Application of Energy Storage Systems for Frequency Regulation Service

Transcription

1 Applicatio of Eergy Storage Systems for Frequecy Regulatio Service Yaa Su, Shahab Bahrami, Vicet W.S. Wog, ad Lutz Lampe Departmet of Electrical ad Computer Egieerig, The Uiversity of British Columbia, Vacouver, Caada {ysu, bahramis, vicetw, Abstract Frequecy cotrol aims to maitai the omial frequecy of the power system through compesatig the geeratio-load mismatch. I additio to fast respose geerators, eergy storage systems ca be exploited to provide frequecy regulatio service due to their fast rampig characteristic. I this paper, we propose a solutio to leverage eergy storage systems deployed i the distributio etworks for secodary frequecy regulatio service by cosiderig the ucertaity i system disturbaces, the eergy storage availability, ad the AC power flow model. I particular, we tackle the ucertaity i the frequecy deviatios ad alleviate the problem associated with the limited eergy storage capacity by usig a risk miimizatio techique. We formulate a liear program to determie the frequecy regulatio sigals to schedule the eergy storage systems by adoptig the cocept of coditioal value-at-risk (CVaR). It eables us to miimize the risk of deviatio from the omial frequecy after performig frequecy regulatio, while satisfyig the operatio costraits of the distributio etwork. Simulatios are performed o a IEEE 37-bus test feeder with three eergy storage systems that participate i the frequecy regulatio service. Results show that by usig the proposed approach, the chargig/dischargig of the eergy storage systems ca be scheduled to regulate the frequecy, ad the risk of eergy storage systems ot beig able to cotribute to future regulatio service ca be reduced. I. INTRODUCTION With the fast proliferatio of itermittet reewable eergy sources ad fluctuatios i load demad, power systems eed to withstad a icreasig umber of disturbaces that may affect the system frequecy. This requires a series of cotrol actios over a cotiuum of time usig differet strategies [1]. Whe the system frequecy deviates from its omial value (e.g., 50 Hz), the primary frequecy cotrol takes place withi the first few secods to stabilize the itercoectios. The secodary frequecy cotrol is the used to restore the system frequecy to its omial value. The system operator uses automatic geeratio cotrol (AGC) to compute the area error cotrol (ACE) sigals for frequecy regulatio. The ACE sigals idicate the amout of active power that should be ijected ito or absorbed from the power grid i order to restore the system frequecy to its omial value. The evolvig regulatory frameworks such as the recet orders issued by the Uited States (U.S.) Federal Eergy Regulatory Commissio (FERC) ope the acillary services market for ew techologies such as eergy storage systems [2] [4]. Specifically, the fast rampig characteristic of eergy storage systems makes them a attractive alterative to provide rapid ad accurate frequecy regulatio i respose to the ACE sigals issued by the system operator. There are several challeges for the system operator to leverage eergy storage systems for secodary frequecy regulatio service. First, the system operator has ucertaity about the system disturbaces, ad thus the frequecy chages i realtime operatio. The iteded service operatio cycle should be divided ito short frequecy cotrol itervals for the system operator to compesate frequecy deviatios i time if eeded. Secod, i each frequecy cotrol time slot, computig the ACE sigal for regulatio service is otrivial as it depeds o the power flow chages i the distributio etworks, which are affected by the chargig demad fluctuatios i the eergy storage systems to provide regulatio service. Third, the power flow costraits i the distributio etwork ca limit the schedulig flexibility of eergy storage systems for frequecy regulatio. The system operator eeds to satisfy the operatio costraits imposed by the distributio etwork for providig secodary frequecy regulatio service. Fourth, a eergy storage system may ot be able to participate i the regulatio service due to the limited battery