Keywords

1 Introduction

The increasing emission of greenhouse gases caused by industrialization and transport sector requires the development of viable solutions to mitigate environment degradation [1]. In view of this, the integration of renewable energy sources (RES), namely solar photovoltaic (PV) panels and wind turbines contributes to a clearer environment [2, 3]. Moreover, the power management from RES can be efficiently achieved in a DC grid, due to its high controllability and absence of harmonic currents and reactive power [4, 5]. For this reason, a PV-based grid can be implemented, for instance, in fast charging stations, whose energy extracted from solar PV panels is used to not overload the power grid and to charge the electric vehicle batteries [6,7,8]. However, the interface of RES demands efficient power converters to attend the innumerous failures that can occur either in the power converters or in the DC grid [9, 10]. Due to this fact, it is a constant challenge for researchers to develop solutions to respond to unavoidable failures [11]. In the presence of failures, the power semiconductors that constitute the power converters, and its drivers are quite vulnerable [12,13,14]. To circumvent those problems caused by the presence of failures in the power converters or in the DC grid, the development of fault-tolerant converters is required [15]. This type of topologies can require additional hardware in order to guarantee the normal operation under fault conditions, avoiding the damage of adjacent hardware [16,17,18]. Due to the necessity of additional hardware, the development of fault-tolerant converters can lead to increased costs, namely sensors to the application of fault diagnostic strategies or the introduction of power semiconductors [19, 20]. Despite that, the damage caused by non-fault-tolerant converters can be more expensive and harmful [21].

In this paper, a non-isolated three-level DC-DC converter integrated in a bipolar DC grid is presented. The DC-DC converter is used to interface RES, namely solar PV panels [22] as demonstrated in Fig. 1. The main application of this DC-DC converter is to continuously extract, considering the weather scenarios, the maximum energy from PV panels at each moment. However, the aim of this paper is analyzing the behavior of the three-level DC-DC converter in the presence of failures in the positive, neutral, and negative wires of the bipolar DC grid. Thus, it is proved the fault-tolerance of the DC-DC converter, without adding any electronic components.

The presented paper is organized as follows: In Sect. 2 are described in detail the operation modes of the non-isolated three-level DC-DC converter in normal conditions and in the presence of a failure in the DC wire. Furthermore, it is described the adopted control strategy to extract energy from the solar PV panels (boost-mode). In Sect. 3 are discussed the simulations results for steady-state and transient-state operations of the three-level DC-DC converter under normal and fault conditions. Finally, Sect. 4 presents the main conclusions.

Fig. 1.
figure 1

Electric schematic of the three-level DC-DC converter interfacing solar PV panels connected to a bipolar DC power grid.

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2 Operating Principles of the Three-Level DC-DC Converter

This section presents a detailed description of the different operation modes of the three-level DC-DC converter under normal and fault conditions. In normal conditions, there is not any fault in the bipolar DC grid, whereas in fault conditions are presented three possible failures: (a) a failure in the positive wire of the bipolar DC grid; (b) a failure in the neutral wire of the bipolar DC grid; (c) a failure in the negative wire of the bipolar DC grid.

2.1 Operation Modes in Normal Conditions

The presented three-level DC-DC converter integrated in a bipolar DC-DC converter aims to extract the energy from the solar PV panels. The topology demonstrated in Fig. 1 consists of two power semiconductors totally controlled (IGBTs in this case), two diodes, two inductors and a split DC-link. The output voltages, vconv1 and vconv2, depend on the states of the semiconductors S1 and S2 and the DC-link voltage. In case of the semiconductors S1 and S2 are disabled, the current flows through the diodes D1 and D2. The value of vconv1 is +vdc1 and vconv2 is +vdc2. If the semiconductors S1 and S2 are enabled, vconv1 and vconv2 are zero. When the diode D1 is directly polarized and the semiconductor S2 is enabled, vconv1 is +vdc1 and vconv2 is zero. Finally, if S1 is enabled and D2 is directly polarized, vconv2 assumes the value of +vdc2 and vconv1 is zero. The values  +vdc1 and +vdc2 corresponds to +vdc/2 since the capacitors C1 and C2 of the DC-link are equal.

