computational methods for sustainable energyzkolter/ijcai13/tutorial.pdf · computational methods...
TRANSCRIPT
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
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
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?
You: need to supply power to the country
5,500 power plants (925 GW capacity)
Data: U.S. Energy Informational Administration, 2010 U.S. Census, Institutefor Electric Efficiency, Argonne National Labs
J. Zico Kolter
Why computation/AI?
You: need to supply power to the country
5,500 power plants (925 GW capacity)
83m residential and 5m commerical/industrial buildings (768 GW peak demand)
Data: U.S. Energy Informational Administration, 2010 U.S. Census, Institutefor Electric Efficiency, Argonne National Labs
J. Zico Kolter
Why computation/AI?
You: need to supply power to the country
5,500 power plants (925 GW capacity)
83m residential and 5m commerical/industrial buildings (768 GW peak demand)
172k miles of transmission lines
Data: U.S. Energy Informational Administration, 2010 U.S. Census, Institutefor Electric Efficiency, Argonne National Labs
J. Zico Kolter
Why computation/AI?
You: need to supply power to the country
5,500 power plants (925 GW capacity)
83m residential and 5m commerical/industrial buildings (768 GW peak demand)
172k miles of transmission lines
49 GW of installed wind/solar capcity
Data: U.S. Energy Informational Administration, 2010 U.S. Census, Institutefor Electric Efficiency, Argonne National Labs
J. Zico Kolter
Why computation/AI?
102
34
567
89 10
2
34
567
89 10
2
34
567
89 10
2
34
567
89 10
2
34
567
89
You: need to supply power to the country
5,500 power plants (925 GW capacity)
83m residential and 5m commerical/industrial buildings (768 GW peak demand)
172k miles of transmission lines
30m installed smart meters
49 GW of installed wind/solar capcity
Data: U.S. Energy Informational Administration, 2010 U.S. Census, Institutefor Electric Efficiency, Argonne National Labs
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
Outline
• Introduction to sustainable energy and the smart grid
• Three highlighted topics:
– Power generation and demand forecasting
– Energy disaggregation
– Control in the smart grid
• 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
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
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Hour of Day
Hou
rly D
eman
d (G
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J. Zico Kolter
Possible features: previous day’s power
0 5 10 15 201.5
1.6
1.7
1.8
1.9
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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
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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
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Hour of Day
Pow
er (
GW
)
ActualPredicted
5 10 15 20
1.4
1.6
1.8
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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
)
ActualPredicted
Predictions for several days
J. Zico Kolter
5 10 15 200
0.05
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0.15
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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
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
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
• Introduction to sustainable energy and the smart grid
• Three highlighted topics:
– Power generation and demand forecasting
– Energy disaggregation
– Control in the smart grid
• Final thoughts
J. Zico Kolter
Energy disaggregation
J. Zico Kolter
J. Zico Kolter
J. Zico Kolter
RefrigeratorWasher/DryerLightingComputer...
5.6410.2315.209.40
J. Zico Kolter
J. Zico Kolter
J. Zico Kolter
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er (
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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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er (
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Power signal for refrigerator
J. Zico Kolter
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er (
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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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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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Power (watts)
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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er (
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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
Research directions for AI
• 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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er (
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ts)
unassignedkitchen outletsmicrowavewasher dryer
True breakdown Our approach
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Unassignedkitchen outletsfurnacebath gfimicrowavekitchen outletswasher dryer
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er (
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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
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
• 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
The challenge of electrical grid control
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You: need to supply power to the country
5,500 power plants (925 GW capacity)
83m residential and 5m commerical/industrial buildings (768 GW peak demand)
172k miles of transmission lines
30m installed smart meters
49 GW of installed wind/solar capcity
Data: U.S. Energy Informational Administration, 2010 U.S. Census, Institutefor Electric Efficiency, Argonne National Labs
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
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1
1.5
2
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3
3.5
Hour
Val
ue
Slow Ramping GeneratorFast Ramping GeneratorPumped Storage EnergyBattery Energy
J. Zico Kolter
Research directions for AI
• 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
• 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
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