A Wavelet-Based Data Compression Technique ... - Semantic Scholar
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IEEE TRANSACTIONS ON SMART GRID, VOL. 2, NO. 1, MARCH 2011
A Wavelet-Based Data Compression Technique for Smart Grid Jiaxin Ning, Member, IEEE, Jianhui Wang, Member, IEEE, Wenzhong Gao, Member, IEEE, and Cong Liu, Member, IEEE
Abstract—This paper proposes a wavelet-based data compression approach for the smart grid (SG). In particular, wavelet transform (WT)-based multiresolution analysis (MRA), as well as its properties, are studied for its data compression and denoising capabilities for power system signals in SG. Selection of the Order 2 Daubechies wavelet and scale 5 as the best wavelet function and the optimal decomposition scale, respectively, for disturbance signals is demonstrated according to the criterion of the maximum wavelet energy of wavelet coefficients (WCs). To justify the proposed method, phasor data are simulated under disturbance circumstances in the IEEE New England 39-bus system. The results indicate that WT-based MRA can not only compress disturbance signals but also depress the sinusoidal and white noise contained in the signals. Index Terms—Data compression, disturbance analysis, wavelet transform.
I. INTRODUCTION
T
HE AGING electric power infrastructure is confronting increasing obstacles to accommodate complex customer demands and emerging technologies. Higher-level usages of renewable energy sources (RESs), flexible alternating current transmission systems (FACTSs), and plug-in hybrid electric vehicles (PHEVs) call for intelligent, real-time, and robust operation, protection, and control of the power grid. In this context, the smart grid (SG) is proposed to change the overall pattern of power grid operation and management in favor of obtaining economic efficiencies, robust control, and environmental benefits. It is desirable that the overall performance of bulk power systems is essentially augmented by SG technologies in a dynamic, adaptive, and optimal manner with greater reliability and stability and more flexible compatibility with existing and future technologies. The concept of SG is to establish the seamless communication throughout each level of the power grid in order to reinforce the transparency and mobility of power grid information and, therefore, to be able
Manuscript received October 05, 2010; accepted October 27, 2010. Date of publication December 10, 2010; date of current version February 18, 2011. Paper no. TSG-00151-2010. J. Ning is with EnerNex Corporation, Knoxville, TN, USA (e-mail: [email protected]). J. Wang and C. Liu are with Argonne National Laboratory, Argonne, IL, USA (e-mail: [email protected]; [email protected]). W. Gao is with Department of Electrical and Computer Engineering, University of Denver, Denver, CO, USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSG.2010.2091291
to coordinate system operation and management throughout all levels of the power grid. Recent studies focus on the technical transition from the conventional power grid to the SG. In other words, many studies have been carried out to observe how grid performance can be improved in a communication-guaranteed and intelligence-enabled environment. Concerning the transmission level(s) of the power grid, the operation and control of huge amounts of RES penetration [1], [2], wide-area protection and control [3], [4], and the regulation of energy storage systems (ESSs) [5] draw significant research interest in the context of SG. In [6] and [7], the functionalities and applications of the smart transmission systems are synthesized and anticipated. Apart from the concerns above, this paper focuses on the issue of data congestion in SG, given that the overwhelming flows of data may lead to dramatic deterioration in the effectiveness and efficiency of communication in the SG. In the future SG, the data reflecting system statuses across all levels of the grid may be generated by smart metering systems, supervisory control and data acquisition (SCADA) systems, widearea monitoring systems (WAMSs), and other monitoring devices. The huge amounts of data need to circulate and be stored among control centers, utilities, and customers in a near realtime manner. In examining the case of WAMSs, for example, in 2004, the Tennessee Valley Authority (TVA) launched a project called Phasor Data Concentrator (PDC) [8], [9], an effort in collecting electrical information of the grid from phasor measurement units (PMUs), which are the major measuring devices in WAMSs. Currently, 120 PMUs are deployed in the Eastern Interconnection. These PMUs transmit the measurements 30 times per second to the PDC in TVA and the measurement archival rate reaches 150 million times per hour. The storage utilization rate reaches 36 gigabytes per day. Moreover, because this PDC project aims to coordinate the independent system operators (ISOs) and utilities in the Eastern Interconnection, data congestion will also be confronted in the communication system of WAMSs, when such a large number of measurement data are circulating among ISOs and utilities. The overall data size in the future SG is expected to be fairly large as a result of the full implementation of SG techniques in the next few years. Therefore, the use of data compression techniques will be desirable to help mitigate the burden of the communication systems and the storage utilization. In addition to data compression, the valuable information contained in the data should be conserved to the greatest extent possible so as to accurately reflect the system statuses. The basic requirements for data compression can be generalized as follows.
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NING et al.: A WAVELET-BASED DATA COMPRESSION TECHNIQUE FOR SMART GRID
• Power system data can be compressed at the sending terminals so as to inject amounts of data that have been compressed as much as possible into the communication systems. • The compression should keep the valuable information contained in the data. • The compressed data can be near-perfectly reconstructed for analysis when received at receiving terminals. This paper proposes a wavelet-based approach [10] for data compression [11], [12] in the SG context. By a process of multiresolution analysis (MRA), wavelet transform (WT) can orthogonally decompose a time series into scaling coefficients (SCs) and wavelet coefficients (WCs), in which the trivial data points can be deleted such that the overall size of the data can be compressed. And the nature of WT satisfies a near-perfect reconstruction of the time series via an inverse MRA. Moreover, with the rapid development of computing techniques, the algorithm of MRA can be implemented for online applications [13], [14]. Thus, it is feasible to embed a wavelet-based data compression algorithm into the monitoring devices, in which the data can be compressed before it is sent out in order to mitigate the data congestion. In addition, WT is capable of depressing the sinusoidal and “white” noise in the data. This property could benefit the preprocessing of the data in the measuring devices. To justify the proposed approach, this paper utilizes a set of simulated PMU data to discuss the advantages of WT on data compression. The simulated PMU data are obtained from simulations in the Power System Simulator for Engineering (PSS/E). In PSS/E, the dynamic frequency and voltage signals are simulated during system disturbances in the IEEE New England 39-bus system. The disturbances include generation loss and load change, which are major concerns for WAMSs in the interconnected systems. Nevertheless, without loss of generality, the proposed approach is capable of compressing any type of grid signal into the format of a time series. As a byproduct of data compression, the denoising property of WT is also discussed to show the immunity of the proposed approach to the various data noise. The paper is organized as follows: in Section II, WT-based MRA and its properties are briefly introduced; in Section III, the selections of wavelet function and decomposition scale for disturbance signals are conducted for data compression and denoising; in Section IV, a numerical simulation is carried out to justify the effectiveness of WT-based MRA on data compression and denoising; the conclusion is presented in Section V.
