SPACES-2015, Dept of ECE, K L UNIVER

Simulation of Ph

Dhruba Kumar1, Debomita GhoshDepartm

Abstract The advent of phasor measuremesystem is revolutionizing the conventional grid towPhasor measurement units are extremely expensitakes into account many aspects of the power sydisclosed by the manufacturer while estimating phand voltage. This paper aims to build a laboratPMU which can estimate the phasor updatincommercial PMU at the benefit of improvaccuracy, reduced manufacturing cost and information.

Keywords Phasor measurement units (PMmeasurement system (WAMS); recursive algorithalgorithm

I. INTRODUCTION The growing trend of remodeling the power

for quality and uninterrupted power necessitatedarea measurement system (WAMS). Phasor me(PMUs) have the potential to revolutionize tpower system are monitored and controlled [1-6synchronized measurement phasors of voltagesin real-time [7-10]. Synchronization is achstamping the sampled voltage and current signsignals from the global positioning system introduction of PMUs the relative phase posiand currents in different parts of widely spreasystem determines the stability and the dynamicthe system.

This paper provides an experimentationbehavior of phasor updation in PMUs. Previomodel of PMU using recursive and non-recursiphasor updation was developed in LMATLAB/Simulink is more users friendacquisition from an external source is not req[11]. The MATLAB/Simulink program is extimplement the idea of recursive and non-recuThe phasor calculation is performed freshly esuccessive windows for non-recursive algrecursive algorithm only phasor updating is nnew phasor estimation for the new window [12]

The paper is mainly divided into followingSection II corroborates a brief review on norecursive algorithm, Section III details the simuof PMU for phasor updation by both non-recurs

RSITY

15

hasor Measurement Unin MATLAB

h2, Member IEEE, Dusmanta Kumar Mohanta3, Senioment of Electrical and Electronics Engineering

Birla Institute of Technology, Mesra Ranchi, India

ent unit in power wards smart grid. ive devices which

ystem that are not hasors of currents tory prototype of ng process of a ed measurement increased timely

MUs); wide area hm; non-recursive

r system network d the use of wide easurement units the way electric

6]. PMUs provide s and currents all hieved by time nals using timing

(GPS).With the ition of voltages

ad electric power c performance of

n regarding the ously simulation ive algorithm for

LABVIEW, but dly where data quired for testing ensively used to ursive algorithm. ach time for the orithm but for

needed instead of .

g major sections: on-recursive and ulation modeling ive and recursive

algorithm with results and Section research work.

II. REVIEW OF NON-RECURSALGORIT

Phasor is a rotating vector as iphase that is used to represent aPhasors are basic tools for analysis as a mean of representation of sforms of fundamental power frequen

A pure sinusoidal signal with nin (1)

).cos()( += tXtx m Where, Xm is the peak amplitud

phase angle, and is frequency in r

Fig. II: (a) A sinusoid (b) Its PThere are various ways to estim

in this paper DFT based non-recursisimulated. The first step is to take sa

)cos( += nXx mn where, n = 0, 1, 2, 3 (N-Thereafter the phasor is cal

=

=

1

0

1 {cos(2N

nn

N nxN

X

=

+=1

0

){cos(2N

nm nXN

it (PMU)

or Member IEEE

IV concludes the performed

SIVE AND RECURSIVE THM in fig. 1 with magnitude and a sinusoidal varying signal. of AC circuit; it is introduced

steady state sinusoidal wave ncy.

no harmonics is considered as

(1)

de of the sine wave, is the radian per second.

Phasor Representation ate phasor [5], [8], [10], [11], ive and recursive algorithm is amples from x(t) to obtain

(2) 1) lculated as in (3) and (4).

+ )}sin(.) nj (3)

+ )}sin(.){cos( njn (4)

SPACES-2015, Dept of ECE, K L UNIVERSITY

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Two separate calculations are performed for real and imaginarycomponents. The real and imaginary parts are given as in (5) and (6).

= cos2

1 mNc

XX (5)

= sin2

1 mNs

XX (6)

Thus,

==jmN

sNc

N eXXjXX .2

. 111 (7)

The superscript (N-1) signifies that (N-1) is the last sample up to which phasor is calculated [11].

After the calculation of first phasor, two different algorithms are described to update the phasor for successive windows. The simplest way to update the phasor is to calculate it again for new window that is called non-recursive phasor update, and another way is just adding the phasor update to old phasor to get new phasor called as recursive phasor update.

Non-recursive algorithm is the simplest procedure to calculate phasor for each and every window [11]. General equation for non-recursive update is given as in (8).

)exp(.21

0)1( jnxN

XN

nrn

rN=

=

+++ (8)

where, r = -1, 1, 2, 3 It is seen that when r = -1, x0 sample is present on the right

hand side but when r = 0, there is no x0 sample even if total number of samples i.e. N remains same.

