Three-Level Co-optimization Model for Generation Scheduling of Integrated Energy and Regulation Market

MITUBIHI ELECTRIC REEARCH LABORATORIE http://www.merl.com Three-Level Co-optimization Model for Generation cheduling of Integrated Energy and Regulation Market un, H.; Takaguchi,.; Nikovski, D.N.; Hashimoto, H. TR2017-158 Decemer 2017 Astract This paper proposes a three-level co-optimization model for determining energy production and regulation reserve schedule in a day-ahead market y minimizing the total cost of unit commitment, generation dispatch, frequency regulation and performance. The unscented transformation and historical profiles are used to generate scenarios for modelling the fluctuations of intermittent renewale and stochastic loads at different time scales. Through detailed modelling and simulation of generation dispatch and frequency regulation, the determined generation schedule can have sufficient reserve capacity and adequate response speed to deal with the renewale and load variations occurred etween shorter dispatching and regulating intervals, as well as longer scheduling intervals. Numerical results on a 5-us sample system are given to demonstrate the effectiveness of proposed method. IEEE Innovative mart Grid Technologies Conference This work may not e copied or reproduced in whole or in part for any commercial purpose. ermission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is y permission of Mitsuishi Electric Research Laoratories, Inc.; an acknowledgment of the authors and individual contriutions to the work; and all applicale portions of the copyright notice. Copying, reproduction, or repulishing for any other purpose shall require a license with payment of fee to Mitsuishi Electric Research Laoratories, Inc. All rights reserved. Copyright c Mitsuishi Electric Research Laoratories, Inc., 2017 201 Broadway, Camridge, Massachusetts 02139

Three-Level Co-optimization Model for Generation cheduling of Integrated Energy and Regulation Market Hongo un 1, usuke Takaguchi 2, Daniel Nikovski 1, and Hiroyuki Hashimoto 2 1 Mitsuishi Electric Research Laoratories Camridge, MA 02139, UA 2 Advanced Technology R&D Center Mitsuishi Electric Corporation Hyogo 661-8661, Japan Astract This paper proposes a three-level co-optimization model for determining energy production and regulation reserve schedule in a day-ahead market y minimizing the total cost of unit commitment, generation dispatch, frequency regulation and performance. The unscented transformation and historical profiles are used to generate scenarios for modelling the fluctuations of intermittent renewale and stochastic loads at different time scales. Through detailed modelling and simulation of generation dispatch and frequency regulation, the determined generation schedule can have sufficient reserve capacity and adequate response speed to deal with the renewale and load variations occurred etween shorter dispatching and regulating intervals, as well as longer scheduling intervals. Numerical results on a 5-us sample system are given to demonstrate the effectiveness of proposed method. Keywords co-optimization; energy productin; frequency regulation; frequency regulation preformance; generation dispatch; regulation reserve; unit comitment I. INTRODUCTION Independent system operators are responsile for maintaining an instantaneous and continuous alance etween supply and demand of power system through managing the energy and reserve markets, including day-ahead market and real-time market. According to the forecasted or historical load and non-dispatchale generation profiles for next day, the commitment schedule of dispatchale generation units for next 24 hours are determined through solving a security-constrained unit commitment prolem. This task is complicated y the increased presence of distriuted energy resources and the continuing improvements on market regulations. The unpredictale nature of renewale energy sources leads to greater fluctuations in the amount of generated power availale [1]. Meanwhile, the renewale may demonstrate different characteristics in term of fluctuation magnitudes and frequency if its data sets are collected at different sampling rates. A unit commitment schedule, that conventionally determined ased on renewale and load profiles generated at longer time scale might not e optimal when implemented in real time due to the unit s technical constraints such as ramping rates and min up/down times. In addition, the market regulatory rules have also required the generation units rewarded y their services that they have actually provided or achieved in real time [2]. ithout taking the real-time renewale and