Some improved methods for digital network analysis

Arch Computat Methods Eng

et al. 2017

The power flow model performs the analysis of electric distribution and transmission systems. With this statement at hand, in this work we present a summary of those solvers for the power flow equations, in both algebraic and parametric version. The application of the Alternating Search Direction method to the power flow problem is also detailed. This results in a family of iterative solvers that combined with Proper Generalized Decomposition technique allows to solve the parametric version of the equations. Once the solution is computed using this strategy, analyzing the network state or solving optimization problems, with inclusion of generation in real-time, becomes a straightforward procedure since the parametric solution is available. Complementing this approach, an error strategy is implemented at each step of the iterative solver. Thus, error indicators are used as an stopping criteria controlling the accuracy of the approximation during the construction process. The application of these methods to the model IEEE 57-bus network is taken as a numerical illustration.

Section: Y-matrix and Z-matrix Methodsmentioning

confidence: 99%

“…Applying these assumptions to equation (14) and dividing equations by |V k | in both sides, the system to be solved is:…”

Section: Gauss-seidel and Newton-raphson Methodsmentioning

confidence: 99%

Algebraic and Parametric Solvers for the Power Flow Problem: Towards Real-Time and Accuracy-Guaranteed Simulation of Electric Systems

García-Blanco

Dı́ez

Arch Computat Methods Eng

et al. 2017

“…Historically, power flow studies started with Gauss-Seidel (GS) type methods [2,3], Newton-Raphson's methods (NR) [4,5], or fixed point algorithms based on the admittance or impedance matrix, like the Implicit Z bus method (IZB) [6][7][8][9][10][11][12][13][14]. Despite their flexibility and low memory usage, GS methods have low convergence rates compared to NR methods, who enjoy optimal quadratic convergence but come with an increased computational cost due to the need of assembling and solving the Jacobian system at each iteration.…”

Section: Related Workmentioning

confidence: 99%

Unified formulation of a family of iterative solvers for power systems analysis

Electric Power Systems Research

Chinesta

Malik

et al. 2016

This paper illustrates the construction of a new class of iterative solvers for power flow calculations based on the method of Alternating Search Directions. This method is fit to the particular algebraic structure of the power flow problem resulting from the combination of a globally linear set of equations and nonlinear local relations imposed by power conversion devices, such as loads and generators. The choice of the search directions is shown to be crucial for improving the overall robustness of the solver. A noteworthy advantage is that constant search directions yield stationary methods that, in contrast with Newton or Quasi-Newton methods, do not require the evaluation of the Jacobian matrix. Such directions can be elected to enforce the convergence to the high voltage operative solution. The method is explained through an intuitive example illustrating how the proposed generalized formulation is able to include other nonlinear solvers that are classically used for power flow analysis, thus offering a unified view on the topic. Numerical experiments are performed on publicly available benchmarks for large distribution and transmission systems.Peer ReviewedPostprint (author's final draft

“…The standard solvers for the power flow problem are based on the classical methodologies like Newton-Raphson's [1,2] and Gauss-Seidel [3,4] but also on specific approaches like fast decoupled load flow [5,6] or the primitive methods based on admittance or impedance matrices [7][8][9][10][11][12], for instance the Z bus method [13]. See [14] for a review.…”

Section: Introductionmentioning

confidence: 99%

Monitoring a PGD solver for parametric power flow problems with goal‐oriented error assessment

García-Blanco

Numerical Meth Engineering

Chinesta

et al. 2017

This is the peer reviewed version of the following article: [García-Blanco, R., Borzacchiello, D., Chinesta, F., and Diez, P. (2017) Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment. Int. J. Numer. Meth. Engng, 111: 529–552. doi: 10.1002/nme.5470], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5470/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The parametric analysis of electric grids requires carrying out a large number of Power Flow computations. The different parameters describe loading conditions and grid properties. In this framework, the Proper Generalized Decomposition (PGD) provides a numerical solution explicitly accounting for the parametric dependence. Once the PGD solution is available, exploring the multidimensional parametric space is computationally inexpensive. The aim of this paper is to provide tools to monitor the error associated with this significant computational gain and to guarantee the quality of the PGD solution. In this case, the PGD algorithm consists in three nested loops that correspond to 1) iterating algebraic solver, 2) number of terms in the separable greedy expansion and 3) the alternated directions for each term. In the proposed approach, the three loops are controlled by stopping criteria based on residual goal-oriented error estimates. This allows one for using only the computational resources necessary to achieve the accuracy prescribed by the end- user. The paper discusses how to compute the goal-oriented error estimates. This requires linearizing the error equation and the Quantity of Interest to derive an efficient error representation based on an adjoint problem. The efficiency of the proposed approach is demonstrated on benchmark problems.Peer ReviewedPostprint (author's final draft