This paper presents a grid-connected PV system in a centralized configuration constructed through a three-phase dual-stage inverter. For the DC-DC stage the three-phase series resonant converter is chosen thanks to the advantages that it exhibits. However, it is inadequate for the accomplishment of MPPT, due to its efficiency strongly depending on the implemented deadtime and switching frequency. Then, this paper proposes a conceptual modification, that is, a modified dual-stage inverter in which the inverter stage is responsible for both the MPPT and the grid-current control. In addition, the DC-DC converter operates with constant duty cycle and frequency. Such configuration requires a new concept, introduced as Behavior Matching. It serves as a fundamental feature for the DC-DC converter to reproduce the PV array I–V characteristic when they are connected, without control action. The maximum power operating point is found by maximizing the direct axis current, obtained by Park's transformation from the inverter, through the perturbation and observation algorithm. Any specific measurement to realize the MPPT is needed. The galvanic isolation is achieved by using a high-frequency transformer. The structure is appropriate for high power applications, above 10 kW.
1. Introduction
The photovoltaic solar energy represents an emergent technology in function of the continuous fall in the production costs and in the technological progress of the PV modules. This alternative energy can significantly contribute with the reduction in the emission of greenhouse gases in the atmosphere, which attack the environment deeply.
Around 75% of the PV systems installed in the world are grid connected [1]. In the grid-connected PV system, DC-AC converters (inverters) need to realize the grid interconnection, inverting the dc current that comes from the PV array into a sinusoidal waveform synchronized with the utility grid [2, 3]. Besides, the DC-AC converter is used to stabilize the dc-bus voltage to a specific value, because the output voltage of the PV array varies with temperature, irradiance, and the effect of MPPT (maximum power point tracking) [4–23]. The DC-AC conversion systems, depending on its topology, can be classified as presented as follows [24, 25].
Single-stage inverter: in one processing stage, MPPT and grid-current control are handled (Figure 1).
Dual-stage inverter: a DC-DC converter performs the MPPT and a DC-AC one is responsible for the grid-current controlling (Figure 2).
Multistage inverter: various DC-DC converters are used for the MPPT and only one DC-AC converter takes care of the grid-current control (Figure 3).
Single-stage inverter without a DC-DC converter.
Photovoltaic solar energy flowing through two conditioning converters.
Low power DC-DC converters connected to strings and one large DC-AC in the grid interface.
The inverters previously shown give an idea about the control and the DC-DC converters’ application. It is worth to discuss in more details how the PV modules are connected with inverters and these are connected with the grid. There are four configurations commercially accepted [26–30].
Central-plant inverter: usually a large inverter is used to convert DC output power of the PV array to AC power. In this system, the PV modules are serially string and several strings are connected in parallel to a single dc-bus. A single or a dual-stage inverter can be employed. Figure 4 illustrates this configuration.
Multiple-string DC-DC converter: each string has a DC-DC converter, which can be galvanically isolated. There is a common DC link, which feeds a transformerless DC-AC converter. As shown in Figure 5, only the multistage inverter can implement this configuration.
Multiple-string inverter: several PV modules are connected in series on the DC side to form a string. The output from each string is converted to AC through a smaller individual inverter. Many such inverters are connected in parallel on the AC side, as shown in Figure 6. A single or a dual-stage inverter can be employed in this kind of configuration.
Module-integrated inverter: each module has a small inverter, and each one is connected in parallel forming an ac-bus, which is connected to the AC grid. Once more, a single or a dual-stage inverter can be used. Figure 7 shows this configuration.
Central-plant inverter.
Multiple-string DC-DC converter.
Multiple-string inverter.
Module-integrated inverter.
Table 1 summarizes the implementation options of a grid-connected PV power system.
Implementation options of a grid-connected PV power system.
Configurations
Topologies
Single-stage inverter
Dual-stage inverter
Multistage inverter
Central-plant inverter
✓
✓
✗
Multiple-string DC-DC converter
✗
✗
✓
Multiple-string inverter
✓
✓
✗
Module integrated inverter
✓
✓
✗
The high efficiency is one of the most important characteristics of a PV inverter. Thus, whenever possible, these inverters are nonisolated electronic circuits, since a transformer imposes an efficiency drop. This efficiency drop is 2% larger for a low than that for a high-frequency transformer [1]. Hence, when grid isolation is mandatory, the incorporation of a high-frequency transformer is a trend. This implies the need for a DC-DC converter in the structure of the PV power system. The isolated ZVS Full-Bridge DC-DC converter [31–38] is usually used at power levels above 750 W [24], to performer both the MPPT and the galvanic isolation. Commonly, its efficiency ranges from 92% to 93% under a 45% to 100% load condition [39]. This performance is not recommended for high power industrial applications. With nonisolated versions, the efficiency can be increased from 96% to 98% [39].
As an alternative to Full-Bridge based converters, the three-phase conversion has some advantages, such as the following [40].
Reduced switching stresses of the power semiconductor devices.
Reduced size and ratings of associated reactive components.
Better transformer copper and core utilization.
As important as high efficiency, it is the inverter cost. The study in [24] indicates the centralization of inverter (central-plant inverter) for reducing cost, according to plant shown in Figure 4.
From the context previously presented, and considering to improve the volume and weight of the whole system, a dual-stage inverter configured in a central-plant, according to Figures 2 and 4, is proposed in this paper, however, with two basic differences.
(1) Uses a three-phase DC-DC converter in place of a single-phase. In [40], it is demonstrated that the three-phase conversion has some advantages such as the following.
High-frequency transformer reduction in comparison to the transformer used in a Full-Bridge DC-DC converter, operating with the same switching frequency.
Increase of three times in the input and output current frequencies, reducing the size of the filters components.
Better distribution of the losses.
The three-phase isolated DC-DC series resonant converter (SRC3) [41, 42] was applied to act as DC-DC stage. Despite the galvanic isolation, the measured efficiency of the DC-DC stage was limited to 96%–97.5% under a 45%–100% load condition.
(2) The MPPT will not be carried out by a DC-DC stage; it will be performed by the inverter, which is also responsible for the grid-current control. It is important to emphasize that any measurements of voltage or current in the photovoltaic array are made. It is an indirect MPPT, possibly due to the behavior matching between the DC-DC converter output I–V characteristic and the PV array I–V characteristic, when they are connected. Then, behavior matching serves as a fundamental feature for DC-DC converters to reproduce the PV array I–V characteristic without control action. The studies in [43–45] indicate this possibility.
