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A novel control approach for harmonic compensation using switched power filter compensators in micro‐grids

2021; Institution of Engineering and Technology; Volume: 15; Issue: 16 Linguagem: Inglês

10.1049/rpg2.12317

1752-1424

Nima Khosravi, Hamid Reza Abdolmohammadi, Sajad Bagheri, Mohammad Reza Miveh,

Optimal Power Flow Distribution

IET Renewable Power GenerationVolume 15, Issue 16 p. 3989-4005 ORIGINAL RESEARCH PAPEROpen Access A novel control approach for harmonic compensation using switched power filter compensators in micro-grids Nima Khosravi, Nima Khosravi Department of Electrical Engineering, Arak Branch, Islamic Azad University, Arak, IranSearch for more papers by this authorHamid Reza Abdolmohammadi, Hamid Reza Abdolmohammadi orcid.org/0000-0001-6570-2802 Department of Electrical Engineering, Golpayegan University of Technology, Golpayegan, IranSearch for more papers by this authorSajad Bagheri, Corresponding Author Sajad Bagheri s-bagheri@iau-arak.ac.ir orcid.org/0000-0002-3553-5510 Department of Electrical Engineering, Arak Branch, Islamic Azad University, Arak, Iran Correspondence Sajad Bagheri, Department of Electrical Engineering, Arak Branch, Islamic Azad University, Arak 3836119131, Iran. Email: s-bagheri@iau-arak.ac.irSearch for more papers by this authorMohammad Reza Miveh, Mohammad Reza Miveh Department of Electrical Engineering, Tafresh University, Tafresh, IranSearch for more papers by this author Nima Khosravi, Nima Khosravi Department of Electrical Engineering, Arak Branch, Islamic Azad University, Arak, IranSearch for more papers by this authorHamid Reza Abdolmohammadi, Hamid Reza Abdolmohammadi orcid.org/0000-0001-6570-2802 Department of Electrical Engineering, Golpayegan University of Technology, Golpayegan, IranSearch for more papers by this authorSajad Bagheri, Corresponding Author Sajad Bagheri s-bagheri@iau-arak.ac.ir orcid.org/0000-0002-3553-5510 Department of Electrical Engineering, Arak Branch, Islamic Azad University, Arak, Iran Correspondence Sajad Bagheri, Department of Electrical Engineering, Arak Branch, Islamic Azad University, Arak 3836119131, Iran. Email: s-bagheri@iau-arak.ac.irSearch for more papers by this authorMohammad Reza Miveh, Mohammad Reza Miveh Department of Electrical Engineering, Tafresh University, Tafresh, IranSearch for more papers by this author First published: 29 October 2021 https://doi.org/10.1049/rpg2.12317AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract This paper presents a new harmonic compensation system using filter compensator devices in a hybrid micro-grid (MG). In order to reduce the amplitude of current and voltage harmonics, two separate systems, including a switched power filter compensator (SPFC) and a switched active power filter (SAPF) have been used in the AC side of the MG. The gain coefficients of both SAPF and SPFC modules (with different controllers) using meta-heuristic algorithms are optimized and applied for three harmonic loops of voltage, current and controller error to obtain an optimal response for reducing the harmonic amplitude of current and voltage. The objective function, containing controller error, current and voltage harmonics is defined and followed by the optimized coefficients for the PID controller of each of the SAPF and SPFC modules. To find the best answer to this problem, the related gains using four meta-heuristic algorithms, including artificial bee colony (ABC), particle swarm optimization (PSO), harmonic search (HS), and differential evolution (DE) are optimized and compared. The simulation results show that using the proposed method, the total harmonic distortion of the system can be significantly reduced. 1 INTRODUCTION The environmental issues, declining fossil fuel reserves, and stresses in the supply have led to the genesis of small-scale sources of electricity generation and the return to clean energy [1]. Micro-grids (MGs) are unit control systems that enable the supply of electrical energy on a small and medium scale locally. The general structure of an MG is shown in Figure 1. MGs have many advantages such as more reliability, power loss reduction, local voltage support, improved power quality and high-speed communication system [2-5]. However, there exist numerous problems to provide reliable operation for MGs either in the grid-connected or islanded mode that needs to be resolved. Power quality problems, operation and protection challenges of MGs are the areas that require more investigation in MGs. In [6-8], comprehensive reviews of issues such as power management strategies and protection methods in MGs are