Synchronized Processing of Distributed Signals for Smart Grid Applications

Transcription

1 Sychroized Processig of Distributed Sigals for Smart Grid Applicatios Guoyu Tu, Juwei Cao, Seior Member, IEEE, Yuxi Wa, Shuqig Zhag, Member, IEEE, Chao Lu, Seior Member, IEEE, ad Huayig Zhag Abstract-- Due to the ature of geometrically distributio, may smart grid applicatios require data from distributed locatios. The performace of the power system is the highly correlated with the commuicatio etwork that trasmits sesig ad cotrollig sigals. This paper explores the impact of ot oly etwork delays but also sigal sychroizatio processig o power system stabilizatio. Sychroizatio schemes are proposed ad compared to the covetioal scheme by simulatio uder differet etwork coditios. Critical values of system performace are idetified regardig etwork delay. Experimetal results demostrate potetial drawbacks of the covetioal scheme that ca be cosiderably improved by the proposed schemes. It is importat to improve wide area moitorig ad cotrol performace by ot oly reducig etwork delays but also sychroizig sigals with a appropriate tradeoff betwee data accuracy ad timely resposes. Idex Terms-- smart grid; power system stablizatio; sigal sychroizatio; etwork delay I. INTRODUCTION Smart grid eables better eergy efficiecy ad stabilizatio of power systems by utilizig iformatio techology [22]. Wide area moitorig ad cotrol (WAMC) is oe of such smart grid applicatios. I a WAMC system, distributed PMU sigals are collected from differet geographic locatios ad set to a cetralized cotroller via the commuicatio etwork. Sice the power system is dyamic with all kids of icetives ad potetial faults that may deteriorate the system stability, the above procedure is a cotiual ad close-loop feedback cotrol procedure. Issues i a WAMC system are two-fold: cotroller desig ad commuicatio protocol. Researches o cotroller desig have ivestigated critical values of delays for cotroller stability where fixed delays i a sigle iput chael or This work was supported i part by Natioal Natural Sciece Foudatio of Chia (grats No ad No ), Miistry of Sciece ad Techology of Chia uder Natioal 973 Basic Research Program (grat No. 213CB22826), ad Chia Souther Power Grid R&D project (K-SZ212-26). Guoyu Tu ad Juwei Cao is with Research Istitute of Iformatio Techology, Tsighua Uiversity, Beijig 184, P. R. Chia( jcao@tsighua.edu.c). Guoyu Tu ad Juwei Cao is also with Tsighua Natioal Laboratory for Iformatio Sciece ad Techology, Beijig 184, P. R. Chia Yuxi Wa is with Departmet of Automatio, Tsighua Uiversity, Beijig 184, P. R. Chia Shuqig Zhag ad Chao Lu is with Departmet of Electrical Egieerig, Tsighua Uiversity, Beijig 184, P. R. Chia Huayig Zhag is with Shezhe Power Supply Co. Ltd. Chia Souther Power Grid Shezhe 5182, P. R. Chia commo delays i multiple chaels are cosidered [7]-[9]. WAMCs face ew challeges with stochastic ad heterogeeous delays i multiple iput chaels, ad research beyod existig results is required. For the cosequet problems, researches o commuicatio protocol have to take ito cosideratio diversified etwork eviromet. Due to the log distace betwee the cotroller ad the distributed phasor measuremet uits (PMUs) i all regios, the performace of the cotroller is heavily iflueced by the commuicatio etwork. Oe of key impacts is the delay of receivig moitorig sigals from PMUs. Relevat researches o sigal delay geerally fall ito two categories. The first category is o the desig of cotrollers o a predictio basis, such as H cotrollig strategy [7] or the gai tuig method [8] to trade-off delay tolerace ad cotroller performace. The secod category is o the modelig of system delays. The determiistic ad stochastic delays of a sigle chael are calculated based o a queuig etwork [6]. Besides the two categories, a geeric result o system stability with delay is provided i [1]. Theoretic results are oly available for liear ad small scaled etworked cotrol systems. Related reviews are available i [17]-[21]. The above researches have provided results o the sigal delay i a sigle chael. Log delay as compared to the samplig period ad multiple-iput cases remai challeges. I this paper, the WAMC is characterized by the oliear large scales power system ad multiple chaels with asychroously delayed iputs, where theoretical results are itractable. The PMUs are distributed i differet locatios ad