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The subject of this study is a frequency estimation algorithm suitable for grid-connected power converters placed at a weak coupling point of a three-phase electrical distribution system. An upgraded version of the widely used complex least mean squares (CLMS) algorithm for frequency estimation is introduced to cope with different voltage amplitude unbalance and harmonic distortion levels, both frequently present in power system at distribution level. First, it is suggested that the CLMS algorithm uses only a positive phase-sequence component of voltage vector, the component that is inherently symmetrical and by cancelling the phase unbalance preserves the circular vector trajectory in a two-phase αβ-plane. This study shows that it is even possible to use the positive voltage phase-sequence vector extracted using a constant delay block, thus avoiding potential instability issues in the case of signal frequency feedback loop. Second, possible high signal harmonics and signal measurement noise are both removed using low-pass filters prior to CLMS algorithm deployment. Computer simulations and experiments are performed under a variety of conditions to validate the effectiveness of the proposed technique. Experimental results are achieved using the dataset sampled from the actual three-phase grid voltage at distributed level and with data processing done in the LabVIEW software environment.

In this research, the constant type of neutral delay Volterra integro-differential equations (NDVIDEs) are currently being resolved by applying the proposed technique in numerical analysis namely, two-point two off-step point block multistep method (2OBM4). This new technique is being applied in solving NDVIDE, identified as a hybrid block multistep method, developed using Taylor series interpolating polynomials. To complete the algorithm, two alternative numerical approaches are introduced to resolve the integral and differential parts of the problems. Note that the differentiation is approximated by the divided difference formula while the integration is interpolated using composite Simpson’s rule. The proposed method has been analysed thoroughly in terms of its order, consistency, zero stability and convergence. The suitable stability region for 2OBM4 in solving NDVIDE has been constructed and the stability region is built based on the stability polynomial obtained. Consequently, numerical results are presented to demonstrate the effectiveness of the proposed 2OBM4.

This paper presents an efficient numerical approach for first-order delay differential equations containing a piece-wise constant delay. The strategy is based on a five-point hybrid block method that has been developed for ordinary differential equations. We will use the interpolation technique for the evaluation of delay terms that are not defined at the grid points. The main characteristics are discussed, including zero stability, local truncation errors, convergence and stability region. The method is easy to implement, and the numerical experiments show the efficiency and accuracy of the proposed method, compared to other methods appeared in the literature.

Decreasing the circuit dimensions is driving the need for low-k materials with a lower dielectric constant to reduce RC delay, crosstalk, and power consumption. In case of spin-on organosilicate low-k films, the incorporation of a porogen is regarded as the only foreseeable route to decrease dielectric constant of 2.2 or below by changing a packing density. In this study, methyltrimethoxysilane (MTMS)–bis(trimethoxysilyl)ethane (BTMSE) copolymers that had superior mechanical properties than MSSQ (methyl-silsesquioxane) were blended with amphiphilic block copolymers used as sacrificial pore generators. While adding up to 40 wt.% porogen into MTMS:BTMSE = 100:50 matrix, optical, electrical, and mechanical properties were measured and the pore structure was also characterized by positron annihilation lifetime spectroscopy (PALS). The result confirmed that there existed a tradeoff in attaining the low dielectric constant and desirable mechanical strength, and no more pores than necessary to achieve the dielectric objective should be incorporated. When the dielectric constant was fixed to approximately 2.3 by controlling BTMSE and porogen contents simultaneously, the thermo-mechanical properties of the porous films were also investigated for the comparison purpose. Under the same dielectric constant, the concurrent increase in BTMSE and porogen contents led to improvement in modulus measured by the nanoindentation technique but deterioration of adhesion strength obtained by the modified edge lift-off test.