load fluctuations into account in some manners, the gaps or deviations etween day-ahead schedules and real-time dispatch and control hardly e mitigated. There are many approaches availale for solving the stochastic unit commitment prolems, specially targeting for co-optimization of energy and reserve markets, such as [3]- [9]. Most of these approaches are focused on hourly generation and load variations, i.e. variations at scheduling intervals. In light of this, this paper proposes a three-level cooptimization model for determining the optimal energy production and regulation reserve schedule for generation units y minimizing the total cost of unit commitment, generation dispatch, frequency regulation and performance. The unscented transformation method is used to generate sample uncertainty scenario for renewale and load at scheduling intervals, and typical/historical renewale generation and load profiles are used to simulate the load and renewale fluctuations at dispatching and regulating intervals. Through detailed modelling of unit commitment, generation dispatch and frequency regulation in the process of co-optimization, the gaps or deviations etween day-ahead schedules and real-time dispatch and control implementation will e reduced, and thus the system efficiency can e improved and the profits for generation companies can e increased. II. THE ROOED METHOD The co-optimization of the energy production and regulation reserve services in a day-ahead market is proposed to e achieved through a three-level optimization process as shown in Fig. 1, including unit commitment, generation dispatch, and frequency regulation. The generation units are divided into dispatchale units that can perform energy production and regulation reserve tasks, and non-dispatchale generation units, such as renewale units that can only e used as constant powers. ome dispatchale units may do not have frequency regulation capaility, so can only e used for energy production. Based on the needs of system power alance, renewale spillage and load shedding may e used ut at certain penalty charges. A. Uncertainty Modeling The uncertainty of renewale and load at scheduling intervals are modelled through a set of sample uncertainty scenarios that generated ased on unscented transformation technique [10]. Assumed " is the vector of active powers contriuted or consumed y renewale sources or load demands at scheduling interval h, and follows the Gaussian distriution with mean " and covariance Q " : " ~N( ", Q " ) (1a) A set of scenarios, h is created y using a set of (2n1) sample points: " = " " n λ 0 Q " Q " (1)

where, n is the total numer of renewale sources and load demands, λ = α 3 n κ n, α and κ are the parameters that determine the spread of the sigma points around. For example, we set: α = 1.0, κ = 1. The square root of the covariance matrix, Q h can e solved using the Cholesky factorization method. Using For any variale " associated with " according to " = f( " ), its mean vector, " can e determined ased on the sample points of " : 3< " = => ": f ": (1c) where ": is the weight factor for uncertainty scenario h A, "B = λ/ n λ, and ": = 0.5/ n λ if k>0. Dividing the sample points with corresponding forecasted means as shown in (1), we can get a set of scale factors for each uncertainty scenario. Those scaling factors are solely defined y the renewale and load covariance, and can e used to derive the values for uncertainty scenario ased on renewale and load forecasts. Fig.1. Three-level co-optimization model for generation schedulin For a given scheduling interval h, the generation output of renewale r and power demand of load d under uncertainty scenario h A, FGH and FGH can e determined as: FGH = FG α FGH JGH = JG α JGH (2a) (2) where FG and JG, and α FGH and α JGH are the forecasted generations and demands, and scaling factors for renewale r and load d respectively. The renewale and load variations at dispatching and regulating intervals are determined ased on the corresponding variation factors defined ased on the historical profiles. For a dispatching interval m within scheduling interval h and uncertainty scenario h A, the renewale generation and load demand, FGH K and JGH K are determined as: FGH K = FGH 1 β FG,K (3) JGH K = JGH 1 β JGK (3) where β FG,K and β JGK are the renewale and load variation factors to represent the variations at dispatching interval m around average renewale generation and load demand at scheduling level h. imilarly, the renewale generation and load demand at regulating interval s within dispatching interval m of uncertainty scenario h A of scheduling interval h, FGH KM and JGH KM are determined as: FGH