Locaton Identfcaton of Dstrbuton Networ Events Usng Synchrophasor Data Mohammad Farajollah, Alreza Shahsavar, and Hamed Mohsenan-Rad Department of Electrcal and Computer Engneerng, Unversty of Calforna, Rversde, CA, USA e-mals: {mfara006, ashah023}@ucr.edu, and hamed@ece.ucr.edu Abstract Ths paper proposes a novel method to dentfy the locaton of events n power dstrbuton systems. An event s defned broadly here to nclude a change n state of a swtch, a change n voltage, n form of a sag or swell, etc. The proposed method s developed based on the compensaton theorem n crcut theory to generate an equvalent crcut accordng to the pre-event and post-event feeder states. To such am, the post-event voltage devatons from pre-event values are assumed to be measured by dstrbuton-level phasor measurement unts, a..a, mcro-pmus. Importantly, we consder the fact that t s nether economc nor necessary to measure every node s voltage devaton along the feeder to fnd the source and locaton of the event. In fact, we utlze data from as few as only two mcro-pmus, that are nstalled at the begnnng and at the end of the feeder, to dentfy the locaton of an event. The rest of the nformaton collected from the feeder s n form of pseudo-measurements. Despte the natural naccuracy n pseudo-measurements, the proposed hybrd method s robust aganst the pseudo-measurements error. The effectveness of the developed method s demonstrated through smulatng the IEEE 33 bus test system n PSCAD. Keywords: Dstrbuton feeder events, mcro-pmus, data-drven method, locaton dentfcaton, compensaton theorem. I. INTRODUCTION The events at dstrbuton grd are often categorzed nto two man groups; power qualty (PQ) events, such as voltage sag and swell due to capactor ban or load swtchng, and emergency events, such as nterrupton n servce due to fuse blowng or relay and recloser trppng [1]. Hstorcally, the detecton and locaton dentfcaton of emergency events, such as permanent fault events, have been of greater nterest to electrc utltes than the PQ events, because of the need to accelerate the solaton and servce restoraton processes n case of emergency events. However, n recent years, electrc utltes have ncreasngly become nterested n locaton dentfcaton of not only emergency events but also PQ events due to prolferaton of customer devces that are senstve to the power qualty. Broadly speang, the exstng methods to dentfy event locatons at dstrbuton grd, whether of PQ type or emergency type, can be categorzed nto two man groups: mpedancebased and wde-area montorng methods [2]. The former class of methods wor based on calculatng the lne mpedance between the fault locaton and the sensor locaton. Such methods wor well only for permanent faults [3], [4]. The man problem wth the mpedance calculaton methods s that the results are Ths wor was supported n part by NSF grant ECCS 1462530 and DoE grant EE 0008001. The correspondng author s H. Mohsenan-Rad. rarely precse,.e., they dentfy multple possble locatons for the event. These methods are also hghly prone to errors related to measurements and the fault mpedance. As for the wde-area montorng methods, they wor based on the fact that voltages and currents along the feeders fluctuate due to ether PQ events or emergency events. In ths regard, these methods use the pre-event and post-event states of the grd to dentfy the exact locaton of the fault. It s worth mentonng that voltage and current fluctuatons along the dstrbuton feeder greatly depend on the type of the event as well as the locaton of the event. In [5], the pre-event and postevent grd states are used to trac the locaton of the source of dsturbance for voltage sags and shunt capactor swtchng n a power dstrbuton system. The proposed method was based on analyzng the transent behavor of current and voltage waveforms captured by power qualty sensors. Thans to the recent development of the dstrbuton-level phasor measurement unts, a..a, mcro-pmus [6], wde-area montorng methods can now be mplemented n practce. In [7], the authors proposed state estmaton based on mcro- PMU data to dentfy the locaton of permanent faults, whle assumng that all nodes are equpped wth mcro-pmus,.e., the grd s beyond fully observable. Subsequent to a fault, several parallel state estmaton tass are conducted based on dfferent hypothess on fault on dfferent lnes. The locaton of the fault s then deemed dentfed at the lne where the related state estmaton resdual has the mnmum value. Another example to conduct event locaton dentfcaton based on mcro-pmu data was presented n [8]. The focus s on dentfyng PQ events related to the operaton of a capactor ban. In [9]-[10], the authors proposed a voltage measurementbased approach to trac the networ modfcatons and to locate slandng