Computational Methods for Sustainable Energyzkolter/ijcai13/tutorial.pdf · Computational Methods...

Computational Methods forSustainable Energy

J. Zico Kolter

August 5, 2013IJCAI

J. Zico Kolter

Outline

• Introduction to sustainable energy and the smart grid

• Three highlighted topics:

– Power and demand forecasting

– Energy disaggregation

– Control in the smart grid

• Final thoughts

J. Zico Kolter

“Sustainable energy”

“Sustainable development is development that meetsthe needs of the present without compromising theability of future generations to meet their own needs.”

– UN Report “Our Common Future”, 1987

J. Zico Kolter

U.S. energy consumption

1850 1900 1950 20000

0.5

1

1.5

2

2.5

3

3.5

Year

Ave

rage

Pow

er (

TW

)

CoalNatural GasPetroleumHydro / Nuclear / BiomassWind / Solar / Geothermal

Data: U.S. Energy Information AdministrationJ. Zico Kolter

U.S. energy consumption

Hydro2.51

Biomass4.29

Geothermal0.21

Wind0.92

Solar0.11

Nuclear8.44

Coal20.82

NaturalGas

24.65

Petroleum35.97

ElectricityGeneration

39.49

Residential11.79

Commercial8.71

Industrial23.27

Trans-portation

27.45

EnergyServices

41.88

Net ElectricityImports

Estimated U.S. Energy Use in 2010: ~98.0 Quads

Source: LLNL 2011. Data is based on DOE/EIA-0384(2010), October 2011. If this information or a reproduction of it is used, credit must be given to the Lawrence Livermore National Laboratoryand the Department of Energy, under whose auspices the work was performed. Distributed electricity represents only retail electricity sales and does not include self-generation. EIA

reports flows for hydro, wind, solar and geothermal in BTU-equivalent values by assuming a typical fossil fuel plant "heat rate." (see EIA report for explanation of change to geothermal in 2010).The efficiency of electricity production is calculated as the total retail electricity delivered divided by the primary energy input into electricity generation. End use efficiency is estimated as 80% for

the residential, commercial and industrial sectors, and as 25% for the transportation sector. Totals may not equal sum of components due to independent rounding. LLNL-MI-410527

RejectedEnergy56.13

20.59

4.65

1.74

2.36

26.78

0.02

5.06

0.01

0.100.04

0.02

0.03

3.28

4.54

4.95

8.44

0.68

8.11

3.28

7.52

19.13

0.06

1.62

0.44

0.42

0.11

2.23

1.100.38

1.22

0.71

8.01

25.65

9.43

6.97

18.62

6.86

2.49

0.09

0.92

0.15

12.71

Lawrence LivermoreNational Laboratory

J. Zico Kolter

U.S. petroleum production

1900 1920 1940 1960 1980 20000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Year

US

Per

trol

eum

Pro

duct

ion

(TW

)

Data: U.S. Energy Information AdministrationJ. Zico Kolter

Atmospheric carbon dioxide

1000 1200 1400 1600 1800 2000260

280

300

320

340

360

380

400

Year

Atm

osph

eric

CO

2 Con

cent

ratio

n (P

PM

)

Data: NOAA and Eteridge et al., 1998J. Zico Kolter

Atmospheric carbon dioxide

0100200300400500600150

200

250

300

350

400

1000 Years Before Present

Atm

osph

eric

CO

2 Con

cent

ratio

n (P

PM

)

Data: Barnola et al., 2003, Siegenthaler et al., 2005J. Zico Kolter

For additional discussion...

