| Summary: | Off-shore wind power plants can be connected to the on-shore grid using diode rectifier HVdc links. As diode rectifiers are passive converters, off-shore WPPs require grid-forming capability. This paper shows how to improve the WTG dynamic response and the voltage and current harmonic rejection by using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">H</mi><mo>∞</mo></msub></semantics></math></inline-formula>-based controllers. The paper explains how to synthesise three different <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">H</mi><mo>∞</mo></msub></semantics></math></inline-formula> voltage controllers: the first is a single-loop <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">H</mi><mo>∞</mo></msub></semantics></math></inline-formula> controller, the second is a cascaded <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">H</mi><mo>∞</mo></msub></semantics></math></inline-formula> controller and the third is a proportional–resonant controller that is optimised using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">H</mi><mo>∞</mo></msub></semantics></math></inline-formula> synthesis. The three <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">H</mi><mo>∞</mo></msub></semantics></math></inline-formula>-based controllers improve the performance and the robustness obtained with a benchmark case PR controller tuned using the root locus technique. All the controllers are designed in continuous time and implemented in discrete time, applying bilinear discretisation with a sampling rate of 0.25 ms. Detailed PSCAD simulations validate the improvement of the performance and robustness, as well as an improvement in the harmonic rejection. The single <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">H</mi><mo>∞</mo></msub></semantics></math></inline-formula> controller shows the best combined characteristics of all tried controllers, at the expense of losing the separation between voltage and current control loops.
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