scholarly journals Solution of series-parallel photovoltaic arrays model using global optimization algorithms

2020 ◽  
Vol 25 (1) ◽  
pp. 14-22
Author(s):  
Juan David Bastidas-Rodriguez ◽  
Jorge Mario Cruz-Duarte ◽  
Carlos Rodrigo Correa-Cely
Keyword(s):  
Global Optimization ◽  
Nonlinear Equation ◽  
Nonlinear Equations ◽  
Optimization Problem ◽  
Optimization Algorithms ◽  
Computation Time ◽  
Equation System ◽  
System Of Nonlinear Equations ◽  
Electrical Behavior ◽  
Partial Shading

Models of series-parallel (SP) photovoltaic (PV) arrays focus on the system of nonlinear equations that represents the array’s electrical behavior. The solution of the system of nonlinear equations can be posed as an optimization problem and solved with different methods; however, the models do not formulate the optimization problem and do not evaluate different optimization algorithms for its solution. This paper proposes a solution, using global optimization algorithms, of the mathematical model that describes the electrical behavior of a SP generator, operating under uniform and partial shading conditions. Such a model is constructed by dividing the generator into strings and representing each module in the string with the single-diode model. Consequently, for each string a system of nonlinear equations is build applying the Kirchhoff’s laws, where the unknowns are the modules’ voltages. The solution of the resulting nonlinear equation system is posed as an optimization problem, where the objective function is defined as the sum of the squared of each nonlinear equation. Minimum and maximum values of each voltage are defined from the datasheet information of the modules and bypass diodes. As a demonstrative example, we arbitrarily select two well-known algorithms to solve this problem: Genetic Algorithms and Particle Swarm Optimization. Simulation results show that both algorithms solve the optimization problem and allow the reproduction of the generator’s characteristic curves. Moreover, the results also indicate that the optimization problem is correctly defined, which opens the possibility explore other optimization algorithms to reduce the computation time.

scholarly journals Finding the Roots of System of Nonlinear Equations by a Novel Filled Function Method

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Xiang Wang ◽  
You-Lin Shang ◽  
Wei-Gang Sun ◽  
Ying Zhang
Keyword(s):  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Function Method ◽  
Optimization Problem ◽  
Test Problems ◽  
System Of Nonlinear Equations ◽  
Global Optimization Problem ◽  
Filled Function ◽  
Filled Function Method ◽  
Constrained System

We present a novel filled function approach to solve box-constrained system of nonlinear equations. The system is first transformed into an equivalent nonsmooth global minimization problem, and then a new filled function method is proposed to solve this global optimization problem. Numerical experiments on several test problems are conducted and the computational results are also reported.

scholarly journals Optimal Path Analysis for Solving Nonlinear Equations with Finite Local Error

2022 ◽  
Vol 16 ◽  
pp. 94-104
Author(s):  
Xiaoxiao Ma ◽  
Xiaojuan Chen
Keyword(s):  
Nonlinear Equation ◽  
Path Analysis ◽  
Objective Function ◽  
Nonlinear Equations ◽  
Optimal Path ◽  
Optimal Solution ◽  
Equation System ◽  
Local Error ◽  
Analysis Method ◽  
Long Time

Because the traditional method of solving nonlinear equations takes a long time, an optimal path analysis method for solving nonlinear equations with limited local error is designed. Firstly, according to the finite condition of local error, the optimization objective function of nonlinear equations is established. Secondly, set the constraints of the objective function, solve the optimal solution of the nonlinear equation under the condition of limited local error, and obtain the optimal path of the nonlinear equation system. Finally, experiments show that the optimal path analysis method for solving nonlinear equations with limited local error takes less time than other methods, and can be effectively applied to practice

scholarly journals Search for Global Maxima in Multimodal Functions by Applying Numerical Optimization Algorithms: A Comparison between Golden Section and Simulated Annealing

Computation ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 43 ◽  
Author(s):  
Jordan Guillot ◽  
Diego Restrepo-Leal ◽  
Carlos Robles-Algarín ◽  
Ingrid Oliveros
Keyword(s):  
Simulated Annealing ◽  
Numerical Optimization ◽  
Simulated Annealing Algorithm ◽  
Golden Section ◽  
Optimization Algorithms ◽  
Computation Time ◽  
Photovoltaic Module ◽  
Test Scenario ◽  
Partial Shading ◽  
Golden Section Search

