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Confidentiality/date line: 13pt Arial Regular, white Maximum length: 1 line Information separated by vertical strokes, with two spaces on either side Disclaimer information may also be appear in this area. Place flush left, aligned at bottom, 8-10pt Arial Regular, white Indications in green = Live content Indications in white = Edit in master Indications in blue = Locked elements Indications in black = Optional elements Copyright: 10pt Arial Regular, white EE5900 Advanced Embedded System For Smart Infrastructure Electricity Market With Smart Home Integration

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Smart Home Scheduling Basic Idea Pricing for one-day ahead time period Prefer using cheap time interval 2

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Smart Home Scheduling System 3 Power flow Internet Control flow

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Home Appliances in Smart Home Not schedulableRestrictively schedulable Fully schedulable 4

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Variable Frequency Drive 10 cents/kwh 5 cents / kwh 5 kwh 10 kwh Power Powerr Time 12 123 (a) (b) 10 cents/kwh 5 cents / kwh cost = 10 kwh * 10 cents/kwh = 100 cents cost = 5 kwh * 10 cents/kwh + 5 kwh * 5 cents/kwh = 75 cents 5 350 W Power level 500 W 820 W 1350 W

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Smart Home Scheduling Given the pricing curve, to decide –when to launch a home appliance –at what frequency –for how long –subject to scheduling constraints such as start time and end time Targets –Reduce monetary cost of each user –Reduce peak to average ratio of grid energy usage From the utility point of view –Change the pricing curve to guide the usage of grid energy –Result in balanced usage of energy, and thus balanced generation from power plant We will describe the algorithm later. Assume that we have it, then 6

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Key Contribution: What Are We Modeling? Given a pricing curve at the aggregator (community) side, customers will schedule home appliances (i.e., distribute grid energy usage over time intervals) using the smart home scheduling algorithm For each community, there is load distribution over time intervals All the communities will send energy demands per time interval to utilities Utility companies will set their own pricing per time interval. The aggregators can choose to buy from whom, when and how much Utility companies will compete with each other in deciding pricing Aggregators will compete with each other in deciding where to buy When all utilities and aggregators make up the decisions, each aggregator modifies the pricing curve at the aggregator side Repeat until converging to equilibrium 7

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Electricity Market We will model them in a bottom up fashion 8

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Single User Smart Home Scheduling Generators Utility Companies Aggregators Customers Home Appliances 9

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Dynamic Programming For Scheduling Single Appliance 0 t1t2t3t4 Time Schedule the home appliance from the first time interval Energy 10

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Solution Characterization For a solution in time slot i, energy consumption e and cost c uniquely characterize its state Time slot iTime slot i+1 (e i, c i )(e i+1, c i+1 ) 11

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Dynamic Programming For a solution in time slot i, energy consumption e and cost c uniquely characterize its state Time slot iTime slot i+1 (e i, c i )(e i+1, c i+1 ) 12

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Solution Pruning For an time interval, solution (e 1, c 1 ) will dominate solution (e 2, c 2 ), if and only if e 1 ≥e 2 and c 1 ≤c 2. Dominated solutions will be pruned. Time interval (15, 20) (15, 25) (11, 22) 13

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Dynamic Programming Based Appliance Optimization (1,2) (2,4) (3,6) (1,1) (2,2) (3,3) 0 t1 t2 (6, 9) (5, 8) (4, 7) (5, 7) (4, 6) (3, 5) (4, 5) (3, 4) (2, 3) (0,0) (3, 3) (2, 2) (1, 1) –# of distinct power levels = k –# time slots = m Runtime : Price Time Dynamic Programming returns the optimal solution Power levels {1, 2, 3} 14

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Scheduling Multiple Appliances for One User Determine Scheduling Appliances Order Schedule Current Appliance Update Energy Upper Bound of Each Time Interval An appliance Schedule Appliances Not all the appliances processed All appliances processed 15

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Multiple User Smart Home Scheduling Generators Utility Companies Aggregators Customers Home Appliances 16

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Motivation Customer 1 Customer 2 Customer 3............. Game theory is used to handle the interactions among customers. 17

