Optimized PMU placement by combining topological approach and system dynamics aspects

Transcription

1 Optmzed PU placement by combnng topologcal approach and system dynamcs aspects Jonas Prommetta, Jakob Schndler, Johann Jaeger Insttute of Electrcal Energy Systems Fredrch-Alexander-Unversty Erlangen-Nuremberg (FAU) Erlangen, Germany Abstract In ths paper a new Phasor easurement Unt (PU) placement methodology s proposed that combnes approaches based on system dynamcs and based on topologcal analyss. In ths way, the deployment strategy of PUs n a power system can be optmzed. The method ensures the recognton of the most relevant nter-area oscllaton modes from the begnnng whle reachng a fully observable system wth a mnmum number of PUs n the long-term perspectve. To acheve ths, egenvalue analyss s used to dentfy crtcal oscllaton modes n the system and to fnd optmal PU placements for ther recognton. Ths result s then matched wth full observablty solutons obtaned by nteger lnear programmng. The methodology s demonstrated usng the 39-bus New England Test System. Keywords-Optmal PU Placement (OPP); Wde Area ontorng; Egenvalue Analyss; Integer Lnear Programmng; Full Observablty I. INTRODUCTION PUs measure the magntude as well as the phase of voltages and currents n the network. They have varous advantages as compared to classcal remote termnal unts (RTUs) that are usually used for Supervsory Control and Data Acquston (SCADA) systems. The measurements of PUs are tme-stamped and can therefore be synchronzed even f they are transmtted wth dfferent tme delays. They also provde a much hgher reportng rate. Ths enables practcally real-tme measurement and supervson of the system, whch can be crtcal n ncreasngly dynamc power systems [1]. However, PUs and ther communcaton channels are costly, whch s why an optmzed PU placement s needed [2]. Several publcatons have tred to classfy the exstng research on PU placement approaches. In [3], a dstncton s made n topology based and system aspects based algorthms. The former consder manly the topology,.e. whch busbars are connected wth each other by lnes or transformers. The goal s to reach the full observablty of the system wth a mnmum number of PUs. Topology based algorthms typcally formulate the Optmal PU Placement (OPP) problem as a mathematcal optmzaton problem. In [4], these are further classfed nto mathematcal and heurstc algorthms. Short descrptons of dfferent methods for each category are gven. Integer lnear programmng (ILP), a mathematcal algorthm, s explaned and conducted n [5]. In [6] a method s proposed to calculate all equvalent solutons wth the ILP approach. System aspect based algorthms conduct a PU placement wth the goal to observe specfc dynamc phenomena n the system. These algorthms requre varous dynamc system studes. In [7] an approach to dvde all generators nto groups and to select one representatve generator per group to be montored wth a PU s proposed. In [8] three mportant aspects that are generally consdered n combnaton wth PU placement for full observablty are mentoned: Consderaton of zero njecton busses (see [5]) ultstage mplementaton of PUs (see [3]) Redundancy n case of communcaton lne/pu outage (see [2]) The method proposed n ths paper combnes the advantages of topology and system aspects based algorthms for PU placement. On the one hand, nteger lnear programmng s used to calculate all possble solutons. On the other hand, the requred PUs to recognze crtcal power swngs are determned usng egenvalue analyss. In the end the PU placement soluton wth the hghest overlap between these two approaches s selected. Ths combned approach s very flexble snce the method to calculate the full observablty solutons can be adjusted for example to consder aspect 1 or 3. Also the PU locatons for observaton of dynamc processes n the system can be adjusted. Havng an optmal PU placement soluton n mnd from the begnnng, cost savngs can be reached by preventon of redundant nstallaton of PUs. The system dynamcs approach s dscussed n chapter II. The bascs of full observablty and nteger lnear programmng are explaned n chapter III, followed by the presentaton of the combnaton approach of both PU placements. Fnally, the method s verfed n a study case n chapter V.

