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Towards a Universally Applicable Neural State Estimation through Transfer Learning
The transition of the power grid requires new technologies and methodologies, which can only be developed and tested in simulations. Especially larger simulation setups with many levels of detail can become quite slow. Therefore, the number of possible simulation evaluations decreases. One solution to overcome this issue is to use surrogate models, i. e., data-driven approximations of (sub)systems. In a recent work, we built a surrogate model for a low voltage grid using artificial neural networks, which achieved satisfying results. However, there were still open questions regarding the assumptions and simplifications made. In this paper, we present the results of our ongoing research, which answer some of these questions. We compare different machine learning algorithms as surrogate models and exchange the grid topology and size. In a set of experiments, we show that algorithms based on linear regression and artificial neural networks yield the best results independent of the grid topology. Furthermore, adding volatile energy generation and a variable phase angle does not decrease the quality of the surrogate models.
Transfer learning is an emerging topic that may
drive the success of machine learning in research and industry.
The lack of data on specific tasks is one of the main reasons to
use it, since collecting and labeling data can be very expensive
and can take time, and recent concerns with privacy make
difficult to use real data from users. The use of transfer learning
helps to fast prototype new machine learning models using pretrained
models from a source task since training on millions
of images can take time and requires expensive GPUs. In
this survey, we review the concepts and definitions related to
transfer learning and we list the different terms used in the
literature. We bring the point of view from different authors
of prior surveys, adding some more recent findings in order to
give a clear vision of directions for future work in this field of
research.
Academic studies and long-term planning demand for highly sophisticated simulation of distribution system’s usage considering operational actions and repercussions of market driven measures when applied on a large scale. This paper presents enhancements to the SIMONA tool enabling a large-scale distribution system simulation of a lifelike 50,000 nodes model.
In recent years, the distribution grid planning process has faced the big challenge to integrate renewable energy sources in its planning methodology while preserving a secure and stable provision of electricity. With the currently observable efforts to electrify human mobility all around the world, another new challenge arises for the planning and operation of distribution grids. To address these challenges and to leverage the opportunities that are accompanied by them, new methods for the planning of distribution grids as well as planning decision-supportive approaches and algorithms are needed. The presented approach contributes to the described demands by means of a coupled approach, using both distribution grid time series as well as a genetic algorithm to support decision making in the planning process considering not only new assets for grid reinforcements and extensions but also smart-grid and operational opportunities.
Non-intrusive load monitoring (NILM) is a technique to recover source appliances from only the recorded mains in a household. NILM is unidentifiable and thus a challenge problem because the inferred power value of an appliance given only the mains could not be unique. To mitigate the unidentifiable problem, various methods incorporating domain knowledge into NILM have been proposed and shown effective experimentally. Recently, among these methods, deep neural networks are shown performing best. Arguably, the recently proposed sequence-to-point (seq2point) learning is promising for NILM. However, the results were only carried out on the same data domain. It is not clear if the method could be generalised or transferred to different domains, e.g., the test data were drawn from a different country comparing to the training data. We address this issue in the paper, and two transfer learning schemes are proposed, i.e., appliance transfer learning (ATL) and cross-domain transfer learning (CTL). For ATL, our results show that the latent features learnt by a ‘complex’ appliance, e.g., washing machine, can be transferred to a ‘simple’ appliance, e.g., kettle. For CTL, our conclusion is that the seq2point learning is transferable. Precisely, when the training and test data are in a similar domain, seq2point learning can be directly applied to the test data without fine tuning; when the training and test data are in different domains, seq2point learning needs fine tuning before applying to the test data. Interestingly, we show that only the fully connected layers need fine tuning for transfer learning. Source code can be found at https://github.com/MingjunZhong/transferNILM.
