Abstract
Advanced power converters are being developed due to the latest developments in power electronics switches. The matrix converter (MC) assessment is the product of this drastic growth. MC is a bidirectional power flow device with a single-step energy conversion mechanism that operates at variable voltage and frequency. The main drawback of MC is the presence of harmonics due to power electronic device switching. A lot of research has been done to decrease the harmonics content present in the MC, but it is restricted to a certain level only. To overcome this limit, the harmonics are minimized in the MC by incorporating soft computing controllers. This article presents particle swarm optimization (PSO), modified PSO (MPSO), and modified hybrid PSO (MHPSO) based controllers for different loads. The proposed MC with a soft computing controller reduces the harmonics by selecting suitable switching pulses for every sample. The simulations are made using the MATLAB/Simulink environment. The results of the proposed MHPSO controller reduce the THD value from 8.654 with a PSO approach to 7.536 in the presence of nonlinear loads.
1. Introduction
Power electronic converters (PECs) are increasingly used in electric drives due to significant advancements in power semiconductor devices. In everyday life, the efficacy of the advancements intensive current, voltage rating, dependability, and efficiency are rising [1]. PEC, on the contrary, consumes more reactive power, which is hard to manage and they are also producing harmonic content owing to the more switching frequency [2]. The conventional matrix converter (CMC) is an advanced PEC used in power system networks with single-stage conversion, effectively replacing the multistage energy converters [3]. It is built with two-way switches that allow energy to be converted in both directions [4]. Compared to multistage converters, the CMC offers more benefits such as the bidirectional power flow, no DC link capacitor, input and output with sinusoidal signals, improved power factor, less weight, and long life [5]. Because of their benefits, they may be used as future PECs with various applications such as renewable energy, aerospace, intelligent grids, and variable speed drives [6, 7]. With proper control of the switches, the required frequency and output voltage are accessible [8]. The output of CMC contains different types of harmonics and various controllers are used to minimize the same [9]. By adjusting the duty cycle and switching pattern, the pulse width modulation (PWM) approach reduces the harmonics [10]. For variable speed drive applications, the sinusoidal pulse width modulation (SPWM) will produce fewer harmonics [11]. Space vector pulse width modulation (SVPWM) reduces the switching pulses, lowering the switching losses, and enhancing the CMC’s efficiency [12, 13]. The model predictive control (MPC) approach is a straightforward approach for calculating harmonics by adding observers and lowering the number of current and voltage sensors [14]. The approach nevertheless provides a lower harmonic content [15]. The researchers have developed many soft computing strategies in the literature to reduce the harmonics in the grid-connected matrix converters. For optimizing the cost function in soft computing, numerous optimization techniques are suggested, such as PSO [16–34], fuzzy logic [17–31], neuro-fuzzy [18–32], genetic algorithm [19–33],and Hybrid PSO [20], FPSO [30], and crazy PSO [21]. Figure 1 presents various types of control methods for MC.
The proposed study demonstrates the use of PSO, MPSO, and MHPSO soft computing controllers, as well as the design of the MC, for minimizing the harmonic content in the output voltage and input current. Compared to traditional controllers, these soft computing-based technologies are robust in suitably reducing the harmonics. The soft computing methods can identify the optimum solution for each switching state sample selection to achieve a better switching approach in the CMC. The computer findings and the test bench’s designed structure strongly advise that the recommended controllers be utilized to improve the CMC performance. Because of the reactive power requirement, harmonic elimination is one of the primary challenges in the research of CMC when associated with nonlinear loads. The PSO approach’s major weakness is that it allows for premature optimization on a local optimum, which is particularly problematic when studying multiobject functions. The proposed study compensates for these drawbacks with modifications. MPSO and the MHPSO are well-defined approaches in the literature for studying these multiobjective issues. They are used to increase the CMC’s efficiency, allowing the harmonics to be strongly lowered compared to traditional methods.
The major contributions of this research include the following:(i)This research proposes an efficient MHPSO techniques for controlling the harmonics present in the matrix converter fed electric drive system(ii)The proposed method is verified for various static and rotating loads with various switching frequencies and the harmonic content below the IEEE allowable limits was obtained(iii)The comparative assessment of PSO, MPSO, and MHPSO are done in this research and it was found that the MHPSO has efficient control on the harmonics presented due to nonlinear loads(iv)The proposed method is also compared with various methods such as ABC and CPSO and received efficient results for various switching frequencies.
