Impact of Control Loops on the Passivity Properties of Grid-Forming Converters with Fault-Ride through Capability

Due to the increasing integration of renewable energy sources (RES) and a corresponding reduction of conventional generating units, there is nowadays a demand from the power-electronic converters to provide grid-forming properties through proper control of the converter systems. This paper aims to evaluate the impact of various control loops in a grid-forming control strategy equipped with a fault-ride through capability on the passivity properties of the converter system. Through the analysis of the frequency-dependent input admittance of the converter, the main factors affecting the passivity properties are identified. A simplified analytical model is derived in order to propose possible control modifications to enhance the system’s passivity at various frequencies of interest and the findings are validated through detailed time-domain simulations and experimental tests.

Input Admittance, Directivity and Quality Factor of Biconical Antenna of Arbitrary Cone Angle

New analytical expressions and numerical results for the quality factor and directivity as well as computationally convenient expressions for the input admittance of a symmetrical biconical antenna of arbitrary length $L$ and cone angle $\theta_0$ are presented. The quality factor for a wide-angle biconical antenna is shown to very closely approach the Chu's limit of $Q = (kL)^{-1}\{1+(kL)^{-2}\}$. Numerical calculations based on the analytical formula for antenna admittance confirm the conjecture that Foster's reactance theorem remains invalid even for perfectly conducting antennas. Furthermore, the variation of directivity of a wide-angle biconical antenna is a slowly varying function of its electrical length and is shown to depart significantly from that of a thin cylindrical dipole. <br>

Input Admittance, Directivity and Quality Factor of Biconical Antenna of Arbitrary Cone Angle

New analytical expressions and numerical results for the quality factor and directivity as well as computationally convenient expressions for the input admittance of a symmetrical biconical antenna of arbitrary length $L$ and cone angle $\theta_0$ are presented. The quality factor for a wide-angle biconical antenna is shown to very closely approach the Chu's limit of $Q = (kL)^{-1}\{1+(kL)^{-2}\}$. Numerical calculations based on the analytical formula for antenna admittance confirm the conjecture that Foster's reactance theorem remains invalid even for perfectly conducting antennas. Furthermore, the variation of directivity of a wide-angle biconical antenna is a slowly varying function of its electrical length and is shown to depart significantly from that of a thin cylindrical dipole. <br>

Determination of the attenuation coefficients from the measured frequency characteristics of the windings of power transformers. Part 1. Theoretical consideration

To model high-frequency processes and determine the stresses on the internal insulation of transformer windings, reliable high-frequency models of power transformers are required. The accuracy of modeling high-frequency resonance processes in the windings depends on how correctly the model reproduces the natural frequencies and damping of free oscillations in the windings. To construct and verify high-frequency models of power transformers, it is necessary to have experimentally obtained data on the values of damping factors. There is a known method for determining the winding damping factors based on measurements of the voltage transfer functions at the internal points of the windings and their subsequent processing using the vector fitting technique, but its application is not always possible in practice. The article presents the results of theoretical studies performed for a simplified transformer winding equivalent circuit. It is shown that the damping factors can be estimated from the width of the resonance peaks of the frequency responses of the voltage modulus and reactive component at the midpoint of the equivalent circuit, and from the input admittance resistive component and current in the neutral of the considered resonance circuit.

Determination of Damping Factors Based on the Measured Frequency Responses of Power Transformer Windings. Part 2. Analysis of Measurement Results

In the first part of the article, based on the results of theoretical studies performed for a simplified transformer winding equivalent scheme, it was shown that the damping factors can be estimated from the width of the resonant peaks of the frequency responses of the module and the reactive component of the voltage at the midpoint of the equivalent scheme, as well as the active component of the input admittance and neutral current of the considered resonant scheme. In this part of the article, the practical possibility of applying the obtained theoretical relations between the damping factors and the width of resonant peaks in relation to the frequency responses of power transformer windings is considered. The results of calculations of the damping factors at the two power transformers made by using the fitting of the free component of transient voltage and by determining the width of the resonance peaks of the active component of winding neutral current and the voltage transfer function, corresponding to intermediate points of the winding. It is shown that the evaluation of the values of the winding damping factors can be performed as a byproduct of transformer condition assessment by frequency response analysis (FRA).

Dynamic Effect of Input-Voltage Feedforward in Three-Phase Grid-Forming Inverters

Grid-connected and grid-forming inverters play essential roles in the utilization of renewable energy. One problem of such a converter system is the voltage deviations in the DC-link between the source and the inverter that can disrupt the inverter output voltage. A common method to prevent these voltage deviations is to apply an input-voltage feedforward control. However, the feedforward control has detrimental effects on the inverter dynamics. It is shown that the effect of the feedforward in the input-to-output dynamics is not ideal due to the delay in the digital control system. The delay affects the input-to-output dynamics at high frequencies, and only a minor improvement can be achieved by low-pass filtering the feedforward control signal. Furthermore, the feedforward control can remarkably affect the inverter input admittance, and therefore, impedance-based stability problems may arise at the DC interface. This paper proposes a method based on linearization and extra element theorem to model the effect of the feedforward control in the inverter dynamics. Experimental measurements are shown to demonstrate the effectiveness of the proposed model.

Numerical Modelling of Vibration Characteristics of a Partially Metallized Micro Electromechanical System Resonator Disc

In this paper, we report an extension of a polynomial and numerical vibrational characterization of an annular piezoelectric disc resonator partially covered with electrodes. The three governing partial differential equations of motion are solved to provide the frequency response of the piezoelectric disc using a polynomial approach. This method makes use of Legendre polynomials series to express the mechanical displacement components and the electrical potential which are introduced into the equations of motion of the piezoelectric structure. The principal advantage of this method consists of incorporating the electrical source, the boundary and continuity conditions directly into the governing equations by the use of position-dependent physical constants and by a wise choice of the polynomial expansions for the independent variables, the mechanical displacement components and the electrical potential. Both harmonic and modal analyses were studied and are presented. Numerical calculations based on the foregoing method were performed to present resonance and anti-resonance frequencies, electromechanical coupling coefficient, field profiles and electrical input admittance for PIC151 and PZT5A disc resonators with various metallization rates. The high accuracy and reliability of our approach is confirmed via a comparison of our results with their counterparts reported in literature.