# Interlink Converter with Linear Quadratic Regulator Based Current Control for Hybrid AC/DC Microgrid

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Hybrid AC/DC Microgrid Operation

## 3. Droop Control Strategy for Individual Subgrids

#### 3.1. Droop Control of AC Microgrid

_{ac}-Q) droop characteristic curves.

#### 3.2. Droop Control of the DC Microgrid

## 4. IC Control Strategy

#### 4.1. Droop Control Strategy in Hybrid AC/DC Microgrid

#### 4.2. Optimized IC Current Control Using LQR

## 5. Results and Discussion

#### 5.1. Operation Mode Transition from Grid-Connected to Stand-Alone Hybrid Microgrid

#### 5.2. AC Load Increase with Battery Support

_{1}= 5 mH, C = 10 µF, L

_{2}= 5 mH) has been simulated without changing the state space model. By deploying the same LQR gains as in the proposed one with L filter, the controller outputs and system responses are almost the same.

#### 5.3. DC Load Increase without Battery Support

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

$\Delta f$ | frequency deviation on the AC subgrid |

$\Delta {P}_{dc}$ | active power deviation on the DC subgrid |

$\Delta {V}_{dc}$ | bus voltage deviation on the DC subgrid |

$\omega $ | grid angular frequency |

$C$ | DC link capacitance |

${E}_{ac}$ | AC subgrid voltage magnitude |

${E}_{abc}$ | three phase voltage at AC subgrid |

${E}_{d}$ | d-axis AC subgrid voltage |

${E}_{q}$ | q-axis AC subgrid voltage |

${f}_{ac}$ | AC microgrid frequency |

${f}_{m}$ | measured frequency in AC subgrid |

${f}_{max}$ | maximum allowable frequency in AC subgrid |

${f}_{min}$ | minimum allowable frequency in AC subgrid |

${f}_{min,ac}$ | minimum allowable frequency in AC microgrid |

${f}_{ref}$ | reference of frequency in AC subgrid |

${i}_{abc}$ | current at AC side of IC |

${I}_{d}$ | d-axis current at AC side of IC |

${I}_{d,ref}$ | reference of d-axis current at AC side of IC |

${i}_{dc}$ | current at DC side of IC |

${i}_{L,dc}$ | inductor current at DC side of IC |

${I}_{q}$ | q-axis current at AC side of IC |

${I}_{q,ref}$ | reference of q-axis current at AC side of IC |

${L}_{f}$ | filter inductance |

${p}_{abc}$ | gating signal of IC represented in three phase form |

${p}_{dq}$ | gating signal of IC represented in d-q axis |

${P}_{ac}$ | active power generated by the droop control in AC microgrid |

${P}_{dc}$ | active power generated by the droop control in DC microgrid |

${P}_{IC}$ | active power reference of IC |

${P}_{l,dc}$ | active power of DC load |

${P}_{max,ac}$ | maximum active power of the AC droop control scheme |

${P}_{max,dc}$ | maximum active power of the DC droop control scheme |

${P}_{net}$ | net active power in DC subgrid |

${P}_{s,dc}$ | active power of DC source |

${Q}_{ac}$ | reactive power produced by the droop control in AC microgrid |

${Q}_{IC}$ | reactive power reference of IC |

${Q}_{max,ac}$ | maximum reactive power of the AC droop control scheme |

${R}_{dc}$ | voltage-active power droop characteristic in DC microgrid |

${R}_{f}$ | filter resistance |

${R}_{p,ac}$ | frequency-active power droop characteristic in AC microgrid |

${R}_{p1}$ | Frequency-active power droop characteristic of IC |

${R}_{p2}$ | DC voltage-active power droop characteristic of IC |

${R}_{q}$ | AC voltage-reactive power droop characteristic of IC |

${R}_{q,ac}$ | voltage-reactive power droop characteristic in AC microgrid |

${V}_{abc}$ | voltage at AC side of IC |

${V}_{ac}$ | measured AC voltage in AC microgrid |

${V}_{ac,m}$ | measured voltage in AC subgrid |

${V}_{ac,ref}$ | reference voltage in AC subgrid |

${V}_{d}$ | d-axis voltage reference at AC side of IC |

${V}_{dc}$ | measured voltage in DC microgrid |

${V}_{dc,m}$ | measured voltage in DC subgrid |

${V}_{dc,max}$ | maximum allowable voltage in DC subgrid |

${V}_{dc,min}$ | minimum allowable voltage in DC subgrid |

${V}_{dc,ref}$ | reference of voltage in DC subgrid |

${V}_{min,ac}$ | minimum allowable voltage in AC microgrid |

${V}_{min,dc}$ | minimum allowable voltage in DC microgrid |

${V}_{q}$ | q-axis voltage reference at AC side of IC |

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**Figure 15.**Comparison of system responses with PI and LQR controllers when the operation mode changed to stand-alone at 15 s; (

