Joint Optimization of Electricity and Communication Cost for Meter Data Collection in Smart Grid

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1 Receved 3 May 2013; revsed 7 July 2013; accepted 8 July Date of publcaton 18 July 2013; date of current verson 21 January Dgtal Object Identfer /TETC Jont Optmzaton of Electrcty and Communcaton Cost for Meter Data Collecton n Smart Grd PENG LI (Member, IEEE), SONG GUO (Senor Member, IEEE), AND ZIXUE CHENG (Member, IEEE) School of Computer Scence and Engneerng, The Unversty of Azu, Azu-Wakamatsu , Japan CORRESPONDING AUTHOR: S. GUO (sguo@u-azu.ac.jp) ABSTRACT Smart grd s recently proposed as an enhancement for the next generaton power grd. To acheve effcent status montorng, control, and bllng, a large number of smart meters are deployed and they would produce a huge amount of data. To effcently collect them mposes a great challenge on the communcaton networks. In ths paper, we study the effcent meter data collecton problem by explorng the secondary spectrum market n cellular networks. The electrcty power reserved by sendng meter data va leased secondary channels would be charged at a lower prce. Wth the objectve of reducng the overall cost of both power and communcaton, we formulate a problem called cost mnmzaton for meter data collecton (CMM) that s to fnd optmal soluton of channel selecton and transmsson schedulng. The CMM problem under a lnear power prcng model s formulated as a mxed nteger lnear programmng problem and s then solved by a branch-and-bound algorthm. Under a nonlnear power prcng model, we formulate t as a nonconvex mxed nteger nonlnear programmng problem and propose an optmal algorthm by ntegratng the sequental parametrc convex approxmaton method nto the branch-and-bound framework. Extensve smulaton results show that our proposal can sgnfcantly reduce the overall cost. INDEX TERMS Smart grd, meter data collecton, spectrum, optmzaton. I. INTRODUCTION Smart grd s regarded as the next generaton power grd wth a glorous future. In contrast to tradtonal power grd wth a tree-lke herarchcal structure, t uses two-way flows of electrcty and nformaton to create a wdely dstrbuted automated energy delvery system. In smart grd, the Advanced Meterng Infrastructure (AMI) [1], [2] s one of the most crtcal components to acheve effcent status montorng, control and prcng by deployng a large number of smart meters n homes, buldngs and factores. Such smart meters would produce a huge amount of data that should be effcently collected, mposng a great challenge on communcaton networks. Due to securty and cost ssues [3], [4] of current wred communcaton technologes, wreless technologes have been consdered more approprate to be used n smart grd because of ts flexblty, large-coverage and lowcost [5] [8]. In ths paper, we study the effcent meter data collecton problem by explorng the secondary spectrum market n cellular networks [9] [13]. Although the spectrum has become a scarce resource because of boomng growth of varous wreless applcatons, measurement results show that spectrum s under-utlzed n many places [14]. Such an observaton motvates the desgn of a secondary spectrum market, where new servces, such as meter data collecton n smart grd, can access lcensed channels wth approprate payment when they are unused by ther owner. Compared wth other opportunstc channel access schemes, such as cogntve rado, the secondary spectrum market based on contracts can provde stable communcaton servce and easy cost management. All exstng work on secondary spectrum market studes problems from the perspectve of communcaton networks only. When t s appled n meter data collecton for power prcng problem studed n ths paper, the nteracton between power and communcaton networks should be taken nto consderaton. The power prcng model proposed n recent lterature [15], [16] show that the power prce s a decreasng VOLUME 1, NO. 2, DECEMBER IEEE. Translatons and content mnng are permtted for academc research only. Personal use s also permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton. 297

2 L et al.: Jont Optmzaton of Electrcty and Communcaton Cost functon of the amount of collected meter data attached wth power reservaton nformaton. Less power cost s ncurred f more meter data are collected. However, t requres more channels or larger channel capacty, leadng to a hgher communcaton cost. On the other hand, reducng communcaton cost by leasng less channel resources may cause meter data may loss due to congeston, such that the power cost wll be ncreased. Ths tradeoff motvates us to desgn an effcent meter data collecton scheme to mnmze the total cost. To the best of our knowledge, we are the frst to study the beneft of leasng secondary channels for meter data collecton by jontly consderng the power and communcaton cost. The man contrbutons