Off-nominal Frequency Research Articles

A new least squares error based method for accurate phasor estimation of fault currents in series-compensated transmission lines

Phasor estimation of the fundamental component of the fault current is of great importance for the fault location unit in distance relays. In series-compensated transmission lines, the transient component of the fault current may appear in the complicated wave shape of an exponential-sinusoidal function. Thus, phasor estimation is a major challenge owing to the fact that more unknown parameters should be found, especially during off-nominal frequency conditions. Therefore, in this paper, a new method is put forward, on the strength of the least squares error (LSE), in order to accurately estimate the fundamental component phasor of the fault current in a series-compensated transmission line for off-nominal frequency conditions. The performance of the established method is also investigated through extensive simulation studies, taking care of different fundamental components, harmonic contents, and transient components. Moreover, the performance of the proposed method is evaluated for off-nominal frequencies. The results obtained in this study demonstrate that the mean absolute error of the estimated amplitude and phase for the fundamental component is less than 1% and 1°, respectively. Furthermore, the accuracy of the proposed method is not affected by the noise up to a signal-to-noise ratio of 30 dB. Thus, the established method is capable to effectively be employed for the phasor estimation in fault location applications.

Performance enhancement of band-pass FIR filter-based M-class phasor estimation

Abstract The paper presents the performance enhancement of band-pass filter-based M-class phasor estimation. The performance of the M-class phasor estimation using a band-pass FIR filter is enhanced with a magnitude correction factor for the off-nominal frequency range. The band-pass filter is implemented for the phasor estimation with various window functions Tukey, Rife Vincent class-I order-2 (RV2), Hamming, Hanning, Blackman, and Flat-top (FT) and its performance are evaluated under the steady and dynamic state tests prescribed by the standard. A rigorous performance analysis of enhanced phasor estimation using band-pass FIR filter with various window functions is presented with the accuracy indices of total vector error (TVE), frequency error (FE), and rate of change of frequency error (RFE). The result analysis reveals that the performance enhanced phasor estimation using band-pass FIR filter offers significantly less error than reported work at the low sampling rate. The design and performance analysis of the phasor estimation using the band-pass FIR filter is performed in the MATLAB platform.

Delay-Tracking Loop for Frequency Estimation of Grid-Interfaced Inverter Under Distorted Conditions

Fast and accurate frequency estimation is difficult for grid-interfaced inverter under distorted grid conditions with off-nominal frequency. A popular solution considers the multiple second-order generalized integrator-based frequency-locked loop yet can hardly achieve a fast dynamic response under significant phase jump and voltage sag. Another solution uses an adaptive sliding window filter with an additional frequency estimator. However, it is challenging to handle numerical instability due to the adjusting marginally-stable resonator and the accumulation error. This letter proposes a delay-tracking loop to overcome these problems. This loop allows the delay length to track the frequency with an inherent harmonics rejection at off-nominal frequency. At the same time, the fast response speed is maintained, and the marginally stable resonator is avoided. Comparative experimental results validate the above claims.

Single-cycle P Class phasor estimation based on harmonics whitening and off-nominal frequency offset adjustment

Phasor Measurement Units (PMUs) are essential for real-time power system monitoring and control. In this paper, a novel algorithm for protection (i.e., P Class) PMUs is presented. The proposed algorithm consists of four steps: preliminary narrowband disturbance whitening; estimation of the off-nominal fundamental frequency offset through the Interpolated Discrete Time Fourier Transform (IpDFT); data record length adjustment to refine narrowband disturbance whitening over an integer number of fundamental periods; time-domain estimation of the Taylor's series coefficients of the synchrophasor function through a weighted least-squares estimator (after correction of possible static off-nominal deviations). The key novel contribution of the proposed approach is its superior ability to smooth harmonic disturbances over shorter observation intervals than many existing algorithms (which typically require at least two-cycle-long data records to meet P Class accuracy requirements), while ensuring a good tracking capability of transient events with a reasonable execution time. Several simulation and experimental results confirm that, in the case of multi-harmonic distortion, the proposed approach returns more accurate results than both the basic Taylor-series-based Weighted Least-Squares (TWLS) estimator and other whitening-based techniques, while ensuring compliance with P Class specifications even over one-cycle-long data records.