Wind:20 kWh/d

PV, 10 m2/p: 5

PV farm(200m2/p):50 kWh/d

Biomass: food,biofuel, wood,waste incin’n,landfill gas:24 kWh/d

Hydro: 1.5 kWh/d

Shallowoffshorewind:

16 kWh/d

Deepoffshorewind:

32 kWh/d

Wave: 4 kWh/d

Tide:11 kWh/d

Geothermal: 1kWh/d

Solar heating:13 kWh/d

Car:40 kWh/d

Jet flights:30 kWh/d

Light: 4kWh/d

Gadgets: 5

Food, farming,fertilizer:15 kWh/d

Stuff:48+ kWh/d

Transportingstuff: 12 kWh/d

“Defence”: 4

Heating,cooling:37 kWh/d

http://www.withouthotair.com

J. Zico Kolter

http://www.withouthotair.com

Why computation/AI?

You: need to supply power to the country

Data: U.S. Energy Informational Administration, 2010 U.S. Census, Institutefor Electric Efficiency, Argonne National Labs

J. Zico Kolter

Why computation/AI?


5,500 power plants (925 GW capacity)


J. Zico Kolter

Why computation/AI?



83m residential and 5m commerical/industrial buildings (768 GW peak demand)


J. Zico Kolter

Why computation/AI?




172k miles of transmission lines


J. Zico Kolter

Why computation/AI?





49 GW of installed wind/solar capcity


J. Zico Kolter

Why computation/AI?

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30m installed smart meters



J. Zico Kolter

Outline






• Final thoughts

J. Zico Kolter

Outline



– Power generation and demand forecasting



• Final thoughts

J. Zico Kolter

Pittsburgh electricity consumption

0 5 10 15 201

1.5

2

2.5

3

Hour of Day

Hou

rly D

eman

d (G

W)

Feb 9Jul 13Oct 10

Data: PJM http://www.pjm.com J. Zico Kolter

http://www.pjm.com

Electricity forecasting

• One of the most common tasks in energy system scheduling isforecasting how much electricity a region will consume

• Lets us plan, in advance, how we are going to allocategeneration (especially important for slow-starting generators)

• Will need to re-schedule generation in real-time to make up forerrors, but gives a good baseline

J. Zico Kolter

A natural supervised learning setup

• Electricity forecasting is naturally formulated as a multi-outputregression problem

yt = f(xt)

where

– yt ∈ R24 = predicted consumption over the next 24 hours,starting at time t

– xt ∈ Rk = features that can help predict consumption over thenext 24 hours

J. Zico Kolter

Possible features: hour of day

0 5 10 15 201

1.5

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2.5

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Hour of Day

Hou

rly D

eman

d (G

W)

Feb 9Jul 13Oct 10

J. Zico Kolter

Possible features: previous day’s power

0 5 10 15 201.5

1.6

1.7

1.8

1.9

2

2.1

Hour of Day

Hou

rly D

eman

d (G

W)

Feb 12, 2008Feb 13, 2008

J. Zico Kolter

Possible features: temperature

0 20 40 60 80 100

1.5

2

2.5

3

High Temperature (F)

Pea

k H

ourly

Dem

and

(GW

)

J. Zico Kolter

(Multiple) linear regression

• Model predicted consumption as a linear model

yt = ΘTxt

where

– yt ∈ R24 = predicted consumption over the next 24 hours,starting at time t

– xt ∈ Rk = {hour of day, previous 24 hours of power, previous 24hours and next 24 hours of temperature (+ non-linear features)}

– Θ ∈ R24×k regression parameters

J. Zico Kolter

• MATLAB code for electricity forecasting

% file format is: <utc timestamp> <load> <temperature>

data = load('pjm_load_data.txt');

% form output and feature vectors

Y = hankel(data(25:end-23,2), data(end-23:end,2));

X_power = hankel(data(1:end-47,2), data(end-47:end-24,2));

X_temp = hankel(data(1:end-47,3), data(end-47:end,3));

hour = mod(data(1:size(X_power,1),1)/3600,24);

X_hour_of_day = sparse(1:size(hour,1), hour+1, ...

ones(size(hour,1),1));

% multiple linear regression

X = [X_power X_temp X_temp.^2 X_temp.^3 X_hour_of_day];

