SMART home scheduling provides management over the

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1 Tis article as been accepted for inclusion in a future issue of tis journal. Content is final as presented, wit te exception of pagination. IEEE SYSTEMS JOURNAL 1 Game-Teoretic Market-Driven Smart Home Sceduling Considering Energy Balancing Yang Liu, Siyan Hu, Senior Member, IEEE, Han Huang, Senior Member, IEEE, Rajiv Ranjan, Member, IEEE, Albert Y. Zomaya, Fellow, IEEE, and Lize Wang, Senior Member, IEEE Abstract In a smart community infrastructure tat consists of multiple smart omes, smart controllers scedule various ome appliances to balance energy consumption and reduce electricity bills of customers. In tis paper, te impact of te smart ome sceduling to te electricity market is analyzed wit a new smart-ome-aware bi-level market model. In tis model, te customers scedule ome appliances for bill reduction at te community level, wereas aggregators minimize te energy purcasing expense from utilities at te market level, bot of wic consider te smart ome sceduling impacts. A game-teoretic algoritm is proposed to solve tis formulation tat andles te bidirectional influence between bot levels. Comparing wit te electricity market witout smart ome sceduling, our proposed infrastructure balances te energy load troug reducing te peak-to-average ratio by up to 35.9%, wereas te average customer bill is reduced by up to 34.3%. Index Terms Dynamic pricing, electricity market, energy balancing, game teory, smart ome sceduling. Fig. 1. In a smart ome, te ome appliances are connected to te smart ome sceduler by communication network and connected to te distribution system by power line. I. INTRODUCTION SMART ome sceduling provides management over te ome appliances in te smart grid infrastructure. All te ome appliances in a smart ome are connected to a smart ome sceduler and te power line, wic is furter connected to te local distribution network, as sown in Fig. 1. Te data depicted in Fig. 2 indicate tat te energy price at different time slots would be significantly different even in a single day. For tis reason, te smart ome sceduler controls ome appliances and operates tem at te time slots wen energy is not expensive, tus reducing te monetary cost. Tis enables te customers Manuscript received November 18, 2014; revised January 26, 2015; accepted Marc 5, Te work of R. Ranjan was supported by te Australia India Strategic Researc Fund entitled Innovative Solutions for Big Data and Disaster Management Applications on Clouds under Grant AISRF troug te Department of Industry, Australia. (Corresponding autors: Sian Hu and Lize Wang.) Y. Liu and S. Hu are wit te Department of Electrical and Computer Engineering, Micigan Tecnological University, Hougton, MI USA ( yliu18@mtu.edu; siyan@mtu.edu). H. Huang is wit te State Grid Energy Researc Institute, State Grid Corporation of Cina, Beijing , Cina ( uangan@sgeri.sgcc.com.cn). R. Ranjan is wit te Commonwealt Scientific and Industrial Researc Organisation (CSIRO), Canberra, A.C.T. 2600, Australia ( rrajv.ranjan@ csiro.au). A. Y. Zomaya is wit te Scool of Information Tecnologies, Te University of Sydney, Darlington, N.S.W. 2008, Australia ( albert.zomaya@ sydney.edu.au). L. Wang is wit te Scool of Computer Science, Cina University of Geoscience, Wuan, , Cina, and also wit te Institute of Remote Sensing and Digital Eart, Cinese Academy of Sciences, Beijing , Cina ( lize.wang@computer.org). Digital Object Identifier /JSYST Fig. 2. Dynamic energy price provided by Ameren [4]. to sift eavy consumption load from peak price time slots to nonpeak price time slots [1]. Wit an appropriately designed pricing sceme, bot te monetary costs of te customers and te peak-to-average ratio (PAR) of energy demand could be significantly reduced [2]. Tis implicitly elps balance te energy generation and reduces te generation capacity, wic lessens te need of large-scale power plants, tus saving a large amount of construction cost. As sown from te U.S. Energy Information Administration, te total capital cost of building an advanced pulverized coal plant wit a nominal capacity of 650 MW is about 2.1 billion U.S. dollars [3]. Utilizing smart ome sceduling tecniques could largely reduce peak IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See ttp:// for more information.

