1. Monte Carlo Simulation for Energy Risk
Management
Scotty Nelson
January 15, 2013
1

2. Outline of Talk
• Background on Deregulated Power Markets
 Regulated vs. Deregulated Power markets
 Market Structure and Participants
 Risk Exposures
• Decision Making Under Uncertainty
 Deterministic Analysis
 Sensitivity Analysis
 Monte Carlo Simulation
 Optimizing the Decision Making Process
• Monte Carlo Simulation
 Model Specification
 Model Estimation
 Model Simulation
 Calibration
 Benchmarking

3. Analytics for Deregulated Power Markets
• Business questions:
 What is my portfolio worth? (valuation)
 How much of my expected dispatch output should I sell into
the forward market? (hedging)
 How much money can I lose? (risk management)
 What trades should I enter into so I can maximize my profits
and minimize my risk? (portfolio optimization)

4. Background on
Deregulated Power
Markets
4

5. State of Deregulation
Source: Department of Energy
5

6. Regulated vs. Deregulated Power Markets
Regulated Setup Deregulated Setup
Power (MWh)
Generator
Load
Generator Load
Payment ($)
ISO
6

7. Risk Exposure to Power Price Movements
Generator Load
Payoff ($)
Payoff ($)
Power Price ($/MWh) Power Price ($/MWh)

8. Hedge Optimization
8

9. Decision Making
Under Uncertainty
9

10. Decision Making Under Uncertainty
• Risk Drivers
 Deterministic scenario planning models
 Sensitivity analysis
 Monte Carlo simulation
• Optimizing the Decision Making Process
 Unconstrained Optimization
 Constrained Optimization
10

11. Generation (MW)
100
200
300
400
500
600
700
0
1
5
9
13
17
21
25
29
33
37
41
45
49
Dispatch Optimization
53
57
61
65
69
73
77
81
generation
85
89
93
97
eprice
101
105
109
113
117
121
125
129
133
137
11
141
145
149
153
157
161
165
0
30
40
50
60
70
80
10
20
90
100
Power Price ($/MWh)

12. Deterministic Planning Models
• Deterministic planning models
 Pro:
o Simple
 Con:
o How to come up with assumptions?
o Are these assumptions realistic?
o Doesn’t acknowledge uncertainty
o Can lead to biased decisions
12

13. $/MMBtu
0
1
2
3
4
5
6
7
8
9
10/1/2008
12/1/2008
2/1/2009
4/1/2009
6/1/2009
8/1/2009
10/1/2009
12/1/2009
2/1/2010
4/1/2010
6/1/2010
8/1/2010
10/1/2010
12/1/2010
2/1/2011
Historical Henry Hub
4/1/2011
6/1/2011
8/1/2011
10/1/2011
Historical versus expected – Henry Hub
12/1/2011
2/1/2012
Expected Henry Hub
4/1/2012
6/1/2012
8/1/2012
10/1/2012
12/1/2012
13
2/1/2013
4/1/2013
6/1/2013
8/1/2013
10/1/2013
12/1/2013

14. $/MWh
100
150
200
250
300
350
400
450
50
0
10/1/2008
12/1/2008
2/1/2009
4/1/2009
6/1/2009
8/1/2009
10/1/2009
12/1/2009
2/1/2010
4/1/2010
6/1/2010
8/1/2010
10/1/2010
12/1/2010
2/1/2011
Historical West Hub
4/1/2011
6/1/2011
Historical versus expected – West Hub
8/1/2011
10/1/2011
12/1/2011
2/1/2012
Expected West Hub
4/1/2012
6/1/2012
8/1/2012
10/1/2012
14
12/1/2012
2/1/2013
4/1/2013
6/1/2013
8/1/2013
10/1/2013
12/1/2013

15. 100
120
20
40
60
80
0
10/1/2008
12/1/2008
2/1/2009
4/1/2009
heat rate
6/1/2009
8/1/2009
10/1/2009
12/1/2009
2/1/2010
4/1/2010
6/1/2010
8/1/2010
10/1/2010
12/1/2010
2/1/2011
Historical Implied Heat Rate
4/1/2011
6/1/2011
8/1/2011
10/1/2011
12/1/2011
2/1/2012
4/1/2012
Historical implied heat rate versus expected implied
6/1/2012
Expected Implied Heat Rate
8/1/2012
10/1/2012
15
12/1/2012
2/1/2013
4/1/2013
6/1/2013
8/1/2013
10/1/2013
12/1/2013

16. Sensitivity Analysis
• Sensitivity analysis
 Pro:
o Simple
 Con:
o How to create sensitivity scenarios?
o Are these scenarios realistic?
• In general the following does not hold, especially for nonlinear functions
E[𝑓 𝑋 ] ≠ 𝑓(𝐸 𝑋 )
16

