# Three-Phase PV CHB Inverter for a Distributed Power Generation System

^{*}

## Abstract

**:**

## 1. Introduction

^{®}are shown, and numerical results are discussed to verify the effectiveness of the proposed approach in static and dynamic conditions, even under partial shading. Conclusions are drawn in Section 4.

## 2. System Topology and Control Strategy

_{Hi,p}, with i = 1, …, N, and p = 1, 2, 3) of each H-bridge. An inductive filter L is exploited to filter the undesired harmonic components in the grid current.

#### 2.1. CHB Inverter Modeling

_{pvi,p}across the i

^{th}DC-link capacitor, the i

^{th}cell in the p-th leg provides an output voltage v

_{Hi,p}which can assume only three values (0, +v

_{pvi,p}, −v

_{pvi,p}) depending on the state of the four switches S

_{is,p}. Namely, v

_{Hi,p}= 0 if either S

_{i1,p}and S

_{i3,p}or S

_{i2,p}and S

_{i4,p}are in the ON state; v

_{Hip}= +v

_{pvi,p}when both S

_{i1,p}and S

_{i4,p}are ON; v

_{Hi,p}= −v

_{pvi,p}when both S

_{i2,p}and S

_{i3,p}are ON. As a result, the AC v

_{inv,p}waveform is composed by 2N + 1 levels given by the sum of the voltages v

_{Hi,p}.

_{inv,p}across the p-th phase can be written as follows:

_{i,p}can assume three possible values (+1, −1, 0). It is worth noting that in conventional modulation approaches, the cells are either all modulated (as in the phase shifted PWM) [20,38,39,40,41], or none are modulated (as in the level-shifted modulation) [21]. Differently from those approaches, only one set of the modulation factors h is being modulated in our algorithm, so that (1) can be written as

_{i,p}, while h = 0 makes the capacitor to be charged by the PV source. Whether the sign is + or - depends on whether v

_{inv,p}is in the positive half cycle or in the negative half cycle, respectively.

_{i,p}with a continuous switching function ${\overline{h}}_{i,p}$ bounded in the interval [−1, +1]; thus, each leg current i

_{in,p}injected into the grid can be straightforwardly related to the voltages across each cell:

_{pv,i}in accordance with the sum of the references ${v}_{pvi,p}^{ref}$ provided by the MPPT blocks (these blocks—not shown in the figure—perform a standard Perturb and Observe (P & O) algorithm). Unfortunately, in order to ensure the overall stability of the CHB inverter, the tracking voltage ${v}_{pvi,p}^{ref}$ should avoid the case that PV generators operate in the flat region of their I–V curve [42]. As a consequence, a lower boundary has to be defined, also ensuring a proper synthesis of AC-side multilevel waveform.

_{pv,i}are obtained by digitally filtering the 100 Hz ripple, thus improving the quality of the inverter output current in terms of THD [20]. On the other hand, a proper sizing of the DC-link capacitors has been performed to limit the detrimental effect of the 100 Hz oscillation on the MPPT efficiency [1].

_{d}and i

_{q}are achieved by converting the measured grid currents (abc coordinates) into dq coordinates. The outputs of the PI are the inverter reference voltages in dq coordinates, which are then converted to the three-phase reference voltages (abc coordinates); the synchronization of the dq transformation is performed by means of the phase-locked loop (PLL) circuit.

_{0}is added to the direct sequence. Indeed, according to [43], for given power unbalances among the phases, defined as

_{0}allowing the inverter neutral point to move so as to have unbalanced inverter voltages (v

_{inv,p}in Figure 1), while assuring balanced grid currents, can be found in accordance with the following equations:

_{0}are, respectively, the peak value and the phase of v

_{0}, while φ is the phase of the balanced currents.

_{is,p}in (1)) for the IGBTs (Insulated Gate Bipolar Transistor) of Figure 1. This is the innovative core of the present work, because it is at this stage that (thanks to a proper sorting algorithm) it is dynamically decided which cell of each leg has to be driven in PWM mode. Indeed, as is shown in Figure 3, the reference signal entering the PWM block depends on the index K, already defined in (2). The detailed description of the sorting algorithm is given below.