events. In [11], the authors developed an algorthm to dentfy frequent dynamc events. Also, the role of supervsory control for events detecton n mcrogrds was nvestgated n [12]. In ths paper, we propose a method to mae use of voltage and current synchrophasor data to dentfy the locaton of PQ events as well as emergency events. The essence of the proposed method s based on the analyss of the equvalentcrcut for feeder, obtaned by applyng compensaton theorem from crcut theory [13], accordng to the pre-event and postevent feeder states. Our approach s hghly practcal because t requres usng only two phasor measurement devces to dentfy the locaton of an event. The two mcro-pmus are proposed to be nstalled at the begnnng and at the end of the
feeder. The effectveness of the developed method s examned on the IEEE 33 bus test system n PSCAD, followed by senstvty analyss and dscussons on the results. II. EVENT LOCATION IDENTIFICATION METHOD Ths secton descrbes the proposed method for dentfyng the locaton of an event n a dstrbuton feeder. Frst, a basc crcut theorem s ntroduced. The proposed method, then, s developed based on the theorem. Fnally, the proposed algorthm for event locaton dentfcaton s presented. A. Compensaton Theorem An event n a crcut can change all or a subset of nodal voltages and branch currents along the crcut. Accordng to the compensaton theorem [13, pp. 177], once an element changes n a crcut, the amount of changes n the nodal voltages and branch currents can be obtaned through an equvalent crcut, n whch the changed element s replaced wth a current source that njects current at a level equal to the amount of change n the current gong through the element; and all sources are replaced wth ther nternal mpedances. The mportance of the compensaton theorem s n the fact that the analyss of an event through the analyss of such equvalent crcut s easer than through the analyss of the orgnal crcut. As an llustratve example, consder an element wth mpedance Z pre, as shown n Fg. 1(a). Suppose Z post denotes the element mpedance after a change occurs n the element, shown n Fg. 1(b). Let I pre and I post denote the currents that are drawn by the element before and after the change, respectvely. Accordng to the compensaton theorem, the equvalent crcut of ths networ can be obtaned by replacng the changed mpedance element wth current source I = I post I pre, (1) and all sources wth ther nternal mpedances. The equvalent networ, shown n Fg. 1(c), can be used to analyze the changes of the nodal voltages and branch currents,.e., and V s = V post s I sr = I post sr V pre s (2) I pre sr. (3) The proposed applcaton of the compensaton theorem n dstrbuton systems s to dentfy the locaton of an event, of PQ or emergency type, as we next descrbe n detals. B. Proposed Methodology Consder a dstrbuton feeder, such as the one shown n Fg. 2. Suppose two mcro-pmus are nstalled on ths feeder, one at the substaton and one at the end of the feeder. The mcro-pmus record the voltage and current flowng at the downstream and upstream of the feeder. There are n buses across the feeder,.e., between the two mcro-pmus. All loads are assumed to have constant mpedances. In case of a lateral, the lateral s replaced wth ts equvalent admttance. Suppose the feeder experences an event, whether a PQ event or an emergency event, at bus, where {1,...n}. Based on the compensaton theorem, a current source wth current I can be replaced at bus n order to create an equvalent crcut. The nodal voltages and branch currents n the presence of current source I are equal to the changes n nodal voltages and branch currents, obtaned from subtractng pre-event and post-event states. Therefore, we conclude that the voltage and current at the begnnng and at the end of the equvalent feeder are essentally equal to the changes n voltages and currents that are recorded by the mcro-pmus. 1) Forward Nodal Voltages Calculaton: The changes n nodal voltages along the feeder can be calculated by usng the measurements from the mcro-pmu at the begnnng of the feeder, together wth pseudo-measurements, as follows: V f 1 = V u V f 2 = V f 1 + ( I u + I f 1 )Z 1. V f n = V f n 1 + ( I u + I f 1 + + If n 1 )Z n 1 where V f denotes the forward calculated nodal voltage of bus by startng from the begnnng of the feeder, and I f denotes the current njecton at bus. Note that, I f s equal to Y V f, where Y ndcates the equvalent admttance of the lateral, and can be obtaned based on the pseudomeasurements and system voltage. Notatons V u and I u ndcate the dfference between the pre-event and post-event voltage and current, captured by the mcro-pmu nstalled at the begnnng of the feeder. Gven the measurement precson of mcro-pmus and snce bus 1 s where the mcro-pmu at the begnnng of the feeder s nstalled, we set V f 1 equal to the change n voltage recorded by the mcro-pmu at the begnnng of the feeder. In addton, consderng the voltage drop made by the current flowng through the lne wth mpedance Z 1 leads to calculatng V f 2. Smlarly, all the nodal voltages across the feeder can be obtaned from the prevous buses voltage and laterals current herarchcally. 