## Abstract

Daily gas demand in the UK is variable. This is partly due to weather patterns and the changing nature of electricity markets, where intermittent wind energy levels lead to variations in the demand for gas needed to produce electricity. This uncertainty makes it difficult for traders in the market to analyse the market. As a result, there is an increasing need for models of the UK natural gas market that include stochastic demand. In this paper, a Rolling Optimisation Model (ROM) of the UK natural gas market is introduced. It takes as an input stochastically generated scenarios of demand. The outputs of ROM are the flows of gas, i.e., how the different sources of supply meet demand, as well as how gas flows in to and out of gas storage facilities. The outputs also include the daily System Average Price of gas in the UK. The model was found to fit reasonably well to historic data (from the UK National Grid) for the years starting on the 1st of April for both 2010 and 2011. These results allow ROM to be used to predict future flows and prices of gas and to investigate various stress-test scenarios in the UK natural gas market.

This is a preview of subscription content, access via your institution.

## Notes

Ofgem (Office of the Gas and Electricity Markets) regulates the gas and electricity markets in the UK. See: http://www.ofgem.gov.uk/About%20us/Pages/AboutUsPage.aspx,

The UK National Grid is the owner and operator of national transmission system throughout Great Britain.

When simulating stochastic demand for the first day of this process, the error from the previous day is assumed to be zero.

While none of the

*c*_{ p }change with the level of production, it should be noted that in Sections 3.2, 3.3 and 4 the different sources of supply in the UK are broken up into multiple tranches, each with a different cost of production. This implicitly allows the cost of each source of supply to change as the level of production changes.The outputs of ROM include all Lagrange multipliers. However, only those associated with demand constraints are analysed in any detail.

For the first roll of the model, the initial amount of gas in storage is a parameter typically determined using actual storage data.

The Holford MRS facility only became operational in 2012.

sSee: http://www.bblcompany.com/,

The parameters in Table 6 were not obtained from simulated annealing as they were obtained from either the UK National Grid or the UK’s Department of Energy and Climate Change.

The values for UKCS exclude gas that is injected to storage.

The Mean Absolute Percentage Error for source

*l*is \(MAPE^{l}= \sum\limits ^{R}_{r=1}\frac {|Actual^{l}_{r} -Simulated^{l}_{r}|}{\frac {1}{R}\sum\limits ^{R}_{r=1}\sum\limits ^{L}_{l=1} Actual^{l}_{r}. }\).

## References

Abada I, Gabriel S, Briat V, Massol O (2012) A generalized Nash-Cournot model for the northwestern European natural gas markets with a fuel substitution demand function: the GaMMES model. Netw Spat Econ 13: 1–42

Abrell J, Weigt H (2012) Combining energy networks. Netw Spat Econ 12: 377–401

Bazaraa M, Sherali H, Shetty C (1993) Nonlinear programming theory and algoritims. Wiley, New York

Boots M, Rijkers F, Hobbs B (2004) Trading in the downstream European gas market: a successive oligopoly approach. Energy J 25: 73–102

Bopp A, Kannan V, Palocsay S, Stevens S (1996) An optimization model for planning natural gas purchases, transportation, storage and deliverability. Omega Int J Manag Sci 24: 511–522

Butler J, Dyer J (1999) Optimizing natural gas flows with linear programming and scenarios. Decis Sci 30: 563–580

Devine M (2012) Rolling optimisation, stochastic demand modelling and scenario reduction applied to the UK gas market. PhD thesis, Department of Mathematics and Statistics, University of Limerick, Ireland

Egging R, Gabriel S (2006) Examining market power in the European natural gas market. Energy Policy 34: 2762–2778

Egging R, Holz F, Gabriel S (2010) The world gas model: a multi-period mixed complementarity model for the global natural gas market. Energy 35: 4016–4029

Gabriel S, Manik J, Vikas S (2003) Computational experience with a large-scale, multi-period, spatial equilibrium model of the North American natural gas system. Netw Spat Econ 3: 97–122

Gabriel S, Kiet S, Zhuang J (2005a) A mixed complementarity-based equilibrium model of natural gas markets. Oper Res 53: 799–818

Gabriel S, Zhuang J, Kiet S (2005b) A large-scale linear complementarity model of the North American natural gas market. Energy Econ 27: 639–665

GAMS (2012) A user’s guide. GAMS Development Corporation, Washington, DC, available at: http://www.gams.com/dd/docs/bigdocs/GAMSUsersGuide.pdf. Accessed 30 Nov 2012

Holz F, von Hirschhausen C, Kemfert C (2008) A strategic model of European gas supply (GASMOD). Energy Econ 30: 766–788

Honoré (2010) A European natural gas demand, supply, and pricing. Oxford University Press

HCBEC (2007) Energy prices, fuel poverty and ofgem. Eleventh report of the house of commons’ business and enterprise committee of the 2007-08 session. Available at: http://www.publications.parliament.uk/pa/cm200708/cmselect/cmberr/293/293ii. Accessed 30 Nov 2012