2.2 Operation Modes in Fault Conditions

As mentioned previously, the three-level DC-DC converter is connected to a bipolar DC grid composed by three wires (positive, neutral and negative wires), where can occur failures in those wires of the DC grid. In this section is described the different operation modes of the DC-DC converter under fault conditions. Figure 2 demonstrates the operating modes of the DC-DC converter under a failure in the positive wire. As it can be observed, the DC-DC converter presents two different operation modes. In case of the current value from PV panels, ipv, presents a lower value than the reference current, ipv flows through the semiconductor S1 and the diode D2 (Fig. 2(a)), otherwise ipv flows through the semiconductors S1 and S2 (Fig. 2(b)). For both cases, the diode D1 is not conducting due to the presence of a failure in the positive wire, as well as the voltage in capacitor C1 is zero. Despite the failure in the positive wire in the DC grid, the DC-DC converter operates in boost-mode, as it is intended.

Figure 3 shows the operations modes of the three-level DC-DC converter under a failure in the neutral wire. When ipv is lower than the reference current, the current flows through the diodes D1 and D2 and the capacitors C1 and C2 (Fig. 3(a)). Thus, the inductors store the energy until reaching the intended current. Otherwise, ipv flows through the semiconductors S1 and S2 (Fig. 3(b)). Depending on the value of ipv according to its reference, the voltage vconv1 assumes the value +vdc which corresponds to the sum of the voltage vdc1 with the voltage vdc2 or the value zero.

Fig. 2.
figure 2

Operating principles of the three-level DC-DC converter under a failure in the positive wire of the bipolar DC power grid: (a) vconv1 = 0 and vconv2 =  +vdc2; (b) vconv1 = 0 and vconv2 = 0.

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Fig. 3.
figure 3

Operating principles of the three-level DC-DC converter under a failure in the neutral wire of the bipolar DC power grid: (a) vconv1 =  +vdc and vconv2 = 0; (b) vconv1 = 0 and vconv2 = 0.

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Figure 4 presents the operating principles of the three-level DC-DC converter in the presence of a failure in the negative wire of the DC grid. In this case, the output voltage vconv1 assumes the value +vdc1 or zero and vconv2 is zero. Depending on the current value in the inductors relatively to the reference current, there are two possible operation modes. Figure 4(a) shows the operation mode when ipv is lower than the established reference current, where the current from the PV panels flows through D1 and S2. When ipv is higher than the reference current, the current flows through the semiconductors S1 and S2, as demonstrated in Fig. 4(b).

Fig. 4.
figure 4

Operating principles of the three-level DC-DC converter under a failure in the negative wire of the bipolar DC power grid: (a) vconv1 =  +vdc1 and vconv2 = 0; (b) vconv1 = 0 and vconv2 = 0.

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For both situations (normal and fault conditions) the control strategy applied to the three-level DC-DC converter is presented through expression (1). The voltages to be synthetized by the three-level DC-DC converter correspond to vcv_dc1 and vcv_dc2. On the other hand, the voltage in the solar PV panels is presented by vpv and iLx[k] is the current in inductor L1 or L2 at instant [k]. The established reference current that the DC-DC converter must synthetize corresponds to the parameter iLx[k + 1] at instant [k + 1].

$$ v_{cv\_dcx} = v_{pv} - (L_1 + L_2 )f(i_{Lx} [k + 1] - i_{Lx} [k]){,}\quad x = \{ 1{,}2\} $$
(1)

where f is the sampling frequency.

The comparison between vcv_dc1 and vcv_dc2 with two triangular carriers phase shifted 180°, results in the control signals of semiconductors S1 and S2.

3 Simulations of the Three-Level DC-DC Converter

In this section are described the simulation results of the three-level DC-DC converter carried out with the software PSIM. The presented simulation results include the steady-state and transient-state operations in two different scenarios: normal conditions and fault conditions. It is used a voltage source of 100 V to emulate the solar PV panels, since the aim of this paper is the fault analysis of the DC-DC converter, and the maximum power tracking control of PV panels is not in the scope of this paper. Moreover, it is considered a voltage value of 200 V in each DC-link capacitor. The DC-link capacitors, C1 and C2, assume a capacitance value of 8.2 mF and the inductors L1 and L2 have an inductance value of 1.2 mH.

