EE5900 Advanced Embedded
System For Smart Infrastructure
Electricity Market With Smart Home Integration
Smart Home Scheduling Basic Idea
Prefer using
cheap time
interval
Pricing for one-day ahead time period
2
Smart Home Scheduling System
Power flow
Internet
Control flow
3
Home Appliances in Smart Home
Not schedulable
Restrictively schedulable
Fully schedulable
4
Variable Frequency Drive
Power level
350 W
500 W
820 W
1350 W
Powerr
Power
10 cents/kwh 5 cents / kwh
10 cents/kwh 5 cents / kwh
10 kwh
5 kwh
1
2
Time
(a)
cost = 10 kwh * 10 cents/kwh = 100 cents
1
2
(b)
3
Time
cost = 5 kwh * 10 cents/kwh + 5 kwh * 5 cents/kwh
= 75 cents
5
Smart Home Scheduling
 Given the pricing curve, to decide
– when to launch a home appliance
–
–
We will describe the
at what frequency
algorithm later. Assume
for how long
that we have it, then
– 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
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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
Repeat until
converging
to
equilibrium
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
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Electricity Market
Generators
We will model them in
a bottom up fashion
Utilities
Electricity
Market
Aggregators
Renewable
Energy
Customers
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Single User Smart Home Scheduling
Generators
Utility Companies
Aggregators
Customers
Home Appliances
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Dynamic Programming For Scheduling Single Appliance
Energy
0
t1
t2
t3
t4
Time
Schedule the home appliance from
the first time interval
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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 i
Time slot i+1
(ei, ci)
(ei+1, ci+1)
𝑒0 = 0, 𝑐0 = 0
𝑒𝑖+1 = 𝑒𝑖 + 𝑝𝑖+1
𝑐𝑖+1 = 𝑐𝑖 + 𝑝𝑖+1 ∙ 𝛼𝑖+1
for 𝑖 = 1,2, … , 𝑛
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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 i
Time slot i+1
(ei, ci)
(ei+1, ci+1)
𝑒0 = 0, 𝑐0 = 0
𝑒𝑖+1 = 𝑒𝑖 + 𝑝𝑖+1
𝑐𝑖+1 = 𝑐𝑖 + 𝑝𝑖+1 ∙ 𝛼𝑖+1
for 𝑖 = 1,2, … , 𝑛
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Solution Pruning
 For an time interval, solution (e1, c1) will dominate
solution (e2, c2), if and only if e1≥e2 and c1≤c2.
 Dominated solutions will be pruned.
Time interval
(15, 20)
(15, 25)
(11, 22)
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Dynamic Programming Based Appliance Optimization
Power levels {1, 2, 3}
𝛼1 = 2
Price
0
𝛼2 = 1
(3,6)
(3,3)
(2,4)
(2,2)
(1,2)
(1,1)
(0,0)
Dynamic Programming returns
the optimal solution
t1
(0,0)
Runtime :
(6, 9) (5, 7) (4, 5) (3, 3)
(5, 8) (4, 6) (3, 4) (2, 2)
(4, 7) (3, 5) (2, 3) (1, 1)
Time
t2
2
O(m k )
–
# of distinct power levels = k
–
# time slots = m
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Scheduling Multiple Appliances for One User
Appliances
Determine Scheduling
Appliances Order
An appliance
Schedule Current Appliance
Not all the appliances
processed
Update Energy Upper
Bound of Each Time Interval
All appliances processed
Schedule
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Multiple User Smart Home Scheduling
Generators
Utility Companies
Aggregators
Customers
Home Appliances
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Motivation
Price Curve
0
1.5
3
4.5
6
7.5
9
10.5
12
13.5
15
16.5
18
19.5
21
22.5
24
14
12
10
8
6
4
2
0
Customer 1
Customer 2
.............
Customer 3
Game theory is used to handle the interactions among customers.
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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.
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An Example of Equilibrium
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Game Formulation at Community Level
Players: All the customers in the community
Payoff: −
𝑙ℎ,𝑗 𝐶ℎ
𝐿ℎ
Strategy: Scheduling the appliances of all customers to
maximize payoff while the scheduling constraints are
satisfied
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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
Converge
No
Yes
Schedule
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Dynamic Pricing
From ComED Illinois Corporation
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
How to decide the
customers is Lh, theconstant
total
factor ah?
cost (price) is approximately
Ch=ahLh2 at time interval h
 If lh,j denotes the load of
customer j, the customer j
pays lh,j·Ch/Lh
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Top Level
Generators
Utility Companies
Aggregators
Customers
Home Appliances
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Electricity Market
Forward Market
Fixed Amount
Utility
Generator
Cheap
Price
Aggregators
Fixed Cost
Whole Sale Market
Generator
LMP
Utility
Bid
Aggregators
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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.
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Generator Model
Total Price ($)
Forward limit
(kWh)
 Within forward limit, electricity can be generated with low price in
power plant
 Beyond forward limit, it costs much higher to generate electricity
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Utility Buying
Local generator
($)
Forward limit
Remote generator 2
($)
($)
Forward limit
(kWh)
Over buying
Waste
Remote generator 1
sign in a forward
contract with local
generator
Forward limit
(kWh)
(kWh)
Not enough
LMP
Utility
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Illustration of LMP
Local generator
Remote generator 1
10￠/kWh, 100kWh
5￠/kWh, 50kWh
Utility,
100kWh
Remote generator 2
8￠/kWh, 100kWh
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Market Level Modeling and Optimization
Generators
Utility Companies
Aggregators
Customers
Home Appliances
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Strategy of Utilities and Aggregators
Aggregators
Utilities
Price
Adjust price to attract
more demand
Demand
Decide purchase from
each utility to minimize
payment
Conducted in each time slot
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Illustration of Our Model
($)
Utility
Generator
Forward limit
(kWh)
Utility designs the pricing model according to the generator model.
