  The 2019-20 Australia bushfire incurred numerous economic losses and
significantly affected the operations of power systems. A power station or
transmission line can be significantly affected due to bushfires, leading to an
increase in operational costs. We study a fundamental but challenging problem
of planning the optimal power flow (OPF) for power systems subject to
bushfires. Considering the stochastic nature of bushfire spread, we develop a
model to capture such dynamics based on Moore's neighborhood model. Under a
periodic inspection scheme that reveals the in-situ bushfire status, we propose
an online optimization modeling framework that sequentially plans the power
flows in the electricity network. Our framework assumes that the spread of
bushfires is non-stationary over time, and the spread and containment
probabilities are unknown. To meet these challenges, we develop a contextual
online learning algorithm that treats the in-situ geographical information of
the bushfire as a 'spatial context'. The online learning algorithm learns the
unknown probabilities sequentially based on the observed data and then makes
the OPF decision accordingly. The sequential OPF decisions aim to minimize the
regret function, which is defined as the cumulative loss against the
clairvoyant strategy that knows the true model parameters. We provide a
theoretical guarantee of our algorithm by deriving a bound on the regret
function, which outperforms the regret bound achieved by other benchmark
algorithms. Our model assumptions are verified by the real bushfire data from
NSW, Australia, and we apply our model to two power systems to illustrate its
applicability.
