Simulation of Phasor Measurement Unit (PMU) Using Labview Sourav Mondal*, Ch. Murthy#,
D. S. Roy#, D. K. Mohanta*,
Department of Electrical and Electronics Engineering, Birla Institute of Technology, Mesra, Ranchi*, National Institute of Science and Technology, Berhampur#,
[email protected],
[email protected]
Department of Electrical and Electronics Engineering*, Birla Institute of Technology, Mesra, Ranchi*, Department of Computer Science and Engineering#, National Institute of Science and Technology, Berhampur,
[email protected],
[email protected]
Abstract— With the advent of Phasor Measurement Unit in Power System a new dimension has been given to power system monitoring and analysis. In this paper simulation of Nonrecursive and recursive DFT phasor estimation algorithm is done using Labview. The algorithm developed in Labview can be used for real time estimation of phasor by integrating with labview compliant data acquisition system like NI ELVIS kit. Index Terms— Phasor measurement unit, labview, recursive dft algorithm, nonrecursive dft algorithm,
I. INTRODUCTION Phasor measurement of voltages have been of utmost importance for power system planning and operation. Since the phase angle difference in voltages of the terminals of a line governs the real power flow, it is necessary to acquire the phase angle across the buses. A rich body of research interest within the power system parlance has been focused towards PMUs and this is reflected through the number of recent publications in the area of PMU health and reliability analyses [1-4]. Proper PMU functioning largely depends upon its communication infrastructure [5, 6]. Moreover, appropriate placement of PMUs within the power network has become another area of keen research interest [7, 8]. The measurement of phase angles directly from the terminals of buses have been made possible with the advent of PMU technology integrated with GPS for synchronized measurement [9]. PMUs with the help of digital signal processing have very high precision in phasor estimation. Global Positioning System (GPS) provides the time stamp for the measured phasor which may portray the state of a wide area in power system. Measured data with précised time stamp is of great utility as digital fault recorder and also depicts the real time behavior of a power system. PMU data also finds its application in real time dynamics, stability monitoring, state estimation etc. Phasor estimation of voltage and current waveform using DSP technique discussed are in this paper.
II. NONRECURSIVE & RECURSIVE DFT ALGORITHM FOR PHASOR ESTIMATION Any sinusoid can be represented by phasor which is a rotating vector with a fixed amplitude, frequency and phase angle [10]. Phasor representation of a sinusoid is given in Figure 2. The amplitude of the phasor is equal to the rms value of the sinusoid. The phase angle of the phasor is the distance of a point in the sinusoid from the reference. A sinusoid can be given by: sin being the frequency of the signal in radian per second, is the peak amplitude. is the phase angle in radian and The phasor representation of this sinusoid will have an amplitude of Xm/√2 and rotating anticlockwise with a fixed frequency .
Fig. 1.
Phasor representation of A sinusoidal quantity
A sinusoid at nominal frequency f0 is sampled at N times the nominal frequency i.e. Nf0. The sinusoid can be given by: cos 2 M samples of the sinusoid xm :{ m=0, 1… M-1} are obtained from: cos
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To extract the fundamental frequency component from a signal corrupted with other frequency components, set k=1 in equation to obtain the phasor estimate for M data samples [4]. √
cos
√
-
√
sin
√
(1)
Equation (1) is the phasor estimate for fundamental frequency. As new samples arrive it is necessary to update the phasor estimate. The algorithm that does not take into account data from previous window and calculate phasor estimate afresh is called nonrecursive algorithm [10]. The phasor estimate for N samples from n=1 to n=N by non-recursive algorithm is given by: √
∑ cos (2) A modified algorithm which saves computation taking into account data from previous window is called as recursive algorithm [10-14] which can be given by the equation below: √
(3)
can also be real time acquired from a data acquisition system like NI ELVIS which is compliant with Labview. This analog input signal is then converted to discrete signal with A2D VI and stored in an array. Here data window is considered for 12 samples. A user defined VI has to be prepared for calculating the Fourier coefficient of the data samples. Appropriate arithmetic operations are performed to estimate phasor for first data window. The complex term obtained after phasor calculation is converted into polar form and displayed as output. This algorithm is repeated for subsequent data samples. As newer estimate of phasor are performed, the phasor rotates anticlockwise by an angle Ө due to delay of each sample by one sampling angle. The nonrecursive labview model is given in the subsequent Figure 3. For recursive algorithm we need to have a phasor estimate obtained over a data window preferably by nonrecursive algorithm. The above mentioned algorithm is used to generate the first estimate of phasor in the case studies here. Once the phasor has been obtained for one data window, recursive algorithm is used. When phasor estimate is obtained for (N + m-1)th sample, (N + m)th sample is compared with mth sample using suitable mathematical operands provided in the standard library. The difference in the sample value dictates in the updation of new estimates of phasor utilizing Eq. 4.
