Sampling Rate Conversion and Data Synchronization in Big Merging Unit Rukui Tao, Baochen Jiang*, Chengyou Wang School of Mechanical, Electrical & Information Engineering Shandong University at Weihai Weihai 264209, P. R. China
[email protected],
[email protected],
[email protected] the data. However, there exists a problem that the sampling rate conversion and DS process the data respectively.
Abstract—In order to achieve multirate sampling conversion and Data Synchronization (DS) for multi-channel data from Electronic Instrument Transformers (EITs) in power system when the sampled data are outputted to IEDs, Big MU scheme has been proposed. Big MU consists of modules of MUs, multirate conversion and DS. Sampling data of MUs from EITs get through multirate conversion module including interpolation, low-pass FIR filter and decimation to obtain the desired sequence values. However, the multi-channel data after conversion are asynchronous with a unified frequency; DS module is utilized for syncing the asynchronous data. The experimental result shows that the scheme can achieve sampling rate conversion and satisfy the requirement of each harmonic component’s amplitude precision in the IEDs by using module of DS in Big MU.
To solve the above problem, this paper proposes Big MU to integrate the sampling rate conversion and DS, Big MU focuses on the studies of sampling rate conversion based on decimation and interpolation achieving the unified frequency and full digitalization, and DS based on quadratic interpolation for syncing the asynchronous data. II.
A digital system typically consists of EITs, MUs, and IEDs. The common transmission data process is that EITs measure voltage and current values, and send digitalized measurement data to MUs. MUs output the data to the protection IEDs [6].
Keywords-MU; interpolation; FIR filter; decimation; data synchronization.
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However, there are important details that need to be considered when processing the data from EITs.
INTRODUCTION
The sampling rates between EITs and IEDs are different and the data are asynchronous. To communicate with interface between EITs and IEDs, Big MU is used; it can solve the existing problems. Fig. 1 gives a new digital system including Big MU. In the Big MU, MUs receive data from EITs and transmit them to multirate conversion module including interpolation, digital filter (DF) and decimation; and then the asynchronous data after conversion with unified frequency input DS module to realize synchronization; finally the synchronized data are outputted to the protection IEDs.
With the wide application of Electronic Instrument Transformers (EIT) and IEC61850 [1] in substation automation systems, Merging Unit (MU) in process level of IEC61850 has been developed a great deal for digitalized data transmission [2]. IEC has constituted a series of related standards to digital output of EITs. As prescribed in IEC60044-8 [3] and IEC61850, the rated value of output data rate can be 1 kHz, 2.4 kHz, or 4 kHz (50Hz of power frequency system), and digital data of EITs in process level go through MUs to transmit them to IEDs (such as the protection IEDs) in bay level. Electronic Current Transformers (ECTs) of EITs are often provided by different manufacturers, the sampling rates of ECTs are various because of different standards of each manufacture. It is inevitable that the data mismatch situation appears among ECTs, so that it cannot directly transmit the data to IEDs. To achieve the data transmission from ECTs to IEDs, it is necessary to unify the sampling rates, and sync the data after conversion. The direct way for sampling rate conversion adopts D/A and A/D converters. First convert all digitalized data into the analog data through D/A; then use A/D converter changing the analog data into the digital data. But the conversion process needs D/A and A/D converters, which cannot achieve a full digitalization process [4], this paper therefore uses decimation and interpolation method to achieve the full digitalization. Meanwhile, the data after conversion are asynchronous, so Data Synchronization (DS) is used to sync
III.
SAMPLING RATE CONVERSION AND DATA SYNCHRONIZATION
A. Sampling Rate Conversion 1) Decimation and Interpolation The process of reducing sampling rate and removing data redundant is termed as signal decimation [7]. But decimation reduces the sampling rate, which leads to frequency aliasing to affect the data process. In order to avoid frequency aliasing, low-pass filter is needed before debasing sampling rate. The ideal characteristic of digital filter is
⎧⎪1, H1 (e jω ) = ⎨ ⎪⎩0,
*Corresponding author:
[email protected]. This work was supported by the Independent Innovation Foundation of Shandong University (No. 2010ZRJD001).