II. WT-BASED MULTIRESOLUTION ANALYSIS WT-based MRA is illustrated in Fig. 1, where (a) shows the procedure for decomposing a signal, and (b) shows the procedure for reconstructing a signal. and are the low-pass filter and high-pass filter, respectively. The filters are constructed by a scaling function and a wavelet function , satisfying . In Fig. 2, the waveforms and frequency responses of the Order 2 Daubechies (db2) scaling function and wavelet function are shown as an example. The MRA generates SCs or “Approximation” and WCs or “Detail” . SCs represent the
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Fig. 1. Procedure of WT-based MRA. (a) Decomposition. (b) Reconstruction.
Fig. 2. Order 2 Daubechies scaling and wavelet functions and their spectrum. (a) Scaling function of db2. (b) Wavelet function of db2. (c) Low-pass filter of db2 (for decomposition). (d) High-pass filter of db2 (for decomposition).
low-frequency components, and WCs represent the high-frequency components. By transforming a signal, the features of the signal can be extracted from SCs and WCs. To disturbance signals in power systems, WCs are more important because the transient features of the signals are mostly represented by the high-frequency components [15]. Property 1—Nonredundant Transform: WT-based MRA is theoretically a type of nonredundant transform. As indicated by the “ ” shown in Fig. 1(a), a two times downsampling rate is adopted to each scale to ensure the equivalence in the number of sampling points before and after the decomposition. Assuming and contain sampling points at lowest scale , the sampling points at any scale can be written as (1) Therefore, the number of sampling points before and after the decomposition (with an absolute symmetric wavelet function) satisfies (2)
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If the wavelet function is not absolutely symmetric, as in, for example, Daubechies wavelet family (i.e., its near-symmetric property), the relationship in (2) can be expressed as (3) Property 2—Threshold Denoising: A threshold can be applied to depress low-value amplitudes in details, most of which are caused by high-frequency noise. The reconstruction of approximation and details after thresholding can return a cleaner signal with little distortion. Several wavelet-based thresholding methods [16], [17] have been developed. The selection of thresholding methods deserves particular consideration in the future for SG applications. In this paper, universal thresholding is chosen to process disturbance signals because of its computational simplicity and efficiency. Universal thresholding is calculated by (4) where stands for noise variance at scale . The threshold can be applied onto WCs by (5) as follows: (5) After thresholding, the amplitude of WCs beneath the threshold is set to be zero. In this way, the noise is largely depressed because the small amplitudes in WCs usually reflect the major energy of noise [16]. Property 3—Data Compression: After applying (5) to WCs, the low-value amplitudes in WCs are depressed to 0. Because only nonzero points are our interest of analysis, the signal can be compressed by eliminating all zero points in WCs and then can be sent to the receiving end, where the signal can be reconstructed as shown in Fig. 1(b). The question for WT-based MRA is whether or not the meaningful information of power system signals can be retained and maintained after the denoising and compression steps. In the reminder of the paper, a numerical experiment is carried out to check the performance of WT-based MRA to disturbance signals. III. SELECTION OF WAVELET AND DECOMPOSITION SCALE Before WT-based MRT is applied for data compression, the best wavelet function and the optimal decomposition scale need to be carefully selected. Wavelet energy is the index to reflect the energy concentration of WCs on certain scales. The larger the wavelet energy, the more the information is preserved after the decomposition. In this paper, wavelet energy is chosen as the criterion to determine the best wavelet function and the optimal decomposition scale for disturbance signals [15]. The definition of total wavelet energy is given by (6)
Fig. 3. Diagram of IEEE New England 39-bus system.
and wavelet energy in each scale is given by (7) where subscript stands for the scale, and the maximum number of scale is ; subscript stands for the point in WCs; and is the length of WCs at scale . The candidates of wavelet functions consist of Daubechies wavelet family and Symlets wavelet family . stands for the order of the wavelet function. In this paper, db2–db10 and sym2–sym10 are chosen as wavelet candidates. These wavelets have been chosen because they have shown excellent performance in analyzing dynamic signals with discontinuity and abrupt change [18], [19]. The wavelet corresponding to the highest total wavelet energy in (6) is chosen as the best wavelet function, and the scale corresponding to the highest wavelet energy in (7) is chosen as the optimal decomposition scale. The testing disturbance signals are also generated in the IEEE New England 39-bus system (Fig. 3). Three types of disturbances are adopted in this paper: generation loss, load drop, and load surge. Generation loss is generated at Buses 33 and 34, respectively; while load drop and load surge are generated at Buses 16 and 20, respectively. During the simulation, frequency and voltage are recorded at Bus 19. The results are listed in Tables I and II. In Table I, the elements highlighted in yellow indicate the highest wavelet energy of a specific signal corresponding to a certain wavelet function. It can be seen that most of the highest wavelet energy levels of the different signals point to db2 and sym2. Because both wavelets return the same total wavelet energy to all signals, either one can be chosen as the best wavelet for disturbance signals. In this paper, db2 is determined to be the wavelet function for MRA. In Table II, the signals are decomposed by db2 into 6 scales, and it is evident that the wavelet energy at scale 5 is the highest for most of the disturbances. Thus, scale 5 is determined as the optimal decomposition scale for MRA in this paper.
NING et al.: A WAVELET-BASED DATA COMPRESSION TECHNIQUE FOR SMART GRID
RESULTS
DB
OF
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TABLE I SELECTION OF WAVELET FUNCTION
Daubechies wavelet function; SYM
Symlets wavelet function
TABLE II RESULTS OF SCALE SELECTION
GL
frequency; v voltage. generation loss; LD load drop; LS
load surge
IV. NUMERICAL EXPERIMENT In this section, the disturbance signals, simulated in PSS/E, are used as system dynamic signals to test the proposed method. The IEEE New England 39-bus system is adopted as the test system, in which the simulation time step is 0.004167 s (1/4 cycle), and the simulation time is 2 s (equivalent to 482 sample points). The simulation focuses on the first 2 s after disturbances occur, during which the automated system control devices (governor or power system stabilizer) have not responded to the disturbances. The topology of the system is shown in Fig. 3, where “G” stands for generators, “ ” stands for loads, and numbers 1–39 are bus numberings. Without loss of generality, the loss of Generation 4 (denoted as GL4) at Bus 33 is used to test the property of WT-based MRA. The measuring location is supposed to be deployed at Bus 19; and the measurements include frequency and voltage.
