Optimal Allocation of Wind Turbines by Considering Transmission Security Constraints and Power System Stability

Transcription

1 Energes 2013, 6, ; do: /en Artcle OPE ACCESS energes ISS Optmal Allocaton of Wnd Turbnes by Consderng Transmsson Securty Constrants and Power System Stablty Clauda Rahmann 1, * and Rodrgo Palma-Behnke Department of Electrcal Engneerng, Faculty of Mathematcal and Physcal Scences, School of Engneerng, Unversty of Chle, Santago , Chle Center of Energy, Faculty of Mathematcal and Physcal Scences, School of Engneerng, Unversty of Chle (CMM, ISCI, DIE), Santago , Chle; E-Mal: rodpalma@cec.uchle.cl * Author to whom correspondence should be addressed; E-Mal: crahmann@ng.uchle.cl; Tel.: Receved: 10 September 2012; n revsed form: 27 December 2012 / Accepted: 27 December 2012 / Publshed: 14 January 2013 Abstract: A novel optmzaton methodology consstng of fndng the near optmal locaton of wnd turbnes (WTs) on a planned transmsson network n a secure and cost-effectve way s presented on ths paper. Whle mnmzng the nvestment costs of WTs, the algorthm allocates the turbnes so that a desred wnd power energy-penetraton level s reached. The optmzaton consders both transmsson securty and power system stablty constrants. The results of the optmzaton provde regulators wth a support nstrument to gve proper sgnals to WT nvestors, n order to acheve secure and cost effectve wnd power network ntegraton. The proposal s especally amed at countres n the ntal stage of wnd power development, where the WT network ntegraton process can stll be nfluenced by polcy-makers. The proposed methodology s valdated wth a real power system. Obtaned results are compared wth those generated from a busness-as-usual (BAU) scenaro, n whch the WT network allocaton s made accordng to exstng WT proects. The proposed WT network allocaton scheme not only reduces the total nvestment costs assocated wth a determned wnd power energy target, but also mproves power system stablty. Keywords: wnd power; wnd turbne; dynamc response; network plannng; system stablty

2 Energes 2013, Introducton Several countres, all over the World, have declared ambtous energy targets regardng renewable energy penetraton levels to be acheved n the comng years [1,2]. Ths stuaton, together wth favorable condtons for wnd turbne (WT) proects; such as economc subsdes, maturty of the technology, and descendng nvestment costs; wll probably lead to wnd power playng an ncreasng role n electrc power systems of the future [3]. evertheless, an energy target tself does not ensure proper operaton of the system or the optmal use of ts capactes. Internatonal experence has shown that ncreasng use of wnd energy can lead to varous problems n power system securty, both n normal operaton as well as n the case of dsturbances [3 5] usually resultng n addtonal costs. Durng normal operaton, the problems are often related to shortage of transmsson capactes, sometmes even endangerng the accomplshment of the (n 1) securty crteron. Ths stuaton can be found n weak transmsson areas usually at the perphery of the network wth attractve wnd resources, but not enough transmsson capactes to transport the generated energy to dstant load centers [6,7]. As long as the expanson plannng for electrc power systems does not explctly consder the development of renewable energes, these transmsson capacty problems wll contnue to arse durng the next few years. On the other hand, stablty problems are closely related to the relatvely weak dynamc performance of WTs compared to conventonal power plants, arsng as a consequence of dfferent network connecton concepts for WTs, lke the use of nducton generators or power electronc converters [8]. Fault rde-through (FRT) capablty and voltage stablty support are key ssues assocated wth WT dynamcs affectng power system stablty performance. Two dfferent stuatons can arse as a consequence of ncreased use of wnd power: 1. eed for grd renforcements, such as transmsson developments or addtonal equpment to mprove system stablty n order to counteract the negatve effects of WT nectons on the system. 2. Delays or reectons n new WT proects due to poor dynamc performance n case of dsturbances or nsuffcent network capactes at the connecton pont. In both cases addtonal costs are nvolved: n the frst nstance, the addtonal costs are assumed by the power system tself through the grd renforcements. In the second case, the whole socety loses through the hamperng of further wnd power network ntegraton. A key element for wnd power network ntegraton s the optmal explotaton of power system capactes by consderng ts securty constrants. By dong ths, possble addtonal grd renforcement costs generated by WT proects can be avoded, and wnd energy goals can be accomplshed n a secure and cost-effectve way. The subect optmal network allocaton of WT corresponds to a relatvely new subect reported n only a few research contrbutons n the lterature untl now [7,9 11]. In all these references, a methodology for optmal allocaton of wnd capactes usng a lnear programmng approach s presented. evertheless, these nvestgatons consder only statc securty constrants related to transmsson capactes wthout ncludng power system stablty whch s a key ssue affected by hgh penetraton levels of wnd power.

