Toward Coordinated Transmission and Distribution Operations

T o wa rd Coordinated T ransmission and Distrib ution Operati ons Mikhail Bragin, IEEE, Member , Y ury Dv orkin, IEEE, Member . Abstract —Proliferation of smart grid technologies has en - hanced observ abi lity and controllability of distribution systems. If coordinated with the transmission system, resources of both systems can be used mor e efficiently . This paper proposes a model to operate t ransmission and distribution systems in a coordinated manner . The proposed model is solved using a Surrogate Lagrangian Relaxation (SLR) approach. The computational perfo rmance of this approach is compared against existing methods (e.g. sub gradient method). Finally , the usefu lness of the proposed model and solution approach is demonstrated via numerical experiments on the illustrative example and IEEE benchmarks. Index T erms —Distribution system operations, transmission system operations, Surrogate Lagrangian Relaxation. I . I N T RO D U C T I O N Activ e dep loym ent of smar t grid tec hnolog ies in distri- bution systems ha s affected the way h ow these systems interact with the tr ansmission systems. It is anticipated that distrib ution systems o f the fu ture will be equipp ed to acti vely engage in transmission system operation s, [1]. This will require a coordina tion mech anism to co-optimize generation resource s av ailab le in both systems to ach iev e least-cost operation s, while respecting objective function s and satisfying technical constrain ts of each system. Coordinatio n between the transmission and d istribution systems has p reviously b een in vestigated f o r econ omic dis- patch and optimal power flow fra mew orks. References [2], [3] propose a decom position ap proach fo r the coo rdinated econom ic disp a tch of the transmission and distribution sys- tems that can capture h eterogen eous techn ical ch a racteristics of these systems. In [4], th e decomp osition algo rithm fr om [2], [3 ] is improved to han dle A C power flow con stra in ts for both the transmission an d d istribution systems. Th e interac- tions between the tr ansmission a n d distribution system in the electricity market co ntext is studied in [ 5]. T h e commo n cav eat of [2]–[5] is that they do n ot endog enously model binary u nit commitmen t (UC) decisions o n conv entional generato r s. T o our knowledge, there is no appro ach to in- clude binary UC decisions, while c oordin ating transmission and distribution oper a tio ns. Considering b inary UC decisions inv okes a numbe r of challenges. First, it renders a mixed-integer lin e a r pr o gram (MILP) that ca nnot a lways be solved e fficiently with a standard branc h -and- c ut metho d . Second, traditio n al decom- position techn iques, e.g. Lagra ngian Relaxation (LR), ar e notorio u s for th eir unstable and often slo w convergence due to th e zigza g ging effect of Lagrang e multipliers. This paper deals with both ch allenges by using the Surro gate Lagrang ian Relaxation (SLR) [7]. The SLR enforces a “surroga te optimality” co ndition, which guar antees that “surroga te ” subgradient d ir ections f orm acute an gles with directions toward the optimal m ultipliers. Th e “sur r ogate optimality” con dition makes it u nnecessary to solve all decomp o sed subproblem s to o ptimality , thus speedin g up the compu tations. Referen ce [7] deriv es a stepsizing f ormula