KM = FGH 1 β FGK β FGKM (4a) JGH KM = JGH 1 β JGK β JGKM (4) where β FGKM and β JGKM are the renewale and load variation factors for regulating inteval s. B. Unit Commitment The first level of co-optimization is to determine the unit commitment schedule under forecasted ase scenarios and sample uncertainty scenarios for renewale productions and load consumptions. The schedule defines the unit commitment statues and scheduling set points for all dispatchale units, renewale spillages for all renewale units, and load shedding for all loads in each scheduling interval. This level is solved through a master prolem and a set of slave prolems. The master prolem is used to determine the on/off status of dispatchale units, and ase scheduling set points for each generation unit. The slave prolem is used to verify whether the determined unit schedule can withstand certain uncertainty scenarios for each scheduling interval, and determine the sensitives of the generation adjustment cost over scheduling set points given y the determined commitment schedule. The master and slave prolems are iteratively solved to otain a unit commitment schedule with minimum commitment, dispatch and regulation cost. The master prolem in the first level can e formulated as: Minimize c O [ = G>Z C O u C u C \]^u C _`^p C O p C p C F>Z FG p FG C J>Z JG p JG c O` (5a) uject to: p F>Z FG p FG = J>Z JG p JG h (5) r R G J>Z JG p JG h (5c) r R G J>Z JG p JG h (5d) u R GZ RU R u U R R G J>Z JG p JG h (5e) f zg = [ G>Z u RD R u D R s n A>Z GH O`() c GH R G op lm nh (B) lq rn J>Z JG p JG h (5f) () p p c O` (5g) u u R GZ u u = 0 g, h (5h) p p R GZ p p = 0 g, h (5i) p r u R g, h (5j) p r u R g, h (5k) p p R GZ p R GZ r p r G G u R GZ RU R u U R g, h (5l) u RD R u D R g, h (5m) u Rv v>gow r Z u g, h (5n) u Rv v>gw r Z 1 u g, h (5o) FG r, h (5p) JG d, h (5q) p FG p JG π zr p F>Z π zf FG p FG J>Z π zj JG p JG l L O, h (5r) F f " F l L ƒ, h (5s) where, H and K G are total numers of scheduling intervals, and sample uncertainty scenarios at scheduling interval h. G is the total numers of dispatchale generation units. u, u and u are inary variales to indicate the unit committed, started-up and shut-down status. p, p and p andr are the unit scheduling set point for ase,r

case, incremental upward/downward generation changes etween two consecutive scheduling intervals, and the rampup and ramp-down reserve contriutions for generation unit \]^, C _`^, C O andc g.c O, C, C are the start-up cost, shutdown cost, fixed non-load cost, per unit variale cost, per unit ramp-up and ramp-down costs for unit g. RU R and RD R, U R andd R, R and R, UT R and DT R are the upward and downward ramping rate thresholds, start-up and shut-down ramping rate thresholds, maximum and minimal generation outputs, and minimum up and down times for unit g. R is the total numers of renewale generation units. p FG andc FG are the renewale spillage, and per unit spillage cost for renewale r. D is the total numers of loads. p JG andc JG are the load shedding, and per unit shedding cost for load d. L O is the set of overload transmission lines. f zg and F z are the power flows on line l at scheduling interval h and its power flow capacity. π zr, π zf and π zj are the allocation factors of dispatchale generator g, renewale r and load d to the power flow on transmission line l, which can e determined using DC load flow formulations. R G and R G, R G and R G are the required ratios of upward and downward reserves, and O` O` regulation speeds over system net loads. c GH and c GH p are the additional scheduling adjustment, dispatch and regulation cost for scenario h A and its sensitivities over ase scheduling set points. p () O`() O`, c GH and c GH p () are corresponding values determined at last iteration or given initially. As expressed in (5a), the ojective of the master prolem is to minimize the total cost related to commitment schedule for the entire operation cycle, c O. It includes the start-up/shutdown cost, the fixed non-load cost, the variale cost for ase scheduling set point, the ramp up/ down costs etween consecutive scheduling intervals, the spillage cost of intermittent renewale, the cost for load shedding, and the additional scheduling adjustment, dispatch and regulation cost for each sample uncertainty scenario (including the ase case), c O` which are considered as a liner function of scheduling set points using sensitivities of associated cost over ase set points. The master prolem is constrained y system-wide constraints, (5)-(5f), device-wise constraints (5h)-(5s). The system wide constraints include power alance equations, system upward/down regulation capacities and speed