Loading Point Of Power Systems Research Articles

An Efficient Geometric Parametrization Technique for the Continuation Power Flow through the Tangent Predictor

This paper presents a new parameterization scheme to the continuation power flow that allows the complete tracing of P-V curves and the computation of the maximum loading point of power system, without ill-conditioning problems of the Jacobian matrix and without the exchange of parameter. The objective is to present the technique in a clear and didactic way.

Fluxo de carga continuado utilizando estratégia de parametrização geométrica baseada em parâmetros físicos

O fluxo de carga convencional é considerado inadequado para a obtenção do ponto de máximo carregamento devido à singularidade da matriz Jacobiana. Os métodos da continuação são ferramentas eficientes para a solução deste tipo de problema, visto que diferentes parametrizações são utilizadas para evitar a singularidade da matriz. Neste trabalho apresenta-se uma técnica de parametrização geométrica que possibilita o traçado completo das curvas P-V sem os problemas de mal-condicionamento. A técnica proposta associa a robustez com a simplicidade e a facilidade de compreensão. A singularidade da matriz Jacobiana é eliminada pela adição da equação de uma reta que passa por um ponto no plano formado pelas variáveis perdas de potência ativa total e o fator de carregamento, dois parâmetros físicos de fácil compreensão. A técnica, aplicada aos sistemas do IEEE, mostra que as características do fluxo de carga são melhoradas.

An efficient geometric parameterization technique for the continuation power flow

Continuation methods have been shown as efficient tools for solving ill-conditioned cases, with close to singular Jacobian matrices, such as the maximum loading point of power systems. Some parameterization techniques have been proposed to avoid matrix singularity and successfully solve those cases. This paper presents a new geometric parameterization scheme that allows the complete tracing of the P– V curves without ill-conditioning problems. The proposed technique associates robustness to simplicity and, it is of easy understanding. The Jacobian matrix singularity is avoided by the addition of a line equation, which passes through a point in the plane determined by the total real power losses and loading factor. These two parameters have clear physical meaning. The application of this new technique to the IEEE systems (14, 30, 57, 118 and 300 buses) shows that the best characteristics of the conventional Newton's method are not only preserved but also improved.

Parameterized fast decoupled power flow methods for obtaining the maximum loading point of power systems: Part I. Mathematical modeling

The conventional Newton and fast decoupled power flow (FDPF) methods have been considered inadequate to obtain the maximum loading point of power systems due to ill-conditioning problems at and near this critical point. It is well known that the PV and Q– θ decoupling assumptions of the fast decoupled power flow formulation no longer hold in the vicinity of the critical point. Moreover, the Jacobian matrix of the Newton method becomes singular at this point. However, the maximum loading point can be efficiently computed through parameterization techniques of continuation methods. In this paper it is shown that by using either θ or V as a parameter, the new fast decoupled power flow versions (XB and BX) become adequate for the computation of the maximum loading point only with a few small modifications. The possible use of reactive power injection in a selected PV bus ( Q PV) as continuation parameter ( μ) for the computation of the maximum loading point is also shown. A trivial secant predictor, the modified zero-order polynomial which uses the current solution and a fixed increment in the parameter ( V, θ, or μ) as an estimate for the next solution, is used in predictor step. 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 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 enhanced and the region of convergence around the singular solution is enlarged. In addition, it is shown that parameters can be switched during the tracing process in order to efficiently determine all the PV curve points with few iterations.

Parameterized fast decoupled power flow methods for obtaining the maximum loading point of power systems: Part II. Performance evaluation

The parameterized fast decoupled power flow (PFDPF), versions XB and BX, using either θ or V as a parameter have been proposed by the authors in Part I of this paper. The use of reactive power injection of a selected PV bus ( Q PV ) as the continuation parameter for the computation of the maximum loading point (MLP) was also investigated. In this paper, the proposed versions obtained only with small modifications of the conventional one are used for the computation of the MLP of IEEE test systems (14, 30, 57 and 118 buses). 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 with the new approaches are presented and discussed. The results show that the characteristics of the conventional FDPF method are enhanced and the region of convergence around the singular solution is enlarged. In addition, it is shown that these versions can be switched during the tracing process in order to efficiently determine all the PV curve points with few iterations. A trivial secant predictor, the modified zero-order polynomial, which uses the current solution and a fixed increment in the parameter ( V, θ, or μ) as an estimate for the next solution, is used for the predictor step.

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.

A rapid solution for the maximum loading point of a power system

AbstractThis paper presents a new solution method for computing the maximum loading point of a bulk power system under the condition where the loads of the nodes can be parameterized by a scalar which is the loading level of the system.A special loading model, in which the loading level of the system depends on the voltage magnitude of a loading node, is adopted for the purpose of releasing the load‐flow computation from the ill‐condition near and at the maximum loading point. The loading level of the system is unknown in the aforementioned loading model. The maximum loading point is obtained by adjusting the operating parameter so as to achieve the maximum loading.The operating parameter is adjusted in the converging process of the Newton‐Raphson iterative computation. The adjustment is computed based on the least squares estimation using the data set which is obtained from its own iteration process.It is shown in numerical examples that the proposed method is satisfactorily rapid, stable, and accurate.