The traditional dual-stage inverter implements some control strategy in the DC-DC stage [46–50]. In this paper, a conceptual modification is proposed that is called Modified Dual-Stage Inverter [51, 52]. In this new approach, there is no control in the DC-DC stage, the SRC3 operates with constant frequency and duty-cycle, representing a very high efficiency operation. All the control, MPPT, and grid-current are implemented in the DC-AC stage (inverter) that consists of a three-phase bidirectional power flow PWM voltage source inverter (VSI3). This is the principal power electronics circuit of a Three-Phase Grid-Connected PV Power System. Figure 8 shows the basic idea of a modified dual-stage inverter.
Modified dual-stage inverter.
The DC-AC stage performs the MPPT through the P and O method [22, 49, 53–58] to maximize the direct axis current, Id, required for the grid current control. The current Id reflects the active power delivered by the photovoltaic array and is expressed through the inverter modeling, using the Park transformation [59, 60]. Then, the inverter output power is maximized without additional sensors. In a single-stage inverter, this principle can also be used. Figure 9 presents the proposal topology for the dual-stage inverter in a three-phase configuration.
Three-phase dual-stage inverter in centralized configuration.
2. Photovoltaic Array Modelling
It was commented previously that the proposed MPPT is based on the behavior of the photovoltaic array by means of temperature and irradiation variations. Thus, the mathematical model of the PV cells is implemented in the form of a current source controlled by voltage, sensible to two input parameters, that is, temperature (°C) and solar irradiation power (W/m^{2}).
An equivalent simplified electric circuit of a photovoltaic cell is presented in Figure 10.
Equivalent electric circuit of a simplified single-diode model (SSDM) of a PV solar cell.
Although it is a simplified version, this equivalent circuit is enough to represent different types of photovoltaic cells when the temperature effects are considered [61]. From [62], it is verified that the cells of polycrystalline material are contemplated. This material is distinguished because information gotten of datasheet of a polycrystalline module is used in the simulation studies; however, the relevant aspects for the control, shown from the modeling, are not only applied to this type of material.
In a more complete version, the equivalent circuit of Figure 10 has two electrical resistors, Rs and Rp [63–65]. According to [66, 67], both resistors can be neglected. However, it is demonstrated that the series resistor, Rs, has a great impact on the inclination of the I–V characteristic curve, becoming it more accurate between the maximum power operating point and the open circuit voltage. This information can also be found in [68].
Expression (1) can be obtained from Figure 10:
(1)I=Iph-Ir·[eq·(V+I·Rs)/npn·k·T-1],
where V and I: voltage and current across the cell; Iph: photocurrent; Ir: cell reverse saturation current; q: charge of an electron; Rs: intrinsic series resistance of the cell; npn: ideality factor of the p-n junction; k: Boltzmann’s constant; T: temperature.
The photocurrent depends on the solar irradiation and the temperature, given by (2):
(2)Iph=[Isc+α·(T-Tr)]·Psun1000,
where Isc: short-circuit current; α: temperature coefficient of the short-circuit current; Tr: reference temperature, for standard condition; Psun: irradiance level. The standard power is 1000 W/m^{2}.
The reverse saturation current varies according to the temperature, as shown in (3):
(3)Ir=Irr·(TTr)3·e[((q·EG)/(npn·k))·(1/Tr-1/T)],
where Irr: cell reference reverse saturation current; EG: band-gap energy of the semiconductor used in the cell.
These equations can be found in [66, 69]. The solution of (1) takes the characteristic curve for only one photovoltaic cell. However, the model is such that, if connected in a PV array form, it can be treated as only one cell with multiple associations in series and parallel [68]. Thus, the photovoltaic array, corresponding to two parallel-connected strings, is simulated. Each string contains ten modules, which approximately produce the operation voltage of 263 V. Therefore, it is found that a 4 kWp array formed by KC200GT modules from Kyocera. Figures 11 and 12 reflect the behavior obtained with the PV array modeling which is connected to DC-DC converter.
Current-voltage characteristics of photovoltaic array at various irradiance levels.
Current-voltage characteristics of photovoltaic array at various temperatures.
3. Dual-Stage Inverter
It is desired the system to be suitable for high power applications, above 10 kW. Thus, the two stages of the inverter are three-phase configurations.
3.1. DC-DC Stage
When the single-phase DC-DC converter is replaced by a three-phase one, several advantages appear [40]:
faster response times;
low stresses on active devices;
filters components reduction;
high-frequency transformer reduction.
Amongst the three-phase DC-DC converters, most attractive they are those that present soft commutation. This characteristic is important due to be high switching frequency in which they can operate, keeping the high efficiency and the heat sinks size in reasonable levels. In addition, with the rise of the switching frequency, a significant reduction in the transformer size and weight is obtained.
Various three-phase DC-DC converters with soft commutation are available [41, 42, 70–72]. Each of them was evaluated about the efficiency in different input power levels, components number, EMI emission, performance under unbalanced conditions, and power range. The topology that appears to relate the best characteristics for the proposal application in this paper is presented in Figure 13, obtained from [42]. The transformer was replaced by their leakage inductances, Ld.
DC-DC three-phase series resonant converter (SRC3).
The switches are gated by 6 phase-shifted signals. Neglecting the deadtime between two switches in each inverter leg, all switches are turned on exactly half a period.
When the switching frequency, fs, is equal to resonance frequency, fr, the converter operates in ZCS. If fs>fr, the converter operates in ZVS. In this condition, the efficiency is much reduced for low-power transfer [42, 73]. Then
(4)fs=fr=12·π·Ld·Cr,(5)Iin=Ipv=6π2·Rloss(Vin-Vdc′),
where Iin: average input current; Ipv: PV array current; Vdc′: average output voltage of the three-phase bridge rectifier, referred to the primary side; Vin: average DC-DC converter input voltage; Rloss: take all losses into account, such as the conduction and switching losses of the switches and diodes, the dielectric losses of the capacitors, the copper and iron losses of the three-phase transformer, and the conduction losses of wires and connections; Ld: leakage inductance of the transformer; Cr: resonant capacitor.
The transformer turn’s ratio can be defined by the following:
(6)n=N2N1,
where N1: number of turns on the transformer primary winding; N2: number of turns on the transformer secondary winding.
From (5) and (6), (7) and (8) can be found:
(7)Rloss=6π2·Iin(Vin-Vdcn),(8)Vin=π26·Rloss·Iin+Vdcn.
A peculiarity about this converter is that, despite the many advantages that it presents, it is inadequate for the accomplishment of MPPT, due to that its efficiency extremely depends on the implemented deadtime and switching frequency [42]. These variables should not vary. That deficiency can be neglected thanks to the Behavior Matching [44, 45, 51, 52, 74].
