Secure Power Scheduling Auction for Smart Grids Using Homomorphic Encryption

Transcription

1 Secure Power Schedulng Aucton for Smart Grds Usng Homomorphc Encrypton Haya Shajaah, Student Member, IEEE, Ahmed Abdelhad, Senor Member, IEEE, and Charles Clancy, Senor Member, IEEE Abstract In ths paper, we ntroduce a secure energy tradng aucton approach to schedule the power plant lmted resources durng peak hours tme slots. In the proposed aucton model, the power plant servng a power grd shares wth the smart meters ts avalable amount of resources that s expected durng the next future peak tme slot; smart meters expectng a demand for addtonal power durng future peak hours partcpate n the power aucton by submttng bds of ther offered prce for ther requested amount of power. In order to secure the power aucton and protect smart meters prvacy, homomorphc encrypton s used to secure the bddng values and ensure avodng possble nsncere behavors of smart meters or the grd operator (.e. the auctoneer) to manpulate the aucton for ther own benefts. We propose an effcent power schedulng mechansm to dstrbute the operator s lmted resources among smart meters partcpatng n the power aucton. Fnally, we present smulaton results for the performance of our secure power schedulng aucton mechansm. Index Terms Power Schedulng Aucton, Homomorphc Encrypton, Smart Grd I. INTRODUCTION Many power grds experence a faster grow n the consumpton of electrc power compared to the expanson rates of generaton unts. Therefore, mantanng a suffcent relablty of power grds durng peak tme perods has been gven sgnfcant attenton recently [1]. Demand response n smart grds s one of the promsng approaches to mprove power grds relablty. It controls the consumpton of electrc power by users durng peak tme perods and usually provdes lower overall costs. Prce based demand response s the most commonly used approach whch controls and manages users consumpton of electrc power by adoptng a day ahead [2], [3] or real tme [4], [5] desgns for electrcty prces. In ths paper we ntroduce a new secure electrc power management and prcng approach by desgnng a secure power schedulng aucton to schedule the power grd s lmted resources for future peak tme perods. We have focused on desgnng a power aucton that has the followng aucton s favorable economc propertes: ncentve compatble, Pareto effcent and ndvdual ratonal. An effcent aucton desgn needs to make sure that all bdders submt ther true evaluaton bddng values n order to ensure truthfulness n the power aucton. The proposed power aucton uses a payment method that s based on Vckrey-Clarke- Groves (VCG) aucton snce VCG s the only aucton that has proved to satsfy the above economc propertes whle maxmzng the auctoneer s revenue [6], [7]. Even though H. Shajaah, A. Abdelhad, and C. Clancy are wth the Hume Center for Natonal Securty and Technology, Vrgna Tech, Arlngton, VA, USA e-mal: {hayajs, aabdelhad, tcc}@vt.edu. Ths research s based upon work supported by the Natonal Scence Foundaton under Grant No VCG aucton has the aforementoned good propertes, t s vulnerable to back-room dealng between an nsncere auctoneer and greedy bdders who collude wth each other to manpulate the aucton for ther own benefts. For example, the auctoneer may carry out frauds when he overcharges the wnnng bdder f that bdder cannot verfy the actual submtted bds from other bdders. On the other hand, bd rggng occurs when the auctoneer shares the value of the wnnng bd wth certan bdder (a greedy bdder) so that the greedy bdder bds more than hs true evaluaton value to enable the auctoneer to ncrease hs revenue and share the spols wth the greedy bdder. Therefore, VCG aucton cannot be drectly used n the power aucton and provdng a secure power aucton desgn s becomng necessary. In order to ensure bdders prvacy and avod possble back room dealngs, a successful secure aucton desgn needs to enable the auctoneer to decde the wnners and ther chargng prce wthout knowng the bdders actual bds. In ths paper, we desgn a secure power schedulng aucton mechansm to schedule the power plant s lmted electrc power resources durng peak hours tme slots. The proposed mechansm allows the power grd operator to schedule hs expected future avalable