Distribution system state estimation (DSSE) is a core task for monitoring and control of distribution networks. Widely used algorithms such as Gauss-Newton perform poorly with the limited number of measurements typically available for DSSE, often require many iterations to obtain reasonable results, and sometimes fail to converge. DSSE is a non-convex problem, and working with a limited number of measurements further aggravate the situation, as indeterminacy induces multiple global (in addition to local) minima. Gauss-Newton is also known to be sensitive to initialization Hence, the situation is far from ideal. It is therefore natural to ask if there is a smart way of initializing Gauss-Newton that will avoid these DSSE-specific pitfalls. This paper proposes using historical or simulation-derived data to train a shallow neural network to ‘learn to initialize’ -that is, map the available measurements to a point in the neighborhood of the true latent states (network voltages), which is used to initialize Gauss-Newton. It is shown that this hybrid machine learning/optimization approach yields superior performance in terms of stability, accuracy, and runtime efficiency, compared to conventional optimization-only approaches. It is also shown that judicious design of the neural network training cost function helps to improve the overall DSSE performance.
Aim/Purpose
The aim of this study was to analyze various performance metrics and approaches to their classification. The main goal of the study was to develop a new typology that will help to advance knowledge of metrics and facilitate their use in machine learning regression algorithms
Background
Performance metrics (error measures) are vital components of the evaluation frameworks in various fields. A performance metric can be defined as a logical and mathematical construct designed to measure how close are the actual results from what has been expected or predicted. A vast variety of performance metrics have been described in academic literature. The most commonly mentioned metrics in research studies are Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), etc. Knowledge about metrics properties needs to be systematized to simplify the design and use of the metrics. Methodology
A qualitative study was conducted to achieve the objectives of identifying related peer-reviewed research studies, literature reviews, critical thinking and inductive reasoning. Contribution
The main contribution of this paper is in ordering knowledge of performance metrics and enhancing understanding of their structure and properties by proposing a new typology, generic primary metrics mathematical formula and a visualization chart
Findings
Based on the analysis of the structure of numerous performance metrics, we proposed a framework of metrics which includes four (4) categories: primary metrics, extended metrics, composite metrics, and hybrid sets of metrics. The paper identified three (3) key components (dimensions) that determine the structure and properties of primary metrics: method of de-termining point distance, method of normalization, method of aggrega-tion of point distances over a data set. For each component, implementa-tion options have been identified. The suggested new typology has been shown to cover a total of over 40 commonly used primary metrics Recommendations for Practitioners Presented findings can be used to facilitate teaching performance metrics to university students and expedite metrics selection and implementation processes for practitioners Recommendations for Researchers By using the proposed typology, researchers can streamline development of new metrics with predetermined properties Impact on Society The outcomes of this study could be used for improving evaluation results in machine learning regression, forecasting and prognostics with direct or indirect positive impacts on innovation and productivity in a societal sense
Future Research
Future research is needed to examine the properties of the extended metrics, composite metrics, and hybrid sets of metrics. Empirical study of the metrics is needed using R Studio or Azure Machine Learning Studio, to find associations between the properties of primary metrics and their “numerical” behavior in a wide spectrum of data characteristics and business or research requirements
Keywords
performance metrics, error measures, accuracy measures, distance, similarity, dissimilarity, properties, typology, classification, machine learning, regression, forecasting, prognostics, prediction, evaluation, estimation, modeling
To address the issue that the phasor measurement units (PMUs) of wide area measurement system (WAMS) are not sufficient for static state estimation in most existing power systems, this paper proposes a mixed power system weighted least squares (WLS) state estimation method integrating a wide-area measurement system and supervisory control and data acquisition (SCADA) technology. The hybrid calculation model is established by incorporating phasor measurements (including the node voltage phasors and branch current phasors) and the results of the traditional state estimator in a post-processing estimator. The performance assessment is discussed through setting up mathematical models of the distribution network. Based on PMU placement optimization and bias analysis, the effectiveness of the proposed method was proved to be accurate and reliable by simulations of different cases. Furthermore, emulating calculation shows this method greatly improves the accuracy and stability of the state estimation solution, compared with the traditional WLS state estimation.
