# Active and Reactive Power Compensation Control Strategy for VSC-HVDC Systems under Unbalanced Grid Conditions

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Analysis and Control Equations Establishment of Double Frequency Ripple power of VSC

## 3. Power Compensation Strategy for VSC-HVDC via Passivity-Based Control with Disturbance Observer

#### 3.1. PCHD Model of the VSC-HVDC Systems and the Passivity-Based Control Strategy

#### 3.2. Robust Passivity-Based Control Strategy via Disturbance Observer

#### 3.3. Stability Analysis of the Proposed Power Compensation Strategy via Passivity-Based Control with Disturbance Observer

_{M}is derived as

## 4. Simulation Results

#### 4.1. Case 1

_{2}have a drop of 4.23 kV (50%) shown in Figure 5. As for the control system, it remains unchanged with the common vector double loop control during 2.5 s to 3.5 s. After 3.5 s, the proposed power compensation strategy and the conventional resonance compensation strategy are added as the auxiliary controllers respectively for the suppression of the double frequency ripples. The simulation results are shown in Figure 6, Figure 7 and Figure 8.

#### 4.2. Case 2

#### 4.3. Case 3

_{2}. The simulation results with no auxiliary control, the conventional resonance compensation strategy and the proposed passivity-based compensation strategy via disturbance observer are shown in Figure 12, Figure 13 and Figure 14 respectively.

#### 4.4. Comparable Evaluation

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

${U}_{a,b,c}$,${i}_{a,b,c}$ | the three phase voltage and current of the converter |

${E}_{a,b,c}$ | the three phase voltage of the AC grid |

$R,L$ | the per-phase resistance and inductance of the AC filter |

$C$ | the DC filter capacitor |

${U}_{dc},{i}_{dc}$ | the DC voltage and current of the converter |

${P}_{s},{Q}_{s}$ | the transmission active and reactive power of the converter |

${U}_{d},{U}_{q}$ | the d axis and q axis components of VSC voltage |

${i}_{d},{i}_{q}$ | the d axis and q axis components of VSC current |

${E}_{d},{E}_{q}$ | the d axis and q axis components of AC grid voltage |

${P}_{2i},{Q}_{2i}$ | the current-relevant components that cause the double frequency ripples in active and reactive power |

${P}_{2u},{Q}_{2u}$ | the voltage-relevant components that cause the double frequency ripples in active and reactive power |

${u}_{P},{u}_{Q}$ | the double frequency power control inputs of VSC |

$\mathit{J}\left(\mathit{x}\right),{\mathit{J}}_{\mathit{d}}\left(\mathit{x}\right)$ | the original and the desired interconnection matrix |

$\mathbf{\Re}\left(\mathit{x}\right),{\mathbf{\Re}}_{\mathit{d}}\left(\mathit{x}\right)$ | the original and the desired damping matrix |

$\mathit{H}\left(\mathit{x}\right),{\mathit{H}}_{\mathit{d}}\left(\mathit{x}\right)$ | the original and the desired Hamiltonian function |

$\mathit{G}\left(\mathit{x}\right)$ | the coefficient matrix with full rank |

$\widehat{\mathit{w}}$ | the estimation of the disturbance |

$k$ | the internal state of the observer |

$\mathbf{\mu}\left(\mathbf{\chi}\right),\mathit{l}\left(\mathbf{\chi}\right)$ | the observer function and the observer gain |

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**Figure 3.**Zero-pole maps with different parameters. (

**a**) Zero-pole maps with varying r

_{1}. (

**b**) Zero-pole maps with varying r

_{2}. (

**c**) Zero-pole maps with varying l

_{1}. (

**d**) Zero-pole maps with varying l

_{2}.

**Figure 6.**Simulation results with conventional resonance compensation strategy. (

**a**) Simulation results of active and reactive power. (

**b**) Simulation results of double frequency components of active and reactive power.

**Figure 7.**Simulation results with proposed passivity-based power compensation strategy via disturbance observer. (

**a**) Simulation results of active and reactive power. (

**b**) Simulation results of double frequency components of active and reactive power.

**Figure 8.**Simulation results with only passivity-based power compensation strategy. (

**a**) Simulation results of active and reactive power. (

**b**) Simulation results of double frequency components of active and reactive power.

**Figure 9.**The observed and calculated values of the double-frequency voltage disturbance ${w}_{Pu}$ and ${w}_{Qu}$.

**Figure 10.**Simulation results of double frequency components of reactive power with different passivity parameters ${r}_{2}$.

**Figure 11.**Simulation results of double frequency components of reactive power with different observer gain.

**Figure 12.**Simulation results of double frequency ripples in active power. (

**a**) With no auxiliary control. (

**b**) With conventional resonance compensation strategy. (

**c**) With proposed passivity-based compensation strategy via disturbance observer.

**Figure 13.**Simulation results of double frequency ripples in reactive power. (

**a**) With no auxiliary control. (

**b**) With conventional resonance compensation strategy. (

**c**) With proposed passivity-based compensation strategy via disturbance observer.

**Figure 14.**Simulation results of dc voltage. (

**a**) With no auxiliary control. (

**b**) With conventional resonance compensation strategy. (

**c**) With proposed passivity-based compensation strategy via disturbance observer.

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## Share and Cite

**MDPI and ACS Style**

Liu, W.; Zheng, T.; Liu, Z.; Fan, Z.; Kang, Y.; Wang, D.; Zhang, M.; Miao, S.
Active and Reactive Power Compensation Control Strategy for VSC-HVDC Systems under Unbalanced Grid Conditions. *Energies* **2018**, *11*, 3140.
https://doi.org/10.3390/en11113140

**AMA Style**

Liu W, Zheng T, Liu Z, Fan Z, Kang Y, Wang D, Zhang M, Miao S.
Active and Reactive Power Compensation Control Strategy for VSC-HVDC Systems under Unbalanced Grid Conditions. *Energies*. 2018; 11(11):3140.
https://doi.org/10.3390/en11113140

**Chicago/Turabian Style**

Liu, Weiming, Tingting Zheng, Ziwen Liu, Zhihua Fan, Yilong Kang, Da Wang, Mingming Zhang, and Shihong Miao.
2018. "Active and Reactive Power Compensation Control Strategy for VSC-HVDC Systems under Unbalanced Grid Conditions" *Energies* 11, no. 11: 3140.
https://doi.org/10.3390/en11113140