The rapid expansion of renewable energy

particularly wind and photovoltaic (PV) power generation

increases the vulnerability of power systems to persistent low output scenarios (PLOS)

which pose significant security risks. To address uncertainties in the timing

duration

and frequency of PLOS while considering operational non-anticipativity

this paper proposes a multi-stage energy storage planning model incorporating a Markov process. A nested conditional value at risk (CVaR) framework is employed to manage uncertainty. To efficiently solve the large-scale multi-stage mixed-integer stochastic problem

a modified stochastic dual dynamic integer programming (SDDiP) algorithm is proposed. In order to accelerate the convergence speed of the algorithm

techniques such as regularization

dynamic sampling

dynamic cut selection

and parallel computation are designed. Case studies on the IEEE 118-bus system validate the effectiveness of the proposed approach.