# Research on Low Voltage Ride through Control of a Marine Photovoltaic Grid-Connected System Based on a Super Capacitor

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Structure of Marine Photovoltaic Grid-Connected System

## 3. Model and Control Strategy

#### 3.1. Mathematical Model and Maximum Power Point Tracking of the Photovoltaic Cell

_{pv}and I

_{d}are the photo-generated current and current flowing through diode, respectively, and R

_{s}is the series resistance representing the internal loss in Figure 3. With the increase of service time, this value of R

_{s}will increase, and the photovoltaic output power will decrease. R

_{sh}is the side leakage resistance. U and I are the output voltage and current of the photovoltaic cell.

_{0}, A, K, T are respectively the amount of charge (the value is 1.6 × 10

^{−19}), the diode reverse saturation current, the quality factor (the value is between 1–2), the Boltzmann constant (the value is 1.38 × 10

^{−23}), and absolute temperature.

_{sh}is very large, and the value of the series resistance R

_{s}is very small, so the term (U + IR

_{S})/R

_{sh}is often ignored under ideal conditions. The output characteristics of photovoltaic cells in actual working conditions are mainly affected by irradiance and ambient temperature. Let ${I}_{sc}$, ${V}_{sc}$, ${I}_{m}$, ${V}_{m}$ be the short-circuit current, open-circuit voltage, maximum power point current, and maximum power point voltage of photovoltaic cells under standard test conditions (irradiance S = 1000 W/m

^{2}, ambient temperature T = 25 °C, atmospheric quality AM = 1.5). Then Formula (3) is converted into:

^{−}

^{1}, 0.5 m

^{2}/W, and 0.00288 C

^{−}

^{1}, respectively.

#### 3.2. Photovoltaic Cell Simulation Model

^{2}, 700 W/m

^{2}, and 1000 W/m

^{2}, respectively, the changes in the power and current of the photovoltaic array with voltage are as shown in Figure 5.

^{2}, and when the ambient temperature T is 10 °C, 25 °C, and 40 °C respectively, the changes in the power and current of the photovoltaic array with voltage are as shown in Figure 6.

#### 3.3. Inverter Control Strategy

_{d}and i

_{q}on the dq axis to the reference current ${i}_{d}^{\ast}$ and ${i}_{q}^{\ast}$ through the current inner loop. According to instantaneous power theory, the inverter output reference current is

_{d}and u

_{q}are the grid voltage, and v

_{d}and v

_{q}are the inverter voltage control reference values. It can be seen from the equation that there is a strong coupling between the currents of the dq axis, and i

_{d}and i

_{q}need to be decoupled in order to adjust them independently. The current decoupling control principle of i

_{d}and i

_{q}is shown in Figure 7. PI adjustment is used to eliminate static errors, so that i

_{d}and i

_{q}can track to ${i}_{d}^{\ast}$ and ${i}_{q}^{\ast}$ accurately. By introducing the current state feedback through feed-forward decoupling, independent control of the dq axis current can be achieved, and the feed-forward compensation will increase, so that the influence of grid voltage on the control system can be reduced.

_{d}and v

_{q}obtained by current control are transformed by dp inverting to obtain the modulation signal U

_{ref}, and then sinusoidal pulse width modulation (SPWM) is applied to generate 6 PWM signals to control the IGBT of the inverter bridge as on or off. This is to realize the DC to three-phase AC inverter and power output.

#### 3.4. Charge/Discharge Control of Super Capacitor

_{c}and capacitor C

_{sc}in series, in which R

_{c}represents the energy consumption during charging and discharging of the super capacitor, and the bidirectional DC/DC converter adopts a bidirectional half-bridge structure.

#### 3.5. LVRT Control Strategy

_{s}. When the voltage sags, the voltage sag depth is calculated by the voltage amplitude of the phase locking loop circuit. Then, the output of the reactive power reference current ${i}_{q}^{\ast}$ is calculated according to Equation (11).