3.1 Steady-State Operation: Normal and Fault Conditions

Figure 5 shows the steady-state operation of the three-level DC-DC converter in normal conditions, i.e., in the absence of any failure in the DC grid. In this case, it is established a reference current of 10 A. As it can be observed, the ripple frequency of ipv is 40 kHz, which corresponds to the double of the switching frequency (20 kHz). As the DC-DC converter is operating in normal conditions, the voltages synthesized by the DC-DC converter, vconv1 and vconv2, can assume the voltage values of zero and +vdc/2 (200 V). Thus, when the semiconductors S1 and S2 are enabled, vconv1 and vconv2 is zero. If S1 is enabled and S2 is disabled, vconv2 is 200 V and vconv1 is 0 V, otherwise vconv2 is 0 V and vconv1 is 200 V. In this case, the duty-cycle of S1 and S2 is 75%, whose command signals are the result of the comparison with two triangular carriers of 20 kHz 180º phase shifted, resulting in the voltages vconv1 and vconv2.

Figure 6 presents the steady-state operation of the three-level DC-DC converter in normal and fault conditions in the positive wire for a reference current of 8 A. Initially, the three-level DC-DC converter is operating normally until time instant 0.004 s, when a failure occurs in the positive wire of the bipolar DC grid. In the presence of the failure, it can be observed that the ripple frequency of ipv is half the frequency (20 kHz) verified in normal conditions (40 kHz). Since there is a failure in the positive wire of the bipolar DC grid, there is no energy in capacitor C1, so the current never flows through the diode D1 and the energy from the PV panels is not injected into the positive wire of the bipolar DC grid. Thus, vconv1 is 0 V and vconv2 can assume the values 0 V and 200 V. Due to this, the semiconductor S1 is always enabled, and the duty-cycle of S2 is reduced from 75% to 50% to maintain the current value according to its reference. As voltage vconv1 is zero, the ripple of ipv is higher than the current ripple verified for normal conditions. The two possible operation modes for this case are presented in Fig. 2.

Figure 7 shows the steady-state operation of the three-level DC-DC converter in normal and fault conditions in the neutral wire of the bipolar DC grid, for a reference current of 6 A. The three-level DC-DC converter is operating in normal conditions until time instant 0.008 s. However, in the presence of a failure in the neutral wire of the bipolar DC grid, the ripple frequency of ipv changes from 40 kHz to 20 kHz, as observed in the previous case. Moreover, vconv1 assumes the values 0 V and 400 V, whose last value corresponds to the total voltage value of the DC-link, whereas vconv2 is 0 V. On the other hand, as vconv2 assumes the value 0 V the ripple of ipv is higher than the current ripple verified in normal conditions. In the presence of a failure in the neutral wire, both semiconductors S1 and S2 switch and the current flows through D1 and D2, resulting in the operation modes presented in Fig. 3.

Fig. 5.
figure 5

Steady-state operation of the three-level DC-DC converter in normal conditions for a reference current of 10 A.

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Fig. 6.
figure 6

Steady-state operation of the three-level DC-DC converter in normal and fault condi-tions in the positive wire for a reference current of 8 A.

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Figure 8 presents the steady-state operation of the three-level DC-DC converter in normal and fault conditions in the negative wire of the bipolar DC grid, for a reference current of 4 A. As the previous case, the ripple frequency of ipv in the presence of a failure in the bipolar DC grid, changes from 40 kHz to 20 kHz. Due to the presence of a failure in the negative wire of the bipolar DC grid, there is no energy in C2 and the energy from the PV panels is not injected into the negative wire of the bipolar DC grid, so the current in D2, iD2, is 0 A. For this reason, vconv2 is 0 V and vconv1 can assume the values 0 V and 200 V. As voltage vconv2 is 0 V, the ripple of ipv is higher than the current ripple verified for normal conditions. Furthermore, the semiconductor S2 is always enabled, and the duty-cycle of S1 is reduced from 75% to 50% in order to maintain the current value according to its reference. The two possible operation modes for this case are presented in Fig. 4.

Fig. 7.
figure 7

Steady-state operation of the three-level DC-DC converter in normal and fault conditions in the neutral wire for a reference current of 6 A.

