Tri-Stage Cascaded Data Compression Framework for Smart Distribution Systems

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1 Tr-Stage Cascaded Data Compresson Framewor for Smart Dstrbuton Systems Syed Muhammad Atf * and Anees Ahmed 2 Graduate School of Scence and Engneerng, PAF Karach Insttute of Economcs and Technology, Karach, 7590, Pastan (syed.muhammad.atf@gmal.com) 2 Graduate School of Scence and Engneerng, PAF Karach Insttute of Economcs and Technology, Karach, 7590, Pastan (aneesemal@yahoo.com) * Correspondng author Abstract: Modern smart dstrbuton system requres storage, transmsson and processng of bg data generated by sensors nstalled n electrc meters. On one hand, ths data s essentally requred for ntellgent decson mang by smart grd but on the other hand storage, transmsson and processng of that huge amount of data s also a challenge. Ths paper proposes a data compresson technque called Tr Compress that blends three dfferent methods n order to acheve hgh compresson rate for effcent storage and transmsson. It s a lossy data compresson technque. Our smulaton results are excellent,.e. data compresson rato s a low as 00:, and shows that ths technque s far better than contemporary technques. Keywords: Sngular Value Decomposton, Normalzaton and Sparse Matrx Representaton, smart grd, power system montorng, lossy data compresson, bg data, compresson rato. I. INTRODUCTION We are currently lvng n the age of IoT. Le any other aspect of our lfe, power dstrbuton systems are also tang advantage of t. Smart meters are rapdly replacng the conventonal meters that allows power dstrbutons companes to get nsght of user power usage behavor and mae ther decson accordngly. Power grds are not only vtal n dstrbuton system but also very senstve to fluctuatons n demands. Sudden ncrease n demand lead to trppng of grd statons. Unfortunately, ths local falure has cascadng effects under certan crcumstances leadng to a catastrophe such as New Yor power outage 2003 [-3]. Those catastrophc events urges us to desgn and deploy such power dstrbuton system that are smart and ntellgent enough to qucly tae ther decsons both reactvely and proactvely wthout any human nterventon. As a result, a new era of smart power dstrbuton systems begns. They are equpped wth smart meterng system that contnuously provde power usage of ther users. The system then utlzes ths data for operatons le montorng, analyss and control. However, smart meter and other smlar equpment contnuously generate huge amount of data at constant rate that brng the challenges n terms of ther transmsson and storage. Ths paper focus the sad problem and proposed a new soluton named tr compress. As the name suggest ths soluton s the blend of three dfferent methods precsely, Sngular Value Decomposton (SVD), normalzaton and value-ndex sparse matrx representaton. In nature, the proposed technque s loosy data compresson technque. Ths paper s organzed as follows. Secton I has presented the ntroducton. Secton II wll gve related wor. Secton III, the core of ths paper, wll present the proposed dea and technque for data compresson. Secton IV wll expermentally evaluate the newly proposed dea. Secton V wll provde the obtaned results of smulaton. Fnally, secton VI wll conclude the paper. II. RELATED WORK Wth the advancements n smart dstrbutons systems and ntegraton of IoT, the amount of data avalable of storage, transmsson and processng wll become ggantc. Ths challenge draws attenton of many researchers towards the development of data compresson technque that specally cater needs of smart dstrbuton systems [3-9]. Brndha and D. Sundararajan uses dscrete wavelet technques for compresson of data. They uses a b-orthogonal 5/3 splne flter for compresson and able to acheve compresson rato of up to 8:. Phasor measurement unt, a well-nown mage compresson technque, s employed by Klump et al. [9] for compresson of smart grd data that result n obtanng the best CR of 4.35:. However, there s stll a need of hgher CR due to large amount of data whch s specfcally address n ths paper. The nature of data obtan from smart grd system allow us to store t n the form matrx as the data comng from dfferent sensor belong to measurements taen for the same devce at several dfferent tme nstances. Ths