Utility will never get negative profit as long as there is some electricity sold.
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Iterative Procedure of Game
Initialize the demand of aggregators to utilities
If the total demand from utility j decreases, utility j
Each utilitywill
designs
their own
pricingstrategy
strategyf;f
decreases
the pricing
according
to the generator’s
If the
total demand
from utility jprice
increases, utility j
will increase the pricing strategy f;
Each aggregator solves the minimization problem to obtain the
solution of dij according to the pricing strategy f of utilities
Each utility combines all the demands from aggregators
and adjusts the pricing strategy f
Not converge
Each aggregator solves the minimization
problem to obtain the solution of dij according to
the updated pricing strategy f of utilities
Converge
Finish
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Utility Adjusts Pricing in Game
At different iterations of game, utility has different pricing curve for different profits
($)
Generator
Forward limit
(kWh)
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Minimizing Total Payment of Aggregators
f1($)
𝑚
𝑀𝑖𝑛
𝑓𝑗 (𝑑𝑖𝑗 ) , 𝑖 = 1, 2, … , 𝑛
𝑗=1
𝑚
Forward limit
(kWh)
𝑠. 𝑡.
𝑑𝑖𝑗 = 𝐷𝑖 , 𝑖 = 1, 2, … , 𝑛
𝑗=1
f2($)
fj is the pricing function of utility j
dij is the demand that aggregator i buy from utility j
Di is the total demand of aggregator i
m is the total number of utility
n is the total number of aggregator
Forward limit
(kWh)
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How Do Aggregators Distribute Demands?
f1($)
Utility 1
Forward limit (kWh)
f1($)
Utility 2
Forward limit (kWh)
f1($)
Utility 3
Forward limit (kWh)
Aggregator
Given the pricing strategy of utilities, aggregators choose the utility with lowest
price and we propose two models
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Model 1 First In First Schedule
($)
Request sequence:
d2j, d3j, d1j
d2j
d3j
Forward limit
d1j
(kWh)
Utility schedules the demands of aggregators according to the
sequence of request of aggregators
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Model 2 Most Balanced Aggregator First
Load 1
($)
Time
Load 2
Time
d1j
d2j
Forward limit
(kWh)
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.
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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
Payoff:
 1. Utility: 𝑅𝑚 = 𝑓𝑚 ( 𝑛𝑖=1 𝑑𝑖𝑚 ), where dim is the demand of aggregator i
to utility m
 2. Aggregator: −𝐶𝑛 where 𝐶𝑛 is the total payment of aggregator 𝑛
Since utilities play the leading role and aggregators play the following role, this
is a Stackelberg game.
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Game Formulation at Community Level
Players: All the customers in the community
Payoff: −
𝑙ℎ,𝑗 𝐶ℎ
𝐿ℎ
Strategy: Scheduling the appliances of all customers to
maximize payoff while the scheduling constraints are
satisfied
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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
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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 Cn,h for
time interval h, one can set ah=Cn,h/Lh2
– Cn,h is the new cost due to the game between utilities and aggregators
– Lh 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
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Initialization
Community Level
Each aggregator changes community
level pricing
Aggregators distribute demands to
utilities for payment minimization
Customers reschedule smart home
appliances with the new pricing curve
Utilities adjust pricing to attract more
demands
Change of
payment
remains big
Change of
payment is small
enough
Market Level
Change of
system cost is
small enough
Change of
system cost is
big
End
43
Game Architecture
Generators
Adopted LMP
based game
Utility Companies
Stackelberg
Game
Aggregators
Customers
Standard
Nash Game
Home Appliances
44
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 ￠/kWh2 to
0.03 ￠/kWh2 and 0.01 ￠/kWh2 to 0.025 ￠/kWh2 respectively. The upper bound of
the utilities are regulated by the government.
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Background Energy Usage
46
Average Energy Reduction Per Customer
Peak to average
ratio is 2.23
Peak to average
ratio is 1.43
47
Average Monetary Cost Reduction Per Customer
48
Pricing and Load Change During Iterations at A Community
49
Profit (USD)
Profit (USD)
Utility Profit
• With andNowithout
smart home scheduling, utility
Smart Home Scheduling, 1573 in total
150
profit is similar
• The essential reason for total customer payment
100
reduction is due to the reduction in the expense of
generation
50
• With smart home scheduling, the peak generation
is
0 avoided and generation is much more balanced
20
40
60
80
100
• 0With smart
home
scheduling,
generation
is mostly
Time Horizon (15 min)
Smart Home limit
Scheduling,
1397 inquadratic
total
within the forward
where
charge is
150
not applied
100
50
0
0
20
40
60
Time Horizon (15 min)
80
100
50
Balanced Generation
Power Plant 1
Power Plant 2
No Smart Home Scheduling
No Smart Home Scheduling
300
Generation (kWh)
Generation (kWh)
300
200
100
0
0
20
40
60
Time Horizon (15 min)
Smart Home Scheduling
80
0
20
40
60
Time Horizon (15 min)
Smart Home Scheduling
80
100
0
20
40
60
Time Horizon (15 min)
80
100
300
Generation (kWh)
Generation (kWh)
100
0
100
300
200
100
0
200
0
20
40
60
Time Horizon (15 min)
80
100
200
100
0
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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.
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