requirements. The regulation capacities and speeds required for handling the maximum fluctuations of renewale and loads at various sampling intervals. The transmission line security requirements are expressed as power flow equations and limits for the lines. To reduce the computation urden, only equations associated with overload lines are included, and the iterative solution is used until there is no overload existing. The master prolem is related to slave prolems through (4g). ith the determined scheduling set points and unit status, the slave prolem for simulating the system operation under a given uncertainty scenario h A can e formulated as: O` = C O p H F>Z () p H () Minimize c GH C C p R(GH G) C p R(GH G) C FG p FGH p FG J>Z C JG p JGH p JG c GH (6a) uject to: p H F>Z FGH p FGH = J>Z JGH p JGH g (6) f zgh = c () GH Š lm nh (B) lq rnh () p H p H p H = p () p R(GH G) () p H = p R(GZ) p H p H c GH p R(GH G) g (6c) g (6d) p H g (6e) p p R(GH G) u R g (6f) p p R(GH G) u R g (6g) p H () u R(GZ) () U R RU R u g (6h) u RD R u D R g (6i) FGH r (6j) p FGH p JGH JGH d (6k) π zr p H F>Z π zf FGH p FGH J>Z π zj JGH l L O` (6l) p JGH F z f zgh F z l L O` (6m) where L O`is the set of overload lines under scenario h A. p H, p H and p H, p R(GH G) and p R(GH G) are the generation output under scenario h A, the output changes etween the uncertainty scenario and the ase case at previous scheduling interval (h-1), p H and p R(GZ), the output changes etween uncertainty scenario h A and the set point at corresponding scheduling interval h, p H and p. c GH and c GH p H are the additional dispatch and regulation cost for scenario h A and its sensitivities over scheduling set points for the scenario. u (), u (), u (), p () H, c () GH and c () GH p H are corresponding values determined at last iteration or given initially. p FGH, p JGH and f zgh are the renewale spillage for renewale r, load shedding for load d and power flow on line l under scenario h A. The ojective of the slave prolem at the first level is to minimize the total generation adjustment cost for the scenario, c GH O`. Besides the weighted dispatch and regulation costs for each scenario, the uncertainty adjustment cost includes the weighted cost related to the generation output changes etween the previous ase set point and current uncertainty scenario set point, and the current ase set point and current uncertainty scenario set point. It also includes the cost changes for renewale spillage and load shedding etween the ase values determined y the master prolem and the values for the current uncertainty scenario. The slave prolem of the first level is linked with prolems at second and third levels through (6c). The sensitives of generation adjustment cost over ase scheduling set points that used in the master prolem can e determined as: op lm nh Œ (7) (B) = α qrnh β γ lq qr(nh q Œn) r(nh Œn) rn α qrnh, β and γ Œ qr(nh q Œn) r(nh are the dual variales of (6d), Œn) (6f) and (6g) respectively. C. Generation Dispatch The second level of co-optimization is to determine the generation dispatch plans for all dispatch intervals within a given scheduling interval, including the dispatching set points for dispatchale units, renewale spillage and load shedding if needed. The impact of frequency regulation is taken into account through the sensitivities of regulation cost over dispatching set points of dispatchale units. In this level, the

determined unit commitment scheme is checked against dispatch operation scenarios to verify whether the unit commitment schedule satisfying the load and renewale fluctuations that occur at a short timescale, i.e. dispatching interval. The historical renewale generation and load profiles are used to create dispatching scenarios along with the renewale and load forecasts within next operation cycle. The generation dispatch prolem can e formulated as: Minimize c GH uject to: = n K>Z C O RK p H K C RK p H K p H K C O RK p R(KGH) F>Z () C FK C R,K p R(KGH ) p FGH K () p FGH \ J>Z C JK p JGH K p JGH c GH (8a) J>Z m F>Z FGH K p FGH K = JGH K p JGH K (8) n K>Z c \() GH K lm nh (B) lq rnh () p H K p H K \ c GH (8c) p H K = p H p R(KGH ) p R(KGH ) g, m (8d) p H K = p H (KZ) p H K p H K g, m (8e) p H p H p R(KGH ) p R(KGH) u R g, m (8f) u R g, m (8g) () p H K τ GK u R(GZ) RU R u U R g, m (8h) p H K τ GK u RD R u D R g, m (8i) p FGH K FGH r, m (8j) p JGH K JGH d, m (8k) f zgh K = π zr p H K F>Z π zf FGH K p FGH K J>Z π zj JGH K p JGH K m, l L (8l) F z f zgh K F z m, l L (8m) where, M G is total numer of dispatching intervals of interval h. p H K, p R(KGH) and p R(KGH ), p H K and p H K are the dispatching set point, the unit output differences etween the