978-1-4577-0365-2/11/$26.00 ©2011 IEEE
DIGITAL DATA TRANSMISSION PROCESS
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ω ≤π M , otherwise.
(1)
3) Design of Low-pass Filter The design of low-pass filter h(n) is imperative when achieving sampling rate conversion [7]. The general requirements in designing the low-pass filter are: pass area should be as flat as possible; transition area should be as steep as possible; and a filter should be linear phase. FIR filter will be the first choice because it has FIR linear phase characteristic. The frequently-used methods of designing FIR filter include window method, frequency sampling method and Chebyshev approximation optimum equiripple method. The former two methods are easy to design and use. However, shortcomings of the filter using the two methods are that bandpass and stop-pass edge frequencies are not controlled accurately. On the contrary, filter is designed based on Chebyshev approximation optimum equiripple, it can solve the previous problems and obtain better band-pass and stop-pass edge frequencies. The low-pass FIR design is mentioned as in [7].
Figure 1. A new digital system with EITs, Big MU and IEDs.
The decimation process of signal is shown in Fig. 2(a), where ↓M means M times decimation.
B. Data Synchronization (DS) 1) Interpolation Method Interpolation method, which is different from the previous interpolation, is that each channel data among EITs are asynchronous data with the same frequency and transmit to MUs, which enroll a time tag for each data frame, and then data frames are measured at the identical moment by interpolation technology [8]. Fig. 4 depicts sketch map of synchronization using interpolation method, the 1st sampling wave values and the 2nd values are asynchronous with unified frequency. In the 1st wave, is calculated by several around via different interpolation methods. Likewise, in the 2nd wave, is calculated by several around. Hence, we can get the calculated values and at the same moment. However, it must be ensured that each channel data from EITs to MUs have the same time delay or time delay can be measured, which is used to compensate time. In this case, data synchronization can be achieved. Compared with unified clock method, the realization is simpler and the cost is lower.
Figure 2. Decimation and interpolation.
The process of increasing sampling rate so as to add data is termed as interpolation [7]. But interpolation increases the sampling rate, which result in frequency mirror images to hamper the data process. Low-pass filter is used to filter mirror images after adding zeros. The ideal characteristic of the digital filter is ⎧⎪ L, H 2 (e jω ) = ⎨ ⎪⎩0,
ω ≤ π L, otherwise.
(2)
The process of signal interpolation is shown in Fig. 2(b), where ↑L means L times interpolation. 2) Sampling Rate Conversion In IEC60044-8, sampling frequencies of output data in MUs are 1 kHz, 2 kHz, 2.4 kHz, 4 kHz, or 10 kHz. However, the sampling rate is not always integer between MUs and IEDs, so it needs sampling rate conversion to achieve a unified sampling rate. This paper needs multi-channel data for conversion in Big MU. In Fig. 3, x1(n) and x2(n) stand for two channel data from MU1 and MU2, sampling frequencies are f1=4 kHz and f2=2.4 kHz respectively. The two data are interpolated by L1, L2 times; filtered by a low-pass filter h(n) which is designed in the following; decimated with a decimator for M times decimation. At last, the data sequence y(m) are obtained with sampling rate fp= L1f1/M.
Figure 4. Sketch map of interpolation synchronization.
There are various DS methods. Linear interpolation of DS methods has been applied in data synchronization for measuring error as in [5], [9]. However, the precision of linear interpolation is very low, especially measuring higher harmonic, which may make the verdict wrong. So the paper uses quadratic interpolation. 2) Quadratic Interpolation Fig. 5 depicts sketch map of quadratic interpolation. Its principle is: given the function i(t) values: i(t0), i(t1) and i(t2), where t=t0, t1, t2 respectively, using the values can obtain
Figure 3. Sampling rate conversion.
