*6.3. ISIP-OSOP DC-DC Converter SSM Verification*

In this section, the generalized multimodule DC-DC converter SSM is verified using three different models presented in [38–42].

## 6.3.1. Generalized Model Verification with a Two-Module IPOS DC-DC Converter

The proposed configuration in [38] consists of two modules that are connected in parallel at the input side, and series, at the output side, where the modules are FB-PS-based DC-DC converters. In this model, the effect of the ESR *Rc* is ignored, accordingly, when verifying the model presented in [34] with the generalized model, *Rc* should be equated to zero.

By ensuring ICS and OVS, the input current per module is *Iin* <sup>2</sup> . However, the input voltage per module is *Vin*. Regarding the output side, the output voltage per module is *Vo* <sup>2</sup> . However, the output current per module is *Io*. In which, *Vin* is the IPOS input voltage, *Iin* is the IPOS input current, *Vo* is the IPOS output voltage, and *Io* is the IPOS output current. Accordingly, the values for the six parameters that are previously defined are known and shown in Table 2.

**Table 2.** Values for the six parameters for a two-module Input-Parallel Output-Series (IPOS) power converter.


Substituting the six parameters with their values in Equations (109), (112), (117), and (120) and substituting the ESR *Rc* with zero in the generalized transfer functions would result in the transfer functions presented in Table 3.


**Table 3.** Generalized model verification with the two-module IPOS power converter.

As can be seen from Table 3, the derived generalized model matches the model presented in [38], where the *Rd* term in the above transfer functions is substituted with its equivalence <sup>4</sup> *Llk fs <sup>K</sup>*<sup>2</sup> .

6.3.2. Generalized Model Verification with a Three-Module ISOP DC-DC Converter

In this Section, the generalized model is validated with the three-module ISOP power converter model-derived and presented in [39,40]. The three-module ISOP configuration consists of three modules that are connected in series at the input side, and parallel at the output side. In this model, the effect of the ESR *Rc* is considered, accordingly, when verifying the model presented [39] with the generalized model, *Rc* should not be ignored.

By ensuring IVS and OCS, the input voltage per module is *Vin* <sup>3</sup> . However, the input current per module is *Iin*. Regarding the output side, the output current per module is *Io* <sup>3</sup> . However, the output voltage per module is *Vo*. Accordingly, the values for the six parameters that are previously defined are known and shown Table 4.

**Table 4.** Values for the six parameters for a three-module Input-Series Output-Parallel (ISOP) power converter.


Substituting the six parameters with their values in Equations (109), (112), (117), and (120) would result in the transfer functions presented in Table 5.


**Table 5.** Generalized model verification with the three-module ISOP power converter.

As can be seen from Table 5, the derived generalized model matches the model presented in [39,40].

6.3.3. Generalized Model Verification with a Four-Module ISIPOS DC-DC Converter

In this section, the generalized model is validated with the four-module ISIPOS power converter model presented in [41,42].

The four-module ISIPOS configuration consists of four modules that are connected in series and parallel at the input side, and series at the output side. In this model, the effect of the ESR *Rc* is ignored, accordingly, when verifying the model presented in [41] with the generalized model, *Rc* should be equated to zero.

By ensuring IVS, ICS, and OVS, the input voltage per module is *Vin* <sup>2</sup> and the input current per module is *Iin* <sup>2</sup> . Regarding the output side, the output voltage per module is *Vo* <sup>4</sup> . However, the output current per module is *Io*. Accordingly, the values for the six parameters that are previously defined are known and shown in Table 6.

**Table 6.** Values for the six parameters for a four-module Input-Series Input-Parallel Output-Series (ISIPOS) power converter.


Substituting the six parameters with their values in Equations (109), (112), (117), and (120) would result in the transfer functions presented in Table 7.


**Table 7.** Generalized model verification with the four-module ISIPOS power converter.

As can be seen from Table 7, the derived generalized model matches the model presented in [41,42].