3.2. DC-AC Stage
Two new trends for this stage are discussed in [75, 76], using LCL filters on a grid interface and replacing the conventional three-level PWM inverter by a multilevel inverter. The objectives are the same: lower total harmonic distortion (THD) and more compact designs. However, for the application presented in this paper, the three-phase current-controlled voltage-source inverter with L filter is adequate.
The inverters used for grid interfacing are broadly classified as voltage-source inverters (VSI) and current-source inverters (CSI). The control schemes can be classified as current-controlled inverters (CCI) and voltage-controlled inverters (VCI).
PV solar arrays are fairly good approximation to a current source. Then, most PV inverters are voltage source. In addition, with vector modulation [77–82], the THD measured is insignificant when harmonics below the switching frequency are considered.
The current-controlled scheme objective is to control active and reactive components of the current fed into the grid. The current controllers are better suited for the control of power export from PV inverters to the utility grid since they are less sensitive to errors in synchronizing sinusoidal voltage waveforms [83]. The structure of the three-phase current-controlled voltage-source inverter is shown in Figure 14.
Three-phase current-controlled VSI.
Performing a Park transformation, its dynamical model in the dq-frame can be described by the following:
(9)dIddt=VdL+ω·Iq-RL·Id-VdcL·Dd,dIqdt=-ω·Id-RL·Iq-VdcL·Dq,dVdcdt=-IdcCf2+IdCf2·Dd+IqCf2·Dq,
where Id, Iq, Vdc: state variable; Dd, Dq: control variables; L=L1=L2=L3; R=R1=R2=R3: intrinsic resistance of the inductance L1,L2,L3, respectively; Vd, ω: utility grid parameters (Vd=3·Vg, and Vg is the grid rms phase voltage, and ω=2πf, where f is the grid frequency); Idc: average output current of the three-phase bridge rectifier, that is, the average input current of the three-phase VSI.
Since Pg=Vd×Id represents the power that the inverter injects in the grid, the MPPT can be performed perturbing Vdc and observing Id, according to the following:
(10)Vdc(k+1)=Vdc(k)+ΔV·sign[Vdc(k)-Vdc(k-1)]·sign[Id(k)-Id(k-1)].
Setting Vdc, the DC-AC stage defines the DC-DC converter’s input characteristic behavior, who determines the PV array operation point. When Id is maximized, the PV array operates on MPOP. As noted, Id and Vdc, used by MPPT, are state variables employed in the grid-current control, that is, additional hardware is not need. Section 4 explains this behavior in detail, which represents the behavior matching of the proposed dual-stage inverter.
4. Behavior Matching and the MPPT Proposal Technique
The indirect MPPT is a type of tracking that uses the connection between measured variables and the position of the maximum power operating point (MPOP). Some variables as temperature and PV generator’s open circuit voltage are used. It is not a true MPPT technique.
The direct MPPT requires, in principle, a measurement of generator voltage and current as well as a multiplication of these variables [84–95].
In both cases, specific measurements for MPPT are made. In the proposed grid-connected dual-stage inverter, the direct axis current, Id, is observed, which serves for the inverter stage to set Vdc. These actions define the DC-DC converter’s input characteristic behavior, which determines the PV array operation point [96]. When Id is maximized, the PV array operates on MPOP. As noted, the variables used in the MPPT are Id and Vdc, initially employed in the grid current control, that is, any specific measurement for MPPT’s purpose is made.
The DC-DC converter operates with constant duty cycle and frequency. It is designed to work with an efficiency of 97% coupled to the PV array shown in Section 3.1, working under Standard Test Conditions (STC) (irradiance of 1 kW/m^{2}, spectrum of 1.5 air mass, and cell temperature of 25°C), resulting in Rloss = 0.32 Ω and Vdc′ = 255 V. Thus, (5) results in
(11)Iin=1.9(Vin-255).
Equation (11) is drawn in Figure 15. This illustration also demonstrates that when MPPT is put in action by the inverter stage, Vdc vary, it shifts the DC-DC converter input I–V characteristic.
DC-DC converter input I–V characteristic.
The Behavior Matching depends on the DC-DC converter input characteristic at an operation point. Several single and three-phase converters exhibit appropriate input characteristic to present Behavior Matching [45, 50, 94, 97–101]. In the case of SRC3, the input characteristic curve is a straight line with a small inclination.
It is important to register that this inclination favors the MPPT on irradiation variations. If this straight line fall together with the line formed by union of the MPOPs, would not be necessary the intervention of the inverter stage is necessary just in the temperature variations, when Vd must be changed in order to move the straight line for a new position, searching the MPOP. Putting upon Figures 11 and 15, the approaching between the DC-DC converter’s input characteristic and the MPOPs can be found, as shown in Figure 16.
Crossing between SRC3 and 4 kWp PV array I–V characteristic curves.
The PV array operation point is defined by the crossing of its respective I–V characteristic curve with the DC-DC converter input characteristic curve. Then, Ipv and Idc are also defined. Figure 17 presents simulation results where it can be seen that the PV array behavior, represented by its I–V characteristic, is reproduced on the DC-DC stage output terminals, represented by Idc×Vdc. From the controller point of view, Idc×Vdc is similar to Ipv×Vin. Thus, MPPT task is to extract the maximum power of the DC link, or to inject the maximum power in the grid. The strategies are different, but the result is the same: both tune the DC-DC stage input I–V characteristic to the PV array MPP. Therefore, Figure 17 shows that the DC-DC stage’s output has behavior matching that of the PV array’s output terminals.
Behavior matching verifying.
The Behavior Matching Technique bring significant advantages always that the input characteristic curve of the DC-DC converter is located near the MPP of the PV array, for all tracking algorithm range. Step-down DC-DC converters, with similar input Buck behavior, are eligible to integrate a modified dual-stage inverter.
4.1. MPPT Proposed Technique Using P and O Algorithm
The MPPT proposed technique, using P and O algorithm, has the following procedure.
The temperature and the solar irradiation in the PV array modules vary in different ways. The clouds movement can result in brusque alterations in the irradiance level. However, the temperature tends to vary much more slowly.
The MPOP can be tracked by a DC-DC converter through its input characteristic. Since temperature remains constant, there is no necessity for the inverter intervention, whose task is to keep the voltage Vdc clamped in a reference.
However, periodically, the inverter, through a P and O algorithm, regulates the value of Vdc in order to shift the DC-DC converter input characteristic, which can be crossing with the array I–V characteristic far from the MPOP due to a temperature variation. Besides P and O, others algorithms can also be used.
The topology of the inverter is presented in Figure 14, where Va, Vb, and Vc represent the AC grid phase voltages. It is verified that P and O block is fed by the direct axes current, Id, obtained from Park’s transformation. According to [102], the power that the inverter injects in the grid is given by Pg=Vd×Id, where Vd is constant. Thus, the MPPT can be indirectly performed, perturbing Vd and observing Id. The Vd perturbation at the (k + 1)th sampling is given by (10).