2 Tis article as been accepted for inclusion in a future issue of tis journal. Content is final as presented, wit te exception of pagination. 2 IEEE SYSTEMS JOURNAL energy demand, leading to te significant investment savings in building power generation units. Researc on smart ome sceduling focuses on bot single customer smart ome and multiple customer smart omes. In terms of single customer smart ome sceduling, Cen et al. formulated a linear programming problem for smart ome sceduling considering te uncertainty of energy consumption in [1]. In [5], Kim and Poor proposed a Markov cain model of te sceduling problem and developed te backtrack algoritm to solve it based on a decision tresold. In [6], a dynamic programming algoritm was proposed to scedule ome appliances for a single customer considering multiple power levels. In [7], a mixed-integer programming metod was used to andle te constraints suc as uninterruptable setting and sequential operations in te smart ome sceduling problem. In [8], L 1 regulation was deployed to transform a mixed-integer problem into a convex programming problem in order to find te solution of smart ome sceduling more efficiently. All of tese works focus on smart ome sceduling for a single customer. However, in a community, tere are multiple customers, and all te customers compete to use energy in nonpeak price time slots, wic could result in te accumulation of energy load in tese time slots. For tis reason, interactions among multiple customers need to be considered. Most of te existing multiple customer smart ome sceduling tecniques are based on game teory, wic include [2], [9], and [10]. In addition, Ibars et al. formulated te distributed load management problem as a congestion game and proposed a dynamic pricing strategy to discourage te energy consumption at peak ours in [11]. In [12], te veicle-to-aggregator game was modeled to regulate te frequency in te power grid as a potential service in te future veicle-to-grid market. In [13] and [14], pricing strategies were deployed by local aggregators to control te energy load. Since te residential energy load is sifted by smart ome sceduling, an impact propagates to te electricity market, wic is never studied in te existing literatures. On te oter and, electricity market modeling is a wellstudied researc topic. In [15], te electricity market in Nortern Europe was modeled considering various generation resources and transmission protocols. In [16], te agent-based simulation metod was used via te Electricity Market Complex Adaptive System to investigate te influence of price probing strategies on te electricity price and generation profit. In [17], a single buyer market model and a pool market model are compared in terms of generation revenue. In [18], different game-teory-based market models were compared in terms of teir market performance. Te existing works on electricity market modeling use statistical data rater tan te actual beavior on energy consumption of customers [19]. However, tere is no guarantee tat te statistically estimated energy consumption of customers can be actually acieved during power system operation. It means tat te feasibility of tese models cannot be guaranteed. It is wort noting tat demand-side management (DSM) and smart ome sceduling are different. As a top-down energy load management tecnique, te traditional DSM, or precisely direct load control (DLC), intends to balance te energy load Fig. 3. Suppose tat a peak energy load is created between 7:00 P.M. and 9:00 P.M. due to a live TV football game. It cannot be sifted since it will be missed oterwise. troug enabling te utilities to control te energy consumption of te customers. However, as sown in Fig. 3, if most ome appliances can only be operated during a specific time period, energy load will accumulate to peak tere anyway, and te majority of te energy consumption cannot be sifted at all. It means tat te strategies of market to scedule te energy consumption are not applicable witout considering te specific requirements from customers. In contrast to DLC, smart ome sceduling provides a more desirable solution of tis problem in te bottom-up fasion. It encourages te customers to allocate te energy consumption evenly over te time orizon troug dynamic pricing, wic is widely accepted today. Terefore, an electricity market model considering smart ome is crucial in analyzing te modern power system. Energy sceduling is influenced by te market pricing strategy, wic, in turn, affects te electricity price. Tis forms a feedback loop and imposes more callenge to te modeling of electricity market. Te bidirectional interaction between utilities and end users need to be considered. Due to suc a feature of te electricity market, a feedback control system is widely deployed to model te interaction between te suppliers and te consumers. In [20], Voice et al. proposed a feedbackloop-based strategy to manage te microstorage system, were te suppliers use adaptive pricing to interact wit te storage

3 Tis article as been accepted for inclusion in a future issue of tis journal. Content is final as presented, wit te exception of pagination. LIU et al.: GAME-THEORETIC SMART HOME SCHEDULING CONSIDERING ENERGY BALANCING 3 Fig. 4. Simplified power system model consisting of generators, utilities aggregators, and customers. agents. In [13], Kisore and Snyder formulated a Stackelberg game to model te competition between te customers and te retailers for energy load controlling. In [21], Ramcurn et al. designed te control mecanism for green energy considering te feedback between te autonomous energy storage system and te green energy supplier operation. In [22], Kok et al. compared several existing tecniques to use te end-user feedback in smart grids, including automated decentralized control of distributed generation and demand response and control for grid stability and islanding operation. In contrast to tese works, our proposed electricity market model incorporates game teory into te feedback loop to model te competition at bot te market and community levels. To te best of our knowledge, tis paper presents te first study of te impact of smart ome sceduling to electricity market. A bi-level model is proposed, wic takes into consideration smart ome sceduling and competitions among customers at te community level and among multiple communities at te market level. Our contributions are listed as follows. 1) Tis paper is te first work addressing te impact of smart ome sceduling to te electricity market. 2) A bi-level game is formulated, were eac customer competes to minimize its individual monetary cost in te community-level game and eac aggregator competes to minimize te monetary cost of its community in te market-level game. Te bidirectional interaction between te market level and te community level is also modeled. 3) To solve te game formulation, an energy demand partition-based market purcasing algoritm is proposed, and a top-level algoritm to modulate te market purcasing and smart ome sceduling is also proposed. 4) Simulations are conducted using a test case consisting of two utilities and five communities, were eac community contains 400 customers. Te simulation results demonstrate tat comparing wit te tecnique witout smart ome sceduling, te average monetary cost of eac customer is reduced by 31.8% and 34.3% for weekdays and weekends, respectively. Te PAR is reduced by 35.9% and 24.9% for weekdays and weekends, respectively. It is also observed tat te generation is balanced over te time orizon. Te capacity of a power generator is reduced by 29.8% and 24.9% for weekdays and weekends, respectively. Tis paper is organized as follows. In Section II, te preliminaries of te smart ome sceduling infrastructure are presented. In Section III, te proposed electricity market models and corresponding algoritms are described. In Section IV, te results of simulations are presented and analyzed. A summary of work is given in Section V. II. PRELIMINARY A power system consisting of customers, aggregators, utilities, and generators is depicted in Fig. 4. Let te community level refer to te interaction between customers and aggregators, and let te market level refer to te interactions among aggregators, utilities, and generators. A. Community Level 1) Aggregators: Te aggregator provides management over te community. In te community level, te aggregator receives te electricity price from te market and delivers it to te customers. It also collects te energy demand request of eac customer and broadcasts it to all oters. 2) Customers: Te customers are equipped wit smart ome scedulers, wic also excange information wit te aggregator. Te mecanisms of te smart ome sceduler are provided in Section III. Te ome appliances of te customers can generally be divided into tree categories as follows. 1) Te first category contains ome appliances wit multiple power levels tat are automatically scedulable suc as wasing macines, clot driers, plug-in electric veicles (PHEVs), and dis wasers. For tis type of ome appliances, power levels could be adjusted subject to te constraints on start time and deadline, in wic start time is te time point tat a ome appliances can start to work and deadline is te time point tat a ome appliance as to finis working. 2) Te second category contains manually controlled ome appliances suc as TV sets and computers. 3) Te tird category contains ome appliances turned on all day long suc as refrigerators. Te smart ome sceduling tecnique controls tese ome appliances wit different strategies according to teir features.