Last sample in the window being (N + m) the phasor is given as: √
(4)
III. LABVIEW MODELLING OF PMU Labview [11] stands for Laboratory Virtual Instrument Engineering Workbench provided by National Instrument is a programming language with graphical interface based on structured data flow. Labview uses programs represented by icons to create applications. Labview programs are called Virtual Instruments (VI). Labview finds its application in signal processing, data acquisition, hardware control etc. The graphical interface of labview consists of front panel window and block panel window. Block panel is used to connect VIs to construct logical operations. The inputs may be predefined or controlled from the front panel and the output is reflected in the front panel. Labview along with NI ELVIS provides a platform for designing the algorithm, simulating and implementing it in real time. Labview models have been constructed using standard library VIs and user defined VIs. Labview provides option like I/O, System Analysis, Signal Manipulation, Execution Control, arithmetic and comparison operation. All the predefined VIs used have been taken from this standard library. Apart from this some user defined VIs are also used. In the nonrecursive algorithm the input signal can be generated from library VI i.e. Simulate Signal VI. This signal
Fig. 2.
LabView Model for Single Phase Nonrecursive Algorithm
VI. CASE STUDIES
Fig. 3. LabView Model for Single Phase Recursive Algorithm(Stage 1)
A test case has been considered for a 440V (line to line) 50Hz system. The single phase 230V 50Hz system is shown because a three phase system is nothing but a replica of single phase system with each phase displaced by 120o. A 50-Hz signal 230 cos 120 /4 is sampled at a frequency of 600 Hz i.e. 12 samples per cycle are taken. First 20 samples are obtained and phasor estimate through recursive and nonrecursive are evaluated using Eq. 3,4. The data window is of 12 samples. Since phasor estimation is performed over a cycle, the first phasor is obtained after obtaining 12 samples i.e. after one complete cycle of the sinusoid. That is why the first 11 columns of Table I are empty of the recursive and nonrecursive phasor updates. After the first 12 samples are acquired phasor is computed by both the algorithm and is presented in Table I. As stated above phasor estimates obtained from nonrecursive phasor update will have a constant magnitude but will rotate anti-clockwise with each estimate. The phasor output in polar form for recursive and nonrecursive estimates as obtained from Labview front panel are shown. Figure 5, 6 shows phasor estimates for nonrecursive updates and Figure 7, 8 shows phasor estimates for recursive updates. It is evident from Figure 6 that the new phasor has been progressed by 30o from the phasor shown in Figure 5. This doesn’t happen with recursive phasor estimation and both the Figure 7, 8 are identical in spite of the fact that they have been computed over different data windows. Since recursive algorithm performs less computations to estimate phasor, it is way faster than the nonrecursive estimate. TABLE I. PHASOR ESTIMATES
Fig. 4. Labview Model for Single Phase Recursive Algorithm(Stage 2)
Sample no.
Sample xn
Nonrecursive phasor estimate
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
162.635 59.5284 -59.5284 -162.635 -222.163 -222.163 -162.635 -59.5284 59.5284 162.635 222.163 222.163 162.635 59.5284 -59.5284 -162.635 -222.163 -222.163 -162.635 -59.5284
162.635∠45o 162.635∠75o 162.635∠105o 162.635∠135o 162.635∠165o 162.635∠-165o 162.635∠-135o 162.635∠-105o 162.635∠-75o
Recursive phasor estimate 162.635∠45o 162.635∠45o 162.635∠45o 162.635∠45o 162.635∠45o 162.635∠45o 162.635∠45o 162.635∠45o 162.635∠45o
Fig. 7. Phasor estimation using Recursive algorithm for first data window
Fig. 5. Phasor estimation using Nonrecursive algorithm for first data window
Fig. 8. Phasor estimation using Recursive algorithm for second data window
VII. CONCLUSION The nonrecursive and recursive DFT algorithms have been simulated using Labview. The simulated results obtained are found to be similar to those obtained using digital storage oscilloscope. The simulation of PMU in labview gives an insight about working of PMUs. REFERENCES
Fig. 6. Phasor estimation using Nonrecursive algorithm for second data window
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