Aggregated Energy Storage for Power System Frequency Control: A Finite-Time Consensus Approach

Transcription

1 Wang, Yu and Xu, Yan and Tang, Y and Lao, Ka and Syed, Mazheruddn H. and Gullo Sansano, Efren and Burt, Graeme () Aggregated energy storage for power system frequency control : a fnte-tme consensus approach. IEEE Transactons on Smart Grd. ISS 99- (In Press), Ths verson s avalable at Strathprnts s desgned to allow users to access the research output of the Unversty of Strathclyde. Unless otherwse explctly stated on the manuscrpt, Copyrght and Moral Rghts for the papers on ths ste are retaned by the ndvdual authors and/or other copyrght owners. Please check the manuscrpt for detals of any other lcences that may have been appled. You may not engage n further dstrbuton of the materal for any proftmakng actvtes or any commercal gan. You may freely dstrbute both the url ( and the content of ths paper for research or prvate study, educatonal, or not-for-proft purposes wthout pror permsson or charge. Any correspondence concernng ths servce should be sent to the Strathprnts admnstrator: strathprnts@strath.ac.uk The Strathprnts nsttutonal repostory ( s a dgtal archve of Unversty of Strathclyde research outputs. It has been developed to dssemnate open access research outputs, expose data about those outputs, and enable the management and persstent access to Strathclyde's ntellectual output.

2 Aggregated Energy Storage for Power System Frequency Control: A Fnte-Tme Consensus Approach Yu Wang, Member, IEEE, Yan Xu, Member, IEEE, Y Tang, Member, IEEE, and Ka Lao, Member, IEEE, Mazheruddn H. Syed, Student Member, IEEE, Efren Gullo-Sansano, Student Member, IEEE and Graeme Burt, Member, IEEE Abstract In future power systems, wdespread small-scale energy storage systems (ESSs) can be aggregated to provde ancllary servces. In ths context, ths paper ams to ntegrate energy storage aggregators (ESAs) nto the load frequency control (LFC) framework for power system frequency control. Frstly, a system dsturbance observer s desgned to supplement the secondary frequency control, where the ESA can respond to the estmated dsturbance and accelerate the system frequency recovery. Then, wthn the ESA, a fnte-tme leader-follower consensus algorthm s proposed to control the small-scale ESSs va sparse communcaton network. Ths algorthm ensures that the ESAs can track the frequency control sgnals and the state-ofcharge balancng among each ESS n fnte-tme. The external characterstcs of the ESA wll resemble to that of one large-scale ESS. umercal examples demonstrate the convergence of the ESA under dfferent communcaton graphs. The effectveness of the entre framework for power system frequency control s valdated under a varety of scenaros. Index Terms Frequency control, consensus algorthm, energy storage systems, aggregator, demand response. I I. ITRODUCTIO recent years, renewable energy sources (RESs), such as photovoltac (PV) panels and wnd turbnes, have been wdely ntegrated nto power grds []. In Sngapore, the PV penetraton level s expected to ncrease to about % n less than a decade from now on []. Although RESs are envronmentally frendly, ther hgh varablty and uncertanty have ntroduced sgnfcant challenges to power system s operaton and control []. Conventonally, the power mbalance between generaton and load consumpton s addressed by synchronous generators n large power plants. As the ncreasng penetraton level of RESs and subsequent replacement of synchronous generators, not only the system nerta but also the system frequency reserves wll be reduced. When a system dsturbance occurs, a power system wth less nerta and frequency regulaton reserves tends to experence more severe frequency devatons [], []. Therefore, Ths work s supported by Energy Innovaton Research Programme Energy Storage Grant (RFEWT-EIRP-), and also supported n part by the European Lason on Electrcty Commtted Towards longterm Research Actvty (ELECTRA) Integrated Research Program (IRP). Y. Wang, Y. Xu, Y. Tang, and K. Lao are wth School of Electrcal and Electronc Engneerng, anyang Technologcal Unversty, Sngapore. M. Syed, E.Gullo-Sansano, and G. Burt are wth Department of electronc and Electrcal Engneerng, Unversty of Strathclyde, Glasgow, UK. addtonal frequency regulaton resources and correspondng control methods are needed for hgh RES penetrated power systems. Energy storage systems (ESSs) have drawn sgnfcant attenton and have been progressvely deployed n modern power systems, due to ther hgh flexblty to contrbute to power system operaton and control []. The ESSs can be classfed accordng to ther capacty and ownershp. The large-scale centralzed ESSs whch are usually owned by the utlty grd can have the capacty up to tens of MWh. For example, the Energy Market Authorty of Sngapore has rased the target to nstall. MWh sland-wde ESSs by the year of []. The large-scale grd ESSs have been studed n the lterature to mtgate PV/wnd fluctuatons [] and power system frequency regulaton [9]. Except for large-scale ESSs, there are also a large amount of small-scale ESSs wdespread n the power system. The small-scale dstrbuted ESSs such as plug-n electrc vehcles (PEV) and communty ESSs usually have the capacty up to hundreds of kwh []. These small-scale dstrbuted ESSs also have large potental n future frequency ancllary servces market. In the lterature, the moble ESSs provded by PEVs are used for system frequency regulaton through vehcle-togrd or grd-to-vehcle operatons []. The statonary ESSs owned by both the utlty or customers can partcpate n system frequency and voltage regulaton through controlled chargng and dschargng [], []. However, the dstrbuted ESSs located at the demand sde are usually larger n numbers but smaller n capacty. Therefore, ther contrbutons to the power system are hard to account ndvdually. The concept of aggregator offers the feasblty for large number of smallscale ESSs to partcpate n ancllary servces (such as frequency regulaton and restoraton) to gan addtonal ncome [], []. In an aggregator, the geographcally dspersed unts can cooperate to acheve a common obectve through communcaton networks. Correspondngly, the energy storage aggregator (ESA) wll have much larger power and capacty ratng compared to a sngle ESS and t can be vewed as one entty for the system operator. One maor obectve of ths paper s to study the formaton and dynamc response of these ESAs. In terms of control methods, centralzed control structures of ESSs have been proposed n some lteratures for power system frequency control. In [], a fuzzy-logc based control