5. Design Example
The PV array consists of two parallel strings, each with ten KC200GT modules from Kyocera. This PV array defines the nominal input power of the dual-stage inverter, whose value is Pin = 4 kW, with Vin = 263 V and Iin = 15.2 A. The estimated efficiency for the DC-DC stage is ηDC = 97%. Then, the output power of the DC-DC stage is Pdc = 3880 W and the same value in the input of the DC-AC stage is obtained. The switching frequencies of the DC-DC and DC-AC stages are fDC = 40 kHz and fAC = 20 kHz, respectively. The grid rms phase voltage is Vg = 220 V.
5.1. PV Array Parallel Capacitor (Cf1)
The PV array parallel capacitor is obtained from (12), where ΔVin is the peak-to-peak ripple on the DC-DC stage input voltage. The adopted value is ΔVin = 1.0% Vin = 2.63 V:
(12)Cf1≥Iin215·fDC·ΔVin=15.2215·40k·2.63≥672.03nF.
A polyester capacitor of 680 nF is used.
5.2. DC-AC Stage Input Capacitor (Cf2)
According to (13) [73], the input capacitor of the DC-AC stage is obtained. The ripple ΔVCf2 needs to be a magnitude perturbation’s percentage involved in the P and O algorithm. The adopted value is ΔVCf2 = 0.2 V, while the magnitude perturbation is 4 V:
(13)Cf2≥Pdc12·2·Vg·ΔVCf2·fAC=3880122·220·0.2·20k≥259.81μF.
The adopted value of Cf2 is 333 μF, obtained by a series association of three electrolytic capacitors of 1000 μF.
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The grid line inductors are calculated by (15), assuming phase current ripple equal to ΔIL = 0.42 A. This value corresponds to 5% of the peak line current, obtained by (14) and is sufficient to keep the THD below 5% [73]:
(14)ILpk=2·Pdc3·Vg=2·38803·220=8.31A,(15)L=2·Vg4·fAC·ΔIL=2·2204·20k·0.42⇒L=9.3mH.
5.4. Resonant Capacitor (<italic>Cr</italic>)
The three-phase transformer is constructed with three single-phase transformers, in wye connection. The turns ratio is defined by n=N2/N1=3.2. The leakage inductances have been measured to Ld = 3.6 μH. Applying (4), this results in a resonant capacitor of Cr = 4.4 μF, for ZCS operation. Polypropylene capacitors were adopted.
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The average DC-link voltage referred to primary side can be calculated from (16) [73]:
(16)Vdc’=ηDC·Vin=0.97·263⇒Vdc’=255V.
The voltage presented in (16) is raised to Vdc = 816 V by n=3.2. This turns ratio keeps the DC-link voltage above 600 V for all MPPT ranges.
In nominal conditions, to sinusoidal resonant currents, the losses are found around Rloss = 0.32 Ω, according to (7).
5.7. Main Data of the Laboratory Prototype
A SK20GD065 Semikron IGBT module was used. The diode bridge was made with six ultrafast recovery rectifiers FFPF05U120S, of 1200 V and 5 A. A top view of the prototype is depicted in Figure 18.
Laboratory prototype of the modified dual-stage inverter.
6. Simulation and Experimental Results
The specifications of the whole system are given in Section 5.
6.1. DC-DC Three-Phase Series Resonant Converter (SRC3) Performance
A compare unit pertained to a peripheral of the Texas TMS320F2812 controller was configured to generate six gate pulses for SRC3, with duty cycle of 50% and deadtime of 640 ns. The same DSP carried out the grid-current control and the MPPT.
Figure 19 shows the resonant currents. Obviously, the leakage inductances of each phase are not exactly the same. These asymmetries cause small differences in resonant currents amplitudes. However, this has a negligible impact on the SRC3 operation.
Resonant currents under nominal conditions.
Figures 20 and 21 present the input and output currents of the DC-DC stage for different power conditions. These currents have a low ripple and a frequency of six times that of the switching frequency, resulting in a continuous power flux. These features are not common among three-phase DC-DC converters and lead to reduced filter devices. The PV array parallel capacitor is of only 680 nF, for example. The voltage ripple on it is showed in Figure 22. This ripple was produced by the current Iin of Figure 21. It has a negligible impact above PV array efficiency.
Input and output currents of the DC-DC stage and collector-emitter voltage, under nominal conditions.
Input and output currents of the DC-DC stage and collector-emitter voltage, with Pdc = 500 W.
PV array output voltage for Pdc = 500W (400 mV/div).
The ZCS commutation is shown in detail in Figure 23. Unfortunately, the commutation losses drastically increase at low power levels, according to Figure 24. Figure 25 shows the SRC3 efficiency.
Resonant current and collector-emitter voltage, under nominal conditions.
Resonant current and collector-emitter voltage, for Pdc = 500 W.
SRC3 efficiency.
6.2. Behavior Matching
This subsection presents experimental results that validate the Behavior Matching technique.
Figure 26 shows the harmonic spectrum of the voltage across the resonant circuit [42]. The fundamental frequency is 40 kHz, that is, the resonant frequency.
Harmonic spectrum of the voltage across the resonant circuit.
The impact of the voltage harmonic components on the resonant current depends on the resonant circuit quality factor, presented as follows:
(17)Q=2·π·fr·LdRloss.
The requirement of large impedance for frequencies that are different of the resonant frequency is fulfilled when the quality factor Q is high. The value of Q is high in nominal conditions, such as Figure 23. On the other hand, for low SRC3 output power rate, the Q value is low too, according to Figure 24. This occurs due increasing of Rloss for output powers below of approximately 1700 W. Figure 25 points to decreasing of efficiency below this power. Larger Ld could reduce the power from which Rloss rises. The efficiency would be more flat.
Figure 27 depicts the consequence of the resonant current distortion. For high rated power, the ratio Iin/Idc = 3.2 = n. For low rated power, the ratio transformer is affected.
Input and output currents ratio in the DC-DC stage.
In conclusion, when Rloss increases, the equivalent ratio transformer (Iin/Idc) also rises.
Reporting to (8), it is verified that Vin could be continuously reduced with the DC-DC stage output power reduction. This effect is depicted in Figure 28. Thus, variations in Rloss are compensated by variations in the equivalent ratio transformer. Moreover, they have the same cause.
DC-DC converter input I–V characteristics.
The inclination of the SRC3 input I–V characteristic, for all Vdc operation range, is given by (18), obtained from (5). Figure 28 shows experimentally measured points of SRC3 prototype input I-V characteristic
(18)dIndVin=6π2·Rloss=2.3A/V.