resources to the smart grds and charge them for the scheduled resources. It provdes a framework for the power plant s operator, who plays the role of an auctoneer, to manage hs lmted resources effcently and securely. It uses homomorphc encrypton to ensure users prvacy and secure the power aucton whch s vulnerable to fraud of an nsncere auctoneer and bd rggng. II. SYSTEM MODEL AND DESIGN ASSUMPTIONS We consder a power grd consstng of K smart meters (SM)s, denoted n the set K = {1, 2,..., K}, that purchases electrc power from a power plant operator (grd operator). We consder the stuaton where a set of smart meters N = {1, 2,..., N}, N K, are nterested n purchasng addtonal amount of electrc power (n addton to ts regularly scheduled power) from the power plant operator to satsfy the demands of ther commercal or ndustral users durng the next peak hours tme slot. We express the power tradng mechansm by desgnng a secure power aucton. The grd operator plays the role of an auctoneer that auctons ts spare resources to bdders (.e. smart grds n N ). We assume that the grd operator s able to determne ts expected amount of spare resources (electrc power) denoted by R n KW that wll be avalable durng the next peak tme slot. The amount of resources R s dvded nto M electrc power unts (EPU)s. Let M = {1, 2,..., M} denotes the set of avalable EPUs to be auctoned by the grd operator to the N smart meters n the power grd. We assume

2 that the grd operator runs the power schedulng aucton for future peak hours tme slot durng whch a contngency wll occur. Each smart meter can bd for a sngle or multple EPUs from the set M based on ts demand. In the proposed power aucton model, we consder a secure gateway that plays the role of a mddleman between the auctoneer and the bdders. Fgure 1 shows a power grd that conssts of SMs, power plant and secure gateway. The secure gateway announces to the SMs the number of bdders as well as the number of auctoned EPUs. Once the smart meters receve these nformaton, the nterested smart meters submt ther bds (prce) to the auctoneer. Let A = {β 1, β 2,..., β A } be the set of all possble allocatons for the M EPUs that each SM bds for and A s the number of all possble allocatons. For example, n the case of M = {EPU1, EPU2} and N = {1, 2, 3}, then we have A = {β 1 = (2, 0, 0), β 2 = (0, 2, 0), β 3 = (0, 0, 2), β 4 = (1, 1, 0), β 5 = (1, 0, 1), β 6 = (0, 1, 1)}, e.g., β 1 = (2, 0, 0) denotes an allocaton where EPU1 and EPU2 are scheduled for bdder 1 and nothng s scheduled for bdder 2 and bdder 3. Each SM submts an encrypted bd for each allocatons n A where w = [w (β 1 ), w (β 2 ),...] represents the encrypted bds that bdder n N submts for the allocatons n A, e.g. w 2 = [0, 2, 0, 1, 0, 1] ndcates that SM 2 bds 0 for allocaton β 1, 2 for allocaton β 2, 0 for allocaton β 3, 1 for allocaton β 4, 0 for allocaton β 5 and 1 for allocaton β 6. It s assumed that each SM submts same bds for dfferent allocatons n A f the number of EPUs that corresponds to that SM n these allocatons s the same. The bddng values of each SM represent the prce of the EPUs that the SM s bddng for. Ths prce s traffc dependant [8];.e. ncreases when the demand for more EPUs s hgh. Let v (β) denotes the true evaluaton value (bddng prce) of SM for allocaton β and v = [v (β 1 ), v (β 2 ),...] be the true evaluaton vector for SM. Let p denotes the chargng prce of the auctoneer (grd operator) to SM for the scheduled EPUs. Then the utlty of SM s gven by u = v (β) p ;.e. the dfference between the true evaluaton value and the actual prce that the SM pays to the auctoneer for allocaton β. Furthermore, let Rev = =N =1 p represents the power plant s revenue from sellng the auctoned electrc power R. Provdng an effcent contngency management usng a secure power aucton provdes a far schedulng mechansm and helps the grd operator mprove ts proft. It s mportant to take nto consderaton that the grd operator (auctoneer) s prone to fraud. Therefore, an deal power aucton should prevent possble back room dealng by allowng the auctoneer to determne the wnners and ther payments whle the actual bddng values are kept secret from the auctoneer. III. DESIGN CONSIDERATIONS In ths secton, we dscuss some desred propertes