The authors discuss an advanced version of the S matrix method, an eigenvalue technique for the analysis of the steady-state stability (or the stability against small signals) of large power systems. The dynamic characteristics of power systems can be linearly approximated with a set of differential equations. The technique transforms the matrix A into the matrix S and then determines several eigenvalues with the largest absolute values from matrix S that correspond to the dominant eigenvalues of matrix A. In the process of identifying the appropriate eigenvalues, the method uses the refined Lanczos process, which makes high-speed calculation possible through the use of the sparsity and the structural uniformity of matrices. >

A new eigen-analysis method of steady-state stability studies for large power systems: S matrix method

A method of analyzing the small signal stability of very large power systems is described. The method is based on a frequency-domain approach which concentrates on the electromechanical modes of the power system under study. By using a modular modeling concept and an efficient sparsity network solution routine, systems having up to 12000 buses and 1000 detailed generator models can be studied. A comparison is made between eigenvalues calculated by this method and by other existing programs. >

Eigenvalue analysis of very large power systems

As power systems continue to develop, online dynamic security analysis and real-time simulation using parallel computing are becoming increasingly important. This paper presents a novel multilevel partition scheme for parallel computing based on power network regional characteristics and describes the design and implementation of a hierarchical block bordered diagonal form (BBDF) algorithm for power network computation. Some optimization schemes are further proposed to reduce the computation and communication time and to improve the scalability of the program. The simulation results show that, for a large network with 2115 nodes, 2614 branches, 248 generators, and 544 loads, the proposed algorithms and schemes run ten times faster on a cluster system with eight CPUs than on a single CPU. Thus, they satisfy the real-time simulation requirement for large-scale power grids.

A parallel transient stability simulation for power systems

The AESOPS and PEALS algorithms are explained in terms of relatively standard eigenvalue analysis and related to a true Newton iterative scheme. The true Newton scheme requires an additional (or simultaneous) elimination at each iteration but can give a reduction in the number of iterations. The generalized algorithm can be used to compute various modes either separately or simultaneously. A numerical example involving the New England test system of reference is given. >

An explanation and generalization of the AESOPS and PEALS algorithms (power system models)

As power systems continue to develop, realtime simulation and online dynamic security analysis using parallel computing are becoming increasingly important. This paper presents a novel multilevel partition scheme for parallel computing based on power network regional characteristics and describes the design and implementation of a hierarchical block bordered diagonal form (BBDF) algorithm for power network computation. Some optimization schemes are also proposed to reduce the computing and communication time and to improve the scalability of the program. The simulation results of a large network having 10188 nodes, 13499 branches, 1072 generators and 3003 loads show that the proposed algorithms and schemes running on a cluster system with 12 CPUs can provide a 15 times faster speed than the single CPU one, to satisfy the realtime simulation requirements for large scale power grids.

Parallel algorithm and implementation for realtime dynamic simulation of power system

Superconducting Generator (SCG) has many advantages such as small size, high generation efficiency, low impedance, and so on. An improved power system with many potential good properties may be obtained by introduction of SCG. In order to study the behaviors of SCG in power systems, a digital type SCG model for an existing analog type real-time power system simulator is developed in this work, which is suitable for real-time simulations when the generator constants and control systems are changed frequently. By use of the above-mentioned equipments, real-time simulation in cases of SCG with different generator constants and in case of SCG in multi-machine power system has been conducted. The real-time simulation results verify the effects of SCG on power system stability enhancement and show the influence of generator constants on its stability-improving effects.

https://www.jstage.jst.go.jp/article/ieejpes/123/3/123_3_368/_pdf

Real-time Simulation Study on Stability-improving Effects of Superconducting Generator in Power Systems by use of Digital Type Generator Model and Analog Type Power System Simulator

