Ancillary service to the grid from deferrable loads:the case for intelligent pool pumps in Florida

Isaac Newton Institute for Mathematical SciencesWorkshop on Modern Probabilistic Techniques

Sean P. Meyn

Prabir Barooah, Ana Busic, Jordan Ehren, He Hao, and Yashen Lin

Electrical and Computer Engineering

University of Florida

Thanks to NSF, AFOSR, ANR, and DOE / TCIPG

August 14, 2013

Outline

1 The Value of Power – A Short Quiz

2 Controlling the Grid

3 Buildings as Actuators

4 Intelligent Pools in Florida

5 Conclusions & Suggestions

6 References

2 / 57

The Value of Power – A Short Quiz

What is the Value of Power?A short quiz

the value of power depends upon location and context

$69.36

$70.86

$75.19

$69.29

$29.36

3 / 57

The Value of Power – A Short Quiz

What is the Value of Power?A short quiz

the value of power depends upon location and context

$69.36

$70.86

$75.19

$69.29

$29.36

3 / 57

The Value of Power – A Short Quiz

Midwest ISO TodayTypical week in the midwest

Prices depend on time, location and context

4 / 57

The Value of Power – A Short Quiz

Midwest ISO TodayTypical week in the midwest

Prices depend on time, location and context

4 / 57

The Value of Power – A Short Quiz

What is the Value of Power?A short quiz

Wind generationfor one day in the Paci�c Northwest

Price is $20/MWh

0

2000

4000

6000

8000

April 6

MW

1600 MW average output

5 / 57

The Value of Power – A Short Quiz

What is the Value of Power?A short quiz

Wind generationfor one day in the Paci�c Northwest

Price is $20/MWh

0

2000

4000

6000

8000

April 6

MW

1600 MW average output

Value = 1600 MW x 24 hours x $20/MWh = $768,000 ?

6 / 57

The Value of Power – A Short Quiz

What is the Value of Power?A short quiz

Zero net power Price is $20/MWh

−800−600

-1000

−400−200

0200400600800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

7 / 57

The Value of Power – A Short Quiz

What is the Value of Power?A short quiz

Zero net power Price is $20/MWh

−800−600

-1000

−400−200

0200400600800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

Value = 0 MW x 7 days x $20/MWh = $0 ?

True or False?

8 / 57

The Value of Power – A Short Quiz

What is the Value of Power?A short quiz

Zero net power Price is $20/MWh

−800−600

-1000

−400−200

0200400600800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

Value = 0 MW x 7 days x $20/MWh = $0 ?

True or False?8 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Answers to Quiz #1

Wind generationfor one day in the Paci�c Northwest

Price is $20/MWh

0

2000

4000

6000

8000

April 6

MW

1600 MW average output

Value = 1600 MW x 24 hours x $20/MWh = $768,000 ?

9 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Answers to Quiz #1 Wind generation

for one day in the Paci�c Northwest

Price is $20/MWh

0

2000

4000

6000

8000

April 6

MW

1600 MW average output

Value = 1600 MW x 24 hours x $20/MWh = $768,000 ?

Answer: Correct!Electrons are electrons, so add them up, and put them on the market!

Answer: False!!Spring 2012 report from this region:Annual “expected value” of oversupply costs estimated at $12 million peryear, with 300,000 MWh of wind curtailment

The first answer would be correct if we hadinfrastructure in place to mitigate volatility

www.nwcouncil.org/media/11074/2012 1212SupplementalReport.pdf

10 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Answers to Quiz #1 Wind generation

for one day in the Paci�c Northwest

Price is $20/MWh

0

2000

4000

6000

8000

April 6

MW

1600 MW average output

Value = 1600 MW x 24 hours x $20/MWh = $768,000 ?

Answer: Correct!Electrons are electrons, so add them up, and put them on the market!

Answer: False!!Spring 2012 report from this region:Annual “expected value” of oversupply costs estimated at $12 million peryear, with 300,000 MWh of wind curtailment

The first answer would be correct if we hadinfrastructure in place to mitigate volatility

www.nwcouncil.org/media/11074/2012 1212SupplementalReport.pdf

10 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Answers to Quiz #1 Wind generation

for one day in the Paci�c Northwest

Price is $20/MWh

0

2000

4000

6000

8000

April 6

MW

1600 MW average output

Value = 1600 MW x 24 hours x $20/MWh = $768,000 ?

Answer: Correct!Electrons are electrons, so add them up, and put them on the market!

Answer: False!!Spring 2012 report from this region:Annual “expected value” of oversupply costs estimated at $12 million peryear, with 300,000 MWh of wind curtailment

The first answer would be correct if we hadinfrastructure in place to mitigate volatility

www.nwcouncil.org/media/11074/2012 1212SupplementalReport.pdf

10 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Answers to Quiz #2

Zero net power Price is $20/MWh

−800−600

-1000

−400−200

0200400600800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

Value = 0 MW x 7 days x $20/MWh = $0 ?

11 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Answers to Quiz #2 Zero net power

Price is $20/MWh

−800−600

-1000

−400−200

0200400600800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

Value = 0 MW x 7 days x $20/MWh = $0 ?

Answer: Correct!The total power is zero, and the ± 800 MW perturbation isinconsequential given the 8000 MW load

Answer: False!Disturbance to the grid is costly, the actual value is −$500,000 (guess)

Answer: False!!This is the BPA regulation signal! The actual value is ...

12 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Answers to Quiz #2 Zero net power

Price is $20/MWh

−800−600

-1000

−400−200

0200400600800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

Value = 0 MW x 7 days x $20/MWh = $0 ?

Answer: Correct!The total power is zero, and the ± 800 MW perturbation isinconsequential given the 8000 MW load

Answer: False!Disturbance to the grid is costly, the actual value is −$500,000 (guess)

Answer: False!!This is the BPA regulation signal! The actual value is ...

12 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Answers to Quiz #2 Zero net power

Price is $20/MWh

−800−600

-1000

−400−200

0200400600800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

Value = 0 MW x 7 days x $20/MWh = $0 ?

Answer: Correct!The total power is zero, and the ± 800 MW perturbation isinconsequential given the 8000 MW load

Answer: False!Disturbance to the grid is costly, the actual value is −$500,000 (guess)

Answer: False!!This is the BPA regulation signal! The actual value is ...

12 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Answers to Quiz #2

April 3 April 4 April 5 April 6 April 7 April 8 April 9

13 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Answers to Quiz #2

Answer: False!!This is the BPA regulation signal! The actual value is ...

0

2000

4000

6000

8000

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

MW Load

Generationfrom Wind

Balancing reserves deployed

Value no less than the Seattle economy?−800

−600

-1000

−400

−200

0

200

400

600

800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

Curtailment tresholds

14 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Answers to Quiz #2

Answer: False!!This is the BPA regulation signal! The actual value is ...

0

2000

4000

6000

8000

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

MW Load

Generationfrom Wind

Balancing reserves deployed

Value no less than the Seattle economy?−800

−600

-1000

−400

−200

0

200

400

600

800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

Curtailment tresholds

14 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Extra credit: What if one resource cannot provide all of the balancing needs?

BalancingReservesDesired

What’s the value of this:

−800−600

-1000

−400−200

0

0

200400600800

−800−600

-1000

−400−200

200400600800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

MW

15 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Extra credit: What if one resource cannot provide all of the balancing needs?

BalancingReservesDesired

What’s the value of this:

−800−600

-1000

−400−200

0200400600800

−800−600

-1000

−400−200

0200400600800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

MW

16 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Extra credit: What if the shape isn’t quite right?

