<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">JPEE</journal-id><journal-title-group><journal-title>Journal of Power and Energy Engineering</journal-title></journal-title-group><issn pub-type="epub">2327-588X</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/jpee.2023.113001</article-id><article-id pub-id-type="publisher-id">JPEE-123824</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Engineering</subject></subj-group></article-categories><title-group><article-title>
 
 
  Simulation Model for Passive Harmonic Filters Using Matlab/Simulink: A Case Study
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Yonis</surname><given-names>Elmi</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Diaa</surname><given-names>Salman</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref><xref ref-type="corresp" rid="cor1"><sup>*</sup></xref></contrib></contrib-group><aff id="aff2"><addr-line>Department of Electrical and Electronic Engineering, Cyprus International University, Nicosia, Northern Cyprus, 
Mersin, Türkiye</addr-line></aff><aff id="aff1"><addr-line>Faculty of Engineering and Technology, Benadir University, Mogadishu, Somalia</addr-line></aff><pub-date pub-type="epub"><day>22</day><month>03</month><year>2023</year></pub-date><volume>11</volume><issue>03</issue><fpage>1</fpage><lpage>14</lpage><history><date date-type="received"><day>30,</day>	<month>January</month>	<year>2023</year></date><date date-type="rev-recd"><day>20,</day>	<month>March</month>	<year>2023</year>	</date><date date-type="accepted"><day>23,</day>	<month>March</month>	<year>2023</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p>
 
 
  Electrical grid power quality is a global issue. The grid must supply electricity at sinusoidal voltages and currents without frequency or amplitude fluctuations. Harmonics from non-linear loads change the stable reference point voltage waveform and cause other problems. Harmonic reduction is essential for grid health. Electrical and electronic equipment users, manufacturers, and suppliers all contribute. This article presents a case analysis of the plastic processing industry, which has historically struggled with a difficulty related to the fifth harmonic. Unwanted harmonics are reduced by using a single-tuned passive filter, a double-tuned passive filter, and a second-order damped filter. The total harmonic distortion is almost identical, but the second-order damped filter provides the best harmonic mitigation, meeting the requirements of the IEE 519-1992 Standard.
 
</p></abstract><kwd-group><kwd>Harmonic</kwd><kwd> Filters</kwd><kwd> Power System Quality</kwd><kwd> Mitigation</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>1. Introduction</title><p>The existence of harmonics on the electrical grid is among the most significant factors in poor power reliability. Harmonic currents flow inside the power system when non-linear loads are connected [<xref ref-type="bibr" rid="scirp.123824-ref1">1</xref>] , distorting the voltage level waveforms at the common coupling point due to source impedance [<xref ref-type="bibr" rid="scirp.123824-ref2">2</xref>] . One significant effect of harmonics is the potential harm they pose to PCC-connected loads. Joule effect losses are exacerbated in conductors by current harmonics [<xref ref-type="bibr" rid="scirp.123824-ref2">2</xref>] . When a transformer is subjected to harmonics, the losses in its copper windings and core are amplified, leading to an increase in temperature that shortens the transformer’s useful life. Harmonics can limit useable torque and performance in electric motors. Circuit breakers and other safety mechanisms may trip unexpectedly due to harmonics [<xref ref-type="bibr" rid="scirp.123824-ref3">3</xref>] . Harmonics are also problematic for transmission systems. Certain vibrations can cause distortion or disturbance in communications lines [<xref ref-type="bibr" rid="scirp.123824-ref4">4</xref>] . This varies depending on the frequency, the degree of connection, and the responsiveness of the equipment. Still worse, harmonics can cause blackouts by spreading through interconnected electrical sub-grids and causing a breakdown.</p><p>Power networks are experiencing significant levels of undesired harmonic distortion as a consequence of the greater use of non-linear loads and power electronics. It results in more losses, shorter equipment life, and interference with system control, communications, and security [<xref ref-type="bibr" rid="scirp.123824-ref5">5</xref>] . Passive and active filters can be used to enhance power factors and reduce harmonic components. Active filters offer a lot of flexibility, but they also add to the system’s cost and complexity [<xref ref-type="bibr" rid="scirp.123824-ref6">6</xref>] . Passive filters are easier to use and less expensive, and they provide both power factor adjustment and larger current filtering capability [<xref ref-type="bibr" rid="scirp.123824-ref7">7</xref>] . In deployments, when the supply voltage is disrupted, they also minimize harmonic voltages.