Hasan Dag

A new preconditioned conjugate gradient power flow

A new solution methodology for the constant matrix, decoupled power flow problem is presented in this paper. The proposed method uses the conjugate gradient method instead of the traditional direct solution of Ax = b for updating the power flow variables. The conjugate gradient method is accelerated with an approximate inverse matrix preconditioner obtained from a linear combination of matrix-valued Chebyshev polynomials. The new method has been tested on several systems of different sizes. In terms of speed, the method is comparable to the fast decoupled load flow in serial environments, but it is more amenable to parallel and vector processing since it contains only matrix-vector multiplications.

Iterative solver techniques in large scale power system computation

The solution of large sparse linear systems forms the core of power system computations whether it is power flow, state estimation or security assessment (static or dynamic). There is a continuous need to speed-up this process by improved numerical algorithms. Iterative solver techniques based on the Krylov subspace projection method offer an attractive alternative to the traditional LU factorization methods because of the ease of parallelization and/or vectorization. In this paper we review the efforts since the late 80s in applying these techniques to power system problems.

Comparison of Post Outage Bus Voltage Magnitudes Estimated by Harmony Search and Differential Evolution Methods

Contingency studies are indispensable tools of both the power system planning and operational studies. Real time implementation of operational problems makes necessary the use of high speed computational methods while requiring reasonable accuracies. On the other hand, accuracy of the results and the speed of calculation depend on branch outage modeling as well as solution algorithm used. This paper presents a comparison of post outage bus voltage magnitudes calculated by two meta-heuristic approaches; namely differential evolution (DE) and harmony search (HS) methods. The methods are tested on IEEE 14, IEEE 30, IEEE 57, and IEEE 118 bus test systems and the results are compared both in terms of accuracy and calculation speed.

Double branch outage modeling and its solution using differential evolution method

Power system operators need to check the system security by contingency analysis, which requires power flow solutions repeatedly. AC power flow is computationally slow even for a moderately sized system. Thus, fast and accurate outage models and approximated solutions have been developed. This paper adopts a single branch outage model to a double branch outage one. The final constrained optimization problem resulted from modeling is then solved by using differential evolution method. Simulation results for IEEE 30 and 118 bus test systems are presented and compared to those of full AC load flow in terms of solution accuracy.

An approximate inverse preconditioner and its implementation for conjugate gradient method

The conjugate gradient method has been used extensively to solve a given set of (symmetric) positive definite linear equations instead of Gaussians elimination based direct methods, especially for very large systems when parallel solution environment is preferred. The method itself can take many iterations to converge. In order to reduce the number of iterations, i.e., in order to accelerate the rate of convergence of the method, the set of linear equations at hand is preconditioned. We present the implementation results of a previously published approximate inverse preconditioner for the conjugate gradient method. The preconditioner is based on an approximate inverse of the coefficient matrix obtained from a linear combination of matrix-valued Chebyshev polynomials. We implement and test the proposed method on a Sun SMP machine. Because the preconditoner itself contains mainly matrix-matrix products and conjugate gradient method contains mostly matrix-vector products, convincing results are obtained in terms of both speedup and scalability.

Harmony search method based parallel contingency analysis

Power system security management is one of the key problems in power system analysis. Power system management center operators need to simulate contingencies as fast as possible and take the remedial actions in time. These contingency analyses comprise of the outages of the branches, transformers and other power system components. This paper solves branch outage problem using a bounded approach. Harmony search method is used to solve the local constrained optimization problem of the bounded approach. Several outage simulations using IEEE 14, 30, and 118 bus systems are performed and compared against AC power flow in terms of accuracy. In order to speed up the contingency simulation, the problem is also solved in a parallel environment. Speed up results of the IEEE 118 and 300 bus test systems are given.

A parallel implementation of chebyshev preconditioned conjugate gradient method

A parallel implementation for linear set of equations of the form Ax = b is presented in this paper. In this implementation, instead of the traditional direct solution of Ax = b, conjugate gradient method is used. The conjugate gradient method is accelerated with an approximate inverse matrix preconditioner obtained from a linear combination of matrix-valued Chebyshev polynomials. This implementation is tested on a Sun SMP machine. Since conjugate gradient method and preconditioner contain only matrix-vector and matrix-matrix multiplications, convincing results are obtained in terms of both speed and scalability.

Parallel-in-space implementation of transient stability analysis on a Linux cluster with infiniband

On-line transient stability analysis is an inevitable way to provide real time power system security and control. Parallel computing is one of the most viable ways to perform on-line transient stability analysis. This paper presents the performance results of a parallel-in-space algorithm based on a multilevel partitioning scheme on an Infiniband cluster system. The algorithm decreases the transient stability simulation time using METIS for partitioning in conjunction with the linearized update solution process of the Very Dishonest Newton Method when solving the differential-algebraic systems of equations [1]. Two real power systems, a 3493-bus system with 844 generators and a 7935-bus system with 2135 generators, are tested on a Linux-cluster system with 16 nodes. Each node has 2 multicore processors and is connected to each other by Infiniband network. The properties of a test system have a large impact on the performance of the parallel algorithm used, since it affects communication duration.

Post outage bus voltage calculations for double branch outages

Secure operation of electrical power systems is vital, hence fast and accurate post-outage state calculations are important for contingency analysis. Contingency analysis includes simulations of both the single and double branch outages. This paper presents constrained optimization problem of a recently developed double branch outage model. Harmony search algorithm is used as an optimization tool. IEEE 30 Bus Test system simulation results are given, and compared with those of the AC load flow in terms of computational accuracy. Speed test results of IEEE 14, 30, 57, 118 and 300 Bus Test Systems are illustrated and compared with those of the AC load flow calculations.

Sparsity Preserving Computation for Spectral Projectors

Several areas of applications, such as model order reduction, preconditioner design, and eigenvalue problems for spectral projectors can be found in the literature. In this paper, a fast and sparsity preserving approach for computing the spectral projectors is proposed. The suggested approach can be used in both Newton iteration and integral representation based methods. A comparison of the original and the suggested approaches in terms of computation time, sparsity preservation and accuracy is presented in this paper.