Cyberattack on Phase-Locked Loops in Inverter-Based Energy Resources

This article reveals power grid vulnerabilities by manipulating the phase-locked loop (PLL) in an inverter-based energy resource (IBER). An attacker can exploit the off-nominal frequency operation of a power grid coupled with stability and tracking properties of an IBER PLL to manipulate the inverter and grid operations during strong and weak grid conditions. Employing a modified IEEE-14 bus system, simulation studies show that PLL-based attacks can cause: (i) revenue losses to IBER operators in weak and strong grid conditions, (ii) voltage limit violations and voltage profile deterioration at IBER bus under weak grid condition, and (iii) system-wide power-angle instability under weak and strong grid conditions. To detect the PLL-based attack, we propose attack severity index (ASI) by generating a detection error signal from local grid voltage measurements and PLL estimation. The attack is mitigated by incorporating security as an integral part of the PLL design, yielding a security-aware PLL.

Estimation of Symmetrical Component Phasors and Frequency of Three-Phase Voltage Signals Using Transformations

This paper proposes a simple and computationally efficient algorithm for estimating the frequency and symmetrical component phasors from three-phase time-domain voltage signals utilizing the concept of transformation. A simple least-squares algorithm is proposed to extract the frequency of the signal based on its components in the rotating reference frame. Further, it is shown that the positive and negative sequence component phasors can also be extracted by utilizing the trajectory of the three-phase voltage signals in two rotating reference frames. Unlike the existing approaches, the proposed algorithm estimates the frequency and symmetrical component phasors without utilizing any phase-locked loop or complex transformations. The proposed approach is validated using simulation studies carried out on (a) three-phase test signals that comprise of harmonics, off-nominal frequencies, and unbalances and (b) standard test signals indicated in IEEE Std. C37.118.

Design and Implementation of Low-Cost PMU for Off-Nominal Frequency and DDC in Compliance with IEEE C37.118 Standard

The transition of the conventional power grid into the smart grid requires continuous monitoring of integrated grids speared over wide-area through Phasor Measurement Units (PMU). These PMUs additionally perform protection and state estimation functions in the smart grid. This paper discusses implementation of a new phasor estimation method to eliminate the effects of Decaying DC (DDC) component and off-nominal frequencies during the extraction of the phasors from a relaying signal. The practical implementation of the proposed method in a low-cost microcontroller (ESP32-WROOM-32 development board) in compliance with the requirements of IEEE C37.118.1a-2011 standard is also demonstrated. The analysis of various existing algorithms estimating the phasors is carried out. The microcontroller is programmed with the best among the analysed algorithm and its feasibility to function as a proper Phasor Measurement Unit is tested. The newly designed PMU is rigorously tested with different estimation methods compliant with IEEE C37.118a-2011 standard. The comparison of the proposed method with different phasor estimation algorithms is also discussed.

Extended State-Based OSG Configurations for SOGI PLL With an Enhanced Disturbance Rejection Capability

Changes in the orthogonal signal generator (OSG) configuration of the standard second-order generalized integrator-based phase-locked loop (S-SOGI PLL) have shown to offer an improved low-voltage ride-through capability. However, the resulting PLLs: highpass SOGI (H-SOGI) and lowpass SOGI (L-SOGI) PLLs have no dc-offset estimation capability and lack robustness to disturbances. Therefore, this article focuses on maximizing the merits of H-SOGI and L-SOGI PLLs for grid and industrial applications by incorporating dc-offset estimation and enhancing their disturbance rejection capability. Accordingly, two varieties of SOGI PLLs, namely: extended state highpass SOGI (ES-H-SOGI) and extended state lowpass SOGI (ES-L-SOGI) PLLs are proposed. In the proposed PLLs, states of the OSGs are extended to achieve dc-offset estimation and rejection, while frequency-adaptive implementation of the moving average filter (MAF) is developed to achieve complete harmonic rejection at off-nominal frequencies of the input voltage. To alleviate the undesirable effect of the MAF in terms of the PLL's slow transient response, frequency-adaptive implementation of a phase-lead compensator is introduced. In this article, design guideline that achieves an optimal tradeoff between disturbance rejection and dynamic performance in the ES-H-SOGI and ES-L-SOGI PLLs is presented. Finally, experimental comparison between the proposed ES-H-SOGI and ES-L-SOGI PLLs and their ES-S-SOGI PLL counterpart is carried to show that the proposed PLLs outperform the ES-S-SOGI PLL in terms of dynamic performance while achieving enhanced disturbance rejection capability.

