Nash equilibria for load balancing in networked power systems

Lead Research Organisation: Queen Mary, University of London
Department Name: Sch of Mathematical Sciences

Abstract

Power systems must constantly maintain a balance between the instantaneous supply and demand for electricity. Coming technologies such as energy storage and demand-side management promise to make a significant contribution to this balancing challenge. The concept of demand-side management involves the ability of power utilities to influence electricity usage at consumers' premises either through direct control via a telecommunications system, or indirectly through incentives which are usually economic such as variable pricing tariffs. An electrical energy storage unit (such as Tesla's recently announced 'Powerwall', a rechargeable lithium-ion battery product for home use which stores electricity for domestic consumption, load shifting, and backup power) is a buffer used principally or exclusively to counteract the power imbalance between supply and demand. Energy storage technologies are typically reliable and always available, but this is not necessarily true for demand-side management solutions.

The proposed research will explore the dynamic, multi-player, economic and operational 'games' arising when energy storage and demand-side management technologies are applied to power system balancing. We will use a game-theoretical approach to model this, combined with useful mathematical techniques borrowed from the statistical mechanics of complex systems and techniques developed for the analysis of complex networks. The operators of these technologies, as well as the entity responsible for balancing, are treated as agents within one or more markets for electricity. An important concept of solution in the study of these non-zero sum dynamic games is the so-called Nash equilibrium, in which no single player can improve their outcome by altering their decision unilaterally. In other words, a Nash equilibrium is a state in which no player can improve their situation by changing to another strategy. Equilibria are desirable in this context of balancing because they represent sustainable and stable setups. We will investigate the properties of these equilibrium states for a variety of stochastic models relevant in the load balancing context.

By studying dynamic games we will address two fundamental research questions: firstly, how the operators of such new technologies should optimally act, and secondly how they should be appropriately rewarded in order to produce a suitable dynamic equilibrium in the balancing service they can provide. Further, by appropriately extending these games to networks we will explore how the dynamic equilibria change when such technologies are aggregated through third parties. In the most ambitious part of this proposal we will explore the effect of multiplex and evolving network topology when, for example, participation in load balancing is influenced by the participation of peers.

Planned Impact

This proposal includes a specific route to impact through active collaboration with innovative UK companies Future Decisions Ltd (FD) and Upside Energy (UE). In particular our research will guide FD and UE in the design of both contractual relationships and stochastic control systems. Since our focus is on the complex interactions within balancing services contracts, the United Kingdom commercial community (UK plc) will be the main beneficiary of this research. The direct financial beneficiaries from improved power system balancing will be National Grid Plc and UK power system customers; FD, UE and potentially other newly created British demand and storage aggregation companies; and the new 'end user' providers of demand response and storage enabled by the proposed research in collaboration with FD and UE. Since demand response is a clean alternative to electricity generation peaking plant which typically uses fossil fuels, society and the environment will benefit through lower emissions of carbon dioxide and associated pollutants.

There are currently a number of UK initiatives encouraging nationwide investment in demand-side management solutions, including Electricity Market Reform and the Electricity Balancing Significant Code Review. (For the purposes of discussing impact we will not distinguish energy storage from demand reponse as in the scientific Case for Support.) There are already UK companies (Flexitricity, Open Energi, KiWi Power) contracting with relatively large industrial sources of demand response (combined heat and power, hotel chains, wastewater facilities). At the other end of the scale, however, there is the potential for wider participation in demand response by a much larger number of smaller power consumers. This potential has been recognised by innovative UK companies such as FD and UE. FD recently won the opportunity to pilot their demand response solution in the ongoing development of Canary Wharf as part of the Cognicity Challenge smart cities accelerator programme, with a project aggregating demand response from multiple heating, ventilation and air conditioning (HVAC) systems. UE have successfully secured funding from Innovate UK to pilot a virtual energy store aggregating a large number of individual storage devices in a consortium project involving Sharp Laboratories of Europe Ltd; UE have also won a DECC Energy Entrepreneurs award to create an open innovation environment to develop algorithms for portfolio optimisation within their energy store, and the numerical algorithms we develop should contribute directly to this effort. We will work closely with both FD and UE to maximise the impact of the proposed research.

