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Geometric interpretations of the QLMMP, QLMS, and QLMP. Although H is a four-dimensional vector space over R, dn, yn and ∆y all are on the same plane.
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... Additionally, in such situations, the SQVM approach is very effective, because this scheme is less sensitive to the variation of internal signals and also has fewer constraints [23][24][25]. In PV-utility interfaced power system, the harvested solar power is injected to the grid and supplied to loads by utilizing the DC link pre-predictive loop for the solar power. ...
This paper presents a sparse quaternion-valued minimization (SQVM) based control technique of two-stage grid supportive Photovoltaic (PV) power system with power conditioning capabilities. The grid side converter (GSC) is controlled by utilizing a SQVM control technique. The proposed algorithm enables the GSC to mitigate the load harmonics current and provides reactive power compensation at the point of common coupling (PCC). The proposed control is tuned to mitigate the DC offset error, harmonics current and to improve the frequency response of the proposed system. A DC link pre-predictive is incorporated to improve the dynamic response by reducing the burden on the outer Proportional-Integral (PI) voltage controller loop. Further, it is used to extract the fundamental component of load currents for generating the reference currents. An adjustable DC link voltage loop is incorporated in the proposed control technique to adapt the PCC voltage variation, which helps in minimizing the losses of the PV system. For real time execution of the adjustable DC link voltage concept, the DC link voltage is adapted with variation in PCC voltage. The operation and control of the system topology are validated experimentally under various scenarios.
... Therefore, Singh et al. [21] have developed various power quality conditioner devices to address the issues of reactive power compensation and power quality improvement. Moreover, various adaptive filtering techniques are proposed to control these devices and address the issues of power quality [22][23][24]. In this work, an energy-efficient autonomous gridsynchronised two-stage three-phase three-wire (3P3W) distribution system is presented. ...
Abstract This study presents a norm combination constrained set‐membership function (CCSMF)‐based approach for two‐stage photovoltaic (PV) array to be used in the three‐phase three‐wire system. Here, the norm is introduced in the control technique to improve the response of existing approaches. The norm is the addition of the magnitudes of the load current components in a space. It is the most natural way of evaluating the various magnitude of harmonic components. In addition, the CCSMF technique furnishes harmonics disturbance rejection, current compensation, grid currents stabilisation and correction of power factor performances in order to allocate system integrated with residential non‐linear loads. Further, it is used to extract the fundamental component of load currents for generating the reference currents. The range of the amplitude and frequency of the grid voltages are continuously monitored by the limit cycle oscillator‐based algorithm. Under the outage of PV insolation, the voltage source converter (VSC) is switched to the compensator unit, and grid feeds power to the emergency load, which improves the utilisation factor of VSC. The presented system along with the proposed technique is tested in the laboratory and grid current total harmonic distortion is brought down within the limit of the IEEE‐519 standard.
... Quaternions have subsequently found new applications in communications, motion tracking, and biomedical engineering [12]- [16]. There has been extensive work on theory and applications of quaternion-valued filters [17]- [19]. Traditional strictly linear quaternion filters are based on the strictly linear model, given byŷ =ĥ H x, with the input vector x ∈ H M ×1 , the weight vectorĥ ∈ H M ×1 , and the outputŷ ∈ H. ...
... Based on (19) and the orthogonality condition ...
Quaternion adaptive filters have been widely used for processing 3D and 4D phenomena. Deficient length quaternion adaptive filters are explicitly or implicitly used in many practical applications where the length of system impulse response is large or unknown. However, their statistical behaviours are yet to be fully understood. As theoretical results on the class of “full length” quaternion least mean square (QLMS) algorithms do not necessarily apply to their deficient length versions, this paper fills this void and analyses the mean and mean square convergence of the deficient length QLMS algorithms, both for the strictly linear and widely linear cases. Transient and steady-state performance is characterised by exploiting the augmented statistics of noncircular quaternion random vectors. A novel decorrelation technique in the quaternion domain is shown to allow for the development of intuitive closed-form solutions for correlated quaternion Gaussian inputs, thus unveiling the relationship between the algorithm behaviour and the noncircularity of quaternion input data. The analysis also provides a general framework whereby the strictly linear and semi-widely linear QLMS algorithms can be seen as “deficient-length” versions of the widely linear QLMS. Numerical simulations validate the accuracy of the theoretical results and support the behaviour of the considered algorithms.
... Regarding to the problem ii), it is noteworthy that nearend speech in AEC with double-talk is a common source of impulsive noise [9], as well as sudden atmospheric phenomena in telecommunication systems [5]. Although the mean square error (MSE) minimization has been widely used as a statistical measure for the development of adaptive filtering algorithms [10], this cost function is prone to instability in the presence of impulsive noise [11]. This fact claims robust cost functions, such as the maximum correntropy criterion (MCC) [12]. ...
An adaptive algorithm should ideally present high convergence rate, good steady-state performance, and robustness against impulsive noise. Few algorithms can simultaneously meet these requirements. This paper proposes a local and deterministic optimization problem whose solution gives rise to an adaptive algorithm that presents a higher convergence rate in the identification of sparse systems due to the use of the proportionate adaptation technique. In addition, a correntropy-based cost function is employed in order to enhance its robustness against non-Gaussian noise. Finally, the adoption of coefficient reuse approach results in a good system identification performance in steady-state conditions, especially in low SNR scenarios.
Prognostics of bearing degeneration play a crucial role in implementation of systems maintenance strategies. Although numerous classical prognostic models have been developed, these models are carried out based on channel-wise processing and therefore fail to capture the inherent nonlinear and coupling nature of multi-dimensional or multi-channel data. To address this issue, a novel prognostics method based on adaptive quaternion-valued least-mean biquadrate (AQ-LMB) algorithm is proposed for a unified processing of hypercomplex data by the virtue of quaternion algebra. The cost function of the proposed AQ-LMB algorithm is designed via the biquadrate form of system output error to adapt to the more common nonlinear and non-Gaussian data, and the update weight vector is derived through Hamilton calculus instead of traditional complex gradient calculation. First, the time series of health indicators (e.g., root-mean-square, RMS) derived from historical data are decomposed by a nonconvex sparse regularization (SR) algorithm associated with a nonconvex penalty, that is, the low frequency trend component (LFC) and high frequency noise component (HFC) are obtained, then both LFC and HFC are respectively predicted by the AQ-LMB algorithm. The final predicted health indicators can be obtained by integrating the correspondingly predicted LFC and HFC. The separate analysis of both sub-components makes it possible to distinguish their respective contributions to the entire degeneration process, thus avoiding false deviation and improving the prediction accuracy. Finally, the effectiveness of the proposed nonconvex SR and AQ-LMB approach in improving prognostic accuracy is illustrated via three-and four-dimensional run-to-failure datasets of rolling bearing.