presented. The overviews of the MGs control methods are given in [9-13]. Harmonics distortions are one of the main challenges which need to be resolved before MGs become commonplace. Non-linear loads and high penetration level of intermittent renewable energy sources (RESs) are the main cause of harmonics distortions in MGs. Therefore, it is necessary for MGs to propose improved harmonic compensators to avoid a threat to the distribution network in terms of power quality and stability issues. To cope with harmonic distortions in MGs, numerous harmonic compensation approaches are presented in the literature [14-27]. Using the embedded load observer system, MG harmonic compensation can be performed. This control method is able to consider and correct issues such as detection, estimation and, finally, harmonic compensation due to variable loads. Experimental results show that the applied control method is quite effective [14]. The pre-filter phase-locked loop (PLL) has been investigated in terms of inter-harmonic perturbations in order to increase the accuracy of phase extraction in voltage source inverters (VSI) [15]. Harmonic and inter-harmonic detection of the system in power grids is performed using the fast Fourier transform (FFT) algorithm in [16]. A control strategy based on the master/slave method in electronic converters has been used to reduce harmonic components as well as improve power quality in low voltage MGs. The simulation results show the improvement of power quality parameters in the system [17]. New design of AC/DC MGs and deregulated thermal system with the presence of flexible alternating current transmission system (FACTS) devices has been studied in [18-20]. A method has been proposed based on the use of some adjusted harmonic filters to detect MG islanding in [21]. These devices connect to the distributed generation (DG) terminals using the impedance calculation technique to detect islanding mode. Moreover, considering the desired method, the harmonic injection to the end of the source is reduced. The harmonic conditions of AC/DC MGs have been investigated in [22]. In this study, using the active power compensator, the harmonic amplitude of the system has been significantly reduced. Also, some heuristic algorithms have been used to optimize the compensator controller. It seems that it is better to use an element of the same nature to compare the results correctly, but in this study, an element of FACTS is used. A hierarchical control approach combined with a parallel power filter to deal with unbalanced harmonic problems caused by multi-converter-inverter systems is investigated in [23]. The task of the active power filter controller is to calculate and apply sensitive load bus (SLB) compression in case of DG inability. In [24], a shunt active power filter (SAPF) using power theory is reduced the harmonic distortions and improved the quality of islanded an MG according to the IEEE 519–1992 standard. Different approaches regarding active power filter (APF) modelling are presented in [25-27]. The results show that using these techniques can reduce some of the system's parameters such as harmonics and DC bus voltage. FIGURE 1Open in figure viewerPowerPoint The structure of MG (the case study) As mentioned above, various papers have been published on harmonic compensation in MGs. Nowadays, optimization using meta-heuristic algorithms on control devices such as control of inverter-based systems, FACTS etc. is abundantly presented in scientific papers. All of these devices are very complex and expensive in terms of maintenance and operating conditions. Therefore, the main purpose in selecting the filter compensator modules and designing their control method is to cope with all the above-mentioned restrictions. As mentioned earlier, the innovation in this study is the definition of three components of voltage harmonic, current harmonic and controller error as the objective function. The modules used in this study include two switches power filter compensators that optimized by four various algorithms. The control coefficients of each of these modules must comply with all the constraints related to the objective function in order to find the best response (harmonic amplitude reduction). However, some drawbacks such as complexity of control systems for harmonic distortions, the lack of a proper integrated harmonic compensator structure have led to the presentation of new harmonic compensator devices. In this paper, a switched active power filter (SAPF) is used along with the switched power filter compensator (SPFC) to reduce harmonic distortions in MGs. The gains controllers for the SAPF and SPFC are optimized using some heuristic algorithms to attain optimal responses for harmonic compensation. The proposed approach is simulated in a test system and compared with conventional methods. The outcomes confirm that the suggested approach has a great ability to reduce total harmonic distortion of the system. The rest of this paper is organized as follows: Section 2 presents the case study. Section 3 discusses the modelling of MG's components. Section 4 presents proposed compensators. Section 5 introduces a roadmap of problem optimization; Section 6 and Section 7 provide simulations and conclusions, respectively. 