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An Op&miza&on and Monte Carlo Planning Approach for High Penetra&ons
of Intermi;ent Renewables
Elaine K. Hart and Mark Z. Jacobson
INFORMS Annual Mee>ng, Aus>n, TX
November 8, 2010
Atmosphere/Energy Program
Dept. of Civil and Environmental Engineering
Stanford University ABabcdfghiejklSTANFORD UNIVERSITY
AT
M
OSP H E R E / E NERGY
1/15
How can the grid accommodate the intermittency of wind and solar to significantly reduce carbon emissions?
Hart and Jacobson
ABabcdfghiejklThe Challenge
2/15
Low Carbon PorAolio Planning Model
Hart and Jacobson
ABabcdfghiejkl
3/15
• Objective Functions – Cost (including annualized capital, fixed and variable O&M,
fuel, and cost of carbon (in 2050 scenario)
– Approximate Emissions – linear function of natural gas generation and spinning capacity
• Linear Constraints – System-wide power balance – Generator governing equations (affine w.r.t. capacity, fuel)
– Thermal plant ramp rates – Energy (integrated power) constraints
Hart and Jacobson
ABabcdfghiejklProblem Formula&ons
4/15 Hart and Jacobson
ABabcdfghiejklGenerator Technology Models
Hart and Jacobson
ABabcdfghiejklGenerator Technology Models
5/15
• System Load, Irradiance (GHI => DNI, DHI), Wind Speed
• Linear statistical models of the form:
where is comprised of func>ons like:
(a forecast)
(prior forecast error) (diurnal or seasonal bias)
(constant bias)
Use linear regression to find and characterize distribu>on Hart and Jacobson
ABabcdfghiejklRealiza&on Models
6/15
!
f (t) = A(t)! x + ˜ b
!
A(t) = a1(t) a2(t) …[ ]
!
ai(t) = ˆ f (t)ai(t) = ˆ f (t "1) " f (t "1)ai(t) = #(t)ai(t) =1
!
! x
!
˜ b
and is a random variable
To create each realiza&on, at each &me step: -‐Apply linear model -‐Sample the model error distribu>on -‐Impose site-‐site correla>ons where appropriate -‐Apply addi>onal models where necessary -‐eg. GHI => DNI => DHI
Hart and Jacobson
ABabcdfghiejklRealiza&on Produc&on
7/15
!
f (t) = A(t)! x + ˜ b
!
˜ b ~ N 0,"model( )
• Dispatch optimization includes expensive deficit in case of extreme forecast error.
• Deficit signal is used with LOLE to determine necessary spinning reserve capacity and schedule
Defi
cit
Realiza&on 1 Realiza&on 2 Realiza&on 3 Realiza&on N . . .
Maximum required spinning reserve capacity
Hart and Jacobson
ABabcdfghiejklEnsuring System Reliability
8/15
• Load scenarios: – 2005-2006 load data, 2050-2051 load projection
• Renewable Portfolios produced by minimizing: – Cost, Emissions
• Data: – Wind: Western Wind Integration Datasets (NREL, 3TIER)
– Irradiance: NSRDB (NREL) – Load: California ISO OASIS Database
• Solve using CVX (Grant and Boyd, 2010)
[17,520 time steps with 20 realizations each] Hart and Jacobson
ABabcdfghiejklCase Studies
9/15
2005 Scenarios 2050 Scenarios0
50
100
150
200
250
300
350
Capa
city
(GW
)
SolarWindNatural GasGeothermalHydro
Min.Cost
Min.CostMin.
CO2
Min.CO2
2005 Scenarios 2050 Scenarios0
50
100
150
200
250
300
350
400
450
500
Annu
al G
ener
atio
n (!
103 G
Wh)
SolarWindNatural GasGeothermalHydro
Min.Cost
Min.Cost
Min.CO2
Min.CO2
Capacity Genera&on
Hart and Jacobson, 2011. [In Review]!
Hart and Jacobson
ABabcdfghiejklSolved Generator PorAolios
10/15
Carbon-‐Free Genera&on Carbon Emissions
Hart and Jacobson, 2011. [In Review]!
Hart and Jacobson
Carbon Emissions Characteris&cs ABabcdfghiejkl
11/15
0
20
40
60
80
100
2005 Scenario 2050 Scenario
Car
bon-
Free
Gen
erat
ion
(%) Low-Cost
Low-Carbon
0
20
40
60
80
100
2005 Scenario 2050 Scenario
Car
bon
Emis
sion
s (1
06 tC
O2)
Low-Cost
Low-Carbon
5 10 15 200
50
100
150
Hour of Day
Pow
er G
ener
atio
n (G
W)
26!Jul!2051
5 10 15 200
50
100
150
Hour of Day
Pow
er G
ener
atio
n (G
W)
15!Nov!2050
5 10 15 200
50
100
150
Hour of Day
Pow
er G
ener
atio
n (G
W)
01!Jun!2050
5 10 15 200
50
100
150
Hour of Day
Pow
er G
ener
atio
n (G
W)
26!Feb!2050GeothermalWindPhotovoltaicSolar ThermalHydroelectricNatural GasNG ReserveDemand + T&D Losses
Winter
Summer
Spring
Autumn
Hart and Jacobson, 2011. [In Review]!Hart and Jacobson
Example Realiza&ons (2050 Low-‐CO2) ABabcdfghiejkl
12/15
0 0.1 0.2 0.3 0.4 0.5 0.60
50
100
150
200
250
Penetration of Wind and Solar
Carb
on In
tens
ity (t
CO2/G
Wh)
Stochastic SimulationsDeterministic Assumption
Porbolios produced by scaling 2005 low-‐carbon capaci>es uniformly
Stochas&c simula&ons: Monte Carlo simula>on with forecast error
Determinis&c assump&on: Simulate single realiza>on where forecast = actual data
Hart and Jacobson, 2011. [In Review]!Hart and Jacobson
ABabcdfghiejklStochas&c vs. Determinis&c
13/15
• We can provide >99% of generation from non-carbon based generators while meeting an LOLE requirement of 1 day in 10 years
• With conservative assumptions regarding thermal plant operation, can still achieve significant reductions in carbon emissions from base case levels
• Stochastic analyses are needed in system planning
• Low capacity factors will require enhanced capacity markets for thermal plants
Hart and Jacobson
ABabcdfghiejklConclusions
14/15
• Include hour-ahead forecasts • Improve forecast error characterization – Include phase errors
• Improve flexibility of hydroelectric generators • Build participating load and storage models – EV’s, Batteries, Fuel Cells, CAES
Hart and Jacobson
ABabcdfghiejklNext Steps
15/15
Thanks to:
• Gil Masters, Nick Jenkins
• Precourt Ins>tute for Energy Efficiency, Stanford Graduate Fellowship, NSF Graduate Research Fellowship
• Bethany Corcoran, Mike Dvorak, Graeme Hoste, Eric Stoutenburg, John Ten Hoeve
For more informa&on
(and a copy of this presenta>on):
www.stanford.edu/~ehart/
Ques&ons? ABabcdfghiejkl
Hart and Jacobson