</p><p>Passive filtering is the most basic conventional approach for reducing harmonic distortion [<xref ref-type="bibr" rid="scirp.123824-ref8">8</xref>] . The passive filters use passive elements such as resistance, inductance, and capacitance to modulate the harmonics. <xref ref-type="fig" rid="fig1">Figure 1</xref> depicts popular types of passive filters and their setups.</p><p>The single-tuned filter has been the most often used passive filter. When compared to other techniques of minimizing harmonic difficulties, this filter is the simplest and lowest cost [<xref ref-type="bibr" rid="scirp.123824-ref10">10</xref>] . The most frequent and least costly kind of passive filter is the single-series filter. This filter is shunt-connected to the main distribution system and is set to provide low impedance to a certain harmonic frequency. As a result, harmonic currents are redirected from the lowest impedance channel via the filter. It is critical to select the suitable capacitor value for the single-tuned filter design in order to achieve a good power factor at the power</p><p>system [<xref ref-type="bibr" rid="scirp.123824-ref9">9</xref>] .</p><p>The purpose of this research is to discuss the usage of single-tuned passive filters in minimizing harmonics in the plastics manufacturing sector. According to IEEE 519-1992 requirements, the system simulation utilizing Matlab/Simulink simulations resulted in total harmonic distortion (THD) of 15.55 percent, which may be decreased to 4.77 percent harmonics. According to the simulated results, A single-tuned passive filter has the capability of reducing the harmonic currents by 82.23 percent, in addition to a large number of other ordered harmonics ranging from 7% to 8%. This reduction is possible because the current harmonics need to be lowered.</p><p>Reducing equipment harmonic emission, enhancing equipment harmonic sensitivity, and employing other harmonic mitigation strategies are all viable ways to address harmonic issues. The choice between constructing nonlinear devices for low levels of waveform distortion and putting harmonic compensation equipment at the terminals, for instance, needs to be decided during the planning phase of installing nonlinear facility components. This is achieved, for instance, by phase-shifting transformers, converter-bridge control, switch-device off-on capabilities, and filtering [<xref ref-type="bibr" rid="scirp.123824-ref11">11</xref>] .</p><p>On the other hand, Harmonic voltage distortion mitigation techniques and harmonic current distortion mitigation techniques are two subsets of the overall mitigation techniques. Their implementation, through standardization and similar means, is connected to the principle as a whole in order to minimize interference. Harmonic voltage distortion is governed by standard limits. The responsibility for ensuring certain thresholds are not crossed lies with the network operator. The network operator, in turn, might impose restrictions on the amount of harmonic current that can be emitted by structures or large pieces of machinery. Standards establish permissible levels of emissions from portable devices. Moreover, to create a low-impedance channel for a certain harmonic frequency [<xref ref-type="bibr" rid="scirp.123824-ref12">12</xref>] , a tuned LC and high-pass filter circuit is connected in series or parallel to create a passive harmonic filter. If a parallel-connected filtration is installed further upstream in the electricity network, it will increase daily costs in the conductors and other plant items that carry the harmonic currents, despite the fact that eliminating harmonics at their source is the most effective method of reducing harmonic losses in the separated power grid, as stated by [<xref ref-type="bibr" rid="scirp.123824-ref13">13</xref>] . The tournament filter, however, exhibits losses.</p><p>Harmonics mitigation was carried out in this study in the plastic processing industry. The processing machinery that is utilized consists of components of the electrical system that are categorized as either linear load or non-linear load. On the basis of previous studies, a single-tuned passive filter will be utilized to bring about a reduction in harmonics [<xref ref-type="bibr" rid="scirp.123824-ref14">14</xref>] .</p></sec><sec id="s2"><title>2. Procedure</title><sec id="s2_1"><title>2.1. System Description</title><p>In this particular investigation, the removal of harmonics was carried out at a business that processed plastic. The working machine that is used is composed of electrical components that may be categorized as either linear load or non-linear load. A passive filter with a single tuning will be used to cut down on harmonics, as indicated by previous studies.