One of the most important research topics in smart grid technology is load forecasting, because accuracy of load forecasting highly influences reliability of the smart grid systems. In the past, load forecasting was obtained by traditional analysis techniques such as time series analysis and linear regression. Since the load forecast focuses on aggregated electricity consumption patterns, researchers have recently integrated deep learning approaches with machine learning techniques. In this study, an accurate deep neural network algorithm for short-term load forecasting (STLF) is introduced. The forecasting performance of proposed algorithm is compared with performances of five artificial intelligence algorithms that are commonly used in load forecasting. The Mean Absolute Percentage Error (MAPE) and Cumulative Variation of Root Mean Square Error (CV-RMSE) are used as accuracy evaluation indexes. The experiment results show that MAPE and CV-RMSE of proposed algorithm are 9.77% and 11.66%, respectively, displaying very high forecasting accuracy.
6 An innovative short term wind power prediction system is proposed which exploits the learning ability 7 of deep neural network based ensemble technique and the concept of transfer learning. In the proposed 8 DNN-MRT scheme, deep auto-encoders act as base-regressors, whereas Deep Belief Network is used as 9 a meta-regressor. Employing the concept of ensemble learning facilitates robust and collective decision 10 on test data, whereas deep base and meta-regressors ultimately enhance the performance of the proposed 11 DNN-MRT approach. The concept of transfer learning not only saves time required during training of a 12 base-regressor on each individual wind farm dataset from scratch but also stipulates good weight 13 initialization points for each of the wind farm for training. The effectiveness of the proposed, DNN-14 MRT technique is expressed by comparing statistical performance measures in terms of root mean 15 squared error (RMSE), mean absolute error (MAE), and standard deviation error (SDE) with other 16 existing techniques. 17 Keywords-Wind power prediction; sparse denoising auto-encoders; meta-regressor; transfer 18 learning; meteorological properties 19
Machine learning and data mining techniques have been used in numerous real-world applications. An assumption of traditional machine learning methodologies is the training data and testing data are taken from the same domain, such that the input feature space and data distribution characteristics are the same. However, in some real-world machine learning scenarios, this assumption does not hold. There are cases where training data is expensive or difficult to collect. Therefore, there is a need to create high-performance learners trained with more easily obtained data from different domains. This methodology is referred to as transfer learning. This survey paper formally defines transfer learning, presents information on current solutions, and reviews applications applied to transfer learning. Lastly, there is information listed on software downloads for various transfer learning solutions and a discussion of possible future research work. The transfer learning solutions surveyed are independent of data size and can be applied to big data environments.
In a future Smart Grid context, increasing challenges in managing the stochastic local energy supply and demand are expected. This increased the need of more accurate energy prediction methods in order to support further complex decision-making processes. Although many methods aiming to predict the energy consumption exist, all these require labelled data, such as historical or simulated data. Still, such datasets are not always available under the emerging Smart Grid transition and complex people behaviour. Our approach goes beyond the state-of-the-art energy prediction methods in that it does not require labelled data. Firstly, two reinforcement learning algorithms are investigated in order to model the building energy consumption. Secondly, as a main theoretical contribution, a Deep Belief Network (DBN) is incorporated into each of these algorithms, making them suitable for continuous states. Thirdly, the proposed methods yield a cross-building transfer that can target new behaviour of existing buildings (due to changes in their structure or installations), as well as completely new types of buildings. The methods are developed in the MATLAB® environment and tested on a real database recorded over seven years, with hourly resolution. Experimental results demonstrate that the energy prediction accuracy in terms of RMSE has been significantly improved in 91.42% of the cases after using a DBN for automatically extracting high-level features from the unlabelled data, compared to the equivalent methods without the DBN pre-processing.
