Compared with the functional link neural network (FLNN) algorithm, the delayless multi-sampled multiband-structured subband FLNN (DMSFLNN) algorithm provides fast convergence when encountering highly auto-correlated input signals, but there is a compromise between convergence and steady-state performances. Therefore, in order to overcome this flaw, we develop an optimal DMSFLNN (ODMSFLNN) algorithm by minimizing the mean square deviation of the weight vector with respect to the subband gain vectors. Interestingly, a vectorized version is also proposed for the ODMSFLNN algorithm, which aims at reducing computational complexity. Additionally, this paper also presents a stability analysis of this algorithm. Then, considering the impulsive noise environment, we develop two robust variants of ODMSFLNN that are the R-ODMSFLNN-I and R-ODMSFLNN-II algorithms, which are based on the specified robust function and the energy constraint of the weight update increment, respectively. Finally, to resolve that the DMSFLNN algorithm may not exploit cross-terms of input samples in nonlinear active noise control scenarios, we further propose the subband second-order Volterra filter (SSOVF) framework in an analogy way and apply the R-ODMSFLNN-II learning principle to obtain the robust optimal SSOVF algorithm. Simulations in several nonlinear scenarios have shown that the proposed algorithms perform better than their competitors.

Dynamic state estimation (DSE) plays a fundamental role in the monitoring and operation of power systems. Although previous work focuses mainly on traditional synchronous generations, with the increasing penetration of renewables, the estimation of photovoltaic (PV) systems is gaining increasing popularity. However, they primarily address static estimation or adopt an oversimplified dynamic model with a deterministic assumption for solar irradiance. Obviously, this cannot hold in practice, which will inevitably lead to biased estimation results. Facing these problems, this article explores DSE for the first time for a detailed two-stage PV system with the PV array, boost converter, inverter, and filter included. Also, to avoid biased estimation results under solar irradiance variations, we further propose to treat the randomness of solar irradiance as the unknown input of a DSE, which is further analytically merged into the unscented Kalman filter (UKF) framework with an unbiased minimum-variance (UMV) manner. Simulations performed on IEEE standard test systems reveal that even under severe variations of solar irradiation that serve as unknown inputs to the system, the proposed method can produce an unbiased estimate of the dynamic states of the PV, which is also verified in a real-world system. This accurate DSE can serve as a reliable prerequisite for the protection and control of PV-penetrated power systems.

This letter addresses a common issue in engineering applications: unanticipated signal truncation events caused by the mismatch between the operational range of measurement devices and the signals to be measured. Under such circumstances, the conventional normalized subband adaptive filtering (NSAF) algorithm significantly underperforms and may even fail to converge. To tackle this issue, we propose an improved NSAF algorithm. We introduce an expectation maximization framework to address the maximum likelihood estimation before the subband adaptive filter, specifically to handle double-sided signal truncation. This new approach leads to an NSAF for unanticipated truncation (UT-NSAF), which has been theoretically and numerically proven to be unbiased. Importantly, our research demonstrates that UT-NSAF significantly outperforms other algorithms in terms of estimation accuracy and convergence speed. Notably, the steady-state solution of UT-NSAF remains almost unaffected by varying truncation thresholds, showing robustness crucial for dealing with various unexpected signal truncation scenarios in engineering applications.

A phasor measurement unit (PMU) is the core measurement component of power system monitoring and analysis. The placement of PMUs directly impacts the state estimation confidence, and hence the optimal PMU placement (OPP), that, minimizing the number of PMUs and ensuring system observability, is appealing to power engineers. However, the current observability analysis mostly relies on topological methods, which cannot reflect the influence of the operating environment. Moreover, intricate OPP models are driving higher demand for efficient solvers. Confronting these challenges, we propose a reinforcement learning graph convolutional network-deep deterministic policy gradient algorithm-based OPP strategy, which effectively captures the system graph structure and PMU state, thereby independently identifying the PMUs value. Furthermore, the degree of system observability is considered, and three observability quantitative indicators are proposed in the OPP strategy, which will enhance the confidence of the perceived state under complex operating environment. The effectiveness of the proposed strategy have been validated in multiple test systems.

Abstract As an effective control measure to ensure uninterrupted power supply to critical loads under extreme faults, network splitting is of great significance for maintaining system safety and stability. The purpose of this study is to develop a method to accurately and quickly find a reasonable splitting surface and reliably perform network splitting. To address the current problem of poor node classification when splitting, the correlation between nodes is obtained through modal analysis of the system. Node classification criteria are proposed to accurately classify different types of nodes and obtain a suitable splitting space. Based on the node correlation, a splitting adaptation index reflecting the suitability of splitting is proposed. Furthermore, a comprehensive index for the optimisation of the splitting surface is proposed by combining the minimum unbalanced power and the splitting adaptation index, and the splitting surface is quickly determined based on this index. Finally, simulation verification is carried out using the IEEE‐118 standard system, which shows that the method can accurately determine the splitting space and optimise the selection of the splitting surface.

In this paper, we propose a novel normalized subband adaptive filter algorithm suited for sparse scenarios, which combines the proportionate and sparsity-aware mechanisms. The proposed algorithm is derived based on the proximal forward-backward splitting and the soft-thresholding methods. We analyze the mean and mean square behaviors of the algorithm, which is supported by simulations. In addition, an adaptive approach for the choice of the thresholding parameter in the proximal step is also proposed based on the minimization of the mean square deviation. Simulations in the contexts of system identification and acoustic echo cancellation verify the superiority of the proposed algorithm over its counterparts.

In this letter, a two-stage robust unscented unbiased minimum-variance (RU-UMV) estimator is proposed for nonlinear system dynamic state estimation with unknown inputs. In the first stage, by leveraging the statistical linerization and the relationship between unknown input vector and states, we derive a batch-mode regression form. It is shown that the application of weighted least squares for this form yields the same results as the UMV unscented Kalman filter. However, it lacks robustness to outliers. To deal with, robust generalized maximum-likelihood (GM)-estimator together with the projection statistics (PS) is developed, yielding robust state estimates. The latter are further used in the second stage for robust unknown input vector estimation. As a result, both innovation and observation/measurement outliers can be effectively suppressed. Illustrative examples are provided to demonstrate the robustness of the proposed method.

This letter proposes an unscented Kalman filter (UKF)-based unbiased minimum-variance estimation (UMV) method for the nonlinear system with unknown inputs. By utilizing the statistical linearization, the nonlinear system and measurement functions are transformed into a “linear-like” regression form. The latter preserves the nonlinearity of the system and the measurement models. To this end, the unknown inputs can be estimated by the weighted least-squares. This “linear-like” regression form also allows us to resort to the UMV state estimation framework for the development of new nonlinear filter to handle unknown inputs. Specifically, two approaches have been developed: 1) given the estimated inputs, we derive a filter by minimizing the trace of the state error covariance matrix; 2) without input estimation, we derive the filter by minimizing the trace of the state error covariance matrix subject to a constraint imposed on the gain matrix. We prove that these two approaches provide the same results. Numerical results validate the effectiveness of the proposed method.

A bias-compensated normalized subband adaptive filter (BC-NSAF) algorithm is proposed for system identification. In the proposed algorithm, a bias-compensation vector is derived to eliminate the bias caused by the noisy input signals. To estimate the input noise variance, a new estimation method is proposed, which does not require the input-output variance ratio in advance. Simulation results show that the proposed algorithm obtains better convergence performance than the existing algorithms in the presence of noisy input signals.