Integrated Microgrid Expansion Planning in Electricity Market With Uncertainty

Transcription

1 1 Integated Micogid Expansion Planning in Electicity Maket With Uncetainty Aida Khayatian, Student Membe, IEEE, Masoud Baati, Membe, IEEE, and no J. Lim Membe, IEEE Abstact This pape addesses the micogid expansion planning MEP poblem. In such a competitive electicity maket, it will assist ommunity Micogid OMG companies in deciding whethe o not they should invest in micogid installation. A two-stage stochastic optimization appoach is poposed to eliminate the taditional centalized planning which has led to competition among OMGs, Geneation ompanies GENOs, and Tansmission ompanies TRANSOs fo powe delivey. The objective of the two-stage stochastic pogamming model is to maximize the expected evenue fom these thee powe companies while ensuing the cost-effectiveness and eliability of the powe system unde uncetain factos such as load gowth and component outages. The poposed model is solved by decomposing the planning poblem into two stages. The goal of the fist stage is to maximize the pofits of OMGs, GENOs, and TRANSOs; the second stage is to minimize shot-tem opeation cost consideing uncetainty to enhance the eliability of the system. omputational esults fom two IEEE test systems ae pesented to analyze the effectiveness of the poposed appoach. Index Tems Bendes decomposition, component outages uncetainty, electicity maket, micogid expansion planning, ual electification, two-stage stochastic mixed-intege pogamming. c Opeational cost fo imaginay unit $/MWh. D Total demand MW. dt The pesent woth coefficient based on discount ate δ, dt = 1 + δ t 1. in. Investment cost $/MW/yea. ip. Incentive payment $/MW/yea. K. Incidence matix. mc. Maginal opeating cost $/MWh. P DM Local demand in OMG MW. P max. Maximum capacity MW. e. Obtained evenue fom LMP and SMP $/MWh. SF Ŷ Shift facto matix based on powe gid topology. U. Availability status of components G, L, and B. Vaiables: P G Dispatched capacity of geneation MW. P L Tansmission line flow MW. P M Aggegated dispatched capacity of OMG MW. P R Dispatched capacity of imaginay geneation MW. P EX Powe exchange between MG and main gid MW. S Slack vaiables. X, Y, Z Installation status of units, lines, and MGs. α, β, γ, π Dual vaiables. λ, µ System lambda and shadow pice. ϕ Total opeational cost. NOMENLATURE Indices: A symbol to indicate pe-detemined vaiables. b Load block subscipt index, b = {1,..., NLB}, NLB: Numbe of seasons at each yea. andidate unit o line supescipt index. E Existing unit o line supescipt index.. Powe output/outage subscipt indices: Geneato G, Line L, Micogid M, and Imaginay unit R, Bus B. i Geneation unit subscipt index, i = {1,..., NG}, NG: Numbe of units. j Tansmission line subscipt index, j = {1,..., NL}, NL: Numbe of lines. k MG subscipt index, k = {1,..., NM}, NM: Numbe of MGs. n Bus o substation subscipt index, n = {1,..., NB}, NB: Numbe of substations. s Scenaio subscipt index, s = {1,..., S}, S: Numbe of Scenaios. t Time subscipt index, t = {1,..., T }, T: Numbe of planning hoizon yeas. Iteation index. Paametes: T b Time block duation. A. Khayatian and G. J. Lim ae with the Depatment of Industial Engineeing, Univesity of Houston, TX USA akhayatian@uh.edu; ginolim@uh.edu. M. Baati is with the Depatment of Electical and ompute Engineeing, Louisiana State Univesity, LA, mbaati@lsu.edu. I. INTRODUTION Gid modenization has inceased attention in ecent yeas, by evamping the taditional way of supplying and deliveing electicity [1]. Many citical lifeline systems ae dependent on electicity infastuctue, which is subject to an incease in exteme natual disastes and othe majo unexpected disuptions. Theefoe, developing a new electic powe system with the ability to povide eliable, economical, and envionmentally fiendly levels of powe is essential. The taditional powe system can be modenized by utilizing Micogids MG. An MG is an advanced technology that can impove powe system eliability, esiliency, and sustainability. Deploying MGs with the ability to supply local loads is a desiable altenative to pomote ual electification, enegy efficiency, and total cost saving of the system, as well as congestion eduction on tansmission lines and distibution main feedes [2]. In the past, howeve, these ealized abilities wee aely obvious in tems of quantifiable fo powe investos [3]. It motivates us to design a moe pactical and cost-effective powe gid by utilizing MGs based on a capacity maket mechanism. This mechanism povides eal maket pice signals and incentive payment as a guide and encouagement fo powe investos. A community micogid OMG integates Distibuted Enegy Resouces DERs into advanced powe distibution gids. DERs ae the smalle powe esouces include nondispatchable enewable geneation such as the wind and sola units; and

