Ricci flow on quasiprojective manifolds

We consider the Kaehler-Ricci flow on complete finite-volume metrics that live on the complement of a divisor in a compact Kaehler manifold X. Assuming certain spatial asymptotics on the initial metric, we compute the singularity time in terms of cohomological data on X. We also give a sufficient condition for the singularity, if there is one, to be type-II.Comment: final versio

A two level feedback system design to provide regulation reserve

Demand side management has gained increasing importance as the penetration of renewable energy grows. Based on a Markov jump process modelling of a group of thermostatic loads, this paper proposes a two level feedback system design be- tween the independent system operator (ISO) and the regulation service provider such that two objectives are achieved: (1) the ISO can optimally dispatch regulation signals to multiple providers in real time in order to reduce the requirement for expensive spinning reserves, and (2) each regulation provider can control its thermostatic loads to respond the ISO signal. It is also shown that the amount of regulation service that can be provided is implicitly restricted by a few fundamental parameters of the provider itself, such as the allowable set point choice and its thermal constant. An interesting finding is that the regulation provider’s ability to provide a large amount of long term accumulated regulation and short term signal tracking restrict each other. Simulation results are presented to verify and illustrate the performance of the proposed framework

A Packetized Direct Load Control Mechanism for Demand Side Management

Electricity peaks can be harmful to grid stability and result in additional generation costs to balance supply with demand. By developing a network of smart appliances together with a quasi-decentralized control protocol, direct load control (DLC) provides an opportunity to reduce peak consumption by directly controlling the on/off switch of the networked appliances. This paper proposes a packetized DLC (PDLC) solution that is illustrated by an application to air conditioning temperature control. Here the term packetized refers to a fixed time energy usage authorization. The consumers in each room choose their preferred set point, and then an operator of the local appliance pool will determine the comfort band around the set point. We use a thermal dynamic model to investigate the duty cycle of thermostatic appliances. Three theorems are proposed in this paper. The first two theorems evaluate the performance of the PDLC in both transient and steady state operation. The first theorem proves that the average room temperature would converge to the average room set point with fixed number of packets applied in each discrete interval. The second theorem proves that the PDLC solution guarantees to control the temperature of all the rooms within their individual comfort bands. The third theorem proposes an allocation method to link the results in theorem 1 and assumptions in theorem 2 such that the overall PDLC solution works. The direct result of the theorems is that we can reduce the consumption oscillation that occurs when no control is applied. Simulation is provided to verify theoretical results.Comment: the 51st IEEE Conference on Decision and Control,December 10-13, Maui, 201