ARTIFICIAL NEURAL NETWORK APPROACH TO POWER SYSTEM VOLTAGE SECURITY ASSESSMENT

Abstract

Artificial neural networks (ANNs), representing computational paradigms based on biological metaphor, are rapidly gaining popularity among power system researchers. The number of ANN applications to electric power system problems has increased dramatically in recent years, fired by both theoretical and application successes in a variety of disciplines. The specific applications include security assessment, load forecasting, fault diagnosis, alarm processing, optimal capacitor switching, power system stabilizer tuning, detection of harmonic sources, etc. The work undertaken has been remained mainly confined to dynamic and static security aspects of electric power system. Security of the system with respect to dynamic/transient stability, voltage instability and static security in the form of component limit violations owing to contingencies, has been examined by exploiting the excellent pattern matching and nonlinear function encoding capabilities of the ANN. The main point of attraction about these techniques is their computational efficiency compared to classical methods. It makes them potential candidates for on-line application at Energy Management Centers. Dynamic stability of the system is formulated as a classification problem and attempted by Kohonen neural classifier. It maps vectors (representing operating conditions) of N-dimensional space unto 2-dimensional grid of output neurons in a nonlinear way and preserving the topological order of the input vectors. QR algorithm of eigen value determination and transformation of s-matrix method are used to evaluate dynamic stability index for given operating conditions. This index corresponds to the absolute value of most critical eigen value of linearized system matrix in z-plane. The contribution, here include minimizing the error in dynamic stability assessment by optimizing the size and introducing more sensitive information in the training vector. Five types of training vector differing in size and composition are composed based on heuristics and pragmatic considerations. Each type of input feature vector is used to train a separate Kohonen classifier. Finally a performance comparison is made for dynamic stability index estimated by each of the trained network and that computed by conventional method. Out of these five sets, training vector composed of internal machine angle, terminal voltage magnitude and active power generation of the machine in addition to active and reactive power at load buses proved to be the best performer from accuracy and computational point of view. In this part of the work transient stability is formulated as function approximation problem. Feedforward multilayer perceptron (MLP) model is used to encode the function which establishes a relation between transient energy/time margin and prefault system conditions, structure of the fault (type and location), at the specified fault clearing time. Transient energy function method is used to compute energy margin or time margin corresponding to operating conditions generated within the working domain of the system. Adaptive error back propagation algorithm is used to train the MLP. Networks are trained individually for energy margin and time margin respectively. Finally, trained ANNs are compared for their performances based on input features in time and energy domain. Predictions made in energy domain are calibrated into much useful and practical, time domain. Further, in an attempt to improve the prediction accuracy, an alternate neural network model called nonfully connected ANN, is tried out. Supporting network of this model is made to share only those input features which affect the energy/time margin most. It provides additional learning capacity to main ANN. The added capacity allows the model to better correlate the relationship between more pertinent input features ii and energy/time margin. Although it improved the results marginally but at the cost of a slightly increased computational burden. From the test results it can be concluded : (a) It is more appropriate to train ANN in time domain as mean percentage error is consistently less in this domain compared to energy domain and it is of more practical value. (b)Nonfully connected ANN performed better compared to fully connected ANN. Last, but not the least, out of a set of 30 test patterns only one test case is misclassified that too when test point was very close to transient stability limit. It demonstrates the power of the proposed method. Voltage instability is believed to be related to heavily stressed systems with insufficient reactive spare capacity. Basic process contributing to small disturbance voltage instability is essentially steady state in nature. Thus, static analysis can be effectively used to estimate the distance (extra load meeting capacity) of a given operating point from voltage collapse point in terms of system loadings.Homotopy continuation based Newton-Raphson method is used to evaluate this distance and is termed as voltage collapse margin (VCM). Bus power injections and tap settings of on-load tap changers are taken as ANN inputs for voltage instability evaluation. Subsequently input feature vector is augmented by voltage magnitude at critical buses to get improved results. Voltage instability is formulated as a classification as well as function approximation problem to be solved subsequently by Kohonen neural classifier and feedforward MLP model respectively. Former is found to be superior in respect of training time whereas, latter offers excellent interpolation capability for the operating conditions. On the other hand Kohonen net can represent limited number of groups/classes of operating conditions depending upon the number of output neurons. However, the prediction accuracy is found to be better than 1% with either of these models. iii The work is further extended to sensitivity based voltage instability alleviation of power system. An expression is derived to compute the sensitivity of target output (VCM) with respect to input features of trained ANN and finally to control parameters of the system. If a given operating point is estimated close to voltage collapse then the location and magnitude of corrective action (reactive power support) is computed based on the sensitivity of VCM to control parameters so as to alleviate the VCM to pretargeted range. During the course of present work it has been experienced that for large size test systems it becomes increasingly difficult to manage with the size and training time of ANN. Taking into account this aspect of the problem, a statistical approach based on system entropy is proposed to reduce the dimensions and training time of ANN. It also amounts to less amount of information extraction from SCADA data base to evaluate voltage instability. The method when tested on IEEE 30-bus system reduced the input feature size and training time of ANN by 40 to 50 % for prediction accuracy of close to 1%. Static Security assessment is a priori prediction of impending post-contingency security violations. These predictions are useful in both preventive and remedial control. This part of the work deals with the ANN based contingency evaluations of power transmission system for single line contingencies. Performance indices are defined to quantify the violations of branch flow limits, bus voltage limits and generator/bus VAR limits. Each of these performance indices is simulated in terms of precontingency system state and contingency in action. ANNs are trained and tested for all the three indices (line flow, bus voltage and bus reactive power in sum of quadratic terms) simultaneously and taken one at time. Performance of MLP model is compared with that of nonfully connected ANN. Through test results on sample systems of 5-bus (7-line) and IEEE 14-bus (20-line), it has been established that nonfully connected iv ANN definitely performs better than MLP model for the present problem. It is also observed that ANN performs better when trained for one PI at a time. It is further investigated that ANN employing sl-CONE as its basic processing element learns about two times faster compared to MLP and nonfully connected ANN. Through test results it is brought to focus that bus power injection is better option in place of line flow to characterize precontingency state as it reduces the size of input feature vector and training time of ANN for the same level of prediction accuracy. Inclusion of the prefault line flow of the line to be switched off improves the accuracy greatly. The use of system entropy technique for system feature reduction/selection produced remarkable results. It reduced the number of inputs and training time of ANN by more than 50% while keeping prediction error within acceptable level of less than 1%. It will also reduce the security estimation time in real-time environment. The results are tested on IEEE 14-bus and IEEE 30-bus systems. In the presented work pattern matching and nonlinear function approximation capabilities of ANN are exploited to assess the dynamic and static security of electric power system. Accuracy and training time have been the guiding factors while selecting the ANN model and its inputs for a particular application. For larger size test systems a system entropy based statistical approach is evolved to reduce number of inputs to ANN and resultant learning time while keeping the prediction accuracy within acceptable limits. The reported techniques are amenable to on-line applications at energy management centers owing to their computational efficiency. However, for future work it will be of interest and value that developed techniques be programmed on parallel processors and applied to practical size systems. Sensitivity of trained ANN to minor topological changes may be investigated. To reduce training time of ANN scope of genetic algorithm to initialize connection weights of ANN is also recommended for future work.