*Article* **Modeling and Performance Assessment of the Split-Pi Used as a Storage Converter in All the Possible DC Microgrid Scenarios. Part I: Theoretical Analysis**

**Massimiliano Luna 1, Antonino Sferlazza 2,\*, Angelo Accetta 1, Maria Carmela Di Piazza 1, Giuseppe La Tona <sup>1</sup> and Marcello Pucci <sup>1</sup>**


**Abstract:** The integration of an electrical storage system (ESS) into a DC microgrid using a bidirectional DC/DC converter provides substantial benefits but requires careful design. Among such converter topologies, the Split-pi converter presents several merits at the cost of non-isolated operation. However, the few works in the literature on the Split-pi presented only closed-loop control with a single control loop; furthermore, they neglected the reactive components' parasitic resistances and did not perform any experimental validation. This work aimed at investigating the use of the Split-pi converter as a power interface between an ESS and a DC microgrid. Five typical microgrid scenarios are presented, where each of which requires a specific state-space model and a suitable control scheme for the converter to obtain high performance. In this study, two different state-space models of the converter that consider the parasitic elements are presented, the control schemes are discussed, and criteria for designing the controllers are also given. Several simulations, as well as experimental tests on a prototype realized in the lab, were performed to validate the study. Both the simulation and experimental results will be presented in part II of this work. The proposed approach has general validity and can also be followed when other bidirectional DC/DC converter topologies are employed to interface an ESS with a DC microgrid.

**Keywords:** Split-pi; bidirectional converter; electrical storage system; DC microgrid; droop control; current control; feed-forward control

#### **1. Introduction**

Over the last few years, DC distribution in terrestrial and marine power systems has attracted a growing interest in view of the implementation of the smart microgrid paradigm due to its advantages in terms of simpler and more efficient electrical architectures. Consequently, power electronic converters that interface distributed generation units, loads, and above all, electrical storage systems (ESSs) with a common DC bus are the subject of renewed interest [1–3]. ESSs have manifold beneficial impacts on DC microgrids: they allow for improving stability and resiliency, compensate for the intermittency of renewable generation, provide ramping support to generators, and act as backup power sources. Furthermore, ESSs ensure a power buffer that can be leveraged to apply suitable energy management strategies to microgrids. In particular, energy management systems (EMSs) can be used to compute the optimal values of power flows among the microgrid devices, which allow for pursuing chosen objectives, such as a minimum electricity bill, maximum efficiency, minimum fuel consumption, or minimum greenhouse gas emissions [1,4–6].

Depending on the designer's choice, the microgrid voltage can be controlled either stiffly using a single voltage generator or in a droop scheme using one or more voltage

**Citation:** Luna, M.; Sferlazza, A.; Accetta, A.; Di Piazza, M.C.; La Tona, G.; Pucci, M. Modeling and Performance Assessment of the Split-Pi Used as a Storage Converter in All the Possible DC Microgrid Scenarios. Part I: Theoretical Analysis. *Energies* **2021**, *14*, 4902. https://doi.org/10.3390/en14 164902

Academic Editor: Mohamed Benbouzid

Received: 12 July 2021 Accepted: 7 August 2021 Published: 11 August 2021

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generators with a predefined power-sharing ratio, usually in proportion to their power rating (grid-forming generators). When an EMS is used, the other active devices of the microgrid must be controlled as current generators based on the optimal power flows that are computed by the EMS [1,5]. Therefore, depending on the specific configuration, the converter interfacing the ESS with the microgrid must be operated as a stiff voltage generator, a non-stiff voltage generator, or a current generator.

The scientific literature provides several contributions on bidirectional DC/DC converters (BDCs). Reference [7] presented an overview of BDCs, where, besides the review of both non-isolated and isolated configurations, the most relevant control schemes and switching strategies were analyzed. In some applications, galvanic isolation between the input and output side of the converter is required; in such cases, the most frequent choice is the dual active bridge converter (DAB) due to its many advantages [7–9]. However, isolation is mandatory only when very high voltage gain is needed. Non-isolated converters are thus more attractive when the goal is to improve the efficiency, size, weight, and cost of the system [7,10]. A review of non-isolated BDCs topologies was presented in [10]. The advantages and disadvantages of the considered converters were properly highlighted. For example, some converters provide an output voltage with opposite polarity than the input, some draw discontinuous current from the battery, while others require a tapped inductor or exhibit weak regulation capability or a high switch count. Overall, Tytelmaier et al. identified the half-bridge converter (HBC) and the related interleaving variants with coupled inductors as the most promising solutions from the efficiency and robustness standpoints [10]. Furthermore, Odo compared three non-isolated BDC topologies with the classical HBC in terms of their suitability for energy storage in a DC microgrid and identified the cascaded buck-boost HBC topology as the best compromise [11].