The DC-DC converter’s input characteristic has a propitious behavior to MPPT algorithm. Putting Figure 28(Vdc=816V) on the PV array I–V characteristic curves, the proximity between the DC-DC converter’s input characteristic and the MPP loci can be established, as shown in Figure 29. This collaborates with the MPPT performance for fast changes in atmospheric conditions.
Crossing between SRC3 and PV array characteristic curves.
6.3. MPPT Performance
This subsection presents simulation results that reflect the possibility to perform the MPPT using the direct axis current (Id).
The mathematical model of a 4 kWp PV array is accurately implemented in the form of a current source controlled by voltage, sensible to two input variables, that is, temperature and solar irradiation power. This model simulates the physical PV array.
The MPOP’s shift is an almost horizontal line when the temperature changes, see Figure 12. The intersection between the characteristics of the PV array and DC-DC converter can deviates from the MPOP. If Vdc is keeping constant, thus Vin stays, approximately, constant too. This implies that Ipv and the power from PV array (PMPPT) will decrease. Figure 30 shows the consequences of cell’s temperature changes from 25°C to 35°C. The irradiance is 1 kW/m^{2} and the air mass is of 1.5.
Temperature variation and consequences.
In order to solve this problem, the P and O method is put in action in the DC-AC stage, as shown in Figure 31. The P and O parameters are Ta = 50 ms and ΔV = 4 V (ΔV is the perturbation magnitude and Ta is the sampling interval). Thus, in order to maximize the Id current, each 50 ms, the Vdc voltage is perturbed by 4 V on its magnitude. This perturbation can be added or subtracted of Vdc. The MPPT algorithm resolves based on the variation of Id. The system uses a turns ratio transformer of 1 : 3.2. Figure 32 shows a zoom on the PV array characteristic curves with the positions (initial, intermediate, and final) of the operation point.
Execution of the Vdc perturbation and Id observation algorithm.
I–V characteristic curves of the PV array.
Figure 33 depicts the trajectory of the PV array output power (PMPPT) as a consequence of the Vdc adjustments, drawn from Figure 31. The relative tracking error, εR, practically achieves zero in steady state conditions. This occurs due to the shifting of the SRC3 input I–V characteristic close to the MPOP.
MPPT performance.
6.4. Performance of the DC-AC Three-Phase Stage
The DC-AC stage is performed by a three-phase PWM voltage source inverter (VSI3) controlled by current, whom power topology is presented in Figure 14. The space vector modulation (SVM) is used in order to minimize the THD of the grid current.
Figure 34 depicts the utility voltage and the current transferred to the main power supply, both in phase a, for rated power condition. The THD of the voltage and current is shown in Figures 35 and 36, respectively. An efficiency of 95% was obtained for the DC-AC stage, and 92% for the whole system, including the DC-DC stage.
Voltage and current in the main power supply (phase a)-100 V/div; 4 A/div; 2 ms/div.
Voltage harmonic analysis of the main power supply-THD = 3.69%.
Current harmonic analysis of the main power supply-THD = 4.89%, phase angle = −175°.
Figure 37 presents the performance of the utility voltage and utility current (THD of current 4.98%, phase angle = 172°), with 32% of the full power delivery to the grid (around 1300 W). For this power conditions, the whole system efficiency is 90%. Below this power the efficiency decreases drastically.
Utility voltage and utility current with 32% of the full power-100 V/div; 2 A/div; 2 ms/div.
7. Conclusion
In this paper, a modified dual-stage inverter applied to grid-connected photovoltaic systems performed for high power applications has been studied. The modified dual-stage inverter contains DC-DC stage and DC-AC stage. Through the Behavior Matching, the DC-DC stage operates with constant frequency and duty cycle and the DC-AC stage becomes responsible for the maximum power point tracking and grid-current control. I–V characteristic of the PV array was reproduced in the output of the DC-DC stage, without any control, which was defined as Behavior Matching. Some sensors could be avoided because the grid-current control apparatus produces the variables needed for the MPPT. In addition, only one digital controller can generate gate pulses for all transistors of the PV system, which results in simpler and cheaper topology. The Behavior Matching technique allows the construction of the Modified Dual-Stage Inverter.
The three-phase DC-DC series resonant converter switching with constant frequency keeps the structure operating with the maximum efficiency and optimized transformer utilization. The topologies chosen for the converters qualify the modified dual-stage inverter for high power operation. The transformer size can be minimized by the increase of the DC-DC converter switching frequency, which is independent of the DC-AC stage. The filter elements size is also reduced due to the low ripple of DC-DC converter input and output current. As a consequence, an insignificant capacitor was used on implementation of the PV array parallel filter. Two factors mainly contributed with this advantage: the continuous current flux with low ripple and the barrier formed by the resonant circuit to electrical perturbations on DC link that did not affect the primary side voltage bus. Besides, the Series Resonant Converter features a robust operation under unbalanced conditions.
The periodic action of the inverter prevents losses and instability, inherent problems of the P and O technique. When the MPOP is found, the voltage Vdc is clamped, avoiding voltage ripple in the photovoltaic array terminals. Moreover, it can be opted for a small perturbation magnitude, minimizing the steady-state error, since the DC-DC converter is that will response for the fast atmospheric condition changes. As was seen, it possesses an extremely fast dynamics. Although P and O method was used, other techniques are encouraged.
Finally, the author expects that the efficiency and the implementation simplicity of the whole system are advantages that promote its use.
Acknowledgments
The author would like to thank the CNPq and FINEP for the financial support.
