Preventive reinforcement under uncertainty for islanded microgrids with electricity and natural gas networks

Transcription

1 J. Mod. Power Syst. Clean Energy (08) (): Preventve renforcement under uncertanty for slanded mcrogrds wth electrcty and natural gas networks Saeed D. MANSHADI, Mohammad E. KHODAYAR Abstract Ths paper presents an approach to determne the vulnerable components n the electrcty and natural gas networks of an slanded mcrogrd that s exposed to delberate dsruptons. The vulnerable components n the mcrogrd are dentfed by solvng a b-level optmzaton problem. The objectve of the upper-level problem (the attacker s objectve) s to maxmze the expected operaton cost of mcrogrd by capturng the penaltes assocated wth the curtaled electrcty and heat demands as a result of the dsrupton. In the lower-level problem, the adverse effects of dsruptons and outages n the electrcty and natural gas networks are mtgated by leveragng the avalable resources n the mcrogrd (the defender s objectve). The uncertantes n the electrcty and heat demand profles were captured by ntroducng scenaros wth certan probabltes. The formulated b-level optmzaton problem provdes effectve gudelnes for the mcrogrd operator to adopt the renforcement strateges n the nterdependent natural gas and electrcty dstrbuton networks and mprove the reslence of energy supply. The presented case study shows that as more components are renforced CrossCheck date: 8 May 08 Receved: 0 August 07 / Accepted: 8 May 08 / Publshed onlne: August 08 Ó The Author(s) 08 & Mohammad E. KHODAYAR mkhodayar@smu.edu Saeed D. MANSHADI manshad@sdsu.edu Department of Electrcal and Computer Engneerng, San Dego State Unversty, San Dego 98, USA Department of Electrcal Engneerng, Southern Methodst Unversty, Dallas 70, USA n the nterdependent energy networks, the renforcement cost s ncreased and the expected operaton cost as a result of dsrupton s decreased. Keywords Mcrogrd, Renforcement, Natural gas, Electrcty, Delberate dsrupton, Uncertanty Introducton The hgher penetraton level of renewable energy resources requres mproved flexblty measures n the power networks. The relatve low cost and abundance of natural gas fuel resources as a result of recent developments n the extracton technques (hydrofracturng and horzontal drllng), the ncrease n the envronmental concerns n electrcty generaton, and the hgher effcency of gas-fred electrcty generaton technology ncreased the dependence of electrcty nfrastructure system on the natural gas network []. Expected low natural gas prces n the 0 00 s projected to addng 7 GW generaton capacty of natural gas-fred generaton technology annually, whch accounts for 3% of the total annual capacty ncrease []. Such ncreasng trends n natural gas-fred generaton resources led to nvestgatng the nterdependence among the bulk electrcty and natural gas energy systems [3 ]. The nstalled capacty of the combned heat and power (CHP) n the U.S. s 70 GW whch accounts for almost 7% of total generaton capacty []. The CHP generaton technology that s leveraged by the customers n the dstrbuton networks, mproves the energy effcency and further hghlghts the nterdependence among natural gas and electrcty dstrbuton networks. Mcrogrds equpped wth CHP technology, provde the expected relablty and 3

2 Saeed. D. MANSHADI, Mohammad. E. KHODAYAR servce qualty by effectvely coordnatng the operaton among electrcty and natural gas dstrbuton networks. The physcal layer of the electrcty network n mcrogrds that operate n grd-connected or sland mode s composed of demand enttes (consumers), dstrbuted generaton unts, and dstrbuton cables. The natural gas dstrbuton network s composed of the source ponts, gasfred dstrbuted generaton unts, heaters, and natural gas ppelnes. In [], several factors ncludng physcal characterstcs, the operatonal procedures, types of the electrcty generaton plants, and avalablty of electrcty and natural gas supply were addressed as potental factors that affect the operaton of the nterconnected natural gas and electrcty networks. The schedulng of nterdependent energy networks by determnng the optmal couplng matrx and controllng the flow of electrcty, natural gas, and dstrct heat flow s addressed n [7]. It s shown n [8] that the ntegrated operaton of electrcty and natural gas networks wll lead to savngs n energy costs. There are several perceptons of reslence. In [9], reslence