1. Eco-Resort in Half Moon Bay
An eco-resort in Half Moon Bay being constructed wants to operate solely on renewable energy.
Data: Small Hotel and Large Restaurant CBECS data combined with additional load for Aquaponics Farm on
site (additional 14 kWh per hour)
Constraints: 25kWh available each from Heat Pump Water Heater and Electric Vehicle fleet. Maximum of
1.5MWh Pumped Hydro energy storage. Maximum land availability enforced.
Results:
Energy Portfolio with No Land Constraints
Energy Portfolio with 1-Acre Land Constraint
Sensitivity Analysis of Cost to Land Constraints
Optimizing an Energy Portfolio with Renewable Generation and Storage to Minimize Costs
Brock Taute
Department of Civil and Environmental Engineering
Stanford University, Stanford, CA 94305
MODEL
Objective Function:
Min: ∑
"#$#
%#
& + 4 ∑ ( 𝐶, 𝑔, 𝑡 −0 𝐶1 𝑔1 𝑡 )
where i is the subscript for each technology purchased,
X is the amount (in kW for generation technologies and kWh for storage technologies) installed for each technology,
C is the lifetime cost of each technology (also the price of electricity when bought or sold to the grid),
L is the lifetime in years of each technology (assuming a daily cycle for storage technologies), gp and gs are the amounts (kWh) of
electricity bought/sold to/from the grid at time t
The factor of 4 comes in because the analysis is only over a quarter-of-a-year’s worth of time, and the amount of electricity purchased
during this time is assumed to be the same for the entire year.
Decision Variables:
Xi - the amount (in kW for generation technologies and kWh for storage technologies) installed for each technology
Yj,in(t) and Yj,out(t) - the amount of electricity (in kWh) charged and discharged into each storage technology j at each time step
gp(t) and gs(t) - the amount of electricity (in kWh) purchased/sold from/to the grid at each time step
Constraints:
Flow Constraint:
∀ 𝑡 𝑖𝑛 𝑇𝐼𝑀𝐸: 𝐷 𝑡 = ∑ 𝑋& 𝐺& 𝑡& + ∑ ( 𝑌@,BC0 (𝑡)𝜂@ −
EF,#G 0
HF
@ ) + 𝑔,(𝑡) − 𝑔1(𝑡)
Where D(t) is the demand (in kWh) at time t
Gk(t) is the amount of electricity generated at each time step (in kWh) for each kW of the generation technology k installed
𝜂@is the charge and discharge efficiency of each storage type
Power Constraint:
∀ 𝑡 𝑖𝑛 𝑇𝐼𝑀𝐸, ∀ 𝑗 𝑖𝑛 𝑆𝑇𝑂𝑅𝐴𝐺𝐸 :
𝑌@(𝑡)
∆𝑡
≤ 𝑃@ (𝑋@)
Where ∆𝑡 is the time step
𝑃@ is the power ratio (kW/kWh installed) for each storage type j
State of Charge Constraint:
∀ 𝑡 𝑖𝑛 𝑇𝐼𝑀𝐸,∀ 𝑗 𝑖𝑛 𝑆𝑇𝑂𝑅𝐴𝐺𝐸: 𝑌@,BC0 (𝑡) ≤ 𝑆@(𝑡 − ∆𝑡)
Where
0 ≤ Sj(t) = Sj(t−∆𝑡) x (1−! 𝛿j) + 𝑌@,&S(t) −𝑌@,BC0(t) ≤ 𝑋@
𝛿j is the rate of self-discharge for each storage type k
Power Constraint:
∀ 𝑡 𝑖𝑛 𝑇𝐼𝑀𝐸: YCSP,in(t) ≤ XSolTherm(GSolTherm(t))
Installation Maximum Constraint:
∀ 𝑖 𝑖𝑛 𝑇𝐸𝐶𝐻𝑁𝑂𝐿𝑂𝐺𝑌: Xj
≤ Xj,MAX
Land Constraint:
W 𝑋& 𝐹& ≤ 𝐿YZ"
&
Where Fi is the footprint (in ft2/kW) of the installed technology i
LMAX is the total land area available (ft2)
Generation Parameter:
Solar:
∀ 𝑘 𝑖𝑛 𝐺𝐸𝑁𝐸𝑅𝐴𝑇𝐼𝑂𝑁: Gk(t) = Ik(t)
Where Ik(t) is the solar insolation over the last time step (in kWh), (since amount of solar installed is in kW, efficiencies aren’t necessary
in the generation parameter)
Wind:
Gk(t) =
−.0182u(t)5 + 1.4386u(t)4 – 42.536u(t)3 + 563.73u(t)2 – 3019.6u(t) + 5543.6
]^^
∆𝑡
Where u(t) is the wind speed at time t. This is based on a fit to the power curve of the 2.5MW wind turbine at General Electric
Technology Costs Lifetime
(Years)
Charge
Efficiency
(%, as a
decimal)
Self-
Discharge
(%, as a
decimal)
Storage
Power:Energy