</p><p>The assessments of the research object’s harmonic properties were carried out with the assistance of portable measurement instruments and a PCC panel. As a piece of measuring apparatus, we made use of a Metrel MI 2392 Power Q Plus Power Quality Analyzer. In order to get accurate readings from the research item, detailed observations on the PCC load were used. The results of the measurements are presented in <xref ref-type="table" rid="table1">Table 1</xref>, which may be accessed here.</p><p>In this study, it has been assumed that a load with three phases is balanced, although the analysis has only been performed on a single phase. As a direct consequence of this, the data that was utilized for calculating and analyzing was the result of measurements that were made during phase L1.</p></sec><sec id="s2_2"><title>2.2. Identifications of Single-Tuned Passive Filter</title><p>The R, L, and C filters were calculated in this study, to reduce the amount of current harmonics while still making use of the maximum possible current harmonics, which surpassed the harmonic constraints specified by the IEEE 519-1992 standard. The only harmonics of roughly the fifth order that need to be reduced are those. When evaluating the loads for all three stages, a balanced condition is assumed. As a consequence of this, modeling and analysis of the data are only carried out on a single phase, and phase L1 is the one that is selected.</p><p>To calculate the capacitor capacity (Q<sub>c</sub>), the power factor is supposed to be enhanced from pf<sub>1</sub> = 0.94 to pf<sub>2</sub> = 0.99. As a harmonic filter is used, the capacitor capacity required must be calculated [<xref ref-type="bibr" rid="scirp.123824-ref15">15</xref>] :</p><table-wrap id="table1" ><label><xref ref-type="table" rid="table1">Table 1</xref></label><caption><title> Measurement results on the PCC panel using power quality particles [<xref ref-type="bibr" rid="scirp.123824-ref14">14</xref>] </title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Symbol</th><th align="center" valign="middle" >Name</th><th align="center" valign="middle" >Phase 1</th><th align="center" valign="middle" >Phase 2</th><th align="center" valign="middle" >Phase 3</th><th align="center" valign="middle" >Total</th></tr></thead><tr><td align="center" valign="middle" >I</td><td align="center" valign="middle" >Current</td><td align="center" valign="middle" >365.94</td><td align="center" valign="middle" >396.54</td><td align="center" valign="middle" >383.27</td><td align="center" valign="middle" >−A</td></tr><tr><td align="center" valign="middle" >V</td><td align="center" valign="middle" >Voltage</td><td align="center" valign="middle" >234.45</td><td align="center" valign="middle" >235.11</td><td align="center" valign="middle" >238.2</td><td align="center" valign="middle" >−V</td></tr><tr><td align="center" valign="middle" >THD V</td><td align="center" valign="middle" >Voltage THD</td><td align="center" valign="middle" >2.1836</td><td align="center" valign="middle" >1.8068</td><td align="center" valign="middle" >2.2791</td><td align="center" valign="middle" >−%</td></tr><tr><td align="center" valign="middle" >THD V</td><td align="center" valign="middle" >Voltage THD</td><td align="center" valign="middle" >5.1187</td><td align="center" valign="middle" >4.2477</td><td align="center" valign="middle" >5.4279</td><td align="center" valign="middle" >−V</td></tr><tr><td align="center" valign="middle" >THD I</td><td align="center" valign="middle" >Current THD</td><td align="center" valign="middle" >54.004</td><td align="center" valign="middle" >53.819</td><td align="center" valign="middle" >58.332</td><td align="center" valign="middle" >−A</td></tr><tr><td align="center" valign="middle" >THD I</td><td align="center" valign="middle" >Current THD</td><td align="center" valign="middle" >14.93</td><td align="center" valign="middle" >13.707</td><td align="center" valign="middle" >15.399</td><td align="center" valign="middle" >−%</td></tr><tr><td align="center" valign="middle" >Q</td><td align="center" valign="middle" >Reactive Power</td><td align="center" valign="middle" >29.65</td><td align="center" valign="middle" >27.498</td><td align="center" valign="middle" >31.694</td><td align="center" valign="middle" >88.842 kVAR</td></tr><tr><td align="center" valign="middle" >P</td><td align="center" valign="middle" >Active Power</td><td align="center" valign="middle" >80.508</td><td align="center" valign="middle" >89.085</td><td align="center" valign="middle" >85.617</td><td align="center" valign="middle" >255.21 KW</td></tr><tr><td align="center" valign="middle" >DPF</td><td align="center" valign="middle" >Displacement