**1. Introduction**

Low voltage DC microgrids present well-known advantages over AC microgrids, such as increased efficiency, lower cost, simplified power electronic converters and related control systems, as well as easier power flow management. In general, their voltage level depends on the rated power. In fact, for a given power level, a higher voltage allows reducing the circulating currents and, in turn, the cross-section of the conductors; thus, a reduction of volume, weight, and cost can be attained by increasing the voltage level.

DC microgrids in stationary applications are mainly proposed for residential and commercial buildings with load powers ranging from 1 kW to hundreds of kilowatts. As explained in [1–3], several possibilities exist for their rated voltage. Typically, the rated DC voltage is chosen coherently with the standard AC ratings, i.e., 120 V DC, 230 V DC, or 400 V DC. Alternatively, if the DC microgrid is supplied by a passive diode rectifier connected to the mains, its voltage equals the rectified mains (i.e., 170 V DC, 325 V DC, or 566 V DC). Finally, if an active rectifier supplies the DC microgrid and the latter encompasses AC loads supplied by an inverter, slightly higher values than the rectified mains must be chosen to provide a suitable margin for voltage regulation.

As for DC microgrids in mobile applications, whenever possible, 48 V DC is chosen to exploit the advantages of Safety Extra-Low Voltage (SELV) systems. However, the rated

**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 II: Simulation and Experimental Results. *Energies* **2021**, *14*, 5616. https://doi.org/ 10.3390/en14185616

Academic Editor: Mohamed Benbouzid

Received: 12 July 2021 Accepted: 3 September 2021 Published: 7 September 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

power of the electrical equipment used in mobile applications is constantly increasing, and so does the nominal DC voltage. Contrarily to the 270 V DC bus imposed to aircraft and unmanned aerial vehicles (UAVs) by the standard MIL-STD-704F [4], no specific voltage level has been established for marine applications, except for large vessels and cruise ships, where 1 kV or 1.5 kV DC is commonly chosen.

For example, a 120 V DC microgrid supplied the 5 kW load of the small underwater remotely operated vehicle (ROV) described in [5]. Additionally, 200 V DC microgrids were considered as case studies in [6] and [7]. In the first case, a 1 kW docking system with bidirectional wireless power transmission capability was proposed for an autonomous underwater vehicle (AUV). In the other case, a centralized stabilizer was designed for a marine DC microgrid used in offshore and ship applications. A 400 V marine DC microgrid was considered in [8] and [9]. In particular, the microgrid of [8] was supplied by a fuel cell and delivered up to 90 kW to the electrical loads of a sailing boat; instead, the shipboard microgrid of [9] encompassed a 400 kW storage system, and it was studied to devise a power management strategy. A 500 V DC shipboard microgrid with two buses and two synchronous generators with 35 kW of total installed power was considered in [10]. Finally, shipboard microgrids with rated voltage ranging from 700 to 750 V DC were considered as case studies in [11] and [12]. In the first case, the microgrid supplied a 12 kW load connected to a 700 V DC bus, and a distributed secondary control strategy was proposed. In the other case, the microgrid of a ferry vessel was modeled for fuel cell integration studies; three 800 kW fuel cells powered three interconnected DC busbars at 750 V DC.

In any case, DC distribution in terrestrial and marine power systems requires extensive use of power electronic converters to interface distributed generation units, loads, and electrical storage systems (ESSs) [13–15]. In particular, bidirectional DC/DC converters are exploited to integrate ESSs into DC microgrids providing manifold benefits such as improved stability and resiliency, compensation of renewable generator's fluctuations, ramping support to generators, and the possibility to employ suitable energy management systems (EMSs) to optimize microgrid power flows [13,16–18].

Among the several topologies of bidirectional DC-DC power converters, the Split-pi is receiving increasing attention due to its distinct advantages such as high efficiency, reduced switch count, small reactive components and switching noise, as well as suitability for multiphase systems, at the only cost of non-isolated operation [19–27]. However, none of the previous works on the Split-pi focused on the connection to DC microgrids. Furthermore, only three papers proposed applications in which such a converter was not controlled in an open-loop fashion [23,24,26]. Such papers, however, presented only closed-loop applications with a single control loop; furthermore, they neglected the reactive components' parasitic resistances and did not perform any experimental validation.

