A Novel Probabilistic Technique for Optimal Allocation of Photovoltaic Based Distributed Generators to Decrease System Losses

Abstract

This paper presents a novel algorithm for modeling photovoltaic based distributed generators for the purpose of optimal planning of unbalanced distribution networks. The proposed algorithm utilizes sequential Monte Carlo method in order to accurately consider the stochastic nature of photovoltaic based distributed generators. An efficient algorithm based on Firefly optimization method is proposed for optimal placement of photovoltaic based distributed generators in unbalanced distribution network. The proposed optimization algorithm aims to minimize the annual energy loss by determining the optimal locations of photovoltaic distributed generators. The proposed algorithms are implemented in MATLAB environment and tested on the IEEE 37-node feeder. Several case studies are conducted to prove the effectiveness of the proposed algorithms. The results obtained are presented and discussed. IntroductionPhotovoltaic (PV) based power stations are good choice for replacement of the traditional electrical energy generation as it is infinite and less pollutant source of energy. However, due to its stochastic nature, PV increases the network uncertainties.The PV power is difficult to be accurately simulated because it is strongly correlated to the climate, ambient temperature, season, time and geography [1]. Thus, a probabilistic model of the PV power is needed in order to simulate the actual behavior of these stations.Models that considers the stochastic nature of the PV power can be classified into two categories; analytical methods [2-6] and Monte Carlo based techniques [7-10]. Authors in [2] Presented a modeling method that based on dividing the solar irradiance into states; finding the average solar irradiance and consequently the most likely power of each hour of the day after consecutive mathematical equations based on the photovoltaic module. In [3] the stochastic nature of the photovoltaic was handled by offering unsymmetrical two point estimation method and it was compared by symmetrical two point estimation method, Gram-Charlier and Latin Hypercube method. The authors in [4] presents a methodology to model PV based power stations for reliability studies by combining Markov Chain and Monte Carlo method for the generation of a multistate PV model based on the transition probability matrix. Reference [6] presents a chronological probability model of photovoltaic (PV) generation on the basis of conditional probability and nonparametric kernel density estimation. Reference [7] described an approach based on Monte Carlo Method to evaluate the uncertainty of the passive parameters of double diode photovoltaic cell using manufacturer's data for the panels, measured environmental parameters and semi empirical equations. The authors in [8] presents a Monte Carlo based strategy for modeling PV power generators considering their dependency with other renewable sources. In [9] a method based on the pseudo-sequential Monte Carlo simulation technique had been proposed to evaluate the reserve deployment and customers' nodal reliab...

Stochastic Optimal Design of Household-Based Hybrid Energy Supply Systems Using Sample Average Approximation

“…Many stochastic optimization approaches do exist in literature [51]. Among these methods, the Monte Carlo (sample average) approach has been identified as the most robust mechanisms to handle such as complex system with high level of uncertainties [49]. In the next section of this study, we use a stochastic optimization method called the sample average approximation to tackle the uncertainty.…”

“…e study finally concluded that dealing with uncertainties in the design though comes with a high computational cost is much more reliable. Reference [49] looked at a new probabilistic approach to optimally allocate PV distributed generators for the reduction of system losses. ey applied a Monte Carlo approach to model the uncertainties in the RES.…”

“…A complete survey of stochastic methods for HESS could be found in reference [51]. Monte Carlo approach has been identified as the most robust mechanism to handle such as complex system [49]. In summary, most existing design methodologies that addressed this issue ignored the randomness effect in the design [52].…”