capacity. Specifically, the schedulig decisio of a eergy storage system i each cotrol time slot affects the amout of its stored eergy, ad thus the amout of its cotributios i the frequecy regulatio durig the upcomig time slots. There have bee some efforts to address the aforemetioed challeges. Che et al. aalyzed the frequecy regulatio respose by usig eergy storage systems with differet peetratio rates give various system disturbace levels [5]. Zhag et al. compared the performace of usig eergy storage systems to compesate frequecy deviatios i a sigle-area system with covetioal geerators [6]. Zhag et al. proposed a framework to aalyze the optimal plaig ad cotrol strategy of usig eergy storage systems for frequecy regulatio service at the miimum operatio cost [7]. Yao et al. adopted a robust optimizatio framework to schedule eergy storage systems for frequecy regulatio service to maximize the fiacial profits uder the performace-based compesatio scheme [8]. He et al. proposed a real-time cooperatio scheme to coordiate wid turbies ad eergy storage systems for frequecy regulatio [9]. Ta et al. desiged a adaptive feedback cotrol scheme for eergy storage systems to coordiate with wid turbies for providig reliable frequecy acillary service [10]. I geeral, the participatio of the eergy storage systems i frequecy regulatio is a optimal

2 cotrol problem, where the regulatio sigals that are computed based o geeratio-load mismatch are used for schedulig decisios. However, optimizig across frequecy regulatio ad limited eergy storage capacity requires a proper desig of the regulatio sigals, where the eergy storage availability give the ucertaity i system frequecy deviatios should be addressed. Furthermore, the costraits imposed by the distributio etwork should also be cosidered. I this paper, we aim to exploit eergy storage systems i the distributio etwork for secodary frequecy cotrol to miimize the risk of deviatio from the omial value after performig frequecy regulatio. The mai cotributios of this paper are summarized as follows: We determie the ACE sigals to schedule the eergy storage systems to provide frequecy regulatio service by cosiderig the ucertaity i the system disturbaces, the availability of the eergy storage systems, ad the operatio costraits imposed by the distributio etwork. We itroduce a risk assessmet techique to tackle the limited capacity of the eergy storage systems. I particular, we adopt the cocept of coditioal value-at-risk (CVaR) to limit the risk of eergy storage systems ot beig able to cotribute to regulatio service, give the ucertaity i the frequecy deviatios. We evaluate the performace of the proposed frequecy regulatio approach usig simulatios o a IEEE 37-bus test feeder with three eergy storage systems to provide frequecy regulatio. We compare the performace whe differet eergy storage capacities are cosidered. Results show that our risk-averse model based o CVaR successfully reduced the impact of limited eergy storage o restorig the frequecy to its omial value for regulatio service. The rest of the paper is orgaized as follows. Our system model, icludig the distributio etwork model ad eergy storage system s costraits, is itroduced i Sectio II. The schedulig problem of eergy storage systems icorporated with CVaR is discussed i Sectio III. Simulatio results ad performace evaluatios of the proposed framework are preseted i Sectio IV. Sectio V cocludes the paper. II. SYSTEM MODEL Cosider a distributio etwork with a set of buses N ad a set of braches L N N. It cosists of some geerators, loads, ad eergy storage systems. Let N s N deote the set of buses with eergy storage system. The distributio etwork is coected to the trasmissio etwork through a substatio bus. We model the trasmissio etwork by a equivalet virtual geerator that ca iject/absorb active ad reactive power ito/from the distributio etwork [11]. This geerator models the power flow betwee the distributio ad trasmissio etworks. The system operator is resposible for moitorig the real-time system operatio icludig the power grid s frequecy ad power flow. We divide the operatio cycle ito