The motivation behind this research lies in the well-spread news about USA and China’s plans to build bases on the moon within the next 10 years. In this research, we create a mathematical model of efficiency for geometrical solar panels, as well as discuss which locations on the moon may be suitable for placing a non-tracing solar power plant. We consider the North Pole, the Equator and additional locations; and analyze the accumulation of illumination over an 18.6-year period that represents the lunar cycle. The simulation for geometrical panels is based on the etendue, with the panel being the diaphragm and a selected segment of the sky being the source. However, the etendue needs to be modified due to the properties of solar energy. The selected segment of the sky is crafted with careful analysis of the motion of the moon. The difficulty of the model comes from the fact that the motion of the sun on the moon’s sky is subject to change in its speed and direction, which is created by the moon’s libration. In addition, we discuss the change of luminosity of the sun’s light due to the varied distance between the moon and the sun. The simulation was performed using MATLAB and Mathematica.
Previous publications suggest that geometrical solar panels are more efficient in terms of using the mounting space than traditional flat static solar panels. However, previous research does not deeply discuss the questions of the distribution of solar cells on the considered segments of cylinders, cones, spheres, and catenoids. To find the best geometry, we optimize the parameters of various curved surfaces, such as cones and catenoids, for the greatest energy produced per square meter. In practice, these curved solar panels are created by packing flexible fixed size square solar cells onto the curved surface. So, we must also optimize our curved surfaces for their ability to be packed efficiently with square solar cells. Using combinatorial methods, we propose sample solar cells packing and approximate energy production to optimize geometrical solar panels at various geographic locations. These techniques allow us to create more efficient static solar panels and improve the overall value of solar energy.
Development in solar photovoltaic (PV) technology has made it possible to manufacture curved or shaped panels. However, little research has been done on the topic of solar resource for curved surfaces. This project aims to develop a numerical program to estimate solar resource for a curved cylindrical panel on Earth and Mars. Numerical calculations of solar resource were performed through MATLAB using Typical Meteorological Year (TMY) empirical irradiance data for New York City. This data was used as inputs for the code and the solar resource for a cylindrical panel of different curvatures and orientation was calculated using the MATLAB program. The cylindrical surface will be discretized into segments of flat surfaces. The isotropic diffused sky solar irradiance model was then used to calculate total solar resource for the given surface. It was found that as the curvature of the panel increased, the total solar resource per unit surface area decreased while the total solar resource per unit footprint area, which is the area an object occupies on a horizontal surface, increased. In addition to quantifying the performance of a curved surface on Earth and Mars, this work shows the potential of highly efficient non-tracking curved surfaces for collecting solar resource in volume limited situations such as space travel or urban applications. The resource estimation algorithm can also be used to estimate solar resource for commercial applications and system sizing.
The introduction of flexible solar cells embedded in fabrics motivates the search for more efficient solar cell designs than flat panels. The optimal configuration of solar cells should receive the maximal flux density of sunlight rays over the course of a year. There may also be spatial restrictions which only allow the cells to cover an arbitrary roof or area and surrounding structures which cast shadows in that area. So, it is difficult to analytically find the most efficient way to cover an arbitrary surface on Earth with solar cells. The genetic algorithm was used to find the optimal geometry for solar cells that have constant footprints at various latitudes. Random configurations of solar cells covering a constant area evolved into efficient configurations under the guidance of chosen selection, crossover, and mutation mechanisms. The results allow us to cover arbitrary roofs or areas as efficiently as possible, which greatly increases the value of solar energy.
The long-term goal of the project is to create and justify a reliable mathematical model that expresses the efficiency of geometrical shapes of non-tracking flexible solar panels. However, the amount of solar energy absorbed by a non-tracking flexible solar panel depends on many parameters: the direction of the sun beam, reflected light, and temperature, etc., which would make a complete model mathematically complicated. In the current model, we limit our consideration to the direction of the sunbeam. In order to simulate the exposure of the panel, we describe the trajectory of the Sun and base the model on the mathematical flux that uses the sun rays as the vector field. To be precise, the efficiency of a geometrical panel is defined as the flux density, which is the ratio of the mathematical flux and the surface area. Our current model was evaluated for the latitude of New York City and we determined the efficiency of the optimized at panels, cylindrical panels, and conical panels. The analysis was largely done through geometrical studies and numerical integration with software programs Python, Maple, Mathematica, and MATLAB.
The purpose of this research is to analyze mathematically cylindrical shapes of flexible solar panels and compare their efficiency to the flat panels. The efficiency is defined to be the flux density, which is the ratio of the mathematical flux and the surface area. In addition we describe the trajectory of the Sun at specific locations: the North Pole, The Equator and a geostationary satellite above the Equator. The calculations were performed with software: Maple, Mathematica, and MATLAB.
The diversity traffic requirements, reliability communication infrastructure, and the real-time end-to-end (E2E) latencies are some of the major communication challenges to support a diverse set of emerging Internet of Things (IoT) applications include Smart Grid (SG) applications. For instance, using point-to-point fibers between each device and the controller has been reported, previously, as one of the solutions to address the E2E latency requirements. However, even with the fiber capacity, utilizing the technique was limited due to its excessive cost. Hence, using a commercial multiservice cellular network such as Long-Term Evolution (LTE) and Long-Term Evolution-Advanced (LTE-A) is a considerable solution due to the high-performance metrics: high throughput, low latency, higher reliability, and large bandwidth.
In this paper, we propose an uplink LTE Cascaded Priority-based scheduling algorithm (CPb) that supports a diverse set of Smart Grid (SG) applications, and improves the performance metrics compared to other two well-known schedulers, Proportional Fairness (PF) and Round Robin (RR). The proposed CPb algorithm uses a differentiation technique, applying the Time Domain Scheduler (TDS) and the Frequency Domain Scheduler (FDS), to meet the various SG traffic requirements and types for massive Machin-to-Machine (M2M) devices. Four SG traffic types for each M2M device are used in this study: (1) SG delay sensitive event-driven traffic is used as a SG Distribution Automation (DA), (2) Time driven traffic is used for the other SG types of traffic, including video surveillance, (3) Power quality data, and (4) Periodic Advanced Meter Infrastructure (AMI) data. The CPb results show a significant improvement in the performance metrics compared to the PF and RR schedulers, according to the LTE QoS Class Identifier (QCI) parameters.
The purpose of this study is to analyze various surfaces of flexible solar panels and compare them to the traditional at panels mathematically. We evaluated the efficiency based on the integral formulas that involve flux. We performed calculations for flat panels with different positions, a cylindrical panel, conical panels with various opening angles and segments of a spherical panel. Our results indicate that the best efficiency per unit area belongs to particular segments of spherically-shaped panels. In addition, we calculated the optimal opening angle of a cone-shaped panel that maximizes the annual accumulation of the sun radiation per unit area. The considered shapes are presented below with a suggestion for connections of the cells.