2) Bacward Nodal Voltages Calculaton: In a smlar manner, the nodal voltages along the feeder can be calculated by usng the measurements of the mcro-pmu at the end of the feeder, together wth pseudo-measurements, as follows: V b n = V d V b n 1 = V b n + ( I d + I b n)z n 1. V b 1 = V b 2 + ( I d + I b n + + I b 2)Z 1 where V b represents the bacward calculated nodal voltage of bus by startng from the end of the feeder. Here, I b denotes the current njecton at bus, whch s equal to Y V b. Notatons V d and I d ndcate the dfference between preevent and post-event voltage and current, captured by the mcro-pmu nstalled at the end of the feeder. Snce a mcro- PMU s at bus n, we set Vn b equal to the change n the voltage recorded by the mcro-pmu at the end of the feeder. 3) Voltage Comparson: In the two sets of equatons that we obtaned n (4) and (5), t s assumed that for all the laterals the current can be obtaned from the producton of (4) (5)
V pre s I pre sr V pre r V post s I post sr V post r V s Isr V r (All sources are removed) + V pre _ + V post _ + V _ I pre Z pre I post Z post I (a) (b) (c) Fg. 1. An llustraton of compensaton theorem: (a) pre-event networ; (b) post-event networ; (c) equvalent crcut based on compensaton theorem. Y u V u V u I u I u I V d V d I d I d Y d Upstream V 1 V Z V 2 V n-1 1 Z n-1 V n Downstream Y 1 I 1 Y 2 I 2 Y I Y n-1 I n-1 Y n I n Fg. 2. Representaton of a dstrbuton feeder based on compensaton theorem equvalent crcut. Measurements are done by two mcro-pmus. nodal voltage and bus admttance. The calculaton based on such product s vald for all the buses, except for bus n whch the event occurs. At ths bus, current source I njects current nto the equvalent feeder and the producton of voltage and lateral admttance s no longer correct for ths bus current. Therefore, the downstream voltages of bus calculated n equaton (4),.e., { V f +1,, V n f }, and the upstream voltages of bus calculated n equaton (5),.e., { V1 b,, VK 1 b }, are not correct, and they cannot be consdered correct nodal voltages. In other words, we can mae the followng dstnctons across the calculated voltages: { V f 1,, V f }{{}, correct { V1 b,, V 1, b }{{} ncorrect V f +1,, V f n } } {{ } ncorrect V b,, V b n } } {{ } correct The fundamental observaton n (6) s that the calculated voltage at bus n both bacward and forward nodal voltage calculatons s a correct value. In other words, V f b and V are essentally equal, because f they are not equal then at least one of them must be ncorrect, whch s a contradcton. Next, we defne the dscrepancy of the nodal voltages obtaned from both calculatons across all buses as: where V f b V b V f b = V f (6) V b,, (7) s desgnated as the dfference between V f and, defned n (4) and (5), respectvely. Accordng to (6), among all buses, the voltage of bus n the two calculated nodal voltages sets are most smlar; therefore, t s expected that V f b has the mnmum value among all buses: = arg mn V f b. (8) 4) Valdty of the Method: The proposed method s based on the mplct assumpton that the event occurs n the area between the two mcro-pmus. Therefore, before usng the proposed method, we should frst determne whether the event has ndeed occurred n such area. Ths can be done by checng the equvalent upstream and downstream admttances calculated by the two mcro-pmus. The equvalent admttances seen by the mcro-pmus can be calculated as: and Y u = I u V u (9) Y d = I d V d, (10) where Y u and Y d ndcate the equvalent admttances of the upstream and downstream of the feeder n the equvalent crcut, respectvely. If the real parts of Y u and Y d are both postve, then the event s ntated from a pont wthn the area restrcted by mcro-pmus [14]. Otherwse, the event occurred outsde ths area, e.g., somewhere at the transmsson level or at the downstream feeder. C. Proposed Algorthm Once we confrmed that the event has ndeed occurred n the area between the two mcro-pmus, the next step s to calculate the nodal voltages along the feeder through forward calculaton by startng from the begnnng of the feeder, as well as bacward calculaton by startng from the end of the feeder. The exact locaton of the event s then determned to be at the bus where the two calculated nodal voltages by the forward and bacward methods have the most least dscrepancy among all buses. The proposed method s summarzed n Algorthm 1.