2 2 small scale dispatchable esouces such as diesel geneatos, micotubines, and enegy stoage [4]. Although a significant amount of eseach has been epoted in liteatue quantifying and optimizing the benefits of using an MG [5] [9], only a few studies have been dedicated to developing an optimization model of the gid-connected MG investment in the powe maket. Some studies in micogid planning have consideed micogids in islanded mode [7] [9]. These studies have consideed micogid expansion planning MEP sepaately fom geneation expansion planning GEP and tansmission expansion planning TEP in the powe system [10] [14]; Howeve, powe sectos ae not sepaable in a vetically integated utility system [15] [19] and a moden powe maket includes geneation units, tansmission lines, and micogids. Khodaei et al. [19] suggests a model that plans the deployment of MGs in the gid and consides the impact of integated MEP with GEP and TEP unde uncetainties while minimizing the total investment and opeational costs. This pape has pimaily focused on powe expansion planning to minimize the total opeation, investment, and load shedding costs of the system fo MG investment as an altenative to taditional GEP and TEP poblem in electic powe gid. Howeve, in eality, the ownes of GENOs, TRANSOs, and OMGs make decisions on the new component deployment that can maximize thei own pofits in such a competitive electicity maket [20], [21]. The location and capacity of each new MG depend on the financial sustainability of the individual investo s decision. The cost associated with implementing the investment of MG is a geat concen to investos. The main motivation of this pape is to develop a new model fo OMG investos to find optimal installation location, size, and time fo MGs in the electicity maket while maximizing thei pofits. Theefoe, this pape enhances the long-tem micogid planning method pesented in [5], [6], [19], [22] by explicitly addessing competitive capacity and opeation of electicity maket, and micogid fo ual electification. In this pape, a maket-based planning famewok is poposed to integate MEP with coodinated GEP and TEP in a competitive envionment. In the poposed coodinated famewok, planne ISO maintains the system eliability in pedefined acceptable level by eliability evaluation to detemine if and when additional capacity is needed. The powe gid including static netwok flows and gid injections is modeled with D powe flow. The D powe flow is computationally light within the scope of coodinated poblems. Due to the uncetainty of foecasted electical loads and powe system outages of substations, geneation units, and tansmission lines [23], [24], optimization of electic powe ove a planning time hoizon is inheently a stochastic decision poblem. In this egad, we povide a two-stage stochastic mixed-intege pogamming model to addess both uncetainties. The esulting model, howeve, is not easily scalable to moe ealistic poblem instances due to the binay vaiables in the optimization model. To ovecome this issue, a theephase algoithm is developed using Bendes decomposition to account fo long-tem planning while maximizing the total pofits and consideing uncetainty impacts [25] [27]. The poposed algoithm featues a tadeoff between the gained Fig. 1. Aggegated ommunity Micogid achitectue. pofits and the level of eliability in the system. Majo contibutions of this pape include: 1 to pesent optimal maket-based planning and opeation of gid-connected micogids; 2 to utilize coect and effective maket-ointed pice signals to plan powe components in powe gid based on the competitive electicity maket; and 3 to quantify and optimize positive effects of deploying gid-connected micogid on opeating condition and ual electification. The est of this pape is oganized as follows. In section II, ommunity Micogid model is explained. The mathematical fomulations and the poposed solution method ae discussed in section III. Section IV povides numeical studies to examine the efficiency of the poposed method. Section V concludes this pape with futue eseach. II. OMMUNITY MIROGRID MODEL As shown a typical OMG stuctue in Fig. 1, the Depatment Of Enegy DOE defines the OMG as a goup of the aggegated load and aggegated DERs that act as a single contollable entity with espect to the gid at the Point of ommon oupling P [28], [29]. The DOE consides MG as an integated enegy system with the ability to opeate in a gid connected mode o in an islanded mode. Ou appoach offes MGs inteconnection at the Medium-Voltage level with the main gid at the High-Voltage level by taken into consideation the design without consideing details of DERs in OMG. Anothe benefit of consideing the inteconnected MG is inceasing evenue of the OMG by selling suplus electicity to the main gid. Theefoe, a cetaint potion of the load demand at any bus with the connected MG can be supplied by the local MG, and the est of the load demand will be supplied by conventional geneation units though the main gid. P EX in 1 shows the powe exchange between MG k and the main gid. P EX is positive, if MG k supplies its local demand and sends its excess powe output to the main gid. Othewise, it is negative. P Mbks t = P DMbks t + P EXbks t, k, b, s, t 1 III. PROBLEM FORMULATION AND SOLUTION METHODOLOGY Regading Bendes decomposition appoach [25] [27], we popose a pactical optimization appoach in which thee optimization phases ae solved in sequence to addess Investment Planning, Feasibility heck on Reliability, and Optimality heck on Opeation ost as illustated in Fig. 2.

