A modified cascaded h-bridge multilevel inverter based on particle swarm optimisation (PSO) technique

Received Jan 23, 2019 Revised Apr 25, 2019 Accepted May 16, 2019 In this paper, modified multilevel inverter, via addition of an auxiliary bidirectional switch, based on Newton Raphson (NR) and Particle Swarm Optimization (PSO) techniques is presented. The NR and PSO techniques were employed for selective harmonics elimination (SHE) solution in a modified Cascaded H Bridge Multilevel inverter (CHB-MLI). The Selective Harmonic Elimination Pulse-Width Modulation (SHE-PWM) is a powerful technique for harmonic minimization in multilevel inverter. The NR and PSO techniques were used to determine the switching angles by solving the nonlinear equations of the output voltage waveform of the modified CHB-MLI in order to control the fundamental component and eliminate some low order harmonics. The proposed NR and PSO techniques are capable to minimize the Total Harmonic Distortion (THD) of the output voltage of the modified inverter within allowable limits. This paper aims to modeling and simulation by MATLAB of the modified topology of the CHB-MLI for a single-phase prototype for 13-levels. The inverter offers less THD and greater efficiency using PSO control algorithm compared with the NR algorithm. The performance of the proposed controllers based on NR and PSO techniques is verified through simulation.


INTRODUCTION
Multilevel power conversion was first introduced 25 years ago [1]. The general concept involves utilizing a higher number of active semiconductor switches to perform the power conversion in small voltage steps. There are several advantages to this approach when compared with traditional two-level power conversion. The smaller voltage steps lead to the production of higher power quality waveforms and also reduce the dv/dt stresses on the load and the electromagnetic compatibility concerns. Another important feature of multilevel converters is that the semiconductors are wired in a series-type connection, which allows operation at higher voltages. However, the series connection is typically made with clamping diodes, which eliminate over voltage concerns. Furthermore, since the switches are not truly series connected, their switching can be staggered, which reduces the switching frequency and thus the switching losses [2,3]. The harmonic elimination techniques are utilized in multilevel inverters in order to lower harmonic content for improving the output waveform of the voltage inverter, reduce the size of the filter utilized and the level of electromagnetic interference (EMI). Numerous topologies can be used to realize those advantages and can generally be divided into three major categories, namely, diode clamped multilevel inverter DC-MLI, flying capacitor multilevel inverter FC-MLI and separated DC sources cascaded H-bridge CHB-MLI. The type of the MLI which uses a single DC source rather than multiple sources is called the diode-clamped MLI. While, the FC type is designed by series connection of capacitor clamped switching cells. The CHB switches are connected in parallel and series in order to provide high power demand and high-power quality [4][5][6][7][8][9][10], [11,12] Reduced number of switches with installation area and cost as well as simplicity of control system, with a high number of steps associated using a new topology of cascaded multilevel inverter (CHB-MLI) has been presented in [13]. A new topology for current source multilevel inverter (CSI) with reduced number of switches to generate desired output current based on sinusoidal pulse width modulation (SPWM) method has been presented in [14]. This topology employs (n+7)/2 switches and (n−1)/2 current-sharing inductors for an n-level CSI.A 5-level single-phase inverter has been developed by field-programmable gate array (FPGA) by [15]. The digital control technique is generated based on multi carrier PWM in Altera DE2 board, which has many features that implement the system design the simulation and experimental results have been consistent. A seven-level inverter has been simulated by [16] via implementation of PWM techniques to reduce total harmonic distortion (THD). This inverter is implemented on the principle of reducing numbers of switches, thus decreasing number of gate drivers in the circuit. The simulation circuitry basically incorporates DC supply and smaller (CHB-MLI) blocks connected in series to implement its desired stepped output waveform.
In this paper, a modified CHB-MLI based on auxiliary bidirectional switch controlled using NR and PSO techniques for optimisation of the output with 13-levels is implemented based on MATLAB Simulink. Most of the researchers had applied the PSO technique to the single phase conventional CHB-MLIs. The NR and PSO techniques are used to calculate switching angles with the capability to eliminate harmonics in the output of the modified CHB-MLIs. Finally, in this paper, is evaluated and validated through simulation results.