Facto</td><td align="center" valign="middle" >0.95 ind</td><td align="center" valign="middle" >0.96 ind</td><td align="center" valign="middle" >0.95 ind</td><td align="center" valign="middle" >0.95 ind</td></tr><tr><td align="center" valign="middle" >PF</td><td align="center" valign="middle" >Power Factor</td><td align="center" valign="middle" >0.94 ind</td><td align="center" valign="middle" >0.96 ind</td><td align="center" valign="middle" >0.94 ind</td><td align="center" valign="middle" >0.94 ind</td></tr><tr><td align="center" valign="middle" >S</td><td align="center" valign="middle" >Apparent Power</td><td align="center" valign="middle" >85.794</td><td align="center" valign="middle" >93.233</td><td align="center" valign="middle" >91.295</td><td align="center" valign="middle" >270.23 kVA</td></tr></tbody></table></table-wrap><p>Q c = P { tan ( cos − 1 p f 1 ) − tan ( cos − 1 p f 2 ) } (1)</p><p>The capacitor’s reactance (X<sub>c</sub>) can be calculated as in Equation (2) and the capacitance of the capacitor (C) can be calculated as in Equation (3) [<xref ref-type="bibr" rid="scirp.123824-ref15">15</xref>] :</p><p>X C = V 2 Q C (2)</p><p>C = 1 2 π f 0 X C (3)</p><p>Equation (4) is used to calculate the inductor’s reactance (X<sub>l</sub>), L can be calculated as in Equation (5), moreover the value of X<sub>n</sub> can be calculated as Equation (6) [<xref ref-type="bibr" rid="scirp.123824-ref15">15</xref>] :</p><p>X L = X C h n 2 (4)</p><p>X L = w 0 L (5)</p><p>X n = X C X L (6)</p><p>Considering that the quality factor of a single passive filter (Q) is 100, the resistance (R) in the filter can be calculated as follows [<xref ref-type="bibr" rid="scirp.123824-ref15">15</xref>] :</p><p>R = X n Q (7)</p><p>Finally, the total harmonic distortion can be calculated as follows [<xref ref-type="bibr" rid="scirp.123824-ref15">15</xref>] :</p><p>T H D I = [ I r m s I 1 , r m s ] 2 − 1 (8)</p></sec></sec><sec id="s3"><title>3. Results and Discussions</title><sec id="s3_1"><title>3.1. Case 1: Non-Filtered Power System Simulation</title><p>According to the findings of the measurements, <xref ref-type="fig" rid="fig2">Figure 2</xref> depicts a succession of simulated object research systems. <xref ref-type="fig" rid="fig2">Figure 2</xref> shows a simulation of a circuit without a filter. Individual harmonics are displayed in <xref ref-type="table" rid="table2">Table 2</xref> and <xref ref-type="fig" rid="fig3">Figure 3</xref> of the circuit modelling results.</p><p><xref ref-type="table" rid="table2">Table 2</xref> illustrates the simulation results without the use of a harmonic filter; the respondents indicated current harmonic is 15.57 percent, which is 0.62 percent less than the true measurement of 14.95 percent. The simulation circuit of the state of the harmonics in the plastics business, which represents the subject of the research, is illustrated in <xref ref-type="fig" rid="fig2">Figure 2</xref>. Only the first five harmonic orders of the present IHD are shown to be much higher than the IEEE 519-1992 defined range of 14.97 percent, with the permissible limit being set at 7 percent. This is shown in <xref ref-type="table" rid="table2">Table 2</xref>.</p></sec><sec id="s3_2"><title>3.2. Case 2: Single-Tuned Filter Case</title><p><xref ref-type="fig" rid="fig4">Figure 4</xref> is a representation of the circuit schematic that was created using</p><p>Matlab Simulation using a Single-tuned Passive Filter. The components R, L, and C are shown. In a manner analogous to that of the non-filtered simulation, a Single-tuned Passive filter simulation is carried out in a number of steps, and it is then completed by adding an RLC filter in parallel with the load. The RLC</p><table-wrap id="table2" ><label><xref ref-type="table" rid="table2">Table 2</xref></label><caption><title> Simulation results in the absence of harmonic filters (IHDi %)</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >IHD Order</th><th align="center" valign="middle" >Measurement</th><th align="center" valign="middle" >Non-Filtered Simulation</th><th align="center" valign="middle" >IEEE 519-1992 Standard</th></tr></thead><tr><td align="center" valign="middle" >1</td><td align="center" valign="middle" >100.00</td><td align="center" valign="middle" >100</td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >3</td><td align="center" valign="middle" >2.20</td><td align="center" valign="middle" >2.35</td><td align="center" valign="middle" >7.0</td></tr><tr><td align="center" valign="middle" >5</td><td align="center" valign="middle" >14.22</td><td align="center" valign="middle" >14.99</td><td align="center" valign="middle" >7.0</td></tr><tr><td align="center" valign="middle" >7</td><td align="center" valign="middle" >2.35</td><td align="center" valign="middle" >2.48</td><td align="center" valign="middle" >7.0</td></tr><tr><td