Energies 2015, 8, 8020-8051; doi:10.3390/en8088020 Aricle OPEN ACCESS energies ISSN 1996-1073 www.mdi.com/journal/energies Oimal Real-Time Scheduling for Hybrid Energy Sorage Sysems and Wind Farms Based on Model Predicive Conrol Meng Xiong, Feng Gao *, Kun Liu, Siyun Chen and Jiaojiao Dong Sae Key Laboraory for Manufacuring Sysems Engineering, Sysems Engineering Insiue, Xi an Jiaoong Universiy, Xi an 710049, China; E-Mails: mxiong@sei.xju.edu.cn (M.X.); kliu@sei.xju.edu.cn (K.L.); sychen@sei.xju.edu.cn (S.C.); jjdong@sei.xju.edu.cn (J.D.) * Auhor o whom corresondence should be addressed; E-Mail: fgao@sei.xju.edu.cn; Tel.: +86-29-8266-7856; Fax: +86-29-8266-8677. Academic Edior: Frede Blaabjerg Received: 11 June 2015 / Acceed: 26 July 2015 / Published: 3 Augus 2015 Absrac: Energy sorage devices are execed o be more frequenly imlemened in wind farms in near fuure. In his aer, boh umed hydro and fly wheel sorage sysems are used o assis a wind farm o smooh he ower flucuaions. Due o he significan difference in he resonse seeds of he wo sorages yes, he wind farm coordinaion wih wo yes of energy sorage is a roblem. This aer resens wo mehods for he coordinaion roblem: a wo-level hierarchical model redicive conrol (MPC) mehod and a single-level MPC mehod. In he single-level MPC mehod, only one MPC conroller coordinaes he wind farm and he wo sorage sysems o follow he grid scheduling. Alernaively, in he wo-level MPC mehod, wo MPC conrollers are used o coordinae he wind farm and he wo sorage sysems. The srucure of wo level MPC consiss of ouer level and inner level MPC. They run alernaively o erform real-ime scheduling and hen so, hus obaining long-erm scheduling resuls and sending some resuls o he inner level as inu. The single-level MPC mehod erforms boh long- and shor-erm scheduling asks in each inerval. The simulaion resuls show ha he mehods roosed can imrove he uilizaion of wind ower and reduce wind ower sillage. In addiion, he single-level MPC and he wo-level MPC are no inerchangeable. The single-level MPC has he advanage of following he grid schedule while he wo-level MPC can reduce he oimizaion ime by 60%.
Energies 2015, 8 8021 Keywords: wind farm; energy sorage; MPC; hierarchical conrol; ower scheduling; smoohing flucuaion; coordinaion of energy sorage; hybrid ower sysem; oimal energy manage 1. Inroducion Wih he increasing eneraion of wind energy ino ower grids, he negaive influences of wind farms are non-negligible [1,2]. The variabiliy and inermience of wind ower cause flucuaion of he volage and frequency of he grid, affecing he safey of he ower grid [3,4]. Energy sorage sysems have been verified o be an effecive mehod for overcoming hese deficiencies [5 7]. The sysem ha coordinaes a wind farm wih energy sorage sysems can be disached ino ower grids, which is similar o ha of a convenional energy lan [8]. Energy sorage sysems can be classified ino wo general caegories: high ower densiy and high energy densiy yes [9 11]. Moreover, energy sorage sysems can be classified as fas resonse or slow resonse deending on he resonse ime [12]. Because smoohing he comlex flucuaion of wind ower using a single ye of energy sorage is difficul, hybrid energy sorage sysems may be a beer choice for wind farms for boh echnical and economic reasons [13,14]. Wind farm scheduling can be classified ino he day-ahead scheduling and he real-ime scheduling according o he influence of wind ower on he grid [15]. The day-ahead scheduling is emloyed o address he long-erm influence, and he real-ime scheduling is alied o address he shor-erm influence. Boh he day-ahead and he real-ime scheduling have drawn much aenion in recen years [16,17]. The aroaches of model redicive conrol (MPC), fuzzy logic conrol (FLC) [18], dynamic rogramming [19] and mixed-ineger nonlinear rogramming (MINLP) [20] have been used o erform real-ime scheduling. The MPC algorihm has been widely used in indusry cases since is firs alicaion in chemical rocess indusry in 1990. Recenly, MPC has been adoed in ower and renewable energy sysems as well [21 28]. MPC has wo main advanages: he simliciy of handling comlex consrains and real-ime conrol based on rolling horizon oimizaion. Indeed, MPC ransforms a conrol roblem ino an oimizaion roblem [29]. Firs, MPC solves a finie horizon oimizaion roblem wih some fuure informaion a he samling ime, and only he resuls for he curren ime are used. The overall rocedure is hen reeaed a he nex samling ime [18]. The oimal resuls closely describe he acual siuaion because of he look-ahead characerisic of MPC. On he oher hand, oher convenional conrol aroaches such as he roorional inegral derivaive (PID) mehod and fuzzy conrol mehods can also be imlemened in real ime scheduling. However, he PID and fuzzy conrol do no belong o oimal algorihm, and heir scheduling resuls are less han he resuls of MPC. Meanwhile, in his aer he Equaions (15) and (16) are logic consrains, hese logic consrains can be easily fulfilled using a CPLEX oimal ool, which is a common ool used in building MPC model. In conras, hey are hard o erform wih he PID and fuzzy conroller mehods. Moreover, he MPC mehod can easily handle comlex consrains, while he PID and fuzzy conrol have difficuly in handling hem.