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Game Theory For every player in a game, there is a set of strategies and a payoff function, which is the profit of the player. Each player chooses from a set of strategies in order to maximize its payoff. When no player can increase its payoff without decreasing the payoffs of others, Nash Equilibrium is reached. In our problem, a customer is a player, the strategy is the dynamic programming based scheduling, payoff function is the negative of the payment of each customer. 18

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An Example of Equilibrium 19

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Game Formulation at Community Level Players: All the customers in the community Strategy: Scheduling the appliances of all customers to maximize payoff while the scheduling constraints are satisfied 20

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Game Theory Based Multiple User Scheduling Each user schedules their own appliances separately All users share information with each other Each user reschedules their own appliances separately Schedule Converge Yes No 21

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Dynamic Pricing From ComED Illinois Corporation 22 How do we set unit price?

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Load Based Pricing Per Time Interval In a local community, when the total load over all customers is L h, the total cost (price) is approximately C h =a h L h 2 at time interval h If l h,j denotes the load of customer j, the customer j pays l h,j ·C h /L h How to decide the constant factor a h ? 23

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Top Level Generators Utility Companies Aggregators Customers Home Appliances 24

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Electricity Market Forward Market Whole Sale Market Generator Utility Aggregators Fixed Amount Fixed Cost Cheap Price Utility AggregatorsGenerator Bid LMP 25

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An Example Suppose that a utility has a contract with a generator that the generator can provide the utility 100MWh every hour with the price 1 ￠ /kWh. The utility company can sell this 100MWh at a price 1.2 ￠ /kWh. When the demand received by the utility exceeds 100MWh, the utility needs extra amount of energy with a much higher cost and sell it with a much higher price. The 100MWh in the contract is called forward limit. 26

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Generator Model Within forward limit, electricity can be generated with low price in power plant Beyond forward limit, it costs much higher to generate electricity 27 Forward limit (kWh) Total Price ($)

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Utility Buying 28 Forward limit ( kWh ) ($) Forward limit ( kWh ) ($) Forward limit ( kWh ) ($) Local generatorRemote generator 1Remote generator 2 Utility sign in a forward contract with local generator LMP Not enough Waste Over buying

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Illustration of LMP 29 Local generator 10 ￠ /kWh, 100kWh Remote generator 1 5 ￠ /kWh, 50kWh Remote generator 2 8 ￠ /kWh, 100kWh Utility, 100kWh 50kWh

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Market Level Modeling and Optimization Generators Utility Companies Aggregators Customers Home Appliances 30

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Strategy of Utilities and Aggregators Utilities Aggregators Adjust price to attract more demand Decide purchase from each utility to minimize payment Price Demand Conducted in each time slot 31

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Illustration of Our Model 32 Forward limit (kWh) ($) Generator Utility Utility designs the pricing model according to the generator model. Utility will never get negative profit as long as there is some electricity sold.

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Iterative Procedure of Game 33 Each utility designs their own pricing strategy f according to the generator’s price Each aggregator solves the minimization problem to obtain the solution of d ij according to the pricing strategy f of utilities Each utility combines all the demands from aggregators and adjusts the pricing strategy f Each aggregator solves the minimization problem to obtain the solution of d ij according to the updated pricing strategy f of utilities Finish Converge Not converge Initialize the demand of aggregators to utilities If the total demand from utility j decreases, utility j will decreases the pricing strategy f; If the total demand from utility j increases, utility j will increase the pricing strategy f;

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Utility Adjusts Pricing in Game 34 At different iterations of game, utility has different pricing curve for different profits Forward limit (kWh) ($) Generator

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Minimizing Total Payment of Aggregators 35 Forward limit (kWh) f 1 ($) f j is the pricing function of utility j d ij is the demand that aggregator i buy from utility j D i is the total demand of aggregator i m is the total number of utility n is the total number of aggregator Forward limit (kWh) f 2 ($)