On the other hand, the integration of DC-DC bidirectional converters into a DC microgrid requires a careful design of the power converter's control system, depending on how the microgrid voltage is controlled (stiff voltage control by a single generator, multiple droop-controlled voltage generators respecting a predefined power-sharing ratio or masterslave control supervised by an EMS). To the best of the authors' knowledge, no paper in the technical literature presented a comprehensive analysis of all the scenarios in which a bidirectional DC/DC converter can be used to interface an ESS with a DC microgrid. The traced contributions fall into two categories. On the one hand, many authors presented a specific converter topology for microgrid applications but modeled the converter considering its output closed on either a load resistor or an ideal voltage source. Therefore, the respect of the chosen stability margin was not guaranteed in real applications where mixed loads stem from the combination of passive loads, droop-controlled voltage generators, and current sources controlled by EMSs. On the other hand, other authors modeled the whole microgrid based on power system or control approaches with different goals such as assessing stabilization and fault or power management techniques or minimizing circulating currents. Thus, such studies were focused on a higher operation level than the present work.

This paper is the second part of a work aimed at analyzing all the scenarios in which a bidirectional DC/DC converter is used to interface an ESS with a DC microgrid. Part I dealt with the theoretical aspects of the problem [28]. First, the five possible DC microgrid scenarios were identified. Then, it was shown that a specific state-space model and a suitable control scheme were required to obtain high performance from the Split-pi in each scenario. The proposed models (denoted as models A and B) considered the parasitic resistances. The control schemes required two to three control loops plus a feed-forward (FF) action depending on the scenario. Finally, a more complex compensator than a conventional PI regulator was needed for output current control in stiff microgrids.

The present paper completes the study proposed in part I, validating the theoretical analysis based on a comprehensive set of simulations and experimental tests. Due to constraints imposed by the available lab equipment, a 180 V DC, 750 W microgrid was chosen as a case study. It can represent a reduced-power prototype of terrestrial and marine microgrids, e.g., a residential DC microgrid encompassing 120 V AC loads supplied by an inverter or the DC microgrid onboard a small-power ROV or AUV. Such an approach is coherent with [29], in which the microgrid of an electric ferry powered by fuel cells was scaled down to 110 V DC, 500 W to validate a stability enhancement technique. In any case, the choice of the voltage rating of the microgrid does not affect the validity of the conclusions, which can be straightforwardly extended to the whole range of low voltage DC.

A prototype of the Split-pi converter was realized in the lab to interface an emulated 48 V ESS with the 180 V microgrid. Then, several experimental tests were performed to assess the performance in each scenario. The results obtained from the experimental tests were coherent with the simulations and validated the study. Finally, it is worth remarking on the general validity of the proposed approach, which can also be followed when other bidirectional DC/DC converter topologies are employed to interface an ESS with a DC microgrid.

#### **2. Overview of the DC Microgrid Scenarios for the Operation of the Split-pi as an ESS Converter**

The complete theoretical analysis of the DC microgrid scenarios, state-space models, and required control schemes for the Split-pi converter used as an ESS converter (i.e., operating with lower storage-side voltage than grid-side voltage) was presented in Part I of the present work. In the following, only the main concepts will be recalled to ease the interpretation of the simulations and the experimental results.

Five scenarios can be considered depending on the control mode chosen for the storage-side converter (interfacing the ESS) and the grid-side converters (interfacing other microgrid generators, if any). They are described in Table 1, which summarizes the corresponding table reported in Part I of the present work. In particular, the first three columns describe each scenario; the fourth and fifth columns, instead, associate to each scenario the state-space model and the control scheme required for the Split-pi, which were devised in Part I.

For the sake of clarity, the five scenarios are referred to also using 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:



**Table 1.** Possible combinations of microgrid scenarios, converter models, and control schemes for the Split-pi.

Furthermore, a baseline scenario derived from scenario #1 excluding the FF action was also considered for comparison purposes to show the usefulness of such action.

