1

Enabling Localized Peer-to-Peer Electricity TradingAmong Plug-in Hybrid Electric Vehicles Using

Consortium BlockchainsJiawen Kang, Rong Yu, Member, IEEE, Xumin Huang, Sabita Maharjan, Member, IEEE,

Yan Zhang, Senior Member, IEEE, Ekram Hossain, Fellow, IEEE

Abstract—We propose a localized Peer-to-Peer (P2P) electricitytrading model for locally buying and selling electricity amongPlug-in Hybrid Electric Vehicles (PHEVs) in smart grids. Unliketraditional schemes, that transport electricity over long distancesand through complex electricity transportation meshes, our pro-posed model achieves demand response by providing incentivesto discharging PHEVs to balance local electricity demand outof their own self-interests. However, since transaction securityand privacy protection issues present serious challenges, we ex-plore a promising consortium blockchain technology to improvetransaction security without reliance on a trusted third party.A localized P2P Electricity Trading system with COnsortiumblockchaiN (PETCON) method is proposed to illustrate detailedoperations of localized P2P electricity trading. Moreover, theelectricity pricing and the amount of traded electricity amongPHEVs are solved by an iterative double auction mechanismto maximize social welfare in this electricity trading. Securityanalysis shows that our proposed PETCON improves transactionsecurity and privacy protection. Numerical results based on a realmap of Texas indicate that the double auction mechanism canachieve social welfare maximization while protecting privacy ofthe PHEVs.

Index Terms—Energy Internet, plug-in hybrid electric vehicle,decentralized energy trading, consortium blockchain, securityand privacy, double auction.

I. INTRODUCTION

W ITH rapid development of energy harvesting and infor-mation communication technologies, more and more

distributed renewable energy sources are integrated into smartgrids [1]. On one hand, nodes in smart grids can harvestenergy from different renewable energy sources to promotegreener smart grids [2]. On the other hand, smart girds utilizesensors with energy harvesting ability to form wireless sensornetworks for long-term monitoring and remote control [3],[4]. In smart grids, Plug-in Hybrid Electric Vehicles (PHEVs)play key roles in distributed renewable energy transportationand management. PHEVs can not only charge electricity fromhome grid with renewable energy sources [5], but can also

Copyright (c) 2017 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to pubs-permissions@ieee.org.

Jiawen Kang, Rong Yu and Xumin Huang are with School of Automation,Guangdong University of Technology, China (emails: {kjwx886@163.com,yurong@ieee.org, huangxu min@163.com). Sabita Mahajan and Yan Zhangare with University of Oslo and Simula Research Laboratory, Norway (emails:sabita@simula.no, yanzhang@ieee.org). Ekram Hossain is with Department ofElectrical and Computer Engineering, University of Manitoba, Canada (email:Ekram.Hossain@umanitoba.ca).

get electricity from other PHEVs to shift peak load throughvehicle-to-vehicle trading [6].

In social hotspots, e.g., parking lots or charging stations,PHEVs with bidirectional chargers can trade electricity in alocalized Peer-to-Peer (P2P) manner (e.g., vehicle-to-vehicle)[6]. In a conventional power grid, the generated electricityis transported through a complex energy transportation meshresulting in high losses in the T&D network and correspond-ingly low efficiency [5], [7]. Unlike so, PHEVs with surplusenergy can discharge energy to satisfy electricity demand oflocal charging PHEVs, thus balancing electricity supply anddemand locally in hotspots [6].

However, PHEVs with surplus electricity may be not willingto participate as energy suppliers in a localized P2P electricitytrading market due to their concerns either over the lifetimeof the battery or about privacy [5]. In this case, electricitysupply and demand are unbalanced among PHEVs. Moreover,traditional centralized electricity trading relying on a trustedthird party suffers from problems such as single point offailure and privacy leakage [8]. Therefore, it is necessary toencourage more PHEVs to perform discharging by designingproper incentives. In addition, it is important to design a securedecentralized electricity trading system such that the privacyof the PHEVs can be preserved during the trade [8].

Recently, a promising blockchain technology with advan-tages of decentralization, security and trust has been in-troduced for electricity trading. The blockchain is a P2Pdistributed ledger technology, that enables electricity tradingto be executed in decentralized, transparent and secure marketenvironments. A digital currency named “NRGcoin” basedon blockchain protocols was presented for renewable energytrading in smart grids [9]. A demonstration platform forrenewable energy exchange using NRGcoin was proposedin [10]. Authors in [6] utilized a general blockchain withmulti-signature to address transaction security problems indecentralized smart grids. However, the existing methods donot work well in localized P2P electricity trading amongPHEVs because of the disadvantage of high cost associatedwith establishing a blockchain in energy-limited PHEVs.

Motivated by these developments, in this paper, we exploitthe consortium blockchain technology to develop a securelocalized P2P electricity trading system. The consortiumblockchain is a specific blockchain with multiple authorizednodes to establish the distributed shared ledger with moderatecost. Here, the authorized nodes are local aggregators (LAGs).

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A consortium blockchain is established on LAGs to publiclyaudit and share transaction records without relying on a trustedthird party. Energy transaction records among PHEVs areuploaded to the LAGs after encryption. The LAGs run analgorithm to audit the transactions and record them into theshared ledger. This ledger is publicly accessed by PHEVsand LAGs connected to the consortium blockchain. Moreover,since electricity pricing along with the amount of tradedelectricity among PHEVs need to be optimized, an iterativedouble auction mechanism is presented to maximize socialwelfare in the system.

The contributions of this paper are summarized as follows.• Unlike existing blockchain-based energy trading system,

we establish a consortium blockchain based on LAGs toaudit and verify transaction records among PHEVs.

• We design a localized P2P Electricity Trading systemwith COnsortium blockchaiN (PETCON) to achieve trust-ful and secure electricity trading.