2 II. EIGENVALUE ANALYSIS FOR GENERATOR GROUPING A. athematcal prncples Egenvalue analyss provdes a much more systematc and effcent tool for the analyss of dynamc power system behavor than smulatng dsturbances n the tme doman whle observng the system reacton. The system s expressed as a lnearzed state matrx n the frequency doman. Its egenvalues descrbe the possble power oscllaton modes n the system,.e. ther frequency and ther dampng. The correspondng rght egenvectors gve nformaton about the observablty of each mode. They can be used to fnd out where n the system a mode can be best observed and also whch generators swng synchronously or aganst each other. The left egenvectors on the other hand sgnal the controllablty of each mode. Ths s of nterest f for example the locaton of a PSS or FACTS element should be determned [9] [10]. The relatonshp between the th egenvalue matrx A and the rght egenvector, when by (1). For the left egenvector 0, the state, s gven A (1) on the other hand, t holds: A The egenvalues can be real or complex. Real egenvalues descrbe non-oscllatory modes, complex egenvalues on the other hand represent oscllatory modes. Therefore, complex egenvalues are of nterest when lookng for nter-area oscllatons. The egenvalue of mode can be wrtten as n (3). wth (2) j (3) dampng of the oscllaton, frequency of the oscllaton. odes can be dvded nto categores by means of ther frequency. odes wth a frequency of less than 0,1 Hz are typcally controller modes. Swng modes generally le between 0,1 and 3 Hz wth nter-area modes typcally on the lower end of ths range (0,1-0,8 Hz) and regonal modes wth hgher frequences (0,8-3 Hz). From the dampng and frequency, the dampng rato of mode can be calculated accordng to (4), where a dampng rato of less than 5 % s usually vewed as crtcal [9]. 2 2 B. Generator groupng For relable recognton of specfc power swng modes, PUs need to be placed at generators that swng aganst each other. Whle the magntude of the rght egenvector sgnals the observablty of a mode at a certan generator, ts phase ndcates the oscllaton phase and therefore allows the dentfcaton of coherent generator groups that swng n phase wth each other. Snce all generators of a group behave smlarly, t s suffcent to place only one PU at a (4) representatve node of each group. A sensble crteron to select ths representatve node s to choose the generator of the group that has the best observablty and hence a relatvely hgh magntude of the rght egenvector. The generator groupng can be conducted n a step-by-step manner, analyzng all the crtcal modes and categorzng the generators n ever-smaller groups. After ths process t s possble to dentfy a small number of PU locatons that are suffcent to observe the most crtcal power swngs. III. PU PLACEENT FOR FULL OBSERVABILITY A. Full Observablty When placng a PU at a certan busbar, the voltage phasor and all current phasors of outgong lnes can be drectly measured. Addtonally, the voltage phasors at all system nodes connected to the PU busbar through lnes and transformers can be calculated. If the voltage phasors at both ends of a lne or transformer are known, then the current between the two busbars can be calculated. The ablty to drectly or ndrectly measure the voltage phasor on every bus n the system and all lne current phasors s called full observablty and brngs dfferent benefts for the grd operaton, for example as a requrement for basng a SCADA system on PU measurements. It s therefore seen as the long-term am of the PU deployment strategy. [8] B. Integer lnear programmng The descrbed PU placement problem for full observablty can be descrbed as an nteger lnear programmng optmzaton problem whch s expressed mathematcally as n (5). Heren, x s a vector whose entres ndcate whether or not a PU s nstalled at bus by takng the values 1 or 0 respectvely. The vector ntcon defnes whch varables can only be bnary, whch s the case here for all. A and b as well as Aeq and beq are used to defne equalty and nequalty constrants. Fnally, t s possble to defne lower and an upper bounds for every varable usng lb and ub [11]. x x x(ntcon) are ntegers T A x b mn f x subject to x Aeq x beq lb x ub The nequalty constrant Ax b formulates the demand for full observablty usng the connectvty matrx A. In a n-bus system ths matrx s of the form n n [5]. x x (5) 1 f j A 1 f bus and bus j are connected (6) j 0 otherwse Assumng that bus 1 s drectly connected to the busses 2, 3 and 4, the frst lne n Ax b would result n (7), assurng that bus 1 s drectly or at least ndrectly observable. x1 x2 x3 x4 1 (7)