align="center" valign="middle" >9</td><td align="center" valign="middle" >0.84</td><td align="center" valign="middle" >0.91</td><td align="center" valign="middle" >7.0</td></tr><tr><td align="center" valign="middle" >11</td><td align="center" valign="middle" >1.21</td><td align="center" valign="middle" >1.25</td><td align="center" valign="middle" >3.5</td></tr><tr><td align="center" valign="middle" >13</td><td align="center" valign="middle" >1.03</td><td align="center" valign="middle" >1.03</td><td align="center" valign="middle" >3.5</td></tr><tr><td align="center" valign="middle" >15</td><td align="center" valign="middle" >0.49</td><td align="center" valign="middle" >0.52</td><td align="center" valign="middle" >3.5</td></tr><tr><td align="center" valign="middle" >17</td><td align="center" valign="middle" >0.84</td><td align="center" valign="middle" >0.85</td><td align="center" valign="middle" >2.5</td></tr><tr><td align="center" valign="middle" >19</td><td align="center" valign="middle" >1.02</td><td align="center" valign="middle" >1.03</td><td align="center" valign="middle" >2.5</td></tr><tr><td align="center" valign="middle" >21</td><td align="center" valign="middle" >0.24</td><td align="center" valign="middle" >0.28</td><td align="center" valign="middle" >2.5</td></tr><tr><td align="center" valign="middle" >23</td><td align="center" valign="middle" >0.81</td><td align="center" valign="middle" >0.82</td><td align="center" valign="middle" >1.0</td></tr><tr><td align="center" valign="middle" >THD</td><td align="center" valign="middle" >14.95</td><td align="center" valign="middle" >15.57</td><td align="center" valign="middle" ></td></tr></tbody></table></table-wrap><p>value was calculated, and the findings revealed that it was equal to R = 0.0061939, C = 1027.8 F, and L = 0.3943 mH. This value was utilized for the function of the block parameter in the RLC filter.</p><p>The amplitude of a certain harmonic flow is shown in <xref ref-type="table" rid="table3">Table 3</xref>, which was produced as a consequence of current harmonic reduction achieved by simulation with a single-tuned passive filter. The results of modeling the removal of current harmonics using a single-tuned passive filter are presented in <xref ref-type="table" rid="table3">Table 3</xref>. This filter has the potential to reduce the overall percentage of current harmonics from 15.57 percent to 4.7793 percent. The results of the simulation show that the IEEE 519-1992 criteria for the whole IHD Order of harmonics have been satisfied when assessed from individual harmonic currents.</p><p>The waveform of the current that was generated by Matlab/Simulink with a single-tuned passive filter is displayed in <xref ref-type="fig" rid="fig5">Figure 5</xref>. The sinusoidal shape of the resultant waveform signal indicates that the distortion has been isolated from the present harmonic distortion.</p></sec><sec id="s3_3"><title>3.3. Case 3: Double-Tuned Filter Case</title><p>The schematic representation of a Double Tuned Filter used in Matlab Simulation is shown in <xref ref-type="fig" rid="fig6">Figure 6</xref>. This filter consists of series components of R, L, and C, all of which are connected in series with parallel R, L, and C. The simulation of the Double Tuned Filter is carried out in a number of phases, much as the simulation of the non-filtered case, and then a double-tuned filter is added in parallel with the load. The RLC value has been determined and acquired by computation.</p><table-wrap id="table3" ><label><xref ref-type="table" rid="table3">Table 3</xref></label><caption><title> Simulation results for a single-tuned passive filter (IHDi %)</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >IHD Order</th><th align="center" valign="middle" >Single-Tuned Passive Filter Simulation [<xref ref-type="bibr" rid="scirp.123824-ref14">14</xref>]</th><th align="center" valign="middle" >Single-Tuned Passive Filter Simulation “Our Results”</th><th align="center" valign="middle" >IEE 519-1992 Standard</th><th align="center" valign="middle" >Description</th></tr></thead><tr><td align="center" valign="middle" >1</td><td align="center" valign="middle" >100.00</td><td align="center" valign="middle" >100</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >3</td><td align="center" valign="middle" >2.31</td><td align="center" valign="middle" >2.3104</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >5</td><td align="center" valign="middle" >2.66</td><td align="center" valign="middle" >2.6693</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >7</td><td align="center" valign="middle" >2.20</td><td align="center" valign="middle" >2.2013</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >9</td><td align="center" valign="middle" >0.80</td><td