6 research outputs found
Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing
Recent developments in quaternion-valued widely linear processing have
established that the exploitation of complete second-order statistics requires
consideration of both the standard covariance and the three complementary
covariance matrices. Although such matrices have a tremendous amount of
structure and their decomposition is a powerful tool in a variety of
applications, the non-commutative nature of the quaternion product has been
prohibitive to the development of quaternion uncorrelating transforms. To this
end, we introduce novel techniques for a simultaneous decomposition of the
covariance and complementary covariance matrices in the quaternion domain,
whereby the quaternion version of the Takagi factorisation is explored to
diagonalise symmetric quaternion-valued matrices. This gives new insights into
the quaternion uncorrelating transform (QUT) and forms a basis for the proposed
quaternion approximate uncorrelating transform (QAUT) which simultaneously
diagonalises all four covariance matrices associated with improper quaternion
signals. The effectiveness of the proposed uncorrelating transforms is
validated by simulations on both synthetic and real-world quaternion-valued
signals.Comment: 41 pages, single column, 10 figure
Microgrid state estimation and control using Kalman filter and semidefinite programming technique
The design of environment-friendly microgrids at the smart distribution level requires a stable behaviour for multiple state operations. This paper develops a Kalman filter based optimal feedback control method for the microgrid state estimation and stabilization. First, the microgrid is modelled by a discrete-time state space equation. Then the cost-effective smart sensors are deployed in order to obtain the required system information. From the communication point of view, the recursive systematic convolution code is adopted to add the redundancy in the system. At the end, the soft output Viterbi decoder is used to recover the system information from the noisy measurements and transmission uncertainties. Thereafter, the Kalman filter is utilized to estimate the system states, which acts as a precursor for applying the control algorithm. Finally, this paper proposes an optimal feedback control method to stabilize the microgrid based on semidefinite programming. The performance of the proposed approach is demonstrated by extensive numerical simulations
Single Iteration Conditional Based DSE Considering Spatial and Temporal Correlation
The increasing complexity of distribution network calls for advancement in
distribution system state estimation (DSSE) to monitor the operating conditions
more accurately. Sufficient number of measurements is imperative for a reliable
and accurate state estimation. The limitation on the measurement devices is
generally tackled with using the so-called pseudo measured data. However, the
errors in pseudo data by cur-rent techniques are quite high leading to a poor
DSSE. As customer loads in distribution networks show high cross-correlation in
various locations and over successive time steps, it is plausible that
deploying the spatial-temporal dependencies can improve the pseudo data
accuracy and estimation. Although, the role of spatial dependency in DSSE has
been addressed in the literature, one can hardly find an efficient DSSE
framework capable of incorporating temporal dependencies present in customer
loads. Consequently, to obtain a more efficient and accurate state estimation,
we propose a new non-iterative DSSE framework to involve spatial-temporal
dependencies together. The spatial-temporal dependencies are modeled by
conditional multivariate complex Gaussian distributions and are studied for
both static and real-time state estimations, where information at preceding
time steps are employed to increase the accuracy of DSSE. The efficiency of the
proposed approach is verified based on quality and accuracy indices, standard
deviation and computational time. Two balanced medium voltage (MV) and one
unbalanced low voltage (LV) distribution case studies are used for evaluations