of ths paper are summarzed as follows. Frst, we consder meter data collecton based on a two-stage power prcng model, under whch power s suppled wth a lower prce f t s reserved n advance. Thus, f more meter data wth the power reservaton nformaton are collected, less power payment wll be produced, but at a hgher leasng fee for more communcaton channels. Wth the objectve of reducng the total cost, we propose a problem called CMM (Cost Mnmzaton for Meter data collecton) that s to fnd the optmal scheme for channel selecton and transmsson schedulng scheme. Second, we analyze the hardness of the CMM problem by provng ts NP-hardness. Specfcally, we reduce the well-known knapsack problem to a specal case of the CMM problem wth a lnear power prce functon,.e., the power prce lnearly ncreases as the growth of power supply. We solve the CMM problems under both lnear and nonlnear power prcng models. The former s formulated as a mxed nteger lnear programmng (MILP) problem and solved by a branch-and-bound algorthm. To deal wth the latter, we formulate t as a nonconvex mxed nteger nonlnear programmng (MINLP) problem and propose an optmal algorthm by ntegratng the SPCA (Sequental Parametrc Convex Approxmaton) method nto our branch-and-bound framework. Fnally, extensve smulatons are conducted to evaluate the proposed algorthms. The expermental results show that our proposal can sgnfcantly reduce the power and communcaton cost. The rest of ths paper s organzed as follows. Secton II revews the related work. Secton III presents the network model and prcng model. The hardness of the CMM problem s analyzed n Secton IV. Secton V presents optmal algorthms for the CMM problem under both lnear and nonlnear power prcng model. Smulaton results are gven n Secton VI. Fnally, Secton VII concludes ths paper. II. RELATED WORK Smart meterng s the most mportant mechansm used n smart grd for obtanng nformaton from end users devces and applcatons. A Zgbee Advance Meterng Infrastructure (ZAMI) s proposed n [17] for automatc meter data collecton and energy audtng and management. In the ZAMI, the system operates wth multple channels and frequency hoppng and coexsts wth potental nterferers. Garlapat et al. [18] have proposed a Hybrd Spread Spectrum (HSS) based advanced smart meterng nfrastructure that reduces the overhead and latency n data transfer when compared to the use of 3G/4G technologes for smart meter data collecton. Matheson et al. [19] have developed a software system called the meterng data management (MDM) usng the web servce technology to support meter data collecton, valdaton, estmaton, versonng and publshng at Bonnevlle Power Admnstraton. One of ts key features s the valdaton and estmaton of the meter data based on statstcal models. The applcaton of cooperatve transmsson for the meter data collecton n smart grd s ntroduced n [16]. To analyze the relay transmsson strategy of the communty, the noncooperatve game model s formulated, and the Nash equlbrum s consdered as the soluton. Recently, many efforts have been made to use CR (cogntve rado) n smart grd [20], [21]. Sreesha et al. [22] have proposed a mult-layered approach to provde energy and spectrum effcent desgns of cogntve rado based wreless sensor networks at the smart grd utlty. Ther desgn provdes a relable and low-latency routng support for largescale cogntve smart grd networks. Qu et al. [23] have bult a real-tme CR network testbed, whch can help te together CRs n the next-generaton smart grd network. Later, Qu et al. [24] have systematcally nvestgated the dea of applyng CR to smart grd on system archtecture, algorthms, and hardware testbed, and proposed a mcrogrd testbed supportng both power flow and nformaton flow. Furthermore, the concept of ndependent component analyss n combnaton wth the robust prncpal component analyss technque s employed to recover data from the smultaneous smart wreless transmssons n the presence of strong wdeband nterference. Yu et al. [25] have proposed an unprecedented cogntve rado based communcatons archtecture for the smart grd, whch s manly motvated by the explosve data volume, dverse data traffc, and need for QoS support. III. SYSTEM MODEL In ths secton, we frst ntroduce the network model for meter data collecton, and then present the prcng models of both power and spectrum. A. NETWORK MODEL In ths paper, we consder a typcal three-layer wreless network model for meter data collecton n smart grd as shown n Fg. 1. Home area network (HAN): The lowest layer s HAN that connects home applances wth smart meters to support demand response, home energy management, load management, and smart meterng. Short-range or local area wreless technologes, such as ZgBee, Bluetooth, and WF, can be used for HAN [26], [27]. 298 VOLUME 1, NO. 2, DECEMBER 2013

