This paper proposes a new fault location method in radial medium voltage distribution networks. The proposed method only uses the measurement data at the feeder beginning to approximate the characteristic equation showing the dependence between the positive-sequence voltage and phase angle at the monitoring point with the distance to the fault location for each fault type on each line segment. To determine these characteristic equation coefficients, the entire distribution network will be modeled and simulated by four types of faults at different locations along the lines to build the initial database. Based on this database, the mathematical functions in MATLAB software are applied to approximate these coefficients corresponding to each type of fault for each line segment in the network. Then, from the current and voltage measurement data at the feeder beginning, the algorithms of global search, comparison, and fault ranking are used to find out where the fault occurs on the distribution network. Two types of distribution network with and without branches are studied and simulated in this paper to verify and evaluate the effectiveness of the proposed method.

In the paper, maximal values x_e(τ) of the solutions x(t) of the linear differential equations excited by the Dirac delta function are determined. The analytical solutions of the equations and also the maximal positive values of these solutions are obtained. The analytical formulae enable the design of the system with prescribed properties. The complementary case to the earlier paper is presented. In an earlier paper it was assumed that the roots si are different, and now we consider the case when s₁ = s₂  = … = s_n.

The mismatch effect of photovoltaic (PV) arrays due to different illumination intensity has a significant impact on the output characteristics and output power of PV arrays, which is crucial to understand the output characteristics of PV arrays and optimize the array configuration in order to improve the value of the maximum power point. This paper illustrates the short-circuit current mismatch of series circuits, and the open-circuit voltage mismatch of parallel circuits and proposes corresponding solutions for each mismatch phenomenon. The output characteristics of multi-stage series PV arrays and multi-stage parallel PV arrays under complex illumination are analyzed by using the peak point approximation calculation method, and the distribution law of peak voltage points as well as the I-V (Current-Voltage) characteristic equation of each operating section are proposed. On this basis, the output characteristics of 3 x 3 centralized PV arrays are analyzed and verified by simulation. By comparing series and parallel PV arrays with the same condition, as well as several groups of centralized PV arrays with the same topology and different types of illumination distribution, this paper proposes a configuration optimization method for PV arrays. Matlab/Simulink simulation results confirm that the output power of parallel arrays is greater than that of series arrays under the same configuration and illuminationt distribution type, and the peak point is less than that of series arrays under the same configuration and lighting conditions; while in centralized PV arrays, the fewer series modules are shaded, the greater the output power and the less the peak point.