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.
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.
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.
Organisations
- Queen Mary University of London (Lead Research Organisation)
- Max Planck Society (Collaboration)
- Forschungszentrum Jülich (Collaboration)
- FUTURE DECISIONS LTD (Collaboration)
- National Grid UK (Collaboration)
- Upside Ltd. (Collaboration)
- Upside Energy Ltd (Project Partner)
- Future Decisions Ltd (Project Partner)
Publications
Alvarez-Rodriguez U
(2021)
Memory Order Decomposition of Symbolic Sequences
Alvarez-Rodriguez U
(2021)
Memory order decomposition of symbolic sequences.
in Physical review. E
Anvari M
(2022)
Data-driven load profiles and the dynamics of residential electricity consumption.
in Nature communications
Battiston F
(2017)
Layered social influence promotes multiculturality in the Axelrod model.
in Scientific reports
Battiston F
(2017)
Determinants of public cooperation in multiplex networks
Battiston F
(2017)
Determinants of public cooperation in multiplex networks
in New Journal of Physics
Beck C
(2016)
Cosmological flux noise and measured noise power spectra in SQUIDs.
in Scientific reports
Bonaventura M
(2019)
Predicting success in the worldwide start-up network
Bonaventura M
(2020)
Predicting success in the worldwide start-up network.
in Scientific reports
Cencetti G
(2018)
Reactive random walkers on complex networks
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. More recently, the statistical techniques of the original grant project have been applied to a much bigger data-set of measured frequency fluctuations in different synchronous areas. This study was published in Nature Communications in December 2020, verifying with measured data a scaling law that we had conjectured and then mathematically developed while working on the original grant project. |
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 developed a new control algorithm, and this has been 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. In the later stages of the grant project, in 2018/19, we developed and tested together with co-workers from KIT (Karlsruhe Institute of Technology) a new measurement device for frequency fluctuations in power grids. With this device we did measurements of frequency fluctuations in different European power grids, testing for size effects and trading effects as well as for the influence of renewables, and testing with real data some of the theoretical models we had developed. This analysis has led to a highly cited article in the journal Nature Energy in 2018. The statistical techniques that we developed in the original EPSRC grant project have led to the development of a new open-access data base for power grid frequency fluctuations, partially funded by a new grant from the European Commission, which started in June 2019, as a follow-up of the EPSRC funded project, which ended in May 2019. For our most recent study, published in Nature Communications in December 2020, we collected power grid data from 17 locations across three continents and covering 12 synchronous areas - regions containing different power plants and consumers that are connected and operate under the same frequency. To these data sets we applied our novel methods of statistical data analysis. Our study is the first step towards a more collaborative approach to energy research. It is hoped the publicly available data can be used worldwide to design and test new `greener' energy concepts in response to current and future challenges. More recently, in 2022 we looked at the stochastic fluctuations of demand patterns of electricity consumers. We analysed household data from German, Austrian and UK households, and developed new statistical methods to predict more precise demand profiles, as well as predicting the statistics of fluctuations around the average demand profiles. This work appeared as a Nature Commun paper in 2022. With the help of this more recent research, it is possible to give better predictions of electricity demand patterns of consumers, which ultimately can help to avoid switching on 'dirty' power stations, thus reducing the carbon footprint in the long-term. |
First Year Of Impact | 2022 |
Sector | Energy,Environment,Transport |
Impact Types | Societal Economic Policy & public services |
Description | Chair of Statistical and Nonlinear Physics Division of European Physical Society (EPS) |
Geographic Reach | Europe |
Policy Influence Type | Participation in a guidance/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 | 05/2019 |
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 | 07/2016 |
End | 07/2017 |
Title | Open data base analysis of scaling and spatio-temporal properties of power grid frequencies |
Description | This is a set of frequency data for various European and international power grids. We produced it with new measuring devices developed at KIT Karlsruhe. The data are openly accessible upon reasonable request. This data set formed the basis for our paper in Nature Communications 11, 6362 (2020). |
Type Of Material | Data analysis technique |
Year Produced | 2020 |
Provided To Others? | Yes |
Impact | Publication in Nature Communications 2020. |
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 | National Grid UK |
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 | Complexity in Energy 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 | Sattelite conference within the Conference on Complex Systems CCS2020, on the topic 'Complexity in Eneergy Systems'. About 20 speakers gave invited and contributed talks, which were broadcast online. |
Year(s) Of Engagement Activity | 2020 |
URL | https://fhell.github.io/ComplexityInEnergySystems/ |
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 | Scientists publish open resource to help design 'greener' energy systems (QMUL press release) |
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 by the Press Office of Queen Mary University of London about our research on spatio-temporal properties of power grid frequencies published in Nature Communications in December 2020. Simultaneous press releases were presented in London, Karlsruhe, Juelich, Dresden, and Istanbul. |
Year(s) Of Engagement Activity | 2020 |
URL | https://www.qmul.ac.uk/media/news/2020/se/scientists-publish-open-resource-to-help-design-greener-en... |
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 |