1. Introduction
Photovoltaic (PV) installations are a growing market due to the objective of reducing greenhouse emissions by 2030 by, at least, 55% [
1]. In addition, PV installations can be used to replace backup diesel generations, reducing urban pollution in large cities. Additional benefits of PV systems are the availability of solar energy at the production site, avoiding the need of fuel transportation required by traditional diesel generators; better usability of large surfaces such as rooftops; and simple scalability of the PV power generation.
In addition to the modularity, PV installations also require mitigation of the detrimental effect of the partial shading conditions on series-connected PV panels (named strings), in which small shades could significantly reduce the power production [
2]. One suitable solution to mitigate this problem is to introduce voltage equalizers [
2,
3], which provide a path for the current difference between two (or more) series-connected modules. This solution avoids the activation of the bypass diode associated to the shaded module; otherwise, such a module will operate in short-circuit condition without producing power. Those voltage equalizers can be designed with classical inductor switched topologies or using switched capacitor solutions [
2], which reduce the converter size and electromagnetic pollution [
4,
5,
6,
7] but introduce discontinuous input or output currents. However, since the voltage equalizers are designed to interact with series-connected modules, introducing (or subtracting) modules from the PV installation requires a disconnection of the whole string. Finally, voltage equalizers do not introduce a voltage boosting factor; hence, several PV modules must be connected in series to reach the input voltage needed by classical grid-connected inverters.
Another strategy to mitigate the effect of partial shading conditions, and to provide modularity to the PV installation, concerns the use of microinverters [
8]. Those devices enable to easily increase (or decrease) the PV installation depending on changes in the load demand without major changes in the installed devices. Moreover, the microinverter avoids the series connection of PV modules; hence, no bypass diodes are activated, which reduces the impact of partial shading conditions. The classical two-stage microinverter is a small power system formed by a PV module, a first stage to perform the tracking of the maximum power point (MPPT) and the regulation of the PV voltage, and a second stage in charge of the grid synchronization and the regulation of the DC-link between both stages; such a microinverter structure is observed in
Figure 1.
The first stage of the microinverter includes a DC/DC converter to match the PV voltage with the DC-link voltage, as reported in [
8,
9], where that DC/DC converter must be regulated to track the maximum power point (MPP) of the PV source in a particular environmental condition. Such a control system is formed by two components [
9]: an MPPT algorithm, which defines the optimal PV voltage reference
, and a high-bandwidth controller, to ensure that the PV voltage
follows the MPPT reference. The MPPT algorithm usually requires the measurement of the PV voltage and current,
and
, while the controller could require the measurement of additional internal variables of the DC/DC converter such as the inductor current
or DC-link voltage
. Finally, the controller generates the control signal
u of the DC/DC converter.
The grid connection is performed using an inverter, which has two main objectives: interact with the grid to deliver the PV power, and regulate the DC-link voltage. This last objective is very important in PV systems, since the grid interaction forces a single-phase inverter to inject sinusoidal power at double the grid frequency, which produces a sinusoidal voltage oscillation at double the grid frequency in the DC-link. This problem is clearly explained in [
10], where it is demonstrated that such a DC-link voltage oscillation can be translated into the PV voltage, making the MPPT algorithm unstable and avoiding the extraction of the maximum power. In addition, the average value of the DC-link must be regulated to avoid non-feasible operation conditions for the first-stage, e.g., high DC-link voltage that could destroy the DC/DC converter. Therefore, the inverter of the second-stage must regulate the average value of the DC-link voltage, as reported in [
11], where the size of the capacitor defines two main aspects of the DC-link:
The amplitude of the low-frequency voltage oscillations at double the grid frequency, which introduce a perturbation on the first stage, as discussed in [
10]; thus, the controller of the first stage must be designed to avoid the transmission of such a DC-link perturbation into the PV voltage.
The magnitude of the high-frequency voltage ripple generated by the DC/DC converter of the first stage, which introduces high-frequency current harmonics into the second-stage inverter. The current harmonics deteriorate the power quality provided to the inverter, introducing high-frequency noise that could interfere with the inverter control system and sensing circuits.
With the aim of reducing the previous problems, high capacitances are usually adopted to design the DC-link, requiring electrolytic capacitors. For example, the microinverters reported in [
12,
13] consider DC-link capacitors of 2200
F, which is clearly in the electrolytic range. Since electrolytic capacitors have a much higher failure rate in comparison with other technologies such as film capacitors [
10], using large DC-link capacitors introduces a reliability problem to the PV microinverter.