BalancingReservesDesired

What’s the value of this:

−800−600

-1000

−400−200

0

200400600800

−800−600

-1000

−400−200

200400600800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

MW

17 / 57

The Value of Power – A Short Quiz

What is the Value of Power?Extra credit: What if the shape isn’t quite right?

BalancingReservesDesired

What’s the value of this:

Delay is deadlyin a control system

Answer,

−800−600

-1000

−400−200

0

200400600800

−800−600

-1000

−400−200

200400600800

April 3 April 4 April 5 April 6 April 7 April 8 April 9

MW

MW

18 / 57

Controlling the Grid

Desires of Consumers & Suppliers, Error Energy & Volatility

Power ConsumptionQuality of LifePower GridControl

HCΣ

+

−

Controlling the Grid

19 / 57

Controlling the Grid

Controlling the GridThe Grid as a Control System

Dynamics are everywhere

Supply and demand are volatile

Transmission lines are subject to dynamics and constraintsTraditional generators have non convex and dynamic costs

Desires of Consumers & Suppliers, Error Energy & Volatility

Power ConsumptionQuality of LifePower GridControl

HCΣ

+

−

20 / 57

Controlling the Grid

Controlling the GridThe Grid as a Control System

Dynamics are everywhere

Supply and demand are volatileTransmission lines are subject to dynamics and constraints

Traditional generators have non convex and dynamic costs

Desires of Consumers & Suppliers, Error Energy & Volatility

Power ConsumptionQuality of LifePower GridControl

HCΣ

+

−

20 / 57

Controlling the Grid

Controlling the GridThe Grid as a Control System

Dynamics are everywhere

Supply and demand are volatileTransmission lines are subject to dynamics and constraintsTraditional generators have non convex and dynamic costs

Desires of Consumers & Suppliers, Error Energy & Volatility

Power ConsumptionQuality of LifePower GridControl

HCΣ

+

−

20 / 57

Controlling the Grid

Controlling the GridThe Grid as a Control System

Dynamics are everywhere

Supply and demand are volatileTransmission lines are subject to dynamics and constraintsTraditional generators have non convex and dynamic costs

Desires of Consumers & Suppliers, Error Energy & Volatility

Power ConsumptionQuality of LifePower GridControl

HCΣ

+

−

20 / 57

Controlling the Grid

Controlling the GridSo many resources to control!

Dynamics are everywhere

Supply and demand are volatileTransmission lines are subject to dynamics and constraintsTraditional generators have non convex and dynamic costs

Desires of Consumers & Suppliers, Error Energy & Volatility

Power ConsumptionQuality of LifePower GridControl

HCΣ

+

−

Act

uato

rs

1

0

2

3

4

Regu

latio

n (M

W)

5 m

inut

es fr

om P

JM

Two

Wee

ks B

PA (G

W)

−1000

0

1000Hydro, Natural GasFlexible manufacturingHVAC

BatteriesCapacitorsFlywheels

Act

uato

rs Hydro, Natural Gas BatteriesCapacitors Flywheels Flexible manufacturing Brick bakingHVAC Water pumping

How do we harness these actuators?

21 / 57

Controlling the Grid

Controlling the GridSo many resources to control!

Dynamics are everywhere

Supply and demand are volatileTransmission lines are subject to dynamics and constraintsTraditional generators have non convex and dynamic costs

Desires of Consumers & Suppliers, Error Energy & Volatility

Power ConsumptionQuality of LifePower GridControl

HCΣ

+

−

Act

uato

rs

1

0

2

3

4

Regu

latio

n (M

W)

5 m

inut

es fr

om P

JM

Two

Wee

ks B

PA (G

W)

−1000

0

1000Hydro, Natural GasFlexible manufacturingHVAC

BatteriesCapacitorsFlywheels

Act

uato

rs Hydro, Natural Gas BatteriesCapacitors Flywheels Flexible manufacturing Brick bakingHVAC Water pumping

How do we harness these actuators?21 / 57

Controlling the Grid

Controlling the GridSmart Grid Myopia?

Dynamics are everywhere

Supply and demand are volatileTransmission lines are subject to dynamics and constraintsTraditional generators have non convex and dynamic costs

Desires of Consumers & Suppliers, Error Energy & Volatility

Power ConsumptionQuality of LifePower GridControl

HCΣ

+

−

Act

uato

rs1

0

2

3

4

Regu

latio

n (M

W)

5 m

inut

es fr

om P

JM

Two

Wee

ks B

PA (G

W)

−1000

0

1000Hydro, Natural GasFlexible manufacturingHVAC

BatteriesCapacitorsFlywheels

$$$

Act

uato

rs Hydro, Natural Gas BatteriesCapacitors Flywheels Flexible manufacturing Brick bakingHVAC Water pumping

Money and consumer response in the loop ???

No way!

22 / 57

Controlling the Grid

Controlling the GridSmart Grid Myopia?

Dynamics are everywhere

Supply and demand are volatileTransmission lines are subject to dynamics and constraintsTraditional generators have non convex and dynamic costs

Desires of Consumers & Suppliers, Error Energy & Volatility

Power ConsumptionQuality of LifePower GridControl

HCΣ

+

−

Act

uato

rs1

0

2

3

4

Regu

latio

n (M

W)

5 m

inut

es fr

om P

JM

Two

Wee

ks B

PA (G

W)

−1000

0

1000Hydro, Natural GasFlexible manufacturingHVAC

BatteriesCapacitorsFlywheels

$$$

Act

uato

rs Hydro, Natural Gas BatteriesCapacitors Flywheels Flexible manufacturing Brick bakingHVAC Water pumping

Money and consumer response in the loop ??? No way!22 / 57

Controlling the Grid Thank you, Petar and Bill!

Controlling the GridSmart Grid Vision

Dynamics are everywhere

Supply and demand are volatileTransmission lines are subject to dynamics and constraintsTraditional generators have non convex and dynamic costs

Desires of Consumers & Suppliers, Error Energy & Volatility

Power ConsumptionQuality of LifePower GridControl

HCΣ

+

−

1

0

2

3

4

Regu

latio

n (M

W)

5 m

inut

es fr

om P

JM

Two

Wee

ks B

PA (G

W)

−1000

0

1000

Act

uato

rs Hydro, Natural Gas BatteriesCapacitors Flywheels Flexible manufacturing Brick bakingHVAC Water pumping

Our community can solve this, thank you!!23 / 57

Controlling the Grid Literature review

Selected prior work:

. Demand-side management has been employed by utilities for manydecades, mainly for emergency response

. Schweppe et. al. 1980: Frequency responsive thermal loads“Equilibrating forces are obtained over longer time scales (5 minutes and

up) by economic principles through an Energy Marketplace using

time-varying spot prices”

. Andersson, Callaway, Hiskens, Mathieu 2011–: Aggregation of loadsfor regulation (much like this work)

This work: 1. Regulation allocated according to bandwidth of service.2. Intelligence at the loads, with minimal communication.3. Aggreggate model for control by the balancing authority:

Mean-field models for intelligent loads

24 / 57

Controlling the Grid Literature review

Selected prior work:

. Demand-side management has been employed by utilities for manydecades, mainly for emergency response

. Schweppe et. al. 1980: Frequency responsive thermal loads“Equilibrating forces are obtained over longer time scales (5 minutes and

up) by economic principles through an Energy Marketplace using

time-varying spot prices”

