Abstract: The authors propose an Artificial Neural Network (ANN) based approach to Contingency Analysis (CA) in power system. Previous work [1] shown that ANNs may be unable to solve contingency analysis problem when implemented in a traditional way. In order to solve the problem, the authors propose an ANN approach to contingency analysis. The approach is based on problem decomposition. For every high-voltage (HV) line, a local contingency analyser is trained separately. The local analysers consist of two-hidden layer perceptrons trained by backpropagation. The approach is tested on a sample 14-bus (21-lines) real power system. The results show that the new approach is much more efficient than the traditional one.
Keywords: neural network, backpropagation, multi-layer perceptron, contingency analysis, power system control
A reliable, continuous, and effective supply of electric energy is essential for the functioning of modern societies. To enhance service reliability and to reduce damage of equipment, power system contingency analysis is required.
Contingency Analysis (CA) simulates single fault (optionally multiple fault) for each component of a power system. The input to the CA is a description of the state of the power system. For each fault, possible unsafe consequence (line overload, voltage collapse, uncontrolled power system separation, etc.) must be evaluated. Because of combinatorial nature of the problem, traditional methods are not suitable for use in real-time applications.
Intelligent systems are expected as a new methodology for solving difficult problems in power systems. Various 'intelligent' technologies are researched and applied to power system area. Expert systems, Artificial Neural Networks (ANN), fuzzy logic, and evolutionary algorithms are examples of these technologies.
Traditional methods of contingency analysis involve a lot of load flow calculations. As the conventional load flow is an iterative, unreliable, and slow calculation, in recent years there has been an increasing interest in studying new computational models. The ANNs seem to be promising candidates of such applications.
ANN can solve the CA problem quickly compared to the conventional method as load flow (Newton-Raphson, Gauss-Seidl, Fast Decoupled Method). ANNs are build from a large number of simple processing elements which learn and are able to collectively solve complicated and ambiguous problems. However, the main drawback of ANNs is the long training time required. When applying ANN theory to a real power system, the dimensional problem is often encountered. The required memory and learning time increase dramatically with the size of the power system.
Previous work [1] has shown that ANNs may be unable to solve contingency analysis problem when implemented in a traditional way. Test results shown that the approach was suitable for fast on-line detection of a bus separation as a result of line outage. But, the approach was not able to classify line overloads, and/or voltage unsafe increase/decrease. It also suffered from bad generalisation ability.
In order to solve the problem, in this paper the authors propose a different ANN approach to contingency analysis. The new approach is based on problem decomposition. For each HV line in a power system, a particular ANN is used. In other words, each HV line in the power system has its own, local contingency analyser. The analyser is trained to classify power system state after a single line outage within the given area in the power system. The analysers are trained and operate separately, but they collectively solve the contingency analysis problem. Using of local contingency analysers considerably reduces learning time and memory requirements.
Instead of having one ANN (with many hidden units) for the whole power system, the new Power System Contingency Analyser has a simple ANN for each HV line. So, each ANN has been trained to classify emergency states on particular HV line. The main advantage of this approach is that the Contingency Analyser consist of many simple feedforward ANNs, which are much easier to train, update, and maintain than a large ANN. Moreover, the simple classifiers can operate in parallel, which enables Contingency Analyser to act as a part of real-time control system. Such a system is also suitable for hardware implementation.
The design of the ANN approach to contingency analysis started with the creation of training samples. Training and test sets have been obtained using a conventional load flow program, which effectively combines Newton-Raphson, Gauss-Seidl, and Fast Decoupled method. Load flow calculations for different active loads were calculated. Binary codes representing the state of the power system were the target values. The training set for every ANN have contained 50 input-target vector pairs. 15 test pairs, different from those in the training set have been used to test the classification ability and generalisation quality of each classifier. The input vectors for the training and testing sets were normalised. Normalising a vector most often means dividing by a norm of the vector, for example, to make Euclidean length of the vector equal to one. In the ANN literature, normalising also often refers to rescaling by the minimum and range of the vector, to make all the elements lie within a given interval. Standardising a vector most often means subtracting a measure of location and dividing by a measure of scale. Two different types of normalisation were tested, and the better one has been used for final training.
