Taguchi‟s method, pioneered by Dr. Genichi Taguchi and developed as a standardized optimization technique of control parameters in process, is based on the statistical analysis of data and offers a simple means of analysis and optimization of complex systems. Taguchi method is a scientifically disciplined mechanism for evaluating and implementing improvements in products, processes, materials, equipment, and facilities. These improvements are aimed at improving the desired characteristics and simultaneously reducing the number of defects by studying the key variables controlling the process and optimizing the procedures or design to yield the best results.
TM is a statistical method for analyzing experimental data for determining and optimizing the effects and levels of the various factors (parameters) involved in a system, allowing this to be done within less experimentation than in traditional methods. It merges statistical and engineering techniques to increase efficiency and productivity, and minimize costs of products, and manufacturing processes. TM further incorporates a method called parameter design for deciding the best optimal values (levels) of variable control factors which effect final product quality or cost. TM achieves this by experimenting on orthogonal arrays of the control factors of the system, and considering the variation of various noise sources. Basically, selection of an optimal set of values can reduce or minimize the effects of factor errors.
The method is applicable over a wide range of engineering fields that include processes that manufacture raw materials, sub systems, products for professional and consumer markets. In fact, the method can be applied to any process be it engineering fabrication, computer-aided-design, banking and service sectors etc. It has been verified that it greatly improves engineering productivity [H. R. Lochner, 1990].
Figure 3.6: A schematic diagram demonstrating the use of Taguchi’s experiment on various control parameters to minimize the error.
Taguchi method is useful for tuning factors in a given process, that significantly influence the quality of output/product of the process, for best results with minimum error. Figure 3.6 is a schematic diagram demonstrating the use of Taguchi‟s experiment on various control parameters to minimize the overall error of a system or process. The diagram signifies that the various control parameters are considered to greatly affect the output/product of the system or process. Hence, by fine-tuning the values of these parameters by applying Taguchi‟s method, an optimal combination from a set of their pre-determined levels, which offers minimum error, is selected. In general, the total number of combinations is given as in Equation (3.21).
Nc = LP (3.21)
where Nc = total number of experiments (combinations)
L = number of levels for each factor P = number of factors (parameters).
If, for example, there is an experiment requiring 21 factors at 4 different levels, it would require 421 experiments (= 4.3 x 1012) to investigate all the possible combinations. Using Taguchi methods, however, only 64 experiments are required. For this reason, such an array is called a L64 orthogonal array, a type of experiment
where the columns for the independent variables are “orthogonal” to one another. The benefits of such experimentation include:
Conclusions valid over the entire region spanned by the control factors and their settings;
Large saving in the experimental effort; and Easy analysis.
TM is a handy tool to optimize some decisive parameters in neural networks to effectively hit the target. For instance, the usual practice to set the number of hidden layer neurons is „trial and error‟. This practice, however; is inefficient and may not deliver the optimal solution. In the content of this work, Taguchi‟s method is used to optimize the neural network‟s control parameters of each training algorithm used. Specifically, the control parameters used in EBP algorithm are number of hidden neurons (h), learning rate () and momentum term (). Whereas, number of hidden layer neurons (h), decay rate (β), and learning parameter (λ) are used in LM algorithm. And, the control parameters used in RPROP algorithm are initial update value (0), increase factor (+), decrease factor (-), decay factor () and number of hidden layer neurons (h). Among combinations of certain levels of the control parameters, the one with the smallest output error is selected after the Taguchi‟s experiments.
The standard eight step procedures which Taguchi proposed to apply his method for optimizing any process are as follows:
Identify the main function, side effects, and failure mode
Identify the noise factors, testing conditions, and quality characteristics Identify the objective function to be optimized
Identify the control factors and their levels Select the orthogonal array matrix experiment Conduct the matrix experiment
Analyze the data; predict the optimum levels and performance, and Perform the verification experiment and plan the future action.
3.4. SUMMARY
In this Chapter, a review of artificial neural networks fundamental network elements topology, their applications in power system areas have been discussed. And, some of the main training methodologies specifically employed in this study, and data pre- processing and post-processing approaches, that help obtain required results from the neural network, have been described in detail. In addition, in depth analyses of information on Taguchi‟s methodology, the procedures followed and its application in our study have been also discussed.
CHAPTER FOUR
MODEL POWER SYSTEM SIMULATIONS AND DATA GATHERING
4.1. INTRODUCTION
As explained in the previous Chapters, the study is exclusively based on simulation of model power system network while due attention is given for validation of the work with IEEE benchmark electric system network. The simulation process encompasses simulations of model power system network and neural network. The latter is discussed in the next Chapter. The overall flow of the simulation work is shown in Figure 4.1.
Get fault voltage waveforms from CVT Simulate model power
system network by generating faults
Signal pre-processing and feature extraction
Training data Target Train neural network Apply Fast Fourier Transform Use anti- aliasing filter Choose Training Algorithm
Optimize values of the control parameters
Test and validate the neural network Power System Network Simulation
Perform feature selection process, identify the number of data patterns
Apply Taguchi‟s methodology
Neural Network Simulation
Normalize data patterns
Identify the target outputs Obtain test and
validation data
Obtain training data
Identify control parameters of selected algorithm and
neural network
GOAL MET! SAVE NETWROK
Figure 4.1 illustrates an insight of the system simulation and other intermediate processes. To generate sufficient number of data patterns for training the neural network, simulation of a single machine infinite bus (SMIB) power system model by generating a number of faults on the transmission line followed by capturing signal from Capacitor Voltage Transformer (CVT) are performed. The signal conditioning and feature extraction processes are carried out by applying anti-aliasing filter and Fast Fourier Transform respectively. However, anti-aliasing filter, commonly used in practical digital sampling systems to avoid acquiring bad data due to noise factors, has been skipped; yet, many technical articles advised using anti-aliasing filters in practical implementation [Math H. J. Bollen, et al. 2006].
Following the feature extraction, selection of decisive features which are adequate for the neural network to identify one fault from the other, and deciding the number of data patterns required for sufficiently training the neural network are done. Then, the data pass through normalization process (which is discussed later in next Chapter), and get break up into sets of training, testing and validation data.
On the other hand, the selection of suitable algorithm for training the neural network is mandatory. To get the neural network effectively trained, and obtain reasonable outcome with high accuracy, optimization of key parameters of the algorithm and neural network is required which is met by using a robust system parameters design methodology –Taguchi‟s method (Details are discussed in the previous Chapters). The final steps in the whole process are training, testing and validating the neural network for perfection, the return being a fully functional neural network which can make accurate decisions whenever is required.
The simulation results based on SMIB model are validated by following the same process using benchmark IEEE 9-bus and 14-bus electric power systems. This Chapter addresses the major power system simulation case studies on SMIB and IEEE 9-bus system models, particularly, for obtaining data patterns for effectively training the neural network. Moreover, a number of faults are also generated on IEEE 14-bus
electric power system model for testing the robustness and effectiveness of the trained neural networks in the previous models.
4.2. CASE STUDY I: A SINGLE MACHINE - INFINITE BUS SYSTEM