YuanX.ZhangY.Status and opportunities of photovoltaic inverters in grid-tied and micro-grid systemsProceedings of the 5th IEEE Power Electronics and Motion Control ConferenceAugust 20065935962-s2.0-4514912917010.1109/IPEMC.2006.297030KazmierkowskiM. P.MalesaniL.Current control techniques for three-phase voltage-source pwm converters: a surveyKojabadiH. M.YuB.GadouraI. A.ChangL.GhribiM.A novel DSP-based current-controlled PWM strategy for single phase grid connected invertersCostogueE. N.LindenaS.Comparison of candidate solar array maximum power utilization approachesProceedings of the Intersociety Energy Conversion Engineering Conference197614491456LandsmanE. E.BucciarelliL. L.GrossmanB. L.LyonE. F.RasmussenN. E.The energy balance associated with the use of a MPPT in a 100 kW peak power systemProceedings of the IEEE Photovoltaic Specialists ConferenceJanuary 19805235272-s2.0-0018919013SchoemanJ. J.van WykJ. D.A simplified maximal power controller for terrestrial photovoltaic panel arraysProceedings of the 13th Annual IEEE Power Electronics Specialists Conference1982361367ArcidiaconoV.CorsiS.LambriL.Maximum power point tracker for photovoltaic power plantsProceedings of the IEEE Photovoltaic Specialists Conference1982507512HartG. W.BranzH. M.CoxC. H.Experimental tests of open-loop maximum-power-point tracking techniques for photovoltaic arraysCaseM. J.SchoemanJ. J.A minimum component photovoltaic array maximum power point trackerProceedings of the European Space Power ConferenceAugust 1993107110MartinsD. C.WeberC. L.DemontiR.Photovoltaic power processing with high efficiency using maximum power ratio technique1Proceedings of the 28th IEEE Annual Conference of the Industrial Electronics Society (IECON '02)November 2002368372MartinsD. C.de AndradeA. S.BottionA.da SilvaD. P.de SouzaK. C. A.PV solar energy electronics processing system operating at the MPP for commercial refrigerator supply applications1Proceedings of the IEEE Annual Power Electronics Specialists Conference (IEEE-PESC '05)2005217223El-ShibiniM. A.RakhaH. H.Maximum power point tracking techniqueProceedings of Integrating Research, Industry and Education in Energy and Communication Engineering Electrotechnical Conference (MELECON '89)April 198921242-s2.0-0024875928ShmilovitzD.On the control of photovoltaic maximum power point tracker via output parametersFemiaN.PetroneG.SpagnuoloG.VitelliM.Optimization of perturb and observe maximum power point tracking methodCasaroM. M.MartinsD. C.Application of the three-phase series resonant converter in a dual-stage inverter operating without specific sensor to perform the MPPTProceedings of the 33rd Annual Conference of the IEEE Industrial Electronics Society (IEEE-IECON '07)November 2007165016552-s2.0-4994908619610.1109/IECON.2007.4459947CoelhoR. F.ConcerF.MartinsD. C.A study of the basic DC-DC converters applied in maximum power point trackingProceedings of the Brazilian Power Electronics Conference (COBEP '09)October 20096736782-s2.0-7795001778410.1109/COBEP.2009.5347723EsramT.ChapmanP. L.Comparison of photovoltaic array maximum power point tracking techniquesde BritoM. A. G.JuniorL. G.SampaioL. P.e MeloG. A.CanesinC. A.Main maximum Power point tracking strategies intended for photovoltaicProceedings of the Brazilian Power Electronics Conference (COBEP '11)2011524530CoelhoR. F.ConcerF. M.MartinsD. C.A simplified analysis of DC-DC converters applied as maximum power point tracker in photovoltaic systemsProceedings of the 2nd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG '10)June 201029342-s2.0-7795654961010.1109/PEDG.2010.5545753CoelhoR. F.ConcerF. M.MartinsD. C.A MPPT approach based on temperature measurements applied in PV systemsProceedings of the IEEE International Conference on Sustainable Energy Technologies (ICSET '10)December 20102-s2.0-7985148945210.1109/ICSET.2010.5684440CavalcantiM. C.OliveiraK. C.AzevedoG. M. S.NevesF. A. S.Comparative study of maximum power point tracking techniques for photovoltaic systemsCoelhoR. F.ConcerF. M.MartinsD. C.Analytical and experimental analysis of DC-DC converters in photovoltaic maximum power point tracking applicationsProceedings of the 36th Annual Conference of the IEEE Industrial Electronics Society (IEEE-IECON '10)November 2010277827832-s2.0-7875147718110.1109/IECON.2010.5675090CarrascoJ. M.FranqueloL. G.BialasiewiczJ. T.GalvánE.Portillo GuisadoR. C.PratsM. A. M.LeónJ. I.Moreno-AlfonsoN.Power-electronic systems for the grid integration of renewable energy sources: a surveyCasaroM. M.MartinsD. C.Electronic processing of the photovoltaic solar energy in grid connected systemsKasaN.IidaT.ChenL.Flyback inverter controlled by sensorless current MPPT for photovoltaic power systemLiQ.WolfsP.A review of the single phase photovoltaic module integrated converter topologies with three different DC link configurationsCalaisM.MyrzikJ.SpoonerT.AgelidisV. G.Inverters for single-phase grid connected photovoltaic systems—an overviewProceedings of the 33rd Annual IEEE Power Electronics Specialists Conference (IEEE-PESC '02)June 2002199520002-s2.0-0036443174KjaerS. B.PedersenJ. K.BlaabjergF.Power inverter topologies for photovoltaic modules—a reviewProceedings of the 37th IEEE Annual Meeting and World Conference on Industrial Applications of Electrical Energy (IAS '02)October 20027827882-s2.0-0036443035YangB.LiW.ZhaoY.HeX.Design and analysis of a grid-connected photovoltaic power systemSabatéJ. A.VlatkovicV.RidleyR. B.LeeF. C.ChoB. H.Design considerations for high-voltage high-power full-bridge zero-voltage-switched PWM converterProceedings of the IEEE Applied Power Electronics Conference and Exposition (IEEE-APEC '90)1990275284RedlR.SokalN. O.BaloghL.A novel soft-switching full-bridge DC/DC converter: analysis, design considerations, and experimental results at 1.5 kW, 100 kHzRedlR.BaloghL.EdwardsD. W.Optimum ZVS full-bridge DC/DC converter with PWM phase-shift control analysis design considerations, and the experimental results1Proceedings of the 9th Annual IEEE Applied Power Electronics Conference and ExpositionFebruary 19941591652-s2.0-0027928827de SouzaK. C. A.GonçalvesO. H.MartinsD. C.Study and optimization of two dc-dc power structures used in a grid-connected photovoltaic systemProceedings of the 37th IEEE Power Electronics Specialists Conference (IEEE-PESC '06)June 2006152-s2.0-4244913047010.1109/PESC.2006.1712265KocybikP. F.BatesonK. N.Digital