Analog Behavioral Models and the Design of Analog Emulation Engines for Power System Computation

Transcription

1 Analog Behavoral Models and the Desgn of Analog Emulaton Engnes for Power System Computaton Mchael B. Olaleye *, Qngyan Lu and Cha O. Nwanpa Center for Electrc Power Engneerng Department of Electrcal and Computer Engneerng Drexel Unversty, Phladelpha, Pennsylvana 19104, USA and Abstract Ths paper addresses the use of Analog Behavoral Models (ABMs) n an effcent strategy for desgnng analog emulaton engnes for large scale power system computaton. Through dscusson of hstorcal development of analog computaton n power system analyss and ts present resurgence, we present the need for, and applcaton of ABMs for model verfcaton and valdaton pror to full structural desgn and mplementaton. esults of PSpce smulatons of these emulaton crcuts are also presented and compared wth ndustral grade numercal smulatons for valdaton. 1 NTODUCTON Ths paper attempts to address an effcent strategy for desgnng analog emulaton engnes for large scale power system computaton through the use of Analog Behavoral Models (ABMs) of PSpce [1]. Analog emulaton of large power systems as compared to the currently n use numercal/dgtal approaches wll have a clear advantage n computaton tme, whch s faster and ndependent of networ sze and topology []. t must be mentoned that the ABMs approach may be a frst step towards feasble realzaton of an analog emulaton engne bult of real analog components and devces. t does not serve as a substtute for nether the components nor the buldng blocs. Emulaton can be descrbed as an act of a physcal system mtatng a real system. Emulaton n ths paper therefore, s the representaton of physcal characterstcs of a real lfe object (power system) usng an electrc crcut equvalent. The representaton relatonshp could be mathematcal, scaled, or both. The crcut equvalent representaton has wthn t, the model of a real system, as well as a method of ts soluton. The speed of computaton s as quc as the response of the crcut tself; whch could be real-tme, faster or slower than real-tme dependng on the parameters settng. The soluton s contnuous n tme and ampltude. Smulaton on the other hand s an attempt to predct/ replcate aspects of the behavor of a real system by creatng an approxmate (mathematcal) model of t. Ths s done by computer modelng; by wrtng a specal-purpose computer program. The program s composed of equatons that descrbe the functonal relatonshps wthn the real system. When the program s run, the resultng mathematcal dynamcs form an analog of the behavor of the real system, wth the results presented n the form of data. Dfferental SNE Output Keywords: Analog Behavoral Models (ABMs), Analog emulaton, PSpce, Power system computaton, Smulaton Sne Shaper ABM equvalent SN * Mchael B. Olaleye s currently wth Maret Servces Dvson, PJM nterconnecton, Norrstown, PA 19403, USA. olalem@pjm.com Ths artcle s the author's own personal wor, and does not necessarly reflects the thoughts or postons of PJM nterconnecton. Angle nput Fgure 1: Analog and ABM Sne Shaper The need to emulate/smulate large and complex mxed-sgnal systems has prompted the development of hgh-level crcut representaton for analog components; ABMs serve ths purpose. n ths paper, ABMs are used to mae flexble descrptons of electronc components or complex buldng bloc n terms of transfer functon or looup tables. n order words, a mathematcal relatonshp s used to model a crcut segment, so one wll not need to desgn the segment component by component. Fgure 1 shows a sne shaper whch s a devce that outputs sne value of ts nput sgnal. The left sde of Fgure 1 s a modfed Glbert sne shaper [3] bult component by component usng analog devces, and the rght sde of Fgure 1 s an ABM sne shaper [1]. The only smlarty between the two s that they both tae the same nput sgnal and produce the same output. The