1
A Teaching Tool for Phasor Measurement Estimation Daniel Dotta, Member, IEEE, Joe H. Chow, Fellow, IEEE and David B. Bertagnolli Senior Member, IEEE
Abstract—This paper discusses the design and usage of a S IMULINK -based Phasor Measurement Unit (PMU) simulator package 1 . The motivation for developing the package is to provide a flexible environment for teaching phasor measurement and frequency estimation to advanced undergraduate and graduate students, and a knowledge base for research and development. This software allows for the exploration of the algorithms and phenomena involved in the phasor estimation process. The package is built on the S IMULINK platform and is able to process simulated signals as well as measured point-onwave data. The popularity and relevance of the proposed package is validated when considering positive feedback from students. Index Terms—PMU, phasor data processing, power system analysis, phasor estimation algorithms.
I. I NTRODUCTION
T
He use of Phasor Measurement Unit (PMU) data in power system operation is of increasing interest. Power grid operators have started to recognize the potential of this technology and several Wide Area Measurement Systems (WAMS) are being built around the world [1–3]. The number of PMUs installed and connected to WAMS in large power systems, such as in the USA and China, is already over several thousands [3, 4]. Despite the high level of research activities in the development of PMU applications [5], the dissemination of phasor processing techniques within a PMU is quite limited. In addition to being a high-sampling-rate digital recording device with GPS-signal time-tagging, a PMU uses signal processing techniques to provide frequency and phasor information on voltages and currents. The signal processing part is not specified in the IEEE C37.118 Synchrophasor Standard [6]. As a result, there are various implementations with different algorithms and data windows. A good understanding of the tradeoff between various algorithms would be useful to power engineering students who may get involved in the design of the next-generation of power system measurement equipment. This will also help operation and maintenance engineers to recognize and report PMU data issues. This paper reports on a software tool based on the S IMULINK platform that can be used for teaching and research Daniel Dotta is with the Federal Institute of Santa Catarina, Florian´opolis, SC 88020-300, Brazil. (email:
[email protected]). J.H. Chow is with Rensselaer Polytechnic Institute, Troy, NY 12180, USA. (email:
[email protected]). D. Bertagnolli is with ISO-NE, Holyoke, MA 01040, USA. (e-mail:
[email protected]). 1 The
simulator and PMU data is avaible upon request from the first author.
to explore the algorithms involved in the phasor measurement process. The main goal is to replicate the device architecture and conventional algorithms available in the literature. This S IMULINK software platform is an evolution of the M ATLAB software platform presented in [7]. The S IMULINK software platform shows clearly the various functional blocks with in a real PMU, and can be readily used for simulation and symmetrical component analysis. The relevant parameters such as the input sine wave amplitude, frequency, and phase, can be changed on-the-fly. This software tool will provide hands-on experience for understanding the algorithms and tradeoffs involved in the phasor measurement process, such as off-nominal frequency and unbalanced phase operation, and impact of correction factors for off-nominal frequency signal. The paper is organized as follows. In Section II, two approaches to use this software package for teaching are presented. In Section III, the basic architecture of a phasor measurement device is described. In Section IV, a S IMULINKbased PMU simulator is presented. In Section V, the education activities of the proposed approach are presented. In Section VI, the result of the evaluation of this package for students is presented. Conclusions are presented in Section VII. II. P HASOR M EASUREMENT T EACHING The modernization of the power system industry will take engineering professional resources of broad expertise and different profile than previously available [8]. The necessity of modernize the curriculum of power system is already recognized such described in [8] [9]. Different new topics, such as signal processing, information technology, automatic tools etc, need to be incorporated to the power system curriculum to fulfill the educational gap needed for the future technical workforce. One of main challenges is how to incorporate these new topics and concepts to the traditional power system courses. This package was developed to support the teaching of phasor measurement process concept. The reference book used to teach these concepts is ”Synchronized Phasor Measurement and Their Applications” by A. G. Phadke and J. S. Thorp [10]. This can be done in two different approaches based on the time available: 1) Introduce de phasor measurement process, as special topic, in a regular course; 2) A course dedicated to teach phasor measurement process and applications. In first approach, teaching phasor measurement is only part of the broader course. The main phasor measurement concepts