3 3 A. Maste Poblem fo Investment Planning Investment planning aims to maximize the pofits of each GENO, TRANSO, and OMG accoding to the installation location and capacity size. The investment status of geneation units, tansmission lines, and OMG units ae detemined in the maste poblem MP in Phase A. The incentive payment and evenue paametes on the objective function encouage all maket investos to shae moe capacity in the system. How to detemine and update these two paametes based on the eliability evaluation and the opeation cost assessment fo the system by the ISO in the fist and second subpoblem, espectively is explained. The coesponding optimization model is: max I GP G, X, e G, ip G + I LP L, Y, e L, ip L + I M P M, Z, e M, ip M ϕ 2 S.t. 0 PGbit E P E,max, b, i, t 0 PGbit P,max Xt, b, i, t 0 P Mbk t PMk max Zt, b, k, t PLbjt P,max Y t, b, j, t 3 X it X it + 1, i, t Y jt Y jt + 1, j, t Z k t Z k t + 1, k, t 4 The MP is fomulated as a mixed-intege pogamming model. The objective function 2 maximizes the investos pofits by taking the total obtained income and subtacting the opeational cost of the system ϕ in a shot tem system opeation. onstaint set 3 enfoces the poduction capacity limits of all components. onstaint set 4 peseves the status of installed components fo the following yeas. I GP G, X, e G, ip G = T b t [e E GbitPGbit E dt t,b,i + e GbitPGbit + ip Gbi tx it] in itx it dt t,i I LP L, Y, e L, ip L = T b t [e LbjtPLbjt dt t,b,j + ip Lbj ty jt] in jty jt dt t,j I M P M, Z, e M, ip M = t,b,k + ip Mbk tz k t] t,k in k tz k t dt T b t [e Mbk tp Mbk t dt Functions 5-7 epesent the obtained income of the stategic investos including the GENOs, TRANSOs and OMGs, espectively. The fist and second tems in I G epesent the income of using existing and candidate units. The fist tem in I L epesents the income of using candidate lines. The thid tem in I G and second tem in I L epesent the ising income owed to obtained evenue fom incentive payments fo enhancing the system eliability at each iteation. The fist Reliability ut + Incentive Payment GENOs Phase B. SP1: Feasibility heck on Reliability Yes Phase A. MP: Investment Planning TRANSOs X Y Z heck system Feasibility and eliability Update incentive payment Violation? No Phase. SP2: Optimality heck on Opeation ost Optimize Opeation ost shot tem alculate LMP and SMP and Revenue onvege? Yes End of Planning Pocess OMGs Fig. 2. Thee-phase algoithm fo the poposed MG-based planning model. No Optimality ut+ Revenue tem in I M is the OMG s evenue of geneating powe by its DERs. The second tem epesents the geneated incentive payment by the ISO to pomote the OMGs fo installing the new MG in gid buses. The last tem in I G, I L, and I M is the installation cost of the units, lines, and MGs. B. Subpoblem 1: Feasibility heck on Reliability In Phase B, the eliability citeion is checked to ensue the eliability index of the system planning, which is satisfied based on the given aangement of the geneation units, MGs, and tansmission topology. Subpoblem 1, SP 1 bst is given fo each scenaio s, time t, and load block b accoding to the detemined ˆX, Ŷ, and Ẑ, as follow: v bs ˆX t, Ŷ t, Ẑ t = min1 T S + s + 1 T S s 8 S.t. 1 T K GP Gs + K M P Ms D s = 0 9 SF Ŷ K GP Gs + K M P Ms D s S s + PL max 10 SF Ŷ K GP Gs + K M P Ms D s + Ss PL max 11 PGbist E P E,max UGbist E, i 12 PGbist P,max ˆX i tugbist, i; α1bist 13 PLbjst E P E,max ULbjst E, j 14 P Lbjst P,max Ŷj tulbjst, j; β t, 1bjs β 1bjst 15 P Mbks t PMk max Ẑ kt K Mkn U Bbns t, k; γ1kbst 16 n PGbist, E PGbist, P Mbks t, S s +, Ss R +, i, j, k 17 The poposed eliability index is based on the unseved load at each bus of the system. But, the objective function

4 4 8 minimizes tansmission flow congestion. onstaint 9 is system enegy balance. onstaints show that the total optimal tansmission flow congestion is equal to the total nodal eal powe imbalance of the gid. onstaints enfoce the capacity limits egading availability of components. Geneation units, tansmission lines, and substations can be damaged due to an exteme event. Relevant to this issue, uncetain binay paametes U Gbis, U Lbjs, and U Bbns ae detemined using simulation to fomulate the impact of electical failues due to a unexpected distibution system inteuption. Moeove, failue of a substation U Bbjs causes failue of the geneation unit and tansmission lines connected to this substation. This effect of a failue of a substation on the elated components can be calculated using Algoithm 1. Algoithm 1 Substation failue 1: fo b, i, j, s, t do 2: if n KnU Bbnst < 1 then 3: U Gbis 0 4: end if 5: if n KnU Bbnst < 2 then 6: U Lbjs 0 7: end if 8: end fo The powe system eliability assessment is to evaluate the total expected unseved enegy of the system load. The Loss Of Enegy Pobability LOEP index is often used as a pefomance metic to calculate the expected unseved enegy. LOEP is