The design of the filter inductor and the capacitors is described in detail in this section. Additionally, all stressors related to device voltage and current have been thoroughly examined. We have covered the ins and outs of thermal modeling as well as loss analysis for the diodes and switches. The capacitor's design limits the maximum voltage ripple to 10% of its rated value [4].
A. DETERMINATION OF CAPACITOR FOR THE PROPOSED SCMLI.
The capacitance value of the proposed inverter is engineered to provide various voltage levels I output while maintaining an acceptable ripple. The boosted voltage steps in positive and negative cycles are controlled by capacitors C1 and C2, whose capacitance value is mainly influenced by two factors: 1) the time it takes to charge or discharge, and 2) the maximum permissible voltage ripple across them.
1) C1 design
The ripple on capacitor C1 is greatest in zones I and VIII. Reason for the highest level of ripple in zone IV. In zone IV, the highest ripple occurs because capacitor C1 charges capacitor C2 to 0.5Vdc using its maximum energy. Zone I should not be used to drain energy from capacitor C1, as zone IV has already charged capacitor C2. Therefore, just the Longest Discharge cycle (LDC) in zone V is used to determine C1.
The following is the voltage ripple of capacitor C1:-
$$\:\varDelta\:{V}_{c1}=\:\frac{1}{{C}_{1}}{\int\:}_{0}^{\raisebox{1ex}{$\theta\:1$}\!\left/\:\!\raisebox{-1ex}{${\omega\:}_{0}$}\right.}{i}_{c1}\left(t\right)dt$$
1
C1 \(\:\ge\:\frac{{I}_{c1avg}\:x\:\left(\theta\:1\right)}{\varDelta\:{V}_{c1}\left(\omega\:0\right)}\) (2)
Where, \(\:{\theta\:}_{1}={\text{sin}}^{-1}\frac{{A}_{c}}{{A}_{m}}\)
The lowest value of capacitor C1, which is 4000µF, may be obtained from Eq. (2) by plugging in IC1 and the average value from the Simulink results. This was done for ∆V_c1 = 5V. However, in both modeling and experiment, voltage steps have been produced with the enhanced value of 4700 µF. As illustrated in Fig. 3, the voltage ripple that has been measured is 4.1V and 6V, respectively.
2) C2 design
Maximum discharge of capacitor C2¬ occurs in zone IV. 10% is the foundation value for voltage ripple ∆V_c2 in the design of C2.
For zone IV from Fig. 3,
$$\:\varDelta\:{V}_{c2}=\:\frac{1}{{C}_{2}}{\int\:}_{\raisebox{1ex}{${\theta\:}_{2}$}\!\left/\:\!\raisebox{-1ex}{${\omega\:}_{0}$}\right.}^{\raisebox{1ex}{$\theta\:3$}\!\left/\:\!\raisebox{-1ex}{${\omega\:}_{0}$}\right.}{i}_{c2}\left(t\right)dt$$
3
C2 \(\:\ge\:\frac{{I}_{c2avg}\:x\:(\theta\:3-\theta\:2)}{\varDelta\:{V}_{c2}\left(\omega\:0\right)}\) (4)
Where \(\:{\theta\:}_{2}={\text{sin}}^{-1}\frac{2{A}_{c}}{{A}_{m}}\:and\:{\theta\:}_{3}={\text{sin}}^{-1}\frac{3{A}_{c}}{{A}_{m}}\:\)
By plugging in IC2 and the average value from the Simulink findings, we can find the lowest value of C2 from (4), which is 4000 µF, given that ∆V_c2 = 10V. The experiment and simulation utilized the greater value of 4700 µF to generate the voltage steps. Additional evidence of a 9.3V and 10V voltage ripple can be found in Fig. 3.
B. Total Standing Voltage Calculation.
If you want to know how efficient and cost-effective MLI converters are, you need to know the total standing voltage (TSV). Switches with lower ratings and less stress across them might make inverters more cost-effective. It is TSV's job to grade and categorize semiconductor electronics. Among them are diodes and integrated gate bipolar transistors (IGBTs). The standing voltage is the highest potential applied voltage across an off-state semiconductor switch. The MSVs of all the switches are added together to get the total standing voltage (TSV). It is possible to get a ballpark estimate of the total standing voltage by using the current switch states. If the output voltage law is unaffected by the MSV of this particular loop, we can declare switch S1 to be off. Consequently, the above configuration shows the maximum standing voltage across each semiconductor switch.
MVS1 = MVS2 = Vdc (5)
MVS3 = MVS4 = MVS5 = MVS6 = 2Vdc (6)
MVS7 = MVS8 = Vdc / 2 (7)
According to the suggested inverter structure, the inverter's total standing voltage is equal to the maximum standing voltage across all of the switches. As a result, the TSV value corresponds to the standard nine-level topology.