• To optimize electricity pricing and the amount of tradedelectricity among PHEVs in PETCON, an iterative dou-ble auction mechanism is proposed to maximize socialwelfare while protecting privacy of PHEVs.

The rest of this paper is organized as follows. We introducecore system components of PETCON in Section II. Detailedoperations of PETCON are illustrated in Section III. The prob-lem definition and the solution for localized P2P electricitytrading are proposed in Section IV and Section V, respectively.Security analysis and numerical results are shown in SectionVI before the paper is concluded in Section VII.

II. CORE SYSTEM COMPONENTS FOR LOCALIZEDPEER-TO-PEER ELECTRICITY TRADING

A. Entities for PETCON

The model for localized P2P electricity trading amongPHEVs includes the following entities as shown in Fig. 1.1) PHEVs: The PHEVs play different roles in localized P2Pelectricity trading at hotspots: charging PHEVs, dischargingPHEVs, and idle PHEVs. Each PHEV chooses its own roleaccording to current energy state and driving plan. 2) LAGs:LAGs work as energy brokers to provide access points ofelectricity and wireless communication services for PHEVs[11]. Each charging PHEV sends a request about electricitydemand to the nearest LAG. The energy broker does a statisticsof local electricity demand and announces this demand to localPHEVs. PHEVs with surplus electricity submit selling pricesto the broker. The energy broker acts as an auctioneer to carryout an iterative double auction among PHEVs, and matcheselectricity trading pairs of PHEVs. (Details on this auction willbe given in Sections IV and V.) 3) Smart meters: Each chargingpole with a built-in smart meter calculates and records theamount of traded electricity in real time. The charging PHEVspay to the discharging PHEVs according to the records in thesmart meters.

B. Consortium Blockchain for PETCON

Blockchain is an emerging P2P technology for distributedcomputing and decentralized data sharing among network n-

Social hotspot 1 Social hotspot 2

Local aggregator 2 Local aggregator 1

Power grid

Discharging

PHEVs

Charging

PHEVs

Grid substation Grid substation

A A

Energy buffer Energy buffer

A

A

A

A

A

A A

AA

A

A

A

Energy coins Energy coins

Idle PHEVs

Social hotspot 1 Social hotspot 2

Energy DataEnergy coin A Smart meter Switch

Fig. 1: Localized P2P electricity trading among PHEVs.

odes. There is an important transaction audit stage, named con-sensus process, before transaction records form a blockchain.This stage is executed by all nodes in a traditional blockchainwith high cost. In this paper, we use a consortium blockchainthat is a special blockchain to perform consensus process bypre-selected LAGs. These authorized LAGs have right to con-trol the consensus process and write the consortium blockchainwith transactional data during localized P2P electricity trading.The consortium blockchain consists of three main components.

1) Transactions: Electricity trading information and digitalasset records are stored in a consortium blockchain. The trad-ing information includes PHEVs’ pseudonyms used for privacyprotection, data type, metadata tags for raw transactional data,complete index history of metadata, an encrypted linked totransaction records, and a timestamp of transaction generation.The information is encrypted and signed with digital signaturesto guarantee authenticity and accuracy. Here, we will present anew digital cryptocurrency, named energy coin, as the digitalasset to trade electricity.

2) Blocks about transactional data: All raw data of elec-tricity transaction is stored, shared, and audited among autho-rized LAGs. Due to limitation of computation and storage,PHEVs store an index of metadata indicated a location of themetadata for decreasing system cost. The LAGs collect andmanage their own local transaction records. These transactionrecords are encrypted and structured into blocks after being au-dited by all the authorized LAGs (i.e., the consensus process).Each block contains a cryptographic hash to the prior blockin the consortium blockchain for traceability and verification.The blocks are added in a linear chronological order in theconsortium blockchain. After the transaction records have beenadded to the consortium blockchain, the data becomes publicly

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accessible to PHEVs and LAGs in smart grids.3) Proof-of-work: i) Proof-of-work for LAGs about data

audit: Similar to Bitcoin, before a new data being insertedinto immutable data storage, a consensus process carried byauthorized LAGs should be reached by a mechanism namedproof-of-work. The proof-of-work for LAGs about data audit issimilar to traditional proof-of-work in Bitcoin, which generatesa unique hash value with a certain difficulty for each block inthe blockchain. The hash value is used to link a new blockto the prior block. Each authorized LAG in the consortiumblockchain competes to create a block by finding a valid proof-of-work. The fastest LAG is rewarded by a certain amountof energy coins. The LAG audits the transaction records andstructures them into a new block for verification by otherLAGs during consensus process. ii) Proof-of-work for PHEVsabout energy contributions: The discharging PHEV with themost contribution on electricity supply in every LAG is alsorewarded by energy coins, which is an incentive to encouragethem to discharge electricity. The total amount of dischargedenergy is measured and recorded by smart meters, which is thespecific proof-of-work for PHEVs about energy contributions.

III. LOCALIZED PEER-TO-PEER ELECTRICITY TRADINGSYSTEM WITH CONSORTIUM BLOCKCHAIN

A. An Overview of PETCON

As shown in Fig. 2, there are three entities in an LAG,i.e., a transaction server, an account pool, and a memory pool.The transaction server collects energy request from chargingPHEVs and matches electricity trading pairs of PHEVs. Thetransaction server also controls switches of charging poles tofinish localized P2P energy transportation. Each PHEV has anenergy coin account that stores all transaction records, and acorresponding wallet to manage energy coins in the account.Here, we use random pseudonyms as public keys of PHEV’swallet named wallet addresses to replace the true address of thewallet for privacy protection. The mapping relationships aboutwallet addresses and the corresponding energy coin accountare stored in the account pools.

