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This paper demonstrates an energy management method using traffic information for commuter hybrid electric vehicles. A control strategy based on stochastic dynamic programming (SDP) is developed, which minimizes on average the equivalent fuel consumption, while satisfying the battery charge-sustaining constraints and the overall vehicle power demand for drivability. First, according to the sample information of the traffic speed profiles, the regular route is divided into several segments and the statistic characteristics in the different segments are constructed from gathered data on the averaged vehicle speeds. And then, the energy management problem is formulated as a stochastic nonlinear and constrained optimal control problem and a modified policy iteration algorithm is utilized to generate a time-invariant state-dependent power split strategy. Finally, simulation results over some driving cycles are presented to demonstrate the effectiveness of the proposed energy management strategy.

Energy storage and renewable sources play a unique role in the future advances of smart grids. In this article, the optimal scheduling of the energy storage system in a hybrid microgrid is presented considering the uncertainties of the renewable generations and the load. The optimisation problem in this article is non‐linear and non‐convex, therefore conventional optimisation methods such as linear programming (LP) are unable to solve this problem. On the other hand, because of parameters uncertainty, special considerations are required to simulate these parameters. In this regard, a new optimisation algorithm that can solve the non‐linearity and non‐convexity of the objective function is proposed based on the Stochastic Quasi‐Gradient optimisation Method (SQGM). Moreover, the uncertainties of the wind, PV generation, and the load are modelled. Different optimisation algorithms: the conventional Stochastic Dynamic Programming (SDP), the Stochastic Dual Dynamic Programming (SDDP) and the proposed SQGM are compared. A 9‐bus benchmark system with distributed generation units is used to evaluate the optimisation strategies.

1. How climatic changes affect migratory birds remains difficult to predict because birds use multiple sites in a highly interdependent manner. A better understanding of how conditions along the flyway affect migration and ultimately fitness is of paramount interest. 2. Therefore, we developed a stochastic dynamic model to generate spatially and temporally explicit predictions of stop-over site use. For each site, we varied energy expenditure, onset of spring, intake rate and day-to-day stochasticity independently. We parameterized the model for the migration of pink-footed goose Anser brachyrhynchus from its wintering grounds in Western Europe to its breeding grounds on Arctic Svalbard. 3. Model results suggested that the birds follow a risk-averse strategy by avoiding sites with comparatively high energy expenditure or stochasticity levels in favour of sites with highly predictable food supply and low expenditure. Furthermore, the onset of spring on the stop-over sites had the most pronounced effect on staging times while intake rates had surprisingly little effect. 4. Subsequently, using empirical data, we tested whether observed changes in the onset of spring along the flyway explain the observed changes in migration schedules of pink-footed geese from 1990 to 2004. Model predictions generally agreed well with empirically observed migration patterns, with geese leaving the wintering grounds earlier while considerably extending their staging times in Norway.

An optimal switching control formalism combined with the stochastic dynamic programming is, for the first time, applied to modelling life cycle of migrating population dynamics with non-overlapping generations. The migration behaviour between habitats is efficiently described as impulsive switching based on stochastic differential equations, which is a new standpoint for modelling the biological phenomenon. The population dynamics is assumed to occur so that the reproductive success is maximized under an expectation. Finding the optimal migration strategy ultimately reduces to solving an optimality equation of the quasi-variational type. We show an effective linkage between our optimality equation and the basic reproduction number. Our model is applied to numerical computation of optimal migration strategy and basic reproduction number of an amphidromous fish Plecoglossus altivelis altivelis in Japan as a target species.

Wind integration in power grids is challenging because of the uncertain nature of wind speed. Forecasting errors may have costly consequences. Indeed, power might be purchased at highest prices to meet the load, and in case of surplus, power may be wasted. Energy storage may provide some recourse against the uncertainty of wind generation. Because of their sequential nature, in theory, power scheduling problems may be solved via stochastic dynamic programming. However, this scheme is limited to small networks by the so-called curse of dimensionality. This paper analyzes the management of a network composed of conventional power units and wind turbines through approximate dynamic programming, more precisely stochastic dual dynamic programming. A general power network model with ramping constraints on the conventional generators is considered. The approximate method is tested on several networks of different sizes. The numerical experiments also include comparisons with classical dynamic programming on a small network. The results show that the combination of approximation techniques enables to solve the problem in reasonable time.

