# Controller for the Grid-Connected Microinverter Output Current Tracking

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## Abstract

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## 1. Introduction

_{P}is the proportional constant, K

_{r}is the resonant gain and ω is the resonant frequency. Theoretically, the PR controller is characterized by the infinite gain at the resonant frequency (for the standard electric grid ω = 314 rad/s) and, therefore, it should provide a zero steady-state error between the actual output current of the inverter and the current reference. However, the employment of the PR controller is challenging because there are no common tuning methods of controller parameters [32,35].

## 2. Control System for Tracking of the Grid-Connected Microinverter Output Current

_{i}) is the controller output signal value at time moment t

_{i}, and U

_{Ast}is the saw-tooth signal amplitude. The condition U(t

_{i}) ≤ U

_{Ast}has to be satisfied.

## 3. Analysis of the Microinverter Control System Based on the PI Controller

_{P}and K

_{I}are proportional and integral constants, t is time, t

_{0}is the initial time, and e(t) is the control error that acts as the input signal of the controller.

_{P}= 10, K

_{I}= 15. The microinverter output current for the case when the electric grid voltage shape is not distorted is presented in Figure 3. The analysis was provided for the microinverter output current with 200 mA, 400 mA and 600 mA amplitude, that correspond to 32 W, 62 W, and 97 W power delivered to the grid, respectively. It is seen (Figure 3) that the shape of the inverter output current is close to the sine. However, the high-frequency ripples are seen on the current curve. It has been estimated that the amplitude of the ripples strongly depends on the value of the PI controller proportional constant K

_{P}. The ripples decrease if the value of K

_{P}decreases. However, the shape of the current worsens and the phase shift of current is introduced at low K

_{P}. All results presented in the work have been obtained for the 28 kHz switching frequency of inverter switches.

## 4. PI Controller with the Variable Proportional Constant

_{P}. The amplitude of ripples decreases at lower K

_{P}. However, if K

_{P}is too low, the output current amplitude of the microinverter does not reach the set point value. If a higher value of K

_{P}is selected, the ripples of the microinverter output current increase. When evaluating the obtained results, one can assume that at a low current value that is close to zero it is more suitable to use a lower value of K

_{P}and at a high value that is close to the amplitude value it is necessary to select the value of K

_{P}higher.

_{P}should be varied in proportion to the microinverter output current to reduce the ripples of the output current. The control algorithm of the suggested controller, which presents the PI controller with the variable proportional constant K

_{P}= K

_{V}(t) K

_{C}, is as follows:

_{V}(t) and K

_{C}are the time-varying and the constant terms of the proportional constant, respectively. The simulation results of microinveter control system show that low distortions of the microinverter output current shape are reached when K

_{V}(t) during every half period of the current changes in time with the current by the similar law. It was found that the same results are obtained if instead of the pure sinus law its piecewise linear approximation given in Figure 7 is used for the variation of the K

_{V}(t). The piecewise linear approximation was used because it is easier to implement. Equation (6) presents the piecewise linear dependents given in Figure 7. The parameters of piecewise linear approximation of K

_{V}(t) were estimated by variation of approximation parameters by the criterion of minimal THD of microinverter output current.

## 5. Analysis of the Microinverter Control System Based on the PI Controller with the Variable Proportional Constant

_{C}and K

_{I}, at which the THD of the microinverter output current is minimal, i.e., the tuning leads to an optimization task with two variables. Using the univariate search method, the controller parameters were tuned as follows: at the fixed initial K

_{C}= K

_{Ci}value, the K

_{I}= K

_{Io1}value, at which the THD gets minimal, was obtained; at a fixed K

_{I}= K

_{Io1}value, the K

_{C}= K

_{Co1}value, at which the THD gets the minimum, was found. This process was repeated until the minimum THD value was obtained. The optimization procedure was also repeated with different initial K

_{C}= K

_{Ci}values. The obtained values of parameters of PI controller with the variable proportional constant are as follows: K

_{C}= 10, K

_{I}= 15.

