IEOR 180 Senior Project Toni Geralde Mona Gohil Nicolas Gomez Lily Surya Patrick Tam Optimizing Electricity Procurement for the City of Palo Alto
Dec 19, 2015
IEOR 180 Senior Project
Toni GeraldeMona Gohil
Nicolas GomezLily Surya
Patrick Tam
Optimizing Electricity
Procurement for the
City of Palo Alto
Outline
• City of Palo Alto• Energy deregulation• Tradeoffs• Palo Alto’s current decision making
tools• Our linear optimization model• Results
Founded: 1900Area: 26 square milesCustomers: 58,100 including• residential homes• small businesses• corporate offices• manufacturing facilities• excluding Stanford University Campus
Company Background
California Energy
Deregulation• Began January 1, 1998• Open buyer and seller
market for electricity– Purchase Energy $X per
Mega Watt Hour
California Energy Market
Inflexible products:
constant amount/ fixed prices
Forwards
High Load
Load Load
All Week
Flexible products:
variable amounts
Spot market
WAPA
Trade-Offs
• Futures contracts: – safeguard against price spikes versus
cost of premium
• Spot Market– flexibility of amount versus exposure to
risk
Meeting Demand
Time of Day
MW
h
Product II
Spot Market/WAPA
Demand CurveProduct I
Sell to spot
12am 11:59 pm
priP
rod
uc
t III
Palo Alto Model:Challenges
• How much WAPA should be utilized– capacity charge based on maximum amount
• How much to purchase in advance via forwards
• Optimize portfolio with two time periods:– Heavy load hours (HLH)– Light load hours (LLH)
• Purchase options: Forward contracts and WAPA
City of Palo Alto: Current Solution
LLH HLH LLH
Demand curve
MW
Time of day6 am 10 pm
Problem Statement
• Optimize available energy sources with additional energy products and additional time periods to accommodate them: – WAPA – HLH forwards– LLH forwards– E3 blocks– All week forwards
Approach: Linear Program
• Based in Excel and What’s Best Solver
WAPA
E3 I
E3 II
Time
Load
6am 10am 2pm 6pm 10pm
Available Data
• Forecasted Load– Hourly demand for one year
• Forecasted Market Prices• Fixed Contract prices
Model features
• Flexible: Let the user input values for all parameters.
• Accurate: It follows the power demand closely by dividing the month into 150 periods.
• Handle risk: Control exposure to spot market for different demand loads.
• Automated
Decision variables
• Power from WAPAbd
• MAX
• Power from High Load Forward
• Power from Low Load Forward
• Power from All Week Forward
• Power from E3bk
Parameters
• Upper and Lower limit for WAPA
• WAPA capacity cost
• Variable Cost of each product
• Demand Loadbd, during each period
Objective function
MIN Cost of Product bdk * Product bdk
+ (WAPA Capacity Cost * MAX)
- (Load bdk - Product bdk)*Cost Forward bdk
Constraints
• WAPA Upper and Lower limit constraints
• MAX >= WAPAbd.
• Satisfy all demand
• All variables >= 0.
Model: Inputs
Start Date 12/ 1/ 98
WESTERNCapacity cost, $/ KW-mo 5 Upper limit, Kwh 140000Variable cost, $/ MWH 11.236 Lower limit,Kwh 61250Transmission cost 2$/ MWH HIGH LOAD FORWARD LOW LOAD FORWARD
ASK: Price, $/ MWH 20 ASK: Price, $/ MWH 15BID: Price, $/ MWH 21 BID: Price, $/ MWH 16
ALL WEEK FORWARD FORWARD TRANSMISSION COST
ASK: Price, $/ MWH 18BID: Price, $/ MWH 19 Cost, $/ MWH 4
E3 BLOCKSTransaction cost 0.03 Transmission Cost 4
$/ MWHWeek (No transaction cost)
Block 1 2 3 4 5(1) 6AM-10AM 18 18 18 18 18(2) 10AM-2PM 20 20 20 20 20(3) 2PM-6PM 24 24 24 24 24(4) 6PM-10PM 22 22 22 22 22
INPUT PARAMETERS
Quantifying Risk
• Risk Defined:– exposure to spot market
• Risk Implementation– % exposure to spot market
• during high load periods• during normal load periods
Percentage of load EXPOSED to spot market
Definition
High Load 140000
Block Time High Load Normal1 10PM-6AM, Sun. 0% 0%2 6AM-10AM 0% 0%3 10AM-2PM 0% 0%4 2PM-6PM 0% 0%5 6PM-10PM 0% 0%
Percentage
Model: Quantifying Risk
• Risk is the exposure to the spot market
Model: Outputsfor all product-
decision variables
DECISION VARIABLES
WESTERN12/1/98 12/2/98 12/3/98
Block 1 112284.5 112284.5 112284.5Block 2 112284.5 112284.5 112284.5Block 3 112284.5 112284.5 112284.5Block 4 112284.5 112284.5 112284.5Block 5 112284.5 112284.5 112284.5
Maximum 112284.5
HIGH LOAD FORWARD (6 a.m. to 10 p.m.)