2 CASE STUDY The considered case study consists of two parts, a direct current MG (DCMG) consisting of a fuel cell, battery, and photovoltaic (PV). The second part is modelled with an alternating current MG (ACMG) that includes a micro-gas turbine generators (MTGs), wind turbines, and diesel generator. The structure and arrangement of the elements are shown in Figure 2. Also, the SPFC and SAPF have been used to reduce harmonics distortions. The purpose of designing such compensators is to reduce system harmonics by determining and optimizing the multiplication of SPFC and SAPF control gains, which is possible using four algorithms of artificial bee cloning (ABC), particle swarm optimization (PSO), harmony search (HS), and differential evolution (DE). Figure 2 shows the considered case study along with compensating modules. The SPFC and SAPF elements can improve and solve the harmonic (voltage and current) problems. FIGURE 2Open in figure viewerPowerPoint The layout of the compensator system along with other case study components In SPFC, the amount of voltage generated by the inverter will be adjusted using sinusoidal pulse width modulation or DC link voltage control, which will cause phase lag and phase lead ‘Q’ current to flow from the voltage source. The simulation results show that the use of the desired modules can be a modern way to eliminate power quality problems. 3 MODELLING OF MG'S COMPONENTS In the following, the modelling of various DGs in MGs is presented. 3.1 Photovoltaic (PV) system One of the main sources of energy production in MGs is PV system. The PV system is packaged as an integrated system consisting of photovoltaic cells by the maximum power point tracking (MPPT) method [28-30]. MPPT controller in PV system has a higher efficiency of 30% compared to conventional controllers. For a solar module, MPPT follows voltage and current to achieve maximum power and thus absorption. The maximum power point is the product of the voltage of the maximum power point ( V m p p ) in the current of the maximum power point ( I m p p ) [31, 32]. The equivalent circuit of the PV system is shown in Figure 3. The photovoltaic output voltage will be obtained from Equation (1). V p v = A K T c e l n I p h + I o − I c I o − R s I c (1)where A is a constant value for fixing the curve, e is the electron charge (1.602 × 10 − 19 C ), K is the Boltzmann constant value (1.38 × 10 − 23 j k ), I c is output current PV cell, I p h is photocurrent (1 A), I o is reverse diode saturation current (0.2 mA), finally, R s is the series resistor (1 MΩ), V p v its output voltage and T c is the reference temperature (25 °C) PV cell. FIGURE 3Open in figure viewerPowerPoint Equivalent circuit of a PV cell 3.2 Battery and fuel cell Batteries play a significant role in balancing power and regulating DCMG voltage [33]. The biggest difference between a fuel cell and a battery is that a fuel cell is a device that converts the chemical energy of a fuel directly into electrical energy. Four types of fuel cells (FCs) are being developed today. That includes the proton exchange membrane fuel cell (PEMFC), phosphoric acid fuel cell (PAFC), molten carbonate fuel cell (MCFC), and solid oxide fuel cell (SOFC). These cells are divided into two categories of minimum and maximum temperature in terms of performance and operation [34]. The simple PMEFC diagram is shown in Figure 4. The Equation (2) states the chemical reaction of the PEM type: H 2 + 1 2 O 2 → H 2 O + Heat + Electrical energy (2) FIGURE 4Open in figure viewerPowerPoint The simple PMEFC diagram The batteries used in this study are of two types: Nickel-metal hydride with a rated voltage of 280 volts and a capacity of 6.5 (Ah), and the fuel cell with PEMFC typing is 50 kW and 625 V. A boost chopper is used to adjust the DC voltage required during the capacitor. A schematic of a simulated fuel cell with a boost chopper is shown in Figure 5. The open-circuit voltage is as follows: E o c = N E n − − A ln I o (3) A = R T Z α F (4) FIGURE 5Open in figure