An interesting alternative is offered by the Split-pi converter, which is a non-isolated BDC that is based on two cascaded HBCs with a common bulk capacitor instead of a common inductor. As such, it is the dual topology of the cascaded buck-boost HBC that was analyzed in [7,10,11]. The Split-pi was initially developed for electric vehicles and patented in 2004 [12], and it is receiving increasing attention due to its distinct advantages [13–20]. It exhibits high efficiency, like the DAB, but with a reduced switch count (eight vs. four switches, of which, only two are actively commutated). Furthermore, LC filters at both ports of the Split-pi allow for small reactive components and reduce the switching noise. On the other hand, the additional phase delay introduced by such filters can slightly complicate this converter's control with respect to simpler converters [17,18]. Nonetheless, the control of the Split-pi is less complicated than that of the DAB because it requires conventional duty cycle control of the pulse width modulator (PWM) instead of phase shift control. An additional advantage of the Split-pi is its suitability for multiphase systems, where a significant reduction in component size and cost can be attained. These features make it attractive when high power density is required, such as in hybrid electric vehicles, renewable energy systems, and aerospace/marine/military applications [16,17].

Only three papers in the technical literature proposed applications in which the Splitpi converter was not controlled using an open-loop [16,17,19]. The aim of [17] was to study a system in which the Split-pi interfaced a flywheel with a 12 V, 120 W DC bus connecting a photovoltaic generator with a passive load. However, in the related control scheme, only one control loop was active at a time (either for the output voltage or the input current) using a shared controller, and the choice was made using a rule-based approach. Singhai et al. did not focus on a specific application and presented a state-space model of the Split-pi converter and a transfer function to design a closed-loop controller for its output voltage [16]. However, they considered the converter connected to a passive load and neglected the parasitic resistances. Finally, Monteiro et al. considered a Split-pi converter with a multilevel structure and controlled current or voltage in any of the two ports in an open-loop, whereas the common DC-link voltage was controlled in a closed-loop [19]. Only a few details about the control systems were given because the study mainly focused on comparing the multilevel Split-pi topology and the interleaved topology of [20].

Apart from [17], all these works only presented simulation results without experimental validation. Furthermore, they all studied closed-loop control with a single control loop, neglecting the reactive components' parasitic resistances. However, when the converter is used to interface an ESS with an active load, such as a DC microgrid, it is essential to control both the ESS current and the output voltage/current of the converter, as required by the microgrid designer. Furthermore, the parasitic elements cannot be neglected because they affect the losses and the maximum gain attainable using the converter.

To cover these aspects, in this work, the use of the Split-pi converter in such an application was investigated with particular attention to its model, the design of its control system, and the assessment of the expected performance in all the possible microgrid configurations. In this first part of the work, it was shown that the Split-pi must be modeled in two different ways depending on the microgrid scenario and that control schemes involving a different number of control loops are needed. In the case of the output voltage control, a feed-forward action was also required to obtain high performance. Furthermore, it was shown that conventional PI regulators alone were not sufficient to obtain the desired performance for output current control in stiff microgrids. The two statespace models considering the parasitic elements and the transfer functions of interest were given in the study, together with criteria to design the controllers. The chosen case study was a DC microgrid that was representative of both terrestrial and marine applications. In Part II of the work, a comprehensive performance assessment is presented based on simulations and experimental tests that validate the study. Finally, the proposed approach has general validity and can also be followed when other BDC topologies are used to interface a storage system with a DC microgrid.

#### **2. Topology, Operation Modes, and Sizing of the Split-Pi Converter**

The schematic of a symmetrical Split-pi converter is sketched in Figure 1, including its reactive components' parasitic resistances. Such a converter can be viewed as the cascaded connection of a first HBC at port 1, a bulk capacitor, and another HBC at port 2. Since the two HBCs are bidirectional, the whole Split-pi converter is also a BDC. If the two HBCs have equal reactive components, the Split-pi is said to be symmetrical.

**Figure 1.** Schematic of the symmetrical Split-pi converter.

The four switches (S1–S4) were sketched in Figure 1 as ideal switches. In the original formulation of [12], they were implemented using MOSFETs to exploit the advantage of synchronous rectification. According to [12], the Split-pi has four operation modes, depending on the relationship between *V*<sup>1</sup> and *V*<sup>2</sup> and on the power direction, as summarized in the first four rows of Table 1, which is an extension of the table reported in [18]. In this work, the Split-pi converter was used to interface a storage system (connected to port 1) with a DC microgrid (connected to port 2). It is worth noting that, whenever possible, the storage system is chosen so that *V*<sup>1</sup> ≤ *V*<sup>2</sup> for both technical and safety reasons. Hence, the present work considered the Split-pi converter operating in modes 1 and 2.


