Constant Jacobian Matrix Research Articles

A New Fast Decoupled Power Flow Method for Distribution Systems

This paper presents a new, robust, and fast technique to obtain the load flow solution in distribution networks. The proposed method is based on the Newton-Raphson technique using equivalent current-injection and rectangular coordinates. The load flow problem is considered as an optimization problem and is decoupled into two subproblems. The assumptions on voltage magnitudes, angles, and r/x ratios necessary for decoupling the network in the conventional FDPF are eliminated in the proposed method. This method is simple, insensitive to r/x ratios of the distribution lines, and uses a constant Jacobian matrix. It is solved similar to FDPF. Test results of the proposed method on a sample six-node and the IEEE 34-node systems are given to illustrate the superior performance. These results indicate that the proposed method is efficient and accurate and has great potential for online applications.

A novel and fast three-phase load flow for unbalanced radial distribution systems

A novel and fast three-phase load flow algorithm for unbalanced radial distribution systems is proposed in this paper. The proposed method uses branch voltages as state variables and employs the Newton-Raphson (NR) algorithm to solve the load flow problem. By utilizing branch voltages as state variables, a constant Jacobian matrix can be obtained, and a building algorithm for Jacobian matrix is then developed from the observation of the constant Jacobian matrix. A solution technique, which takes the network structure into account to avoid the time-consuming lower and upper triangular (LU) factorization, is also developed. Since the factorization procedure can be avoided, the proposed method can save computation time. For any power system equipment, if its equivalent current injection or admittance matrix can be obtained, it can be integrated into the proposed method. Test results demonstrate that by integrating the Jacobian building algorithm and efficient solution technique, the proposed method is an effective three-phase load flow method and has great potential for real-time use.

Constant Jacobian matrix and its application to fast trajectory simulation of power systems

The speed of simulation of power system dynamics has been one of the topics most concerned with on-line security assessment. This paper proposes a new method for forming the constant Jacobian matrix for enhancing the speed of system simulation. By using the constant Jacobian matrix approach in system simulations, both for post-fault and fault-on duration, simulation efficiency is greatly enhanced. Techniques for speeding up the constant Jacobian matrix approach are discussed. Theoretical analysis is presented to demonstrate how the constant Jacobian matrix approach can be extended to a power system with generator controls. Simulation results with the constant Jacobian matrix approach in the 10-generator New England test system and the North China power system are compared with the results obtained by the use of commercial software BPA.

A Novel and Fast Three-Phase Load Flow for Unbalanced Radial Distribution Systems

A novel and fast three-phase load flow algorithm for unbalanced radial distribution systems is proposed in this paper. The proposed method uses branch voltages as state variables and employs the Newton-Raphson algorithm to solve the load flow problem. By utilizing branch voltages as state variables, a constant Jacobian matrix can be obtained and a building algorithm for Jacobian matrix is then developed from the observation of the constant Jacobian matrix. A solution technique, which takes the network structure into account to avoid the time-consuming LU factorization, is also developed. Since the factorization procedure can be avoided, the proposed method can save computation time. For any power system equipment, if its equivalent current injection or admittance matrix can be obtained, it can be integrated into the proposed method. Test results demonstrate that by integrating the Jacobian building algorithm and efficient solution technique, the proposed method is an effective three-phase load flow method and has great potential for real-time use.

Control of Nonlinear Multivariable Systems Using Direct Fuzzy Learning Method

A learning method that can acquire the control rules in the multi-input multi-output system is presented. Generally, in the control of a multivariable system, the error of the outputs must be transformed into the corrections of the inputs to get the control rules. If we do not know the mathematical modeling equation of the system, we cannot find out the Jacobian matrix to show the output variance with respect to the input variance. However, because it is not necessary to use the exact variable matrix in the learning of the fuzzy rules, this article introduces a method to get a representative constant Jacobian matrix that assures the convergence. Using this constant matrix, the fuzzy rules are successfully obtained. In particular, because many fuzzy subsets must be used in the case of a multivariable system, the optimization technique to minimize the fuzzy rule structure is also applied.

Numerical solution of the RHNC theory for fluids of non-spherical particles near a uniform planar wall

An efficient algorithm, a hybrid of the Picard-type and Newton-Raphson (NR) methods, is developed for solving the reference hypernetted-chain (RHNC) theory for non-spherical particles near a uniform planar wall. The basic idea of the algorithm is also applicable to non-spherical particles near a large macroparticle at infinite dilution. The problem of dipolar hard spheres near a hard wall is chosen here as an example system. A feature of the algorithm is that the Jacobian matrix is determined in the bulk calculation and serves as part of the input data for the wall calculation. Hence, the convergence is achieved in only a single iteration in the inner NR loop regardless of the initial values of the iteration variables. It is shown that the great advantage of the constant Jacobian matrix can be preserved even for general cases of other particle-particle and wall-particle interactions. In the course of the study, we encounter a singular behaviour of the RHNC theory for bulk dipolar hard spheres. Keeping the reduced density, we continue to increase the reduced dipole moment. Then, at a certain point the projections of the rotational invariant expansion of the total correlation function h mm0(r) (m ≠ 0; m = 1,2,3, …) become infinitely long ranged, which causes divergence of their Fourier transforms at zero wave-number, ħ mm0(0). The static dielectric constant and the heat capacity also diverge at that point. The singular behaviour implies the growth of the strong, long-ranged orientational order favouring parallel configuration, and represents a stability limit of the isotropic phase.

Optimal voltage control using a constant sensitivity matrix

Abstract This paper presents a new technique for improving system voltage profiles. Control of the voltage profile is achieved by minimizing the sum of the weighted voltage deviations at the buses using a first-order gradient technique. A constant symmetric load flow model in rectangular coordinates is employed. This permits efficient power computations requiring just four multiplications and a few additions per bus, irrespective of the system size. The constant Jacobian matrix used in load flow is also used in the calculation of the Langrangian multipliers throughout the optimization procedure. These features result in a computationally efficient algorithm. Results for two sample test systems using the proposed algorithm are presented.

On-Line Computation of Phase Shifter Distribution Factors and Lineload Alleviation

This paper presents a new method for the computation of phase shifter distribution factors required for adjusting the phase angles of phase shifters to control the line flows. These factors are computed usingusing the sensitivity matrix, which is tversee in- of the constant Jacobian matrix. Computation of these factors is carried out for both the base case system and the outaged system using the same-sensitivity matrix. The factors so computed are used to alleviate the line overloads leaving the economic generation schedules unaffected. In case the phase angle adjustments of the phase shifters do not reduce the line overloads completely, generation rescheduling and/ or load curtailment is proposed, thus ensuring a secure system operation. The proposed techniques are validated by testing on different test systems.

A reduced gaussian method using constant jacobian matrix for solving network type nonlinear simultaneous equations

A reduced gaussian method using constant jacobian matrix for solving network type nonlinear simultaneous equations