nteror of a behavoral model however, s dfferent n that t s mplemented n terms of algebrac or dfferental equatons rather than physcal analog components. n order words, n a behavoral model, the focus s on the nput/output relatonshp of the bloc. The fundamental advantage of the behavoral modelng technque n top-down desgns s that the smulaton can provde fast predcton of system performance. The approach helps to select proper archtectures for crcut mplementaton and analyze tradeoffs at the early desgn stages. The transstor-level smulaton (bottom-up desgn) comparatvely can be very tedous and cumbersome especally for mxed-sgnal chps contanng a large number of analog components. Under such crcumstances, behavoral models enable desgners to 15th PSCC, Lege, -6 August 005 Sesson 38, Paper 4, Page 1

2 verfy the complex system effcently and result n fast system evaluaton pror to embarng on full structural desgn and mplementaton. n ths paper, ABMs are used as buldng blocs to develop software smulaton of an analog emulaton engne that computes the states and behavors of a power system. Analyss s lmted to load flow only. Ths paper s presented n the followng manner. n the next secton, a bref hstorcal bacground of power system computaton usng analog, the currently-n-use dgtal/numerc counterpart, and the resurgence of analog emulators wll be presented. Secton 3 wll present methodology of power system core computaton usng ABMs. Dscussons on tested sample cases, PSpce smulaton results and results from currently n-use ndustral-grade numercal smulators for the purpose of comparson and valdaton, wll be gven n Secton 4. Fnally, the paper s summarzed n Secton 5. BACKGOUND Smulaton and/or emulaton are ndspensable when dealng wth large-scale power systems. They mae t possble to do essental assessment n power system dspatch, operaton, securty and stablty. Dfferent smulaton/emulaton tools today are bult for dfferent applcatons le transent stablty analyss, fault analyss, power flow studes, operatonal plannng, etc. The hstory of power system technques of smulaton or emulaton dates bac to the start of last century. Krause et al [4] gve a good revew of the subject as do McLaren et al [5]. The buldng of these smulators/emulators has been based ether on analog, dgtal or combnaton of analog and dgtal mplementatons as shown n Fgure. Analog emulaton conssts of buldng a scaled-down model of a real power system. Ths may nclude usng analog devces that represent equatons characterzng dstnct relatonshps wthn the power system. Dgtal smulaton conssts of developng dgtal computer programs that solve networ mathematcal equatons through numercal methods. These smulators/emulators have ther advantages and dsadvantages or short comngs n ther mode of operaton, functonalty, effcency and accuracy. frst emulators were analog. Analog computng devces, nstruments, and machnes have been wdely n use snce ancent tmes. Analog computaton has gone through transtons such as mechancal, electromechancal, electrcal, and electronc developments as depcted n Fgure. Electrcal analog emulaton technques were predomnant from 190 to The earler analog computers were specal or fxed purpose, and then general-purpose. The specal-purpose analog emulator technque forms the bass of both the Power System Transent Networ Analyzer (TNA) and the Hgh Voltage Drect Current (HVDC) analog emulator [6]. Ther mplementatons allow for real-tme or faster than real-tme emulaton however, there were serous lmtatons on the reconfguraton and sze of the system that can be emulated. Ths s because of ther specal purpose bult nature and the technology of devces used. Other dsadvantages of ths mplementaton nclude, but are not lmted to complexty, accuracy and cost of mantenance of the emulator. General-purpose electronc analog computers on the other hand could be used for a varety of applcatons. By alterng the arrangements of nterconnectons