Heterogeneous Delay Tolerant Task Scheduling and Energy Management in the Smart Grid with Renewable Energy
Shengbo Chen
Electrical and Computer Engineering & Computer Science and Engineering
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The Smart Grid Next generation power grid: full visibility and
pervasive control on both supplier and consumers Smart meters
Dynamic electricity prices according to demand Shift demand from peak time
Renewable energy Reduce cost and greenhouse gas emission Energy harvesting: highly dynamic Battery: limited capacity
With these new features and challenges, there is a need for comprehensive solutions for the smart grid
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taskschedule
Model of Information Delivery Real-time communication between operator and consumers
Smart meters Controller: operator/customer side
Operator
Smart Meter 1
Smart home appliances
demandrequests
Smart Meter 2
Controller
demandrequests
taskschedule
Controller
electricityprices
electricityprices
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Energy Supply and Demand
Attributes of energy supply Unlike communication network
— Storable Renewable vs. Non-renewable Intermittent vs. Stable supply
Energy Supply Energy Demand
Energy Management
Attributes of energy demand Time-varying Unpredictable vs predictable Elastic vs. Non-elastic
Random demand meets with possibly uncertain supply
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I. Delay-tolerant Task Scheduling Intuition: Postpone delay-tolerant tasks to the period with low electricity
price E.g. dish washer, washer, electricity vehicle, air conditioner
Objective: Minimize cost of electricity tasks by leveraging the delay tolerance property and renewable energy
Constraints Hard deadlines for job completion Average “dissatisfaction” constraint
Control variables Delay in starting a job Amount of energy drawn/stored from/to the battery in each time slot
Challenges Uncertainty in job arrivals, incoming renewable energy and price of electricity Appliances have diverse electricity usage patterns and scheduling flexibility
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Energy Model
Demand = Supply l(t) = g(t)+b(t)
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Related Works Task scheduling [Koutsopoulos and Tassiulas, 2010]
Convex cost function
Renewable energy management scheme [Neely, 2010] No battery & task scheduling
Dynamic programming technique [Papavasiliou and Oren, 2010] Distribution of power demand needs to be known in advance
Demand peak optimization [Facchinetti and Vedova, 2011]
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Example
Key factors Factor 1: Time-varying electricity price & Delay tolerant property Factor 2: Battery energy management
Electricity Price P(t)
Time1 2 3 4 5 6
1
2
3
4
5
6
7
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Task
Schedules Cost
Non-scheduling $11
Scheduling w F1 $10
Scheduling w F1,F2 $7
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1
, ( ) 1 1 0
1min lim [ ( )
( ) ( )]
tt i
ti
n cTt ti iTs b t t i j
P j s tT
P t b t
E
Problem Statement Models
Electricity price assumed to be known in the near future Dissatisfaction function U
Average dissatisfaction constraint Don’t delay too many jobs
by too much
Cost of electricity
Cost reduction by drawing from battery
Starting delayfor job i arriving in timeslot t
Energydrawn/stored from/to the battery
1 1
1lim sup ( )
tnTt ti i
Tt i
U sT
. .s t
0 t t ti i is d c
max| ( ) | , ( ) ( ), ( ) ( )b t b b t B t b t l t
Job must finish before deadline
Hard deadlineJob duration
Energy constraint
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Solution Methodology Virtual Queue Q(t)
Deal with the average dissatisfaction constraint
Lemma: If the virtual queue is stable, the average dissatisfaction constraint is satisfied
Lyapunov optimization technique Define Lyapunov function Minimize the Lyapunov drift
Q(t) 𝛼1
( )tn
t ti i
i
U s
2 2max max( ) ( ) ( ( ) )L t Q t B t b VP
[ ( 1) ( ) | ( ( ), ( ))]L t L t Q t B t E
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In each time slot, the delay in starting a job is computed as
In each time slot, the battery charge/discharge is given by
Algorithm Sketch
Cost of electricityMeasure of
dissatisfactionfor this job
Measure of accumulated dissatisfaction
max max max*
max
min , ( ) if ( ) ( ) 0,( )
otherwise
b l t b VP B t VP tb t
b
1*
0 0
arg min ( ) ( ) ( )ti
t t ti i i
ct t t t ti i i i i
s d c j
s Q t U s V P j s t
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1* *
1 1 0
max max
1limsup [ ( ) ( ) ( )]
tt in cT
t ti i
T t i j
opt
P j s t P t b tT
DC P b
V
E
Battery level is always bounded: Only require finite battery capacity
Average delay dissatisfaction is always less than Performance is within a constant gap of the optimum
Main Results
max max max( ) 2B t b VP r
Constant gap Diminish as V becomes large
A tradeoff between the battery size and the performance
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Simulation Results Compared to the non-scheduling case
Cost reduction over slots (V=100) Cost reduction versus V
S. Chen, N. Shroff and P. Sinha , “Heterogeneous Delay Tolerant Task Scheduling and Energy Management in the Smart Grid with Renewable Energy,” to appear in IEEE Journal on Selected Areas in Communications (JSAC).S. Chen, N. Shroff and P. Sinha , “Scheduling Heterogeneous Delay Tolerant Tasks in Smart Grid with Renewable Energy,” in Proceeding of IEEE CDC, pp. 1130-1135, Dec, 2012.
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Summary Cost reduction
Leverage dynamic electricity prices and delay-tolerant property Renewable energy and battery
Delay constraints Hard deadlines Average dissatisfaction constraint
Scheme performance is within a constant gap of the optimum The constraint means that we can only draw energy
from the grid ( ) 0g t
What if this constraint does not exist?