Kirkpatrick S, Gelatt C, Vecchi M (1983) Optimization by simulated annealing. Science 220: 671–680

Lise W, Hobbs B (2008) Future evolution of the liberalised European gas market: simulation results with a dynamic model. Energy 33: 989–1004

Lochner S, Bothe D (2009) The development of natural gas supply costs to Europe, the United States and Japan in a globalizing gas market-model-based analysis until 2030. Energy Policy 37: 1518–1528

Metropolis N, Rosenbluth A, Rosenbluth M, Teller A (1953) Equation of state calculations by fast computing mechanics. J Chem Phys 21: 1087–1092

Perner J (2002) Die Langfristige Erdgasversorgung Europas, Schriften des Energiewirtschaftlichen Instituts, Band 60, Munchen

Perner J, Seeliger A (2004) Prospects of gas supplies to the European market until 2030-results from the simulation model EUGAS. Util Policy 12: 291–302

Seeliger A (2006) Entwicklung des weltweiten Erdgasangebots bis 2030-Eine modellgestutzte Prognose. Oldenburg Verlag, Munich

Siddiqui S, Gabriel S (2012) An SOS1-based approach for solving MPECs with a natural gas market application. Netw Spat Econ 13: 205–227

The Baker Institute World Gas Trade Model (2005) Available at: http://www.bakerinstitute.org/publications/the-baker-institute-world-gas-trade-model-biwgtm. Accessed 30 April 2013

UK National Grid (2011a) UK National Grid’s development of energy scenarios. Available at: http://www.nationalgrid.com/NR/rdonlyres/C934D455-1438-4949-A7CD-3FE781FE39E8/47855/DevelopmentofEnergyScenariosTBE2011.pdf. Accessed 30 Nov 2012

UK National Grid (2011b) UK National Grid’s future energy scenarios, Available at: http://www.nationalgrid.com/uk/Electricity/Operating+in+2020/UK+Future+Energy+Scenarios.htm. Accessed 30 Nov 2012

UK National Grid (2011c) UK National Grid’s gas ten year statement. Available at: http://www.nationalgrid.com/NR/rdonlyres/E60C7955-5495-4A8A-8E80-8BB4002F602F/50703/GasTenYearStatement2011.pdf. Accessed 30 Nov 2012

DUKES (2010) UK’s Department of Energy and Climate Change Digest of United Kingdom energy statistics (DUKES) Available at: http://www.decc.gov.uk/assets/decc/Statistics/publications/dukes/348-dukes-2010-printed.pdf. Accessed 30 Nov 2012

DECC (2011a) UK’s Department of Energy and Climate Change Digest of United Kingdom energy statistics (DUKES) Available at: http://www.decc.gov.uk/assets/decc/11/stats/publications/2310-dukes-2011-internet-booklet.pdf. Accessed 30 Nov 2012

DUKES (2011b) UK’s Department of Energy and Climate Change Electricity market reform white paper. Available at: http://www.decc.gov.uk/assets/decc/11/policy-legislation/EMR/2210-emr-white-paper-full-version.pdf. Accessed 30 November 2012

DUKES (2012) UK’s Department of Energy and Climate Change Digest of United Kingdom energy statistics (DUKES) Available at: http://www.decc.gov.uk/assets/decc/11/stats/publications/dukes/5954-dukes-2012-chapter-4-gas.pdf. Accessed 30 Nov 2012

## Acknowledgments

This work is funded by Science Foundation Ireland under programmes MACSI 06/MI/005 and 09/SRC/E1780. The authors would also like to thank Bord Gáis Energy for their contributions, in particular Gavin Hurley.

## Author information

### Authors and Affiliations

### Corresponding author

## Appendix A: Analysis of Karush-Kuhn-Tucker conditions

### Appendix A: Analysis of Karush-Kuhn-Tucker conditions

In this section, a small algebraic example illustrates the fact that changing the production costs of ROM, without altering the merit order, does not affect the volumes but does change the marginal supply cost. Consider the following problem:

subject to:

where \(Q_{1,2}\) represent production levels, \(c_{1,2}\) represent the costs associated with them and represent \(Q^{max}_{1,2}\) represent maximum production levels. The variables in the parentheses, alongside constraints (19)–(21), represent the Lagrange multipliers associated with that constraint. The Karush-Kuhn-Tucker conditions for optimality (Bazaraa et al. 1993) associated with this problem are:

as well as constraints (19)–(21). These conditions show that the optimal production levels depend on the production capacities and the demand whereas the price associated with meeting demand (\(\lambda _{D}\)) depends on costs.

## Rights and permissions

## About this article

### Cite this article

Devine, M.T., Gleeson, J.P., Kinsella, J. *et al.* A Rolling Optimisation Model of the UK Natural Gas Market.
*Netw Spat Econ* **14**, 209–244 (2014). https://doi.org/10.1007/s11067-013-9216-4

Published:

Issue Date:

DOI: https://doi.org/10.1007/s11067-013-9216-4

### Keywords

- Rolling optimisation
- UK natural gas market
- Stochastic demand scenarios