between the computng elements, they could be set up, or programmed to solve many dfferent problems [7]. ts dsadvantages whch nclude sze and accuracy were nfluenced more by the technology of the tme. Fgure 3 depcts structural comparson between old and proposed technologes of analog emulaton engne for power system computaton. Old Technology G1 1 G 3 Proposed Technology 000 Mcroelectroncs/ VLS (analog VLS) VLS Chp Perod Pre 190 Mechancal Analog Electrcal/Electroncs Analog Electro-mechancal Analog Dgtal (numercal) Hybrd (analog/dgtal) Power System Computaton Hardware Technology Fgure : Tme Lne of Hardware Technology Technology has naturally been an mportant factor n the development of power system computaton tools. The Fgure 3: Comparson of Old and Proposed Technology n the late fftes began the applcaton of dgtal computers to solvng power system problems. Due to hgher precson, flexblty and ease of smulatng larger systems, dgtal smulators began to replace analog emulators. However, one of the most sgnfcant dsadvantages of software based smulators relates to the speed at whch they operate. They are lmted by the cloc rate, - the number of steps that can be executed n a second. For example, present cloc rates though fast, do not allow for real-tme computaton of large-scale power systems. 15th PSCC, Lege, -6 August 005 Sesson 38, Paper 4, Page

3 V m = ( Pm) e = ( Pe) S1 0 S = ( m e) S S1 = 1Ω 0 g 1 st nd C1 C V0 ( δ ) Consequently, dgtal smulatons are severely lmted n tme-crtcal applcatons le on-lne montorng and control. Followng the advent of the dgtal computer emerged the hybrd computer. Hybrd computers combned the fast computaton features of analog wth the logc and accuracy of dgtal computers. Ths technque greatly enhanced the effcency of once-pure-analog emulators such as power system transent networ analyzer (TNA) [8]. However, the sze of hybrd TNA emulator depends largely on the wor requred of t. That s, the larger the real power system networ to be emulated, the larger the emulator. There are extensve and ever contnung efforts to mprove and expand the capabltes and applcatons of dgtal (numercal) smulators; to acheve the goal of realtme. Some of the efforts nclude: () fast decoupled power flows; () sparse matrx computaton technques to reduce the elements to be computed as zero elements tae tme and spaces; () parallel processng usng multple hgh speed CPU s; (v) LU decomposton to help avod nverson of large matrces that proves cumbersome and tme consumng [9]. But the cloc rate stll lmts the effects of the enhancements. More so, Newton-aphson method whch s the most wdely used method for solvng smultaneous nonlnear algebrac equatons n power systems s sequental. t uses a successve approxmaton procedure based on an ntal estmate of the unnown and the use of Taylor s seres expanson. Stage ABMs Feasblty Exploraton ABMs A ( ) sn V 0 Stage V VLS Development G1 VLS Chp Power System Emulator Analog Control Sgnals 1 3 Load G Analog Measurement Sgnals MUX MUX DAC ADC Stage PC Board Prototype Generator Modules Computer nterface VLS Chp Networ Modules Stage VLS Desgn Fgure 4: Developmental Stages of an Analog Emulator There has been recent advancement n the areas of mcroelectroncs and VLS technology that allows hundreds of thousands to mllons of actve components (most often transstors) to be placed on a chp on the order of 100 mm n area and 0.5 mm thc [10]. Analog technology s now a vable canddate for mplementng power system emulator. Other examples of applcaton of analog mplementaton are n domans such as neural modelng, vsual processng, and assocatve memores [10]. The goal of mang real-tme computaton a realty may well requre a rebrth of technology that many consder obsolete n ths era of dgtal computer analog computers (emulators). Therefore the focus of ths paper s the feasblty exploraton of desgn of analog emulaton engne for power systems computaton