#### 2.2. The Sorting Algorithm

_{inv,p}can be synthesized by adding up the output voltages v

_{Hi}of K-1 cells (by permanently connecting them) plus one cell in PWM mode, while the others are kept in the zero output voltage state. The new idea is to determine—in every control cycle—the state of each cell depending on the voltage error $\Delta {v}_{i,p}={v}_{pvi,p}^{ref}-{v}_{pvi,p\_f}$ between the reference ${v}_{pvi,p}^{ref}$ given by the MPPTs and the filtered actual v

_{pvi,p}.

## 3. Numerical Analysis

^{®}(2012a, Mathworks, Natick, MA, USA) environment. The simulated circuit was a three-phase system with three solar panels connected to each phase, each of them feeding a devised H-bridge, so that single-panel conversion was investigated. It was built by exploiting both specially suited elemental blocks taken from the Xilinx [44] library and custom homemade Verilog [45] modules. The main advantage of this approach is that the control code could be straightforwardly implemented on a Xilinx field-programmable gate array (FPGA) platform; moreover, it allowed very realistic simulations because the actual behavior of the hardware implementation of the control code on the FPGA was emulated by performing the circuit synthesis.

^{2}) was considered, all of the P–V curves coincide each other; thus, for example, the P–V curves of the three solar panels connected to the first leg (Figure 5a) are represented by a unique curve.

_{o}(see Equation 4) is set to zero. The observed time interval of 100 ms corresponds to a MPPT period, while the switching frequency was f = 5 kHz. Moreover, the THD values of the phase currents and voltages have been calculated up to the 40th harmonic, as defined by the standard rules. The numerical results for the three-phase currents are 0.23%, 0.28%, and 0.27%, while for the modulated voltages they are 5.76%, 5.77%, and 6.40%.

_{inv,p}of the multilevel inverters are also unbalanced. As explained in the previous section, the equilibrium of the three grid currents is achieved thanks to the addition of the homopolar voltage component v

_{o}. The effectiveness of this strategy is clearly visible in Figure 9, showing the superposition of the grid currents with the grid voltages, and Figure 10 showing the phase relation among the grid currents and the modulated voltages corresponding to three phase legs. In particular, from Figure 10b it can be seen that the zero-sequence injection provides no more balanced modulated voltages while assuring balanced currents. The THD values of the phase currents and voltages have been calculated up to the 40th harmonic, as for the uniform case. The numerical results are 0.60%, 0.68%, and 0.47% for the three-phase currents, while for the modulated voltages they are 5.60%, 6.00%, and 6.20%.

^{2}to 400 W/m

^{2}in a time interval starting at 0.4 s and ending at 0.8 s, so that the MPP of that panel changed from 73 W to 40 W. From Figure 11, we observe that the MPP of the shaded panel is correctly tracked during time; at the same time, the power factor is unity in all three legs (Figure 12).

_{ds,max}= 150 V, I

_{d,max}= 170 A @ 25 °C, typical R

_{ds,ON}= 4.8 mΩ), powered an individual PV panel. The behavior of the PV panel was described by a circuital model with the same parameters reported in Table 1 and an irradiance of 800 W/m

^{2}. As in the Matlab/Simulink simulations, the CHB inverter was equipped with a 5 mH line inductor. Moreover, the PSpice simulation was conducted at a higher switching frequency (i.e., 10 kHz instead of 5 kHz) in order to deeply stress the switching behavior. Numerical results showed that the proposed modulation strategy allows a decrease of about 50% of the overall power dissipation, thus making the efficiency pass from 98.8% in the PS-PWM case to 99.4%.

## 4. Conclusions

^{®}and PSpice analysis, showing the capability of system to take all relevant parameters under control: power factor, balance of the currents, solar panel maximum power points, and dynamic power losses.