During a localized P2P electricity trading, PHEVs firstchoose their own roles according to electricity demand andenergy states. Charging PHEVs request energy from localdischarging PHEVs. LAGs work as energy brokers for PHEVsto execute energy bidding and transaction through an iterativedouble auction mechanism. After that, the charging PHEVspay to the discharging PHEVs using energy coins. With thehelp of proof-of-work for LAGs about data audit, transaction-related data in every LAG is audited and verified through aconsensus process among authorized LAGs.

B. Operation Details of PETCON

1) System initialization and key generation: In PETCON,we utilize elliptic curve digital signature algorithm and asym-metric cryptography for system initialization [8]. Each PHEVbecomes a legitimate entity after registration on a trustedauthority, such as a government department. A PHEV Vi withtrue identity IDi joins the system and gets its public/privacy

Account poolMemory pool

Wallet

Transaction server

(Controller)

Wallet

Local aggregator

Energy coins

Electricity

Transaction

records

V1 V2

V2 V1

V1 V2

Consortium

Blockchain

Charging PHEVDischarging PHEV

Transaction

records

Fig. 2: Localized P2P electricity trading using energy coins.

key and certificate (denoted as PKi, SKi and Certi, respec-tively). Certi can be used to uniquely identify the PHEVthrough binding registration information of the PHEV (e.g.,license plate number). Vi requests a set of ν wallet addresses{WIDi,k}νk=1 from the authority. The authority generatesa mapping list {PKi, SKi, Certi, {WIDi,k}νk=1}. When Viexecutes system initialization, Vi uploads wallet addressesbeing used to the account pool of its nearest LAG. Vi checksthe integrity of its wallet, and downloads the last data aboutits wallet through a memory pool. The memory pool stores alltransaction records in the consortium blockchain.

2) Choosing different roles in electricity trading: Duringelectricity trading, PHEVs are divided into two groups (i.e.,charging PHEVs and discharging PHEVs) according to theircurrent energy states and future driving plans. PHEVs withsurplus electricity may become discharging PHEVs to meetlocal electricity demands of charging PHEVs.

3) Selling and buying energy: Charging PHEVs send elec-tricity requests including the amount of electricity and ex-pected serving time to the transaction server of an LAG.The transaction server works as a controller to count thetotal electricity demands and broadcasts this demand to localdischarging PHEVs. The discharging PHEVs determine theirselling electricity and give responses back to the controller.The controller matches the electricity supply and demandamong PHEVs. Here, we use a double auction mechanism toexecute energy bidding, negotiation and transactions amongPHEVs. More details on the double auction mechanism willbe given in Sections IV and V.

4) Paying and earning energy coins: After electricity trad-ing, a charging PHEV pays for the energy transaction througha wallet address of a discharging PHEV as shown in Fig. 2.The charging PHEV transfers energy coins from its walletto the given wallet address. The discharging PHEVs obtainthe last blockchain from the memory pool of LAGs to ver-ify the payment. The charging PHEVs generate transactionrecords, and the discharging PHEVs verify and digitally signthe transaction records and thus upload them to LAGs for

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audit. To balance electricity demand and supply, by providingincentives, we stimulate discharging PHEVs to meet localdemand. During a certain period, the discharging PHEV withthe most contribution on electricity supply in every LAG isrewarded by energy coins according to the proof-of-work forPHEVs about energy contributions.

5) Building blocks and finding proof-of-work: LAGs collectall local transaction records in a certain period, and thenencrypt and digitally sign these records to guarantee authen-ticity and accuracy. The transaction records are structured intoblocks as shown in Fig. 3. Each block contains a cryptographichash to the prior block in the consortium blockchain. Similarto Bitcoin, the LAGs try to find their own valid proof-of-work (i.e., a hash value which meets a certain difficulty).An LAG calculates the hash value of its block based on arandom nonce value x and the previous block hash value,timestamp, transactions’ merkle root and so on (denoted asp data) [12]. Namely, Hash(x + p data) < Difficulty.Here, Difficulty is a number controlled by system to adjustthe speed of finding out a specific x.

6) Carrying out consensus process: The fastest LAG witha valid proof-of-work (i.e., x) becomes a leader of the cur-rent consensus process. The leader broadcasts block data,timestamp and its proof-of-work to other authorized LAGsfor verification and audit. These LAGs audit the block dataand broadcast their audit results with their signatures to eachother for mutual supervision and verification. After receivingthe audit results, each LAG compares its result with othersand sends a reply back to the leader. This reply includes theLAG’s audit result, comparison result, signatures, and recordsof received audit results. The leader does statistics of receivedreplies from LAGs. If all the LAGs agree on the block data,the leader will send records including current audited blockdata and a corresponding signature to all authorized LAGsfor storage. After that, this block is stored in the consortiumblockchain in a chronological order, and the leader is awardedby energy coins. Once the authorized LAGs formation iscomplete and remains almost constant, the total time neededfor reaching consensus of one new block is about 1 minuteregardless of the network size [13]. If some LAGs don’tagree on the block data, the leader will analyze the auditresults, and send the block data to these LAGs once again foraudit if necessary. Moreover, according to audit results andcorresponding signatures, compromised LAGs will be foundout and held accountable.