Theta = X \ Y;

Y_pred = X*Theta;

J. Zico Kolter

5 10 15 201

1.5

2

Hour of Day

Pow

er (

GW

)

ActualPredicted

5 10 15 201.4

1.6

1.8

2

Hour of Day

Pow

er (

GW

)

ActualPredicted

5 10 15 20

1.4

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Hour of Day

Pow

er (

GW

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ActualPredicted

5 10 15 20

1.2

1.4

1.6

1.8

2

Hour of Day

Pow

er (

GW

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ActualPredicted

Predictions for several days

J. Zico Kolter

5 10 15 200

0.05

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0.15

0.2

0.25

Prediction Horizon (Hours)

Roo

t Mea

n S

quar

ed E

rror

(G

W)

All featuresHour of day onlyHour of day + previous powerHour of day + temperature

Errors omitting various features

J. Zico Kolter

From demo to state-of-the-art

• With a few additions, this is a state-of-the-art, deployed system:

– PJM Manual 19: Load Forecasting and Analysis. PJM. Availableat: http://www.pjm.com/~/media/documents/manuals/m19.ashx

– Neural network, additional features forweekdays/weekends/holidays, more nuanced treatment oftemperature (heating/cooling degree days)

• A huge existing literature on the topic:Soliman, S. A. and Al-Kandari, A. M. (2010). Electrical LoadForecasting: Modeling and Model Construction. Elsevier.

J. Zico Kolter

http://www.pjm.com/~/media/documents/manuals/m19.ashx

Renewable generation forecasting

• Can apply the exact same methodology to forecast thegeneration of uncertain sources like wind or solar power

• Some work in the area, but a much more recent topic:

– A. Costa, et al. A review on the young history of the wind powershort-term prediction. Renewable and Sustainable EnergyReviews, 12(6):17251744, 2008.

– C. Monteiro, et al. Wind power forecasting: state-of-the-art2009. Technical report, Argonne National Laboratory (ANL),2009

– Kaggle Global Energy Forecasting Competition, 2013.http://gefcom.org

J. Zico Kolter

http://gefcom.org

Research directions for AI

• How do we make multiple predictions across spatially-similarregions?

• How do we deal with uncertainty in the predictions?

• How can we use these predictions to actually optimally schedulegeneration (more on this later)

J. Zico Kolter

Large-scale probabilistic forecasting

• Some of our recent work on the topic:M. Wytock, J.Z. Kolter. Sparse Gaussian conditional randomfields: Algorithms, theory, and application to energy forecasting.ICML, 2013.

J. Zico Kolter

• Algorithm: sparse conditional Gaussian random field (SGCRF)

x1 x2

· · ·

xnx3

y1

· · ·

y2 ypy3

• Mathematical formulation:

p(y|x) ∼ exp{−yTΛy − 2yTΘx

}, Λ ∈ Rp×p,Θ ∈ Rp×n

• Train using maximum likelihood estimation with `1regularization on Λ and Θ

minimizeΛ,Θ

log p(Y |X) + λ(‖Λ‖1 + ‖Θ‖1)

J. Zico Kolter

Performance on wind forecasting

10−2

10−1

100

0.2

0.3

0.4

0.5

λ

MS

E

SGCRFLS

• Least-squares here uses highly tuned features, got 5th place inKaggle Global Energy Forecasting Competition.

J. Zico Kolter

Performance on load forecasting

10−3

10−2

10−1

0.04

0.06

0.08

0.1

0.12

λ

MS

E

SGCRFPJM forecast

• “PJM” is deployed solution at utility.

J. Zico Kolter

Summary: energy forecasting

• Application: Predicting future demand on the electrical grid, orfuture generation of renewable sources

• Algorithm: Supervised learning techniques for forecasting;recent work involving large-scale probabilistic modeling

J. Zico Kolter

Outline



– Power generation and demand forecasting



• Final thoughts

J. Zico Kolter

Energy disaggregation

J. Zico Kolter

J. Zico Kolter

RefrigeratorWasher/DryerLightingComputer...