Algorthm 1 Event Locaton Identfcaton Input: Mcro-PMUs measurements, pseudo-measurements. Output: The locaton of an event. 1: Obtan Y u and Y d, as n (9) and (10), respectvely. 2: f R{Y u } < 0 or R{Y d } < 0. then 3: The change s not between the two mcro-pmus. 4: else 5: Obtan vector V f usng (4). 6: Obtan vector V b usng (5). 7: Obtan vector V f b usng (7). 8: Obtan the event locaton usng (8). 9: return 10: end f III. CASE STUDIES Ths secton demonstrates the effectveness of the proposed event locaton dentfcaton method by applyng t to the IEEE 33 bus test system. The sngle lne dagram of the feeder s shown n Fg. 3, and the relevant techncal data can be found n [15]. In below, followng a bref descrpton over the mplementaton of the developed method on ths test system, smulatons results for dfferent types of events and varous under-contngency senstvty analyses to examne the effect of dfferent parameters on the method robustness are presented. A. Implementaton of the Method on IEEE 33 bus The IEEE 33 bus test feeder s smulated n PSCAD [16], and the voltages and currents of bus 1 and bus 18 are read as pre-event measurements at the begnnng and at the end of the feeder, whch are deemed to be provded by mcro-pmu 1 and mcro-pmu 2. By applyng an event at a defned bus, the feeder s agan smulated and smlar to the orgnal feeder, the post-event measurements are obtaned. The dscrepancy of preevent and post-event measurements s recorded to be used by the proposed method, accordng to the equvalent-crcut that s formed based on the compensaton theorem. Ths equvalentcrcut conssts of a man feeder wth 18 buses, n whch the laterals are deemed equvalent admttances connected to the man feeder buses. The tas here s to dentfy the locaton of an event on the man feeder by usng Algorthm 1. B. Case I: PQ Event The PQ event n ths case study s n form of a typcal load swtchng acton. A 60 VA load, wth power factor 0.95, s swtched on at a certan bus on the man feeder. Note that the total loadng of the feeder s 4.5 MV A. The swtchng of such a small load does not cause major dsturbance, snce the connected load s only 1.33% of total loadng. Table I shows the results for the case where the PQ event happens at bus 9. We can see that, V f b has ts mnmum value, 0.2 V, at bus 9,.e., the forward and bacward voltage calculatons have ther smallest msmatch at bus 9. Accordngly, Algorthm 1 dentfes bus 9 as the locaton of the event, whch s correct. The second smallest voltage msmatch occurs at bus 10 wth value 8.9 V, whch s consderably greater than the msmatch at bus 9. Such large dfference between the frst and the second largest voltage msmatches provdes a relable margn to accurately dstngush the locaton of the event. Next, the same type of PQ event s smulated to occur at two other locatons.,.e., buses 3 and 15. The results are shown n Fgure 4, and the curves are related to msmatch vectors. Accordng to the curve assocated wth the event at bus 3, the msmatch vector has the mnmum value at bus 3. It means that the two nodal voltage vectors at bus 3 have the most smlarty, whch results n Algorthm 1 to correctly dentfy bus 3 as the locaton of the event. Smlarly, for the curve assocated wth the event at buses 9 and 15, the msmatch vectors carry ther mnmum at the bus where the event occurs. We can see that, as we move away from the bus undergong the event, the values of msmatch ncrease. Thus, Algorthm 1 accurately dentfes the locaton of the PQ event n all three cases. C. Case II: Emergency Event In ths study, an emergency event s defned as a fault occurrence whch sgnfcantly changes the value of currents and voltages along the feeder. Here, a fault wth the resstance of 1 Ω s consdered as an