http://www.div-portl.org Postprint This is the ccepted version of pper presented t IEEE PES Generl Meeting. Cittion for the originl published pper: Mhmood, F., Hooshyr, H., Vnfretti, L. (217) Sensitivity Anlysis of PMU-Fed Stedy Stte Model Synthesis Method for Active Distribution Networks. In: IEEE N.B. When citing this work, cite the originl published pper. Permnent link to this version: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:div-2224
Sensitivity Anlysis of PMU-Fed Stedy Stte Model Synthesis Method for Active Distribution Networks Frhn Mhmood KTH Royl Institute of Technology Stockholm, Sweden Emil: frhnm@kth.se Hossein Hooshyr KTH Royl Institute of Technology Stockholm, Sweden Emil: hosseinh@kth.se Luigi Vnfretti KTH Royl Institute of Technology Stockholm, Sweden Emil: luigiv@kth.se Abstrct The purpose of this pper is to crry out sensitivity nlysis of method tht performs stedy stte model synthesis (SSMS) of ctive distribution networks using Syncrophsor Mesurements. An extended version of the Totl Vector Error (TVE) is used s metric to evlute how sensitive the output of the SSMS method is to the chnges in the inputs to the method. Loction of PMUs in the system, system operting point, nd occurrence of different disturbnces re considered s the input to the SSMS method. The sensitivity nlysis is performed through severl cse studies ech contining chnges in one of the inputs. Index Terms-- ctive distribution network, model synthesis, PMU, sensitivity nlysis. I. INTRODUCTION Sensitivity nlysis is the study of how the uncertinty in the output of mthemticl model or system cn be distributed to different sources of uncertinty in its inputs [1]. A relted prctice is uncertinty nlysis, which hs greter focus on uncertinty quntifiction nd propgtion of uncertinty. Idelly, uncertinty nd sensitivity nlysis should be run in tndem. Sensitivity nlysis of method cn be performed by reclculting its outputs for considerble number of times under different ssumptions nd then nlyzing how their ccurcy is impcted. This study is useful for vriety of purposes including Testing the robustness of the outputs in the presence of vrious uncertinties. Identifying the method s inputs tht cuse substntil uncertinty in the outputs nd should therefore be considered for enhncing robustness. Serching for different types of errors in the outputs. A. Motivtion nd Previous Work With the increse of intermittent genertion sources in distribution networks, it is becoming necessry for Trnsmission System Opertors (TSOs) to hve n ccurte model of their distribution networks. Mesurements from Phsor Mesurement Unit (PMU) from multiple loctions in the distribution network cn be exploited to be used for model synthesis of ctive distribution networks. In this context, stedy stte model synthesis (SSMS) method is introduced in [2] which synthesizes three-phse stedy stte equivlent model of the distribution network. Although performnce nlysis of the method is presented in [2] using hrdwre-inthe-loop (HIL) simultion setup, yet there ws need to perform detiled sensitivity nlysis of the proposed SSMS method to know how sensitive the output of the method is to the chnges in its inputs. The ppliction of sensitivity nlysis in power system hs been extensively discussed in literture [] [4] [5]. In [], sensitivity nlysis is pplied to evlute the vrition of totl genertion cost with respect to chnge in rective power, for determining the optiml loction of the cpcitor bnks in the network. The influence of prmeter perturbtions on power system stbility limit hs been discussed in [4]. In [5], sensitivity nlysis on the ccurcy of different dc power-flow models is presented. B. Pper Contributions In this pper, sensitivity nlysis of the SSMS method (presented in [2]) hs been crried out. Moreover, the pper proposes methodology to perform sensitivity nlysis on PMU dt-bsed pplictions such s the proposed SSMS method. The pper begins by summrizing the concept of stedy stte model synthesis in Section II. In Section III, methodology to perform sensitivity nlysis on the SSMS ppliction is presented. Section IV describes the HIL reltime simultion setup used for sensitivity nlysis of the SSMS ppliction. Section V presents the results from the sensitivity nlysis on the SSMS ppliction. Conclusions re drwn in Section VI. II. THE STEADY STATE MODEL SYNTHESIS METHOD Assuming tht PMU mesurements re vilble t the boundry buses of distribution network, three-phse stedy stte equivlent model cn be synthesized s illustrted in Fig. 1. As the operting conditions of the system chnges, the