## 6. Conclusions

- The most popular controllers used for tracking of the grid-connected photovoltaic inverter output current in the industrial microinverters are PI and PID controllers.
- The distortions of the grid-connected microinverter output current shape can be reduced when the proportional constant of the PI controller during every half period of the current changes in time with the current by the similar law.
- The variation of the proportional constant in the proposed modification of the PI controller is realized by the introduction of the time-varying term, which varies according to the law presented by the piecewise linear approximation of the sinus.
- The employment of the proposed PI controller with the variable proportional constant for tracking of the grid-connected photovoltaic microinverter output current instead of the ordinary PI controller allows us to reduce the THD of the output current by 30% at 32 W, by 48% at 62 W, and by 40% at 97 W load power when the electric grid voltage has a pure sinus shape and by 7% at 32 W, by 33% at 62 W and by 26% at 97 W—in the case when the grid voltage is distorted by the third- and fifth-order harmonics.
- The experimental investigation results prove the superiority of the PI controller with the variable proportional constant over the ordinary PI controller.
- The implementation of the proposed controller is more complicated as compared to the ordinary PI controller because the proportional constant in the proposed controller varies in time according to a certain law.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Block diagram of a single stage photovoltaic microinverter based on a couple of two-switch DC–DC flyback converters in the Matlab/Simulink environment.

**Figure 3.**The microinverter output current (black curves) when using the PI controller at different load power: (

**a**) 32 W; (

**b**) 62 W; (

**c**) 97 W. Red curves represent the electric grid voltage.

**Figure 4.**Spectra of the output current of the microinverter based on the PI controller at the load power: (

**a**) 32 W; (

**b**) 62 W; (

**c**) 97 W in the case when the electric grid voltage shape is not distorted.

**Figure 5.**The microinverter output current (black curves) when using the PI controller at a different load power: (

**a**) 32 W; (

**b**) 62 W; (

**c**) 97 W. The electric grid voltage (red curves) is distorted by third- and fifth-order harmonics.

**Figure 6.**Spectra of the output current of the microinverter based on the PI controller at the load power: (

**a**) 32 W; (

**b**) 62 W; (

**c**) 97 W. The electric grid voltage is distorted by third- and fifth-order harmonics.

**Figure 8.**The microinverter control system based on the PI controller with the variable proportional constant (the proposed PI controller is depicted with the darker background).

**Figure 9.**The microinverter output current (black curves) when using the PI controller with the variable proportional constant at different load power: (

**a**) 32 W, (

**b**) 62 W; (

**c**) 97 W. Red curves represent the electric grid voltage.

**Figure 10.**The spectra of the output current of the microinverter based on the PI controller with the variable proportional constant at the load power: (

**a**) 32 W; (

**b**) 62 W; (

**c**) 97 W) in the case when the electric grid voltage shape is not distorted.

**Figure 11.**The microinverter output current (black curves) when using the PI controller with the variable proportional constant at different load power: (

**a**) 32 W, (

**b**) 62 W; (

**c**) 97 W. The electric grid voltage (red curves) is distorted by the 3rd and 5th harmonics.

**Figure 12.**The spectra of the output current of the microinverter based on the PI controller with the variable proportional constant at the load power: (

**a**) 32 W; (

**b**) 62 W; (

**c**) 97 W for the electric grid voltage distorted by the third- and fifth-order harmonics.

**Figure 13.**The microinverter output current (black curves) when using the ordinary PI controller (

**a**) and the PI controller with the variable proportional constant (

**b**). Red curves represent the electric grid voltage.

Component | Parameter | Value |
---|---|---|

Flyback transformer | Magnetic inductance | 36 µH |

Primary winding active resistance | 0.01 Ω | |

Secondary winding active resistance | 0.47 Ω | |

Transformation ratio | 1:12 | |

Capacitor of CL filter | Capacitance | 200 nF |

Inductor of CL filter | Inductance | 330 µH |

**Table 2.**Types and parameters of transistors and diodes used in the output stage of the microinverter experimental model.

Component | Type | Parameters |
---|---|---|

Q1, Q2, Q3, Q4 | IRF3205 | 55 V; 110 A |

Q5, Q6 | 2SK2717 | 900 V; 5 A |

D1, D2 | FUF5408 | 1000 V; 3 A |

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**MDPI and ACS Style**

Bielskis, E.; Baskys, A.; Valiulis, G.
Controller for the Grid-Connected Microinverter Output Current Tracking. *Symmetry* **2020**, *12*, 112.
https://doi.org/10.3390/sym12010112

**AMA Style**

Bielskis E, Baskys A, Valiulis G.
Controller for the Grid-Connected Microinverter Output Current Tracking. *Symmetry*. 2020; 12(1):112.
https://doi.org/10.3390/sym12010112

**Chicago/Turabian Style**

Bielskis, Edvardas, Algirdas Baskys, and Gediminas Valiulis.
2020. "Controller for the Grid-Connected Microinverter Output Current Tracking" *Symmetry* 12, no. 1: 112.
https://doi.org/10.3390/sym12010112