Investigating optimal strategies for power storage facilities

Abstract

The variation in electricity generation is increasing significantly as the UK transitions to a renewable based energy grid, introducing logistical challenges in balancing the supply and demand of electricity. These challenges can be overcome through the use of power storage facilities, which ensure that electricity can be generated when possible and provided to the grid when needed. Private investment in power storage facilities must be encouraged through studies of their profitability, for which suitable methodologies must be developed, with facilities aiming to identify optimal strategies which maximise profits by considering the values of different actions and acting in a manner which adds the most value to the facility. The value of the facility is dependent upon the excess demand - the difference between the demand and supply - of electricity, with increasing excess demand leading to higher prices of electricity. Whilst the value of charging and discharging are known for each facility and given by payoff functions, the value of waiting has historically required assuming the form of the stochastic process assumed to underlie excess demand data and the estimation of parameter values from which the value of waiting can be calculated. Instead, this thesis employs an empirical approach to directly estimate the value of waiting from historical excess demand data. The methodology is derived using traditional stochastic control techniques requiring the underlying process only to be volatile in some manner and non-explosive, requiring no set form or even the existence of a canonical form which means it is suitable for application on data-sets where the underlying dif fusion is unknown such as with excess demand. With an eye on the continued development of power storage technologies a development of standard ‘bang-bang’ models which only consider complete actions is introduced that allows for the consideration of partial actions, allowing for more accurate modelling of developing power storage technologies with quick reaction times to changes in excess demand levels. Furthermore, variations in facility efficiency and electricity pricing - and the resulting effects on the optimal control strategy - with respect to different factors are considered through their affects on the payoff functions, alongside the potential interaction between factors to provide a methodology to define a complete optimal control strategy.