D.A. Alves

Continuation fast decoupled power flow with secant predictor

The conventional Newton and fast decoupled power flow methods are considered inadequate for obtaining the maximum loading point of power systems due to ill-conditioning problems at and near this critical point. At this point, the Jacobian matrix of the Newton method becomes singular. In addition, it is widely accepted that the P-V and Q-/spl theta/ decoupling assumptions made for the fast decoupled power flow formulation no longer hold. However, in this paper, a new fast decoupled power flow is presented that becomes adequate for the computation of the maximum loading point by simply using the reactive power injection of a selected PV bus as a continuation parameter. Besides, fast decoupled methods using V and /spl theta/ as parameters and a secant predictor are also presented. These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained for the IEEE systems (14 and 118 buses) show that the characteristics of the conventional method are enhanced and the region of convergence around the singular solution is enlarged.

Real power losses reduction and loading margin improvement via continuation method

This letter presents an alternative approach for reducing the total real power losses by using a continuation method. Results for two simple test systems and for the IEEE 57-bus system show that this procedure results in larger voltage stability margin. Besides, the reduction of real power losses obtained with this procedure leads to significant money savings and, simultaneously, to voltage profile improvement. Comparison between the solution of an optimal power flow and the proposed method shows that the latter can provide near optimal results and so, it can be a reasonable alternative to power system voltage stability enhancement.

A Parameterization Technique for the Continuation Power Flow Developed from the Analysis of Power Flow Curves

This paper presents an efficient geometric parameterization technique for the continuation power flow. It was developed from the observation of the geometrical behavior of load flow solutions. The parameterization technique eliminates the singularity of load flow Jacobian matrix and therefore all the consequent problems of ill-conditioning. This is obtained by adding equations lines passing through the points in the plane determined by the loading factor and the total real power losses that is rewritten as a function of the real power generated by the slack bus. An automatic step size control is also provided, which is used when it is necessary. Thus, the resulting method enables the complete tracing of P-V curves and the computation of maximum loading point of any electric power systems. Intending to reduce the CPU time, the effectiveness caused by updating the Jacobian matrix is investigated only when the system undergoes a significant change. Moreover, the tangent and trivial predictors are compared with each other. The robustness and simplicity as well as the simple interpretation of the proposed technique are the highlights of this method. The results obtained for the IEEE 300-bus system and for real large systems show the effectiveness of the proposed method.

Parameterized fast decoupled load flow for tracing power systems bifurcation diagrams

The conventional Newton and fast decoupled load flow methods are considered to be inadequate to obtain the maximum loading point due to ill-conditioning problems at and near this critical point. At this point the Jacobian matrix of the Newton-Raphson method becomes singular, and the assumptions made for the fast decoupled formulation no longer hold. However, as shown in this paper, with small modifications these methods become adequate for the computation of the complete bifurcation diagrams. They are also adequate for obtaining a single solution near the nose point or at the lower part of PV curve with flat start initialization. These new methods are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained for the IEEE systems (14, 30, 57 and 118 buses) show that the characteristics of the conventional methods are preserved.

A new approach to the solution of the optimal power flow problem based on the modified Newton's method associated to an augmented Lagrangian function

This paper presents a new algorithm for the optimal power flow problem. The algorithm is based on Newtons method which works with an Augmented Lagrangian function associated with the original problem. The function aggregates all the equality and inequality constraints and is solved using the modified-Newton method. Test results have shown the effectiveness of the approach using the IEEE 30 and 638 bus systems.

Alternative parameters for the continuation power flow method

Abstract The conventional Newtons method has been considered inadequate to obtain the maximum loading point (MLP) of power systems. It is due to the Jacobian matrix singularity at this point. However, the MLP can be efficiently computed through parameterization techniques of continuation methods. This paper presents and tests new parameterization schemes, namely the total power losses (real and reactive), the power at the slack bus (real or reactive), the reactive power at generation buses, the reactive power at shunts (capacitor or reactor), the transmission lines power losses (real and reactive), and transmission lines power (real and reactive). Besides their clear physical meaning, which makes easier the development and application of continuation methods for power systems analysis, the main advantage of some of the proposed parameters is that its not necessary to change the parameter in the vicinity of the MLP. Studies on the new parameterization schemes performed on the IEEE 118 buses system show that the ill-conditioning problems at and near the MLP are eliminated. So, the characteristics of the conventional Newtons method are not only preserved but also improved.

A geometric interpretation for transmission real losses minimization through the optimal power flow and its influence on voltage collapse

Abstract This work presents an approach for geometric solution of an optimal power flow (OPF) problem for a two bus system (a slack and a PV busses). Additionally, the geometric relationship between the losses minimization and the increase of the reactive margin and, therefore, the maximum loading point, is shown. The algebraic equations for the calculation of the Lagrange multipliers and for the minimum losses value are obtained. These equations are used to validate the results obtained using an OPF program.

Study of alternative schemes for the parameterization step of the continuation power flow method based on physical parameters, part I: Mathematical modeling

The conventional power flow method is considered to be inadequate to obtain the maximum loading point because of the singularity of Jacobian matrix. Continuation methods are efficient tools for solving this kind of problem since different parameterization schemes can be used to avoid such ill-conditioning problems. This paper presents the details of new schemes for the parameterization step of the continuation power flow method. The new parameterization options are based on physical parameters, namely, the total power losses (real and reactive), the power at the slack bus (real or reactive), the reactive power at generation buses, and transmission line power losses (real and reactive). The simulation results obtained with the new approach for the IEEE test systems (14, 30, 57, and 118 buses) are presented and discussed in the companion paper. The results show that the characteristics of the conventional method are not only preserved but also improved.

Esquemas alternativos para o passo de parametrização do método da continuação baseados em parâmetros físicos

The conventional load flow method is considered to be inadequate to obtain the maximum loading point (MLP) of power systems, due to the singularity of Jacobian matrix. Continuation methods are efficient tools for solving this kind of problem, since parameterizations techniques can be used to avoid such singularities. In this paper new options for the parameterization step are presented. It is shown that variables with clear physical meaning can be utilized to parameterize the power flow equations. The following variables have been tested: total real and reactive power losses, real and reactive power at the slack bus, reactive power at generator buses, and transmission line real and reactive power losses. The proposed parameterization schemes simplify the implementation of a continuation power flow, and make it easier for power engineers to understand its mathematical definition, since it uses physically meaningful parameters rather than purely mathematical and complex variables. Results obtained with the new parameterization techniques for the IEEE test systems (14, 30, 57 and 118 buses) show that the convergence characteristics of the conventional power flow method are improved at the MLP vicinity. In addition, it is shown that the proposed parameters can be switched during the tracing of the PV curve in order to efficiently determine all its points with few iterations. Several tests are carried out to compare the performance of the proposed parameterization schemes for the continuation load flow method.

An improved parameterization technique for the Continuation Power Flow

Continuation methods have been long used in P-V curve tracing due to their efficiency in the resolution of ill-conditioned cases, with close to singular Jacobian matrices, such as the maximum loading point of power systems. Several parameterization techniques have been proposed to avoid matrix singularity and successfully solve those cases. This paper presents a simple geometric parameterization technique to overcome the singularity of the Jacobian matrix by the addition of a line equations located at the plane determined by a bus voltage magnitude and the loading factor. This technique enlarges the set of voltage variables that can be used to whole P-V curve tracing, without ill-conditioning problems and no need of parameter changes. Simulation results, obtained for large realistic Brazilian and American power systems, show that the robustness and efficiency of the conventional power flow are not only preserved but also improved.