Study On Small Signal Stability Of Time-delayed Power System

Time delays are often considered as the cause of system instability and oscillation.So it is very important to explore the dynamical behaviors in time-delay dynamicsystems. In this thesis, small signal stability of time-delayed power system are deeplystudied. Some issues are involoved, including but not limit, model improvement,eigenvalue locus tracing, dynmaics behaviour and bifurcation analysis. Main work ofthis thesis is as following:1. Two new models suitable for power system stability analysis with consideringtime delays are derived. They are constraint time-delayed ordinary differentialequation model (abbr. CTODE) and constraint time-delayed differential algebraicequation model (abbr. CTDAE). In these two models, dimension of the time-delayedequation is significantly reduced so as to speed up the calculation efficiency. Detailderivations to their nonlinear and incremental linear forms are given. And, some oftheir good features are discussed. A typical simple time-delayed dynamic system andsingle-machine-infinite-bus system are selected to validate the new models throughLyapunov-Krasovskii criterion. It is revealed that some unnecessary calculations inthe analysis can be avoided to achieve higher efficiency based on new models,especially when the dimension of time-delayed variables is far smaller than the one ofthe state variables.2. A prediction-correction based approach to trace the practical eigenvaluespectrum of power system with time delays is presented. System eigenvalues withouttime delay is first gotten. Time delays are then increased tardily to get the predictiveresult by the predicting process. And then, an optimal model is used as the predictor toget the final result. WSCC3-generator-9-bus system is used to validate the proposedmethod. It can be found that eigenvalue locus of the time-delayed power system canbe traced precisely. And, in the simulation, two new type bifurcations in the time-delayed system are found. They are oscillation disappearance bifurcation(ODB) andoscillation emergence bifurcation(OEB).3. Mechanism of ODB and OEB bifurcations are discussed and analyzed.Definitions of these two bifurcations are first given according to the change of systemeigenvalues. Then, an approach to determine the occurrence of OEB bifurcation indynamic systems with single time delay is given. In the derivation, information of thedisappearance and emergence of the real solution branches in the Lambert W functionis used. One-dimensional, two-deimensional time-delayed systems and WSCC3- generator-9-bus power system with single time delay are used to validate the givenapproach. It can be found that the given method can correctly determine the OEBbirurcation. Since OEB and ODB bifurcations have close relationship to theemergence and disappearance of system oscillation modes, study of this thesis ishelpful to power system stability analysis with time delays.