Multi-Objective Optimization of the Safe Operation of the Electrical Distribution System by Placing D-FACTS and Network Reconfiguration

The distribution networks of agglomerated areas of the developing countries are generally the seat of overloads, voltage drops, and untimely interruptions of the power supply. This paper consisted of optimizing the grid topology and placement of a DSTATCOM in a SBEE real distribution network in order to improve its technical performance. The modified ant colony algorithms solved this difficult combinatorial problem, which integrated among the criteria, the minimization of the losses and the deviation of the node voltages under operational constraints about distribution networks operation. According to the results obtained, the optimization of the topology of a distribution network and the placement of DSTATCOM contributed qualitatively to improve the losses, voltage and stability plans of the Togba distribution network. Actually, the hybridization of optimization means such as the placement of DSTATCOM and the reconfiguration of the networks applied to the Togba HVA network made the power of DSTATCOM optimization possible by almost 50.71% and reduce losses to 83.57%. The implementations of those algorithms are very efficient and effective, and can be implemented to help distribution system operators, developing countries and in particular, the operators of the Beninese Electric Power Company to perform their electrical network.


Introduction
In the context of the liberalization of the energy sector, with the strong competition that follows it, the regulators have become very demanding in front of electricity companies. These requirements are driven not only by the urgent need to preserve fossil energy resources for future generations, but are also concerned about the quality of the product served to the consumer. Indeed, the electrical industry is subject to the laws and principles that govern both the physical characteristics of the product and the realization of the expectations of public services and consumers. The regulation is aimed at the general well-being that is the benefit of consumers and operators [1].
To achieve this, companies use several techniques to improve energy systems, including topology optimization, FACTS devices insertion, decentralized generation, placement of capacitors and inductors to control the transit of reactive and active power in the electrical networks. The hybridization of these means or the coupling of two different types of FACTS not only improves the technical performances but also contributes to reduce the computer drifts, the early convergences and the suboptimality of the solutions found [2].
Although the FACTS devices arising from the development of power electronics components, they constitute, nowadays, the effective means, to improve the technical performance of the transmission and distribution networks, their dimensioning and their location in the networks have led to other difficult optimization issues that network operators will have to face. In addition, in order to exploit the distribution networks, with greater profitability, the network operators use equipment such as SCADA and DMS that allow their automation and the control of all operating parameters. They consist among other functions in the automatic selection of the switches to be opened in order to minimize the active and reactive losses as much as possible and to supply healthy customers with a departure in case of occurrence of a disturbance. This complex function is part of the family of difficult optimization problems and whose metaheuristics provide global solutions, and can guide decision-makers to make optimal choices. Moreover, the imbalance between reactive energy production and its consumption disrupts the maintenance of losses and voltage profiles within acceptable tolerances. In this context, the supply of good quality energy customers is one of the major problems of energy companies in order to meet the requirements of the system regulator and reliability and performance of their system. The solutions to this concern are often sought after by the authors who use metaheuristic methods to combine many actions to optimize the operational safety of electrical infrastructures.
In 2016, Radhika et al. [3] used cuckoo search algorithms (CSA) to reconfigure and place a FACTS in a distribution network. Watcharakorn Pinthurat & al in 2018 [4], proposed an algorithm hybridization (PSO and AG) to optimize the operation of an electrical network by optimal positioning of a DG and reconfiguring it. Hajar Bagheri Tolabi & al [5] proposed an ACO metaheuristic method Venkateswarlu & al [6] investigated the impact of a SVC and a DG on a distribution network and found that the optimal placement of a SVC and a DG significantly improves the ability of a transfer of an electrical network. JUNJIRO SUGIMOTO proposed in [7] the taboo search method to search the optimal position of a SVC and SVR in an electrical installation already constituted by a DG.
M. A. Tayyab & al. [8] show the effects of DG and SVC in a distribution network depending on their position. In this one, Yuvaraj & al [9] proposed a metaheuristic based on the light search algorithm to optimize the placement of DSTAT-COM, and a DG in an electrical network, taking into account the variations of the load. Jai Govind Singh & al [10] proposed another analytical method for optimal placement of a DSTATCOM and SVC to ensure the safety of the system in the event of sudden modifications in its characteristics. In 2013, Oloulade et al. [11] proposed a method for a DSTATCOM placement in a distribution network in order to improve the quality of customer supply. R. Sinirvassa [12] used bee colony to reconfigure the 33-bus network and found that this proposed method is efficient and effective. K. SURESHKUMAR et al. used the differential evolution technique to reconfigurate a distribution network.
This paper is devoted to optimizing the placement of a D-FACTS in a distribution network and reconfiguring its topology using a metaheuristic based on ant colony. The following part of the paper is constituted in point 2 by the driving difficulties faced by the operators, in 3 by the method used for the calculation of the power flow and the network stability, in 4 by the DSTATCOM modeling. Points 5, 6 and 7 present the ant colony algorithms, the simulation results and discussions then the conclusion.