s defned as the capablty of a system to wthstand major dsruptons wth acceptable degradaton n performance and capablty to recover wthn acceptable tme and cost. In [0], reslence s defned as the ablty to prepare and adapt to the evolvng condtons, wthstand the dsruptons, and recover rapdly from them. Ths paper adopted the frst defnton of reslence; therefore, the vulnerable components n slanded mcrogrds are determned to avod the dsrupton n servce as a result of delberate dsruptons. Reslence n electrcty network was addressed by several publcatons [ ]. In [], a smulaton-based approach s proposed to address the margn and senstvty of the electrcty dstrbuton network wth respect to the resources for repar and recovery. The proposed model could be used for dstrbuton system operators to assess the ablty of the system to accommodate large dsturbances by adjustng system repar resources. A two-step stochastc programmng framework s proposed n [] to mtgate the socoeconomc cost of mcrogrds that are exposed to the stochastc natural dsasters. The proposed approach showed the potental of mcrogrds for mprovng the reslence of the electrcty network. In [3], statc power system vulnerablty s addressed usng a b-level optmzaton problem wth transmsson lne swtchng. The objectve s to determne the most destructve nterdcton plan wth the hghest loss of load n the power network. An mproved nterdcton model that dentfes maxmal electrc grd attacks n short-term (seconds to mnutes) and medum term (mnutes to days) s addressed n []. The proposed model dentfes the potental cascadng falures that may lead to large blackouts. In [], a tr-level defender-attacker-defender model s proposed and solved usng the column and constrant generaton methodology for mprovng the grd survvablty under contngences. The reslence of natural gas network s addressed n [] by procurng a response strategy to energy shortage and evaluatng ts quantfed effectveness n varous scenaros. Whle earler research nvestgated the reslence of electrcty networks aganst delberate dsruptons, the nteracton among electrcty and natural gas networks to provde effectve reslence measures should be further nvestgated [7]. Ths paper addresses the renforcement strateges n slanded mcrogrds wth electrcty and natural gas dstrbuton networks, that are exposed to delberate dsruptons consderng the uncertantes n electrcty and heat demand. The presented framework dentfes the crtcal components that should be renforced to ensure the energy supply contnuty n the mcrogrd s dstrbuton network whle capturng the uncertantes mposed by volatlty of electrcty and heat demands. Problem formulaton The problem s formulated as a b-level optmzaton problem that yelds the vulnerable components n the mcrogrd wth electrcty and natural gas dstrbuton network. The preventve renforcement strateges n the nterdependent electrcty and natural gas networks are procured by dentfyng the vulnerable components and the potental consequences of dsruptons n an slanded mcrogrd. The objectve of the upper-level problem s to maxmze the expected operaton cost of the mcrogrd by dsruptng the vulnerable elements n the electrcty and natural gas networks consderng lmted resources for such dsruptons. The objectve of the lower-level problem s to mnmze the expected operaton cost of the slanded mcrogrd once t s exposed to the delberate dsruptons. As shown n Fg.,by ncorporatng the dualty theory, the b-level optmzaton problem s formulated as a sngle level mxed nteger programmng (MIP) problem. The objectve functon of the MIP problem s the same as the objectve functon of the upperlevel problem as gven n (). max OP pr ¼ t ( j q t " P e;d F c; þvoll h j P e ;t þ VOLL e P e;d þ F c;k P h k;t ðþ k #) P h;d P h;d where s the ndex for the gas-fred dstrbuted generaton unt; l s the ndex for the electrcty dstrbuton lne; p s 3

