Design of a New Under Frequency Load Shedding Algorithm Using EMD and FSD Methods

Transcription

1 Desgn of a ew Under Frequency Load Sheddng Algorthm Usng EMD and FSD Methods J. Sadeh,*, A. Sohel 2, E. Afshar 3 Department of Electrcal Engneerng, Faculty of Engneerng, Ferdows Unversty of Mashhad Mashhad, Iran sadeh@um.ac.r, 2 soheladel@stu.um.ac.r, 3 ehsan.afshar@ut.ac.r Abstract In ths paper a new under frequency load sheddng algorthm s ntroduced and smulated on the IEEE 39-Bus test system. Usng multple load estmators and arrangng busbar technques reduces the probablty of over or under sheddng durng the process. Selectng the optmum place for load sheddng can have an mpact on the frequency at steady state. The man advantages and dsadvantages of conventonal, new schemes and the proposed algorthm have also been dscussed throughout the paper. Keywords-Underfrequency load sheddng, estmate magntude of dsturbance (EMD), frequency seconds deravtve (FSD), load sheddng I. ITRODUCTIO Early power grds were bult at small levels, dstrbuted and n close range to each other. Therefore mantanng and controllng of them was smple. Over the years as the demand for sutable electrc energy ncreased power grds became larger, nterconnected and more complex than ever, requrng complcated controllng and protecton systems to mantan the stablty of the power grd. As the dependency to a relable power source ncreases the goal to operate the power grd under secure condtons becomes more and more concernng. owadays power grds are forced to operate at ever smaller reserve capacty and stablty margns []. A wde range of protecton schemes have been mplemented to reach and hold ths goal. One of these schemes whch are lsted as the last resort of the power system s known as Under Frequency Load Sheddng (UFLS) [2]. UFLS s a procedure to prevent frequency drops facng a dangerous mbalance n generaton and load due to a cascadng fault n the power system or large generator trp [3]. The man goal can be descrbed as gradually dsconnectng pre-defned amounts of load (n early schemes) to make up for the mbalance created by the lack of generaton. Several dfferent under frequency load sheddng methods have been demonstrated n [4-8]. In most cases the mbalance s determned by solvng the generator swng equaton usng dfferent nonlnear mathematcal methods [9-]. In other cases extra parameters such as rate of change of frequency and voltage have proven to play a very mportant role n defnng the optmal amount and place for dsconnectng loads [2-3]. Also n [4] the predcton of mnmum frequency usng frequency second dervatve (FSD) has shown to play a role n estmatng the magntude of total mbalance and also determnng the amount of load to be shed from the power system. However, n ths procedure a mathematcal approxmaton method s requred whch n ths paper a new Radal Bass Functon (RBF) nterpolaton method s ntroduced and mplemented thorough out the algorthm to precsely predct the mnmum frequency reached. *Correspondng Author /4/$ IEEE Conventonal load sheddng algorthms used parameters such as frequency and loadng factor (L) to determne sutable amount of load to be shed [5-6]. In [7] a load sheddng method s ntroduced usng Estmatng Magntude of Dsturbance (EMD) as load estmator and the voltage stablty VQ margn as the arrangng parameter.in some of the lteratures the lowest economc loss and socal mpact has been selected as the prortzaton method for arrangng busbars [8]. Implementaton of ths method would requre a wde study n dfferent loads n the regon and ther economc loss due to sudden sheddng. The presented algorthm n [9] has focused on the mnmum frequency threshold and number of steps requred for optmum load sheddng. The regresson tree s a new method ntroduced n [20] whch the mnmum frequency s predcted after a generaton outage to calculate the necessary load sheddng amount. In another approach, the Kalman flter s used [2] to estmate the frequency and ts rate of change usng voltage samples of the power grd. Also, n an approach whch s presented n [22], a new load sheddng scheme s ntroduced by consderng the load frequency characterstcs. Moreover, under frequency load sheddng methods have been demonstrated wth self-healng capabltes n [23]. Ths algorthm has been tested on a 79-bus test system wth 20 generaton machnes, whch actvates after a sudden lack of generaton and dvdes the power grd nto some small controllable slands and snce these slands have a much smaller nerta constant revvng system frequency wll be much easer. Several solutons have been ntroduced to the dsturbance estmator problems usng artfcal neural networks [24], fuzzy logc [25] and genetc algorthm [26]. The desgn of a UFLS scheme begns by answerng the questons of how much?, where?, when? and s t enough?. The man goal of ths