#### **3. Overview of the Chosen Case Study and Droop Characteristics of the Storage-Side and Grid-Side Converters**

The considered case study encompassed a 48 V, 750 W storage system interfaced with a 180 V DC microgrid using a Split-pi converter. As explained in the Introduction, it can represent a reduced-power prototype of terrestrial and marine microgrids. Figure 1 shows the schematic of the Split-pi converter, which was sized for the chosen case study in Part I of the present work. Its main parameters are summarized in Table 2. Furthermore, in Part I of the work, five control systems were designed, i.e., one for each specific scenario. It was assumed that the converter supplied its rated power without an external current or voltage generator. The latter was seen as a disturbance, which the control system had to compensate promptly. Furthermore, suitably wide stability margins were imposed, so the designed controllers were also effective at lighter loads.

**Figure 1.** Schematic of the Split−pi converter.

For a proper interpretation of the simulation results, it is worth recalling the droop characteristics of both the storage converter and the voltage generator of the microgrid. As for the storage converter, its droop characteristic was defined by *Eds* = 180 V and *Rds* = 0 in scenario #1 (SS-GN); in scenarios #2 (SD-GN) and #3 (SD-GD), instead, it was expressed by *Eds* = 180 V and *Rds* = 2.2 Ω, i.e., imposing a 5% voltage reduction at the nominal current. As for the equivalent voltage generator of the microgrid, its droop parameters were equal to those of the storage converter in scenario #4 (SC-GD). Instead, in scenario #3 (SD-GD), they were expressed by *Ed* = 198 V and *Rd* = 9 Ω; thus, the storage system did not supply any power for half the rated load of the microgrid, as desired. Finally, in scenario #5 (SC-GS), a constant voltage generator *Ed* = 180 V was considered to model the microgrid's stiff voltage generator.


**Table 2.** Main parameters of the Split-pi converter.

#### **4. Simulation Results**

Several simulations were performed to assess the performance of the controlled system in all the scenarios. The circuit model was implemented using PLECS based on the electrical parameters of Table 2, whereas the control system was realized in Simulink. The simulation parameters set in the Simulink environment were the following:


The default values were confirmed for the other Simulink parameters, as well as for the PLECS parameters. The obtained simulation results are presented and commented on in the following.

#### *4.1. Validation of FF Action and Performance Assessment in Scenario #1 (SS-GN)*

As a starting point to prove the advantage of the FF action, the baseline scenario in which the storage converter supplied a microgrid stiffly at 180 V was simulated. Besides the passive load, a current generator was also present in the microgrid. Only the two innermost control loops for *IL*<sup>1</sup> and *V*<sup>2</sup> were employed, the FF action was disabled, and the system was described by state-space model A.

The waveforms of the most meaningful electrical and control quantities are shown in Figures 2 and 3a. Before t = 0.2 s, the converter output was at a steady state with the following values of load resistance, load power, and external current reference: *R=Rn*, *P=Pn*, and *I* = 0. Then, a representative sequence of *R* and *I* values was applied, as shown in Table 3. From t = 0.2 s to t = 0.6 s, the load was passive and exhibited two stepwise variations from the rated power almost to a no-load condition and vice versa. At t = 0.6 s, the load resistance was kept constant, but the external current reference was increased to supply the load fully; hence, the converter's output current dropped to zero. Then, at t = 0.8 s, the converter operated again with a very low load, so the external current was almost entirely fed back to the converter to recharge the storage system at full power. At t = 1 s, the load power was increased to its rated value. Finally, the sequence applied during the remaining time intervals was such that the external current generator started and stopped recharging the storage system at full power while the load resistance was the rated one.

**Figure 2.** Baseline performance without FF action: (**a**) output current and load current; (**b**) input inductor current; (**c**) external generator's current; (**d**) duty cycle.