1.1. Literature Review
This subsection discusses different approaches, reported in literature, to face the previous considerations.
The microinverter reported in [
8] adopts a DC/DC boost converter for the first stage, which provides the boosting factor needed to match the PV voltage and the DC-link voltage. The first stage has no high-frequency controller; hence, the boost converter can be perturbed by the low-frequency oscillations present in the DC-link, and no global stability of the first stage is ensured. Finally, this solution adopts an incremental conductance (INC) MPPT algorithm. The microinverter presented in [
12] is also based on an open-loop boost converter with no global stability ensured; however, in this case, a large electrolytic capacitor is used to reduce the DC-link voltage oscillations at the expense of reliability; finally, the perturb and observe (P&O) MPPT algorithm is used to maximize the power production. The work reported [
14] also considers a grid-connected PV system; the first stage of this solution is formed by a boost converter in open-loop with a capacitive DC-link, where the duty cycle is defined by a predictive MPPT algorithm. In this case, the voltage oscillations at the DC-link are mitigated by using a three-phase inverter, which requires balanced power flows in each phase to ensure a small oscillation magnitude. Since three-phase networks are not common in urban/residential power systems, this solution is restricted to industrial environments. Finally, the design of the power stage is not discussed.
Another approach is reported in [
9], where a flyback converter is adopted. The first stage of this solution includes a sliding-mode controller (SMC) to mitigate the DC-link voltage oscillations, thus avoiding the need for large electrolytic capacitors. However, the flyback converter requires the use of a high-frequency transformer, which introduces electromagnetic pollution that could affect the sensors of the system. Instead, the work reported in [
15] adopts both the boost converter and SMC into the first stage to ensure stability. The SMC is designed considering a resistive load to simplify the analysis. Despite changes on the resistive load being considered, such an approximation does not correctly represent the input of a grid-connected inverter; thus, no global stability can be ensured. In addition, the boost converter design is not analyzed; thus, no guidelines concerning the design of the passive elements are provided. Similar problems are found in [
11], where an SMC is designed for the boost converter in the first stage, ensuring stability of both the converter and P&O MPPT algorithm, but the design of the power stage is not discussed.
The work reported in [
16] succeeds in providing design equations for the first-stage converter (with a boost topology). As in the case of [
15], a resistive load model is used to represent the second stage; thus, those results are not easily applicable to real PV microinverters. Moreover, the work reported in [
16] adopts a robust-direct-adaptive controller (RDAC), but the calculation of the controller parameters is not discussed. Finally, an MPPT algorithm similar to the P&O solution is adopted. The work discussed in [
13] is also based on a boost converter, where the first stage is regulated using a mixed proportional–integral (PI)-P&O controller, but the system stability is not formally analyzed. Moreover, the converter design is not discussed. The solution reported in [
17] is also based on a boost converter and an SMC; however, in this case, an additional PI controller is introduced. The main advantage of this solution is the use of a particle swarm optimization (PSO) to obtain the optimal controller parameters; however, the converter design is not discussed and the global stability of the system is not formally demonstrated. Finally, the work reported in [
18] presents a first stage based on a boost converter controlled by an SMC and a P&O algorithm. This solution considers an accurate model for the DC-link, and the stability of the PV system is formally demonstrated. However, the design of the converter elements is not taken into account, and the output current of this first stage is discontinuous.
From the previous discussions, the following conclusions are obtained:
The boost converter is the most widely adopted solution to develop PV microinverters. Nonetheless, a design procedure for the converter elements, based on the particular requirements of the PV installation, is needed.
The SMC is widely adopted in PV systems due to its robustness to parametric changes and satisfactory rejection of environmental perturbations. However, the global stability is not ensured; thus, the associated mathematical analysis is needed.
The low-frequency voltage oscillations at the DC-link, caused by the grid connection of the second stage, must be reduced or mitigated. This can be performed by implementing the DC-link with a large electrolytic capacitor at the expense of reliability or by using high-bandwidth controllers in the first stage.
The solutions previously discussed are based on DC/DC converters with discontinuous output current, requiring large DC-link capacitors to reduce the high-frequency current harmonics introduced to the second stage.
The P&O algorithm is the most widely used solution in PV microinverter applications due to its efficiency and simplicity, followed by the INC solution.