2
are presented in classroom and the package is used at home, following the educational activities presented in Section V, executed as homework. The second approach is to prepare an exclusive course of Synchronized Phasor Measurement technology when you have time to spend in classroom to execute the PMU Simulator. The first approach was used in RPI using a primitive version of this simulator, the second approach was applied for students from IFSC (Federal Institute of Santa Catarina) and University of S˜ao Paulo (USP-SC) at IFSC. The packaged is composed by an only file and can easily simulated by students using their own laptops being useful for both approaches. The results of feedback from students is presented in the Section VI. The other successful works in this area and the comparison with the presented package are discussed as follow. A. Research and Development PMU Projects The limitations of closed source philosophy under which commercial PMU devices are developed lead a number of universities to develop an open model for PMU technology [11]. Successful projects such as GridTRAK PMU [12], DTU PMU [13] and OpenPMU [11] presented interesting results emulating commercial PMUs. The main goal of these projects is to develop an open and low-cost PMU device improving the innovation of research projects in the area. All these projects, using different approaches, present all the modules necessary to emulate a commercial PMU such as hardware, software and GPS receiver to set up the GPS clock. The data is exported using the IEEE standard C37.118. The necessity of hardware component may bring some difficulties to application of these projects in teaching classes since you need laboratory environment prepared (sometimes not available in developing countries). Hardware devices can also make the student lose their focus on methodologies and may not be easily run in out of laboratory environments (at home for example). To overcome these issues a S IMULINK PMU simulator is proposed. The motivation to design this package, using S IMULINK, came after the development of a research oriented M ATLAB PMU Simulator presented in [7]. The research oriented version was developed to test filtering designs [14] and help the understanding of the methodologies involved in the phasor measurement process. A primitive version of the research oriented version of the PMU Simulator presented in [7] was shamefully applied in classroom. However it was verified that better results could be achieve using S IMULINK diagram. Although the projects could be accomplished solely using the MATLAB command language, operations with S IMULINK diagram removed most of the drudgery of keeping track of the block-diagram and feedback structure, reducing the possibility of errors. This was an important consideration when students of different background were not proficient MATLAB users. The PMU S IMULINK Simulator proposed in this paper is composed by one file (S IMULINK diagram block) that can easily run in a student laptop. The package was design to understand the main methodologies involved in the phasor measurement process. However, if the the intention
is to really explore all the PMU components and not only the methodologies involved such as the GPS receiver issues and the standard C37.118 the other research projects are more suitable. III. BASIC P HASOR M EASUREMENT A RCHITECTURE Figure 1 shows a general block diagram of a PMU [15]. The proposed PMU simulator is shown in Figure 2, with three main computing blocks • Phasor estimation using Discrete Fourier Transform (DFT) • Frequency estimation • Post-processing including calibration factors and filtering Not included in the PMU simulator are the input signal antialiasing filter, the GPS-based timing signal generator, and the A/D converter for sampling the filtered input signal. The purpose of the PMU simulator is to explore the phasor and frequency estimation, and the techniques involved in correcting the phasor estimation under off-nominal frequency operation. To simplify the proposed simulator, two assumptions are made: • the sampling rate is uniform • anti-aliasing filtering has been applied to the input signals Note that non-uniform sampling schemes based on the estimated system frequency have been proposed [17, 18]. The technicalities of these schemes are quite advanced and the implementations of such schemes can be quite difficult. A. Phasor Estimation The function of this phasor estimation block is to compute the amplitude and phase of an input signal at the fundamental frequency using DFT. The non-recursive DFT algorithm is given by √ N −1 2πn 2 X k (1) xk+n e−j N X = N n=0 where k is the first sample in the data window, and N is the number of samples in a cycle of the fundamental frequency component. If a recursive DFT approach is used, care must be taken so that the algorithm does not accumulate truncation errors during long-term operation. B. Frequency Estimation In normal power system operation, the power system frequency seldom stays exactly at the nominal system frequency (50 or 60 Hz). The frequency measurement is important because the phasor is a steady-state representation so correction must be done in the presence of frequency deviations. This Sampling Clock
x(t)
Fig. 1.