PMU sigals are set from differet commuicatio chaels. Due to various traffics i these chaels, a commo delay is isufficiet to characterize the asychroous sigals from various chaels. Sychroizatio of asychroous sigals from multiple chaels is the focus of this work. Three schemes that provide differet tradig off betwee data accuracy ad timely cotrol respose are proposed ad compared. This tradeoff is the major problem arises i the sychroizatio process, which ca be explaied as follow. Sice the closed loop sigal processig is cotiuous, its real-time performace is importat for timely feedback cotrollig commads. However, durig a certai samplig iterval, there is o guaratee that the sigals from all sources are available. Waitig for the missig sigals is equivalet to icrease the time delay, whereas it loses the accuracy to estimate these missig sigals. The real-time performace ad the data accuracy is thus to be tradeoff by ay sychroized processig schemes. I this paper, a WAMC across multiple provices ad its /16/$ IEEE

2 power flow oscillatio betwee two subets is studied. Historical data are used i simulatio to recreate icetives ad faults that lead to oscillatios. A well-desiged cetral cotroller is applied. To evaluate differet sychroizatio processig schemes proposed herei, the stabilizatio performace of the whole system is ivestigated uder a variety of etwork coditios. The rest of paper is orgaized as follows. Sectio II provides a detailed descriptio to the WAMC system. I Sectio III, etwork delay models ad differet sychroizatio processig approaches are elaborated with observatios i practice. Numerical simulatio results ad their aalysis are illustrated i Sectio IV. It cocludes i Sectio V. II. THE WAMC SYSTEM A. WAMC of Chia South Power Grid The WAMC system of Chia Souther Power Grid across two provices is take as a case study i this work [23]. The frequecy differece betwee subets will lead to power oscillatio betwee these subets ad make the power system ustable. The frequecies of differet regios i the power system are moitored ad to be cotrolled to be cosistet i this WAMC system. As illustrated i 错误! 未找到引用源 below, PMU measuremets of four buses are selected to represet the frequecies of two regios where they located, two PMUs for each regio. The average frequecy of the two locatios represets the frequecy i their regios. Those sigals are set to a cetralized cotroller through the commuicatio etwork with 1ms samplig itervals. O detectig differece, the cetralized cotroller starts to stabilize the system by sedig back cotrollig sigals to selected local motors i each regio separately so as to reduce the differece. Differece of the average frequecies of the two regios is to be cotrolled to withi.2% stadard frequecy, that is,.1hz. B. Dampig Cotroller The average frequecy of a regio is calculated from the selected PMU measuremets distributed i this regio. By comparig the average frequecies i regio 1 ad regio 2, the cotroller derives the correspodig sigals to cotrol the local motors as below shows. Fig. 2. The basic structure of a WAMCs dampig cotroller. The Chia Souther Power Grid i study cosists of 1392 odes, 2371 buses, ad two high voltage DC trasmissio lies. For such a realistic system, the optimal cotroller is hardly attaiable. The cotroller used i the testig is a combiatio of suboptimal oes uder typical seasoal patters. I a ideal case where o etwork delay exists, this dampig cotroller is supposed to stabilize the system withi two secods uder a give set of failure modes, ad reduces the system trasit time back to stabilizatio. Just like other WAMC applicatios which are affected by the commuicatio etwork, such as badwidth, routig etc. [3], this feedback cotrol i the power system is also affected by the etwork eviromet, ad its performace of stabilizig a power system will ot reach the same level as i a ideal eviromet [4]. The performace of this techique depeds o three aspects: the desig of cotrollers, the schemes for the data trasmissio, ad the traffic o the commuicatio etwork. I desigig the cotrollers, H cotrol has bee studied for the sigle delay i a sigle chael or the commo delay i multiple chaels [7]- [9]. It should be oted that the delays are ot fixed due to the time-variat etwork eviromet. It is thus challegig to desig a cotroller for ucertai delays. The delay of sigals received by the cotroller is also affected by differet schemes, especially, differet ways of hadlig usychroized ad missig sigals from differet chaels. The scheme desig also has to take ito cosideratio the ucertai etwork traffic. I the studies o traffic shapig, the traffic models are established based o aalytical models or commercial software [1][2]. C. System Performace Metrics A compariso of system dyamics with ad without the dampig cotroller is show i. The dyamic with cotroller is i the ideal etwork eviromet of o delays. Fig. 1. Magetizatio as a fuctio of applied field. (Note that "Fig." is abbreviated ad there is a period after the figure umber followed by two spaces.) /16/$ IEEE