2 form dataset representaton s the most approprate for SVD, a wdely used technque n the feld of mage compresson and many other [-4]. Ths paper s utlze SVD for compresson of data of smart grd systems. The reason s that t provde us a good tradeoff between nformaton loss and degree of acheved compresson. It s possble n case of smart grd data as t generally used by applcatons for montorng and plannng purposes that do not requre hgh precson data. by t respectvely where S be the dagonal matrx of dmenson m by t that dagonal entres are arranged n descendng order. Fg. 3 s gvng a pctoral representaton of ths factorzaton. However, the effectve dmenson of U, S and V matrces are m by r, r by r and r by t where r s the ran of the matrx. It s noteworthy that here we use matrx V wth dmenson r by t for convenent. It s equvalent to V T of dmenson t by r that s conventonally used n lterature. III. PROPOSED SOLUTION In ths secton, we explan our tr-stage cascaded data compresson framewor va sngular value decomposton (SVD), normalzaton and sparse matrx representaton (see Fg..). The subsecton A wll explans how SVD wll be utlzed n our data compresson framewor model to acheve data compresson. Subsecton B wll elaborates the second stage of our model.e. normalzaton for effcent representaton of data obtan after apply SVD n the frst stage whereas subsecton C provdes detal regardng the thrd stage of our model that explots sparse matrx representaton for compressed data obtaned from second stage so that data can be stored or transmtted n ts most compressed form. Data from sensors Sngular Value Decomposton Fg. 2 SVD of matrx. Fg. 3 Representaton of data as matrx. In essence, SVD represents a matrx as the sum of ran one matrces ordered n descendng order of ther respectve frobenus norm. r u v Normalzaton Sparse Matrx Representaton Fnal Compress Data Fg. Data Compresson Framewor. A. Sngular value decomposton (SVD) Let be the data collected from dfferent sensors at regular tme ntervals. Ths data can be consders as a matrx of dmenson m by t where m s number of meterng devces equpped wth sensors and t s the tme stamps as depcted n Fg. 2. Sngular value decomposton (SVD) wll degenerate ths matrx nto three matrces U, S and V where U and V be the orthogonal untary matrces of dmenson m by m and t Fg. 4 Typcal decrease n ordered sngular values. Snce U and V are untary matrces.e. ther column has unt L2 norm, so ther correspondng sngular value n the dagonal matrx S wll represent the frobenus norm of respectve sum term. Fg. 4 s llustratng the typcal decay (decrease) n the sngular values n SVD. 2

3 Hence, a matrx can be well approxmated by the frst few terms. Let be approxmated as by the top sngular values then () u v or n matrx notaton ^ U V Where the dmenson of U, Σ and V are m by, by and by t respectvely and. r. The storage or transmsson capacty requred for wthout any manpulaton s: space( ) mt (3) (2) However, the storage or transmsson capacty requred for, the approxmaton of, s: space( But, ) space( U space( space U ) m ) ) space( V ) (4) ( (5) space( ) (6) space V ) t Hence, space( ( (7) ) m t ( m t) (8) Therefore, we have compressed data s comparng to.e. space() < space() provded that m t/(m++t)t < or equvalently << r m. B. Normalzaton Data comng from sensors n electrcal devces as n our case s manly wattage, voltage and current usage.e. t s numercal n nature. Such a data s typcally stored or transmtted by computng devces n floatng pont format or mantssa exponent format, a wdely used standard for ths format s IEEE 754. However, blndly usng ths format s not good n our case because of reason that people n vcnty usually have smlar rage of electrcal devce as well as smlar electrcal usage behavor. It leads us to the concluson that the varaton n obtaned data wll be at most order of two or so. It s an deal condton where technque le normalzaton can be readly use for data compresson. Normalzaton s way of representng decmal pont numercal data. It transforms the entre data, by smply multply them sutable powers of ther system radx, so 3 ther exponents become dentcal. Ths transformatons generally leads to precson loss. However, ths precson loss s neglgble when varaton n data s vary low. Normalzaton allows us to transmt or store the exponent part of data only once as t s now common. Ths leads to sgnfcant reducton n the sze of that that need to be store or transmtted. For example there s 25% reducton n the sze of data after normalzaton f the data s represented n sngle precson floatng pont IEEE 754 format as mantssa to exponent rato n ths format s 3:. C. Sparse Matrx Representaton Spare matrx s ones that vast number of entres are zeros. It s not a good dea to store (transmt) all the entres of such a matrx. Instead, one can store (transmt) a sparse matrx effcently f t just store (transmt) only non-zero entres along wth ther ndces (postons) n the matrx. It leads to reducton n sze of data provded the amount of space requred for zero entres s more than that requred for ndex value representaton of non-zero entres of the gven sparse matrx. The matrx of our data s well sparse n nature because most of the electronc (electrcal) devces such as water pumpng machne, ron, mcrowave oven, televson etc. typcally used only very small fracton of tme. So, U and V matrces obtaned after apply SVD of ths data wll also be sparse matrces.e. most of the entres n most of the column of U (resp. most of the entres n most of the rows of V ) wll be zero. Thus, ndex value representaton of U and V matrces wll lely lead to sgnfcant data compresson. IV. SIMULATION AND EPERIMENTAL RESULTS In ths secton, we wll present results obtaned from smulaton conducted to chec the valdty of our proposed tr-stage cascaded data compresson framewor specfcally talored for smart dstrbuton (grd) system. We use TU Darnstadt tracebase data set. It s a freely avalable dataset that can be obtaned from [5-6]. In our smulaton study, we use data of fve dfferent devces namely DVD player, Subwoofer, TV and vacuum cleaner. There are total 80 devces precsely 28 DVD player, 2 Subwoofer, 6 TV and 24 vacuum cleaner. The wattage usage of these 80 devces