**Figure 3.** Grid voltage overshoot: (**a**) in baseline scenario; (**b**) in scenario #1 (SS−GN).


**Table 3.** Transitions considered in the baseline scenario and scenarios #1 (SS-GN) and #2 (SD-GN).

The normalized waveform of grid voltage is presented in Figure 3a and shows that the converter's output voltage was correctly regulated at the desired steady-state value as the passive/active load varied. As shown in Figure 2, the current loop dynamics were fast enough to track *IL*1,*ref* instantly. However, the voltage waveform exhibited significant under- and overshoots due to load variations, as shown in Figure 3a. In particular, the maximum overshoot and undershoot were 20% and −29%, respectively. On the other hand, the microgrid usually has an allowed transient voltage tolerance of ±20% around its nominal voltage, so it would have been automatically de-energized by the protection devices, causing severe inconvenience.

A significant improvement of the system response can be achieved using the FF action; therefore, such action was enabled in the first three scenarios of Table 1, starting from scenario #1 (SS-GN). The difference between such a scenario and the baseline one is only the inclusion of the FF action. The related simulation results are shown in Figures 3b and 4. As shown in Figure 4d, the FF action varied the duty cycle instantaneously to compensate for the load variation. Consequently, the waveforms of *IL*1, *I2*, and *IR* were pretty squared (Figure 4a,b), and the resulting output voltage exhibited acceptable over/undershoots (5% and −8.8%), as shown in Figure 3b. Thus, a correct operation of the microgrid was attained.

#### *4.2. Performance Assessment in Scenario #2 (SD-GN)*

Unlike the first scenario, in scenario #2 (SD-GN), the storage converter was controlled using a droop scheme with *Rd* = 0, i.e., with three control loops (*IL*1, *V*2, and droop) plus the FF action. All the other parameters, including the initial conditions and load sequence, were kept unchanged. The microgrid voltage was not constant at 180 V at steady-state due to the droop control; thus, the actual load power was slightly lower than the value reported in Table 3 depending on voltage reduction, as expected.

The simulation results in terms of grid voltage waveforms are shown in Figure 5. The converter's output voltage (*V*2) quickly tracked the reference voltage (*V*2*ref*) computed according to the droop characteristic during the entire timeframe. In particular, the voltage variation was ±5% when the storage system was discharged/recharged at the rated current, as expected based on the droop characteristic. The over/undershoot superimposed to the steady-state voltage variation was less than ±1.66%. Thus, the microgrid voltage stayed within ±7% of its rated value even during transients. The input/output currents and duty cycle were not shown because their waveforms were like those obtained in scenario #1 (SS-GN).

**Figure 4.** Performance obtained in scenario #1 (SS−GN): (**a**) output current and load current; (**b**) input inductor current; (**c**) external generator's current; (**d**) duty cycle.

**Figure 5.** Performance obtained in scenario #2 (SD−GN): (**a**) actual and reference grid voltage; (**b**) grid voltage overshoot.

#### *4.3. Performance Assessment in Scenario #3 (SD-GD)*

In this scenario, both the storage converter and the equivalent voltage generator of the microgrid were controlled in droop mode with non-null droop resistances. Furthermore, the presence of an equivalent current generator in the microgrid was considered as well. The two droop characteristics were chosen so that the storage system did not supply any power for half the microgrid's rated load, as described in Section 3. Again, before t = 0.2 s, the converter output was at steady-state with the following values of load resistance, load power, and external current reference: *R=Rn*, *P=Pn*, and *I* = 0. However, the storage system delivered about half the rated power in this scenario, and the equivalent voltage generator supplied the remaining quota.

The load sequence that was applied to the converter after t = 0.2 s is shown in Table 4. It is like that of Table 3, with additional conditions in which the passive load drew half the rated power. Furthermore, the current reference values were chosen to inject the maximum allowed current that did not overload the droop-controlled generator and the storage system.


