In power distribution systems with multiple time-varying harmonic sources, to address the limitation in the accuracy of harmonic power flow (HPF) calculations due to the difficulty in accurately obtaining harmonic source and system models, this paper proposes a high-accuracy time-varying probabilistic harmonic power flow (PHPF) calculation method based on iterative correction of the harmonic coupling matrix model (HCMM). First, the harmonic-coupled HPF equation of the system is established. Second, the HCMM is iteratively corrected using time-series measurements of node voltages and currents, and adaptive time-segmentation is performed according to the variation characteristics of harmonic source voltages and currents. Finally, to overcome the limitations of the independence assumption and symmetric distribution assumption, the point estimation method is improved based on Nataf–Cholesky transform decoupling and asymmetric sampling, achieving high-accuracy PHPF calculation. In the IEEE-33 and IEEE-123 bus test systems, the relative errors of voltage total harmonic distortion obtained by the proposed method are below 1%, significantly better than the traditional PHPF calculation method (about 10%), with an accuracy improvement of about 10 times. In addition, the actual distribution system is used to verify the performance of the proposed method.

With the large-scale integration of new energy sources into power grids, the level of disturbances in new power systems has gradually increased. The disturbances in the 9-150 kHz frequency band may exceed the limit values of the electromagnetic compatibility in the IEC 61000-2-2 standard. However, methods for measuring disturbances in this band are still under development. Currently, IEC SC77A/WG9 is developing a quasi-peak (QP) measurement method of disturbances in the 9-150 kHz band for the IEC 61000-4-30 standard. Therefore, this paper proposes a 9-150 kHz QP measurement method (compressed sensing-phase-locked loop, CS-PLL method) that conforms to the framework of the IEC 61000-4-30 standard. The phase-locked loop (PLL) disturbance tracking part of the method enables disturbance tracking with less computation, whereas frequency pre-estimation effectively shortens the PLL method adaptation process and reduces the measurement uncertainty at short window lengths. After simulation and experimental signal verification, the combination of frequency pre-estimation and the PLL method can achieve a measurement uncertainty of less than 5% in a 200 ms QP measurement window. This meets the measurement window length proposal of the IEC 61000-4-30 standard framework and the measurement uncertainty proposal for this frequency band.

High-Frequency Oscillation (HFO) has a broad frequency band and the spectrum is prone to spectral interference. Detecting HFO accurately within a very short time window is a challenging task. Existing HFO detection methods cannot guarantee the reliability of results under dense harmonic/interharmonic interference. This paper proposes a joint detection method combining Kaiser window-based S-transform (KST) and the Prony algorithm, referred to as KST-Prony. First, the KST is applied for time-frequency analysis, where ridge extraction is used to obtain key information and reconstruct oscillatory components, enabling the separation of HFO from the fundamental and other harmonic phasors. Subsequently, the Prony algorithm is employed to identify the oscillation parameters. An adjustment factor is introduced for the Kaiser window in KST, and the Kaiser window is adaptively adjusted according to the HFO frequency to meet different detection requirements. Case studies demonstrate that the proposed method can accurately identify the amplitude, frequency, and damping factor of the HFO. Even in the presence of dense harmonic and interharmonic interference, it can avoid detection errors caused by spectral aliasing and exhibits strong robustness against noise interference.

Accurate calculation of time-varying probabilistic harmonic power flow (PHPF) in distribution systems is essential for reliable assessing harmonic pollution, and for supporting harmonic mitigation and power-quality improvement. To address the bias in PHPF caused by the pronounced time-varying characteristics of network topology and harmonic-source operating states in modern distribution systems, this paper proposes a high-accuracy time-varying PHPF method based on multi-time-scale decomposition. First, at the long-time scale, an event-triggered adaptive time-segmentation mechanism is constructed, utilizing accumulated statistics from measurement data to decompose a long-time period into multiple sub-time periods. Second, within each sub-time period, a recursive calculation method for the harmonic coupling matrix is proposed based on sliding-window least squares, where a single-sample update is adopted to avoid repeated model reconstruction and computation. Finally, a Markov chain is introduced to describe the state transitions of harmonic sources, estimating the state transition probability matrix and state occupancy probability, and constructing a point estimation method considering multiple state transitions to obtain the output statistics. In the IEEE-33 bus and IEEE-123 bus test feeders, Monte Carlo simulation results are used as benchmarks to verify the accuracy of the proposed method when harmonic parameter characteristics are rapidly time-varying.