**Table 1.** Summary of the operating modes of the Split-pi converter.

The Split-pi components can be sized according to the classical formulas used for buck and boost converters [17,21]. Specifically, the minimum inductance value is expressed by (1) for both boost and buck operations; on the other hand, the minimum capacitance of the input and output capacitors *Ce* can be computed using (2), which is valid for a buck converter, whereas the minimum value of the bulk capacitance *C* is expressed by (3), which is valid for a boost converter:

$$L\_{\rm min} = \frac{100 \text{ V}\_2 (1 - d)d}{2 F\_{\rm sw} r\_{\rm I} \rho\_{\rm I} I\_1} \,\text{}\,\text{}\,\text{}$$

$$C\_{\mathfrak{e}\_r \min} = \frac{100(1 - d)}{8 F\_{\text{sw}}^2 r\_{\text{rc}} v\_{\text{rc}} d},\tag{2}$$

$$C\_{\rm min} = \frac{100 \ I\_2 d}{F\_{\rm sur} r\_{v\%} V\_2}. \tag{3}$$

In (1), (2), and (3), *Fsw* is the switching frequency; *d* is the duty cycle; *V*<sup>2</sup> and *I*<sup>2</sup> are the output voltage and current, respectively; *I*<sup>1</sup> is the input current; *ri*% is the desired inductor current ripple; and *rv*% and *rve*% are the desired voltage ripple values on the bulk and external capacitors, respectively.

### **3. Possible DC Microgrid Scenarios, Load Models, and Required Control Schemes for the ESS Converter**

In the present study, it was supposed that the Split-pi converter was used to interface an ESS with a DC microgrid. Under this hypothesis, several scenarios could be considered depending on the control mode chosen for both the storage-side converter and the grid-side converters interfacing other microgrid generators, if any. Depending on the combinations of the control modes of such converters, five scenarios were identified and, for each of them, a different type of load model and control scheme must be used. The different DC microgrid scenarios and the required load models and control schemes are discussed in the following subsections.

### *3.1. Possible DC Microgrid Scenarios*

In general terms, one of the following situations can occur as a control mode for the microgrid converters:


is possible only with a single master); the others (i.e., the slaves) behave as current generators and are managed by an EMS to pursue one or more predefined goals.

Therefore, three control modes are possible for both the storage-side and grid-side converters: stiff droop control, non-stiff droop control, and current control. The five scenarios resulting from the combinations of the control modes of such converters are described in the first three columns of Table 2. For the sake of clarity, such scenarios are referred to also by means of an abbreviation in the form Sx-Gy, where x and y specify the control mode for the storage-side and the grid-side converters, respectively. The range of options for x is:


**Figure 2.** Equivalent active load transformations for non-stiff and stiff microgrids: (**a**) general load model for storage converter; (**b**) equivalent load model considered in scenarios #1–#4; (**c**) equivalent load model considered in scenario #5.

**Table 2.** Possible combinations of microgrid scenarios, converter and load models, and control schemes for the Split-pi.


As for the options for y:


#### *3.2. Possible Load Models for the ESS Converter*

The dynamic behavior of the storage converter is affected by the load that it must supply, which depends not only on the passive loads of the DC microgrid but also on the possible presence of grid-side generators. In the most general case, the load for the ESS converter can be modeled following these steps: (1) aggregating all the droop-controlled generators of the microgrid using Thevenin's theorem, obtaining parameters *Ed* and *Rd*; (2) combining all the current-controlled generators managed by the EMS to compute the overall current *I*; (3) including an aggregated passive load *Rload*. The resulting circuit model is shown in Figure 2a. However, it is convenient to reduce such a model to a suitable equivalent form comprising only one generator. Toward this aim, it is necessary to distinguish between the five scenarios. In scenarios #3 (SD-GD) and #4 (SC-GD), using Norton's theorem, the couple *Ed*, *Rd* can be substituted with an equivalent current generator *Ed*/*Rd* and a parallel-connected resistance *Rd*. Then, the load can be reduced to that of Figure 2b with the following assumptions: *Ieq* = *I* + *Ed*/*Rd* and *R* = *Rload*//*Rd*, where // denotes the parallel connection of circuit elements. In scenarios #1 (SS-GN) and #2 (SD-GN), the same scheme of Figure 2b can be used assuming *Ieq* = *I* and *R* = *Rload*. Furthermore, in scenario #5 (SC-GS), the converter's output voltage is set equal to *Ed* because *Rd* = 0. Since both *Rload* and *I* are now parallel connected to an ideal voltage generator, they do not influence the converter's dynamics. Thus, the load can be modeled as shown in Figure 2c.

**Figure 3.** Control scheme that is used for the voltage control of the ESS converter in scenarios #1 (SS-GN), #2 (SD-GN), and #3 (SD-GD).

**Figure 4.** Control scheme that is used for the current control of the ESS converter in scenarios #4 (SC-GD) and #5 (SC-GS).

In the following, the state-space model of the storage converter connected to the load of Figure 2b is denoted as model A, whereas model B refers to the converter connected to the load of Figure 2c. The derivation of such models is given in Section 4. The relationship between the possible DC microgrid scenarios and the storage converter and load models is described in the first five columns of Table 2. It is worth noting that the value of the equivalent load resistance *R* considered in scenarios #3 (SD-GD) and #4 (SC-GD) is much lower than that of scenarios #1 (SS-GN) and #2 (SD-GN) because it results from the parallel connection of *Rload* and *Rd*. Finally, the last column of Table 2 reports the required control scheme for the ESS converter in each microgrid scenario according to the considerations given in the following section.