1.2. Contributions of the Proposed Solution
The solution proposed in this paper improves the first stage of PV microinverters by enabling the implementation of a non-electrolytic DC-link using a new approach: developing the first stage using a non-electrolytic-capacitor (NEC) boost converter, which provides continuous output current, thus decreasing the DC-link capacitor needed to reduce the high-frequency current harmonics introduced to the second stage. This approach uses the NEC boost converter with non-pulsating and ripple-free output current proposed in [
19], which introduces an improved impedance network (over the Z-network of the classical boost converter) but without changing the voltage conversion ratio and keeping the continuous input current condition. In addition, the PV system based on the NEC boost topology is analyzed in detail to provide a mathematical model and a comprehensive design procedure.
Moreover, the operation complexity of the NEC boost converter requires a suitable control system to guarantee the global stability of the PV system; thus, an SMC is designed to regulate the NEC boost converter and to guarantee global stability to the PV installation. This proposed SMC also enables rejecting the low-frequency perturbations present in the DC-link due to the grid connection. Finally, the formal proof of the global stability is developed.
1.3. Manuscript Organization
The remainder of the paper is organized as follows.
Section 2 presents a detailed analysis of the proposed PV system, describing the main objectives of the NEC boost converter into the PV system. Moreover, the non-linear model of the PV system is calculated.
Section 3 describes the design of the SMC including the mathematical analyses needed to provide global stability. This section also describes the practical implementation of the SMC using an analog circuit.
Section 4 proposes a method to design the dynamic behavior of the PV system, based on a cascade voltage controller, which is needed to ensure the stability of the MPPT algorithm. In addition, the implementation of the complete control structure is summarized in a block diagram. Then,
Section 5 illustrates the design procedure using a realistic application example, which includes the calculation of the parameters for both the NEC boost converter and SMC, including the verification of the global stability equations.
Section 6 presents the validation of the theoretical analyses using realistic and detailed circuital simulations in the commercial power electronics simulator PSIM [
20], which is used in literature to validate theoretical expressions developed for design and control of other PV microinverters; examples of such validations are reported in [
9,
21]. Finally, the conclusions close the paper.
5. Design Procedure and Application Example
The PV system is designed depending on the operation conditions required by the PV panel and grid-connected inverter (or micro/nanogrid). For this application example, a BP585 PV panel is selected to be interfaced with a
V DC-link, which is common for low-voltage nanogrids and some commercial inverters (e.g., ATO-GTI-300 inverter), but any other panel and bus voltage can be considered depending on the application. The datasheet parameters of the BP585 PV panel are reported in
Table 1 [
33].
The first step to design the PV system is to define the desired current and voltage ripples. Taking into account that the P&O algorithm could provide a precision higher than 99%, as demonstrated in the works reported in [
27,
28], the PV voltage ripple must be lower than 1% of the optimal operation voltage, which in
Table 1 is
= 18 V. Therefore, this example considers the desired peak-to-peak ripple of the PV voltage equal to 0.1% of
, i.e.,
mV.
The main advantage of the NEC boost converter, in comparison with the classical boost converter, is the capability to provide a continuous current to the output DC bus. This is possible since the current provided by the NEC boost converter is
, which is continuous when the ripple
(24) of that current is smaller than the average value
. Therefore,
will be designed to provide a continuous current for at least 75% of the irradiance space:
Figure 12 shows the electrical characteristics of the PV panel for the maximum irradiance possible (1000 W/m
), and for the 75% (750 W/m
), 50% (500 W/m
), and 25% (250 W/m
) of such an irradiance space. Thus,
must be designed to provide
for irradiances
W/m
(green zone of
Figure 12). For irradiances
W/m
, the
current will be discontinuous (red zone of
Figure 12), but the power provided to the DC-link will be low; thus, the high-frequency current components will also have a low impact on the DC-link. Finally,
could be designed to impose a continuous current for a larger irradiance space depending on the requirements of the second stage.
The MPP conditions of the PV panel under an irradiance of 250W/m
are
A and
V, which produce a duty cycle
for the NEC boost converter (22); those values assume a temperature of 25
C (i.e., the STC temperature considered in the datasheet). For different temperature conditions, the MPP current and voltage can be extracted from experimental measurements or estimated using a model parameterized at the desired temperature. Then, using expressions (
18) and (21) it is calculated the average value of
as
A. Therefore, the current ripple on
must be
A when
W/m
.
