Abstract
This article presents a systematic robust current control design approach for three-phase voltage-source converters. Robustness is guaranteed by combining intrinsic passive properties of the impedance uncertainty at the point of common coupling together with stability results from a passivity-based control theory. This approach ensures stability against typical uncertainty sources at mid and high frequencies, such as cable resonances or other converters interaction, with significant less conservative performances than the obtained with the traditional robust control theory. The approach uses multiobjective controller synthesis formulation that allows us to logically combine robustness requirements with performance objectives avoiding heuristic iteration over the control structure and parameters. The controller synthesis is performed by means of a nonsmooth <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> optimization technique that tunes all free parameters of a vector-based controller function, which constraints its structure. This results in a synthesized controller with lower order than those obtained with convex optimization definitions of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> control problem. The design methodology is validated in time and frequency domain by means of theoretical analysis and experimental results with three usual grid filters: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL,</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLCL</i> .
Highlights
T HE increasing presence of voltage-source converters (VSCs) in power systems has placed its stability against grid uncertainties under intense study [1], [2]
One of the main sources of uncertainty, due to the interaction with other VSCs connected to the point of common coupling (PCC) and intrinsic parameters in transformers and electric connections, is the equivalent grid impedance
The size of such passivity shortage relies on the dynamic behavior of Syo→i2, which depends on the desired performance objectives and the presence of filters in the measured variables as well as PCC voltage feed-forward
Summary
T HE increasing presence of voltage-source converters (VSCs) in power systems has placed its stability against grid uncertainties under intense study [1], [2]. The main theoretical approach is based on linear matrix inequalities (LMIs) derived from positive-real lemma and bounded-real lemma [24] This approach requires convex optimization-based controller synthesis that, presents important practical problems as an inherent conservativeness [25] and, again, high-order resulting controllers that are prone to numerical instability. This article considers a close but alternative procedure that relies on nonsmooth optimization techniques [26], [27], which have been successfully applied in other problems [28], [29] to find feasible solutions This approach allows evaluating and enforcing of the required passivity constraint and performance objectives [14] to tune the selected controller structure.
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