Fig. 4. Frequency and voltage responses at Bus 19 to GL4.
In Fig. 4, the frequency and voltage at Bus 19 during GL4 at 0.5 s of simulation time are illustrated. At the moment a disturbance occurs, both frequency and voltage experience an abrupt drop in their values; and then, both variables start low-frequency oscillation because of the transient response of the system. The WT-based MRA to the frequency and voltage are shown in Figs. 5 and 6, respectively. The Order 2 Daubechies wavelet is chosen as the wavelet function, and scale 5 is selected as the maximum decomposition scale. From Figs. 5(a) and 6(a), it can be seen that both frequency and voltage have abrupt change in the waveforms at 0.5 s due to the disturbance. Figs. 5(b) and 6(b) are the SCs of frequency and voltage signals which approximate envelops of the signals and, thus, represent the low-frequency features of the signals. Note that the absolute amplitude of SCs only reflects the distribution of signal’s energy at scale 5 after the transform and have no direct relationship with its amplitude in time domain. In practice, the signal needs to be reconstructed
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TABLE III COMPARISON OF DATA LENGTHS BEFORE AND AFTER WT
Fig. 5. WT-based MRA to frequency. (a) Frequency signal. (b) Approximation at scale 5. (c) Detail at scale 5. (d) Detail at scale 4. (e) Detail at scale 3. (f) Detail at scale 2. (g) Detail at scale 1.
Fig. 7. The testing frequency signals. (a) The original signal. (b) The signal mixed with 60-Hz periodic noise with the amplitude of 0.1. (c) The signal mixed with the white noise with the amplitude of 0.05.
Fig. 6. WT-based MRA to voltage. (a) Voltage signal. (b) Approximation at scale 5. (c) Detail at scale 5. (d) Detail at scale 4. (e) Detail at scale 3. (f) Detail at scale 2. (g) Detail at scale 1.
to utilize its actual amplitude in time domain. In Figs. 5(c)–(g) and 6(c)–(g), the WCs of frequency and voltage signals are displayed. The WCs reflect the high-frequency features of the signals at each scale because the nonzero points of WCs are only localized around 0.5 s. At different scales, the WCs exhibit different values because of the filter property that varies across scales. In the previous section, scale 5 has been proven to be the optimal decomposition scale for disturbance signals. Therefore, in Figs. 5(c) and 6(c), one can see that a distinguishable amplitude in accurately indicates the occurrence of the disturbance at 0.5 s. At other scales (see in Figs. 5(d)–(g) and 6(d)–(g)), although the large amplitudes of WCs appear around the disturbance moment, the accuracy is incomparable to scale 5. It seems that, in Figs. 5(g) and 6(g), can also indicate the occurrence of the disturbance. However, a finer observation of reveals that it is less precise than and the amplitude of at 0.5 s is less noticeable than as well. This feature of can be used for signal recognition and other quantitative analysis. In Table III, the lengths (standing for one-dimensional data size) of frequency signals and the lengths of SCs and WCs are listed, respectively. Table III shows that there are 10 more sampling points after the decomposition. Although Daubechiesbased WT is not a perfect nonredundant transform because of its near-symmetric property as explained by (3), the redundant
Fig. 8. Denoising to the frequency signal mixed with the periodical noise. (a) The original signal. (b) The signal mixed with the periodical noise. (c) WCs of the original signal. (d) WCs of the polluted signal.
points are trivial when compared with the total length of the signal (10 points versus 482 points). Denoising is often introduced into signal processing to counteract the pollution of noise to the signal. In power systems, the noise is usually sorted into two types: periodical noise and white noise. In this paper, the 60 Hz periodical noise and the white noise are mixed with the frequency signal to justify the denoising of WT-based MRA. In Fig. 7, the frequency signal shown in Fig. 4 and its polluted mixtures with 60-Hz periodic noise with the amplitude of 0.1 and the white noise with the amplitude of 0.05 are plotted. The polluted signals are decomposed by a db2 wavelet into 5 scales. Universal thresholding are applied to the WCs by (5). In Figs. 8 and 9, the WCs at scale 5 are exhibited for both the original signal and the polluted signal after the denoising. Comparing the amplitude of (c) and (d) in Figs. 8 and 9, it can be
NING et al.: A WAVELET-BASED DATA COMPRESSION TECHNIQUE FOR SMART GRID
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Fig. 9. Denoising to the frequency signal mixed with the white noise. (a) The original signal. (b) The signal mixed with the white noise. (c) WCs of the original signal. (d) WCs of the polluted signal.
Fig. 11. Denoising results for the signal polluted by the white noise. (a) The original signal. (b) The polluted signal. (c) The reconstructed signal after denoising.
TABLE IV LENGTH OF THE COMPRESSED SIGNAL
TABLE V SNR RATIO AND RMS ERROR BEFORE AND AFTER DENOISING
the periodical noise;
the white noise.
after the denoising and compression is listed in Table V, as well as the root-mean-square (rms) error, criterion for signal distortion, between the original signal and the reconstructed signal. Table V shows that the SNR is improved up to two times compared to the ratio before denoising. In addition, the rms error is improved by about 10 times. WT-based MRA provides excellent performance in terms of depressing noise, as well as reducing signal distortion. V. CONCLUSION
Fig. 10. Denoising results for the signal polluted by the periodical noise. (a) The original signal. (b) The polluted signal. (c) The reconstructed signal after denoising.