viewerPowerPoint Equivalent circuit of a fuel cell where R = 8.3145 J/(mol K), F = 96,485 As/mol, the number of moving electrons (z,) E n is Nernst voltage, the thermodynamics of the voltage of the cells and depends on the partial pressure of the reactants, temperature, etc. exchange current( I o ), charge transfer coefficient ( α) depending on the electrode type, the catalyst used and the temperature (T). The V f c fuel cell voltage is as follows: V f c = E o c − V A c t i v a t i o n L o s s − V O h m i c L o s s − V C o n c e n t r i o n L o s s (5) V A c t i v a t i o n L o s s = A l o g I f c + I n I o (6) V O h m i c L o s s = R m I f c + I n (7) V C o n c e n t r i o n L o s s = B l o g 1 − I f c + I n I l (8)where V C o n c e n t r a t i o n L o s s unit is (V), B is a constant. 3.3 Wind turbine Wind turbines are an undeniable component of clean energy. The main concern in the wind energy industry is reforming the amount of production of this energy, extraction and how to control the performance of wind turbines [35]. The layout and type of connection of these systems are shown in Figure 6. Therefore, the mechanical power of this unit will be obtained from Equation (9). P m = 1 2 ρ A C p λ , β V w 3 (9) FIGURE 6Open in figure viewerPowerPoint The structure of the used wind turbine In this equation, ρ is air density (kg/ m 3 ), A is the rotor displacement point ( m 2 ), V w is the wind speed (m/s), and C p ( λ , β ) is the power factor (ranging from 0.25 to 0.45) that depends on the function of λ and the angle of the screw β [36, 37]. 3.4 Micro-gas turbine generator Today, in some industries, high-speed generators which are called MTGs are introduced as new energy sources, especially in the robotics industry. These sources can have speeds of 20 × 10 4 rpm to 40 × 10 4 rpm in the class of 500 W [38]. This study uses MTGs with a capacity of 20 kW to 100 kW. 4 PROPOSED COMPENSATORS In the following, in this section, each of the filter devices will be examined along with the type of control system used in them. 4.1 Switched power filter compensator The elements used in the SPFC include a series capacitive bank, two parallel capacitive banks and a tuned arm power filter [39]. The equivalent circuit of SPFC is shown in Figure 7. The energy discharge path for parallel capacitive elements will be performed by a two-pulse diode rectifier circuit with ‘R’ and ‘L’ branches; the circuit is formed by the arm power filter on the DC rectifier side. Transistor switches (S1 and S2) are controlled by two switch outputs (P1 and P2). The applied output pulse is self-generated by the PID signal, which is optimized by a set of meta-heuristic algorithms to find the best response. In describing PWM output, two modes can be considered. First, it is assumed that the volume P1 is lower than P2, therefore, the resistance and induction of the arm filter will act quickly. Finally, a set of combined capacitors will be used for compensation and storage activities for AC production sources. Second, if the value of P1 is higher than P2, then the resistance and inductance of both are connected to the circuit as a tuned arm filter. FIGURE 7Open in figure viewerPowerPoint The SPFC structure 4.1.1 SPFC controller The SPFC controller is shown in Figure 8. The error ( e s p f c ) after optimization by intelligent algorithms is the input of PID control and includes three errors, voltage stabilization loop error ( e v s p f c ) , current limiting error ( e I s p f c ) and dynamic power loop error ( e P s p f c ) . The resulting global error ( e s p f c ) is depicted in Figure 8 e s p f c = γ v s p f c e v s p f c + γ I s p f c + e I s p f c + γ P s p f c e P s p f c (10) e v s p f c = V s p f c r e f − V s p f c 1 1 + s T 1 V s p f c b a s e (11) e I s p f c = I p f c s I s p f c b a s e 1 1 + s T 1 1 − 1 1 + s T 2 (12) e P s p f c = V s p f c V s p f c b a s e × I s p f c I s p f c b a s e 1 − 1 1 + s T 2 (13) FIGURE 8Open in figure viewerPowerPoint The block diagram control of SPFC The parameters ( γ v s p f c ), ( γ I s p f c ), and ( γ P s p f c ) are the basic coefficients to achieve the best value of the control loops. Also, T 1 and T 2 are time constants. The PWM control signal of the SPFC (system control voltage) is regulated by a time-domain for the PID controller as follows. Finally, a command pulse from PWM only closes one of the S 1 or S 2 keys. V c t = k p e s p f c t + k i ∫ 0 t e s p f c t d t + k d d e s p f c t d t (14) 4.2 Switched active power filter The function of the SAPF is to improve the power quality and remove power system harmonics. In the form of a shunt connection, it is assumed that the ohmic charge thyristor