. Andersson, Callaway, Hiskens, Mathieu 2011–: Aggregation of loadsfor regulation (much like this work)

This work: 1. Regulation allocated according to bandwidth of service.2. Intelligence at the loads, with minimal communication.3. Aggreggate model for control by the balancing authority:

Mean-field models for intelligent loads

24 / 57

Controlling the Grid Literature review

Selected prior work:

. Demand-side management has been employed by utilities for manydecades, mainly for emergency response

. Schweppe et. al. 1980: Frequency responsive thermal loads“Equilibrating forces are obtained over longer time scales (5 minutes and

up) by economic principles through an Energy Marketplace using

time-varying spot prices”

. Andersson, Callaway, Hiskens, Mathieu 2011–: Aggregation of loadsfor regulation (much like this work)

This work: 1. Regulation allocated according to bandwidth of service.2. Intelligence at the loads, with minimal communication.3. Aggreggate model for control by the balancing authority:

Mean-field models for intelligent loads

24 / 57

Controlling the Grid Literature review

Selected prior work:

. Demand-side management has been employed by utilities for manydecades, mainly for emergency response

. Schweppe et. al. 1980: Frequency responsive thermal loads“Equilibrating forces are obtained over longer time scales (5 minutes and

up) by economic principles through an Energy Marketplace using

time-varying spot prices”

. Andersson, Callaway, Hiskens, Mathieu 2011–: Aggregation of loadsfor regulation (much like this work)

This work: 1. Regulation allocated according to bandwidth of service.2. Intelligence at the loads, with minimal communication.3. Aggreggate model for control by the balancing authority:

Mean-field models for intelligent loads

24 / 57

Buildings as Actuators

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

MW

0

−800

−600

−400

−200

200

400

600

800

Buildings as Actuators

25 / 57

Buildings as Actuators Why Buildings?

HVAC flexibility to provide additional ancillary service

◦ Buildings consume 70% of electricity in the USHVAC contributes to 40% of the consumption.

◦ Buildings have large thermal capacities: Small variations in mass flowrate do not change the indoor environment

◦ Modern buildings have responsive equipment

26 / 57

Buildings as Actuators Why Buildings?

HVAC flexibility to provide additional ancillary service

◦ Buildings consume 70% of electricity in the USHVAC contributes to 40% of the consumption.

◦ Buildings have large thermal capacities: Small variations in mass flowrate do not change the indoor environment

◦ Modern buildings have responsive equipment

26 / 57

Buildings as Actuators Why Buildings?

HVAC flexibility to provide additional ancillary service

◦ Buildings consume 70% of electricity in the USHVAC contributes to 40% of the consumption.

◦ Buildings have large thermal capacities: Small variations in mass flowrate do not change the indoor environment

◦ Modern buildings have responsive equipment

26 / 57

Buildings as Actuators Frequency regulation from buildings

Building Thermal DynamicsFor control?

Feedforward control architecture; an add-on to the existing control system

Grid Regulation Signal

Desires of Consumers & Suppliers, Error

Error

HappyConsumers

Energy & Volatility

Feedforward power deviation

Power GridGrid Control

HC+

−Σ Σ

Act

uato

r

HVAC

−1000

0

1000

PIBuildingControl

27 / 57

Buildings as Actuators Frequency regulation from buildings

Building Thermal DynamicsFor control?

Feedforward control architecture; an add-on to the existing control system

Grid Regulation Signal

Desires of Consumers & Suppliers, Error

Error

HappyConsumers

Energy & Volatility

Feedforward power deviation

Power GridGrid Control

HC+

−Σ Σ

Act

uato

r

HVAC

−1000

0

1000

PIBuildingControl

27 / 57

Buildings as Actuators Frequency regulation from buildings

Building Thermal DynamicsFeedforward control architecture; an add-on to the existing control system

How to we prevent a fight between our control system and theirs?

Feedforward control viewed as a disturbance by the existing HVAC PI controller?

Solution: Restrict to BW that is unseen by existing building PI control

Power to Fan Speed

Power to TemperatureMag

nitu

de(d

B)

Frequency (Hz) 10010−3 1600

14

0

−20

20

−40

−60

Bandwidth for Ancillary Service from Commercial Buildings

Within this frequency band,

Current HVAC control systems do not attempt to reject disturbances

Temperature is insensitive to fan-speed variations

28 / 57

Buildings as Actuators Frequency regulation from buildings

Building Thermal DynamicsFeedforward control architecture; an add-on to the existing control system

How to we prevent a fight between our control system and theirs?

Feedforward control viewed as a disturbance by the existing HVAC PI controller?

Solution: Restrict to BW that is unseen by existing building PI control

Power to Fan Speed

Power to TemperatureMag

nitu

de(d

B)

Frequency (Hz) 10010−3 1600

14

0

−20

20

−40

−60

Bandwidth for Ancillary Service from Commercial Buildings

Within this frequency band,

Current HVAC control systems do not attempt to reject disturbances

Temperature is insensitive to fan-speed variations

28 / 57

Buildings as Actuators Frequency regulation from buildings

Building Thermal DynamicsFeedforward control architecture; an add-on to the existing control system

How to we prevent a fight between our control system and theirs?

Feedforward control viewed as a disturbance by the existing HVAC PI controller?

Solution: Restrict to BW that is unseen by existing building PI control

Power to Fan Speed

Power to TemperatureMag

nitu

de(d

B)

Frequency (Hz) 10010−3 1600

14

0

−20

20

−40

−60

Bandwidth for Ancillary Service from Commercial Buildings

Within this frequency band,

Current HVAC control systems do not attempt to reject disturbances

Temperature is insensitive to fan-speed variations

28 / 57

Buildings as Actuators Frequency regulation from buildings

Building Thermal DynamicsFeedforward control architecture; an add-on to the existing control system

How to we prevent a fight between our control system and theirs?

Feedforward control viewed as a disturbance by the existing HVAC PI controller?

Solution: Restrict to BW that is unseen by existing building PI control

Power to Fan Speed

Power to TemperatureMag

nitu

de(d

B)

Frequency (Hz) 10010−3 1600

14

0

−20

20

−40

−60

Bandwidth for Ancillary Service from Commercial Buildings

Within this frequency band,

Current HVAC control systems do not attempt to reject disturbances

Temperature is insensitive to fan-speed variations28 / 57

Buildings as Actuators Experiments

Pugh Hall @ UFHow much ancillary service can we extract from a campus building?

40,000 sq. ft. building at the University of Florida campus in Gainesville

29 / 57

Buildings as Actuators Experiments

Pugh Hall @ UFHow much?

0 500 1500 2500 3500 Time (s)

−4

−2

0

2

4

0

−0.1

0.2

0.1◦

Fan Power Deviation Regulation Signal

kWD

egre

es C

Temperature Deviation

. One AHU fan with 25 kW motor:> 3 kW of regulation reserve

. Pugh Hall (40k sq ft, 3 AHUs):> 10 kW

Indoor air quality is not affected

. 100 buildings:> 1 MW

That’s just using the fans!

30 / 57

Buildings as Actuators Experiments

Pugh Hall @ UFHow much?

0 500 1500 2500 3500 Time (s)

−4

−2

0

2

4

0

−0.1

0.2

0.1◦

Fan Power Deviation Regulation Signal

kWD

egre

es C

Temperature Deviation

. One AHU fan with 25 kW motor:> 3 kW of regulation reserve

. Pugh Hall (40k sq ft, 3 AHUs):> 10 kW

Indoor air quality is not affected

. 100 buildings:> 1 MW

That’s just using the fans!

