scholarly journals Distributed Weighted Least-Squares and Gaussian Belief Propagation: An Integrated Approach

2021 ◽  
Author(s):  
Dino Zivojevic ◽  
Muhamed Delalic ◽  
Darijo Raca ◽  
Dejan Vukobratovic ◽  
Mirsad Cosovic
Keyword(s):  
Least Squares ◽  
Large Scale ◽  
Belief Propagation ◽  
Weighted Least Squares ◽  
Measurement Data ◽  
Integrated Approach ◽  
Factor Graph ◽  
State Variables ◽  
Large Scale Systems ◽  
Distributed Approach

The purpose of a state estimation (SE) algorithm is to estimate the values of the state variables considering the available set of measurements. The centralised SE becomes impractical for large-scale systems, particularly if the measurements are spatially distributed across wide geographical areas. Dividing the large-scale systems into clusters (\ie subsystems) and distributing the computation across clusters, solves the constraints of centralised based approach. In such scenarios, using distributed SE methods brings numerous advantages over the centralised ones. In this paper, we propose a novel distributed approach to solve the linear SE model by combining local solutions obtained by applying weighted least-squares (WLS) of the given subsystems with the Gaussian belief propagation (GBP) algorithm. The proposed algorithm is based on the factor graph operating without a central coordinator, where subsystems exchange only ``beliefs", thus preserving privacy of the measurement data and state variables. Further, we propose an approach to speed-up evaluation of the local solution upon arrival of a new information to the subsystem. Finally, the proposed algorithm provides results that reach accuracy of the centralised WLS solution in a few iterations, and outperforms vanilla GBP algorithm with respect to its convergence properties.

scholarly journals Distributed Weighted Least-Squares and Gaussian Belief Propagation: An Integrated Approach

2021 ◽  
Author(s):  
Dino Zivojevic ◽  
Muhamed Delalic ◽  
Darijo Raca ◽  
Dejan Vukobratovic ◽  
Mirsad Cosovic
Keyword(s):  
Least Squares ◽  
Large Scale ◽  
Belief Propagation ◽  
Weighted Least Squares ◽  
Measurement Data ◽  
Integrated Approach ◽  
Factor Graph ◽  
State Variables ◽  
Large Scale Systems ◽  
Distributed Approach

The purpose of a state estimation (SE) algorithm is to estimate the values of the state variables considering the available set of measurements. The centralised SE becomes impractical for large-scale systems, particularly if the measurements are spatially distributed across wide geographical areas. Dividing the large-scale systems into clusters (\ie subsystems) and distributing the computation across clusters, solves the constraints of centralised based approach. In such scenarios, using distributed SE methods brings numerous advantages over the centralised ones. In this paper, we propose a novel distributed approach to solve the linear SE model by combining local solutions obtained by applying weighted least-squares (WLS) of the given subsystems with the Gaussian belief propagation (GBP) algorithm. The proposed algorithm is based on the factor graph operating without a central coordinator, where subsystems exchange only ``beliefs", thus preserving privacy of the measurement data and state variables. Further, we propose an approach to speed-up evaluation of the local solution upon arrival of a new information to the subsystem. Finally, the proposed algorithm provides results that reach accuracy of the centralised WLS solution in a few iterations, and outperforms vanilla GBP algorithm with respect to its convergence properties.

scholarly journals Distributed Weighted Least-Squares and Gaussian Belief Propagation: An Integrated Approach

2021 ◽  
Author(s):  
Dino Zivojevic ◽  
Muhamed Delalic ◽  
Darijo Raca ◽  
Dejan Vukobratovic ◽  
Mirsad Cosovic
Keyword(s):  
Least Squares ◽  
Large Scale ◽  
Belief Propagation ◽  
Weighted Least Squares ◽  
Measurement Data ◽  
Integrated Approach ◽  
Factor Graph ◽  
State Variables ◽  
Large Scale Systems ◽  
Distributed Approach