3 Frequecy Differece cotrol without delay o cotrol Time (ms) Fig. 3. System dyamics compariso (o cotrol vs. cotrol uder zero delays). To ivestigate the impact of etwork delays ad sychroizatio processig o the cotrollig performace, the performace metric for system stability is used for evaluatio purpose, which is defied below: 2 s dt t where s stads for frequecy differece betwee two regios. As show i, the trasitio process is as short as two secods. I fact, if the system caot be stabilized withi two secods, it fails i most cases. Thus we calculate the performace metric over a period of 2 millisecods. This performace metric represets the waste of eergy durig the stabilizig process. The smaller is the better the cotrollig performace. D. Commuicatio Network ad Issues therei Amog all types of commuicatio liks for PMU sigals, optic-fiber cables are widely applied for their iterferece immuity. Besides its high iitial ivestmet, oly a very small part of badwidth is occupied by PMU sigals i WAMC [5], which itroduces ecoomic wastes. There are two ways to efficietly utilize the massive badwidth that optic fiber cables provide. The first way is to replace the dedicated badwidth by other low cost istallatio, especially whe more samplig locatios of PMU are added to the whole system. Secodly, the badwidth ca be shared with data traffic of other secodary applicatios. The cosequet issue with either of the two ways is the icrease of commuicatio delays, sice delays play a critical role i WAMC for it elarges the timelag of the cotroller that corrects power grid istabilities ad oscillatios. As poited i [5], the lik delay ca be calculated by summatio of the fixed delay associated with trasducers used, DFT processig, data cocetratio ad multiplexig, the lik propagatio delay, the trasmissio delay ad a stochastic jitter. I additio to such a lik delay, the sychroizatio delay has to be cosidered ad is the focus of this paper. The samplig data from differet PMUs are all labeled with GPS time stamp before deliverig. Differece of GPS time stampig is igored here ad the samplig PMU sigals with the same time stamp are regarded as sychroous data of the same time. As those sychroous data are set from differet PMU locatios, they arrived at the cetralized cotroller with differet commuicatio delays. These delayed sigals from all chaels have to be sychroized agai before the cotroller ca derive a output. The sychroizatio delay therefore comes from the differece of commuicatio delays i multiple iput chaels of the cotroller. III. NETWORK DELAYS AND SIGNAL SYNCHRONIZATION A. Delay Modes The major delays i cocer are categorized ito three modes: lik delays, pure radom delays ad delays due to secodary applicatios that share badwidth with the cotrollig sigals. I this work, sice WAMC uses dedicated chaels for commuicatio, we maily cosider pure radom delays. B. Sychroizatio Schemes Suppose there are N chaels of sigals, that is, the cotroller has N iputs. The sigal of time t from chael is deoted as S (t). The set of received sigals from all the N chaels is deoted as a available set A. Sigals i A are available for sychroizatio processig ad ca be set as the iput of the cotroller. I view of the low sigal utilizatio of the widely applied scheme Drop i practice, we propose herei three differet schemes for receivig asychroous sigals, SCH (sigle chael history), SCI (sigle chael iterpolatio) ad SCI-T (sigle chael iterpolatio with timestamp). Drop I the covetioal method Drop, if ay of the latest sigals are missig at t, cotroller iputs x (t) are set to be zero for all. It writes as: x ( t) s ( t ) I, 1 s( t1) A, t1=max{ s( ) A}, 1,, N where I {} is the idicatig fuctio, takig oe if {} is true ad takig zero otherwise. It ca be see that whe