that guarantee s the convergence and qu a ntifiable solu tio n accuracy withou t requ iring any knowledge of the optimal dual Lagrang ian fun ction. Previously , th e SLR was applied to large-scale transmission UC m odels [8], [9], even with A C power flows [ 1 0]. This paper p roposes a m o del to coo rdinate the transmis- sion and distribution systems, which accounts f or bin ary UC decision s an d power flow ph ysics. The model is solved using the SLR. Our case study d escribes th e co st an d computatio nal perfo rmance o f the pro posed coo rdination and solution tec h nique. I I . M O D E L This paper con siders a power system layout typical to the US power sector, where mu ltiple distribution systems are c onnected to the single transmission system . Th e tran s- mission system is oper a te d by the tr ansmission system operator (T SO) using a wholesale electricity market. E ach distribution system is operated by the distribution system operator (DSO) that dispatches its own gene r ation and can also participate in the wholesale electricity market. A. Pr eliminaries Let B [ · ] , I [ · ] and L [ · ] be the sets of buses, g enerators an d lines in dexed by b , i , and l , where superscript [ · ] den otes the transmission (T) and distribution ( D) system. Let J be the set of d istribution system s indexed b y j . The tran smission system an d each distribution system ar e then gi ven by graphs G T = ( B T , L T ) and G D j = ( B D j , L D j ) . Graph G T is chosen to be loopy (meshed) and G D j is chosen to be tree (radial) to represent comm on top ologies of the transmission and distribution sy stem s. Grap h G T and each gr a ph G D j have strictly one connec tio n point at th e root bus of G D j . The root bus of each distribution system is den oted as b 0 ,j . T o denote the con nection between the tran smission and distribution systems, w e use in d ex j ( b ) , which is interpreted as distribution system j is connected to tran smission bus b . The set of tra nsmission buses that have distribution systems is d enoted as ˆ B T . Acti ve an d r eactiv e power variables are distinguished by superscripts p and q. B. DSO Model The following model is f ormulated for e ach distribution system in dividually a n d therefore index j is omitted for the sake of clarity . The DSO aims to maximize th e social welfare in the distribution system by supplying its d emand using av ailable distribution and wholesale market resources: max  o D  = max  X b ∈B L p b T − X i ∈I D C g i g p i + λ b 0 ( p ↑ b 0 − p ↓ b 0 )  . ( 1 ) The first term in (1) represents the p ayment co llected by the DSO from consumers based on their a cti ve power consump tion L p b and flat- rate tariff T . The seco nd ter m accounts f or the pro d uction cost o f co n ventional gene r ators located in the distribution system an d is computed based on their incremental gen e ration co st C g i and acti ve power output g p i . The th ird term acco unts for the co st of transactions perfor med by the DSO in th e wholesale electricity market. V ariables p ↓ b 0 and p ↑ b 0 represent th e capacity b id/offered by the DSO in the wholesale market, while λ b 0 denotes the locational marginal price (L MP) at the transmission bus, which is connected to the r o ot bus of the distribution sy stem. Thus, p ↑ b 0 > 0 indicates that the DSO offers to sell electricity in the wholesale ma r ket, while p ↓ b 0 > 0 signals that