**Table 4.** Transitions considered in scenario #3 (SD-GD).

The simulation results for this scenario are shown in Figure 6. At t = 0.2 s, the external current reference was null while the load resistance doubled; hence, the converter's output current dropped to zero, as expected. At t = 0.4 s, the converter operated almost at no load, so the storage system was recharged at about half power. Then, at t = 0.6 s, the equivalent current generator injected current into the grid providing excess power; hence, the storage system was recharged at full power. From t = 0.8 s to t = 1.2 s, the load power increased from low to medium to high. The equivalent current generator injected constant current, so the charging power progressively decreased as the load power increased. Finally, at t = 1.2 s, the external current generator charged the storage system at the maximum power level besides supplying the rated load.

As in the previous scenario, the converter's output voltage quickly tracked the reference voltage computed according to its droop characteristic based on the output current; however, in scenario #3, the current also depended on the droop characteristic of the equivalent voltage generator. In particular, Figure 6d shows that the voltage variation of the microgrid was even lower compared to scenario #2 (SD-GN): from −2% to 5% at steadystate with minimal over/undershoots (i.e., less than ±1.05%). Finally, the waveforms of the input inductor current *IL1* and the duty cycle *d* were not shown because they were like those obtained in scenario #1 (SS-GN).

**Figure 6.** Performance obtained in scenario #3 (SD−GD): (**a**) output current and droop-controlled generator's current; (**b**) actual and reference grid voltage; (**c**) external generator's current and load current; (**d**) grid voltage overshoot.

#### *4.4. Performance Assessment in Scenario #4 (SC-GD)*

In scenario #4 (SC-GD), the voltage was regulated by the microgrid's equivalent voltage generator controlled in droop mode with non-null droop resistance. In contrast, the storage converter was operated as a current-controlled source based on a reference given by the EMS. Therefore, the control system of the Split-pi converter encompassed two loops for *IL*<sup>1</sup> and *IL*2, respectively. Furthermore, the presence of an equivalent external current generator in the microgrid was also considered.

The simulation results for this scenario are shown in Figure 7. Before t = 0.2 s, the converter output was at steady-state with the following values of load resistance, output current reference, and external current reference: *R=Rn*, *I*2*ref* = 0, and *I* = 0. In other words, the storage system and the external current generator delivered no power while the load was supplied entirely by the equivalent voltage generator. Then, a representative sequence of *R*, *I*2*ref* , and *I* values was applied, as shown in Table 5.

**Figure 7.** Performance obtained in scenario #4 (SC−GD): (**a**) actual and reference output current; (**b**) load current; (**c**) droop-controlled generator's current and external generator's current; (**d**) grid voltage overshoot.


**Table 5.** Transitions considered in scenario #4 (SC-GD).

The load resistance kept the same value from t = 0.2 s to t = 1.2 s while the external current generator's reference progressively increased. Each time, the output current reference was set to the maximum value (either positive or negative) that respected the following conditions: it was compatible with the current combination of *R* and *I*, and it did not overload the droop-controlled generator and the storage system. From t = 1.2 s to t = 1.8 s, the load resistance was increased almost to a no-load condition, and the reference for the external current generator was progressively incremented. Again, the output current reference was set to the maximum value that did not overload the droop-controlled generator and the storage system; however, only negative values were allowed because of the no-load condition.

All the grid-side current transients were fast and clean even though challenging perturbations were applied, i.e., stepwise variations of circuit parameters. As for the microgrid voltage variation, Figure 7d shows that it went from −5.14% to 0% at steadystate with minimal over/undershoots, as expected. The FF action was not used with current-mode control; thus, the waveform of *IL*<sup>1</sup> was like that obtained in the baseline scenario, and the waveform of the duty cycle was flat around its rated value.

#### *4.5. Performance Assessment in Scenario #5 (SC-GS)*

In this scenario, the storage converter was operated as a current-controlled source under the supervision of the EMS and connected to a microgrid in which one voltage generator was droop controlled with *Ed* = 180 V and *Rd* = 0 (stiff microgrid). Hence, model B was considered to design the control system. The initial condition was *I*2*ref = 0*. Then, starting from t = 0.2 s, the same sequence of *I*2*ref* as in scenario #4 (SC-GD) was applied, i.e., the one reported in the last column of Table 5. The simulation results for this scenario in terms of grid-side currents are shown in Figure 8 and confirmed the good system performance. The microgrid voltage *V*<sup>2</sup> was perfectly constant at 180 V because the voltage generator was controlled stiffly. Again, since the FF action was not used with current-mode control, the waveform of *IL*<sup>1</sup> resembled that obtained in the baseline scenario. Furthermore, the duty cycle waveform was even flatter compared to the previous scenario because the converter had stiff voltages at both ports.

