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function is generated to guide adaptive adjustment of fault data before to be put into the instrument, which makes the whole instrumentation system show linear performance so that the distortion of the output waveform is constrained greatly. A simulation using fault recording data is carried out, whose results demonstrate the feasibility and validity of application of WPNN on relay protection testing of power system, and a prototype with the proposed approach has been put into practical operation. 2 Construction of WPNN
WPNN is the development of wavelet neural network (WNN). WNN can be viewed as the combination of reconstructions using wavelet basis of orthogonal wavelet spaces of L2?R? based on multi-resolution analysis (MRA) [8], [9], [10]. As everyone knows, wavelet space can be decomposed further using wavelet packet, so signals can be decomposed in more frequency bands to increase frequency resolution than by MRA. Therefore, selecting best wavelet packet basis to be network neuron’s activation function will obtain better time-frequency localization property and approximation ability for the network. So WPNN utilizes wavelet packet basis extracting feature of input signal and neural network in WPNN takes charge of information identification, i.e., WPNN can be divided into two parts: wavelet packet feature extraction and neural network information identification, which is shown in Fig.1.
Throughout the paper, Z denotes the set of all integers. Let???? 和
?un????n?Zdenote wavelet basis and wavelet packet generated from ???? respectively.
The structure design of WPNN consists of following three primary steps:
Step 1. Calculating scale range: Using ?t1,t2? and ?tmin,tmax? to denote the time extent of ????and the goal system f?i?, their energy concentrating areas of frequency extent can be estimated with training data, which are expressed as
?f1,f2? and ?fmin,fmax?separately. According to the properties of Fourier transform,
with the increase of the wavelet scale j, frequency extent will expand by 2j, i.e., frequency extent of ?j??? is ?2jf1,2jf2?. Therefore the wavelet scale j
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contains a finite range for covering ?fmin,fmax?,and it can be calculated by below:
???fmax??? fmin???J??j???int???log,intlog2??2?????ff?12???????Where int??and int?? denote choosing smaller or bigger integer value nearby respectively.
Step 2. Selecting best wavelet packet basis: Shannon entropy criterion is introduced to calculating the entropies for the set of coefficients of each node in scale range getting in step1. Then, replace the parent nodes by the two children nodes directly below it if the sum of children’s entropies is less than that of parent. In this method, we can uncover the set of minimum entropy basis, which can be denoted as follows:
U?une,je,1?e?E,e?Z
??Where E is the number of best wavelet packet basis.
Step 3. Determination of number of nodes: This step is also can be seen as determination of translation factor k for each wavelet scale j. It is known as that the time extent of wavelet packet ?un????n?Z{ ( )} is invariable with n changes, so the time extent of wavelet packet basis
un,j??? can be expressed as
?2?jthe increase or decrease of k, the extent slides on the time ?t1?k?,2?j?t2?k?? .With
axis. For covering the time area ?tmin,tmax? of f???, range of k is determined as:
K??k??int??2j?tmin?t1,int??2j?tmax?t2??????
By the three steps above, the structure and parameters of first part of WPNN (feature extraction) can be definitely determined. So the second part (information identification) can be viewed as a simple three-layered neural network with known input value, whose connection rights w( n , j , k )are also that of WPNN. The whole structure of WPNN is thus of the following form, and is illustrated in Fig.1.
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3 Overall Scheme of Relay Protection Testing Instrument
As referred in introduction, the non-linear distortion of output waveform is the most serious problem for relay protection testing. Aiming at this problem, a new scheme of closed-loop relay protection testing instrument is proposed as shown in Fig.2.
Double CPUs configuration including upper-controller and lower-amplifier is applied in this system.
Upper-controller adopts high-performance portable computer or embedded computer as its core, which realizes data acquisition, fault analysis and integrated control.Besides, it can also adjust sampling frequency, value, releasing speed or harmonic content of the input data according to the
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requirements of testing. And a suit of protection testing digital simulation software is successfully embedded into uppercontroller of the instrument. It can simulate the testing process before analog testing on the digital platform, which improves the flexibility and repeatability and avoids potential harm to the tested equipments [11].
Lower-amplifier mainly consists of Digital Signal Processing (DSP) chip, array of Intelligent Power Modules (IPM), and feedback circuit. DSP receives data form upper-controller computer through CAN bus and generates PWM (Pulse Width
Modulation) pulse by regular sampling method, and IPM is drove by the PWM pulse to realize power amplification. Feedback circuit is designed to sample the output signals to compose closed-loop configuration, which mainly takes charge of the transformation of amplitude and polarity.
For eliminating non-linear distortion, an algorithm of digital closed-loop modification is used based on the proposed hardware [12], which can be described as follow:Identify the lower-amplifier part with training data and establish an input-output model for the instrumentation system. By comparing the identification model’s output with idea output, an adjusting function is generated to guide adaptive adjustment of fault data in numeric area before being to be input to the instrument, so that the output waveform can furthest approach to ideal value. It is clear that accurate identification of system is of great importance in the algorithm, and WPNN can be applied to complete this task because of its excellent time-frequency localization property and approximation ability.
4 Procedure of the Algorithm with WPNN
The procedure of digital closed-loop modification with WPNN is shown in Fig.3,which can be explained like that: Some random sampling points within the effective range are input to the actual instrument with proposed configuration and the output waveform is recorded using the feedback circuit. The group composing by the sampling data and their corresponding feedback is regarded as training data set. An identification model fid??? is established by the training data set as substitute of unknown non-linear performance fid??? of instrument’s
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