set T = {1,..., T } of T time slots. Each time slot correspods to a short frequecy cotrol iterval (e.g., 15 miutes), durig which the system operator performs frequecy regulatio. At the begiig of time slot t T, the system operator observes the system frequecy deviatio ad activates the primary frequecy cotrol. The participatig geerators will respod withi few secods (e.g., 10 secods). Although the primary frequecy cotrol ca maitai the frequecy withi a certai rage, it may ot be able to restore the system frequecy to its omial value. Let ω(t) deote the system frequecy deviatio from the omial value after performig the primary frequecy regulatio i time slot t. I the ext step, the system operator uses the eergy storage systems for the secodary frequecy cotrol to restore the system frequecy. Let ω reg (t) deote the chage i the system frequecy i time slot t after performig the secodary frequecy regulatio. If ω reg (t) = ω(t), the system frequecy is restored to its omial value. The system operator computes the ACE sigal for each bus with eergy storage system to obtai the amout of active power that the correspodig eergy storage system should absorb from or iject ito the power grid. I the followig subsectio, we discuss how the system operator ca determie the ACE sigals. A. Computig the ACE Sigal To achieve the frequecy chage ω reg (t) i time slot t T, the system operator determies the ACE sigal for each bus. If the eergy storage systems participate i the frequecy regulatio service, the power flow i the distributio lies will chage. I particular, the ijected active power at bus N i time slot t T will chage from its scheduled value p ij (t) to p ij (t) after performig the frequecy regulatio. Let p ij (t) = p ij (t) p ij (t) deote the chage i the ijected active power at bus N i time slot t T after performig the secodary frequecy regulatio. I time slot t T, the ACE sigal correspodig to the eergy storage system at bus N s is equal to the chage i the chargig demad from the scheduled value p s (t) to p s (t). We have [12, p. 489] β ω reg (t) + p ij (t) = p s (t) p s (t), N s, (1) where β is the frequecy bias factor of bus N. It depeds o the characteristics of the geerator ad load coected to bus. I particular, for the secodary frequecy cotrol, the geerator at bus N ca be modeled by its speeddroop characteristic ϕ, which reflects the speed regulatio due to goveror actios [12, p. 477]. The load at bus N ca be modeled by its dampig coefficiet ψ, which is the ratio betwee the chage i the load ad the chage i the frequecy [12, p. 473]. The frequecy bias factor of bus ca be obtaied as β = 1 ϕ + ψ. Equatio (1) implies that whe the ACE sigal for a bus with eergy storage system is positive (egative), the eergy storage system decreases (icreases) its chargig power ad provides regulatio up (dow) service. The ACE sigal is zero if there is o eergy storage system

3 at bus i time slot t T. We have β ω reg (t) + p ij (t) = 0, N \ N s. (2) Computig the ACE sigals ad the frequecy chage ω reg (t) i (1) ad (2) is a otrivial task as it depeds o the distributio etwork power flow. I the followig subsectio, we provide a liearized AC power flow model to determie the chage i the ijected active power ito the buses durig the frequecy regulatio service. B. Distributio Network Model I a distributio etwork, the ratio betwee the resistace ad iductace of the lies ca be large. Hece, the system operator uses AC power flow model i the distributio etwork. The AC power flow equatios are o-covex ad difficult to be solved i a timely fashio. Similar to [13], we use a liear model to approximate the AC power flow i the distributio etwork. Let p ij (t) = (p ij (t), N ) ad q ij (t) = (q ij (t), N ) deote the vectors of ijected active power p ij (t) ad reactive power q ij (t) ito bus N i time slot t T, respectively. Let v(t) = ( v (t), N ) ad θ(t) = (θ (t), N ) deote the vectors of voltage magitude v (t) ad phase agle θ (t) of bus N i time slot t T, respectively. Give the the real ad reactive parts of the etry (m) i bus admittace matrix Y, deoted by G m ad B m, respectively, as well as the shut susceptace ad coductace at