the atio of the Expected Unseved Enegy EUE to the total enegy demand of the system. The LOEP index detemines eliability violation based on the total unseved load at each load block b fo each yea t, and each scenaio s, which is associated with tansmission congestion, and contingencies on geneation units, lines and MGs. The total unseved load is automatically calculated by 8. When the expected atio of total unseved enegy ove the total equied enegy is geate than the theshold value of LOEP, E s [ˆv bs t T b t/l bs t T b t] LOEP, the eliability cut 18 will be geneated and added to the MP. This will foce the investos to evisit and modify the values of X, Y, and Z to educe the expected unseved enegy. The cut 18 is calculated based on Bendes decomposition appoach. The cut is a function of the dual vaiables α 1, β 1, and γ 1 of constaints 13, 15 and 16 contain pe-detemined vaiables X, Y, and Z, espectively. These pe-detemined vaiables ae sent by the MP 2. E s[ i + j + k α1bistp,max UGbist X it ˆX i t β t + 1bjs β 1bjstP,max ULbjst Y jt Ŷ j t γ1bkstp Mk max U Bbnk st Z k t Ẑ kt + ˆv bs ˆX t, Ŷ t, Ẑ t] LOEP E[L bs t], b, t. 18 The MP 2 with this added eliability cut 18 may esult in diffeent optimal solutions. Note that the main objective of the MP is a pofit maximization fo each investo. In ode to take the impact of the eliability cut into account in the investo s decision making poblem, the eliability cut must be pojected into the pofit function of each investo in MP 2. This can be viewed as an incentive payment, which is called an incentive eliability signal. Paticulaly, the ISO is authoized to establish a powe system planning incentive pogam to suppot the installation of additional geneation esouces and an adaption of cetain advanced powe geneation technologies to impove the global eliability of the powe gid. This incentive eliability signal encouages powe investos to expand moe capacity to the locations with weak powe. The esulting MIP investment poblem with this signal equies adding an additional pai of linea constaints 0 X, Y, Z 1 to fomulation 2. This evised model is solved and the coesponding dual vaiable π of constaint 18 is calculated to update the incentive eliability income fo each investo, at each block b, and pe yea t in 19. [ ] ip Gbit = πbte s α1bistp,max UGbist [ ] ip Lbit = πbte s β 1bjst + β t P,max 1bjs ULbjst ip Mbit = π bte s [γ 1bkstP max Mk U Bbnk st] 19 The incentive payment functions 19 updates at each iteation by multiplying the dual vaiable π, which can be intepeted as the pice of one unsatisfied load MW to the expected value of exta added capacity of candidates. The incentive payment fo a new capacity investment is updated in the objective function of MP as an incentive eliability signal fo all paticipants by the ISO.. Subpoblem 2: Opeation ost hecking The system opeation cost including the total shot un maginal cost of all existing and installed candidate capacities of is minimized in Phase. Subpoblem 2, SP 2 bst at each load block b in yea t fo each scenaio s is fomulated as: w bs ˆX t, Ŷ t, Ẑ t = min mc E GbitPGbist+ E i mc GbitPGbist + mc LbjtPLbjst j + k S.t. mc Mbk tp Mbks t + n c RP Rbns t 20 1 T K GP Gs + K M P Ms + K RP Rs D s = 0, λ s 21 SF E Ŷ P Rs + K GP Gs + K M P Ms D s P E,max Ls ; µ E E s 22 SF Ŷ P Rs + K GP Gs + K M P Ms D s PLs ; µ s 23 0 PGbist E P E,max UGbist E, i 24 0 PGbist P,max ˆX i tugbist, i; α2bist 25 0 PLbjst P,max Ŷj tulbjst, j; β2bjst 26

5 5 0 P Mbks t PMk max ktu Bbnk st, k; γ2bkst 27 0 P Rbns t, n 28 The objective function 20 is the total opeation cost of the system. It should be noted that the consideed uncetainties may cause the unexpected unseved load in some scenaios. To povide feasibility of the opeational cost poblem, an amount of imaginay geneation units ae consideed as eseve to seve the esidual unseved enegy of the system at each buses. onstaint 21 epesents enegy balance of the system and constaints indicate components capacity limits. The ISO simulates enegy payment fo all paticipants based on the nodal Locational Maginal Pices LMP and line Shadow Maginal Pices i.e., SMP as a evenue signal [30]. LMP eflects the maginal cost of supplying one unit of inceased enegy at a specific bus and SMP is the maginal cost of supplying the next incement of maximum line capacity. The λ E s, and µ s ae dual vaiables of constaints 21-23, epesent system lambda, shadow pice of existing and candidate lines, espectively. The expected LMP and SMP ae calculated fom λ E s, and µ s LMP [ = E s λ s + λ ] cong,s λ cong,s = SFs T Ŷ [ SMP = E s µ s µ s µ s ] µ s 31 Futhemoe, the geneated optimality cut 32 fo all scenaios sends to MP at each iteation based on Bendes decomposition, whee ϕ calculates the system opeational cost in the objective function 2. E s[ i + j + k α2bistp,max UGbist X it ˆX i t β2bjstp,max ULbjst Y jt Ŷ j t γ2bkstp Mk max U Bbnzst Z k t Ẑ kt + ŵ bs ˆX t, Ŷ t, Ẑ t] ϕ, b, t 32 By the Duality theoem [27], ou poposed algoithm povides uppe and lowe bounds to the solution in each iteation. Once the opeation cost poblem is solved, the lowe and uppe bounds to the solution should be calculated. The uppe bound 33 and lowe bound 34 solutions at the th iteation update with total obtained income of all maket paticipants and total system opeation cost. ρ uppe =I GP G 1, ˆX 1, e G 1, ip G 1 +I LP L 1, Ŷ 1, e L 1, ip L 1 +I M P M 1, Ẑ 1, e M 1, ip M 1 ϕ 33 ρ lowe =I GP G, ˆX, e G, ip G + I LP L, Ŷ, e L, ip L +I M PM, Ẑ, e M, ip M E s [w bs ˆX ] t, Ŷ t, Ẑ t b,t 34 The algoithm continues until the stopping citeion 35 is met, whee ε is a small toleance value between and [26], [31]. We set ε at ρ uppe ρ lowe /ρ uppe ε 35 Algoithm 2 depicts all calculation steps descibed above in ou poposed algoithm and it is self-explanatoy. Algoithm 2 The poposed algoithm 1: Initialize ε,, ˆX, Ŷ, Ẑ, ρ lowe, ρ uppe, ˆv bs, 2: while ρ uppe ρlowe /ρ uppe > ε do 3: while ˆv bs > ε do 4: Solve 8 fo all b, t, and s to obtain optimal ˆv bs t and dual vaiables α1bist, β t, 1bjs β 1bjst, γ1kbst. 5: Geneate eliability Bendes cut 18. 6: Add the geneated cut to MP 2. 7: Solve elaxed MP 2 to obtain the dual value πbt of eliability cut 18. 8: Update incentive payments ip G, ip L, ip M at 2 9: by : Solve 2 to obtain optimal ˆX t, Ŷ t, Ẑ t. 11: end while 12: Solve 20 fo all b, t, and s to obtain optimal ŵ bs t and dual vaiables λ s, µ E E s, α 2bis t, β t, 2bjs β 2bjs t, γ 2bkst. 13: Geneate optimality cut : Add the geneated cut to MP 2. 15: alculate LMP and SMP by 29 and 31, espectively. 16: Update e G, e L, e M based on calculated LMP and SMP. 17: : Solve 2 to obtain optimal ˆX t, Ŷ t, Ẑ t. 19: alculate ρ uppe and ρ lowe by 33 and : end while IV. ASE STUDIES This section pesents numeical esults fom two case studies based on the IEEE six-bus and modified 118-bus test systems descibed in [32]. Model 2-35 has been solved using PLEX [33] unde GAMS [34] on a Linux seve with 24 pocessos at 2.53 GHz and 128 GB of RAM. A. Six-Bus System A six-bus test system is consideed [21], whee it has seven existing and seven candidate lines, thee existing and eleven candidate units and one candidate OMG. One candidate OMG is connected to bus 3. The loads ae located at buses 3, 5, and 6. Moe details of the test system and the figue can be found in [32]. The following model paametes ae given as inputs: the planning hoizon is ten yeas, thee ae fou load blocks, the base yea peak load is 25 MW, and the base yea enegy demand is GWh, the LOEP is at 5% fo all load blocks at evey planning yea, and the discount ate δ is assumed at 5%, which is used fo net pesent value calculation. A nomal pobability distibution function with 0 mean and 0.01 standad deviation values ae used to geneate andom values fo peak load and load gowth ate at each load block. A unifom pobability distibution function in the ange

6 6 TABLE I INSTALLATION YEAR OF ANDIDATE GENERATION UNITS AND OMG G1 G3 G4 G5 G6 G7 G8 MG ase ase TABLE II INSTALLATION YEAR OF ANDIDATE TRANSMISSION LINES L1 L2 L3 L4 L5 L6 L7 ase ase TABLE III TOTAL OPERATION OSTS AND UNSERVED ENERGY ase 0 ase 1 ase 2 ase 3 Total Op. cost$ Unseved enegymwh of 0 and 1 is used to andomize the component outages. One thousand scenaios ae geneated using the Latin Hypecube Sampling pogam to epesent the uncetainties in demand and component outages [35]. Recall that the scenaio eduction is applied to educe the computation effots while maintaining the solution accuacy using the SENRED tool [36]. Thus, the initially geneated 1000 scenaios wee educed to 10 scenaios using SENRED and moe details can be found in [32]. Five case studies ae designed to study model pefomance based on two factos: load gowth and component outages uncetainty and OMG planning conditions. Unde the assumption that OMG planning is consideed in the model, the fist two cases compae the diffeence between two modeling appoaches: a deteministic model and a stochastic model The second two cases ae to show the model pefomance when OMG planning is not consideed. The last case is studied to obseve the effect of OMG planning on diffeent locations. ase 0 Deteministic model with OMG planning. ase 1 Stochastic model with OMG planning. ase 2 Deteministic model without OMG planning. ase 3 Stochastic model without OMG planning. ase 4 Stochastic model with mutliple OMG planning. The expeiment esults ae pesented in Tables I and II which summaize the installation yea of candidate geneation units, OMGs and tansmission lines esults fo ase 0 and ase 1. ase 0 Deteministic model with OMG planning: The goal of this model is to detemine the coodinated investment planning of thee powe company investos by maximizing thei pofits. This model is solved by ou poposed algoithm without consideing uncetainties. In the oiginal six-bus test system, the