control of a ZVS full-bridge DC-DC converter2Proceedings of the 10th Annual IEEE Applied Power Electronics ConferenceMarch 19956876932-s2.0-0029232263JangY.JovanovićM. M.A new family of full-bridge ZVS convertersde SouzaK. C. A.dos SantosW. M.MartinsD. C.A single-phase active power filter based in a two stages grid-connected PV systemProceedings of the 35th Annual Conference of the IEEE Industrial Electronics Society (IEEE-IECON '09)November 20091141192-s2.0-7795152303910.1109/IECON.2009.5414792de SouzaK. C. A.dos SantosW. M.MartinsD. C.Active and reactive power control in a single-phase grid-connected PV system with optimization of the ferrite core volumeLeeJ. P.MinB. D.KimT. J.YooD. W.YooJ. Y.A novel topology for photovoltaic DC/DC full-bridge converter with flat efficiency under wide PV module voltage and load rangeZiogasP. D.PrasadA. R.ManiasS.Analysis and design of a three-phase off-line DC/DC converter with high frequency isolationProceedings of the IEEE Conference Record of the Industry Applications Society Annual Meeting (IAS '88)1988813820de DonckerR. W. A. A.DivanD. M.KheraluwalaM. H.A three-phase soft-switched high-power-density DC/DC converter for high-power applicationsJacobsJ.AverbergA.de DonckerR.A novel three-phase DC/DC converter for high-power applicationsProceedings of the IEEE 35th Annual Power Electronics Specialists Conference (PESC '04)June 2004186118672-s2.0-8744220418CasaroM. M.MartinsD. C.Application of the three-phase series resonant converter in a dual-stage inverter operating without specific sensor to perform the MPPTProceedings of the 33rd Annual Conference of the IEEE Industrial Electronics SocietyNovember 2007165016552-s2.0-4994908619610.1109/IECON.2007.4459947CasaroM. M.MartinsD. C.Grid-connected PV system: introduction to behavior matchingProceedings of the 39th Annual IEEE Power Electronics Specialists ConferenceJune 20089519562-s2.0-5234909138810.1109/PESC.2008.4592052CasaroM. M.MartinsD. C.NathwaniJ.NgA. W.Paths to sustainable energyKjaerS. B.PedersenJ. K.BlaabjergF.A review of single-phase grid-connected inverters for photovoltaic modulesLiJ.ZhuoF.LiuJ.WangX.WenB.WangL.NiS.Study on unified control of grid-connected generation and harmonic compensation in dual-stage high-capacity PV systemProceedings of the IEEE Energy Conversion Congress and Exposition (IEEE-ECCE '09)September 2009333633422-s2.0-7244918229610.1109/ECCE.2009.5316516CasaroM. M.MartinsD. C.Architectural and control contributions for PV grid-connected systems applying dual-stage invertersProceedings of the 14th IEEE International Conference on Electronics, Circuits and Systems (IEEE-ICECS '07)December 20078618642-s2.0-5064911235010.1109/ICECS.2007.4511127FemiaN.PetroneG.SpagnuoloG.VitelliM.A technique for improving P&O MPPT performances of double-stage grid-connected photovoltaic systemsCruz MartinsD.DemontiR.Grid connected PV system using two energy processing stagesProceedings of the 29th IEEE Photovoltaic Specialists ConferenceMay 2002164916522-s2.0-0036953407CasaroM. M.MartinsD. C.Behavior Matching as fundamental feature to obtain a modified dual-stage inverterProceedings of the IEEE International Symposium on Industrial Electronics (ISIE '08)July 2008242624312-s2.0-5784909964410.1109/ISIE.2008.4676951CasaroM. M.MartinsD. C.Grid-connected PV system using a three-phase modified dual-stage inverterProceedings of the Brazilian Power Electronics Conference (COBEP '09)October 20091671732-s2.0-7794996611810.1109/COBEP.2009.5347762PetroneG.SpagnuoloG.VitelliM.A multivariable perturb-and-observe maximum power point tracking technique applied to a single-stage photovoltaic inverterNasrA.AliA.SaiedM. H.MostafaM. Z.Abdel-MoneimT. M.A survey of maximum ppt technique of PV systemsProceedings of the IEEE Energy TechMay 2012LiuF.KangY.ZhangY.DuanS.Comparison of P&O and hill climbing MPPT methods for grid-connected PV converterProceedings of the 3rd IEEE Conference on Industrial Electronics and Applications (IEEE-ICIEA '08)June 20088048072-s2.0-5194910836210.1109/ICIEA.2008.4582626FemiaN.PetroneG.SpagnuoloG.VitelliM.Optimizing duty-cycle perturbation of P&O MPPT technique3Proceedings of the 35th Annual IEEE Power Electronics Specialists Conference (IEEE-PESC '04)June 2004193919442-s2.0-8744267298AzevedoG. M. S.CavalcantiM. C.OliveiraK. C.NevesF. A. S.LinsZ. D.Evaluation of maximum power point tracking methods for grid connected photovoltaic systemsProceedings of the 39th Annual IEEE Power Electronics Specialists ConferenceJune 2008145614622-s2.0-5264914747910.1109/PESC.2008.4592141KumariJ. S.BabuD. C. S.BabuA. K.Design and analysis of P&O and IP&O MPPT technique for photovoltaic systemCampbellS.ToliyatH. A.DSP-based electromechanical motion controlSchonardieM. F.MartinsD. C.Application of the dq0 transformation in the three-phase grid-connected PV systems with active and reactive power controlProceedings of the Annual IEEE International Conference on Sustainable Energy Technologies (IEEE-ICSET '08)November 200818232-s2.0-6294918933110.1109/ICSET.2008.4746965XiaoW.LindM. G. J.DunfordW. G.CapelA.Real-time identification of optimal operating points in photovoltaic power systemsTsunoY.HishikawaY.KurokawaK.Temperature and irradiance dependence of the I-V curves of various kinds of solar cellsProceedings of the 15th International Photovoltaic Science & Engineering Conference (PVSEC '05)2005422423VillalvaM. G.GazoliJ. R.FilhoE. R.Comprehensive approach to modeling and simulation of photovoltaic arraysCoelhoR. F.ConcerF. M.MartinsD. C.A proposed photovoltaic module and array mathematical modeling destined to simulationProceedings of the IEEE International Symposium on Industrial Electronics (IEEE-ISIE '09)July 2009162416292-s2.0-7795014906810.1109/ISIE.2009.5214722HernanzJ. A. R.MartinJ. J. C.BelverI. Z.LesakaJ. L.GuerreroE. Z.PerezE. P.Modelling of photovoltaic moduleProceedings of the International Conference on Renewable Energy an Power Quality2010HusseinK. H.MutaI.HoshinoT.OsakadaM.Maximum photovoltaic power tracking: an algorithm for rapidly changing atmospheric conditionsMutohN.OhnoM.InoueT.A method for MPPT control while searching for parameters corresponding to weather conditions for PV generation systemsGowJ. A.ManningC. D.Development of a photovoltaic array model for use in power-electronics simulation studiesHuaC.LinJ.ShenC.Implementation of a DSP-controlled photovoltaic system with peak