Fig. 9.30 shows the nominal power losses, the total volume and the total active mass as functions of f_sw for 2L-VSR with SPWM. Since SPWM with a V_LL,N of 690 V is considered, then the 3.3 kV/1500 A IGBT module should be used (as it can be observed from Fig. 9.23(a)) and f_sw is limited to 2 kHz. In addition, the minimum f_sw is limited to around 700 Hz because of the maximum relative inductor voltage constraint (which requires the maximum inductance value (L_F,max) for the given δiL of 20%).

Fig. 9.30(a) shows how the different components contribute to the total nominal losses. It is observed that the capacitor loss contribution is very low compared with the inductor and switch valves' losses. Also, it can be noted that increasing f_sw beyond around 1.36 kHz will require connecting two modules in parallel per valve and therefore it increases in the valve losses abruptly.

Fig. 9.30(b,c) shows the total volume and active mass, respectively, and the contribution of each component. It can be observed that the inductor represents the main contribution to the total mass and volume in the 2L-VSC with the characteristics indicated in Table 9.7. Also, it is noted that as f_sw increases the required inductance and capacitance value decrease and therefore the inductor/capacitor volume and mass decrease.

The evaluations of η, ρ and γ as functions of f_sw are presented in Fig. 9.31. It can be noted that aiming to maximize η and ρ (or γ) are two conflicting objectives. The maximum η of 97.5% is obtained for converter design with f_sw of 700 Hz, but at the same f_sw the minimum ρ and γ are obtained.

On the other hand, as can be observed from Fig. 9.31, the maximum values of ρ and γ (1.93 MW/m³ and 1.28 MW/t, respectively) are obtained when the maximum f_sw (2 kHz) is considered; however a considerable reduction in nominal η (from 97.5% to 93.7%) is necessary if the converter is switched at 2 kHz.

The influence of the maximum δiL (δiL,max) on the nominal power losses, the total volume and total active mass are illustrated in Fig. 9.32, when an f_sw of 1.25 kHz is kept constant in the converter design. It can be noted from Fig. 9.32 that the variation of δiL,max only has a relevant influence on the AC inductor filter design. The inductor mass and volume decrease as the converter design allows a higher δiL, but the inductor losses increases.

Fig. 9.33 shows the evaluation of the nominal η, ρ and γ as function of δiL,max for f_sw of 1.25 kHz. Similarly to the case of f_sw variation (Fig. 9.31), it can be noted that targeting to maximize η and ρ (or γ) are two conflicting objectives from the point of view of δiL,max restriction. A reduction of 10% on δiL,max restriction (from 20% to 30%) will cause a reduction of 0.75% to η and an increase of 23% and 33% to ρ and γ of the converter, respectively.

Finally, the optimized design of the 1-MW 690-V 2L-VSC with SPWM and operated as rectifier, taking into account different f_sw and δiL, is plotted in Fig. 9.34. The design cases from Fig. 9.31 (δiL=0.2) and Fig. 9.33 (f_sw = 1.25 kHz) are also included in Fig. 9.34. The relationship between η and ρ for the space of solution is presented in Fig. 9.34(a), which also shows the η–ρ Pareto-front for the rectifier mode 2L-VSC (black curve). The ρ–γ Pareto-front and ρ–γ relationship for the space of solution are presented in Fig. 9.34(b).

It is possible to observe from Fig. 9.34(a), how variations on δiL have a notorious impact on ρ, but little influence on η, when f_sw is kept constant. Also, it can be noted from Fig. 9.34(a), how n_p is needed to fulfil thermal constraints and has a significant impact on the η–ρ space of solutions, which is clearly divided according to n_p with the highest efficiencies for the solutions with one module. Additionally, when two IGBT modules are parallel connected, an increase in f_sw has a small impact on ρ but a large influence on η.