Energies 2015, 8 8022 The alicaion of he MPC mehod o conrol energy sorage sysems and wind farms has been sudied by many invesigaors. In he research, hey emloyed he muli-level hierarchical MPC [24,30 32] or one-level MPC [25 27] according o he difference in conrol archiecures. Wei e al. roosed a wo-level hierarchical MPC o reduce he MPC oimizaion ime [24]. In his alicaion, energy sorage is used o coordinae wind-solar subsysems o oimize he roducion of desalinaed waer and he waer and sorage requiremen is me. The uer level is modeled as a long-imescale roblem, while he lower level is a shor-imescale roblem. The oimized uer level resuls are used as he inu of he lower level. In [25], he archiecure of he MPC is single-level. A wind-baery oimizaion model is esablished for a sorage sysem and wind farm o conduc scheduling in he same manner as a radiional lan does. Oher lieraure is available on real-ime scheduling involving fuzzy logic conrol and dynamic rogramming. Lei e al. resened a wo-level dynamic rogramming o manage a wind farm and a sorage sysem [33], in which he uer level is imlemened over he whole eriod o obain he reference rajecory and he lower level is imlemened for real-ime oeraion. In [28], a combinaion of he MPC mehod wih fuzzy logic conrol was roosed, in which MPC is used for real-ime conrol o achieve he oimizaion objecive, and a fuzzy logic conroller adjuss he ower reference o increase he lifeime of he sorage sysem. In [24], he auhor ook advanage of wo-ime-scale roery of he dynamics of he inegraed sysem o imrove he comuaional efficiency of he conrol roblem formulaion. This meri has reduced he comuaion burden of he mehod, and now i can be imlemened in real ime sysem. However, we hink his mehod could exis a demeri in running sabiliy. In exreme condiion, he redicion error could lead o he oimal mode failure in finding feasible soluion. In [25], he meri of he aer is resened wih a hird-order baery model and a sae sace is used o describe he baery model. Addiionally, auhor has also found ha he redicion horizon of MPC is an imoran arameer ha conribues o he scheduling erformance. The demeri of his aer could be ha he baery energy sorage sysem (BESS) charge/discharge frequency is relaively high. Thus, he limi consrain of charge/discharge frequency should be added in his model. In [28], he meri of he mehod is ha MPC mehod is combined wih fuzzy logic conrol (FLC) mehod o conrol he wind farm and energy sorage. The combinaion of he wo mehods is a novel way, and he resuls have demonsraed ha he wind farm revenue has been imroved by 3%. The demeri of his aer is ha auhors ado single sorage raher han wo yes of sorage. The hybrid sorage has more advanages han single ye energy sorage, and hese advanages can assis he wind farm in following scheduling. In [33], he auhor has succeeded in overcoming he dilemma of he conflic beween long horizon and redicion accuracy. The mehod is very useful in conrolling sohisicaed sysem consised by wind farm and energy sorage. However, we hink here was a minor unreasonable descriion in he baery model. We believe ha he baery ough is o occuy only one of he hree saes a any given ime: charge, discharge, or shu-down, while according o he baery mode (Equaion (5)) a baery can be in charge and discharge sae simulaneously, herefore we hink he auhor may have negleced his minor oin in his model. Alhough many researchers have invesigaed he managemen of a wind farm wih a single ye of sorage based on MPC, few researchers have sudied a wind farm wih a hybrid sorage sysem based on MPC, esecially when he hybrid sorage sysem includes umed hydro sorage. A baery sorage sysem may be more racical han a umed hydro sorage sysem; however, here are some secial
Energies 2015, 8 8023 cases in which a baery sorage sysem canno relace a umed hydro sorage sysem. For examle, on an isolaed island, umed hydro sorage serves as no only energy sorage bu also a reservoir for local ciizens. Moreover, he umed hydro sorage sysem has some advanages such as large sorage caaciy, high efficiency, maure consrucion echnology, relaively low caial cos er uni of energy and ime-shifing beween wind generaion and demand rofiles. The urose of his aer is o resen wo MPC models o be imlemened in wind farms wih hybrid sorage sysems including a umed hydro sorage sysem and a fly wheel sysem. The MPC models resened consider he ower characerisics of wind farms and hybrid sorage sysems, and he resuls confirm he efficiency of he MPC model. The meri of roose mehod is as follows: Firs, wo yes of energy are adoed. Second, he MPC mehod is used o smooh wind ower flucuaion. Finally, wo ye of MPC mehods are discussed and comared. The conribuions are lised as follows: (1) We have adoed a fas resonse seed energy sorage and a slow resonse seed energy sorage o smooh he shor erm and he long erm wind ower flucuaions, resecively. Due o he wo differen resonse seeds, how o ge he wo energy sorages o cooerae is a roblem for real ime scheduling. We have exloied he modulariy of wind farms based on he MPC mehod wih wo yes of sorage o solve he roblem. (2) We resen ha he MPC redicion horizon should be wo hours according o he wind farm ower secrum densiy and redicion error. (3) Addiionally, we have imlemened a wo-level MPC o reduce he oimal comuaion ime. The exerimenal resuls are close o ha of a single-level MPC. The single-level MPC has is own advanages in following he grid lan. The wo-level MPC canno be subsiued for single-level MPC, and vice versa. (4) Two sound conclusions are drawn hrough heory analyses and simulaions: One is ha he decision values of he umed sorage are no sensiive o he flywheel caaciy. The oher is ha in some siuaions, wind ower generaion being sen o he grid is sacrificed o reduce he wind curailmen. The res of his aer is organized as follows. In Secion 2, he roblem o be addressed is described. In Secion 3, he sysem configuraion and oeraing rocess are given. In Secion 4, he roosed sysem model is described. In Secion 5, he numerical resuls are resened. Finally, he conclusions are resened in Secion 6. 2. Problem Descriion In his aer, wo yes of energy sorage sysems were used o assis a wind farm in smoohing he ower flucuaions. One of he key issues is how he wo energy sorage sysems cooerae wih each oher o erform such ower smoohing. In he case of hybrid sorage sysems, i is imoran o deermine wheher common or secial decision-making rocesses exis when a umed hydro sorage sysem is relaced by anoher high-energy densiy sorage sysem. In he following aragrahs, we sae he characerisics of wind ower and energy sorage sysems firs and hen deermine he relaionshi beween hem. Finally, some useful resuls and suggesions were obained.
Energies 2015, 8 8024 2.1. Characerisics of Wind Power Wind ower flucuaions consis of wo overlaing ars: macro-meeorological flucuaions and micro-meeorological flucuaions [34]. Figure 1 shows he wind flucuaions decomosed ino macro-meeorological flucuaions and micro-meeorological flucuaions. From Figure 1, i can be seen ha he macro-meeorological flucuaions are relaively slow and smooh and dislay he rend of wind ower generaion. In addiion, he macro-meeorological flucuaions vary over a large band from 0 o 22 MW, while he micro-meeorological flucuaions are relaively fas and shar and vary over a relaively narrow band of around 2.5 MW. These observaions indicae ha wo yes of sorage sysems can be used o smooh hese wo flucuaions. One ye of sorage is alied o address macro-meeorological flucuaions; in his case, he sorage should be a high energy densiy ye wih a large ower and caaciy, bu is resonse seed may be slow. The oher ye of sorage is used o address he micro-meeorological flucuaions; in his case, he sorage sysem requires he caabiliy of raidly changing ower, bu a large caaciy is no needed. 30 25 Power/M W 20 15 10 5 wind macro wind micro wind 0 0 500 1000 1500 /min Figure 1. Decomosiion of wind ower flucuaions. 2.2. Characerisics of Tyical Energy Sorage Sysems Table 1 shows some characerisics of yical energy sorage sysems. Pumed hydro sorage has large ower and caaciy. However, is resonse ime is long due o he high ineria of waer urbines and some securiy consideraions. Addiionally, umed hydro sorage may be forbidden from swiching from umed mode o generaion mode (and vice versa) wihin a shor ime frame [35]. As a resul, in his aer, we ado he reasonable assumion ha he umed hydro sorage only has ermission o change is oeraing sae once each half hour and ha he changing ime occurs a he beginning of he half hour (Assumion 1). This assumion can enable umed hydro sorage easy o conrol and oerae safely. Noe ha for he umed hydro sorage, he erm change sae means ha he umed hydro sorage changes he generaion mode ino umed mode, and vice versa. Moreover, he erm also means ha he umed hydro sorage changes he ower value of generaion or uming. For fly wheel, he meaning of he erm is similar o ha for umed hydro sorage.