seen that the thresholding does not affect the property of WCs. The value of WC at 0.5 s remains the same and accurately indicates the occurrence moment of the disturbance. This result is important because WCs contain most of the high-frequency information, which helps us recognize the dynamic feature of the signal. After denoising, the nonzero points in WCs from scale 1 through scale 5 can be extracted so as to compress the length of the original WCs. The lengths of the compressed WCs are listed in Table IV, which shows that the lengths of the compressed WCs are reduced by around 1/5.4 times in comparison with the original WCs. Figs. 10 and 11 show the reconstructed signals after the denoising and compression. One can see that the signals are recovered although there is slight distortion. The signal-to-noise (SNR) ratio, criterion for denoising, before and
This paper proposes a WT-based MRA to perform data compression in the smart grid context. The proposed approach is capable of effectively compressing the size of disturbance signals as well as depressing sinusoidal and white noise in the signals. The Order 2 Daubechies wavelet and scale 5, respectively, as the best wavelet function and the optimal decomposition scale for disturbance signals has been selected according to the criterion of the maximum wavelet energy of wavelet coefficients. A numerical simulation is conducted to exhibit the properties of WT-based MRA for data compression and denoising. The analysis for the results shows the effectiveness of WT-based MRA on data compression and denoising for disturbance signals. Without loss of generality, the proposed method can be implemented in smart grid to mitigate data congestion and improve data transmission and quality. REFERENCES [1] X. P. Zhang, “A framework for operation and control of smart grids with distributed generation,” in IEEE Power Energy Soc. Gen. Meet. —Conv. Del. Elect. Energy 21st Century, 2008, pp. 1–5. [2] C. W. Potter, A. Archambault, and K. Westrick, “Building a smarter smart grid through better renewable energy information,” in IEEE/PES Power Syst. Conf. Expo., 2009, pp. 1–5. [3] S. Wang and G. Rodriguez, “Smart RAS (Remedial Action Scheme),” in Proc. Innovative Smart Grid Technol., 2010, pp. 1–6.
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[4] K. Heussen, A. Saleem, and M. Lind, “Control architecture of power systems modeling of purpose and function,” in Proc. IEEE Power Energy Soc. Gen. Meet., 2009, pp. 1–8. [5] K. Moslehi and R. Kumar, “A reliability perspective of the smart grid,” IEEE Trans. Smart Grid, vol. 1, no. 1, pp. 57–64, Jun. 2010. [6] A. Bose, “Smart transmission grid applications and their supporting infrastructure,” IEEE Trans. Smart Grid, vol. 1, no. 1, pp. 11–19, Jun. 2010. [7] Z. Jiang, F. Li, and W. Qiao et al., “A vision of smart transmission grids,” in IEEE Power Energy Soc. Gen. Meet., 2009, pp. 1–10. [8] [Online]. Available: http://openpdc.codeplex.com/ [9] B. Fardanesh, S. Zelingher, and A. P. Sakis Meliopoulos et al., “Multifunctional synchronized measurement network [power systems],” IEEE Comput. Appl. Power, vol. 11, no. 1, pp. 26–30, Jan. 1998. [10] S. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 11, no. 7, pp. 674–693, Jul. 1989. [11] S. Santoso, E. J. Powers, and W. M. Grady, “Power quality disturbance data compression using wavelet transform methods,” IEEE Trans. Power Del., vol. 12, no. 3, pp. 1250–1257, 1997. [12] T. B. Littler and D. J. Morrow, “Wavelets for the analysis and compression of power system disturbances,” IEEE Trans. Power Del., vol. 14, no. 2, pp. 358–364, 1999. [13] M. Forghani and S. Afsharnia, “Online wavelet transform-based control strategy for UPQC control system,” IEEE Trans. Power Del., vol. 22, no. 1, pp. 481–491, 2007. [14] O. A. S. Youssef, “Combined fuzzy-logic wavelet-based fault classification technique for power system relaying,” IEEE Trans. Power Del., vol. 19, no. 2, pp. 582–589, 2004. [15] J. Ning, “Wide-area monitoring and recognition for power system disturbances using data mining and knowledge discovery theory,” Ph.D. dissertation, Tennessee Technol. Univ., Cookeville, TN, Aug. 2010. [16] X. Zhang and M. D. Desai, “Adaptive denoising based on SURE risk,” IEEE Signal Process. Lett., vol. 5, no. 10, pp. 265–267, 1998. [17] H. Krim, D. Tucker, and S. Mallat et al., “On denoising and best signal representation,” IEEE Trans. Inf. Theory, vol. 45, no. 7, pp. 2225–2238, 1999. [18] L. Zhang and P. Bao, “Edge detection by scale multiplication in wavelet domain,” Pattern Recognit. Lett., vol. 23, no. 14, pp. 1771–1784, Dec. 2002. [19] J.-W. Hsieh, M.-T. Ko, and H.-Y. M. Liao et al., “A new wavelet-based edge detector via constrained optimization,” Image Vis. Comput., vol. 15, no. 7, pp. 511–527, Jul. 1997.
Jiaxin Ning (S’08–M’10) received the B.S. and M.S. degrees in electrical engineering from Chongqing University, China, in 2004 and 2007, respectively, and the Ph.D. degree in electrical engineering from Tennessee Technological University, Cookeville, in 2010. He is currently a Senior Consultant on electric power research, engineering, and consulting at EnerNex Corporation, Knoxville, TN. His scope of work covers modeling and simulation of renewable energy sources, power system operation and control, and power quality analysis.
Jianhui Wang (M’07) received the B.S. degree in management science and engineering and M.S. degree in technical economics and management from North China Electric Power University, China, in 2001 and 2004, respectively, and the Ph.D. degree in electrical engineering from Illinois Institute of Technology, Chicago, in 2007. He is currently an Assistant Computational Engineer with the Decision and Information Sciences division at Argonne National Laboratory, Argonne, IL. Dr. Wang is the Chair of the IEEE Power & Energy Society (PES) power system operation methods subcommittee and Cochair of an IEEE task force on integration of wind and solar power into power system operations. He is an editor of the IEEE TRANSACTIONS ON SMART GRID.
Wenzhong Gao (S’00–M’02–SM’03) received the M.S. and Ph.D. degrees in electrical and computer engineering specializing in electric power engineering from Georgia Institute of Technology, Atlanta, in 1999 and 2002, respectively. His current teaching and research interests include renewable energy and distributed generation, smart grid, power-system protection, power-electronics applications in power systems, power-system modeling and simulation, and hybrid electric propulsion systems.
Cong Liu (S’08–M’10) received the B.S. and M.S. degrees in electrical engineering from Xi’an Jiaotong University, China, in 2003 and 2006, respectively, and the Ph.D. degree from Illinois Institute of Technology, Chicago, in 2010. Currently, he is a Postdoctoral Appointee in the Decision and Information Sciences Division, Argonne National Laboratory, Argonne, IL. His research interests include power systems and natural gas systems analysis, optimization, and operation.
