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. In [
28], the optimal placement and sizing of capacitor banks and inverter-based DGs was employed by biogeography-based optimization (BBO) algorithm considering the harmonic content of the DGs at different load levels. In [
29], the authors presented an economic study that approved the economic benefits of using passive filters especially in the case of the nonlinear loads that exceed 1 MVA. In [
30], the design of single tuned filters was carried out by using ETAP software in distribution systems with PV systems to eliminate the harmonics and their impact on the system. A comprehensive analysis of the single tuned filter parameters selection and its effect on the harmonic mitigation is presented in [
16].
As illustrated in the abovementioned literature review, non-linear loads and renewable energy sources can increase the harmonic distortion in distribution systems, which leads to harmful effects on the system power quality. In this paper, a proposed method is introduced for simultaneously determine the optimal design, number, and placement of single tuned harmonic filters by using the Water Cycle Algorithm (WCA) which is implemented as a multi-objective optimization algorithm. The harmonic spectrums of the inverter-based DGs implement in the distribution system are considered beside the harmonic emissions from the nonlinear loads. This study is considered a multidimensional study as it achieves both technical and economic merits throughout the objectives that include minimizing: the total harmonic distortion, cost of power loss and that of the filter investment cost, and improvement of the voltage profile. Harmonic load flow with and without a filter is implemented for analyzing the systems’ harmonics. The effect of harmonic spectrums of the DGs on the harmonic distortion in the system is studied through two cases studied.
The organization of the current paper is ordered as follow:
Section 2 presents the problem formulation,
Section 3 presents the optimization algorithm and electric scheme representation,
Section 4 presents, the proposed filters planning procedure,
Section 5 presents the application of the proposed method,
Section 6 presents simulation results and discussion, and
Section 7 presents the conclusions.
4. Proposed Filters Planning Procedure
Figure 6 shows the flowchart that describes the planning procedure of the STF. Where, the proposed filter planning procedure for harmonic mitigation has the following steps:
Step 1: Randomly initialize the initial set of raindrops that has a size of
Npop.
Step 2: Checking the following constraints:
where
ft is the tuned harmonic order.
Step 3: Evaluate the fitness of each raindrop by the following steps:
Calculating filter parameters which consist of (series of R, L, and C)
where
Xc is the capacitive reactance and
is the capacitor reactive power rating in kVAr.
where
XL is the inductive reactance.
where
QF is the quality factor of the filter, and f
0 is the fundamental harmonic frequency.
- (1)
Carrying out harmonic power flow calculation based on the backward/forward sweep power flow for balanced radial distribution feeders [
35], Power flow analyses are carried before and after adding the filters into the system.
- (2)
Calculating fitness function using the harmonic power flow results.
- (3)
Checking the buses’ voltage, THD, and IHD constraints. If any solution doesn’t satisfy any of the constraints, putting the value of its fitness function equals infinity. So, it will not be selected as a minimum solution.
Step 4: Getting the personal best data and storing its controlled variables data as:
Step 5: Applying the WCA to generate a new set of solutions.
Step 6: Repeating steps from 2 to 5 till reaching the maximum iterations number.
5. Applications
The proposed method is applied according to two cases studied as follows:
Case 1: Optimal planning of single-tuned filters without considering the harmonic spectrum of the DG units.
Case 2: Optimal planning of single tuned filters with considering the harmonic spectrum of the DG units.
The type of nonlinear load is assumed to be a six-pulse inverter that has a harmonic spectrum as shown in
Table 1 [
30]. The harmonic spectrum of the inverter-based DGs is also considered as shown in
Table 2 [
28]. DGs are placed nearby the heavy loads to reduce the power losses and improve the voltage profile [
9]. For considering a high penetration of DGs, the total capacity of the DGs is assumed to be 40% of the total demand and divided equally into four units. The proposed method considered all the odd harmonic orders from 3rd up to the 25th harmonic order.
The weighting factors k1, k2, and k3 are considered equal to 0.5, 0.3, and 0.2, respectively. The WCA is implemented in MATLAB software using m-file code taking the total initial number of raindrops equals to 100 (one sea, 9 rivers, and 90 streamers). The evaporation condition dmax is considered to be 1 × 10−4, and the iterations number is 50.