Energies 2015, 8 8025 The fly wheel has low caaciy and fas resonse seed, as indicaed in Table 1. The resonse ime of a fly wheel is 0.05 s. For convenional scheduling rocesses, he fly wheel is regarded as a fas sorage device, and i can change is oeraing sae a any scheduling ime (Assumion 2). In his aer, we assume ha he scheduling inerval is five minues and he scheduling horizon is one day or 24 h (Assumion 3). Table 1. Characerisics of yical energy sorage yes. Tye Energy Power Resond Power Energy Efficiency Life (year Densiy Densiy ime (MW) (MWh) (%) or cycle) (Wh/kg) (W/kg) (s) Pumed hydro 0 1800 >200 0.5 1.5-75 10 600 50 y Comressed air 0 300 0 105 30 60 10 100 64 1 600 30 y SMES 0 10 0 1 30 100 10 4 10 5 95 0.005 30 y Fly wheel 0 5 0 10 5 10 10 2 10 3 93 0.05 20 y Suer ca 0 0.3 0 10 <50 0 4000 98 0.05 10 5 c Baery 0 50 0 100 30 200 0 500 70 0.02 3000 c 2.3. Relaionshi beween Wind Power Flucuaion and Sorage Sysems As menioned above, a umed hydro sorage is used o address he macro-meeorological flucuaions. According o Assumion 1, umed hydro sorage changes is work sae once each half hour o handle hour-level flucuaions. In addiion, i has high ower and high caaciy characerisics, which assis umed sorage in a smooh wide band of wave. A fly wheel is suiable for dealing wih urbulence due o is fas resonse and low ower characerisics. Subsiuing comressed air sorage for umed hydro sorage aears o be feasible because hey have similar arameers. If we subsiue a baery for umed sorage, we mus consider wheher he baery can have boh high ower and high caaciy. Even if a baery sysem has sufficien ower and caaciy, he conrol of he baery will be challenging. 2.4. The Princile of Choosing Predicion Horizon In his aer, he lengh of he redicion horizon is deended on he wind ower secrum densiy and he ye of energy sorage. We exlain he reason as following: Firs, for fly wheel sorage, i mainly deals wih he urbulence due o is fas resonse seed and low ower characerisics. Pumed sorage handles macro meeorological flucuaion due o is slow resonse seed and high ower characerisics. Turbulence belongs o minue-level flucuaion, and macro meeorological flucuaion is hour-level or day-level flucuaion. Therefore, he lengh of he redicion horizon should be hour-level, if he MPC conroller is conrolling he umed sorage. Second, he wind farm ower secrum densiy curve was shown in Figure 2. The macro meeorological flucuaion is relaively low frequency and huge energy, herefore, i should belong o he lef ar of he curve. The urbulence is relaively high frequency and low energy, so i should belong o he righ ar of he curve. In Figure 2, One hour window means ha he lengh of he MPC redicion horizon is one hour, and Two hour window means ha he lengh of MPC redicion horizon is wo hours. One hour window conains much urbulence and lile macro
Energies 2015, 8 8026 meeorological flucuaion; on he conrary, he Two hour window includes much urbulence and some macro meeorological flucuaion. According o hese observaions, we decided o choose wo hours as he MPC redicion horizon. Finally, we undeniably agree ha he hree hour soluion is also feasible, erha i is beer han he wo hours soluion because i conains more macro meeorological flucuaions. However, he redicion accrual of hree hours is worse han wo hours, which is no beneficial for he real ime scheduling. Thus, o balance he redicion accrual and macro meeorological flucuaions, we choose he wo hour soluion. 10 7 Power secral densiy/mw 2 10 6 10 5 10 4 10 3 10 2 X: 0.0001389 Y: 7.366e+004 Two hours window One hour window X: 0.0002778 Y: 635.4 10 1 10-5 10-4 10-3 10-2 Frequency/Hz Figure 2. Wind ower secrum densiy curve. 3. The Sysem Configuraion and Oeraing Process In his secion, wo yes of sysem configuraions are resened because MPC mehods include a convenional MPC (single-level MPC) and a hierarchical MPC (muli-level MPC). The single-level MPC sysem configuraion is shown in Figure 3a, and he wo-level MPC sysem configuraion is shown in Figure 3b. 3.1. Single-Level Sysem Configuraion and Oeraing Process Figure 3a shows ha he single-level sysem consiss of a wind farm, a hybrid sorage sysem, a grid, and an MPC conroller. The single-level MPC oeraing rocess is resened as follows: Firs, he MPC obains he available informaion, such as he curren wind ower, forecased wind ower, energy levels in he wo energy sorage sysems, grid lan and working saes of he wo energy sorages (umed mode or generaion mode, charging mode or discharging mode). Second, he MPC makes oimal decisions based on his informaion and hen imlemens he acions based on hese decisions. Noe ha only he curren ime oimal decisions can be made. The wo above-menioned se are reeaed when he nex scheduling ime arrives.