The electrical scheme of
Figure 3 shows that the ripple of the PV current is shared between
and
currents; hence,
is selected to ensure a balanced sharing of the current ripple, which is confirmed by expressions (
23) and (24). On the other hand, the voltage of the internal capacitor
affects the derivative of both
and
, as reported in (
9) and (10); hence,
must be designed to have a small voltage ripple
. Therefore,
is selected as 10% of the steady-state value of
, which, according to expression (19), is equal to 48 V. In addition, the switching frequency of the NEC boost converter is selected to be below 100 kHz, which ensures the correct operation of commercial MOSFETs as observed in the implementation of the boost converter reported in [
25]. Finally,
Table 2 summarizes the design characteristics for the NEC boost converter for this example.
Applying Equation (24) leads to a minimum
inductance of 147
H; so, the commercial values
H are selected. Similarly, applying Equation (25) leads to a minimum
capacitance of
F, selecting a commercial value
F for this application. The
capacitance is calculated from Equation (
26) using the values of
, which results in a minimum capacitance of
F; thus, the commercial value
F is adopted.
The parameters of the P&O algorithm are calculated following the procedure proposed by Femia et al. in [
34], obtaining a perturbation period
s and a perturbation magnitude
mV. Since Femia also demonstrated that the settling time of the PV voltage must be shorter than
to ensure the P&O stability, such a settling time is defined as
s
. Concerning the SMC, Equation (
54) is used to calculate the hysteresis width needed to limit the switching frequency under 100 kHz, obtaining
A. Then, the voltage controller parameters are calculated from Equations (60) and (
64) to ensure the desired
value, obtaining
A/V and
kA/V.
It is important to remark that the global stability of the SMC is ensured when the dynamic restrictions (
47) and (48) are fulfilled. Those limits depend on the derivative of the PV current, which can be analyzed using the ideal single diode model, whose parameters are calculated following the procedure reported in [
35]:
, where
,
V
, and the short-circuit current is considered proportional to the irradiance condition
S as
. Then, the PV current derivative is
, where
is proportional to the derivative of the irradiance
. In order to test the proposed solution under strong perturbations, a very fast change on the irradiance condition
(W/m
)/ms is considered, which corresponds to a change of one sun in a single millisecond, i.e., from fully irradiated to completely shaded in one millisecond. Evaluating the limits given in (
47) and (48) results in
A/
s
A/
s, but with the aim of imposing a single dynamic limit, the most restrictive condition is selected as
A/
s. The current reference
is provided by the voltage controller as
; thus, the dynamic limitation must be described in terms of the voltage reference
. Deriving the previous expression for
, and replacing
(change on the reference imposed by the P&O) and
(sum of the current ripples in
and
), leads to the dynamic restrictions on the voltage reference to ensure the stability of the SMC as follows:
Evaluating the previous expression results in the dynamic restriction
V/
s, which must be imposed into the reference generated by the P&O algorithm. Such a limitation can be implemented in analog form using operational amplifiers, e.g., using the circuit reported in [
36], or by embedding it into the digital processor used to implement the P&O algorithm. This application uses the second option since the digital processor is already needed to execute the P&O algorithm, thus avoiding the use of additional hardware. Such a digital limitation is implemented using expression (
66), which generates a ramp with slope
to impose the desired perturbation magnitude
; this expression accounts for both positive and negative perturbations.
Finally, the designed parameters for both the NEC boost converter and SMC are reported in
Table 3, and the design process of those parameters is summarized in the flowchart of
Figure 13: the PV panel used in the installation and the maximum switching frequency supported by the MOSFETs must be defined; then, the PV model parameters are calculated using the procedure reported in [
35]. Using the previous information, the values for the inductors of the NEC boost converter are calculated using expressions (
18)–(24). The next step is to calculate the
capacitor using expression (25), and the input capacitor
is designed from Equation (
26). The voltage and current that must be supported by both semiconductors are calculated from (
27) to (30), which are needed to select the MOSFET and diode. The parameters of the P&O algorithm are calculated using the procedure reported in [
34], and the settling time
of the PV voltage must be defined to ensure the P&O stability (
). Using expression (
54), the hysteresis width
H of the SMC is calculated, and the voltage controller parameters
and
are calculated using expressions (60) and (
64). The control system design is finalized with the calculation of the dynamic limits for the voltage reference using Equations (
47), (48), and (
65), which is implemented using the difference equation given in (
66).