4 Tis article as been accepted for inclusion in a future issue of tis journal. Content is final as presented, wit te exception of pagination. 4 IEEE SYSTEMS JOURNAL B. Market Level Here, te market activities are discussed, including te trading between utilities and generators and te trading between utilities and aggregators. In terms of te trading between utilities and generators, two types of markets, including forward market and wolesale market [23], are modeled. In different types of markets, te utilities and generators ave a different trading price, wic is also a reference for te utilities to set te selling price to te aggregators. 1) Utilities Versus Generators: Utilities make profits troug purcasing electricity energy from generators and selling it to aggregators. In te forward market, eac utility as a contract wit its local generator, according to wic te utility purcases a certain amount of energy from te local generator wit a fixed total price. Te energy amount is defined as te forward limit. If te requested amount exceeds te forward limit, te utility purcases te rest of te energy demand in te wolesale market, were te price is muc iger. In tat situation, te utility can coose to purcase from eiter te local generator or remote generators according to te locational marginal price (LMP) [24]. 2) Utilities Versus Aggregators: In te trading between utilities and aggregators, an aggregator purcases energy from utilities to satisfy te total energy demand of te community. Among all te available utilities, te aggregator cooses te ones wit te lowest prices to minimize te total monetary cost of te community. Te specific pricing strategy is presented in Section III. III. PROPOSED MODEL AND ALGORITHMS Here, te analytical models in community and market levels are proposed. In terms of smart ome sceduling and market trading, two optimization problems are formulated, respectively, based on wic te bi-level game is developed. A bi-level algoritm consisting of a smart ome sceduling algoritm and a market purcasing algoritm is proposed to solve te optimization problems. Trougout tis paper, te index of communities is denoted by n {1, 2,...,N}, te index of utilities is denoted by m {1, 2,...,M}, and te index of time slots is denoted by {1, 2,...,H}. In te community n,te index of customers is denoted by q {1, 2,...,Q n }. Notations are summarized in Table I. A. Community-Level Model Te community-level model used in tis paper adopts te one from our previous work [25]. For completeness, we include some details as follows. In te community n, te total monetary cost is defined as a convex function of te total load at eac time slot in order to discourage te accumulation of energy load in any single time slot. Tere are various pricing models in existing literature, including te quadratic pricing model in [10], te linear pricing model in [1], te piecewise convex pricing model in [26], and te piecewise linear pricing model provided by Britis Columbia Hydro Corporation [10]. Te quadratic function C,n = a,n L 2,n is adopted in tis paper TABLE I LIST OF NOTATIONS [10]. At te time slot, C,n is te total monetary cost in te community n, L,n is te total energy load, and a,n is te unit energy price, wic converts energy consumption to monetary cost. Among te customers in tis community, te expense is sared based on te individual energy consumption suc tat if te energy consumption of te customer q is l q, at te time slot, te monetary cost is C,n l q, /L,n. For te customer q, denote te set of ome appliances by A q. For ome appliance i A q, denote te set of power levels by E i. At te time slot, te ome appliance i A q works in te power level x i E i, wic denotes te energy consumption in a single time slot. Te ome appliance i is operated between te earliest start time ts i and te latest end time te i, wereas te required energy consumption is w i. Since eac customer aims to minimize its individual monetary cost, te optimization problem of customer q in community n is formulated as [25] min B. Market-Level Model s.t. H =0 te i C,n l q, L,n =ts i x i w i x i = l q, i A q Q n l q, = L,n q=1 x i E i. (1) Te market competition is modeled ere. At eac time slot, te aggregators purcase electricity energy from te utilities based on te energy demand of te customers. 1) Market Operation of Utility: Te selling pricing of utilities is based on te buying price from te generators. For tis reason, te revenue of te utilities could be divided into two parts, including te estimated cost and te expected profit. For te utility m, wen te amount of energy sold is equal to te

5 Tis article as been accepted for inclusion in a future issue of tis journal. Content is final as presented, wit te exception of pagination. LIU et al.: GAME-THEORETIC SMART HOME SCHEDULING CONSIDERING ENERGY BALANCING 5 C. Game Formulation Here, te competitions in te community and market levels are modeled as a bi-level game. At te community level, eac customer competes to reduce its individual monetary cost troug selecting te power levels. At te market level, eac aggregator competes to reduce te total monetary cost of its community troug planning purcasing from te utilities. Te complete game model is formulated as follows. Bi-Level Game Model Fig. 5. Revenue and local buying cost of utility m versus energy demand corresponding to (2). forward limit d ref m,, it is expected to make a profit as muc as b ref m,, wic is called te reference profit. As sown in Fig. 5, p m is te buying cost on te forward contract, and a m(d,m) 2 is te estimated buying cost wen te amount of purcased energy exceeds te forward limit. Given te total energy demand d,m, te pricing function of utility m is defined as p ref d,mb Rm m + m, = a m(d,m) 2 + m, d ref, d,m d ref m, (2), d,m >d ref m,. ref d,mbm, d ref m, In order to make Rm a continuous function of d,m,setp m = a m(d ref m, )2. Wen energy demand d,m d ref m,, te utility m could purcase tis amount of energy in te forward market and sell it to te aggregators. Te buying cost for te utility m to keep te forward contract is p m wit te expected profit of ref d,mbm, /dref m,. Wen d,m >d ref m,, te utility m estimates te buying cost as a m(d,m) 2, wic is te generation cost of te ref local generator. Te expected profit is d,mbm, /dref m,. Wile te buying price from te generators witin te forward limit is always p m, beyond te forward limit, te trading between utilities and generators is operated based on te LMP wit discrete bidding as discussed in [24]. Eac generator posts a price table based on te incremental price. A generator needs to satisfy te total request of te local utility before supplying te request of utilities in remote areas. Te details are provided in [24, C ]. 