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Fig. 8.
figure 8

Steady-state operation of the three-level DC-DC converter in normal and fault conditions in the negative wire for a reference current of 4 A.

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3.2 Transient-State Operation: Normal and Fault Conditions

Figure 9 illustrates the transient-state operation of the three-level DC-DC converter in normal conditions. Initially, the reference current is 10 A and it is reduced to 8 A at time instant 0.002 s. In this case, the transition time takes 25 µs. Moreover, the ripple frequency of ipv is 40 kHz, i.e., the double of the switching frequency. As the three-level DC-DC converter is operating in normal conditions, the output voltages, vconv1 and vconv2, assume the values 0 V and 200 V. When S1 and S2 are enabled, vconv1 and vconv2 are zero. If S1 is enabled and S2 is disabled, vconv2 is 200 V and vconv1 is 0 V, otherwise vconv2 is 0 V and vconv1 is 200 V. The duty-cycle of S1 and S2 is 75%.

Figure 10 shows the transient-state operation of the three-level DC-DC converter in the presence of a failure in the positive wire of the bipolar DC grid. At time instant 0.0055 s the reference current is reduced to 6 A, whose transition time is 50 µs. The transition time verified is higher than in normal conditions (25 µs). Moreover, the ripple of ipv is the same verified in fault conditions, i.e., the ripple is higher than in normal conditions. This is since the output voltage vconv1 is 0 V, where S1 is always enabled and there is no energy injected into the positive wire of the bipolar DC grid. So, iD1 is 0 A and the current flows through S1 and S2 or S1 and D2.

Fig. 9.
figure 9

Transient-state operation of the three-level DC-DC converter in normal conditions for reference currents of 10 A and 8 A.

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Fig. 10.
figure 10

Transient-state operation of the three-level DC-DC converter in the presence of a failure in the positive wire of the DC power grid for reference currents of 8 A and 6 A.

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Figure 11 presents the transient-state operation of the three-level DC-DC converter in the presence of a failure in the neutral wire of the bipolar DC grid. Initially, the established reference current is 6 A and at time instant 0.0095 s the reference current is reduced to 4 A, whose transition time took 25 µs. As mentioned above, in the presence of a failure in the neutral wire of the bipolar DC grid, vconv1 assumes the values 0 V and 400 V and vconv2 is 0 V. As vconv2 is null, the ripple of ipv is higher than the current ripple verified in normal conditions.

Figure 12 illustrates the transient-state operation of the three-level DC-DC converter in the presence of a failure in the negative wire of the bipolar DC grid. At time instant 0.0135 s the reference current changes from 4 A to 2 A, whose transition time is 50 µs. In the presence of a failure in the negative wire of the bipolar DC grid, vconv1 assumes the values 0 V and 200 V and vconv2 the value 0 V. In this case, the energy is injected from the PV panels into the bipolar DC grid, through the semiconductors S2 and S1 or S2 and D1.

Despite the presence of failures in the positive, neutral or negative wire of the bipolar DC grid, ipv follows correctly the reference current.

Fig. 11.
figure 11

Transient-state operation of the three-level DC-DC converter in the presence of a failure in the neutral wire of the DC grid for reference currents of 6 A and 4 A.

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Fig. 12.
figure 12

Transient-state operation of the three-level DC-DC converter in the presence of a failure in the negative wire of the DC power grid for reference currents of 4 A and 2 A.

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4 Conclusions

In this paper, a three-level DC-DC converter is analyzed in normal and fault conditions connected to a bipolar DC power grid. The three-level DC-DC converter aims to interface solar photovoltaic (PV) panels into a bipolar DC power grid. The presented DC-DC converter is analyzed in normal conditions considering steady-state and transient-state operations. The results are compared with the DC-DC converter operating in the presence of a failure, individually, in the positive, neutral and negative wires of the DC grid. Moreover, the validation was performed for different values of the reference currents. It is demonstrated that, despite the presence of failures in the bipolar DC grid, the current from the PV panels, ipv, correctly follows the established reference current. However, the ripple of ipv is higher in presence of failures than in normal operating conditions, but analyzing the presented simulation results, this aspect is not critical. As shown, the three-level DC-DC converter presents good results in normal and in the fault conditions reported in this paper, without compromising the power extraction from the solar PV panels.