the DSO bids to purchase e le c tr icity No te (1) n eglects the fixed co st of conventional g enerator s as it is normally negligible fo r distribution gener a tors. The output of distribution gen e rators is constra ined as: G p i ≤ g p i ≤ G p i , ∀ i ∈ I D , (2) G q i ≤ g q i ≤ G q i , ∀ i ∈ I D , (3) where the minimum an maximum acti ve power limits are G p i and G p i , while th e minim um a nd m aximum r eactiv e power limits are G q i and G q i . sSince this pa p er considers a single- period o ptimization, the eco nomic dispa tc h constraints do not include inter-temporal limits (e.g. ramp limits). Since th e distribution system is assume d to have a radial topolog y , AC power flows can be modeled using an exact second-o rder conic (SOC) rela x ation; interested reader s are referred to [6] for details of this relaxation given b elow:  ( f p l ) 2 + ( f q l ) 2  1 a l ≤ v s ( l ) , ∀ l ∈ L D , (4) v r ( l ) − v s ( l ) = 2( R l f p l + X l f q l ) − a l ( R 2 l + X 2 l ) , ∀ l ∈ L D , (5) ( f p l ) 2 + ( f q l ) 2 ≤ S 2 l , ∀ l ∈ L D , (6) ( f p l − a l R l ) 2 + ( f q l − a l X l ) 2 ≤ S 2 l , ∀ l ∈ L D (7) V b ≤ v b ≤ V b , ∀ b ∈ B D . (8) Eq. (4) r epresents a relaxed expression for the curren t squared in branch l , denoted by auxiliary variable a l , variables f p l and f q l denote a ctiv e and reactive power flows across line l , and v s ( l ) is the voltage magn itude a t the sending en d of line l . The sendin g and receiving buses of branch l are denoted as s ( l ) and r ( l ) , respectively . Eq. (5) relates the send ing and r eceiving bus voltages squared v s ( l ) and v r ( l ) via the voltage drop across branc h l , where parameters R l and X l are the r eactanace an d impedan ce of branch l . Since the power flow at th e sendin g an d receiving buses of each bran ch l differs due to losses incu r red by transmission, the appar e n t power flow limit S l is enfo rced for the send ing and receiving buses separ ately in (6) an d (7). The b u s v o ltages ar e con strained in (8), where v b denotes voltages squared limited by V b and V b , see [6]. W ith the exception of the root bus, which is discussed below , the nodal power balance is enforced as: f p l | s ( l )= b − X l | r ( l )= b ( f p l − a l R l ) − X i ∈I U b g p i + L p b + v b G l | s ( l )= b = 0 , ∀ b ∈ B D \  b 0  , (9) f q l | s ( l )= b − X l | r ( l )= b ( f q l − a l X l ) − X i ∈I U b g q i + L q b − v b B l | s ( l )= b = 0 , ∀ b ∈ B D \  b 0  , (10) where L p b and L q b denote the active and reactiv e power consump tion at bus b an d G l is the condu ctance of bran c h l . In case o f the r oot bus, (9) and (10) transform into: − X l | r ( l )= b 0 ( f p l − a l R l ) − p ↑ b 0 + p ↓ b 0 + v b 0 G l | o ( l )= b 0 = 0 , (11) − X l | r ( l )= b 0 ( f q l − a l X l ) − v b 0 G l | o ( l )= b 0 = 0 . (12) Eq. (11) includes the power exchange with the transmission system based on the capacity bid ( p ↑ b 0 ) and o ffered ( p ↓ b 0 ) by the DSO in the electricity market. Since the DSO is assumed to meet its own reactive power need s, the reactive power balance fo r the root bus in ( 12) has no reacti ve power exchange with the transmission system. Since the ph ysical interface between th e tran smission and distribution sy stems is lim ited, p ↓ b 0 and p ↑ b 0 are limited as: 0 ≤ p ↑ b 0 ≤ P j ( b ) , (13) 0 ≤ p ↓ b 0 ≤ P j ( b ) , (14) where P j ( b ) and P j ( b ) is the acti ve p ower