power trackingPrasadA. R.ZiogasP. D.ManiasS.A three-phase resonant PWM DC-DC converterProceedings of the 22nd Annual IEEE Power Electronics Specialists Conference (PESC '91)June 19914634732-s2.0-0026236041BhatA. K. S.ZhengL.Analysis and design of a three-phase LCC-type resonant converterProceedings of the 27th Annual IEEE Power Electronics Specialists ConferenceJanuary 19962522582-s2.0-0029727132OliveiraD. S.Jr.BarbiI.A three-phase ZVS PWM DC/DC converter with asymmetrical duty cycle associated with a three-phase version of the hybridge rectifierCasaroM. M.CasaroM. M.MartinsD. C.Behavior matching technique applied to a three-phase grid-connected PV systemPrroceedings of the IEEE International Conference on Sustainable Energy Technologies (ICSET '08)November 200812172-s2.0-6294916163610.1109/ICSET.2008.4746964BlaabjergF.TeodorescuR.ChenZ.LiserreM.Power converters and control of renewable energy systemsProceedings of the International Conference on Performance Engineering (ICPE '04)2004I2I20SelvarajJ.RahimN. A.Multilevel inverter for grid-connected PV system employing digital PI controllerHolmesD. G.The general relationship between regular-sampled pulse-width-modulation and space vector modulation for hard switched converterProceedings of the IEEE Conference Record of the Industry Applications Society Annual Meeting (IEEE-IAS '92)199210021009BlaabjergF.FreyssonS.HansenH. H.HansenS.New optimized space vector modulation strategy for a component minimized voltage source inverterProceedings of the 10th Annual IEEE Applied Power Electronics Conference (APEC '95)March 19955775852-s2.0-0029213209HalkosaariT.TuusaH.Optimal vector modulation of a pwm current source converter according to minimal switching lossesZhouK.WangD.Relationship between space-vector modulation and three-phase carrier-based PWM: a comprehensive analysisBatistaF. A. B.BarbiI.Space vector modulation applied to three-phase three-switch two-level unidirectional PWM rectifierLegaA.MengoniM.SerraG.TaniA.ZarriL.General theory of space vector modulation for five-phase invertersProceedings of the IEEE International Symposium on Industrial Electronics (ISIE '08)July 20082372442-s2.0-5784910178910.1109/ISIE.2008.4677169RashidM. H.JungY.SoJ.YuG.ChoiJ.Improved perturbation and observation method (IP&O) of MPPT control for photovoltaic power systemsProceedings of the 31st IEEE Photovoltaic Specialists ConferenceJanuary 2005178817912-s2.0-27944435396TeulingsW. J. A.MarpinardJ. C.CapelA.O'SolluivanD.New maximum power point tracking systemProceedings of the 24th Annual IEEE Power Electronics Specialist ConferenceJune 19938338382-s2.0-0027867378MidyaP.KreinP. T.TurnbullR. J.ReppaR.KimballJ.Dynamic maximum power point tracker for photovoltaic applicationsProceedings of the 27th Annual IEEE Power Electronics Specialists ConferenceJanuary 1996171017162-s2.0-0029726710KuoY. C.LiangT. J.ChenJ. F.Novel maximum-power-point-tracking controller for photovoltaic energy conversion systemKimT. Y.AhnH. G.ParkS. K.LeeY. K.A novel maximum power point tracking control for photovoltaic power system under rapidly changing solar radiationProceedings of the IEEE International Symposium on Industrial Electronics Proceedings (ISIE '01)June 2001101110142-s2.0-0034852732LiuX.LopesL. A. C.An improved perturbation and observation maximum power point tracking algorithm for PV arraysProceedings of the 35th Annual IEEE Power Electronics Specialists ConferenceJune 2004200520102-s2.0-8744267294DorofteC.BorupU.BlaabjergF.A combined two-method MPPT control scheme for grid-connected photovoltaic systemsProceedings of the European Conference on Power Electronics and ApplicationsSeptember 20051102-s2.0-33947634125JaenC.MoyanoC.SantacruzX.PouJ.AriasA.Overview of maximum power point tracking control techniques used in photovoltaic systemsProceedings of the 15th IEEE International Conference on Electronics, Circuits and Systems (IEEE-ICECS '08)September 2008109911022-s2.0-5784909325310.1109/ICECS.2008.4675049FarandaR.LevaS.MaugeriV.MPPT techniques for PV systems: energetic and cost comparisonProceedings of the IEEE Power and Energy Society General Meeting—Conversion and Delivery of Electrical Energy in the 21st CenturyJuly 2008Pittsburgh, Pa, USA162-s2.0-5234910963210.1109/PES.2008.4596156Lopez-SeguelJ.SelemeS. I.Donoso-GarciaP.MoraisL. F.CortizoP.MendesM. S.Comparison of MPPT approaches in autonomous photovoltaic energy supply system using DSPProceedings of the IEEE International Conference on Industrial Technology (IEEE-ICIT '10)March 2010114911542-s2.0-7795439662610.1109/ICIT.2010.5472594ScarpaV. V. R.SpiazziG.BusoS.Low complexity MPPT technique exploiting the effect of the PV cell series resistanceProceedings of the 23rd Annual IEEE Applied Power Electronics Conference and Exposition (IEEE-APEC '08)February 2008195819642-s2.0-4704910039110.1109/APEC.2008.4522996FemiaN.PetroneG.SpagnuoloG.VitelliM.Optimizing sampling rate of P&O MPPT techniqueProceedings of the 35th Annual IEEE Power Electronics Specialists Conference (PESC '04)June 2004194519492-s2.0-8744230787CasaroM. M.MartinsD. C.New method of MPPT application for dual-stage invertersProceedings of the Brazilian Power Electronics Conference2007676681LopezH. F. M.VieroR. C.ZollmannC.TonkoskiR.ReckzielgelL.GomesH.Dos ReisF. S.Analog signal processing for photovoltaic panels grid-tied by Zeta converterProceedings of the IEEE Electrical Power and Energy Conference (IEEE-EPEC '09)October 2009162-s2.0-7795144559310.1109/EPEC.2009.5420961MartinsD. C.DemontiR.Interconnection of a photovoltaic panels array to a single-phase utility line from a static conversion system3Proceedings of the 31st Annual IEEE Power Electronics Specialists Conference200012071211Cruz MartinsD.DemontiR.Photovoltaic energy processing for utility connected system2Proceedings of the 27th Annual Conference of the IEEE Industrial Electronics Society (IEEE-IECON '01)December 2001129212962-s2.0-0035695469KjaerS. B.PedersenJ. K.BlaabjergF.Power inverter topologies for photovoltaic modules—a review2Proceedings of the 37th IEEE Conference Record of the Industry Applications Society Annual Meeting (IEEE-IAS '02)October 20027827882-s2.0-0036443035MartinsD. C.DemontiR.RütterR.Analysis of utility interactive photovoltaic generation system using a single power static inverterProceeding of the 28th IEEE Photovoltaic Specialists Conference (IEEE-PVSC '00)200017191722BorgonovoD.