2) Market Operation of Aggregator: In te market level, aggregators purcase electricity energy from te utilities to meet te energy demand of teir communities. Te amount of energy purcased by aggregator n from utility m is denoted by d n,m suc tat d,m = N n=1 d n,m. Similar to witin a community, if multiple aggregators purcase from utility m, tey sare te total expense proportionally based on te trading amount wit m. Te total demand of an aggregator is denoted by d n,, were d n, = M d n,m. Wit te aforementioned definitions, te monetary cost minimization problem is formulated as min s.t. d n,m N n=1 d n,m R m d n,m = d n,. (3) Community Level: 1) Players: Customers. 2) Payoff functions: H =0 3) Optimization problem: min s.t. H =0 te i C,n l k, L,n C,n l q, L,n =ts i x i = w i x i = l q, i A q Q n l q, = L,n q=1 were C,n = a,n L 2,n 4) Decision Variables: x i Market Level: x i E i 1) Players: Aggregators. 2) Payoff functions: M (d n,m/ N 3) Optimization problem: min M d n,m N n=1 d n,m R m m, d ref m, n=1 d n,m)r m s.t. M d n,m = d n, were p ref d,mbm, Rm m +, d,m d ref d = ref m, m, ( ) a 2 ref d,mb m d,m +, d,m >d ref m, 4) Decision Variables: d n,m As mentioned in Section II-A, eac customer aims to reduce te electricity bill troug assigning te working power levels of te ome appliances given te electricity price in te community level. Note tat te sceduling of eac customer impacts te electricity bills of eac oter. Tis naturally leads to te competition between tem modeled by te communitylevel game. Similarly, eac aggregator determines te energy purcasing from eac utility to minimize te total monetary

6 Tis article as been accepted for inclusion in a future issue of tis journal. Content is final as presented, wit te exception of pagination. 6 IEEE SYSTEMS JOURNAL solution of d n,m tat minimizes te total monetary cost M R m due to te convexity of te problem. 2) Step 2: A closed-form solution of te pure strategy Nas equilibrium is sown for te aforementioned problem. In order to provide a closed-form solution, we solve te market-level game based on te assumptions as follows for simplicity. a) Te forward limit is set as d ref m, =0. Witout loss of generality, we can andle te problem similarly wen d ref m, 0. b) At time slot, te two aggregators ave te same energy demand tat d 1, = d 2, = = d N,. Based on te aforementioned assumptions, eac aggregator aims to minimize te individual monetary cost. However, one can sow tat te solution of problem Fig. 6. Bi-level game model. cost of te local community. It is formulated as a game since te purcasing of eac aggregator impacts eac oter as well. Te two levels interact based on te electricity pricing and energy demand. Te electricity pricing in eac community is determined by te aggregator resulting from te competition of te market-level game. In return, te market-level game is based on te real-time energy demand in eac community, wic is te result of te competition in te community-level game. For eac level, a pure strategy Nas equilibrium exists. Te Nas equilibrium of te community-level game as been proved by several existing works, including [10] and [27]. In tis paper, we prove te existence of Nas equilibrium of our market-level game in two steps. In te first step, we sow tat tere exists a global optimal solution of d n,m, wic minimizes te total monetary cost of all te aggregators. In te second step, we sow a closed-form solution of te pure strategy Nas equilibrium for our problem. 1) Step 1: Tere exists a global optimal solution of d n,m tat minimizes te total monetary cost of all te aggregators. In our formulation, te aggregators determine te energy purcasing d n,m to minimize te individual monetary cost. Given te energy demand of eac community at eac time slot, te monetary cost of eac aggregator m is M (d n,m/ N n=1 d n,m)r m. Te total monetary cost of all te aggregators is calculated as N n=1 d n,m N n=1 d n,m R m = R m, (4) wile d n,m is constrained by d n,m = d n,. (5) Note tat R m is a convex function of d n,m, te linear combination of multiple suc functions is also convex. Since te constraint conditions are linear, tere exists a min s.t. R m d n,m = d n, (6) is a Nas equilibrium of te market-level game. In order to simplify te analytical presentation, assume N =2and M =2. However, te solution can be generalized to any N and M. Using Lagrangian relaxation, te problem (6) is rewritten as min a 1 ( d 1,1 +d ) 2+a ( 2,1 2 d 1,2 +d 2 2,2) + λ 1 ( d 1, d 1,1 d 1,2) +λ2 ( d 2, d 2,1 d 2,2). (7) It is easy to derive d 1,1 + d 2,1 = a ( 2 d 1, + d2, ) a 1 + a 2 d 1,2 + d 2,2 = a ( 1 d 1, + d2, ) a 1 + a 2 d 1,1 + d 1,2 = d 1, d 2,1 + d 2,2 = d 2,. (8) Tus, te energy purcasing d n,m can minimize te total monetary cost as long as te constraints (8) are satisfied. A possible solution is d 1,1 = d 2,1 = a ( 2 d 1, + d2, ) 2 ( a 1 + ) a 2 d 1,2 = d 2,2 = a ( 1 d 1, + d2, ) 2 ( a 1 + ). (9) a 2 Wit tis solution, te individual monetary cost of eac aggregator is also minimized. Suppose tat aggregator 1 aims to cange te purcasing amount d 1,1 and d 1,2 to