existing lines ae congested because the existing line capacities ae not enough to supply the demand at load buses. Hence, a new component investment is needed to satisfy load demand and elieve the tansmission line congestion. The solution esults show the deteministic eliability citeion 18 is violated in the fist iteation of the algoithm. This fact foces ISO to activate incentive payment as an incentive eliability signal to encouage the investos of candidate lines 2-7. As it is shown in Table II, the obtained solution poposes the installation of L2-L7 in Yea 1. Accoding to tables I- II, ou investment plan pefes to constuct the lines moe than geneatos. This is because the opeation and investment costs ae cheape compaed to the candidate geneatos and micogid. The plan suggests the installation of geneation units G1, G3, and G5-G7. Fo example, thee ae two candidate geneatos G1 and G2 connected to bus 1, whee G1 is consideed to be installed at yea 1. G1 offes a less expensive opeation cost and highe geneation capacity compaed to G2. Summing up all these, fom the investos viewpoint, we can claim that ou model selects the moe pofitable offes based on maket pospective while consideing the system eliability. Fom the OMG point of view, MG is installed at yea 1, at the ealiest yea. MG investment is moe pofitable; howeve, thee ae two othe candidate geneation units G2 and G4 with a highe capacity and smalle investment cost. These esults veify that the installation of MG with the ability to supply the local load and lowe opeational cost educes the tansmission line investment cost as well as the system opeational cost by $ This is a consequence of local supplying. ase 1 Stochastic model with OMG planning: The coodinated planning of thee powe companies is applied unde uncetainties. The solution of the stochastic model in Tables I and II suggests installing the additional candidate geneation units G4 and G8 and hastening the installation of G5 and G6. Even though G4 and G8 ae the most expensive candidate units, the eliability constaint 18 foces the investos to install them. Because they ae associated with lowe Foced Outage Rate FOR. Adding moe eliable geneatos with less FOR to the netwok will educe the total powe mismatch consideing powe outages. As compaed with ase 0, geneatos ae installed ealie in ase 1 due to an anticipated highe amount of unseved enegy unde uncetainties. As a esult, thee is an incease in powe supply by 18.50MWh to satisfy the system eliability level. In ase 0, the solution pocess equied fouteen pice signal loop iteations to check opeational cost in Phase which is taken seconds to solve. ompaed to the esults of ase 0, ase 1 equied six pice signal loop iteations and took seconds to convege. onsequently, the solution time is highe in ase 1, even though the scenaio eduction is applied. Figue 3 shows that the stochastic model s PU solution time inceases exponentially as the numbe of scenaios. It indicates the impotance of scenaio eduction on PU calculation time. ase 2 Deteministic model without OMG planning: The esult of this case is given in Table III, it shows 24.74% total opeation costs addition compaed with ase 0. ase 3 Stochastic model without OMG planning: The geneation and tansmission expansion planning poblem is solved without consideing the MG installation. The solution esult shows that applying OMG educed the expected amount of unseved enegy by 11.92%, because the OMG supplies the local load without using tansmission lines that inheently have the possibility of outage. Anothe facto affecting the investment decision of MG is the impact of the electicity maket LMP in a shot tem opeation. at the local OMG. Figue 4 illustates the expected LMP at bus 3 fo block 1 fo ase 1 and 3. The expected LMP

7 7 MP Objective $ No. of educed scenaios Fig. 3. The equied PU time to solve the poposed model based on numbe of scenaios. 200 ase ase 1 LMP $/MWh Yea Fig. 4. LMP ove planning yeas at bus 3 fo the fist load block. TABLE IV INSTALLATION YEAR OF ANDIDATE GENERATION UNITS AND OMGS G1 G3 G4 G5 G6 G7 G8 M1 M2 ase ase ase TABLE V TOTAL OPERATION OSTS AND UNSERVED ENERGY ase 1 ase 4-1 ase 4-2 Total Op. cost$ Unseved enegymwh pofiles fo othe blocks ae the same as block 1. This figue veifies that in ase 1 the MG installation at yea 2 ceates lowe LMP at bus 3 $47.677/MWh in compaison to ase 3, without MG $48.127/MWh. Theefoe, MG investment impoves the LMP pofile fluctuation at lowe level values ove the planning hoizon. ase 4 Stochastic model with mutliple OMG planning.: In this case as well as the initial MG candidate at bus 3, one moe MG is added into the system in two diffeent locations: 1 bus 5 and 2 bus 3. Table IV-V shows the esult of ou investment plan fo ases 1 and 4. In ase 4-1, the plan pefes to install second MG at yea 1 in bus 5. As a esult, second MG helps to educe the expected unseved