3 Energes 2013, Ths work presents an optmzaton methodology to fnd the near optmal locaton of WTs on a planned transmsson network n a secure and cost-effectve way. The algorthm allocates the turbnes so that a desred wnd power energy-penetraton level s reached whle mnmzng the WT nvestment costs. The man contrbuton s to propose an optmzaton algorthm able to combne both transmsson securty and power system stablty constrants. The proposal s especally amed at countres n the frst stage of wnd power development, where the WT network ntegraton process can stll be nfluenced by polcy makers, and where the expanson plannng for the power system stll does not ncorporate the development of renewable energes. Ths s the case, for nstance, n several Latn Amercan countres, where such a methodology could be of prme mportance to ensure a cost-effectve development of wnd power n the comng years. evertheless, t s mportant to note that makng the best choce for the WT network allocaton s relevant for every power system. Ths paper s organzed as follows: n Secton 2 the methodologcal approach for optmal network allocaton of WTs s presented. The power system used to valdate the methodology s presented n detal n Secton 3. The results obtaned are gven n Secton 4. Fnally the pertnent conclusons are presented n Secton Methodologcal Approach for Optmal Allocaton of WTs n the etwork 2.1. Introducton The proposed methodology for optmally allocatng the WTs on a planned transmsson network s shown n Fgure 1. The optmzaton mnmzes the WT nvestment costs needed to reach a desred wnd energy-penetraton level. The optmzaton ncludes transmsson securty and power system stablty constrants. Dfferent WT technologes can be consdered by the methodology. Snce the optmzaton problem s carred out on a planned transmsson network, t could be possble to have a locaton wth favorable wnd condtons, but not enough transmsson capactes. In such a case, another locaton could be selected durng the optmzaton process, even f ts wnd potental s less attractve. In an extreme stuaton, f the total exstng system capactes are not suffcent to acheve the orgnal wnd energy target, less WT capacty wll be nstalled. The optmzaton process s dvded nto two man phases. In the frst stage, the algorthm allocates the turbnes by consderng only transmsson network securty constrants for a whole operatve year based on (n 1) securty crtera. The valdty of the obtaned soluton s verfed n a second phase n whch the stablty of the power system s tested. If the soluton s not feasble due to poor dynamc performance of the power system, the whole optmzaton process s run agan consderng addtonal system stablty constrants. The process runs teratvely untl all system securty restrctons (statc and dynamc) are fulflled Theory behnd the etwork Securty Constrants The transmsson network securty constrants consdered n ths work are based on (n 1) securty crtera. The constrants are calculated for each lne and transformer of the network at each hour of the year by consderng ts transmsson capacty lmt and ts hourly power flows. To do ths, a complete network model s used.

4 Energes 2013, Fgure 1. Methodologcal approach for WT network allocaton. Wnd data Load data etwork data Connecton ponts for WTs Intal soluton for WT allocaton Gx,Tx expanson plan Unt commtment Formulaton of (statc) securty constrants Power system stablty constrants Lnear optmzaton o WT dstrbuton equal to the soluton before? Yes o Iteratve process 1 Update of the wnd power nectons Dynamc analyss of crtcal contngences Stable? FRT requrements for WTs Optmal WT allocaton Iteratve process 2 The power flows of each element are determned based on the DC load flow [12]. The dea behnd ths s to use a lnear, non-teratve power flow algorthm, where the Jacoban matrx of the system does not need to be recalculated at each teraton. The smulaton tmes are then sgnfcantly reduced compared to the full nonlnear AC power flow algorthm, allowng the generaton of thousands of securty constrants for a whole operatve year. If a network wth nodes s consdered, the vector [P] contanng the power nectons at each node s gven by: P B (1) where s the phase angle vector and [B'] s the reduced Jacoban matrx whose elements are gven by: 1 xk B k 1 1 xk f f k k Addtonally, the power flowng between buses p and q (beng ether a lne or transformer), usng the DC power flow equatons, s: (2)

5 Energes 2013, pf pq p q (3) x pq If Equatons (1) and (3) are combned, the power flow between buses p and q can be rewrtten as: pf pq 1 Bp P B q 1 where P s the power necton at bus. The power flow of each element of the network s thus a lnear P 1 combnaton of the power nectons x pq 1 1 P. Equaton (4) can be wrtten n matrx form as follows: pf AP 2.3. Intal Soluton for WT Allocaton Unt Commtment (4) (5) The formulaton of the transmsson securty constrants based on Equaton (4) requres the hourly power nectons at each node of the network obtaned from a year-long unt commtment study. However, snce the WT network dstrbuton s not known before the optmzaton process s completed; an ntal soluton for the WT allocaton problem must be assumed. Based on ths, a representatve annual tme-seres contanng the total hourly wnd power nectons nto the system can be generated and used to carry out an ntal hourly unt commtment study for the entre year. The frst step of the methodology s therefore to determne an ntal soluton for the WT allocaton problem. To do ths, potental places for the nstallaton of the turbnes must be establshed. Snce the evaluaton of every possble connecton pont s not vable, the methodology only consders a lmted set of places n whch the wnd potental s especally hgh. Wth the set of connecton ponts for WTs, the wnd tme-seres at each of these locatons, and the load data of the system, an ntal soluton for the WT allocaton problem can be obtaned. The ntal soluton must satsfy the wnd power energy penetraton target gven by the equaton below: I T 1 1 C E E T (6) The defnton of the varables appearng n Equaton (6) s presented n Table Formulaton of (Statc) Securty Constrants Based on the unt commtment study and ts nput data, the transmsson network securty constrants can be formulated for each hour of the year. To do ths, Equaton (5) must be rewrtten n order to dstngush between power nectons of conventonal power plants or loads and wnd power: pf AP AP I WT The frst term on the rght sde of Equaton (7) ncludes the power nectons of conventonal power plants and loads (P), whle the second one ncludes only the wnd power nectons (P WT ). Snce the nectons of conventonal power plants are known from the hourly unt commtment study, and the load profle at each network bus s assumed to be avalable n the nput data, both contrbutons to the II (7)