Energies 2015, 8 8027 (a) (b) Figure 3. Sysem configuraion. (a) Single-level sysem configuraion; (b) Two-level sysem configuraion. 3.2. Two-Level Sysem Configuraion and Is Oeraing Process In hierarchical sysems, a number of regulaors erform heir conrol acions a differen imescales. This aroach can be useful when he overall rocess under conrol is characerized by slow and fas dynamic behavior [29]. In his aer, umed hydro sorage is a slow form of sorage, and he fly wheel is a fas form of sorage according o he resonse ime. Therefore, hierarchical MPC is adoed o resen he sysem. This wo-level sysem is comosed of a wind farm, a hybrid sorage sysem, a grid, an MPC1 conroller, and an MPC2 conroller, as shown in Figure 3b. To undersand he cooeraion beween he MPC1 conroller and MPC2 conroller, he above-menioned Assumions 1, 2 and 3 mus be exlained in deail. Assumion 3 is ha he scheduling inerval is 5 min; Assumion 2 is ha a fly wheel can change is oeraing sae a any scheduling ime inerval. Assumion 1 which is crucial, is ha he umed sorage canno change is oeraing sae wihin a 30 min eriod unil he nex 30 min eriod sars. In oher words, umed hydro sorage can change is oeraing sae only a he beginning of he 30 min eriod and mus hen mainain is oeraing sae unil he 30 min eriod ends. Noe ha 30 min corresonds o six scheduling inervals. The level of MPC 1 is regarded as he inner level or shor-erm level, and he level of MPC 2 is viewed as he ouer level or long-erm level. Similar o he convenional hierarchical MPC, in his aer, he long-erm MPC oeraes by firs making decisions and hen ransmiing some decisions o he shor-level MPC; ha is, informaion is ouu from he long-erm MPC and hen inu o he shor-erm MPC [29]. The wo-level MPC oeraing rocess is resened as follows: Firs, he long-erm MPC (MPC 2) runs and makes decisions. Some decisions are hen ransmied o he shor-erm MPC (MPC 1), and furher decisions are made. Second, when he nex scheduling inerval arrives, he long-erm MPC (MPC 2) so working, and hen he shor-erm MPC (MPC 1) sars working. MPC 1 makes decisions and hen erforms hem. If a new 30 min eriod arrives, he firs se is reeaed, or else he second se is reeaed.
Energies 2015, 8 8028 There are hree ways o communicae beween he wo conrollers. The hree ways are Eherne communicaions, global sysem for mobile communicaions (GSM) and saellie communicaion echnology, resecively. Eherne communicaion soluion is he cheaes soluion among he hree ways, and he saellie communicaion soluion is he mos exensive soluion. We consider he hree following imlemen cases: If inerne is available in he umed sorage saion and he fly wheel saion hen Eherne communicaion is recommended. If he mobile signals exiss in he umed sorage saion and he fly wheel saion, hen GSM communicaion is adoed. Oherwise, he saellie communicaion has o be chosen. In his aer, he wo conrollers communicae once every five minues, he seed of above hree echnologies is fas enough o ensure synchronizaion of heir communicaion. Meanwhile, i also ossible o ado some roocols in he sofware o ensure synchronizaion for examle, he shake hand roocol is a common way o synchronize communicaion. 4. Sysem Model In Secion 2 (Problem descriion), he cooeraion beween he umed hydro sorage and he fly wheel sorage was noed. However, he rocess and deails of he cooeraion based on rolling oimizaion have no ye been addressed. The rolling oimizaion lays a significan role in MPC. When alying MPC mehod o wind farm and hybrid energy sorage, which consis of a fas resonse seed sorage and a slow resonse seed sorage, wo yes of MPC mehods can be imlemened. One ye is single-level MPC mehod, and he oher is wo-level MPC mehod. For single-level MPC mehod, a wo ime scales roblem will be me due o wo kinds of resond seeds of energy sorage. To overcome his roblem, single-level MPC mehod mus divide he roblem ino several siuaions, and for every siuaion, a model is used o describe i. The models are carried ou in urn according o he siuaions. In conras, wo-level MPC mehod is suiable for he hybrid sorages. Ouer level and inner level MPC run alernaively o erform real-ime scheduling. Therefore, in his secion, we firs analyze he rocess and deails of he cooeraion based on wo yes of MPC mehod and hen aem o use he oimizaion model and he sae-sace mehod o reresen he rocess in deail. The single-level MPC mehod is addressed and hen wo-level MPC mehod is discussed below. 4.1. Single-Level MPC Mehod Before he rolling oimizaion rocess is analyzed, some basic informaion mus be given. We assume ha he redicion horizon is equal o he conrol horizon and each of hem are wo hours. The samle ime is 5 min. Le s = 0 when MPC conroller begins o work, where s reresens he serial number of he scheduling inerval. Two hours are equal o weny-four scheduling inervals. The rincile of rolling oimizaion is as follows: Firs, a he curren ime, he MPC conroller samles he curren inerval informaion, and redics he informaion for he nex wo hours. Second, MPC erforms on-line oimizaion.
Energies 2015, 8 8029 Finally, MPC makes he curren ime decisions. The above rocess is reeaed on he arrival of he nex scheduling inerval. Alhough he rincile is easy and clear, i will become relaively comlex, once i is imlemened o hybrid energy sorage, which has significanly differen resonse seeds. For undersanding he rincile, we will firs analyze a simle examle, and hen we will exlain he comlex rocess. The simle examle is ha he umed hydro sorage is relaced by a baery. From Table 1, he resonse seed of he fly wheel is almos equal o ha of he baery; herefore, a any scheduling inerval, he baery and fly wheel are ready o change heir work saes according o he oimal resuls. In conras, according o assumion 1, he umed sorage is no ready o change is work sae a any scheduling inerval. In oher words, a any scheduling inerval, we have he conrol righ o change he fly wheel and baery, bu we have almos los he conrol righ for umed sorage. Therefore, when he rincile is alied o he baery and he fly wheel, i is a simle examle, and he analysis rocess is as follows: MPC conroller samles, forecass, execue on line oimizaion and roduces he resuls. The MPC conroller reeas he above rocess on he nex scheduling inerval. Therefore, he MPC conroller always erforms he same se of acions a any scheduling inerval. The rocess is shown in Figure 4. Figure 4. Single-level MPC erforming rolling oimizaion (based on baery and fly wheel). In Figure 4, a any scheduling inerval, he conex of MPC conroller erforming is similar. When he rincile is alied o umed sorage and fly wheel, he rocess will become relaively comlex, due o he conrol righ of he umed sorage. According o Assumion 1, he umed sorage is under conrol a every saring half an hour, consequenly, when s is 0, 6, 12, 18, 24, boh he umed sorage and he fly wheel are under conrol. The conrol righ siuaion is similar o ha of baery and fly wheel. Any oher ime, he wo siuaions are differen. The deails are shown in Figure 5. Figure 5 schemaically shows he rocess by which he single-level MPC erforms he rolling oimizaion. Change means ha, a he beginning of his half-hour eriod, he umed sorage can change oeraing sae once; hold on means ha, in he scheduling inerval, umed hydro sorage canno change is oeraing sae; and Case 0 5 denoes he difference condiions. The difference beween Figure 4 and Figure 5 is significan. The main reasons for his difference are as follows:
Energies 2015, 8 8030 When s = 0 (Case 0), he MPC conroller sars working, samles and redics informaion, erforms on-line oimizaion, and hen sends is oimizaion decisions o he umed hydro sorage and he fly wheel. The umed hydro sorage sysem receives and execues he decisions. Once he umed sorage changes is oeraing sae, i mus remain in he sae unil he half-hour eriod ends. In oher words, when s = 1, 2 5, he umed hydro sorage canno change is oeraing sae for x min, where x is 25, 20, 15, 10, and 5, resecively. For examle, in Figure 5, Case 3 shows ha he umed hydro sorage canno change is oeraing sae for he firs 15 min, bu i can change is oeraing sae once when he new half-hour eriod begins. Figure 5. Single-level MPC erforming rolling oimizaion (based on umed sorage and fly wheel). We can also exlain he above rocess in a differen way: when s = 0 (Case 0), he MPC conroller, fly wheel, and umed hydro sorage sar working, he MPC conroller rovides he decision, and hen he fly wheel and umed hydro sorage sysems erform he acions based on he decision. In Case 0, he decision variable of umed sorage belongs o he conrol variable. Once he umed sorage changes is oeraing sae, i mus remain in his sae for half an hour. In he following Cases 1 5, he decision variable of he umed sorage is a consan a he iniial ime, no a variable. In oher words, in Cases 1 5, he variable of umed sorage does no ake ar in he on-line oimizaion, and i is assigned according o he value of Case 0. When s = 1, 2 5, he corresonding condiions are Case 1 Case 5, and when s = 6, he corresonding condiion is Case 0. The relaionshi beween s and he case can be described by Equaion (1): Case n mod( s,6) (1) where mod is he remainder oeraor, and he relaionshi is shown in Figure 6.
