712 research outputs found
Interior HW^{1,p} estimates for divergence degenerate elliptic systems in Carnot groups
Let X_1,...,X_q be the basis of the space of horizontal vector fields on a
homogeneous Carnot group in R^n (q<n). We consider a degenerate elliptic system
of N equations, in divergence form, structured on these vector fields, where
the coefficients a_{ab}^{ij} (i,j=1,2,...,q, a,b=1,2,...,N) are real valued
bounded measurable functions defined in a bounded domain A of R^n, satisfying
the strong Legendre condition and belonging to the space VMO_{loc}(A) (defined
by the Carnot-Caratheodory distance induced by the X_i's). We prove interior
HW^{1,p} estimates (2<p<\infty) for weak solutions to the system
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A novel Q-limit guided continuation power flow method for voltage stability analysis
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Voltage security assessment is becoming a more and more important issue due to the fact that electrical power systems are more prone to voltage instability under increased demand, and it can be time-consuming to determine the actual level of voltage security in large power systems. For this reason, this thesis presents a novel method for calculating the margin of voltage collapse that is based on the Continuation Power Flow (CPF) method. The method offers a flexible and reliable solution procedure without suffering from divergence problems even when near the bifurcation point. In addition, the new method accounts for reactive power limits. The algorithmic continuation steps are guided by the prediction of Q-limit breaking point. A Lagrange polynomial interpolation formula is used in this method in order to find the Q-limit breaking point indices that determine when the reactive power output of a generator has reached its limit. The algorithmic continuation steps will then be guided to the closest Q-limit breaking point, consequently reducing the number of continuation steps and saving computational time. The novel method is compared with alternative conventional and enhanced CPF methods. In order to improve CPF further, studies comparing the performance of using direct and iterative solvers in a power flow calculation have also been performed. I first attempt to employ the column approximate minimum degree (AMD) ordering scheme to reset the permutation of the coefficient matrix, which decreases the number of iterations required by iterative solvers. Finally, the novel method has been applied to a range of power system case studies including a 953 bus national grid transmission case study. The results are discussed in detail and compared against exiting CPF methods
On the spectrum of operators concerned with the reduced singular Cauchy integral
We investigate spectrums of the reduced singular Cauchy operator and its real and imaginary components
Multi-GradSpeech: Towards Diffusion-based Multi-Speaker Text-to-speech Using Consistent Diffusion Models
Recent advancements in diffusion-based acoustic models have revolutionized
data-sufficient single-speaker Text-to-Speech (TTS) approaches, with Grad-TTS
being a prime example. However, diffusion models suffer from drift in training
and sampling distributions due to imperfect score-matching. The sampling drift
problem leads to these approaches struggling in multi-speaker scenarios in
practice. In this paper, we present Multi-GradSpeech, a multi-speaker
diffusion-based acoustic models which introduces the Consistent Diffusion Model
(CDM) as a generative modeling approach. We enforce the consistency property of
CDM during the training process to alleviate the sampling drift problem in the
inference stage, resulting in significant improvements in multi-speaker TTS
performance. Our experimental results corroborate that our proposed approach
can improve the performance of different speakers involved in multi-speaker TTS
compared to Grad-TTS, even outperforming the fine-tuning approach. Audio
samples are available at https://welkinyang.github.io/multi-gradspeech
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