3 Preventve renforcement under uncertanty for slanded mcrogrds wth electrcty and Input data of electrcty load, dstrbuted energy resource (DER), heat load data, and dstrbuton components Input data of electrcty load, DER, natural gas load data, and dstrbuton components B-level optmzaton problem Upper-level problem (MIP): Maxmze the operaton cost wth lmted resources for dsruptons Lower-level problem (MIP): Mnmze the operaton cost Natural gas flow constrants AC power flow constrants Prmal dual representaton of lower-level problem Equvalent sngle level mxed nteger lnear programmng (MILP) problem maxmzng the operaton cost of the mcrogrd subjected to: Prmal and dual representaton of AC power flow constrants Dsrupton resource constrant Prmal and dual representaton of Natural gas flow constrants Fg. Soluton framework for the proposed b-level optmzaton problem the ndex for the natural gas ppelne; t s the ndex for scenaro. The producton cost functon for gas-fred dstrbuted generaton unt and heater k are presented by F c; and F c;k. The ndces for electrcty and heat energy are presented by e and h. In addton, the value of lost load for electrcty and heat demands are shown by VOLL e and VOLL h respectvely. The probablty of scenaro t s shown as q t. The generaton dspatch of gas-fred dstrbuted generaton s shown as P e ;t, the electrcty and heat demand at node j n scenaro t are shown as P e;d and P h;d respectvely. The served electrcty and heat demand at node j n scenaro t are shown as P e;d and P h;d respectvely. The generated heat by heater k at node j n scenaro t s shown as P h k;t. The resources for dsrupton are lmted by () where M s the total avalable resources for dsrupton. The requred resources to renforce gas-fred dstrbuted generaton unts, dstrbuton lnes and natural gas ppelnes are shown by M, M l, and M p respectvely. NG M ð U Þþ NL þ NP p l M l ð UY l Þ M p UZ p M ðþ The decsons on dsruptng gas-fred dstrbuted generaton unts, dstrbuton lnes, and natural gas ppelnes are represented by the bnary varables U, UY l, and UZ p respectvely. Here, 0 ndcates that the component s dsrupted and consequently unavalable, and ndcates that the component s not dsrupted and s avalable. The total number of gas-fred dstrbuted generaton unts, electrcty dstrbuton lnes, and natural gas ppelnes are shown by NG, NL, and NP respectvely. The objectve of the lower-level problem s gven n (3), where the expected operaton cost OP pr of the mcrogrd exposed to dsrupton s mnmzed. As formulated n (3), the objectve of the lower-level problem s to mnmze the expected operaton cost of the mcrogrd. mn ( OP pr ¼ t j q t P e;d " þvoll h j F c; P e ;t þ VOLL e P e;d þ F c;k P h k;t ð3þ k #) P h;d P h;d The expected operaton cost s determned by the probablty assocated wth each scenaro, the generaton cost of gas-fred dstrbuted generaton unts and heaters n addton to the penalty assocated wth the electrcty and heat demand curtalments n each scenaro. Here, the constrants assocated wth the lower-level problem are gven n () () where the dual varables of the equalty and nequalty constrants are shown by l, k, c and s. The real and reactve power njecton at node j, are presented by P nj and Q nj, as shown n () and () respectvely. GG j P e ;t GG j Q e ;t Pe;d Qe;d ¼ P nj ¼ Q nj k k ðþ ðþ where P e ;t and Q e ;t are the decson varables assocated wth the real and reactve dspatch of gas-fred dstrbuted generaton unt that s connected to node j n scenaro t respectvely. Furthermore, generaton unt belongs to the group of generators that s connected to the node j as shown 3

4 Saeed. D. MANSHADI, Mohammad. E. KHODAYAR by GG j. The served real and reactve electrcty demand at node j n scenaro t are shown by P e;d and Q e;d respectvely. The real and reactve generaton dspatch of gas-fred dstrbuted generaton unts are lmted by () and (7). P mn U P e ;t Pmax U ðl ;t ; l;t Þ ðþ Q mn U Q e ;t Qmax U l ;t ; l;t ð7þ The real and reactve generaton capacty of the gasfred dstrbuted generaton unt are shown as P max and Q max respectvely. Smlarly, P mn and Q mn are the mnmum real and reactve generaton capacty of gasfred dstrbuted generaton unt, respectvely. It s assumed that the demand s curtalable and the real and reactve electrcty demand curtalment at node j s no more than to the real and reactve electrcty demand as presented by (8) and (9) respectvely. 