A limitation faced by the utilities when monitoring the voltages and power flow, i.e. its state, in their distribution system is that metering is expensive to install and maintain. Thus, mathematical methods to calculate the state of the network from minimal measurements are highly desirable. This paper presents a modification of the traditional technique to estimate the static state of a power system, improving its robustness to measurement deficiency. A significant improvement to the traditional technique it the elimination of the requirement that the monitored power system's state must be fully observable. The technique is applied in two stages. Firstly, a Newton iteration, which uses singular value decomposition to generate the Moore- Penrose inverse of the input's Jacobian matrix. Secondly, an analytic sensitivity analysis determining the observability of variables calculated from the partially observable system state.
This work proposes an innovative method based on autoencoders to perform state estimation in distribution grids, which has as main advantage the fact of being independent of the network parameters and topology. The method was tested in a real low voltage grid (incorporating smart grid features), under different scenarios of smart meter deployment. Simulations were performed in order to understand the necessary requirements for an accurate distribution grid state estimator and to evaluate the performance of a state estimator based on autoencoders.
The distribution system state estimation problem seeks to determine the network state from available measurements. Widely used Gauss-Newton approaches are very sensitive to the initialization and often not suitable for real-time estimation. Learning approaches are very promising for real-time estimation, as they shift the computational burden to an offline training stage. Prior machine learning approaches to power system state estimation have been electrical model-agnostic, in that they did not exploit the topology and physical laws governing the power grid to design the architecture of the learning model. In this paper, we propose a novel learning model that utilizes the structure of the power grid. The proposed neural network architecture reduces the number of coefficients needed to parameterize the mapping from the measurements to the network state by exploiting the separability of the estimation problem. This prevents overfitting and reduces the complexity of the training stage. We also propose a greedy algorithm for phasor measuring units placement that aims at minimizing the complexity of the neural network required for realizing the state estimation mapping. Simulation results show superior performance of the proposed method over the Gauss-Newton approach.
Contemporary power grids are being challenged by rapid and sizeable voltage fluctuations that are caused by large-scale deployment of renewable generators, electric vehicles, and demand response programs. In this context, monitoring the grid's operating conditions in real time becomes increasingly critical. With the emergent large scale and nonconvexity however, existing power system state estimation (PSSE) schemes become computationally expensive or often yield suboptimal performance. To bypass these hurdles, this paper advocates physicsinspired deep neural networks (DNNs) for real-time power system monitoring. By unrolling an iterative solver that was originally developed using the exact AC model, a novel model-specific DNN is developed for real-time PSSE requiring only offline training and minimal tuning effort. To further enable system awareness even ahead of the time horizon, as well as to endow the DNNbased estimator with resilience, deep recurrent neural networks (RNNs) are also pursued for power system state forecasting. Deep RNNs leverage the long-term nonlinear dependencies present in the historical voltage time series to enable forecasting, and they are easy to implement. Numerical tests showcase improved performance of the proposed DNN-based estimation and forecasting approaches compared with existing alternatives. In real load data experiments on the IEEE 118-bus benchmark system, the novel model-specific DNN-based PSSE scheme outperforms nearly by an order-of-magnitude its competing alternatives, including the widely adopted Gauss-Newton PSSE solver.
The problem of state estimation for unobservable distribution systems is considered. A deep learning approach to Bayesian state estimation is proposed for real-time applications. The proposed technique consists of distribution learning of stochastic power injection, a Monte Carlo technique for the training of a deep neural network for state estimation, and a Bayesian bad-data detection and filtering algorithm. Structural characteristics of the deep neural networks are investigated. Simulations illustrate the accuracy of Bayesian state estimation for unobservable systems and demonstrate the benefit of employing a deep neural network. Numerical results show the robustness of Bayesian state estimation against modeling and estimation errors and the presence of bad and missing data. Comparing with pseudo-measurement techniques, direct Bayesian state estimation via deep learning neural network outperforms existing benchmarks.