prmeters of the equivlent model re updted in rel-time. The reders re referred to [2] for the detils of the SSMS method. V 1 bc <δ 1 bc PMU1 I 1 bc <φ 1 bc Any feeder configurtion with n rbitrry combintion of lod nd DG PMU2 I N bc <φ N bc V N bc <δ N bc V. bc bc <δ I bc <φ bc V bc bc 2 <δ 2 I2 bc <φ 2 bc PMU N PMU As illustrted in Fig. 2, the end-to-end TVE consists of the following two TVEs:. PMU TVE The difference between the true phsor, tht is in our cse existing in the simultion environment, nd the phsor estimted by the PMU is defined s PMU TVE s shown in Fig. 2. This TVE cn occur due to the phse ngle error tht is the product of instrumenttion chnnels nd improper timing sources of the PMU [7]. In our experimentl setup, explined in Section IV, the rel-time simultor nd the PMUs hve different dynmic rnge on voltge nd current rtings. This cn lso contribute s source of PMU TVE. In ddition, the current mplifiers re sources of phse ngle errors, which in turn my cuse PMU TVE. V 1 <δ 1 I 1 <φ 1 R X V R X <δ I <φ R X I 2 <φ 2 V 2 <δ 2 V R <δ 1 X 1 I <φ. RN-2 X N-2 I N <φ N VN <δ N b. Field Appliction TVE The difference between the phsor estimted by the PMU nd the phsor reproduced by the synthesized model is defined s Field Appliction TVE. This type of TVE is minly the product of the SSMS ppliction estimtion errors. The reduced stedy stte equivlent model for phse E <δ Fig. 1. Synthesized model bsed on N number of PMU mesurement points III. METHODOLOGY FOR SENSITIVITY ANALYSIS OF THE SSMS METHOD The min outputs of the SSMS method, summrized in the previous section, re the voltge nd current phsors reproduced by the synthesized model. This section presents methodology to nlyze how the ccurcy of these outputs is influenced by different inputs of the SSMS method. A. End-to-End Totl Vector Error (TVE) The ccurcy of the SSMS outputs cn be mesured using n extended revision of the TVE concept introduced in [6]. This extended revision, clled end-to-end TVE in this study, is defined s the mesure of the difference between the theoreticl phsor vlue of the signl being mesured nd the reproduced version of the sme phsor, s shown below TVE Where Vˆ r ( n ) V ( n ) r Vˆ( n i ) V ( n ) i end to end ( n) ( Vˆ( n) V ( n)) ( Vˆ( n) V ( n)) 2 2 r r i i 2 2 V ( n) V ( n) r i Rel prt of the reproduced voltge Rel prt of the true (ctul) voltge Imginry prt of the reproduced voltge Imginry prt of the true (ctul) voltge (1) Estimted phsor End-to-End TVE by field Appliction Field Appliction TVE True phsor Fig. 2. Types of TVEs PMU TVE Estimted phsor by PMU B. Methodology for Clculting End-to-End TVE The end-to-end TVE cn be clculted by running the SSMS ppliction in HIL simultion setup (explined in Section IV). The HIL setup is used for rel-time simultion of the grid model whose synthesized reduced model is of interest. As shown in Fig., through the HIL setup, the estimted voltge nd current phsors t the boundry buses of the grid model re fed to the SSMS ppliction which estimtes the prmeters of the reduced equivlent model. These prmeters re sequentilly updted in rel-time s soon s ny chnge in the operting point of the system occurs. The resulting rry of the prmeters is fed to reduced equivlent version of the grid model. The reduced model is then simulted to reproduce the corresponding voltge nd current phsors. The reproduced voltge nd current phsors re then compred to their true vlues in order to clculte the end-to-end TVE using (1).