For recursive phasor estimation, phasor is calculated for X N-1 only and then X N is calculated by adding phasor update to it [11]. In general for recursive phasor estimation the formula is given as in (9).

jrrrN

rNrN exxN

XX +++

+= ).(2)1( (9)

where, r = 0, 1, 2, 3 If r represents the present state, (r-1) represents the past

state. By comparing equation (8) & (9) it is clear that, for recursive estimation present output (XN+r) depends on past output (XN+(r-1)) and present input, and for non-recursive phasor estimation present output depends only on present input as there is no (r-1) phasor present in the equation. Recursive phasor estimation is faster compared to non- recursive phasor estimation as phasor calculation is not performed in each step. If the sine wave is not continuous there is a small error in phasor updating part in case of recursive phasor estimation and the error goes on increasing. This error is not present in non-recursive phasor update. The phasor for a constant sinusoid remain

stationary for recursive phasor estimation and rotates counter clock wise by sampling angle

N 2= for non-recursive

phasor estimation.

Based on this algorithm, simulation model is done in the preceding section.

III. SIMULATION MODEL OF PMU FOR RECURSIVE AND NON-RECURSIVE ALGORITHM AND RESULTS

Simulation model for PMUs is developed as in fig 2(a) and fig 2(b) for recursive and non- recursive algorithm. Two inputs signals: one analog sinusoidal signal provided as an input to the PMU and the other is synchronizing signal of 1pps from global positioning system (GPS). The GPS signal which acts as an input to the phase lock oscillator outputs a sampling signal whose phase is same as the GPS signal but frequency is different i.e. sampling frequency. The sampling signal is fed to the sample and hold element placed inside the A/D converter to obtain the samples x0, x1, x2xN-1. From the sampling signal a sequence n = 0, 1, 2, 3N-1 is evaluated inside the CPU module using time stamp subsystem which is needed to calculate another (N1) sequence { )exp( jn ; (n = 0, 1, 2,..,N-1)}. Next

)exp( jn is multiplied with corresponding xn and summed up to N-1 samples to get the phasor (X N-1) for the first windows. X N-1 is same for recursive and non recursive algorithm. After calculating X N-1 magnitude and phase angle block gives the final output. Fig. 2 shows a view of a single phase PMU operating at nominal frequency.

For calculating XN new window is created consisting {x1, x2, x3,, xN} for non-recursive phasor estimation. It is found that x0 is not present but xn is present which was not there in the first window. Phasor estimation is then performed with these samples. By this way XN+1, XN+2, , XN+11 is calculated and the non-recursive algorithm is reset and the same process is performed for the next (N = 12) windows.

While applying recursive algorithm, XN is calculated by adding phasor update with XN-1 as mentioned in equation (9) with r = 0. As x0 is present in the second window the phasor cannot rotate by an angle (2 /N=360o/12=30o). After the phasor estimation, magnitude and angle is calculated. The magnitude is the r.m.s. value of the signal and angle is the phase angle.

Twelve samples per cycle are taken by the A/D converter so

the sampling time becomes 600

11250

1=

second. Phasors

obtained are plotted on compass plot as in fig. 3 (a) and fig. 3(b) also sample values with phasors are tabulated as in table 1. The recursive plot has only one phasor with length

2100 and angle

45o. The non-recursive plot has twelve phasors. Each phasor leads the previous phasor by 30o. If simulation time is increased

SPACES-2015, Dept of ECE, K L UNIVERSITY

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Fig. 2: (a) PMU Model for Recursive Algorithm

Fig. 2: (b) PMU Model for Non-Recursive Algorithm

to generate thirteenth phasor it is overlapped with the first phasor and so on.

Thus for non-recursive algorithm the magnitude is fixed but the angle increases each phasor.

Fig. 3: (a) Recursive phasor estimation

Fig. 3: (b) Non-recursive phasor estimation

On the other hand recursive phasor estimation results in constant magnitude and phase angle.

In1

In2

Out1

Out2

In1

In2

Out1

Out2

SPACES-2015, Dept of ECE, K L UNIVERSITY

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Table 1: Results for non-recursive and recursive algorithm

Time (sec)

Sample Value

Recursive Phasor

Estimation

Non-Recursive Phasor

Estimation Magni tude

Angle Magni tude

Angle

0 70.7107 0 0 0 0 0.0016667 25.8819 0 0 0 0 0.0033333 -25.8819 0 0 0 0

0.005 -70.7107 0 0 0 0 0.0066667 -96.5926 0 0 0 0 0.0083333 -96.5926 0 0 0 0

0.01 -70.7107 0 0 0 0 0.0116667 -25.8819 0 0 0 0 0.0133333 25.8819 0 0 0 0

0.015 70.7107 0 0 0 0 0.0166667 96.5926 0 0 0 0 0.0183333 96.5926 70.7107 45 70.7107 45

