Simplified Volterra Model Research Articles

Frequency-Domain Nonlinear Modeling Approaches for Power Systems Components—A Comparison

Harmonic simulations play a key role in studying and predicting the impact of nonlinear devices on the power quality level of distribution grids. A frequency-domain approach allows higher computational efficiency, which has key importance as long as complex networks have to be studied. However, this requires proper frequency-domain behavioral models able to represent the nonlinear voltage–current relationship characterizing these devices. The Frequency Transfer Matrix (FTM) method is one of the most widespread frequency domain modeling approaches for power system applications. However, others suitable techniques have been developed in the last years, in particular the X-parameters approach, which comes from radiofrequency and microwave applications, and the simplified Volterra models under quasi-sinusoidal conditions, that have been specifically tailored for power system devices. In this paper FTM, X-parameters and simplified Volterra approaches are compared in representing the nonlinear voltage –current relationship of a bridge rectifier feeding an ohmic-capacitive dc load. Results show that the X-parameters model reaches good accuracy, which is slightly better than that achieved by the FTM and simplified Volterra models, but with a considerably larger set of coefficients. Simplified Volterra models under quasi-sinusoidal conditions allows an effective trade-off between accuracy and complexity.

Nonlinear Behavioral Modelling of Voltage Transformers in the Frequency Domain: Comparing Different Approaches

Instrument transformers suffer from weak nonlinearities, which may have a significant impact on harmonic measurements. Therefore, their detailed characterization should be based on a nonlinear model instead of a mere measurement of the frequency response function. Starting from this assumption, this article compares different models that can be employed to represent the behavior of voltage transformers (VTs): simplified Volterra models, frequency transfer matrixes (FTMs), and spectral linearization approximation; an inductive VT has been considered as a case study. The results highlight that the FTM approach is significantly affected by the range of variation of the fundamental component, while remarkable accuracy can be reached with the spectral linearization approximation at the expense of complexity. On the other hand, simplified Volterra models allow obtaining an effective tradeoff between the achieved accuracy and the number of coefficients.

Behavioral Representation of a Bridge Rectifier Using Simplified Volterra Models

Studying the propagation of harmonics in power grids represents a very important task nowadays. However, this demands for nonlinear models of power system devices representing a critical tradeoff between the accuracy and the computational cost. Simplified Volterra models with quasi-sinusoidal excitation have been recently proposed and they appear to be particularly suitable for the purpose. In this paper, these models have been applied to predict, for a given input voltage, the current harmonics of a full-bridge rectifier feeding an ohmic-capacitive load. Accuracy has been evaluated by means of both numerical simulations and experiments. Robustness has also been assessed by considering a set of realistic voltage waveforms different from those employed for the identification. Results highlight the remarkable accuracy of the proposed models in spite of the relatively small set of coefficients to be identified. This feature is extremely important when models have to be employed in frequency-domain simulations of large networks.

On-line fault detection technique for voltage transformers

Conventional voltage transformers (CVTs) are still widely used as transducers in power networks, thanks to their high reliability, insulation capability, low drift over time and temperature. Their rugged construction is very often used as justification for skipping periodical tests and calibrations, that require putting them off-line, thus avoiding a time-consuming and expensive procedure. For this reason, in the last years, a growing interest has been addressed towards the study of online diagnostic and calibration procedures. The typical approach is based on the frequency response analysis that permits, under sinusoidal excitation, to detect possible deterioration of the behavior of CVT. Anyway, the real interest is to check the CVT fleet already installed and operating on the grid without requiring their disconnection from the grid. As well known, distribution grid voltage features a non negligible harmonic distortion, which may allow the online evaluation of the frequency response of the transformer, by simply connecting a reference transducer. Unfortunately, being the harmonics much lower than the fundamental, this approach cannot be employed in a straightforward way because of the nonlinear behavior of the CVT. This paper proposes an innovative condition monitoring technique of CVTs based on a simplified Volterra model. This opens the way to a new approach to the on-site characterization of CVTs, exploiting the actual voltage of the grid and thus not requiring its disconnection.

Calibration of pipeline ADC with pruned Volterra kernels

A Volterra model is used to calibrate a pipeline ADC simulated in Cadence Virtuoso using the STMicroelectronics CMOS 45 nm process. The ADC was designed to work at 50 MSps, but it is simulated at up to 125 MSps, proving that calibration using a Volterra model can significantly increase sampling frequency. Equivalent number of bits (ENOB) improves by 1–2.5 bits (6–15 dB) with 37–101 model parameters. The complexity of the calibration algorithm is reduced using different lengths for each Volterra kernels and performing iterative pruning. System identification is performed by least squares techniques with a set of sinusoids at different frequencies spanning the whole Nyquist band. A comparison with simplified Volterra models proposed in the literature shows better performance for the pruned Volterra model with comparable complexity, improving linearity by as much as 1.5 bits more than the other techniques.

Simplified Modeling and Identification of Nonlinear Systems Under Quasi-Sinusoidal Conditions

This paper proposes a simplified Volterra model able to represent the steady-state behavior of nonlinear systems in quasi-sinusoidal conditions. A wide class of nonlinear systems can be modeled using the conventional Volterra approach, but as the order of nonlinearity or the memory length increases, the number of coefficients grows exponentially, thus making the identification of the Volterra model troublesome. By considering a system whose input is a periodic signal containing a main frequency component which is much higher than the others, it is possible to drastically reduce the number of coefficients of its frequency-domain Volterra model without affecting the model accuracy. The proposed technique is particularly suitable to represent the behavior of the electrical devices connected to the ac mains, since they typically operate in quasi-sinusoidal conditions. In particular, its application to voltage and current transducers takes on great importance in the field of instrumentation and measurement, since it allows overcoming their usual characterization. Thanks to the proposed model, dynamics and nonlinearities can be considered simultaneously, while avoiding the complexity usually associated with the conventional Volterra approach. For example, the proposed technique is applied to model a Hammerstein system, which is often employed to represent the behavior of electrical devices, and the results are deeply discussed.

A Behavior Level Analytical Method of Electromagnetic Susceptibility for Radio Frequency Receiver

Based on simplified Volterra model, a behavior-level simulation analysis approach of electromagnetic susceptibility (EMS) for radio frequency (RF) receiver is presented in this article. Third order simplified Volterra model is adopted to analyze receiver EMS. A general criterion for EMS is proposed according to EMS response characteristics in frequency domain, and then the simulation flow charts for calculating susceptibility thresholds are given. This approach is superior to the previous EMS analysis method on receiver, which mainly relies on experiments but lack simulation analysis. Take the dual frequency GPS receiver and zero IF receiver interfered by continue wave as examples for in-band and out-of-band susceptibility threshold calculation. Simulation results show that the proposed method is not only valid and effective, but also reduces the internal storage and simulation time, which is suitable to RF receiver EMS analysis and practical in engineering and technology field.