5.6410.2315.209.40

J. Zico Kolter

J. Zico Kolter

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Wat

ts)

J. Zico Kolter

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J. Zico Kolter

A slightly simpler problem...

• Given power traces for a single device, determine if it is a givendevice (e.g. a refrigerator) or not

• Often used as a sub-step of a full energy disaggregationalgorithms

J. Zico Kolter

1000 2000 3000 4000 5000 6000 70000

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250

Time (seconds)

Pow

er (

wat

ts)

Power signal for refrigerator

J. Zico Kolter

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Constructing features from power signal

J. Zico Kolter

Refrigerator vs. other devices

120 140 160 180 200 220 240

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1500

2000

2500

Power (watts)

Dur

atio

n (s

econ

ds)

Other devicesRefrigerator

J. Zico Kolter

• MATLAB code for classifying devices (using YALMIPoptimization library to solve SVM)

% file format: <power> <duration> <+1/-1 for fridge>

data = load('device_signals.txt');

X = data(:,1:2);

y = data(:,3);

m = size(X,1);

% construct kernels and outputs

X = (X - repmat(mean(X),m,1)) ./ repmat(std(X),m,1);

sig = 1.0;

C = 100;

K = exp(-sqdist(X', X')/(2*sig^2)) + 1e-2*eye(m);

% solve SVM

a = sdpvar(m,1);

solvesdp([], a’*K*a + C*sum(max(0,1-y.*(K*a))), ...

sdpsettings('solver', 'sedumi'));

Y_pred = sign(K*double(a));

J. Zico Kolter

120 140 160 180 200 220 240

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1000

1500

2000

2500

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Dur

atio

n (s

econ

ds)

Kernelized SVM, Gaussian kernel (σ = 1.0)

J. Zico Kolter

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Dur

atio

n (s

econ

ds)

Kernelized SVM, Gaussian kernel (σ = 0.2)

J. Zico Kolter

Standard approach for energy disaggregation

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• State of the art (for 20+ years, e.g. Hart 1992): classify edgesin power signal, integrate to determine breakdown of energy.

• A recent survey: M. Ziefman and K. Roth. Nonintrusiveappliance load monitoring: Review and outlook. IEEETransactions on Consumer Electronics, 57(1):7684, 2011.

J. Zico Kolter


• Probabilistic disaggregation using source separation techniques(standard classification approach very sensitive to errors)

• Unsupervised/semi-supervised learning of appliance models

• Determining best feedback methods for giving information tousers

J. Zico Kolter

Disaggregation with Factorial HMMs

• Some of our recent work on the topic:J.Z. Kolter and T. Jaakkola. Approximate inference in additivefactorial HMMs. AISTATS, 2012.

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x(1)t−1 x

(1)t x

(1)t+1

yt−1 yt yt+1

x(2)t−1 x

(2)t x

(2)t+1

Factorial hidden Markov model(FHMM)

J. Zico Kolter

x(1)t−1 x

(1)t x

(1)t+1

yt−1 yt yt+1

x(2)t−1 x

(2)t x

(2)t+1

• Challenge: Inference (determining the most likely discretestates given observed output) is intractable for FHMMs

• Algorithmic work: New methods for approximate inference inFHMMs, based upon convex relaxations

J. Zico Kolter

• The trick: look at a probabilistic formulation in terms of thedifferences in total power

• Write inference as optimization problem

minimizeµ

T−1∑t−1

((yt+1 − yt)−

∑i

θTi µ(i)t

)2

subject to µ(i)t ∈ {0, 1}, ∀i, tµ

(i)1:T−1 “valid”, ∀i

where µ variables represent indication function of state changeand θ parameters denote mean power outputs