0 P e;d 0 Q e;d P e;d P e;d Q e;d Q e;d l ; 3 l 3 l ; l ð8þ ð9þ The real and reactve electrcty demand n scenaro t at node j s represented by P e;d and Q e;d, respectvely. The admttance of the dstrbuton lne s calculated n (0), consderng the bnary varables assocated wth the dsruptons n the dstrbuton lne. y j;o ¼ g j;o þ jb j;o ¼ r j;ouy j;o rj;o þ j x j;ouy j;o x j;o rj;o þ ð0þ x j;o where y j;o, g j;o, b j;o, r j;o, x j;o are admttance, conductance, susceptance, resstance, and reactance of dstrbuton lne that connects node j to node o. The lnearzed AC power flow for real/reactve power njecton s shown n () and () as suggested n [8]. P nj ¼ V Gj;j Q nj þ NB oo¼j ð Þ G j;o V þ V o;t þ Bj;o h h o;t ¼ V Bj;j þ NB þ G j;o h h o;t oo¼j ð Þ B j;o V þ V o;t k k 3 ðþ ðþ where V and V o;t are the voltage magntudes on nodes j and o; h and h o;t are the voltage angles on nodes j and o; NB s the total number of nodes; G j;o and B j;o are the elements of conductance and susceptance matrces. The real, reactve and apparent power transmtted through the dstrbuton lne s gven n (3), () and () respectvely. PL t j;o ¼G j;o V V o;t þ Bj;o h h o;t k j;o ;t ð3þ QL t j;o ¼ B j;o V V o;t þ Gj;o h h o;t k j;o ;t SL t j;o ¼ PLt j;o þ n j;oql t j;o k j;o 7;t ðþ ðþ In (3) (), the real, reactve, and apparent power transferred on the lne between nodes j and o for scenaro t are shown by PL t j;o, QLt j;o, SLt j;o, respectvely. In (), the auxlary parameter n s determned by the demand power factor as dscussed n [8]. The apparent power that flows n the dstrbuton lne (SL t j;o ) s lmted by the capacty of the dstrbuton lne (SL max j;o ) as expressed n (). SL max j;o SLt j;o SLmax j;o l j;o ;t ; lj;o ;t ðþ The lmtatons on the voltage phase angle and magntude n dstrbuton network are gven n (7) and (8), where V max, V mn, h max, h mn are the maxmum and mnmum voltage magntudes and maxmum and mnmum voltage phase angles respectvely. The nodal natural gas flow balance at node j s shown by (9). h mn h h max V mn V V max A j v s;t sgs j Ph k;t khh j Cgh k ¼ pp F;j f p;t þ l ; l l ; 7 l 7 j;o þ j;o Pe ;t C GG j ge pp T;j f p;t c ð7þ ð8þ ð9þ The njected and wthdrawn volumes of natural gas at node j are equal. The natural gas s used to produce heat and electrcty at CHP unts wth respectve converson factors. Here s s the ndex for natural gas resource, GS j s the group of all natural gas resources that are connected to the node j, A j s the node-natural gas resource connectvty matrx, and v s;t s the volume of natural gas supply s n scenaro t. The natural gas flow n ppelne p that connects the nodes j and o n scenaro t, s f p;t j;o and the set of ppelnes startng from node j and endng to node j are shown by P F;j and P T;j respectvely. The set of heaters at node j s presented by HH j. Here Cgh k s the natural gas-toheat converson coeffcent for heater k and Cge s the natural gas-to-electrcty converson coeffcent for gasfred dstrbuted generaton. The avalablty of natural gas 3

5 Preventve renforcement under uncertanty for slanded mcrogrds wth electrcty and 7 ppelnes s determned by the dsrupton decsons gven n (0), where the maxmum natural gas flow on ppelne p that lnks node j and o. s gven by f p;max j;o. f p;max j;o UZ p f p;t j;o f p;max j;o UZ p s j;o ;t ; sj;o ;t ð0þ The mpact of nodal natural gas pressure on the natural gas flow among nterconnected nodes j and o s gven n (), where p j s the natural gas pressure at node j, p 0 j s the ntal natural gas pressure on node j, C p s a constant whch s determned by the physcal characterstcs of natural gas ppelne p, and K s a large number. f p;t j;o K UZ C p p 0 p jp p 0 op rffffffffffffffffffffffffffffffffffffffffffffffffffff o;t p 0 j p 0 ðþ o f p;t j;o þ K UZ p s j;o ;t ; sj;o ;t The natural gas pressure at node j s lmted by () where p max and p mn are the maxmum and mnmum pressure n the natural gas dstrbuton network. The served heat demand at node j (P h;d j ) s lower than the total heat demand (P h;d j ), as gven by (3). p mn p p max P h;d P h;d s s 3 ; s 3 ðþ ð3þ The capacty of natural gas supply s further lmted by (), where v max s and v mn s are the maxmum and mnmum volume of natural gas resource s. If all electrcty of a node s curtaled, the heat demand wll be also curtaled as shown n (). The heat demand s served ether by the CHP unt as the b-product of electrcty generaton or by burnng natural gas n heater as shown n (). Here, Cgh s the natural gas-to-heat converson coeffcent for gas-fred dstrbuted generaton unt. v mn s v s;t v max s s s;t ; ss;t ðþ P h;d KP e;d s ðþ 0 P h;d ðc gh ÞPe ;t GG Cgh þ khh j P h k;t s 7 ; s 7 ðþ The dual formulaton of the lower-level problem s gven n (7) (3), where the objectve of the dual form of the lower-level problem (OP dual ) s gven n (7) and the constrants of the dual problem are represented n (8) (3). max OP dual ¼ t þ Q mn U l ;t ( ðp mn U l ;t Qmax U l ;t Þþ j Pmax U l ;t ðp e;d j l 3 Qe;D j l G j;j k 3 þ B j;jk Ph;D j s þ Vmn l 7 Vmax l j 7 þ hmn l h max l þ pmn s 3 pmax s 3 Þ þ j oj¼o ð Þ s j;o;t þ s j;o;t þ s GG k v mn s s s;t f p;max j;o UZ p s j;o;t þ s j;o;t SL max j;o ) vmax s s s;t C þ gh s 7 ¼ q t of c; P e ;t =ope ;t ðk Þþl;t GG k k C ge c l j;o;t þ l ;t P e ;t þ l j;o;t l;t l;t ¼ 0 Qe ;t K UZp l þ 3 l 3 þ Ks ¼qt VOLL e P e;d l þ l ¼ 0 Qe;d k þ k 3 ¼ 0 Pnj k þ k ¼ 0 Qnj G j;j k NB oo¼j ð Þ 3 þ l l 7 G j;o k 3 þ ko;t 3 þ G j;o k j;o;t k o; NB oo¼j ð Þ 7 þ B j;jk Bj;o k þ ko;t Bj;o k j;o;t þ k o; B j;o k 3 þ ko;t 3 Gj;o k B j;o k j;o;t k o; Gj;o k j;o;t þ l l ¼ 0 h k j;o;t k j;o;t 7 ¼ 0 PL j;o;t k j;o;t n j;o k j;o;t 7 ¼ 0 QL j;o;t ð7þ ð8þ ð9þ ð30þ ð3þ ð3þ ð33þ ¼ 0 V ð3þ ko;t k o; k j;o;t 7 þ l j;o;t l j;o;t ¼ 0 SL j;o;t ð3þ ð3þ ð37þ ð38þ 3