IV. PROBLEM DEFINITION FOR ELECTRICITY TRADING

In this section, we present the problem definition aboutelectricity pricing and the amount of traded electricity amongPHEVs to maximize overall social welfare (i.e., the sum ofnonlinear utilities of PHEVs). In each hotspot region, anLAG can communication with any local PHEVs to establish areal-time electricity trading market. LAGs facilitate electricitytrading between any charging PHEV and any dischargingPHEV in the network [14]. A local aggregator LAGn acting asan energy broker manages local PHEVs to execute electricitytrading operations. A set of LAGs (denoted as ι) is indexed

Discharging PHEVs Charging PHEVs

Transaction

record

Transaction

record

Local aggregator

Fig. 3: Structure of our proposed consortium blockchain.

by n, where n ∈ ι∆= {1, 2...n}. Let us denote a set of

charging PHEVs in LAGn as υ ∆= (CV n

i |i ∈ C, n ∈ ι),C ={0, 1, 2, ..., I}. The discharging PHEVs in LAGn are denotedas ψ ∆

= (DV nj |j ∈ Z, n ∈ ι),Z = {0, 1, 2, ..., J}. cn,min

i andcn,maxi are the minimum and maximum of electricity demand

for CV ni ∈ R in LAGn, respectively. LAGn must provide

cn,mini energy to CV n

i for normal driving.Here, cnij is the electricity demand of CV n

i for dischargingPHEV DV n

j in LAGn. The electricity demand vector of CV ni

is Cni

∆= {cnij |j ∈ Z}. In LAGn, the total electricity demand

of all charging PHEVs is Cn ∆= {Cn

i |i ∈ C}. We define theenergy state of CV n

i before charging as STOni . EV cap

i is thebattery capacity of CV n

i . The satisfaction function of CV ni is

Ui(Cni )=wi ln(η

J∑j=1

cnij − cn,mini + 1), (1)

where η is average charging efficiency from dischargingPHEVs to CV n

i . wi =τ

STOni

is the charging willingness ofCV n

i , and τ is a constant.For the discharging PHEVs, dnji is the amount of electricity

supply from discharging PHEV DV nj to CV n

i in LAGn. The

electricity supply vector of DV nj is Dn

j∆= {dnji|i ∈ R}. In

LAGn, the total electricity supply of all discharging PHEVsis Dn ∆

= {Dnj |j ∈ Z}. The maximum of electricity supply for

a discharging PHEV in LAGn is Dn,maxj . In LAGn, the cost

function of DV nj is

Lj(Dnj )=l1

I∑i=1

(dnji)2 + l2

I∑i=1

dnji, (2)

where l1 and l2 are cost factors. Here, l1 > 0.Since the local charging PHEVs want to maximize their

utilities while the local discharging PHEVs try to minimizetheir cost, LAGn working as the energy broker not only triesto meet the demand of charging PHEVs, but also maximizeelectricity allocation efficiency. From a social perspective,the localized P2P electricity trading should maximize socialwelfare and achieve effective market equilibrium [15]. The

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energy broker addresses the social welfare maximization prob-lem (denoted as SW ) to allocate energy between dischargingPHEVs and charging PHEVs. Here, the objective function ofsocial welfare problem is expressed as follows:

SW : maxCn,Dn

I∑i=1

Ui(Cni )−

J∑j=1

Lj(Dnj ). (3)

Subject to: cn,mini ≤ η

J∑j=1

cnij ≤ cn,maxi ,∀i ∈ C,

I∑i=1

dnji ≤ Dn,maxj , ∀j ∈ Z,

ρdnji = cnij , ∀i ∈ C, ∀j ∈ Z,cnij ≥ 0, ∀i ∈ C, ∀j ∈ Z.

(4)

Here, ρ is average electricity transmission efficiency of thelocal electricity trading. The objective function in Eq. (3) isstrictly concave with compact and convex constraints, so thereexists a unique optimal solution using Karush-Kuhn-Tucker(KKT) conditions [16]. We carry out relaxation of constraintsyielding the following Lagrangian L1:

L1(Cn,Dn,α,β,γ,λ,µ) =

I∑i=1

Ui(Cni )−

J∑j=1

Lj(Dnj )+

I∑i=1

αi(cn,mini − η

J∑j=1

cnij) +

I∑i=1

βi(η

J∑j=1

cnij − cmaxi,n )

+

J∑j=1

γj(

I∑i=1

dnji −Dmaxj,n ) +

J∑j=1

I∑i=1

λij(ρdnji − cnij)−

J∑j=1

I∑i=1

µijcnij .

(5)Here, αi, βi, γi, λij , and µij are Lagrange multipliers for theconstraints in Eq. (4). The corresponding sets are α, β, γ, λ,and µ. From the stationary conditions, the optimal solution ofSW meets following conditions:

∇cnijL1(C

n,Dn,α,β,γ,λ,µ) =ηwi

ηJ∑

j=1

cnij − cn,mini + 1

−ηαi + ηβi − λij − µij = 0,(6)

∇dnjiL1(C

n,Dn,α,β,γ,λ,µ) = −2l1dnji − l2 + γj

+λijρ = 0.(7)

For the social welfare maximization problem, it is necessaryfor the energy broker to obtain true and complete informationof all PHEVs’ utility and cost functions, and thus to solvethe problem using Eqs. (6) and (7). The complete informationof PHEVs includes current energy state, battery capacity andso on, which is private information for PHEVs. However,the PHEVs may not be willing to provide the above privateinformation to the energy broker. To address the issue, theenergy broker needs to design a mechanism to extract hid-den information from the PHEVs. As each PHEV tries to

maximize its own utility, the PHEVs are price taking entitiesthat make the electricity trading market competitive. A doubleauction is efficient to elicit the hidden information in a real andcompetitive electricity trading market with enough PHEVs,which is individually rational and weakly budget balanced[17]. The individually rational and weakly budget balancedcharacteristics of double auction mean that the PHEVs bidtruthfully according to privacy information and the energy bro-ker would not lose money to conduct the auction, respectively.

V. ITERATIVE DOUBLE AUCTION MECHANISM

In this section, an iterative double auction mechanism isproposed to elicit hidden information about PHEVs to energybrokers in order to maximize social welfare. In a hotspot, anenergy broker acts as an auctioneer to perform an iterativedouble auction according to buying prices from chargingPHEVs and selling prices from the discharging ones. In thisway, the auctioneer determines the final trading prices and theamount of traded electricity, which is useful to avoid directlyrevealing private information of PHEVs during electricitytrading. More specifically, each charging PHEV CVi submitsa bid price bij ≥ 0 for each discharging PHEV DVj to theauctioneer. And each discharging PHEV DVj also submitsa bid price sji ≥ 0 for each charging PHEV CVi to theauctioneer. After receiving these bid prices, the auctioneersolves an optimal energy allocation problem based on the bidsfrom PHEVs, and thus allocates electricity for every PHEV toachieve effective market equilibrium [17].