2nd window

- - 70.7107 45 70.7107 45 0.02 70.7107 70.7107 45 70.7107 75

3rd window

- - 70.7107 45 70.7107 75 0.0216667 25.8819 70.7107 45 70.7107 105

4th window

- - 70.7107 45 70.7107 105 0.0233333 -25.8819 70.7107 45 70.7107 135

5th window

- - 70.7107 45 70.7107 135 0.025 -70.7107 70.7107 45 70.7107 165

6th window

- - 70.7107 45 70.7107 165 0.0266666

7 -96.5926 70.7107 45 70.7107 -165 7th

window - - 70.7107 45 70.7107 -165

0.02833333 -96.5926 70.7107 45 70.7107 -135

8th window

- - 70.7107 45 70.7107 -135 0.03 -70.7107 70.7107 45 70.7107 -105

9th window

- - 70.7107 45 70.7107 -105 0.0316667 -25.8819 70.7107 45 70.7107 -75

10th window

- - 70.7107 45 70.7107 -75 0.0333333 25.8819 70.7107 45 70.7107 -45

11th window

- - 70.7107 45 70.7107 -45 0.035 70.7107 70.7107 45 70.7107 -15

12th window

- - 70.7107 45 70.7107 -15 0.0366667 96.5926 70.7107 45 70.7107 15

IV. CONCLUSION The phasor estimation algorithms are simulated and

verified in MATLAB/Simulink. The developed PMU provides phase information i.e., both magnitude and phase angle. In application point of view for wide area measurement system (WAMS) recursive algorithm will prove to be a better method than non-recursive algorithm. This is because comparison of phase angle in between the different remote locations is easier and accurate because of constant phase angle differences.

REFERENCES [1] Soumik Das, Debomita Ghosh, T. Ghose and D.K. Mohanta,

Simulation of Wide Area Measurement System with Optimal Phasor Measurement Unit Location, International conference on signal processing and integrated networks (SPIN-2014), Noida, India, pp. 226-230, 20-21 February 2014.

[2] I. Kamwa, S. R. Samantaray, and G. Joos, Optimal Integration of Disparate C37.118 PMUs in Wide-Area PSS With Electromagnetic Transients. IEEE transactions on power systems, vol. 28, no. 4, pp- 4760-4770 November 2013..

[3] Debomita Ghosh, Chandan Kumar, T. Ghose and D.K. Mohanta, Performance Simulation of Phasor Measurement Unit for Wide Area Measurement System, In: Proceedings of international conference on control, instrumentation, energy and communication (CIEC-2014), Kolkata, India, pp. 297-300, 31 Jan. 02 February 2014.

[4] D. Ghosh, T. Ghose, D K Mohanta, Communication Feasibility Analysis for Smart Grid with Phasor Measurement Units, IEEE Transactions on Industrial Informatics, vol. 9, no. 3, pp. 1486-1496, August 2013.

[5] M. H. Cintuglu, and O. A. Mohammed, Simulation of Digitalized Power System Using PMU and Intelligent Control, Industry Applications Society Annual Meeting, Lake Buena Vista, FL. pp- 1-8. 6-11 October 2013.

[6] W. Rahman, M. Ali, A. Khan, H. Rahman, K. Haider, M. Iqbal, A. Zeb, H. Ahmad, Z. Ali, PMUs Advance Control for Power System Wide area Monitoring Protection using MATLAB/SIMULINK. Canadian Journal on Electrical and Electronics Engineering vol. 3, no. 6, July 2012.

[7] G. Missout and Girard, Measurement of bus voltage angle between Montrel and Septles,IEEE transaction on Power Apparatus and System. vol. 99, no-2, pp-536-539, March 1980.

[8] G. Missout, J. Beland, G. Bedard and Y. Lafleur, Dynamic measurement of the absolute voltage angle on transmission lines, IEEE transaction on Power Apparatus and System. vol.100, no.11, pp. 4428-4434 November 1981.

[9] C37.118-2005 - IEEE Standards for Synchrophasors for Power System, IEEE power engineering power system relaying society, pp. 1-57, 03 April 2006.

[10] M. Adamiak, B. Kasztenny, and W. Premerlani. Synchrophasors: definition, Measurement and application, Proceedings of the 59th annual Georgia Tech Protective Relaying, Atlanta, GA, 2005.

[11] S. Mondal, Ch. Murty D. S. Roy, D. K. Mohanta, Simulation of Phasor Measurement Unit (PMU) Using Labview. 14th International Conference on Environment and Electrical Engineering (EEEIC-2014), Krakow pp-164-168, 10-12 May 2014.

[12] A. G. Phadke and J. S. Throp Synchronised Phasor Measurement and their application, Springer, 2008.

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