30 / 57

Buildings as Actuators Experiments

Pugh Hall @ UFHow much?

0 500 1500 2500 3500 Time (s)

−4

−2

0

2

4

0

−0.1

0.2

0.1◦

Fan Power Deviation Regulation Signal

kWD

egre

es C

Temperature Deviation

. One AHU fan with 25 kW motor:> 3 kW of regulation reserve

. Pugh Hall (40k sq ft, 3 AHUs):> 10 kW

Indoor air quality is not affected

. 100 buildings:> 1 MW

That’s just using the fans!

30 / 57

Buildings as Actuators Beyond fans

HVAC is more than fansRegulation from chillers in U.S. commercial buildings

Frequency band

f ∈ [1/(60 min), 1/(3 min)]

Capacity

12 GW

No impact on indoor climate

31 / 57

Buildings as Actuators Beyond fans

HVAC is more than fansRegulation from chillers in U.S. commercial buildings

Frequency band

f ∈ [1/(60 min), 1/(3 min)]

Capacity

12 GW

No impact on indoor climate

31 / 57

Intelligent Pools in Florida

−600−400−200

0200400600

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

MW

Intelligent Pools in Florida

32 / 57

Intelligent Pools in Florida Pools today

One Million Pools in FloridaPools Service the Grid Today

On Call1: Utility controls residential pool pumps and other loads

Used only in times of emergency — Activated only 3-4 times a year

Opportunity: FP&L already has their hand on the switch of nearly onemillion pools!

1Florida Power and Light, Florida’s largest utility.www.fpl.com/residential/energysaving/programs/oncall.shtml

33 / 57

Intelligent Pools in Florida Pools today

One Million Pools in FloridaPools Service the Grid Today

On Call1: Utility controls residential pool pumps and other loadsUsed only in times of emergency — Activated only 3-4 times a year

Opportunity: FP&L already has their hand on the switch of nearly onemillion pools!

1Florida Power and Light, Florida’s largest utility.www.fpl.com/residential/energysaving/programs/oncall.shtml

33 / 57

Intelligent Pools in Florida Pools today

One Million Pools in FloridaPools Service the Grid Today

On Call1: Utility controls residential pool pumps and other loadsUsed only in times of emergency — Activated only 3-4 times a year

Opportunity: FP&L already has their hand on the switch of nearly onemillion pools!

1Florida Power and Light, Florida’s largest utility.www.fpl.com/residential/energysaving/programs/oncall.shtml

33 / 57

Intelligent Pools in Florida Pools today

One Million Pools in FloridaHow Pools Can Regulate The Grid

1,5KW 400V

Needs of a single pool

. Filtration system circulates and cleans: Average pool pump uses1.3kW and runs 6-12 hours per day, 7 days per week

. Pool owners are oblivious, until they see frogs and algae

. Pool owners do not trust NSA or the local utility – Privacy is a bigconcern

Control strategy

. Privacy and smooth behavior of the aggregate: randomization.

. Minimal communication: Each pool pump should know the needs ofthe grid, and the status of the pool under its care.

:

34 / 57

Intelligent Pools in Florida Pools today

One Million Pools in FloridaHow Pools Can Regulate The Grid

1,5KW 400V

Needs of a single pool

. Filtration system circulates and cleans: Average pool pump uses1.3kW and runs 6-12 hours per day, 7 days per week

. Pool owners are oblivious, until they see frogs and algae

. Pool owners do not trust NSA or the local utility – Privacy is a bigconcern

Control strategy

. Privacy and smooth behavior of the aggregate: randomization.

. Minimal communication: Each pool pump should know the needs ofthe grid, and the status of the pool under its care.

:

34 / 57

Intelligent Pools in Florida Pools today

One Million Pools in FloridaHow Pools Can Regulate The Grid

1,5KW 400V

Needs of a single pool

. Filtration system circulates and cleans: Average pool pump uses1.3kW and runs 6-12 hours per day, 7 days per week

. Pool owners are oblivious, until they see frogs and algae

. Pool owners do not trust NSA or the local utility – Privacy is a bigconcern

Control strategy

. Privacy and smooth behavior of the aggregate: randomization.

. Minimal communication: Each pool pump should know the needs ofthe grid, and the status of the pool under its care.

:

34 / 57

Intelligent Pools in Florida Pools today

One Million Pools in FloridaHow Pools Can Regulate The Grid

1,5KW 400V

Needs of a single pool

. Filtration system circulates and cleans: Average pool pump uses1.3kW and runs 6-12 hours per day, 7 days per week

. Pool owners are oblivious, until they see frogs and algae

. Pool owners do not trust NSA or the local utility – Privacy is a bigconcern

Control strategy

. Privacy and smooth behavior of the aggregate: randomization.

. Minimal communication: Each pool pump should know the needs ofthe grid, and the status of the pool under its care.

:

34 / 57

Intelligent Pools in Florida Pools today

One Million Pools in FloridaHow Pools Can Regulate The Grid

1,5KW 400V

Needs of a single pool

. Filtration system circulates and cleans: Average pool pump uses1.3kW and runs 6-12 hours per day, 7 days per week

. Pool owners are oblivious, until they see frogs and algae

. Pool owners do not trust NSA or the local utility – Privacy is a bigconcern

Control strategy

. Privacy and smooth behavior of the aggregate: randomization.

. Minimal communication: Each pool pump should know the needs ofthe grid, and the status of the pool under its care.

:34 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaRandomized Control Architecture

0 1 2 T−1 T. . .

T

On

O�012T−1

...

Markovian model for an individual pool; nominal transition matrix PControlled transition matrix P

Cost function: balance needs of grid and needs of pool,

Cost = Needs of Grid + Deviation from nominal behavior

= −z × [Power consumption] + dist.(P , P )

Parameter z positive or negative: Common signal to all pools.Distance function “dist.” to be determined

35 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaRandomized Control Architecture

0 1 2 T−1 T. . .

T

On

O�012T−1

...

Markovian model for an individual pool; nominal transition matrix PControlled transition matrix P

Cost function: balance needs of grid and needs of pool,

Cost = Needs of Grid + Deviation from nominal behavior

= −z × [Power consumption] + dist.(P , P )

Parameter z positive or negative: Common signal to all pools.Distance function “dist.” to be determined

35 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaRandomized Control Architecture

0 1 2 T−1 T. . .

T

On

O�012T−1

...