Operation Issues on Distribution Network of SBEE
Electrical network operations are made of all the actions to be taken to maintain the supply of electrical energy at a good quality level and to effectively restore the electricity supply when it has been interrupted [13]. Actually, the detection

Stability Margin of a Distribution Network
Voltage static stability in a distribution network has become an important concern for utilities today because of its impact on the quality and reliability of electricity supply. The companies then express the need to evaluate the stability of their system in order to predict the contingencies and to elaborate the means of safeguarding them. In the literature, there are several stability margin assessment methods, whose performances are variously appreciated by the authors. In this paper, we will use the continuous power flow method which consists of a reformulation of the power equations by integrating the load parameters to evaluate the stability margin of a HVA distribution network of the SBEE which is our case study.
with: The indices L, G and T respectively correspond to the load node, generation node (balance node) and injection node (PV node).
To simulate the different load variation cases, the power flow equations are modified as follows: Then, the equations above modified can be written: ΔBase S : Apparent power chosen to provide an appropriate scale. If "F" is used as the set of equations, then, the system described above represents a set of nonlinear equations expressed by and it is applied the process of prediction and correction to solve these equations.
The calculation algorithm of the Continuous Power Flow (Algorithm 1) is essentially based on the prediction-correction method and is as follows: Inputs: Node data (P, Q, type), Line data (R, X), Number of iterartion N. Outputs: V, δ, λ.

Modeling of DSTATCOM
The DSTATCOM is a device illustrated in Figure 1  Step 1: Compute V 0 and δ 0 to execute the algorithm described in subsection 2.4.2; Step 2: Reformulate the power flow equations to integrate the parameter λ using Equations (4) - (7); As long as dλ ≠ 0 and k <N do Step 3: Prediction of the new solution Step 4: Calculate the tangent vector using the equation Step 5: Predict the next solution based on the equation Step 6: Fix the solution Step 7: Correct the error on the predicted solution by solving the 2.32 system Step 8: Choose the next continuous parameter based on the components of the tangent vector ( )    By separating real parts and imaginary parts of Equation (10), we obtain the Equations (11) and (12): Data: The unknowns: Then, the Equations (11) and (12) become respectively the Equations (13) and (14): We can draw 1 x respectively in Equations (13) and (14) We also obtain: x represents he initial conditions before the placement of DSTATCOM, the chosen Equation (19) is: Next,

Distribution Network Reconfiguration
The

Ant Colony Algorithm
Ants are social insects whose physical or behavioral characteristics have long fascinated researchers. Ant colony algorithms typically use the behavior of real ants to solve combinatorial optimization problems. It can be reduced in search of the shortest path through graphs based on the behavior of the ants that in their displacement mark the way with glands contained in their abdomen called pheromones. The amount of pheromone depends on the length of the path and the amount of food found. The pheromone evaporates over time if others are deposited there. The path of pheromones leading to food sources will be more frequented by ants. In practical terms, ant movements are characterized as a stochastic procedure Journal of Power and Energy Engineering for solutions around a graph such as G = {N, C} where "N" is the set of nodes and C is the set of paths given by losses in the branches. Ants move according to a probabilistic decision rule are based on pheromone trails, ant condition and problem constants. The algorithm developed on the basis of the principles mentioned above is described as follows: Algorithm 3. Main algorithm: Simultaneous optimization (Reconfiguration-Placement) Step 1: Initialize the first iteration t = 1 Initialize pheromones: Update tie-switches Step 3: Look for a single path from a given node to the source node with excluded open switches Step 4: Rearrange loads from end-of-branch nodes-save new topology Step

Simulation Parameters
The choice of parameter values determines the quality of solutions to be obtained in a simulation process. In fact, incorrect parameter settings or inappropriate choices can lead to suboptimal solutions. The table shows the values of the parameters chosen.

Validation of the Results
For validation purposes, we tested the tool designed under the MATLAB environment. For this purpose, it is tested on the standard 33-bus network.  It is observed from Table 2 that the 33-bus network whose losses in the initial configuration are evaluated at 214.72 kW have been increased to 139.5 kW by using the differential evolution algorithm in [9] for the reconfiguration with    Sinirvassa applied the bee colony-based algorithm to reconfigure the 33 node network and found that the losses are also 139.

Application of ACO on the 41-Bus Network of SBEE
The diagram of Figure 4 shows a          configuration associated with the placement simultaneously contributes not only to qualitatively improve the technical performance of the network but also to optimize the size of DSTATCOM. This action reduces the operating costs while improving the quality of the energy supply delivered. However, the reconfiguration will have to be a period cooperation to adapt to the consumption profile and to contend with the damage of the cut-off devices.

Conclusion
In this paper, the improved ant colony algorithm is used to solve the problem of topology optimization and placement of a DSTATCOM in a real distribu-

Conflicts of Interest
The authors declare no conflicts of interest regarding the publication of this paper.