6 Energes 2013, power flows n the network [term I of Equaton (7)] can be calculated easly by usng Equaton (4). However, the WT network dstrbuton s stll not known untl the optmzaton process s completed; therefore the wnd power contrbuton to power flows [term II of Equaton (7)] cannot be determned. The second term of Equaton (7) s used to formulate the transmsson network securty constrants to be consdered n the WT allocaton problem. The constrants are calculated for hourly power flows at each lne and transformer of the network. The wnd power necton at locaton and hour t 0 s gven by (see Table 1 for varables defnton): P WT t 0 T E 1 t 0 C (8) Consderng Equatons (7) and (8), the power flows of each element n the network at t 0 can be wrtten as: ~ pf t A P t At C (9) where C s a vector of dmenson 1 contanng the nstalled capacty of wnd power at each network bus. Each component of C assocated wth a network bus where non-wnd power nstallaton s consdered, s zero for every case. mn max If pf and pf are vectors contanng the mnmal and maxmal transmsson capacty of each element of the network, the general form of the transmsson securty constrants s gven by: mn ~ max pf A P t A C pf 0 t 0 ~ (10) R A C R 1 t0 t0 2 t0 In Equaton (10) t s assumed that transmsson lnes have the same transmsson capacty (gven by the worst case scenaro) throughout the year, and thus no dynamc ratng s consdered. The ncorporaton of a dynamc ratng model for transmsson lnes can be ncorporated easly nto the mn max optmzaton process by makng both vectors pf and pf of Equaton (10) tme-dependent Lnear Optmzaton The optmzaton mnmzes the WT nvestment costs n order to reach a desred wnd-energy penetraton level. The mnmzaton of the nvestment costs s ustfed snce no transmsson network renforcement or expansons are consdered n the optmzaton process; thus, the only pertnent costs to be ncluded are the nvestment costs of the WTs themselves. The WT nvestment cost must nclude nstallaton costs (ncludng transportaton, and land costs), nterconnecton costs to the transmsson system (connecton lnes, power statons), and other costs that could arse at each partcular place. If all relevant costs are consdered, the optmzaton process should reasonably reflect the trend to be followed by WT nvestors n a compettve envronment. Assumng that the nvestment cost of the WT technology at locaton s drectly proportonal to the nstalled capacty, the optmzaton problem can be formulated as follows: I T mn v C (11) 1 1

7 Energes 2013, I T 1 1 C E E T (12) ~ R1 t A t C R2 t (13) t 1, The defntons of the varables appearng prevously are gven n Table 1. It s mportant to note that economes of scale can also be ncluded n the optmzaton process by updatng the nvestment costs accordng to obtaned wnd farm szes. Table 1. Varables defnton. Varable I T v C E T E pf pf mn max Defnton umber of places for WT nstallaton umber of WT technologes consdered by the methodology Investment cost at locaton of the WT technology (USD/MW) Installed capacty at locaton of the WT technology (n MW) Tme-seres for 1 MW of the WT technology at locaton (vector of dmenson 8,760 1 n MWh) WT energy target (MWh) Vector contanng the mnmal transmsson capacty of each element of the network Vector contanng the maxmal transmsson capacty of each element of the network Equaton (12) represents the wnd power energy penetraton target over the whole year and Equaton (13) the transmsson securty constrants. If n L and n T are the number of lnes and transformers n the network, a total of 2 n L n T 8760 transmsson securty constrants s consdered n the optmzaton process. If these transmsson securty constrants were not ncluded, the optmzaton would allocate all WTs n that network area wth the hghest capacty factor. As can be seen from Equatons (11) (13), ths frst stage of the optmal WT network allocaton s a lnear optmzaton problem n whch the optmzaton varables are the WT capactes at each locaton. As wth any other lnear optmzaton problem, ths can be solved usng dfferent optmzaton technques Iteratve Process 1 As can be seen n Fgure 1, once a soluton for the WT network allocaton problem s obtaned, the methodology verfes f ths soluton s equal to that used n the unt commtment study n order to avod wnd power necton dscrepances. If both solutons dffer, an updated annual tme-seres contanng the total wnd power nectons (by consderng the current soluton of the WT allocaton problem) s generated and used to carry out a new year-long unt commtment study. Ths process runs teratvely untl the WT network allocaton used for the unt commtment study s the same as that obtaned by the lnear optmzaton; consequently, no power system mbalances emerge.

8 Energes 2013, Iteratve Process 2 The valdty of the soluton obtaned n the lnear optmzaton process s verfed n a second phase where the stablty of the power system s tested (Iteratve process 2). For ths dynamc study, stablty ssues are fully taken nto account; therefore, voltages at all system buses are determned based on AC load flow equatons. Dfferent nvestgatons have shown that among the stablty problems arsng as a consequence of the dynamc performance of WTs, those related to voltage stablty are of maor mportance when consderng power system securty [13,14]. Ths s especally true for WTs based on nducton generators, whose dynamc response to voltage dps s characterzed by sgnfcant reactve power consumpton [15]. Ths behavor can be found not only n fxed speed nducton generators, but also n varable speed WTs based on doubly fed nducton generators wth crowbar. Voltage stablty support provded by WTs s also a key ssue n ths context. Even n the case of modern WTs wth power electronc converters, ther capablty to support voltage stablty cannot be compared wth the tradtonal support provded by conventonal power plants. The man reason for ths s the need to lmt the n-feed current of the WTs durng dsturbances as a consequence of: (1) techncal margns of the electronc power devces and (2) need to preserve transent stablty of the wnd park [16]. By contrast, conventonal power plants are characterzed by a huge overloadng capacty for a relatvely wde tme wndow [17]. Consderng these ssues, the dynamc analyss of the power system put specal emphass on those components and mechansms of the system that contrbute to the characterzaton of the voltage stablty. evertheless, ths specal emphass on voltage stablty should not be understood as a reecton of other dynamc phenomena of the power system lke voltage collapse or transent nstabltes. In fact, the models used n the dynamc smulatons must be able to properly reflect all components and mechansms that contrbute to the characterzaton of all knd of nstabltes. As explaned n the followng, the focus on voltage stablty has only a drect effect on the selecton of the crtcal contngences and operatng ponts to smulate, but not n the dynamc models. Although the dynamc analyss of each hour of the year for all possble contngences would be desrable, the dynamc smulaton of all scenaros under these crcumstances would lead to a sgnfcant number of smulatons. Consderng that each dynamc smulaton s a hghly computatonally demandng task, system stablty of power systems s always tested only for a partcular set of contngences and operatng condtons (hours) of the year. By ths way, the amount of dynamc smulatons can be sgnfcantly reduced. The selecton of the system condtons to smulate must be based on a worst case scenaro crteron. The man dea s to fnd out the worst condtons that the power system could experence accordng to the obectves of the study. In ths context, and consderng that the focus of the present work s wth respect to mantanng voltage stablty, the selecton of the crtcal contngences (CC) and hours of the year s based on the followng consderatons: Selecton of hours of the year: To properly defne the most crtcal hours of the year, t s necessary to study a varety of load, wnd, and generaton patterns whch s done wth help of the unt commtment study. When the analyss s focused on voltage stablty, a usual operatng condton to smulate s the peak load of the system, n whch case the network can be consdered to be n a hghly stressed stuaton. Addtonally, n the present work, those hours of the year characterzed by maxmum wnd power necton are also consdered to be crtcal operatng

9 Energes 2013, ponts due to the consumpton of reactve power by the WTs under low voltage stuatons and the lmted number of conventonal power plants that would be operatng to support voltage stablty. Selecton of contngences: When selectng the contngences the same crteron s used,.e., the set of contngences s determned based on a worst case scenaro. A sound method to select the crtcal contngences must take nto account the needs of the study and the characterstcs of the power system tself. Dfferent approaches have been proposed n lterature for the determnaton of the CC [12]. In ths work, the selecton of the CC s focused on voltage stablty problems and therefore short crcuts at key network buses (from a voltage stablty vewpont) and lne outages are ncluded n the study. Short crcuts appled at the connecton pont of each wnd park are also consdered a worst case scenaro regardng voltage stablty due to the reactve power consumpton of WTs after the fault clearance Power System Stablty Constrants For each selected operatng pont (hours of the year), the selected contngences are smulated n order to verfy the dynamc performance of the power system. If one or more of these contngences leads to power system nstablty, the obtaned soluton for the WT allocaton problem s not feasble, and the lnear optmzaton must be completed agan by consderng addtonal power system stablty constrants (see Fgure 1). The addtonal constrants nclude lmtaton of WT nectons at those buses leadng to system nstablty. Two categores of stablty constrants are consdered: 1. Constrants regardng frequency stablty: Most up-to-date grd codes around the world defne Fault Rde-Through (FRT) requrements where the mmedate dsconnecton of WTs n case of voltage dps s no longer admtted [18,19]. These requrements nfluence the occurrence probablty of scenaros wth massve dsconnecton of WTs and therefore have a drect mpact on system frequency stablty. Although ths work put specal emphass on voltage stablty ssues, t s mportant to consder frequency stablty constrants f such scenaros want to be avoded. Thus the maxmum MW of wnd power that can be dsconnected at the same tme must be lmted. In ths work, ths s done by consderng the prmary power reserves (PPR) of the system. Consder C * as a soluton of the lnear optmzaton process (before the dynamc analyss). If contngency χ leads to a WT dsconnecton hgher than PPR, an addtonal system securty constrant s ncorporated nto the optmzaton process accordng to: k C k PPR where k denotes those network buses at whch the contngency χ leads to smultaneous dsconnecton of the WTs. 2. Constrants regardng voltage stablty: Dependng on the WT technology and the FRT requrements n force, mportant problems could arse wth the voltage stablty of the power system f reactve power reserves are not suffcent. Ths can become extremely mportant n cases of WTs based on nducton generators and demandng FRT requrements wth large (14)

