Multi-objective planning model for simultaneous reconfiguration of power distribution network and allocation of renewable energy resources and capacitors with considering uncertainties

This research develops a comprehensive method to solve a combinatorial problem consisting of distribution system reconfiguration, capacitor allocation, and renewable energy resources sizing and siting simultaneously and to improve power system's accountability and system performance parameters. Due to finding solution which is closer to realistic characteristics, load forecasting, market price errors and the uncertainties related to the variable output power of wind based DG units are put in consideration. This work employs NSGA-II accompanied by the fuzzy set theory to solve the aforementioned multi-objective problem. The proposed scheme finally leads to a solution with a minimum voltage deviation, a maximum voltage stability, lower amount of pollutant and lower cost. The cost includes the installation costs of new equipment, reconfiguration costs, power loss cost, reliability cost, cost of energy purchased from power market, upgrade costs of lines and operation and maintenance costs of DGs. Therefore, the proposed methodology improves power quality, reliability and security in lower costs besides its preserve, with the operational indices of power distribution networks in acceptable level. To validate the proposed methodology's usefulness, it was applied on the IEEE 33-bus distribution system then the outcomes were compared with initial configuration.

DISTRIBUTED MONITORING SYSTEM RELIABILITY ESTIMATION WITH CONSIDERATION OF STATISTICAL UNCERTAINTY

Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.

Economic Dispatch of Electrical Power System Based on the Multi-objective Co-evolutionary Algorithm

It is important to distribute the load efficiently to minimize the cost of the economic dispatch of electrical power system. The uncertainty and volatility of wind energy make the economic dispatch much more complex when the general power systems are combined with wind farms. The short term wind power prediction method was discussed in this paper. The method was based on the empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD). Furthermore,the effect of wind farms on the traditional economic dispatch of electrical power system was analyzed. The mathematical model of the economic dispatch was established considering the environmental factors and extra spinning reserve cost. The multi-objective co-evolutionary algorithm was used to figure out the model. And the results were compared with the NSGA-Ⅱ(non-dominated sorting genetic algorithm-Ⅱ) to verify its feasibility.

Linear regression under model uncertainty

We reexamine the classical linear regression model when it is subject to two types of uncertainty:(i)some covariates are either missing or completely inaccessible,and(ii)the variance of the measurement error is undetermined and changing according to a mechanism unknown to the statistician.By following the recent theory of sublinear expectation,we propose to characterize such mean and variance uncertainty in the response variable by two specific nonlinear random variables,which encompass an infinite family of probability distributions for the response variable in the sense of(linear)classical probability theory.The approach enables a family of estimators under various loss functions for the regression parameter and the parameters related to model uncertainty.The consistency of the estimators is established under mild conditions in the data generation process.Three applications are introduced to assess the quality of the approach including a forecasting model for the S&P Index.

Multi-timescale optimization scheduling of interconnected data centers based on model predictive control

With the promotion of“dual carbon”strategy,data center(DC)access to high-penetration renewable energy sources(RESs)has become a trend in the industry.However,the uncertainty of RES poses challenges to the safe and stable operation of DCs and power grids.In this paper,a multi-timescale optimal scheduling model is established for interconnected data centers(IDCs)based on model predictive control(MPC),including day-ahead optimization,intraday rolling optimization,and intraday real-time correction.The day-ahead optimization stage aims at the lowest operating cost,the rolling optimization stage aims at the lowest intraday economic cost,and the real-time correction aims at the lowest power fluctuation,eliminating the impact of prediction errors through coordinated multi-timescale optimization.The simulation results show that the economic loss is reduced by 19.6%,and the power fluctuation is decreased by 15.23%.

Survey on normal distributions,central limit theorem,Brownian motion and the related stochastic calculus under sublinear expectations

This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It's type.The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems.

Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle

In this paper, sampled-data based average-consensus control is considered for networks consisting of continuous-time first-order integrator agents in a noisy distributed communication environment. The impact of the sampling size and the number of network nodes on the system performances is analyzed. The control input of each agent can only use information measured at the sampling instants from its neighborhood rather than the complete continuous process, and the measurements of its neighbors＇ states are corrupted by random noises. By probability limit theory and the property of graph Laplacian matrix, it is shown that for a connected network, the static mean square error between the individual state and the average of the initial states of all agents can be made arbitrarily small, provided the sampling size is sufficiently small. Furthermore, by properly choosing the consensus gains, almost sure consensus can be achieved. It is worth pointing out that an uncertainty principle of Gaussian networks is obtained, which implies that in the case of white Gaussian noises, no matter what the sampling size is, the product of the steady-state and transient performance indices is always equal to or larger than a constant depending on the noise intensity, network topology and the number of network nodes.

On Representation Theorem of G-Expectations and Paths of G-Brownian Motion

We give a very simple and elementary proof of the existence of a weakly compact family of probability measures {Pθ ： θ∈θ} representing an important sublinear expectation- G-expectation E[·]. We also give a concrete approximation of a bounded continuous function X（ω） by an increasing sequence of cylinder functions Lip（Ω） in order to prove that Cb（Ω） belongs to the completion of Lip（Ω） under the natural norm E[｜·｜].