enegy and total opeation costs by % and 6.998%, espectively. Howeve, fom ase 4-2, it can be concluded that inceasing the penetation of MG not necessaily causes a significant eduction in the unseved enegy because both MGs ae connected at bus 3. Accumulation MG in bus 3, due to the congestion of the netwok cannot significantly impove the system load satisfaction. Theefoe, the penetation and spead of MGs ove the powe gid may have a significant impact on less tansmission congestion and moe total load seving in whole system. PU time s a % OMGs GENOs 68% b % 71% c % 91% Fig. 5. Ratio of used capacity of OMGs and GENOs in the system to seved enegy with diffeent MGs investment cost: a $600, b $800, c $2,000/MWh/yea It should be emphasized that the opeation cost of existing tansmission line is not consideed in the objective function of SP2. The existing liteatue has been veified that moe than 80% of the total expansion planning cost belongs to geneation units [37]. The optimization esults also show less congestion and geneation costs with maginally geate total opeation cost in compaing to anothe case when the opeation cost of existing tansmission line is consideed on the objective function SP2. In this case, the value of feedback pice signals to candidate tansmission line investos in MP will be deceased in the wake of lowe congestion pices. Theefoe, deployment of new candidate tansmission line will be also diminished. onsequently, the SP2 utilizes the full capacity of the existing tansmission line to satisfy the total demand in the system instead of the new candidate tansmission lines. In addition to above consequences, the computational effot is petty much less and the PU calculation time becomes faste. Note that consideing the exising lines opeation cost in 20 esults in 1.7% total cost saving, howeve, it aises the computational time by %. B. 118-Bus System A modified IEEE 118-bus system is analyzed to study the pefomance of the poposed solution appoach. The system includes 118 buses, 53 existing geneation and 10 candidate geneation units, and 180 existing and 5 candidate lines [32]. The MGs can be deployed at a selected subset of the buses and the MG s maginal cost is assumed to be $1/MWh. Fou load blocks ae assumed fo a 10-yea planning hoizon. FORs of geneation units and tansmission lines ae 4% and 1%, espectively. The initial system peak load is 3, 000 MW and the initial enegy demand is 21, 576 GWh with an annual load and enegy gowth ate of 5%. One thousand scenaios on demand and component outages ae geneated and wee educed to ten scenaios using SENRED. The pobability of each educed scenaio is pesented in Table VI. We analyzed the model sensitivity of changing investment cost fo MG in thee diffeent cases as shown in Fig. 5 and Table VII. The sensitivity analysis is done fo low, medium, and high MG investment costs: $600, 800, and 2000/MWh/yea. The last thee columns of Table VII show the installation yea of MGs fo each case. In the case of $600/MWh/yea, five MGs ae to be installed in yeas 1, 4, 5, and 7, while only one MG MG2 is suggested fo installation in yea 1 when the investment cost is $2, 000/MWh/yea. This makes economic sense because it is less pofitable to have MGs installed when the investment cost of MG is highe. Figue 5 illustates

8 8 TABLE VI PROBABILITY OF EAH SENARIO AFTER SENARIO REDUTION Scenaio Pobability Scenaio Pobability TABLE VII OMG INSTALLATION YEAR Bus apacity. Inv. ost $/MWh/yea MW MG MG MG MG MG the influence of MG investment cost on the penetation of GENOs and OMGs in the system. Unde the scenaio of $600/MWh/yea Fig. 5 a, GENOs supplied 68% of the total amount of seved enegy and OMGs supplied 32%. Howeve, the shae of supplied enegy by these two esouces changed to 91% GENOs and 9% OMGs when the MG installation cost was inceased to $2, 000/MWh/yea. Rual electification povides few incentives fo business development such as GENOs and TRANSOs due to the high investment cost associated with tansmission lines and low density custome basis pe squae mile [2]. Nevetheless, OMGs offe enewable geneation with the capability of installing MGs at a emote egion. To examine the impact of ou poposed famewok on ual electification, bus 12 is elected at a emote location in the netwok, with % of load facto. Even though the $2, 000/MW/yea investment cost on a MG is much moe expensive than a candidate geneation unit [32], the installation of MG at bus 12 MG2 is still pofitable in yea 1, because thee ae multiple benefits to have MG2 fo the powe system opeato and its investo. Benefits include 1 unseved enegy eduction by 11.23% in emote aeas, 2 $ cost savings coesponding to ejection of additional geneation units and additional tansmission lines in emote aeas, and 3 the highest incentive payment paid by ISO to MG2 investo is 50.92% geate than the next highest incentive payment to anothe maket