6. Validation Using Circuital Simulations
The validation of the proposed PV system is performed using realistic and detailed simulations in the commercial power electronics simulator PSIM [
20], which is used by several industries due to the capability to simulate the non-linear behavior of the MOSFET and diode, parasitic effects, and even emulate microprocessors using a C-code interface.
The detailed circuital simulation is carried out using the circuital description of the PV system given in
Figure 2. The controller block of such a figure is formed by the complete structure depicted in
Figure 11, which uses the switching circuit of
Figure 9 to generate the control signal
u of the NEC boost converter. Finally, the circuital simulation is configured using the parameters for both the NEC boost converter and SMC reported in
Table 3, while the switching circuit is supplied with a
V power source and implemented using a Zener diode with
V, resulting in
k
and
k
.
Figure 14 shows the PSIM implementation of the PV system based on the NEC boost converter, including the SMC: in this circuit, the implementation of both the voltage controller and the calculation of the switching function
are performed in an emulated microprocessor, which acquires the required signals using Analog-to-Digital converters (ADC) and delivers the output
using a Digital-to-Analog converter (DAC).
Appendix A reports the C code developed for the microprocessor, which can be used to implement those processes in any real device programmable in C language.
The main advantage of the NEC boost converter concerns the reduced harmonic content introduced to the output DC bus in comparison with the classical boost topology. Such a condition is tested by comparing the performance of the proposed NEC solution with an equivalent PV system based on a boost converter: to provide a fair comparison, the boost converter is designed to provide the same current and voltage ripple to the PV panel; therefore, the capacitor and inductor of the boost topology are
F and
H, respectively. The design of such a boost inductor is also fair in terms of stored energy, as discussed in
Section 2.2: the boost inductor stores almost the same energy as the two inductors of the NEC option. In fact, for a duty cycle of 50%, both
and
support half of the PV current, resulting in a combined stored energy of
, where
F; the energy stored in the inductor of the boost current is
, which is the same. In the extreme case of the MPP at the highest irradiance (1000 W/m
), the duty cycle is
, which results in a combined energy of the NEC converter inductors equal to
, which is only 5.5% higher than the energy stored in the inductor of the boost converter.
Figure 15 reports the circuital simulations of the PV systems based on both the NEC and classical boost converters performed in PSIM. The detailed simulations confirm the desired condition for the PV voltage ripple, previously reported in
Table 2: the peak voltage ripple is
mV
mV. Such a value exhibits an error of 2.5% with respect to the theoretical value calculated from (
26), which is mainly caused by the changes on the switching frequency introduced by the SMC. Moreover, the figure confirms that both the NEC and classical boost converters provide the same voltage and current ripples at the PV panel side, verifying the correct design of the classical boost converter and NEC converter input capacitor. The ripple magnitudes of the inductor current reported in this simulation have errors equal to 2.98% with respect to the theoretical values calculated from (
23) and (24), which are also caused by the changes on the switching frequency.
The simulation results of
Figure 15 confirm the advantage of the NEC topology over the classical boost option: the current delivered to the DC bus by the NEC boost converter (which corresponds to
) is continuous, while the current delivered by the classical boost topology (which corresponds to diode current) is discontinuous. In order to provide a numerical comparison, the RMS and DC values of those output currents are calculated: for the NEC boost converter, they are
A and
A, while for the classical boost converter they are
A and
A. Then, the AC components of the output currents are
A for the NEC topology and
A for the boost converter, calculated from
. Therefore, the proposed PV system based on the NEC boost converter introduces nine times less (1/9) undesired current harmonics than a PV system based on the classical boost converter, thus providing a much better power quality to the DC bus or grid-connected inverter. This reduction in the AC current component has a difference of 8% with respect to the values calculated from (
39) and (40), which is caused by the change on the duty cycle from
(used in the comparison of
Section 2.2) to
(set by the MPPT algorithm at 1000 W/m
).
The simulation results also report a switching frequency equal to
kHz at
W/m
, which confirms the fulfillment of the practical restriction imposed in
Table 2 for the switching frequency (
kHz). Finally,
Table 2 reports that the current of
in the NEC boost converter must fulfill
A at
W/m
to ensure a continuous output current for 75% of the irradiance space (as described in
Figure 12). This is verified by
Figure 15, which shows (in the bottom waveforms) the behavior of both inductors’ currents in the NEC boost converter at
W/m
, confirming the desired condition. In conclusion, the simulation results reported in
Figure 15 confirm the correct design of
,
, and
for the NEC boost converter.
