# Voltage Stability Assessment of AC/DC Hybrid Microgrid

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## Abstract

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## 1. Introduction

- (1)
- This manuscript investigates the modeling of AC/DC hybrid microgrids with different types of power electronic devices and power generation, including a traditional power generator, a battery energy storage system (BESS), and PV generation.
- (2)
- The power converters are modeled using the circuit averaging method, which greatly reduces the runtime of software simulation.
- (3)
- We discuss the stability of AC/DC hybrid microgrids when a fault or disturbance happens. The voltage nadir is examined to evaluate the transient stability of the microgrid.
- (4)
- Droop control is adopted to regulate the power flow and alleviate voltage instability. We formulate an equivalent control diagram to develop sensitivity analysis instead of using the original microgrid simulation.

## 2. Materials and Methods

#### 2.1. A Typical Architecture of an AC/DC Hybrid Microgrid

#### 2.2. The Operation of an AC/DC Microgrid

- (1)
- Start the BESS integrated with a grid-forming converter, which support the bus voltage at the main bus of the DC microgrid.
- (2)
- Launch the PV system integrated with a grid-following converter. It follows the bus voltage regulated by the BESS and can track the maximum power point if needed.
- (3)
- When the DC microgrid is in the steady state, connect it to the AC microgrid by enabling the grid-following power inverter to interface the AC/DC sides.

#### 2.3. The Modeling of BESS and PV

#### 2.4. Circuit Averaging Model of Power Converter

- (1)
- In the first case, we assume ${V}_{s1}\left(t\right)=0,\text{}\left(n+1-D\right){T}_{s}t\left(n+1\right){T}_{s}$. Hence,$$\langle {V}_{1}\left(t\right)\rangle \&=\frac{1}{{T}_{s}}{{\displaystyle \int}}_{t-{T}_{s}}^{t}{V}_{s1}\left(\tau \right)d\tau =\frac{1}{{T}_{s}}{{\displaystyle \int}}_{n{T}_{s}}^{\left(n+1-D\right){T}_{s}}{V}_{2}\left(t\right)dt$$

- (2)
- In the second case, we assume ${V}_{s1}\left(t\right)={V}_{2}\left(t\right)$. Similarly, we also obtain$$\langle {V}_{1}\left(t\right)\rangle \&=\frac{1}{1-D}\langle {V}_{2}\left(t\right)\rangle $$

- (1)
- In the first case, we assume ${i}_{s2}\left(t\right)=0,\text{}\left(n+1-D\right){T}_{s}t\left(n+1\right){T}_{s}$. Hence,$$\langle {i}_{2}\left(t\right)\rangle \&=\frac{1}{{T}_{s}}{{\displaystyle \int}}_{t-{T}_{s}}^{t}{i}_{2}\left(t\right)dt=\frac{1}{{T}_{s}}{{\displaystyle \int}}_{n{T}_{s}}^{\left(n+1-D\right){T}_{s}}{i}_{1}\left(t\right)dt$$

- (2)
- In the second case, we assume ${i}_{s2}\left(t\right)={i}_{1}\left(t\right)$. Similarly, we obtain$$\langle {i}_{2}\left(t\right)\rangle \&=\frac{1}{1-D}\langle {i}_{1}\left(t\right)\rangle $$

#### 2.5. AC/DC Interfacing Power Inverter

## 3. Discussion

#### 3.1. Stability Analysis with Faults

#### 3.1.1. The Effects of an AC-Side Fault on the Stability of the DC Side

- (1)
- In the AC microgrid, the voltage has no fault component whereas the current has observable fault components. Two phases of the current increase a lot when the fault occurs.
- (2)
- The AC/DC interfacing inverter still works well as in the normal operating condition.
- (3)
- In the DC microgrid, both the main bus voltage and the power output of the generation systems have very small oscillations. Considering that the oscillation of the main bus voltage is within 5%, the DC loads can still work in the normal condition in most cases.

- (1)
- In the AC microgrid, both the voltage and the current have observable fault components. However, unlike the case with a single phase-to-ground fault, the fault current does not show any increase. Therefore, some devices on the AC side possibly still work as in the normal condition if the fault does not last long, but it may bring challenges to fault detection.
- (2)
- Both the voltage and the current of the AC/DC interfacing inverter become distorted. The fault current shows sharp spikes.
- (3)
- In the DC microgrid, both the main bus voltage and the power output of the generation systems have tremendous spikes, which could destroy the whole power grid. A fault protection scheme specialized for the DC microgrid is required.