emergency event. The value of the fault current vares from roughly 800 to 3000 A wth respect to the locaton of fault along the feeder. Ths hgh level of current magntude maes sure that the fault current would be enough to be qualfed as an emergency event. Agan, three dfferent locatons are examned as the locaton of the event,.e., ncludng bus 3, 9, and 15. Fg. 5 depcts the curves assocated wth the msmatch vectors. As shown, for each event, the curve has ts mnmum value at the bus n whch the fault occurs. It s also obvous that by gong far from the locaton of the fault, the values of msmatch vectors ncrease. It s nterestng to compare the amount of voltage msmatch V f b n Fgures 4 and 5. Clearly, the voltage msmatch s much larger for the emergency event than for the PQ event. That means, there s a much greater margn of accuracy n dentfyng the correct locaton for emergency events; therefore, t s very unlely for the locaton of an emergency event to be dentfed ncorrectly. D. Under-Contngency Senstvty Analyss In practce, the utlty s nowledge about system parameters s not perfect. The range of uncertanty vares for dfferent types of parameters; nevertheless, for a defned level of parameters accuracy, the robustness of the proposed method aganst the parameter varatons should be determned. In order to do so, ths secton conducts some under-contngency senstvty analyses to nvestgate the mpact of dfferent parameters uncertanty on the proposed method s effectveness. Recall that the proposed method maes use of four prncpal parameters: mpedances of the dstrbuton lnes, pseudomeasurements, current synchrophasor measurements, and voltage synchrophasor measurements. For each system parameter, Mont Carlo approach s used to generate dfferent scenaros based on the errors n the system parameter. Table II shows the results obtaned from the lnes mpedance varatons. As shown, for lnes mpedance error wth 10%
19 20 21 22 26 27 28 29 30 31 32 33 Sub. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 23 24 25 µpmu 1 µpmu 2 Fg. 3. The under-study feeder that s smulated n PSCAD. Three dfferent event scenaros are smulated at buses 3, 9, and 15. TABLE I CALCULATED NODAL VOLTAGE VECTORS AND CORRESPONDING MISMATCH VECTOR Bus # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 V f 4.3 4.8 7.9 10.4 12.9 19.2 22.6 27.1 35.5 44.0 45.3 47.9 60.5 66.4 72.0 78.6 93.6 100.5 V b 42.5 42.1 40.6 39.8 39.0 37.1 36.8 36.3 35.7 35.1 35.0 34.9 34.3 34.1 33.9 33.8 33.6 33.6 V f b 38.2 37.3 32.7 29.4 26.1 17.9 14.2 9.2 0.2 8.9 10.3 13.0 26.2 32.3 38.1 44.8 60.0 66.9 120 100 Bus 3 Bus 9 Bus 15 16000 14000 Bus 3 Bus 9 Bus 15 Voltages Msmatch( V f-b ) 80 60 40 20 Voltages Msmatch( V f-b ) 12000 10000 8000 6000 4000 2000 0 2 4 6 8 10 12 14 16 18 Bus number 0 2 4 6 8 10 12 14 16 18 Bus number Fg. 4. Results assocated wth three dfferent locatons of PQ event. Fg. 5. Results assocated wth three dfferent locatons of emergency event. standard devaton, nearly 95.5% of the event locaton dentfcatons are done correctly, and just n 2.5% of the results, the locaton of events s wrongly dentfy, n whch the neghborng buses are wrongly dentfed as the bus where the event occurs. Also, wth ths range of error, the locaton of the event s dentfed to be no more than one bus away form the true locaton of the event, mplyng that n the worst case, the event locaton mght be dentfed at the neghborng buses. By ncreasng the error n lnes mpedance, the results demonstrate a satsfyng estmaton of the event locaton dentfcaton. For nstance, for lnes mpedance error wth 50% standard devaton, roughly 50% of event locatons are found correctly, and just 13% of the events locaton are wrongly dentfed at the buses beyond the neghborng