A Cascaded Integral Action Based Filter for Distorted Conditions

This article proposes a cascaded integral action-based filter by relying on the orthogonal output of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T/4$</tex-math></inline-formula> delay block. The proposed filter employs an integrator together with mechanisms involving feedback of the filtered signal and feedforward of its orthogonal input. Based on this approach, the proposed filter addresses the problem of initial state when applying a direct integral action to a sinusoidal voltage. More so, the proposed filter provides notch filtering characteristics at certain harmonic frequencies, thereby achieving improved harmonic rejection in comparison to existing second-order generalized integrator filter. Without frequency adaptivity, the proposed filter achieves fast response, and more importantly, provides excellent filtering of harmonic components at off-nominal frequencies of the supply voltage. Furthermore, dc-offset rejection in the proposed filter is considered together with its FLL implementation for frequency, phase angle, and amplitude estimations. Linearized model and stability evaluation of the proposed filter’s FLL are presented while detailed analytical, simulation, and experimental validation of the proposed filter’s performance for applications involving voltage parameter estimation for synchronization purposes and reference signal generation are provided. Results obtained demonstrate superiority of the proposed filter in terms of harmonic rejection and estimation speed when compared to existing filtering techniques.

Decaying DC Offset Current Mitigation in Phasor Estimation Applications: A Review

Decaying DC (DDC) offset current mitigation is a vital challenge in phasor current estimation since it causes malfunctioning/maloperation of measurements and protection systems. Due to the inductive nature of electric power systems, the current during fault inception cannot change immediately and it contains a transient oscillation. The oscillatory component acts similar to an exponential DC signal and its characteristics depend on the X/R ratio of the system, fault location, and fault impedance. DDC attenuates accurate phasor estimation, which is pivotal in protection systems. Therefore, the DDC must be eliminated from the fault current (FC) signal. This paper presents an overview of DDC mitigation methods by considering different groups—before the discrete Fourier transform (pre-DFT), after the discrete Fourier transform (post-DFT), the least square-based (LS-based), and other methods. Through a comprehensive review of the existing schemes, the effects of noise, harmonics, multiple DDCs (MDDCs), and off-nominal frequency (ONF) on the accuracy of DDC estimation, were recognized. A detailed discussion (along with some simulation results) are presented to address the main advantages/disadvantages of the past studies. Finally, this paper presents a few suggestions for future researchers, for researchers to investigate more implementable solutions in this field.

Quasi Type-1 PLL With Tunable Phase Detector for Unbalanced and Distorted Three-Phase Grid

Out of various moving average filter (MAF)-based phase-locked-loop (PLL), quasi type-1 PLL (QT1-PLL) is widely adopted due to its fast dynamic performance, implementation simplicity, and harmonics rejection abilities. However, the performance of QT1-PLL deteriorates in the presence of an off-nominal frequency unbalanced grid voltage component. Moreover, the sensitivity towards the fundamental frequency negative sequence (FFNS) component is high. Hence, this paper proposes a novel enhanced QT1-PLL solution that is insensitive to unbalance in the grid voltage signal during off-nominal frequency conditions. The proposed adaptive phase detector makes it possible to estimate both the fundamental frequency positive sequence (FFPS) and FFNS components with a high degree of immunity against harmonics. Notably, the pre-loop separation of the FFPS and the FFNS components helps suppress the second harmonic oscillations for improving the parameter estimation accuracy. The loop-filter design of QT1-PLL remains unaffected and requires a proportional gain to estimate the fundamental phase and frequency information. To address the DC offset issue, a modified delayed signal cancellation method is also proposed, which can theoretically eliminate the DC offset for any arbitrary delay length. A small-signal model of the proposed PLL is developed for the sake of stability analysis. Comparative numerical simulation and experimental results are provided with various variants of QT1-PLLs to demonstrate the performance improvement achieved with the proposed technique.

Enhanced Grid Synchronization Technique Based on Frequency Detector for Three-Phase Systems

An adaptive cascaded delayed signal cancellation (CDSC) method relying on a simple frequency detector is combined with a third-order function for three-phase grid synchronization application. In this article, the proposed synchronization technique shows a high degree of insensitivity to harmonics at both nominal and off-nominal frequency environments. When compared to a similar method relying on adaptive CDSC and phase-locked loop (CDSC-PLL), the proposed technique generates alike results but demands less computational effort due to avoiding real-time evaluation of computationally demanding trigonometric functions and square root operation. Moreover, unlike the CDSC-PLL method, the proposed one eliminates the interdependent loops exist between the phase and frequency estimation, thus a simpler tuning process is achieved. In addition, the proposed method stays away from the tuning of the loop filter in the PLL by removing the phase loop. The usefulness of the proposed method is established by both simulation and experimental results.