scheduling set point p H and the dispatching set point, the unit output changes etween two consecutive dispatching intervals, m and (m-1), p H Kandp H (KZ). The per unit ramp up/down costs and renewale spillage and load shedding costs can e determined ased on corresponding values per scheduling interval and pre-determined conversion factors. \ c GH is the cost related to frequency regulation for the scheduling interval h, and expressed using the sensitivity of cost related to dispatching interval, c GH K over generation output at the dispatching interval, p H K. L is the set of overload lines. τ GK is the ratio of length of dispatching interval over length of scheduling interval, and used to convert ramping thresholds from per scheduling interval to per,p JGH K dispatching interval. p FGH K and f zgh Kare the renewale spillage for renewale r, load shedding for load d and power flow on line l at dispatch interval m under scenario h A. The ojective of generation dispatch is to minimize the total as cost related to generation dispatch and regulation, c GH shown in (8a). The cost includes the additional cost incurred y the generation output changes etween the scheduling set point and dispatching set point, and the set points etween two consecutive dispatching intervals. It is also included the cost changes for renewale spillages and load shedding etween the determined values for the scheduling interval and the values for the dispatching interval. The sensitivities of generation dispatch and regulation cost over scheduling set points are determined as: Š lm nh (B) = α qrnh β q r( ŒnH ) γ q r( ŒnH ) lq rnh n Œ K>Z (9) α, β qrnh q and γ Œ r( ŒnH q ) r( ŒnH are the dual variales of ) (8d),(8f) and (8g) respectively. D. Frequency Regulation The third level of co-optimization is to determine the generation frequency regulation schemes to maintain qualified system frequency in each regulating interval. In this level, the frequency regulation is used to simulate the power system to deal with fluctuations in load and renewale that occur at a much faster timescale, i.e. regulating interval. The historical profile of load and generation for this timescale are used to determine the expected frequency regulation and performance cost for each dispatchale unit. The generation regulation setting points (determined y secondary frequency control) are first determined ased on load and renewale variations and frequency requirements for each regulating interval. The performance for generation units to follow the regulation setting points (implemented y primary frequency control) are then measured y the sum of deviation of setting points and actual achieved mechanical outputs of generation units. The frequency regulation is formulated as: Minimize c \ GH K = n C O RM p H MK C M>Z RM p H MK C O RM p H M C () RM p H M F>Z C FM p FGH KM p FGH K J>Z C JM p JGH KM p JGH K c GH K (10a) uject to: K f GH KM n M>Z K f c GH KM p JGH KM J>Z p H KM n Œ H n H r F>Z FGH KM p FGH K J>Z 1 K f GH KM JGH KM p JGH K K f J>Z p JGH KM g, s (10) f GH KM f GH KM f s (10c) p H KM = p H K p H KM p H KM = p H K MZ š lm nh B p lq H KM rnh p H (MK) p H KM () u n Œ H n H R,G p H K p H K p H KM p H (MK) c GH K (10d) g, s (10e) p H KM g, s (10f) r = p H KM g, s (10g) u R g, s (10h) u R g, s (10i) p H (MK) p H (MK) () p H KM τ GM u R(GZ) RU R u () U R g, s (10j) p H KM τ GM u RD R u D R g, s (10k) p FGH KM FGH KM r, s (10l) p JGH KM JGH KM d, s (10m) f zgh KM = π zr p H KM F>Z π zf FGH KM p FGH KM J>Z π zj JGH KM p JGH KM l L \, s (10n) F z f zgh KM F z l L \, s (10o) where, GK is total numer of regulating intervals of dispatching interval m within scheduling interval h. p H KM, p H (MK) and p H (MK), and p H KMand p H KM are the generation output at regulating interval s, the upward

and downward output differences etween the dispatching and regulating intervals, p H KM andp H K, and the upward and downward regulating set point (i.e. generation control command) changes etween two consecutive regulating intervals, s and (s-1), p H KM and p H K MZ. L \ is the overload line set. τ GM is the ratio of length of regulation interval over length of scheduling interval, and used to convert ramping thresholds from per scheduling interval to per regulation interval. f GH KM and f are the system frequency deviation (away from system rated frequency), and its allowed threshold. K is system load frequency sensitivity coefficient, and DR ž is the generation unit droop (in M/HZ). p FGH KM, p JGH KM and f zgh KM are the renewale spillage for renewale r, load shedding for load d and power flow on line l at regulation interval s. The ojective for frequency regulation is to minimize