**a**) active power injection of IC; (

**b**) reactive power injection of IC; (

**c**) AC subgrid frequency and (

**d**) DC subgrid voltage.

**Figure 16.**Control performance comparison between PI and LQR in the first scenario (1) current tracking (2) d-q frame voltage at point of common coupling (PCC) to AC subgrid (3) closed loop output. (

**a**) PI controller; (

**b**) LQR; (

**c**) PI controller; (

**d**) LQR; (

**e**) PI controller; (

**f**) LQR.

**Figure 20.**Comparison of system responses with PI and LQR controllers when AC load increased to maximum loading point at 10 s; (

**a**) active power injection of IC; (

**b**) reactive power injection of IC; (

**c**) AC subgrid frequency and (

**d**) DC subgrid voltage.

**Figure 21.**Control performance comparison between PI and LQR in the second scenario (1) current tracking (2) d-q frame voltage at point of common coupling (PCC) to AC subgrid (3) closed loop output. (

**a**) PI controller; (

**b**) LQR; (

**c**) PI controller; (

**d**) LQR; (

**e**) PI controller; (

**f**) LQR.

**Figure 22.**Active power flow in AC subgrid when the DC load was increased and there was no battery support.

**Figure 23.**Reactive power flow in AC subgrid when the DC load was increased and there was no battery support.

**Figure 24.**Active power flow in DC subgrid when the DC load was increased and there was no battery support.

**Figure 25.**Comparison of system responses with PI and LQR controllers LQR when DC load increased and there was no battery support at 10 s; (

**a**) active power injection of IC; (

**b**) reactive power injection of IC; (

**c**) AC subgrid frequency and (

**d**) DC subgrid voltage.

**Figure 26.**Control performance comparison between PI and LQR in the third scenario (1) current tracking (2) d-q frame voltage at point of common coupling (PCC) to AC subgrid (3) closed loop output. (

**a**) PI controller; (

**b**) LQR; (

**c**) PI controller; (

**d**) LQR; (

**e**) PI controller; (

**f**) LQR.

Scenario | Disturbance | Transient Time | Operation Mode | Operating Point | ||
---|---|---|---|---|---|---|

Before Transient | After Transient | Before Transient | After Transient | |||

I | Operation mode transition | 15 s | Grid-connected | Stand-alone | Maximum | Maximum |

II | AC load increase | 10 s | Stand-alone | Stand-alone | Normal | Maximum |

III | DC load increase | 10 s | Stand-alone | Stand-alone | Normal | Normal |

No | LQR with Exponential Weighting | PI Controller |
---|---|---|

1 | Power is transferred between subgrids rapidly and stably | Power is transferred between subgrids rapidly but not as stable as LQR controller |

2 | The hybrid microgrid operates robustly against various operation conditions | The hybrid microgrid operation is limited in maximum loading point |

3 | During transition mode from grid connected to stand-alone operation, the transient response is high but smooth | During transition mode from grid connected to stand-alone operation, the transient response is low but not smooth |

4 | Easy to adjust LQR parameters for MIMO systems | Hard to adjust PI parameters for MIMO systems |

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**MDPI and ACS Style**

Aryani, D.R.; Kim, J.-S.; Song, H.
Interlink Converter with Linear Quadratic Regulator Based Current Control for Hybrid AC/DC Microgrid. *Energies* **2017**, *10*, 1799.
https://doi.org/10.3390/en10111799

**AMA Style**

Aryani DR, Kim J-S, Song H.
Interlink Converter with Linear Quadratic Regulator Based Current Control for Hybrid AC/DC Microgrid. *Energies*. 2017; 10(11):1799.
https://doi.org/10.3390/en10111799

**Chicago/Turabian Style**

Aryani, Dwi Riana, Jung-Su Kim, and Hwachang Song.
2017. "Interlink Converter with Linear Quadratic Regulator Based Current Control for Hybrid AC/DC Microgrid" *Energies* 10, no. 11: 1799.
https://doi.org/10.3390/en10111799