A deep learning model for gas storage optimization

Abstract

To the best of our knowledge, the application of deep learning in the field of quantitative risk management is still a relatively recent phenomenon. In this article, we utilize techniques inspired by reinforcement learning in order to optimize the operation plans of underground natural gas storage facilities. We provide a theoretical framework and assess the performance of the proposed method numerically in comparison to a state-of-the-art least-squares Monte-Carlo approach. Due to the inherent intricacy originating from the high-dimensional forward market as well as the numerous constraints and frictions, the optimization exercise can hardly be tackled by means of traditional techniques.

Reservoir optimization and Machine Learning methods

“…As the problem is Markovian in (S, Q) where Q is the storage level, we can introduce as in [BE+06] a feed forward networks φ θi i with parameters θ i per time step i as an operator from R 2 to R approximating a transformation of the control u i . There are many ways to deal with the constraints imposed on the level of the storage (Q has to stay positive and below Q max ): among them clipping the control, penalization of the objective function are possible but the best approach (we won't report results on less effective approaches) consists in using the [Cur+21] approach. First we introduce for a given i in 0, .…”

“…At last in a very recently article, [Cur+21] studies the valuation and hedging of a gas storage using a single optimization approximating the control at each time step by some neural networks as in [BE+06]. They also propose to "merge" the network between different time steps (so introducing a dependence on time in a network shared between different time steps).…”

“…This kind of approach merging all time steps (so using a single neural network shared between all time steps) is the one proposed in [FMW19] for risk valuation or [CWNMW19] for BSDE resolution: they show that its gives better stabilized results on these problems. The present article studies first the "Global Valuation" method (GV) of one or many storage using the global approach used in [BE+06] and [Cur+21] testing different formulations and network to represent the control. This type of resolution is impossible to use on real problem involving optimization for example on the global year on an hourly basis for one storage, or the global year even on a daily basis when many storages are linked together: this is for example the case for the valuation of a high number of batteries with a management having an influence on the price of electricity as it would the case for some windmill fields with batteries.…”

“…This choice is driven but the fact that, in practice, it is the main concern associated to this kind of management. Introducing some hedging strategies as proposed in [Cur+21] leads to the need to use a risk function to discriminate an optimal strategy. Another important point associated with this choice is the fact that we can implement multi storage optimization problems that can easily be reduced to a one storage optimization permitting to get a reference by the classical dynamic programming approach using regressions.…”

A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection

“…For instance X max = 0 corresponds to the much simpler problem without storage nor control of the valuation of a wind power park. See also [22,43]. To represent the almost sure constraint 0 ≤ X t ≤ X max we choose as constrained function…”