This letter proposes a wideband oscillation detection method that reframes the detection problem as an algorithm adaptation for sinusoidal and damped sinusoidal under different amplitude ratios. Building on this framework, the classification iterative-interpolated discrete Fourier transform (C-iIpDFT) algorithm is proposed. The algorithm classifies the damped sinusoidal and sinusoidal component based on the property of spectral amplitude differences and adjusts the iIpDFT framework to enhance its suitability for wideband oscillation detection. Meanwhile, considering the coupling effects of multiple input variables, the algorithm parameters were optimized through sensitivity analysis. Simulation results show that the classification-based iteration effectively optimises the iterative performance, achieving high detection accuracy for frequency, amplitude, damping factor, and phase in two typical scenarios, while maintaining robustness against noise interference.

The sudden change of the region of attraction (ROA) under parameter variation can be ascribed to global bifurcations. When global bifurcations involve chaotic attractors, their inherent randomness and suddenness may cause catastrophic threat to large-disturbance voltage stability. In the subcritical Hopf bifurcations, the unstable limit cycles surrounding stable equilibrium points will bring instability risks to the post-fault system through boundary crises. To this end, this paper proposes the partitioning method of the voltage stability dynamic security region considering boundary crises (BC-VSDSR). In theoretical analysis, the occurrence mechanism of boundary crises is studied based on manifold analysis. Then, the numerical analysis method of boundary crises is studied based on the homoclinic Melnikov method. In simulation analysis, the effects of various bifurcations due to parameter variations on the large-disturbance voltage stability of a direct-drive wind power grid-connected system are researched. Meanwhile, combined with state space analysis, the impact of boundary crisis on the ROA is studied. Finally, the BC-VSDSR in the space of power injections is divided. The division of BC-VSDSR helps guide the parameter adjustment to ensure the voltage stability in actual operation.

As power electronic equipment becomes increasingly prevalent, interharmonic disturbances have emerged as a major obstacle to achieving precise synchrophasor measurement. To overcome this limitation, this work introduces a novel dynamic synchrophasor estimation approach utilizing the Iterative Symmetric Taylor Weighted Least Squares (I-STWLS) technique. By employing a Taylor series to represent the dynamic signal and applying iterative estimation through symmetrically weighted least squares, the proposed algorithm is able to mitigate the impact of negative frequency components and substantially enhance phasor estimation precision. Performance validation through simulations-conducted for both steady-state and dynamic conditions as prescribed in IEEE/IEC 60255-118-1, such as tests for frequency deviation and ramping-shows that ISTWLS consistently delivers highly accurate results, maintaining TVE, FE, and RFE well within the required limits. Furthermore, the method demonstrates considerable resistance to interharmonic interference and fully satisfies the criteria for both M-class and Pclass PMUs, indicating its significant promise for practical engineering use.

It is crucial to reduce the substantial line loss in distribution networks in power utility.It is the premise to develop a model to describe the loss characteristics that constitute the targeted and comprehensive loss mitigation decision.In this study,a general line loss probability density distribution model is proposed based on state identification in the power distribution area.Firstly,a line loss state identification method based on the C-vine Copula model is proposed to overcome the low accuracy of the existing models caused by ignoring the different characteristics of the different states when calculating the loss.Secondly,a general line loss rate probability density distribution model,including the optimal selection of the probability density function and parameter estimation of the proposed model,is presented to reflect different loss distribution characteristics under different line loss states of the power distribution area.Finally,the accuracy and validity of the proposed method is verified using the measured data across two years of a power distribution area in southwest China.

From the perspective of nonlinear dynamics and bifurcation theory, this paper analyzes the impact of time delay on small-signal stability region of doubly-fed induction generator (DFIG) grid-connected power system. Firstly, the differential-algebraic equation model of the system is established. It is theoretically demonstrated that time delay will affect the bifurcation behavior of the system, especially the degenerate Hopf bifurcation (DHB) under a specific time delay. Then, the time delay, the injected DFIG mechanical power, and the load reactive power are chosen as the bifurcation variables. The bifurcation diagram is obtained through bifurcation analysis, which can determine the multi-parameter small-signal stability boundary of the system. Finally, the impact of single and multiple time delays on the stability region is analyzed through the stability boundary. It is found that the DHB due to the time delay variation induces a hole effect in the system stability region. Moreover, increasing the time delay may also improve the system stability margin. The findings of this study have significant guiding implications for multi-time delay system parameter adjustment.

Under the new power system with a large number of new energy sources connected to the grid, the research on system stability faces new problems. The occurrence of global bifurcation phenomena will cause sudden changes in the system's attraction domain, affecting system stability. When the system undergoes subcritical Hopf bifurcation, the unstable limit cycle generated will affect the original stable and unstable manifolds, causing sudden changes in the system's attraction domain. The sudden change in the stability of the limit cycle and the coexistence of different system bifurcation parameters will also affect the attraction domain. This paper proposes a method based on manifold analysis and bifurcation theory to explore the mechanism by which limit cycles affect the attraction domain and their impact on voltage stability under large disturbances. First, the power system equations are analyzed to study the bifurcation phenomena and the impact of limit cycles on stability. In the case analysis, the bifurcation analysis method is used to observe the system's state space diagram to study the influence mechanism of limit cycles under different parameters, and the bifurcation diagram is drawn to study the impact of the limit cycle and its sudden change caused by subcritical Hopf bifurcation on voltage stability, and to determine the voltage stability change range. This method has important guiding significance for understanding the mechanism and impact of subcritical Hopf bifurcation.