3 IEEE TRANSACTIONS ON L et al.: Jont Optmzaton of Electrcty and Communcaton Cost FIGURE 1. Network model. Neghborhood area network (NAN): Multple homes form a communty that s served by a data aggregator unt (DAU), whch collects meter data from HAN gateways va NAN n a sngle- or multple-hop manner. Wde area network (WAN): WAN s at the top layer and forwards the collected meter data at DAUs to a remote power management system (PMS). Long-dstance communcaton technologes, e.g., 3G or satellte, should be used n WAN for coverage consderaton [28], [29]. In contrast to HAN and NAN that can be easly constructed usng dedcated hardware wth low cost, WAN needs the support of hgh-end communcaton technologes that are shared by multple servces. Thus, the communcaton cost cannot be neglected n WAN. Under ths model, we explot the secondary spectrum market n cellular networks for meter data collecton. Specfcally, we consder a WAN that conssts of a base staton and a set of n DAUs S = {s1, s2,..., sn }. There are a set of secondary channels B = {b1, b2,..., bm } avalable n the network, whch can be rented by DAUs. Due to geographcal dfferences, the set of accessble channels at s S, whch s denoted by B(s ), may be dfferent at each DAU. We let cj denote capacty of the wreless lnk from DAU s to the base staton under channel bj. Each DAU s equpped multple antennas such that t can work on multple channels smultaneously. Each channel can accommodate multple DAUs as long as the sum of ther transmsson rate does not exceed the channel capacty. each DAU s collects an amount of R meter data, ncludng a total power demand D, from ts communty. The collected data at DAUs should be forwarded to PMS wthn tme T over leased cellular channels, whose capacty, unfortunately, may not be always enough to support R data transmsson due to lmted channel resource and communcaton cost consderaton. As a result, packets at DAU s are unformly abandoned such that only a porton of data s successfully delvered to PMS, leadng to only d D power demand successfully receved by PMS n the frst stage. In the second stage, the reserved power of each communty s suppled wth a lower prce. If the reserved power s not enough, addtonal power wll be bought at a hgher prce. To descrbe ths power prcng model, we defne two functons fr (x) and fa (x), fr (x) fa (x), such that ther dervatves characterze the prcng rate of electrcty use n reserved and exceedng porton, respectvely. Lettng g(d, x) be the power prce to communty s wth actual power demand x whle only d receved by PMS, we therefore have: 0 g(d, x) f (x), x d, = r0 fa (x), otherwse. x After solvng ths dfferental equaton, we obtan the power prce wth demand D as: g(d, D ) = fa (D ) fa (d ) fr (d ). (1) Two typcal forms of functon fa /fr have been descrbed by a lnear [16] and a nonlnear model [30] [32]. The former requres payment lnearly proportonal to the power usage,.e., each unt of power s charged wth the same prce. The latter dscourage excessve electrcty use by applyng a nonlnear, e.g., exponental, prcng model. It has recently been adopted by many electrcty companes as a measure to reduce power usage. Wthout loss of generalty, we consder fa (x) = αfr (x), α > 1 n our model. In the followng, fr (x) and fa (x) n both lnear and nonlnear forms wll be studed. Lnear power prce functon: As shown n Fg. 2, fr (x) s gven as fr (x) = pe x n a lnear form [16], where pe s unt prce for reserved power. After substtutng t nto (1), g(d, D ) can be expressed as: g(d, D ) = pe d + αpe (D d ), B. PRICING MODEL The two-stage power prcng model [15], [16] has receved an ncreasng attenton because t provdes ncentves for effcent electrcty use. In such model, power supply s charged n a perod-by-perod manner, where each perod may last several hours or days accordng to the strategy adopted by PMS. In the frst stage, users reserve power supply from power generators before each perod. For ths purpose, VOLUME 1, NO. 2, DECEMBER 2013 (2) where the two terms n rght-hand represent the payment of reserved power d and addtonal porton D d, respectvely. Nonlnear power prce functon: In addton to the smple lnear prcng model, functons fr (x) s often modelled n nonlnear forms [30] [32],.e., fr (x) = eλx 1, λ 1 as shown n Fg. 3. Accordng to (1), the power prce functon g(d, D ) can be expressed as: g(d, D ) = α(eλd 1) (α 1)(eλd 1). (3) In addton to power cost, communcaton cost A s ncurred by leasng wreless channels connectng DAUs and 299