Single contracts for large-scale demand response with, say, a wastewater treatment plant have the advantage of relatively high technical predictability plus the involvement of just two parties in operational decision making. In contrast, coordinating demand response from a large number of small power consumers involves a potentially large number of decision makers plus dynamic stochasticity concerning its technical response. Our proposed mathematical modelling of the interactions within balancing services contracts as a dynamic stochastic game, particularly taking account of network topologies induced by aggregators such as FD and UE, is therefore timely. It is important since the existence of suitable Nash equilibria in such games will have the impact of indicating potentially practically usable and commercially successful operational and contractual arrangements. These arrangements will themselves be enabled by the corresponding numerical feedback control solutions obtained in the proposed research. We aim to generate short-term impact with the supporting companies and longer term impact with the wider industry.

Publications

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Battiston F (2017) Determinants of public cooperation in multiplex networks in New Journal of Physics

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Bonaventura M (2020) Predicting success in the worldwide start-up network. in Scientific reports

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Cencetti G (2018) Reactive random walkers on complex networks in Physical Review E

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De Angelis T (2017) Optimal entry to an irreversible investment plan with non convex costs in Mathematics and Financial Economics

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De Angelis T (2017) Optimal entry to an irreversible investment plan with non convex costs in Mathematics and Financial Economics

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Iacopini I (2019) Simplicial models of social contagion. in Nature communications

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Iacopini I (2018) Network Dynamics of Innovation Processes. in Physical review letters

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Jizba P (2018) Transitions between superstatistical regimes: Validity, breakdown and applications in Physica A: Statistical Mechanics and its Applications

 
Description We have developed new mathematical models to better understand load balancing problems in the electricity markets, using multilayer network approaches and stochastic analysis. A major new result of our research, published in the prestiguous journal Nature Energy in January 2018, is that both renewables and trading have a big impact on the statistics of frequency fluctuations in the power grid. We compared the statistics of various European, American, and Japanese power grids, and found subtle differences. What is very interesting is that the statistics is non-Gaussian and can be described by so-called superstatistical models. Using these models, one can provide better estimates of the risk of large fluctuations of the frequency around its mean value of 50 Hz, and develop suitable control algorithms.
We have also been comparing the efficiency of different control algorithms arising in the context of demand response. A concrete result deals with the optimal control of a commercial
building's thermostatic load for off-peak demand response. Another interesting result of our research relates to the intermittent statistical properties of power production by renewables (wind energy). We have found that the persistence statistics of low-wind and high-wind situations in Europe is characterized by power law tails that can be related to a superstatistical modelling approach.
Exploitation Route Our findings provide new methods for demand control and storage, for example in the framework of the recent Demand Turn Up initiative of National Grid. They give the basis for new control algorithms that can be further optimized and applied by our project partners Upside Energy Ltd and Future Decisions Ltd.
Sectors Energy,Environment

URL https://iaciac.github.io/lobanet/
 
Description We have developed a new control algorithm, and this is being used by our project partner Future Decisions Ltd as a tool to develop an optimized regulation of air condition and cooling of professional buildings in the Demand Turn Up initiative of National Grid. Our analysis of frequency fluctuation statistics of various European power grids is very useful in this context, as frequency fluctuations around 50 Hz mirror demand and supply fluctuations within the grid, which the Demand Turn Up Initiave of National Grid aims to smoothen. Also, Future Decisions Ltd were able to improve and control air quality in a particular building owned by a big company, using similar tools.
First Year Of Impact 2017
Sector Energy,Environment
Impact Types Economic

 
Description Chair of Statistical and Nonlinear Physics Division of European Physical Society (EPS)
Geographic Reach Europe 
Policy Influence Type Participation in a advisory committee
Impact enabling cooporation and career progress for physicists
URL http://www.eps.org/snpd
 
Description member of EPS HORIZON 2050 advisory panel
Geographic Reach Europe 
Policy Influence Type Membership of a guideline committee
 
Description Impact Acceleration Fund
Amount £5,000 (GBP)
Organisation Queen Mary University of London 
Sector Academic/University
Country United Kingdom
Start 03/2018 
 
