Direct AC voltage control for grid-forming inverters

Abstract

Grid-forming inverters usually use inner cascaded controllers to regulate output AC voltage and converter output current. However, at the power transmission system level where the power inverter bandwidth is limited, i.e., low switching frequency, it is difficult to tune controller parameters to achieve the desired performances because of control loop interactions. In this paper, a direct AC voltage control-based state-feedback control is applied. Its control gains are tuned using a linear quadratic regulator. In addition, a sensitivity analysis is proposed to choose the right cost factors that allow the system to achieve the imposed specifications. Conventionally, a system based on direct AC voltage control has no restriction on the inverter current. Hence, in this paper, a threshold virtual impedance has been added to the state-feedback control in order to protect the inverter against overcurrent. The robustness of the proposed control is assessed for different short-circuit ratios using small-signal stability analysis. Then, it is checked in different grid topologies using time domain simulations. An experimental test bench is developed in order to validate the proposed control.

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Acknowledgements

This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 691800. This paper reflects only the author’s views, and the European Commission is not responsible for any use that may be made of the information it contains.

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Correspondence to Taoufik Qoria.

Appendix

Appendix

Augmented state-space control matrices:

$$ x^{\text{T}} =\left[ \begin{array}{*{20}c} {\begin{array}{*{20}c} {\Delta i_{\text{sd}} } & {\Delta i_{\text{sq}} } & {\Delta e_{\text{gd}} } & {\Delta e_{\text{gq}} } & {\Delta i_{\text{gd}} } & {\Delta i_{\text{gq}} } \\ \end{array} \Delta \zeta_{\text{d}} \Delta \zeta_{\text{q}} \ldots } \\ { \Delta \delta \Delta p_{\text{mes}} \Delta q_{\text{mes}} } \\ \end{array} \right]$$
$$ A_{{{\text{aug}}_{ 1 1} }} = \left[ {\begin{array}{*{20}c} { - \frac{{R_{{{\text{f}}_{ } \omega_{\text{b}} }} }}{{L_{\text{f}} }} + \frac{{\omega_{\text{b}} K_{11} }}{{L_{\text{f}} }}} & {\omega_{ } \omega_{\text{b}} + \frac{{\omega_{\text{b}} K_{12} }}{{L_{\text{f}} }}} & { - \frac{{\omega_{\text{b}} }}{{L_{\text{f}} }} + \frac{{\omega_{\text{b}} K_{13} }}{{L_{\text{f}} }}} \\ { - \omega_{ } \omega_{\text{b}} + \frac{{\omega_{\text{b}} K_{21} }}{{L_{\text{f}} }}} & { - \frac{{R_{{{\text{f}}_{\text{pu}} \omega_{\text{b}} }} }}{{L_{\text{f}} }} + \frac{{\omega_{\text{b}} K_{21} }}{{L_{\text{f}} }}} & { + \frac{{\omega_{\text{b}} K_{21} }}{{L_{\text{f}} }}} \\ {\frac{{\omega_{\text{b}} }}{{C_{\text{f}} }}} & 0 & 0 \\ \end{array} } \right] $$