• Key property: if only one device changes state at any giventime, we can relax problem to linear program; solvingoptimization problem typically results in integral solutions

J. Zico Kolter

Performance

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unassignedkitchen outletsmicrowavewasher dryer

True breakdown Our approach

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Unassignedkitchen outletsfurnacebath gfimicrowavekitchen outletswasher dryer

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unassignedbath gfimicrowavefurnacekitchen outletskitchen outletswasher dryer

Event-based Structured mean fieldJ. Zico Kolter

Performance

Circuit Our Method Previous approx Event-basedMicrowave 98% / 66% 97% / 4% 98% / 28%Bath GFI 83% / 71% 50% / 9% 23% / 21%

Kitchen Outlets 38% / 13% 10% / 48% 57% / 15%Furnace 92% / 71% 13% / 15% 25% / 71%

Kitchen Outlets 45% / 16% 13% / 24% 27% / 11%Washer / Dryer 99% / 73% 89% / 77% 95% / 64%

Total 87% / 60% 36% / 45% 49% / 53%

Performance on example circuits in a home over two weeksAll data available at: http://redd.csail.mit.edu

J. Zico Kolter

http://redd.csail.mit.edu

Summary: energy disaggregation

• Application: Understand breakdowns of power from smartmeters

• Algorithm: Supervised learning for classifying devices, hiddenMarkov models and approximate inference approaches for sourceseparation in factorial HMMs

• Additional work: A great deal of follow on work, using REDDdata set, or other domains (e.g. conference paper at IJCAI onwater disaggregation)

J. Zico Kolter

Outline






• Final thoughts

J. Zico Kolter

The challenge of electrical grid control

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J. Zico Kolter

• Generators has very different costs, greenhouse emissions, andramp rates

• Transmission lines have different physical properties andcapacities

• Power can’t be “routed” like packets, obeys laws of physics

• Wind and solar provide “free” power (at least at operationtime), but are non-dispatchable, intermittent, and can’tcurrently be stored economically

• Emerging ability to also control load through “demandresponse”

J. Zico Kolter

Everything you ever wanted to know aboutpower systems but were afraid to ask

• Voltage: electric potential energy, 1 volt = 1 joule/coulomb

• Current: flow of charge, 1 ampere = 1 coulomb/second

• Ohm’s law: i = v/R

• Power: p = vi

J. Zico Kolter

• Alternating current (AC) systems: v(t) = v cos(ωt+ θ), v =voltage magnitude, ω = frequency, θ = phase/voltage angle

• Represent using complex numbers: v = vejθ, j =√−1

• Ohm’s law: i = Y v, where Y is admittance Y = 1/(R+ jX),X is reactance, X = ωL− 1

ωC , L is inductance and C iscapacitance

• Power: s = vi (· is complex conjugate), has both real andimaginary components, called real and reactive powerrespectively

J. Zico Kolter

• Power network: i ∈ Cn, v ∈ Cn

• Ohm’s law + Kirchoff’s voltage law: i = Y v where

Yk` =

{ − 1Rk`+jXk`

k 6= ` (0 if k, ` not connected)∑s 6=k

1Rsk+jXsk

k = `

• Flow over line via Ohm’s law: ik` = vk−v`Rk`+jXk`

J. Zico Kolter

• Power: s = diag vi = diag vY v

• Power flow: given some know powers/voltages, solve(non-linear) equation s = diag vY v

• Optimal power flow (OPF): Solve some optimization problem(e.g. minimize generation cost) subject to power flow constraint