17. Monte Carlo Simulation
• Monte Carlo simulation
 Pro:
o Realistic representations of possible states of the world (this could actually happen)
o Correlations are maintained
o Can benchmark against actual price distributions
 Cons:
o Complex, slow
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18. Optimizing the Decision Process
• Given the prices, we want to optimize a decision process
• Example:
 European Call Option
o Value a call option, value=max(P-K,0)  simple decision rule, if P>K then exercise,
otherwise don’t
o Decisions today don’t impact decisions tomorrow
 Power Plant
o Operational constraints  can’t turn on and off instantly
o How to optimize the decision process, given that decisions today impact possible
decisions tomorrow?
o Answer is provided through dynamic programming
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19. Generation (MW)
100
200
300
400
500
600
700
0
1
5
9
13
17
21
25
29
33
37
41
45
49
Dispatch Optimization
53
57
61
65
69
73
77
81
generation
85
89
93
97
eprice
101
105
109
113
117
121
125
129
133
137
19
141
145
149
153
157
161
165
0
30
40
50
60
70
80
10
20
90
100
Power Price ($/MWh)

20. Monte Carlo
Simulation
20

21. Monte Carlo Framework
- Model Specification
- Specify a model of the fundamental risk drivers
- Model Estimation
- Estimate the unknown parameters of the model
- Simulation
- Simulate the risk drivers
- Calibration
- Use any known information to calibrate the simulations, to match observed real world
quantities
- Decision Making
- Optimize the decision process
- Summarize
- Summarize the outcomes (e.g. using probability distributions)

22. Overview of PowerSimm Processes
WX Sim Load Sim
Spot Price Sim
Calibrated Spot
Dispatch
Price Data
Forward Price
Sim
Portfolio
Summarization
22

23. Marginal Price of Electricity
Demand
Supply
P2
Marginal price
$/MWh
of electricity
P1
Baseload (Coal) Midmerit (CC) Peakers (CTs)
MW

24. 100
20
40
80
120
60
0
1/1/2007
Weather – historical relationships
5/19/2007
10/1/2007
2/12/2008
LAX Max DB 6/25/2008
11/6/2008
100
120
20
40
60
80
0
3/20/2009
0
9/1/2009
1/13/2010
7/27/2010
50 12/8/2010
4/21/2011
9/2/2011
1/14/2012
USC Max DB
5/27/2012
100
150
CAMPUS
AIRPORT
INTERNATIONAL
DOWNTOWN L.A./USC

25. Weather – modelling – vector autoregression
𝑈𝑆𝐶 𝐷𝐵 𝑡 = 𝑓(𝑈𝑆𝐶 𝐷𝐵 𝑡−1 , … , 𝑈𝑆𝐶 𝑀𝑎𝑥𝐷𝐵 𝑡−𝑙 ,
𝐿𝐴𝑋 𝐷𝐵 𝑡 , … , 𝐿𝐴𝑋 𝐷𝐵 𝑡−𝑙 )
+𝜀 𝑡,1
𝐿𝐴𝑋 𝐷𝐵 𝑡 = 𝑓(𝑈𝑆𝐶 𝐷𝐵 𝑡−1 , … , 𝑈𝑆𝐶 𝑀𝑎𝑥𝐷𝐵 𝑡−𝑙 ,
𝐿𝐴𝑋 𝐷𝐵 𝑡 , … , 𝐿𝐴𝑋 𝐷𝐵 𝑡−𝑙 )
+𝜀 𝑡,2
𝜺~𝑁(0,Ω)

26. Weather – simulated temperature – temporal
correlations

27. Weather – simulated temperature – benchmarking

28. Load – historical relationships
Summer Load Profile Winter Load Profile
Load vs Temperature

29. Load – modelling – model specification
𝐿𝑜𝑎𝑑 𝑡
= 𝑓 𝑀𝑜𝑛𝑡ℎ 𝑡 , 𝐷𝑂𝑊𝑡 , 𝐻𝑜𝐷 𝑡 , 𝑀𝑎𝑥𝐷𝐵 𝑡 + 𝜀 𝑡

30. Load – benchmarking simulations

31. Load – benchmarking simulations
31

32. Spot Prices – historical relationships

33. Spot Prices – modelling
𝑃𝑜𝑤𝑒𝑟 𝑡 = 𝑓 𝐿𝑜𝑎𝑑 𝑡−1 , 𝑃𝑜𝑤𝑒𝑟 𝑡−1 , 𝐺𝑎𝑠 𝑡−1 + 𝜀 𝑡,1
𝐺𝑎𝑠 𝑡 = 𝑓 𝐿𝑜𝑎𝑑 𝑡−1 , 𝑃𝑜𝑤𝑒𝑟 𝑡−1 , 𝐺𝑎𝑠 𝑡−1 + 𝜀 𝑡,2

34. Spot Prices – simulation results

35. Wrapup
35

36. Analytics for Deregulated Power Markets
• Business questions:
 What is my portfolio worth? (valuation)
 How much of my expected output should I sell into the
forward market? (hedging)
 How much money can I lose? (risk management)
 What trades should I enter into so I can maximize my profits
and minimize my risk? (portfolio optimization)

37. What is My Portfolio Worth?
Gross Margin At Expected
Risk Value of
Portfolio
37

38. How Sensitive is My Portfolio To Prices?
Sensitivity of gross
margin = $19 million
per $/MWh
Optimal forward sale = ~1500 MW
38

39. Questions?
Scotty Nelson
snelson@ascendanalytics.com
39