2. Modeling of Matrix Converter
This design incorporates most of the CMC regular operations, such as frequency control, voltage magnitude, and input power factor. For CMC output and input voltage, current basic components, the CMC must be within the dqo reference frame (9–14). The transformation matrix must meet the following conditions.(i)Duty cycle restrictions(ii)Controlled output voltages and frequency with sinusoidal nature(iii)Controllable power factor with the sinusoidal input current.
The transformation matrix (1) and (2) individually satisfies the first two conditions:, , , , , , , , and .
To satisfy all three conditions, the individual transformation matrix must be combined with the first two conditions (1) and (2) to form a new transformation matrix (12),where a = parameter of constant change between 0 and 1.
This depends on the alesina venturini approach, which was developed in 1981. The final duty ratio should be lower than one and should be the sum of both individual duty ratios. The input and output voltages of CMC are represented in the following equations [4, 5]:
Output current and input current of CMC are as follows:where φi is the input phase anglewhere DPFin = cos (φi) and DPFout = cos (φo).
Using the above mathematical modeling, the output voltage and input current quantities are estimated with the help of optimized transformation matrix. There are two types of matrix converters [22].(1)Conventional matrix converter (CMC)(2)Indirect matrix converter (IMC)
The CMC achieves frequency and voltage conversion in a single stage, while the IMC obtains voltage and current in two steps without a DC link or storage parts. If both converters are controlled using a single modulation approach, the output power quality is the same and two converters require identical filters at input [23]. Figure 2 depicts a three-phase CMC with an induction motor load. It consisted of nine bidirectional switches controlled by the 27 regular switching positions, as in Figure 3 and an input filter for lowering the harmonics [24]. The two-way switches enable electricity to flow in two directions and link any input phase to the output phase at any moment. It is important to remember that input parameters should never be shorted and yield phases should not be opened during switching [25]. The block diagram of the direct matrix converter is shown in Figure 4 and its simple mathematical model is represented in Figure 5. To get the proper representation of a present commutation environment that determines the switch positions, the following equation is used:
The affinity among yield current and input voltage are obtained by direct solution as in the following equation:
Because of the lack of the link DC capacitor, protection is rugged in CMC and commutation with current is problematic due to the lack of a freewheeling channel [3]. As a result, the following considerations are made for matrix converter commutation techniques, short circuits among any two phases should not appear since strong circulating currents might harm the switching devices [4]. Because greater output voltages may damage the switching devices, the commutation must not create any pauses in output currents.
Equations (17)–(19) represent the dynamics in the input voltage, input current, and output voltages, derived from Figure 5.
3. Proposed MHPSO Optimization Method
The test bench system under consideration in this research has a 3-phase 33 CMC fed by a three-phase supply via a harmonic filter to run a rotating load induction motor to get variable voltage and current [7, 8]. Table 1 lists the test system parameters. This article proposes MPSO and MHPSO swarm optimization-based control approaches to regulate the switching states PSO. Figure 1 depicts the existing control approaches and the suggested methods for the optimum switching positions. Figure 4 illustrates the advanced optimized switching approach with the proposed swarm optimization controller. Swarm optimization-based methods will work depending on the food-searching nature of wild animals, which may solve the issue according to the specified rules and practices [16].
3.1. Particle Swarm Optimization (PSO) Approach
The researchers Kennedy and Eberhart devised the PSO approach in 1995, with the base of the food-searching performance of bird flocks [26]. It differs from the other optimization methods due to its faster reaction time, better solutions, fewer programming codes, and fewer parameters. This approach employs the particles that generate the hidden solutions. Each particle moves through open space at a constant velocity that can be modified by prior experience. At (t + 1) th iteration, the draught condition of ith element of group xi with element velocity vi is defined as follows:where R1 and R2 = random numbers, t = 1, 2, 3, … , n, where n is the swarm size, C1 and C2 = position constants, ω = inertia weight factor, Gbest = best particle of swarm, and besti = the good previous state of the ith agent
Figure 6(a) shows the flowchart of the PSO strategy with the initial weight ω ranging between 0.4 and 0.9. Various steps involved in the PSO approach are as follows:
(a)
(b)
Step 1. Using velocities and state variables, searched agents are arbitrarily produced. The state of an ith particle can be recognized as follows:
Step 2. The velocity of the given agent can be customized by the use of equation (20).
Step 3. A velocity, which moderately obtains the situation near Pbest and Gbest is modified by equation (21). The amendment of search agents by PSO and the nature of agents in an investigated area progress towards the most excellent arrangement.
