连续潮流法,通过追踪PV曲线来获取临界点。但对于高维电力系统,这种方法计算速度较慢,难以满足实时电压稳定评估的要求。为减少评估时间,应用快速且可靠的评估技术是很重要的。
支持向量机是新一代的机器学习算法,以统计学习理论作为其理论基础,其训练等价于解决一个二次规划问题,采用结构风险最小化原则,具有预测能力强、全局最优及收敛速度快等显著特点。因此,本文提出了一种基于支持向量机的静态电压稳定评估方法,并建立了电压稳定评估的支持向量机模型。从测试结果看,支持向量机模型经过训练后可以实时地根据系统运行状态估算系统的电压稳定临界点。该方法充分发挥支持向量机在解决高维、非线性和有限样本问题方面体现出的优势,保证了电压稳定评估模型的泛化能力,具有较快的评估速度和较高的预测精度。将支持向量机模型与BP人工神经网络模型进行了比较,结果证明,利用支持向量机模型进行电压稳定临界点预测比利用人工神经网络模型具有更高的拟合精度。
为了降低输入空间的维数,本文提出用主成分分析对数据进行特征提取,将提取出的包含样本数据信息的主元送入支持向量机进行训练。这样既结合了主成分分析的特征提取能力,又利用了支持向量机良好的非线性函数逼近能力。通过实际算例分析,验证了该方法在保证预测精度的同时可有效降低输入空间的维数。
Voltage collapse has become one of the most important problems which have threatened the operation safety of electric power systems. It is necessary to evaluate the distance between the operation state and the voltage critical point in order to escape from the voltage collapse.
By means of calculating the critical point, the loading margin to voltage collapse can be determined. But at the critical point, the Jacobian matrix of conventional power flow equations becomes singular. The continuation power flow method of getting the critical point by tracing the PV curve has been applied to overcome this difficulty. The calculation speed of this method is slow for power systems with high dimension, so it is difficult to realize real-time voltage stability assessment. The application of a faster and more reliable evaluation technique is very important to shorten the evaluation time.
Support vector machine(SVM), a method based on statistics learning theory, is a machine learning algorithm of the new era. It equals to solving a quadratic programming problem in the principle of minimum structural risk. This algorithm is featured with strong forecasting ability, global optimization and fast speed of approaching, etc. Hence a method of model construction which based on SVM is presented for the power system static voltage stability assessment, and a SVM model for voltage stability assessment is established in this dissertation. Basing on the operation state, the critical point can be estimated by the model being trained according to the test results. This method takes full advantage of SVM's ability to solve the problems with high dimension, nonlinear and small sample. Hence, with quicker assessment speed and higher forecast precision, better generalization ability is guaranteed. Compared with ANN model, it can be seen that SVM model has higher precision.
In this dissertation, the features of the data set are extracted by using principle component analysis to reduce the input dimension. Then the principle component containing the information of sample data is sent to support vector machine for training. This proposal combines the feature extraction ability of principle component analysis together with the excellent nonlinear function approaching ability of support vector machine. The empirical results show that with high forecast precision, the input dimension can be reduced by this method.
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