Note tht s indicted in Fig., the SSMS sensitivity nlysis is performed by clculting the end-to-end TVE versus different inputs such s the loction of PMUs, system operting points, nd occurrence of different disturbnces. Inputs to the SSMS method Different PMU Loction Different Nture of disturbnce Different operting point of the system Grid model(ctul) is simulted using HIL setup phsor V t Bus A SSMS Method Estimted prmeters of the reduced equivlent model Phsor I t Bus A Reduced equivlent grid model is simulted phsor V t Bus A Phsor I t Bus A Phsors V & I of the true model End-to-End TVE Clcultions ccording to eqution(1) Phsors V & I of the equivlent model Fig.. Methodology for clculting end-to-end TVE C. End-to-End TVE s Evlution Metric As mentioned before, the end-to-end TVE is selected in this study s the evlution metric for the sensitivity nlysis of the results produced by the SSMS method. We hve defined % men error requirement for the endto-end TVE 1 in this study. In other words, we would like the SSMS outputs, i.e. the reproduced phsors, to hve limited sensitivity to the chnges in the SSMS inputs (i.e. loction of PMUs, system operting points, nd occurrence of different disturbnces) such tht the end-to-end TVE remins within %. The bsis of this requirement is s follows: DC Power flow models vilble in literture cn hve more thn 15.7 % error [5]. As SSMS is method to synthesize stedy stte models of the ctive distribution network, hving % end-to-end TVE for estimted prmeters still provides much better ccurcy of the reduced equivlent models thn power flow models. % is n cceptble vlue becuse end-to-end TVE contins PMU TVE, which is not relted to the performnce of the trget ppliction. Specificlly, in our cse, the mount of phse ngle error generted by instrumenttion nd difference in dynmic rnge of the 1 Observe tht requirements in terms of ech type of TVE defined could be imposed nd ssessed. However, such work would require dditionl experimentl tests. Further work in this re will be crried out in future publictions. rtings of different equipment increse the end-to-end TVE. IV. HIL REAL-TIME SIMULATION SETUP This section describes the HIL rel-time simultion setup for ccessing the performnce of SSMS method. As shown in Fig. 4, grid model is simulted using the OPAL-RT rel-time simultor. The mesured voltges nd currents re fed to PMUs through the nlogue output ports of the OPAL-RT simultor nd the mplifiers. As the figure shows, Syncrophsors re sent to Phsor Dt Concentrtor (PDC) which strems the dt over TCP/IP to worksttion computer holding Sttnett s Synchrophsor Development Kit (S DK) [8]. S DK serves s rel-time dt meditor tht prses the PDC dt strem nd mkes it vilble to the SSMS ppliction in LbVIEW environment. As shown in Fig. 4, different types of TVEs explined in Section III cn be visulized. Opl-RT Simultor PMU TVE V1 I1 Voltge & Current Amplifier V2 I2 Voltge & Current Grid model Amplifier simulted in rel-time PMU 1 SEL-PDC 57 PMU 2 End-to-End TVE PDC Strem S DK rel-time dt meditor Field Appliction TVE Fig. 4. HIL simultion setup showing different types of TVEs V. SENSATIVITY ANALYSIS OF THE SSMS METHOD SSMS Appliction Field Applictions Fig. 5 shows single digrm of grid network model, which hs been dopted from n ctive distribution network model, presented in [9]. The grid model is used to crry out different cse studies to show how sensitive the output of the SSMS method is with respect to the chnges in its inputs. In [2], SSMS method is vlidted by the grid model, shown in Fig 5. Therefore, ny chnges in the grid model cn be EPS Sttic lod Dynmic lod Voltge regultor Wind frm 11 1 12 1 15 14 Legend Cpcitor bnk Circuit breker FOP Recloser PMUs Loction sets 1 2 858 86 86 84 84 IEEE 4 - Bus LS2 (PMU 2) LS (PMU 2) RBTS Test Feeder 862 822 888 82 88 82 LS1 (PMU 1) LS1 (PMU 2) LS (PMU 1) 818 852 86 88 812 824 826 16 8 82 814 85 816 81 856 CS1: Wind Power 828 8 854 Curtilment LS2 (PMU 1) 864 848 846 844 Fig. 5. Single-line digrm of grid network 842 CS2: Feeder Disconnects (Event 1) CS2: Wind Turbine Disconnection (Event 2)
