We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Renewable energy, such as hydro power, photovoltaics and wind turbines, has become the most widely applied solutions for addressing issues associated with oil depletion, increasing energy demand and anthropogenic global warming. Solar and wind energy are strongly dependent on weather resources with intermittent and fluctuating features. To filter these variabilities, battery energy storage systems have been broadly accepted as one of the potential solutions, with advantages such as fast response capability, sustained power delivery, and geographical independence. During the implementation of battery energy storage systems, one of the most crucial issues is to optimally determine the size of the battery for balancing the trade-off between the technical improvements brought by the battery and the additional overall cost. Numerous studies have been performed to optimise battery sizing for different renewable energy systems using a range of criteria and methods. This paper provides a comprehensive review of battery sizing criteria, methods and its applications in various renewable energy systems. The applications for storage systems have been categorised based on the specific renewable energy system that the battery storage will be a part. This is in contrast to previous studies where the battery sizing approaches were either arranged as an optimised component in renewable systems or only accounted for one category of renewable system. By taking this approach, it becomes clear that the critical metrics for battery sizing, and by extension the most suitable method for determining battery size, are determined by the type of renewable energy system application, as well as its size. This has important implications for the design process as the renewable energy system application will drive the battery energy storage system sizing methodology chosen.

Battery energy storage system size determination in renewable energy systems: A review

Evaluating challenges to Industry 4.0 initiatives for supply chain sustainability in emerging economies

Battery energy storage systems have gained increasing interest for serving grid support in various application tasks. In particular, systems based on lithium-ion batteries have evolved rapidly with a wide range of cell technologies and system architectures available on the market. On the application side, different tasks for storage deployment demand distinct properties of the storage system. This review aims to serve as a guideline for best choice of battery technology, system design and operation for lithium-ion based storage systems to match a specific system application. Starting with an overview to lithium-ion battery technologies and their characteristics with respect to performance and aging, the storage system design is analyzed in detail based on an evaluation of real-world projects. Typical storage system applications are grouped and classified with respect to the challenges posed to the battery system. Publicly available modeling tools for technical and economic analysis are presented. A brief analysis of optimization approaches aims to point out challenges and potential solution techniques for system sizing, positioning and dispatch operation. For all areas reviewed herein, expected improvements and possible future developments are highlighted. In order to extract the full potential of stationary battery storage systems and to enable increased profitability of systems, future research should aim to a holistic system level approach combining not only performance tuning on a battery cell level and careful analysis of the application requirements, but also consider a proper selection of storage sub-components as well as an optimized system operation strategy.

https://www.mdpi.com/1996-1073/10/12/2107/pdf

Lithium-Ion Battery Storage for the Grid—A Review of Stationary Battery Storage System Design Tailored for Applications in Modern Power Grids

The journal’s scope ranges from mathematical foundations of the field to algorithm and software development, and from benchmark examples to case studies of practical applications in structural, aero-space, mechanical, civil, chemical, naval and bioengineering. Fields such as computer-aided design and manufacturing, uncertainty quantification, artificial intelligence, system identification and modeling, inverse processes, computer simulation, bio-mechanics, bio-medical applications, nano-technology, MEMS, optics, chemical processes, computational biology, meta-modeling, DOE and active control of structures are covered when the topic is closely related to the optimization of structures or fluids. Structural and Multidisciplinary Optimization publishes original research papers, review articles, industrial applications, brief notes, educational articles, book reviews, conference diary, forum section, discussions on papers, authors ́ replies, obituaries, announcements and society news. The journal does not consider papers directly related to weapon and military applications.

Structural and Multidisciplinary Optimization

Systematic literature review of decision support models for energy-efficient production planning

On the use of waste heat in a two-stage production system with controllable production rates.

Over the last decade, manufacturing companies have identified renewable energy as a promising means to cope with time-varying energy prices and to reduce energy-related greenhouse gas emissions. As...

Flow shop scheduling with grid-integrated onsite wind power using stochastic MILP.

This paper adopts a single-period newsvendor model with supply uncertainties to be used for optimally sizing an electrical energy storage system (EESS) for an apartment house with a photovoltaic system. Hence, typical inventory cost components and supply chain characteristics are translated into the EESS application. The results show that existing research approaches for inventory management can be adapted to determine the optimal size of an EESS. The proposed EESS-sizing procedure takes into account the total cost of the storage system including energetic losses as well as the costs for energy supply from the own energy systems and from the energy supplier.

K. Biel

Papers

Systematic literature review of decision support models for energy-efficient production planning

On the use of waste heat in a two-stage production system with controllable production rates.

Flow shop scheduling with grid-integrated onsite wind power using stochastic MILP.

Using inventory models for sizing energy storage systems: An interdisciplinary approach

Dynamic scheduling of a flow shop with on-site wind generation for energy cost reduction under real time electricity pricing