Step 4. The objective utility is derived by commencing the fitness task. The objective function of every agent in the initial state is obtained using the mathematical modeling of CMC. The primary best is set as Gbest.
Objective function = minimum of () + δ (number of switching states), where δ is the normalization factor.
Step 5. To update the states of various particles for every calculation, the objective function values are obtained, as shown in Figure 7.
Step 6. If the terminating criteria were obtained, the procedure terminates.
3.2. Modified Particle Swarm Optimization (MPSO)
To use the historical history of locations and velocities, the arithmetic average is imposed in Gbest and Pbest and velocities renew computations, as shown in figure 6(b). The first three Pbest iterations are calculated and kept in an array for the following iteration. To obtain the novel Pbest value, the arithmetic average is applied to the past iteration and stores the Pbest value. As a result, the same algorithm is used to calculate Gbest and velocity updates [27].
3.3. Modified Hybrid Particle Swarm Optimization (MHPSO)
Applying the MPSO approach resulted in a quick improvement in solution quality [27]. Local search techniques will answer the optimization issue early [28]. MHPSO [29] is a novel optimization approach designed more efficiently by combining the benefits of both local search and PSO techniques. The comparison of various fitness parameters such as the number of particles, computational time, and the number of iterations are presented for the proposed three methods as illustrated in Table 2. As a result, the MHPSO algorithm functions in two stages, as shown in Figure 8.
4. Simulation Results and Discussion
Each of the suggested techniques was implemented on the CMC structure presented in Figure 2. The inertia weight is critical for PSO convergence in recent PSO algorithms. The initial weight controls the effect of past velocity histories on the present particle. Similarly, the particle contains the trade-off surrounding the swarm’s worldwide and regional inspection abilities. An adequate recognition of the inertia weight offers balance among the local and global exploration qualifications, reducing the iterations necessary to get the best output. The highest weight is set at 0.9, while the lowest is set to 0.4.
C1 and C2 are both taken as 2. The available requirements of R1 and R2 are random variables evenly distributed in the range of [0, 1]. Figures 9–14 depict the output voltage and current waveforms of an induction motor load with three suggested methods. Each method’s voltage THD values are 9.02, 8.12, and 7.68, respectively, as shown in Table 3. Figures 15–17 present the fitness parameters of the three algorithms when compared at 100 Hz, 50 Hz, and 5 Hz, respectively. Figure 18 shows the loading of the MC. Figure 19 describes the input voltage and current waveforms for no-load and full-load conditions. Table 4 provides a comparison of the proposed MHPSO for induction motor load with ABC and CPSO [24] for RL load and shows the suggested methods for achieving better fitness values under dynamic load conditions. The input current and voltage waveforms from Figures 9–14 represent the power factor as unity on the input side. For the reasons stated, the program must be as brief as feasible to create a strong switching position for the CMC. The suggested MHPSO has the intrinsic benefit of having a small programmatic code with improved THD and less number of parameters. Table 5 presents various existing methods associated with the projected technique and concludes that the anticipated scheme will reduce the THD to a low value.
(a)
(b)
5. Conclusion
The suggested three soft computing switching generation techniques enhance the CMC system control behavior. The proposed controllers will connect the three reference currents of the system and effectively deliver exhorted outputs at the given frequency. The overall assessment of the methods reveals that MHPSO’s control behavior is better than the other PSO and MPSO strategies. As a result, the output voltage THD is reduced from 21.761% to 7.68%. Although the comparison findings had less harmonic data, the suggested methods were evaluated on the induction motor load, whereas the previous relevant works were done on the RL Load. Future academics can construct sophisticated CMC control systems using various new soft computing technologies.
Abbreviations
| fo: | Load frequency |
| q: | Modulation index |
| : | Input angular frequency |
| Vim: | Peak input voltage |
| Vo (t): | Output voltage |
| Vi (t): | Input voltage |
| Vs (t): | Source voltage |
| Lf: | Filter inductance |
| Rf: | Filter resistance |
| io (t): | Output current |
| W: | Inertia weight factor |
| Cf: | Filter capacitance |
| Is (t): | Input current |
| fs: | Source frequency |
| C1, C2: | Position constants |
| Vom: | Peak output voltage |
| Sit: | Switching state of ith particle |
| LL: | Load inductance |
| RL: | Load resistance |
| Vit: | Velocity of the ith particle |
| R1, R2: | Random values |
| Vit+1: | Updated velocity of the ith particle |
| Gbestit: | Global best particle in swarm |
| bestit: | Individual best particle. |
Data Availability
The data used to support the study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.