On the other hand, an increase in f_sw or δiL,max will improve ρ and γ, as can be observed from Fig. 9.34(b), but it decreases the nominal η of the solution, as it is shown in Fig. 9.34(a). Also, a variation in f_sw has more impact on γ than ρ, as can be noted from Fig. 9.34(b). The ρ–γ Pareto-front (in Fig. 9.34(b)) of the solutions is short compared with the η–ρ Pareto-front (in Fig. 9.34(a)), which shows that ρ and γ are highly correlated.

Figs 9.35 and 9.36 show a comparison of the three modulation strategies (SPWM, SVPWM and SFTM) in terms of η (top), ρ (middle) and γ (bottom), respectively, as functions of f_sw for VSR and VSI. It can be noted that solutions based on SVPWM and SFTM will leave better solutions than those based on SPWM for the range of f_sw considered. Also, SVPWM and SFTM modulations allow 1.7 kV/3600 A IGBT modules to used for a V_LL,N of 690 V, as was analysed from Fig. 9.23(b), and therefore frequencies higher than 2 kHz can be considered.

The SFTM looks to be the best modulation in terms of the three performance indices, as can be noted from Figs 9.35 and 9.36, for VSR and VSI, respectively. Comparing Figs 9.35 and 9.36, it can be noted that VSI can achieve higher values for each performance indice than VSR. However, it should be noted that this conclusion is limited to the system parameters and design constraints considered (Table 9.7).

As noted previously for the SPWM, an increase in f_sw will improve ρ and γ of the converter with a reduction of the nominal η. However it can be noted, from Figs 9.35 and 9.36, that there is an optimal f_sw beyond which ρ or γ will decrease. In the case of VSR with SFTM, the maximum ρ (3.55 MW/m³) and γ (2.62 MW/t) are obtained for the same f_sw of 3.79 kHz. In the case of VSI with SFTM, the maximum ρ (3.76 MW/m³) is obtained for f_sw = 3.79 kHz, but the maximum γ (2.77 MW/t) is obtained for the maximum possible f_sw (4 kHz), which indicates that the IGBT technology limits the maximum γ.

Fig. 9.37 shows the influence of the modulation method on the η–ρ Pareto-front for VSR (Fig. 9.37(a)) and VSI (Fig. 9.37(b)). It is clear that SFTM will give the best trade-off between η and ρ, and only comparable solutions are obtained with SVPWM for small values of f_sw, which imply low ρ.

The ρ–γ Pareto-front of 2L-VSC with the three modulation strategies is shown in Fig 9.38(a,b) for VSR and VSI, respectively. Again, SFTM presents the best trade-off between ρ and γ, where the Pareto-front is obtained for the solution with the highest switching frequencies.

Finally, an optimized design of a 2L-VSR is done for different converter nominal power and the parameters and constraint presented in Table 9.7. It is assumed that 2L-VSR is interfacing a wind power generator with an equivalent generator inductance per phase of 1e-4 = 10⁻⁴ = 0.0001 in per unit, which is assumed to be the same value for all the nominal power. This low inductance value has been chosen in order to acquire higher inductance values in the input filter and therefore see how the performance indices are affected when the switching frequency is changed.

Fig. 9.40 shows the results of the optimized selection of f_sw as a function of P_N when SVPWM is selected for 2L-VSR. Fig. 9.40(a) shows the selecting of f_sw based on four criteria to maximize η, ρ, γ or Λ. Fig. 9.40(b) presents the number of IGBT modules in parallel connection needed when f_sw is selected to maximize Λ.

The nominal η, ρ and γ, as functions of the nominal power, are shown in Fig 9.40(c,d,e), respectively. Each of these figures includes the maximum possible value (by selection of the corresponding f_sw in Fig. 9.40(a)) and the value obtained when f_sw is selected to maximize Λ.

The results of the optimized selection of f_sw as function of P_N when SFTM is selected for 2L-VSR are shown in Fig. 9.41. Since SFTM is more efficient than SVPWM for the given power factor (0.85), then higher f_sw can be used for SFTM and therefore higher ρ and γ are obtained with the same nominal η.