bus, deoted by b ad g, respectively, the liearized AC power flow model i time slot t T is obtaied as follows [ p ij (t) q ij (t) ] [ ] [ ] B G = θ(t), (3) G B v(t) where the th diagoal elemet of matrices B ad B is B ad B b, respectively. The o-diagoal elemet i row ad colum m of B ad B is B m. Similarly, the th diagoal elemet of matrices G ad G is G ad G g, respectively, ad the o-diagoal elemet i row ad colum m of G ad G is G m. I time slot t T, the liearized active ad reactive power flow through lie (, m) L with resistace R m ad reactace X m ca be obtaied as follows. p m (t) = R m ( v (t) v m (t) ) + X m (θ (t) θ m (t)) Rm 2 + Xm 2, (4) q m (t) = X m ( v (t) v m (t) ) R m (θ (t) θ m (t)) Rm 2 + Xm 2. (5) The apparet power flow s m (t) = p 2 m(t) + qm(t) 2 is upper bouded by s max m. This costrait ca be liearized by a piecewise approximatio of the circular boudary usig a regular polygo with cetral agle α. For (, m) L, we have p m (t) cos(hα) + q m (t) si(hα) s max m, (6) where h = { 0, 1,..., 2π }. The voltage magitude at bus α N i time slot t T is bouded by the limits v mi ad v max. We have v mi v (t) v max. (7) Costraits (3) (7) ca be used by the system operator to determie the feasible power flow withi the distributio etwork durig the secodary frequecy regulatio i time slot t. There are some operatio costraits for a eergy storage system, which are described i the followig subsectio. C. Eergy Storage System s Operatio Costraits I time slot t T, the power ratig of the eergy storage system at bus N s has limits p s,mi < 0 ad p s,max > 0. p s,mi p s (t) p s,max, N s. (8) Besides, the chage i the chargig power of a eergy storage system is subject to the ramp up ad dow ratig limits p s,mi < 0 ad p s,max > 0 due to the limits i its mechaical iertia. For t T \ {1}, we have p s,mi p s (t) p s (t 1) p s,max, N s, (9) ad p s,mi p s (1) p s,max, N s. If there is o eergy storage system coected to bus N \ N s, the p s,mi = p s,max = 0. Let E iit 0 deote the iitial eergy level of the eergy storage system at bus N s at the begiig of the operatig cycle T. The stored eergy i the battery util time slot t T is oegative ad upper bouded by the limit E max. We have 0 E iit t k=1 ps (k) E max, N s. (10) Costraits (8) (10) guaratee that the eergy storage systems operate withi their physical rage to provide regulatio. III. PROBLEM FORMULATION AND SOLUTION APPROACH I this sectio, we preset how the system operator determies the chargig/dischargig of the eergy storage systems to provide secodary frequecy regulatio service. Costraits (9) ad (10) imply that the operatio of a eergy storage system i curret time slot t T affects its eergy level durig the upcomig time slots T (t+1) = {t+1,..., T } T. Hece for the frequecy regulatio i curret time slot t, the system operator eeds to take ito accout the chages i the chargig/dischargig power of the eergy storage systems over curret time slot t ad upcomig time slots k T (t+1). If the system operator is aware of the profile of the system frequecy deviatios ω(t) = ( ω(t),..., ω(t )), the it ca solve the followig optimizatio problem to determie the chargig/dischargig profile p s (t) = (p s (t),..., p s (T )) of the eergy storage system at bus N s. miimize p s (t), N s, ω reg (τ), τ {t,...,t } ω reg (τ) + ω(τ) (11) τ=t subject to costraits (1) (10) for time slots {t,..., T }, where is the absolute value. Note that the system operator may ot be able to restore the system frequecy to its omial value (i.e., ω reg (τ) ω(τ) for the time slots τ

