Optimal Generation Expansion Planning Model of a Combined Thermal-wind-PV Power System Considering Multiple Boundary Conditions: A Case Study in Xinjiang, China

Background The scarcity of fossil fuels and their high emissions impact on the environment have forced the rapid development of renewable energy. Wind and photovoltaic power play a more and more important role in today's power system because of their clean and renewable characteristics. However, with the large-scale grid connection of wind and photovoltaic power, the contradiction between renewable energy and thermal power is becoming more and more serious. The unreasonable planning of power generation resources has also caused a lot of waste of electric power.Methods To solve this problem, this paper comprehensively considers the construction and operation costs of power plants, and constructs an optimal generation expansion planning model of a combined thermal-wind-PV power system with the objective of minimizing total cost. The planning is calculated under the boundary conditions of ensuring the safe operation of the power grid and taking into account the share requirement, utilization requirements and construction requirements for renewable energy. The model is applied to the self-use and external power plants in Xinjiang.Results The results show that this generation expansion plan can reduce the total cost of the power plants while ensuring the load demand. The renewable energy has also received more consumption share and its abandonment rate has dropped significantly. Numerical examples show that the optimization model has good applicability.Conclusion The proposed optimization model can realize the coordinated development of three types of power sources under multiple boundary conditions, which can not only guarantee the economy of power construction, but also take into account the optimization of environmental benefits. Reasonable generation expansion planning can improve energy efficiency, achieve clean and low carbon in the process of power generation, and promote the sustainable development of society.

A Meshless Method Based on Radial Basis and Spline Interpolation for 2-D and 3-D Inhomogeneous Biharmonic BVPs

This paper presents a meshless method which, at the first step, utilises the radial basis functions collocation scheme to approximate the unknown function at specific nodal points. The difficulty of these biharmonic-type problems is the multiple boundary conditions, as well as high derivatives terms. The inhomogeneous biharmonic equation is replaced by two Poisson equations of an intermediate function where Neumann’s boundary conditions is of second derivatives. It uses the imposed-kernel technique (IKT) to overcome multiple boundary conditions where Neumann’s boundary conditions is of first derivatives. In the next step, our meshless approach uses two- and three-dimensional cubic spline interpolation to get smooth, approximate solutions for the 2-D and 3-D inhomogeneous biharmonic-type problem, respectively. Numerical experiments are included to demonstrate the reliability and efficiency of this method.

Computational Elastic Rod Model Applied to DNA Looping

DNA is a long flexible biopolymer containing genetic information. Proteins often take advantage of DNA’s inherent flexibility to perform their cellular functions. Here we present selected results from our computational studies of the mechanical looping of DNA by the Lactose repressor protein. The Lactose repressor resides in the bacterium E. coli and deforms DNA into a loop as a means of controlling the production of enzymes necessary for digesting lactose. We examine this looping process using a computational rod model [1–3] to understand the strain energy and geometry for the resultant DNA loops. Our model captures the multiple looped conformations of the molecule arising from both multiple boundary conditions and geometric nonlinearities. In addition, the model captures the periodic variation of strain energy with base-pair length as suggested by repression experiments (see, for example, [4, 5]).