Analog Filter
A/D Converter
PMU General Blocks
Frequency Estimator
x(k)
Digital Filter
Phasor Estimator
X(k)
3
filtering
X
N +n
=X
N + n −1
X ntrue =
− j 2π n 2 (x + − x )e N N N +n n
Xn Pn
C. Post-Processing
Post-Processing
X nest
xn (t )
Filtering*
DFT
Frequency estimation
2
X nfiltering X
1
∆ω
X ntrue
Look up table with calibration factor
Pn
Under off-nominal frequency operation, the post-processing block is necessary to correct for the effects caused by the leakage phenomenon, resulting from the truncation of sampled data outside the data window. Consequently, the estimated phasor (X est ) is attenuated by two complex gains, Pn and Qn such as, X est = Pn X true + Qn X true
&ŝůƚĞƌŝŶŐΎ (Α) ǀĞƌĂŐĞ&ŝůƚĞƌ (Β) tŝŶĚŽǁŝŶŐ ;Ϳ>ĞĂƐƚ^ƋƵĂƌĞƐ
Fig. 2.
∆t − sampling period N (ω − ω0 )∆t (ω −ω0 ) ∆t sin Fixed j ( N −1) 2 2 N - window size }e Pn = { (ω − ω0 )∆t N sin ∆ω = ω − ω0 ≅ 0 2
Phasor processing algorithm for uniform sampling [16]
deviation can be small, when subject to random load variation, or large, during loss of generation disturbances. Thus, the frequency estimation methodology plays a key role in the phasor computation process. An interesting discussion of the power system frequency concept is found in [15]. Frequency measurement on a power system is not an instantaneous measured value, like that obtained from a machine speed sensor installed on the shaft of a generator. Instead, frequency is calculated from a voltage waveform data window. Several frequency measurement methodologies can be found in the literature [19–23]. The phasor-based method [20, 22, 23] is chosen as the frequency estimator for the PMU Simulator. This method, commonly used in commercial PMUs, is a byproduct of the phasor estimation and provides satisfactory performance under large frequency variation and noisy environment. This method, originally proposed in [24], defines frequency as the speed of rotation of a phasor. The main idea is to calculate the positive-sequence voltage phasor for a balanced system operating at off-nominal frequency, while still using the nominal frequency-based DFT and samples. The method proposed in [24] is based on a fixed-frequency model. The method implemented in the PMU Simulator here is described in [22], which considers the effect of dynamic frequency in the algorithm. In [22], the authors mathematically prove that frequency can be accurately measured using sample phasor measurement series, shown in Figure 3, where (A,B) and (D,E) are phasor measurement samples, N is the size of the data window for phasor calculation, and M is the size of the data window for frequency calculation. The frequency deviation is computed as ∆ω =
0
N-1
A
B
Fig. 3.