Non-intrusive load monitoring (NILM) is a technique for analyzing changes in the voltage and current flowing through the main feeder and determining the appliances in operation as well as their energy consumption. With the increase in amount and type of electric loads nowadays, it is of increasing significance to extract unique load signatures and build robust classification models for NILM. However, the electric loads of different households differ materially from each other, which makes it difficult to collect enough label data and train classification models with strong representation and generalization ability. In this paper, a voltage-current (V-I) trajectory enabled transfer learning method has been proposed for NILM. Different from the existing methods, a deep learning model pretrained on a visual recognition dataset is transferred to train the classifier for NILM, linking the knowledge between different domains. Moreover, the V-I trajectory is also transferred to visual representation by color encoding, which not only enhances the load signature’s uniqueness but also enables the NILM implementation of transfer learning. The experimental results on NILM datasets show that the proposed method significantly improves the accuracy and can be efficiently generalized compared with state-of-art methods.
As a new classification platform, deep learning has recently received increasing attention from researchers and has been successfully applied to many domains. In some domains, like bioinformatics and robotics, it is very difficult to construct a large-scale well-annotated dataset due to the expense of data acquisition and costly annotation, which limits its development. Transfer learning relaxes the hypothesis that the training data must be independent and identically distributed (i.i.d.) with the test data, which motivates us to use transfer learning to solve the problem of insufficient training data. This survey focuses on reviewing the current researches of transfer learning by using deep neural network and its applications. We defined deep transfer learning, category and review the recent research works based on the techniques used in deep transfer learning.
The expected increase in uncertainty regarding energy consumption and production from intermittent distributed energy resources calls for advanced network control capabilities and (household) customer flexibility in the distribution network. Depending on the control applications deployed, grid monitoring capabilities that accurately capture the system operation state are required. In order to establish such monitoring capabilities, several technical and legal challenges relating to monitoring accuracy, user privacy, and cost efficiency need to be tackled. As these aspects have complex mutual interdependencies, a universal approach for realising distribution network monitoring is not straightforward. Therefore, this article highlights these issues and proposes a method to evaluate monitoring accuracy and the proportionality of personal data processing, and to illustrate the interdependencies between finding the legal grounds for data processing and the monitoring accuracy the processed data produces. To illustrate the method, several test cases are presented, in which the accuracy of network monitoring is assessed for different measurement configurations, followed by an analysis on the legality of the configurations.
Large scale smart meter deployments have resulted in popularization of sensor-based electricity forecasting which relies on historical sensor data to infer future energy consumption. Although those approaches have been very successful, they require significant quantities of historical data, often over extended periods of time, to train machine learning models and achieve accurate predictions. New buildings and buildings with newly installed meters have small historical datasets that are insufficient to create accurate predictions. Transfer learning methods have been proposed as a way to use cross-domain datasets to improve predictions. However, these methods do not consider the effects of seasonality within domains. Consequently, this paper proposes Hephaestus, a novel transfer learning method for cross-building energy forecasting based on time series multi-feature regression with seasonal and trend adjustment. This method enables energy prediction with merged data from similar buildings with different distributions and different seasonal profiles. Thus, it improves energy prediction accuracy for a new building with limited data by using datasets from other similar buildings. Hephaestus works in the pre- and post- processing phases and therefore can be used with any standard machine learning algorithm. The case study presented here demonstrates that the proposed approach can improve energy prediction for a school by 11.2% by using additional data from other schools.
The rapid development in smart grids needs efficient state estimation methods. This paper presents a novel
method for smart grid state estimation (e.g., voltages, active and reactive power loss) using artificial neural
networks (ANNs). The proposed method which is called SE-NN (state estimation using neural network)
can evaluate the state at any point of smart grid systems considering fluctuated loads. To demonstrate the
effectiveness of the proposed method, it has been applied on IEEE 33-bus distribution system with different data resolutions. The accuracy of the proposed method is validated by comparing the results with an exact power flow method. The proposed SE-NN method is a very fast tool to estimate voltages and re/active power loss with a high accuracy compared to the traditional methods.
