A new method is presented for calculating the nose curves and critical loading conditions of power systems. The nose curve (PV curve), which donates the relationship between total load and system voltages, is calculated by a new approach based on the homotopy continuation method. The critical loading condition, which might be called the bifurcation point, is also calculated precisely as the final point of the nose curve. This method does not require an exhausting cut-and-try process or a rough-approximation process. It is based on the conventional Newton-Raphson load flow calculation, but it overcomes the numerical difficulties associated with the singularity of the Jacobian matrix. The results of applying the proposed method to the IEEE 118-bus system and to other large practical systems (e.g., a 496-bus system) verify its robustness and feasibility. >

Calculation of critical loading condition with nose curve using homotopy continuation method

A knowledge of the structure of the boundary of solutions of the power flow problem is important when analyzing the robustness of operating points. This paper proposes a predictor-corrector technique to assist in exploring that structure. Points on the solution boundary satisfy the power flow equations together with an equation which forces the power flow Jacobian to be singular. Curves of such points result from freeing two parameters of the system. The proposed technique follows those curves. A simple example is used to illustrate the complex nature of the power flow solution space.

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Exploring the Power Flow Solution Space Boundary

This paper provides a comprehensive list of books, reports, workshops and technical papers related to voltage stability and security

Bibliography on voltage stability

The authors present preliminary results in a computer program aimed at energy function analysis of transient behavior of power systems with nonlinear loads. The model, which preserves the network structure, is of a differential-algebraic type. This introduces some new analytical issues, but the concepts permit the establishment of a connection between transient (angle) stability, multiple stable equilibria, and voltage behavior. A practical method for determining and classifying the equilibrium points of the model is developed. >

Energy functions, transient stability and voltage behaviour in power systems with nonlinear loads

As systems become more heavily loaded, nonlinearities play an increasingly important role in power system behavior. Modeling must accurately reflect component and system response. Analysis tools should combine to work reliably even under extreme system conditions, providing accurate predictions of power system behavior. The paper considers some power system modeling issues and presents an overview of the source of nonlinearities in power systems. It then considers industry accepted analysis techniques, as well as those techniques that are more research orientated. The influence of nonlinearities on these tools is explored.

Analysis tools for power systems-contending with nonlinearities

The global response of a power system to variations in the node constraints is considered. The relation of specific system variables to independent node parameters is calculated using a numerical technique which provides a generalization of the elementary power circle diagram. Curves which show system performance during disturbances, tradeoffs between design parameters, voltage stability limits and multiple power flow solutions are produced. The theory of the method is presented through geometrical concepts, and its application is illustrated with several examples.

G. B. Price

Papers

A Generalized Circle Diagram Approach For Global Analysis Of Transmission System Performance