7 Tis article as been accepted for inclusion in a future issue of tis journal. Content is final as presented, wit te exception of pagination. LIU et al.: GAME-THEORETIC SMART HOME SCHEDULING CONSIDERING ENERGY BALANCING 7 d 1,1+Δd and d 1,2 Δd, respectively. Tus, te individual monetary costs before and after making tis cange are Cost 1 = a ( 1 d 1,1 +d ) 2,1 d 1,1 +a ( 2 d 1,2 +d ) 2,2 d 1,2 (10) Cost 1 = a ( 1 d 1,1 +d 2,1+Δd )( d 1,1+Δd ) + a ( 2 d 1,2 +d 2,2 Δd )( d 1,2 Δd ) (11) respectively. Troug canging te energy purcase by Δd, te individual monetary cost is increased by Cost 1 Cost 1 = ( a 1 +a 2) Δd 2 +Δd ( a 1d 2,1 a 2d ) 2,2 +2Δd(a 1d 1,1 a 2d 1,2) = ( a 1 + a 2) Δd 2 > 0. (12) Tus, eac aggregator cannot unilaterally decrease te individual monetary cost in tis situation. Tus, (d 1,1,d 1,2,d 2,1,d 2,2) is a pure strategy Nas equilibrium of te market-level game. One can similarly extend tis proof for any value of N and M. D. Community-Level Algoritm At te community level, te customers scedule teir ome appliances in order to minimize teir individual monetary costs. Given te electricity price, eac customer solves te optimization problem (1) to set power levels and operation time of eac ome appliance. Te dynamic programming algoritms proposed in our previous work [25] are used to solve te smart ome sceduling problems among multiple customers. E. Market-Level Algoritm At te market level, eac aggregator purcases electricity energy from te utilities in order to minimize te monetary cost and satisfy te total demand of its community. Since te total selling price of a utility is based on te total energy demand, te trading amount of one aggregator wit a utility influences te monetary cost of te oter aggregators. A distributed market purcasing algoritm is proposed to provide te solution of purcasing for eac aggregator. Wit te feedback from te utilities, te aggregator n computes d n,m tat minimizes te monetary cost of its own community assuming te purcasing of te oter aggregators is fixed. Tis is repeated until tere is no cange in te monetary costs of te aggregators. For eac utility, te pricing function R m is a piecewise convex function suc tat it is a quadratic function wen te total energy demand exceeds te forward limit, and it is linear oterwise. Tis makes te objective function of eac aggregator more complex. To andle te optimization problem of aggregators flexibly, an energy demand partition tecnique is used in te market purcasing algoritm. Te energy demand partition-based market purcasing algoritm is given in Algoritm 1. Witin eac iteration, te aggregator n divides te total demand d n, into K n pieces, were eac piece is d n, /K n. Te aggregator n maintains [d n,1,d n,2,...,d n,m ] as te decision array. Eac time, te aggregator cooses a utility to purcase te energy piece k {1, 2,...,K n } to minimize te current monetary cost. Assuming tat te aggregator n purcases te kt piece of energy from utility m, te pricing of utility m is canged according to (2). Tus, te aggregator n cooses te current ceapest utility to purcase te (k +1)t piece of energy. Tis is repeated until te total amount of energy demand is placed. A complete description of te algoritm is presented in Algoritm 1. In order to implement te aforementioned procedure, we introduce a bidding array [d n,1,d n,2,...,d n,m ] and temporary monetary cost [tc 1, tc 2,...,tc M ] as temporary variables. Te algoritm initializes in lines 1 and 2. In line 7, te aggregator places te energy piece k to eac utility and obtains te corresponding temporary monetary cost tc m in line 8. In line 11, te aggregator cooses te utility ˆm wit te minimum temporary monetary cost to purcase te energy piece k. Subsequently, te decision array is updated in line 12. Algoritm 1 Market Purcasing Algoritm 1: Initialize d n,m =0,d n,m = d n,m 2: Utilities initialize price 3: loop 4: for n =1:N do 5: for k =1:K n do 6: for m =1:M do 7: d n,m = d n,m +(d n, /K n ) 8: Get temporary monetary cost tc m = M i=1 (d n,i/ N n=1 d n,i)r i from utilities according to (2) and (3) 9: d n,m = d n,m 10: end for 11: ˆm =argmin m} m 12: d n, ˆm = d n, ˆm 13: end for 14: end for 15: if No cange in monetary costs ten 16: Break loop 17: end if 18: end loop F. Top-Level Algoritm Wile te algoritms are provided to solve te smart ome sceduling problem and te market purcasing problem, respectively, te bidirectional influence between te levels sould be considered. Te electricity price is needed for te communities to conduct smart ome sceduling, and te energy demand is needed for te trading operation in te market. A top-level algoritm is proposed to link smart ome sceduling and market purcasing togeter, wic is given in Algoritm 2. In line 1, a,n is initialized. From line 3 to line 5, te dynamic programming algoritm in [25] is called to solve te smart ome sceduling problem under te current pricing. In line 6, Algoritm 1 is called to solve te market purcasing problem. Since te aggregators can only obtain te total monetary cost from te market, it is converted into unit price in line 7. Wen te energy load of community n is L,n and te total monetary cost is C,n at time slot, a,n is updated as

8 Tis article as been accepted for inclusion in a future issue of tis journal. Content is final as presented, wit te exception of pagination. 8 IEEE SYSTEMS JOURNAL TABLE II DAILY ENERGY CONSUMPTION AND RUN TIME OF AUTOMATICALLY CONTROLLED HOME APPLIANCES Fig. 7. Proposed algoritm consists of te smart ome sceduling algoritm in te community level and te market purcasing algoritm in te market level. Te two levels are linked togeter as a loop to emulate te bidirectional influence of eac oter. a,n = C,n /L 2,n, wic is to be used in te next iteration. Te complete algoritm flow is sown in Fig. 7. Algoritm 2 Top-Level Algoritm 1: Initialize community level unit energy price a,n 2: loop 3: for n =1:N do 4: Call Dynamic Programming Algoritm in [25] to compute sceduling in community n 5: end for 6: Call Algoritm 1 to get te pricing in te market 7: Update community level pricing according to a,n = C,n /L 2,n 8: if Not converging ten 9: Continue 10: else 11: Exit and keep te current solution 12: end if 13: end loop IV. CASE STUDY Here, simulations are conducted, and te impact of smart omes to te electricity market is analyzed. A. Simulation