limit between distribution system j and transmission bus b . C. TSO Model As in (1), the TSO aims to m aximize the social welfare in th e transmission system, which can be forma lized as: max  o T  =  X b ∈B T C b b L p b − X i ∈I T C o i g p i (15) + X b ∈ ˆ B T  C ↓ j ( b ) p ↓ j ( b ) − C ↑ j ( b ) p ↑ j ( b )  . The first term in ( 1 5) represents the p ayment collected from consumer s connected directly to the transmission system based on their acti ve p ower con sumption L p b and pr ice bids C b b . Th e secon d term represents the cost of offers by conv entional gene r ation resources comp u ted based on th e ir offered price C o i and power pro duction g p i . Th e third ter m is th e cost of active power exchan ge between the TSO and DSO, where C ↓ j ( b ) and C ↑ j ( b ) are th e price bid s and offers of the DSO j located at transmission bus b . The d ispatch of conventional g enerators is constrained as: G p i ≤ g p i ≤ G p i x i , ∀ i ∈ I T , (16) where x i ∈  0 , 1  is a b inary (on/o ff) de c ision on conven- tional generato rs. Since this paper conside rs a single - period case, inter-temporal r a mp limits and m in imum u p an down times of conv entional gener ators are omitted. The network constrain ts are modeled using th e D C p ower flow approxima tio n to accoun t for a me sh ed topolo gy as customarily used in market c learing p rocedu r es: f p l = 1 X l ( θ o ( l ) − θ r ( l ) ) , ∀ l ∈ L T , (17) − F l ≤ f p l ≤ F l , ∀ l ∈ L T , (18) where (17) computes the active power flow in line l and the active power flow limit F l on each lin e l is enfo rced in (18). The noda l active p ower balance is then modeled for transmission buses without and with interconnected distribution systems in (19) and (20): X i ∈ I b g p i + X l | r ( l )= b f p l − X l | o ( l )= b f p l − L p b = 0 , ∀ b ∈ B T \  ˆ B T  , (19) X i ∈I b g p i + X l | r ( l )= b f p l − X l | o ( l )= b f p l + p ↑ j ( b ) − p ↓ j ( b ) − L p b = 0 , ∀ b ∈ ˆ B T : ( λ b ) , (20) where λ b is a L agrang ian m ultiplier of the power balan ce constraint, i.e. th e wholesale LMP , at the transmission bus with an interconnected distribution system . V ariables p ↑ j ( b ) and p ↓ j ( b ) in (2 0) denote the power exchnag e with distribu- tion system as seen from th e transmission side. Th erefore, as in (13)-(14), these flows are constrain ed: 0 ≤ p ↓ j ( b ) ≤ P j ( b ) , ∀ b ∈ ˆ B T , (21) 0 ≤ p ↑ j ( b ) ≤ P j ( b ) , ∀ b ∈ ˆ B T . (22) D. Coordinated TSO-DSO Model Operating decisions of the TSO and multiple DSOs can be c oordin a ted by solving the following prob lem: Eq. (1)-(14) , ∀ j ∈ J , (23) Eq. (15)-(22) , (24) p ↓ b 0 ,j ( b ) = p ↓ j ( b ) , ∀ b ∈ ˆ B T : ( ψ ↓ b 0 ,j ) , (25) p ↑ b 0 ,j ( b ) = p ↑ j ( b ) , ∀ b ∈ ˆ B T : ( ψ ↑ b 0 ,j ) . (26) Eq. (23) and (24) list all DSO and TSO problems, while (2 5) and (26) en f orce the power exchanges between the DSO and TSO pr oblems. Note that ψ ↓ b 0 ,j and ψ ↑ b 0 ,j denote Lagr a nge multipliers of respecti ve con stra ints. The prob le m in (23)- (26) canno t be solved ef ficiently for large-scale instances using off-the-shelf solution strategies. Furthermo re, it is im- portant to p reserve the distributed nature of the coordinatio n process between the TSO and DSOs. This m otiv ates an iter- ativ e SLR-b ased solution tech nique described in Section II I. I I I . S O L U T I O N T E C H N I Q U E The p roposed SLR-based solu tion techniq ue is illustrated in Fig. 1 and each step is detailed below: 1) Initia lization: Set the iteration coun te r k = 0 . Stepsize s 0 are in itialized as in [7] an d pena lty co- efficient c 0 is chosen as in [11]. Also, initialize λ 0 b 0 ,j , ψ 0 , ↓ b 0 ,j , ψ 0 , ↑ b 0 ,j , p 0 , ↓ b 0 ,j , p 0 , ↑ b 0 ,j , p 0 , ↓ j ( b ) , p 0 , ↑ j ( b ) . 