3 for wnd farms and ESSs wthn the load frequency control (LFC) scheme has been proposed. In [], a master-slave based centralzed control of dstrbuted ESS has been proposed for mtgatng voltage and frequency devatons. Smlarly, a centralzed coordnated control for EVs and ESSs partcpatng n LFC has been presented n []. The maor concern of the centralzed control structure s the requrement of a central communcaton nfrastructure. Ths bottleneck lmts the support for plug-and-play functons whch s hghly desred for wdespread dstrbuted devces. As an alternatve method, dstrbuted control has rased consderable attenton n the power system communty. Unlke the centralzed control, ths control scheme does not need full communcaton access as each controllable devce only communcates wth ts neghbours, whch s more sutable for wdespread dstrbuted resources n the dstrbuton network. The dea of consensus based dstrbuted control s to acheve far utlzaton of avalable devces by exchangng nformaton through sparse communcaton networks. Ths control algorthm has frstly been appled to dstrbuted control for a group of PV systems and ESSs for dstrbuton networks voltage control n [], [9]. In [], the leader-follower consensus control of responsve load aggregators has been proposed for LFC. Ths research work has been further extended n [], where a compound control strategy ncludng model predctve control and consensus-based dstrbuted control has been desgned to control ESSs n LFC scheme. The state-of-charge (SoC), as the key performance ndcator of ESSs s not consdered n [9], []. Besdes, the convergence of the above method n fnte-tme s not guaranteed. As a result, the convergence tme may be too long, and the frequency performance cannot be satsfactory. By contrast, the fnte-tme consensus can ensure the convergence of partcpants n fnte tme, whch can effectvely enhance the overall system dynamc performance. In [], a fnte-tme dstrbuted cooperatve voltage unbalance compensaton method for mcrogrd s proposed. In [], a fnte-tme dstrbuted voltage and frequency restoraton strategy s proposed for slanded AC mcrogrds. Yet so far, lttle research has been reported usng the fnte-tme consensus approach to control both the power outputs and SoCs for an aggregator of ESSs smultaneously. Compared wth prevous research, the contrbuton of ths paper s twofold: ) a novel frequency control framework s proposed to ntegrate the ESA nto the power system LFC. A system dsturbance observer s proposed to supplement the secondary frequency control of ESA. The hgh-frequency system dsturbance n one control area can be extracted and compensated by the ESA. Compared wth the conventonal proportonal-ntegral (PI) based secondary frequency control methods, the proposed control scheme explots the full potental of fast response speed of ESAs, thereby mprovng system frequency recovery speed; ) a leader-follower fntetme consensus algorthm s proposed to control ESSs n the ESA. Ths algorthm ensures power trackng and SoC balancng of ESSs n fnte-tme, allowng for desred dynamc performance to be obtaned through a proper desgn. For the proposed consensus-based ESA, frst, a vrtual leader wll update the reference power and energy states based on the frequency control sgnal. Then the reference states are receved by the pnnng ESSs and transmtted to all ESSs through predefned communcaton networks. The power and energy states of each ESS wll reach consensus at steady-state. Compared wth the exstng method, the benefts of the proposed ESA wth fnte-tme power trackng and SoC balancng are: () t avods unntentonal swtchng off of certan ESSs when they reach ther SoC lmts, () the ESA can mantan a larger power ratng for a longer tme, () t s convenent for the upper level controller to manage the SoCs of the entre aggregator, and (v) t offers plug-and-play capablty,.e. when a new ESS ons the aggregator for frequency control, ts SoC can autonomously be balanced wth other ESSs. II. PROPOSED FREQUECY COTROL FRAMEWORK A. System Overvew An overvew of the proposed frequency control framework s shown n Fg.. As hghlghted n Fg., there are two contrbutons of ths paper: () a novel frequency control framework that ncorporates a system dsturbance observer to supplement the secondary frequency control, and () a leaderfollower fnte-tme consensus algorthm to control ESSs wthn an ESA. In ths secton, the mult-area LFC model and the proposed dsturbance observer are ntroduced. The detaled desgn of the ESA based on fnte-tme consensus algorthm s presented n Secton III. Under the proposed frequency control framework, the frequency control sgnal of the ESA s comprsed of two parts: () The AGC sgnal from the secondary frequency control wth a predefned partcpaton factor ESA. It should be noted that the AGC sgnal s shared by both generators and ESAs n each control area. () The system dsturbance sgnal estmated by the system dsturbance observer. The obectve of ths desgn s to accelerate the frequency recovery speed as compared to the conventonal PI based secondary frequency control methods. The frequency control sgnal of the ESA s further shared among each ESS through the proposed fnte-tme consensus algorthm. System Dsturbance Observer Secondary Control (AGC) Bandpass Flter Proposed Dsturbance Observer Prmary Control Communcaton etwork ESS ESS... ESS n Energy Storage Aggregator Fg.. An overvew of the proposed frequency control framework.