the sigals from all chaels are ot received all together, the icomplete sigals are igored uder Drop scheme. The waste of data prevets the fuctioig of cotroller. The three schemes proposed below compesate the missig data to put the cotroller ito fuctioig. SCH To reduce the waste of received sigals, Sigle Chael History (SCH) scheme compesates missig sigals with the latest historical data i the same chael. The iput of cotroller is writte as: s ( t ) t max{ s ( ) A} 1 1 [, t] x ( t), otherwise Such a approximatio caot avoid asychroous ad iaccurate iputs, but is expect to provide prompt cotrollig output. SCI Rather tha usig historical data directly as a substitute for the missig data as i SCH scheme, Sigle Chael Iterpolatio (SCI) estimates the missig data by the liear iterpolatio of the latest two sigals available i the same chael, which writes: s( t1) s( t1) A s( t2)( t1 t3) s( t3)( t2 t3) x( t) s( t1) A ad t2, t3, t2 t3 otherwise where t = max{ ( ) } 1 s A /16/$ IEEE

4 t max{ s ( ) A} 2 [, t1 ].45.4 t max{ s ( ) A} 3 [, t2 ] This liear iterpolatio utilizes two latest sigals received to estimate the missig data of the latest received sigals. This estimatio of cotroller iput is expected to be more closed to the missig data at t. SCI-T Differet from all the previous schemes that compesate the missig data amog the latest received sigals, Sigle Chael Iterpolatio with Timestamp (SCI-T) takes ito cosideratio the timestamp of the curret time t. That is, it estimates the sigals of curret timestamp t to elimiate the latecy due to etwork delay. Specifically, s t2 t t3 s t3 t t2 t2 t3 s ( t) s( t) A ( )( ) ( )( ) x ( t) s( t) A ad t2, t3, otherwise where t max{ s ( ) A} 2 3 [, t] [, t2 ] t max{ s ( ) A} I case that the latest sigal arrives without delays or the delay is less tha the samplig period, SCI-T reduces to SCI. IV. EXPERIMENTAL RESULTS I the simulatio experimets, system performace is tested ad compared with these sychroizatio schemes uder a set of delay cofiguratios specified hereafter. A recorded fault from real historical data is used to geerate the sceario where the system starts to oscillate. I differet delay patters, commo radom umbers are used to geerate the stochastic delay sequeces. The results will demostrate the characteristics of differet sychroizatio schemes uder the same delay cofiguratios. A. Critical value of the system tolerace For compariso purpose, the system stability performace is explored uder fixed delays ad delays of all iput chaels are set to be the same. The plots below depict the system performace curve ad the critical value of maximal delay is 15ms for curret stabilizatio cotroller Delay (ms) Delay (ms) Fig. 4. Critical value: System stabilizatio performace with commo delays of icreasig meas uder curret cotroller. B. Results of differet sychroizatio schemes I -, the error bars of the stability performace metric of the system are plotted. They characterize the performace of differet sychroizatio schemes uder delays of icreasig meas ad a commo variace 25/3. The mea delay rages from 5ms to 1ms with icreasig step 5ms. With icreasig delays, all the schemes degrade i terms of the icreasig. As poited out i Subsectio IV..A, the system tolerace of sychroous delays is 15ms. I this testig, the system tolerace is expected to be less tha 15ms regardig asychroous sigals. For Drop, SCH ad SCI schemes, a slight chage appears o the curves at 65ms, ad obvious chages ca be observed at 85ms for all of the four schemes. Whe delays approach 1ms, scheme Drop ad SCI-T fail to stabilize the system o some sample paths. The failed sample paths are excluded i geeratig the error bar, ad the correspodig poits o the error bar are marked with a red asterisk. Drop It ca be see i that alog with the icreasig mea delays, the covetioal Drop schemes oscillates ad degrades gradually. To demostrate the oscillatio, its performace error bar with uit icreasig steps of mea delays is plotted i The oscillatio is due to the Drop scheme itself ad the period of the oscillatio is due to the system samplig period. With Drop scheme, sigals will be igored whe they do ot arrive o time all together ad the cotroller will ot take effect. I this WAMC system, samplig sigals of PMU are set every 1ms. Correspodigly, the cotroller receives iput sigals every 1ms. If the delayed sigals arrive i the same samplig iterval, o matter how much the