2) So lve the DS O p r oblem: The following p roblem is solved for each DSO in a par allel man ner ( ∀ j ∈ J ) max o D j ( g i , p ↑ b 0 ,j , p ↓ b 0 ,j ) + ψ k, ↓ b 0 ,j ( p ↓ b 0 ,j − p ↓ ,k − 1 j ( b ) ) + c k 2 | p ↓ ,k − 1 b 0 ,j − p ↓ ,k − 1 j ( b ) || p ↓ b 0 ,j − p ↓ ,k − 1 j ( b ) | + ψ k, ↑ b 0 ,j ( p ↑ b 0 ,j − p ↑ ,k − 1 j ( b ) ) + c k 2 | p ↑ ,k − 1 b 0 ,j − p ↑ ,k − 1 j ( b ) || p ↑ b 0 ,j − p ↑ ,k − 1 j ( b ) | , (27) Eq. (1) − (1 4) . (28) Since (25)-(26) are relaxed, the deviations from the TSO power flows a t th e previous iterations, p ↓ ,k − 1 j ( b ) and p ↑ ,k − 1 j ( b ) , are penalized in (27). A s in [9], th e absolu te value penalties are u sed to a void unn ecessary linear ization. 3) So lve the TS O pr oblem: Follo wing the DSO problems, optimized values of p ↑ ,k b 0 ,j , p ↓ ,k b 0 ,j are used in the TSO problem: Initialize λ 0 b 0 ,j , ψ ↑ , 0 b 0 ,j , ψ ↓ , 0 b 0 ,j , s 0 , c 0 , p 0 , ↓ b 0 ,j , p 0 , ↑ b 0 ,j , p 0 , ↓ j ( b ) , p 0 , ↑ j ( b ) Solve the DSO pro b lem, eq. (2 7)-(28) Solve the TSO pro blem, eq . (3 0)-(32) Update λ k b 0 ,j , ψ ↑ ,k b 0 ,j , ψ ↓ ,k b 0 ,j , s k , c k , α k Stop? End p ↑ ,k b 0 ,j , p ↓ ,k b 0 ,j f k l , v k b , a k l , θ k b p ↑ ,k b 0 ,j , p ↓ ,k b 0 ,j , p ↑ ,k j ( b ) , p ↓ ,k j ( b ) k = k + 1 Fig. 1: F lowc hart of the proposed SLR-based solution technique. max  L c k ( λ k b 0 ,j , ψ ↑ ,k b 0 ,j , ψ ↓ ,k b 0 ,j ; p ↑ ,k b 0 ,j , p ↓ ,k b 0 ,j ; (29) f l , g l , θ b , p ↑ j ( b ) , p ↓ j ( b ) )  , (30) Eq. (16) − (19) , (2 1) − (22) , (31) ˜ L c k ( λ k b 0 ,j , ψ ↑ ,k b 0 ,j , ψ ↓ ,k b 0 ,j ; p ↑ ,k b 0 ,j , p ↓ ,k b 0 ,j ; f k l , g k l , θ k b , p ↑ ,k j ( b ) , p ↓ ,k j ( b ) ) > ˜ L c k ( λ k b 0 ,j , ψ ↑ ,k b 0 ,j , ψ ↓ ,k b 0 ,j ; p ↑ ,k b 0 ,j , p ↓ ,k b 0 ,j ; f k − 1 l , g k − 1 l , θ k − 1 b , p ↑ ,k − 1 j ( b ) , p ↓ ,k − 1 j ( b ) ) , (32) where L c k is the au gmented Lagr angian fun c tion, and ˜ L c k is th e surrog ate augme nted dual value. The value o f ˜ L c k is defined as th e value of (2 9) f o r its cu r rent feasible solutio n . Eq. (3 2) represents th e “surro g ate op tim ality” cond ition from [ 9]. As in Step 2, we relax and penalize constrain ts (20 ) and (25 )-(26) with in the augm e nted Lagrang ian function L c k . The penalization is implemented as discussed in [9]. Due to th e p agination lim it, we o mit the p rocedu r e to deriv e the exact expressions fo r L c k and ˜ L c k and refer interested readers to [9] for details. 4) Upd ate: Using the DSO and TSO solutions o btained at iteration k , the following par ameters are upd ated: c k +1 = c k β , β > 1 , (33) ψ ↓ ,k +1 b 0 ,j = ψ ↓ ,k b 0 ,j + s k ( p ↓ ,k b 0 ,j − p ↓ ,k j ( b ) ) , (34) ψ ↑ ,k +1 b 0 ,j = ψ ↑ ,k b 0 ,j + s k ( p ↑ ,k b 0 ,j − p ↑ ,k j ( b ) ) , (35) λ k +1 b 0 ,j = λ k b 0 ,j + s k ˜ h b 0 ( g p ,k i , f p ,k l , p ↑ ,k b 0 ,j , p ↓ ,k b 0 ,j ) , (36) s k +1 = α k s k × × || ˜ H ( g p ,k i , f p ,k l , p ↑ ,k b 0 ,j , p ↓ ,k b 0 ,j , p ↑ ,k b ( j ) , p ↓ ,k b ( j ) ) || 2 || ˜ H ( g p ,k +1 i , f p ,k +1 l , p ↑ ,k +1 b 0 ,j , p ↓ ,k +1 b 0 ,j , p ↑ ,k +1 b ( j ) , p ↓ ,k +1 b ( j ) ) || 2 , (37) where α k is a step-sizing parameter α k = 1 − 1 M k 1 − 1 /k r , M > 1 , r > 0 . (38) V alue ˜ h b 0 ( g p,k i , f p,k l , p ↑ ,k b 0 ,j , p ↓ ,k b 0 ,j ) is defined as the level of constraint violation fo r a feasible solutio n of (2 9 ) defined for each distribution system as: ˜ h b 0 ( g p,k i , f p,k l , p ↑ ,k b 0 ,j , p ↓ ,k b 0 ,j ) = X i ∈I b 0 g p,k i + X l | r ( l )= b 0 f p,k l − X l | o ( l )= b 0 f p,k l + p ↑ ,k b 0 ,j − p ↓ ,k b 0 ,j − L p b 0 . (39) According ly , vector ˜ H ( g p ,k i , f p ,k l , p ↑ ,k b 0 ,j , p ↓ ,k b 0 ,j , p ↑ ,k b ( j ) , p ↓ ,k b ( j ) ) is the surrogate subg r adient dire c tio n. Each compo nent of th is vector represents the con straint violation of (20 ) an d (25)- (26). The procedu re describ ed in Step 1- 4 r epeats u ntil the stopping criteria are satisfied such as CPU time, value of the surrog ate subgradien t norm , or the duality gap, [7]. I V . C A S E S T U DY A. Illustrative E xample Fig. 2 describ e s th e illustrati ve test system. The transm is- sion system inclu d es on e transmission line between nodes 1 and 2 with F 1 − 2 = 10 0 MW . The loads c o nnected directly to the tra nsmission system ar e L p 1 = 100 MW and L p 2 = 200 MW . The operating r ange of G1 and G2, i.e. the rang e between their min imum and maximu m power outputs, is  5 , 75  MW and  5 , 15  MW , respectiv ely , and their price of fers are C o 1 = $1 6 /MW and C o 1 = $6 /MW . Each distribution system ne e ds to supply L p 3 = L p 4 = 10 MW . Generators G3 and G4 hav e the o perating ran ge  10 , 120  MW ea c h with the increm ental costs of C o 3 = $6 /MW an d C o 4 = $4 /MW . For clar ity it is assume d that the d istribution system has no reactive power loads, a s well as power flow and voltage limits. The optim a l d ispatch is G 1 = 65 MW , G 2 = 15 MW , G 3 = 120 MW , and G 4 = 120 MW and th e L MPs are λ 1 = λ 2 = $16 /MW . Note G1 is a price-maker as other generato r s are at their power output limit. T h e power flo w in line between no des 1 and 2 is 7 5 MW , and the power flows in distribution lines 1-3 and n ode 2- 4 are 110 MW each. Fig. 3 compares the conver gence of the propo sed SLR-b ased approa c h obser ved at e a ch iteration with the sub gradien t method, a common algor ithmic ben chmark . Relativ e to th e benchm a rk, the pr oposed ap proach req u ires fewer iteratio n s to ach iev e a higher accuracy of the optim al solution, e.g . DSO-1 DSO-2 G4 2 4 G3 1 3 G1 G2 Load 4 TSO Load 3 Load 1 Load 2 Fig. 2: An illustrativ e example with t wo distribu tion systems (DSO- 1 and DSO-2) connected to the transmission system (T SO-1). 0.000001 0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 0 100 200 300 400 Distance to the optimum Iteration number Surrogate Lagrangian Relaxation Subgradient Method Fig. 3: Con verge nce of the proposed SLR-based approach com- pared t o the con ver gence of the subgradinet method. 