Energies 2015, 8 8031 Figure 6. Relaionshi beween s and he case. In Figure 6, he Ci reresen Case i, he roll oimizaion based umed sorage and fly wheel is reeaed afer six scheduling inervals. 4.2. Single-Level MPC Sae-Sace and Oimizaion Model 4.2.1. Single-Level MPC Sae-Sace Model The following simle linear dynamic equaions based on he single-level sysem configuraion are considered: Equaion (2) describes he assignmen rocess for wind ower. wind a fa (2) f 1 (3) Equaion (3) describes he comosiion rocess for sysem oal generaion [28]. a E 1 E η1 (4) η Equaion (4) describes energy balance of he umed hydro sorage a ime. Equaion (5) describes he energy balance of he fly wheel a ime. From Equaion (2), can be reresen as: Subsiuing ino Equaion (3), we obain: 4 2 f fw fw fa E 1 E η3 (5) η (6) wind a fa wind a fa f 1 (7) Subsequenly, he discree-ime five-order dynamic equaion of he wind ower wih hybrid sorages can be wrien as follows: X( k1) AX( k) B1 u( k) B2 ε( k) fa k 1 1 1 1 1 f k 1 000 k k 1 a Ek1 010 Ek 0 0 η1 0 k 0 η wind (8) k fw fw 2 E 001 0 k1 E k k η 3 0 0 0 η k 4
Energies 2015, 8 8032 and: yk ( ) C X( k) k k 100Ek fw Ek (9) Consrains including logic consrains are difficul o resen. However, logic consrains can be easily formulaed in a rogramming model. Therefore, in his aer, a rogramming model is used. 4.2.2. Single-Level MPC Programming Model (a) Objecive Funcion of he Model The objecive funcion includes hree sub-objecives: he sysem generaes ower sricly according o he grid lan (he firs sub-objecive); reduces he quaniy of wind curailmen (he second sub-objecive); and imroves he raio of (he hird sub-objecive). The reasons for he firs and second sub-objecives are obvious, and he reason for he hird sub-objecive is ha here is a loss of energy when wind ower is sored ino he energy sorage sysem and is hen generaed from he energy sorage sysem, i.e., he hird sub-objecive can imrove he wind energy uilizaion efficiency. The objecive funcion is as follows: s lan (10) 0 min N w 1 w 2 w 3 where N (N = 23) is he redicion horizon of he MPC and w 1, w 2, and w 3 are osiive weigh facors of he sub-objecives. The choice of he weigh facor is mainly based on on-sie demand. w 1, w 2, and w 3 can be relaced by w 1 (), w (), and 2 w () 3, showing ha he weigh facors are relaed o ime. We will examine he differences caused by he differences beween w() and 1 w 1 in he simulaion resuls. (b) Consrains of he model (1) The assignmen rocess of wind ower is described in Equaion (2). (2) The comosiion rocess of he sysem oal generaion is described in Equaion (3). (3) The energy balances of he umed hydro sorage and he fly wheel are resened in Equaions (4) and (5), resecively. (4) The uer and lower bounds of umed sorage decision variable are: min max a a a min max E E E min max [0, 23] [0, 23] [0,23] (11) The lef side of he inequaliy resens he lower bounds, while he righ side dislays he uer bounds. (5) The uer and lower bounds of he fly wheel decision variable are described as follows:
Energies 2015, 8 8033 f f f min max fa fa fa min max E E E fw fw fw min max [0, 23] [0, 23] [0, 23] (12) The lef side of he inequaliy resens he lower bounds, while he righ side dislays he uer bounds. (6) The umed hydro sorage occuies only one of hree saes a any given ime: generaion, uming, or shu-down. The consrain is as follows: a ( 0) + = =0 1 ( ) [0, 23] (13) a where ( 0) and ( 0) are logical exressions. If, a a ime when he umed sorage is in a a umed sae, is greaer han 0, hen he logical exression ( 0) is evaluaed as 0; oherwise, i is 1. If, a a ime when he umed sorage is in he generaion sae, is greaer han 0, hen he logical exression ( 0) is evaluaed as 0; oherwise, i is 1. If he sum of he wo logical exressions is greaer han 1, he umed hydro sorage can only be in one of hree saes. (7) The fly wheel sorage occuies only one of hree saes a any given ime: charge, discharge, or shu-down. The consrain is as follows: fa f ( 0) + = =0 1 [0, 23] ( ) (14) where fa ( 0) and f ( = =0) are logical exressions analogous o hose for he umed sorage. (8) Wind delivered direcly o grid canno exceed generaion lan: [0, 23] lan Wih he hel of he sub-objecive in he objecive funcion, he consrains can ensure ha is close o he ower lan and imrove he uilizaion raio of wind ower. These benefis are ossible because he wind ower is direcly injeced ino he grid and he insufficien ar of he demand is comensaed by he energy sorage sysem when he wind ower is less han ower lan. Moreover, when he wind ower exceeds he ower lan, can only be close o he generaion lan o mee he sub-objecive and Equaion (15). (9) Consrains of Assumion 1: Assumion 1 is ha umed sorage can change is oeraing sae a he beginning of a new half-hour eriod and hen remain in his sae unil he half-hour eriod ends. Meanwhile, as shown in Figure 5, Assumion 1 is classified ino six cases, as described in he following: The case 0 consrain can be obained according o Figure 5 Case 0. where x sands for eiher (15) x x x x x x Case0 : 1 2 3 4 5 ( 0,6,12,18) (16) a or, is he number of ime series, he origin of is s, and is in he range of 0 23 (wo hours). The Equaion (16) describe he umed sorage mus kee work sae unchanging in half hour, and he secific oimal value is decided by he oimal model. Therefore, in Case 0, he umed sorage is under conrol. Meanwhile, Equaion (16) shows he redicion horizon is wo hours, and i is a long-erm oimizaion. Noe ha, on he o of Figure 5, he horizonal axis is