ϕD−E − ϕA−B M ∆t
(M+N-1)/2
M
C
D
Phasor-Based Frequency Estimation [22]
(2)
M+N-1
E
(3)
where Pn =
(
Qn =
(
0 )∆t sin N (ω−ω 2
N sin
(ω−ω0 )∆t 2
0 )∆t sin N (ω+ω 2
N sin
(ω+ω0 )∆t 2
)
)
ej(N −1)
(ω−ω0 )∆t 2
e−j(N −1)
(ω+ω0 )∆t 2
(4)
(5)
From Equation (4), the effects of the complex gain Pn (shown in Figure 2) can be readily computed from the sampling window size (N ), the frequency deviation (∆ω), and the sampling period (△t) [10]. The magnitude of Pn is an attenuation factor, and the phase angle of Pn is a constant offset in the measured phase angles. As the window size (N ) and sampling period (△t) are fixed, Pn can be readily estimated for a frequency range and stored in a table (Block 1 in Figure 2). In real-time, frequency deviation estimation is necessary to compute the correct Pn value. The complex gains Qn introduces a variation at frequency 2ω0 + ∆ω ≃ 2ω0 in the estimated single-phase phasor. In contrast to a static offset, this oscillation is not readily removed. A conventional way to minimize its influence is to use a three-point-average filter [10]. Other filtering techniques are described in [14]. IV. S IMULINK - BASED PMU S IMULATOR A S IMULINK PMU simulator suitable for exploring the phasor measurement estimation process is shown in Figure 4. The simulator works with single-phase and three-phase measurement signals, allowing positive-sequence phasor estimation. Step and ramp (frequency modulation) frequency disturbances can be simulated to observe the influence of the complex gains (Pn and Qn ) and filtering in the phasor estimation process. Processing of real point-on-wave data can also be realized. The main features of the PMU Simulator are: • Non-Recursive DFT • Off-nominal frequency operation • Unbalanced input signals • Symmetrical components estimation • Pn and Qn complex gains effects • On-the-fly frequency changes. The main goal of the simulator is to show the PMU performance under off-nominal frequency operation. It is important to understand how a steady-state phasor concept can be applied under off-nominal frequency environment. Two frequency disturbances are considered and can be chosen using Switch 1 in Figure 4: step and ramp. The level of the disturbance can also be selected in the main window using Switch 2 in Figure 4.
4
PMU Simulink Simulator 0 SP_MF
Step
SP_MnF
Disturbance
1 Switch 1
Ramp
PS_M PS_Md PS_A
SP_MF SP_MnF PS_M PS_Md PS_A
60 Nominal Frequency
Frequency Goal
PS_Ad
•
PS_Ad
D. Frequency Estimation •
Switch 2
59
Frequency Deviation
PMU
FD
Ploting Area
Frequency Goal
Fig. 4.
estimation block. The negative- and zero-sequence components are also computed. Pedagogy: They are useful for exploring unbalanced power system operation, especially in distribution systems. The second harmonic ripple show up in all symmetrical components.
Main Window
The frequency level can also be changed on-the-fly. A variety of signals are available for plotting: single-phase and positivesequence magnitude and angle with and without filtering, and down-sampled positive-sequence magnitude and phase. To understand the internal PMU operation a user can click on the main block to gain access to the internal S IMULINK blocks. The software blocks and algorithms involved in the S IMULINK PMU simulator are shown in Figure 5 and are described as follows. A. Three-Phase Sinusoidal Wave Generation • Function: In this block the sinusoidal waves in threephase power systems are generated and the disturbance types are processed. Real data files can also be used. • Pedagogy: The three-phase signal magnitude and phase can be changed allowing unbalanced operation. A bias factor can also be set to introduce off-set and noise in the sinusoid waves. B. Phasor Estimation • Function: The function consists of three single-phase estimation, using a data buffer of window size (N ). This data frame is sent to the FFT block. The nonrecursive DFT algorithm described in Section III-A is used . The estimation using rectangular coordinates is computed for each new data window. The FFT block output consists of N harmonic frequency spectral values. In the phasor estimation process only the fundamental component is used so an extra block is used to extract the first harmonic. The Gain block represents the constant √ 2/N described in Equation 1. • Pedagogy: The influence of the window size (N ) can be explored showing the effect of considering multiple cycles on the phasor estimation as well as the magnitude of the other DFT spectral values under noise environment. C. Symmetrical Component Calculation • Functions: The positive-, negative-, and zero-sequence components are estimated in the this block. The main output is the positive-sequence phasor used for the frequency
•
Functions: The frequency is estimated using the positivesequence phasor angle following the algorithm described in Section III-B. The first block converts the phasor from rectangular to polar coordinates and extracts the angle. This angle is sent to a buffer block where the sampled phasor measurement series is created. The data set is sent to a M ATLAB function that processes the data and estimates the frequency deviation in Hz. The frequency deviation is used to estimate the complex gain Pn . Pedagogy: The data window size for the frequency calculation M can be changed and its influence can be checked in the phasor estimated.