4 L et al.: Jont Optmzaton of Electrcty and Communcaton Cost channel selecton to mnmze communcaton cost stll exsts. In ths paper, the total cost mnmzaton problem n meter data collecton, whch s also referred to as CMM, can be defned as follows. Gven a WAN consstng a base staton, a set of DAUs, and several avalable channels, the CMM problem s to select a set of channels and fnd a transmsson schedulng of DAUs on these channels to mnmze total cost M. FIGURE 2. FIGURE 3. Lnear power prcng model. Nonlnear power prcng model. remote PMS. Let p c j be the payment of usng channel b j durng tme T. Note that a channel s the mnmum trade unt n spectrum market consdered n our model,.e., once DAUs decde to rent a channel b j, they should pay p c j even f ths channel s not fully utlzed. The total cost M n tme T s calculated by summng power and communcaton cost,.e., M = g(d, D ) + A. (4) We observe from (2) and (3) that lower power cost can be acheved f more power reservaton data are forwarded to PMS, however, more channels requred for such data lead to hgher communcaton cost. Even for forwardng a fxed amount of data, the challenge of IV. HARDNESS ANALYSIS In ths secton, we prove the CMM problem NP-hard. Theorem 1: The CMM problem s NP-hard. Proof: In order to prove an optmzaton problem NPhard, we need to show the NP-completeness of ts decson form, whch s formalzed as follows. The CMM_D problem INSTANCE: Gven a WAN consstng a base staton, a set of n DAUs S, and a set of avalable channels B, a prce functon g(d, D ), a constant M. QUESTION: Is there a channel purchase scheme and a transmsson schedulng such that the total cost M M? It s easy to see that the CMM_D problem s n NP class as the objectve functon assocated wth a gven channel purchase scheme and a transmsson schedulng can be evaluated n a polynomal tme. The remanng proof s done by reducng the well-known knapsack problem wth dentcal prce-per-pound to the CMM_D problem. The knapsack problem INSTANCE: Gven a set of tems = {φ 1, φ 2,..., φ m }, where tem φ j has value v j and sze w j, a knapsack capacty W, and a constant V. QUESTION: Is there a subset such that φ j w j W and φ j v j V? We now descrbe the reducton from the knapsack problem to an nstance of the CMM_D problem. We consder a lnear power prcng functons g(d, D ) shown n (2) n our proof. The process of nstance constructon s shown as follows. Step 1: for each tem φ j n, we create a channel b j wth prce p c j = w j, whch can be accessed by all DAUs wth dentcal channel capacty c j = c j = v j, 1 n; Step 2: the sum of power demand from all communtes s V,.e., 1 n D = V ; Step 3: we let M = p e V + W ; Step 4: set the value of α to a large number such that the power cost wll exceed M f demands are not fully delvered to PMS. In the followng, we only need to show that the knapsack problem has a soluton f and only f the resultng nstance of CMM_D problem has a channel selecton and a transmsson schedulng that satsfy total cost constrant. Frst, we suppose that there exsts a subset such that φ j w j W and φ j v j V. The correspondng soluton of CMM_D problem s a subset B B such that the total cost s calculate 300 VOLUME 1, NO. 2, DECEMBER 2013

5 L et al.: Jont Optmzaton of Electrcty and Communcaton Cost IEEE TRANSACTIONS ON by: M = 1 n g(d, D ) + A = [p e d + αp e (D d )] + p c j b j B 1 n = αp e 1 n αp e 1 n D + (1 α)p e 1 n d + b j B p c j D + (1 α)p e b j B c j + b j B p c j = αp e V + (1 α)p e v j + φ j αp e V + (1 α)p e V + W = p e V + W. b j B p c j Then, we suppose that the CMM_D problem has a soluton B B such that M M. Due to the large α, all demand should be delvered to PMS. Thus, n the correspondng soluton, we have: v j = c j = D V. (5) φ j b j B 1 n can be formulated as: mn g + A, 1 n 0 1 n subject to x j y j 1 j m, (7) x j = 0 1 n, b j / B(s ), (8) d TD x j c j 1 n, (9) R 1 j m d D 1 n, (10) g p e d + αp e (D d ) 1 n, (11) A y j p b j. (12) 1 j m Multple DAUs workng on a common channel should share ths channel accordng to tme dvson, whch leads to constrant (7). The power demand delvered by any DAU s s determned by transmsson rate and can not exceed D, represented by constrants (9) and (10), respectvely. Constrants (11) and (12) represent the power and communcaton cost, respectvely. The formulated CMM problem s n a form of mxed nteger lnear programmng (MILP) that can be solved by a branch-and-bound algorthm shown n Algorthm 1. We use P to denote a problem set wth an upper bound U and a lower bound L of the optmal soluton that are tghtest found On the other hand, the communcaton cost should be no greater than W, whch lead to: w j = p c j W. (6) φ j b j B Thus, the CMM_D problem n decson form s NPcompleteness and ts orgnal optmzaton problem CMM s NP-hard. V. SOLVING THE CMM PROBLEM In ths secton, we solve the CMM problem under both lnear and nonlnear power prcng models. A. LINEAR POWER PRICING MODEL We defne a varable y j for channel selecton,.e., { 1, f channel bj s selected, y j = 0, otherwse. Snce each DAU s allowed to transmt on multple channels, we defne x j to denote the tme fracton of DAU s workng on channel b j. By lettng g denote the power cost of DAU s, the CMM problem usng lnear power prce functon Algorthm 1 Solvng the CMM problem 1: P = {P 0 }, U = ; 2: set l P0 as the optmal soluton of the relaxed problem P 0 ; 3: whle P = do 4: select a problem P P wth the mnmum l P and let L = l P ; 5: set u P as the soluton of P usng roundng; 6: f u P < U then 7: u = u P, U = u P ; 8: f L (1 ɛ)u then 9: return the (1 ɛ)-optmal soluton u ; 10: else 11: remove all problems P P wth l P (1 ɛ)u; 12: end f 13: end f 14: select the maxmum unfxed varable y j from the results of the relaxed problem P and remove P from P; 15: construct a problem P 1 wth y j = 1 and solve t to obtan l P1. 