10 Energes 2013, voltage dps to rde through. To ensure voltage stablty of the system, scenaros of hgh reactve power consumpton by WTs should be avoded. In ths context, f a contngency leads to a voltage nstablty stuaton, the WT nectons at those buses/locatons leadng to the nstablty are reduced untl no nstablty arses. Snce voltage stablty s a local phenomenon; the prevously mentoned approach can be easly ustfed. The addtonal constrant n ths case s smlar to Equaton (14). 3. Case Study The optmzaton methodology proposed n ths work s valdated through the man Chlean transmsson system (SIC) at year The valdaton s made based on the power system expanson plan establshed by the Chlean atonal Energy Commsson [20]. Although the system stll shows low penetraton levels of wnd power (200 MW representng less than 2% of the whole nstalled capacty), t s expected that wnd energy wll play an ncreasng role n the future power system of Chle. The numbers confrm ths hypothess: Untl December 2011, there had been approxmately 2,000 MW of WT proects for nterconnecton at the SIC and there are stll more under study [21]. The Chlean case s a good example of a transmsson network presentng several locatons wth notable capacty factors for WT proects, but wth mportant techncal constrants hamperng ts defntve network ntegraton. Transmsson system capacty constrants (especally n the northern part of the system where some of the best wnd resources of the country are concentrated), and voltage stablty problems due to the longtudnal structure of the system [22,23] are some of the crtcal problems to be consdered Chlean Central Interconnected System (SIC) The SIC s a medum-szed solated power system characterzed by long dstances between maor load centers and generaton areas. Long transmsson lnes are dstnctve of the system coverng a total length of 2,200 km. The voltages n the bulk network are from 110 kv to 500 kv wth nearly 750 buses. In order to llustrate the network structure, a smplfed dagram s shown n Fgure 2. The system s composed of hydroelectrc and thermal power statons. Hydroelectrc power plants are concentrated manly n the south of the country, comprsng about 50% of the whole nstalled capacty Developed Investgatons The optmzaton methodology to fnd the near optmal allocaton of WTs s appled to the man Chlean transmsson system at year For comparson purposes a BAU scenaro s consdered n whch the WT network dstrbuton s determned followng a portfolo of WT proects [21]; therefore no optmzaton for the WT network allocaton s realzed. The BAU scenaro s characterzed by an nstalled capacty of 1220 MW of WTs based on nducton generators coverng 6% of the total energy demand at year In order to compare the BAU scenaro wth the scenaro consdered by the optmzaton, the optmzaton methodology s appled at year 2015 by consderng a wnd energy target of 6%.

11 Energes 2013, Fgure 2. Schematc of the Chlean transmsson network kv 220 kv 154 kv 110 kv Hydroelectrc power plant Thermal power plant WT locaton Two possble WT technologes are consdered by the methodology: Fxed Speed Inducton Generators (FSIG), and Doubly Fed Inducton Generators (DFIG). Ths s ustfed snce no WT proect based on synchronous generators wth full converter has been offcally presented untl the present; hence, t can be assumed that the wnd power network ntegraton n Chle s gong to be characterzed n the md-term by connecton of WTs based on nducton generators. It s mportant to note, however, that although for the present case study only WTs wth nducton generators are consdered, the methodology allows consderng dfferent technologes as long as the pertnent power curve and dynamc model are avalable for the unt commtment and dynamc analyss respectvely. Fve network connecton ponts for WTs are consdered n the optmzaton process (see Fgure 2), all of them concdng wth connecton ponts of the WT proects n the BAU scenaro. Although some nterestng places n terms of wnd potental were detected n other areas, partcular factors of these locatons make the related WT proects not very attractve from an economc pont of vew, and were therefore dscarded. Table 2 shows the average capacty factor at each of these locatons by consderng 1 MW turbne of FSIG and DFIG. A set of 20 crtcal contngences was selected for the dynamc analyss of the power system ncludng three-phase short crcuts appled at the connecton pont of each wnd park. Due to the mportance of the FRT requrements for WTs n power system dynamc performance, the methodology s appled for two FRT requrements (see Fgure 3).

