# Optimal Harmonic Mitigation in Distribution Systems with Inverter Based Distributed Generation
## 1 Introduction  
Nowadays, distribution system power quality is one of the most important challenges, especially after the widespread use of harmonic sources in distribution systems which is considered as one of the most effective factors on power quality [1]. Harmonics presence in the distribution system can result in excessive losses, system equipment's overheating, and damage [2]. Consequently, to keep the distribution system reliable and working at a high performance, harmonics levels should be kept within the allowable limits approved in the international standards [3]. However, due to the widespread of power electronics devices and nonlinear loads in the distribution system, harmonics levels in the distribution system may exceed the standard limits. Therefore, harmonic mitigation becomes more interesting in distribution systems to decrease distortion levels and enhance system performance [4]. On the other hand, huge efforts have been exerted for increasing the penetration of distributed generation units (DGs) in the distribution systems especially the renewable DGs which are inverter-based such as PV and wind generation sources [5]. The presence of DGs in distribution systems provides many technical, environmental, and economic merits [6; 7; 8; 9], but on the other hand, the harmonic content of the inverter-based DGs may increase the harmonic distortion problem in the distribution system [10; 11]. To effectively analyze the harmonic distortion in the distribution systems, load-flow and harmonic load flow studies are of prime importance. Therefore, various load flow and harmonic load flow methods are presented for analyzing different topologies of radial distribution systems as in [12; 13; 14; 15]. Further, to solve the harmonic distortion problem, several methods had been proposed [16; 17]. In [18], 12-Pulse Rectifiers were used to reduce the amount of generated harmonics, but this technique requires special cooling systems. However, the active filter can be considered as an effective method for harmonic damping in distribution systems [19], it is considered an uneconomic method due to its high cost. Single tuned passive harmonic filters still one of the most common methods for harmonic mitigation due to their effectiveness and economic benefits. The single tuned passive filters are designed to trap the harmonic in the filter-branch depending on the low impedance of the filter-branch at the tuned harmonic order [20]. Various methods were developed for the optimal design of passive harmonic filter based on optimization techniques such as particle swarm optimization [20], simulated annealing [21], and fuzzy linear programming [22]. Such optimization techniques are considered for solving this nonlinear problem which has a very large search space. Therefore, these techniques are considered as a fast, robust, and accurate method to solve this type of problem. Selecting the optimal placement of the harmonic filters in the system has an essential effect on the system harmonic mitigation. Authors in [23] presented a method for single-tuned filter placement in a small distribution system based on a genetic algorithm to reduce the harmonic distortion. In [24], the authors presented a method for determining the optimal allocation of passive filters in an industrial distribution network based on the harmonic similarity metric. In [25], the authors presented two sensitivity indices as a guide for the passive filter placement problem which can determine the sensitive buses for filter placement. In [26], a multi-objective optimization problem was considered for solving the optimal planning problem of passive filter considering specific harmonic orders without considering the harmonic distortion resulted from DG units. In [27], simultaneously planning of both inverter-based DGs and passive filters in the distorted distribution system are considered for minimizing THD and power loss.