A. Entities in the Double Auction Mechanism

1) Charging PHEVs: The bid price vector of CVi forbuying energy in LAGn is Bn

i∆= {bnij |j ∈ Z}. All bid prices of

charging PHEVs in LAGn are denoted as Bn ∆= {Bn

i |i ∈ C}.CVi needs to solve the following optimal electricity buyingproblem (EB, buyer) to determine its optimal bid price:

EB : maxBn

i

[Ui(Cni )− payi(Bn

i )], (8)

where payi(Bni ) is the payment function of CVi given by the

auctioneer.2) Discharging PHEVs: The bid price vector of DVj for

selling electricity in LAGn is denoted as Snj

∆= {snji|i ∈ C}.

The bid price matrix of selling electricity is Sn ∆= {Sn

j |j ∈ Z}.DVj solves an optimal electricity selling problem (ES, seller)to determine its optimal bid price as follows:

ES : maxSn

j

[Rewj(Snj )− Lj(D

nj )], (9)

where Rewj(Snj ) is a reward function of DVj given by the

auctioneer.3) Auctioneer: The bid price matrices from charging and

discharging PHEVs are submitted to the auctioneer for per-forming an iterative double auction mechanism with multipleiterations. The buyers and sellers respectively solve theirown optimal electricity buying and selling problems at eachiteration to update bid price vectors according to the auction-eer’s newly allocated demand and supply, respectively. The

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auctioneer solves the following optimal allocation problem Ato calculate the amount of traded electricity [18]:

A : maxCn,Dn

I∑i=1

J∑j=1

[bnij lncnij − snjidnji], (10)

subject to the same constraints in Eq. (4). From Eq. (10), if thebid prices of charging and discharging PHEVs are given, theauctioneer can solve Problem A. Note that both Problems Aand SW have the same constraints. Problem A is also strictlyconcave, which ensures that there exists a unique optimalsolution for A. For Eq. (10), we carry out constraint relaxationthrough Lagrangian L2. To ensure that the optimal solutionof Problem A also solves Problem SW , it is necessary thatall KKT conditions along with the stationary conditions arematched for both Problem A and Problem SW . Therefore,L2 and L1 have the same Lagrange multipliers. Applying thestationary conditions yield

∇cnijL2(C

n,Dn,α,β,γ,λ,µ) =bnijcnij− ηαi + ηβi

−λij − µij = 0,

(11)

∇dnjiL2(C

n,Dn,α,β,γ,λ) = −snji + γj + λijρ = 0. (12)

As the KKT conditions are the same, clearly, from Eqs. (6),(7), (11), and (12), it is known that

bnij =ητcnij

(ηJ∑

j=1

cnij − cn,mini + 1)STOn

i

,(13)

snji = 2l1dnji + l2. (14)

Note that, if the bid prices of charging and discharging PHEVs,respectively, satisfy Eqs. (13), and (14), both the optimalsolution of Problem A and Problem SW are the same.

B. Pricing Rules

The payment function of CVi and the reward function ofDVj are, respectively, expressed as

payi(Bni ) =

J∑j

bnij , (15)

Rewj(Snj ) =

I∑i

(snji)2

4l1+ rmin

j . (16)

For stimulation, rminj is a minimum reward for a discharging

PHEV owing to the participation in local electricity trading.Theorem 1: The pricing rules based on Eqs. (15), and (16)

make the optimal buying price and optimal selling price satisfyEqs. (13), and (14), respectively.

Proof: For CVi, the optimal buying price satisfies thefollowing condition from Eq. (8),

∂Ui(Cni )

∂bnij− ∂payi(B

ni )

∂bnij= 0. (17)

According to Eq. (15), we obtain, ∂Ui(Cni )

∂bnij=

∂Ui(Cni )

∂cnij

∂cnij∂bnij

=∂payi(B

ni )

∂bnij= 1. Hence,

bnij =∂Ui(C

ni )

∂cnijcnij =

ητcnij

(ηJ∑

j=1

cnij − cn,mini + 1)STOn

i

. (18)

Here, Eq. (18) and Eq. (13) are the same.For DVj , the optimal buying price satisfies the following

condition from Eq. (9),

∂Rewj(Snj )

∂snji−∂Lj(D

nj )

∂snji= 0 (19)

According to Eq. (16), we obtain,∂Lj(D

nj )

∂snji=

∂Lj(Dnj )

∂dnji

∂dnji

∂snij=

∂Rewj(Snj )

∂snji=

snji2l1. Thus, we have

∂dnji∂snij

=snji

2l1(2l1dnji + l2). (20)

Based on the Eq. (20), we consider that there exist linearcorrelations between snji and dnji. We can easily obtain that,

snji = 2l1dnji + l2. (21)

Eq. (21) and Eq. (14) are also the same. It is known that thepricing rules based on Eq. (15) and Eq. (16) can make optimalprices satisfy Eq. (13) and Eq. (14), respectively.

