A Theorem on Power Superposition in DC Networks

The superposition theorem, a particular case of the superposition principle, states that in a linear circuit with several voltage and current sources, the current and voltage for any element of the circuit is the algebraic sum of the currents and voltages produced by each source acting independently. The superposition theorem is not applicable to power, because it is a non-linear quantity. Therefore, the total power dissipated in a resistor must be calculated using the total current through (or the total voltage across) it. The theorem proposed and proved in this paper states that in a linear DC network consisting of resistors and independent voltage and current sources, the total power dissipated in the resistors of the network is the sum of the power supplied simultaneously by the voltage sources with the current sources replaced by open circuit, and the power supplied simultaneously by the current sources when the voltage sources are replaced by short-circuit. This means that the power is superimposed. The theorem can be used to simplify the power analysis of DC networks. The analysis results are validated via numerical examples.

A Theorem on Power Superposition in DC Networks

The superposition theorem, a particular case of the superposition principle, states that in a linear circuit with several voltage and current sources, the current and voltage for any element of the circuit is the algebraic sum of the currents and voltages produced by each source acting independently. The superposition theorem is not applicable to power, because it is a non-linear quantity. Therefore, the total power dissipated in a resistor must be calculated using the total current through (or the total voltage across) it. The theorem proposed and proved in this paper states that in a linear DC network consisting of resistors and independent voltage and current sources, the total power dissipated in the resistors of the network is the sum of the power supplied simultaneously by the voltage sources with the current sources replaced by open circuit, and the power supplied simultaneously by the current sources when the voltage sources are replaced by short-circuit. This means that the power is superimposed. The theorem can be used to simplify the power analysis of DC networks. The analysis results are validated via numerical examples.

Traveling wave based fault location for power transmission lines using morphological filters and clarke modal components

This article presents a fast and accurate fault location approach for power transmission lines based on the theory of traveling waves. In fact, when faults occur, they give rise to transient voltages and currents that propagate at a speed close to that of light along the transmission line as traveling waves. Moreover, according to the superposition theorem, each of these transients is a combination of a steady-state quantity and an incremental quantity. These transient signals measured at both ends of the line are first transformed to the Clarke (0-α-β components) components in order to categorize the type of faults, and then multi-scale morphological gradient filters are used to extract equivalent quantities to the incremental quantities to form what are called characteristic signals. These latter will be used to identify the fault location according to the proposed algorithm.

Modeling Tide–Induced Groundwater Response in a Coastal Confined Aquifer Using the Spacetime Collocation Approach

This paper presents the modeling of tide–induced groundwater response using the spacetime collocation approach (SCA). The newly developed SCA begins with the consideration of Trefftz basis functions which are general solutions of the governing equation deriving from the separation of variables. The solution of the groundwater response in a coastal confined aquifer with an estuary boundary where the phase and amplitude of tide can vary with time and position is then approximated by the linear combination of Trefftz basis functions using the superposition theorem. The SCA is validated for several numerical examples with analytical solutions. The comparison of the results and accuracy for the SCA with the time–marching finite difference method is carried out. In addition, the SCA is adopted to examine the tidal and groundwater piezometer data at the Xing–Da port, Kaohsiung, Taiwan. The results demonstrate the SCA may obtain highly accurate results. Moreover, it shows the advantages of the SCA such that we only discretize by a set of points on the spacetime boundary without tedious mesh generation and thus significantly enhance the applicability.

Ohm’s law and electric circuits

This chapter considers various simple dc and ac circuits which contain at least one active element (always a voltage source) and passive elements (resistors, capacitors and inductors) arranged in different combinations to form a bilateral network. The notions of complex voltage, complex current and complex impedance are introduced and then used in the ensuing analysis. Some standard ‘network theorems’ including Kirchhoff’s rules, the delta-star transformation, Thevenin’s theorem and the superposition theorem are employed. Included in the questions are circuits involving bridges, filters, audio amplifiers and transformers. Important topics such as series and parallel resonance in LRC circuits are also considered along the way. Much of the laborious algebra involved in manipulating the complex quantities above is avoided by relegating this task to Mathematica.