Real-time wavelet-based adaptive algorithm for low inertia AC microgrids power measurements

This paper proposes a real-time wavelet-based power estimator using a real-time modified stationary discrete wavelet packet transform (RT-MSDWPT). The proposed method overcomes the conventional SDWPT main constraints of power estimations related to the lack of reactive power flow direction and susceptibility to off-nominal frequency operation. The introduction of a digital sampling-shifting of a quarter of the fundamental, applied to the filtered voltages, assures the reactive power flow direction. Additionally, the insertion of an adaptive sampling time procedure based on the power grid frequency estimation mitigates the errors introduced by the network frequency deviations. These modifications make the RT-MSDWPT suitable for being embedded into the standard hierarchical power flow control strategies of ac microgrids. Experimental results assessed using an ac microgrid laboratory setup, operating under different operational scenarios, demonstrate the feasibility of the proposed solution.

A robust and accurate discrete Fourier transform‐based phasor estimation method for frequency domain fault location of power transmission lines

Frequency domain methods had been commonly used in power transmission line fault location. To improve the accuracy of frequency domain fault location methods, this paper studies a robust and accurate discrete Fourier transform (DFT)-based phasor estimation method. First, this paper analyses the deviation characteristics of DFT output phasors caused by decaying DC components with data window sliding. Based on these characteristics, this paper employs rotation factor computation to construct linear equations for the purpose of estimating the accurate fundamental frequency phasor during fault transient process. In this way, the accurate fundamental frequency phasor can be calculated by a two-step linear operation. Furthermore, to eliminate the effect of off-nominal frequency, the proposed method adjusts frequency deviation by using interpolation method. To further enhance the robustness for frequency domain fault location, the PauTa criterion is used to exclude the anomalous equations in the phasor estimation process. Finally, electro-magnetic fault simulation is used to evaluate the proposed method. The test results demonstrate that the proposed method improve the accuracy of fault location during the fault transient process.

Enhanced Single-Phase Phase Locked Loop Based on Complex-Coefficient Filter

Complex coefficient filters (CCFs) are widely used for phase-locked loop (PLL) in three-phase power systems, while its usage is largely sparse in the single-phase domain. Single-phase CCF-PLLs so far reported in the literature do not yield satisfactory performances at off-nominal frequency conditions, which is a crucial PLL attribute. Whether they are a suitable filtering technique of choice for single-phase PLL is yet to be formally documented in a methodological way. In this regard, this article derives an enhanced version of the single-phase CCF-PLL (ECCF-PLL), which is able to provide accurate estimation of grid parameters in dynamically changing grid frequency environment. The proposed ECCF-PLL is then numerically and experimentally compared with few other single-phase PLLs to gauge its efficacy and suitability. The test shows the advantage of harmonic robustness from ECCF-PLL, which is specifically useful in a weak grid.

A Tuned Whitening-Based Taylor-Kalman Filter for P Class Phasor Measurement Units

Protection-oriented (P Class) phasor measurement units (PMUs) are required to reconcile high measurement accuracy and low latency in order to promptly detect possible anomalous operating conditions in power systems. Most of the existing estimators of synchrophasor magnitude, phase, frequency, and rate of change of frequency (ROCOF) of voltage or current AC waveforms need to acquire the samples of at least two power line cycles to meet the P Class requirements specified in the IEEE/IEC Standard 60255-118-1:2018. In this article, instead, a multistep technique based on the combination of multiple signal classification (MUSIC), narrowband disturbance whitening, and Taylor–Kalman Filtering (TKF) is proposed to maximize accuracy even over one-cycle-long observation intervals. Both MUSIC and disturbance whitening rely on a common theoretical framework (i.e., signal and noise vector subspace decomposition) and they are applied to compensate for the detrimental effect of off-nominal frequency deviations and harmonic distortion, respectively. The use of cascaded dynamic estimators such as the TKF is motivated by the need to track possible in-band amplitude and phase oscillations or step-like changes with low latency. While the basic TKF is very sensitive to possible narrowband disturbances, the tuned whitening-based TKF (TW-TKF) described in this article ensures superior accuracy under the influence of harmonics and amplitude or phase step changes, with just a minor performance degradation in the other P Class testing conditions reported in the IEEE/IEC Standard 60255-118-1:2018.