IEEE TRANSACTIONS ON SMART GRID, VOL. 2, NO. 1, MARCH 2011
A Wavelet-Based Data Compression Technique for Smart Grid Jiaxin Ning, Member, IEEE, Jianhui Wang, Member, IEEE, Wenzhong Gao, Member, IEEE, and Cong Liu, Member, IEEE
Abstract—This paper proposes a wavelet-based data compression approach for the smart grid (SG). In particular, wavelet transform (WT)-based multiresolution analysis (MRA), as well as its properties, are studied for its data compression and denoising capabilities for power system signals in SG. Selection of the Order 2 Daubechies wavelet and scale 5 as the best wavelet function and the optimal decomposition scale, respectively, for disturbance signals is demonstrated according to the criterion of the maximum wavelet energy of wavelet coefficients (WCs). To justify the proposed method, phasor data are simulated under disturbance circumstances in the IEEE New England 39-bus system. The results indicate that WT-based MRA can not only compress disturbance signals but also depress the sinusoidal and white noise contained in the signals. Index Terms—Data compression, disturbance analysis, wavelet transform.
I. INTRODUCTION
T
HE AGING electric power infrastructure is confronting increasing obstacles to accommodate complex customer demands and emerging technologies. Higher-level usages of renewable energy sources (RESs), flexible alternating current transmission systems (FACTSs), and plug-in hybrid electric vehicles (PHEVs) call for intelligent, real-time, and robust operation, protection, and control of the power grid. In this context, the smart grid (SG) is proposed to change the overall pattern of power grid operation and management in favor of obtaining economic efficiencies, robust control, and environmental benefits. It is desirable that the overall performance of bulk power systems is essentially augmented by SG technologies in a dynamic, adaptive, and optimal manner with greater reliability and stability and more flexible compatibility with existing and future technologies. The concept of SG is to establish the seamless communication throughout each level of the power grid in order to reinforce the transparency and mobility of power grid information and, therefore, to be able
Manuscript received October 05, 2010; accepted October 27, 2010. Date of publication December 10, 2010; date of current version February 18, 2011. Paper no. TSG-00151-2010. J. Ning is with EnerNex Corporation, Knoxville, TN, USA (e-mail: [email protected]). J. Wang and C. Liu are with Argonne National Laboratory, Argonne, IL, USA (e-mail: [email protected]; [email protected]). W. Gao is with Department of Electrical and Computer Engineering, University of Denver, Denver, CO, USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSG.2010.2091291
to coordinate system operation and management throughout all levels of the power grid. Recent studies focus on the technical transition from the conventional power grid to the SG. In other words, many studies have been carried out to observe how grid performance can be improved in a communication-guaranteed and intelligence-enabled environment. Concerning the transmission level(s) of the power grid, the operation and control of huge amounts of RES penetration [1], [2], wide-area protection and control [3], [4], and the regulation of energy storage systems (ESSs) [5] draw significant research interest in the context of SG. In [6] and [7], the functionalities and applications of the smart transmission systems are synthesized and anticipated. Apart from the concerns above, this paper focuses on the issue of data congestion in SG, given that the overwhelming flows of data may lead to dramatic deterioration in the effectiveness and efficiency of communication in the SG. In the future SG, the data reflecting system statuses across all levels of the grid may be generated by smart metering systems, supervisory control and data acquisition (SCADA) systems, widearea monitoring systems (WAMSs), and other monitoring devices. The huge amounts of data need to circulate and be stored among control centers, utilities, and customers in a near realtime manner. In examining the case of WAMSs, for example, in 2004, the Tennessee Valley Authority (TVA) launched a project called Phasor Data Concentrator (PDC) [8], [9], an effort in collecting electrical information of the grid from phasor measurement units (PMUs), which are the major measuring devices in WAMSs. Currently, 120 PMUs are deployed in the Eastern Interconnection. These PMUs transmit the measurements 30 times per second to the PDC in TVA and the measurement archival rate reaches 150 million times per hour. The storage utilization rate reaches 36 gigabytes per day. Moreover, because this PDC project aims to coordinate the independent system operators (ISOs) and utilities in the Eastern Interconnection, data congestion will also be confronted in the communication system of WAMSs, when such a large number of measurement data are circulating among ISOs and utilities. The overall data size in the future SG is expected to be fairly large as a result of the full implementation of SG techniques in the next few years. Therefore, the use of data compression techniques will be desirable to help mitigate the burden of the communication systems and the storage utilization. In addition to data compression, the valuable information contained in the data should be conserved to the greatest extent possible so as to accurately reflect the system statuses. The basic requirements for data compression can be generalized as follows.
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NING et al.: A WAVELET-BASED DATA COMPRESSION TECHNIQUE FOR SMART GRID
• Power system data can be compressed at the sending terminals so as to inject amounts of data that have been compressed as much as possible into the communication systems. • The compression should keep the valuable information contained in the data. • The compressed data can be near-perfectly reconstructed for analysis when received at receiving terminals. This paper proposes a wavelet-based approach [10] for data compression [11], [12] in the SG context. By a process of multiresolution analysis (MRA), wavelet transform (WT) can orthogonally decompose a time series into scaling coefficients (SCs) and wavelet coefficients (WCs), in which the trivial data points can be deleted such that the overall size of the data can be compressed. And the nature of WT satisfies a near-perfect reconstruction of the time series via an inverse MRA. Moreover, with the rapid development of computing techniques, the algorithm of MRA can be implemented for online applications [13], [14]. Thus, it is feasible to embed a wavelet-based data compression algorithm into the monitoring devices, in which the data can be compressed before it is sent out in order to mitigate the data congestion. In addition, WT is capable of depressing the sinusoidal and “white” noise in the data. This property could benefit the preprocessing of the data in the measuring devices. To justify the proposed approach, this paper utilizes a set of simulated PMU data to discuss the advantages of WT on data compression. The simulated PMU data are obtained from simulations in the Power System Simulator for Engineering (PSS/E). In PSS/E, the dynamic frequency and voltage signals are simulated during system disturbances in the IEEE New England 39-bus system. The disturbances include generation loss and load change, which are major concerns for WAMSs in the interconnected systems. Nevertheless, without loss of generality, the proposed approach is capable of compressing any type of grid signal into the format of a time series. As a byproduct of data compression, the denoising property of WT is also discussed to show the immunity of the proposed approach to the various data noise. The paper is organized as follows: in Section II, WT-based MRA and its properties are briefly introduced; in Section III, the selections of wavelet function and decomposition scale for disturbance signals are conducted for data compression and denoising; in Section IV, a numerical simulation is carried out to justify the effectiveness of WT-based MRA on data compression and denoising; the conclusion is presented in Section V.