4 B. Mult-Area LFC Model wth ESAs Consder an nterconnected power system wth M control areas ndexed by =,, M. The LFC model, ncludng RESs and ESAs, of the th control area s presented n Fg.. The am of prmary control s to contan the frequency devaton caused by power mbalance n any control area, whle the secondary control,.e. automatc generaton control (AGC), ams to recover the frequency back to the nomnal value []. The system dynamcs of the th area can be represented by the followng dfferental equatons: D f& ( t) f( t) H Pm ( t) PL, ( t) PRES, ( t) Pte, ( t) PESA, ( t) H () Ta P& m ( t) Pm ( t) Pg ( t) P& g ( t) () T T T b b b P& g ( t) Pg ( t) Pc ( t) f ( t) () T T RT g g g M P& te, ( t) T ( f ( t) f ( t)) (), where f s the change n system frequency, P c denotes control effort of secondary control, P m and P g are the devatons of generator mechancal output and valve poston, respectvely. H, D, R, T g T a and T b are the system nerta, load dampng coeffcent, speed droop, governor and turbne tme constants, respectvely. P L,, P RES,, P te, and P ESA, are power varatons of loads, RESs, te-lne and ESAs, respectvely, whch can be vewed as external dsturbances to the system. The control nput for the secondary control s called area control error (ACE) and can be defned as ACE ( t) B f ( t) P ( t) () te, where B the frequency bas factor. In the LFC model, (proportonal ntegral) PI control s commonly utlzed for the secondary control, whch s to elmnate the ACE for each control area. The PI based AGC controller can be desgned as P ( t) K ACE ( t) K ACE ( t) () c P I where K P and K I are the proportonal and ntegral gans, respectvely. In practcal condton, the frequency recovery tme by secondary frequency control can be as long as mn. Tradtonally, synchronous generators n large power plants are responsble for frequency control caused by the load varaton n the power system. As the penetraton of RESs ncrease rapdly n power systems, addtonal dsturbances have been added to the orgnal LFC model. Gven the hgh controllablty, flexblty, and scalablty of ESAs, addtonal frequency support can be provded by ESAs. C. Proposed Dsturbance Observer The proposed dsturbance observer s comprsed of a dsturbance observer and a band-pass flter n seres. The followng sub-sectons explan the detaled desgn of the proposed dsturbance observer. Dsturbance Observer: The desgn obectve of the dsturbance observer s to estmate the real power varatons of the control area wthn whch t s deployed, n real-tme. Usng system dynamcal equatons ()-() n th control area, a state-space model th control area can be obtaned as follows: &x ( t) A x ( t) B ( t) F P ( t) () d where the state varable x f Pm P g, the system nput Pc, the system dsturbance Pd PRES, PL, P P. It s noted that the power output of ESA s also te, ESA, ncluded n the system dsturbance. Thus, wth proper control of the ESA, the observed system dsturbance can be reduced. D H H Ta Ta A, RT gtb T b Tb TgT, B b Tg RT g T g T F. H Wth the state space model () of the th area, the system dsturbance observer can be desgned as []: xˆ & ( ) ˆ ( ) ( ) ˆ t A x t B t Fd ( t) R( y ( t) yˆ ( t)) () yˆ ( t) Cxˆ ( t) where C s an dentty matrx, C = dag{,, }, R s constant gan matrx, d ˆ s the estmated system dsturbance. Wth the estmated states x ˆ, the system dsturbance can be estmated as follows: ˆ d ( t) ( t) + Mxˆ ( t), (9) &( ) ( ˆ ( ) ( ) ˆ & ( )) ˆ t M A x t B t Fd t d ( t) where s an auxlary varable, M s a constant gan matrx. Defnng the state estmaton error and dsturbance estmaton error as x x xˆ and d d dˆ, the output estmaton error can be obtaned wth Cx. T Wth () and (9), the estmated state error dynamcs become: &x ( t) ( A RC ) x ( t) F d ( t) () Combnng the dsturbance estmaton error and state estmaton error: &( t) A ( t) () T where x d and = A RC F A. MRC The egenvalues of the matrx A can be placed arbtrarly by selectng the gan matrxes R and M as: det[ si A ] ( s ) () m

5 where are the desred egenvalues of the system. Through the egenvalue palcement n (), the desred dynamcs of system dsturbance observer can be desgned. Band-Pass Flter: A band-pass flter s desgned to extract the magntude of system dsturbance to be compensated by the ESA wthn the control area. The functon of the band-pass fler s llustrated n Fg.. The key dea s to decompose the estmated system dsturbance, where the hgh-frequency components of system dsturbance wthn the passband [f L, f H ] wll be sent to the ESA. Therefore, the ESAs can respond to sudden system dsturbance and mprove the system frequency response. The very hgh-frequency components of system dsturbance [f H, ] can be vewed as system nose, whle the low-frequency components wthn [, f L ] can be compensated by conventonal generators. Generally, f H s selected to be larger than the recprocal of response tme of the ESA and f L s selected to cover the most senstve frequency band []. Ampltude (db) db -db Stopband Compensated by generators fl Passband Compensated by ESAs Fg.. The functon of the band-pass flter. fh Stopband db System nose III. FIITE-TIME COSESUS-BASED ESA f(hz) In a realstc power grd, the small-scale ESSs are usually owned by customers that lack drect communcaton wth the AGC controller. In ths condton, the ESSs can be sparsely connected to form an ESA, whch can partcpate n system frequency servces as an entty. In ths secton, detaled desgn of the ESA based on the fnte-tme consensus approach and ts characterstcs wll be ntroduced. A. Communcaton etwork Prelmnares The communcaton network of an aggregated ESSs (denoted by =,,..., ) can be descrbed by a graph, whch s defned as G = (V, E) wth a set of nodes V = {v, v,,v } and a set of edges E = V V. Each node s assgned to an ESS n the ESA, and edges represent communcaton lnks for data exchange. If communcaton lnks are bdrectonal, (v, v ) E (v, v ) E, the graph s sad to be undrected. Otherwse, t s drected. A drected graph s sad to have a spannng tree, f there s a root node, such that there s a drected path from the root to any other node n the graph. A matrx called adacency matrx A = [a ] where a can be defned as a, f ( v, v ) E =, otherwse. () The n-degree matrx of G s defned as = dag{} wth =. The Laplacan matrx can be represented as a, L l = n () a, The Laplacan matrx L has