Distributed Power Flow and Distributed Optimization - Formulation, Solution, and Open Source Implementation

Solving the power flow problem in a distributed fashion empowers different grid operators to compute the overall grid state without having to share grid models-this is a practical problem to which industry does not have off-the-shelf answers. In cooperation with a German transmission system operator we propose two physically consistent problem formulations (feasibility, least-squares) amenable to two solution methods from distributed optimization (the Alternating direction method of multipliers (ADMM), and the Augmented Lagrangian based Alternating Direction Inexact Newton method (Aladin)); with Aladin there come convergence guarantees for the distributed power flow problem. In addition, we provide open source matlab code for rapid prototyping for distributed power flow (rapidPF), a fully matpower-compatible software that facilitates the laborious task of formulating power flow problems as distributed optimization problems; the code is available under https://github.com/KIT-IAI/rapidPF/. The approach to solving distributed power flow problems that we present is flexible, modular, consistent, and reproducible. Simulation results for systems ranging from 53 buses (with 3 regions) up to 4662 buses (with 5 regions) show that the least-squares formulation solved with aladin requires just about half a dozen coordinating steps before the power flow problem is solved.Comment: 35 pages, 6 figures, 7 tables, journal submissio

Distributed AC Optimal Power Flow for Generic Integrated Transmission-Distribution Systems

Coordination of transmission and distribution power systems is increasingly critical in the context of the ongoing energy transition. However, traditional centralized energy management faces challenges related to privacy and/or sovereignty concerns, leading to growing research interests in distributed approaches. Nevertheless, solving distributed AC optimal power flow (OPF) problems encounters difficulties due to their nonlinearity and nonconvexity, making it challenging for state-of-the-art distributed approaches. To solve this issue, the present paper focuses on investigating the distributed AC OPF problem of generic integrated transmission-distribution (ITD) systems, considering complex grid topology, by employing a new variant of the Augmented Lagrangian based Alternating Direction Inexact Newton method (ALADIN). In contrast to the standard ALADIN, we introduce a second-order correction into ALADIN to enhance its numerical robustness and properly convexify distribution subproblems within the ALADIN framework for computing efficiency. Moreover, a rigorous proof shows that the locally quadratic convergence rate can be preserved for solving the resulting distributed nonconvex problems. Extensive numerical simulations with varying problem sizes and grid topologies demonstrate the effectiveness of the proposed algorithm, outperforming state-of-the-art approaches in terms of numerical robustness, convergence speed, and scalability

Hypergraph-Based Fast Distributed AC Power Flow Optimization

This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex relationships between subgrids can be expressed as hyperedges. Then, a hypergraph-based distributed sequential quadratic programming (HDQ) approach is proposed to handle the reformulated problems, and the hypergraph-based distributed sequential quadratic programming (HDSQP) is used as the inner algorithm to solve the corresponding QP subproblems, which are respectively condensed using Schur complements with respect to coupling variables defined by hyperedges. Furthermore, we rigorously establish the convergence guarantee of the proposed algorithm with a locally quadratic rate and the one-step convergence of the inner algorithm when using the Levenberg-Marquardt regularization. Our analysis also demonstrates that the computational complexity of the proposed algorithm is much lower than the state-of-art distributed algorithm. We implement the proposed algorithm in an open-source toolbox, i.e., rapidPF, and conduct numerical tests that validate the proof and demonstrate the great potential of the proposed distributed algorithm in terms of communication effort and computational speed

Application of Machine Learning Algorithms to Predict Central Lymph Node Metastasis in T1-T2, Non-invasive, and Clinically Node Negative Papillary Thyroid Carcinoma

Purpose: While there are no clear indications of whether central lymph node dissection is necessary in patients with T1-T2, non-invasive, clinically uninvolved central neck lymph nodes papillary thyroid carcinoma (PTC), this study seeks to develop and validate models for predicting the risk of central lymph node metastasis (CLNM) in these patients based on machine learning algorithms. Methods: This is a retrospective study comprising 1,271 patients with T1-T2 stage, non-invasive, and clinically node negative (cN0) PTC who underwent surgery at the Department of Endocrine and Breast Surgery of The First Affiliated Hospital of Chongqing Medical University from February 1, 2016, to December 31, 2018. We applied six machine learning (ML) algorithms, including Logistic Regression (LR), Gradient Boosting Machine (GBM), Extreme Gradient Boosting (XGBoost), Random Forest (RF), Decision Tree (DT), and Neural Network (NNET), coupled with preoperative clinical characteristics and intraoperative information to develop prediction models for CLNM. Among all the samples, 70% were randomly selected to train the models while the remaining 30% were used for validation. Indices like the area under the receiver operating characteristic (AUROC), sensitivity, specificity, and accuracy were calculated to test the models' performance. Results: The results showed that ~51.3% (652 out of 1,271) of the patients had pN1 disease. In multivariate logistic regression analyses, gender, tumor size and location, multifocality, age, and Delphian lymph node status were all independent predictors of CLNM. In predicting CLNM, six ML algorithms posted AUROC of 0.70–0.75, with the extreme gradient boosting (XGBoost) model standing out, registering 0.75. Thus, we employed the best-performing ML algorithm model and uploaded the results to a self-made online risk calculator to estimate an individual's probability of CLNM (https://jin63.shinyapps.io/ML_CLNM/). Conclusions: With the incorporation of preoperative and intraoperative risk factors, ML algorithms can achieve acceptable prediction of CLNM with Xgboost model performing the best. Our online risk calculator based on ML algorithm may help determine the optimal extent of initial surgical treatment for patients with T1-T2 stage, non-invasive, and clinically node negative PTC