buses. Ths ndcates that even wth a large range of errors n lnes mpedance, a great porton of wrong dentfcatons are related to dentfyng the neghborng buses as the locaton of the event. Table III provdes the results correspondng to pseudo- measurements. In networs that are not fully observable, the exact values of power njectons at buses are not defned. In ths regard, the pseudo-measurements are defned as power njectons at the buses whch are mostly obtaned va hstorcal data and the capacty of dstrbuton transformers nstalled at the begnnng of laterals. Therefore, pseudo-measurements are prone to a large range of errors. As the results shown, errors wth 20% standard devaton does not have any effect on the accuracy of the method, and for the errors wth standard devatons up to 60%, the worst wrong dentfcaton s related to neghborng buses. Accordngly, the proposed method s hghly robust aganst the pseudo-measurements error. Table IV and V represents the results related to the errors n the current and voltage measurements, respectvely. In ths study, t s assumed that the mcro-pmus serve as the only measurement devces. These devces are hghly accurate and the range of ther error s even less than the commercal PMUs already used n transmsson level. Here, the standard devaton of errors consdered for mcro-pmus are related to
TABLE II METHOD EFFECTIVENESS AGAINST LINES IMPEDANCE ERROR WITH DIFFERENT STANDARD DEVIATIONS Error of Correct One Bus One Bus Maxmum Lne Impedanec Locaton Error Error Error 10% 97.42% 2.58% 0% 1 bus 20% 83.50% 16.29% 0.21% 2 buses 30% 69.98% 26.87% 3.15% 3 buses 40% 59.78% 32.67% 7.55% 4 buses 50% 49.73% 37.22% 13.05% 5 buses TABLE III METHOD EFFECTIVENESS AGAINST PSEUDO-MEASUREMENTS ERROR WITH DIFFERENT STANDARD DEVIATIONS Error of Pseudo- Measurement Correct Locaton One Bus Error One Bus Error Maxmum Error 20% 100% 0% 0% 0 bus 40% 99.55% 0.45% 0% 1 bus 60% 96.28% 3.72% 0% 1 bus 80% 91.1% 8.89% 0.01% 2 buses 100% 85.85% 13.97% 0.18% 2 buses total vector error whch ncludes both the magntude and angle errors. We can clearly see that the error n voltage phasors has greater effect on the method s accuracy than the error n current phasors. Ths fact s so desred, because usually the currents phasors are perturbed by the noses whch are dffcult to get fltered, whle the voltage measurements do not contan such level of nose, so they can be used wth more confdence. IV. CONCLUSIONS Ths paper proposed a novel method, based on an nnovatve applcaton of the compensaton theorem n crcut theory combned wth mang effectve use of data from mcro-pmus, to dentfy the locaton of events n dstrbuton systems, whether of PQ type events or emergency type events. Based on the smulaton results n PSCAD, f the networ s correctly modeled and the pseudo-measurements are precsely obtaned, TABLE IV METHOD EFFECTIVENESS AGAINST CURRENT MEASUREMENTS ERROR WITH DIFFERENT STANDARD DEVIATIONS Error of Correct One Bus One Bus Maxmum Current Phasor Locaton Error Error Error 0.2% 99.79% 0.21% 0% 1 bus 0.4% 93.01% 6.99% 0% 1 bus 0.6% 82.64% 16.89% 0.47% 2 buses 0.8% 73.22% 24.05% 2.73% 3 buses 1.0% 57.87% 32.47% 9.66% 4 buses TABLE V METHOD EFFECTIVENESS AGAINST VOLTAGE MEASUREMENTS ERROR WITH DIFFERENT STANDARD DEVIATIONS Error of Correct One Bus One Bus Maxmum Voltage Phasor Locaton Error Error Error 0.2% 97.92% 2.08% 0% 1 bus 0.4% 83.29% 16.56% 0.15% 2 buses 0.6% 68.91% 28.83% 2.26% 3 buses 0.8% 56.72% 36.10% 7.18% 4 buses 1.0% 40.27% 39.36% 20.37% 5 buses the proposed method accurately estmate the exact locaton of the event. However, n practce, the networ modelng and pseudo-measurements are prone to a level of naccuracy. 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