C. Algorithm Implementation

According to the proposed mechanism, the charging PHEVsand the discharging PHEVs submit initial bid price vectors(i.e., Bn and Sn) based on their preferences to the auctioneerin the first iteration. Through these initial bid prices, theauctioneer solves Problem A to allocate the electricity demandand supply based on their individual bids. The auctioneerbroadcasts a new allocation solution to the charging and dis-charging PHEVs. Then these PHEVs solve their own ProblemES and Problem EB in order to obtain optimal bid pricesfor the next iteration. The auctioneer checks a terminationcondition of Algorithm 1 based on newly submitted bidprices from the PHEVs. Here, the termination condition is thatwhether the newest bid prices satisfy the convergence criteria(i.e., RDB < ε and RDS < ε) or not. If not, the entities inthis algorithm repeatedly execute the above steps. ProblemsEB, ES, and A can be solved through multiple iterations.Here, ε determines the execution time of Algorithm 1 andaccuracy of final results. When ε becomes smaller, the finalresults will get closer to the optimal values but increase timeand iterations of the algorithm. Selection of the value of ε isa tradeoff between time and accuracy of the algorithm.

In addition, auctioneers monitor localized P2P electricitytrading in real time. When some unexpected events happen,e.g., abrupt disconnection of scheduled PHEVs, a trigger willbe activated. Then the auctioneers may restart Algorithm1 and reinitialize parameters on demand. A new electricitytrading procedure is executed in time. Besides, similar to thatin [6], we consider that few PHEVs suddenly leave fromscheduled trades in parking lots during a specified scheduling

7

Algorithm 1 Iterative Double Auction Algorithm

// RDB =∣∣∣bn(t)

ij − bn(t−1)

ij

∣∣∣ /bn(t)

ij , RDS =∣∣∣sn(t)

ji − sn(t−1)

ji

∣∣∣ /sn(t)

ji .

1: Input: ε, η, τ, STOn;2: Initialization: Bn

(0)

,Sn(0)

, t← 0, flag ← 1, trigger ←0 ;

3: while flag and ∼ trigger do4: if Participating PHEVs of current localized P2P elec-

tricity trading change then5: trigger ← 1, and the auctioneer terminates the

procedure and prepares to restart Algorithm 1.6: else7: Based on Bn(t) and Sn(t), the auctioneer solves

Problem A to get Cn(t)

and Dn(t)

, and then broad-casts the optimized results to charging PHEVs anddischarging PHEVs, respectively.

8: Based on Cn(t)

and Dn(t)

, charging PHEVs computetheir optimal bid prices Bn

(t+1)

through solvingProblem EB, and submit them to the auctioneer;

9: Based on Cn(t)

and Dn(t)

, discharging PHEVs com-pute their optimal bid prices Sn

(t+1)

through solvingProblem ES, and also submit them to the auctioneer;

10: t← t+ 1;11: if RDB < ε and RDS < ε, then12: flag ← 0, t← t− 1.13: end if14: end if15: end while16: Output: Cn(t),Dn(t),Bn(t+1),Sn(t+1)

time period. The abruptly disconnected PHEVs will be heldaccountable and will be made pay for a penalty of disconnec-tion. This algorithm is performed with acceptable overheadsin practice with low frequency of restart. More details on theiterative double auction are given in Algorithm 1.

According to Eqs. (18) and (21), it is known that each PHEVwill bid truthfully and maximize their own utilities throughsolving Problems EB and ES. Each PHEV’s utility is non-negative. Our proposed auction is weakly budget balanced be-cause the auctioneer does not suffer any loss while conductingthe iterative double auction. Therefore, our proposed auctionis truthful, individually rational, weakly budget balanced. Thisauction can achieve an optimal energy allocation solutionwith optimal social welfare in the energy market, where theauctioneer does not have complete information about PHEVs’utility and cost functions for privacy protection [14], [17].

VI. SECURITY ANALYSIS AND NUMERICAL RESULTS

A. Security Analysis

PETCON has defense ability against many traditional se-curity attacks through standard cryptographic primitives in-cluding asymmetric and symmetric key-based encryption.Meanwhile, the adversary cannot simulate an entity or forgemessages of an entity due to its attached digital signatures inthe messages.

Fig. 4: Distribution of parking lots in the real map of Texas.

PETCON can also satisfy the following blockchain-relatedsecurity requirements: 1) Without reliance on the only trustedthird party: PHEVs trade electricity in a P2P manner withouta third party to make system robust and scalable. 2) Privacyprotection: Due to the iterative double auction mechanism,PHEVs only submit bid prices to the auctioneer withoutprivate information during trading. All energy coin accountsof PHEVs are pseudonymous by multiple wallet addresses, itis useful to protect identity privacy and account security. 3)Wallet security: Without corresponding keys and certificates,no adversary can open a PHEV’s wallet and steal energycoins from the wallet. 4) Transaction authentication: With thehelp of proof-of-work, all transaction data is publicly auditedand authenticated by authorized LAGs. It is impossible tocompromise all entities in our system due to overwhelmingcost. 5) Data unforgeability: The decentralized nature ofconsortium blockchain combined with digitally-signed trans-actions ensure that an adversary cannot pose as the user orcorrupt the network, as that would imply the adversary forgeda digital signature, or gained control over the majority ofsystem resources. 6) No double-spending: Energy coin relieson digital signatures to prove ownership and a public historyof transactions to prevent double-spending.

B. Numerical Results

We evaluate the performance of the proposed iterativedouble auction mechanism based on a real dataset [19] in areal urban area of Texas [20]. The latitude of observed areais from 30.256 to 30.276, and the longitude is from -97.76 to-97.725. The observed area is approximately 2.22× 3.88 km2

including 58 parking lots (Fig. 4). We formulate electricityconsumption behavior of PHEV as recorded in [19] and realdata analysis in [6]. Therefore, we set the battery capacityof the PHEVs to 24 KWh. The minimum and maximum ofelectricity demand for charging PHEVs are [5, 10] KWh and[12, 18] KWh, respectively. The maximum of electricity supplyfor discharging PHEVs is [10, 20] KWh. The cost factors ofcost function, i.e., l1 and l2 in Eq. (2), are set to 0.01 and0.015, respectively. The average charging efficiency η is 0.8

8

1 5 10 15 20 25 3018

19

20

21

22

23

24

25

Iteration

Soc

ial w

ealfa

re

(a)

PETCON P2P energy trading0

2

4

6

8

10

12

14

16

18

20

Algorithm comparison

Ave

rage

con

verg

ed it

erat

ions

Algorithm 1 in PETCON (ε=0.01)The proposed algorithm in [6]

(b)

Fig. 5: (a) Evolution of social welfare with PETCON, (b)comparison between algorithms in terms of iterations.

and the average electricity transmission efficiency ρ is 0.9.The minimum reward for a discharging PHEV rmin

j randomlyranges from 1 to 2 dollars. The convergence threshold ε is0.001. We take a parking lot with 35 charging PHEVs and 45discharging in LAG1 as an example.