Sell energy back to the grid!
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II. Energy Trading
Intuition: Dynamic electricity price combining an energy storage battery implies a trading opportunity (similar to stock)
Objective: Maximize the profit by opportunistically selling energy to the grid
Control variables Amount of energy drawn/stored from/to the battery in each time slot
Challenges Uncertainty of incoming renewable energy, price of electricity and
energy demand
Energy selling price is always less than the energy buying price
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Example
Key factors: Time-varying electricity price & Battery energy management
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( )1
1max lim [ ( )( ( ) ( ) )
( )( ( ) ( )) ]
T
Tb tt
P t l t b tT
P t l t b t
E
Problem Statement Models
Energy selling price is smaller by a factor of Energy demand l(t) is exogenous process
Profit of selling energy
Cost of buying energy from the grid
Energydrawn/stored from/to the battery
Battery level
Maximal output of the battery. .s tmax| ( ) |b t b
( ) ( )b t B t
(0,1)
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Denote
In each time slot, the energy allocation is given as follows Case 1: If
Case 2: If
Case 3: If
Algorithm Sketch
Sell: Price is high orbattery level is high
Buy: Price is low andbattery level is low
Equal: Price and battery level are mild
max max
max max
( ) ( ) ( )
( ) ( ) ( )
t VP t B t VP b
t V P t B t VP b
( ) ( ) 0t t
0 ( ) ( )t t
*max( )b t b
*max( )b t b
( ) 0 ( )t t *
max( ) min{ , ( )}b t b l t
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Battery level is always bounded: Only require finite battery capacity
Asymptotically close to the optimum as T tends to infinity
Main Results
max max max( ) 2B t b VP r
* *
1
1limsup [ ( )( ( ) ( ) ) ( )( ( ) ( )) ]
T
T t
opt
P t l t b t P t l t b tT
DC
V
E
Diminish as V becomes large
A tradeoff between the battery size and the performance
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Simulation Results Compared to the greedy scheme: first use the renewable energy
for the demand, and sell the extra if any
Annual profit versus Beta (V=1000) Annual profit versus V (Beta=0.8)S. Chen, N. Shroff and P. Sinha , “Energy Trading in the Smart Grid: From End-user’s Perspective,” to appear in Asilomar Conference on Signals, Systems and Computers, 2013. (Invited paper)
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Open Problems Different Model
Preemptive & non-preemptive HVAC system optimization
Game theory based schemes The behavior of large number of customers can influence the
market price
Network Economics
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Low-Latency Algorithm in Cloud Storage
Objective: Developed a queueing delay optimal algorithm for downloading data in cloud storages by leveraging multiple parallel threads and FEC codes
System model (n,k) codes
Requestarrivals
Queue
Queueing Delay
…
Threads
Dispatcher
Read Time
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When k = 1, given that the downloading time of each individual thread is i.i.d. following exponential distribution and the arrival process is Poisson, any work-conserving scheme is throughput optimal and also delay optimal.
When k > 1, given that the downloading time of each individual thread is i.i.d. following exponential distribution and the arrival process is Poisson process, the greedy scheme is delay optimal.
Main Results
S. Chen, L. Huang and X. Liu, “Optimal-Latency Data Retrieving Scheme in Storage Clouds by Leveraging FEC Codes,” under submission, 2013.G. Liang, S. Chen and U. Kozat, “On Using Parallelism and FEC in Delivering Reliable Delay Performance over Storage Clouds: A Queueing Theory Perspective,” under submission, 2013.
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Energy allocation and routing schemes in rechargeable sensor networks
Objective: Maximize the total
utility/throughput performance for
a rechargeable sensor network
Main results Finite time-horizon
—Optimal Offline: Shortest path
Infinite time-horizon—Simple asymptotically optimal
S. Chen, P. Sinha, N. Shroff, and C. Joo, “A Simple Asymptotically Optimal Energy Allocation and Routing Scheme in Rechargeable Sensor Networks,” Proc. of IEEE INFOCOM, Orlando, Florida, pp 379-387, Mar 2012. S. Chen, P. Sinha, N. Shroff, and C. Joo, “Finite-Horizon Energy Allocation and Routing Scheme in Rechargeable Sensor Networks,” Proc. of IEEE INFOCOM, Shanghai, pp 2273-2281, April 2011.S. Chen, P. Sinha, N. Shroff, and C. Joo, “A Simple Asymptotically Optimal Joint Energy Allocation and Routing Scheme in Rechargeable Sensor Networks,” Under Minor Revision, Transactions on Networking.
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Lifetime Tunable Design in WiFi Objective: Improve the system performance for energy-
constrained WiFi devices Resulting scheme
Near-optimal proportional-fair utility performance for single access point scenarios
Alleviating the near-far effect and hidden terminal problem in general multiple AP scenarios
Performance improvement Lifetime: high energy efficiency by avoiding idle listening Fairness: providing high priority to the low throughput devices Throughput: smaller collision probability
S. Chen, T. Bansal, Y. Sun, P. Sinha and N. Shroff, “ Life-Add: Lifetime Adjustable Design for WiFi Networks with Heterogeneous Energy Supplies,” To appear in proceedings of Wiopt 2013.
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Thank you
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Cost of electricity
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System Model
Demand = Supply l(t) = g(t)+b(t)
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System Model
g(t) = l(t)-b(t)