3 Snce all constrants can be formulated as shown n ths example no equalty constrants are needed for the calculaton of a full observablty soluton. Ths means that the entres of Aeq and beq are 0. Because all varables x are bnary, lower and upper lmtatons of 0 and 1 respectvely are adequate. C. ultple solutons Calculaton of multple solutons can be a more complex task, snce tools lke atlab often stop after fndng the frst soluton. To get all possble and equally optmzed solutons t s then necessary to calculate agan wth strcter constrants. One approach s to stepwse prohbt the placement of a PU at busbars suggested by prevous solutons. As ths has to be done for every new soluton that s found, a recursve algorthm s requred to calculate the full set of solutons. To set ths further constrant the equalty constrants can be used. If no PU should be placed at bus then and beq 0 Aeq, 1 fulflls ths requrement. After every calculaton of the recursve algorthm t s necessary to check f a new soluton can be found wth the addtonal constrants and f the number of requred PUs s equal to the mnmum. As t s possble that the same soluton s obtaned multple tmes, duplcates have to be fltered [6]. IV. COBINATION OF APPROACHES A. ultstage mplementaton As t was mentoned before PU placement n two steps s suggested. Snce the number of PUs needed to observe the system dynamcs s much lower than for full observablty solutons, t s suggested to start wth them. But snce the fnal placement soluton s known already these PUs wll not turn out to be redundant. B. axmum overlap soluton The frst approach to combne the PU placement based on system aspects and on the topology (full observablty) s to calculate the overlaps of both solutons n order to dentfy the soluton wth the hghest percentage of overlap. In case that the requred PUs from the system dynamcs approach are not contaned n any soluton of the topologcal approach,.e. no overlaps of 100 % s obtaned, t s possble to ncrease the number of PUs by the mssng requred locatons. C. New calculaton wth further constrants If the amount of addtonal PUs s greater than one, a new run of the full observablty calculaton should be started wth the constrant of placng PUs at the requred busbars. There s the possblty that a soluton wth a PU number that s only slghtly hgher than the mnmal number can be found to be the better soluton. In ths case the overall number of PUs could be less than takng the mnmal number and addng the requred PUs. other busbars than those found n the system dynamcs study whle stll beng able to observe the power swngs n the system to a satsfyng degree. V. STUDY CASE To valdate the presented concept the method s appled to the 39-bus New England Test System, shown n Fg. 1. The test system conssts of 10 generators and 46 lnes on a 345 kv voltage level and a 10 kv voltage level on the low voltage sde of the machne transformers. Generator 10 represents the aggregaton of the resdual system connected to busbar 39 wth ts dynamc behavor. A. Egenvalue analyss for generator groupng The test system s studed wth the dynamc power system analyss tool PSS NETOAC. Wth the ntegrated egenvalue analyss functon (NEVA) the egenvalues and egenvectors of the test system are calculated. In Fg. 2 all modes that have been calculated wth NEVA are vsualzed n the complex S-plane. odes wth a dampng rato below 5 % (see dashed 5 % solne) are marked n red. From the dfferent oscllaton frequences, controller modes and swng modes can clearly be dfferentated n the dagram. Snce controller modes do not represent a rsk of nstablty, only the swng modes are of nterest for the dynamc supervson of a system. [9] G10 #1 #30 #2 G1 #39 #4 #9 #5 Fg. 1. #8 #7 #37 G8 #25 #26 #28 #29 #3 #6 #18 #31 G2 #12 #14 #17 G3 #27 #16 #15 #11 #13 #20 #10 #32 G5 #24 #21 #19 #23 39-bus New England Test System wth fnal PU placement #34 #33 G4 #22 #38 #35 #36 G9 G6 G7 PU D. Soften the requrements on PU locaton If t s the overall goal to keep the number of PUs to the absolute mnmum for full observablty, further system study s necessary. It has to be studed f PUs can be nstalled on

