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USAEE/IAEE
ErnestoGuzman,Ph.D.
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USAEE/IAEEDiagnostic metrics for the adequate development of
efficient-market baseload natural gas storage capacity
Ernesto Guzman, Ph.D.
Colorado School of Mines
November 13, 2017
Contact: eguzman.phd@gmail.com
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USAEE/IAEE
ErnestoGuzman,Ph.D.
Question
Lit review
Methodology
Findings
Operations
Predictions
Metrics
Conclusions
Backup
Non-binding
Binding
Metrics
References
Introduction
Research QuestionWhat diagnostic metrics can be used to assess the adequatedevelopment of efficient-market baseload natural gas storagecapacity?
MotivationAnalytical tools for the aforementioned assessment are notfound in the literature. FERC can use them to monitorpotential and unintended deterrent effects of their ownregulatory policies on natural gas storage development.
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USAEE/IAEE
ErnestoGuzman,Ph.D.
Question
Lit review
Methodology
Findings
Operations
Predictions
Metrics
Conclusions
Backup
Non-binding
Binding
Metrics
References
Literature Review
No direct precedent in literature of commodity storage.
1 [Pyatt, 1978]:
• Minimizing production cost Vs. maximizing profit.
2 [Williams and Wright, 1991]:
• Classic textbook on structural models of storage.
3 [Schroder-Amundsen, 1991]:
• Constrained production, storage, and distribution.
4 [Urıa and Williams, 2007]:
• Influence of NYMEX futures in net injection profiles.
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USAEE/IAEE
ErnestoGuzman,Ph.D.
Question
Lit review
Methodology
Findings
Operations
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Non-binding
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Intertemporal Choice Model
1 Optimal control approach
2 Storage operator (single agent)
3 Benevolent planner or monopolist
4 Control variable: Withdrawal/injection flows u
5 State variable: Natural gas inventory N
6 One-year planning horizon
7 Seasonal demand (sine)
8 Inelastic constant supply
9 Binding and non-binding storage capacity operations:• Binding inventory level N• Minimum non-binding storage capacity SC
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USAEE/IAEE
ErnestoGuzman,Ph.D.
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Model Introduction
Seasonal (inverse) demand Pt is represented by the linear form
Pt(QDt ) = A · St − B · QD
t
Seasonality factor St is represented by the sinusoidal form
St = 1− a · sin bt
a Seasonal amplitudeb Factor normalizing planning horizon over one seasonal
cycleQD
t Quantity demanded (consumption)A Reservation priceB Constant (inverse) demand slope
Constant and perfectly inelastic supply is Q0.
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USAEE/IAEE
ErnestoGuzman,Ph.D.
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Lit review
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Seasonal Demand and Perfectly Inelastic Supply
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USAEE/IAEE
ErnestoGuzman,Ph.D.
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Seasonality Factor
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ErnestoGuzman,Ph.D.
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Binding Storage Capacity Operation ModelUnder Monopoly
max
∫ T
0−u · Pt (Q0 − u) dt
s.t. N = u and N (0) = 0 N (T ) = 0
Upper constraint: N ≤ N ⊥ θUt ≥ 0
Lower constraint : −N ≤ 0 ⊥ θLt ≥ 0
θUt Lagrangian multiplier of upper constraint.
θLt Lagrangian multiplier of lower constraint.
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USAEE/IAEE
ErnestoGuzman,Ph.D.
Question
Lit review
Methodology
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Operations
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Metrics
Conclusions
Backup
Non-binding
Binding
Metrics
References
Binding Storage Capacity Operation ModelUnder Perfect Competition
max
∫ T
0
[A · St · (Q0 − u)− B
2· (Q0 − u)2
]dt
s.t. N = u, N (0) = 0, N (T ) = 0
Upper constraint: N ≤ N ⊥ θUt ≥ 0
Lower constraint: −N ≤ 0 ⊥ θLt ≥ 0
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USAEE/IAEE
ErnestoGuzman,Ph.D.
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Lit review
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Results
Four variables for each market environment changing over time:
P Price
u Storage flow (control variable)
N Inventory level (state variable)
θ Shadow value of inventory
Four stages:
A Injection
B Binding storage capacity
C Withdrawal
D Stockout
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ErnestoGuzman,Ph.D.