$$ A_{{{\text{aug}}_{ 1 2} }} = \left[ {\begin{array}{*{20}c} {\frac{{\omega_{b} K_{14} }}{{L_{\text{f}} }}} & {\frac{{\omega_{b} K_{15} }}{{L_{\text{f}} }}} & {\frac{{\omega_{b} K_{16} }}{{L_{\text{f}} }}} & { - \frac{{\omega_{b} K_{I11} }}{{L_{\text{f}} }}} & { - \frac{{\omega_{b} K_{I12} }}{{L_{\text{f}} }}} \\ { - \frac{{\omega_{\text{b}} }}{{L_{\text{f}} }} + \frac{{\omega_{\text{b}} K_{21} }}{{L_{\text{f}} }}} & {\frac{{\omega_{\text{b}} K_{21} }}{{L_{\text{f}} }}} & { + \frac{{\omega_{b} K_{21} }}{{L_{\text{f}} }}} & { - \frac{{\omega_{\text{b}} K_{I21} }}{{L_{\text{f}} }}} & { - \frac{{\omega_{\text{b}} K_{I21} }}{{L_{\text{f}} }}} \\ {\omega_{ } \omega_{b} } & { - \frac{{\omega_{\text{b}} }}{{C_{{f_{ } }} }}} & 0 & 0 & 0 \\ 0 & 0 & { - \frac{{\omega_{\text{b}} }}{{C_{\text{f}} }}} & 0 & 0 \\ 0 & { - \frac{{R_{{{\text{c}}_{ } \omega_{\text{b}} }} }}{{L_{\text{c}} }}} & {\omega_{ } \omega_{\text{b}} } & 0 & 0 \\ \end{array} } \right] $$
$$ A_{\text{aug13}} = \left[ 0 \right]_{3 \times 3} $$
$$ A_{{{\text{aug}}_{ 2 1} }}^{\text{T}} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ {\frac{{\omega_{\text{b}} }}{{C_{\text{f}} }}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ { - \omega_{ } \omega_{b} } & {\frac{{\omega_{\text{b}} }}{{L_{\text{c}} }}} & 0 & 1 & 0 & 0 & {\omega_{\text{c}} I_{{{\text{g}}_{\text{d}} 0}} } & { - \omega_{\text{c}} I_{{{\text{g}}_{\text{q}} 0}} } \\ \end{array} } \right] $$
$$ A_{{{\text{aug}}_{ 2 2} }} = \left[ {\begin{array}{*{20}c} 0 & 0 & { - \frac{{\omega_{\text{b}} }}{{C_{\text{f}} }}} & 0 & 0 \\ 0 & { - \frac{{R_{{{\text{c}}_{ } \omega_{\text{b}} }} }}{{L_{\text{c}} }}} & {\omega \omega_{\text{b}} } & 0 & 0 \\ {\frac{{\omega_{b} }}{{L_{\text{c}} }}} & { - \omega_{0} \omega_{b} } & { - \frac{{R_{{c_{ } \omega_{b} }} }}{{L_{\text{c}} }}} & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ {\omega_{\text{c}} I_{{{\text{g}}_{\text{q}} 0}} } & {\omega_{\text{c}} E_{{{\text{g}}_{\text{d}} 0}} } & {\omega_{\text{c}} E_{{{\text{g}}_{\text{d}} 0}} } & 0 & 0 \\ {\omega_{\text{c}} I_{{{\text{g}}_{\text{d}} 0}} } & {\omega_{\text{c}} E_{{{\text{g}}_{\text{q}} 0}} } & { - \omega_{\text{c}} E_{{{\text{g}}_{\text{d}} 0}} } & 0 & 0 \\ \end{array} } \right] $$
$$ A_{{{\text{aug}}_{ 2 3} }} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 \\ {\frac{{V_{{{\text{pccd}}_{ 0} }} \sin \left( {\delta_{0} } \right)\omega_{\text{b}} }}{{L_{c} }}} & { - \omega_{\text{b}} I_{{{\text{gq}}0}} } & 0 \\ {\frac{{V_{{{\text{pccd}}_{ 0} }} \cos \left( {\delta_{0} } \right)\omega_{b} }}{{L_{c} }}} & {\omega_{\text{b}} I_{\text{gd0}} } & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & { - m_{\text{p}} } & 0 \\ 0 & { - \omega_{\text{c}} } & 0 \\ { - \omega_{\text{c}} } & 0 & 0 \\ \end{array} } \right] $$

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Qoria, T., Li, C., Oue, K. et al. Direct AC voltage control for grid-forming inverters. J. Power Electron. 20, 198–211 (2020). https://doi.org/10.1007/s43236-019-00015-4

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Keywords

  • Power transmission system
  • 2-Level voltage source inverter
  • Grid-forming control
  • State-feedback control
  • Small-signal stability analysis
  • Current limitation
  • Transient power coupling