4 {t,..., T }) due to the costraits imposed by the distributio etwork ad the eergy storage systems. Therefore, i problem (11), the system operator aims to miimize the differece betwee the regulated frequecy ad the system frequecy deviatios. I problem (11), it is assumed that the system operator is aware of the profile of the system frequecy deviatios ω(t). However, i practice, the system operator observes oly the actual system frequecy deviatio i curret time slot t ad has ucertaity about the frequecy chages i upcomig time slots k T (t + 1). The system operator ca use the historical data record of the system frequecy fluctuatios to obtai a presumed frequecy deviatio profile ˆω(t + 1) for the uderlyig system. Nevertheless, the presumed system frequecy deviatio profile ˆω(t + 1) = ( ˆω(t + 1),..., ˆω(T )) may be differet from the realized frequecy deviatio profile ω(t + 1) = ( ω(t + 1),..., ω(t )) i upcomig slots k T (t+1). Hece, the system operator eeds to implemet a proper mechaism to determie the close-to-actual frequecy deviatio profile ˆω(t + 1) usig the historical data record. We itroduce the risk measure CVaR to determie the presumed profile ˆω(t + 1). The system operator ca use CVaR to limit the likelihood of large differece betwee the presumed frequecy deviatio profile ˆω(t + 1) ad the realized frequecy deviatio profile ω(t + 1). Note that for upcomig time slots k T (t + 1), the presumed deviatio value ˆω(k) may be differet from the actual frequecy deviatio of the system ω(k). Let f( ˆω(t + 1), ω(t + 1)) deote a real-valued fuctio that captures the differece betwee the profile of presumed frequecy chages ˆω(t+1) ad the profile of realized frequecy chages ω(t + 1). For t T \ {T }, we have f( ˆω(t + 1), ω(t + 1)) = k=t+1 ˆω(k) ω(k). (12) Give the cofidece level δ (0, 1) ad vector ˆω(t + 1) i time slot t T, we defie the value-at-risk (VaR) as VaR δ ( ˆω(t + 1)) = mi{η Pr{f( ) η} < 1 δ}, (13) where η is the miimum threshold, for which the probability that f( ˆω(t + 1), ω(t + 1)) η is less tha 1 δ. For the cofidece level δ (0, 1) ad vector ˆω(t + 1) i time slot t T, the CVaR ca be defied as follows CVaR δ ( ˆω(t + 1)) E{f( ˆω(t + 1), ω(t + 1)) f( ˆω(t + 1), ω(t + 1)) VaR δ ( ˆω(t + 1))}, (14) where E { } is the expectatio over the radom variable ω(t + 1). CVaR is a covex fuctio ad ca be miimized usig samplig techiques especially whe the probability distributio of the ucertai variables is ot available [14]. Note that CVaR is the expectatio over the scearios, where f( ˆω(t + 1), ω(t + 1)) is greater tha VaR. Thus, CVaR is always greater tha or equal to VaR, ad miimizig CVaR results i a low VaR as well. We use the set of J {1,..., J} samples ω j (t + 1) of the radom variable ω(t + 1) from the historical record. We obtai Pr{ ω j (t + 1)}, the probability of the sceario with sample ω j (t + 1). The CVaR for cofidece level δ ad vector ˆω(t + 1) ca be obtaied as [14] where CVaR δ ( ˆω(t + 1)) = mi η R Γ δ ( ˆω(t + 1), η), (15) Γ δ ( ˆω(t + 1), η) = η + j J Pr{ ω j (t + 1)} (1 δ) [ f( ˆω(t + 1), ω j (t + 1)) η ] +. (16) The system operator itroduces fuctio Γ δ ( ˆω(t + 1), η) with a weight coefficiet κ 0 to the objective fuctio of problem (11) to miimize the risk of differece betwee the presumed frequecy deviatio profile ˆω(t + 1) ad the realized frequecy deviatio profile ω(t + 1). The optimizatio problem for the system operator at each cotrol time slot t ca be formulated as follows. miimize ω reg (t) + ω(t) + T ω reg (k) + ˆω(k) p s (t), N, k=t+1 ω reg (t), ω reg (k), k T (t+1), + κγ δ ( ˆω(t + 1), η) ˆω(t+1), η (17) subject to costraits (1) (10) for time slots {t,..., T }. To trasform problem (17) ito a liear program, we itroduce oegative auxiliary variables γ(t) ad γ(k), k {t + 1,..., T } for the term ω reg (t) + ω(t) ad ω reg (k) + ˆω(k), respectively. We itroduce oegative auxiliary variables λ j (k), j J, k {t + 1,..., T } for the term ˆω(k) ω j (k) i f( ˆω(t + 1), ω j (t + 1)). We also itroduce auxiliary variable µ j (t), j J to upper boud each term [ f( ˆω(t + 1), ω j (t + 1)) η ] +. We defie vectors γ(t) = (γ(t),..., γ(t )), λ j (t + 1) = (λ j (t + 1),..., λ j (T ), j J ), ad µ(t + 1) = (µ j (t + 1), j J ). Problem (17) ca be rewritte as miimize γ(τ)+κ (η + p s (t), N, τ=t ˆω(t+1), η, ω reg (t), ω reg (k), k T (t+1), γ(t), λ j (t+1), µ(t) j J Pr{ ω j (t + 1)} ) µ j (t + 1) (1 δ) subject to costraits (1) (10) for time slots {t,..., T }, γ(t) ω reg (t) + ω(t) γ(t), γ(k) ω reg (k) + ˆω(k) γ(k), k T (t + 1), λ j (k) ˆω(k) ω j (k) λ j (k), k T (t + 1), λ j (k) η µ j (t + 1). k=t+1 (18) Problem (18) is a liear program ad ca be solved efficietly to determie the optimal schedulig profile p s,opt (t) of the eergy storage system at bus i each cotrol time slot t.