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How Do Aggregators Distribute Demands? 36 Given the pricing strategy of utilities, aggregators choose the utility with lowest price and we propose two models Aggregator Forward limit (kWh) f 1 ($) Utility 1 Forward limit (kWh) f 1 ($) Utility 2 Forward limit (kWh) f 1 ($) Utility 3

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Model 1 First In First Schedule 37 Forward limit (kWh) ($) d 2j d 3j Utility schedules the demands of aggregators according to the sequence of request of aggregators Request sequence: d 2j, d 3j, d 1j d 1j

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Model 2 Most Balanced Aggregator First 38 Forward limit (kWh) ($) d 1j d 2j Utility schedules the demands of aggregators according to the rate of balance of aggregators, where rate of balance is current demand over total demand of aggregators. Time Load 1 Time Load 2

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Game Formulation at Market Level Player: Utility and Aggregator Strategy: 1. Utility: Decide price both within and beyond forward limit 2. Aggregator: Decide the amount of energy to buy from each utility Strategy: 1. Utility: Decide price both within and beyond forward limit 2. Aggregator: Decide the amount of energy to buy from each utility Since utilities play the leading role and aggregators play the following role, this is a Stackelberg game. 39

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Game Formulation at Community Level Players: All the customers in the community Strategy: Scheduling the appliances of all customers to maximize payoff while the scheduling constraints are satisfied 40

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Interaction Between Market Level and Community Level Market Level Price Schedule Community Level Impact of market pricing to customers Customers feedback to market 41

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Between Aggregator and Customer Assume that the aggregator makes no or fixed profit from customers Since the payment from the aggregator n to all utilities is C n,h for time interval h, one can set a h =C n,h /L h 2 –C n,h is the new cost due to the game between utilities and aggregators –L h is the old load from all the customers inside community n Due to the changes in the pricing curve, the customers will redistribute the load during time intervals 42

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Aggregators distribute demands to utilities for payment minimization Each aggregator changes community level pricing Customers reschedule smart home appliances with the new pricing curve Change of system cost is big Utilities adjust pricing to attract more demands Change of payment is small enough Change of payment remains big Change of system cost is small enough End Community Level Market Level Initialization 43

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Game Architecture Generators Utility Companies Aggregators Customers Home Appliances Stackelberg Game Standard Nash Game Adopted LMP based game 44

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Case Study The testcase in our study –One day time horizon with the time interval of 15 minutes time –2 utilities –5 communities where each one has an aggregator and 400 smart home customers –Each customer has 5 flexible appliances including dish washer, washing machine, dryer and charger –The daily consumption of these appliances varies from 1kWh to 5kWh, and the run time under the normal power level varies from 45 minutes to 2 hours The market assumption –In the forward market, the unit price of the 2 utilities are in the range 1 ￠ /kWh to 3 ￠ /kWh and 1.2 ￠ /kWh to 2.6 ￠ /kWh, respectively. –In the whole sale market, the slopes of unit price are in the range 0.012 ￠ /kWh 2 to 0.03 ￠ /kWh 2 and 0.01 ￠ /kWh 2 to 0.025 ￠ /kWh 2 respectively. The upper bound of the utilities are regulated by the government. 45

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Background Energy Usage 46

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Average Energy Reduction Per Customer 47 Peak to average ratio is 2.23 Peak to average ratio is 1.43

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Average Monetary Cost Reduction Per Customer 48

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Pricing and Load Change During Iterations at A Community 49

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Utility Profit 50 With and without smart home scheduling, utility profit is similar The essential reason for total customer payment reduction is due to the reduction in the expense of generation With smart home scheduling, the peak generation is avoided and generation is much more balanced With smart home scheduling, generation is mostly within the forward limit where quadratic charge is not applied

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Balanced Generation 51 Power Plant 1Power Plant 2

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Conclusion This work is to evaluate the impact of the smart home scheduling to the whole power system. –The complete power system model is provided with integration of smart home –Provide two level game structure for electricity market –Stackelberg game to model market level –Standard game to model community level –Design the dynamic programming and distributed algorithm for the game Smart home scheduling can reduce the payment of customers payment by about 30%, and reduce peak to average ratio by about 35% in the power system. The energy generation is also much more balanced. 52

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