propertes that all row sums of L are zero. For the system wth a leader (labelled as node ), the nteracton topology can be expressed by drected graph G, whch contans orgnal graph G, node v and edges (v, v ) from node v to other nodes. The leader can send nformaton to followers, but not vce versa. The matrx G = dag{g, g, g } s used to descrbe whether each follower drectly receve nformaton from the leader, where g, f ( v, v) =, otherw se. () One mportant property to guarantee that the leaderfollower consensus algorthm wth graph G wll convergence s that the graphg contans a spannng tree rooted at node and all the egenvalues of matrx L+G have postve real parts []. B. Fnte-Tme Consensus Algorthm for ESA In ths paper, a fnte-tme leader-follower consensus algorthm s proposed to control each ESS n the ESA. Compared to other consensus algorthms, the fnte-tme consensus approach guarantees the power trackng and SoC balancng of each ESS n fnte-tme. The modellng and desgn of fnte-tme consensus based ESA are llustrated as below. The real power output of th ESS s determned by: where ESS, P ( t) p ( t) P () ESS, ESS, P s the power ratng (MW) of th ESS. p s the power state of the communcaton agent assocated wth th ESS. p [-, ] n practcal applcaton consderng the power lmts of ESS. The SoC of th ESS can be estmated as: where ESS, P () t T ESS, SoC ( t) SoC () dt t CESS, () C and SoC () are the capacty (MWh) and ntal SoC of the th ESS. s the chargng or dscharng effcency of the th ESS. C s multpled by to convert the unts ESS, from hours to seconds. Defne an energy state e whch s equal to the SoC of th ESS. e [, ] consderng the capacty lmts of ESS. Combnng () wth () and dfferentatng t wth respect to tme, the relatonshp between p and e s expressed as: P p () t e& ( t) K p ( t) () ESS, CESS, ESS, where K ESS, s a coeffcent between p and e. In ths paper, t s assumed that the power output of each ESS s rated at C, whch means P and ESS, C have the same value but dfferent ESS,

6 unts, and =.9 s of the same value for each ESS n one ESA. Consderng the control nput dynamcs of power state, the ESA can be modelled as a group of homogenous double ntegral systems as follows: e& ( t) KESS p ( t),,...,. (9) p& ( t) u( t) where e and p are the energy and power states and u s the control nput of th ESS. A leader s defned as a controller whch can receve the upper level control sgnal (frequency control sgnal n ths paper). The leader wll update the reference power state and energy state of the ESA as follows: e& ( t) K ESS p ( t) * PESA () t () p ( t) PESA where e and p are reference energy and power states of the * P ESA s the system frequency control sgnal and the power ratng of the ESA, whch s equal to P ESS,. leader. PESA s Therefore, the research problem can be formulated as desgnng a leader-follower fnte-tme consensus control for a group of ESSs wth model (9) and () n an ESA. For an ESA formulated by (9) and (), the leaderfollower fnte-tme consensus s acheved, f for any ntal states, there exsts a T [, ], such that lm e ( t) e ( t), lm p ( t) p ( t) tt tt e ( t) e ( t), p ( t) p ( t), t T,,,.... () In order to acheve (), the leader-follower fnte-tme consensus control protocol s desgned as follows: u ( t) a ( sg( e ( t) e ( t)) ) g ( sg( e ( t) e ( t)) ) a ( sg( p ( t) p ( t)) ) g ( sg( p ( t) p ( t)) ) () where the functon sg( x) x sgn( x), x denotes the absolute value of varable x, and sgn(.) denotes the sgn functon.,, are control gans to be selected,,, (,), and / ( ). The settlng tme T satsfes the nequalty []: V () T c ( ) () where V(x) s a postve defnte functon defned n a neghbourhood of the orgn, and real number c>. The stablty of system (9) and () wth the protocol () can be proved usng Lyapunov s second method by properly selectng Lyapunov functon. The detaled proof s gven n Appendx. C. umercal Illustratons Ths secton ams to show the dynamcs of power and energy states and valdate control effectveness under dfferent communcaton graphs. The control algorthm s tested under two drected communcaton graphs ( G and G ), as shown n Fg.. In G, ode (ESS ) s consdered as a pnnng node whch can receve the nformaton from the leader labelled as. Other ESSs are connected n a drected lne as shown n Fg. (a). In G, odes and are both pnng nodes Whle other ESSs are connected n two drected lnes as shown n Fg. (b). The convergence of each ESS wth communcaton graphs G and G are shown n Fg. and Fg., respectvely. The fgures are drawn wth T ca =.s, e =. and =., =., =.. There s a step change n p from to. at s. The ntal energy states of each ESS are [.,.,.,.9,.,.,.,.] and ntal power state for all s. (a) Fg.. Communcaton network represented by two drected graph. Power state (p.u.) Energy state (p.u.) Tme (s) Fg.. Convergence speed of ESA wth communcaton graphg. Power state (p.u.) Energy state (p.u.) (b) Tme (s) Fg.. Converge speed of ESA wth communcaton graphg.

7 The results n Fg. and Fg. are further llustrated n tme sequence: ) <t<s. At the begnnng, the energy state of each ESS s not equal. Although the reference power state s durng ths perod, each ESS stll need to charge or dscharge n order to balance the energy state. As shown n Fg. and Fg., both G and G wll converge to consensus and satsfy () n fnte-tme. In Fg., the convergence of ESSs s not symmetrcal as graph G s unbalanced. Whle n Fg., the convergence of ESSs - and ESSs - become symmetrcal as these two sub-groups have same topologes n graph G. The sum of power state for all ESSs n graph G remans, whch s preferred as t s not desred that the SoC balancng nfluences the external characterstcs of the ESA. ) s<t<s. As the consensus s reached n the frst tme perod, the power and energy states of each ESS are equalzed. When there s a step change of p from to. at s, all ESSs start to track the new reference power state. Because the energy states are balanced durng ths perod, the power states of ESSs wll converge to p much faster. The overshoot of G s smaller than G, as the connecton of last node n G s actually shorter than G. From the numercal llustraton, t s valdated that both G and G can converge n the fnte-tme. However, G s preferred as t can reach consensus wth smaller overshoot and does not nfluence the external power response of the ESA. G wll be adopted n