Development Of Structure-Induced Bifurcation And Advanced Continuation Power Flow And Its Applications On Voltage Stability Analysis

A peculiar bifurcation, structure-induced bifurcation in large-scale power systems is studied and illustrated in this paper. Structure-induced bifurcation is different from traditional bifurcations such as saddle-node bifurcations and Hopf bifurcations, in which one of the system eigenvalues crosses the imaginary axis as parameters vary. On the other hand, structure-induced bifurcation in power systems occurs while the real parts of all of its corresponding eigenvalues remain negative. Physically speaking, a structure-induced bifurcation in power system occurs due to load increases (parameter variation); causing one or more generators reach their reactive power (also termed Q) limits which in turns changes the underlying power flow equations (i.e. the vector field is altered).Continuation power flow is a powerful tool to simulate power system steady-state stationary behaviors with respect to a given power injection variation scenario. Power injection variations include both load variation and real generation scheduling in power systems. This tool has been implemented in several commercial packages for generating P-V curves. Continuation power flow methods have been studied extensively in power system community and have their theoretical roots in algebraic topology and differential topology. From system analysis viewpoint, continuation power flow methods have been applied to power system voltage stability analysis and available power transfer analysis. Improvements of continuation power flow methods can have significant impacts on power system analysis and control.An advanced continuation power flow with nonlinear predictor and hybrid correct is proposed in this dissertation. Based on the advanced continuation method, impacts of nonlinear load variation directions and composite load model on voltage stability are analyzed. Structure-induced bifurcation which induced voltage immediate instability by reactive power limit of generation is studied. The applicability of look-ahead load margin with composite load model and generation reactive power limit is testified.The main contents and contributions of this dissertation are summarized as follows:(1) A structure-induced bifurcation, a local bifurcation of non-smooth nonlinear systems, is studied and illustrated on electric power system models. Physically speaking, a structure-induced bifurcation in power system occurs due to load increases and when one or more generators reach their reactive power limits. The consequence of structure-induced bifurcation is an immediate instability induced by generator reactive power limits. It is numerically shown that structure-induced bifurcation can occur at small power systems and large-scale power systems. A practical power system, a 5500-dimension power system is used to illustrate that structure-induced bifurcation is quite common in power systems. Furthermore, it is shown that structure-induced bifurcation is robust to a local open bifurcation set. In other words, structure-induced bifurcation in power system persists under different directions of load increases.(2) The power injection region for unconstrained power flow equations can be quasi-convex, while the region is nonconvex when generation reactive power limit is considered. Traditionally, the bifurcation boundary is associated with singularity of the power flow Jacobian matrix, and it separates the areas where the specified nodal powers are consistent and inconsistent. This boundary can be associated with the saddle node bifurcations and under certain conditions voltage collapse boundaries. While we know that structure-induced bifurcation may be encountered when generation reactive power limit is considered. Then the bifurcation boundary can include saddle node bifurcation or structure-induced bifurcation. The power injection region is the region enclosed by the bifurcation boundary. That is, the power flow solution is feasible when the power injections are contained by the bifurcation boundary. In this paper, the power injection region is studied in both small power systems and large-scale power systems. The nonconvexity of power injection region when Q limit is considered is a challenge to the application of convex optimization in power system programming problem.(3) While continuation power flow methods have been implemented in several commercial packages, they may be still too slow for on-line applications. This dissertation aims to improve continuation power flow methods mainly on their speed and to a less extent, on its reliability. Nonlinear predictors are developed based on the Polynomial interpolations. Our numerical studies show that Continuation power flow with the proposed nonlinear predictors can be much faster than that with traditional linear predictors such as tangent or secant predictors. Of the nonlinear predictors, 2nd-order polynomial approximation based and 3rd-order based nonlinear predictors show their superior performance in speed. Continuation power flow with 2nd-order nonlinear predictors is generally slightly faster than that with 3rd-order nonlinear predictors. In addition, a hybrid corrector is developed and incorporated into continuation power flow. It is numerically shown on several test systems ranging from 118-bus to 1648-bus that continuation power flow with the proposed hybrid corrector can be much faster than that with traditional correctors such as Newton method and the Fast decoupled method. Finally, an improved continuation power flow with the developed nonlinear predictor and hybrid corrector is presented and evaluated.(4) Continuation Power Flow with nonlinear load variation and generation re-dispatch patterns is developed in this dissertation. The power injection variations are determined by both load variation and real generation dispatch in power systems. To model power injection variations, a piecewise linear model in the power injection space is used to model nonlinear load variations while the economic dispatch or other generation scheduling schemes is applied to determine the participation factor of each generator. The newly-improved continuation tool is applied to test the impacts of nonlinear power injection variations on load margin. Our numerical studies indicate that power injection directions can significantly affect the load margin to nose point, and the difference between uniform power injection direction and nonlinear power injection variations can be significantly different.(5) While it has been widely accepted that the constant P-Q load model leads to conservative load margin calculation of voltage stability, lately the studies show that induction motor loads can lead to an even more conservative load margin calculation. Another load margin index caused by induction motor load is proposed in this dissertation. The impacts of composite load model (the composite of ZIP and induction motor load models) on the load margin of voltage stability are analyzed. In order to take into consideration the composite load model, a new set of parameterized power flow equations is derived. A procedure of integrating composite load model is integrated into continuation power flow to model the load increase. Numerical studies indicate that the load margin with composite load model can be significantly different with that with constant P-Q load model. These numerical results are contradicted to the belief that constant P-Q leads to conservative load margin calculation of voltage stability.(6) The impacts of generation reactive power limits and composite load model on critical bus and reactive power margin are studied in this thesis. The critical bus can be identified by voltage change method or sensitivity method. Apply a fictitious synchronous condenser at the critical bus and control the voltage at a certain range, the V-Q curve can be obtained by plotting the voltage magnitude at the critical bus and the corresponding reactive power output of the synchronous condenser. The reactive power margin is defined as the negative of the value of the synchronous condenser output at the minimum point of the V-Q curve of the base case. The numerical studies show that the composite load model and generation reactive power limits have significantly impacts on the V-Q curve and reactive power margin.(7) Traditionally, look-ahead load margin is applied to contingency screening and ranking for on-line voltage security assessment due to its speediness. In this dissertation, the robustness and speed of look-ahead method is testified when composite load model and generation reactive power limit are considered. The reactive power margin of generation is used to predict whether the bifurcation type is saddle node bifurcation or structure-induced bifurcation. The numerical studies show that the computation time can be significantly decreased with look-ahead step length control method.(8) The multi-stage method to analysis the contingency screening and ranking are advised in this paper. In order to rapidly and accurately screen and rank contingency, a lot of fast algorithms such as reactive power loss and sensitivity method, are studied. An outage of either transmission line or transformer changes the pattern of the power flow in the network. A large amount of power might be routed through a sub section of the network resulting in larger branch angles and thereby producing more reactive power losses. This action leads to shortage of reactive power in the network leading to voltage collapse. But contingency ranking based on reactive power loss method can not reflect the load increasing information. The aim of sensitivity method is to compute a single nose curve and associated sensitivities to use these to quickly estimate the change in the loading margin to voltage collapse for any line outage. Compared with reactive power loss method, contingency ranking based on sensitivity method consume less computation time, while the sensitivity method can not obtain the severe contingency that the immediately voltage collapse once contingency is encountered. In this paper, multi-stage method is proposed to screen and rank contingency in voltage stability analysis. The first stage is advised to use the hybrid method of sensitivity method and reactive power loss method, the second stage is suggested to use look-ahead load margin method, the exact continuation powr flow method is proposed to rank contingency in the last stage.