Accurately measuring wideband harmonics and interharmonics requires the balancing of high-frequency resolution with minimal computation time. Frequency-band segmentation methods use multiple filters, making them prone to filtering errors. On the basis of the measurement requirements for harmonics and interharmonics across different frequency bands below 150 kHz, a differential frequency resolution measurement method is proposed. The proposed method is based on the framework of the International Electrotechnical Commission (IEC) 61000-4-30 standard. The harmonic components are initially estimated by the weighted least squares method, and the results are iteratively corrected via phase rotation and spectral energy superposition. The results show that the proposed method meets the accuracy requirements of the IEC 61000-4-30 standard for Class A power quality measurement algorithms across all frequency bands. Compared to the method recommended in the IEC 61000-4-30 standard, the proposed method increases accuracy without significantly increasing the computation time.

A phasor measurement unit (PMU) is a basic tool for synchrophasor estimation in modern power systems. The large-scale integration of power electronic devices in modern power systems results in DC offset on the AC side. In addition, with the rapid development of high-voltage DC transmission projects, the decay time of the DC offset in the system has further increased, which severely affects the estimation accuracy of the M-class PMU. When DC offset and out-of-band interference (OOBI) such as interharmonics coexist, the errors in the time-frequency domain convolution and higher-order matrix inversion increase. The errors of the M-class PMUs are further amplified as a result. Existing methods are ineffective in addressing this challenge. To address this problem, this paper proposes an algorithm based on polynomial fitting and three-point interpolation. First, the iterative elimination concept is employed to restructure DC offset. The initial estimation of the synchrophasor is subsequently performed via linear Bessel interpolation. Finally, the conditional iterative optimization is used for the second estimation of the synchrophasor. The simulation scenarios are designed based on Standard IEC/IEEE 60255-118-1, and the results show that the proposed algorithm can accurately estimate with OOBI and DC offset.

High-frequency electromagnetic radiation pose significant challenges to the stability and security of modern power systems, particularly with the increasing penetration of power electronic devices and renewable energy sources. Electromagnetic radiation exhibit a broad frequency range and are susceptible to noise and harmonic interference. To address this issue, this paper proposes the MSSKST-Prony method, which combines the Multi-Synchronous Squeezed Kaiser-S Transform (MSSKST) with Prony parameter estimation. MSSKST enhances time-frequency energy concentration through multiple squeezing stages, effectively suppressing spectral leakage and noise interference. Subsequently, ridge extraction and component reconstruction techniques separate oscillation modes, followed by Prony estimation for precise identification of amplitude, frequency, and damping parameters. Simulation results under static and harmonic disturbance conditions demonstrate significant advantages over traditional FFT and Prony methods, with outstanding robustness in noisy environments.

A power system is a strongly nonlinear dynamic system, and traditional small disturbance stability analysis cannot reflect the dynamic characteristics of the system under uncertain disturbances. This paper proposes a robust practical stability region (RPSR) partitioning method that considers uncertain disturbances to address the uncertainty of wind power injections and load volatility in wind power systems. First, a disturbance model of the wind turbine generator access system is constructed on the basis of perturbation theory to investigate the effects of uncertainty disturbances on the dynamic characteristics of the system. Second, through bifurcation analysis and limit cycle (L-cycle) tracking, a comprehensive bifurcation diagram that considers the variation trend of the L-cycle amplitude is drawn. Combined with the variation trend of the L-cycle, the RPSR of the system under uncertain disturbances is partitioned. Case studies of dual-machine system and multimachine system explore the new concept of the RPSR. Last, numerical simulations are used to verify the effectiveness of the analysis results and the proposed method.

Connecting a large number of distributed photovoltaics (PVs) and energy storage systems (ESSs) to a distribution network enables the mitigation of harmonic issues through grid-connected inverters with active topology. In this paper, we propose an optimization model for harmonic mitigation based on PV-ESS collaboration. The objective function is to minimize the total cost of harmonic mitigation, to ensure that the harmonic emission levels of all nodes in the network do not exceed the limit required by the IEEE standard. The constraint conditions include the fundamental frequency and harmonic power flow, voltage, mitigation performance, power for PV and ESS inverters, and cost constraints. The model is solved to obtain the amount of harmonic compensation currents and the unit price of the harmonic mitigation service of different inverters at different times. Finally, the validity of the proposed model is verified by the modified IEEE 13 node test feeder.