the smulaton tests n Secton IV. Generally, the dynamcs of the ESA are nfluenced by factors such as communcaton rate, graph and control protocol. IV. SIMULATIO TESTS In ths secton, a varety of scenaros are tested to valdate the proposed frequency control framework. The LFC model and the proposed ESA are mplemented n Matlab/Smulnk. To evaluate the performance of the proposed method, both system contngency and normal operaton scenaros have been consdered. The smulaton has been frst conducted n sngle LFC area, and then extended to mult-lfc areas. The LFC system under consderaton s a per-unt system wth S base = MVA. The parameters of the proposed method are shown n Table I. The parameters of the three-area LFC are shown n Table II [9]. The parameters of each test case are shown n Table III. It s assumed that n one control area all the ESSs are aggregated nto one ESA. The capacty of the ESA (C ESA ) n Area s.mwh, wth eght ESSs of capacty [.,.,.,.,.,.,.,.] MWh. Whle the capacty of the ESA n Area s scaled up to. MWh. TABLE I PARAMETERS OF PROPOSED METHOD Parameter Value Band-pass flter (f L, f H).Hz, Hz Fnte-tme consensus control (,, ).,.,. Communcaton rate (T ca).s TABLE II PARAMETERS OF THREE-AREA POWER SYSTEM Area o. H (p.u./hz)... D (p.u./hz)... T a (s). T b (s) T g (s)... R (Hz/p.u.).. B (p.u./hz)..9. T (p.u./hz)... C ESA (MWh).. TABLE III PARAMETERS OF EACH TEST CASE Test Case Load Varaton (P L,) PV Varaton (P RES) ESA Capacty # At s, to. MW.A.. MWh n Area # Fg. 9 Fg. 9. MWh n Area # At s, to. MW n Area ; At s, to 9. MW n Area A. Test Case : System Contngency.A.. MWh n Area ;. MWh n Area In test case, the dynamc performance of the proposed method s nvestgated under system contngency condton n a sngle area power system. Area wth. MWh ESA, as n Table II, s consdered wth ntal SoCs of ESSs as %. A load dsturbance of. MW at s emulates the contngency. The system frequency responses under orgnal control scheme wthout ESA, wth ESA but wthout the dsturbance observer, and the proposed control scheme are compared n Fg.. Upon occurrence of the dsturbance at, the frequency of the system begns to drop. The dynamcs of the ESA s manly governed by the proposed dsturbance observer other than AGC sgnal n ths condton. As a result, t can be observed that both the frequency nadr and the frequency devaton recovery wthn the allowable range (±. Hz) are evdently mproved wth the proposed control scheme. The performance of the system dsturbance observer s shown n Fg.. The parameters of matrxes M and R are chosen as M = [-, -, -] and R = dag{,, } accordng to () and (). In ths condton, the egenvalues = -., = -,, = -.±. are assgned to the dsturbance observer and the system () s stable. It can be notced that the estmated system dsturbance can track the actual system dsturbance after a short tme. The partcpaton of the ESA n conuncton wth the proposed dsturbance observer actually reduces the total system dsturbance as compared to the load step of. MW, thereby mprovng the frequency response. The power output of each ESS n the ESA durng ths process s shown n Fg.. As shown n Fg., each ESS can respond fast to the load change and reach ts mum power output when there s a large system dsturbance. The response speed of each ESS s determned by control protocol () as well as communcaton graphs. The mum power ratng of each ESS s also reflected n Fg., whch s the same as the

8 capacty of each ESS mentoned before. As the ESA s desgned to compensate the power varaton rather than the steady-state dsturbances, the band-pass fler wll reduce the power output of each ESS from s. Correspondngly, the dsturbance n Fg. wll gradually ncrease after s due to the reducton of power output from the ESA Proposed method ESA w/o observer Orgnal scheme (w/o ESA) -. Tme (s) Fg.. The frequency response under a step load change. Dsturbance (MW) Load step Actual dsturbance Observed dsturbance -. Tme (s) Fg.. Perfomance of the proposed dsturbance observer Tme (s) Fg.. The power output of each ESS n the ESA. B. Test Case : ormal Operaton In test case, the normal operaton study s conducted to further nvestgate the dynamc performance of the proposed method. The same sngle area system s consdered as n test case. The one-hour PV and load varaton profles used n ths case are shown n Fg. 9. The PV data wth -second resoluton was measured on June by EPRI []. The PV profle has very hgh fluctuatons whle the load profle s much smoother. The ntal SoC of each ESS n the ESA s [%, %, %, 9%, %, %, %, %]. In ths test case, the AGC partcpaton factors of ESAs and generators are ESA =. and G =.9, respectvely. Power Varatons (MW).... PV Load Tme (s) Fg. 9. One-hour PV and load varaton profles. Fg. (a)-(c) show system frequency devatons wth the orgnal control scheme, wth ESA but wthout observer, and wth the proposed control scheme, respectvely. Comparng Fg. (a)-(c), t can be observed that frequency devatons are mtgated much more effectvely wth the proposed method. The frequency devatons can be regulated n an allowable range (±. Hz) wth the.mwh ESA usng the proposed method. Furthermore, total power output of the ESA wth and wthout the proposed dsturbance observer s compared n Fg.. The results are correspondng to (b) and (c) n Fg.. The ESA wll react faster wth the proposed observer, thus the system frequency devaton becomes smaller (a) Orgnal scheme (w/o ESA) (b) ESA w/o observer (c) Proposed method (wth observer) Tme (s) Fg.. Frequency devatons wth and wthout proposed method Proposed method ESA w/o observer -. Tme (s) Fg.. Total power output of the ESA wth and wthout system dsturbance observer. The power output and SoC profles of each ESS n the ESA n ths test case s shown n Fg. and, respectvely. Intally, the SoC dfferences between each ESS are large. Therefore, the SoC balancng effect domnates the ESS dynamcs. The power sharng among each ESS s much nfluenced n order to balance SoCs. Whle the total power output of the ESA stll follows the frequency control sgnal. As the SoC of each ESS gradually become equalzed durng the operaton, the power sharng among each ESS become proportonal to ther power ratng, same as Fg. n test case. It can be also observed from Fg. that each ESS n the ESA responds to sudden PV fluctuaton to mtgate the frequency devatons.