4 s recorded for the entre day after about every 8s. MAE Compressed Fle Sze after(n B) Compresson Rato after (at all stages) SVD Normalzaton Sparse Matrx Representaton SVD Normalzaton Sparse Matrx Representaton :.89 00:.77 00: :4.2 00: : : : : : : : : : : : : : : : : : : :30.43 Table Summarzed results of tr-stage cascaded data compresson framewor. Thus, our test data matrx has dmenson of 80 by Ths data matrx requres 792KB when store as csv fle format. We desgn a MatLab code to evaluate our methodology. As, our compresson framewor s loosy n nature so a matrc s requred to quanttatvely measure the loss of nformaton durng compresson. We use MAE as a matrc to measure the loss of nformaton durng compresson. It s defned as: MAE ( ) mt m t (9) j (, j) (, j) Table summares the results of smulaton study. The sze n KB requred to store compressed verson of data matrx n csv fle format s recorded after each of the three stage n our model. You may observe that compresson rato of decreases as number of ran one matrces n SVD summaton use for approxmaton ncreases. It s expected as ncrease n a wll ncrease the dmenson of U, S and V that n turn ncrease the sze of fle. However, hgher value of means better approxmaton of gven data or less loss of nformaton. Therefore, there s a steady declne n MAE as the value of ncreases. It means that a tradeoff s requred between compresson rato requred to acheve and loss of nformaton whle usng our framewor. One have to compromse on the precson of data when requre hgher compresson. Normalzaton stage always able to further compress the data obtan from SVD stage. However, ts compresson ablty s less than both stage one and two. Spare matrx representaton always dramatcally compress the data due to hgh level of sparsty present n the data. You may conclude from table that one that ths stage always compress the data obtan from stage two by 00% or more. V. CONCLUSION Ths paper presents a lossy data compresson framewor that s specally talored by eepng need hgh data compresson needs of smart power dstrbuton system. The framewor compresses the data n three dfferent stages usng dfferent technques. In the frst stage, t explot redundancy n the data usng SVD for compresson. The second stage apples normalzaton on resultng data whereas the thrd stage transforms the compressed output of second stage nto ts equvalent ndex value sparse matrx representaton. Our smulaton results shows that ths tr stage cascaded data compresson framewor s very effcent and may even produce promsng compresson rato of 00:. REFERENCES [] Marx, Melssa A., Carla V. Rodrguez, Jane Greeno, Debjan Das, Rchard Heffernan, Adam M. Karpat, Farzad Mostashar, Sharon Balter, Marcelle Layton, and Don Wess. "Darrheal llness detected through syndromc survellance after a massve power outage: New Yor Cty, August 2003." Amercan Journal of Publc Health, vol. 96, no. 3, pp , [2] Anderson, G. Brooe, and Mchelle L. Bell. "Lghts out: mpact of the August 2003 power outage on mortalty n New Yor, NY." Epdemology (Cambrdge, Mass.) vol. 23, no. 2, pp. 89, 202. [3] Ln, Shao, Barbara A. Fletcher, Mng Luo, Robert Chnery, and Syn-An Hwang. "Health mpact n New Yor Cty durng the Northeastern blacout of 2003." Publc Health Reports vol. 26, no. 3, pp , 20. [4] M. Rngwels, C. Renner, A. Renhardt, A. Wegel, and V. Turau, The Htchher s gude to choosng the compresson algorthm for your smart meter data, Proceedngs of IEEE Internatonal Energy Conference and Exhbton, 4

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