delays are, these sigals are treated by the cotroller as sychroized sigals that arrive together ad the cotroller takes effect. While whe the delays of PMU sigals distribute over more tha oe period, the probability becomes small for all sigals arrive withi the same samplig period, which meas the cotroller is less likely to take effect alog the ru. From, it ca be see that the period of oscillatio is 1ms, equivalet to the samplig period. The high peaks of, that is, the low peaks of cotrollig effects, take place whe the mea delays are multiple of 1ms; ad the cotrary performace takes place whe the mea delay is at the middle of the 1ms samplig periods. Furthermore, all peaks icrease with the mea delay icreases, the performace get worse gradually, but still, the oscillatio domiates the degradatio over the icreasig etwork delays. Besides the above drawbacks, this covetioal Drop scheme is ot good eough compared to other schemes. It does ot provide good stability performace eve whe the delays are still small. It also fails i stabilizig the system whe the mea delay is larger tha 85ms. The geeral improvemet by /16/$ IEEE

5 the proposed schemes below ca be as large as about te times i terms of. SCH It ca be see that SCH method archives better stability performace tha the covetioal Drop scheme i terms of. SCH s performace degrades gradually with the icreasig mea delays. For delay larger tha 8ms, SCH worses rapidly i terms of mea ad variace of Mea Delays (ms) Fig. 5. Drop performace error bar with delays of icreasig meas ad a commo variace Mea Delays (ms) Fig. 6. Drop performace error bar with delays of uit icreasig mea ad a commo variace * * Mea Delays (1ms) Fig. 9. SCI-T performace error bar with delays of icreasig mea ad commo variace. V. CONCLUDING REMARKS This paper presets experimetal study results o sigal sychroizatio for a dampig cotrol applicatio i smart grid. I presece of radom ad o-uiform delays of multiple iput chaels, the system tolerace for delays is decreased, ad the critical values o delay tolerace deped o the sychroizatio scheme beig applied. A sychroizatio scheme has to tradeoff the loss of either accuracy or striget time requiremets. With covetioal schemes, if sigals of a commo timestamp from differet iput chaels arrive with differet delays ad caot serve as the cotroller s iputs, they are either igored or beig waited till all are available. That is, the sigal accuracy remais. I this paper, three schemes that provide more timely cotrollig respose are proposed ad compared with the covetioal scheme Drop i the testig. The three schemes SCH, SCI ad SCI-T compesate the missig sigals, respectively, with historical data, with liear iterpolatio ad with liear iterpolatio weighted by time stamp. With differet approximatios to the origial sychroous sigals from the sourcig PMUs, these schemes offer differet tradeoffs betwee data accuracy ad timely cotrol respose, which ca be roughly illustrated by below. Drop SCH SCI SCI-T * Mea Delays (ms) Fig. 7. SCH performace error bar with delays of icreasig mea ad commo variace Mea Delays (1ms) Fig. 8. SCI performace error bar with delays of icreasig mea ad commo variace. Data accuracy Timely cotrol Fig. 1. Illustratio of tradeoffs betwee accuracy of approximated sychroous sigals ad timely cotrol respose that differet sychroizatio schemes offer. Numerical testig results demostrate that timely respose is importat for this real-time cotrollig applicatio. SCH ad SCI schemes achieve better performace amog the four. I geeral, the improvemet by SCH/SCI ca be as large as te times i terms of the performace metric, i additio to the lower possibilities i failig to stabilize the system. Refereces [1] M. Cheie, I. Al Khatib, J. Ivaovski, V. Made, ad L. Nordstrom, PMU Traffic Shapig i IP-based Wide Area Commuicatio, Proc. 5th It. Cof. o Critical Ifrastructure (CRIS), pp. 1-6, 21. [2] M. Cheie, E. Karam, ad L. Nordstrom, Modelig ad Simulatio of Wide Area Moitorig ad Cotrol Systems i IP-based Networks, Proc. IEEE Power & Eergy Society Geeral Meetig, pp. 1-8, 29. [3] A. G. Phadke ad J. S. Thorp, Commuicatio Needs for Wide Area Measuremet Applicatios, Proc. 5th It. Cof. o Critical Ifrastructure (CRIS), 21. [4] M. Cheie, L. Nordstrom, ad P. Johso, Factors i Assessig Performace of Wide Area Commuicatio Networks for Distributed /16/$ IEEE

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