Long‐term multireservoir operations optimization is challenging for existing optimization methods such as stochastic dynamic programming (SDP) and implicit stochastic programming (ISP) suffering from excessive computing time requirements. More difficult is to tackle a risk‐based optimization problem and provide an efficient frontier of the objective function for multireservoir systems. The Fletcher–Ponnambalam (FP) method is an explicit stochastic optimization method suitable for multireservoir operations optimization which faces no curse of dimensionality of SDP and has no need for scenario generations of ISP, thus is extremely fast. Earlier implementations have developed expressions for mean and variance of storages and releases, including deficits and surpluses, to estimate fairly accurate values of the linear and quadratic objective functions when compared with other well‐known methods. This paper introduces analytical derivations of hydropower equations to be used in the recent extension of the FP method and applies it to a long‐term operations optimization problem of a three‐reservoir system in Iran. The objective function is to maximize the expected value of the annual energy, which is a multiplicative nonlinear function of both releases and storage levels. The computational results from simulations for the 60 years of available inflow data for the chosen multireservoir system using the policies derived by the FP, ISP, and SDP methods were compared. The solution qualities were nearly the same, but the FP method has tremendous speedups over the other methods. Secondly, expressions for the variances of monthly energy productions were derived to compute efficient frontier for risk‐return tradeoffs of annual energy to guide decision makers. Plain Language Summary Optimizing long‐term operations for multiple reservoirs is difficult with traditional methods like stochastic dynamic programming (SDP) and implicit stochastic programming (ISP) because they require a lot of computing time. It's even harder to address risk‐based optimization and to create an efficient frontier, which shows the best trade‐offs between different goals. The Fletcher–Ponnambalam (FP) method is a fast and effective solution that doesn't suffer from the complexity issues of SDP and doesn't need scenario generations like ISP. Previous versions of the FP method could accurately estimate values using mean and variance of storage and releases. This paper improves the FP method by introducing new hydropower equations and applies it to optimize a three‐reservoir system in Iran over 60 years of inflow data. The goal is to maximize annual energy, a complex function of water releases and storage levels. The FP method produced solutions comparable in quality to SDP and ISP but was much faster. Additionally, new calculations for monthly energy variance were developed to help make better risk‐return decisions for annual energy production. Key Points Analytic expressions are derived for the moments of energy function to be used in hydropower multireservoir operations optimization, not considered before The derived expressions for the second moment of the generated energy is used to produce efficient frontier easily for annual hydroenergy production function The Fletcher–Ponnambalam (FP) results are better than stochastic dynamic programming and comparable to implicit stochastic programming but much faster than these methods

In this paper, we consider a project-based organization that deals with an assignment problem in which a set of projects must be assigned to a group of project managers. This assignment is done based on the relative contributions of projects to the organizational mission and a matching score between each pair of a project and a project manager. We assume that some projects are deterministic, and the organization has signed their corresponding contracts while others are stochastic, i.e. the organization has submitted bids for these projects and may or may not win them in the future. Furthermore, we consider a finite planning horizon and presume a predetermined start time for each deterministic and stochastic project. We develop two models including a multi-stage stochastic integer programming model and a stochastic dynamic programming model to solve the problem. The latter shows better performance for small-size and less complex instances whereas the former gives better performance for more complex instances. We also developed a heuristic algorithm to solve large-size and more complex instances. Computational results indicate that the developed heuristic algorithm can reach near-optimal solutions in reasonable CPU run times and dominates the two other solution approaches particularly for large-size instances.

