Dr Huikang Liu, Research Associate in the Analytics and Operations Group at Imperial College Business School, discusses the role of optimisation under uncertainty in the long-term planning of future energy systems. Huikang works on Project 5 of IDLES, which aims to quantify the benefits of forward-looking strategies over incremental “greedy” strategies for the design of future energy systems.

Future plans almost inevitably involve uncertainty, and the design of sustainable future energy systems is no different. When deciding which energy sources to use, where and how to build power plants and which transmission lines to build or upgrade, we should account for the uncertainty inherent in the future demand for energy, the emergence of future technologies (such as electric vehicles), behavioural changes (such as the current move towards working from home), as well as various operational aspects (such as the failure of power plants and/or transmission lines in addition to the intermittent nature of many renewable sources of energy).

Unfortunately, taking decisions under uncertainty is an inherently difficult undertaking. Mathematically speaking, uncertainty is modelled through random variables whose interplay is characterised by probability distributions, and prudent decisions today have to anticipate that future decisions can be taken under the benefit of knowing the values of some (but typically not all) of these random variables. This means that future decisions are functions of the realisations of these random variables, and optimising over the associated functional spaces is hard — this is the well-known curse of dimensionality. As part of Project 5 of IDLES, I investigate how tractable decisions (that scale to industry-size problems) can be found in this setting that benefit from rigorous performance guarantees with respect to the optimal decisions that can typically not be determined with today’s computing infrastructures.

A promising strategy in this regard is the class of factored Markov decision processes. A Markov decision process characterises the uncertain evolution of a system (such as an energy system serving a country) through a set of states (that characterise the potential states of the system, such as the available power plants and transmissions lines as well as the current demand), a set of actions (which describe the investment and operational decisions available to the decision maker) as well as transition probabilities (which elucidate how the interplay of states and actions characterise the evolution of the system). While Markov decision processes offer a very natural way to describe and solve dynamic decision problems involving uncertainty, they suffer from the aforementioned curse of dimensionality: the description (and solution) of a Markov decision process typically grows exponentially in the description of the underlying system.

To combat the curse of dimensionality, factored Markov decision processes have emerged as a promising strategy to exploit the structure inherent in many real-life systems. Factored Markov decision processes assume that the state of a system can often be meaningfully approximated by the interplay of the states of several sub-systems (e.g., different regions of the energy system) that evolve largely independently. Exploiting this structure often leads to an exponential reduction in the description of the system, which is then accompanied by a similar reduction in the solution effort. In the past, factored Markov decision processes have enjoyed significant attention in the Computer Science community, and I am exploring how the methods and tools of optimisation theory can help to leverage these developments in energy systems.

About IDLES Project 5

Project 5 of the Integrated Development of Low-Carbon Energy Systems (IDLES) programme is addressing the risk and ambiguity present in long-term energy planning, and the challenges associated with the large scale of the optimisation problems (due to the long time horizons and interconnected nature of the energy systems). Insights obtained from our models will help identify strategically important technologies and solutions as cost-effective options for energy system decarbonisation, thus guiding investors and policy makers by quantifying the benefits of investing in certain infrastructure assets ahead of their full utilisation.