6 8 Saeed. D. MANSHADI, Mohammad. E. KHODAYAR 0 s j;o;t c p p 0 s j;o;t j rffffffffffffffffffffffffffffffffffffffffffffffffffff so; s o; B p 0 0 A þ s 3 p p A j c sgs j p 0 j o p 0 o ss;t þ ss;t ¼ 0 v s;t j s 3 ¼ 0 ð39þ ð0þ c þ c pp f ;j pp t;j ðþ þ s j;o;t s j;o;t s j;o;t þ s j;o;t ¼ 0 f p j;o;t s ð c khh j s þ s 7 s 7 ¼q t VOLL h P h;d Cgh k þ s 7 Þ¼q tof c; P h k;t =op h k;t P h k;t ðþ ð3þ As the decsons on bnary varables were made n the upper-level problem, these varables are fxed n the lowerlevel problem and t s possble to formulate the dual form of the lower-level problem [9]. In other words, the lowerlevel problem s reflected as a set of constrants that ensures the feasblty of the decsons made n the upper-level problem. The dual formulaton of the lower-level problem s used to transform the lower-level optmzaton problem nto a set of constrants. In addton to the prmal and dual constrants of the lower-level problem, the strong dualty condton that s shown n (), s formulated as a constrant. Ths constrant shows that the objectve of the prmal form of the lower-level problem s equal to the objectve of ts dual form. Therefore, the lower-level problem s formulated as a set of constrants represented by () (), (8) (3) and (). The constrants () () are correspondng to the prmal form of the lower-level problem, whle (8) (3) are assocated wth the dual form. In (3), Cgh k s a constant representng the converson factor of natural gas to heat for heater k. The left-hand sde of ths constrant s lnear. The rght-hand sde s the dervatve of cost functon wth respect to the heat energy for heater k whch s the margnal cost for the heater. Assumng a quadratc cost functon, the margnal cost functon s also a lnear functon. Therefore, the rght-hand sde of ths equaton s lnear. The margnal cost functon can be approxmated by pece-wse lnear representaton. Here, the lower-level problem s represented by a set of prmal and dual constrants whch form the feasble regon for the upper-level problem. Usng the prmal and dual constrants, the b-level optmzaton problem s transformed nto a sngle level optmzaton problem. OP prmal ¼ OP dual ðþ In the presented formulaton, all nonlnear terms are transformed nto lnear form. In ths secton, the nonlnear constrants are lsted and the lnearzaton approach s presented. These nonlnear terms are formed as a result of bnary to contnuous varable multplcaton n the dual formulaton and the AC power flow constrants. In (7) there are three types of bnary-to-contnuous terms, whch are assocated wth the generator, dstrbuton lne, and ppelnes, respectvely. The bnary decson varables assocated wth the electrcty dstrbuton lnes are ncorporated n the admttance matrx as llustrated n (0). The constrants () () contan 0 bnary-tocontnuous terms and (3) and (3) have 8 dstngushed bnary-to-contnuous terms. As mentoned n the prevous part, (0) and () are the lnearzed form of the nonlnear formulaton (). Once the bnary varable (UZ p )n() s set to one, the frst equalty constrant wll be presented as two nequalty constrants as shown n () where both nequalty constrants are bndng. Once the bnary varable (UZ p ) s set to zero, the nequalty constrants gven n () are relaxed,.e. the natural gas flow n the dsrupted ppelne that connects two nodes s not dependent on the dfference between the nodal pressures at the nodes. Also, the natural gas flow s set to zero as shown n (0). Other bnary-to-contnuous nonlnear terms are lnearzed usng the same technque. 