Multistage stochastic integer programming (MSIP) combines the difficulty of uncertainty, dynamics, and non-convexity, and constitutes a class of extremely challenging problems. A common formulation for these problems is a dynamic programming formulation involving nested cost-to-go functions. In the linear setting, the cost-to-go functions are convex polyhedral, and decomposition algorithms, such as nested Benders’ decomposition and its stochastic variant, stochastic dual dynamic programming (SDDP), which proceed by iteratively approximating these functions by cuts or linear inequalities, have been established as effective approaches. However, it is difficult to directly adapt these algorithms to MSIP due to the nonconvexity of integer programming value functions. In this paper we propose an extension to SDDP—called stochastic dual dynamic integer programming (SDDiP)—for solving MSIP problems with binary state variables. The crucial component of the algorithm is a new reformulation of the subproblems in each stage and a new class of cuts, termed Lagrangian cuts, derived from a Lagrangian relaxation of a specific reformulation of the subproblems in each stage, where local copies of state variables are introduced. We show that the Lagrangian cuts satisfy a tightness condition and provide a rigorous proof of the finite convergence of SDDiP with probability one. We show that, under fairly reasonable assumptions, an MSIP problem with general state variables can be approximated by one with binary state variables to desired precision with only a modest increase in problem size. Thus our proposed SDDiP approach is applicable to very general classes of MSIP problems. Extensive computational experiments on three classes of real-world problems, namely electric generation expansion, financial portfolio management, and network revenue management, show that the proposed methodology is very effective in solving large-scale multistage stochastic integer optimization problems.

The size of the fuel cell and battery of a Fuel Cell Hybrid Electric Vehicle (FCHEV) will heavily affect the overall performance of the vehicle, its fuel economy, driveability, and the rates of fuel cell degradation observed. An undersized fuel cell may experience accelerated ageing of the fuel cell membrane and catalyst due to excessive heat and transient loading. This work describes a multi-objective design exploration exercise of fuel cell size and battery capacity comparing hydrogen fuel consumption, fuel cell lifetime, vehicle mass and running cost. For each system design considered, an individually optimised Energy Management Strategy (EMS) has been generated using Stochastic Dynamic Programming (SDP) in order to prevent bias to the results due to the control strategy. It has been found that the objectives of fuel efficiency, lifetime and running cost are largely complimentary, but degradation and running costs are much more sensitive to design changes than fuel efficiency and therefore should be included in any optimisation. Additionally, due to the expense of the fuel cell, combined with the dominating effect of start/stop cycling degradation, the optimal design from an overall running cost perspective is slightly downsized from one which is optimised purely for high efficiency.

Adaptation planning for water resource systems is fraught with significant challenges, arising from uncertainties associated with diverse climate change scenarios, varying model structures, and Internal Climate Variability (ICV), often captured through multiple initial condition runs. ICV, typically considered irreducible, has received significant attention for state and derived hydrological variables. However, its implications and role in regional decision‐making remain elusive. Here, we develop an integrated framework to incorporate uncertainties through hydrological modeling combined with a suite of multi‐objective stochastic optimization techniques. This approach is applied to design optimal operating policies for the Sardar Sarovar Dam in Gujarat, India, a multipurpose infrastructure of national importance to meet flood control, hydroelectric generation and domestic, industrial, and irrigation water demands while accounting for two future climate change scenarios, SSP245 and SSP585, with 49 different initializations of each scenario to represent the ICV. We employ Sampling Stochastic Dynamic Programming to incorporate ICV by considering multiple initializations simultaneously, in contrast to Stochastic Dynamic Programming, which evaluates realizations individually. We show that despite the wide range of uncertainties, optimal operating policies can be designed to meet the various demands with reliability of 100%, 59%, and 27% for domestic, irrigation, and industrial water demand, respectively, when all scenarios are considered simultaneously. Our study advocates for the systematic inclusion of a wide array of climate model outputs, emphasizing that such integration is essential not only for crafting robust operating policies, but also for the reliability assessment of current operating policies in light of changing climate and demand scenarios.