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)