Energies 2015, 8 8034 he ime series axis, and we use s o reresen he ime series. The definiion of s is differen from ha of. s = 0 means he sysem has sared; however, = 0 denoes he firs scheduling inerval for rolling oimizaion. = 1 reresens he second scheduling inerval, and = 23 reresens he las wo-hour scheduling inerval. For examle, Case 3 in Figure 5, he MPC sysem has erformed hree scheduling inervals; hus, s = 3, whereas we regard he firs scheduling inerval for rolling oimizaion as = 0. The funcion of s is o deermine he cases he MPC condiion corresonds o (see Equaion (1)). In case 0, 0,6,12,18 reresen four iniial oins of a half-hour eriod, and a he iniial oin of he half- hour eriod, he umed hydro sorage can change is oeraing sae. x x x x x x 1 2 3 4 5 indicaes ha umed hydro sorage mus remain in he same oeraing sae for 30 min (six scheduling inervals), and he oimal oeraing sae is deermined by rolling oimizaion. The Case 1 consrain can be obained from Figure 5, Case 1. where x _ iniial Case1: ( 0) x x x x x x 1 2 3 4 _ iniial x x x x x x 5 6 7 8 9 10 ( 0, 6,12) is he umed hydro sorage oeraing sae a he beginning of he half-hour eriod. x x x x x x 1 2 3 4 _ iniial ( 0) means ha, for his insance of rolling oimizaion, he umed sorage decision variable is consan a he iniial ime ( = 1 4). x x x x x x In ( 0,6,12) 5 6 7 8 9 10, ( 0,6,12) means ha, when = 5, 11, 17, a new half-hour eriod begins, and he umed hydro sorage can change is oeraing sae. x x x x x x In ( 0,6,12) x x x x x x 5 6 7 8 9 10, 5 6 7 8 9 10 means ha he umed hydro sorage mus remain in he same oeraing sae for 30 min (six scheduling inervals), and he oimal oeraing sae is deermined by rolling oimizaion. The consrain of Case 2 can be obained according o Figure 5. x x x x x Case2 : ( 0) 1 2 3 _ iniial x x x x x x 4 5 6 7 8 9 x x 22 23 ( 0,6,12) x x x x x x x x x x x 1 2 3 _ iniial ( 0) and ( 0,6,12) 4 5 6 7 8 9 refer o x x x Equaion (17). 22 23 means ha, a he las wo-hour scheduling inerval, 22 should be equal x o 23, and he decision values are deermined by rolling oimizaion. The consrain of Case 3 can be obained according o Figure 5: x x x x Case3: ( 0) 1 2 _ iniial x x x x x x 3 4 5 6 7 8 x x x 21 22 23 ( 0,6,12) Please refer o Equaion (18). The consrain of Case 4 can be obained according o Figure 5. (17) (18) (19)
Energies 2015, 8 8035 Case4 : ( 0) x x x 1 _ iniial ( 0,6,12) x x x x x x 2 3 4 5 6 7 x x x x 20 21 22 23 Please refer o Equaion (18). The consrain of Case 5 can be obained according o Figure 5. x x Case5: ( 0) _ iniial ( 0,6,12) x x x x x x 1 2 3 4 5 6 x x x x x 19 20 21 22 23 (20) (21) Please refer o Equaion (18). 4.3. Two-Level Rolling Oimizaion As menioned in Secion 3.2, a hierarchical MPC is adoed o resen he sysem considered in his sudy. MPC 1 mainly conrols he fly wheel, and MPC 2 mainly manages he umed hydro sorage. In conras, he single-level MPC manages boh he umed hydro sorage and he fly wheel. The umed hydro sorage sysem and one of he MPC conrollers are regarded as he ouer level, and he fly wheel sorage sysem and he oher MPC conroller are regarded as he inner level. The ouer level and inner level run alernaively o erform real-ime scheduling. Firs, he ouer level runs for one scheduling inerval for oimizaion and hen so, hus obaining long erm scheduling resuls and sending some resuls o he inner level as inu. Nex, he inner level erforms a shor-erm scheduling ask. For a real-ime scheduling sysem, he soluion seed is one of he imoran sysem characerisics. In Figure 7, for Case 0, he conrol horizon is wo hours, and he wo-hour eriod is useful for umed sorage because umed sorage mainly addresses he slow flucuaion. To obain he slow flucuaion by decomosing he wind ower, his relaively long conrol horizon is essenial. However, because he flywheel mainly manages urbulence flucuaions, he wo hour eriod is unnecessary for he following reasons: (1) he urbulence flucuaion is difficul o forecas, i.e., he accuracy decreases wih an increase in he redicion horizon; and (2) he soluion ime increases wih an increase in he redicion horizon. We reduce he redicion horizon when he fly wheel is used. In oher words, he redicion horizon of he fly wheel (MPC 1) decreases significanly, and he redicion horizon of he umed hydro sorage (MPC 2) remains unchanged. The reducion of he fly wheel (MPC 1) redicion horizon is erformed in he wo-level rolling oimizaion, as shown in Figure 7. From Figure 7, i can be noed ha a he beginning of scheduling (Case 0), MPC 2, which manages he umed hydro sorage, is on and MPC 1 is off. The MPC2 conroller makes decisions based on he wo-hour redicion horizon. The decisions include a key one ha is he decision of umed sorage. The umed sorage decision is ransmied o he inner MPC (MPC 1) as an inu value. In Cases 1 5, he umed sorage value is a consan, no a decision variable a he iniial ime. Moreover, he redicion of MPC1 is 25, 20, 15, 10, 5 min for he differen cases for he above reasons.