II. WT-BASED MULTIRESOLUTION ANALYSIS WT-based MRA is illustrated in Fig. 1, where (a) shows the procedure for decomposing a signal, and (b) shows the procedure for reconstructing a signal. and are the low-pass filter and high-pass filter, respectively. The filters are constructed by a scaling function and a wavelet function , satisfying . In Fig. 2, the waveforms and frequency responses of the Order 2 Daubechies (db2) scaling function and wavelet function are shown as an example. The MRA generates SCs or “Approximation” and WCs or “Detail” . SCs represent the
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Fig. 1. Procedure of WT-based MRA. (a) Decomposition. (b) Reconstruction.
Fig. 2. Order 2 Daubechies scaling and wavelet functions and their spectrum. (a) Scaling function of db2. (b) Wavelet function of db2. (c) Low-pass filter of db2 (for decomposition). (d) High-pass filter of db2 (for decomposition).
low-frequency components, and WCs represent the high-frequency components. By transforming a signal, the features of the signal can be extracted from SCs and WCs. To disturbance signals in power systems, WCs are more important because the transient features of the signals are mostly represented by the high-frequency components [15]. Property 1—Nonredundant Transform: WT-based MRA is theoretically a type of nonredundant transform. As indicated by the “ ” shown in Fig. 1(a), a two times downsampling rate is adopted to each scale to ensure the equivalence in the number of sampling points before and after the decomposition. Assuming and contain sampling points at lowest scale , the sampling points at any scale can be written as (1) Therefore, the number of sampling points before and after the decomposition (with an absolute symmetric wavelet function) satisfies (2)
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If the wavelet function is not absolutely symmetric, as in, for example, Daubechies wavelet family (i.e., its near-symmetric property), the relationship in (2) can be expressed as (3) Property 2—Threshold Denoising: A threshold can be applied to depress low-value amplitudes in details, most of which are caused by high-frequency noise. The reconstruction of approximation and details after thresholding can return a cleaner signal with little distortion. Several wavelet-based thresholding methods [16], [17] have been developed. The selection of thresholding methods deserves particular consideration in the future for SG applications. In this paper, universal thresholding is chosen to process disturbance signals because of its computational simplicity and efficiency. Universal thresholding is calculated by (4) where stands for noise variance at scale . The threshold can be applied onto WCs by (5) as follows: (5) After thresholding, the amplitude of WCs beneath the threshold is set to be zero. In this way, the noise is largely depressed because the small amplitudes in WCs usually reflect the major energy of noise [16]. Property 3—Data Compression: After applying (5) to WCs, the low-value amplitudes in WCs are depressed to 0. Because only nonzero points are our interest of analysis, the signal can be compressed by eliminating all zero points in WCs and then can be sent to the receiving end, where the signal can be reconstructed as shown in Fig. 1(b). The question for WT-based MRA is whether or not the meaningful information of power system signals can be retained and maintained after the denoising and compression steps. In the reminder of the paper, a numerical experiment is carried out to check the performance of WT-based MRA to disturbance signals. III. SELECTION OF WAVELET AND DECOMPOSITION SCALE Before WT-based MRT is applied for data compression, the best wavelet function and the optimal decomposition scale need to be carefully selected. Wavelet energy is the index to reflect the energy concentration of WCs on certain scales. The larger the wavelet energy, the more the information is preserved after the decomposition. In this paper, wavelet energy is chosen as the criterion to determine the best wavelet function and the optimal decomposition scale for disturbance signals [15]. The definition of total wavelet energy is given by (6)
Fig. 3. Diagram of IEEE New England 39-bus system.
and wavelet energy in each scale is given by (7) where subscript stands for the scale, and the maximum number of scale is ; subscript stands for the point in WCs; and is the length of WCs at scale . The candidates of wavelet functions consist of Daubechies wavelet family and Symlets wavelet family . stands for the order of the wavelet function. In this paper, db2–db10 and sym2–sym10 are chosen as wavelet candidates. These wavelets have been chosen because they have shown excellent performance in analyzing dynamic signals with discontinuity and abrupt change [18], [19]. The wavelet corresponding to the highest total wavelet energy in (6) is chosen as the best wavelet function, and the scale corresponding to the highest wavelet energy in (7) is chosen as the optimal decomposition scale. The testing disturbance signals are also generated in the IEEE New England 39-bus system (Fig. 3). Three types of disturbances are adopted in this paper: generation loss, load drop, and load surge. Generation loss is generated at Buses 33 and 34, respectively; while load drop and load surge are generated at Buses 16 and 20, respectively. During the simulation, frequency and voltage are recorded at Bus 19. The results are listed in Tables I and II. In Table I, the elements highlighted in yellow indicate the highest wavelet energy of a specific signal corresponding to a certain wavelet function. It can be seen that most of the highest wavelet energy levels of the different signals point to db2 and sym2. Because both wavelets return the same total wavelet energy to all signals, either one can be chosen as the best wavelet for disturbance signals. In this paper, db2 is determined to be the wavelet function for MRA. In Table II, the signals are decomposed by db2 into 6 scales, and it is evident that the wavelet energy at scale 5 is the highest for most of the disturbances. Thus, scale 5 is determined as the optimal decomposition scale for MRA in this paper.
NING et al.: A WAVELET-BASED DATA COMPRESSION TECHNIQUE FOR SMART GRID
RESULTS
DB
OF
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TABLE I SELECTION OF WAVELET FUNCTION
Daubechies wavelet function; SYM
Symlets wavelet function
TABLE II RESULTS OF SCALE SELECTION
GL
frequency; v voltage. generation loss; LD load drop; LS
load surge
IV. NUMERICAL EXPERIMENT In this section, the disturbance signals, simulated in PSS/E, are used as system dynamic signals to test the proposed method. The IEEE New England 39-bus system is adopted as the test system, in which the simulation time step is 0.004167 s (1/4 cycle), and the simulation time is 2 s (equivalent to 482 sample points). The simulation focuses on the first 2 s after disturbances occur, during which the automated system control devices (governor or power system stabilizer) have not responded to the disturbances. The topology of the system is shown in Fig. 3, where “G” stands for generators, “ ” stands for loads, and numbers 1–39 are bus numberings. Without loss of generality, the loss of Generation 4 (denoted as GL4) at Bus 33 is used to test the property of WT-based MRA. The measuring location is supposed to be deployed at Bus 19; and the measurements include frequency and voltage.
