Abstract-Stability analysis of power-converter-based AC systems poses serious challenges not only because of the non-linear nature of power converters, but also because linearisation is not generally applied around a steady-state operating point, as in the DC case, but around a time-periodic operating trajectory. Typical examples are single-phase and unbalanced three-phase systems. In this paper, two general methods to assess stability of the aforementioned systems are presented. Both are based on the Linear Time Periodic (LTP) systems theory. The first is model-based and relies on the evaluation of the eigenvalues of the linearised model, assuming a complete knowledge of the parameters. By contrast, the second proposes a set of smallsignal current injections to measure the Harmonic Impedances and applies the LTP Nyquist Criterion, so that stability of the system can be assessed with a black-box approach, without relying on knowledge of the system parameters. The basic LTP systems theory is reviewed in order to provide a mathematical justification for the second method. As case study, a simple network, consisting of a source full-bridge converter in AC voltage-control mode and a load full-bridge converter in AC current-control mode including PLL, is considered. Analytical results based on average modelling and simulations based on both average and switching models are presented, showing good accuracy in the identification of the stability thresholds for both the proposed methods.

A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. Abstract-Stability analysis of power converters in AC networks is complex due to the non-linear nature of the conversion systems. Whereas interactions of converters in DC networks can be studied by linearising about the operating point, the extension of the same approach to AC systems poses serious challenges, especially for single-phase or unbalanced three-phase systems. A general method for stability analysis of power converters suitable for single-phase or unbalanced AC networks is presented in this paper, based on Linear Time Periodic (LTP) theory. A singlephase grid-connected inverter with PLL is considered as case study. It is demonstrated that the stability boundaries can be precisely evaluated by the proposed method, despite the nonlinearity introduced by the PLL. Simulation and experimental results from a 10kW laboratory prototype are provided to confirm the effectiveness of the proposed analysis.

This paper presents the first experimental validation of the stability analysis based on the online measurement of harmonic impedances exploiting the Linear Time Periodic (LTP) approach, applied to AC networks of power converters. Previous publications have provided the theoretical framework for the method, enabling the stability assessment of an unknown system adopting a blackbox approach, relying only on injected perturbations and local measurements. The experimental case study considered in this paper comprises two single-phase converters, one acting as source subsystem and the other as load subsystem. A third converter, the Stability Measurement Unit (SMU), is controlled to inject small current perturbations at the point of common coupling (PCC).From the measured small-signal perturbations of PCC voltage, source current and load current, the harmonic impedances of source and load subsystems are calculated. The LTP Nyquist Criterion is then applied to the ratio of the two harmonic impedances in order to assess the stability of the whole system. Theoretical and experimental results from a 5 kW laboratory prototype are provided and confirm the effectiveness of the method. In addition, the measurements do not require sophisticated equipment or control boards and can be easily performed from data sampled by commercial micro-controllers.

Abstract-A general method for the stability analysis of power converters is presented in this paper. The method is based on Harmonic Linearisation and Linear Time Periodic (LTP) analysis techniques and a single-phase grid-feeding inverter with PLL is considered as case study. Although stability analysis has been developed using the average model of the converter, the obtained results can be extended to the switching model and it is possible to evaluate precisely the boundary between stability and instability.

In recent years, a considerable effort has been made to minimise the size of DC-link capacitors in single-phase activefront-ends (SP-AFE), to reduce cost and to increase power density. As a result of the lower energy storage, a high-bandwidth outer DC voltage control loop is required to respond to fast load changes. Linearised modelling is usually performed according to the power-balance method and the control is designed using LTI techniques. This is done assuming negligible voltage ripple at twice the grid frequency, and the model is considered valid up to the grid frequency. However, its precise validity limits are usually unknown and the control design becomes empirical when approaching these boundaries. To overcome this drawback, Linear Time Periodic (LTP) theory can be exploited, defining the range of validity of the LTI model and providing precise stability boundaries for the DC-link voltage loop. The main result is that LTP models more accurately describe the system behaviour and provide superior results compared to the LTI ones. Theoretical analysis, simulations and extensive experimental tests on a 10 kW converter are presented to validate the claims.

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