align="center" valign="middle" >0.7998</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >11</td><td align="center" valign="middle" >1.17</td><td align="center" valign="middle" >1.175</td><td align="center" valign="middle" >3.5</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >13</td><td align="center" valign="middle" >1.00</td><td align="center" valign="middle" >1.009</td><td align="center" valign="middle" >3.5</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >15</td><td align="center" valign="middle" >0.47</td><td align="center" valign="middle" >0.46</td><td align="center" valign="middle" >3.5</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >17</td><td align="center" valign="middle" >0.81</td><td align="center" valign="middle" >0.8099</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >19</td><td align="center" valign="middle" >0.99</td><td align="center" valign="middle" >0.987</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >21</td><td align="center" valign="middle" >0.23</td><td align="center" valign="middle" >0.23</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >23</td><td align="center" valign="middle" >0.78</td><td align="center" valign="middle" >0.775</td><td align="center" valign="middle" >1.0</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >THD</td><td align="center" valign="middle" >4.77</td><td align="center" valign="middle" >4.7793</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr></tbody></table></table-wrap><p><xref ref-type="table" rid="table4">Table 4</xref> is an illustration of the size of individual harmonic flow that occurs as a consequence of current harmonic reduction achieved by simulation utilizing a double-tuned filter. The results of modeling current harmonic reduction using a double-tuned filter are presented in <xref ref-type="table" rid="table4">Table 4</xref>. This filter may reduce total current harmonics from 15.57 percent to 4.82096 percent, therefore achieving the goal of current harmonic minimization. When looked at from the perspective of single harmonic currents, the results of the simulation show that the IEEE 519-1992 criteria has been satisfied by the whole IHD Order of harmonics.</p><p><xref ref-type="fig" rid="fig7">Figure 7</xref> is a representation of the current waveform that was generated by</p><table-wrap id="table4" ><label><xref ref-type="table" rid="table4">Table 4</xref></label><caption><title> Double tuned filter simulation results (IHDi %)</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >IHD Order</th><th align="center" valign="middle" >Double Tuned Filter</th><th align="center" valign="middle" >IEE Standard</th><th align="center" valign="middle" >statues</th></tr></thead><tr><td align="center" valign="middle" >1</td><td align="center" valign="middle" >100</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >3</td><td align="center" valign="middle" >2.3114</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >5</td><td align="center" valign="middle" >2.6594</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >7</td><td align="center" valign="middle" >2.25</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >9</td><td align="center" valign="middle" >0.797</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >11</td><td align="center" valign="middle" >1.275</td><td align="center" valign="middle" >3.5</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >13</td><td align="center" valign="middle" >1.00</td><td align="center" valign="middle" >3.5</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >15</td><td align="center" valign="middle" >0.47</td><td align="center" valign="middle" >3.5</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >17</td><td align="center" valign="middle" >0.81</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >19</td><td align="center" valign="middle" >0.98</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >21</td><td align="center" valign="middle" >0.24</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >23</td><td align="center" valign="middle" >0.78</td><td align="center" valign="middle" >1.0</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >Total THD</td><td align="center" valign="middle" >4.82096</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr></tbody></table></table-wrap><p>Matlab/Simulink while using a double-tuned filter. This waveform demonstrates that the resultant signal has a sinusoidal shape, which is an indication that the system has been isolated from current harmonic interference.