## 4. System Simulation and Analysis

#### 4.1. Simulation Parameters Design

#### 4.2. Simulation Results Analysis

^{2}, and it started to fluctuate randomly at 100 s. At 200 s, the value of the irradiance stabilized again at 500 W/m

^{2}.

^{2}, ambient temperature T = 25 °C) in the example simulation. The voltage variation curve of the marine power grid is shown in Figure 16. Three-phase symmetric voltage sag occurred at 0.5 s with a 35% sag depth, and it returned to normal at 0.8 s. The simulation results are shown in Figure 17, Figure 18, Figure 19, Figure 20, Figure 21 and Figure 22.

- (1)
- In case of grid voltage sag, it can be seen from Figure 20a and Figure 21 that the inverter operates under unit power factor without LVRT control in grid-connected system and does not output reactive power, but the active output power drops slightly due to voltage sag. As shown in Figure 17a, Figure 18a and Figure 20a, as the photovoltaic array continues to work at the maximum power state, an imbalance between the input power and output power appears on the DC bus side, and the power difference acts on the DC bus, and the DC bus voltage presents a rapid upward trend. The DC bus voltage increases because the input power of the inverter is greater than the output power. In order to ensure the power balance between the DC input and the AC output of the inverter, the output current of the inverter will increase to 1.4 pu, which exceeds the rated operating current and causes the inverter to be off-gird due to overcurrent protection, thus increasing the fault range.
- (2)
- With LVRT control, the photovoltaic controller still operates in MPPT mode during voltage sag. According to Figure 17b and Figure 18b, in order to prevent the inverter from being off-grid due to output overcurrent during voltage sag, the inverter reduces the active power output and its output current is always less than 1.1 pu. During the fault period, the super capacitor absorbs the energy difference between the inverter and the controller, so that the DC bus voltage remains stable. The dynamic and static response is ideal, with the overshoot of the DC bus less than 5%, the adjustment time less than 0.1 s, and the steady-state voltage basically remaining at 380 V. It can be seen from Figure 19 and Figure 22 that the inverter adjusts the distribution of active and reactive power when the grid voltage sags, with the power factor decreasing from 1 to 0.77 and the voltage sag increasing from 150 V to 156 V. The control strategy can absorb excess photovoltaic energy through the super capacitor adjustment system, greatly reduce the voltage rise of the DC bus of the photovoltaic power generation system, and maintain the grid-connected current below the limit current value. After the fault is removed, the marine diesel/photovoltaic grid-connected power system will quickly return to the normal working state, enhancing the low voltage ride-through capability of the system.

## 5. Conclusions

- (1)
- The use of super capacitors for ship energy storage can keep the DC bus voltage stable and reduce the power injected into the photovoltaic inverter.
- (2)
- The inverter can realize the independent control of dq axis current. At the same time, the feedforward compensation of the grid voltage is added, which reduces the influence of the grid voltage on the control system.
- (3)
- When the ship grid voltage fluctuates, the photovoltaic grid-connected system control strategy automatically adjusts the distribution of active power and reactive power to help restore the grid voltage.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

I_{pv,}V_{pv} | PV source output voltage andcurrent | ${I}_{sc}^{\ast}$ | Reference current |

I_{d} | Current flowing through the diode | i_{s} | Current of the inverter operating at unity power factor |

R_{s} | Series resistance characterizing internal loss | C_{1} | Photovoltaic controller capacitor |

R_{sh} | Bypass leakage resistance | L_{1} | Photovoltaic controller inductance |

U | PV cell output voltage | D | Photovoltaic controller duty cycle |

I | PV cell output current | C_{dc} | Photovoltaic controller DC bus capacitor |

i_{d} | Stator d-axis current component | C_{2} | Bidirectional DC/DC converter capacitor |

i_{q} | Stator q-axis current component | L_{2} | Bidirectional DC/DC converter inductor |

u_{d} | Grid d-axis voltage | K_{p1} | Voltage outer loop proportional coefficient |

u_{q} | Power grid q axis voltage | Ki_{1} | Integral coefficient of voltage outer loop |

v_{d} | Stator d-axis reference voltage | K_{p2} | Current inner loop proportional coefficient |

v_{q} | Stator q-axis reference voltage | K_{i2} | Current inner loop integral coefficient |

