A Mixed-integer Linear Programming Model for Defining Customer Export Limit in PV-rich Low-voltage Distribution Networks

A photovoltaic (PV)-rich low-voltage (LV) distribution network poses a limit on the export power of PVs due to the voltage magnitude constraints. By defining a customer export limit, switching off the PV inverters can be avoided, and thus reducing power curtailment. Based on this, this paper proposes a mixed-integer nonlinear programming (MINLP) model to define such optimal customer export. The MINLP model aims to minimize the total PV power curtailment while considering the technical operation of the distribution network. First, a nonlinear mathematical formulation is presented. Then, a new set of linearizations approximating the Euclidean norm is introduced to turn the MINLP model into an MILP formulation that can be solved with reasonable computational effort. An extension to consider multiple stochastic scenarios is also presented. The proposed model has been tested in a real LV distribution network using smart meter measurements and irradiance profiles from a case study in the Netherlands. To assess the quality of the solution provided by the proposed MILP model, Monte Carlo simulations are executed in OpenDSS, while an error assessment between the original MINLP and the approximated MILP model has been conducted.</p

A Mixed-integer Linear Programming Model for Defining Customer Export Limit in PV-rich Low-voltage Distribution Networks

A photovoltaic (PV)-rich low-voltage (LV) distribution network poses a limit on the export power of PVs due to the voltage magnitude constraints. By defining a customer export limit, switching off the PV inverters can be avoided, and thus reducing power curtailment. Based on this, this paper proposes a mixed-integer nonlinear programming (MINLP) model to define such optimal customer export. The MINLP model aims to minimize the total PV power curtailment while considering the technical operation of the distribution network. First, a nonlinear mathematical formulation is presented. Then, a new set of linearizations approximating the Euclidean norm is introduced to turn the MINLP model into an MILP formulation that can be solved with reasonable computational effort. An extension to consider multiple stochastic scenarios is also presented. The proposed model has been tested in a real LV distribution network using smart meter measurements and irradiance profiles from a case study in the Netherlands. To assess the quality of the solution provided by the proposed MILP model, Monte Carlo simulations are executed in OpenDSS, while an error assessment between the original MINLP and the approximated MILP model has been conducted.</p

Tensor Power Flow Formulations for Multidimensional Analyses in Distribution Systems

In this paper, we present two multidimensional power flow formulations based on a fixed-point iteration (FPI) algorithm to efficiently solve hundreds of thousands of power flows in distribution systems. The presented algorithms are the base for a new TensorPowerFlow (TPF) tool and shine for their simplicity, benefiting from multicore \gls{cpu} and \gls{gpu} parallelization. We also focus on the mathematical convergence properties of the algorithm, showing that its unique solution is at the practical operational point, which is the solution of high-voltage and low-current. The proof is validated using numerical simulations showing the robustness of the FPI algorithm compared to the classical \gls{nr} approach. In the case study, a benchmark with different PF solution methods is performed, showing that for applications requiring a yearly simulation at 1-minute resolution the computation time is decreased by a factor of 164, compared to the NR in its sparse formulation

Methodology to Evaluate the Residential Electrical Stock Appliances According to Socioeconomic Status

This paper attempts an understanding of the use of stock electrical appliances in the city of Bogot´a D.C. We developed a methodology based on Colombia's National Quality of Life (NQL) 2016, the methodology uses a questionnaire survey focused on information related to: type of residential building, appliances stock, socioeconomic status and income, among others. The proposed study explains the relationship between appliance stock and socioeconomic status, income, and type of household by using an econometric energy model. The results obtained have a potential application in energy planning strategies and policies, especially for lowest social status. Keywords: Electrical stock appliances, socioeconomic status, econometric energy model. JEL Classifications: C50; D12; Q40 DOI: https://doi.org/10.32479/ijeep.717

Clasificador No Lineal Basado en Redes Neuronales con Funciones de Base Radial para Implementación en Sistemas de Punto Fijo

Para implementar máquinas inteligentes, es común requerir de sistemas de clasificación que sean eficientes y realizables en plataformas con bajo nivel de procesamiento. En este trabajo se presenta un método de diseño para estimar los parámetros de un clasificador basado en redes neuronales con funciones de base radial para ser implementado en sistemas de procesamiento digital con punto fijo. En principio, usando métricas estadísticas se obtiene el número de centroides necesarios para llevar las clases a un espacio que las haga linealmente separables, posteriormente aplicando el algoritmo k-medias se estima la ubicación de los centroides. Se determina la distancia de los puntos de entrenamiento a cada centroide, y usando aproximación por mínimos cuadrados se calculan los pesos de la función de salida. De esta manera, se obtiene un clasificador con una complejidad computacional reducida que permita ser usado en sistemas con requerimientos de bajo nivel de procesamiento como los de tiempo real.Implementation of intelligent machines requires of efficient classification systems under limited computational resources. Thisstudy introduces a method for estimating the parameters of Radial Basis Function Neural Network (RBF-NN) that can be implemented on a fixed point processor. First, the number of hidden nodes is chosen based on statistics of the mapped data points. A k-means search is then carried out to determine the location of each node. The hidden units mapping corresponds to the Euclidean distance of their centers to each data point, the weights of the output sum are obtained by solving a linear least squares problem. With this procedure, a low computational cost classifier can be readily implemented on a low capacity platform for real time applications