Optimization Framework for Frequency and Parameter Estimation in Low-Inertia Power Systems for Fast-Frequency Support

This paper presents a new numeric technique to estimate the operating power system frequency. The technique employs a recurrent scheme which consists of a tunable input FIR filter, frequency calculator and an averaging output filter. The recurrent structure ensures that power system frequency is efficiently tracked while minimizing signal distortions arising from harmonic and noise effects. The performance of the developed technique has been thoroughly investigated using computer simulations, and the results are provided. The effectiveness of the proposed technique is demonstrated by comparing it with three different methods reported in the literature. An experimental setup is successfully developed to evaluate the practical operation of the estimator corroborating the performance during simulations. It was confirmed that the proposed estimator performs well during static and dynamic conditions which makes it useful for the estimation of online power system frequency.

This paper describes the design, analysis and computational aspects of a technique for the measurement of power system voltage, current and frequency. This technique can be used in a digital AVR for the state estimation of turbine-generator terminal quantities or in a digital relay for protection of a power system. This technique provides fast and accurate estimation of power system frequency, and is used in a Kalman-filtering algorithm to estimate power system voltage and current signals. Practical considerations such as the effect of power system harmonics, noise, frequency changes, mechanical and electrical load changes are taken into account during implementation of this technique. Several computer simulation tests are presented to highlight the usefulness of the technique. Simulation results show that the technique can simultaneously estimate the amplitude and frequency of a sinusoidal signal, even in the case that the signal is distorted by harmonics or noise or encounters frequency changes.

Effective frequency estimation has become one of the great challenges in power systems especially in future smart grid systems due to their varying topology and tenable supply-demand mismatch. In this paper, we have presented a Matrix pencil method (MPM) based technique for real-time frequency estimation in balanced and unbalanced power systems by exploiting widely linear model of power system. Comparison of this method was performed with recently developed CLMS and ACLMS techniques based on strictly and widely linear modeling respectively. It was observed that MPM demonstrates significantly better estimation accuracy and time resolution compared to these techniques.

The paper proposes an extended complex Kalman filter and employs it for the estimation of power system frequency in the presence of random noise and distortions. From the discrete values of the 3-phase voltage signals of a power system, a complex voltage vector is formed using the well known /spl alpha//spl beta/-transform. A nonlinear state space formulation is then obtained for this complex signal and an extended Kalman filtering approach is used to compute the true state of the model iteratively with significant noise and harmonic distortions. As the frequency is modeled as a state, the estimation of the state vector yields the unknown power system frequency. Several computer simulations test results are presented in the paper to highlight the usefulness of this approach in estimating near nominal and off-nominal power system frequencies.

Dynamic variation in power system frequency is required to be estimated for implementing the correcting measures. This paper presents power system frequency estimation by using RLS-Adaline and KF-Adaline algorithms. In the proposed hybrid approaches the weights of the Adaline are updated using RLS/KF algorithms. Frequency of power system signal is estimated from final updated weights of the Adaline. The performances of the proposed algorithms are studied through simulations for several critical cases that often arise in a power system. These studies show that the KF-Adaline algorithm is superior over the RLS-Adaline in estimating power system frequency. Studies made on experimental data also support the superiority.

An accurate dynamic estimation of frequency and magnitude parameters (actual power-line frequency and actual power-line voltages or currents) is very important for different applications in power systems, such as frequency and magnitude relay protection, harmonics and quality of power in transient regimes, especially for local power systems with external UPS (uninterruptible power supply) synchronization (for example, by diesel-generator). Investigated methods and algorithms are modifications of OPD (orthogonal phasor decomposition) and IZC (integrating zero crossing) for frequency estimation and modifications of DFT (discrete Fourier transform) with interpolation in time or frequency domain, or alternatively, with pre-tuned prefilters, for magnitude (harmonics) estimation. Some aspects of choice and optimization of the above DSP (digital signal processing) methods and algorithms were described before in publications, but without comparison of their characteristics, which are the main subject of the proposed publication. Obtained simulation results can be used for improvement of chosen algorithms and their real time applications.

A new technique for estimating the frequency in power system is proposed in this paper. The standard recursive least squares (RLS) has the fast rate of convergence and is not sensitive to variations in the eigenvalue spread of the correlation matrix of the input vector, however, the tracking performance of RLS is limited in nonstationary condition. State space recursive least squares (SSRLS) technique allows the designers to choose an appropriate model to describe the information of system, so it can track the time-varying system. Considering the unbalance faults in power system, the complex voltage vector model formed by alphabeta - transformation is used as the frequency estimation model. On the other hand, the exponent-smoothing technique can reduce the errors caused by noise and oscillatory, so it is natural to use the exponent-smoothing technique to adjust the phase estimated by SSRLS. The results show that the proposed method based on SSRLS and exponent-smoothing technique gives the accurate frequency estimation even under the low signal-to-noise and the nonstationary condition.

In this paper a new improved recursive Newton type algorithm suitable for measurement applications in power systems is presented. It is used for power system frequency, phasors and spectra estimation. The recursive form of Newton type algorithm is improved with a strategy of sequentially tuning the forgetting factor. By this, the main algorithm properties, speed of convergence and accuracy, are significantly improved. The results of computer simulation, laboratory testing and off-line full-scale real-life data processing are given to show the main algorithm features.

This paper proposes an assessment framework for branch parameter estimation of power systems, based on which the estimation accuracy can be improved and the estimation reliability can be ensured. The proposed framework comprises three parts: 1) Parameter credibility assessment to evaluate the credibility of original parameters in the case that their true values are unknown; 2) estimation accuracy assessment to provide quantitative information about the validity of the estimation; 3) parameter dominance assessment to find out the key parameters for the estimation. This framework can be incorporated into the conventional parameter estimation process easily such that the accuracy and reliability of the estimation are improved. The implementation problems are addressed in details. Tests are carried out on the IEEE 14-bus system, IEEE 30-bus system, and IEEE 300-bus system to show the correctness and effectiveness of the proposed assessment framework.

Wide-range, fast and robust estimation of power system frequency

The utilization of Clarke's transformation in the estimation of power system frequency provides the classical single-phase methods with more robustness because the estimated frequency is computed using the information provided by the three-phase voltage. This approach is particularly important when asymmetric sags generate zero voltage in one of the three phases. In addition, the proposed algorithm exhibits good behavior during dynamic conditions. The Clarke components of the voltage signals are then used to compute the frequency of the system following an iterative approach based on a proportional-integral-derivative controller. The inverse component of the voltage is also used in order to detect unbalanced conditions. The proposed algorithm has been put to the test with distorted three-phase voltage supplied by an arbitrary waveform programmable power supply and with different signals generated with an Alternative Transients Program-Electromagnetic Transients Program model.

Precise tracking of frequency is essential for accurate phasor estimation at off nominal frequencies. In this paper, a simple approach for real time frequency estimation involving interpolation of DFT coefficients corresponding to fundamental and two adjacent bins is presented. In particular, quadratic interpolation method is adopted to estimate the frequency. The quadratic interpolation formulation widely adopted in signal processing framework may not be adequate for frequency estimation of power system signals. The modifications required to improve the accuracy are presented. Results on standard test signals and simulated waveforms of practical equivalent systems of Indian grid are presented to validate the proposed approach.

Frequency estimation in wind farm integrated systems using artificial neural network

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a reference manual for the commands specification for the DAKOTA software, providing input overviews, option descriptions, and example specifications.

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a developers manual for the DAKOTA software and describes the DAKOTA class hierarchies and their interrelationships. It derives directly from annotation of the actual source code and provides detailed class documentation, including all member functions and attributes.