Fig. 5(a) shows the convergence evolution of social welfareachieved by our Algorithm 1. Note that the social welfarerapidly converges close to the optimal one (i.e., the dottedline) after 12 iterations. Fig. 5(b) shows iteration convergencecomparison between Algorithm 1 used for PETCON and theP2P energy trading algorithm in [6]. After 1000 experiments ofelectricity trading with different energy demands from PHEVs,the average converged iterations of Algorithm 1 is 11.9, whichis 36.7% less than that in [6]. From the figures, it is clear thatour proposed Algorithm 1 is faster than the algorithm in [6].

Fig. 6 shows performance comparison between our PET-CON and a hybrid energy trading model in [7]. In thehybrid energy trading model, energy buyers can not onlytrade electricity with local energy seller but also with thesmart grid. Unlike so, we focus on localized P2P electricitytrading between charging PHEVs (i.e., energy buyers) and

0.12 0.16 0.2 0.24 0.280.12

0.13

0.14

0.15

0.16

0.17

0.18

Sell−out price of the smart grid for energy buyers (dollar/KWh)

Ave

rage

buy

ing

pric

e of

ene

rgy

buye

rs (

dolla

r/K

Wh)

0.12 0.16 0.2 0.24 0.2815

16

17

18

19

20

21

0.12 0.16 0.2 0.24 0.2815

16

17

18

19

20

21

Ave

rage

tran

smitt

ed e

lect

ricity

from

ene

rgy

selle

rs a

nd s

mar

t grid

(K

Wh)

Buying price of energy buyers (EBs) in [7]

Buying price of EBs in PETCON

Transmitted electricity from energy sellers (ESs) in [7]

Transmitted electricity from ESs in PETCON

(a)

0.08 0.1 0.12 0.14 0.160.12

0.13

0.14

0.15

0.16

0.17

Buy−back price of the smart grid for energy sellers (dollar/KWh)

Ave

rage

sel

ling

pric

e of

ene

rgy

selle

rs (

dolla

r/K

Wh)

0.08 0.1 0.12 0.14 0.1610

11

12

13

14

15

0.08 0.1 0.12 0.14 0.1610

11

12

13

14

15

Ave

rage

am

out o

f ava

ilabl

e el

ectr

icity

for

ener

gy b

uyer

s (K

Wh)

Selling price of energy sllers (ESs) in [7]

Selling price of ESs in PETCON

Available electricity for energy buyers (EBs) in [7]

Available electricity for EBs in PETCON

(b)

Fig. 6: (a) Average buying price and transmitted electricity,(b) average selling price and available electricity.

discharging PHEVs (i.e., energy sellers) with 90% electricitytransmission efficiency [21]. While there exist high energytransmission losses between the smart grid and energy buyersand sellers resulting in low transmission efficiency (only 70%)[21]. Fig. 6(a) shows that when the sell-out price of thesmart grid for energy buyers is smaller than that of localdischarging PHEVs, the energy buyers obtain more benefits in[7] because of lower average buying price. However, becauseof high transmission losses, the average amount of transmittedelectricity from both energy sellers and the smart gird is higherthan that of PETCON. If the sell-out price of the smart gridis too high, the energy buyers will buy electricity from localenergy sellers instead of the smart grid in [7], then obtain thesame benefits as our PETCON. Similar results can be found inFig. 6(b). Although the average selling price of energy sellersincreases with the increasing buy-back price given by the smartgrids in [7], the average available electricity for energy buyersis decreasing because of higher energy losses during electricitytransmission. Therefore, compared with the trading model in[7], our PETCON has less energy loss and higher electricityutilization efficiency from the system’s perspective.

9

5 10 15 20 25 300.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Iteration

The

am

ount

of t

radi

ng e

lect

ricity

(K

Wh)

Charging electricity of CV1Discharging electricity of DV1

(a)

5 10 15 20 25 302

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

Iteration

Ave

rage

pay

men

t/rew

ard

(dol

lar)

Average payment of CVsAverage reward of DVs

(b)

Fig. 7: Evolution of (a) amount of trading electricity and (b)average payment and average reward of PHEVs.

Fig. 7(a) shows the convergence evolution of charged elec-tricity and discharged electricity among PHEVs. Here, werandomly choose a charging PHEV (CV1) and a dischargingPHEV (DV1) to observe their convergence evolution. Theamount of CV1’s charged electricity from all the dischargingPHEV converges when the number of iterations is 25, whileDV1 also finally converges after 30 iterations. Fig. 7(b) showsthe convergence evolution of average payment for 35 chargingPHEVs and average reward of 45 discharging PHEVs. Theaverage payment of charging PHEVs for discharging PHEVsfinally converges to 2.50 dollars. And the average reward ofdischarging PHEVs converges to 2.04 dollars after a few itera-tions. The difference between payment of charging PHEVs andreward of discharging PHEVs is the benefit of the auctioneer.