16: f l P1 < (1 ɛ)u, then put P 1 nto P; end f 17: construct a problem P 2 wth y j = 0 and solve t to obtan l P2. 18: f l P2 < (1 ɛ)u, then put P 2 nto P; end f 19: end whle 20: return the (1 ɛ)-optmal soluton u ; VOLUME 1, NO. 2, DECEMBER

6 L et al.: Jont Optmzaton of Electrcty and Communcaton Cost so far. Intally, P only ncludes the orgnal problem, denoted by P 0. For any P P, the correspondng relaxed problem can be easly solved and the optmal soluton serves as an lower bound, denoted as l P, of the soluton to the orgnal problem. Then, the algorthm proceeds teratvely as follows. In each round, we fnd a problem P P wth mnmum l P and then set L = l P. Whle any feasble soluton of P can serve as an upper bound, the one obtaned usng roundng under the satsfacton of all constrants s used and denoted by u P. The smallest upper bound U s updated from lne If the performance gap between L and U s less than a predefned small number ɛ, a (1 ɛ)-optmal soluton u s returned. Otherwse, we fnd the maxmum unfxed varable y j from the results and create two subproblems P 1 and P 2 by fxng y j to 1 and 0, respectvely. If the results of relaxed P 1 and P 2 are less than (1 ɛ)u, they are put nto the problem set P. B. NONLINEAR POWER PRICING MODEL Smlar wth the formulaton under lnear power prcng model, we also defne y j (1 j m) and x j (1 n, 1 j m) for channel selecton and transmsson schedulng, respectvely, such that the CMM problem under nonlnear power prcng model can be formulated as: mn g + A, subject to 1 n ( g α(e λd 1) ) ln + 1 λd 1 α 1 n, (13) (7) (10), and (12). We observe that above formulaton s a nonconvex mxed nteger nonlnear programmng (MINLP), whch s dffcult to be solved, due to constrant (13), whose left sde s denoted by H (g ). To deal wth ths challenge, we explore the SPCA (Sequental Parametrc Convex Approxmaton) method [33] whose basc dea s to teratvely solve the resultng lnear programmng (LP) problem by replacng orgnal nonconvex constrants wth lnear ones untl a converged soluton s acheved. At each teraton, a new lnear constrant s constructed such that the correspondng lne s tangent to the curve defned by the nonconvex constrant at the pont, whch s a soluton obtaned n the prevous teraton. By applyng the SPCA technque, the relaxed CMM problem (.e., all nteger varables are relaxed to real ones), denoted as CMM_R, can be quckly solved. Specfcally, n the k-th teraton, we replace nonconvex constrant (13) by z(g ḡ (k 1) ) zḡ (k 1) + ln(zḡ (k 1) Q ) λd, (14) Q where z = 1 α 1 and Q = zα(e λd 1) 1. We denote the left sde of (14) as h (k) (g ), n whch ḡ (k 1) denotes the optmal soluton of varable g obtaned n the (k 1)-th teraton. As shown n Fg. 4, after solvng the correspondng lnear programmng n the k-th teraton, we construct a new lnear constrant h (k+1) (g ) to approxmate (14) FIGURE 4. Illustraton of the SPCA method. n the next teraton. The algorthm to solve the CMM_R problem s formally descrbed n Algorthm 2, n whch CMM_R(k) and (k) are the problem formulaton and ts optmal soluton n the k-th teraton, respectvely. Snce the ntal value of ḡ (0) can be set as an arbtrary postve number, we set ḡ (0) = e λd 1. Algorthm 2 Solvng the CMM_R problem 1: k = 0, =, (0) = 0, ḡ (0) = e λd 1(1 n) 2: whle (k) > ξ do 3: = (k), 4: k = k + 1 5: obtan (k) as well as ḡ (k) (1 n) by solvng the followng LP problem wth relaxed varables: 6: end whle CMM_R(k) : mn 1 n g + g c s.t. (7) (10), (12) and (14). In the followng theorem, we show that the soluton obtaned by Algorthm 2 satsfes the Karush Kuhn Tucker (KKT) condtons,.e., the frst-order necessary condtons for a soluton n nonlnear programmng to be optmal [34]. Theorem 2: The soluton of the CMM_R problem obtaned by Algorthm 2 satsfes the Karush Kuhn Tucker (KKT) condtons. Proof: For any feasble pont (ḡ (k 1), h (k 1) (ḡ (k 1) )), we update the lnear constrant for the CMM_R formulaton n Algorthm 2. As guaranteed by the analyss n [33], the concluson s acheved when the nonlnear functon, whch s denoted by H (g ), and ts approxmated lnear functon h (k) (g ) have the same values at g = ḡ (k 1) for the orgnal and ther frst-order dfferental functons, respectvely. 302 VOLUME 1, NO. 2, DECEMBER 2013

