Elias Kaufhold

The growth of renewables in public energy networks requires suitable strategies to assess the stable operation of the respective power electronic devices, e.g., inverters. Different assessment methods can be performed with regard to the available knowledge and the assessment objective, e.g., a specific frequency range or the input signal characteristics that are typically classified into small-signal and large-signal disturbances. This paper addresses the limits of the measurement-based small-signal stability analysis in the harmonic frequency range of commercially available single-phase inverters for photovoltaic applications. The harmonic stability is analyzed, and the results for a sinusoidal background voltage and distorted background voltages are assessed based on measurements. The measurements prove that even in the harmonic frequency range, the harmonic stability analysis can only provide a sufficient but not a necessary condition in terms of the statement towards an instable operation.

The growth of renewables in the energy sector, e.g., in public low-voltage networks, leads to an increasing share of installed power electronic devices, e.g., inverters for photovoltaic applications. To rely on these devices, suitable analyses have to be performed. This includes studies of the device stability in the harmonic frequency range, i.e., above 50 Hz up to 2 kHz. State-of-the-art time-domain studies for harmonic stability analyses require detailed knowledge about the inverter design. Black-box studies must identify the inverter characteristics in the laboratory, which can differ depending on specific operating points, i.e., specific operating powers. This study analyzes the operating-point dependency of inverters on the critical inductance values of the network impedance, e.g., the inductances at which the inverter is expected to become unstable. Measurements are performed for three operating powers of an unknown, commercially available single-phase inverter to validate the critical inductances. Two further commercially available inverters and four simulative implementations are analyzed as well with regard to the critical inductance and the critical frequency. The results demonstrate the importance of considering a representative range of operating powers of the inverter for the small-signal stability analysis.

This paper presents a framework to assess the grid compatibility of single-phase inverters connected to public low voltage network, which is characterized by a stable operation at reasonable emission. The assessment is based on considering emission, immunity and stability. The state of the art for commercially available devices relies only on the classical, impedance-based stability analysis based on the Nyquist criterion. However, experiences have shown that this is not sufficient for a statement towards the stable operation of an inverter, since the stable operation can also be affected by other factors than the network impedance, e.g. a background voltage distortion. Exemplary laboratory measurements of two commercially available single-phase PV inverters are presented to validate the statement by showing that despite the impedance-based stability criterion is met, inverters can still trip in presence of a high background voltage distortion. The paper concludes that the immunity of the inverter with regard to the voltage distortion at the point of connection (PoC) is additionally of importance for its stable operation.

The increasing number of installed renewable power generators, e.g. photovoltaic systems, leads to a significant growth of power electronic devices, especially in public low voltage networks. To analyze and assess the harmonic emission and the harmonic stability, i.e. the device characteristics in the frequency range up to 2 kHz, suitable device representations are required. The representation of commercially available devices is limited to black-box models since their detailed design is unknown. For the parametrization of the respective small signal models, all relevant impact factors on the model have to be known. Consequently, this paper studies the impact of the DC power on the small signal model of single-phase photovoltaic inverters. The paper presents a quantitative assessment of three commercially available inverters in terms of their frequency-dependent small signal characteristics. The linear time-invariant and the linear-time periodic device characteristics are analyzed in terms of their absolute and their relative deviations between different DC powers. The results demonstrate the importance of considering the DC power level for accurate frequency domain models in harmonic studies.

The growth of renewable energy generators in public energy networks demands suitable approaches to simulate future power grids, e.g. low voltage networks. One main distributed energy generator are small power photovoltaic systems interconnected by single-phase inverters. The increasing penetration of such inverters requires models that are suitable for large-scale studies. This study analyses the aggregation characteristics based on time domain simulations. The results suggest that under specific circumstances the aggregation of multiple inverters connected at the same point having similar output power can be approximated by multiplying the individual inverter characteristics. In case the inverters have different output powers a simple aggregation is not possible.

This paper presents the use of a modular time domain model to study the interaction of single-phase photovoltaic inverters in public low voltage networks. Currently, specific time domain implementations of individual inverters are designed and studied from a power electronics perspective. If circuit and controller are unknown, e.g. for commercially available photovoltaic inverters, time domain modelling is not possible and measurement-based black-box models in frequency domain have to be used. This paper proposes a modular modelling approach for generating a large and realistic set of different inverter implementations for general and probabilistic system-level studies of their interaction in public low voltage networks. The modular model can be used for time domain studies but also enables to derive frequency domain models as required in case of large-scale studies. It is shown in frequency domain that the modular model represents adequately commercially available devices, which have been characterized by black-box measurements in the laboratory.

A photovoltaic inverter (PVI) may enter operational instability region based on grid supply conditions, such as the presence of voltage waveform distortions and high grid impedance, especially when the actual power output of the PVI is low. This paper considers evaluation and modelling of one commercially available 3-phase PVI, for which laboratory tests showed instability when it was operating with a low power output and connected to a distorted voltage supply. A full switching model of the considered PVI is developed using simulated and measured frequency-based impedance plots, which are also used to calculate approximate values of the PVI output filter, as well as the type and parameters of its control. Afterwards, the operational stability of the PVI is evaluated using impedance-based and Nyquist stability criteria.

Battery energy storage systems are a key enabling component for the transition from passive to active distribution grids. Therefore, the number of battery energy storage systems is expected to increase exponentially in the near future. As such systems consist of grid-side power electronic frontends, this increase drives the need for accurate harmonic models that can be used in power system studies to analyze the future impact on harmonic levels and harmonic stability. The aim of this study is to develop a measurement based black-box model of a single-phase commercial battery energy storage system in frequency domain. A comparison is made between harmonic characteristics in charging and discharging mode, which evaluates the requirement for different models for the two operating modes.

The increasing share of power electronic (PE) devices in public electricity networks has increased the chance of harmonic instabilities, which are caused by the interaction of the device control with the network impedance. Usually, the detailed internal design of PE devices is not available and only measurement-based black-box approaches are feasible for the analysis of harmonic instabilities. A major drawback of such black-box approaches is the need for expensive programmable grid simulators. To overcome that issue, this article proposes a new approach to identify the sensitivity of a PE device for harmonic instabilities, which solely requires two air coils and which can simply be connected to any available power supply including the low voltage (LV) network. By systematically increasing the resulting inductance of air coils, the proposed method is able to identify the frequency regions that are critical with regard to the harmonic stability of the PE device. Critical frequency regions are determined by analyzing the measurement results in time-frequency domain using the estimation of signal parameters via rotational invariance techniques (ESPRITs). The proposed method is applied to a commercially available single-phase photovoltaic (PV) inverter. The critical frequency region has been determined at around 500 Hz, which is confirmed by formal stability analysis.