Setup In our generated bencmark, tere are two utilities and five communities, were eac community consists of 400 customers. Eac customer is equipped wit bot automatically controlled ome appliances and manually controlled ome appliances. Te daily energy consumption and execution duration of automatically controlled ome appliances are given in Table II, wic is obtained from te data provided by [3], [10], [28], and [29]. In te simulation, te execution period and energy consumption are randomly cosen from te corresponding Fig. 8. Background consumption on weekdays and weekends, wic are created by te manually controlled ome appliances. ranges provided in te table wit a uniform distribution. For eac customer, te energy consumption of te manually controlled ome appliances is fixed, wereas te energy consumption of automatically controlled ome appliances is sceduled by te smart sceduling algoritm. Since te energy consumption profile created by te manually controlled ome appliances is not cangeable, it is called background energy consumption. Two different scenarios, including weekdays and weekends, are considered in te bencmark. Generally speaking, people use te ome appliances more on weekends tan weekdays. For tis reason, in te simulation, more ome appliances are operated on weekends, and te execution durations are longer tan weekdays. Fig. 8 depicts te average background energy consumption of one customer on weekdays and weekends, respectively. Tey are generated according to [3], [28], and [30]. Te peak energy consumption appears from evening to nigt wen most people are off work at ome. Tere is also a lower peak energy consumption during te daytime around te noon. Te energy consumption starts to increase from te morning and reaces te peak around te noon. For eac utility, te parameters in (2) are set according to te following rules. 1) Te purcasing cost p m witin te forward limit is set according to te average energy demand at eac time slot and te generation cost. 2) Te purcasing price a m beyond te forward limit is set according to te generation cost. For utility 1, te parameters are set as p 1 = $30,b ref 1, = $10, and

9 Tis article as been accepted for inclusion in a future issue of tis journal. Content is final as presented, wit te exception of pagination. LIU et al.: GAME-THEORETIC SMART HOME SCHEDULING CONSIDERING ENERGY BALANCING 9 Fig. 9. Average energy consumption of a customer on weekdays. Fig. 11. Energy generation of generator 1 on weekdays. Fig. 12. Energy generation of generator 2 on weekdays. Fig. 10. Average monetary cost of eac customer on weekdays. a 1 =0.12$/kW 2. For utility 2, te parameters are set as p 2 = $33,b ref 2, = $10, and a 2 =0.13$/kW 2. Te sceduling time is 24 from 12 A.M. of te current day to 12 A.M. next day, wic is divided into 15-min time slots. Te simulation results for weekdays are presented as follows. Te average energy consumption profile for a customer is sown in Fig. 9. Wit smart ome sceduling, te energy consumption is balanced over te time orizon. Tis reduces te PAR by 35.9%, from 2.23 to 1.43, wic is also te reduction rate of te peak of te total generation requirement. Note tat te monetary cost at a time slot will be even iger as te energy consumption accumulates. Wen smart ome sceduling is applied, te energy consumption of te automatically controlled ome appliances is sceduled at te time slots witout eavy background load. Tus, te energy load is sifted off te peak, wic results in balanced energy usage. As sown in Fig. 10, te average monetary cost of eac customer is also evenly distributed due to te balancing of te energy consumption. Te monetary cost of all te customers over te wole time orizon is reduced by 31.8%, from $5.43 to $3.71. Since te total energy cost is independent of smart ome sceduling, te reduction of total monetary is due to te mitigation of te ig purcasing price in te market. Te energy generation of te two generators over te time orizon are sown in Figs. 11 and 12. Te generated energy is balanced among all time slots, wic demonstrates tat smart ome sceduling can implicitly elp balance te energy generation. As obtained from Figs. 11 and 12, te peak generation of generator 1 is reduced by 36.0%, from 271 to 174 kw, and te peak generation of generator 2 is reduced by 29.8%, from 272 to 191 kw. Our iterative algoritm is effective in balancing te energy consumption from iteration to iteration. As an example, te energy consumption of community 1 in four consecutive iterations is summarized in Fig. 13, wic clearly sows tat te energy consumption becomes more and more balanced during te optimization.

10 Tis article as been accepted for inclusion in a future issue of tis journal. Content is final as presented, wit te exception of pagination. 10 IEEE SYSTEMS JOURNAL Fig. 13. Total energy consumption of community 1 in four consecutive iterations. Fig. 14. Average energy consumption of te customers on weekends. Fig. 16. Energy generation of generator 1 on weekends. Fig. 15. Average monetary cost of eac customer on weekends. B. Results for Weekends Fig. 14 sows te average energy consumption of eac customer wit and witout smart ome sceduling, respectively. Similar to te result for weekdays, smart ome sceduling elps balance te energy load. However, comparing wit Fig. 9, te total energy consumption is increased because te ome appliances are operated longer. On weekends, te PAR is 1.23 wit smart ome sceduling, wereas it is 1.62 witout smart ome Fig. 17. Energy generation of generator 2 on weekends. sceduling, wic is a 24.9% reduction. As sown in Fig. 15, on weekends, te total monetary cost of customer is reduced by 34.3%, from $7.10 to $4.66, by smart ome sceduling. Te energy generation of te two generators on weekends is sown in Figs. 16 and 17. Similar to te results on weekdays, te generation is more balanced resulting from smart ome sceduling. For generator 1, te peak generation is reduced by 24.1%, from 253 to 192 kw. For generator 2, te peak generation is reduced by 24.9%, from 253 to 190 kw.