12 Energes 2013, Table 2. Varables defnton. Locaton Average capacty factor (%) Fgure 3. FRT requrements for WTs used n the optmzaton process. 100 Voltage U/U n % FRT 1 FRT Tme (ms) As explaned n Secton 2.8, f system stablty s threatened for a gven contngency, the soluton for the WT allocaton problem s not feasble, and the optmzaton s completed agan by consderng addtonal stablty constrants. Regardng the frequency stablty constrants, a prmary power reserve (PPR) of 200 MW was consdered n the smulatons. In ths context, t s mportant to note that: Low voltage stuatons lead to dsconnecton of wnd parks based on FSIGs. Wnd parks based on DFIGs are able to rde through grd faults and therefore no dsconnecton takes place n cases of dsturbances. In ths way, the nstalled capacty of wnd parks based on FSIGs wll be lmted accordng to the PPR n order to ensure frequency stablty Dynamc Model of WTs In the present subsecton only the man ssues regardng the WT models used n the dynamc smulatons are presented. More detals can be found n [23,24]. The WT model s comprsed of aerodynamc, mechancal, and electrcal models. A ptch angle control s mplemented to lmt the generator speed n normal operaton as well as n cases of dsturbances. An actuator dsc concept s taken nto account n the aerodynamc model under the assumpton of constant wnd velocty. The drve tran s approxmated by a two mass model (one mass to represent the turbne rotor nerta and the other representng the generator rotor nerta). Both masses are connected by a flexble low-speed shaft characterzed by stffness and dampng. As s usual n

13 Energes 2013, fundamental frequency smulatons, the generator dynamc s smplfed by neglectng stator transents (thrd order model). In the case of a WT based on DFIGs the use of power converters durng normal operaton enables the DFIGs to operate at optmal rotor speed thus maxmzng the power generaton. In case of voltage dps, hgh over-currents n the rotor and/or over-voltages at the DC lnk could damage the converters. Therefore, a protecton system s ncluded. A common protecton system s an external rotor mpedance known as a crowbar crcut. When a fault s detected, the protecton system acts by short-crcutng the generator rotor through the crowbar. Once the rotor sde converter s blocked, the DFIG wll operate lke a typcal nducton generator; meanng that the controllablty of actve and reactve power s lost. When the fault s cleared and the termnal voltage s recovered, the crowbar s dsconnected and the DFIG can resume normal operaton very quckly. 4. Obtaned Results 4.1. Optmal Allocaton of WTs Table 3 shows a summary of the results obtaned from the applcaton of the optmzaton methodology n the SIC by consderng a wnd power energy target of 6% and two FRT requrements (see Fgure 3). The data of the BAU scenaro s also shown n the table only for comparson purposes. Table 3. Summary of obtaned results. Installed capacty (MW) Investment cost Scenaro FRT requrement FSIG DFIG Total (Mll. Euros) FRT ,204 1,080 Wth optmzaton FRT ,242 1,062 BAU ,220 1,094 Results shown n Table 3 confrm that the use of the optmzaton methodology reduces the total costs assocated wth a determned energy target. Although the cost dfferences compared wth the BAU scenaro are not sgnfcant, the dfferences regardng dynamc system performance must be taken nto account (see next subsecton). In ths frst stage of the WT network allocaton process, the optmzaton deals wth the trade-off between nvestment costs and energy generated by each WT technology. Obtaned results ndcate that at ths stage the optmzaton gves prorty to network ntegraton of FSIGs. Therefore t can be concluded that for the present study, the hgher total annual energy of DFIGs (per nstalled MW) compared to FSIGs, does not compensate for ts hgher nvestment costs. However, ths stuaton cannot be generalzed snce t depends on energy prce, wnd potental, characterstcs of the WTs locaton, and the nvestment cost tself, leadng to the concluson that under dfferent condtons, the hgher nvestment costs of DFIGs could eventually be compensated by ts greater effcency. Table 3 also shows that the optmzaton methodology consderng FRT 1 nvolves hgher nvestment cost than when FRT 2 s consdered. Ths s because FRT 1 ntroduces more strngent requrements for WTs by forcng them to sustan operaton even f the voltage at the connecton pont decreases to zero. If large voltage dps must be rdden through, problems may arse by connectng low

