Modeling and Control of PMSG-Based Variable-Speed Wind Turbine

Abstract

This chapter presents a control scheme of a variable-speed wind turbine with a permanent-magnet synchronous-generator (PMSG) and full-scale back-to-back voltage source converter. A comprehensive dynamical model of the PMSG wind turbine and its control scheme is presented. The control scheme comprises both the wind-turbine control itself and the power-converter control. In addition, since the PMSG wind turbine is able to support actively the grid due to its capability to control independently active and reactive power production to the imposed set-values with taking into account its operating state and limits, this chapter presents the supervisory reactive-power control scheme in order to regulate/contribute the voltage at a remote location. The ability of the control scheme is assessed and discussed by means of simulations, based on a candidate site of the offshore wind farm in Jeju, Korea.

Appendices

Appendix

Base values

$$\begin{aligned} S_{b} & = 2 {\text{MVA}},\quad V_{b} = 690 {\text{V}},\quad \omega_{b} = 2\pi f(rad/\sec ),\quad f = 60 {\text{Hz}}, \\ {\text{V}}_{\text{d}c} & = 800 {\text{V,}}\quad Z_{b} = {{\left( {{{V_{b} } \mathord{\left/ {\vphantom {{V_{b} } {\sqrt 3 }}} \right. \kern-0pt} {\sqrt 3 }}} \right)} \mathord{\left/ {\vphantom {{\left( {{{V_{b} } \mathord{\left/ {\vphantom {{V_{b} } {\sqrt 3 }}} \right. \kern-0pt} {\sqrt 3 }}} \right)} {i_{b} }}} \right. \kern-0pt} {i_{b} }},\quad L_{b} = {{Z_{b} } \mathord{\left/ {\vphantom {{Z_{b} } {\omega_{b} }}} \right. \kern-0pt} {\omega_{b} }},\quad C_{b} = {1 \mathord{\left/ {\vphantom {1 {\left( {Z_{b} \omega_{b} } \right),}}} \right. \kern-0pt} {\left( {Z_{b} \omega_{b} } \right),}} \\ T_{b} & = {{S_{b} } \mathord{\left/ {\vphantom {{S_{b} } {\omega_{b} }}} \right. \kern-0pt} {\omega_{b} }},\quad J_{b} = {{S_{b} } \mathord{\left/ {\vphantom {{S_{b} } {\left( {\omega_{b}^{2} } \right)}}} \right. \kern-0pt} {\left( {\omega_{b}^{2} } \right)}},\quad i_{\text{d}c} = {{S_{b} } \mathord{\left/ {\vphantom {{S_{b} } {{\text{V}}_{\text{d}c} }}} \right. \kern-0pt} {{\text{V}}_{\text{d}c} }}, \\ Z_{\text{d}c} & = {{{\text{V}}_{\text{d}c} } \mathord{\left/ {\vphantom {{{\text{V}}_{\text{d}c} } {i_{\text{d}c} }}} \right. \kern-0pt} {i_{\text{d}c} }},\quad L_{{{\text{d}}c}} = {{Z_{{{\text{d}}c}} } \mathord{\left/ {\vphantom {{Z_{{{\text{d}}c}} } {\omega_{b} }}} \right. \kern-0pt} {\omega_{b} }},\quad C_{\text{d}c} = {1 \mathord{\left/ {\vphantom {1 {\left( {Z_{\text{d}c} \omega_{b} } \right)}}} \right. \kern-0pt} {\left( {Z_{\text{d}c} \omega_{b} } \right)}} \\ \end{aligned} $$

Infinite bus voltage and maximum operating limit of VSC (pu)

$$ {\mathbf{v}}_{\text{d}q,IB} = \left[ {\begin{array}{*{20}c} {1.15} & {0.5} \\ \end{array} } \right],\;S_{\hbox{max} } = 1 $$

Line parameter (pu)

$$ \begin{aligned} R_{TL} & = 0.0059,\quad L_{TL} = 0.1132,\quad C_{TL} = 0.025,\quad R_{ca} = 0.006, \\ L_{ca} & = 0.003,\quad C_{ca} = 0.042,\quad R_{\text{filt}} = 0.014,\quad L_{\text{filt}} = 0.175, \\ R_{tr1} & = 0.0003,\quad L_{tr1} = 0.001,\quad R_{tr2} = 0.0005,\quad L_{tr2} = 0.004 \\ \end{aligned} $$

PMSG (pu)

$$ R_{s} = 0.042,\quad L_{ds} = 1.05,\quad L_{qs} = 0.75,\quad \psi_{m} = 1.16 $$

Controller gains (pu)

• A. Generator-side converter:

  Controllers PI1 and PI3: $k_{p} = 0.2952,\quad k_{i} = 12.4832$

  Controllers PI2 and PI4: $k_{p} = 21.5,\quad k_{i} = 11.5$

• B. Grid-side converter:

  Controllers PI5 and PI6: $k_{p} = 0.7147,\quad k_{i} = 7.1515$

  DC link module: $v_{\text{d}c}^{ref} = 1.16,\quad C_{\text{d}c} = 0.1,\quad k_{p} = 0.9544,\quad k_{i} = 7.8175$

• C. Reactive power controllers: $k_{p} = 0.001,\quad k_{i} = 120$

Future Work

This work provides a feasibility study for dynamic modeling and voltage control for wind farm based on simulation. This work will be applied to a demonstration project in order to validate the dynamic modeling and also voltage control and expand its application.