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amplifier in the algorithm. And then compare the output of fid??? to the idea output, and construct an adjusting function to compensate the initial to be put into the instrumentation system for realizing the goal of constraining distortion of output waveform greatly.
Accurate system identification and acquirement of adjusting function are two the key points of the algorithm.
With its excellent time-frequency localization property and approximation ability, WPNN is used to establish the identification model for the system. Select a suitable mother wavelet function and estimate the frequency domain of the non-linear performance f??? with training data set. Network structure and neurons number of WPNN can be determined by the method proposed in the second section, and the connection weights of WPNN can be trained by some optimization algorithm, e.g.,back propagation (BP), genetic algorithm (GA), and etc.
And the adjusting function is obtained by the method of iterative modification. As shown in Fig.3, xi denotes a certain data point of the fault data to be input to the instrument and fid?xi? is its output amplified by the identified model fid???. The difference δ of fid?xi? and idea amplifying value Axi, where A is the idea amplification factor, is used to adjust the original data
xi toxi*. And then setting xi* as initial point, repeat the process above until
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δ meets the precision requirement. The last δ is recorded into adjusting value form and the last xi*will be input to the testing instrument to realize fault waveform amplification.
This algorithm is essentially a compensating method for the non-linear performance of the amplifier, which makes the instrumentation system show linear characteristics on the whole, so that the non-linear error of output waveform can be greatly reduced. 5 Simulation Results
To testify the effectiveness of applying WPNN on relay protection testing of power system, a simulation experiment is carried out using actual fault data recorded in a certain region of Jiangxi Province. Following the procedure mentioned above, an identification model is established using WPNN based on the training data and the compensating value related to each sampling data can be calculated by close-loop modifying, which is draw out in Fig.4. The results show that the identification model can accurately approximate the simulated non-linear performance and its tracking error is within 0.1%.
Fig.5 displays a segment of initial input data of the simulation and its adjustment process by the compensating value. The initial data is a phase current of a current oscillation fault, whose maximum reaches up to 10A. And in peak
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or vale points, input data has bigger compensating value because of more serious non-linear attenuation.
The comparison of output waveform with and without the method proposed in the paper is shown as Fig.6. Results from the analysis of the waveforms indicate that 1) Because of non-linear performance of amplifier, the distortion will inevitably come into being in the output waveform which possibly leads to false relay protection testing conclusions; 2) By using system identification and close-loop modification, the root mean square error of output waveform reduces from 2.09 to 0.76. The distortion is constrained so greatly that the output waveform could simulate the power fault exactly, 3) and the compensation function is most remarkable especially at the points near peak or vale value.
6 Conclusion
(1) A novel neural networks, WPNN, with best wavelet packet basis as neuron’s activation function is introduced in the paper, which has normative procedures of structure design and accurate system approximation performance.
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(2) In this study, WPNN is applied to resolve the output waveform’s distortion problem of protective relaying testing instrument. The simulation results prove its feasibility and validity and a prototype with the proposed algorithm has now put into practical operation.
(3) WPNN has excellent capability of approximating the complex nonlinear system, so it can also be applied to other modeling or optimizing problems in power system such as pattern recognition, fault diagnosis, load forecasting and data compress.
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