Probbility Density Probbility Density Probbility Density Probbility Density considered s the inputs to the SSMS method. Three vrible inputs re considered in this study: chnge in the system operting point, occurrence of different disturbnces in the grid network, nd chnge in the loction of the PMUs instlled in the network. For cse study 1, the experiment is repeted 125 times (for ech step decrese in wind power). Wheres, for cse study 2 nd cse study, the experiment is repeted 4 times ech. The sensitivity of the output of the SSMS method to these inputs is shown in the following cse studies. A. Cse Study 1: Chnge in system operting point This Cse Study shows how sensitive the output of SSMS method is with respect to chnges in the system operting point. The chnges re relized by pplying power decrese of.5 MW (16% of the totl lod) in 5 steps (.75 MW in ech step) to the wind turbine connected t node 854 in Fig. 5. The sensitivity of the output of the SSMS method is evluted by clculting the men, mximum nd minimum vlues of the end-to-end TVE for ech step decrese in the wind power genertion. The results re summrized in Tble I. The lrgest men vlue of the end-to-end TVE for ll the voltge nd current phsors is 2.72 %. Note tht in this cse study the PMUs re instlled t nodes 814 nd 852. The stndrd devition (SD) is clculted for ech voltge nd current phsor. The mximum vlue of SD of end-to-end TVE is.4644 %, which shows the uncertinty in the output of the SSMS method is smll. The probbility distributions for the end-to-end TVE for both voltge nd current phsors, for both PMU 1 nd PMU 2, re plotted nd re shown in Fig. 6. The top plots correspond to the voltge phsors nd the bottom plots re for the current phsors. 9 8 7 6 5 4 2 1 TABLE I End-to-end TVE for Cse Study 1 (Number of trils=125 for ech step decrese in wind power) Phsors End-to-end TVE (%) Men Mx Min SD V1.1184.1564.14.14 I1 2.72.7165 1.6429.4644 V2 1.6486 1.7288 1.5818.416 I2 1.4972 1.6172 1.426.559 TVE for Voltge Phsor for PMU 1.8.1.12.14.16.18 TVE for V1 (%) 4 5 25 2 15 1 5 TVE for Voltge Phsor t PMU 2 1.5 1.55 1.6 1.65 1.7 1.75 1.8 TVE for V2 (%) B. Cse Study 2:Occurnce of Disturbnces The sensitivity of the output of the SSMS method is nlyzed by pplying two types of disturbnces in the grid model (shown in Fig. 5). The following two events were creted: Event 1: Disconnection of lterl feeder t bus 84 Event 2: Loss of 1 MW wind genertion t bus 854 The end-to-end TVE is clculted for three different time periods, listed in Tble II, to nlyze the sensitivity of the SSMS output with respect to these two events. TABLE II Different time periods in Cse Study 2 No. Detils of the Sections 1 Before Event 1 2 Between Event 1 & Event 2 After Event 2 For ech time period, men, mximum nd minimum vlues of the end-to-end TVE for ech voltge nd current phsor were clculted. Note tht in this cse study the PMUs re instlled t nodes 814 nd 852. The results re summrized in Tble III. As shown in the tble, the lrgest men vlue of the end-to-end TVE is.549 % for ll the voltge nd currents phsors for both PMUs. Moreover, SD is clculted for ech phsor for both PMUs. The mximum vlue for SD of the end-to-end TVE, for ll phsors of both PMUs is.449 %. The results from Tble III show tht the end-to-end TVE remins in the permissible rnge despite the occurrence of the two disturbnces. Phsors V1 I1 V2 I2 TABLE III End-to-end TVE for Cse Study 2 (Number of trils=4) Sections End-to-end TVE (%) Men Mx Min SD 1.1267.16.1.251 2.182.1672.151.218.1186.1486.896.19 1 2.5192 2.991 2.116.284 2.549.6 2.176.449 1.455 1.674 1.952.162 1 1.6448 1.68 1.611.29 2 1.6259 1.665 1.64.211 1.726 1.7592 1.724.16 1 1.4878 1.5671 1.49.265 2 1.744 1.784 1.76.27 1.5624 1.5862 1.5442.12 4 TVE for Current Phsor t PMU 1 TVE for Current Phsor t PMU 2.5 2.5 2 1.5 1 25 2 15 1 C. Cse Study : Chnge in PMU Loction In this cse study, the loction of ech pir of PMUs (used in the SSMS method) is vried, s shown in the grid model in.5 5 1 1.5 2 2.5.5 4 4.5 TVE for I1 (%) 1. 1.4 1.5 1.6 1.7 TVE for I2 (%) Fig. 6. Probbility distribution of end-to-end TVEs for Cse Study 1
