Hopf Bifurcation In Power System Research Articles

Variable step-size prediction–correction homotopy method for tracking high-dimension Hopf bifurcations

A new algorithm named prediction–correction homotopy continuation method (PC-HCM) is proposed to track Hopf bifurcations in power systems. To overcome the calculation burden of conventional method, the secant prediction method is proposed to track Hopf bifurcation homotopy path. And the automatic step-size control strategy is produced to implement the step-by-step correction, which ensures the calculation accuracy and speed. Simulation results with WSCC 3-machine 9-bus system and NewEngland 39-bus system indicate that the proposed PC-HCM can trace Hopf bifurcations quickly and accurately.

New technique for computation of closest Hopf bifurcation point using real-coded genetic algorithm

Hopf bifurcation in power systems leads to oscillatory instability, and it is desirable to operate the system with sufficiently large loading margin to Hopf bifurcation. A new technique to determine the shortest distance to Hopf bifurcation is developed. The problem of determining the closest Hopf bifurcation point is formulated as an optimisation problem and solved using real-coded genetic algorithm. The advantage of this method is that it is capable of handling various operational constraints and can determine the closest Hopf bifurcation point accurately even if the hypersurface is not smooth. The proposed approach has been applied on two-area and IEEE 14-bus test systems. The details of implementation and simulation results are presented. The effect of load modelling on closest Hopf bifurcation point is also investigated for various loading patterns.

Some Design and Simulation of Sliding Mode Variable Structure Control for Hopf Bifurcation in Power Systems

In power systems, the Hopf bifurcation (HB) can occur before the saddle-node bifurcation (SNB) and be-comes one of main reasons of voltage instability and collapse, so the bifurcation control for HB has impor-tant significance in improving power system voltage stability. In this paper, the numerical bifurcation analy-sis software MATCONT was used to study bifurcation behavior of a single-machine dynamic-load (SMDL) system with SVC, and the simulation analysis results show that a unstable Hopf bifurcation (UHB) point oc-curring before SNB point and engendering potential harm to voltage stability. To delay or eliminate the UHB phenomenon and enhance voltage stability of the SMDL system with SVC, we designed a sliding mode variable structure controller. The switching function and control variables of the controller are clearly de-scribed and the derivations are directly provided in detail in this paper. The MATLAB simulation results prove that the designed controller can eliminate the UHB point effectively and ensure safe and stable opera-tion of the system.

Control of Hopf Bifurcation in Power System

In power system, when the overload of large-scale power grid results in serious disaster, the nonlinear dynamic bifurcation is obvious. It will be effective to delay the occurrence of bifurcation through the bifurcation control method, so workers have enough time to take protective measures. We can also design an appropriate controller to prevent these kinds of dangerous disaster effectively. This paper outlines a number of common bifurcation control method, and use one of these method to design a bifurcation controller so as to control the hopf bifurcation in power system and make a Simulation on it.

Reliable prediction of Hopf bifurcation in power systems

In this study, a new index for detection and prediction of oscillatory instabilities associated with HOPF bifurcation (HB) in power systems is proposed. Conventional indices could just predict HB in the heavy load conditions. The proposed index has a wider linear range and therefore prediction of system behavior at a wider range of load changes (even in lightly load condition) is provided. Consequently, the power system operators have more time to make the proper decisions to prevent HB. Conventional indices use critical eigenvalue pair of the state matrix to predict HB. This pair possesses biggest real parts among all eigenvalue pairs. However, sometimes this pair might not reach the imaginary axis before other eigenvalues. Therefore, they are not representative for HB eigenvalues which can lead to HB (This pair of eigenvalues could not be considered as HB eigenvalues). In this study, proposed index uses HB eigenvalue pair of state matrix to predict HB and two criteria are used to recognize HB eigenvalue pair. The first criterion is based on the proximity of the pairs of complex eigenvalue to the imaginary axis and the second criterion is based on the speed and the direction of the eigenvalues’ movement towards the imaginary axis. Also, in this study, Matrix Reciprocal Condition Number Estimate (MRCNE) instead of minimum singular value decomposition is used to determine proximity of matrix to singularity. This estimation causes faster calculation without missing considerable accuracy. In order to demonstrate the effectiveness and accuracy of the proposed index, the new method is tested on the IEEE-14 bus and WSCC-9 bus test systems and results are presented. Results indicate that the proposed index has wider linear range and could predict HB in lower load level.

WAMS-based monitoring and control of Hopf bifurcations in multi-machine power systems

A method is proposed to monitor and control Hopf bifurcations in multi-machine power systems using the information from wide area measurement systems (WAMSs). The power method (PM) is adopted to compute the pair of conjugate eigenvalues with the algebraically largest real part and the corresponding eigenvectors of the Jacobian matrix of a power system. The distance between the current equilibrium point and the Hopf bifurcation set can be monitored dynamically by computing the pair of conjugate eigenvalues. When the current equilibrium point is close to the Hopf bifurcation set, the approximate normal vector to the Hopf bifurcation set is computed and used as a direction to regulate control parameters to avoid a Hopf bifurcation in the power system described by differential algebraic equations (DAEs). The validity of the proposed method is demonstrated by regulating the reactive power loads in a 14-bus power system.

Avoiding Hopf Bifurcations in Power Systems via Set-Points Tuning

This paper presents a methodology to control Hopf bifurcations in power systems based on several control actions, as reactive power compensation, LTC switching, load shedding, and adjustment of set-point values of automatic voltage regulators and governors. This approach is suited to large power systems since it includes a detailed system modeling, where the bifurcation diagrams are obtained directly from the DAE representation. Results are presented for two systems: the New England test system and the Southern Brazil power system.

Degenerate Hopf bifurcations in power systems

The occurrence of degenerate Hopf bifurcations in power systems is considered and this phenomenon is explored analytically using the Lyapunov-Schmidt reduction method and by simulation. A qualitative method that uses system trajectory data to classify the type of degenerate Hopf bifurcation is proposed. >