Allocation to High Load Forward 56346.75
LOW LOAD FORWARD (10 p.m. to 6 p.m.)
Allocation to Low Load Forward 14178.5
ALL WEEK FORWARD (24 hours a day, 7 days a week)
Allocation to All Week Forward 0
E3 BLOCKSBlock Week 1 Cost6AM-10AM 0 -$ 10AM-2PM 0 -$ 2PM-6PM 0 -$ 6PM-10PM 0 -$
Total -$
12/4/98 12/5/98 12/6/98 12/7/98112284.5 112284.5 112284.5 108148.625112284.5 112284.5 112284.5 112284.5112284.5 112284.5 112284.5 112284.5112284.5 112284.5 112284.5 112284.5112284.5 112284.5 112284.5 112284.5
Total Cost Western 1,614,778.87$ Capacity Cost 561,422.50$
Total Cost High Load Forward 608,544.90$
Total Cost Low Load Forward 88,473.84$
Total Cost All Week Forward -$
Week 2 Cost Week 30 -$ 00 -$ 00 -$ 00 -$ 0
Total -$ Total
Total Cost E3 Blocks -$
Model Outputs:
the costs for different products
Objective Function $1,809,351.92
Minimized
LOAD - POWER BOUGHT
Day 1 2 3Block 1 -13139.25 -11321.125 -8175Block 2 -39857 -37829.5 -37147.5Block 3 -7472 -2043.75 -8426Block 4 -12084.25 0 -8733Block 5 -12680.25 -48.75 -3434.75
Expected Revenue
Date 12/01/98 12/02/98 12/03/98Block 1 1997166 1720811 1242600Block 2 3507416 3328996 3268980Block 3 717312 196200 808896Block 4 1353436 0 978096Block 5 1318746 5070 357214
Sum Of The Expected Revenue 502,445.68$
The Option to Sell Back
Negative means unused capacity
Unused capacity multiplied by the
corresponding price
Revenue from selling back
The portfolio of electricity procurement for Dec 1998
-40%
-20%
0%
20%
40%
60%
80%
100%
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
date
per
cen
tag
e o
f d
iffe
ren
t p
rod
uct
s
Sell back toMarket
E3 blocks
LL Forward
HLForward
WAPA
Chart Output: Percentage of
different products
Quantifying Results
Model Comparison• Run models under various scenarios
– Heavy load– Light load – Normal load
• Calculate cost reduction under new model
Model Comparison
• Based on same inputs– prices– forecasted demand
• Compare models against an actual load– Actual load = average load during
time intervals utilized in UCB model
Model Comparison
• UCB Model is inherently better than Palo Alto’s current Model.
Time
Load
6am 10am 2pm 6pm 10pm
Monthly Savings
0
500000
1000000
1500000
2000000
2500000
$
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
1998 Electricity Costs
Annual Savings
$24,000,000.00
$24,200,000.00
$24,400,000.00
$24,600,000.00
$24,800,000.00
$25,000,000.00
$25,200,000.00
$25,400,000.00
$25,600,000.00
$25,800,000.00
$26,000,000.00
$26,200,000.00
1998
1998 Annual Cost
Palo Alto Model
UCB Model
UCB Model withRevenue
Reduction in Variance
Palo AltoUCB
6am-10am
10am-2pm
2pm-6pm
6pm-10pm
10pm-6am
-
100,000,000.00
200,000,000.00
300,000,000.00
400,000,000.00
500,000,000.00
600,000,000.00
Comparison of Variance (March)
Summary of Results
• UCB Model Savings– $1.121 million for 1998– 4% cost reduction
• UCB with revenue Model– additional $180,762 for 1998– additional 1% cost reduction
• Reduction in Variance
Benefits of UCB Model
• Utilizes all available procurement options
• Low Run-time • Partitions day into finer time
intervals– more closely follows demand curve– reduction in variance from actual load
• Reduction in risk