that are taken nto consderaton n the proposed power schedulng aucton. Frst, we dscuss the payment rule that the auctoneer adopts to determne the chargng prce that the SMs pay for the scheduled EPUs. Then we dscuss the securty and prvacy challenges that need to be addressed n the aucton Fg. 1. Power grd that conssts of smart meters, power plant and secure gateway. desgn. Fnally, we provde some background on homomorphc encrypton. Smart Meter A. VCG Based Payment Rule As mentoned before, our goal s to desgn a power schedulng aucton that maxmzes the power plant revenue. Therefore, we adopt the payment rule of VCG aucton snce VCG aucton s proven to be Pareto effcent [9]. In order for a SM to maxmze ts utlty, t has to bd wth ts true evaluaton value regardless of the bddng strateges of other bdders [10]. In the proposed power aucton desgn, we use a payment rule that s based on VCG aucton mechansm [11] where each bdder s charged a prce that s equvalent to the dfference between the socal welfare wth and wthout that bdder s partcpaton n the aucton. Each SM submts ts encrypted bddng vector w for the allocaton set A. Let β A be a Pareto effcent allocaton that the auctoneer selects where β s defned as β = arg max β A w (β). (1) The auctoneer schedules the EPUs n M to the SMs n N based on allocaton β. Furthermore, when SM s not partcpatng n the aucton then the correspondng allocaton A s defned as β β = arg max β A w j (β). (2) The prce that SM s charged by the auctoneer for allocaton β s equvalent to p = j j w j (β ) j w j (β ). (3) Then the utlty of SM s u = v (β ) p. By usng the payment method expressed n equaton 3, the aucton has no postve transfers (.e. p 0 N and other desred economc propertes can be satsfed as mentoned before. B. Securty and Prvacy Consderatons One of the most mportant features of the proposed power schedulng aucton s provdng a suffcent level of securty n order to enable a relable and effcent schedulng of the auctoneer s resources. On the other hand, t s mportant to provde the SMs wth a suffcent level of prvacy by usng a cryptosystem that allows bdders to submt ther encrypted bddng values whle keepng the actual values unknown to

3 the auctoneer and other bdders n order to thwart backroom dealng such as bd-rggng between the bdders and the auctoneer and possble fraud of an nsncere auctoneer. Bd-rggng can occur f the nsncere auctoneer that s aware of the bdders actual bddng values colludes wth certan bdder, for the beneft of both, by sharng wth hm the bddng values of other bdders and manpulate the aucton. On the other hand, frauds of the nsncere auctoneer occurs f the auctoneer manpulates the chargng prce and overcharges the wnners n order to ncrease ts revenue whch results n a bad utltes for the wnners. Therefore, t s mportant for a power schedulng aucton to use a mechansm that allows the auctoneer to determne the maxmum bd wthout knowng the actual bddng values. C. Homomorphc Encrypton As mentoned before, homomorphc encrypton s adopted n our aucton desgn. Homomorphc encrypton s used when there s a requrement to perform certan operatons whle the nputs are not dsclosed. There are many schemes for homomorphc encrypton. In the proposed aucton desgn we adopt Paller cryptosystem [12], [13]. By usng Paller cryptosystem, the encrypton functon E(.) of plantexts x 1 and x 2 s addtvely homomorphc,.e. E(x 1 + x 2 ) = E(x 1 )E(x 2 ). Wth the ndstngushablty property of Paller cryptosystem, f a plantext x s encrypted twce the resultng two cyphertexts are dfferent from each other makng t not possble for anyone to dstngush ther orgnal plantexts unless decryptng the two cphertexts. In addton, wth the self blndng property of Paller cryptosystem, t s possble to compute dfferent cphertext E (x) from the cphertext E(x) wthout knowng the decrypton key of the plantext. IV. SECURE POWER SCHEDULING AUCTION MECHANISM Gven that the grd operator who plays the role of an auctoneer could be a prvate entty, the aucton s prone to fraud from an nsncere auctoneer. Therefore, preventng possble nsncere behavor from the auctoneer s essental. In order to enable an effcent secure schedulng process of the power plant s resources, t s mportant to desgn a secure power aucton that enables the