5 IV. PERFORMANCE EVALUATION We evaluate the performace of the proposed frequecy regulatio approach o a IEEE 37-bus distributio test feeder [15] with three eergy storage systems. The test feeder is show i Fig. 1. The equivalet virtual geerator to model the trasmissio etwork is coected to the substatio bus 37. For coveiece, voltage magitudes are i per-uit (pu) with a 4.8 kv base. The base power of the system is 100 kva. The slack bus is the substaio bus, i.e., its voltage magitude is 1 pu ad its phase agle is zero. The eergy storage systems are located at buses 13, 23, ad 31. We assume that o geerator or frequecy sesitive load is coected to buses withi the distributio etwork, ad thus we set the frequecy bias factor to β = 0, = 1,..., 36. The frequecy bias factor β of the substatio bus = 37, where the virtual geerator is coected, is set to pu/hz [16, p. 24]. Sice high frequecy deviatios occur durig peak load hours, we cosider a six-hour operatio period ad divide it ito 24 frequecy cotrol time slots, where oe cotrol time slot is 15 miutes. To obtai the load profile over the operatio cycle, we use the database for Otario [17] over time iterval [4 pm, 9 pm] o May 2, We scale the load demad to make the average demad at each bus over the operatio cycle equal to its correspodig spot load specified i [15]. We use the measuremet data i [18] to obtai J = 50 samples of frequecy deviatio. The cofidece level δ is set to be Uless stated otherwise, the weight coefficiet κ is set to be 1. We first preset the frequecy regulatio performace whe eergy storage systems of differet sizes are used. If the system operator has perfect kowledge about the frequecy chages, the it determies the chargig/dischargig of the eergy storage systems at the begiig of the operatio cycle ad schedules them to restore the frequecy to its omial value accordigly. If the system operator has ucertaity about the frequecy chages, the it solves problem (18) at each time slot to regulate the frequecy. Fig. 2(a) shows the results whe the eergy storage systems are small size with E13 max = 10 kwh, ad E23 max = E31 max = 5 kwh. It ca be observed that the system operator either with perfect kowledge or with ucertaity about the frequecy chages caot regulate the frequecy i most of the time slots, due to the striget operatio costraits of the eergy storage systems. Fig. 2(b) shows the results whe the eergy storage systems are medium size with E max 13 = 50 kwh, ad E max 23 = E max 31 = 30 kwh. The system operator with perfect kowledge about the frequecy chages ca regulate the frequecy i most of the time slots. I time slot 11, the frequecy is ot regulated because the eergy storage systems discharge to be able to perform regulatio durig time slots 12 ad 13 whe chargig is eeded. With ucertaity about the frequecy chages, the system operator ca also regulate the frequecy almost similar to the sceario with perfect kowledge except durig time slots 10 to 13, whe the frequecy has experieced high deviatios. Fig. 2(c) shows the results whe the eergy storage systems are large size with E max 13 = 150 kwh, ad E max 23 = E max 31 = Fig. 1. IEEE 37-bus distributio test feeder used i the simulatio, with the equivalet virtual geerator coected to the substatio bus 37, ad three eergy storage systems at buses 13, 23, ad 31, respectively. 