9 Tme (s) Fg.. Power output of each ESS n test case State-of-charge (%) 9 Converged Tme (s) Fg.. SoC profle of each ESS n test case. C. Test Case : Mult-Area Power System In test case, the system contngency study s extended to mult- LFC areas to further nvestgate the performance of the proposed method. The structure of the studed three-area nterconnected power system s depcted n Fg.. In test case, t s assumed that there s. MWh ESA n Area and. MWh ESA n Area. There are step load dsturbances of. MW at s n Area and 9. MW at s n Area. The proposed dsturbance observer wll estmate the system dstance n each control area for correspondng ESA. Other smulaton condtons are the same as n test case. Te lne Te lne Area - Area - Area Te lne - Fg.. The structure of the studed three-area power system Tme (s) Fg.. Total power output of ESAs n Area and Area. Fg. shows the total power output of ESAs under step load changes n Area and Area, respectvely. The ESAs n Area and Area wll respond to the system dsturbance n the respectve control area, as shown n Fg.. Fg. shows the frequency response n each control area of test case. As shown n Fg., the sudden load changes wll nfluence the frequency n not only the same area, but also the nterconnected power systems. The frequency response of each control area can be mproved wth the proposed observer and fnte-tme consensus-based ESAs. Area Area (a) Area (b) Area (c) Area Proposed method w/o ESA -. Tme (s) Fg.. Frequency response of each control area. D. Control Algorthm Comparsons In ths sub-secton, the proposed fnte-tme consensus control protocol s compared to a commonly utlzed consensus control protocol for the second order mult-agent system reported n [9]. Compared to the fnte-tme approach n ths paper, the control protocol n [9] s lnear and nfnte-tme. For system (9) and (), the control protocol n [9] can be expressed as: u ( t) k a ( e ( t) e ( t)) g ( e ( t) e ( t)) k a ( p ( t) p ( t)) g ( p ( t) p ( t)) where k and k are control gans to be selected () -. (b) ESA Power Ouput.... Proposed method Method n [9] -. Tme (s) Fg.. Comparson wth the method n [9]. (a) frequency response. (b) ESA power output. Frstly, the performance of protocol () n [9] and the proposed protocol () are compared under system contngency scenaro n test case. The comparson results of frequency response and ESA power output are shown n Fg.. The control gans of protocol () s selected as k =, k =. As shown n Fg. (a), t can be found that the proposed method mproves the frequency nadr as compared to the method n [9]. Correspondngly, the power output of (a) Frequency response

10 9 the ESA under the proposed method also reacts faster than the method n [9], as shown n Fg. (b). Secondly, the protocol () n [9] s compared aganst the proposed control protocol under the normal operaton scenaro n test case. The results of Secton IV-B serve as a base reference,.e., the convergence tme for protocol () s s (as seen n Fg. ) and the mum power overshoot observed s. MW (for ESS as seen n Fg. ). The study s undertaken n two steps and the performance n terms of convergence tme and system overshoot are compared. In order to ensure the same convergence tme (s) as n test case, the control gans of protocol () are tuned as k =, k =. As shown n Fg. 9, the SoC of each ESS can converge at s, the same as n Fg.. However, the power overshoots n Fg. durng the convergence are much hgher than n Fg., whch even reach the power lmts of the ESSs. It can therefore be sad that the proposed method presents smaller system overshoot under the same convergence tme. In order to ensure the same mum power overshoot (. MW of ESS-) as n test case, the control gans of protocol () are tuned as k =, k =. As shown n Fg., mum power overshoot s. MW, the same as n Fg.. However, the SoC (or system) n Fg. converges much slower as compared to Fg.. amely, the proposed method can provde faster convergence speed under the same system overshoot Large power overshoot -. Tme (s) Fg.. Power output of each ESS wth protocol () (k =, k =). State-of-charge (%) 9 Converged Tme (s) Fg. 9. SoC profle of each ESS wth protocol () (k =, k =) Tme (s) Fg.. Power output of each ESS wth protocol () (k =, k =). State-of-charge (%) 9 Slow convergence Tme (s) Fg.. SoC profle of each ESS wth protocol () (k =, k =). The advantages of the fnte-tme approach compared wth the common used method n [9] are summarzed as follow. In case of a system contngency, the ESA wth the proposed fnte-tme approach has faster response of power output, thus far mproves the system frequency response. Under the normal operaton, the ESS wth proposed fnte-tme approach presents smaller power overshoot and faster convergence. Smaller power overshoot and faster convergence are desred for operaton of ESA as: () ESSs wthn the ESA have a lower chance to reach the power lmts durng the operaton and () any newly oned ESS can attan faster SoC balancng, ensurng plug-and-play capablty. V. COCLUSIO In ths paper, a new frequency control framework wth fnte-tme consensus-based ESA has been proposed to mprove the power system frequency response n the presence of stochastc renewable power generaton. The total frequency control sgnal for ESA s determned by both AGC commands and the proposed dsturbance observer. The control protocol usng a leader-follower fnte-tme consensus algorthm has been proposed to aggregate ESSs n one control area nto an ESA. The dynamc response or external characterstc of the ESA s determned by ts communcaton graph and control protocol settngs. Smulaton results have shown that the system frequency response can be mproved by usng the proposed dsturbance observer and fnte-tme consensus-based ESA. The proposed method s effectve for both power system contngency and normal operaton condtons. The ESA can track the frequency control sgnal and the SoC of each ESS can be balanced n fnte-tme durng the operaton. The proposed method has been extended to mult-area power systems. The comparatve studes valdate the advantages and necessty of the proposed method. The research results valdate that the proposed method s an effectve way to ncorporate wdespread ESSs for power system frequency control. APPEDIX A. Globally Asymptotcally Stablty Let pˆ ( t) p( t) p ( t), eˆ ( t) e( t) e ( t), the system (9) and () becomes eˆ & ( ) ˆ t KESS p ( t), pˆ & ( ) ˆ t u( t),...,. ()