The purpose of a state estimation (SE) algorithm is to estimate the values of the state variables considering the available set of measurements. The centralised SE becomes impractical for large-scale systems, particularly if the measurements are spatially distributed across wide geographical areas. Dividing the large-scale systems into clusters (\ie subsystems) and distributing the computation across clusters, solves the constraints of centralised based approach. In such scenarios, using distributed SE methods brings numerous advantages over the centralised ones. In this paper, we propose a novel distributed approach to solve the linear SE model by combining local solutions obtained by applying weighted least-squares (WLS) of the given subsystems with the Gaussian belief propagation (GBP) algorithm. The proposed algorithm is based on the factor graph operating without a central coordinator, where subsystems exchange only ``beliefs", thus preserving privacy of the measurement data and state variables. Further, we propose an approach to speed-up evaluation of the local solution upon arrival of a new information to the subsystem. Finally, the proposed algorithm provides results that reach accuracy of the centralised WLS solution in a few iterations, and outperforms vanilla GBP algorithm with respect to its convergence properties.

Distributed Weighted Least-Squares and Gaussian Belief Propagation: An Integrated Approach

2021 ◽  
Author(s):  
Dino Zivojevic ◽  
Muhamed Delalic ◽  
Darijo Raca ◽  
Dejan Vukobratovic ◽  
Mirsad Cosovic
Keyword(s):  
Least Squares ◽  
Belief Propagation ◽  
Weighted Least Squares ◽  
Integrated Approach

A Decentralized Multivariable Robust Adaptive Voltage and Speed Regulator for Large-Scale Power Systems

2013 ◽  
Vol 14 (1) ◽  
pp. 41-56 ◽  
Author(s):  
Francis A. Okou ◽  
Ouassima Akhrif ◽  
Louis A. Dessaint ◽  
Derrick Bouchard
Keyword(s):  
Power Systems ◽  
Power System ◽  
Large Scale ◽  
Matching Condition ◽  
Algebraic Riccati Equation ◽  
Linear Component ◽  
State Variables ◽  
Large Scale Systems ◽  
Robust Adaptive ◽  
Excitation Parameters

Abstract This papter introduces a decentralized multivariable robust adaptive voltage and frequency regulator to ensure the stability of large-scale interconnnected generators. Interconnection parameters (i.e. load, line and transormer parameters) are assumed to be unknown. The proposed design approach requires the reformulation of conventiaonal power system models into a multivariable model with generator terminal voltages as state variables, and excitation and turbine valve inputs as control signals. This model, while suitable for the application of modern control methods, introduces problems with regards to current design techniques for large-scale systems. Interconnection terms, which are treated as perturbations, do not meet the common matching condition assumption. A new adaptive method for a certain class of large-scale systems is therefore introduces that does not require the matching condition. The proposed controller consists of nonlinear inputs that cancel some nonlinearities of the model. Auxiliary controls with linear and nonlinear components are used to stabilize the system. They compensate unknown parametes of the model by updating both the nonlinear component gains and excitation parameters. The adaptation algorithms involve the sigma-modification approach for auxiliary control gains, and the projection approach for excitation parameters to prevent estimation drift. The computation of the matrix-gain of the controller linear component requires the resolution of an algebraic Riccati equation and helps to solve the perturbation-mismatching problem. A realistic power system is used to assess the proposed controller performance. The results show that both stability and transient performance are considerably improved following a severe contingency.

The inverse modeling problem

SIMULATION ◽  
1970 ◽  
Vol 15 (6) ◽  
pp. 264-268 ◽  
Author(s):  
Bernard C. Patten
Keyword(s):  
Real World ◽  
Inverse Modeling ◽  
Simulation Modeling ◽  
Large Scale ◽  
State Variables ◽  
Large Scale Systems ◽  
Natural Systems ◽  
Valid Model ◽  
The Relationship ◽  
Definite Solution

In simulation modeling of very large-scale systems, such as social and natural systems, reductions in scale must be so severe that state variables of the abstraction (model) often cannot be translated back to variables that have real-world significance. Model behavior may not much resemble anything that occurs naturally. If y is a real system and x a model of it, the two can be viewed as related by a set of homomorphic corres pondences M. Then, xMy means x "is a model of" y. Behavior of x pertains to that of y only as M is a valid model, and the relationship is implicit in an inverse model M-1, defined from the fact that xMy implies yM-1x (y "is modeled by" x). To make it explicit, that is to interpret model behavior in terms of real-world variables, means in some sense to be able to identify M-1. One approach to estimating it is suggested, but a definite solution is not reached.

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