11 Tis article as been accepted for inclusion in a future issue of tis journal. Content is final as presented, wit te exception of pagination. LIU et al.: GAME-THEORETIC SMART HOME SCHEDULING CONSIDERING ENERGY BALANCING 11 V. C ONCLUSION In a smart community infrastructure tat consists of multiple smart omes, smart controllers scedule various ome appliances to balance energy consumption and reduce te electricity bills of customers. Tis paper analyzes te impact of te smart ome sceduling to te electricity market. It also proposes a new smart-ome-driven bi-level market model were te customers scedule ome appliances for bill reduction at te community level, wereas aggregators minimize te energy purcasing expense from utilities at te market level, bot of wic consider te smart ome sceduling impacts. A gameteoretic algoritm is proposed to solve tis formulation, wic andles te bidirectional influence between te community level and te market level. As demonstrated by simulation results, te average monetary cost of customers is reduced by 31.8% on weekdays and by 34.3% on weekends. In addition, te PAR for te energy consumption is reduced by 35.9% on weekdays and by 24.9% on weekends. Furtermore, te peak generation requirement can be reduced by 29.8% on weekdays and by 24.9% on weekends. REFERENCES [1] X. Cen, T. Wei, and S. Hu, Uncertainty-aware ouseold appliance sceduling considering dynamic electricity pricing in smart ome, IEEE Trans. Smart Grid, vol. 4, no. 2, pp , Jun [2] A. Mosenian-Rad and A. Leon-Garcia, Optimal residential load control wit price prediction in real-time electricity pricing environments, IEEE Trans. Smart Grid, vol. 1, no. 2, pp , Sep [3] [Online]. Available: ttp:// [4] [Online]. Available: ttp:// [5] T. Kim and H. Poor, Sceduling power consumption wit price uncertainty, IEEE Trans. Smart Grid,vol.2,no.3,pp ,Sep [6] L. Liu, X. Yang, H. Huang, and S. Hu, Smart ome sceduling for cost reduction and its implementation on FPGA, J. Circuit, Syst. Comput., vol. 24, no. 4, pp. 1 15, [7] K. Sou, J. Weimer, H. Sandberg, and K. Joansson, Sceduling smart ome appliances using mixed integer linear programming, in Proc. IEEE CDC-ECC, 2011, pp [8] K. Tsui and S. Can, Demand response optimization for smart ome sceduling under real-time pricing, IEEE Trans. Smart Grid, vol. 3, no. 4, pp , Dec [9] A. Mosenian-Rad, V. Wong, J. Jatskevic, and R. Scober, Optimal and autonomous incentive-based energy consumption sceduling algoritm for smart grid, in Proc. ISGT, 2010, pp [10] A. Mosenian-Rad, V. Wong, J. Jatskevic, R. Scober, and A. Leon-Garcia, Autonomous demand-side management based on game-teoretic energy consumption sceduling for te future smart grid, IEEE Trans. Smart Grid, vol. 1, no. 3, pp , Dec [11] C. Ibars, M. Navarro, and L. Giupponi, Distributed demand management in smart grid wit a congestion game, in Proc. IEEE Int. Conf. SmartGridComm, 2010, pp [12] C. Wu, A. Mosenian-Rad, and J. Huang, Veicle-to-aggregator interac tion game, IEEE Trans. Smart Grid, vol. 3,no.1,pp ,Mar [13] S. Kisore and L. Snyder, An innovative RTP-based residential power sceduling sceme for smart grids, in Proc. IEEE ICASSP, 2011, pp [14] S. Bu, F. Yu, and P. Liu, Dynamic pricing for demand-side management in te smart grid, in Proc. IEEE Online Conf. GreenCom, 2011, pp [15] T. Aigner, H. Faramand, and T. Gjengedal, Modeling te nortern European electricity market, in Proc. IEEE Power Energy Soc. Gen. Meet., 2012, pp [16] G. Knezevic, K. Fekete, and S. Nikolovski, Applying agent-based modeling to electricity market simulation, in Proc. Int. Conv. Inf. Commun. Tecnol. Electron. MIPRO, 2010, pp [17] M. Hassan, M. Abdulla, A. Arifin, F. Hussin, and M. Majid, Electricity market models in restructured electricity supply industry, in Proc. IEEE Int. PECon, 2008, pp [18] E. Bompard, Y. Ma, R. Napoli, G. Gross, and T. Guler, Comparative analysis of game teory models for assessing te performances of network constrained electricity markets, IET Gener., Transmiss. Distrib., vol. 4, no. 3, pp , [19] J. Zang, J. Fuller, and S. Eledli, A stocastic programming model for a day-aead electricity market wit real-time reserve sortage pricing, IEEE Trans. Power Syst., vol. 25, no. 2, pp , May [20] T. Voice, P. Vytelingum, S. D. Ramcurn, A. Rogers, and N. R. Jennings, Decentralised control of micro-storage in te smart grid. in Proc. AAAI Conf. Artif. Intell., 2011, pp [21] S. D. Ramcurn, P. Vytelingum, A. Rogers, and N. R. Jennings, Agentbased omeostatic control for green energy in te smart grid, ACM Trans. Intell. Syst. Tecnol., vol. 2, no. 4, p. 35, Jul [22] K. KoK et al., Smart ouses for a smart grid, in Proc. Int. Conf. Exib. Elect. Distrib., Part 1, 2009, pp [23] X. Guan, J. Wu, F. Gao, and G. Sun, Optimization-based generation asset allocation for forward and spot markets, IEEE Trans. Power Syst., vol. 23, no. 4, pp , Nov [24] D. Kirscen and G. Strbac, Fundamentals of Power System Economics. Hoboken, NJ, USA: Wiley, [25] L. Liu, Y. Zou, Y. Liu, and S. Hu, Dynamic programming based game teoretic algoritm for economical multi-user smart ome sceduling, in Proc. IEEE Int. MWSCAS, 2014, pp [26] S. Caron and G. Kesidis, Incentive-based energy consumption sceduling algoritms for te smart grid, in Proc. IEEE Int. Conf. SmartGridComm, Oct 2010, pp [27] C. Wu, H. Mosenian-Rad, J. Huang, and A. Wang, Demand side management for wind power integration in microgrid using dynamic potential game teory, in Proc. IEEE GC Wksps, 2011, pp [28] [Online]. Available: ttp:// [29] K. Herter, P. McAuliffe, and A. Rosenfeld, Observed temperature effects on ourly