A Robust Half-Cycle Single-Phase Prefiltered Open-Loop Frequency Estimator for Fast Tracking of Amplitude and Phase

This article presents a fast phase-locking and amplitude detection scheme for single-phase applications. The proposed scheme employs a pseudo-rectification process in order to generate even harmonics from the grid signal. The dc-offset component present in the grid signal increases the sensitivity of the pseudo-rectification process, and the design of the prefiltering stage must, therefore, be completely focused on the rejection of dc-offset and the even-harmonics. The application of a half-cycle (HC) prefilter would consequently appear to be a highly attractive option as regards improving the dynamic response time and even harmonic rejection abilities. However, the elimination of the dc-offset component and the estimation of phase and amplitude information is still a very challenging task. The aforementioned issues are addressed by employing an HC comb filter and an HC nonadaptive Lyapunov orthogonal signal generator. The estimation of single-phase grid parameters is thereby made simpler by employing an improved open-loop frequency estimation, which is capable of providing accurate frequency deviation information with good precision. The research shown herein also reveals that the estimation of the amplitude and phase information differs slightly from the usual mathematical notations owing to the pseudo-rectification method adopted in the proposed work. Note that the prefiltering stage is nonadaptive in nature, which may lead to steady-state errors in the amplitude and phase information under off-nominal frequency conditions. An online mathematical correction approach dependent on frequency deviation is, therefore, employed in order to obtain the error-free amplitude and phase information. Finally, the robustness of the current proposal is validated by experimentally comparing several known grid parameter estimation schemes using a real-time controller.

IIR Cascaded-Resonator-Based phasor estimation

The multiple-resonator (MR) filter structure has been proposed in previous works as a convenient approach to the dynamic harmonic analysis. Later, the cascaded-resonator (CR)-based filters for the off-nominal frequency harmonics analysis, MR-based like, has been proposed. In this article, the aim is to use the infinite-impulse-response (IIR) CR-based filters for a single phasor estimation, instead of a dead-beat observer (i.e. the FIR filter) for a full spectrum estimation. Filter coefficients of the IIR filter transfer function are derived through the minimax optimization. This way, both the flatness in the passband and the attenuation in the stopband are significantly improved simultaneously.

An Error Demodulation Technique for Single-Phase Grid Synchronization/LVRT Applications

This paper proposes a nonadaptive error demodulation technique with which to track the amplitude, the phase and the frequency information of the grid voltage for single-phase applications. A nonadaptive comb filter, Lyapunov’s estimation law, and half-cycle moving average filters are exploited in order to reconstruct the fundamental orthogonal components. The proposed nonadaptive Lyapunov filter has good bandpass filtering characteristics, thus allowing the rapid rejection of the dc-offset and the harmonics. The proposed open-loop phase angle deviation algorithm is, moreover, a rescuer as regards estimating the fundamental frequency deviation, signifying that it correctly compensates the estimated amplitude and the phase angle information through the use of a mathematical regression approach under off-nominal frequency conditions.

A Third-Order MAF Based QT1-PLL That is Robust Against Harmonically Distorted Grid Voltage With Frequency Deviation

The quasi-type-l phase-locked loop (QT1-PLL) is a grid synchronization technique that has become very popular in recent years thanks to its attractive performance such as easy implementation, fast dynamic response, and good accuracy in steady-state operation. However, it is still vulnerable to operation under harmonically distorted grid voltages with frequency drift. This paper proposes a novel QT1-PLL based synchronization algorithm that makes an appropriate combination of two filters’ types: an in-loop third-order moving average filter (MAF) with a reduced window width, and a simplified second-order fast delayed signal cancellation (FDSC) based prefiltering stage. The proposed PLL is named third-order MAF based QT1-PLL (TQT1-PLL). Though both TQT1-PLL's filters do not need any adaptive algorithm, it is able to reject non-triplen odd-harmonics and the fundamental frequency negative sequence (FFNS) even under grid frequency drift. Its correct operation is confirmed through numerical simulations and real-time implementation on a digital signal processor (DSP). Moreover, the obtained results confirm its ability to reduce the ripple in the estimated frequency and phase under distorted grid voltages and off-nominal frequency operation. Authors show also through an analytical development that the topology of the proposed TQT1-PLL can be extended to enable the rejection of the DC-offset.