Constant Source Power Research Articles

Blow-up of p-Laplacian evolution equations with variable source power

We study the blow-up and/or global existence of the following $p$-Laplacian evolution equation with variable source power $$u_t(x,t)=\textrm{div}(| \nabla u|^{p-2} \nabla u)+u^{q(x)} \quad\textrm{in} \quad\Omega \times (0,T),$$ where $ \Omega$ is either a bounded domain or the whole space $\mathbb{R}^N$, and $ q(x)$ is a positive and continuous function defined in $ \Omega$ with $0＜q_-=\inf q(x)\leq q(x)\leq \sup q(x)=q_+＜\infty$. It is demonstrated that the equation with variable source power has much richer dynamics with interesting phenomena which depends on the interplay of $q(x)$ and the structure of spatial domain $ \Omega$, compared with the case of constant source power. For the case that $\Omega$ is a bounded domain, the exponent $p-1$ plays a crucial role. If $q_+>p-1$, there exist blow-up solutions, while if $q_+＜p-1$, all the solutions are global. If $q_->p-1$, there exist global solutions, while for given $q_-＜p-1＜q_+$, there exist some function $q(x)$ and $\Omega$ such that all nontrivial solutions will blow up, which is called the Fujita phenomenon. For the case $\Omega= \mathbb{R}^N$, the Fujita phenomenon occurs if $1＜q_-\leq q_+\leq p-1+p/N$, while if $q_->p-1+p/N$, there exist global solutions.

Present point of view about the instantaneous reactive power theory

The instantaneous reactive power theory has been the most used in nonlinear load compensation with active power filters (APF). Its application to APF control allows constant source power to be obtained after compensation in a simple way. It works optimally with balanced and sinusoidal source voltage, but not so good with unbalanced or non-sinusoidal source voltage. Although the p–q theory obtains constant source power in all the cases, in the second one the source current obtained is not balanced and sinusoidal. On the other hand, some researches argue that it is not a complete power theory because it does not assign a physical meaning to the power terms. Necessary modifications in the original formulation to treat compensation under any condition of voltage supply are discussed. Moreover, here, it is reformulated in phase coordinates, which allows a simpler treatment for analysing the different compensation strategies. On the other hand, from the power point of view, it is proved that the introduction of instantaneous imaginary power makes p–q formulation a formal theory of electric power in three-phase system. Finally, compensation strategies are applied to a practical power system and the results are presented.

Instantaneous Reactive Power Theory: A Reference in the Nonlinear Loads Compensation

The instantaneous reactive power theory was published 25 years ago, in an IEEE Transactions. Since then, it has been the most used in nonlinear load compensation with active power filters. Its application allows constant source power to be obtained after compensation in a simple way. Moreover, some researches have showed up some limitations of the theory, i.e., it goes optimally with source voltage balanced and sinusoidal, but not so good with source voltage unbalanced and/or nonsinusoidal, since the source current obtained is not balanced and sinusoidal. This paper presents a new compensation strategy in phase coordinates, equivalent to the original theory's one. Its simplicity, due to the nonnecessity of coordinate mathematical transformation, makes easier the modifications necessary to obtain alternative compensation objectives. In this way, this paper presents those modifications and derives compensation strategies that obtain alternative compensation objectives: unity power factor or balanced and sinusoidal source current. Finally, compensation strategies are applied to a practical power system, and the results are presented.

Effect of capacitive coupling on inductively coupled fluorocarbon plasma processing

This article describes results obtained using various plasma and surface diagnostics in a study of inductively coupled fluorocarbon plasmas in which the amount of capacitive coupling was systematically varied. It is found that the plasma density decreases while the electron temperature increases as the amount of capacitive coupling is increased at a constant source power level. The rate at which the dielectric coupling window is eroded is found to scale with both the peak-to-peak rf voltage and the ion current density, and the dielectric window erosion is found to influence the resulting plasma gas-phase chemistry. The changes in plasma electrical and chemical characteristics have a large impact on the surface processes occurring in inductively coupled fluorocarbon plasmas such as fluorocarbon deposition, fluorocarbon etching, SiO2 etching and Si etching. Further, we show how the selective SiO2-to-Si etch process changes with varying capacitive coupling.