usng ABMs. Fgure 4 gves a pctoral summary of developmental stages to the goal - mplementaton of analog emulator on a VLS chp. The methodology of mplementaton of power system core computaton s dscussed next. 3 METHODOLOGY OF COE COMPUTATONS USNG ABMs Analog Behavoral Models (ABMs) of PSpce are used to buld a scaled-down model of a real power system. Ths may nclude usng ABMs that represent equatons characterzng dstnct relatonshps wthn the power system. The approach s only for the purpose of desgn feasblty studes. The man advantage s that t gves a clearer pcture of the end goal, desgn layouts and ntrcaces of crcut connectons. P m H d δ = P ( ) ( 0) m Pe δ D = π f dt P e Pm - mechancal nput power Pe - electrcal output power δ - power angle (el. radans) H - per unt nerta constant f - electrcal frequency E - nternal gen. voltage V - bus voltage - current Y - element of Ybus 0 The per-unt swng equaton Pe = e{ E } P = e( V ) Q= m( V ) = Y V S L - constant power load SL = PL jql Fgure 5: Bloc Dagram of Core Computaton Methodology of an Analog Emulator E E δ δ V Generator Transmsson Lnes Load Power system core computaton methodology mplemented n the desgn of analog emulaton goes through three major steps. These steps are llustrated n Fgure 5. The assumptons made and detal processes are dscussed n [11] and [], respectvely. Step 1: Calculatng complex voltage out of generator The generator bloc solves the swng equaton (dynamc) wth resultng power angle, δ. The power angle combnes wth desred voltage magntude to gve a complex voltage out of a generator. Step : Calculatng currents n the networ The nodal and generator nduced voltages nteract wth transmsson lne mpedance and load (f not lumped wth lne mpedance) to produce complex current flowng n any branch. Usng admttance for smplcty and expressng n rectangular form, current s computed as n Fgure 5. As depcted n Fgure 6, t wll requre four separate networs n order to emulate complex current flowng on any branch. The approach of dc-resstve networ as proposed by Fred et al [11] s used. Transformaton of the transmsson lne complex mpedance to ts resstve value for real and magnary 15th PSCC, Lege, -6 August 005 Sesson 38, Paper 4, Page 3

4 part s through ts complex conjugate as shown n equaton 1. = YV = ( Yr jy)( Vr jv) = ( VY r r VY ) jvy ( r VY r) Networ 1 Networ 3 Networ Networ 4 r Fgure 6: Complex Current Computaton Methodology Y Y Y 1 1 jx Z jx X = = Yr X X = ( ) = Y X = = = e m (1) The real power out of each generator n the system s calculated as the real part of the product of generator termnal voltage and complex conjugate of the generator current: { } { } { } { } { } P = e E = e E e m E m (3) e g g g g g g The swng equaton descrbes the dynamcs of a generator. ts nput s a mechancal power from prme mover and whch s assumed constant. The output of a generator s an electrcal power, whch changes n accordance wth the state of the networ. The swng equaton s a second order dfferental equaton and ts soluton s the power angle of the generator. The power angle combnes wth generator nternal voltage to constantly update the generator termnal voltage and hence the generator current. Fgure 8 descrbes the contnuous cycle of power system core computaton. Combnng equaton 1 wth Fgure 6, we can show the mplementaton of complex current computaton as descrbed n Fgure 7. P m Swng Equaton δ Networ 1 Networ = VY r r = V r X = = X VY V X Networ 3 X = VY r = Vr X Networ 4 = = V VY r V V r V V r V V r j Fgure 7: Complex Current Computaton mplementaton Ths means that the real part of complex current flowng n any branch s gven by the sum of component currents n networs 1 and, and the magnary part as the dfference between component currents n networs 4 and 3, as descrbed n equaton. = j r r V = = where subscrpts r and represent real and magnary part, respectvely.,,, V represent the four DC networs. Step : Computaton of generator