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quadratic polynomial; then the theoretical value can be calculated at t moment by the obtained polynomial, as shown in Fig. 5. The actual sampling values have been measured before interpolation. Difference between the actual sampling value and the theoretical value at t moment is the interpolation error. When the interpolation error is small, it is very good for the actual sampling value to fit the theoretical value; otherwise it is very poor. This shows that error magnitude reflects the performance of quadratic interpolation [8].
Big MU syncs the asynchronous data after conversion at the unified frequency. A. Convert Multirate into Uniform Sampling Rate In this section, fault currents I1 and I2 with 4 kHz and 2.4 kHz will be converted into I10=I20 with 2 kHz. According to the previous analysis, the interpolation factors L1 and L2 are set to 3, 5 respectively and the decimation factor M is set to 6. The low-pass filter is designed by using Chebyshev approximation optimum equiripple. By changing filter length N and comparing with calculated results, it is appropriate to take N=45. The first original signal by L1 times interpolation, DF, M time decimation converts to the low sampling rate signal, shown as in Fig. 7(a); the second original signal also converts to the low sampling rate signal, which equals the first low sampling rate, shown as in Fig. 7(b). Frequency spectrums of the first original signal I1(f) and the corresponding low sampling rate signal I10(f) are shown in Fig. 7(c). There is a good match in the frequency range from 0 Hz to 500 Hz between I1(f) and I10(f). Simultaneously, the results of the second original signal I2(f) and the corresponding low sampling rate signal I20(f) are similar shown as in Fig. 7(d). The results show that sampling rate conversion process reserves the low frequency of the first original signal and the second original signal accurately and filters the high frequency successfully.
Figure 5. Sketch map of quadratic interpolation.
Quadratic interpolation error has higher precision than the linear interpolation, as in [8]. It is more suitable to measure higher harmonic for DS, and the interpolation error can be controlled in the range of allowable error in power system. ALGORITHM SIMULATION
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In standard IEC60044-8, sampling frequency of MUs is 2 kHz, 2.4 kHz, 4 kHz, or 10 kHz. Sampling rates of the IEDs are 1.2 kHz, 1.6 kHz, 2 kHz, and 3.2 kHz. Fig. 6(a) and (b) shows fault currents I1 and I2 from two actual waveforms, whose sampling rates are 4 kHz and 2.4 kHz respectively. It is assumed that the sampling rates of MU1 from EIT1 data is 4 kHz, and MU2 from EIT2 data is 2.4 kHz. The sampling time is 0.04s including fault current time. Meanwhile, the requirement of sampling rate in the protection IEDs is 2 kHz.
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Figure 7. Sampling rate conversion of I1 and I2 to I10 and I20.
Figure 6. Fault currents from actual waveforms.
B. Data Synchronization According to the previous multirate sampling, I10 and I20 can be obtained as shown in Fig. 8. But these sampling data are
Apparently, on one hand, Big MU converts the different sampling rates into uniform sampling rate. On the other hand,
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V.
In this paper, the sampling rate conversion based on interpolation, decimation and DS for digital relay protection have been studied. Big MU including modules of MUs, sampling conversion and data synchronization has also been proposed, aiming at improving the calculation efficiency. When the data from EITs transmit to the protection IEDs, Big MU processes the data to the protection IEDs for synchronization with unified frequency. Big MU converts the multirate data to the same sampling rate from EITs; syncs the asynchronous data with the same frequency and transmits to the IEDs. Experimental results show that the proposed scheme has higher efficiency in achieving the sampling rate conversion and data synchronization, and it can satisfy the requirement of power system.
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Asynchronous data I10, I20 with the unified frequency are synchronized by using quadratic interpolation. I1s and I2s are the synchronized data, as shown in Fig. 9 (a) and (b), where I10 and I20 are the converted data. Compared with I1s and I10, I2s and I20, the instantaneous errors are obtained respectively, as shown in Fig. 9(c) and (d). The maximum instantaneous error requirement of power system for the protection IEDs is less than 0.1 from fundamental harmonic to quintuple harmonic. It is obvious that the error is fit for the requirement of power system. 500
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