USAEE/IAEE. Diagnostic metrics for the adequate development of efficient-market baseload natural gas storage capacity.

Transcription

1 USAEE/IAEE Diagnostic metrics for the adequate development of efficient-market baseload natural gas storage capacity Colorado School of Mines November 13, 2017 Contact: 1 / 28

2 Introduction Research What diagnostic metrics can be used to assess the adequate development of efficient-market baseload natural gas storage capacity? Motivation Analytical tools for the aforementioned assessment are not found in the literature. FERC can use them to monitor potential and unintended deterrent effects of their own regulatory policies on natural gas storage development. 2 / 28

3 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 [Uría and Williams, 2007]: Influence of NYMEX futures in net injection profiles. 3 / 28

4 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 and non-binding storage capacity operations: inventory level N Minimum non-binding storage capacity SC 4 / 28

5 Model Introduction Seasonal (inverse) demand P t is represented by the linear form P t (Qt D ) = A S t B Qt D Seasonality factor S t is represented by the sinusoidal form S t = 1 a sin bt a b Q D t A B Seasonal amplitude Factor normalizing planning horizon over one seasonal cycle Quantity demanded (consumption) Reservation price Constant (inverse) demand slope Constant and perfectly inelastic supply is Q 0. 5 / 28

6 Seasonal Demand and Perfectly Inelastic Supply 6 / 28

7 Seasonality Factor 7 / 28

8 Storage Capacity Operation Model Under Monopoly T max u P t (Q 0 u) dt 0 s.t. N = u and N (0) = 0 N (T ) = 0 Upper constraint: N N θ U t 0 Lower constraint : N 0 θ L t 0 θ U t θ L t Lagrangian multiplier of upper constraint. Lagrangian multiplier of lower constraint. 8 / 28

9 Storage Capacity Operation Model Under Perfect Competition T max [A S t (Q 0 u) B2 ] (Q 0 u) 2 dt 0 s.t. N = u, N (0) = 0, N (T ) = 0 Upper constraint: N N θ U t 0 Lower constraint: N 0 θ L t 0 9 / 28

10 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 storage capacity C Withdrawal D Stockout 10 / 28

11 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, Q 0 5 NG flow Initial inventory, N (0) 0 NG volume 11 / 28

12 Operation profiles with 25% NSC under PC 12 / 28

13 Operation Profiles with 25% NSC under Monopoly 13 / 28

14 Working Gas in Underground Storage ( ) 14 / 28

15 Henry Hub Forward Curves (2014, 2015) 15 / 28

16 First Diagnostic Metric Actual vs. Theoretical Storage Capacity 16 / 28

17 Second Diagnostic Metric Actual vs. Theoretical Maximum Seasonal Price Spread (MSPS) 17 / 28

18 Third and Fourth Diagnostic Complement the first two metrics Market power in storage operations when and [ ( corr P t, Qt D ) ] > 0 [ corr (P t, N t ) > 0]. 18 / 28

19 Four diagnostic metrics were formulated based on: 1 Market equilibrium of storage capacity investments 2 Maximum seasonal price spread (MSPS) 3 Correlation between price and consumption 4 Correlation between price and inventory can be adjusted for seasonal amplitude uncertainty can be used by agencies like FERC Follow-up research: 1 Adjust metrics for asymmetric seasonality 2 Explain forward curve shape at Henry Hub and others 19 / 28

20 s s Colorado School of Mines November 13, 2017 Contact: eguzman.phd@gmail.com 20 / 28

21 Slides Slides Colorado School of Mines November 13, 2017 Contact: 21 / 28

22 Slides storage capacity operations (1/2) Market Equilibrium Q 0 bounds for interior solution Under monopoly Q b Q 0 ( A B Q b) where Q b = aa 2B Under perfect competition 2Q b Q 0 A B where Q b = aa 2B Storage flow u = Q b (sin bt) u = 2u Quantity demanded Qt D = Q 0 u Qt D = Q 0 u Price P t = P 0 B u P t = P 0 (Q 0 ) Min. non-binding storage capacity SC = aa bb SC = 2 SC Inventory levels N t = SC 2 (1 cos bt) 22 / 28

23 Slides storage capacity operations (2/2) Market Equilibrium Profit Welfare Other equations Under monopoly Under perfect competition π = BQ2 b 2 T π s = 0 W M = W NSO BT Q2 b Ws = W NSO + BT Qb 2 P 0 (Q 0 ) = A [ B Q 0 and W NSO = T Q 0 A B 2 Q ] 0 23 / 28

24 Slides SCO: Stages A and B Under Perfect Competition and Monopoly Perfect Competition Variable Stage A Stage B t (τ 1, τ 2 ) [τ 2, τ 3 ] P P I [= P τ1 (Q 0 )] P t (Q 0 ) u 1 [ B PI P t (Q 0 ) ] > 0 0 N f (τ 1, t) N θt U 0 Ṗ (Q 0 ) 0 Monopoly P 1 [ 2 PI + P t (Q 0 ) ] P t (Q 0 ) u 1 2 u 0 N 1 2 f (τ 1, t) N θt U 0 Ṗ (Q 0 ) 0 24 / 28

25 Slides SCO: Stages C and D Under Perfect Competition and Monopoly Perfect Competition Variable Stage C Stage D t (τ 3, τ 4 ) [τ 4, T ] [0, τ 1 ] P P W [= P τ3 (Q 0 )] P t (Q 0 ) u 1 [ B PW P t (Q 0 ) ] < 0 0 N N + f (τ 3, t) 0 θt U 0 0 Monopoly P 1 [ 2 PW + P t (Q 0 ) ] P t (Q 0 ) u 1 2 u 0 N N f (τ 3, t) 0 θt U / 28

26 Slides First Diagnostic Metric Actual vs. Theoretical Storage Capacity Where actual storage capacity (ASC) falls ASC < SC EQ SC EQ ASC SC EQ Storage Capacity Adequacy (Qualification) Insufficient (Red flag) May be subject to market power (Yellow flag) Potential issues Physical constraints in the natural gas infrastructure or regulatory deterrents. Market power or any of the above. SC EQ < ASC Sufficient (Green flag) Excessive investment that may not be recovered. 26 / 28

27 Slides Second Diagnostic Metric Actual vs. Theoretical Price Fluctuations Where actual annual price spread (APS) falls APS > aa (1 + sin bτ 1) MBSC (τ 1) APS aa (1 + sin bτ 1) Storage Capacity Adequacy (Qualification) Insufficient (Red flag) May be subject to market power (Yellow flag) Potential issues Physical constraints in the natural gas infrastructure or regulatory deterrents. Market power or any of the above. APS < MBSC (τ 1) N.A. Inconsistent estimates. 27 / 28

28 Slides Cited I Pyatt, G. (1978). Marginal costs, prices, and storage. The Economic Journal, 88: Schroder-Amundsen, E. (1991). Seasonal Fluctuations of Demand and Optimal Inventories of a Non-Renewable Resource Such as Natural Gas. Resources and Energy, 13(3): Uría, R. and Williams, J. (2007). The supply of storage for natural gas in california. The Energy Journal, 28(3): Williams, J. C. and Wright, B. D. (1991). Storage and Commodity Markets. Cambridge University Press, Cambridge, 1st edition. 28 / 28