the total cost related to frequency regulation, c \ GH K. It includes the cost related to mismatch etween the dispatching set point and generation output at the regulating interval, and regulation set point changes etween two consecutive regulating intervals, and cost changes related to renewale spillage and load shedding. It also includes the additional cost related to frequency regulation performance, c GH K. The costs related to primary frequency regulation performance for all regulating intervals in the dispatching interval m and scheduling interval h, c GH K is expressed as a linear function of generation set point at the regulation interval using the sensitivity of related cost for the regulation interval over generation set point at the regulation interval, c GH KM p H KM. The constraints for frequency regulation include power alance requirement with frequency changes for interval s (10), and generation droop control equation (10g). The cost for primary frequency regulation performance is defined as: O c GH KM = C M max 0, p H KM p H KM C M max 0, p H KM p H KM (11) O C M and C M are per unit upward/downward mismatch costs etween frequency regulation setting points, p H KM and generation mechanical outputs, p H KM. The sensitivities of primary frequency regulation cost over dispatching set points are determined as: lm nh (B) = α β qrnh q γ Œ M>Z rnh q ( Œ ) rnh (12) ( Œ ) lq rnh n α qrnh, β q and γ Œ rnh q ( Œ ) rrnh are the dual variales of ( Œ ) (10e),(10h) and (10i) respectively. The aility of a generator in following the frequency regulation signal depends on its technology and physical characteristics. ithout loss of generality, we consider a governor-turine control model for each generator where a speed governor senses the changes in its power command set points, i.e., the frequency regulation set points, p GH KM(t) and converts them into valve actions. A turine then converts the changes in valve positions into changes in mechanical power output, i.e., generation signal p GH KM(t). The relationship etween the incremental changes of mechanical output and control signal, p GH KM(t)and p GH KM(t)is descried as: 1 T J w R 1 T J Jv R p Jv GH KM(t) = p GH KM(t) (13) For a given regulating interval s, the mechanical output of generator g can e determined as: M p GH KM = p GH K p GH K p GH K Z >Z ( Œ ) ( Œ ) δ i = 1 T ª Š R e r T w ª ª R e r δ i u t τ M (i 1) (14a) / T R T R w (14) u(t)is a unit step function, δ i is the generation regulation achieving ratio for regulation interval i. The sensitivity of frequency regulation performance cost over regulation setting points is determined according to: š lm nh = δ s C M O max 0, q rn H lq nh C M max 0, q «rn H q rnh q rnh q rnh «q rnh q «rnh q rnh «(15) III. NUMERICAL EAMLE The proposed method has een tested on a 5-us system as shown in Fig. 2. The system has 2 dispatchale units (located at Bus-1, and Bus-2), 1 non-dispatchale unit (located at Bus-5), 2 loads (located at Bus-3 and Bus-4), and 5 lines. All lines have same impedance and capacity as 0.01j0.1 p.u. and 50 M respectively. Fig. 2 also shows the maximal and minimal outputs of generation units, and the ase power consumption/generation for the loads/renewales. The scheduling, dispatching and regulating intervals are set as 1 hour, 15 minutes and 15 seconds respectively. Fig.2. 5-Bus test system that used in this paper Fig. 3 gives the typical daily generation and load profiles sampled once per 15 seconds, and the values at vertical axis are the ratios of actual values with corresponding ase values. Those profiles are used to derive the dispatching and regulating variation factors for renewale and loads. The standard deviations of hourly renewale and load variation are assumed to e 10% of their hourly average values. Those standard deviations are used to generate the covariance matrix and define the scaling factors for sample uncertainty scenarios. The parameters for generation units are given in Tale I. Both generation units have een running for 10 hours. The test results are summarized in Tale II. The required upward/downward regulation reserve capacity and speed ratios are 10%, and the allowed maximum frequency deviation is 1.0Hz. The system load frequency sensitivity coefficient is 5%/HZ. There are two cases in the tale. The generation schedule of Case I is determined y ignoring the impacts of generation dispatch and frequency regulation. In comparison, the impacts generation dispatch and frequency regulation are modelled when determining the generation schedule for Case II. The determined daily schedule of generation energy production and regulation reserve for Case II are depicted in Fig. 4.