bridge rectifier is considered as a non-linear load on the three-phase AC voltage. This non-linear load will cause a non-sinusoidal current from the main source. The APF eliminates the disadvantages of a passive filter using a power inverter. The shunt active power filters act as a non-linear load parallel to the current source, and it has a good performance in eliminating harmonic currents [40, 41]. The series active and passive power filter topologies are shown in Figure 9. The APF is used to drop harmonic current and perform reactive power compensation. In the APF, the inverter is controlled to produce a compensating current that is equal but opposite to the harmonic and reactive currents generated by the non-linear load. In this condition, the main source current will be sinusoidal and synchronous with the phase current source. The main purpose of using the APF is to compensate for harmonics and reactive power, thereby eliminating the undesirable effects of the non-ideal primary source with three-phase balanced sinusoidal currents having a single power factor. As stated in the series APF, it reduces harmonics above the voltage source, and the output voltage will be sinusoidal [42]. The issue of harmonic distortion is one of the power quality problems in the system. Another practical topic of power quality is dynamic voltage restorer (DVR), which is tried to be presented here with a practical example of its performance in response to the active power filter module. The following relations of the mentioned subject will be presented: U L = U 1 R = const . (15) FIGURE 9Open in figure viewerPowerPoint Series active and passive power filter topologies If the DVR output voltage effective values define the first and ninth harmonic values, respectively, U F , U 1 R and U n , then it will be concluded as: U F 2 = ( U 1 R − U 1 ) 2 + ∑ n = 2 ∞ U n 2 (16) If k considerer as the ratio between the effective reference voltage value and the first harmonic of the voltage source: k = U 1 R U 1 (17) It can be deduced from Equations (16) and (17): U F = U 1 k − 1 2 + k h 2 (18) So, the ratio of DVR apparent power, with S F index and apparent load power (S) will be: S F 2 S 2 = U 1 2 k − 1 2 + k h 2 I ′ 2 U 1 2 + ∑ n = 2 ∞ U n 2 I 2 = k − 1 2 + k h 2 1 + k h 2 (19) The graphically restored forms of the dynamic voltage state resulting from Equations (20) and (21) are shown in Figures 10 and 11. To better understand, Figure 10 shows the exponential changes between the two components of the system's apparent power with respect to the voltage value. In the following, each of the mentioned components has a conversion ratio. For example, the apparent power of the system, including the ratio of the apparent power of the dynamic voltage restorer to the apparent power of the load, will be defined. k is the ratio between the effective values of the reference voltage (the preliminary defined one) and the first harmonic of the grid voltage. The results of Figure 10 will be obtained by setting the parameters of the apparent power dynamic voltage restorer ( S F ), the apparent power of the load, and the constant-coefficient (Kh) by placing it in Equation (20). S F S = k − 1 2 + k h 2 1 + k h 2 (20) U L U = U 1 R U = k 1 1 + k h 2 (21) FIGURE 10Open in figure viewerPowerPoint Series active power filters (dynamic voltage restorer-graphics in accordance with Equation (20)) FIGURE 11Open in figure viewerPowerPoint Series active power filters (dynamic voltage restorer-graphics in accordance with Equation (21)) 4.2.1 SAPF controller The SAPF controller first calculates the difference between the desired voltage characteristic and the actual voltage. Therefore, the actual voltage deficiency is injected by the SAPF model. Typically, the input pulse is generated for VSI operation as a series APF by one of the PWM techniques [43, 44]. Finally, the voltage of this module will be transmitted and injected by the transformers to the voltage source. In fact, the control method used in this study is the identity vector template generation (IVTG). The use and implementation of IVTG will eliminate the harmonic nature of the MG voltage at the point of common coupling (PCC). The block diagram of the SAPF is shown in Figure 12. The source voltage with the reference voltage of the MG for the first phase represented by α can be expressed as Equation (22). V s α ω t = V s α 1 + V s α 2 + V s α 0 + V s α h (22)where V s α 1 , V s α 2 , V s α 0 and V s α h will be defined as positive, negative, zero, and harmonic voltage sequences, respectively. Find the harmonic content of α from Equation (23). V s α h = ∑ n = 2 ∞ V s α n sin n ω t + θ n α (23) FIGURE 