8 C p p 0 j p p 0 o p o;t >< sffffffffffffffffffffffffffffffffffffffffffffffffffffffffff f p j;o;t ¼ UZ p ¼ p 0 j p 0 ðþ o >: 0 UZ p ¼ 0 The preventve renforcement strategy s procured through several steps n whch the reslence of mcrogrd at each step s measured based on the renforcement strategy for generaton and dstrbuton components. Fgure shows the process to mprove the reslence of the mcrogrd usng successve renforcements. The soluton of the b-level optmzaton problem at each step procures the vulnerable components that should be renforced n the next step. The teratve process for renforcng the energy converson and dstrbuton components contnues untl the operator s antcpated level of reslence s acheved. In order to quantfy the reslence measure, the reslence ndex (r) s formulated as (). Here, c and c 0 are the expected operaton costs of the mcrogrd n normal and contngency condtons respectvely and M s the total avalable resources for dsruptons. The reslence ndex shows the vulnerablty of mcrogrd to delberate dsruptons at each step. The lower the reslence ndex s, the more vulnerable the mcrogrd s 3

7 Preventve renforcement under uncertanty for slanded mcrogrds wth electrcty and 9 Renforce the dsrupted components Fg. Preventve renforcement procedure N The scenaro wth hghest expected operaton cost for the mcrogrd exposed to dsrupton Is desred level of reslency satsfed? Y Determne the best renforcement plan Table Electrcty and natural gas networks characterstcs ID From node To node Length (m) SL max (kva) L L L L L L L L L L L L L P P P P P 0 0 P P C p f max (SCM) to delberate dsruptons. Therefore, the reslence ndex ncreases as the mcrogrd components are renforced aganst dsruptons. r ¼ e c 0 c M ðþ 3 Case study In the case study, an slanded mcrogrd wth 3 nodes, 3 electrcty dstrbuton lnes, 3 electrcty demands, 7 heat demands, 7 natural gas ppelnes, and CHP unts s consdered. The converson effcency of natural gas to electrcty and natural gas to heat for each CHP s 3% and 0% respectvely. The data related to the natural gas ppelnes and the electrcty dstrbuton lnes, as well as the characterstcs of CHP unts, are presented n Tables and respectvely. As the equpment used for heat transfer (such as pumps or fans) use electrcty, dsrupton n electrcty supply at nodes that result n total electrcty demand curtalment wll also cause total curtalment of heat demand. The electrcty and heat demands and ther respectve values of lost load (VOLL) are lsted n Table 3. The assgned VOLL determnes the promnence of demands to be served. Here, the constant of natural gas, c p, s dependent on length, frcton, dameter, temperature, and gas composton [0]. The total avalable natural gas s equal to 0 standard cubc meter (SCM) n ths case study. The phase angles, voltage magntude, and natural gas pressure at nodes are restrcted between - p to p, per unt, to 7 bar, respectvely. The resstance and nductve reactance of the dstrbuton network cables are r ¼ 0:098 =000 m and x ¼ 0:3 =000 m respectvely. CPLE. s used as the solver for ths case study. The dsrupton costs for generators, natural gas ppelnes, and electrcty dstrbuton lnes are $00, $300 and $00 respectvely. The requred resources to dsrupt gasfred dstrbuted generaton unt, dstrbuton lne and natural gas ppelne are 0 tmes hgher than the renforcement cost. The avalable budget for dsrupton n slanded Table CHP unt characterstcs Unt P max ðkw) P max ðkw) F c, ( /kwh) F c, ( /kwh) Cge ðscm/kwhþ Cge ðscm/kwhþ G G G G G

8 30 Saeed. D. MANSHADI, Mohammad. E. KHODAYAR Table 3 Electrcty and heat demand Node ID P e;d (kw) Q e;d (kvar) VOLL e ($/kwh) P h;d (MBtu) VOLL h ($/MBtu) p 0 m (bar) Table Outcome of sequental preventve renforcement Step Operaton cost ($) Reslence ndex (r) Dsrupted component Total renforcement cost ($) L, P, G L, L7, P L, L9, L0, L, P L, L9, G L, L, L0, P L, P L8, P L3, L G L L mcrogrd s $0000. The followng cases were consdered to evaluate the effectveness of proposed preventve renforcement strategy on enhancng the energy supply reslency: Case Sequental renforcement of electrcty and natural gas networks (determnstc soluton). Case Sequental renforcement of electrcty and natural gas networks (stochastc soluton). 