#### 3.1.2. The Effects of a DC-Side Fault on the Stability of the AC Side

#### 3.2. Stability Analysis with Disturbances

#### 3.3. Voltage Instability Alleviation with Droop Control

#### 3.3.1. Power Flow Management Using Droop Control

#### 3.3.2. The Evaluation of Stability Using Voltage Nadir

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**The equivalent modeling of a boost converter. (

**a**) Switch model of a boost converter; (

**b**) Averaged circuit model of a boost converter.

**Figure 9.**Performance when a single phase-to-ground fault occurs on the AC side. (

**a**) Signals at Bus 6; (

**b**) Signals at AC/DC interfacing Bus 8; (

**c**) Signals at DC bus; (

**d**) Power output of the BESS; (

**e**) Power output of the PV generation.

**Figure 10.**Performance when a phase-to-phase fault occurs on the AC side. (

**a**) Signals at Bus 6; (

**b**) Signals at AC/DC interfacing Bus 8; (

**c**) Signals at DC bus; (

**d**) Power output of the BESS; (

**e**) Power output of the PV generation.

**Figure 11.**Performance when a line disconnection fault occurs on the DC side. (

**a**) Signals at Bus 6; (

**b**) Signals at AC/DC interfacing Bus 8; (

**c**) Signals at DC bus; (

**d**) Power output of the BESS; (

**e**) Power output of the PV generation.

**Figure 12.**Performance when a ground fault occurs on the DC side. (

**a**) Signals at Bus 6; (

**b**) Signals at AC/DC interfacing Bus 8; (

**c**) Signals at DC bus; (

**d**) Power output of the BESS; (

**e**) Power output of the PV generation.

**Figure 13.**Performance when a DC-side surplus load happens. (

**a**) Signals at Bus 6; (

**b**) Signals at AC/DC interfacing Bus 8.; (

**c**) Signals at DC bus; (

**d**) Power output of the BESS; (

**e**) Power output of the PV generation.

**Figure 14.**Performance when the PV operation environment changes. (

**a**) Signals at Bus 6; (

**b**) Signals at AC/DC interfacing Bus 8; (

**c**) Signals at DC bus; (

**d**) Power output of the BESS; (

**e**) Power output of the PV generation.

**Figure 15.**Performance when an AC-side load shedding happens. (

**a**) Signals at Bus 6; (

**b**) Signals at AC/DC interfacing Bus 8; (

**c**) Signals at DC bus; (

**d**) Power output of the BESS; (

**e**) Power output of the PV generation.

**Figure 20.**Voltage nadir measured in the Simulink simulation. (

**a**) Power output of the PV generation; (

**b**) Signals at DC bus.

Cut-off voltage (V) | 90 |

Fully charged voltage (V) | 139.6785 |

Nominal discharge current (A) | 347.8261 |

Internal resistance (Ohms) | 0.0015 |

Capacity (Ah) at nominal voltage | 723.4783 |

Exponential zone [voltage (V), capacity (Ah)] | 29.6463, 39.30435 |

Maximum power (W) | 250.205 |

Cells per module (Ncell) | 96 |

Open circuit voltage Voc (V) | 37.4 |

Short-circuit current Isc (A) | 8.63 |

Voltage at maximum power point Vmp (V) | 30.7 |

Current at maximum power point Imp (A) | 8.15 |

Temperature coefficient of Voc (%/deg.C) | −0.34 |

Temperature coefficient of Isc (%/deg.C) | 0.05 |

Fault Location | Fault Type | AC-Side | DC-Side | Inverter |
---|---|---|---|---|

AC-side | Single p-g | faulty | normal | normal |

p-p | faulty | severe | faulty | |

Double p-g | faulty | severe | faulty | |

Three-phase | severe | |||

DC-side | Line disconnection | normal | normal | normal |

Ground | normal | severe | normal |

Disturbance Location | Disturbance Type | DC-Side | AC-Side |
---|---|---|---|

DC-side | A surplus load | Voltage dip | Normal |

Operational environment changes | Voltage dip | Normal | |

AC-side | Load shedding | Normal | Power regulation |

Load Disturbance | 2.0 kW | 4.0 kW | 1.5 kW | 0.5 kW | |
---|---|---|---|---|---|

Microgrid simulation | Steady-state voltage before disturbance | 0.9989 | 0.9989 | 0.9989 | 0.9989 |

Voltage nadir | 0.9845 | 0.9691 | 0.9879 | 0.9953 | |

Steady-state voltage after disturbance | 0.9898 | 0.9731 | 0.9920 | 0.9966 | |

Control diagram | Steady-state voltage before disturbance | 0.9996 | 0.9996 | 0.9996 | 0.9996 |

Voltage nadir | 0.9822 | 0.9657 | 0.9865 | 0.9952 | |

Steady-state voltage after disturbance | 0.9904 | 0.9816 | 0.9927 | 0.9973 | |

RMSE (%) | 0.0333 | 0.1933 | 3.7007 × 10^{−15} | 0.0433 |

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## Share and Cite

**MDPI and ACS Style**

Chang, F.; O’Donnell, J., Jr.; Su, W. Voltage Stability Assessment of AC/DC Hybrid Microgrid. *Energies* **2023**, *16*, 399.
https://doi.org/10.3390/en16010399

**AMA Style**

Chang F, O’Donnell J Jr., Su W. Voltage Stability Assessment of AC/DC Hybrid Microgrid. *Energies*. 2023; 16(1):399.
https://doi.org/10.3390/en16010399

**Chicago/Turabian Style**

Chang, Fangyuan, John O’Donnell, Jr., and Wencong Su. 2023. "Voltage Stability Assessment of AC/DC Hybrid Microgrid" *Energies* 16, no. 1: 399.
https://doi.org/10.3390/en16010399