11 The control protocol () becomes uˆ ( t) a ( sg( eˆ ( t) eˆ ( t)) ) ( sg( pˆ ( t) pˆ ( t)) ) g ( ( ˆ ( )) ( ( ˆ sg e t sg p ( t)) )) Choose a Lyapunov functon V V V V V n pˆ, n n eˆ eˆ eˆ V a ( sg( s) ) ds, n V pˆ ( sg( s) ) ds. Take the dervatve of V V& V& V& V& pˆ ( ( ˆ ˆ ) ( ( ˆ ˆ a sg e e sg p p ) ) g ( ( ˆ ) ( ˆ sg e sg p ) ) a ( ˆ ˆ ) ( ˆ ˆ p p sg e e ) ) g pˆ sg( eˆ ) pˆ ( ˆ ˆ ) ( ˆ asg p p gsg p ) a ( ˆ ˆ ) ( ˆ ˆ p p sg p p ) ) n g pˆ sg( pˆ ) a ( ˆ ˆ ) ( ˆ ˆ p p sg p p ) ) () Accordng to Lyapunov s second method for stablty, V V&. Therefore, the system () wth the control protocol () s stable. Furthermore, note that V&, f and only f ˆ ˆ whch mples pˆ &,,,.... p p, pˆ & ( t) a ( sg( eˆ ( t) eˆ ( t)) sg( pˆ ( t) pˆ ( t)) ) g ( ( ˆ ( )) ( ˆ sg e t sg p ( t)) ) a sg( eˆ ( t) eˆ ( t)) g sg( eˆ ( t)) It follows p a sg( e ( t) e ( t)) g sg( e ( t)) ( ) ( ) ( ) ˆ ˆ ˆ ˆ a ˆ ˆ ˆ ˆ ˆ ˆ e e sg e e ge sg e Equalty above mples that eˆ eˆ whch means the system wll converge to e e, p p at steady-state. Thus the system () wth control protocol () s globally asymptotcally stable. B. Locally Fnte-tme Stablty If the equlbrum of a control s globally asymptotcally stable and locally fnte-tme convergent, then the control s globally fnte-tme stable []. Ths follows the prncple that globally asymptotcal stablty mples fnte-tme convergence to any gven bounded neghborhood of the equlbrum. Wth the prevous proof of globally asymptotc stablty, the fnte-tme convergence of the system () wth control protocol () s proved as below. Lemma. (Lasalle s Invarance Prncple) k Let x(t) be a soluton of x& f ( x), x() x R, where f : U R k s contnuous wth U an open subset of R k, and let V : U R k be a locally Lpschtz functon such that D + V (x(t)), where D + denotes the upper Dn dervatve. Then, denotng the postve lmt set as + (x ), + (x ) U s contaned n the unon of all solutons that reman n S = {x U : D + V (x) = }. Defnton. (Homogenety wth dlaton) A functon V(x) of x R k s homogeneous of degree homogeneous of degree wth dlaton coeffcents (r,..., r r r k ), f (,..., k V x xk ) V( x),. If r =... = r k =, then the dlaton s called trval. Consder k-dmensonal system x& f ( x), x ( x,..., x ) T R k () A contnuous vector feld f(x) = (f (x),..., f k (x)) T homogeneous of degree R wth dlaton (r,..., r k ), f f x x f x. r r (,..., k k) ( ), System () s called homogeneous f ts vector feld s homogeneous. Moreover, k x& f ( x) fˆ ( x), ˆ(), k f x R () s called locally homogeneous f f s homogeneous of degree R wth dlaton (r,..., r k ) and ˆf s a contnuous vector feld satsfyng ˆ ( r,..., rk f x xk ) r lm, x. (9) Lemma. Suppose system () s homogeneous of degree wth dlaton (r,..., r k ), f s contnuous and x = s ts asymptotcally stable equlbrum. If homogenety degree <, the equlbrum of system () s fnte-tme stable. s

12 Moreover, f (9) holds, then the equlbrum of system () s locally fnte-tme stable. The we can get system wth varables ( eˆ, eˆ ˆ ˆ ˆ ˆ,..., en, p, p,..., pn) s homogeneous of degree wth dlaton (,,...,,,,..., ). Therefore, accordng to Lemma, the system wth control law s locally fnte-tme stable. Therefore, system () wth control protocol () s globally fnte-tme stable. In other words, we have eˆ eˆ, pˆ pˆ,, =,..., n fnte-tme. Ths completes the proof. REFERECES [] A. M. Bouzd, et. al., A survey on control of electrc power dstrbuted generaton systems for mcrogrd applcatons, Renewable Sustanable Energy Revews, vol., pp., Apr.. [] ext-generaton electrcty: The emergng negawatt and mcropower revolutons. [Onlne]. Avalable: [] H. Bevran, A. Ghosh, and G. Ledwch, Renewable energy sources and frequency regulaton: Survey and new perspectves, IET Renewable Power Generaton, vol., no., pp., Sep.. [] V. Knap, et. al., Szng of an energy storage system for grd nertal response and prmary frequency reserve, IEEE Trans. Power systems, vol., o., pp., Dec.. [] P. Kundur, Power System Stablty and Control. ew York, Y, USA: McGraw-Hll, 99. [] S. Vazquez, S. M. Lukc, E. Galvan, L. G. Franquelo, and J. M. Carrasco, Energy storage systems for transport and grd applcatons, IEEE Trans. Industral Electroncs, vol., no., pp. 9, Dec.. [] Launch of Sngapore's Frst Utlty-Scale Energy Storage System. [Onlne]. Avalable: Storage%Systems%Test-Bed%Meda%Release.pdf [] X. J. L, D. Hu, and X. K. La, Battery energy storage staton (BESS)- based smoothng control of photovoltac (PV) and wnd power generaton fluctuatons, IEEE Trans. Sustanable Energy, vol., no., pp., Mar.. [9] L. Mao, J. Y. Wen, C. Y. Yue, et al., Coordnated control strategy of wnd turbne generator and energy storage equpment for frequency support, IEEE Trans. Industry Applcatons, vol., no., pp., Jan.. [] U. C. Chukwu and S. M. Mahaan, VG parkng lot wth PV rooftop for capacty enhancement of a dstrbuton system, IEEE Trans. Sustanable Energy, vol., no., pp. 9-, Sep.. [] X. H. Lu, A. Achhorn, L. M. Lu, and H. Lu, Coordnated control of dstrbuted energy storage system wth tap changer transformers for voltage rse mtgaton under hgh photovoltac penetraton, IEEE Trans. Smart Grd, vol., no., pp. 9-9, Feb.. [] M. J. E. Alam, K. M. Muttaq, and D. Sutanto, Mtgaton of rooftop solar PV mpacts and evenng peak support by managng avalable capacty of dstrbuted energy storage systems, IEEE Trans. Power Systems, vol., no., pp., ov.. [] L. Gkatzks, K. Iordans, and S. Theodoros, The role of aggregators n smart grd demand response markets IEEE Journal on Selected Areas n Communcatons, no., vol., pp. -, Jul.. [] S. Burger, et al. The