Hydropower plant operation reorganizes the temporal and spatial distribution of water resources to promote the comprehensive utilization of water resources in the basin. However, a lot of uncertainties were brought to light concerning cascade hydropower plant operation with the introduction of the stochastic process of incoming runoff. Therefore, it is of guiding significance for the practice operation to investigate the stochastic operation of cascade hydropower plants while considering runoff uncertainty. The runoff simulation model was constructed by taking the cascade hydropower plants in the lower reaches of the Lancang River as the research object, and combining their data with the copula joint function and Gibbs method, and a Markov chain was adopted to construct the transfer matrix of runoff between adjacent months. With consideration for the uncertainty of inflow runoff, the stochastic optimal operation model of cascade hydropower plants was constructed and solved by the SDP algorithm. The results showed that 71.12% of the simulated monthly inflow of 5000 groups in the Nuozhadu hydropower plant drop into the reasonable range. Due to the insufficiency of measured runoff, there were too many 0 values in the derived transfer probability, but after the simulated runoff series were introduced, the results significantly improved. Taking the transfer probability matrix of simulated runoff as the input of the stochastic optimal operation model of the cascade hydropower plants, the operation diagram containing the future-period incoming water information was obtained, which could directly provide a reference for the optimal operation of the Nuozhadu hydropower plant. In addition, taking the incoming runoff process in a normal year as the standard, the annual mean power generation based on stochastic dynamic programming was similar to that based on dynamic programming (respectively 305.97 × 108kW⋅h and 306.91 × 108kW⋅h), which proved that the operation diagram constructed in this study was reasonable.
Close-to-nature management (CTNM) is the most promising option for plantation silviculture and has received widespread attention in recent years. Stand density is a key variable in CTNM, as it directly influences growth and yield. Research for the optimal density that maximizes the total harvest has been ongoing. In this paper, a dynamic programming model was applied to the CTNM of Phoebe bournei plantations for the first time to solve the problem of stand density and target tree density control. This paper took Phoebe bournei plantations in Jindong Forest Farm of Hunan Province as the research object. Based on the data of seven consecutive years from 2015 to 2021, Richard’s growth equation was used to fit the height growth equation and basal area growth equation of Phoebe bournei. Stand growth was divided into five development stages according to the forest growth process and characteristics. Stand density and basal area were selected as two-dimensional state variables, and the maximum total harvest in the entire stand growth process was used as the objective function to establish a dynamic programming model. The optimal stand density and target tree density at each growth stage of the stand under three different site conditions were determined. According to the results obtained, the objective forest shape was designed for the stand under three types of site conditions, which can provide a theoretical basis for the CTNM of Phoebe bournei plantations to make the stand achieve the maximum harvest.
There is a growing interest in using electric vehicles (EVs) and drones for many applications. However, battery-oriented issues, including range anxiety and battery degradation, impede adoption. Battery swap stations are one alternative to reduce these concerns that allow the swap of depleted for full batteries in minutes. We consider the problem of deriving actions at a battery swap station when explicitly considering the uncertain arrival of swap demand, battery degradation, and replacement. We model the operations at a battery swap station using a finite horizon Markov decision process model for the stochastic scheduling, allocation, and inventory replenishment problem (SAIRP), which determines when and how many batteries are charged, discharged, and replaced over time. We present theoretical proofs for the monotonicity of the value function and monotone structure of an optimal policy for special SAIRP cases. Because of the curses of dimensionality, we develop a new monotone approximate dynamic programming (ADP) method, which intelligently initializes a value function approximation using regression. In computational tests, we demonstrate the superior performance of the new regression-based monotone ADP method compared with exact methods and other monotone ADP methods. Furthermore, with the tests, we deduce policy insights for drone swap stations.