14 Energes 2013, cost WT technologes lke FSIGs due to ther hgh reactve power consumpton under severe faults. The network ntegraton of FSIGs s thus lmted due to power system stablty constrants. Snce no addtonal nvestments n dynamc reactve power support devces are consdered, the wnd power energy target can only be acheved through network ntegraton of DFIGs; a more expensve WT technology. The Table 4 shows the WT network dstrbuton for each scenaro. As before, the WT dstrbuton n the case of the BAU scenaro s shown only for comparson purposes. As can be seen, hgh capacty factor locatons (grouped on buses 2, 3, and 5) are fully used by the optmzaton methodology to acheve the energy target whle lower capacty factor areas (connecton pont 4) are not used. The logc behnd the mnmzaton of the nvestment costs,.e., to use areas wth hgher capacty factors, s thus verfed n the methodology. Table 4. WT dstrbuton (MW). Connecton pont WT technology Scenaro Wth optmzaton BAU FRT 1 FRT 2 - FSIG DFIG FSIG DFIG FSIG DFIG FSIG DFIG FSIG DFIG Dynamc Analyss of the Power System A smplfed model of 250-busbars of the Chlean network was mplemented n the power system smulaton tool DIgSILET Power Factory [25] for dynamc analyss of the crtcal contngences. The model consders addtonal generaton capacty whch s expected to come onlne by 2015, as well as the decommssonng plan of conventonal power plants. The planned nstalled capacty s about 15 GW for an estmated peak load of 9 GW. The developed model ncludes 170 synchronous generators representng the conventonal power plants of the year 2015, and about 100 consumpton centers dstrbuted throughout the system. The smulatons are made by consderng a converter ratng for DFIGs of 30% of the generator capacty, whle the compensaton of FSIGs s made usng statc var compensators (SVC) rated at 40% of the wnd farm capacty. Usng the smplfed model of 250-busbars of the Chlean SIC, a dynamc analyss of the crtcal contngences was realzed. At ths stage of the optmzaton, new constrants may be mposed dependng on system performance n the dynamc analyss. In general, the dynamc smulatons lead to a reducton of the nstalled capacty of FSIGs due to voltage stablty problems n the power system. For nstance, Fgure 4

15 Energes 2013, shows the voltage of the wnd park connected at bus 1 when applyng a three-phase short crcut at t = 0.05 ms durng 150 ms. The fgure shows system response for each scenaro by consderng both FRT requrements presented n Fgure 3 (FRT1 and FRT2). It can be seen that unlke the BAU scenaro, n both cases n whch the optmzaton methodology s appled, no voltage nstablty appears. Ths s, however, an expected result snce the optmzaton process s realzed by consderng power system stablty constrants, meanng that no nstabltes should arse. Fgure 4. Voltage at connecton pont of the wnd park connected at bus 1. Voltage at bus U/Un [%] (%) BAU - FRT1 BAU - FRT2 Wth optmzaton - FRT1 Wth optmzaton - FRT Tme [s] (s) The fgure above shows that f FRT 1 s consdered n the BAU scenaro, the short crcut leads to large voltage oscllatons durng the frst seconds after the fault clearance. Ths s caused by torsonal oscllatons of the shaft, a typcal characterstc of FSIGs durng large dsturbances. Snce no decouplng between WT and electrcal network exsts, these oscllatons are drectly reflected n the system. After ths transent perod has ded down, the voltage s no longer controlled and the system becomes unstable (ths s clear when observng the progressve and uncontrollable declne n voltage). The power system s, thus, not able to mantan stablty n the BAU scenaro f WTs must sustan operaton when the voltage at the connecton pont decreases to zero. Consderng ths dynamc performance, addtonal equpment to mprove power system stablty would be needed n order to counteract the negatve effects of the WT nectons. As a consequence, f the BAU scenaro wth FRT 1 takes place, addtonal costs for the power system must be taken nto account. On the other hand, f FRT 2 s consdered (.e., WTs are dsconnected from the grd when the voltage at the connecton pont decreases below 0.2 p.u.), stablty problems are not experenced by the power system. These results confrm that system dynamc performance under hgh penetraton levels of wnd power s extremely dependent on the FRT requrements n force: the lower the voltage dp to rde through by the WT, the greater the effort demanded from the turbne. Ths s especally true n case of FSIGs due to ts dynamc performance durng low voltage stuatons. Thus, dependng on the FRT requrements and the