Fig. 3. Renewale and Load rofiles Attriute Ramping Rate (M/min) tart-up/shutdown ramping rate (M/min) Governor time constant (s) Turine time constant (s) Tale I. Generation Unit arameters Generation Unit Generation Bus Attriute Unit Bus Bus-1 Bus-2 Bus-1 Bus-2 1.33 3.33 2.66 6.66 1 0.5 12 6 Droop 10% 10% tart-up costs (k$) 0.4 0.2 hut-down costs (k$) Fixed cots(k$/h) ariale cots (k$/mh) Ramping Costs (k$/m/h) Regulation performance cost (k$/mh) min up/down time(h) (a). Generation Unit at Bus-1 0.2 0.1 0.2 0.1 0.02 0.04 0.02 0.01 0.01 0.02 4/2 2/1 (). Generation Unit at Bus-2 Fig. 4. Generation schedule for energy production and regulation reserve Case I II Unit On chedule (Hrs) Bus-1: 0-23 Bus-2:0-3,7-20 Bus-1: 0-23 Bus-2: 0-3,7-21 Tale II. Test Cases and Results Cost Contriutions (k$) Unit Generation Frequency Commitment Dispatch Regulation Total 37.26 0.47 3.82 41.6 37.27 0.46 1.94 39.7 Compared with Case I, Case II has committed the generation unit at Bus-2 operating one more hour, ut has less additional frequency regulation cost at third level. It is shown that the total cost of Cast II is 1.9 k$ (i.e. 4.75%) less than Case I. This result has preliminarily demonstrated the advantages for using three-level co-optimization model. I. CONCULUION This paper has proposed a three-level co-optimization model for generation scheduling in a day-ahead market. The impacts of renewale and load fluctuations at three different time scales have een taken into account. Through detailed modelling of unit commitment, generation dispatch and frequency regulation in the process of co-optimization, the gaps or deviations etween day-ahead schedules and real-time dispatch and control have een effectively mitigated, and thus the system efficiency can e improved and the profits for generation companies can e maximized. The preliminary results have demonstrated the effectiveness of the proposed method. Future work may include developing more efficient algorithm, testing on practical systems, and more detailed modelling of unit start-up, and shut-down process. REFERENCE [1] J. Morales, A. Conejo, and J. erez-ruiz, Economic aluation of Reserves in ower ystems ith High enetration of ind ower, IEEE Transactions on ower ystems, vol. 24, no. 2, pp. 900 910, May 2009. [2] Frequency Regulation Compensation in the Organized holesale ower Markets, Oct. 2011 [Online]. Availale: http://www.ferc.gov/whatsnew/comm-meet/2011/102011/e-28.pdf. [3] D. Gan, E. Litvinov, A lost opportunity cost model for energy and reserve co-optimization, IEEE ower Engineering ociety ummer Meeting, vol. 3, pp. 1559-1564, 2002. [4] un Tiam Tan, and Daniel. Kirschen, Co-optimization of Energy and Reserve in Electricity Markets with Demand-side articipation in Reserve ervices, 2006 IEEE E ower ystems Conference and Exposition, pp. 1182-1189. [5]. ong and J. Fuller, ricing energy and reserves using stochastic optimization in an alternative electricity market, IEEE Transactions on ower ystems, vol. 22, no. 2, pp. 631 638, May 2007. [6] U. Ozturk, M. Mazumdar, and B. Norman, A solution to the stochastic unit commitment prolem using chanced constrained programming, IEEE Transactions on ower ystems, vol. 19, no. 3, pp. 1589 1598, Aug. 2005. [7] L. u, M. hahidehpour, and T. Li, tochastic security-constrained unit commitment, IEEE Transactions on ower ystems, vol. 22, pp. 800 811, 2007. [8]. Ruiz, C. hilrick, E. Zak, K. Cheung, and. auer, Uncertainty management in the unit commitment prolem, IEEE Transactions on ower ystems, vol. 24, no. 2, pp. 642 651, May 2009. [9] E.M. Constantinescu,. M. Zavala,M. Rocklin,. Lee, and M. Anitescu, A computational framework for uncertainty quantification and stochastic optimization in unit commitment with wind power generation, IEEE Transactions on ower ystems, vol. 26, no. 1, pp. 431 441, Fe. 2010. [10]. arkka, On unscented Kalman filtering for state estimation of continuous-time nonlinear systems, IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1631 1641, 2007.