# F. J. Toledo's research while affiliated with Universidad Miguel Hernández de Elche and other places

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## Publications (31)

In this paper it is provided a new, the first one as far as the authors knowledge, parametrization of the I-V curve associated to the photovoltaic (PV) single-diode model (SDM), which is the most common model in the literature to analyze the behavior of a PV panel. The SDM relates, through a transcendental equation with five parameters to be determ...

p>In this paper it is provided a new, the first one as far as the authors knowledge, parametrization of the I-V curve associated to the photovoltaic (PV) single-diode model (SDM), which is the most common model in the literature to analyze the behavior of a PV panel. The SDM relates, through a transcendental equation with five parameters to be dete...

p>In this paper it is provided a new, the first one as far as the authors knowledge, parametrization of the I-V curve associated to the photovoltaic (PV) single-diode model (SDM), which is the most common model in the literature to analyze the behavior of a PV panel. The SDM relates, through a transcendental equation with five parameters to be dete...

This article revisits the objective function (or metric) used in the extraction of photovoltaic (PV) model parameters. A theoretical investigation shows that the widely used current distance (CD) metric does not yield the maximum likelihood estimates (MLE) of the model parameters when there is noise in both voltage and current samples. It demonstra...

The objective of this paper is to provide the exact sets of initial data ensuring the convergence or divergence of a special class of real towers of powers and logarithms. All the terms forming these towers have a common value except the cusp element, that is indeed the initial data of the sequences defining the towers. The results obtained will be...

The photovoltaic (PV) single-diode model is the most widely used to characterize the behavior of a PV panel because it combines high precision with moderate difficulty. Lots of methods to obtain the model parameters use optimization techniques that require the resolution of the characteristic equation thousands of times; therefore, it is essential...

The objective of this paper is to determine all the possible combinations of the five parameters of the single-diode model (SDM) of a photovoltaic panel when only the following three important points (remarkable points) of a I–V curve, namely, short circuit, maximum power and open circuit points, are available, usually from manufacturer's datasheet...

The present paper is devoted to the computation of the Lipschitz modulus of the optimal value function restricted to its domain in linear programming under different types of perturbations. In the first stage, we study separately perturbations of the right-hand side of the constraints and perturbations of the coefficients of the objective function....

The final goal of the present paper is computing/estimating the calmness modulifrom below and above of the optimal value function restricted to the set of solvable linear problems.Roughly speaking, these moduli provide measures of the maximum rates of decrease and increaseof the optimal value under perturbations of the data (provided that solvabili...

From a computational point of view, this paper provides a significant advance in the study of the calmness property of ordinary (finite) linear programs under canonical perturbations (i.e., perturbations of the objective function coefficient vector and the right-hand side of the constraint system). In the recent literature we find, for both the fea...

This paper presents a System-on-Chip design for real-time satellites photovoltaic curves telemetry. In these applications, the limitation of memory and communication bandwidth makes quite difficult to store and to transmit the whole characteristic I-V curve of any solar section in real-time. The proposed solution is based on the real-time calculati...

This paper introduces the concept of critical objective size associated with a linear program in order to provide operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping under uniqueness of nominal optimal solution and pertu...

In this paper, the five parameters of the solar cell single-diode model are analytical and quasi-explicitly extracted for the first time, just using the coordinates of four arbitrary points of the characteristic I–V curve and the slopes of the curve in these points. The new method presented, called Analytical and Quasi-Explicit (AQE) method, is exa...

This paper provides operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping in linear optimization under uniqueness of nominal optimal solutions. Our analysis is developed in two different parametric settings. First, in the...

One of the most important models to predict the electrical behavior of a photovoltaic (PV) module is the so-called single-diode model. This model is derived from the electrical equivalent circuit formed by a current source in parallel with one diode, a shunt resistor and a series resistor. The model equation depends on five parameters, if these par...

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides...

This paper was originally motivated by the problem of providing a point-based formula (only involving the nominal data, and not data in a neighborhood) for estimating the calmness modulus of the optimal set mapping in linear semi-infinite optimization under perturbations of all coefficients. With this aim in mind, the paper establishes as a key too...

This paper characterizes the calmness property of the argmin mapping in the framework of linear semi-infinite optimization problems under canonical perturbations; i.e., continuous perturbations of the right-hand side of the constraints (inequalities) together with perturbations of the objective function coefficient vector. This characterization is...

This paper presents a practical implementation of a photovoltaic I-V curves and maximum power point estimation algorithm (IVMPPE). The IVMPPE estimates the I-V curve and sets the operation of the solar panels at a voltage that extracts the maximum available power without tracking. The operation is based on solving the parameters of the solar array...

In this paper, a new real-time curve fitting method for photovoltaic (PV) modules is presented. The method solves the four-parameters photovoltaic cell model without scanning the entire I–V curve, without sensing irradiance or temperature and with no need of any manufacturer data. Only six pairs of voltage and current coordinates are needed to obta...

This article extends some results of Cánovas et al. [M.J. Cánovas, M.A. López, J. Parra, and F.J. Toledo, Distance to ill-posedness and the consistency value of linear semi-infinite inequality systems, Math. Prog. Ser. A 103 (2005), pp. 95–126.] about distance to ill-posedness (feasibility/infeasibility) in three directions: from individual perturb...

In this article, some sensitivity analysis of the dual optimal value in linear semi-infinite optimization is carried out via the notion of primal/dual asymptotic solution. The sensitivity results are then applied to derive some Hoffman-type inequalities (error bounds). Like in [Renegar, J., 1994, Some perturbation theory for linear programming. Mat...