The 110 kV real power system shown in Fig.1. has been used to test the effectiveness of the new method. The system consists of 14 buses and 21 lines. In this system, only single line outages have been considered.
Fig.1. Sample Power System
The ANN has 13 inputs (active loads on buses) and 3 output neurones. During tests the number of neurones in the first and the second hidden layer varied from 5 to 60. Test result shows that the sufficient number of hidden units is 15. The results for ANNs with 60 neurones in the hidden layers are shown in Fig. 2.
Backpropagation (BP) algorithm with momentum and adaptive learning rate was used to learn the two-hidden layer perceptron. The backpropagation learning algorithm is the most widely used training algorithm in multi-layer feedforward networks. Initial conditions for two-hidden layer perceptron can be chosen more favourably than by using purely random numbers. The Nguyen-Widrow initial conditions are used for speeding up learning of the network. A method called momentum decrease BP’s sensitivity to small details in the error surface. This helps the network avoid getting stuck in shallow minima which would prevent the network from finding a lower error solution. The training time can also be decreased by the use of an adaptive learning rate which attempts to keep the learning step size as large as possible while keeping learning stable. The learning rate is made responsive to the complexity of the local error surface. Tangens-sigmoid function was used as a transfer function in hidden units.
ANNs have been trained to classify power system state when presented with active powers (loads) on buses. Three possible unsafe consequences of a simple line outage have been considered:
The following training parameters have been used:
| maximum number of training epochs | 15000 |
| error goal | 0.025 |
| learning rate | 0.02 |
| momentum | 0.95 |
| learning rate incrementation | 1.05 |
| learning rate decrementation | 0.7 |
| error ratio | 1.04 |
The ANN approach to CA has been implemented on a conventional personal computer. The ANN Contingency Analyser and a program which has been used to test the performance and reliability of ANNs have been developed and trained using MATLAB Neural Network Toolbox.
The trained networks operated adequately. The simulation result shows that the proposed ANN Contingency Analyser can be used for fast on-line analysis in power system and is much more faster than traditional approaches.
The training and test results are shown on Fig.2. The test results show that the proposed approach is suitable for fast on-line detection of unsafe consequences of a power line outage in power systems.
| Line No. | No. of Epochs | Flops | Sum Squared Error | Overloads Detected [%] | Voltage out of Range [%] | Bus Separation [%] |
|---|---|---|---|---|---|---|
| 1 | 15000 | 2.142 109 | 0.0513 | 86.67 | 100 | 100 |
| 2 | 15000 | 2.142 109 | 0.0678 | 100 | 100 | 100 |
| 3 | 15000 | 2.142 109 | 0.2823 | 66.67 | 100 | 100 |
| 4 | 15000 | 2.142 109 | 0.1436 | 86.67 | 100 | 100 |
| 5 | 15000 | 2.142 109 | 0.1755 | 80 | 100 | 100 |
| 6 | 14144 | 2.020 109 | 0.0249 | 73.33 | 100 | 100 |
| 7 | 10134 | 1.448 109 | 0.0249 | 80 | 100 | 100 |
| 9 | 11805 | 1.686 109 | 0.0249 | 100 | 100 | 100 |
| 13 | 15000 | 2,142 109 | 0.0511 | 66.67 | 100 | 100 |
| 18 | 7976 | 1.139 109 | 0.0249 | 86.67 | 100 | 100 |
Fig.2. Training and Test Results
In this paper, an improved technique for fast on-line contingency analysis using ANNs has been described. The proposed approach is based on multi-layer perceptrons trained by backpropagation to contingency analysis. Each HV line in power system has its own contingency classifier. The classifiers are trained separately. When properly trained, the classifiers operate in parallel, which enables the Contingency Analyser to act as a tool in a real-time control system. The approach has been tested on real power system which consists of 14 buses and 21 lines. The results show that the proposed approach is much more efficient than the traditional one.
E-mail: bencr@hotmail.com
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