In this paper, we propose a fast algorithm for computing the spectral radii of symmetric nonnegative tensors. In particular, by this proposed algorithm, we are able to obtain the spectral radii of weakly reducible symmetric nonnegative tensors without requiring the partition of the tensors. As we know, it is very costly to determine the partition for large-sized weakly reducible tensors. Numerical results are reported to show that the proposed algorithm is efficient and also able to compute the spectral radii of large-sized tensors. As an application, we present an algorithm for testing the positive definiteness of Z-tensors. By this algorithm, it is guaranteed to determine the positive definiteness for any Z-tensor.

Recent developments in electrical power grids have witnessed high utilization levels of renewable energy sources (RESs) and increased trends that benefit the batteries of electric vehicles (EVs). However, modern electrical power grids cause increased concerns due to their continuously reduced inertia resulting from RES characteristics. Therefore, this paper proposes an improved fractional-order frequency controller with a design optimization methodology. The proposed controller is represented by two cascaded control loops using the one-plus-proportional derivative (1 + PD) in the outer loop and a fractional-order proportional integral derivative (FOPID) in the inner loop, which form the proposed improved 1 + PD/FOPID. The main superior performance characteristics of the proposed 1 + PD/FOPID fractional-order frequency controller over existing methods include a faster response time with minimized overshoot/undershoot peaks, an ability for mitigating both high- and low-frequency disturbances, and coordination of EV participation in regulating electrical power grid frequency. Moreover, simultaneous determination of the proposed fractional-order frequency controller parameters is proposed using the recent manta ray foraging optimization (MRFO) algorithm. Performance comparisons of the proposed 1 + PD/FOPID fractional-order frequency controller with existing PID, FOPID, and PD/FOPID controllers are presented in the paper. The results show an improved response, and the disturbance mitigation is also obtained using the proposed MRFO-based 1 + PD/FOPID control and design optimization methodology.

In this paper, we present a new maximum power point tracking (MPPT) algorithm that can identify whether a boost converter is operating in continuous conduction mode (CCM) or discontinuous conduction mode (DCM). The conventional MPPT algorithm assumes that the converter is always in CCM mode, even though this is not always the case. The converter can enter DCM mode due to factors such as the inductor size, irradiance and temperature conditions, voltage step size of the algorithm, and operating point of the PV array. In the proposed work, the conduction mode of a boost converter is evaluated under different conditions. The region of the I–V curve where the converter is likely to operate in DCM mode is identified and a mathematical expression developed in this work is then used to detect the conduction mode of the converter. The proposed algorithm incorporates this expression into a modified perturb and observe (P&O) algorithm. In each iteration, the algorithm first detects the conduction mode of the converter. If the converter is in DCM mode, the algorithm takes a large voltage step to force the converter back into CCM mode, i.e., into the constant current region. The proposed MPPT algorithm was tested using simulation experiments, and the results show that the proposed algorithm can significantly improve the efficiency of the MPPT process.

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