**Figure 8.** Performance obtained in scenario #5 (SC−GS): (**a**) actual and reference output current; (**b**) droop-controlled generator's current.

#### *4.6. Comparison among the Five Scenarios*

The results obtained in the five scenarios were summarized in Table 6 for a comparison. The chosen metrics were the maximum charging/discharging power, the percentage voltage variation against *V*2*n*, and the output voltage and current settling time. The latter metric is defined as the time after which the output variable enters and remains within a specified error band after applying an instantaneous stepwise input. The simulation results showed that some applied stimuli determined no difference between the steadystate value after the transition and the initial value. Therefore, the error band was defined summing/subtracting a fixed quantity to/from the steady-state value, as if it was a measurement error. Such a quantity was 0.01·*V*2*<sup>n</sup>* for the output voltage and 0.01·*I*2*<sup>n</sup>* for the output current.


#### **Table 6.** Result comparison in the five scenarios.

It is worth remarking that, in general, the microgrid designer cannot freely choose from all five scenarios due to system constraints. For example, the first three scenarios are impracticable if the designer decides to put the ESS converter under the control of an EMS; on the other hand, only the first and last scenarios are practicable if a stiff microgrid is to be designed. Thus, the proposed comparison can provide helpful information when the designer is not obliged to choose a specific scenario.

According to Table 6, the fastest performance was achieved in scenario #1 at the expense of the voltage variation, which can reach −8.8%. This behavior descended from the simplicity of such a scenario. Comparing scenarios #1 and #2 shows that introducing a virtual droop resistance dampened the system response and slightly reduced the maximum charging/discharging power as a side effect. Thus, the microgrid's voltage variation decreased, and the settling time increased for both *V*<sup>2</sup> and *I*<sup>2</sup> (+ 238% and +278%, respectively).

The use of more than one droop-controlled generator in the microgrid has pros and cons. In fact, in scenario #3, the maximum discharging power of the ESS was halved by design; thus, the ESS and its converter were partly underutilized. On the other hand, a halved maximum voltage reduction was exhibited, and the maximum settling time of *V*<sup>2</sup> decreased significantly (i.e., −52% and −86% compared to scenarios #1 and #2, respectively). The settling time reduction was achieved because the voltage waveform's peak did not surpass the tolerance band. Instead, the maximum settling time of *I*<sup>2</sup> stayed almost constant.

Comparing scenarios #2 and #3 with the last two scenarios showed a slight reduction of the settling time of *I*2. Instead, a comparison between scenarios #4~#5 and scenario #1 revealed an increase of such a metric equal to +200% and +240%, respectively. As for the percentage voltage variation and the settling time of *V*<sup>2</sup> in scenario #4, they both exhibited intermediate values compared to scenarios #2 and #3. Finally, scenario #5 presented no voltage variation thanks to the stiff control of the microgrid.

Summing up, the following guidelines can be given for the considered case study. If the ESS converter must be controlled by an EMS, the response time of *I*<sup>2</sup> is around 50 ms, whereas that of *V*<sup>2</sup> does not exceed 15 ms and depends on the stiffness of the microgrid. Otherwise, the ESS converter should be operated in scenario #1 to achieve the fastest performance, i.e., around 15 ms response time for both *V*<sup>2</sup> and *I*2. In such a scenario, the ESS converter is the only voltage source of the microgrid and is controlled stiffly. If these two conditions cannot be met, the response time of *I*<sup>2</sup> worsens significantly (around 60 ms), and the waveform of *V*<sup>2</sup> depends on a compromise: lower voltage variation and better dynamic performance come with a partial underutilization of the ESS.