</p></sec><sec id="s3_4"><title>3.4. Case 4: Second Order Damped Filter Case</title><p><xref ref-type="fig" rid="fig8">Figure 8</xref> depicts the Matlab Simulation circuit drawing employing a second-order damped filter with series components of C and parallel R, L. Second Order Damped Filter simulation is performed in numerous stages, similar to non-filtered simulation, and then augmented with second-order damped filter in tandem with the load. The RLC value was computed as follows:</p><p>The following values that are taken from the single-tuned filter are the same as what we need for the second-order damped filter:</p><p>X C = 3.0969423   Ω</p><p>C = 1027.8   μ F</p><p>X L = 0.12385692   Ω</p><p>L = 0.3943   mH</p><p>X n = 0.6193365278</p><p>If we assume that the quality factor of a single-tuned passive filter, denoted by Q, is equal to five, then we may compute the value of resistance, denoted by R, in the filter as follows [<xref ref-type="bibr" rid="scirp.123824-ref15">15</xref>] :</p><p>R = X n Q (9)</p><p>Then, R = 0.6193365278 &#215; 5 = 3.096682639 Ω.</p><p><xref ref-type="table" rid="table5">Table 5</xref> displays the intensity of single harmonic flow as a result of current harmonic reduction by simulation using a second-order damped filter. <xref ref-type="table" rid="table5">Table 5</xref> shows the results of modelling current harmonic elimination with a second-order damped filter, which may minimize overall current harmonics from 15.57 percent to 4.677307 percent. The simulation findings reveal that the complete IHD Order of harmonics has met the IEEE 519-1992 requirement when viewed from single harmonic currents.</p><p><xref ref-type="fig" rid="fig9">Figure 9</xref> is a depiction of the current waveform that was created using Matlab/second Simulink’s order damped. This waveform reveals that the resultant signal has a sinusoidal shape, which indicates that the system has been isolated from harmonic current interference.</p><table-wrap id="table5" ><label><xref ref-type="table" rid="table5">Table 5</xref></label><caption><title> Second order damped filter simulation results (IHDi %)</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >IHD Order</th><th align="center" valign="middle" >Second Order Damped Filter</th><th align="center" valign="middle" >IEE Standard</th><th align="center" valign="middle" >Statues</th></tr></thead><tr><td align="center" valign="middle" >1</td><td align="center" valign="middle" >100</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >3</td><td align="center" valign="middle" >2.3</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >5</td><td align="center" valign="middle" >2.52</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >7</td><td align="center" valign="middle" >2.2</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >9</td><td align="center" valign="middle" >0.73</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >11</td><td align="center" valign="middle" >1.270</td><td align="center" valign="middle" >3.5</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >13</td><td align="center" valign="middle" >1.00</td><td align="center" valign="middle" >3.5</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >15</td><td align="center" valign="middle" >0.48</td><td align="center" valign="middle" >3.5</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >17</td><td align="center" valign="middle" >0.80</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >19</td><td align="center" valign="middle" >0.97</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >21</td><td align="center" valign="middle" >0.25</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >23</td><td align="center" valign="middle" >0.7</td><td align="center" valign="middle" >1.0</td><td align="center" valign="middle" >Satisfied</td></tr><tr><td align="center" valign="middle" >Total THD</td><td align="center" valign="middle" >4.677307</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr></tbody></table></table-wrap><table-wrap id="table6" ><label><xref ref-type="table" rid="table6">Table 6</xref></label><caption><title> Comparison between the four cases</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >IHD Order</th><th align="center" valign="middle" >Non-Filtered Simulation</th><th align="center" valign="middle" >Single-Tuned Passive Filter</th><th align="center" valign="middle" >Double Tuned Filter</th><th align="center" valign="middle" >Second Order Damped Filter</th><th align="center" valign="middle" >IEE 519-1992 Standard</th><th align="center" valign="middle" >Description</th></tr></thead><tr><td align="center" valign="middle" >1</td><td align="center" valign="middle" >100</td><td align="center" valign="middle" >100</td><td align="center" valign="middle" >100</td><td align="center" valign="middle" >100</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >3</td><td align="center" valign="middle" >2.35</td><td align="center" valign="middle" >2.3104</td><td align="center" valign="middle" >2.3114</td><td align="center" valign="middle" >2.3</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >5</td><td align="center" valign="middle" >14.99</td><td align="center" valign="middle" >2.6693</td><td