paper s to ntroduce a new under frequency load sheddng algorthm combnng the effectveness of prevous schemes and elmnatng ther man dsadvantages. The proposed scheme uses multple mbalance estmaton and busbar arrangng methods, whch each estmaton technque s actvated dependng on the fault nfluence over the power system frequency. Determnng the ntaton frequency and selectng the optmum busbar poston for dsconnectng loads have been tested and compared through several fault condtons. The fnal program was smulated and tested through the IEEE ewengland 39-Bus system usng DIgSILET Power factory and MATLAB as data acquston and processng unts. The rest of paper s organzed as follows. In Secton II the defnton and characterstcs of specal protecton schemes (SPS) followed by the man requrements for communcatons and UFLS programng s dscussed. The UFLS scheme s proposed n Secton III by descrbng the man estmatng and arrangng methods. Specfcaton and features of IEEE ew England 39-Bus s defned n Secton IV. Smulaton results contanng the comparson of load sheddng amount based on

2 frequency ntaton and busbar arrangng method are presented n Secton V and fnally the concluson s presented n Secton VI. II. SPECIAL PROTECTIO SCHEMES (SPS) System protecton schemes are a wde range of protecton strateges desgned and mplemented to detect uncommon and rregular condtons, causng unusual stress to the power system [7]. The most common protecton schemes used are under voltage and under frequency load sheddngs. Prelmnary work on the load sheddng scheme started n 950 s [6]. Followng the 965 ortheast blackout, applcaton of under frequency load sheddng became accepted utlty practce. As power systems have matured, however, voltage problems are often lkeler than slandng wth a large generaton-load mbalance [27]. Under voltage load sheddng s a partal soluton to voltage stablty challenges analogous to the use of under frequency load sheddng n other crcumstances. Typcally, load sheddng protects the power system aganst excessve frequency or voltage declne by attemptng to balance real and reactve power supply and demand n the system. Common dsturbances that can cause ths condton to occur nclude faults, loss of generaton, swtchng errors, lghtnng strkes, etc [28]. There has been three approaches to the load sheddng algorthms, namely; Tradtonal, Semadaptve and Adaptve Under Frequency Load Sheddng. The system frequency s the only parameter used n the Tradtonal Load Sheddng schemes. After the frequency drops to a certan amount, a predefned amount of load wll be dsconnected through several steps from the power system. Prelmnary and fnal steps usually nclude smaller portons of loads to be shed. Even though the mplementatons of these schemes were farly smple but the possblty to shed nsuffcent or excessve load s very hgh and ths s consdered as the man dsadvantage. Sem-adaptve schemes on the other hand, take the frequences rate of change nto account to shed an amount of load adequate to the dsturbance sgnfcance. Although ths approach helps to dstngush between small and large dsturbances but the man dsadvantage of over or under sheddng makes t unsutable n most cases. Adaptve load sheddng s the most complete algorthm among other desgns. Ths scheme uses the frequency and ts rate of change not only to determne the magntude of dsturbance but also to determne the optmum place for sheddng ths overload, elmnatng any chance of over or under sheddng n case of system dsturbances. The man dsadvantages of ths algorthm were the complexty of mplementaton and the lack of hgh speed communcaton networks. Specal Protecton Schemes (SPS) can also be categorzed under Response-based/Event-based or Centralzed/Local schemes [29-30]. In response-based schemes, response of the system to dsturbances s used to make decsons. Input sgnal of the system may be voltage, frequency, etc. However, n event-based protecton schemes decson s based on the state of specfc elements n the system such as mportant transmsson lnes or generators whch s transmtted to control center va a communcaton lnk [7]. III. DESIG OF A EW UFLS ALGORITHM As mentoned n prevous sectons the under frequency load sheddng scheme s the systems fnal getaway plan or n other words, the last resort aganst cascadng faults resultng n power system blackouts n scenaros whch a large porton of generaton s lost due to generator trp or dsconnecton of transmsson lnes. The frequency wll drop dangerously f the reserve power or other protecton schemes fal to mantan power system stablty. The declne n frequency depends on varous parameters, such as system nerta, fault duraton, magntude of dsturbance, and poston on the grd. The proposed method n ths paper uses two dsturbance estmators known as Estmaton of Magntude of Dsturbance (EMD) and Frequency Second