0 4 8 12 16 0 4 8 12 16 λ 2 λ 1 Surrogate Lagrangian Relaxation Subgradient method Fig. 4: Con ver gence of the Lagrangian multipliers λ 1 and λ 2 (LMPs at node 1 and node 2) to their optimal v alue of $16/MW . after 400 iter ations the a c c uracy gain is ro ughly 100 x. Fig. 4 shows how λ 1 and λ 2 conv erge to their optimal values o f $16/MW . As shown in Fig. 4, the SL R re d uces zigzaging of Lagrang ian multipliers relative to the standard subgradien t method, which improves its conv ergence (Fig. 3). B. IEEE Benchma rk This section uses the IEEE 118-bus data [1 2] for the transmission system and each distribution system is mod- eled using the 34-bus IEEE distribution da ta [13]. In the following simulations we in crease the number of distribution systems co n nected to the transmission system and compare the results to the case when th e TSO and DSO are oper- ated without coo r dination. When add ed to the transmission system at a given bus, the distribution system is assum ed to fully replace the transmission lo a d at that bus. Each distri- bution system is assumed to h ave the same top ology an d the loads in each distribution system are scaled p ropor tionally to match the total transmission load in the case when the transmission and distribution systems are not co o rdinated . T able I sum marizes the c o st sa vings o btained with the propo sed TSO-DSO coordin ation, as co mpared to th e case without any coo rdination , and co m puting times o btained with th e pr oposed solutio n techniqu e. As the numb er of DSOs coord inated with the T SO increases, the relative TSO and DSO cost savings b oth increase. Howe ver, the TSO cost sa vings are rou ghly one ord er of magn itude grater than the DSO savings. Th is observation suggests tha t the T SO stand s to benefit to a larger extent from the propo sed coo rdination and there f ore there is a need to d esign appro priate in centive mechanisms to engage DSOs in the prop osed coord ination. T ABLE I. C O S T S A V I N G S A N D C O M P U T I N G T I M E S O B TA I N E D W I T H T H E P RO P O S E D T S O - D S O C O O R D I N AT I O N . # of DSOs TSO cost savin gs, % DSO* cost savin gs, % CPU time (s) 1 0.82% 0.06% 2 2 0.82% 0.05% 4 4 0.82% 0.06% 5 8 0.86% 0.07% 45 16 1.61% 0.19% 112 32 3.11% 0.18% 234 64 4.29% 0.29% 422 * Refers to the tota l cost of all DSOs cooridnat ed with the TSO. The computing times also increase with the number of DSOs engaged in the pro posed coordin a tio n; however , the pro- posed solu tion techn ique is cap able of solvin g all in stances within a reasonable amount of time. V . C O N C L U S I O N & F U T U R E W O R K This pap er presents an model to coordina te transmission and distrib ution system, wh ile c o nsidering binary UC de- cisions. W e solve the propo sed model using the Surrogate Lagrang ian Relaxation. Our case study demon stra te s that both th e tran smission and distribution systems benefit from the p roposed co ordinatio n. W e also show that the proposed SLR solution techniqu e outper forms existing meth ods. The p r oposed mode l p oints to multiple d irections for further investigation. First, it is imp ortant to extend th e propo sed model to a multi-perio d framew ork and include relev an t inter-tempor al constraints. Extending the model to multiple time per iods will also require accountin g for demand - and su pply-side un c e rtainty in both the transmis- sion and distribution system. It will also be imp o rtant to refine the accuracy of AC an d DC power flow models used in this work and av oid making restrictive assumptio ns on the sy stem topo logy (me sh ed or radial) . Fin ally , the propo sed model and solution techniq ue can be extended to a decentralized decision-makin g framework to respect priv acy concern s of the DSO and TSO oper ators. R E F E R E N C E S [1] H. 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