Iterative solver techniques in fast dynamic calculations of power systems

Kulkarni, A.; Pai, M.A.; Sauer, Peter W.

doi:10.1016/s0142-0615(00)00066-1

Cited by 19 publications

(11 citation statements)

References 10 publications

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“…In [21], a method is proposed to update the Jacobian matrix whenever the rate of convergence slows down, which is referred to as the 'dishonest' Newton method.…”

Section: Nr Solution Methodsmentioning

confidence: 99%

Revisiting the power flow problem based on a mixed complementarity formulation approach

Pirnia

Cañizares

Bhattacharya

2013

IET Generation, Transmission & Distribution

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A novel optimisation-based model of the power flow (PF) problem is proposed using complementarity conditions to properly represent generator bus voltage controls, including reactive power limits and voltage recovery processes. This model is then used to prove that the Newton-Raphson (NR) solution method for solving the PF problem is basically a step of the generalised reduced gradient algorithm applied to the proposed optimisation problem. To test the accuracy, flexibility and the numerical robustness of the proposed model, the IEEE 14-bus, 30-bus, 57-bus, 118-bus and 300-bus test systems and large real 1211-bus and 2975-bus systems are used, benchmarking the results of the proposed PF model against the standard NR method. It is shown that the proposed model yields adequate solutions, even in the case when the NR method fails to converge.

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“…In [21], a method is proposed to update the Jacobian matrix whenever the rate of convergence slows down, which is referred to as the 'dishonest' Newton method.…”

Section: Nr Solution Methodsmentioning

confidence: 99%

Revisiting the power flow problem based on a mixed complementarity formulation approach

Pirnia

Cañizares

Bhattacharya

2013

IET Generation, Transmission & Distribution

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“…The Krylov subspace methods have been developed and perfected since early 1980's for the iterative solution of the linear problem Ax b for large, sparse and nonsymmetric Amatrices. The approach is to minimize the residual r in the formulation of r b Ax (Kulkarnil, Pai, & Sauer, 2001). Because these methods form a basis, it is clear that this method converges in N iterations when N is the matrix size.…”

Section: Review Of Krylov Subspace Methodsmentioning

confidence: 99%

Available Transfer Capability Calculation

Hojabri¹,

Hizam²

2011

Applications of MATLAB in Science and Engineering

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“…More than 50% reduction of computation cost was obtained in their work, compared with Newton-LU method. Pai et al [11][12][13] successfully used a similar method to solve the nonlinear equations arising from implicit trapezoidal method in TDS. With good preconditioners and dishonest preconditioner technique, the Newton-GMRES method obtained significant performance improvement compared with the Newton-LU method [13].…”

Section: Introductionmentioning

confidence: 99%

“…Pai et al [11][12][13] successfully used a similar method to solve the nonlinear equations arising from implicit trapezoidal method in TDS. With good preconditioners and dishonest preconditioner technique, the Newton-GMRES method obtained significant performance improvement compared with the Newton-LU method [13]. Recently, Zhang and Chiang [14] proposed a Fast Newton-FGMRES algorithm to solve largescale power flow problems.…”

Section: Introductionmentioning

confidence: 99%

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Updating preconditioner for iterative method in time domain simulation of power systems

Wang

Xue

Lin

et al. 2011

Sci. China Technol. Sci.

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The numerical solution of the differential-algebraic equations (DAEs) involved in time domain simulation (TDS) of power systems requires the solution of a sequence of large scale and sparse linear systems. The use of iterative methods such as the Krylov subspace method is imperative for the solution of these large and sparse linear systems. The motivation of the present work is to develop a new algorithm to efficiently precondition the whole sequence of linear systems involved in TDS. As an improvement of dishonest preconditioner (DP) strategy, updating preconditioner strategy (UP) is introduced to the field of TDS for the first time. The idea of updating preconditioner strategy is based on the fact that the matrices in sequence of the linearized systems are continuous and there is only a slight difference between two consecutive matrices. In order to make the linear system sequence in TDS suitable for UP strategy, a matrix transformation is applied to form a new linear sequence with a good shape for preconditioner updating. The algorithm proposed in this paper has been tested with 4 cases from real-life power systems in China. Results show that the proposed UP algorithm efficiently preconditions the sequence of linear systems and reduces 9%-61% the iteration count of the GMRES when compared with the DP method in all test cases. Numerical experiments also show the effectiveness of UP when combined with simple preconditioner reconstruction strategies. differential-algebraic equations, GMRES, updating preconditioner, power system simulation Citation:Wang K, Xue W, Lin H X, et al. Updating preconditioner for iterative method in time domain simulation of power systems.

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Iterative solver techniques in fast dynamic calculations of power systems

Cited by 19 publications

References 10 publications

Revisiting the power flow problem based on a mixed complementarity formulation approach

Revisiting the power flow problem based on a mixed complementarity formulation approach

Available Transfer Capability Calculation

Updating preconditioner for iterative method in time domain simulation of power systems

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