E. Table Lookup •
•
Functions: The main goal of this block is the estimation of the complex gain Pn used for correct the phasor under off-nominal frequency operation. This complex gain is estimated from frequency deviation and the window size (N ) following the Equation 4. With the complex gain estimation the positive-sequence phasor is calibrated and converted to polar coordinates. Pedagogy: The calibration factor can be turned of to check their influence in the single-phase and positive sequence estimation.
F. Downsampling •
•
Functions: In this block the phasors are downsampled to generate the real PMU output. A sample is picked up every N points of a phasor, decreasing the sampling rate from N ∗ fnominal to fnominal .2 Pedagogy: The phasor estimated before the downsampling can be check and the influence of the downsampling block as a filter can be studied.
G. Single-Phase Processing •
Functions: A separate block for single-phase phasor processing is necessary because of the second harmonic oscillation introduced by the complex gain Q at offnominal frequencies. The effect of the complex gain Q is automatically compensated in the positive sequence estimation. The processing starts with the calibration regarding the effects of the complex gain P . After the phasor is converted into polar coordinates, the traditional three-point average filter is applied for second harmonic filtering. The intent is to show the second harmonic
2 Note that some commercial PMUs computes phasors directly at the nominal sampling rate fnominal .
5
Phasor A CF
1 SP_MF
SP_MF SP_MnF
2 SP_MnF
Single-PhaseProcessing 3 PS_M 2 Frequency Goal
Phase A Frequency
Phase A
Phasor A
Phasor A
Phase B
Phase B
Phasor B
Phasor B
PS_M P_PS
1 Disturbance
Type
Phase C
Three-Phase Signal Producer
Fig. 5.
Phase C
Phasor C
Phasor Estimation
Phasor C
Symmetrical Components
FD
FD
PS_M
PS_Md
4 PS_Md
PS_A
PS_Ad
6 PS_Ad
PS_A
Lookup Table
Frequency Estimation
Downsampling 5 PS_A
7 Frequency Deviation
Main Components
Downsampling Angle - Ramp Disturbance
effect comparing single-phase phasor magnitude with and without filtering at off-nominal frequencies. Pedagogy: Different sets of filtering can be introduced to check their influence in the single-phase estimation.
V. E XAMPLES OF E DUCATIONAL ACTIVITIES In this section, educational components using the PMU simulator are illustrated. In the examples, the nominal system frequency is 60 Hz, for the simulated signals, a sampling rate of 32 points per cycle, that is, 1920 Hz is used.
150
100
50
Angle (degrees)
•
CF
P_ PS P_PS
0
−50
−100
−150
1.5
2
2.5
3
3.5
4
4.5
Time (s)
1) Step Disturbance: A three-phase system is used to show the positive-sequence estimation performance. A frequency step (Switch 1 set on step) of one Hz (Switch 2 set on 59) is applied after two seconds. This feature is suitable for understanding the angle behavior under off-nominal frequency operation. After the disturbance application, the phasor angle starts to decrease linearly following the frequency drop. A frequency deviation of 1 Hz corresponds to an angle variation of 2π/sec. The student can also observe the angle jumping from -180 to 180 degrees. 2) Ramp Disturbance: In this case, a positive 1 Hz ramp frequency disturbance is applied (Switch one in ramp position) between two and three seconds. The performance of the positive-sequence angle is shown in Figure 6. Different from the frequency step case, the angle shows a parabolic behavior under the frequency ramp period (23 seconds). The system acceleration is positive (frequency rising) so the position (angle) is increasing. 3) Complex Gain Influence: The complex gain Qn , a second harmonic oscillation, does not affect the positive sequence phasor performance because it is filtered by the three-phase estimation. The influence of the complex gain Pn under off-nominal frequency operation, when the calibration block is not considered, is shown in Figure 7. During the offnominal frequency operation the leakage phenomena result in a attenuation of the magnitude of the phasor.