align="center" valign="middle" >2.6594</td><td align="center" valign="middle" >2.52</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >7</td><td align="center" valign="middle" >2.48</td><td align="center" valign="middle" >2.2013</td><td align="center" valign="middle" >2.25</td><td align="center" valign="middle" >2.2</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >9</td><td align="center" valign="middle" >0.91</td><td align="center" valign="middle" >0.7998</td><td align="center" valign="middle" >0.797</td><td align="center" valign="middle" >0.73</td><td align="center" valign="middle" >7.0</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >11</td><td align="center" valign="middle" >1.25</td><td align="center" valign="middle" >1.175</td><td align="center" valign="middle" >1.275</td><td align="center" valign="middle" >1.270</td><td align="center" valign="middle" >3.5</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >13</td><td align="center" valign="middle" >1.03</td><td align="center" valign="middle" >1.009</td><td align="center" valign="middle" >1.00</td><td align="center" valign="middle" >1.00</td><td align="center" valign="middle" >3.5</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >15</td><td align="center" valign="middle" >0.52</td><td align="center" valign="middle" >0.46</td><td align="center" valign="middle" >0.47</td><td align="center" valign="middle" >0.48</td><td align="center" valign="middle" >3.5</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >17</td><td align="center" valign="middle" >0.85</td><td align="center" valign="middle" >0.8099</td><td align="center" valign="middle" >0.81</td><td align="center" valign="middle" >0.80</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >19</td><td align="center" valign="middle" >1.03</td><td align="center" valign="middle" >0.987</td><td align="center" valign="middle" >0.98</td><td align="center" valign="middle" >0.97</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >21</td><td align="center" valign="middle" >0.28</td><td align="center" valign="middle" >0.23</td><td align="center" valign="middle" >0.24</td><td align="center" valign="middle" >0.25</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >23</td><td align="center" valign="middle" >0.82</td><td align="center" valign="middle" >0.775</td><td align="center" valign="middle" >0.78</td><td align="center" valign="middle" >0.7</td><td align="center" valign="middle" >1.0</td><td align="center" valign="middle" >Match</td></tr><tr><td align="center" valign="middle" >THD</td><td align="center" valign="middle" >15.57</td><td align="center" valign="middle" >4.7793</td><td align="center" valign="middle" >4.82096</td><td align="center" valign="middle" >4.677307</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr></tbody></table></table-wrap></sec><sec id="s3_5"><title>3.5. Comparison between the Four Cases</title><p><xref ref-type="table" rid="table6">Table 6</xref> shows the final comparison between the three filters single-tuned passive filter, double-tuned filter and the second-order damped filter and non-filtered case. Since the filters were designed to overcome the fifth harmonic effect which does not match the IEE standards. The results for all filters satisfy the requirements and give almost similar results of harmonic mitigation; however, the second-order damped filter outperforms the other filters.</p></sec></sec><sec id="s4"><title>4. Conclusion</title><p>Harmonics are periodic waves with frequencies that are integral multiples of the basic power line frequency component. They are consequences of contemporary electronic components. Hence it is vital to mitigate harmonics and provide harmonic reduction measures. This research provides a case study of the plastic processing industry which used to face a problem in terms of the fifth harmonic. Three filters were used to mitigate the undesirable harmonics: single-tuned passive filter, double-tuned filter and second-order damped filter. The results give almost similar THDi, however, the second-order damped filter provides the optimum harmonic mitigation, which satisfies IEE 519-1992 Standard.</p></sec><sec id="s5"><title>Conflicts of Interest</title><p>The authors declare no conflicts of interest regarding the publication of this paper.</p></sec><sec id="s6"><title>Cite this paper</title><p>Elmi, Y. and Salman, D. (2023) Simulation Model for Passive Harmonic Filters Using Matlab/Simulink: A Case Study. Journal of Power and Energy Engineering, 11, 1-14. https://doi.org/10.4236/jpee.2023.113001</p></sec></body><back><ref-list><title>References</title><ref id="scirp.123824-ref1"><label>1</label><mixed-citation publication-type="other" xlink:type="simple">Lumbreras, D., Gálvez, E., Collado, A. and Zaragoza, J. 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