SWITCHING OPERATION MODES OF MODIFIED CHB-MLIS FOR 13-LEVELS
The switching mode operation of the proposed single-phase modified CHB-MLI for 13-levels can be illustrated in Figure 1. As previously mentioned, the proposed topology adopts a full-bridge configuration with an auxiliary circuit comprising four diodes and a switch which generates half-level DC bus voltage. Figure 2 shows the timing diagram or switching pattern for all switches employed in the modified CHB-MLI. The output voltages of the modified CHBMLI for 13 levels can be summarized as described in Table 1. The present work presents a 13-level PWM inverter with output voltages Vdc, Vdc/2, Vdc/3, Vdc/4, 0, -Vdc/4, -Vdc/3, -Vdc/2 and -Vdc. Surely that increasing the number of output levels of an inverter would reduce its harmonic content.  Voltage State S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 Vo

ANALYSIS OF THE PROPOSED TOPOLOGIES OF THE MODIFIED CHB-MLI FOR 13-LEVELS
A. Fourier Series for the Output Voltage of the Proposed Modified CHB-MLI for 13-Level: The equations for 13-levels based on the Fourier series are described below [20]: where: : Voltage of each voltage source that was in unity : Switching angles i =1,2…6.
From (1), six equations were resulted, one for controlling the fundamental component 1 st and others for eliminating the 3 th , 5 th , 7 th , 9 th and 11 th harmonics.
where m = V1/(2Vdc/ ), and it is related to the modulation index mi by mi = m/s, where 0 < mi <1. An objective function is then needed for the optimisation procedure selected as a measure of effectiveness of eliminating selected order of harmonics while maintaining the fundamental component at a pre-specified value. Therefore, this function is defined as: The optimal switching angles are obtained by minimising (4) subjected to the constraint 0 <θ 1 <θ 2 <θ 3 <θ 4 _ … <θ s < /2, and consequently the required harmonic profile is achieved. The main challenge is the non-linearity of the transcendental set of (4), as most iterative techniques can be used with five and 13levels of the modified CHB-MLI as shown in Figure 3 and each step is explained, General flowchart of the PSO of the modified CHB-MLI as shown in Figure 4.

NR Technique
The values of the switching angles 1, 2, 3 , 4, 5, and 6 can be chosen by solving the transcendental equations using a modulation index formula (5) to obtain the suitable.
Where, mi is the modulation index For the angles θ 7 until θ 24 can be obtained by referring the output waveform of 13-levels of the modified CHB-MLIs theory in Figure 5. The procedure of detecting attributes and configuration of a system is called optimisation. For a 13-level single phase inverter, only five harmonics can be eliminated which are the 3 rd , 5 th , 7 th , 9 th , and 11 th harmonics. Thus, the switching angles can be found by solving the transcendental equations by using NR technique. These switching angles are then examined for their corresponding THD given by: The effect of optimised angles for 13-levels are 1 , 2 , 3 , 4 , 5 , 6, on the THD and the modulation index. By using MATLAB coding for number of iterations, it can be easily find that the modulation index is equal to 0.949 and the corresponding THD value of output voltage with 13-levels is equal to 6.18 %.

Yes
Calculate Objective Function using Eq.

No
Update the Velocity and Position by using Eq. .

PSO Technique
PSO has become a very popular technique in solving non-linear optimization problems. Among many types of evolutionary algorithms, particle swarm is preferred primarily because of its computational efficiency, simplicity and ability to avoid local optima. The PSO has the following key advantages over other evolutionary optimization techniques [17][18][19][20]. The PSO algorithm is required to solve nonlinear equations based on SHE algorithm for solving the transcendental equations in order to optimize best switching angles. The number of iteration in the algorithm is solved using MATLAB coding to get better angles for eliminating specific unwanted harmonics. The iteration PSO algorithm can be described by the following steps: Step 1: Initialise the system parameters such as velocity vector Vi, location vector Xi, personal best particle vector Pi, particle inertia weight C0, and global best vector Pg. Assign the values of generations as 100, population size as 40, cognitive parameter C1 as 0.5 and social parameter C2 as 1.25.
Step 2: Check for the case 0 < (C1 + C2) < 2 and (C1 + C2)/ 2 < C0 < 1, if the two cases are satisfied then the system will be guaranteed to converge to a stable equilibrium point. If false, go to Step 1.
Xij (t+1) = Xij (t) + Vij (t+1) (8) where i is the particle index, j is the index of parameter of concern to be optimized, x is the position of the ith particle and jth parameter, k is the discrete time index, V is the velocity of the ith particle and jth parameter, P is the best position found by the ith particle and jth parameter (personal best), G is the best position found by swarm (global best), C is a random uniform number between [0,1] applied to the ith particle.
Step 7: Check for the case P(xi) < P(Pi), if i = i + 1 not satisfied then execute to Step 3.
Step 8: If the produced location of the particle is the best then update by change with the previous location as Pi =Xi.
Step 9: Update the global best location as Pg = min (P neighbor).
Step10: Switching angles are optimized as the best. Accomplish the solution of the problem. The general flowchart of the PSO of the modified CHB-MLI is shown in Figure 5.