## Author Contributions

## Conflicts of Interest

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**Figure 5.**Sunny case: the operating point position corresponding to three panels in the p-th phase leg (namely, panel 1, p (pink squares), panel 2, p (orange circles), and panel 3, p (green triangles)) is highlighted with respect to the individual panel P–V curves (solid line). (

**a**) Phase leg 1; (

**b**) phase leg 2; (

**c**) phase leg 3.

**Figure 6.**Sunny case: time behavior of the output currents compared to the grid voltages related to (

**a**) phase 1; (

**b**) phase 2; and(

**c**) phase 3.

**Figure 7.**Sunny case: comparison among (

**a**) phase currents i

_{grid, p}; and (

**b**) phase modulated voltages v

_{inv,p}.

**Figure 8.**Partial shading: the operating point position corresponding to three panels in the p-th phase leg (namely, panel 1, p (pink squares), panel 2, p (orange circles), and panel 3, p (green triangles)) is highlighted with respect to the individual panel P–V curves. The solid-line P–V curves correspond to the panels under sunny conditions, while the dashed lines describe panels 2, 1 and 2, 2 under partial shading conditions. (

**a**) Phase leg 1; (

**b**) phase leg 2; (

**c**) phase leg 3.

**Figure 9.**Partial shading: time behavior of the output currents compared to the grid voltages related to (

**a**) phase 1; (

**b**) phase 2; and (

**c**) phase 3.

**Figure 10.**Partial shading: comparison among (

**a**) phase currents i

_{grid, p}; and (

**b**) phase modulated voltages v

_{inv,p}.

**Figure 11.**Dynamic partial shading: the operating point position corresponding to three panels in the p-th phase leg (namely, panel 1, p (pink squares), panel 2, p (orange circles), and panel 3, p (green triangles)) is highlighted with respect to the individual panel P–V curves. The solid line P–V curves correspond to the panels 1, p, 2, p, and 3, p under sunny condition, while the dashed line describes panel 2, p under partial shading condition. (

**a**) Phase leg 1; (

**b**) phase leg 2; (

**c**) phase leg 3.

**Figure 12.**Dynamic partial shading: time behavior of the output currents compared to grid voltages related to (

**a**) phase 1; (

**b**) phase 2; and (

**c**) phase 3.

**Figure 13.**Dynamic partial shading: comparison among (

**a**) phase currents i

_{grid,p}; and (

**b**) phase modulated voltages v

_{inv,p}.

Parameter Description | Value |
---|---|

Line inductance L (mH) | 5 |

DC-link capacitance C_{i,j} (mF) | 4.32 |

Carrier frequency (kHz) | 5 |

Parameter Description | Value |
---|---|

Inherent diode saturation current (A) | 1e-9 |

Series resistance (Ω) | 2 |

Shunt resistance (kΩ) | 7 |

Ideality factor | 1.06 |

Photogenerated current (A) | 4.8 |

Number of cells | 72 |

Phase | 1 | 2 | 3 |
---|---|---|---|

cell 1 | 625 W/m^{2} | 625 W/m^{2} | 425 W/m^{2} |

cell 2 | 300 W/m^{2} | 425 W/m^{2} | 425 W/m^{2} |

cell 3 | 625 W/m^{2} | 625 W/m^{2} | 425 W/m^{2} |

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**MDPI and ACS Style**

Guerriero, P.; Coppola, M.; Di Napoli, F.; Brando, G.; Dannier, A.; Iannuzzi, D.; Daliento, S.
Three-Phase PV CHB Inverter for a Distributed Power Generation System. *Appl. Sci.* **2016**, *6*, 287.
https://doi.org/10.3390/app6100287

**AMA Style**

Guerriero P, Coppola M, Di Napoli F, Brando G, Dannier A, Iannuzzi D, Daliento S.
Three-Phase PV CHB Inverter for a Distributed Power Generation System. *Applied Sciences*. 2016; 6(10):287.
https://doi.org/10.3390/app6100287

**Chicago/Turabian Style**

Guerriero, Pierluigi, Marino Coppola, Fabio Di Napoli, Gianluca Brando, Adolfo Dannier, Diego Iannuzzi, and Santolo Daliento.
2016. "Three-Phase PV CHB Inverter for a Distributed Power Generation System" *Applied Sciences* 6, no. 10: 287.
https://doi.org/10.3390/app6100287