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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.

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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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ErnestoGuzman,Ph.D.

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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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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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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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ErnestoGuzman,Ph.D.

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Seasonal Demand and Perfectly Inelastic Supply

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Seasonality Factor

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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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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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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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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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Operation profiles with 25% NSC under PC

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Operation Profiles with 25% NSC under Monopoly

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Working Gas in Underground Storage (2015-2016)

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Henry Hub Forward Curves (2014, 2015)

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First Diagnostic MetricActual vs. Theoretical Storage Capacity

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ErnestoGuzman,Ph.D.

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Second Diagnostic MetricActual vs. Theoretical Maximum Seasonal Price Spread (MSPS)

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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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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.

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Lit review

Methodology

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Operations

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Metrics

Conclusions

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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.

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Lit review

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Conclusions

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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.

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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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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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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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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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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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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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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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