Dervatve (FSD), three arrangng busbar methods and a smple relaton to dvde the mbalance calculated by the estmators between the busbars selected wth hgher prorty. As such the man parts of the algorthm can be explaned n the followng subsectons: A. Estmatng Magntude of Dsturbance (EMD) For faults or dsturbances relatvely small compared to total generaton, the proposed scheme uses the EMD method whch s based on the generator swng equaton. Equaton () shows the lnearzed form of ths equaton for the th Generator: 2H df pm p e p dst f dt = = =, 2,3,..., () n where pm represents the mechancal power nput by the turbne n pu, pe s the electrc power usage output n pu, p the total mbalance n pu, H s the nerta constant of the dst th generator n seconds, f s the frequency and f n s the rated value n Hz. By summng () for the overall generators the followng expresson for the total mbalance between generaton and load forms: 2 H = df c df c Pdst = pdst = = α (2) = fn dt dt Snce the frequency of equvalent nerta center, f c and constant α can be calculated n advanced they can be treated as known parameters of the equaton. They are defned as below: fc = H f H (3) = = and α = 2 H f (4) = n A negatve value of df /dt wll mply that the electrc power usage seen from the machnes pont of vew s greater than the mechancal power nput of the turbne. In other words an overload wll occur, resultng n the reducton of system frequency. Because of the turbne, generator and other control elements of system dynamcs, the presented statements are only vald momentarly after fault occurrence [3]. B. Frequency Second Dervatve (FSD) Accordng to gathered data from past blackouts, small faults can lead to cascadng events dsconnectng a large amount of generaton from load. Snce the response of power system frequency s manly unknown, the proposed algorthm uses the frequency second dervatve to predct the total mbalance throughout the grd. Fg. shows the possble dfferent mpacts of dsturbances on the frequency and ts frst and second dervatve.

3 It can be seen that the power system response through the frequency and ts rate of change are hghly unpredctable. On the other hand the frequency second dervatve shows promsng results. Snce the overall behavor of ths parameter does not change sgnfcantly, t can be used as bass to predct the mnmum frequency reached.the man goal of ths method s based on fndng a sutable mathematcal expresson descrbng the frequency second dervatve response. By calculatng ths equaton and usng numerc ntegraton, the mnmum frequency can be estmated.in ths paper a new RBF fttng method s used to estmate the overall characterstcs of the frequency second dervatve. The followng equaton shows the general form of ths equaton: M fˆ( x ) = α jφ ( x x j ) (5) f ˆ( x) j= represents the selected functon for estmatng the frequency second dervatve.also, φ( x) s known as the base functon whch can be dfferent dependng on the data set avalable, α j s a numercal constant, x j s the j th data and the dstance between x and x j through space or surface s shown by x x j. The frequency second dervatve form Fg. can be descrbed as an exponental behavor throughout the data set. Therefore, the Gaussan base functon s used for the purpose of ths paper. After calculatng the estmated functon and usng numerc ntegraton the mathematcal representaton for system frequency wll form. Fndng the mnmum of ths functon wll show the lowest frequency predcted to reach. By expandng (5) and usng the second dervatve data gathered from dfferent buses we have: φ( x x ) φ( x x ) φ( x x ) α f ( x ) 2 M φ( x x ) φ( x x ) φ( x x ) α ) f ( x M 2 2 = φ( x x ) φ( x x ) φ( x x ) α f ( x ) 2 M M M M M M The element of the th row and j th column represents the value of the Gaussan expresson at x x j. It can be seen that the coeffcent matrx s dagonally symmetrc, thus usng ths method wll ncrease calculaton speed due to the transform of the equatons to smple lnear systems. A smple relaton between the mnmum frequency estmated and the total load to be shed from the power system must form. A lnear curve s selected over other possble curves, whereas t has been shown that dfferent slopes do not much affect the total load-sheddng amount [4]. Fg. 2 shows the total amount of load to be shed n respect to the mnmum frequency calculated usng FSD for a 60Hz system. After determnng the amount of load to be shed ether wth EMD or FSD, the queston of where s the optmum poston to dsconnect ths load? comes to mnd. In the proposed algorthm three arrangng busbar methods are ntroduced and programed. The busbars are arranged usng. df/dt and dv/dt, 2. Magntude of V and df/dt and 3. Electrc dstance:. In the frst approach the program sorts the busbars n two separate sngle column matrxes usng ther rate of change n frequency and voltage, therefore the busbars wth hgher senstvty wll be ranked hgher. A hgh change of rate would mply that the fault has a hgher (6) Sheddng Amount [% total system load] mpact on the selected busbar. The program then adds the poston of busbars from each matrx. The busbar wth the lowest sum wll represent the hghest senstvty to frequency and voltage among others. 