TSVproposed module = \(\:\sum\:_{i=1}^{8}{MVS}_{i}\) = 11Vdc, (8)
The following is the proposed MLI's total standing voltage (TSV) as a percentage of the maximum output voltage (TSVp.u):
TSVp.u = \(\:\frac{TSV}{{V}_{0},\:max}\) (9)
Where TSVp.u is 5.5.
As a percentage, the voltage stress distribution across each switch can be determined by dividing the total converter standing voltage by the maximum static voltage (MSV) across all of the switches. At 2Vdc, the greatest voltage stress that switches S7 and S8 undergo representing 25% of the entire voltage stress—is 50%. While all six switches were subjected to the full voltage stress, switches S1, S2, S3, S4, and S6 were only subjected to half of it. Figure 3 shows the prevalence of voltage stress as well as the percentage of stress that each switch has encountered. Because they share the voltage stress effectively, the inverter is able to use more switches and low-TSV dc sources.
There is a distinct distribution of the total supply voltage (TSV) across the inverter switches. There is a 100% voltage stress on half of the inverter's switches. Concurrently, topologies grow in size and cost due to the requirement for high-rated switches and the fact that 25% of switches undergo minimum voltage stress [15]. The inverter is both simple and inexpensive because it uses switches with varying ratings.
C. COST FUNCTION
In order to determine the appropriate applicable MLI, several factors are considered when calculating the cost function (CF). These factors include the total standing voltage (TSV), the number of switches (Ns), the driver (NGd), the capacitor (Nc), the main and auxiliary diodes (ND and NAD), and the number of switches. The following is the formula for calculating the CF of an inverter:
CF = (Ns + NGd + NDc + Nc + β*TSV) (10)
The total standing voltage is given more weight than the component count when β is used as the weighting factor. The inverter's structural qualities are improved by a low value of CF. The CF per level is the metric that is utilized for comparison. Accordingly, the cost function is computed at β = 0.5 and 1.5.
CF (β = 0.5) = 25.5, CF/level = 2.83 (11)
CF (β = 1.5) = 36.5, CF/level = 4.05 (12)
D. Loss Analysis
When adding together the power losses in all of the semiconductor devices in the dc-ac converter, we get the total loss[16]. The suggested inverter experiences power loss due to switching and conduction losses.
i) Switching Loss
Whenever a switch goes from being on to off, or back again, it loses some of its power. For a given switch, the overlapping waveforms of current and voltage are considered during the changeover. One way to calculate the overall switching loss of all n system modules is to
Psw,N = \(\:\frac{1}{2}\sum\:_{N=1}^{4N+6}\left[{V}_{0}{I}_{0}\right({t}_{on}+{t}_{off}\left){f}_{sw}\right]\) (13)
The voltage stress across the semiconductor switch (V0), the current flowing through it (I0), and the timings ton and toff, which represent the on and off states of the switch, are equal. Here, fsw is the switching frequency.
ii) Conduction Loss
For one-way operation, the proposed design makes use of switches that are integrated gate bipolar transistors (IGBTs) with antiparallel diodes. In an MLI switch, the total loss of conduction power is the sum of the losses of the integrated gate bipolar transistor (IGBT) and the diode. It is possible to determine the IGBT and diode's conduction loss via
Pon, IGBT = Von, IGBT I(t) + RIGBT Iα+1(t), (14)
Pon, Diode = Von, Diode I(t) + RDiode I2(t) (15)
In the conduction period (on state), the voltage across the IGBT is denoted as Von, IGBT, while the voltage across the diode is denoted as Von, Diode. The characteristic of an IGBT, where A is a constant, defines the sinusoidal current I(t) that flows through a switch with a maximum current of Im. Just so we're clear, (Non, IGBT) represents the number of IGBTs and (Non, diode) represents the number of diodes. Accordingly, the suggested topology's average conduction power loss (Pc,avg) is
Pc, avg = \(\:\frac{1}{\pi\:}\int\:{(N}_{on,IGBT}{P}_{on,IGBT})+\left({N}_{on,diode}{P}_{on,diode}\right)dwt\) (16)
All of the module failures By adding the two losses from equations 13 and 16, we get the total losses, or plosses.
Plosses = Psw + Pc, avg. (17)
The process of determining switch loss using the PLECS program is illustrated in Fig. 4. Calculation of the losses in the proposed module is done in the PLECS-based simulation model. A switch thermal module characteristic (IKY50N120CH3) is used to conduct the analysis. A good approximation of the suggested module converters' efficient distribution has been derived using datasheets supplied by power semiconductor manufacturers. The suggested module's power loss study is conducted on an input power of 1 kW with an RL load. Figure 4 shows the distribution of losses and the consequence of each switch's particular loss.
(A) (B)
Figure 5 (A) Dispersion of Losses Among Switches (B) Total loss of inverter.
An efficiency of 97.6% is achieved with power semiconductor switches, with a total loss of 23.5W for a resistive inductive load. The distribution of the inverter's total conduction and switching losses is shown in Fig. 5(B). We find that switching losses account for only 6% of total losses, which is significantly lower than conduction losses, which account for 94% of inverter losses.