power plant s operator to determne the wnners and the resource prce wthout knowng the orgnal bds. By makng the auctoneer only able to explot the wnners and ther payments, t s then not possble for hm to conduct bd-rggng or fraud. Once the power aucton s performed, the power plant s operator schedules each of the wnnng SMs for the correspondng EPUs and charges t for the scheduled resources. The proposed power aucton leverages homomorphc encrypton through Paller cryptosystem to provde a secure and honest aucton mechansm by avodng possble frauds and bd-rggng. The procedure of the proposed secure power aucton s presented n the followng steps: 1. The auctoneer generates a prvate and publc keys of Paller cryptosystem and shares hs publc key x (.e. x 0) wth the SMs n the power grd. 2. Each SM n N submts ts true evaluaton bddng values n w = v to a buffer that encrypts these values usng Paller cryptosystem and creates cphertexts. Let the bddng value w(β) of allocaton β be equvalent to m such that 1 m s where s s any number that s large enough to cover all possble bddng values for the allocaton of the EPUs. Let E(x) be the Paller encrypton of the publc key x 0, the buffer creates a vector of cphertexts e(m) for bddng value m where e(m) s gven by e(m) = (e 1,..., e s ) = (E(x),..., E(x), E(0),..., E(0) ). (4) }{{}}{{} m s m Furthermore, the auctoneer creates N +1 representng vectors E T = E(O), E 1 = E(O),...,E N = E(O) (.e. N s the number of bdders). The sze of E equals A and the ntal O(β) equals 0;.e. E(O) = {e(0), e(0),.., e(0)}. Each SM;.e. the j th SM n N keeps ts encrypted bddng vector w j secret by addng t to all representng vectors except E j. Once performng ths addton process by each SM n N, the auctoneer obtans E T = ( e(w (β 1 )),..., e(w (β A ))). (5) By applyng the homomorphc addton property, E T can be expressed as E T = (e( w (β 1 )),..., e( w (β A ))) = E( w ), (6) and the auctoneer also has E j = E( j w ) for (1 j N). 3. The secure gateway adds a random constant θ(β) = r to each of E T, E 1,..., E N to obtan E( w + θ) and E( j w + θ) j and sends them to the auctoneer. 4. The auctoneer determnes the maxmum sum value of the masked bds accordng to the followng equaton: k = max β A ( = max β A ( w (β) + θ(β)) w (β)) + r, where k can be determned by the auctoneer by takng the product of the encrypted values n E T, whch s equvalent to A n=1 e( N =1 w (β n )+r), and fndng the maxmum element n that product. 5. The auctoneer decrypts the k th element of each vector e( w (β) + θ(β)) n E T for all the allocatons n A. Its decrypted value wll be equvalent to zero or x. The allocaton that has a decrypton value equvalent to x,.e. β, s the one that maxmzes w. The auctoneer consders β to be the wnnng allocaton and schedules ts resources to the correspondng SMs accordng to β. 6. In order for the auctoneer to fnd ts chargng prce for each wnnng SM, the auctoneer decrypts e( z w (β ) + θ) of E z (.e. SM z s a wnnng one) and fnds the value ( z w (β ) + θ). The auctoneer then fnds the maxmum value of the product of the encrypted elements max β A ( z w (β) + r) = ( z w (α z) + r). (7)

4 The auctoneer calculates the chargng prce that each of the wnnng SMs needs to pay for the scheduled EPUs accordng to the followng equaton p z = ( z w (β z) + r) ( z w (β ) + r). (8) where SM z s a wnnng bdder that pays a prce p z for ts scheduled EPUs. Fgure 2 shows the procedure of the proposed secure power schedulng aucton. Auctoneer (Power Plant Operator) Power Plant Revenue SM 4 SM 3 SM 2 SM Number of EPUs Secure Gateway Fg. 3. The auctoneer s revenue for dfferent number of bdders wth the auctoned EPUs changng from 1 to Smart Meter (Bdder) Smart Meter (Bdder) Bdders (SMs) Satsfacton SM 4 SM 3 SM 2 SM Smart meters submt ther encrypted bddng vectors to the auctoneer Secure Power Aucton The Auctoneer runs a secure power aucton Each smart meter (bdder) s scheduled the power unts t won and charged the correspondng prce Number of EPUs Fg. 4. Bdders satsfacton wth the auctoned EPUs changng from 1 to 15. Fg. 2. Procedure of the proposed secure power schedulng aucton. V. SIMULATION RESULTS In ths secton, we present the performance of the proposed power schedulng aucton. Two performance metrcs are