Quasi-Newton Power Flow Using Partial Jacobian Updates

Purpose -The purpose of this work is that of providing the guidelines of an efficient implementation of power flow computations using the MATLAB computation environment. Design/methodology/approach -The goal of obtaining high efficiency from MATLAB programs often proves elusive unless special care is taken in exploiting the vectorising capability of MATLAB programming. In the present paper the implementation of Newton-Raphson power flow in MATLAB is examined with particular emphasis on the way of obtaining a vectorisable code capable of achieving effective numerical performance by exploiting its formulation in terms of complex variables. Findings -Tests on actual networks with up to 1,300 buses are presented. They show that the complex power flow is as efficient as the best implementations of the Newton Raphson power flow using real variables, as long as the operations involved are reordered with the aim of exploiting the vectorisation capabilities of the MATLAB environment. Originality/value -It is shown that improved numerical efficiency in the MATLAB can be obtained through its formulation in terms of complex variables. The complex Newton-Raphson load flow, not very common in practical uses, is shown to have many desirable qualities from the point of view of MATLAB programming and is presented in detail. IntroductionSince its early versions, MATLAB has provided scientists and technicians with a very powerful language for numerical computing and data presentation. Its basic capabilities in matrix algebra have been continuously extended with the addition of specialized toolboxes covering many areas of scientific computing, also including control systems and power system analysis.The addition of an efficient support for sparse matrix manipulation makes it possible to design MATLAB programs (M-files) for such specialized computations as power flow, state estimation and power system dynamics, cutting down the time for programming and debugging the code. Furthermore, MATLAB not only appeared as a useful tool for testing methods and ideas in view of an implementation using other programming languages, but it could be adopted as a platform for software applications development.Obtaining high performance from MATLAB programs, however, is not always straightforward. The key-point of efficient programming lies in making systematic use of the vector syntax of the MATLAB language (MathWorks, 2010); all numerical operations are more efficiently executed if they are expressed in the form of matrix or vector operations with speed-ups exceeding one order of magnitude with respect to non-vector code. As a result, the potential of MATLAB programming mostly depends on the programmer's ability of re-thinking solution algorithms originally designed for scalar efficiency, in a vector-oriented mode (MathWorks, 2010;Alvarado, 1999).

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“…This technique, based on the Quasi-Newton concept proposed in Semlyen and De Leon (2001), can be easily adapted to the complex power flow.…”

Section: 3mentioning

confidence: 99%

MATLAB implementation of the complex power flow

Granelli

Montagna²

2013

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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“…when bus type switching from PV to PQ is due to reactive limit violations) or when the number of iterations exceeds a predefined threshold value. This procedure, known as the 'dishonest Newton method' [11], often enables a considerable reduction in the computing time. Therefore the purpose of this section is to evaluate the proposed parameterisation techniques, and to compare their performance by considering two procedures.…”

Section: Influence Of Using a Constant Jacobian Matrixmentioning

confidence: 99%

“…when there is a change in the bus type from PV to PQ because of their reactive limits violations) [11], as opposed to updating it at every iteration.…”

Section: Introductionmentioning

confidence: 99%

Improved geometric parameterisation techniques for continuation power flow

Neto

Alves

2010

IET Gener. Transm. Distrib.

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This study presents efficient geometric parameterisation techniques for the continuation power flow. The Jacobian matrix singularity is eliminated by the addition of the line equations which pass through the points in the plane determined by the variables loading factor and the sum of nodal voltage magnitudes, or angles, of all system buses. These techniques enable the complete tracing of P-V curves and the computation of the maximum loading point for any power system, including those with voltage instability problems that have the strong local characteristics, for which the global parameterisation techniques are considered inadequate. An efficient criterion to change the set of lines, based on the analysis of the total power mismatch evolution, is also defined. The obtained results show that the characteristics of Newton's conventional method are preserved and the convergence region around the Jacobian matrix singularity is enhanced. The computational time required to trace the P-V curve can also be reduced, without losing robustness, when the Jacobian matrix is updated only after the system undergoes a significant change.

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“…Direct methods [1][2][3][4] are based on direct matrix multiplication, where loop impedance matrix are being formulated by using special topology of distributed networks that requires tremendous computation work for the formation of loop, matrix inversion and renumbering of nodes. Whereas fast-decoupled and Newton-Raphson methods [5][6][7][8] requires the formulation of Jacobian matrix as well as its lower and upper triangular (LU) factorization that demands more time for calculations and it also requires special treatment for ill-conditioned systems [9]. Papers [31,32] presents a method for calculating the power flow in distribution networks considering uncertainties in the distribution system.…”

Section: Introductionmentioning

confidence: 99%