100 kwh. It ca be observed that the frequecy regulatio performace is similar to the sceario with perfect kowledge except i a few time slots such as 8 ad 18. Thus, we coclude that whe the size of the eergy storage systems decreases, the system operator may fail to restore the frequecy durig time slots with high frequecy chages due to the operatio limits of the eergy storage systems ad the ucertaity issues. To further study the impact of the eergy storage capacity o the frequecy regulatio performace, we compare the average regulated frequecy deviatio from the omial value after performig the regulatio with three eergy storage systems of differet sizes durig the operatio cycle, as show i Fig. 3. The capacity ad the iitial chargig eergy level of the small, medium ad large eergy storage are set to be the same as the eergy storage used i Fig. 2. We ca observe that the regulated frequecy deviatio icreases as the eergy storage capacity decreases. As illustrated, whe the size of the eergy storage deceases by half, the regulated frequecy deviatios icreases by 50%. Whe the size of the eergy storage deceases by 90%, the regulated frequecy deviatios icreases by 350%. Fially, we study the impact of the weight coefficiet κ o the frequecy regulatio performace. Fig. 4 shows the CVaR versus the regulated system frequecy deviatio from the omial value, give the frequecy deviatios observed i Fig. 2. It ca be observed that whe κ icreases from 0 to 10, the value of CVaR decreases from 1.39 Hz to 0.29 Hz. This idicates that the system operator becomes more coservative about the expected future frequecy chages i the system whe makig curret schedulig decisios for the eergy storage systems to provide frequecy regulatio. As illustrated, beig more coservative with a larger value of κ makes the system operator to reduce the expectatios about the future frequecy chages, ad the deviatio of the regulated system frequecy from the omial value thus icreases. V. CONCLUSION I this paper, we formulated a liear program to schedule the eergy storage systems i the distributio etwork to provide frequecy regulatio. We desiged the ACE sigals for secodary frequecy regulatio service, while takig ito accout the eergy storage availability, the AC power flow i the distributio etwork as well as the ucertaities i

6 System Frequecy (Hz) Frequecy Deviatio With Perfect Kowledge With Ucertaity Frequecy Cotrol Time Slot CVaR (Hz) κ=0 System Frequecy (Hz) System Frequecy (Hz) (a) Frequecy Deviatio With Perfect Kowledge With Ucertaity Frequecy Cotrol Time Slot (b) Frequecy Deviatio With Perfect Kowledge With Ucertaity Frequecy Cotrol Time Slot (c) Fig. 2. Frequecy regulatio by usig (a) three small eergy storage systems with their iitial eergy level E13 iit = 5 kwh, Eiit 23 = 2.5 kwh, ad Eiit 31 = 5 kwh, (b) three medium eergy storage systems with their iitial eergy level E13 iit = 25 kwh, Eiit 23 = 15 kwh, ad Eiit 31 = 30 kwh, (c) three large eergy storage systems with their iitial eergy level E13 iit = 100 kwh, E23 iit = 75 kwh, ad Eiit 31 = 100 kwh. Regulated Frequecy Deviatio (Hz) Small Medium Large Eergy Storage System Capacity Fig. 3. The regulated frequecy deviatio after performig the regulatio by usig three eergy storage systems with differet sizes. the frequecy chages. Our problem formulatio captured the risk of eergy storage systems ot beig able to participate i the regulatio service based o CVaR. By usig liear approximatio of the AC power flow model ad sample average approximatio of CVaR, our problem could be solved efficietly. Simulatio