Description Marie Curie Fellowship
Amount € 212,000 (EUR)
Organisation European Union 
Sector Public
Country European Union (EU)
Start 06/2019 
End 05/2021
 
Description Queen Mary research enabling fund
Amount £8,000 (GBP)
Organisation Queen Mary University of London 
Sector Academic/University
Country United Kingdom
Start 08/2016 
End 07/2017
 
Description Collaboration with Forschungszentrum Juelich 
Organisation Julich Research Centre
Country Germany 
Sector Academic/University 
PI Contribution Joint paper in Nature Energy, with Dirk Witthaut
Collaborator Contribution Data analysis
Impact Joint publication: Nature Energy 3, 119-126 (2018)
Start Year 2017
 
Description Collaboration with MPI Goettingen 
Organisation Max Planck Society
Department Max Planck Institute for Dynamics and Self-Organization
Country Germany 
Sector Academic/University 
PI Contribution Joint paper in Nature Energy with Benjamin Schaefer and Marc Timme
Collaborator Contribution Data analysis
Impact Nature Energy 3, 119-126 (2018)
Start Year 2017
 
Description Future Decisions Ltd 
Organisation Future Decisions Ltd
Country United Kingdom 
Sector Private 
PI Contribution Research discussions and intellectual input. During our meetings we had discussions on load balancing problems that are of interest for the building control systems developed by Future Decisions Ltd.
Collaborator Contribution Future Decisions has some time series data at hand that we could analyse.
Impact Stochastic modelling techniques have been fine-tuned
Start Year 2016
 
Description National Grid 
Organisation The National Grid Co plc
Country United Kingdom 
Sector Private 
PI Contribution We organized a joint workshop in Wokingham at the control centers of National Grid, bringing together academics and people from the energy industry interested in mathematical modelling of energy markets.
Collaborator Contribution National Grid was co-organizer of this workshop joint with Queen Mary Univ London and Edinburgh universities
Impact Slides from the talks at the workshop can be found at the above workshop website
Start Year 2017
 
Description Upside Energy 
Organisation Upside Ltd.
Country New Zealand 
Sector Private 
PI Contribution Research discussions and intellectual input on load balancing and storage options: Paying people not to use energy, and how to model it mathematically
Collaborator Contribution Information about the details of Upside's business concept
Impact New mathematical models including energy storage
Start Year 2016
 
Description Conference Organisation of 1st EPS Statistical and Nonlinear Physics Conference Krakow 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact 120 scientists discussed stochastic modelling methods and statistical physics approaches
Year(s) Of Engagement Activity 2017
 
Description Conference on Dynamics of Complex Systems 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact The meeting further developed applications of complex systems research and sparked scientific discussions and interactions.
Year(s) Of Engagement Activity 2016
URL https://www2.warwick.ac.uk/fac/sci/maths/research/events/2015-16/nonsymposium/dcs/
 
Description Conference organization: Statistical Physics of Complex Systems 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Conference "Statistical Physics of Complex Systems", PI was main organizer. This took place at Nordida/Stockholm. 200 participants, mainly academics working on sttaistical physics methods for general complex systems.
Year(s) Of Engagement Activity 2019
URL https://indico.fysik.su.se/event/6502/
 
Description Press release: Impact of renewables and trading on power grid frequency fluctuations 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact Press release about the 2018 Nature Energy paper dealing with impact of renewables and trading on power grid frequency fluctuations
Year(s) Of Engagement Activity 2018
URL http://www.qmul.ac.uk/media/news/2018/se/impact-of-renewables-and-trading-on-power-grid-frequency-fl...
 
Description Workshop: Mathematics and Economics of Energy Markets 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Industry/Business
Results and Impact About half of the audience were from the energy industry, the other half were academics, postdocs, and PhD students from
universities. We discussed a variety of
problems relevant for energy markets, with emphasis on practical relevance of mathematical models, and fine-tuning of models to the needs of
the energy industry.
Year(s) Of Engagement Activity 2017
URL https://iaciac.github.io/lobanet/events/
 
Description organization of power grid workshop 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact organized workshop on power grid dynamics at Nordita, Stockhom (9 May 2019).
Year(s) Of Engagement Activity 2019