Mineral Characteristics and Metamorphic Evolution of Pelitic Gneiss in Wulashan Area, Central Inner Mongolia

Wulashan Neoarchean peliticgneiss is exposed in the eclogite gneiss formation of Wulashan group in central Inner Mongolia. It is the most widely distributed plutonic metamorphic rock in Wulashan formation. The main lithology is biotite garnet monzonite gneiss. Through detailed petrological observation, this paper makes a systematic mineral chemical analysis of typical metamorphic minerals, and studies their metamorphic evolution characteristics and tectonic significance. The results show that the pelitic gneiss in the eclogite gneiss formation of Wulashan group has experienced four metamorphic evolution stages, and its metamorphic conditions are limited by metamorphic mineral thermobarometer inversion: early progressive metamorphic stage (M1), its mineral assemblage is characterized by core garnet + biotite + plagioclase + quartz ± sillimanite; The mineral assemblage of the peak metamorphic stage (M2) is characterized by garnet + sillimanite + biotite + plagioclase + quartz + potassium feldspar. The temperature and pressure conditions of this stage are T= 771~870℃, p = 7.5~11.2 Kb; The post peak near isothermal decompression stage (M3) is characterized by the coronal structure of cordierite at the edge of garnet. Its mineral assemblage is garnet + cordierite + biotite + plagioclase + quartz ± sillimanite. The temperature and pressure conditions of this stage are T= 750~800℃, p = 6.1~7.0 Kb; The mineral assemblage in the late cooling stage (M4) is characterized by garnet + biotite + plagioclase + quartz + magnetite ± K-feldspar. The temperature and pressure conditions in this stage are T= 650~659℃, p= 4.3~4.8 Kb. The metamorphic evolution P-T track of argillaceous gneiss has a clockwise pattern of nearly isothermal depressurization. It shows that the Wulashan group in the late Neoarchean in Wulashan area experienced the dynamic process of crustal subduction and thickening followed by exhumation and uplift

The complete chloroplast genome sequence of Machilus robusta W. W. Smith (Lauraceae) from Jiangxi Province, China

Machilus robusta W. W. Smith is an evergreen plant distributed in the Yangtze River Basin and the south regions of China. Here we analyzed the complete chloroplast (cp) genome sequence of M. robusta to determine its structure and evolutionary relationship to other Lauraceae. The cp genome is 152,737 bp in length and has an overall GC content of 39.2% The genome includes a large single-copy (LSC) region of 93,706 bp and a small single-copy (SSC) region of 18,885 bp, and these are separated by a pair of inverted repeats (IRs) of 20,073 bp. The cp genome contains 128 genes, including 83 protein-coding, 37 tRNAs, and 8 rRNAs. Phylogenetic analysis based on complete cp genome sequences fully resolved M. robusta in a clade with M. balansae. This work provides new molecular data for evolutionary studies of the Lauraceae

Deep Hypothermic Circulatory Arrest Does Not Show Better Protection for Vital Organs Compared with Moderate Hypothermic Circulatory Arrest in Pig Model

Background. Continued debates exist regarding the optimal temperature during hypothermic circulatory arrest in aortic arch repair for patients with type A aortic dissection. This study seeks to examine whether the use of moderate hypothermic circulatory arrest in a pig model provides comparable vital organ protection outcomes to the use of deep hypothermic circulatory arrest. Methods. Thirteen pigs were randomly assigned to 30 minutes of hypothermic circulatory arrest without cerebral perfusion at 15°C (n = 5), 25°C (n = 5), and a control group (n = 3). The changes in standard laboratory tests and capacity for protection against apoptosis in different vital organs were monitored with different temperatures of hypothermic circulatory arrest management in pig model to determine which temperature was optimal for hypothermic circulatory arrest. Results. There were no significant differences in the capacity for protection against apoptosis in vital organs between 2 groups (p > 0.05, respectively). Compared with the moderate hypothermic circulatory arrest group, the deep hypothermic circulatory arrest group had no significant advantages in terms of the biologic parameters of any other organs (p > 0.05). Conclusions. Compared with deep hypothermic circulatory arrest, moderate hypothermic circulatory arrest is a moderate technique that has similar advantages with regard to the levels of biomarkers of injury and capacity for protection against apoptosis in vital organs