Markovian model for an individual pool; nominal transition matrix PControlled transition matrix P

Cost function: balance needs of grid and needs of pool,

Cost = Needs of Grid + Deviation from nominal behavior

= −z × [Power consumption] + dist.(P , P )

Parameter z positive or negative: Common signal to all pools.Distance function “dist.” to be determined

35 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaRandomized Control Architecture

Cost function designed to balance needs of grid and needs of pool,

Cost = Needs of Grid + Deviation from nominal behavior

= −z × [Power consumption] + dist.(P , P )

Conditional costs, given X(t) = x:

κ(x) = I{

Pool is off}∣∣∣x∝ −(Power consumption)

∣∣∣x

Relative entropy,

dist.(P , P )∣∣∣x

= D(P (x, · )‖P (x, · ))

36 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaRandomized Control Architecture

Cost function designed to balance needs of grid and needs of pool,

Cost = Needs of Grid + Deviation from nominal behavior

= −z × [Power consumption] + dist.(P , P )

Conditional costs, given X(t) = x:

κ(x) = I{

Pool is off}∣∣∣x∝ −(Power consumption)

∣∣∣x

Relative entropy,

dist.(P , P )∣∣∣x

= D(P (x, · )‖P (x, · ))

36 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaRandomized Control Architecture

Cost function designed to balance needs of grid and needs of pool,

Cost = Needs of Grid + Deviation from nominal behavior

= −z × [Power consumption] + dist.(P , P )

Conditional costs, given X(t) = x:

κ(x) = I{

Pool is off}∣∣∣x∝ −(Power consumption)

∣∣∣x

Relative entropy,

dist.(P , P )∣∣∣x

= D(P (x, · )‖P (x, · ))

36 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaRandomized Control Architecture

Cost function designed to balance needs of grid and needs of pool,

Cost = Needs of Grid + Deviation from nominal behavior

= −z × [Power consumption] + dist.(P , P )

Conditional costs, given X(t) = x:

κ(x) = I{

Pool is off}∣∣∣x∝ −(Power consumption)

∣∣∣x

Relative entropy,

dist.(P , P )∣∣∣x

= D(P (x, · )‖P (x, · ))

36 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaRandomized Control Architecture

Cost for given state and transition matrix P :

Cost∣∣∣x

= zκ(x) +D(P (x, · )‖P (x, · ))

If π denotes the invariant measure for P , then

Cost(P ) = z〈π, κ〉+DDV(P‖P )

Donsker-Varadhan rate function:

DDV(P‖P ) =∑x,y

π(x)(P (x, y) log

[ P (x, y)P (x, y)

])

Minimization over P is obtained as an eigenvector problem (Todorov).

37 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaRandomized Control Architecture

Cost for given state and transition matrix P :

Cost∣∣∣x

= zκ(x) +D(P (x, · )‖P (x, · ))

If π denotes the invariant measure for P , then

Cost(P ) = z〈π, κ〉+DDV(P‖P )

Donsker-Varadhan rate function:

DDV(P‖P ) =∑x,y

π(x)(P (x, y) log

[ P (x, y)P (x, y)

])Minimization over P is obtained as an eigenvector problem (Todorov).

37 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaRandomized Control Architecture

Cost for given state and transition matrix P :

Cost∣∣∣x

= zκ(x) +D(P (x, · )‖P (x, · ))

If π denotes the invariant measure for P , then

Cost(P ) = z〈π, κ〉+DDV(P‖P )

Donsker-Varadhan rate function:

DDV(P‖P ) =∑x,y

π(x)(P (x, y) log

[ P (x, y)P (x, y)

])

Minimization over P is obtained as an eigenvector problem (Todorov).

37 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaRandomized Control Architecture

Cost for given state and transition matrix P :

Cost∣∣∣x

= zκ(x) +D(P (x, · )‖P (x, · ))

If π denotes the invariant measure for P , then

Cost(P ) = z〈π, κ〉+DDV(P‖P )

Donsker-Varadhan rate function:

DDV(P‖P ) =∑x,y

π(x)(P (x, y) log

[ P (x, y)P (x, y)

])

Minimization over P is obtained as an eigenvector problem (Todorov).

37 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaEigenvector Problem

. Scaled transition matrix:

P (x, y) = exp(−zκ(x))P (x, y)

. Eigenvector equation: P v = λv

. Eigenvalue: λ = e−η∗, where η∗ the optimal average cost.

. Optimizer: Twisted transition matrix,

P (x, y) =1λ

1v(x)

P (x, y)v(y)

See Kontoyiannis & M. for theory and approximations for P

38 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaEigenvector Problem

. Scaled transition matrix:

P (x, y) = exp(−zκ(x))P (x, y)

. Eigenvector equation: P v = λv

. Eigenvalue: λ = e−η∗, where η∗ the optimal average cost.

. Optimizer: Twisted transition matrix,

P (x, y) =1λ

1v(x)

P (x, y)v(y)

See Kontoyiannis & M. for theory and approximations for P

38 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaEigenvector Problem

. Scaled transition matrix:

P (x, y) = exp(−zκ(x))P (x, y)

. Eigenvector equation: P v = λv

. Eigenvalue: λ = e−η∗, where η∗ the optimal average cost.

. Optimizer: Twisted transition matrix,

P (x, y) =1λ

1v(x)

P (x, y)v(y)

See Kontoyiannis & M. for theory and approximations for P

38 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaEigenvector Problem

. Scaled transition matrix:

P (x, y) = exp(−zκ(x))P (x, y)

. Eigenvector equation: P v = λv

. Eigenvalue: λ = e−η∗, where η∗ the optimal average cost.

. Optimizer: Twisted transition matrix,

P (x, y) =1λ

1v(x)

P (x, y)v(y)

See Kontoyiannis & M. for theory and approximations for P

38 / 57

Intelligent Pools in Florida MDP model for a single pool

A Single Pool in FloridaEigenvector Problem

. Scaled transition matrix:

P (x, y) = exp(−zκ(x))P (x, y)

. Eigenvector equation: P v = λv

. Eigenvalue: λ = e−η∗, where η∗ the optimal average cost.

. Optimizer: Twisted transition matrix,

P (x, y) =1λ

1v(x)

P (x, y)v(y)

See Kontoyiannis & M. for theory and approximations for P

38 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

Aggregate model: output Y (t) = proportion of pools off.

If every pool operates according to Pz, then Y (t) ≈ 〈πz, κ〉 (large t).

Transient behavior requires state evolution: Given initial distribution µ0,

µt(x) =∑x0∈X

µ0(x0)P tz(x0, x)

Next step: Relax assumption that z is a constant.New interpretation: {zi} control signal broadcast by balancing authority

39 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

Aggregate model: output Y (t) = proportion of pools off.If every pool operates according to Pz, then Y (t) ≈ 〈πz, κ〉 (large t).

Transient behavior requires state evolution: Given initial distribution µ0,

µt(x) =∑x0∈X

µ0(x0)P tz(x0, x)

Next step: Relax assumption that z is a constant.New interpretation: {zi} control signal broadcast by balancing authority

39 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

Aggregate model: output Y (t) = proportion of pools off.If every pool operates according to Pz, then Y (t) ≈ 〈πz, κ〉 (large t).

Transient behavior requires state evolution: Given initial distribution µ0,

µt(x) =∑x0∈X

µ0(x0)P tz(x0, x)

Next step: Relax assumption that z is a constant.New interpretation: {zi} control signal broadcast by balancing authority

39 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

Aggregate model: output Y (t) = proportion of pools off.If every pool operates according to Pz, then Y (t) ≈ 〈πz, κ〉 (large t).

Transient behavior requires state evolution: Given initial distribution µ0,

µt(x) =∑x0∈X

µ0(x0)P tz(x0, x)

Next step: Relax assumption that z is a constant.New interpretation: {zi} control signal broadcast by balancing authority

39 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

New interpretation: {zi} control signal broadcast by balancing authority

Distribution evolution of the state:

µt(x) =∑{xi}∈X

µ0(x0)Pz0(x0, x1)Pz1(x1, x2) · · · Pzt−1(xt−1, x)

Average number of pools pumps that are not operating,

yt =∑x

µt(x)κ(x)

{µt} viewed as a state process that is under our control through {zt}.Mean-field model (“NLMP”)

Question: How to control this complex nonlinear system?