results showed that our risk-averse model for the system operator ca successfully schedule the eergy storage systems to restore the curret frequecy deviatio, while takig ito accout the risk of the eergy storage system ot beig able to participate i the frequecy regulatio i the upcomig time slots. ACKNOWLEDGEMENT This work has bee supported by the Natural Scieces ad Egieerig Research Coucil of Caada (NSERC). REFERENCES [1] B. J. Kirby, Frequecy regulatio basics ad treds, U.S. Departmet of Eergy, Dec κ=0.01 κ=0.5 κ=0.1 κ=1 0.5 κ=2 κ=5 κ= Regulated Frequecy Deviatio (Hz) Fig. 4. The tradeoff betwee the regulated frequecy deviatios ad CVaR whe three small eergy storage systems are used for frequecy regulatio with differet weight coefficiet κ. [2] D. Hedberg, M. Emett, G. Sodeberg, N. McItire, R. Gramlich, ad R. Kodziolka, FERC order 890: What does it mea for the west? Natioal Associatio of Regulatory Utility Commissioers (NARUC), Natioal Wid Coordiatig Collaborative (NWCC), ad the Wester Goverors Associatio, Tech. Rep., Feb [3] U.S. Federal Eergy Regulatory Commissio (FERC), Frequecy regulatio compesatio i orgaized wholesale power markets, Washigto, DC, USA, FERC 755, Dockets RM AD , Oct [4] M. Kiter-Meyer, Regulatory policy ad markets for eergy storage i North America, Proc. of the IEEE, vol. 102, o. 7, pp , Jul [5] S. Che, T. Zhag, H. B. Gooi, R. D. Masiello, ad W. Katzestei, Peetratio rate ad effectiveess studies of aggregated BESS for frequecy regulatio, IEEE Tras. o Smart Grid, vol. 7, o. 1, pp , Ja [6] F. Zhag, Z. Hu, X. Xie, J. Zhag, ad Y. Sog, Assessmet of the effectiveess of eergy storage resources i the frequecy regulatio of a sigle-area power system, accepted for publicatio i IEEE Tras. o Power System, [7] Y. J. Zhag, C. Zhao, W. Tag, ad S. H. Low, Profit maximizig plaig ad cotrol of battery eergy storage systems for primary frequecy cotrol, accepted for publicatio i IEEE Tras. o Smart Grid, [8] E. Yao, V. W. S. Wog, ad R. Schober, Robust frequecy regulatio capacity schedulig algorithm for electric vehicles, IEEE Tras. o Smart Grid, vol. 8, o. 2, pp , Mar [9] G. He, Q. Che, C. Kag, Q. Xia, ad K. Poolla, Cooperatio of wid power ad battery storage to provide frequecy regulatio i power markets, accepted for publicatio i IEEE Tras. o Power Systems, [10] J. Ta ad Y. Zhag, Coordiated cotrol strategy of a battery eergy storage system to support a wid power plat providig multi-timescale frequecy acillary services, IEEE Tras. o Sustaiable Eergy, vol. 8, o. 3, pp , Jul [11] D. Pudjiato, C. Ramsay, ad G. Strbac, Virtual power plat ad system itegratio of distributed eergy resources, IET Reewable Power Geeratio, vol. 1, o. 1, pp , Mar [12] A. J. Wood, B. F. Wolleberg, ad G. B. Sheblé, Power Geeratio, Operatio, ad Cotrol, 3rd ed. Joh Wiley & Sos, [13] N. Cai, Y. Tia, ad J. Mitra, Optimal brach umberig for UPFC beefit study, i Proc. of North America Power Symposium (NAPS), Charlotte, NC, Oct [14] A. J. Coejo, M. Carrió, ad J. M. Morales, Decisio Makig Uder Ucertaity i Electricity Markets. Spriger, [15] IEEE Power ad Eergy Society distributio test feeders, [Olie]. Available: [16] H. Bevrai, Robust Power System Frequecy Cotrol. Spriger, [17] IESO, Hourly Otario ad market demads, year to date. [Olie]. Available: [18] FINGRID, Frequecy measuremet data. [Olie]. Available: system maagemet/maitaiie of balace betwee electricity cosumptio ad productio/frequecy measuremets data/pages/default.aspx