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Model Input Parameters
Parameter Name Value Parameter Units
Time horizon, T 12 Months
Seasonal amplitude, a 0.5 Unitless
Reservation price, A 20 USD / NG flow
Demand slope, B 2 USD / NG flow
Constant supply, Q0 5 NG flow
Initial inventory, N (0) 0 NG volume
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USAEE/IAEE
ErnestoGuzman,Ph.D.
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Operation profiles with 25% NSC under PC
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USAEE/IAEE
ErnestoGuzman,Ph.D.
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Conclusions
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Binding
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Operation Profiles with 25% NSC under Monopoly
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USAEE/IAEE
ErnestoGuzman,Ph.D.
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Non-binding
Binding
Metrics
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Working Gas in Underground Storage (2015-2016)
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USAEE/IAEE
ErnestoGuzman,Ph.D.
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Lit review
Methodology
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Conclusions
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Non-binding
Binding
Metrics
References
Henry Hub Forward Curves (2014, 2015)
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USAEE/IAEE
ErnestoGuzman,Ph.D.
Question
Lit review
Methodology
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Conclusions
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Non-binding
Binding
Metrics
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First Diagnostic MetricActual vs. Theoretical Storage Capacity
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USAEE/IAEE
ErnestoGuzman,Ph.D.
Question
Lit review
Methodology
Findings
Operations
Predictions
Metrics
Conclusions
Backup
Non-binding
Binding
Metrics
References
Second Diagnostic MetricActual vs. Theoretical Maximum Seasonal Price Spread (MSPS)
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USAEE/IAEE
ErnestoGuzman,Ph.D.
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Methodology
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Metrics
Conclusions
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Non-binding
Binding
Metrics
References
Third and Fourth Diagnostic MetricsComplement the first two metrics
Market power in storage operations when
[corr
(Pt ,Q
Dt
)> 0]
and
[|corr (Pt ,Nt)| > 0] .
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USAEE/IAEE
ErnestoGuzman,Ph.D.
Question
Lit review
Methodology
Findings
Operations
Predictions
Metrics
Conclusions
Backup
Non-binding
Binding
Metrics
References
Conclusions
• Four diagnostic metrics were formulated based on:
1 Market equilibrium of storage capacity investments2 Maximum seasonal price spread (MSPS)3 Correlation between price and consumption4 Correlation between price and inventory
• Metrics can be adjusted for seasonal amplitude uncertainty
• Metrics can be used by agencies like FERC
• Follow-up research:
1 Adjust metrics for asymmetric seasonality2 Explain forward curve shape at Henry Hub and others
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Questions
ErnestoGuzman,Ph.D.
Question
Lit review
Methodology
Findings
Operations
Predictions
Metrics
Conclusions
Backup
Non-binding
Binding
Metrics
References
Questions
Ernesto Guzman, Ph.D.
Colorado School of Mines
November 13, 2017
Contact: eguzman.phd@gmail.com
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Backup Slides
ErnestoGuzman,Ph.D.
Question
Lit review
Methodology
Findings
Operations
Predictions
Metrics
Conclusions
Backup
Non-binding
Binding
Metrics
References
Backup Slides
Ernesto Guzman, Ph.D.
Colorado School of Mines
November 13, 2017
Contact: eguzman.phd@gmail.com
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ErnestoGuzman,Ph.D.
Question
Lit review
Methodology
Findings
Operations
Predictions
Metrics
Conclusions
Backup
Non-binding
Binding
Metrics
References
Non-binding storage capacity operations (1/2)
MarketEquilibrium
Undermonopoly
Under perfectcompetition
Q0 bounds forinterior solution
Qb ≤ Q0 ≤(AB − Qb
)where Qb = aA
2B
2Qb ≤ Q0 ≤ AB
where Qb = aA2B
Storage flow u∗ = Qb · (sin bt) u∗∗ = 2u∗
Quantitydemanded
QD∗t = Q0 − u∗ QD∗∗
t = Q0 − u∗∗
Price P∗t = P0 − B · u∗ P∗∗
t = P0 (Q0)
Min. non-bindingstorage capacity
SC ∗ = aAbB SC ∗∗ = 2 · SC ∗
Inventory levels Nt = SC2 (1− cos bt)
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ErnestoGuzman,Ph.D.