40 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

New interpretation: {zi} control signal broadcast by balancing authorityDistribution evolution of the state:

µt(x) =∑{xi}∈X

µ0(x0)Pz0(x0, x1)Pz1(x1, x2) · · · Pzt−1(xt−1, x)

Average number of pools pumps that are not operating,

yt =∑x

µt(x)κ(x)

{µt} viewed as a state process that is under our control through {zt}.Mean-field model (“NLMP”)

Question: How to control this complex nonlinear system?

40 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

New interpretation: {zi} control signal broadcast by balancing authorityDistribution evolution of the state:

µt(x) =∑{xi}∈X

µ0(x0)Pz0(x0, x1)Pz1(x1, x2) · · · Pzt−1(xt−1, x)

Average number of pools pumps that are not operating,

yt =∑x

µt(x)κ(x)

{µt} viewed as a state process that is under our control through {zt}.Mean-field model (“NLMP”)

Question: How to control this complex nonlinear system?

40 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

New interpretation: {zi} control signal broadcast by balancing authorityDistribution evolution of the state:

µt(x) =∑{xi}∈X

µ0(x0)Pz0(x0, x1)Pz1(x1, x2) · · · Pzt−1(xt−1, x)

Average number of pools pumps that are not operating,

yt =∑x

µt(x)κ(x)

{µt} viewed as a state process that is under our control through {zt}.Mean-field model (“NLMP”)

Question: How to control this complex nonlinear system?

40 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

New interpretation: {zi} control signal broadcast by balancing authorityDistribution evolution of the state:

µt(x) =∑{xi}∈X

µ0(x0)Pz0(x0, x1)Pz1(x1, x2) · · · Pzt−1(xt−1, x)

Average number of pools pumps that are not operating,

yt =∑x

µt(x)κ(x)

{µt} viewed as a state process that is under our control through {zt}.

Mean-field model (“NLMP”)

Question: How to control this complex nonlinear system?

40 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

New interpretation: {zi} control signal broadcast by balancing authorityDistribution evolution of the state:

µt(x) =∑{xi}∈X

µ0(x0)Pz0(x0, x1)Pz1(x1, x2) · · · Pzt−1(xt−1, x)

Average number of pools pumps that are not operating,

yt =∑x

µt(x)κ(x)

{µt} viewed as a state process that is under our control through {zt}.Mean-field model (“NLMP”)

Question: How to control this complex nonlinear system?

40 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

New interpretation: {zi} control signal broadcast by balancing authorityDistribution evolution of the state:

µt(x) =∑{xi}∈X

µ0(x0)Pz0(x0, x1)Pz1(x1, x2) · · · Pzt−1(xt−1, x)

Average number of pools pumps that are not operating,

yt =∑x

µt(x)κ(x)

{µt} viewed as a state process that is under our control through {zt}.Mean-field model (“NLMP”)

Question: How to control this complex nonlinear system?

40 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

Question: How to control this complex nonlinear system?

zt yt

One Million Pools

Proportion of pools o�:

µt+1 = µtPzt

41 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model

Question: How to control this complex nonlinear system?

yt

yt

zt

= 〈µt, κ〉

Control @ Utility

Gain

One Million Pools

Disturbance to be rejected

Proportion of pools o�

desired

µt+1 = µtPzt

42 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Linear approximation

Question: How to control this complex nonlinear system?

Distribution evolution is linear in the state, and nonlinear in control:

µt+1 = µtPzt

Linearization for small zi, and µ0 ∼ π,

µt+1 ≈ µt[P + zt∆] ≈ µtP + ztπ∆

Derivative ∆ based on Poisson’s equation – see Kontoyiannis & M.Evolution approximated by linear state space modelControl should be easy if this is a “nice” linear system

43 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Linear approximation

Question: How to control this complex nonlinear system?

Distribution evolution is linear in the state, and nonlinear in control:

µt+1 = µtPzt

Linearization for small zi, and µ0 ∼ π,

µt+1 ≈ µt[P + zt∆] ≈ µtP + ztπ∆

Derivative ∆ based on Poisson’s equation – see Kontoyiannis & M.Evolution approximated by linear state space modelControl should be easy if this is a “nice” linear system

43 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Linear approximation

Question: How to control this complex nonlinear system?

Distribution evolution is linear in the state, and nonlinear in control:

µt+1 = µtPzt

Linearization for small zi, and µ0 ∼ π,

µt+1 ≈ µt[P + zt∆] ≈ µtP + ztπ∆

Derivative ∆ based on Poisson’s equation – see Kontoyiannis & M.

Evolution approximated by linear state space modelControl should be easy if this is a “nice” linear system

43 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Linear approximation

Question: How to control this complex nonlinear system?

Distribution evolution is linear in the state, and nonlinear in control:

µt+1 = µtPzt

Linearization for small zi, and µ0 ∼ π,

µt+1 ≈ µt[P + zt∆] ≈ µtP + ztπ∆

Derivative ∆ based on Poisson’s equation – see Kontoyiannis & M.

Evolution approximated by linear state space model

Control should be easy if this is a “nice” linear system

43 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Linear approximation

Question: How to control this complex nonlinear system?

Distribution evolution is linear in the state, and nonlinear in control:

µt+1 = µtPzt

Linearization for small zi, and µ0 ∼ π,

µt+1 ≈ µt[P + zt∆] ≈ µtP + ztπ∆

Derivative ∆ based on Poisson’s equation – see Kontoyiannis & M.

Evolution approximated by linear state space modelControl should be easy if this is a “nice” linear system

43 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Numerical Example

Linearization for small zi, and µ0 ∼ π,

µt+1 ≈ µtP + ztπ∆ , yt = 〈µt, κ〉

Choice for P?Consider symmetric nominal model,

00

0.5

1

Pool pump o� for i hours2412 i

0 1 2 T−1 T. . .

T

On

O�012

2

T−1

...

For each z, the transition matrix Pz is defined by a “twisted” model

44 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Numerical Example

Linearization for small zi, and µ0 ∼ π,

µt+1 ≈ µtP + ztπ∆ , yt = 〈µt, κ〉 Choice for P?

Consider symmetric nominal model,

00

0.5

1

Pool pump o� for i hours2412 i

0 1 2 T−1 T. . .

T

On

O�012

2

T−1

...

For each z, the transition matrix Pz is defined by a “twisted” model

44 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Numerical Example

Linearization for small zi, and µ0 ∼ π,

µt+1 ≈ µtP + ztπ∆ , yt = 〈µt, κ〉

Choice for P?Consider symmetric nominal model,

00

0.5

1

Pool pump o� for i hours2412 i

0 1 2 T−1 T. . .

T

On

O�012

2

T−1

...

For each z, the transition matrix Pz is defined by a “twisted” model

44 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Numerical Example

Linearization for small zi, and µ0 ∼ π,

µt+1 ≈ µtP + ztπ∆ , yt = 〈µt, κ〉

Choice for P?Consider symmetric nominal model,

00

0.5

1

Pool pump o� for i hours2412 i

0 1 2 T−1 T. . .

T

On

O�012

2

T−1

...

For each z, the transition matrix Pz is defined by a “twisted” model44 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Numerical Example

For each z, the transition matrix Pz is defined by a “twisted” model

Pool pump o� for i hours24120

0.5

1

z =- 6z =

- 4

z = 4

z = 0

z = 6

Pz ≈ P + z∆

45 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Steady-State Approximations

The optimal cost η∗z and aquadratic approximation

η∗(zz

)

η0z

η0z

− 12 ς 2

0z2

−10 −5 5 10

−6

−4

−2

2

4

Approximation of thesteady-state probability thata pool-pump is operating

−10 −8 −6 −4 −2 0 2 4 6 8 10 z

P{pool is on}1− (η0 − zς2

0 )

0

0.5

1

46 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Steady-State Approximations

The optimal cost η∗z and aquadratic approximation

η∗(zz

)

η0z

η0z

− 12 ς 2

0z2

−10 −5 5 10

−6

−4

−2

2

4

Approximation of thesteady-state probability thata pool-pump is operating

−10 −8 −6 −4 −2 0 2 4 6 8 10 z

P{pool is on}1− (η0 − zς2

0 )

0

0.5

1

46 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Linear System Analysis

Linearization is Minimum phase!