Energies 2015, 8 8036 Figure 7. Two-level MPC erforming rolling oimizaion. Le s be equal o 0, corresonding o he ime when he sysem is se ino oeraion. The wo-level rolling oimizaion rocess is resened as follows: Firs (Se 1), when s = 0, he condiion is Case 0. Only he MPC 2 conroller is available, and he MPC 1 does no make sysem decisions. The MPC 2 conroller obains informaion, which is similar o ha of he single-level aroach; nex, MPC 2 makes oimal decisions and hen erforms hese decisions. In addiion, he umed hydro sorage oeraing sae is hen ransferred o he MPC 1 conroller. The main urose of he firs se is o carry ou a long-erm and a look-ahead disach when he sysem begins o work. Because he oimal resuls conain some of he fuure informaion, he resuls can indicae he endency of curren values. The long-erm rolling oimizaion is used o conduc he macro meeorological flucuaions by conrolling he umed sorage. In Se 1, he umed sorage obains an oimal resul, and in case 0, he umed sorage in under conrol. We can use he following equaion o describe he under conrol umed sorage. x x x x x x Case0 : 1 2 3 4 5 ( 0,6,12,18) (22) The Equaion (22) describes ha he umed sorage mus kee he work sae unchanged for half an hour, and he secific oimal value is decided by he oimal model. Therefore, in case 0, he umed sorage is under conrol. Meanwhile Equaion (22) also shows ha he redicion horizon is wo hours, and i is a long-erm oimizaion. Second (Se 2), when s = 1, he condiion is Case 1. MPC 2 does no make sysem decisions, and MPC 1 akes charge of making decisions. The MPC 1 conroller obains informaion (exce for he umed hydro sorage informaion). MPC 1 hen makes oimal decisions (exce for umed hydro sorage decisions) and erforms acions based on he decisions. Noe ha he MPC 1 conroller canno be in charge of he umed hydro sorage. The main urose of he second se is o carry ou a shor-erm and a look-ahead disach when he sysem coninues o work. The shor-erm rolling oimizaion is used o deal wih he urbulences by conrolling he fly wheel. In Case 1, he umed sorage ariciaed in scheduling; however, he ower value of umed sorage was no decided in
Energies 2015, 8 8037 Case 1, and i is u o Case 0. In Case 1, he decision rocess of he umed sorage can be described by he following equaion: where x _ iniial x x x x x x Case1: 0 1 2 3 4 _ iniial (23) is he umed hydro sorage oeraing sae a he beginning of he half-hour eriod. means ha, for his insance of rolling oimizaion, he x x x x x x 0 1 2 3 4 _ iniial umed sorage decision variable is consan a he iniial ime. In Equaion (23), he redicion horizon is 25 min, his indicaed ha he comuaion burden is significan less han ha of Case 0. This is main reason ha wo-level MPC is adoed o conrolling wind farm and hybrid sorages. Third (Se 3), when s is in he range of 2 5, he condiions are Cases 2 5, resecively, and MPC 1 and MPC 2 oerae as in Se 2. Finally, when s = 6, a new 30 min eriod sars, and MPC1 and MPC 2 reea Se 1 (Case 0). The relaionshi beween s and he cases is exressed by Equaion (1). Figure 8 shows he work sequence of MPC1 and MPC2. In Figure 8, when s = 0, s = 6, s = 12, a new 30 min eriod has arrived, and a hese scheduling inervals, MPC 2 sars o work, while MPC 1 so working. When s is in he range of 1 5, 7 11,, MPC 2 so working, and MPC 1 sars o work. Noe ha a any scheduling inerval, only one MPC conroller is working. Figure 8. Collaboraion diagram for MPC 1 and MPC 2. 4.4. Two-Level MPC Sae-Sace and Oimizaion Model 4.4.1. Two-level MPC sae-sace model (a) Sae-sace of MPC 2 In Figure 7 Case 0, MPC 2 is working, while MPC 1 is no working. Case 0 is similar o Case 0 for he single-level MPC. Therefore, he sae-sace of he long-erm MPC (MPC 1) can be reresened by Equaions (8) and (9). (b) Sae-sace of MPC 1 In Cases 1 5, he umed hydro sorage mus remain in is oeraing sae a he iniial ime, and he decision value of he umed hydro sorage is consan. The samle dynasic equaions are similar o Equaions (4), (5), and (7), and he differences are he decision variables of he umed hydro sorage. The equaion for is similar o Equaion (7). The fly wheel energy balance equaion is similar o Equaion (5). The umed hydro sorage energy balance equaion is similar o Equaion (4).
Energies 2015, 8 8038 Subsequenly, he discree-ime hree-order dynamic equaion of he wind ower wih hybrid sorages can be wrien as follows: Xk ( 1) A Xk ( ) Buk ( ) B ε( k) 1 2 1 1 1 E 010 E η 0 0 0 0 E E fa wind k1 000 k k 1 1 1 k fw fw f a k1 k 3 k k η 4 001 k k k 0 0 0 0 η1 k η 2 (24) and he ouu equaion is: yk ( ) C X( k) k k fw 100Ek Ek (25) 4.4.2. Two-Level MPC Programming Model (a) Programming Model of MPC2 The rogramming model of MPC2 is similar o ha of single-level MPC Case 0; herefore, he objecion and consrains can be reresened by Equaions (10) (16). (b) Programming Model of MPC1 MPC 1 addresses Cases 1 5. In hese cases, he umed hydro sorage variable is a consan. (1) MPC1 Objecive Funcion of he Model (2) MPC1 Consrains min N w 1 w 2 w 3 s lan (26) 0 Equaions (11) (15) are also he consrains of MPC 1 because he redicion horizon is reduced significanly, i.e., i is smaller han ha of he single-level MPC, as described in Table 2. Table 2. Parameers for differen cases of wo-level model redicive conrol (MPC1). Parameer Case 0 Case 1 Case 2 Case 3 Case 4 Case 5 N 23 4 3 2 1 0 0 23 0 4 0 3 0 2 0 1 0 variable Consan Consan Consan Consan consan x The MPC1 consrains of Assumion 1 are resened as follows: x x x x x x Case1: 0 1 2 3 4 _ iniial (27) x x x x x Case 2 : 0 1 2 3 _ iniial (28) x x x x Case3: 0 1 2 _ iniial (29)