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Non-binding storage capacity operations (2/2)
MarketEquilibrium
Undermonopoly
Under perfectcompetition
Profit π∗ =BQ2
b2 T πs = 0
WelfareWM = WNSO + 3
4BT · Q2b
W ∗∗s = WNSO + BT · Q2
b
Other equationsP0 (Q0) = A− B · Q0 and
WNSO = T · Q0
[A− B
2 · Q0
]
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ErnestoGuzman,Ph.D.
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Binding SCO: Stages A and BUnder Perfect Competition and Monopoly
Perfect CompetitionVariable Stage A Stage B
t ∈ (τ1, τ2) ∈ [τ2, τ3]
P∗∗ P I [= Pτ1 (Q0)] Pt (Q0)
u∗∗ 1B
[P I − Pt (Q0)
]> 0 0
N∗∗ f (τ1, t) N
θU∗∗t 0 P (Q0) ≥ 0
Monopoly
P∗ 12
[P I + Pt (Q0)
]Pt (Q0)
u∗ 12u
∗∗ 0
N∗ 12 f (τ1, t) N
θU∗t 0 P (Q0) ≥ 0
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ErnestoGuzman,Ph.D.
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Binding SCO: Stages C and DUnder Perfect Competition and Monopoly
Perfect CompetitionVariable Stage C Stage D
t ∈ (τ3, τ4) ∈ [τ4, T ] ∧ [0, τ1]
P∗∗ PW [= Pτ3 (Q0)] Pt (Q0)
u∗∗ 1B
[PW − Pt (Q0)
]< 0 0
N∗∗ N + f (τ3, t) 0
θU∗∗t 0 0
Monopoly
P∗ 12
[PW + Pt (Q0)
]Pt (Q0)
u∗ 12u
∗∗ 0
N∗ N + 12 f (τ3, t) 0
θU∗t 0 0
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ErnestoGuzman,Ph.D.
Question
Lit review
Methodology
Findings
Operations
Predictions
Metrics
Conclusions
Backup
Non-binding
Binding
Metrics
References
First Diagnostic MetricActual vs. Theoretical Storage Capacity
Where actualstorage capacity
(ASC) falls
Storage CapacityAdequacy
(Qualification)Potential issues
ASC < SC∗EQ
Insufficient (Redflag)
Physical constraints inthe natural gasinfrastructure or
regulatory deterrents.
SC∗EQ ≤ ASC ≤ SC∗∗
EQ
May be subject tomarket power(Yellow flag)
Market power or anyof the above.
SC∗∗EQ < ASC
Sufficient (Greenflag)
Excessive investmentthat may not be
recovered.
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ErnestoGuzman,Ph.D.
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Lit review
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Backup
Non-binding
Binding
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Second Diagnostic MetricActual vs. Theoretical Price Fluctuations
Where actual annualprice spread (APS)
falls
Storage CapacityAdequacy
(Qualification)Potential issues
APS >aA (1 + sin bτ1)
Insufficient (Redflag)
Physical constraints inthe natural gasinfrastructure or
regulatory deterrents.
MBSC (τ1) ≤ APS ≤aA (1 + sin bτ1)
May be subject tomarket power(Yellow flag)
Market power or anyof the above.
APS < MBSC (τ1) N.A.Inconsistentestimates.
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ErnestoGuzman,Ph.D.
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Lit review
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Non-binding
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References
References Cited I
Pyatt, G. (1978).Marginal costs, prices, and storage.The Economic Journal, 88:749 – 762.
Schroder-Amundsen, E. (1991).Seasonal Fluctuations of Demand and Optimal Inventoriesof a Non-Renewable Resource Such as Natural Gas.Resources and Energy, 13(3):285–306.
Urıa, R. and Williams, J. (2007).The supply of storage for natural gas in california.The Energy Journal, 28(3):31–50.
Williams, J. C. and Wright, B. D. (1991).Storage and Commodity Markets.Cambridge University Press, Cambridge, 1st edition.
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