Nash equilibria for load balancing in networked power systems

电力系统必须始终在电力的瞬时供需之间保持平衡。能源储存和需求侧管理等即将到来的技术有望为这一平衡挑战做出重大贡献。需求侧管理的概念涉及电力公用事业公司通过电信系统直接控制或通过通常是经济的激励措施(如可变定价电价)间接影响用户场所的电力使用的能力。电能存储单元(如特斯拉最近发布的可充电锂离子电池产品Powerwall，用于存储供家庭消费、负载转移和备用电源的电力)主要或仅用于抵消供需之间的电力失衡。能源存储技术通常是可靠的，并且始终可用，但对于需求侧管理解决方案来说，情况并非如此。这项研究将探索储能和需求侧管理技术应用于电力系统平衡时所产生的动态、多人、经济和可操作的‘博弈’。我们将使用博弈论方法对此进行建模，并结合借用复杂系统统计力学的有用数学技术和为分析复杂网络而开发的技术。这些技术的运营商以及负责平衡的实体被视为一个或多个电力市场的代理人。在这些非零和动态博弈的研究中，一个重要的解的概念是所谓的纳什均衡，在这个均衡中，任何一个参与者都不能通过单方面改变他们的决策来改善他们的结果。换句话说，纳什均衡是一种状态，在这种状态下，任何玩家都不能通过改变策略来改善自己的状况。在这种平衡的背景下，平衡是可取的，因为它们代表了可持续和稳定的设置。通过研究动态博弈，我们将解决两个基本的研究问题：第一，这些新技术的运营商应该如何最优地采取行动；第二，他们应该如何获得适当的报酬，以便在他们所能提供的平衡服务中产生合适的动态均衡。此外，通过将这些游戏适当地扩展到网络，我们将探索当这些技术通过第三方聚合时，动态均衡是如何变化的。在本提案最雄心勃勃的部分中，我们将探索多路复用和不断演变的网络拓扑的影响，例如，当参与负载平衡时，对等方的参与会产生影响。

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.