−1 0 1−1

0

1

Real Part

Imag

inar

y Pa

rt

Solidarity of linear and nonlinear models:

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

Inpu

t zLine

ar R

espo

nse

Mar

kov

Resp

onse

10%

20%

30%

40%

50%

60%

70%

80%

0 500 1000 Time in hours

47 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Linear System Analysis

Linearization is Minimum phase!

−1 0 1−1

0

1

Real Part

Imag

inar

y Pa

rt

Solidarity of linear and nonlinear models:

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

Inpu

t zLine

ar R

espo

nse

Mar

kov

Resp

onse

10%

20%

30%

40%

50%

60%

70%

80%

0 500 1000 Time in hours

47 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Grid-level PI Control

Minimum phase suggests a simple control law should work

Assumption: Pools check the regulation signal each half hour, but theyhave no common clock (addresses delay at grid level)PI Control:

zt = ket + kIeIt

where e = ydesired − y and

eIt =t∑0

ei

48 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Grid-level PI Control

Minimum phase suggests a simple control law should work

Assumption: Pools check the regulation signal each half hour, but theyhave no common clock (addresses delay at grid level)

PI Control:zt = ket + kIe

It

where e = ydesired − y and

eIt =t∑0

ei

48 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Grid-level PI Control

Minimum phase suggests a simple control law should work

Assumption: Pools check the regulation signal each half hour, but theyhave no common clock (addresses delay at grid level)

PI Control:zt = ket + kIe

It

where e = ydesired − y and

eIt =t∑0

ei

48 / 57

Intelligent Pools in Florida Mean-field model for one million pools

Reconsidering One Million PoolsMean-Field Model: Grid-level PI Control

PI Control takes care of low-pass BPA regulation:

−200

−100

0

100

200

July 18 July 20July 19 July 21 July 23July 22 July 24

Reference Output deviation (in MWs)

MW

49 / 57

Conclusions & Suggestions

Conclusions & Suggestions

50 / 57

Conclusions & Suggestions

Smart Grid 2020A playground for control theory

Baseline generationVolatility from natureConsumer demand (est.)

Power ConsumptionQuality of Life

Power Grid

Increasing timescale of ancillary service

GovernorsFlywheels

Coal GenerationFlexible Manufacturing

Distributed Data Centers

CapacitorBanks

Hydro Generation Gas Turbine Generation

Heating, Ventillation & Cooling

BatteriesPool Pumps

51 / 57

Conclusions & Suggestions

Smart Grid 2020A playground for control theory

Baseline generationVolatility from natureConsumer demand (est.)

Power ConsumptionQuality of Life

Power Grid

Increasing timescale of ancillary service

GovernorsFlywheels

Coal GenerationFlexible Manufacturing

Distributed Data Centers

CapacitorBanks

Hydro Generation Gas Turbine Generation

Heating, Ventillation & Cooling

BatteriesPool Pumps

Open problems near the pool

. Network issues: Needs of the grid are regional.

. Communication architecture: Local and global signals(such as local voltage?

. Consumer risk: On average, quality of service is perfect,but for one pool... frogs and algae?

. Grid-level risk: ???

52 / 57

Conclusions & Suggestions

Smart Grid 2020A playground for control theory

Baseline generationVolatility from natureConsumer demand (est.)

Power ConsumptionQuality of Life

Power Grid

Increasing timescale of ancillary service

GovernorsFlywheels

Coal GenerationFlexible Manufacturing

Distributed Data Centers

CapacitorBanks

Hydro Generation Gas Turbine Generation

Heating, Ventillation & Cooling

BatteriesPool Pumps

Open problems near the pool

. Network issues: Needs of the grid are regional.

. Communication architecture: Local and global signals(such as local voltage?

. Consumer risk: On average, quality of service is perfect,but for one pool... frogs and algae?

. Grid-level risk: ???

52 / 57

Conclusions & Suggestions

Smart Grid 2020A playground for control theory

Baseline generationVolatility from natureConsumer demand (est.)

Power ConsumptionQuality of Life

Power Grid

Increasing timescale of ancillary service

GovernorsFlywheels

Coal GenerationFlexible Manufacturing

Distributed Data Centers

CapacitorBanks

Hydro Generation Gas Turbine Generation

Heating, Ventillation & Cooling

BatteriesPool Pumps

Open problems near the pool

. Network issues: Needs of the grid are regional.

. Communication architecture: Local and global signals(such as local voltage?

. Consumer risk: On average, quality of service is perfect,

but for one pool... frogs and algae?

. Grid-level risk: ???

52 / 57

Conclusions & Suggestions

Smart Grid 2020A playground for control theory

Baseline generationVolatility from natureConsumer demand (est.)

Power ConsumptionQuality of Life

Power Grid

Increasing timescale of ancillary service

GovernorsFlywheels

Coal GenerationFlexible Manufacturing

Distributed Data Centers

CapacitorBanks

Hydro Generation Gas Turbine Generation

Heating, Ventillation & Cooling

BatteriesPool Pumps

Open problems near the pool

. Network issues: Needs of the grid are regional.

. Communication architecture: Local and global signals(such as local voltage?

. Consumer risk: On average, quality of service is perfect,but for one pool...

frogs and algae?

. Grid-level risk: ???

52 / 57

Conclusions & Suggestions

Smart Grid 2020A playground for control theory

Baseline generationVolatility from natureConsumer demand (est.)

Power ConsumptionQuality of Life

Power Grid

Increasing timescale of ancillary service

GovernorsFlywheels

Coal GenerationFlexible Manufacturing

Distributed Data Centers

CapacitorBanks

Hydro Generation Gas Turbine Generation

Heating, Ventillation & Cooling

BatteriesPool Pumps

Open problems near the pool

. Network issues: Needs of the grid are regional.

. Communication architecture: Local and global signals(such as local voltage?

. Consumer risk: On average, quality of service is perfect,but for one pool... frogs and algae?

. Grid-level risk: ???

52 / 57

Conclusions & Suggestions

Smart Grid 2020A playground for control theory

Baseline generationVolatility from natureConsumer demand (est.)

Power ConsumptionQuality of Life

Power Grid

Increasing timescale of ancillary service

GovernorsFlywheels

Coal GenerationFlexible Manufacturing

Distributed Data Centers

CapacitorBanks

Hydro Generation Gas Turbine Generation

Heating, Ventillation & Cooling

BatteriesPool Pumps

Open problems near the pool

. Network issues: Needs of the grid are regional.

. Communication architecture: Local and global signals(such as local voltage?

. Consumer risk: On average, quality of service is perfect,but for one pool... frogs and algae?

. Grid-level risk: ???

52 / 57

Conclusions & Suggestions

Smart Grid 2020A playground for economists

TOU prices for peak shaving, and

Contracts for real-time demand-response services

Successful contracts today: Constellation Energy, Alcoa, residential pool

pumps, commercial buildings ...

