Development of methodology for determining a-parameters of an asymmetric rail line

The article considers the methodology of forming the matrix of A-parameters of a rail line, represented by a multi-pole equivalent circuit. It is shown that when using a four-pole equivalent circuit of a rail line in case of violation of the equipotentiality of the circuit, it is impossible to take into account the flow of current along bypass paths, along the earth path, and the influence of adjacent track circuits. A multi-pole equivalent circuit of a rail line is represented as a 2x4 pole, in the rail lines of which self-induction EMF sources are included, and an earth path is used as the second wire. An equivalent multi-pole of equivalent circuit is represented by two groups of poles – at the input and output of the rail line, including one common (ground). The parameters of all elements of the equivalent multi-pole circuit are presented in the form of matrices, which makes it possible to analyze the state of the rail lines when changing the primary parameters of the rail multi-pole in a wide range. Using Kirchhoff's laws and solving a system of ordinary differential equations, the A-parameters of a rail multi-pole are obtained.

Dynamical Effects of Offset Terms on a Modified Chua’s Oscillator and Its Circuit Implementation

This paper addresses the effects of offset terms on the dynamics of a modified Chua’s oscillator. The mathematical model is derived using Kirchhoff’s laws. The model is analyzed with the help of the maximal Lyapunov exponent, bifurcation diagrams, phase portraits, and basins of attraction. The investigations show that the offset terms break the symmetry of the system, generating more complex nonlinear phenomena like coexisting asymmetric bifurcations, coexisting asymmetric attractors, asymmetric double-scroll chaotic attractors and asymmetric attraction basins. Also, a hidden attractor (period-1 limit cycle) is found when varying the initial conditions. More interestingly, this latter attractor coexists with all other self-excited ones. A microcontroller-based implementation of the circuit is carried out to verify the numerical investigations.

Fractional order differential calculus applied on decision making system to smart grid management via decision trees

This article portrays the relationship between fractional order differential calculus and the computational intelligence method, applying it to the improvement of intelligent systems. The Kirchhoff Laws, represented by second order differential equations, were solved via non-integer order differential calculus. The results obtained were used in the implementation of decision trees, which allowed the decision rules to be incorporated into the controllers. The results obtained by mathematical modeling did magnify the information extracted from Kirchhoff's Laws. Due to the gain magnitude of this information, the decision trees were obtained with greater precision and accuracy. In this way, it was achieved to build a hybrid system capable of being used in the development of controllers automata that has the lower response time and highest efficiency.

Heisenberg Operator Approach: Nano-Mechanical Oscillator (Part 2) and the Quantum LC Circuit

With the knowledge of the new design rules in Chapter 7, we use this new insight to find the eigenvectors for the nano-vibrator problem, and then we use the same approach to examine the quantum LC circuit. While the usual approach is to use Kirchhoff’s laws to analyze a simple circuit classically, we first see that Hamilton’s equations can in fact be used, giving the same classical result. But then, using the new design rules and the knowledge of the total energy in the circuit, we identify a canonical coordinate and a conjugate momentum that have nothing to do with real space and motion of a particle of mass m. At the same time, consistent with the Schrödinger picture, we continue to see that the time evolution of an observable such as position, x(t), or current, i(t), is not part of the solution. Given that Hamilton’s equations give the same result as Kirchhoff’s law but the quantum solution does not, reinforces the idea that the quantum description is showing features that cannot be imagined with a viewpoint based on classical (i.e. non-quantum) analysis.

An improved backward/forward sweep power flow method based on network tree depth for radial distribution systems

This paper presents an improved load flow technique for a modern distribution system. The proposed load flow technique is derived from the concept of the conventional backward/forward sweep technique. The proposed technique uses linear equations based on Kirchhoff’s laws without involving matrix multiplication. The method can accommodate changes in network structure reconfiguration by involving the parent–children relationship between nodes to avoid complex renumbering of branches and nodes. The IEEE 15 bus, IEEE 33 bus and IEEE 69 bus systems were used for testing the efficacy of the proposed technique. The meshed IEEE 15 bus system was used to demonstrate the efficacy of the proposed technique under network reconfiguration scenarios. The proposed method was compared with other load flow approaches, including CIM, BFS and DLF. The results revealed that the proposed method could provide similar power flow solutions with the added advantage that it can work well under network reconfiguration without performing node renumbering, not covered by others. The proposed technique was then applied in Tanzania electric secondary distribution network and performed well.

Nonlinear Membrane Circuit Loaded on a Lossy Transmission Line without the Heaviside’s Condition

The paper deals with transmission lines terminated by a nonlinear circuit describing a simplified model of membrane. This means that all elements of the membrane circuit are nonlinear ones as follows: in series connected LR-loads parallel to C-load. Using the Kirchhoff’s laws we formulate boundary conditions. For lossy transmission lines systems with the Heaviside’s condition, the mixed problem is considered in previous papers. The main goal of the present paper is to investigate the same problem for lossy transmission lines without the Heaviside’s condition. We reduce the existence of solution of the more complicated mixed problem for such a system to the existence of fixed point of an operator acting on a suitable function space. Then by ensuring the existence of this fixed point we obtain conditions for existence of a generalized solution of the mixed problem. The obtained conditions are easily verifiable. We demonstrate the advantages of our method by a numerical example.