Fig. 4. Frequency and voltage responses at Bus 19 to GL4.
In Fig. 4, the frequency and voltage at Bus 19 during GL4 at 0.5 s of simulation time are illustrated. At the moment a disturbance occurs, both frequency and voltage experience an abrupt drop in their values; and then, both variables start low-frequency oscillation because of the transient response of the system. The WT-based MRA to the frequency and voltage are shown in Figs. 5 and 6, respectively. The Order 2 Daubechies wavelet is chosen as the wavelet function, and scale 5 is selected as the maximum decomposition scale. From Figs. 5(a) and 6(a), it can be seen that both frequency and voltage have abrupt change in the waveforms at 0.5 s due to the disturbance. Figs. 5(b) and 6(b) are the SCs of frequency and voltage signals which approximate envelops of the signals and, thus, represent the low-frequency features of the signals. Note that the absolute amplitude of SCs only reflects the distribution of signal’s energy at scale 5 after the transform and have no direct relationship with its amplitude in time domain. In practice, the signal needs to be reconstructed
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TABLE III COMPARISON OF DATA LENGTHS BEFORE AND AFTER WT
Fig. 5. WT-based MRA to frequency. (a) Frequency signal. (b) Approximation at scale 5. (c) Detail at scale 5. (d) Detail at scale 4. (e) Detail at scale 3. (f) Detail at scale 2. (g) Detail at scale 1.
Fig. 7. The testing frequency signals. (a) The original signal. (b) The signal mixed with 60-Hz periodic noise with the amplitude of 0.1. (c) The signal mixed with the white noise with the amplitude of 0.05.
Fig. 6. WT-based MRA to voltage. (a) Voltage signal. (b) Approximation at scale 5. (c) Detail at scale 5. (d) Detail at scale 4. (e) Detail at scale 3. (f) Detail at scale 2. (g) Detail at scale 1.
to utilize its actual amplitude in time domain. In Figs. 5(c)–(g) and 6(c)–(g), the WCs of frequency and voltage signals are displayed. The WCs reflect the high-frequency features of the signals at each scale because the nonzero points of WCs are only localized around 0.5 s. At different scales, the WCs exhibit different values because of the filter property that varies across scales. In the previous section, scale 5 has been proven to be the optimal decomposition scale for disturbance signals. Therefore, in Figs. 5(c) and 6(c), one can see that a distinguishable amplitude in accurately indicates the occurrence of the disturbance at 0.5 s. At other scales (see in Figs. 5(d)–(g) and 6(d)–(g)), although the large amplitudes of WCs appear around the disturbance moment, the accuracy is incomparable to scale 5. It seems that, in Figs. 5(g) and 6(g), can also indicate the occurrence of the disturbance. However, a finer observation of reveals that it is less precise than and the amplitude of at 0.5 s is less noticeable than as well. This feature of can be used for signal recognition and other quantitative analysis. In Table III, the lengths (standing for one-dimensional data size) of frequency signals and the lengths of SCs and WCs are listed, respectively. Table III shows that there are 10 more sampling points after the decomposition. Although Daubechiesbased WT is not a perfect nonredundant transform because of its near-symmetric property as explained by (3), the redundant
Fig. 8. Denoising to the frequency signal mixed with the periodical noise. (a) The original signal. (b) The signal mixed with the periodical noise. (c) WCs of the original signal. (d) WCs of the polluted signal.
points are trivial when compared with the total length of the signal (10 points versus 482 points). Denoising is often introduced into signal processing to counteract the pollution of noise to the signal. In power systems, the noise is usually sorted into two types: periodical noise and white noise. In this paper, the 60 Hz periodical noise and the white noise are mixed with the frequency signal to justify the denoising of WT-based MRA. In Fig. 7, the frequency signal shown in Fig. 4 and its polluted mixtures with 60-Hz periodic noise with the amplitude of 0.1 and the white noise with the amplitude of 0.05 are plotted. The polluted signals are decomposed by a db2 wavelet into 5 scales. Universal thresholding are applied to the WCs by (5). In Figs. 8 and 9, the WCs at scale 5 are exhibited for both the original signal and the polluted signal after the denoising. Comparing the amplitude of (c) and (d) in Figs. 8 and 9, it can be
NING et al.: A WAVELET-BASED DATA COMPRESSION TECHNIQUE FOR SMART GRID
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Fig. 9. Denoising to the frequency signal mixed with the white noise. (a) The original signal. (b) The signal mixed with the white noise. (c) WCs of the original signal. (d) WCs of the polluted signal.
Fig. 11. Denoising results for the signal polluted by the white noise. (a) The original signal. (b) The polluted signal. (c) The reconstructed signal after denoising.
TABLE IV LENGTH OF THE COMPRESSED SIGNAL
TABLE V SNR RATIO AND RMS ERROR BEFORE AND AFTER DENOISING
the periodical noise;
the white noise.
after the denoising and compression is listed in Table V, as well as the root-mean-square (rms) error, criterion for signal distortion, between the original signal and the reconstructed signal. Table V shows that the SNR is improved up to two times compared to the ratio before denoising. In addition, the rms error is improved by about 10 times. WT-based MRA provides excellent performance in terms of depressing noise, as well as reducing signal distortion. V. CONCLUSION
Fig. 10. Denoising results for the signal polluted by the periodical noise. (a) The original signal. (b) The polluted signal. (c) The reconstructed signal after denoising.