Efficiency loss2, but utility and consumers each have reliable services

New smart appliances that can facilitate these contracts

Control theory to make this all work:

We don’t know why the grid is so robust today. Introducingall of these dynamics will lead to new control challenges.

Energy policy that is guided by an understanding of both physics andeconomics

Thank You!

2Extra credit: define efficiency53 / 57

Conclusions & Suggestions

Smart Grid 2020A playground for economists

TOU prices for peak shaving, and

Contracts for real-time demand-response services

Successful contracts today: Constellation Energy, Alcoa, residential pool

pumps, commercial buildings ...

Efficiency loss2, but utility and consumers each have reliable services

New smart appliances that can facilitate these contracts

Control theory to make this all work:

We don’t know why the grid is so robust today. Introducingall of these dynamics will lead to new control challenges.

Energy policy that is guided by an understanding of both physics andeconomics

Thank You!

2Extra credit: define efficiency53 / 57

Conclusions & Suggestions

Smart Grid 2020A playground for economists

TOU prices for peak shaving, and

Contracts for real-time demand-response services

Successful contracts today: Constellation Energy, Alcoa, residential pool

pumps, commercial buildings ...

Efficiency loss2, but utility and consumers each have reliable services

New smart appliances that can facilitate these contracts

Control theory to make this all work:

We don’t know why the grid is so robust today. Introducingall of these dynamics will lead to new control challenges.

Energy policy that is guided by an understanding of both physics andeconomics

Thank You!

2Extra credit: define efficiency53 / 57

Conclusions & Suggestions

Smart Grid 2020A playground for economists

TOU prices for peak shaving, and

Contracts for real-time demand-response services

Successful contracts today: Constellation Energy, Alcoa, residential pool

pumps, commercial buildings ...

Efficiency loss2, but utility and consumers each have reliable services

New smart appliances that can facilitate these contracts

Control theory to make this all work:

We don’t know why the grid is so robust today. Introducingall of these dynamics will lead to new control challenges.

Energy policy that is guided by an understanding of both physics andeconomics

Thank You!

2Extra credit: define efficiency53 / 57

Conclusions & Suggestions

Smart Grid 2020A playground for economists

TOU prices for peak shaving, and

Contracts for real-time demand-response services

Successful contracts today: Constellation Energy, Alcoa, residential pool

pumps, commercial buildings ...

Efficiency loss2, but utility and consumers each have reliable services

New smart appliances that can facilitate these contracts

Control theory to make this all work:

We don’t know why the grid is so robust today. Introducingall of these dynamics will lead to new control challenges.

Energy policy that is guided by an understanding of both physics andeconomics

Thank You!

2Extra credit: define efficiency53 / 57

Conclusions & Suggestions

Control TechniquesFOR

Complex Networks

Sean Meyn

Pre-publication version for on-line viewing. Monograph available for purchase at your favorite retailer More information available at http://www.cambridge.org/us/catalogue/catalogue.asp?isbn=9780521884419

Markov Chainsand

Stochastic Stability

S. P. Meyn and R. L. Tweedie

August 2008 Pre-publication version for on-line viewing. Monograph to appear Februrary 2009

π(f

)<∞

∆V (x) ≤ −f(x) + bIC(x)

‖P n(x, · )− π‖f → 0

supCE

x [Sτ

C(f)]

<∞

References

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References

References: Economics

G. Wang, M. Negrete-Pincetic, A. Kowli, E. Shafieepoorfard, S. Meyn, and U. Shanbhag.Dynamic competitive equilibria in electricity markets. In A. Chakrabortty and M. Illic,editors, Control and Optimization Theory for Electric Smart Grids. Springer, 2011.

M. Negrete-Pincetic and S. Meyn. Where is the Missing Money? The impact of generationramping costs in electricity markets. In preparation, 2012.

G. Wang, A. Kowli, M. Negrete-Pincetic, E. Shafieepoorfard, and S. Meyn.A control theorist’s perspective on dynamic competitive equilibria in electricity markets. InProc. 18th World Congress of the International Federation of Automatic Control (IFAC),Milano, Italy, 2011.

S. Meyn, M. Negrete-Pincetic, G. Wang, A. Kowli, and E. Shafieepoorfard. The value ofvolatile resources in electricity markets. In Proc. of the 10th IEEE Conf. on Dec. andControl, Atlanta, GA, 2010.

I.-K. Cho and S. P. Meyn. Efficiency and marginal cost pricing in dynamic competitivemarkets with friction. Theoretical Economics, 5(2):215–239, 2010.

U.S. Energy Information Administration. Smart grid legislative and regulatory policies andcase studies. December 12 2011.http://www.eia.gov/analysis/studies/electricity/pdf/smartggrid.pdf

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References

References: Demand Response

H. Hao, A. Kowli, Y. Lin, P. Barooah, and S. Meyn Ancillary Service for the Grid ViaControl of Commercial Building HVAC Systems. ACC 2013 (much more on our websites)

S. Meyn, P. Barooah, A. Busic, and J. Ehren. Ancillary service to the grid from deferrableloads: the case for intelligent pool pumps in Florida. IEEE Conference on Decision &Control (invited), 2014

P. Xu, P. Haves, M. Piette, and J. Braun, Peak demand reduction from pre-cooling withzone temperature reset in an office building, 2004.

D. Callaway and I. Hiskens, Achieving controllability of electric loads. Proceedings of theIEEE, vol. 99, no. 1, pp. 184–199, 2011.

D. Watson, S. Kiliccote, N. Motegi, and M. Piette, Strategies for demand response incommercial buildings. In Proceedings of the 2006 ACEEE Summer Study on EnergyEfficiency in Buildings, August 2006.

S. Kundu, N. Sinitsyn, S. Backhaus, and I. Hiskens, Modeling and control ofthermostatically controlled loads, Arxiv preprint arXiv:1101.2157, 2011. [Online]. Available:http://arxiv.org/abs/1101.2157

S. Koch, J. Mathieu, and D. Callaway, Modeling and control of aggregated heterogeneousthermostatically controlled loads for ancillary services, in Proc. PSCC, 2011, pp. 1–7.

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References

References: Markov Models

I. Kontoyiannis and S. P. Meyn. Spectral theory and limit theorems for geometricallyergodic Markov processes. Ann. Appl. Probab., 13:304–362, 2003.

I. Kontoyiannis and S. P. Meyn. Large deviations asymptotics and the spectral theory ofmultiplicatively regular Markov processes. Electron. J. Probab., 10(3):61–123 (electronic),2005.

E. Todorov. Linearly-solvable Markov decision problems. In B. Scholkopf, J. Platt, andT. Hoffman, editors, Advances in Neural Information Processing Systems 19, pages1369–1376. MIT Press, Cambridge, MA, 2007.

M. Huang, P. E. Caines, and R. P. Malhame. Large-population cost-coupled LQG problemswith nonuniform agents: Individual-mass behavior and decentralized ε-Nash equilibria.IEEE Trans. Automat. Control, 52(9):1560–1571, 2007.

H. Yin, P. Mehta, S. Meyn, and U. Shanbhag. Synchronization of coupled oscillators is agame. Automatic Control, IEEE Transactions on, 57(4):920–935, 2012.

P. Guan, M. Raginsky, and R. Willett. Online Markov decision processes withKullback-Leibler control cost. In American Control Conference (ACC), 2012, pages1388–1393, 2012.

V.S.Borkar and R.Sundaresan Asympotics of the invariant measure in mean field modelswith jumps. Stochastic Systems, vol. 2, no. 2, pp.322-380, 2012.

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