The stable operation of the proposed PV system is also confirmed by the simulation results of
Figure 16, which verify that the ripple condition for
, given in
Table 2, is fulfilled with an error of 4.5% with respect to the theoretical value calculated from (25), thus confirming the correct design of
. In addition,
Figure 16 also reports the same steady-state value given in (19) and (20) for
and
, respectively, and the relation given in (21) for the inductor currents; therefore, the stable operation of the NEC boost converter is confirmed. Finally, this simulation also reports the waveform of the switching function
, thus validating the correctness of the control law defined in Equation (
51). In conclusion, the simulation results reported in both
Figure 15 and
Figure 16 confirm the correct design of both the NEC boost converter and switching circuit.
A second simulation was carried out to test both the stability and dynamic performance of the proposed control system. This new simulation introduces a change of
in the voltage reference to test the controller’s ability to ensure the desired settling time
defined in
Table 3.
Figure 17 reports the detailed simulation results, where the reference change is imposed at
ms with the derivative defined in
Table 3 (dashed black waveform
), i.e.,
V/
s. This simulation also includes the verification of the theoretical dynamic behavior of the PV voltage reported in Equation (
58), which was evaluated using the parameters of
Table 3 to obtain the numerical version
for this particular example:
The simulation results reported in
Figure 17, at the top, show the correct prediction of the PV voltage (
in blue trace) provided by the theoretical transfer function
(red trace), which exhibits an absolute-relative-error (
68) of 0.52% that is mainly caused by the switching ripple, thus confirming the correctness of the voltage design dynamics proposed in
Section 4. For the calculation of the ARE,
corresponds to the voltage obtained in the PSIM circuital simulation, while
corresponds to the theoretical value.
The waveforms in
Figure 17 also confirm the correct tracking on the reference (
in dashed black trace) with the desired settling time
s, which validates the accurate voltage control design proposed in
Section 4.1. The compensation of such a reference change is introduced, by the voltage controller, into the SMC by means of the current reference
, which acts on the switching circuit by means of the switching function
. The simulation results show the waveform of
, where the voltage controller compensation can be observed.
It is worth noting that this accurate regulation of the PV voltage is performed in presence of a large perturbation in the output voltage
(i.e., the DC-link). In this example, the perturbation is equal to a 25% peak-to-peak sinusoidal oscillation at double the grid frequency (120 Hz), which corresponds to the perturbation introduced by a grid-connected inverter with a non-electrolytic DC-link. This perturbation is large in comparison with the DC-link oscillations considered for the validation of other first-stage solutions:
Table 4 reports some examples of the peak-to-peak oscillation amplitudes adopted in literature to validate the first stage of microinverters, which are between 1.9 and 500 times smaller than the oscillation adopted in this example, thus requiring a much larger DC-link capacitor. This comparison provides a measurement of the reduction in the DC-link capacitance requirements obtained with the solution proposed in this paper.
The simulation results given in
Figure 17 also report the duty cycle produced by the SMC, where no saturation occurs (
), confirming that the equivalent control condition analyzed in
Section 3.3 is fulfilled. In addition,
Figure 17 reports the output current
of the NEC boost converter, which is always continuous as expected, hence, providing a much better power quality in comparison with the classical boost converter. Moreover, it is observed that the SMC modulates into
(and
d) the perturbation present on
, thus avoiding the transmission of such a perturbation into the PV voltage, which ensures stable operation of the PV module even under large output voltage oscillations. Finally, the waveform of the switching function
is always trapped inside the desired hysteresis band
with
A; this confirms that both the reachability and transversality conditions analyzed in
Section 3.1 and
Section 3.2 are always fulfilled. In conclusion, the previous results validate the global stability of the SMC in presence of large perturbations, and verify the correct design of the voltage controller to impose the desired behavior to the PV voltage.
