A convex chance-constrained model for reactive power planning

Abstract

The present study evaluated the effectiveness of a dicalcium and tetracalcium phosphatebased desensitizer in reducing dentin permeability in vitro. Dentin fluid flow was measured before and after treatment of dentin with patent dentinal tubules using 1 or 3 applications of the dicalcium and tetracalcium phosphate containing agent Teethmate TM (TM) and comparing the results with two sodium fluoride varnishes Vella TM (VLA) and Vanish TM (VAN), after storage in artificial saliva for 24 h, 48 h and 7 days. Significant differences were observed among the 4 methods employed for reducing dentin permeability (p < 0.001) and the 3 posttreatment times (p < 0.001). VLA and VAN never achieved 50% permeability reductions consistently in any of the 3 time periods. Only the calcium phosphate-based desensitizer applied for 3 times consistently reduced dentin permeability by 50% after 24 h. When applied once, the permeability reduction of TM increased progressively over the 3 time periods. After 7 days, only one and three applications of the calcium phosphate-based desensitizer consistently reduced dentin permeability by more than 50%. Permeability reductions corresponded well with scanning electron microscopy examination of dentinal tubule orifice occlusion in dentin specimens treated with the agents. Overall, the dicalcium and tetracalcium phosphate-based desensitizer is effective in reducing dentin permeability via a tubule occlusion mechanism. The ability of the agent to reduce dentin permeability renders it to be potentially useful as a clinical dentin desensitizing agent, which has to be confirmed in future clinical studies. By contrast, the two sodium fluoride varnishes are not effective in dentin permeability reduction and should be considered as topical fluoride delivering agents rather than tubular orifice-blocking agents.

A Type-2 Fuzzy Chance-Constrained Fractional Integrated Modeling Method for Energy System Management of Uncertainties and Risks

“…Figure 4 presents the relevant economic parameters for electricity demand forecasting. This is assuming that emission constraints can be violated under three specified p levels ( p = 0.01, 0.05, and 0.1, known as significance levels) [6]. ) of renewable energy leads to the slightly higher total system cost than the lower share ( = 15%  ) scenario under all levels.…”

“…Koltsaklis and Georgiadis presented a mixed-integer stochastic programming method for Greek electricity generation expansion planning [5]. López et al formulated a long-term reactive electricity investment planning model using a stochastic mixed-integer programming method [6]. Cai et al put forward an interval fuzzy random programming model to identify optimal strategies for energy management systems planning under uncertainties [7].…”

Efficient samplings in stochastic optimization for reactive power planning problems

“…The location of the reactive power compensation is described by binary variables, representing the presence of e Congrès de maîtrise des risques et de sûreté de fonctionnement -Saint-Malo 11-13 octobre 2016 capacitor/reactor banks connected to a node of the grid, while the other variables (complex voltages, active and reactive power generation, reactive compensation size etc) are continuous variables. Moreover, due to the uncertain context, this stochastic OPF (SOPF) is subject to stochastic constraints instead of classical deterministic ones (Lopez et al, 2015 andYang et al, 2006).The Chance Constrained Programming (CCP) approach is generally used to take this stochastic dimension into account. Stochastic RPP problems were already discussed in (Zhang et al, 2007), (Lopez et al, 2015), (Yang et al, 2006), (Ugranli et al, 2015), (Liu et al, 2015) and (Fang et al, 2015) where several methods to model the uncertainties and solve the RPP problem were developed.…”

“…Moreover, due to the uncertain context, this stochastic OPF (SOPF) is subject to stochastic constraints instead of classical deterministic ones (Lopez et al, 2015 andYang et al, 2006).The Chance Constrained Programming (CCP) approach is generally used to take this stochastic dimension into account. Stochastic RPP problems were already discussed in (Zhang et al, 2007), (Lopez et al, 2015), (Yang et al, 2006), (Ugranli et al, 2015), (Liu et al, 2015) and (Fang et al, 2015) where several methods to model the uncertainties and solve the RPP problem were developed. In those papers, samples of the uncertainties are generated from probability density functions (pdf) but there are no details on the choice and number of samples necessary to efficiently characterize the uncertainties.…”

“…The variables allowing controlling the voltages in the grid are the generation units voltages and the reactive power compensation. Transformer taps are not included in this model but could be considered with appropriate modifications [Lopez, 2015]. This stochastic MINLP is thus composed of 2*n*N equality constraints (Eq.…”