Fig. 6.
Positive Sequence Angle from Ramp Disturbance Positive Sequence Magnitude 1.0002 1.0001
Magnitude (pu)
A. Positive-Sequence Phasor Computation
1 0.9999 0.9998 0.9997 0.9996 0.9995 0.9994 1.8
Fig. 7.
1.9
2
2.1
2.2
2.3
Time (s) Complex Gain Pn Influence from Step Disturbance
B. Single-Phase Phasor Computation For the step disturbance, the influence of the complex gain Qn is clearly observed in the single-phase phasor estimation under off-nominal frequency and is shown in Figure 8. In this example the influence of the complex gain is clearly revealed in the phasor magnitude before the filtering and downsampling blocks. A second harmonic of 120 Hz shows up in the phasor magnitude without filtering (blue curve). The phasor magnitude after filtering is shown in the red curve. The singlephase phasor performance after filtering and downsampling is
6
Zero-Sequence Component
Single-Phase Magnitude Filtering No Filtering
1.008
0.0291
Magnitude (pu)
1.006
Magnitude (pu)
1.004 1.002 1 0.998
0.029 0.0289 0.0288 0.0287
0.996 0.0286 0.994
1.8
1.9
2
2.1
2.2
2.3
Time (s)
0.992
Fig. 11. Zero-sequence phasor magnitude under off-nominal and unbalanced operation
0.99 1.99
2
2.01
2.02
2.03
2.04
2.05
2.06
2.07
Time (s) Load Rejection Test - Generator Voltages
Fig. 8.
1
Single-Phase Phasor Magnitude Estimation Single-Phase Filtering and Downsampling
Magnitude (pu)
0.5
1.01
Mangnitude (pu)
Va Vb Vc
1.005
0
−0.5
1
−1 0.3
0.995
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.4
Time (sec) 0.99
Fig. 12.
Three-Phase Real Voltage Data
0.985 2
2.5
3
3.5
4
Time (s)
Fig. 9.
D. Real Data
Single-Phase Phasor Magnitude Estimation with Downsampling
shown in Figure 9. A low-amplitude oscillation at 2 Hz is observed. C. Unbalanced Operation In this example, the phasor magnitudes are changed in the Signal Generator block to simulate a 5% unbalanced in the three-phase signals, as shown in Figure 10. The positive- and zero-sequence phasor magnitude are shown in Figures 10 and 11, respectively. Note that the second-harmonic components will not be canceled in the positive-sequence calculation under unbalanced operation. An oscillation of 2 Hz is evident under off-nominal frequency operation.
Real digital data files can be also processed by the PMU Simulator. The data was recorded at 48 points per cycle, that is, a sampling rate of 2.88 kHz. The results are presented as follows. 1) Generator load rejection: A three-phase real digital data acquired during a generator load rejection test is processed by the simulator. The three-phase voltage and current data acquired during the fault are shown in Figures 12 and 13, respectively. It should be noted that the load rejection happened around 0.35 s., the voltage wave exhibits some spikes related with the circuit breaker misoperation. In the current plots the breaker
Load Rejection Test - Generator Currents 1.5
1
Positive Sequence - Unbalanced Operation
0.5
Magnitude (pu)
1.0002
Magnitude (pu)
Ia Ib Ic
1
0.9998
0
−0.5 0.9996 −1 0.9994 1.5
2
2.5
3
3.5
4
4.5
Time (s)
Fig. 10. Positive-sequence phasor magnitude under off-nominal and unbalanced operation
−1.5 0.3
0.31
0.32
0.33
0.34
0.35
Time (sec)
Fig. 13.