Energies 2015, 8 8039 x x x Case 4 : 0 1 _ iniial (30) x x Case5: 0 _ iniial (31) The meanings of he five consrains are he same as hose in Equaion (17). 5. Simulaion Resuls and Discussion To verify he roosed scheduling mehod, exensive simulaions are erformed based on an acual wind farm using MATLAB (R2011a) and Clex (12.4) sofware. The daa used in his sudy are obained from he ower generaion daa for a wind farm in Inner Mongolia, China, wih an insalled caaciy of 50 MW. The samling ime of he MPC is 5 min. The simulaions have a duraion of 24 h and include a oal of 288 es oins in oal. A each samling oin, he forecas ower daa of he wind farm is required, and hese daa can be obained from he redicion sofware or algorihm [36]. In his aer, hese daa are obained by adding random noise o he ower daa of a real wind farm. The arameers of umed sorage and flywheel sorage are lised in Table 3. The arameers of he hybrid sorage sysems are aken from our revious sudy [37]. In [33], we considered he minimized invesmen and he maximized revenue of hybrid sorage sysems. A wind farm ower daase covering a one-year imesan is used o obain he oimal sorage. Table 3. Parameer reresenaions of he umed sorage saion and he fly wheel ower saion. Tye Charging Power (MW) Discharging Power (MW) Iniial Energy (MWh) Minue Energy (MWh) Maximum Energy (MWh) Efficiency (η1, η2) Efficiency (η3, η4) Pumed sorage 100 100 100 20 200 0.87 0.85 Fly wheel 10 10 2.5 0.0 5 0.95 0.95 The aim of his research was o resen wo MPC models o manage a wind farm and a hybrid sorage sysem. In Secion 5.1, he simulaion resuls of he single-level MPC are comared wih hose of he wo-level MPC. 5.1. Simulaion Tes for Three Sub-Objecives Based on Single-Level and Two-Level MPC Three sub-objecives were esed under he condiion ha w1 = 0.9, w2 = 1.0, and w3 = 0.1, where w1, w2, and w3 are he weighing coefficiens of hree sub-objecives. Noe ha in Secion 5.1, he weighing coefficiens are consans; however, in Secion 5.2, he values of hese coefficiens vary wih ime. Figure 9 shows he ime hisories of he ower signals over he 24 h simulaion ime. Three ower signals are shown: he lan ower of he grid lan (solid, red), he single-level generaion ower of he wind-sorage sysem (dash-lus, black), and he wo-level generaion ower of he wind-sorage sysem (dash-do, gray). From Figure 9, i can be noed ha he single-level follows he lan closely, exce for some oins. From he magnified views of differen areas, clearly does no follow he lan clearly a 655, 680 or 710 min. Two ossible reasons for he differences beween he single-level and lan are as follows: (1) he caaciy of fly wheel sorage is close o sauraion in hese momens, srongly limiing
Energies 2015, 8 8040 he charging abiliy, and (2) he weigh of wind curailmen (w2 = 1.0) is greaer han ha of he difference beween and lan (w1 = 0.9). I seems ha a difference beween he lan and should be ermied, for reducing wind curailmen. Moreover, he wo-level also follows he lan closely, exce for he ime oins of 640, 655, 670, 680, 685, and 710. However, he wo-level fails o follow he lan comleely a he 880-minue oin. I is likely ha he single-level MPC mehod erformed beer han he wo-level MPC mehod in erms of following he lan. A ossible exlanaion for his behavior is ha he redicion horizon of he single-level MPC is longer han ha of he wo-level MPC, as shown in Figures 5 and 7. 16 15 lan single-level wo-level 13.8 13.6 Zoom in 880 895 Power/ M W 14 13 12 15 Zoom in 11 14 620640660680700720 10 0 500 1000 1500 / min Figure 9. Simulaion resul for he firs sub-objecive. The wo-level MPC mehod has he benefi of reducing he soluion ime. For he wo-level mehod, he average comuing ime of a scheduling inerval is aroximaely 12.1 ms, while for he single-level MPC mehod, he ime is 33.6 ms. In oher words, he wo-level mehod significanly reduces he comuing ime by aroximaely 64%. The resul of he second sub-objecive is as follows. In Figure 10, wo ower signals are deiced: he single-level wind curailmen () (solid-lus, black) and he wo-level wind curailmen (dash-do, gray). Figure 10 shows he resuls of he wind curailmen of he single-level MPC mehod vs. ha of he wo-level MPC mehod. For boh mehods, he ime of occurrence of wind curailmen is nearly he same, and he amoun of single-level is aroximaely he same as ha of he wo-level. The amoun of single-level is 11.68 MW, corresonding o 0.3% wind energy during a day, while ha of wo-level is 10.35 MW, corresonding o 0.26% wind energy. The resuls sugges ha for he second sub-objecive, he wo-level MPC mehod may be slighly beer han he single-level MPC mehod. This wase of wind-sourced energy can be aribued o wo main reasons: (a) he fly wheel is almos full, and (b) alhough he umed hydro sorage has a large amoun of unused sorage, i is consrained by Assumion 1, which does no allow i o use he excess wind energy. Taking he single-level MPC as an examle, he following exlains he reason for he firs wind curailmen. As shown in Figure 10, he firs wind curailmen occurs a minue 435 (inerval 88),
Energies 2015, 8 8041 s = 88. From Equaion (1), we know ha umed hydro sorage is in Case 4, i.e., i remained unchanged from 420 o 445 min (six scheduling inervals, half hour). Some basic informaion is rovided as follows. 1.5 single-level wo-level Power/ M W 1 0.5 Figure 10. Simulaion resul for he second sub-objecive. wind lan Table 4 indicaes ha he wind ower is greaer han he grid lan ( ), and he excess wind wind a fa wind energy mus be sored in he sorage sysems. In Equaion (4) ( ), is 20.15 MW; is 12.18 MW, due o he hird sub-objecive and consrains (Equaion (17)); a is fw assigned as 6.39 MW according o assumion 1. Based on Equaion (7) and E 1 5.0MW h, fw E 4.809MW h, we can calculae fa as 0.66 MW. Finally, based on Equaion (4) and he above wind fa resuls (,, ), we can calculae as 0.93 MW. a, 0 0 500 1000 1500 /min Table 4. Analysis on he cause of he wind curailmen. Values lan wind a fa E fw E Time(min) 435 440 445 450 455 /MW 12.18 12.19 12.20 12.21 12.26 /MW 20.15 20.16 16.26 18.45 17.39 /MW 12.18 12.19 9.86 12.21 12.26 /MW 6.39 6.39 6.39 4.51 4.51 /MW 0.66 2.42 0 1.73 0.62 /MW h 98.58 99.03 99.48 99.80 100.1 /MW h 4.809 5.0 4.80 4.93 4.98 The resul of he hird sub-objecive is shown as follows: Figure 11 shows he wind ower ha is direcly sen o he grid (). Moreover, Figure 11 shows ha he single-level is equal o he wo-level. The reason for his may be as follows: wind lan is he hird sub-objecive. When (he inequaliy means he wind ower is less han he grid demand; hus, he sorage sysems mus release energy o comensae for he missing energy beween a fa he wind ower and he grid demand in oher words, in his siuaion,,, are equal o 0), o maximize wind a fa wind, and mee he consrain, should be equal o.