Fig 5. This is to investigte how sensitive the SSMS output is with respect to the mesurement points, tht is the PMU loction. In this cse study, the following Loction Sets (LS) re selected: Loction Set 1: PMU 1 t node 814 PMU 2 t node 852 Loction Set 2: PMU 1 t node 8 PMU 2 t node 84 Loction Set : PMU 1 t node 8 PMU 2 t node 84 For ech PMU loction set (LS), men, mximum nd minimum vlues of end-to-end TVE for voltge nd current phsors for both PMU 1 nd PMU 2 were clculted. The results re summrized in Tble IV. As shown in the tble, the lrgest men vlue of the End-to-End TVE is 2.5192 % for ll the voltge nd currents phsors for both PMUs. Moreover, SD is clculted for ech LS for the voltge nd the current phsors for both PMUs. The mximum vlue for SD for ll the phsors for both PMUs is.284 %. The results from Tble IV show tht the end-to-end TVE does not chnge much by chnging the PMU loction set in the network, which indictes tht the output of SSMS method is impervious to different PMU loctions in the network. Phsors V1 I1 V2 I2 TABLE IV End-to-end TVE for Cse Study (Number of trils=4) PMU End-to-end TVE (%) Loction Set Men Mx Min SD 1.1267.16.1.251 2.5.69.47.56.55.8.412.1 1 2.5192 2.991 2.116.284 2 2.4842 2.866 1.8817.2727 1.6148 1.7428 1.54582.6 1 1.6448 1.68 1.611.29 2 1.6164 1.662 1.587.24 1.5254 1.67248 1.64415.8 1 1.4878 1.5671 1.49.265 2 1.4667 1.4825 1.4476.1218 - - - - the end-to-end TVE before nd fter the disturbnces. In ddition, it ws shown tht the end-to-end TVE does not chnge much by chnging the loction of the PMUs in the grid. In summry, the results of the cse studies show tht the output of the SSMS method is quite impervious to the chnges in its inputs, which indictes the robustness of the method. ACKNOWLEDGMENT This work ws supported in prt by the FP7 IDE4L project funded by the Europen Commission nd the STndUp for Energy Collbortion Inititive. REFERENCES [1] Sltelli, A.; Rtto, M.; Andres, T.; Cmpolongo, F.; Criboni, J.; Gtelli, D.; Sisn, M.; Trntol, S. (28). Globl Sensitivity Anlysis: The Primer. John Wiley & Sons. [2] F. Mhmood; H. Hooshyr; J. Lvenius; P. Lund; L. Vnfretti, "Reltime Reduced Stedy Stte Model Synthesis of Active Distribution Networks Using PMU Mesurements," in IEEE Trnsctions on Power Delivery, in press, erly ccess vilble t http://ieeexplore.ieee.org/xplore/home.jsp. [] J. Chureemrt nd P. Churueng, "Sensitivity nlysis nd its pplictions in power system improvements," Electricl Engineering/Electronics, Computer, Telecommunictions nd Informtion Technology, 28. ECTI-CON 28. 5th Interntionl Conference on, Krbi, 28, pp. 945-948. [4] Michele Brucoli, Bruno Mione, Ernesto Mrgrit nd Frncesco Torelli, "Sensitivity nlysis in power system dynmic stbility studies," Electric Power Systems Reserch, 1981. Elsevier Sequoi S.A., Lusnne, pp. 59-66. [5] Yingying Qi; Di Shi; Tylvsky, D., "Impct of ssumptions on DC power flow model ccurcy" North Americn Power Symposium (NAPS), 212, vol., no., pp.1-6, 9-11 Sept. 212. [6] IEEE Std C7.118, IEEE stndrd for syncrophsor mesurements for power systems no. 2, pp. 1 211, 26. [7] R. S. Singh, H. Hooshyr nd L. Vnfretti, "Assessment of time synchroniztion requirements for Phsor Mesurement Units," PowerTech, 215 IEEE Eindhoven, Eindhoven, 215, pp. 1-6. [8] L. Vnfretti, V. H. Arstrnd, M. S. Alms, V. S. Peric, J. O. Gjerde, A softwre development toolkit for rel-time synchrophsor pplictions, in Proc. IEEE PowerTech, 21. [9] H. Hooshyr, F. Mhmood, L. Vnfretti, M. Budette, Specifiction, implementtion, nd hrdwre-in-the-loop rel-time simultion of n ctive distribution grid, Elsevier Sustinble Energy, Grids nd Networks (SEGAN), Volume, September 215, Pges 6-51. VI. CONCLUSIONS This pper hs presented sensitivity nlysis of method tht performs stedy stte model synthesis (SSMS) of ctive distribution networks using synchronized phsor mesurement dt. The originl TVE concept ws extended (end-to-end TVE) to serve s n evlution metric in the sensitivity nlysis. A methodology for sensitivity nlysis of the SSMS ppliction ws presented nd performed through three different cse studies. The presented results show tht the method s output djusted to the chnges in operting point of the system well nd provided cceptble vlues for