value of aggregators n electrcty systems, MIT workng paper,. [] S. Q. Zhang, Y. Mshra, and M. Shahdehpour, Fuzzy-logc based frequency controller for wnd farms augmented wth energy storage systems, IEEE Trans. Power Systems, vol., no., pp. 9-, Mar.. [] S. J. Lee, et al. Coordnated control algorthm for dstrbuted battery energy storage systems for mtgatng voltage and frequency devatons, IEEE Trans. on Smart Grd, vol., no., pp. -, May. [] J. Zhong, et al. Coordnated control for large-scale EV chargng facltes and energy storage devces partcpatng n frequency regulaton, Appled Energy, vol., pp. -, Jun.. [] H. H. Xn, Z. H. Qu, J. Seuss, and A. Maknounnead A self-organzng strategy for power flow control of photovoltac generators n a dstrbuton network, IEEE Trans. Power Systems, vol., no., pp. -, Aug.. [9] G. Mokhtar, A. Ghosh, G. ourbakhsh, and G. Ledwch, Smart robust resources control n LV network to deal wth voltage rse ssue, IEEE Trans. Sustanable Energy, vol., no., pp. -, Oct.. [] J. Q. Hu, et al. Improvng frequency stablty based on dstrbuted control of multple load aggregators, IEEE Trans. Smart Grd, ov.. [] Wen, Guanghu, et al. Frequency regulaton of source-grd-load systems: A compound control strategy, IEEE Trans. Industral Informatcs, vol., no., pp. 9-, Feb.. [] F. Guo, C. Wen, J. Mao, and Y. Song, Dstrbuted secondary voltage and frequency restoraton control of droop-controlled nverter-based mcrogrds, IEEE Trans. Industral Electroncs, vol., no., pp. -,. [] S. Zuo, A. Davoud, Y. Song, and F. L. Lews, Dstrbuted fnte-tme voltage and frequency restoraton n slanded AC mcrogrds IEEE Trans. Industral Electroncs, vol., no., pp. 9-99,. [] D. Gnoya, P. D. Shendge, and S. B. Phadke, State and extended dsturbance observer for sldng mode control of msmatched uncertan system, Journal of Dynamc Systems, Measurement, and Control, vol., no., Jul.. [] C. Luo, H. Banakar, B. Shen and B. T. Oo, Strateges to Smooth Wnd Power Fluctuatons of Wnd Turbne Generator, n IEEE Trans. Energy Converson, vol., no., pp. -9, June. [] H. Zhang, F. L. Lews, and Z. Qu, Lyapunov, adaptve, and optmal desgn technques for cooperatve systems on drected communcaton graphs, IEEE Trans. Industral Electroncs, vol. 9, no., pp.,. [] S. Yu, and X. Long, Fnte-tme consensus for second-order mult-agent systems wth dsturbances by ntegral sldng mode, Journal of Automatca, vol., pp. -, Apr.. [] -second resoluton data, EPRI. [Onlne]. Avalable: [9] S. Qang, J. Cao, and W. Yu, Second-order leader-followng consensus of nonlnear mult-agent systems va pnnng control, Systems & Control Letters, vol. 9, no.9, pp. -, Sep.. [] X. Wang, and Y. Hong, Fnte-tme consensus for mult-agent networks wth second-order agent dynamcs, IFAC Proceedngs Volumes, vol., no., pp. -9, Dec.. Yu Wang (S -M ) receved the B.Eng. degree from Wuhan Unversty, Wuhan Chna n, and the M.Sc. and Ph.D. degree from anyang Technologcal Unversty, Sngapore n and, respectvely. He s currently a research fellow n anyang Technologcal Unversty, Sngapore. Hs research nterests nclude dstrbuted control n power systems, energy storage systems and smart grds. Yan Xu (S -M ) receved the B.E. and M.E degrees from South Chna Unversty of Technology, Guangzhou, Chna n and, respectvely, and the Ph.D. degree from The Unversty of ewcastle, Australa, n. He s now the anyang Assstant Professor wth the School of Electrcal and Electronc Engneerng, anyang Technologcal Unversty, Sngapore. He was prevously wth the Unversty of Sydney, Australa. Hs research nterests nclude power system stablty and control, mcrogrd and multenergy network, and data-analytcs for smart grd. Y Tang (S M ) receved the B.Eng. degree n electrcal engneerng from Wuhan Unversty, Wuhan, Chna, n, and the M.Sc. and Ph.D. degrees n power engneerng from the School of Electrcal and Electronc Engneerng, anyang Technologcal Unversty, Sngapore, n and, respectvely. Ka Lao (M ) receved the B.E. and Ph.D. degrees from Southwest Jaotong Unversty, Chengdu, Chna, n and, respectvely. He s currently a Research Fellow n the School of Electrcal and Electronc Engneerng, anyang Technologcal Unversty, Sngapore. Hs research nterests nclude power system stablty and control, and renewable energy. Mazheruddn H. Syed (S ) receved hs B.E. degree n Electrcal and Electroncs Engneerng from Osmana Unversty, Inda, n and hs M.Sc. degree n Electrcal Power Engneerng from Masdar Insttute of Scence and Technology, UAE. Presently, he s a research assstant at the

13 Insttute for Energy and Envronment, the Unversty of Strathclyde, Scotland, workng towards hs Ph.D. Hs research nterests nclude demand sde management, decentralzed and dstrbuted control, and power hardware n the loop smulatons. Efren Gullo-Sansano (S ) receved hs M.Sc. degree n Electrcal Power Engneerng from the Unversty of Strathclyde, Glasgow, Scotland, n. He s currently a research assstant wth the Insttute for Energy and Envronment at the Unversty of Strathclyde, Scotland, where he s pursung a Ph.D. degree n electrcal power systems. Hs current research nterests nclude the testng and valdaton of dstrbuted energy resources and power electroncs, power hardware n the loop, dstrbuted control, and ancllary servces. Graeme M. Burt (M 9) receved the B.Eng. degree n electrcal and electronc engneerng, and the Ph.D. degree n fault dagnostcs n power system networks from the Unversty of Strathclyde, Glasgow, U.K., n 9 and 99, respectvely. He s currently a Professor of electrcal power systems at the Unversty of Strathclyde where he co-drects the Insttute for Energy and Envronment, drects the Rolls-Royce Unversty Technology Centre n Electrcal Power Systems, and s lead academc for the Power etworks Demonstraton Centre (PDC). In addton, he serves as spokesperson for the board of DERlab e.v., the assocaton of dstrbuted energy laboratores. Hs research nterests nclude the areas of power system protecton and control, dstrbuted energy, and expermental valdaton.