VII. CONCLUSION

We have proposed a localized P2P electricity trading modelfor PHEVs in smart grids. A consortium blockchain hasbeen exploited to design a localized P2P electricity tradingsystem, where charging and discharging PHEVs can tradeelectricity without reliance on a trusted third party. In thismodel, an iterative double auction mechanism for charging and

discharging PHEVs is presented to maximize social welfare.The LAGs work as auctioneers to carry out the double auctionamong PHEVs according to their bid prices, which does notrequire private information about PHEVs. Security analysisshows that our proposed method can improve transactionsecurity and privacy protection. Numerical results based on areal map indicate that the iterative double auction mechanismmaximizes the social welfare.

VIII. ACKNOWLEDGMENT

The work is supported in part by programs of NSFC underGrant nos. 61422201, 61370159 and U1301255, U1501251,the Science and Technology Program of Guangdong Provinceunder Grant no. 2015B010129001, Special-Support Project ofGuangdong Province under grant no. 2014TQ01X100, HighEducation Excellent Young Teacher Program of GuangdongProvince under grant no. YQ2013057, Science and TechnologyProgram of Guangzhou under grant no. 2014J2200097, and ispartially supported by the projects 240079/F20 funded by theResearch Council of Norway.

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BIOGRAPHIES

Jiawen Kang received the M.S. degree from theGuangdong University of Technology, China in2015. He is now pursuing his Ph.D. degree inGuangdong University of Technology, China. Hisresearch interests mainly focus on security andprivacy protection in wireless communications andnetworking.

Rong Yu (S’05-M’08) received his Ph.D. degreefrom Tsinghua University, China, in 2007. Afterthat, he worked in the School of Electronic andInformation Engineering of South China Universityof Technology. In 2010, he joined the Instituteof Intelligent Information Processing at GuangdongUniversity of Technology, where he is now a fullprofessor. His research interest mainly focuses onwireless communications and networking, includingcognitive radio, wireless sensor networks, and homenetworking. He is the co-inventor of over 30 patents

and author or co-author of over 100 international journal and conferencepapers. He was the member of home networking standard committee in China,where he led the standardization work of three standards.

Xumin Huang is now pursuing his Ph.D. degreein Guangdong University of Technology, China. Hisresearch interests mainly focus on network per-formance analysis, simulation and enhancement inwireless communications and networking.

Sabita Maharjan (M’09) received her Ph.D. degreein Networks and Distributed Systems from Uni-versity of Oslo, and Simula Research Laboratory,Norway, in 2013. She is currently a Senior ResearchScientist in Simula Research Laboratory, Norway.She worked as a Research Engineer in Institute forInfocomm Research (I2R), Singapore in 2010. Shewas a Visiting Scholar at Zhejiang Univeristy (ZU),Hangzhou, China in 2011, and a Visiting ResearchCollaborator in University of Illinois at UrbanaChampaign (UIUC) in 2012. She was a Postdoctoral

Fellow at Simula Research laboratory, Norway from 2014 to 2016. Hercurrent research interests include wireless networks, network security andresilience, smart grid communications, cyber-physical systems, machine-to-machine communications, and software defined wireless networking.

Yan Zhang (SM’10) is Full Professor at the Depart-ment of Informatics, University of Oslo, Norway.He received a PhD degree in School of Electrical& Electronics Engineering, Nanyang TechnologicalUniversity, Singapore. He is an Associate TechnicalEditor of IEEE Communications Magazine, an Edi-tor of IEEE Transactions on Green Communicationsand Networking, an Editor of IEEE CommunicationsSurveys & Tutorials, an Editor of IEEE Internet ofThings Journal, and an Associate Editor of IEEEAccess. He serves as chair positions in a number of

conferences, including IEEE GLOBECOM 2017, IEEE VTC-Spring 2017,IEEE PIMRC 2016, IEEE CloudCom 2016, IEEE ICCC 2016, IEEE CCNC2016, IEEE SmartGridComm 2015, and IEEE CloudCom 2015. He servesas TPC member for numerous international conference including IEEEINFOCOM, IEEE ICC, IEEE GLOBECOM, and IEEE WCNC. His currentresearch interests include: next-generation wireless networks leading to 5G,green and secure cyber-physical systems (e.g., smart grid, healthcare, andtransport). He is IEEE VTS (Vehicular Technology Society) DistinguishedLecturer. He is also a senior member of IEEE, IEEE ComSoc, IEEE CS,IEEE PES, and IEEE VT society. He is a Fellow of IET.

Ekram Hossain (F’15) received the Ph.D. degree inelectrical engineering from the University of Victo-ria, Canada, in 2001. He has been a Professor withthe Department of Electrical and Computer Engi-neering, University of Manitoba, Winnipeg, Canada,since 2010. He has authored/edited several booksin these areas. His current research interests includedesign, analysis, and optimization of wireless/mobilecommunications networks, cognitive radio systems,and network economics. He is currently a member(Class of 2016) of the College of the Royal Society

of Canada. He is a member of the IEEE Press Editorial Board. He servesas the Editor-in-Chief of the IEEE Communications Surveys and Tutorialsand an Editor of the IEEE Wireless Communications. He has received severalresearch awards including the IEEE Communications Society Transmission,Access, and Optical Systems Technical Committee’s Best Paper Award inIEEE Globecom in 2015, the University of Manitoba Merit Award forResearch and Scholarly Activities in 2010, 2014, and 2015, the 2011 IEEECommunications Society Fred Ellersick Prize Paper Award, and the IEEEWireless Communications and Networking Conference 2012 Best PaperAward. He served as an Area Editor of the IEEE Transactions on WirelessCommunications in resource management and multiple access from 2009to 2011, an Editor of the IEEE Transactions on Mobile Computing from2007 to 2012, and an Editor of the IEEE Journal on Selected Areas inCommunications-Cognitive Radio Series from 2011 to 2014. He was theDistinguished Lecturer of the IEEE Communications Society from 2012to 2015. He is currently a Distinguished Lecturer of the IEEE VehicularTechnology Society. He is also a Registered Professional Engineer in theprovince of Manitoba, Canada.