real power and swng equaton update r () cosδ snδ cosδ snδ E g E g E g E g e{y} Networ 1 m{y} Networ m{y} Networ 3 e{y} Networ 4 - e{ g } m{ g } Fgure 8: Generator eal Power Computaton Methodology Fgure 9 descrbes the dc-networ equvalent of a real power system bus and condtons for ts mplementaton. Analyzng a sample power system and consderng an arbtrary bus wth ts complex voltage values, we have V 4 networs wth 4 buses:,, and as equvalents. For feasble bus voltages, the followng condtons must be satsfed: V = V = V r V = V V = V t s then and only then that the current computaton methodology descrbed n secton 3 wll yeld accurate and feasble values. The feasble bus voltages condton s realzable wth a constant PQ-load model []. Among other attrbutes of an analog emulator that contrbute greatly to ts versatlty are the scale factors. Scale factors are constants that relate the values of the varables on the emulator to the values of the varables n the real system under study. The choce of proper scale X X P e (3) 15th PSCC, Lege, -6 August 005 Sesson 38, Paper 4, Page 4

5 factors s an mportant consderaton n obtanng satsfactory results []. Power System Bus V V jv = r DC Networ Approach Equvalent V Bus complex voltage ( V ) eal part of bus voltage ( V r ) magnary part of bus voltage ( V ) Complex power njecton nto the bus ( S) Complex power njecton out of the bus ( S) Fgure 9: Computatonally Feasble Bus Voltage 4 CASE STUDES AND ESULTS Cases studed whch nclude 3-bus, 6-bus and 14-bus lossy and lossless power systems were mplemented usng ABMs of PSpce. ABMs substtute real analog crcut mplementaton of the mathematcal equatons and scaled relatonshp that descrbe the states of the power system cases and emulate ther behavors. Power flow test were conducted on each of the cases. Smlar cases were tested on ndustral grade numercal smulaton software, PowerWorld v9.1 [1] and Power System Smulaton for Engneerng (PSS/E) v.8.1 [13], for benchmarng. For the valdaton process, the followng parameters were measured and/or calculated and compared wth the benchmars. δ Voltage angle dfference between generator. j1 buses j and 1 (j =, 3, );. Load bus complex voltage;. Current magntude flowng n each branch. Smulaton results obtaned from the analog emulaton engnes mplemented on ABMs of PSpce and that of the benchmars are presented n Tables 1 through 4. t must be mentoned that the followng lmtatons were encountered durng measurements (or computatons) of the benchmars parameters: The PowerWorld Smulator [1] computes only magntude of a branch current; The PSSE [13] provdes a bus voltage angle to one decmal place, and only the magntude of a branch current. From the Tables, we conclude that the emulaton results compares favorably. Ths confrms the valdty of the methodology as well as the technque of mplementaton. P (1 pu : 1 A) Q δ V (1 radan : 1 volt) V (1 A : 1 volt) Fgure 10: Varable epresentaton n Analog Emulator V Smulaton outputs of analog emulator were measured n rectangular form and/or radans. Conversons to polar representaton and/or degree were made for easy comparsons wth the benchmars. Also, for convenence and effcent analog emulaton mplementaton, certan power system varables and parameters were represented by other crcut varables. Fgure 10 summarzes varable representatons used n ths wor. Snce converson rato used between current-voltage or power-current s 1:1, obtaned values reman representatve n quantty. Table 1: Summary esults for 3-bus Power System (lossless system) (δ 1 ) n degree 0.94º 0.9º 0.94º Load Bus (V3) Voltage º º º Current n Branch _ (, A) Current n Branch 1_ (, A) Current n Branch _ (, A) Table : Summary esults for 3-bus Power System (lossy system) (δ 1 ) n degree 0.65º 0.6º 0.65º Load Bus (V3) Voltage º º º Current n Branch _ (,A) Current n Branch 1_ (,A) Current n Branch _ (,A) Table 3: Summary esults for 6-Bus Power System (Lossy System) -.10º (δ 1 ) n degree -.10º -.10º -.71º (δ 31 ) n degree -.7º -.71º Load Bus (V4) º º º Load Bus (V5) º º º Load Bus (V6) º º º Current n Branch 1_ (, A) Current n Branch 1_ (, A) Current n Branch _ (, A) Current n Branch _ (, A) Current n Branch 3_ (, A) th PSCC, Lege, -6 August 005 Sesson 38, Paper 4, Page 5