MODELLING OF THE PROPOSED MODIFIED CHB-MLI
MATLAB/SIMULINK software was used to model the proposed topologies of the modified CHB-MLI for 13, levels. Figure 6 shows the circuit diagram of the proposed single-phase modified CHB-MLI for 13-levels. The configuration of this model consists of conventional inverter with 12 switches in addition to a 3-bi-directional switch. This paper aims to develop a PSO algorithm based on the SHE technique for getting the best firing angles for harmonics elimination and compare it with the conventional NR algorithm. The system operation was simulated at low switching frequency. In this simulation, the model, has three DC supply of 300V each. Generator pulse block is used to procedure the switching pattern for generating switching pulses necessary to control the switches of the MLI based on the NR and PSO algorithms. A resistor of 100kΩ will be used as a load to the proposed inverter model. The maximum output phase voltage of the modified CHB-MLI is 900 volts with frequency of 50Hz. The series connected DC bus capacitors C1 and C2 ere 2500e-6F, which split the DC bus voltage for each cell into: VDC/2, 0, -VDC/2. The middle point n of the capacitors is defined as the neutral point.

SIMULATION RESULTS OF MODIFIED CHB-MLI FOR 13-LEVELS WITH mi=0.81 USING NR AND PSO ALGORITHMS
In order to obtain the optimization of the output of the single-phase modified CHB-MLI with 13-levels, the switching angles based on the NR and PSO algorithms were calculated. Based on the simulation model, Figure 7, Figure 8 and Figure 9 show the timing diagram of the switches in the single-phase modified CHB-MLI of 13-levels. There are 3 cells available in the configuration of the proposed inverter shown in the methodology of Figure 6.
Each cell comprises five switches, including bi-directional switch, namely e.g. for the first cell has the switches S1, S2, S3, and S4 and the bi-directional switch S5. From these figures, it is noted that the 15 switches have equal switching periods using a switching frequency of 2500 Hz. The switching angles of the inverter were  The obtained timing diagram for the optimization of output voltage waveform of the single-phase 13level modified CHB-MLI using the NR technique has been produced as shown in Figure Error! No text of specified style in document. 10. In order to eliminate the specific order harmonics of the inverter output, the SHE technique of the fundamental switching frequency scheme is used. In this paper, the single-phase modified CHB-MLI with equal DC sources based on the super capacitors [18,19] is utilized. The output voltage harmonic spectra of the single-phase modified CHB-MLI using the NR were obtained through simulation as shown in Figure  Error

EFFICIENCY OF THE MODIFIED CHB-MLI
Actually, the efficiency of the inverter simply can be defined as the process of converting the DC power into an AC power during the conversion of the power in the system, and there are power losses available, these losses would change as a heat, making the inverter heated, and causing reduction in its operational life time. The drop in the inverter output power controlled with both algorithms NR and PSO will cause its efficiency to be reduced as shown in Figure Error! No text of specified style in document.18, but the efficiency performance of the inverter under the PSO controller is better than the NR one due to effect of the optimization. The DC input power doesn't convert completely into AC output power; part of which is converted into losses. These losses are produced depending on the materials nature of inverter switches as well as the harmonic content, THD of its output. This makes inverter under the PSO control is better than the NR control. Figure 18. Efficiency of the 13-level modified CHB-MLI for versus technique PSO and NR

CONCLUSIONS
The simulation results showed that the higher level of the modified inverter will produce lower harmonics content in its output voltage waveform using the both NR and PSO techniques. However, the PSO technique produce lower content of harmonics (THD) compared to NR technique due to switching angles of the PSO technique is more accurate and thus, more efficient in eliminating lower order harmonics. Its proved that the proposed PSO technique produced the best switching angles. Voltage harmonics within an electrical power system