A novel methodology for power loss allocation of both passive and active power distribution systems

This paper presents a new active power loss allocation (LA) scheme for fair allocation of losses among the end-user with due consideration to deregulation in power supply. In this deregulated environment, the developed technique assigns losses judiciously because it has simplified the difficulties lying with the division of cross-term power loss equation analytically without any assumptions and approximations. Further, it establishes a direct relationship between two end-voltages of a branch and its subsequent load currents, in terms of node-injected complex powers. This LA scheme assigns losses to the network participants with due consideration to their demands, power factors, and geographical locations in the network. Again, the strategy followed for remuneration of distributed generators (DGs) awards all benefits of network loss reduction (NLR) to the DG owners in terms of incentives/penalties after analyzing their actual impact towards system loss reduction. The effectiveness of the proposed method is not only investigated at different load levels but also with various types of DG power injection using a 33-bus radial distribution network (RDN) with/without DGs. The comparison results obtained signify the novelty of the present technique in contrast to other discussed established methods.

Investigation of the solution relative convergence when calculating step irregularities in the transmission line by the partial domain method using the energy orthogonality condition

The absolute convergence of diffraction problems on stepwise irregularities in transmission lines using the energy orthogonality condition is beyond doubt. In this article, we consider the question of relative convergence and investigate the dependence of the accuracy of the obtained solution on the order of the reduced system, i.e., on the number of waves taken into account in the connected transmission lines. We believe that the most accurate results for a finite number of waves taken into account in the connected waveguides are obtained when the complex powers of the waves propagating in both waveguides are equal. In this case, for the phase constants the relation is valid: β εμjm j j Sk ωεμ β2 k k  kn2   , β εμkn k k Sj ωεμ β2 j j  jm2  where βjm – the phase constant of a wave with maximum number m considered in a waveguide j; βkn – the phase constant of a wave with maximum number n considered in a waveguide k; Sj, Sk – the cross-sectional areas of waveguides j and k, respectively. Using the result of Weyl's spectral theorem, we obtain: N N S Sjk   j k34 , where Nj, Nk – number of considered waves in waveguides j and k, respectively. When calculating step irregularities, when the areas of the connected waveguides differ significantly from each other, the number of waves taken into account in the field expansions must be taken sufficiently large to ensure equality of the tangential components of the field at the interface. The use of the relations obtained in the article allows you to choose this number as optimal, and to achieve the specified accuracy of the solution with a smaller number of waves taken into account, which leads to a reduction in time and computational resources.

Alternating current regimes in linear electric circuits according to the relativistic circuit theory

The paper presents some new chapters of the relativistic circuit theory, which are part of the special theory of relativity. It explores the alternating current regimes in the linear electric circuits, which are moving with very high speeds less than the speed of light. In the paper a large group of basic problems, connected with the relativistic fundamental laws in the time domain and in phasor form for the linear electric circuits are observed. The relativistic forms of the phasors of the basic quantities of the electric circuits (currents, voltages), the complex powers and the relativistic relations of the basic parameters of the circuits (angular frequencies, phases, phase shifts, reactances, susceptances, impedances, admittances) are presented, too. Additionally, some phenomena as resonances and transient processes in fast moving linear electric circuits are observed, as well. All the formulas in the paper are extracted consecutively and they are followed by explanations in full details. The final results are supported by many simple examples about fast moving linear electric circuits.

On -modules related to the -function and Hamiltonian flow

Let $f$ be a quasi-homogeneous polynomial with an isolated singularity in $\mathbf{C}^{n}$. We compute the length of the ${\mathcal{D}}$-modules ${\mathcal{D}}f^{\unicode[STIX]{x1D706}}/{\mathcal{D}}f^{\unicode[STIX]{x1D706}+1}$ generated by complex powers of $f$ in terms of the Hodge filtration on the top cohomology of the Milnor fiber. When $\unicode[STIX]{x1D706}=-1$ we obtain one more than the reduced genus of the singularity ($\dim H^{n-2}(Z,{\mathcal{O}}_{Z})$ for $Z$ the exceptional fiber of a resolution of singularities). We conjecture that this holds without the quasi-homogeneous assumption. We also deduce that the quotient ${\mathcal{D}}f^{\unicode[STIX]{x1D706}}/{\mathcal{D}}f^{\unicode[STIX]{x1D706}+1}$ is nonzero when $\unicode[STIX]{x1D706}$ is a root of the $b$-function of $f$ (which Saito recently showed fails to hold in the inhomogeneous case). We obtain these results by comparing these ${\mathcal{D}}$-modules to those defined by Etingof and the second author which represent invariants under Hamiltonian flow.

Complex powers of eta-function

We derive a formula for complex powers of the [Formula: see text]-function using the identities for a vertex operator algebra correlation functions in terms of [Formula: see text]-functions obtained in the self-sewing procedure of the torus to form a genus two Riemann surface.

Social Pharmacopeias

This chapter traces the strategies that Caribbean ritual specialists used to create substances and objects with bodily effect. It shows how ritual practitioners modeled the power of medicinal substances and power objects on the basis of myriad encounters with cosmopolitan therapeutic communities in Caribbean lands. The power of healing substances resided in the tactics that practitioners used to claim privileged access to nature’s secrets, to its blessings and terrifying truths. The chapter shows how the tracing of the history of seventeenth-century Caribbean materials with bodily effects necessitates the plotting of maps of social realities and competition that go beyond a study of European appropriation and interpretation of “exotic” materials.These substances’ effectiveness was inextricably linked to the local realities within which practitioners deployed them. Caribbean substance specialists worked in communities that were unstable and continuously engaged in exchanges and appropriations. The specialized and complex powers of the substances and power objects they crafted for specific Caribbean rich and vibrant social spaces were, thus, not always geographically portable.