Ratio
(kW/kWh)
Footprint (ft2/kW
of generation,
ft2/kWh of storage)
CdTe
Photovoltaics
$1750/kW 27 NA NA NA 86.11
Mono-Silicon
Photovoltaics
$3000/kW,
$.05/kWh
33 NA NA NA 54.41
Concentrated
Solar Thermal
$6000/kW,
$.09/kWh
30 NA NA NA .1176
Wind $2680/kW,
$.04/kWh
20 NA NA NA .7
LithiumIon
Batteries
$250/kWh 10 .93 4E-5 .33 0 (In households)
Hydrogen Fuel
Cells
$250/kWh 27 .60 0 .1 .35879
Molten Nitrate
SaltsThermal
Storage
$.12.kWh 30 .99 .1 2 0 (Assumed in
Solar Thermal)
Pumped Hydro $100/kWh 75 .85 0 .5 0 (Underground)
Electric Vehicles 0 (Already
assumed in
analysis)
20 .93 4E-5 .33 0 (On the road or
in garages)
Heat Pump Water
Heaters
0 (Already
assumed in
analysis)
20 .9 .1 1 0 (In houses)
DATA
Technology:
Data from NREL Cost Reports and Spec Sheets from Manufacturing Companies
Resources:
Typical Meteorological Year data at hourly intervals from weather reports at local weather station Spring
Valley, CA
Cross-Referenced with NREL Solar and Wind Maps
Demand:
The hourly demand predicted by Energy Plus simulations using Commercial Building Energy Consumption
Survey data and San Francisco T.M.Y. information
INTRODUCTION
• There are many reasons to incorporate renewable energy into a location’s energy portfolio.
• Environmental Concern
• Cheaper Electricity
• Grid Independence
• In all cases, finding the most cost effective solution is difficult and may be the reason that renewable
energy implementation at a site never takes place.
• Variable Resource Availability
• Many Different Technologies to Consider
• Seasonal Demand Changes
• Optimizing an energy portfolio for cost ensures the renewable energy integration yields the most value
possible.
• Automating the process of picking technologies removes any bias toward one technology.
• Playing with constraints and running sensitivity analyses allows for many different factors to be weighted
when making a decision.
• Having a model that has access to a lot of data from reliable sources simplifies the process of determining
which technologies to install and makes renewable energy more accessible.
• Having a model that operates quickly and cheaply makes the value of distributed renewable energy more
clear.
22501.6
1338.69
5552.25
25
25 1500 153.426 CdTe
MonoSi
SolTherm
Wind
CSP
Fuel Cell
EV
HPWH
Hydro
Lithium Ion
787.36
18001.2
1378.42
4719.65
CdTe
MonoSi
SolTherm
Wind
CSP
Fuel Cell
EV
HPWH
Hydro
Lithium Ion
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 10 20 30 40 50
Annual Cost of Electricity
($ Million)
Acres of Land Available for Installations
CONCLUSIONS
Model
• Robust models are useless if there isn’t enough operating power to run them in a timely
fashion.
• Simplifications can make a model much more useful while still providing accurate results.
Trial
• Cheaper energy solutions often occupy more land
• Solar thermal technology becomes advantageous when large amounts of storage are needed,
due to its cheap thermal storage aspect
• Combinations of wind and solar technology enable the best value.
FUTURE WORK
• Create an online user face to operate the model
• Automate the process of collecting data on locations and simulating load profiles
• Incorporate energy efficiency projects into the objective function
• Find more data to model residential building loads
RESOURCES
NREL Solar Cost Analysis, NREL Wind Cost Analysis, CBECS-EIA, Energy Plus, Spring Valley Weather Station
Tesla, Sun Power, First Solar, GE, EPS