Nash equilibria for load balancing in networked power systems

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.

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.