Probabilistic Analysis of Rechargeable Batteries in a Photovoltaic Power Supply System Page: 4 of 15
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The present investigation creates a model for maximum battery capacity and cycle life
using an artificial neural network (ANN). Specifically data obtained either experimentally or
synthetically are used to create an ensemble of data that serves as exemplars for training the
ANN. These ensembles contain various discharge profiles, including periods of deep discharge,
for a particular type of battery. The ANN is used to reckon damage to potential maximum battery
capacity caused by deep discharge. In summary, battery damage is modeled as deterministic.
The power supplied by the photovoltaic system is modeled as a stochastic process.
Because solar insolation varies randomly as a function of time and is equal to or less than some
theoretical maximum value, the stochastic process, typically, does not have a probability density
function that is symmetric in its states and, therefore, is not modeled as Gaussian. In this work an
approach that employs a Markov process is used to simulate components of the solar data. The
load is modeled as deterministic in ihis study.
All these elements are combined into a single framework to yield a stochastic model for
the photovoltaic power supply and energy storage system. The model is operated on the Monte
Carlo principle to yield realizations of the stochastic processes characteristic of the operational
phenomena, and these can be analyzed using the tools of classical statistics and random signal
analysis to infer the probabilistic behavior of the system. Ultimately the model can be used to
design and optimize the power supra ly system.
Mathematical descriptions of subsystem behavior are presented in the following section
along with some relations required to describe system interactions. Next a numerical example is
presented. Finally, some conclusions are drawn and presented.
MATHEMATICAL MODEL OF A POWER SUPPLY/STORAGE/LOAD SYSTEM
Our objective is to model and simulate a renewable energy supply and storage system.
The particular system consists of four parts: a solar resource model, a photovoltaic power
conversion model, a rechargeable battery energy storage model, and a load model. We provide
the details of the individual subsystem models then combine the components into a model of the
overall system. The solar resource is modeled as a random process, and we develop the
capability to generate realization of the solar radiation from the random source. These
realizations are used as the system input, along with a deterministic load, that drives response in
the battery storage system. Equations that permit simulation of battery behavior are solved for
specific load and insolation inputs, and the results are used in a Monte Carlo framework to
characterize system behavior.
The Solar Resource Model
The first subcomponent to be modeled is the power source of the photovoltaic system: the
sun. The amount of solar energy available on a given surface area is particularly important. This
is the solar insolation, and it is measured in units of power per area-i.e., units of W-hr/m2,
BTU/ft2-hr, etc. There exist many sets of measured data that are readily available from local,
state, and federal agencies. These data include values of global, direct, and diffuse solar radiation
(either measured with a pyranometer or calculated) and can be used to calculate the solar energy
received by a solar array (or collector) (1) or to guide the development of an insolation model. A
model was developed to calculate the solar energy received by a flat plate collector tilted at an
angle and located at arbitrary latitude. Equation 1 identifies fundamental quantities and their
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Barney, P.; Ingersoll, D.; Jungst, R.; O'Gorman, C.; Paez, T.L. & Urbina, A. Probabilistic Analysis of Rechargeable Batteries in a Photovoltaic Power Supply System, article, November 24, 1998; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc667911/m1/4/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.