A modified sequence domain impedance definition and its equivalence to the dq-domain impedance definition for the stability analysis of AC power electronic systems

Representations of AC power systems by frequency dependent impedance equivalents is an emerging technique in the dynamic analysis of power systems including power electronic converters. The technique has been applied for decades in DC-power systems, and it was recently adopted to map the impedances in AC systems. Most of the work on AC systems can be categorized in two approaches. One is the analysis of the system in the \textit{dq}-domain, whereas the other applies harmonic linearization in the phase domain through symmetric components. Impedance models based on analytical calculations, numerical simulation and experimental studies have been previously developed and verified in both domains independently. The authors of previous studies discuss the advantages and disadvantages of each domain separately, but neither a rigorous comparison nor an attempt to bridge them has been conducted. The present paper attempts to close this gap by deriving the mathematical formulation that shows the equivalence between the \textit{dq}-domain and the sequence domain impedances. A modified form of the sequence domain impedance matrix is proposed, and with this definition the stability estimates obtained with the Generalized Nyquist Criterion (GNC) become equivalent in both domains. The second contribution of the paper is the definition of a \textit{Mirror Frequency Decoupled} (MFD) system. The analysis of MFD systems is less complex than that of non-MFD systems because the positive and negative sequences are decoupled. This paper shows that if a system is incorrectly assumed to be MFD, this will lead to an erroneous or ambiguous estimation of the equivalent impedance

Automatic power sharing modification of P/V droop controllers in low-voltage resistive microgrids

Microgrids are receiving an increasing interest to integrate the growing share of distributed generation (DG) units in the electrical network. For the islanded operation of the microgrid, several control strategies for the primary control have been developed to ensure a stable microgrid operation. In lowvoltage microgrids, active power/voltage (P/V ) droop controllers are gaining attention as they take into account the resistive nature of the network lines and the lack of directly-coupled rotating inertia. However, a problem often cited with these droop controllers is that the grid voltage is not a global parameter. This can influence the power sharing between different units. In this paper, it is investigated whether this is actually a disadvantage of the control strategy. It is shown that with P/V droop control, the DG units that are located electrically far from the load centres automatically deliver a lower share of the power. This automatic power sharing modification can lead to decreased line losses, thus, an overall better efficiency compared to the methods that focus on perfect power sharing. In this paper, the P/V and P/f droop control strategies are compared with respect to this power sharing modification and the line losses

Effect of control method on impedance-based interactions in a buck converter

All the interconnected regulated systems are prone to impedance-based interactions making them sensitive to instability and transient-performance degradation. The applied control method affects significantly the characteristics of the converter in terms of sensitivity to different impedance interactions. This paper provides for the first time the whole set of impedance-type internal parameters and the formulas according to which the interaction sensitivity can be fully explained and analyzed. The formulation given in this paper can be utilized equally either based on measured frequency responses or on predicted analytic transfer functions. Usually, the distributed dc-dc systems are constructed by using ready-made power modules without having thorough knowledge on the actual power-stage and control-system designs. As a consequence, the interaction characterization has to be based on the frequency responses measureable via the input and output terminals. A buck converter with four different control methods is experimentally characterized in frequency domain to demonstrate the effect of control method on the interaction sensitivity. The presented analytical models are used to explain the phenomena behind the changes in the interaction sensitivity

Impedance analysis of harmonic resonance in HVDC connected Wind Power Plants

During the last years the development of HVDC connected offshore wind power plants increased. As the first wind farms of this type were commissioned, an unexpected phenomenon occurred. Electrical harmonic resonance in offshore AC grid led to outages of the HVDC transmission system. The thesis introduces the phenomenon and compare different methods of its analysis. The study focuses on harmonic frequencies identification excited through the resonance phenomena between the elements within WPP's inner AC network. The analysis includes observations from three tested topology cases by different methods: frequency sweep and harmonic resonance modal analysis. The comparison is performed for diverse converter models: voltage source based, current source based and nonlinear impedance model obtained by harmonic linearization method. The results of the analysis are verified by the outcome attained in DIgSILENT Power Factory software. The study also includes the stability analysis based on Nyquist criterion and interpreted in Bode diagrams. Furthermore, the result of investigation exposes the clues for possible subsequent implementation of harmonic filters as well as for beneficial control of converters. Feasible measures for resonance mitigation from literature are described and proposed

Demonstration of sustained and useful converter responses during balanced and unbalanced faults in microgrids

In large power grids where converter penetration is presently low and the network impedance is predominantly reactive, the required response from converters during faults is presently specified by phrases such as “maximum reactive output”. However, in marine and aero power systems most faults are unbalanced, the network impedance is resistive, and converter penetration may be high. Therefore a balanced reactive fault current response to an unbalanced fault may lead to over-voltages or over/under frequency events. Instead, this paper presents a method of controlling the converter as a balanced voltage source behind a reactance, thereby emulating the fault response of a synchronous generator (SG) as closely as possible. In this mode there is a risk of converter destruction due to overcurrent. A new way of preventing destruction but still providing fault performance as close to a SG as possible is presented. Demonstrations are presented of simulations and laboratory testing at the 10kVA 400V scale, with balanced and unbalanced faults. Currents can be limited to about 1.5pu while still providing appropriate unbalanced fault response within a resistive network