For nearly 20 years the Test Feeder Working Group of the Distribution System Analysis Subcommittee has been developing openly available distribution test feeders for use by researchers. The purpose of these test feeders is to provide models of distribution systems that reflect the wide diversity in design and their various analytic challenges. Because of their utility and accessibility, the test feeders have been used for a wide range of research, some of which has been outside the original scope of intended uses. This paper provides an overview of the existing distribution feeder models and clarifies the specific analytic challenges that they were originally designed to examine. Additionally, the paper will provide guidance on which feeders are best suited for various types of analysis. The purpose of this paper is to provide the original intent of the Working Group and to provide the information necessary so that researchers may make an informed decision on which of the test feeders are most appropriate for their work.
State estimation and power flow analysis are important tools for analysis, operation and planning of a power system. In this paper, a new state estimation method based on the extended weighted least squares (WLS) method for considering both measurement errors and model inaccuracy is presented. Two bus, three bus, and IEEE 14 bus test cases are employed to evaluate the accuracy of the method. The comparison results show that the extended WLS method may outperform traditional WLS approach when the model is not accurate. In addition, this paper investigates a method based on Z matrix to implement power flow in a transmission system with multiple types of loads (e.g. constant PQ, constant impedance and constant current magnitude loads or mixed loads). The load flow results demonstrate that the method is effective and easy to implement when composite load types exist in the system. Our studies also show that it may be possible that multiple solutions exist for a power flow problem.
This paper addresses the problem of meter placement for distribution system state estimation (DSSE). The approach taken is to seek a set of meter locations that minimizes the probability that the peak value of the relative errors in voltage magnitudes and angle estimates across the network exceeds a specified threshold. The proposed technique is based on ordinal optimization and employs exact calculations of the probabilities involved, rather than estimates of these probabilities as used in our earlier work. The use of ordinal optimization leads to a decrease in computational effort without compromising the quality of the solution. The benefits of the approach in terms of reduced estimation errors is illustrated by simulations involving a 95-bus UKGDS distribution network model.
With the increasing role of computational modeling in engineering design, performance estimation, and safety assessment, improved methods are needed for comparing computational results and experimental measurements. Traditional methods of graphically comparing computational and experimental results, though valuable, are essentially qualitative. Computable measures are needed that can quantitatively compare computational and experimental results over a range of input, or control, variables to sharpen assessment of computational accuracy. This type of measure has been recently referred to as a validation metric. We discuss various features that we believe should be incorporated in a validation metric, as well as features that we believe should be excluded. We develop a new validation metric that is based on the statistical concept of confidence intervals. Using this fundamental concept, we construct two specific metrics: one that requires interpolation of experimental data and one that requires regression (curve fitting) of experimental data. We apply the metrics to three example problems: thermal decomposition of a polyurethane foam, a turbulent buoyant plume of helium, and compressibility effects on the growth rate of a turbulent free-shear layer. We discuss how the present metrics are easily interpretable for assessing computational model accuracy, as well as the impact of experimental measurement uncertainty on the accuracy assessment.
A major assumption in many machine learning and data mining algorithms is that the training and future data must be in the same feature space and have the same distribution. However, in many real-world applications, this assumption may not hold. For example, we sometimes have a classification task in one domain of interest, but we only have sufficient training data in another domain of interest, where the latter data may be in a different feature space or follow a different data distribution. In such cases, knowledge transfer, if done successfully, would greatly improve the performance of learning by avoiding much expensive data-labeling efforts. In recent years, transfer learning has emerged as a new learning framework to address this problem. This survey focuses on categorizing and reviewing the current progress on transfer learning for classification, regression, and clustering problems. In this survey, we discuss the relationship between transfer learning and other related machine learning techniques such as domain adaptation, multitask learning and sample selection bias, as well as covariate shift. We also explore some potential future issues in transfer learning research.