4 ζ = 5 % Frequency Group 1 G10 Group 2 G1 G2 G3 G4 G5 G6 0.6 G7 G8 G Fg. 3. ode shape of most domnant mode Sgma [rad/s] Fg. 2. Vsualzaton of egenvalues n complex S-plane Table 1. Frequency and dampng values of all modes ode type f [Hz] ζ [%] ω [rad/sec] σ [rad/sec] Controller modes Swng modes In Table 1 the 20 modes that were calculated by egenvalue analyss are lsted, categorzed n controller modes and swng modes. Analyss of the rght and left egenvectors of the nne swng modes shows whch generators partcpate n whch mode and moreover whch generator groups swng aganst each other. It turns out that there exsts one mode (shaded n gray n Table 1) whch shows a sgnfcant value of observablty at all generators. Generators G1 to G9 all swng synchronously aganst G10. Ths s vsualzed n Fg. 3. The magntude of the black fracton of the crcles equvalents the magntude of the respectve rght egenvector entry of the specfed generator. A quarter of a crcle equvalents a magntude of 1. The drecton of the black segment represents the phase of the rght egenvector. Supplementary smulatons n the tme-doman revealed that ths mode s ndeed the most domnant one whch gets almost always excted when a dsturbance occurs n the system. Therefore, observaton of ths power swng s found to be of prmary mportance n ths power system. Ths means that n both groups a representatve generator for PU placement has to be selected. Snce Group 1 conssts of only one Generator the frst PU has to be nstalled at Generator 10. From Group 2 Generator 5 and Generator 9 are selected as ths s where the hghest observablty values are found for ths mode. Snce PUs are regularly nstalled on the hgh-voltage sde ths means that PUs have to be nstalled at busbars 20, 29 and 39. B. PU placement for full observablty Wth the PU placement for the test system that was determned n the prevous secton t s possble to observe the most mportant power swng mode n the system. However, the system s not fully observable. As t was descrbed n secton III, the full observablty problem can be formulated as an nteger lnear programmng optmzaton problem. The ntlnprog functon of atlab was used for ths paper to calculate the full observablty solutons for the test system. The parameters of the functon can be seen below. The nputs A and b have to be multpled by negatve one because the nput format of ntlnprog defnes a turned nequalty sgn as compared to the equatons n secton III. X ntlnprog( f, ntcon, A, b, Aeq, beq, lb, ub ) (8)

5 Wth ths functon only one possble soluton s calculated. To calculate all solutons, the functon has to be used multple tme wth added constrants as has been explaned n secton III. The mnmum number of PUs n the test system was determned to be 13. In total, 48 solutons for full observablty wth 13 PUs were found (see Appendx, Table 5). C. Combnaton of approaches The results of the two approaches for the 39-bus test system are shown n Table 2. Table 2. Results of both approaches PU placement acc. to Egenvalue analyss PUs at Busses 20, 29, 39 Full observablty 13 PUs n total A comparson of the PU locatons that have been obtaned from the egenvalue analyss wth the 48 solutons for full observablty has been conducted. It showed all 48 solutons have an overlap of at least 33,3 % because n every soluton a PU s nstalled at busbar of the solutons have a 66,6 % overlap wth a PU at busbar 20 as well. But no soluton places a PU at busbar 39. Soluton no. Table 3. Example for overlap calculaton Full observablty Overlap [%] 1 2, 6, 9, 12, 14, 17, 22, 23, 29, 32, 33, 34, 37 33,3 % 6 2, 6, 9, 10, 11, 14, 17, 19, 20, 22, 23, 29, 37 