7 L et al.: Jont Optmzaton of Electrcty and Communcaton Cost IEEE TRANSACTIONS ON These can be verfed by: h (k) (ḡ (k 1) h (k) (ḡ m 1 ) = H (ḡ (k 1) ) = ln(zḡ (k 1) Q ), ) = H (ḡ m 1 z ) = zḡ (k 1). Q Note the KKT condtons are satsfed only for the relaxed problem, referred to as CMM_R here, not for the MINLP problem. Although Algorthm 2 returns a soluton satsfyng the KKT condtons, we fnd out that t s always the global optmal soluton emprcally through extensve numercal experments. In order to solve the orgnal CMM problem, we ntegrate Algorthm 2 nto the branch-and-bound framework shown n Algorthm 1 by solvng each relaxed problem n problem set P usng Algorthm 2. To apply our proposal n practce, we frst need to collect the nformaton from both network and power systems, such as avalable channels and power prce model. Then, the proposed algorthm s executed n a centralzed manner. After obtanng optmzaton results, we negotate wth the network servce provder to lease the selected channels such that the transmsson schedulng can be appled n these channels to acheve the mnmum total cost. VI. PERFORMANCE EVALUATION In ths secton, we conduct extensve smulatons to evaluate the performance of the proposed algorthm. Smulaton setup s frst ntroduced and then the results under dfferent network parameters are presented. A. SIMULATION SETTINGS In our smulaton settng, the total power demand of each communty s dstrbuted wthn range [1, 5] accordng to random unform dstrbuton. The power prce p e s set to $1. The capacty of each channel s specfed as a unform dstrbuton n the range [1,5]. Snce there s no exstng algorthms for the CMM problem that s frst nvestgated n our paper, we propose three heurstc algorthms n the followng to compare aganst our proposal that s denoted as CMM_optmal. CMM_EC: all meter data are transfered to PMS regardless of how many channels are used. CMM_CC: t does not forward any data such that the communcaton cost s zero. CMM_1/2: t sends half of the meter data to the PMS. Our proposed optmal algorthm s referred to CMM_optmal. Note the all results n the followng are obtaned by averagng 50 random network nstances. B. SIMULATION RESULTS We frst nvestgate the effect of number of channels on the total cost. The values of α and λ are set to 2 and 50, respectvely. The channel prce s a Gaussan dstrbuton wth mean 3 and varance 0.5. When the number of DAU s 30, as shown n Fg. 5, the total cost of CMM_optmal, CMM_1/2 and FIGURE 5. The total cost versus dfferent number of channels. (a) Lnear power prcng model. (b) Nonlnear power prcng model. CMM_EC decreases as the number of channels grows from 10 to 50 under both lnear and nonlnear power prcng models. For example, the total cost of CMM_optmal s n 10-channel networks under lnear power prcng models, and when channel number ncreases to 50, ths number decreases to 75.5, by about 60%. Smlar observaton are made for the nonlnear power prcng model. That s because more channels provde more chances for DAUs to select cheap channels wth hgher capacty. The performance of CMM_CC shows horzontal lnes under both models snce t does not affected by the number of channels n the network. We then evaluate the total cost under dfferent number of DAUs by fxng the number of channels to 30. As shown n Fg. 6(a), the total cost of all schemes grows as the number of DAUs ncreases snce more DAUs brng more power demands. For example, the total cost of CMM_CC s 59.1 when there are 10 DAUs. The correspondng performance of CMM_EC and CMM_optmal s only ts 65% and 59%, respectvely. When the number of DAUs grows VOLUME 1, NO. 2, DECEMBER

8 L et al.: Jont Optmzaton of Electrcty and Communcaton Cost FIGURE 6. The total cost versus dfferent number of DAUs. (a) Lnear power prcng model. (b) Nonlnear power prcng model. FIGURE 7. The total cost versus dfferent value of α. (a) Lnear power prcng model. (b) Nonlnear power prcng model. to 50, the performance of CMM_EC, CMM_optmal, and CMM_CC s 4.5, 3.8, and 5.1 tmes of that under 10-DAU networks, respectvely. We have smlar observatons under nonlnear power prcng model and the cost growth s sharper because of the exponental power prce functon. The nfluence of α to the total cost s nvestgated by changng ts value from 1.4 to 2.2. The results under 30 DAUs and 30 channels are shown n Fg. 7. In both Fg. 7(a) and 7(b), the performance of CMM_EC shows as horzontal lnes because t forwards all meter data to PMS such that ts power prce s determned only by p e. The total cost of CMM_CC ncreases lnearly to α under both models snce all power s charged wth αp e per unt. We notce that whle the total cost of CMM_optmal shows as an ncreasng functon of α as well, the growth rate decreases under larger α. That s because our algorthm wll forward more data to PMS under larger α such that the power cost wll be reduced. For example, the total cost of CMM_optmal s 33.1 and 88.2 under α = 1.4, and exhbt a growth of 266% and 184% when α ncreases to 2.2, as shown n Fg. 7(a) and 7(b), respectvely. Fnally, we