In the field of engineering when a situation is not resolved analytically, efforts are made to develop methods that approximate a possible solution. These efforts have originated the numerical methods known at present, which allow formulating mathematical problems that can be solved using logical and arithmetic operations. This paper presents a comparison between the numerical optimization algorithms golden section search and simulated annealing, which are tested in four different scenarios. These scenarios are functions implemented with a feedforward neural network, which emulate a partial shading behavior in photovoltaic modules with local and global maxima. The presence of the local maxima makes it difficult to track the maximum power point, necessary to obtain the highest possible performance of the photovoltaic module. The programming of the algorithms was performed in C language. The results demonstrate the effectiveness of the algorithms to find global maxima. However, the golden section search method showed a better performance in terms of percentage of error, computation time and number of iterations, except in test scenario number three, where a better percentage of error was obtained with the simulated annealing algorithm for a computational temperature of 1000.

A Fixed-Point Iteration Method With Quadratic Convergence

2012 ◽  
Vol 79 (3) ◽  
Author(s):  
K. P. Walker ◽  
T.-L. Sham
Keyword(s):  
Fixed Point ◽  
Nonlinear Equations ◽  
Unit Root ◽  
Iteration Method ◽  
Equation System ◽  
Higher Order ◽  
Iteration Algorithm ◽  
System Of Nonlinear Equations ◽  
Fixed Point Iteration ◽  
Root Functions

The fixed-point iteration algorithm is turned into a quadratically convergent scheme for a system of nonlinear equations. Most of the usual methods for obtaining the roots of a system of nonlinear equations rely on expanding the equation system about the roots in a Taylor series, and neglecting the higher order terms. Rearrangement of the resulting truncated system then results in the usual Newton-Raphson and Halley type approximations. In this paper the introduction of unit root functions avoids the direct expansion of the nonlinear system about the root, and relies, instead, on approximations which enable the unit root functions to considerably widen the radius of convergence of the iteration method. Methods for obtaining higher order rates of convergence and larger radii of convergence are discussed.

scholarly journals On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mudassir Shams ◽  
Naila Rafiq ◽  
Nasreen Kausar ◽  
Praveen Agarwal ◽  
Choonkil Park ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Basin Of Attraction ◽  
Numerical Test ◽  
Computational Cost ◽  
System Of Nonlinear Equations ◽  
Single Root ◽  
Root Finding

AbstractIn this article, we construct a family of iterative methods for finding a single root of nonlinear equation and then generalize this family of iterative methods for determining all roots of nonlinear equations simultaneously. Further we extend this family of root estimating methods for solving a system of nonlinear equations. Convergence analysis shows that the order of convergence is 3 in case of the single root finding method as well as for the system of nonlinear equations and is 5 for simultaneous determination of all distinct and multiple roots of a nonlinear equation. The computational cost, basin of attraction, efficiency, log of residual and numerical test examples show that the newly constructed methods are more efficient as compared to the existing methods in literature.

scholarly journals A Solution of Implicit Model of Series-Parallel Photovoltaic Arrays by Using Deterministic and Metaheuristic Global Optimization Algorithms

Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 801
Author(s):  
Luis Miguel Pérez Archila ◽  
Juan David Bastidas-Rodríguez ◽  
Rodrigo Correa ◽  
Luz Adriana Trejos Grisales ◽  
Daniel Gonzalez-Montoya
Keyword(s):  
Optimization Problem ◽  
Reference Model ◽  
Optimization Algorithms ◽  
Trust Region ◽  
Computation Time ◽  
Optimization Methods ◽  
Systems Of Nonlinear Equations ◽  
Implicit Model ◽  
Current Voltage ◽  
Simulation Results

The implicit model of photovoltaic (PV) arrays in series-parallel (SP) configuration does not require the LambertW function, since it uses the single-diode model, to represent each submodule, and the implicit current-voltage relationship to construct systems of nonlinear equations that describe the electrical behavior of a PV generator. However, the implicit model does not analyze different solution methods to reduce computation time. This paper formulates the solution of the implicit model of SP arrays as an optimization problem with restrictions for all the variables, i.e., submodules voltages, blocking diode voltage, and strings currents. Such an optimization problem is solved by using two deterministic (Trust-Region Dogleg and Levenberg Marquard) and two metaheuristics (Weighted Differential Evolution and Symbiotic Organism Search) optimization algorithms to reproduce the current–voltage (I–V) curves of small, medium, and large generators operating under homogeneous and non-homogeneous conditions. The performance of all optimization algorithms is evaluated with simulations and experiments. Simulation results indicate that both deterministic optimization algorithms correctly reproduce I–V curves in all the cases; nevertheless, the two metaheuristic optimization methods only reproduce the I–V curves for small generators, but not for medium and large generators. Finally, experimental results confirm the simulation results for small arrays and validate the reference model used in the simulations.