Power systems have become very large, and in addition the forthcoming open electricity market will make power system operation more complex. Therefore, power system operation must become more efficient and flexible. Very fast power system simulation is a means of achieving more sophisticated power system on-line monitoring and control, and parallel computing is a key technology for very fast power system simulation. This paper proposes an efficient and fast parallel network calculation algorithm that will contribute to the development of fast power system simulation programs. Numerical examples show that the proposed method using six processors is about 4.0 times as fast as the usual serial algorithm when applied to a large-scale radial power system and about 3.2 times as fast when applied to a large-scale loop power system. © 2001 Scripta Technica, Electr Eng Jpn, 135(3): 26–36, 2001

Parallel processing of network calculations in order to speed up transient stability analysis

Conventional methods for dynamic stability analysis such as the eigenvalue method (QR method), frequency response method, direct numerical integration method, etc., are not applicable to very large-scale systems because of limitations of memory capacity, computing time, and computation accuracy. To analyze a larger power system, it is necessary to take advantage of sparsity and regularity of matrices and to derive eigenvalues more efficiently (that is, with smaller memory capacity and shorter computing time). In this paper, we propose a new method which transforms the eigenvalue with the smallest real part (poorest attenuation component) to the eigenvalue of largest absolute value of a new matrix. We call the new matrix, Stability matrix (S-matrix) and call the proposed method, the S-method. The theoretical background of the S-method is presented and the effectiveness of the S-method is shown.

Analysis of dynamic stability of power system by a new eigenvalue method

An eigenvalue estimation method for small signal stability analysis of electric power systems is proposed. The method, called the Mode Coupling Method, is used to estimate efficiently the nonlinear change of the eigenvalue with respect to the change of parameter. The eigenvalue sensitivity analysis method, which has been used to estimate the change of the eigenvalue, is a method of linear estimation of the change of the eigenvalue. However, the eigenvalue frequently shows a strong nonlinear change, and therefore the calculation efficiency and speed were insufficient in the conventional method. In the Mode Coupling Method, the most important modes and those most related to the major mode under consideration are first selected. Next, these two or more selected modes are coupled and the new eigenvalues of the coupled matrix are calculated, providing good estimation of the new eigenvalues. The size of the coupled matrix is very small. We can consider mutual interaction between important modes. Thus, this is a powerful method in which nonlinear estimation of eigenvalues is possible. When the QR method is used, the calculation time for eigenvalue analysis is proportional to the third power of the size of the matrix. The size of the matrix used for the mode coupling method is approximately 1/6 of the original value. Therefore, the computing time for eigenvalue estimation becomes less than 1% of the original computing time. The computational accuracy of the proposed method is verified with the IEEJ EAST30 standard power system model. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 174(1): 10–16, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/ eej.21037

Development of an eigenvalue estimation method (Mode Coupling Method) for small signal stability analysis of power system

This paper presents a new method of unbalanced load flow calculation to improve complexity by the method of advanced symmetrical coordinates. Usually, the electric power system has been calculated only by the positive phase sequence component on the assumption that three-phase transmission lines and loads are balanced. However, many ultrahigh-voltage transmission lines are not transposed, and therefore mutual inductances cause negative sequence currents in the trunk transmission system. Negative sequence currents cause heating of generators and transformers, and therefore the three-phase sequence component should be calculated accurately. We examined the fast computation and good convergence performance of unbalanced load flow calculation by models of three-phase transmission lines, transformers, and loads. The proposed method is not the phase coordinate system but the method of symmetrical coordinates. This technique decreases numerical complexity by the use of a simplified Jacobian matrix. The convergence performance of this method is inferior to that of the usual Newton–Raphson method. As a consequence, the problem of poor convergence performance is alleviated by a technique for the newly developed deceleration Newton method. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 174(1): 17–24, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.21034

Naoyuki Uchida

Papers

Real-time Simulation Study on Stability-improving Effects of Superconducting Generator in Power Systems by use of Digital Type Generator Model and Analog Type Power System Simulator

Parallel processing of network calculations in order to speed up transient stability analysis

Analysis of dynamic stability of power system by a new eigenvalue method

Development of an eigenvalue estimation method (Mode Coupling Method) for small signal stability analysis of power system

Fast computation and stable convergence technique for unbalanced load flow calculation in large‐scale systems