study the effect of channel prce on the total cost by changng ts mean value from 1 to 5. As shown n Fg. 8, the total cost of CMM_EC, CMM_1/2 and CMM_optmal ncreases as the mean value grows under both lnear and nonlnear power prcng models. For example, n Fg. 8, ther total cost s 45.3 and 31.2, respectvely, when mean value s 1. When we set the mean value to 5, ther total cost ncreases to and 144.3, respectvely. Moreover, the performance gap between CMM_EC and CMM_optmal becomes larger as the growth of mean value. Snce CMM_CC does not forward any meter data, t has no communcaton cost such that ts performance shows as a horzontal lne under dfferent channel prces. To evaluate the performance of the SPCA method, we show the dstrbuton of teratons n Fg. 9. When the error bound ξ s set to 0.1, the number of teratons s no greater than 12 over 90% executons. As we reduce the value of ξ to 0.01, ths percentage decreases to 55%, but there are about 90% executons can acheve ths bound wthn 16 teratons. 304 VOLUME 1, NO. 2, DECEMBER 2013

9 L et al.: Jont Optmzaton of Electrcty and Communcaton Cost IEEE TRANSACTIONS ON reducng the total cost, we propose a problem called CMM (Cost Mnmzaton for Meter data collecton) that s to fnd the optmal scheme for channel selecton and transmsson schedulng scheme. Ths problem s formulated based on a three-layer network model and a two-stage prcng model, and s proved to be NP-hard. Under lnear power prcng model, t s formulated as a mxed nteger lnear programmng problem and solved by a branch-and-bound algorthm. Under nonlnear power prcng model, we formulate t as a nonlnear mxed nteger programmng (MINLP) problem and propose an optmal algorthm by ntegratng SPCA method n our branch-and-bound framework. Fnally, smulaton results show that the proposed algorthm can sgnfcantly reduce the overall cost. FIGURE 8. The total cost versus dfferent mean of channel prce dstrbuton. (a) Lnear power prcng model. (b) Nonlnear power prcng model. Cumulatve Fracton of teratons FIGURE Number of teratons ξ=0.001 ξ=0.01 The dstrbuton of teratons of SPCA method. VII. CONCLUSION In ths paper, we nvestgate the effcent meter data collecton problem n smart grd by explorng the secondary spectrum market n cellular networks. Wth the objectve of REFERENCES [1] D. Hart, Usng am to realze the smart grd, n Proc. IEEE Power Energy Soc. Gen. Meetng, Convers. Del. Electr. Energy 21st Century, Jul. 2008, pp [2] D. Reken and M. Walker, Ultra low frequency power-lne communcatons usng a resonator crcut, IEEE Trans. Smart Grd, vol. 2, no. 1, pp , Mar [3] W. Lu, H. Wdmer, and P. Raffn, Broadband PLC access systems and feld deployment n European power lne networks, IEEE Commun. Mag., vol. 41, no. 5, pp , May [4] N. Pavldou, A. Han Vnck, J. Yazdan, and B. Honary, Power lne communcatons: State of the art and future trends, IEEE Commun. Mag., vol. 41, no. 4, pp , Apr [5] P. Parkh, M. Kanabar, and T. Sdhu, Opportuntes and challenges of wreless communcaton technologes for smart grd applcatons, n Proc. IEEE Power Energy Soc. Gen. Meetng, Jul. 2010, pp [6] P. L and S. Guo, Delay mnmzaton for relable data collecton on overhead transmsson lnes n smart grd, n Proc. ComComAp, Apr. 2013, pp [7] C. Hochgraf, R. Trpath, and S. Herzberg, Smart grd charger for electrc vehcles usng exstng cellular networks and SMS text messages, n Proc. 1st IEEE Int. Conf. SmartGrdComm, Oct. 2010, pp [8] U. Deep, B. Petersen, and J. Meng, A smart mcrocontroller-based rdum satellte-communcaton archtecture for a remote renewable energy source, IEEE Trans. Power Del., vol. 24, no. 4, pp , Oct [9] S. Y. Hu and K.-H. Yeung, Challenges n the mgraton to 4G moble systems, IEEE Commun. Mag., vol. 41, no. 12, pp , Dec [10] E. Kavurmacoglu, M. Alanyal, and D. Starobnsk, Competton n secondary spectrum markets: Prce war or market sharng? n Proc. IEEE Int. Symp. DYSPAN, Oct. 2012, pp [11] H. Bogucka, M. Parzy, P. Marques, J. Mwangoka, and T. Forde, Secondary spectrum tradng n TV whte spaces, IEEE Commun. Mag., vol. 50, no. 11, pp , Nov [12] P. L, S. Guo, Y. Xang, and H. Jn, Uncast and broadcast throughput maxmzaton n amplfy-and-forward relay networks, IEEE Trans. Veh. Technol., vol. 61, no. 6, pp , Jul [13] P. L, S. Guo, W. Zhuang, and B. Ye, On effcent resource allocaton for cogntve and cooperatve communcatons, IEEE J. Sel. Areas Commun., to be publshed. [14] R. Murty, R. Chandra, T. Moscbroda, and P. Bahl, SenseLess: A database-drven whte spaces network, IEEE Trans. Moble Comput., vol. 11, no. 2, pp , Feb [15] J. Cabero, A. Ballo, S. Cersola, M. Ventosa, A. Garca-Alcalde, F. Peran, and G. Relano, A medum-term ntegrated rsk management model for a hydrothermal generaton company, IEEE Trans. Power Syst., vol. 20, no. 3, pp , Aug [16] D. Nyato and P. Wang, Cooperatve transmsson for meter data collecton n smart grd, IEEE Commun. Mag., vol. 50, no. 4, pp , Apr [17] H. Y. Tung, K. F. Tsang, and K. L. Lam, Zgbee sensor network for advanced meterng nfrastructure, n ICCE Conf. Dg. Tech. Papers, Jan. 2010, pp VOLUME 1, NO. 2, DECEMBER