seen that the thresholding does not affect the property of WCs. The value of WC at 0.5 s remains the same and accurately indicates the occurrence moment of the disturbance. This result is important because WCs contain most of the high-frequency information, which helps us recognize the dynamic feature of the signal. After denoising, the nonzero points in WCs from scale 1 through scale 5 can be extracted so as to compress the length of the original WCs. The lengths of the compressed WCs are listed in Table IV, which shows that the lengths of the compressed WCs are reduced by around 1/5.4 times in comparison with the original WCs. Figs. 10 and 11 show the reconstructed signals after the denoising and compression. One can see that the signals are recovered although there is slight distortion. The signal-to-noise (SNR) ratio, criterion for denoising, before and
This paper proposes a WT-based MRA to perform data compression in the smart grid context. The proposed approach is capable of effectively compressing the size of disturbance signals as well as depressing sinusoidal and white noise in the signals. The Order 2 Daubechies wavelet and scale 5, respectively, as the best wavelet function and the optimal decomposition scale for disturbance signals has been selected according to the criterion of the maximum wavelet energy of wavelet coefficients. A numerical simulation is conducted to exhibit the properties of WT-based MRA for data compression and denoising. The analysis for the results shows the effectiveness of WT-based MRA on data compression and denoising for disturbance signals. Without loss of generality, the proposed method can be implemented in smart grid to mitigate data congestion and improve data transmission and quality. REFERENCES [1] X. P. Zhang, “A framework for operation and control of smart grids with distributed generation,” in IEEE Power Energy Soc. Gen. Meet. —Conv. Del. Elect. Energy 21st Century, 2008, pp. 1–5. [2] C. W. Potter, A. Archambault, and K. Westrick, “Building a smarter smart grid through better renewable energy information,” in IEEE/PES Power Syst. Conf. Expo., 2009, pp. 1–5. [3] S. Wang and G. Rodriguez, “Smart RAS (Remedial Action Scheme),” in Proc. Innovative Smart Grid Technol., 2010, pp. 1–6.
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[4] K. Heussen, A. Saleem, and M. Lind, “Control architecture of power systems modeling of purpose and function,” in Proc. IEEE Power Energy Soc. Gen. Meet., 2009, pp. 1–8. [5] K. Moslehi and R. Kumar, “A reliability perspective of the smart grid,” IEEE Trans. Smart Grid, vol. 1, no. 1, pp. 57–64, Jun. 2010. [6] A. Bose, “Smart transmission grid applications and their supporting infrastructure,” IEEE Trans. Smart Grid, vol. 1, no. 1, pp. 11–19, Jun. 2010. [7] Z. Jiang, F. Li, and W. Qiao et al., “A vision of smart transmission grids,” in IEEE Power Energy Soc. Gen. Meet., 2009, pp. 1–10. [8] [Online]. Available: http://openpdc.codeplex.com/ [9] B. Fardanesh, S. Zelingher, and A. P. Sakis Meliopoulos et al., “Multifunctional synchronized measurement network [power systems],” IEEE Comput. Appl. Power, vol. 11, no. 1, pp. 26–30, Jan. 1998. [10] S. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 11, no. 7, pp. 674–693, Jul. 1989. [11] S. Santoso, E. J. Powers, and W. M. Grady, “Power quality disturbance data compression using wavelet transform methods,” IEEE Trans. Power Del., vol. 12, no. 3, pp. 1250–1257, 1997. [12] T. B. Littler and D. J. Morrow, “Wavelets for the analysis and compression of power system disturbances,” IEEE Trans. Power Del., vol. 14, no. 2, pp. 358–364, 1999. [13] M. Forghani and S. Afsharnia, “Online wavelet transform-based control strategy for UPQC control system,” IEEE Trans. Power Del., vol. 22, no. 1, pp. 481–491, 2007. [14] O. A. S. Youssef, “Combined fuzzy-logic wavelet-based fault classification technique for power system relaying,” IEEE Trans. Power Del., vol. 19, no. 2, pp. 582–589, 2004. [15] J. Ning, “Wide-area monitoring and recognition for power system disturbances using data mining and knowledge discovery theory,” Ph.D. dissertation, Tennessee Technol. Univ., Cookeville, TN, Aug. 2010. [16] X. Zhang and M. D. Desai, “Adaptive denoising based on SURE risk,” IEEE Signal Process. Lett., vol. 5, no. 10, pp. 265–267, 1998. [17] H. Krim, D. Tucker, and S. Mallat et al., “On denoising and best signal representation,” IEEE Trans. Inf. Theory, vol. 45, no. 7, pp. 2225–2238, 1999. [18] L. Zhang and P. Bao, “Edge detection by scale multiplication in wavelet domain,” Pattern Recognit. Lett., vol. 23, no. 14, pp. 1771–1784, Dec. 2002. [19] J.-W. Hsieh, M.-T. Ko, and H.-Y. M. Liao et al., “A new wavelet-based edge detector via constrained optimization,” Image Vis. Comput., vol. 15, no. 7, pp. 511–527, Jul. 1997.
Jiaxin Ning (S’08–M’10) received the B.S. and M.S. degrees in electrical engineering from Chongqing University, China, in 2004 and 2007, respectively, and the Ph.D. degree in electrical engineering from Tennessee Technological University, Cookeville, in 2010. He is currently a Senior Consultant on electric power research, engineering, and consulting at EnerNex Corporation, Knoxville, TN. His scope of work covers modeling and simulation of renewable energy sources, power system operation and control, and power quality analysis.
Jianhui Wang (M’07) received the B.S. degree in management science and engineering and M.S. degree in technical economics and management from North China Electric Power University, China, in 2001 and 2004, respectively, and the Ph.D. degree in electrical engineering from Illinois Institute of Technology, Chicago, in 2007. He is currently an Assistant Computational Engineer with the Decision and Information Sciences division at Argonne National Laboratory, Argonne, IL. Dr. Wang is the Chair of the IEEE Power & Energy Society (PES) power system operation methods subcommittee and Cochair of an IEEE task force on integration of wind and solar power into power system operations. He is an editor of the IEEE TRANSACTIONS ON SMART GRID.
Wenzhong Gao (S’00–M’02–SM’03) received the M.S. and Ph.D. degrees in electrical and computer engineering specializing in electric power engineering from Georgia Institute of Technology, Atlanta, in 1999 and 2002, respectively. His current teaching and research interests include renewable energy and distributed generation, smart grid, power-system protection, power-electronics applications in power systems, power-system modeling and simulation, and hybrid electric propulsion systems.
Cong Liu (S’08–M’10) received the B.S. and M.S. degrees in electrical engineering from Xi’an Jiaotong University, China, in 2003 and 2006, respectively, and the Ph.D. degree from Illinois Institute of Technology, Chicago, in 2010. Currently, he is a Postdoctoral Appointee in the Decision and Information Sciences Division, Argonne National Laboratory, Argonne, IL. His research interests include power systems and natural gas systems analysis, optimization, and operation.