The need for higher frequency in state estimation execution covering larger supervised networks has led to the investigation of faster and numerically more stable state estimation algorithms. However, technical developments in distributed energy management systems based on fast data communication networks open up the possibility of parallel or distributed state estimation implementation. In this paper, this possibility is exploited to derive a solution methodology based on conventional WLS distributed state estimation algorithms and an intelligent ANN technique. Numerical experiments show suitable performance of the proposed method with regard to estimation accuracy, convergence robustness and computational efficiency. The above methods are demonstrated with IEEE 37 bus distributed distribution system with comparison of simulated estimated outputs.
Along with the large-scale implementation of distributed generators, the current distribution networks have changed gradually from passive to active operation. State estimation plays a vital role to facilitate this transition. In this paper, a suitable state estimation method for the active network design is proposed. The method takes advantages of the multi-agent system technology to compute iteratively local state variables by neighbors' data measurements. The accuracy and complexity of the proposed estimation are investigated through on-line simulation with a 5-bus test network.
Recent developments in the solution methods for state estimation are reviewed. Concepts of decoupling, ill-conditioning and robustness in state estimation are discussed. Derivations of decoupled estimators, stable estimators and robust estimators are reviwed. Future directions for research are suggested.
We discuss and compare measures of accuracy of univariate time series forecasts. The methods used in the M-competition as well as the W-competition, and many of the measures recommended by previous authors on this topic, are found to be degenerate in commonly occurring situations. Instead, we propose that the mean absolute scaled error become the standard measure for comparing forecast accuracy across multiple time series. (c) 2006 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.
The problem of real-time estimation of the state of a power system is treated from the point of view of the theory of least-squares estimation (Kalman-Bucy filtering). Since under normal operating conditions, the power system behaves in a quasi- static manner, a simple model for the time behavior of the power system is derived. This model, together with the real-time measurement system, enables the design of a tracking state-estimator algorithm. The proposed algorithm has several advantages over the previously suggested static estimator algorithm in regard to its computational aspects, real-time implementation, and the accuracy of the estimated state.
The ac power flow problem can be solved efficiently by Newton's method. Only five iterations, each equivalent to about seven of the widely used Gauss-Seidel method, are required for an exact solution. Problem dependent memory and time requirements vary approximately in direct proportion to problem size. Problems of 500 to 1000 nodes can be solved on computers with 32K core memory. The method, introduced in 1961, has been made practical by optimally ordered Gaussian elimination and special programming techniques. Equations, programming details, and examples of solutions of large problems are given.
A comprehensive approach to implement monitoring and state estimation in distribution grids with a low number of measurements
- J.-H Menke
- Universität Kassel
Real-time power system state estimation and forecasting via deep neural networks
- L Zhang
- G Wang
- G B Giannakis
Beobachtbarkeit und steuerbarkeit in energiesystemen - eine handlungsanalyse der dena-plattform systemdienstleistungen
- H Seidl
- S Mischiner
- R Heuke
The influence of pattern similarity and transfer learning upon training of a base perceptron B2
- bozinovski
Verfahren zur Zustandsschätzung und ihr Beitrag zum Engpassmanagement in Mittelspannungsnetzen
- A Brüggemann
Transfer learning for non-intrusive load monitoring
- M Incecco
- S Squartini
- M Zhong
Error modeling in distribution network state estimation using rbf-based artificial neural network
- marzouni
Introduction to Simulink with Engineering applications
- S T Karris
A survey on deep transfer learning
- C Tan
- F Sun
- T Kong
- W Zhang
- C Yang
- C Liu
Beobachtbarkeit und steuerbarkeit in energiesystemen - eine handlungsanalyse der dena-plattform systemdienstleistungen
- seidl
Real-time power system state estimation and forecasting via deep neural networks
- zhang