residential electric load reduction in response to an experimental critical peak pricing tariff, U.S. Dept Energy, Ernest Orlando Lawrence Berkeley Nat. Lab., Berkeley, CA, USA, [30] P. Asare et al., Real time pricing of electric power, Scool Elect. Eng., Purdue University, West Lafayette, IN, USA, Yang Liu received te B.S. degree from te Huazong University of Science and Tecnology, Wuan, Cina, in He is currently working toward te P.D. degree in electrical engineering at Micigan Tecnological University, Hougton, MI, USA. His researc focuses on smart ome systems, cyber pysical systems, and big data analysis. Siyan Hu (SM 10) received te P.D. degree in computer engineering from Texas A&M University, College Station, TX, USA, in He is currently an Associate Professor wit te Department of Electrical and Computer Engineering, Micigan Tecnological University, Hougton, MI, USA. He was a Visiting Professor at IBM Researc (Austin) during summer of His researc interests are in te area of computer-aided design of VLSI circuits, cyber pysical systems, and smart ome cybersecurity, were e as publised over 80 tecnical papers in refereed journals and conferences. Dr. Hu as served as General Cair, Tecnical Program Committee (TPC) Cair, TPC Subcommittee Cair, Session Cair, and TPC Member for various conferences for more tan 70 times. He is an Associate Editor or Guest Editor of te IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS PART II, IEEE TRANSACTIONS ON COMPUTERS, IEEE TRANSACTIONS ON COMPUTER- AIDED DESIGN, IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS,and ACM Transactions on Embedded Computing Systems. He was a recipient of te ACM SIGDA Ricard Newton DAC Scolarsip (as te Faculty Advisor), te Faculty Invitation Fellowsip from te Japan Society for te Promotion of Science, and te National Science Foundation CAREER Award.

12 Tis article as been accepted for inclusion in a future issue of tis journal. Content is final as presented, wit te exception of pagination. 12 IEEE SYSTEMS JOURNAL Han Huang (SM 08) received te P.D. degree from New York University Polytecnic Scool of Engineering, Brooklyn, NY, USA, in He is currently te Deputy Director of te Smart Grid Researc Department, State Grid Energy Researc Institute, State Grid Corporation of Cina, Beijing, Cina. He as publised various papers in books, journals, conferences, and worksops. His researc interests include smart grids, power systems, and power electronics. Rajiv Ranjan (M 08) received te P.D. degree in engineering from te University of Melbourne, Parkville, Australia, in He is a Researc Scientist and a Julius Fellow at te Computational Informatics Division, Commonwealt Scientific and Industrial Researc Organisation (CSIRO; formerly known as CSIRO ICT Centre). He as publised 62 scientific peer-reviewed papers (7 books, 25 journals, 25 conferences, and 5 book capters). His expertise is in datacenter cloud computing, application provisioning, and performance optimization. Dr. Ranjan as been invited to serve as te Guest Editor for leading distributed systems journals, including te IEEE TRANSACTIONS ON CLOUD COMPUTING, Future Generation Computer Systems, andsoftware Practice and Experience. One of is papers was in 2011 s top computer science journal, i.e., te IEEE COMMUNICATION SURVEYS AND TUTORIALS. His -index is 20, wit a lifetime citation count of more tan 1660 (Google Scolar). His papers ave also received more tan 140 ISI citations. Seventy percent of is journal papers and 60% of conference papers ave been A /A ranked ERA publication. Albert Y. Zomaya (F 04) received te P.D. degree from te Department of Automatic Control and Systems Engineering, Seffield University in Seffield, U.K. He is currently te Cair Professor of Hig Performance Computing and Networking at te Scool of Information Tecnologies, Te University of Sydney, Sydney, Australia. He is also te Director of te Centre for Distributed and Hig Performance Computing, wic was establised in late He as publised more tan 500 scientific papers and articles and is te autor, coautor, or editor of more tan 20 books. His researc interests are in te areas of parallel and distributed computing and complex systems. Prof. Zomaya is a Cartered Engineer and a Fellow of te American Association for te Advancement of Science and Te Institution of Engineering and Tecnology (U.K.). He served as te Editor in Cief of te IEEE TRANS- ACTIONS ON COMPUTERS ( ). He currently serves as te Editorin-Cief of Springer s Scalable Computing and is an Associate Editor of 22 leading journals, suc as te ACM Computing Surveys, IEEE TRANSACTIONS ON COMPUTATIONAL SOCIAL SYSTEMS, IEEE TRANSACTIONS ON CLOUD COMPUTING, andjournal of Parallel and Distributed Computing. Hewasa recipient of te IEEE Tecnical Committee on Parallel Processing Outstanding Service Award in 2011, te IEEE Tecnical Committee on Scalable Computing Medal for Excellence in Scalable Computing in 2011, and te IEEE Computer Society Tecnical Acievement Award in Lize Wang (SM 09) received te B.Eng. degree (wit onors) and te M.Eng. degree from Tsingua University, Beijing, Cina, and te Dr. Ing. degree (magna cum laude) in applied computer science from te University Karlsrue (now Karlsrue Institute of Tecnology), Karlsrue, Germany. He is a 100-Talent Program Professor at te Institute of Remote Sensing and Digital Eart, Cinese Academy of Sciences, Beijing, and a CuTian Cair Professor at te Scool of Computer Science, Cina University of Geosciences, Wuan, Cina. Prof. Wang is a Fellow of Te Institution of Engineering and Tecnology and te Britis Computer Society.