3. Case The renforcement strategy s contnued untl no generaton, dstrbuton and natural gas ppelne can be dsrupted consderng the avalable resources for the attacker. Table shows a selected number of steps n the sequence of renforcements n the mcrogrd s electrcty and natural gas network. As shown n ths table, as more renforcements were made through the steps, the operaton cost of the mcrogrd decreases as a result of less electrcty and heat demand curtalment and reducton n the number of vulnerable components n the electrcty and natural gas networks. For example, at step of renforcement, the operaton cost s decreased from $ to $ as a result of less electrcty and heat demand curtalment. The electrc load curtalment at step s 88 kw whch s decreased from 7 kw n step 3. The developed renforcement strategy at ths step led to mprovement n the reslence ndex. The reslence ndex s ncreased from 0.8 at step 3 to at step. The ncrease n the reslence ndex requres more nvestment n renforcng the electrcty and natural gas network components. As shown n Table, the renforcement cost s ncreased from $9000 at step 3 to $38000 at ths step. The ncrease n the renforcement cost s because of renforcng L, L, L0 n electrcty dstrbuton network and P7 n the natural gas dstrbuton network. As shown n Table, the renforcement cost ncreases wth the ncrease n the number of renforced components. 3. Case In ths case, the uncertantes n demand were captured n mcrogrds by generatng 3000 scenaros usng Monte Carlo smulaton. The error n the forecasted demand s determned by employng truncated normal dstrbuton wth a mean value equals to the forecasted demand and a standard devaton equals to 0% percentage of the forecasted demand. As such problem has a large computaton burden whle there are several smlar scenaros n whch can be reduced to much smaller number of scenaros. Fast backward, fast backward/forward and fast backward/ backward are among selected scenaro reducton technques. Here, backward/forward method s utlzed to procure twelve dstrct scenaros. The probablty of the scenaro dscussed n Case s % and eleven other scenaros have the probablty of %,.%,.%, %, 3%, 3%, 0%, 7.%, 7.%, 8% and 8%. In step 0, the mpact of dsrupton on electrcty and natural gas networks s evaluated wth no preventve renforcement n these networks. In normal condton and before any dsruptons, the expected operaton cost of the mcrogrd s $30. The vulnerable components, n ths step, consderng the budget attack as $0000, are dstrbuton lnes L7 as well as the ppelne P and gas-fred unt G3. The delberate dsrupton n ths step wll lead to electrcty and heat demand curtalments n all nodes. The expected operaton cost ncreases from $30 n normal condton to 3

9 Preventve renforcement under uncertanty for slanded mcrogrds wth electrcty and 3 $8,098 n ths step. Fgure 3 shows the topology of the network wth the presumed outages. As shown n ths fgure, the electrcty demands n all nodes are curtaled as there s no gas supply for G, G, G, G and G3 s dsrupted. The heat demands n nodes, -, 8, 9,, and 3 are curtaled as dsrupton of P prevent natural gas delvery to these nodes. The reslence ndex, n ths step, s In the frst step of renforcement, dstrbuton lnes L7 as well as the ppelne P and gas-fred unt G3 are renforced. Therefore, the dsrupton cost for the renforced lne s $3000, the dsrupton cost for ppelne P s $7000, and the dsrupton cost for gas-fred unt G3 s $9000. In the frst step, the dstrbuton lnes L, L, and L7 as well as ppelne P3 are dsrupted. Fgure shows the topology of the network wth the presumed outages. As the natural gas ppelne P3 supples nodes, 8, 9, and n the natural gas network of the mcrogrd, dsrupton of ths ppelne wll lead to electrc and heat load curtalment at these nodes. The heat load on nodes,, 8, 9, and are curtaled, as electrcty curtalment n node led to heat curtalment on ths node. In ths step, the electrcty network of the mcrogrd s dvded nto three electrcally slanded networks consstng of nodes {,,, 3}, nodes {3, } and nodes {,, 7, 8, 9, 0, }. The operaton cost, n ths step, s $33 and the reslence ndex s Gas supply P P 3 P3 P7 9 P P P G Fg. 3 Dsrupton n step 0 of Case Gas supply P 3 P7 P P3 9 P P P Fg. Dsrupton n step of Case G3 3 L3 L7 G L 3 8 L L L G 8 L0 L 7 L8 G 0 9 L3 L L9 3 G3 7 L3 L G 3 8 L L L G L8 L 7 L0 G G L9 L3 L Table shows the steps n the sequence of renforcements n the mcrogrd s electrcty and natural gas network consderng the uncertantes n mcrogrd s demand. Because of the uncertanty n demand, the expected operaton cost at ntal step of renforcement s ncreased compared to the determnstc soluton. The expected operaton cost of the mcrogrd at step 0 s $8098 whch s.8% more than that n Case. In addton, the expected operaton of the mcrogrd wth reslency ndex equal to one s 8.8% hgher than the operaton cost n Case. Table Outcome of sequental preventve renforcement wth uncertantes n demand Step Operaton cost ($) Reslence ndex r Dsrupted component Total renforcement cost ($) G3, L7, P L, L, L7, P L, L8, P L8, P L0, L, L, P P, L9, L0, L L9, P L, P, P L0, P G, G L, L, L L, L3, L, P G, L, L P G L, L L, G L G G P P G L L L G L L3, L L L L L L