6 Table 4: Summary esults for 14-Bus Power System (Lossless) (δ 1 ) n degree -1.08º -1.1º -1.08º (δ 31 ) n degree -0.75º -0.8º -0.75º (δ 61 ) n degree -8.09º -8.1º -8.09º (δ 81 ) n degree -7.30º -7.3º -7.30º Load Bus (V4) Voltage º º º Load Bus (V5) Voltage º º º Load Bus (V7) Voltage º º º Load Bus (V9) Voltage º º º Load Bus (V10) º º º Load Bus (V11) º º º Load Bus (V1) º º º Load Bus (V13) º º º Load Bus (V14) º º º Current n Branch 1_ (, A) Current n Branch _ (, A) Current n Branch 5_4 6.5 (, A) Current n Branch 4_ (, A) SUMMAY Analog Behavoral Models of PSpce smulaton software s a very effcent tool. Among advantages are that t gves opportunty to test drve deas, t ads n explorng the effects of modfcatons, and etc. However, t should be mentoned that ABMs and PSpce smulaton tool are n no way a substtute for real analog bloc or analog emulaton engne. These tools are free of nose, crosstal or nterference. For real analog mplementaton, ssues le component varatons, stray conductve paths, and others have to be dealt wth. Technology has naturally been an mportant factor n the development of power system computaton tools. The mplementatons have gone through varous stages of development. Evoluton of mcroelectroncs and VLS technology whereby mllons of actve components can be placed on a chp on the order of 100 mm n area and 0.5 mm n thcness, now cause the resurgence of what was once consdered old technology analog computaton. Ths latest technology maes analog emulaton a vable canddate for qucer computaton of power system states and behavors consderng ts ntrnsc massvely parallel collectve processng capablty. ACKNOWLEDGMENT The authors would le to than the Department of Energy for the fnancal support under Grant No. CH EFEENCES [1] Capture CS verson 9..3, Cadence Desgn Systems, nc. [] M.B. Olaleye and C.O. Nwanpa, Analog Behavoral Models for the Purpose of Analog Emulaton of Large Scale Power Systems, The Proceedngs of the 36th North Amercan Power Symposum (NAPS), pp , August 004. [3] B. Glbert, A monolthc Mcrosystem for Analog Synthess of Trgonometrc Functons and Ther nverses, EEE Journal of Sold State Crcuts, Vol. SC-17, No. 6, pp , December 198. [4] P.C. Krause, T.A. Lpo and D.P. Carroll, Applcatons of Analog and Hybrd Computaton n Electrc Power System Analyss, Proceedngs of the EEE, Vol. 6, No. 7, July [5] P.G. McLaren, P. Forsyth, A. Pers and P.. Bshop, New Smulaton Tools for Power Systems, Transmsson and Dstrbuton Conference and Exposton, 001. EEE/PES, vol. 1, 8, pp , Oct- Nov, 001. [6] A. Greenwood, Electrcal Transents n Power Systems. nd Edton, John Wley & Sons, nc., New Yor, 1991 [7] G.A. Korn and T.M. Korn, Electronc Analogue Computers (D-C Analogue Computers), McGraw- Hll, New Yor, nd edton, [8] M. Hraam and W. Neugebauer, Transent Networ Analyzer Operaton wth Dgtal Computer Control and Analyss, EEE Transactons on Power Apparatus and Systems, Vol. PAS-100, No. 4, Aprl [9] M. Crow, Computatonal Methods for Electrc Power Systems. CC Press, 003. [10]. W. Newcomb and J.D. Lohn, Analog VLS for Neural Networs n Handboo of Bran Theory and Neural Networs, M. Arbb Ed., Bradford Boos, MT Press, [11]. Fred,.S. Cheraou, C.C. Enz, A. Germond, and E.A. Vttoz, Approaches for Analog VLS Smulaton of the Transent Stablty of Large Power Networs, EEE Transactons on Crcuts and Systems-: Fundamental Theory and Applcatons, Vol. 46, No.10, pp , October [1] PowerWorld Smulator v.9.1, PowerWorld Corporaton, Champagn L. [13] Power System Smulator for Engneerng (PSS/E) , Power Technologes, nc. 15th PSCC, Lege, -6 August 005 Sesson 38, Paper 4, Page 6