12Open in figure viewerPowerPoint The block diagram control of the SAPF Similarly, the equations for the other two phases will be formulated as follows: V s β ω t = V s β 1 + V s β 2 + V s β 0 + V s β h (24) V s γ ω t = V s γ 1 + V s γ 2 + V s γ 0 + V s γ h (25) The sine voltage of the detection domain in the PCC will be obtained by the voltages of all three phases, respectively and finally it will be compared to the desired value range. The voltage vector generated using this approach is known as the IVTG by the following equations: ρ α = sin ω t (26) ρ β = sin ω t − 120 o (27) ρ γ = sin ω t + 120 o (28) In the block diagram, the parameter V L m represents the peak load voltage value. To increase the required load voltage, the set of the above equations will be multiplied by the parameter V L m (with a fixed term) and finally, the input voltages to the controller hysteresis will be obtained as follow: V L α ∗ ω t = V L m ρ α = V L m sin ω t (29) V L β ∗ ω t = V L m ρ β = V L m sin ω t − 120 o (30) V L γ ∗ ω t = V L m ρ γ = V L m sin ω t + 120 o (31) The gate signal pulses are generated by the hysteresis controller for the VSI (compare reference load voltages with actual load voltages). Ultimately this process enables the control of the desired goals. 5 ROADMAP OF PROBLEM OPTIMIZATION In this section, the desired objective function and methods for optimizing the SAPF and SPFC control gain coefficients will be explained. The target functions will be defined as follows: Min ( ζ ) = min ∑ i = 1 3 a i ζ i (32) 0 < a i ≤ 1 (33)where ζ i will be as follows: ζ 1 is the global error of the compensation, equal to: ζ 1 = e a (34) In Equation (34), the e a is the global error value of the SAPF and SPFC controllers. ζ 2 and ζ 3 are the total voltage and current harmonics on the ACMG side, respectively: ζ 2 = T H D V (35) T H D V < T H D y , m a x (36) T H D V = ∑ h = 2 n V h 2 V 1 (37) ζ 3 = T H D i (38) T H D i < T H D i , m a x (39) T H D i = ∑ h = 2 n I h 2 I 1 (40) The objective performance of the problem defined is examined by keeping the following constraints. If the AC busbar voltage of the ACMG side is V A C M G , and the DC busbar voltage of DCMG is V D C M G , The constant voltage between AC and DC busbars and will be: Δ V A C M G , Δ V D C M G (41) Δ V A C M G = V A C M G − V A C M G r e f (42) Δ V D C M G = V D C M G − V D C M G r e f (43) The power factor on the side of the AC busbars, as defined below: P F A C M G ≥ P F A C M G r e f (44) The total harmonic distortion, a waveform depending on the type of voltage or current being a parameter, will be obtained from Equations (35)–(40). Finally, the roadmap related to what this study has done and implemented is shown in the flowchart in Figure 13. FIGURE 13Open in figure viewerPowerPoint Flowchart of the case study roadmap 5.1 Optimization algorithms Today, many methods and techniques such as Monte Carlo, genetic algorithms, etc. are used in optimization and problem-solving [45]. In this study, based on the content and best output, four algorithms PSO, HS, DE, and ABC are used to determine the best SAPF and SPFC controllers coefficients gains to reduce the harmonic oscillations of the system, which will be discussed further in each of these algorithms. 5.1.1 ABC algorithm The artificial bee colony (ABC) algorithm is an optimization solution that simulates the behaviour of a bee colony, and was used for the first time in 2005. The ABC has three types of bees, worker bees; this focus is on collecting food and bringing it to the hive from a specific food source, observational bees, which roam among worker bees to determine whether a food source is still worth using and, finally, bee-keepers looking for new food sources [46]. 5.1.2 PSO algorithm Particle swarm optimizing (PSO) is one of the smart algorithms that have been used extensively in the field of harmonic system optimization [47]. In the PSO algorithm, all the particles are looking for the best point; each time the motion is made the particles calculate their fitness function. Every particle that has the best fitness (closest to the answer) alerts the other particles and moves the particle toward that particle. The particles update their velocity and position in terms of absolute and local solutions. 5.1.3 HS algorithm The harmony search (HS) algorithm is inspired by music to get the best answer. The HS algorithm is the best strategy for converting qualitative research trends into quantitative processes, and it is tangible optimization. Harmony memory consideration rate (HMCR) and pitch adjusting rate (PAR) parameters, which are two parameters between zero and one, in the next step, a harmonic me