Optimal Sizing of Photovoltaic Generation in Radial Distribution Systems Using Lagrange Multipliers

Abstract

The integration of renewable distributed generation into distribution systems has been studied comprehensively, due to the potential benefits, such as the reduction of energy losses and mitigation of the environmental impacts resulting from power generation. The problem of minimizing energy losses in distribution systems and the methods used for optimal integration of the renewable distributed generation have been the subject of recent studies. The present study proposes an analytical method which addresses the problem of sizing the nominal power of photovoltaic generation, connected to the nodes of a radial distribution feeder. The goal of this method is to minimize the total energy losses during the daily insolation period, with an optimization constraint consisting in the energy flow in the slack bus, conditioned to the energetic independence of the feeder. The sizing is achieved from the photovoltaic generation capacity and load factors, calculated in time intervals defined in the typical production curve of a photovoltaic unit connected to the distribution system. The analytical method has its foundations on Lagrange multipliers and relies on the Gauss-Jacobi method to make the resulting equation system solution feasible. This optimization method was evaluated on the IEEE 37-bus test system, from which the scenarios of generation integration were considered. The obtained results display the optimal sizing as well as the energy losses related to additional power and the location of the photovoltaic generation in distributed generation integration scenarios.

Reduction of Emission Cost, Loss Cost and Energy Purchase Cost for Distribution Systems With Capacitors, Photovoltaic Distributed Generators, and Harmonics

“…The simulations are performed by coding program on MATLAB ver.2017 on a personal computer with 1.8 GHz and 8.0 GB. ~1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 In addition to the use of proper update mechanisms, these algorithms are also based on randomization factors such as the use of random scaling factors from 0 to 1, and the use of randomly picked solutions from current population. Thus, one computation run is not high enough to reach the most optimal solution and obtained results from the sole run cannot reflect the performance of applied algorithms.…”

“…However, this algorithm is quite complicated, the convergence speed is relatively slow, and its performance is easily affected by the initial parameters. Moreover, there are other positive methods also used in the studies [16][17]. In [16], the optimal sizing of the photovoltaic system has also been proposed by using Lagrange Multipliers (LM).…”

“…Moreover, there are other positive methods also used in the studies [16][17]. In [16], the optimal sizing of the photovoltaic system has also been proposed by using Lagrange Multipliers (LM). This work minimized the total energy loss during the daily insolation period in various scenarios with test system of 37 buses.…”

Optimal Location and Sizing of BESS for Performance Improvement of Distribution Systems with High DG Penetration

“…Energy storage system (ESS) is increasingly being incorporated into distribution systems to solve the aforementioned problems and provide different technical and economic benefits [8][9][10][11][12]. Moreover, ESS also reduces power losses [13][14][15][16], improves voltage profile or alleviates voltage deviation [17,18], achieves peak shaving [19], mitigates reverse power flow [20], and decreases system cost [21].…”

Optimal Siting and Sizing of Battery Energy Storage Systems for Distribution Network of Distribution System Operators

“…Therefore, energy storage systems (ESSs) have an important role and have been used in distribution networks with the connected RESs to overcome the drawbacks of RES. Additionally, the ESS can balance the electrical power supply and demands [5], improve voltage deviation [6,7], reduce power loss [8][9][10][11], reduce peak demand by storing electrical energy during an off-peak time and supplying electric power during peak time [12,13], and use for many objectives including voltage deviation improvement, power loss reduction, and peak demand reduction [14][15][16].…”