10 3 Saeed. D. MANSHADI, Mohammad. E. KHODAYAR Smlar to Case, as more renforcements were made through the steps, the expected operaton cost of the mcrogrd decreases because of less electrcty and heat demand curtalment and reducton n the number of vulnerable components n the electrcty and natural gas networks. The expected operaton cost mcrogrd at step s sgnfcantly decreased (.e..8%) compared to that n step 3 and the reslency ndex s ncreased from 0.00 at step 3 to 0.00 at step. Concluson Ths paper presents an approach for strategc renforcement and optmal operaton of mcrogrds wth electrcty and natural gas networks that are exposed to delberate dsruptons consderng the uncertantes n electrcty and heat demand. The output of the presented approach determnes the hghest expected operaton cost of the mcrogrd as a result of the delberate dsrupton. A renforcement strategy s proposed based on the determned vulnerable components n the nterdependent electrcty and natural gas networks. As a result of the proposed renforcement strategy, the cost of dsrupton for the renforced components s ncreased and therefore, the dsrupted components are less vulnerable to outages n next teratons. Consequently, the penalty assocated wth the curtaled demand s decreased through the teratons as shown n a case study. The proposed reslence measure shows the reslence of the mcrogrd as t s exposed to delberate dsruptons. It s shown that as more components are renforced n the mcrogrd s nterdependent energy networks, the renforcement cost s ncreased and the expected operaton cost s decreased. Open Access Ths artcle s dstrbuted under the terms of the Creatve Commons Attrbuton.0 Internatonal Lcense ( creatvecommons.org/lcenses/by/.0/), whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded you gve approprate credt to the orgnal author(s) and the source, provde a lnk to the Creatve Commons lcense, and ndcate f changes were made. References [] Krupnck AJ (0) Wll natural gas vehcles be n our future? Resources for the Future. Resources/Pages/8-Natural-Gas-Vehcles.aspx. Accessed Mar 07 [] Internatonal energy lookout 0. U.S. Energy Informaton Admnstraton, DOE/EIA-0383 [3] u, Ja H, Chang HD et al (0) Dynamc modelng and nteracton of hybrd natural gas and electrcty supply system n mcrogrd. IEEE Trans Power Syst 30(3): [] Shahdehpour M, Fu Y, Wedman T (00) Impact of natural gas nfrastructure on electrc power systems. Proc IEEE 93():0 0 [] Zhang, Che L, Shahdehpour M et al (07) Relablty-based optmal plannng of electrcty and natural gas nterconnectons for multple nodes. IEEE Trans Smart Grd 8():8 7 [] EIA (0) Combned heat and power technology flls an mportant energy nche. detal.cfm?d=80. Accessed Mar 07 [7] Gedl M, Andersson G (00) Operatonal and structural optmzaton of mult-carrer energy systems. 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MANSHADI receved the Ph.D. degree from Southern Methodst Unversty, Dallas, USA, n 08; the M.S. degree from the Unversty at Buffalo, the State Unversty of New York (SUNY), Buffalo, USA, n 0; and the B.S. degree from the Unversty of Tehran, Tehran, Iran, n 0 all n electrcal engneerng. He was a Postdoctoral Fellow at the Unversty of Calforna, Rversde. He s currently an Assstant Professor wth the Department of Electrcal and Computer Engneerng, San Dego State Unversty, San Dego, USA. Hs research nterests nclude smart grd, mcrogrds, ntegratng renewable and dstrbuted resources, and power system operaton and plannng. 3

11 Preventve renforcement under uncertanty for slanded mcrogrds wth electrcty and 33 Mohammad E. KHODAYAR receved the B.S. and M.S. degrees n electrcal engneerng from Amrkabr Unversty of Technology (Tehran Polytechnc) and Sharf Unversty of Technology, respectvely; and the Ph.D degree n electrcal engneerng from Illnos Insttute of Technology, Chcago, USA, n 0. He was a Senor Research Assocate n the Robert W. Galvn Center for Electrcty Innovaton at Illnos Insttute of Technology. He s currently an Assstant Professor wth the Department of Electrcal Engneerng, Southern Methodst Unversty, Dallas, USA. Hs research nterests nclude power system operaton and plannng. 3