Non-intrusive load monitoring is a technique for monitoring the operating conditions of electrical appliances by collecting the aggregated electrical information at the household power inlet. Despite several studies on the mining of unique load characteristics, few studies have extensively considered the high computational burden and sample training. Based on low-frequency sampling data, a non-intrusive load monitoring algorithm utilizing the graph total variation (GTV) is proposed in this study. The algorithm can effectively depict the load state without the need for prior training. First, the combined $K$-means clustering algorithm and graph signals are used to build concise and accurate graph structures as load models. The GTV representing the internal structure of the graph signal is introduced as the optimization model and solved using the augmented Lagrangian iterative algorithm. The introduction of the difference operator decreases the computing cost and addresses the inaccurate reconstruction of the graph signal. With low-frequency sampling data, the algorithm only requires a little prior data and no training, thereby reducing the computing cost. Experiments conducted using the reference energy disaggregation dataset and almanac of minutely power dataset demonstrated the stable superiority of the algorithm and its low computational burden.

Accurate harmonic modeling is key for the assessment and mitigation against harmonic issues. Existing modeling methods face difficulties in reflecting the influence of uncertain factors such as operating states of the harmonic source, resulting in poor accuracy. To address this problem, we propose in this study a general harmonic probability model (GHPM) based on operating states identification. Firstly, a load operating state identification algorithm is described, to support modelling according to the different operating states. Secondly, the proposed GHPM is presented. It includes the possible probability density function of the emission by the typical harmonic sources, which overcomes the poor generality of the traditional methods. Furthermore, this study proposes the parameter estimation method of the proposed GHPM based on the monitored data. Finally, the proposed method is verified by a 110 kV steelmaking plant, PV power station and wind farm in Central China, and the IEEE 13-bus test system. The effects of practical issues are also discussed to show the applicability of the proposed method.

The existing division of system stability region does not fully consider the influence of nonlinear characteristics of the system. To address the challenge that it is difficult to inscribe the stability region of wind power grid-connected systems accurately and quantitatively, this article proposes a nonlinear system multi-parameter practical stability region analysis method based on limit cycle amplitude tracking. Firstly, the nonlinear dynamic model of multi-machine system with doubly fed induction generator (DFIG) is established, and the bifurcation diagram of the system is obtained by nonlinear analysis of the model. Then, the limit cycle-parameter diagram is obtained by tracking the limit cycle of the Hopf bifurcation point of the system, and the problem of how the system oscillation evolves with the change of operating parameters is analyzed. Afterwards, the single parameter practical stability region of the nonlinear system is obtained by combining the system equilibrium manifold. Finally, the multi-parameter practical stability region of the nonlinear system is obtained by the three-dimensional bifurcation map with the system time delay, DFIG output active power and reactive load as the bifurcation parameters. The division of the stability region has important guiding significance for the parameter adjustment in the actual operation of the system.

电网工频时变将导致固定采样率下的非同步采样现象,降低谐波检测精度.A类谐波测量仪器通过硬件锁相克服了该问题,但高昂的价格使其难以广泛应用于实际工程.在嵌入式系统中通过合理的算法校正非同步采样结果,实现谐波的准确测量,能够有效降低设备成本.首先分析频谱泄漏抑制条件与多点变换谐波测量算法特性,研究不同变换点数对频谱的影响,推导在不同采样条件下的最佳变换点数选择式.其次提出优先计算基波及低次奇次谐波频率的平均参考工频优化算法,进一步改善了整体计算效果.最后在STM32嵌入式系统上实现了算法.模拟数据计算及LED灯谐波检测实验结果均验证了在非同步采样下,基于该算法的嵌入式系统谐波测量的高精度性与高可靠性.

Due to the limitation of frequency resolution and the spectrum leakage caused by signal windowing, the spectrums of harmonic and interharmonic components with close frequencies overlap each other. When the dense interharmonic (DI) components are close to the harmonic spectrum peaks, the harmonic phasor estimation accuracy is seriously reduced. To address this problem, a harmonic phasor estimation method considering DI interference is proposed in this paper. Firstly, based on the spectral characteristics of the dense frequency signal, the phase and amplitude characteristics are used to determine whether DI interference exists in the signal. Secondly, an autoregressive model is established by using the autocorrelation of the signal. Data extrapolation is performed on the basis of the sampling sequence to improve the frequency resolution and eliminate the interharmonic interference. Finally, the estimated values of harmonic phasor, frequency and rate of change of frequency are obtained. The simulation and some experimental results demonstrate that the proposed method can accurately estimate the parameters of harmonic phasors when DIs exist in the signal, and has a certain anti-noise capability and dynamic performance.