66,6 % Snce the number of addtonally requred PUs s not greater than one, a new calculaton would be redundant. Therefore, t s necessary to study f a PU can be placed on a busbar other than busbar 39 whle stll obtanng the requred nformaton to observe the power swngs n the system. In Fg. 4 the frequency at bus 39 s compared to the two adjacent busses 1 and 9 durng the domnant mode n a tmedoman smulaton. It can be seen that the frequency oscllaton at those adjacent busses s much less pronounced than at bus 39. However, the power swng recognton n establshed phasor data processng software s normally done usng the voltage angle dfference. From Fg. 5 t can be seen that the swng n the voltage angle dfference s only slghtly less pronounced when usng adjacent busses, but stll sgnfcant enough for successful swng recognton. It can also be seen that the sgnals measured at bus 1 and 9 are almost dentcal. Checkng the overlap wth the full observablty solutons agan would suggest to place the PU at bus 9 snce t occurs n all solutons and bus 1 n none. Table 4 shows the overlap percentage for two example solutons. Consequently, soluton number 6 s chosen as the fnal PU placement. Ths placement s llustrated n Fg. 1. Soluton no. Table 4. Second overlap calculaton Full observablty Overlap [%] 1 2, 6, 9, 12, 14, 17, 22, 23, 29, 32, 33, 34, 37 66,6 % 6 2, 6, 9, 10, 11, 14, 17, 19, 20, 22, 23, 29, % Frequency devaton at bus 39 [mhz] Frequency devaton at bus 1 [mhz] Frequency devaton at bus 9 [mhz] Tme [sec] Fg. 4. Frequency devaton at bus 20 [mhz] Frequency devaton at bus 29 [mhz] Frequency at adjacent busses 1 and 9 durng domnant mode Voltage anlge dfference bus 39 and 20 [ ] Voltage anlge dfference bus 1 and 20 [ ] Voltage anlge dfference bus 9 and 20 [ ] Fg. 5. Comparson of voltage angle dfference between bus 39, 1 and 9 to bus 20 durng domnant mode

6 VI. SUARY Wth the ncreasng mportance of Wde Area easurement Systems (WAS), cost effectve and techncally optmzed PU deployment strateges are needed. Several approaches for optmal PU placement that serve dfferent requrements exst. In ths paper, a combnaton of two methods was proposed to harness the benefts of both. The am was to fnd a small set of PUs for montorng the most crtcal power swng modes already from the begnnng of PU deployment and to combne t wth a full observablty soluton as a long-term goal. Ths way, the SCADA systems can beneft from near real-tme data from PUs to a maxmum degree and n an economcal way. The suggested method was thoroughly dscussed n theory and demonstrated on the 39-bus New England Test System. APPENDIX Table 5. Full observablty solutons for New England Test System No. Busbar numbers wth PU REFERENCES [1] J. achowsk, J. Balek, and J. Bumby, Power system dynamcs: stablty and control: John Wley & Sons, [2] S. Akhlagh, N. Zhou, and N. E. Wu, Eds., PU placement for state estmaton consderng measurement redundancy and controlled slandng IEEE Power and Energy Socety General eetng (PESG), [3] V. S. S. Kumar and D. Thukaram, Eds., Approach for ultstage Placement of Phasor easurement Unts Based on Stablty Crtera, [4] N.. anousaks, G. N. Korres, and P. S. Georglaks, Eds., Taxonomy of PU Placement ethodologes, [5] B. Xu and A. Abur, Eds., Observablty analyss and measurement placement for systems wth PUs, [6] N. Xa and H. B. Goo, Eds., Observablty analyss of PU placement: ultple-soluton studes IEEE PES Innovatve Smart Grd Technologes, [7] S. Yang, B. Zhang,. Hojo, and K. Yamanaka, Eds., An optmal scheme for PU placement based on generators groupng IEEE PES Asa-Pacfc Power and Energy Engneerng Conference (APPEEC), [8] A. Bswal and H. D. athur, Eds., Identfcaton of optmal locatons of PUs for WAPAC n smart grd envronment Internatonal Conference on Technologcal Advancements n Power and Energy (TAP Energy), [9] Infrastructure & Ctes Sector Smart Grd Dvson, Onlne Documentaton NEVA PSS NETOAC Egenvalue Analyss. [10] P. Kundur, N. J. Balu, and. G. Lauby, Power system stablty and control: cgraw-hll New York, [11] athworks, xed-nteger lnear programmng (ILP). [Onlne] Avalable: Accessed on: ay