paticipant. This high payment is because MG2 enhanced the system eliability LOEP by at emote bus 12. Hence, ual electification can be enhanced by investing on OMGs if it is pofitable. These esults show that ou poposed model not only educes investment cost as well as unseved enegy, but also enhances the system eliability in emote location of powe gid. As the netwok size gets lage, the computational buden to solve the coesponding optimization model can become moe challenging. Fo the 118-bus system, the oiginal model without consideing paamete uncetainty took 16 minutes to solve, while ou poposed stochastic appoach with educed scenaios found the optimal solution in 6 minutes. Futhemoe, Fig. 6 shows pogession of the poposed solution appoach until it conveges. It displays the stopping citeion 35 and the opeation cost ove iteation. The algoithm Stopping iteion Iteation Fig. 6. onvegence fo the 118-bus system. Op.ost Stop i conveged with a negligible gap at at iteation 6. The cost made a big jump to $3.7, at iteation 3 and finally conveged to $3.7, at the final iteation. Fom the esults pesented in Table I to VII, the following obsevations can be made egading competitive makets. a Even at a highe investment cost, a OMG is an excellent altenative to taditional powe esouces unde exteme events because those events can cause a powe outage. Since MGs do not ely on the tansmission system, having OMGs can decease the unseved enegy and enhance the system eliability. b Having coect and effective pice signals is a key facto fo a successful electicity maket. LMP is the basis fo maket-based congestion management and achieving maket efficiency. OMGs can help tansmission congestion eduction and minimize the consequence of tansmission outages in the netwok. Due to the fact that a highe tansmission line congestion leads to a highe LMP value, the LMP value is a good indicato to identify potential locations fo OMGs installation. Hence, OMG is installed at highly congested locations based on the LMP signal and educes the LMP. c Having OMGs in the powe netwok can enhance ual electification. In many cases, OMGs can be sufficient enough to supply electicity to ual aeas whee the load is elatively low. As a esult, it will eliminate the need fo extending taditional powe esouces, which ae often expensive to install and maintain. Although simila obsevations have been made in pevious studies, they focused pimaily on a system-wide pespective, not on competitive electicity makets. V. ONLUSION In this pape, a new two-stage stochastic pogamming model fo integating OMG with GENO and TRANSO as powe investos was intoduced based on electicity maket unde uncetainty. This model povides appopiate maket pice signals fo all investos to detemine thei investment status based on maximizing pofits as well as keeping the eliability and opeational cost of the powe system at acceptable levels. The poposed model was applied to two modified IEEE test systems. The esults illustate that integating enegy initiative esouces with taditional esouces enhances the eliability and educes high opeational cost of the system. Moeove, adding OMGs can enhance ual electification. 2 0 Opeation ost $

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Available: [33] The ILOG PLEX, [Online]. Available: poducts/cplex/. [34] R. E. Rosenthal, GAMS: A Uses Guide, GAMS Development opoation, Washington, Sep [35] G. D. Wyss and K. H. Jogensen, A uses guide to LHS: Sandias Latin hypecube sampling softwae. SAND , Sandia National Laboatoies, Albuqueque, NM, [36] GAMS/SENRED Documentation [Online]. Available: [37] B. Alizadeh and S. Jadid. Reliability constained coodination of geneation and tansmission expansion planning in powe systems using mixed intege pogamming, IET Gen. Tans. Dist., vol. 5.no. 9, pp , Sep Aida Khayatian is a Ph.D. student in the Industial Engineeing Depatment at the Univesity of Houston, Houston. He eseach inteests include Micogid and integated esouce planning. Masoud Baati eceived the Ph.D. degee in electical engineeing fom Illinois Institute of Technology, hicago, in Pesently, he is a eseach and instuctional assistant pofesso in the Electical and ompute Engineeing Depatment at Univesity of Houston, Houston. His eseach inteests include micogid opeation and planning, micoeconomics, mathematical modeling and multiple infastuctue assesment. no J. Lim is a pofesso and chai of industial engineeing, and Hai and Anjali Faculty Fellow at the Univesity of Houston. He holds a Ph.D. in Industial Engineeing fom Univesity of Wisconsin-Madison. His eseach inteest lies in developing optimization techniques fo solving lage scale decision making poblems in aeas such as netwok esiliency, supply chain unde disuption and tanspotation netwoks. His cuent eseach pojects include obust optimization in tanspotation poblems, smat pots, and scheduling. His addess is ginolim@uh.edu.