A third simulation scenario was designed to evaluate the performance of the complete PV system, including the action of the P&O algorithm. Such a simulation, reported in
Figure 18, considers fast changes on the irradiance condition (i.e., high derivatives of 1000 (W/m
)/ms) to test the correct performance of the control system. In particular, the irradiance starts at the highest value possible (1000 W/m
), falling to the lowest irradiance considered in this example (250 W/m
); then, the irradiance changes to 500 W/m
and, finally, to 750 W/m
. The results of this simulation confirm the correct operation of both the P&O algorithm and control system: the PV voltage (
) exhibits a 3-point behavior around the MPP voltage (
) for each irradiance condition, thus ensuring that the P&O reference (
) reaches the optimal operation condition for every irradiance value as demonstrated in [
27,
37]. This optimal condition is also confirmed by the power produced by the PV panel (
), which always reaches the maximum power possible (
) for every irradiance value. Finally, in the
ms of this simulation, the complete PV system extracts
of the maximum energy available, which puts into evidence the correct operation of the system.
Therefore, the simulation scenarios presented in this section validate the following conditions:
The design process for the NEC boost converter is correct.
The mathematical analysis of the SMC is correct and practically verifiable.
The design process for the SMC is correct, ensuring the global stability of the PV system even under the presence of large perturbations.
The design process for the voltage controller is correct, ensuring the tracking of the reference with the desired settling time.
The designed PV system, based on the NEC boost converter, ensures the extraction of the maximum PV power and provides a continuous current to the DC-link, resulting much better power quality in comparison with the classical boost converter.
7. Conclusions
This paper proposes a new solution for the first stage of a PV microinverter, which enables the reduction of the DC-link capacitor to non-electrolytic values, thus improving the system reliability. This solution is based on the NEC boost converter and an SMC, providing a precise design process for the complete solution.
The NEC boost converter provides continuous input and output currents, similar to the Cuk converter, but without the voltage inversion, hence simplifying the sensing circuits. Moreover, the proposed PV system imposes lower stress in the internal capacitor and input inductor in comparison with the Cuk converter. The continuous current condition provided by the NEC converter could be also useful to design battery chargers/dischargers, since high-frequency current harmonics affect both the battery health and the DC bus power quality. In addition, the voltage conversion ratio is the same one obtained with a boost converter; hence, the NEC boost topology can be used to replace classical boost converters in existing applications. This could improve the overall efficiency because the RMS current provided by the NEC boost converter is lower than the RMS current provided by the classical boost option, which reduces the ohmic losses on the elements of the second stage. Despite the additional complexity of the NEC boost converter, the paper presents a detailed modeling set formed by the switched model, the averaged model, and the steady-state relations. Those models can be used to design new control strategies for the proposed first PV stage.
The global stability of the proposed SMC was mathematically demonstrated, which enables the first stage to be used in any operation condition including fast-changing irradiance. Moreover, this SMC enables the proposed PV system to be scaled to any power level. However, the dynamic limitation introduced by the reachability conditions must be taken into account in the design; thus, a prior knowledge is needed of the fastest irradiance change to be experimented. This aspect was taken into account in the step-by-step design procedure proposed for the PV system.
The implementation of the proposed control system mixes both analog and digital circuits, which provides flexibility to include additional features such as diagnostic algorithms or more complex MPPT algorithms. In fact, one future improvement is to study the inclusion of MPPT algorithms designed for partially shaded PV systems, which could improve the microinverter’s flexibility by enabling the connection of small PV arrays.
In any case, the results obtained in the circuital simulations were satisfactory, since all the theoretical predictions were confirmed with realistic and non-linear simulations. Those results provide confidence to the proposed solution, since the commercial power electronics simulator has been also adopted to validate other microinverters reported in literature. However, the experimental implementation of the proposed first stage will have some challenges that must be addressed in future developments. For example, the resolution of the comparator used in the switching circuit could modify the switching frequency; thus, a safety margin must be introduced into the calculation of the hysteresis width. Another implementation problem to face is the tolerances of the electronics devices; thus, safety margins on the ripple requirements must be also introduced. The largest implementation problem will be the microprocessor interface with the analog circuitry, since the resolution of both the ADC and DAC will introduce errors into the switching function calculation: 10-bit resolution (usually provided in microcontrollers at 5 V) could introduce mV errors, which is half of the PV voltage ripple; instead, the suggested microprocessor TMS320F28335 has 12-bit resolution, which only introduces mV errors, but at a higher cost in comparison with a traditional microcontroller. Therefore, the correct selection of the microprocessor will have a large impact on the operation of the proposed PV system. Finally, the parasitic losses on the inductors and semiconductors will affect the converter efficiency; hence, a correct balance between low parasitic resistances and element cost must be achieved.