A probabilistic dynamic security assessment of large power systems using artificial neural networks

Due to extensive utilization of intermittent energy sources in recent years, probabilistic dynamic security assessment has attracted much more attention. Conventional deterministic studies may not provide accurate security assessments for the power systems under uncertainties. Therefore, probabilistic approaches are necessary for decision makers to take appropriate preventive control actions based on more reliable assessments. In this thesis, a new methodology is proposed to perform probabilistic security assessment for one forecasted operating point of a large power system. This approach can be applied for both transient and small-signal angle stability analyses. The main uncertainty in a power system originates from the uncertainties of loads and wind generation units; therefore, the active power output of wind generation units and active power demand of loads are considered as random variables. The main purpose of the proposed methodology for dynamic security assessment of a large power system is to compute the risk for one forecasted operating condition. In order to compute the risk, probability distribution of the system's dynamic performance is required. To obtain the probability distribution of the system performance, Monte-Carlo simulation method is used with some additional efforts to increase the accuracy and to decrease the computational burden of the process. To obtain the probability distribution of the system performance more precisely, left tailed region of the distribution is fitted by a Generalized Pareto (GP) distribution and the remaining part is fitted by a normal distribution. For fitting the GP distribution, an exceedance sample, which can be obtained by a time consuming process if dynamic simulations are solely used to distinguish each exceedance instance, is required. To decrease the computational burden of the exceedance sample generation process, machine learning approaches such as neural-networks and feature selection methods are utilized. xxii The procedure starts with the creation of a dataset for training a neural network. The trained neural network is utilized to predict the system performance of an operating point for an exceedance sample generation process. The exceedance sample involves instances which result in system performances below a predefined threshold. Due to the fact that most of these instances have a low probability to be sampled, a large number of instances must be examined in order to get a reasonably large sample. However, using dynamic simulations to directly distinguish all the instances in such a large sample would not be suitable for online applications. Instead of the extensive dynamic simulations requiring an excessive computational effort, the trained neural network is used to generate an exceedance sample with a proper size as it predicts the system performance of each operating point more efficiently. Latin Hypercube Sampling technique is used to sample the space of random variables evenly and produce instances of the dataset for training the neural network. For each instance, Optimal Power Flow solution is found and new operating points are obtained. For each operating point produced, a series of dynamic simulations is applied and the system performance is computed. Since the initial dataset created for training the neural network will most likely involve features which are not relevant to the system performance, a reliable and fast feature selection algorithm, namely Relief, is used to find the relevant features. Thus, with this approach the accuracy of the neural network can be improved as its training time is reduced. The next step of the methodology is to generate instances by an appropriate MonteCarlo sampling technique and to obtain an initial probability distribution of the system performance. Gibbs sampling technique, which is a type of Markov-Chain MonteCarlo sampling method, is used to generate the operating conditions which are used to fit a normal distribution for the system performance. Considering the existence of correlation between the random variables, Gibbs sampling is selected as an appropriate method to produce new operating conditions. For each newly produced operating condition, an Optimal Power Flow (OPF) solution is found and the system performance for the resulting operating point is computed by dynamic simulation. xxiii The required number of operating points for Gibbs sampling is determined according to the sample standard deviation of the system performance and specified error and confidence level. The sample standard deviation of the system performance is calculated based on the previously generated training dataset for the neural network. In this study, the maximum tolerable error and the confidence level are specified as 5% and 95%, respectively. It means that we are 95% sure that error we make is less than 5%. The exceedance sample which is required for Generalized Pareto (GP) distribution fitting is produced with the help of trained neural network. First, a large number of instances is generated by LHS method and, then, we randomly select one instance at a time, without a replacement, as a candidate exceedance instance. The performance of each selected instance is predicted by the trained neural network. If the system performance is less than the specified threshold, this candidate is included in the exceedance sample; otherwise it is discarded. The system performance of each exceedance instances are also computed through dynamic simulation, which also confirm their exceedance. This process continues until the required number of exceedance instances are collected. The system performance at these operating points are used to fit the GP distribution. The overall probability distribution of the system performance is obtained by combining the two fitted (normal and GP) distributions above for a given forecasted operating condition. A risk analysis has been done to give a probabilistic security assessment for the forecasted operating condition. In order to perform the risk analysis, a severity function related to the system performance is selected. In this study, the severity function is the combination of a unit step and a quadratic function. The product of the probability density function of the system performance and the corresponding severity function is used to calculate the risk of the forecasted operating condition.