• But non-linear equations is nasty, so we can simplify (assumevoltages equal, transmission lines have no resistance justreactance, small angle approximation) to get

p = Bθ, Bk` =

{ − 1Xk`

k 6= `∑s 6=k

1Xsk

k = `

called (in the worst naming convention ever) DC power flow

J. Zico Kolter

An example of DC OPF

• An example optimal power flow optimization problem

minimizepG,θ

n∑i=1

ci(pGi )

subject to Bθ = pG − pL

pG ≤ pG ≤ pG

|Bij(θi − θj)| ≤ F ij

where pG, θ ∈ Rn are optimization variables; B ∈ Rn×n is DCapproximate admittance matrix; pL ∈ Rn is a vector of loads ateach node; pG, pG ∈ Rn are generator upper and lower bounds;and Fij is the power capacity of the transmission line betweennodes i and j

J. Zico Kolter

IEEE 30 bus test system

J. Zico Kolter

• MATLAB code for DC optimal power flow

% load electrical network data from file

[B, p, gen, base_mva] = load_cdf_dc('ieee30cdf.txt');

n = size(B,1);

p_load = max(-p,0);

p_gen = sdpvar(n,1);

theta = sdpvar(n,1);

% set up costs and constraints

cost1 = p_gen(gen(1)) + p_gen(gen(1))^2;

cost2 = 0.5*p_gen(gen(2)) + 2*p_gen(gen(2))^2;

const = [B*theta == p_gen - p_load;

theta(1) == 0;

p_gen(setdiff(1:n,gen)) == 0;

abs(B(1,2)*(theta(1) - theta(2))) <= 0.9];

% solve optimization problem

solvesdp(const, cost1 + cost2, ...

sdpsettings('solver', 'sedumi'));

J. Zico Kolter

Beyond static optimal power flow

• Introduce receding horizon model predictive control objective

minimizepG1:T ,θ1:T

T∑t=1

c(pGt )

with power flow constraints

Bθt = pGt − pLt , t = 1, . . . , T

• Since we don’t know the future loads pLt , we use our loadforecasting methods to make the best predictions

J. Zico Kolter

Integrating renewables

• Additional wind power term

Bθt = pGt + pWt − pLt ,pWt ≤ pWt , t = 1, . . . , T

• Wind acts like a negative load,can’t be controlled, so still mustbe forecast

J. Zico Kolter

Storage

• Battery power

Bθt = pGt + (pBoutt − pBin

t )− pLt

• With battery dynamics

EBt+1 = EBt + 0.9pBint − pBout

t

and constraint that EBt ≥ 0.

J. Zico Kolter

Evolution of power and storage

4000 4050 4100 4150 4200 4250 43000

0.5

1

1.5

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2.5

3

3.5

Hour

Val

ue

Slow Ramping GeneratorFast Ramping GeneratorPumped Storage EnergyBattery Energy

J. Zico Kolter


• Load and renewables are inherently uncertain, how do we dealwith this uncertainty in optimization? −→ stochasticprogramming

• Generator costs are not really convex, many power plants havefixed startup time with zero generation −→ integer programming

• These systems are run in markets, how do we ensure thegenerators provide “accurate” costs? −→ game theory andmechanism design

• How will intelligent control strategies interact with each other?−→ multi-agent systems

J. Zico Kolter

Summary: energy forecasting

• Application: Methods for allocating power in large powernetworks with multiple constraints

• Algorithmic approach: Model predictive control techniques forfast online resource allocation

J. Zico Kolter

Outline






• Final thoughts

J. Zico Kolter

Final thoughts

• Energy issues pose some of the greatest challenges currentlyfacing society

• These have traditionally been viewed as physical or policychallenges

• Increasingly, prevalance of data means that computationalmethods have the potential to transform these domains as well

J. Zico Kolter

Some resources/venues

• Forecasting: International Journal of Forecasting, PES GlobalEnergy Forecasting Competition (likely to run again in 2013,check Kaggle.com).

• Disaggregation: REDD data set(http://redd.csail.mit.edu), International Workshop onNon-intrusive load monitoring

• Smart grid: IEEE Transactions on Smart Grid, IEEETransactions on Power Systems, IEEE Conference on Smart GridCommunications

J. Zico Kolter

http://redd.csail.mit.edu

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