Practical Application of Global Optimization to the Design of Offshore Structures

2004 ◽  
Author(s):  
Lothar Birk ◽  
Gu¨nther F. Clauss ◽  
June Y. Lee
Keyword(s):  
Global Optimization ◽  
Optimization Algorithms ◽  
Computation Time ◽  
Offshore Structures ◽  
Deterministic Algorithm ◽  
Assessment Tools ◽  
Design Stage ◽  
Overall Design ◽  
Hull Design ◽  
Quadratic Programming Method

The paper presents improved methods and new results on the introduction of formal optimization strategies into the design of offshore structures. The hull design stage is singled out from the overall design process and automated by introducing parametric shape generation, numeric hydrodynamic analysis and assessment tools as well as Nonlinear Programming algorithms for process control. The investigation compares the performance of three different optimization algorithms within a shape optimization framework. The classical deterministic Sequential Quadratic Programming method competes with two so called global optimization algorithms: The popular Genetic Algorithm and the more exotic Adaptive Simulated Annealing. The applications show that significant improvements of seakeeping qualities are obtained in either case. As expected, the global methods require definitely more computation time than the deterministic algorithm. Furthermore the global methods do not always produce better results, which makes a careful choice of the optimization algorithm mandatory. Guidelines for an efficient application are given in the conclusions.

scholarly journals New Multi-Step Iterative Methods for Solving Systems of Nonlinear Equations and Their Application on GNSS Pseudorange Equations

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 5976
Author(s):  
Kalyanasundaram Madhu ◽  
Arul Elango ◽  
René Jr Landry ◽  
Mo’tassem Al-arydah
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Computation Time ◽  
Efficiency Index ◽  
Systems Of Nonlinear Equations ◽  
Test Problems ◽  
System Of Nonlinear Equations ◽  
Additional Function ◽  
Computation Efficiency ◽  
Global Navigation Satellite

A two-step fifth and a multi-step 5+3r order iterative method are derived, r≥1 for finding the solution of system of nonlinear equations. The new two-step fifth order method requires two functions, two first order derivatives, and the multi-step methods needs a additional function per step. The performance of this method has been tested with finding solutions to several test problems then applied to solving pseudorange nonlinear equations on Global Navigation Satellite Signal (GNSS). To solve the problem, at least four satellite’s measurements are needed to locate the user position and receiver time offset. In this work, a number of satellites from 4 to 8 are considered such that the number of equations is more than the number of unknown variables to calculate the user position. Moreover, the Geometrical Dilution of Precision (GDOP) values are computed based on the satellite selection algorithm (fuzzy logic method) which could be able to bring the best suitable combination of satellites. We have restricted the number of satellites to 4 to 6 for solving the pseudorange equations to get better GDOP value even after increasing the number of satellites beyond six also yields a 0.4075 GDOP value. Actually, the conventional methods utilized in the position calculation module of the GNSS receiver typically converge with six iterations for finding the user position whereas the proposed method takes only three iterations which really decreases the computation time which provide quicker position calculation. A practical study was done to evaluate the computation efficiency index (CE) and efficiency index (IE) of the new model. From the simulation outcomes, it has been noted that the new method is more efficient and converges 33% faster than the conventional iterative methods with good accuracy of 92%.

scholarly journals A Novel Filled Function Method for Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Liuyang Yuan ◽  
Qiuhua Tang
Keyword(s):  
Global Optimization ◽  
Nonlinear Equations ◽  
Function Method ◽  
Optimization Problem ◽  
Constrained Systems ◽  
Systems Of Nonlinear Equations ◽  
Test Problems ◽  
Global Optimization Problem ◽  
Filled Function ◽  
Filled Function Method

A novel filled function method is suggested for solving box-constrained systems of nonlinear equations. Firstly, the original problem is converted into an equivalent global optimization problem. Subsequently, a novel filled function with one parameter is proposed for solving the converted global optimization problem. Some properties of the filled function are studied and discussed. Finally, an algorithm based on the proposed novel filled function for solving systems of nonlinear equations is presented. The objective function value can be reduced by quarter in each iteration of our algorithm. The implementation of the algorithm on several test problems is reported with satisfactory numerical results.

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