A New and Efficient Nonlinear Solver for Load Flow Problems

Khoso, A. H.; Shaikh, Muhammad Mujtaba; Hashmani, Ashfaque Ahmed

doi:10.48084/etasr.3604

Cited by 8 publications

(2 citation statements)

References 15 publications

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“…The binary variables, which are the decision variables of the problem, are related to the location of the PV units. On the other hand, their continuous part is provided by the solution to the power flow formulation, which corresponds to a nonlinear problem given the nature of its equations [ 32 , 33 ]. The complete optimization model will be formulated in the complex domain to simplify the mathematical power flow solution associated with the slave stage [ 13 ].…”

Section: Mathematical Formulationmentioning

confidence: 99%

Optimal Design of PV Systems in Electrical Distribution Networks by Minimizing the Annual Equivalent Operative Costs through the Discrete-Continuous Vortex Search Algorithm

Cortés-Caicedo

Molina-Martin

Grisales-Noreña

et al. 2022

Sensors

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This paper discusses the minimization of the total annual operative cost for a planning period of 20 years composed by the annualized costs of the energy purchasing at the substation bus summed with the annualized investment costs in photovoltaic (PV) sources, including their maintenance costs in distribution networks based on their optimal siting and sizing. This problem is presented using a mixed-integer nonlinear programming model, which is resolved by applying a master–slave methodology. The master stage, consisting of a discrete-continuous version of the Vortex Search Algorithm (DCVSA), is responsible for providing the optimal locations and sizes for the PV sources—whereas the slave stage employs the Matricial Backward/Forward Power Flow Method, which is used to determine the fitness function value for each individual provided by the master stage. Numerical results in the IEEE 33- and 69-node systems with AC and DC topologies illustrate the efficiency of the proposed approach when compared to the discrete-continuous version of the Chu and Beasley genetic algorithm with the optimal location of three PV sources. All the numerical validations were carried out in the MATLAB programming environment.

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Section: Mathematical Formulationmentioning

confidence: 99%

Optimal Design of PV Systems in Electrical Distribution Networks by Minimizing the Annual Equivalent Operative Costs through the Discrete-Continuous Vortex Search Algorithm

Cortés-Caicedo

Molina-Martin

Grisales-Noreña

et al. 2022

Sensors

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show abstract

“…Las variables binarias, que son las variables de decisión del problema y están relacionadas con la ubicación de las unidades fotovoltaicas. Por otro lado, las variables de naturaleza continua están dadas por las variables eléctricas en el problema de flujo de potencia, el cual corresponde a un problema no lineal dado el producto de entre voltajes en las ecuaciones de balance de potencia [25].…”

Section: Modelo De Optimización Matemáticounclassified

Integración Óptima de Generadores Fotovoltaicos en Sistemas de Distribución DC a través de la Aplicación del Algoritmo de Optimización Aritmética Modificado

Losada

Jaramillo

Montoya

2022

TecnoL.

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En este artículo se aborda el problema de ubicación y dimensionamiento óptimo de generadores fotovoltaicos (PV) en redes de corriente continua (CC) con el objetivo de minimizar los costos de inversión y operación de la red para la empresa de distribución de energía en un horizonte de operación de 20 años. Este problema es presentado mediante un modelo matemático de programación no lineal entera mixta (PNLEM), el cual se resuelve mediante la aplicación de una metodología de optimización del tipo maestro-esclava. La etapa maestra corresponde a una versión mejorada del algoritmo de optimización aritmética que incluye una etapa de exploración y explotación del espacio de solución que involucra la generación de nuevas soluciones a partir de la aplicación de funciones de distribución gaussiana alrededor de actual en cada iteración . En la etapa esclava se emplea el algoritmo de flujo de potencia especializado para redes de CC, el cual permite evaluar cada posible solución obtenida de la etapa maestra en relación con la ubicación (nodos) y el dimensionamiento de los generadores PV (tamaños), y verificar que todas las restricciones asociadas al modelo de PNLEM se cumplan. El resultado principal de esta investigación corresponde a una metodología mejorada basada en la combinación del algoritmo de optimización aritmética y las funciones de distribución gaussiana para mejorar las etapas de exploración y explotación del espacio de soluciones y encontrar soluciones de mejor calidad que las reportadas en la literatura especializada. En conclusión, los resultados numéricos en los sistemas de prueba IEEE 33 e IEEE 69 nodos demostraron que el algoritmo de optimización propuesto mejoró los resultados existentes en la literatura especializada para la ubicación y el dimensionamiento de fuentes PV en sistemas de distribución de CC, lo cual genera un nuevo punto de referencia para futuras investigaciones en esta temática.

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Some Efficient Mathematical Programming Techniques for Balancing Equations of Complex Chemical Reactions

Yousaf¹

2020

JMCMS

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The equations of chemical reactions usually describe the breakup of some desired or consequent products and the breakup of reactants used in chemical reactions. Usually, the equations in skeleton form are unbalanced, and a deeper analysis requires the balanced form which is not quite easy for complex reactions. In instances, the balancing can be done quickly with hit and trial and simple logic. In such cases, the trials are found not attractive, although they are helpful at a simple level at an advanced level they become more tough and unpredictable. For complex cases, many mathematical techniques can be used for balancing equations of chemical reactions. In this study, some efficient mathematical techniques are suggested which can be more suitable from all perspectives to balance chemical equations and to provide a case to case recommendations for the practitioners. Particularly, we suggest and utilize the linear algebra Gauss elimination (LA-GE) and the linear programming two-phase (LP-2P) approaches to successfully for chemical equation balancing. A number of chemical equations have been taken from literature to see the performance of both approaches. The advantages and disadvantages of both approaches are discussed, mainly with the computer programming in MATLAB and TORA systems, and an exhaustive comparison based on floating point operations (FLOPS) is carried out. The recommendations will prove fruitful for the practitioners for using efficient and yet simpler mathematical programming techniques for the balancing of equations of chemical reactions in the future.

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A New and Efficient Nonlinear Solver for Load Flow Problems

Cited by 8 publications

References 15 publications

Optimal Design of PV Systems in Electrical Distribution Networks by Minimizing the Annual Equivalent Operative Costs through the Discrete-Continuous Vortex Search Algorithm

Optimal Design of PV Systems in Electrical Distribution Networks by Minimizing the Annual Equivalent Operative Costs through the Discrete-Continuous Vortex Search Algorithm

Integración Óptima de Generadores Fotovoltaicos en Sistemas de Distribución DC a través de la Aplicación del Algoritmo de Optimización Aritmética Modificado

Some Efficient Mathematical Programming Techniques for Balancing Equations of Complex Chemical Reactions

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