Fast Real-Time DC State Estimation in Electric Power Systems Using Belief Propagation

We propose a fast real-time state estimator based on the belief propagation algorithm for the power system state estimation. The proposed estimator is easy to distribute and parallelize, thus alleviating computational limitations and allowing for processing measurements in real time. The presented algorithm may run as a continuous process, with each new measurement being seamlessly processed by the distributed state estimator. In contrast to the matrix-based state estimation methods, the belief propagation approach is robust to ill-conditioned scenarios caused by significant differences between measurement variances, thus resulting in a solution that eliminates observability analysis. Using the DC model, we numerically demonstrate the performance of the state estimator in a realistic real-time system model with asynchronous measurements. We note that the extension to the AC state estimation is possible within the same framework.Comment: 6 pages; 7 figures; submitted in the IEEE International Conference on Smart Grid Communications (SmartGridComm 2017

Physically Equivalent Intelligent Systems for Reasoning Under Uncertainty at Nanoscale

Machines today lack the inherent ability to reason and make decisions, or operate in the presence of uncertainty. Machine-learning methods such as Bayesian Networks (BNs) are widely acknowledged for their ability to uncover relationships and generate causal models for complex interactions. However, their massive computational requirement, when implemented on conventional computers, hinders their usefulness in many critical problem areas e.g., genetic basis of diseases, macro finance, text classification, environment monitoring, etc. We propose a new non-von Neumann technology framework purposefully architected across all layers for solving these problems efficiently through physical equivalence, enabled by emerging nanotechnology. The architecture builds on a probabilistic information representation and multi-domain mixed-signal circuit style, and is tightly coupled to a nanoscale physical layer that spans magnetic and electrical domains. Based on bottom-up device-circuit-architecture simulations, we show up to four orders of magnitude performance improvement (using computational resolution of 0.1) vs. best-of-breed multi-core machines with 100 processors, for BNs with about a million variables. Smaller problem sizes of ~100 variables can be realized at 20 mW power consumption and very low area around a few tenths of a mm2. Our vision is to enable solving complex Bayesian problems in real time, as well as enable intelligence capabilities at a small scale everywhere, ushering in a new era of machine intelligence

Distribuirana estimacija stanja u elektroenergetskimn sistemima upotrebom probabilističkih grafičkih modela

We present a detailed study on application of factor graphs and the belief propagation (BP) algorithm to the power system state estimation (SE) problem. We start from the BP solution for the linear DC model, for which we provide a detailed convergence analysis. Using BPbased DC model we propose a fast real-time state estimator for the power system SE. The proposed estimator is easy to distribute and parallelize, thus alleviating computational limitations and allowing for processing measurements in real time. The presented algorithm may run as a continuous process, with each new measurement being seamlessly processed by the distributed state estimator. In contrast to the matrixbased SE methods, the BP approach is robust to illconditioned scenarios caused by significant differences between measurement variances, thus resulting in a solution that eliminates observability analysis. Using the DC model, we numerically demonstrate the performance of the state estimator in a realistic real-time system model with asynchronous measurements. We note that the extension to the non-linear SE is possible within the same framework. Using insights from the DC model, we use two different approaches to derive the BP algorithm for the non-linear model. The first method directly applies BP methodology, however, providing only approximate BP solution for the non-linear model. In the second approach, we make a key further step by providing the solution in which the BP is applied sequentially over the non-linear model, akin to what is done by the Gauss-Newton method. The resulting iterative Gauss-Newton belief propagation (GN-BP) algorithm can be interpreted as a distributed Gauss- Newton method with the same accuracy as the centralized SE, however, introducing a number of advantages of the BP framework. The thesis provides extensive numerical study of the GN-BP algorithm, provides details on its convergence behavior, and gives a number of useful insights for its implementation. Finally, we define the bad data test based on the BP algorithm for the non-linear model. The presented model establishes local criteria to detect and identify bad data measurements. We numerically demonstrate that the BP-based bad data test significantly improves the bad data detection over the largest normalized residual test.Glavni rezultati ove teze su dizajn i analiza novih algoritama za rešavanje problema estimacije stanja baziranih na faktor grafovima i „Belief Propagation“ (BP) algoritmu koji se mogu primeniti kao centralizovani ili distribuirani estimatori stanja u elektroenergetskim sistemima. Na samom početku, definisan je postupak za rešavanje linearnog (DC) problema korišćenjem BP algoritma. Pored samog algoritma data je analiza konvergencije i predloženo je rešenje za unapređenje konvergencije. Algoritam se može jednostavno distribuirati i paralelizovati, te je pogodan za estimaciju stanja u realnom vremenu, pri čemu se informacije mogu prikupljati na asinhroni način, zaobilazeći neke od postojećih rutina, kao npr. provera observabilnosti sistema. Proširenje algoritma za nelinearnu estimaciju stanja je moguće unutar datog modela. Dalje se predlaže algoritam baziran na probabilističkim grafičkim modelima koji je direktno primenjen na nelinearni problem estimacije stanja, što predstavlja logičan korak u tranziciji od linearnog ka nelinearnom modelu. Zbog nelinearnosti funkcija, izrazi za određenu klasu poruka ne mogu se dobiti u zatvorenoj formi, zbog čega rezultujući algoritam predstavlja aproksimativno rešenje. Nakon toga se predlaže distribuirani Gaus- Njutnov metod baziran na probabilističkim grafičkim modelima i BP algoritmu koji postiže istu tačnost kao i centralizovana verzija Gaus-Njutnovog metoda za estimaciju stanja, te je dat i novi algoritam za otkrivanje nepouzdanih merenja (outliers) prilikom merenja električnih veličina. Predstavljeni algoritam uspostavlja lokalni kriterijum za otkrivanje i identifikaciju nepouzdanih merenja, a numerički je pokazano da algoritam značajno poboljšava detekciju u odnosu na standardne metode