16 Energes 2013, characterstcs of the transmsson system, the wnd power network ntegraton based on FSIGs could only be realzed f addtonal nvestments for mprovng system stablty are consdered. Consequently, for a scenaro wth non-addtonal transmsson nvestments, as consdered n the present work, the wnd power ntegraton based on FSIGs must be lmted due to voltage stablty constrants. Comparng wth the case when the WTs are dstrbuted accordng to the proposed optmzaton methodology, t can be seen that even when the most strngent FRT requrements are consdered (.e., FRT 1), no nstablty arses. However, the amount of FSIGs connected at bus 1 n ths case must be reduced from 84 MW to 34 MW (see Table 4). On the other hand, f FRT 2 s consdered no nstablty s experenced by the system and the amount of FSIGs connected at bus 1 can be ncreased untl 200 MW. Ths confrms that system dynamc response depends n a complex manner on the network dstrbuton of the wnd power, WT technology, and the grd requrements n force. Hence, no general concluson regardng the effects of WTs on power system dynamc performance can be made. Indeed, ndependent studes for each power system taken nto account the characterstcs of the wnd power network development and the power system tself must be carred out when defnng proper sgnals to WT nvestors to acheve secure and cost effectve wnd power network ntegraton. 5. Conclusons In ths work, a novel optmzaton methodology for fndng the near optmal allocaton of WTs on a planned transmsson network was developed. The algorthm allocates the turbnes so that a desred wnd energy-penetraton level s reached whle mnmzng the WT nvestment costs. The man contrbuton s to propose an optmzaton algorthm that combnes both transmsson securty and power system stablty constrants. The proposal s amed especally at countres n the prmary stage of wnd power development, where the WT network ntegraton process can stll be nfluenced by polcy makers and where the expanson plannng for the power system stll does not ncorporate the development of renewable energes. The methodology s a support nstrument for regulators to generate polcy strateges amng to gve proper sgnals to WT nvestors n order to reach the desred wnd power network ntegraton. The strateges can be defned through changes and adaptatons of the regulatory framework n the electrcty market,.e., tenderng processes for WT proects, feed-n tarffs wth locaton sgnals, warrantes found for nvestment promoton, dfferentated taxes, etc. As a result, prce sgnals wll be followed by the agents n the market leadng to secure and cost-effectve WT network development. Based on system development, new adaptatons or adustments of the regulatory framework can be made at regular tme ntervals. The proposed methodology s valdated wth a real power system. Obtaned results are compared wth those generated from a BAU scenaro n whch the WT network allocaton s made accordng to exstng WT proects. From the economc vewpont, results ndcate that the WT network allocaton scheme obtaned through the proposed optmzaton methodology not only reduces the total nvestment costs assocated wth a wnd energy target, but also reduces the need for addtonal grd renforcements to ensure power system stablty. Therefore, optmal use of power system capactes and wnd resources s realzed by ensurng system securty. The dynamc smulatons show that the effects of wnd power on system stablty depend strongly on the WT network allocaton, WT technology, and

17 Energes 2013, the FRT requrements n force. The mportance of consderng power system stablty constrants when plannng the wnd power network ntegraton process s thus verfed. As future work, the methodology can be mproved further f addtonal network renforcements are explctly consdered durng the optmzaton process n order to counteract possble negatve effects of WTs, or to permt wnd power network ntegraton at those locatons where transmsson capactes are not suffcent. Acknowledgment The authors would lke to acknowledge the support of the Chlean Councl of Scentfc and Technologcal Research, COICYT (Fondecyt # ) and the Complex Engneerng Systems Insttute (ICM: P F, COICYT: FBO16) n the realzaton of ths work. References 1. Doherty, R.; O Malley, M. A new approach to quantfy reserve demand n systems wth sgnfcant nstalled wnd capacty. IEEE Trans. Power Syst. 2005, 20, Kark, R.; Po, Hu; Bllnton, R. A smplfed wnd power generaton model for relablty evaluaton. IEEE Trans. Energy Convers. 2006, 21, Meegahapola, L.; Flynn, D. Impact on Transent and Frequency Stablty for a Power System at Very Hgh Wnd Penetraton. In Proceedngs of 2010 IEEE Power Energy Socety General Meetng, Mnneapols, M, USA, July Energewrtschaftlche Planung für de etz-ntegraton von Wndenerge n Deutschland an Land und Offshore bs zum Jahr 2020 [In German]; Deutsche Energe-Agentur GmbH: Berln, Germany, Erlch, I.; Wnter, W.; Dttrch, A. Advanced Grd Requrements for the Integraton of Wnd Turbnes nto the German Transmsson System. In Proceedngs of 2006 IEEE Power Engneerng Socety General Meetng, Montreal, Canada, June Ackermann, T. Wnd Power n Power Systems; Wley: Chchester, UK, Burke, D.J.; O Malley, M.J. Optmal Frm Wnd Capacty Allocaton to Power Systems wth Securty Constrants. In Proceedngs of 2009 IEEE/PES Power Systems Conference and Exposton (PSCE 09), Seattle, WA, USA, March We, Q.; Harley, R.G. Effect of Grd-Connected DFIG Wnd Turbnes on Power System Transent Stablty. In Proceedngs of 2008 IEEE Power and Energy Socety General Meetng Converson and Delvery of Electrcal Energy n the 21st Century, Pttsburgh, PA, USA, July Burke, D.J.; O Malley, M.J. Maxmzng frm wnd connecton to securty constraned transmsson networks. IEEE Trans. Power Syst. 2010, ck, M.; Rahy, G.H.; Hossenan, S.H.; Fallah, F. Wnd power optmal capacty allocaton to remote areas takng nto account transmsson connecton requrements. IET Renew. Power Gener. 2011, 5,

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