Three-Phase Real Current Data
0.36
0.37
0.38
0.39
7 Real Data - Frequency Deviation 9
5
Number of Votes
Frequency Deviation (Hz)
8
4
3
2
7 6 5 4 3 2
1
1 0
0 0.3
0.4
0.5
0.6
0.7
0.8
0.9
Time (s)
Fig. 14.
Fig. 17.
Positive-Sequence Component
3
Rating
4
5
Student Feedback
to evaluate their learning outcome from lab exercises using this tool. These 15 students came from Federal Institute of Santa Catarina (IFSC) and University of S˜ao Paulo (USPSC), Brazil. The tool was rated on a scale of 1 to 5 (5 being excellent). The evaluation results are presented in the horizontal axis in Figure 17, while the vertical axis represents the number of participates who voted for this specific rating. It is evident that the popularity of the tool. The average rating of the tool course is more than four.
0.9 0.8
Magnitude (pu)
2
Frequency Performance
1
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.3
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.4
0.41
VII. C ONCLUSIONS
Time (s)
Fig. 15.
Positive-Sequence Component of Current
misoperation can be also observed. The frequency estimation before and after the disturbance is shown in Figure 14. Following the load rejection, the frequency rises significantly because the generator is operating with no load. As expected there is a delay related to the actuation of the speed governor. The positive- and negative-sequence magnitude from the current phasor estimation is presented in Figures 15 and 16. The breaker is clearly observed in the increase of negativesequence component around 0.37 s. VI. T EACHING T OOL S TUDENT E VALUATION An important part of this process in to evaluate this package from the students perspective. In 2013, 15 students were asked
In this paper a PMU S IMULINK simulator was presented. The aim of this software is to aid in the understanding of the behavior of algorithms internal to the PMU and to grasp key factors affecting their performance under off-nominal frequency operation. The PMU simulator is useful for academics and professionals who would like to understand the concepts involved in the phasor estimation process carried out by PMUs. The data block S IMULINK environment allows a better understanding of the algorithms and data flow involved in the phasor measurement process. This open environment also provides an easy access to the signals the user wants to observe. The quality and relevance of this package courses is validated when considering the positive feedback from students of different universities. ACKNOWLEDGMENT The authors gratefully acknowledge the financial support of the Brazilian Government Research Agency (CNPq) grant 201249/2011-1 and the Engineering Research Center Program of the NSF and the DoE under Award Number EEC1041877 and the CURENT Industry Partnership Program. The authors also gratefully acknowledge Dr. Jay Murphy for the discussions on phasor measurement estimation and Professor Rodrigo A. Ramos from USP-SC for sending students to participate of package evaluation.
Negative-Sequence Component 0.35
0.3
0.25
Magnitude (pu)
1
1
0.2
0.15
R EFERENCES
0.1
0.05
0 0.3
0.32
0.34
0.36
0.38
Time (s)
Fig. 16.
Negative-Sequence Component of Current
0.4
0.42
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Daniel Dotta received his PhD Degree in Power System Engineering in 2009, from the Federal University of Santa Catarina, Florianpolis, Brazil. He has been on the faculty at the Federal Institute of Santa Catarina since 2006. Currently he is doing his sabbatical at Renssenlaer Polytechnic Institute (RPI), Troy, NY, USA.
Joe H. Chow received his MS and PhD degrees from the University of Illinois, Urbana-Champaign. After working in the General Electric power system business in Schenectady, he joined Rensselaer Polytechnic Institute in 1987, and is a professor of Electrical, Computer, and Systems Engineering. His research interests include multivariable control, power system dynamics and control, voltage-source converter-based FACTS controllers, and synchronized phasor data applications.
David Bertagnolli is a principal engineer with ISO-New England, the Independent System Operator for the New England bulk electric power system. Mr. Bertagnolli holds a Bachelors degree in electrical engineering from the University of Illinois and a Masters degree from Columbia University. He is registered as a Professional Engineer in the State of Connecticut and a senior member of the Institute for Electrical and Electronics Engineers.