2. To arrange the busbars usng ther voltage magntude and rate of change n frequency the program dvdes the busbars n separate matrxes wth voltage ranges of ( ), ( ), (0.95-) and greater than pu. Afterwards the busbars are sorted by df/dt n each matrx separately. The fnal arrangement wll be created by attachng each matrx to the begnnng of the next range startng from the lowest voltage. Snce motorzed loads wll stall under voltage magntude of 0.8 pu, they have the hghest prorty. 3. Electrc dstance s the thrd crtera for arrangng busbars. Ths method uses the Z bus matrx as the bass of calculatng and defnng busbars nearest to fault. Frst the algorthm removes busbars wth no loads or loads marked as vtal; afterwards the remanng busbars are sorted accordng to the Z bus matrx. The closer the load or busbar s to the fault, the hgher the senstvty of that busbar wll be Fg.. Impact of dsturbance on frequency and ts frst and second dervatve Sheddng Area Load Sheddng Amount Usng FSD Safe Area Mnmum Frequency Value Forcast [Hz] Fg.2. Determnng total sheddng amount from mnmum frequency estmaton Dependng on the amount of mbalance estmated n the prevous secton, the number of selected busbars vares to carry of the load sheddng process. Table I shows the proposed selecton of busbars by ths algorthm: Table I. umber of busbar selected n dfferent dsturbance estmatons

4 Estmated Dsturbance umber of Busbars Selected Lower than 60MW 60MW 300MW 3 300MW 600MW 5 Hgher than 600MW 7 After determnng the mbalance throughout the grd and the optmum poston to shed ths load from, a relaton must be formed to determne each of the hgh ranked busbars share. In ths algorthm, equaton (7) s assgned for carryng out ths goal: dp ( ) V dv (7) P = p dst dp (( ) V ) dv = In whch dp s defned as dv dp = VY j cos( δ δ j θj ) dv (8) where δ and δ are the voltage angles of busses and j, Y j j s the admttance magntude for the connectng lne between the and j busbars and θ s the respected angle. p j dst represents the load mbalance calculated n each cycle of the program (f more than one cycle s requred) and P s the amount of load assgned to be shed from the th busbar selected from the arranged matrx. C. Proposed Method Flowchart The majorty of the process s dscussed n ths secton. Snce mentoned before an UFLS algorthm should be complete and consder as much scenaros as possble. A complete cycle of the proposed algorthm s shown n Fg. 3.As shown, by montorng the frequency (f) and the rate of change of frequency (df/dt), the scheme actvates when the frequency exceeds ether one of thresholds of f th or f th2. If frequency ncreases a certan level a sgnal of over generaton wll be send to control turbne nput power, n other cases when frequency drops below f th2 (frequency ntaton), t would ndcate that the spnnng reserve and other controllng schemes faled to control the generaton outage and the UFLS procedure begns. After consderng the rate of change of frequency at fault tme, the program wll decde f whether Method I or Method II s necessary for estmatng the total mbalance n the power grd. The mportance of consderng motorzed and vtal loads can be seen n both estmaton methods. In the proposed scheme shown n Fg. 3, f the frequency rate of change remans negatve after sheddng loads from ether methods, the algorthm wll send a sgnal to begn slandng procedure to break the grd nto smaller and more controllable systems. In each sland dependng on them beng ether Generaton Rch or Load Rch, approprate actons wll take place. Snce the majorty and behavor of frequency after slandng s unknown, the proposed method for UFLS n each sland s FSD. Fg. 3. Flowchart of the proposed UFLS algorthm IV. IEEE 39-BUS EW EGLAD The IEEE 39-Bus ew England System was frst ntroduced by Prof. Gerry Heydt from Perdue Unversty [32]. It shows the structure of the 960 ew England power grd, whch only contans dstrbuton voltage level. The man property of ths system s the avalablty of the generator dynamc nformaton. Snce the generators are the key elements n all dynamc studes, the complexty of the dynamc study s determned by the number of generators. Ths test power system conssts of 0 synchronous machnes, 6250 MW actve power and 390MVar reactve power usage, 46 transmsson lnes, 2 transformers whch 0 of them are Generator Step-Up (GSU) transformers. Fg. 4 shows the sngle lne dagram of the ew England 39-Bus power system. V. SIMULATIO RESULTS Smulatons on dfferent scenaros have been done on the 39-Bus ew England power system. In ths secton we examne and compare the man aspects and advantages of the proposed method. Three scenaros have been selected as follow:

5 Loss of G0 (250 MW) Loss of G06 (650 MW) Cascadng effect of losng G07 and G02 (230 MW The followng parameters are analyzed throughout the smulaton:. Frequency ntaton mpact on calculatng the total mbalance 2. Accuracy of the FSD method usng RBF fttng 3. Impact of dfferent arrangng methods on the steady state frequency 59.5 Hz, but the frequency wll stll reman under the threshold value. After a small delay for gatherng new data the program wll dsconnect a second amount of load to meet wth the stablty condtons. C. Cascadng effect of losng G07 and 02 After the dsconnecton of Generator o. 02, Generator o. 07 wll face an overload and wll trp shortly after. By losng these two generators 9.68% of total generatons are dsconnected. The mbalance estmator shows a load sheddng of 584 MW n frst and 88 MW n second steps. Table III. Comparson of dfferent frequency ntatons on total load sheddng estmaton Intaton Executon Steps Arrangng Frequency Frst Second Method I 57.5 Hz 239. MW - (df/dt and 58.5 Hz MW - dv/dt) 59.5 Hz MW - Arrangng Method II (df/dt and v ) Intaton Executon Steps Frequency Frst Second 57.5 Hz 239. MW Hz MW Hz MW 60 MW Fg.4. IEEE 39-Bus ew England test system [33] A. Loss of G0 (250MW) By losng G0 ether to generator trp or dsconnecton on the outgong feeders, 4% of total actve power wll be lost. After the frequency drops below 57.5 Hz the mbalance estmaton procedure starts. Snce the dsturbance does not create a large df/dt, the algorthm automatcally selects the EMD method to calculate the total mbalance. Table II shows the result for runnng the EMD method: Table II. Smulaton results for generaton outage of 250MW Arrangng Crtera Load to be shed Selected bus o. df/dt and dv/dt 39. MW o. 25 v and df/dt 39. MW o. Even though the smulaton has been done for the arrangements by electrc dstances, the results were mostly not converged, because the test system does not have enough lne connectons to ncrease the probablty of havng multple dsconnecton busbar optons at fault presence usng ths method. Electrc dstance can prove to be sutable for large and hghly ntertwned systems. Fg.5 shows the mpact of the generator outage and the response after dsconnectng the estmated load to be shed. By actvatng the FSD method manually and processng the gathered data, the mnmum frequency estmated wll result n Hz whch compared to the actual mnmum frequency (59.47 Hz) from Fg. 5 shows promsng results. B. Loss of G06 (650MW) By dsconnectng generator o. 06, 0.4% of total system generaton s lost. Table III shows the total amount of load mbalance n respect to the frequency ntaton.as seen from the table, the hgher the frequency ntaton s selected the more sgnfcant the rate of change n frequency would be and therefore the program would requre sheddng more loads to mantan the stablty of the power grd. Fg. 6 shows the result of mplementng the estmated mbalance.even though a large porton of load s beng shed for the frequency ntaton of Frequency[Hz] Frequency[Hz] Frequency[Hz] Arrangng Method I Arrangng Method II o Load Sheddng Tme[s] Fg. 5. Frequency response of power system to the lack of generaton of 250MW and frequency ntaton of 59.5 Hz Hz 58.5 Hz 59.5 Hz Tme[s] Fg.6. Comparng frequency responses due to 650MW generaton outage n dfferent frequency ntatons Arrangng Method I Arrangng Method II Tme[s] Fg.7. Comparng frequency steady state by usng dfferent arrangng busbar methods Fg.7 shows the frequency response of the power grd to the dsconnecton of 772 MW load usng two dfferent arrangng methods. Even though n both condtons the amount of load

6 shed was the same, the steady state frequency s dfferent. Choosng the rate of change n frequency and voltage has proven to show a better effect. VI. COCLUSIO In ths paper a new adaptve Under Frequency Load Sheddng scheme has been ntroduced for protecton aganst cascadng and catastrophc faults usng two mbalance estmators (EMD & FSD) and three arrangng busbar methods. Each method s actvated automatcally dependng on the mpact of dsturbance over the system frequency (df/dt). The fnal program was tested offlne on the IEEE ew England system, comparng the results n three dfferent scenaros. The effects of dfferent ntaton frequences have been dscussed and judgng by the results, 57.5 Hz would ndcate the optmum frequency to begn UFLS procedure snce t would requre much less load to be shed and create a sutable tme delay for the algorthm to gather and process data. Usng two dsturbance estmators (EMD and FSD) reduces the probablty of over or under sheddng of loads. 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