10 L et al.: Jont Optmzaton of Electrcty and Communcaton Cost [18] S. Garlapat, H. I. Volos, T. Kurugant, M. R. Buehrer, and J. H. Reed, PHY and MAC layer desgn of hybrd spread spectrum based smart meter network, n Proc. IEEE IPCCC, Dec. 2012, pp [19] D. Matheson, C. Jng, and F. Monforte, Meter data management for the electrcty market, n Proc. Int. Conf. Probablstc Methods Appl. Power Syst., Sep. 2004, pp [20] A. Ghassem, S. Bavaran, and L. Lampe, Cogntve rado for smart grd communcatons, n Proc. IEEE SmartGrdComm, Oct. 2010, pp [21] X. Ma, H. L, and S. Djouad, Networked system state estmaton n smart grd over cogntve rado nfrastructures, n Proc. 45th Annu. CISS, Mar. 2011, pp [22] A. Sreesha, S. Somal, and I.-T. Lu, Cogntve rado based wreless sensor network archtecture for smart grd utlty, n Proc. IEEE Long Island Syst., Appl. Technol. Conf., May 2011, pp [23] R. C. Qu, Z. Chen, N. Guo, Y. Song, P. Zhang, H. L, and L. La, Towards a real-tme cogntve rado network testbed: Archtecture, hardware platform, and applcaton to smart grd, n Proc. IEEE Workshop Netw. Technol. SDR Netw., Jun. 2010, pp [24] R. Qu, Z. Hu, Z. Chen, N. Guo, R. Ranganathan, S. Hou, and G. Zheng, Cogntve rado network for the smart grd: Expermental system archtecture, control algorthms, securty, and mcrogrd testbed, IEEE Trans. Smart Grd, vol. 2, no. 4, pp , Dec [25] R. Yu, Y. Zhang, S. Gjessng, C. Yuen, S. Xe, and M. Guzan, Cogntve rado based herarchcal communcatons nfrastructure for smart grd, IEEE Netw., vol. 25, no. 5, pp. 6 14, Sep./Oct [26] H. Farhang, The path of the smart grd, IEEE Power Energy Mag., vol. 8, no. 1, pp , Jan./Feb [27] P. Y, A. Iwayem, and C. Zhou, Developng ZgBee deployment gudelne under WF nterference for smart grd applcatons, IEEE Trans. Smart Grd, vol. 2, no. 1, pp , Mar [28] V. C. Gungor and F. C. Lambert, A survey on communcaton networks for electrc system automaton, Comput. Netw., vol. 50, no. 7, pp , May [29] Y. Hu and V.-K. L, Satellte-based nternet: A tutoral, IEEE Commun. Mag., vol. 39, no. 3, pp , Mar [30] Á. Cartea and P. Vllaplana, Spot prce modelng and the valuaton of electrcty forward contracts: The role of demand and capacty, J. Bank. Fnance, vol. 32, no. 12, pp , [31] M. R. Lyle and R. J. Ellott, A smple hybrd model for power dervatves, Energy Econ., vol. 31, no. 5, pp , [32] P. Skantze, A. Gubna, and M. Ilc, Bd-based stochastc model for electrcty prces: The mpact of fundamental drvers on market dynamcs, Energy Labs. Pubs., MIT, Cambrdge, MA, USA, Tech. Rep. EL , [33] A. Beck, A. Ben-Tal, and L. Tetruashvl, A sequental parametrc convex approxmaton method wth applcatons to nonconvex truss topology desgn problems, J. Global Optm., vol. 47, no. 1, pp , May [34] S. Boyd and L. Vandenberghe, Convex Optmzaton. Cambrdge, U.K.: Cambrdge Unv. Press, PENG LI (S 12 M 13) receved the B.S. degree from the Huazhong Unversty of Scence and Technology, Wuhan, Chna, n 2007, the M.S. and Ph.D. degrees from the Unversty of Azu, Azu- Wakamatsu, Japan, n 2009 and 2012, respectvely, where he s currently a Post-Doctoral Researcher. Hs current research nterests nclude networkng modelng, cross-layer optmzaton, network codng, cooperatve communcatons, cloud computng, smart grd, performance evaluaton of wreless and moble networks for relable, energy-effcent, and cost-effectve communcatons. SONG GUO (M 02 SM 11) receved the Ph.D. degree n computer scence from the Unversty of Ottawa, Ottawa, ON, Canada, n He s currently a Senor Assocate Professor wth the School of Computer Scence and Engneerng, Unversty of Azu, Azu-Wakamatsu, Japan. Hs current research nterests nclude protocol desgn and performance analyss for relable, energy-effcent, and cost effectve communcatons n wreless networks. He s an Assocate Edtor of the IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS and an Edtor of Wreless Communcatons and Moble Computng. He s a senor member of the ACM. ZIXUE CHENG (M 95) receved the master s and doctor s degrees n engneerng from the Tohoku Unversty, Senda, Japan, n 1990 and 1993, respectvely. He joned the Unversty of Azu, Azu-Wakamatsu, Japan, n 1993, as an Assstant Professor, became an Assocate Professor n 1999, and has been a Full Professor snce Hs current research nterests nclude desgn and mplementaton of protocols, dstrbuted algorthms, dstance educaton, ubqutous computng, ubqutous learnng, embedded systems, functonal safety, and Internet of Thngs. He served as the Drector of Unversty-Busness Innovaton Center from 2006 to 2010, and has been the Head of the Dvson of Computer Engneerng, Unversty of Azu, snce He s a member of ACM, IEICE, and IPSJ. 306 VOLUME 1, NO. 2, DECEMBER 2013