Reliability Constrained Optimal Design of Distributed Generators in Power System Under Load and Wind Turbine Generation Uncertainty

Power systems are designed to meet power demands of the communities with high reliability. Distributed generators (DGs) could play an essential role in improving the power system reliability and resilience. To date, influence of the uncertainty of the DGs to power system reliability has not been well addressed. Consequently, placement of the DGs considering reliability constraints may not be optimally conducted. This paper proposes reliability analysis and design of power systems under time-dependent load uncertainty and wind power generation uncertainty using an efficient uncertainty quantification (UQ) method, i.e., the eigenvector dimension reduction (EDR) method. Furthermore, binary particle swarm optimization (B-PSO) is proposed to address the optimal placement of DGs considering the reliability constraint. Two case studies, including an IEEE 14-bus power system and an IEEE 57-bus power system, are used to demonstrate the effectiveness of the proposed methodology.

Stacking Yield Prediction of Package-on-Package Assembly Using Uncertainty Propagation Analysis—Part II: Implementation of Stochastic Model

The stochastic model for yield loss prediction proposed in Part I is implemented for a package-on-package (PoP) assembly. The assembly consists of a stacked die thin flat ball grid array (TFBGA) as the top package and a flip chip ball grid array (fcBGA) as the bottom package. The top and bottom packages are connected through 216 solder joints of 0.5 mm pitch in two peripheral rows. The warpage values of the top and bottom package are calculated by finite element analysis (FEA), and the corresponding probability of density functions (PDFs) are obtained by the eigenvector dimension reduction (EDR) method. The solder ball heights of the top and bottom package and the corner pad joint heights are determined by surface evolver, and their PDFs are determined by the EDR method, too. Only 137 modeling runs are conducted to obtain all 549 PDFs in spite of the large number of input variables considered in the study (27 input variables). Finally, the noncontact open-induced staking yield loss of the PoP assembly is predicted from the PDFs.

Stacking Yield Prediction of Package-on-Package Assembly Using Advanced Uncertainty Propagation Analysis: Part I Stochastic Model Development

A comprehensive stochastic model is proposed to predict Package-on-Package (PoP) stacking yield loss. The model takes into account all pad locations at the stacking interface while considering the statistical variations of the warpages and the solder ball heights of both top and bottom packages. The goal is achieved by employing three statistical methods: (1) an advanced approximate integration-based method called eigenvector dimension reduction (EDR) method to conduct uncertainty propagation (UP) analyses, (2) the stress-strength interference (SSI) model to determine the noncontact probability at a single pad, and (3) the union of events considering the statistical dependence to calculate the final yield loss. In this first part, theoretical development of the proposed stochastic model is presented. Implementation of the proposed model is presented in a companion paper.

Reliability Analysis With Model Uncertainty Coupling With Parameter and Experiment Uncertainties: A Case Studyof 2014 Verification and Validation Challenge Problem

A validation strategy with copula-based bias approximation approach is proposed to address the 2014 Verification and Validation (V & V) challenge problem developed by the Sandia National Laboratory. The proposed work further incorporates model uncertainty into reliability analysis. Specific issues have been addressed including: (i) uncertainty modeling of model parameters using the Bayesian approach, (ii) uncertainty quantification (UQ) of model outputs using the eigenvector dimension reduction (EDR) method, (iii) model bias calibration with the U-pooling metric, (iv) model bias approximation using the copula-based approach, and (v) reliability analysis considering the model uncertainty. The proposed work is well demonstrated in the challenge problem.