consdered: power plant s revenue and SMs satsfacton. Let W denotes the set of all wnnng SMs. The power plant s revenue s gven by Rev = W p (.e. the sum of all wnnng SMs chargng prces) and the SMs satsfacton s represented by the sum of all wnnng SMs utltes dvded by the sum of all SMs evaluaton values that s gven by W u / N v. We ran Monte Carlo Smulaton for dfferent number of SMs that are bddng for the auctoneer s resources and the results are averaged over the ndependent runs n whch the bddng values of the SMs are generated randomly and the two performance metrcs are evaluated. Smulaton results are represented for each of the four cases: N = 2 SMs (bdders), N = 3 SMs, N = 4 SMs and N = 5 SMs. Fgure 3 shows that the auctoneer s revenue ncreases when the number of SMs (bdders) ncreases. Ths s expected as the auctoneer s revenue ncreases wth more bdders requestng more resources. In Fgure 4, we show that the bdders satsfacton ncreases as the number of EPUs ncreases untl the bdders satsfacton saturates when each SM s assgned the number of EPUs t bds for. Fgure 4 also shows that for the same amount of the auctoneer s avalable resources R, the bdders satsfacton s hgher when there are less number of bdders partcpatng n the power aucton. VI. CONCLUSION In ths paper, we have proposed a secure power schedulng aucton that enables an effcent power schedulng mechansm to schedule the power plant s lmted resources durng peak hours tme slots. We have taken nto consderaton possble nsncere behavor of the auctoneer and desgned a power aucton that prevents possble frauds and bd-rggng between an nsncere auctoneer and greedy bdders. The proposed power aucton leverages homomorphc encrypton through Paller cryptosystem to keep the SMs bddng values unknown to the auctoneer whle the auctoneer s stll able to fnd the wnnng SMs. We showed through smulatons that the proposed power aucton provdes suffcent revenue for the power plant and satsfactory utltes for the SMs whle provdng a secure power schedulng aucton aganst possble back room dealngs. REFERENCES [1] P. Y, X. Dong, A. Iwayem, C. Zhou, and S. L, Real-tme opportunstc schedulng for resdental demand response, Smart Grd, IEEE Transactons on, vol. 4, pp , March [2] A.-H. Mohsenan-Rad, V. Wong, J. Jatskevch, R. Schober, and A. Leon-Garca, Autonomous demand-sde management based on game-theoretc energy consumpton schedulng for the future smart grd, Smart Grd, IEEE Transactons on, vol. 1, pp , Dec [3] C. Joe-Wong, S. Sen, S. Ha, and M. Chang, Optmzed day-ahead prcng for smart grds wth devce-specfc schedulng flexblty, Selected Areas n Communcatons, IEEE Journal on, vol. 30, pp , July [4] J. H. Yoon, R. Baldck, and A. Novoselac, Dynamc demand response controller based on real-tme retal prce for resdental buldngs, Smart Grd, IEEE Transactons on, vol. 5, pp , Jan 2014.

5 [5] S. L, D. Zhang, A. Roget, and Z. O Nell, Integratng home energy smulaton and dynamc electrcty prce for demand response study, Smart Grd, IEEE Transactons on, vol. 5, pp , March [6] R. Weber, Aucton Theory: By Vjay Krshna. Academc Press, 2002, Games and Economc Behavor, vol. 45, no. 2, pp , [7] T. Groves, Incentves n teams, Econometrca, vol. 41, p , [8] A. Abdel-Had and C. Clancy, A Robust Optmal Rate Allocaton Algorthm and Prcng Polcy for Hybrd Traffc n 4G-LTE, n PIMRC, [9] W. Vckrey, Counterspeculaton, Auctons and Compettve Sealed Tenders, Journal of Fnance, pp. 8 37, [10] A. Abdelhad, H. Shajaah, and C. Clancy, A multter wreless spectrum sharng system leveragng secure spectrum auctons, IEEE Transactons on Cogntve Communcatons and Networkng, vol. 1, pp , June [11] N. Nsan, T. Roughgarden, É. Tardos, and V. V. Vazran, Algorthmc Game Theory. New York, NY, USA: Cambrdge Unversty Press, [12] P. Paller, Publc-key cryptosystems based on composte degree resduosty classes, n Proceedngs of the 17th Internatonal Conference on Theory and Applcaton of Cryptographc Technques, EUROCRYPT 99, (Berln, Hedelberg), pp , Sprnger-Verlag, [13] P. Paller and D. Pontcheval, Effcent publc-key cryptosystems provably secure aganst actve adversares, n Advances n Cryptology - ASIACRYPT99 (K.-Y. Lam, E. Okamoto, and C. Xng, eds.), vol of Lecture Notes n Computer Scence, pp , Sprnger Berln Hedelberg, 1999.