${i}_{d}^{\ast}$ | Stator d-axis reference current | C_{3} | Inverter filter capacitor |

${i}_{q}^{\ast}$ | Stator q-axis reference current | L_{3} | Inverter filter inductor |

U_{ref} | Modulated signal | K_{p3} | Power outer ring proportional coefficient |

R_{c} | Super capacitor model equivalent resistance | K_{i3} | Power outer loop integral coefficient |

C_{sc} | Equivalent capacitance of the supercapacitor model |

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**Figure 1.**Low voltage ride through curve [17].

**Figure 13.**The frequency changes of the ship’s power grid. (

**a**) Not connected to a super capacitor, (

**b**) Connected to a super capacitor.

**Figure 14.**The Phase voltage change of ship power grid. (

**a**) Not connected to a super capacitor, (

**b**) Connected to a super capacitor.

Performance Comparison | Charging Time/(s) | Discharge Time/(s) | Power Density/(W/kg) | Charge and Discharge Efficiency/(%) | Product Maintenance | Service Life/(Years) |
---|---|---|---|---|---|---|

Lithium battery | (3.6~18) × 10^{3} | (1.08~10.8) × 10^{3} | <10^{3} | 70–85 | high cost | 4–6 |

Super capacitor | 0.3~30 | 0.3~30 | <10^{4} | 85–98 | low cost | 10–15 |

String Relationship | Total Power/kW | Open Circuit Voltage/V | Short Circuit Current/A | Peak Voltage/V | Peak Current/A |
---|---|---|---|---|---|

18 series 20 parallel | 102.7 | 712.8 | 188.2 | 570.6 | 180 |

Equipment | Parameter | Value | Unit |
---|---|---|---|

Photovoltaic controller | C_{1} | 1.7 | mF |

L_{1} | 16 | µH | |

D | 0.1% | - | |

C_{dc} | 10 | mF | |

Bidirectional DC/DC converter | IGTT switching frequency | 4 | kHz |

C_{2} | 1 | mF | |

L_{2} | 3 | mH | |

K_{p}_{1} | 0.8 | - | |

K_{i}_{1} | 100 | - | |

K_{p}_{2} | 0.2 | - | |

K_{i}_{2} | 30 | - | |

Super capacitor | Operating voltage range | 240~300 | V_{DC} |

Energy storage capacity | 6 | kWh | |

Maximum output current limit | 400 | A | |

Inverter | C_{3} | 20 | µF |

L_{3} | 0.5 | mH | |

K_{p}_{3} | 0.01 | - | |

K_{i}_{3} | 3 | - | |

K_{p}_{2} | 120 | - | |

K_{i}_{2} | 5 | - |

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## Share and Cite

**MDPI and ACS Style**

Wang, S.; Tang, X.; Liu, X.; Xu, C.
Research on Low Voltage Ride through Control of a Marine Photovoltaic Grid-Connected System Based on a Super Capacitor. *Energies* **2022**, *15*, 1020.
https://doi.org/10.3390/en15031020

**AMA Style**

Wang S, Tang X, Liu X, Xu C.
Research on Low Voltage Ride through Control of a Marine Photovoltaic Grid-Connected System Based on a Super Capacitor. *Energies*. 2022; 15(3):1020.
https://doi.org/10.3390/en15031020

**Chicago/Turabian Style**

Wang, Shihao, Xujing Tang, Xionghang Liu, and Chen Xu.
2022. "Research on Low Voltage Ride through Control of a Marine Photovoltaic Grid-Connected System Based on a Super Capacitor" *Energies* 15, no. 3: 1020.
https://doi.org/10.3390/en15031020