This paper deals with the so-called total ill-posedness of linear optimization problems with an arbitrary (possibly infinite) number of constraints. We say that the nominal problem is totally ill-posed if it exhibits the highest unstability in the sense that arbitrarily small perturbations of the problem’s coefficients may provide both, consistent...

We consider the parametric space of all the linear semi-infinite programming problems with constraint systems having the same index set. Under a certain regularity condition, the so-called well-posedness with respect to the solvability, it is known from Cánovas et al. [2] that the optimal value function is Lipschitz continuous around the nominal pr...

We consider the parameter space of all the linear inequality systems, in the n-dimensional Euclidean space and with a fixed index set, endowed with the topology of the uniform convergence of the coefficient
vectors. A system is ill-posed with respect to the consistency when arbitrarily small perturbations yield both consistent
and inconsistent syst...

We characterize those linear optimization problems that are ill-posed in the sense that arbitrarily small perturbations of the problem’s data may yield both, solvable and unsolvable problems. Thus, the ill-posedness is identified with the boundary of the set of solvable problems. The associated concept of well-posedness turns out to be equivalent t...

In this paper we measure how much a linear optimization problem, in Rn, has to be perturbed in order to loose either its solvability (i.e., the existence of optimal solutions) or its unsolvability property. In other words, if we consider as ill-posed problems those in the boundary of the set of solvable ones, this paper deals with the associated di...

In this paper we consider the parameter space of all the linear inequality systems, in the n-dimensional Euclidean space, with a fixed and arbitrary (possibly infinite) index set. This parameter space is endowed with the topology of the uniform convergence of the coefficient vectors by means of an extended distance. Some authors, in a different con...

## Citations

... Other methods to compute the Euclidean distance from a point to an I-V curve suffer again in providing a solution without checking if it really is the global minimum, which occurs particularly when multiple candidates are available. It is the case of the system of two nonlinear equations formed by the SDM equation and the necessary optimality condition, or a recent method which reduces the previous system in a one-variable equation based on the so-called diode voltage ( [3]). To avoid any problem and be sure that the distance computed is the minimum possible, a robust strategy is proposed in the current paper based on a new, as far as we know unique, parametrization of the SDM (Section 2), which allows to reduce the calculation of the Euclidean distance to compute the roots of a one-variable function. ...

... Ishaque et al., relies on the data provided by Villalva et al. [21], while Biswas et al., does not make any reference to the bounds used to determine these parameters. The information and methodology provided by these studies is limited, and the criteria for the selected limits used in the algorithms indicated by the state-of-the-art is studied by some authors like Toledo et al. [22] using an analytical approach. However, the boundaries calculus method addressed by Toledo et al., presents inconsistencies for certain SPVMs since it is not capable of providing a finite value for the maximum limit of the shunt resistance. ...

... Condition (ii) in the next theorem appeals to indexation function (9). ...

... Moreover, for a fixed objective function (respectively, for a fixed RHS) the corresponding 'partial' optimal value function is piecewise linear and convex (respectively, concave) on its effective domain (which is a convex polyhedral set), hence globally Lipschitzian there, see, e.g., [10,Chapter 6], [1,Chapter 5.5] or [16,17]. For recent detailed discussions of the history of Lipschitz analysis in linear optimization, we refer to the papers [4,5]. ...

... The way to increase the output power of cracked solar cells is using aggregate power electronic devices, such as a systemon-chip proposed by R. Gutierrez et al. [20]. Other approaches also suggest using neural-network-based control algorithms [21], [22]. ...

... Let us prove that there exists a neighborhood U of x along with > 0 such that (20) holds for all x ∈ U and all a ∈ ℝ n with ‖a − a‖ < . To do this we appeal to [10,Theorem 3], which shows -adapted to our current notation-that each S(a) is indeed a subregularity constant itself with an associated neighborhood U a , which -see formula (8) in that paper-, taking into account (11) and the 'slack relationship ...

... The authors of [11] also adopted the principle of the point selection strategy of [9,10], but the location of the six points selected for fitting was sparser. The authors of [12] used four arbitrary points on the I-U curve jointly with the slopes of the I-U curve at these points. The four points were selected differently for different tests. ...

... The development of condition measures in optimization was pioneered by Renegar [22,24,25] and has been further advanced by a number of scholars. Condition measures provide a fundamental tool to study various aspect of problems such as the behavior of solutions, robustness and sensitivity analysis [7,18,20,23], and performance of algorithms [5,14,15,19,21,25]. Renegar's condition number for conic programming is defined in the spirit of the classical matrix condition number of linear algebra, and is explicitly expressed in terms of the distance to infeasibility, that is, the smallest perturbation on the data defining a problem instance that renders the problem infeasible [24,25]. ...

... Rights reserved. modulus are given in [6,Section 5] to the computation of some constants related to the convergence of certain optimization methods. The first one is focused on a particular procedure described in [19,Section 3.1] for a descent method, and the second deals with a concrete regularization scheme for mathematical programs with complementarity constraints introduced in [17]. ...

... minimize c x subject to a t x ≤ b t , t ∈ T, for a compact indexing set T and continuous functions a and b on T . Relation (1.1) was the main ingredient in [4][5][6] to derive point-based explicit expressions for the so-called calmness moduli of the associated feasible and optimal solutions set-valued mappings; we refer to [9][10][11] for more details on this calmness property. For instance, if F a : C(T, R) → R n denotes the feasible set-valued mapping F a (b) := {x ∈ R n : a t x ≤ b t ∀t ∈ T }, b ∈ C(T, R), then the calmness modulus of F a at a point (b,x) belonging to its graph, defined as ...