| Power flow computation is a fundamental tool in power system analysis.However, power grids are still fast developing and becoming much larger in scale andcomplexity, which brings in a great pressure on the traditional power flow calculation.In particular, behaviors of the system become more and more nonlinear (especially inheavy loading conditions), resulting in more frequent divergence for conventionalpower flow methods. Therefore, development of robust yet efficient power flowmethods to overcome these issues becomes a necessity. To this end, this dissertationinvestigates some novel power flow methods with solid theoretical foundations ofnonlinear dynamical systems. The main works and contributions are summarized asfollows:(1) The properties of the convergence regions of Newton power flow method arefirst studied in the variable state space. Convergence regions of Newton power flowmethod are numerically characterized, along with analysis regarding their propertieson base-case condition and varied loading conditions. These results reveal the root ofsensitiveness to initial points and loading conditions of the conventional Newtonpower flow method.(2) A dynamical trajectory-based power flow method is introduced to solve thepower flow problem. The basic idea of the proposed method is to convert the powerflow problem into the solution problem of a properly constructed dynamic system;accordingly, computing a power flow solution corresponds to computing a stableequilibrium point (SEP) in the dynamical system. Therefore, when an SEP is obtainedby tracing the trajectory of the dynamic system, a power flow solution is found, too.Firstly, the basic idea of the proposed method is introduced and its features andadvantages are analyzed. In the following, several typical dynamic systems arestudied in terms of two aspects:1) their applicability to different power flow problems,and2) the relationships between their SEPs and power flow solutions. Afterwards, theproposed method is applied to the multiple-solution problem and the detailedapproach is investigated. Numerical results show that the proposed method can solvedivergent cases of Newton method because of bad initialization or the ill-conditioning,which reveals the effectiveness and robustness of the proposed method. (3) The convergence region of the dynamical trajectory-based power flow methodis in essence the stability region of the constructed dynamical system. The stabilityregions of several typical dynamical systems are numerically characterized indifferent loading conditions. It is revealed that proposed method possesses a near-byproperty, and the convergence of the proposed method is insensitive to initial pointsand loading conditions, given an appropriate formulated dynamical system. Beingsuch a dynamical system, the quotient gradient system (QGS) formulation is provedto satisfy the theorem of characterization of stability boundaries. Based on this, asystematic approach is developed to characterize the stability boundary of QGS.(4) A dynamical Trajectory-based Unified power flow method, namely the TJUmethod for short, is proposed by uniquely combining static method and dynamicmethods. In the methodology aspect, the proposed method consists of three majorstages: the exact trajectory stage, the inexact trajectory stage and the fast approachingstage. Based on this, two integral schemes are designed according to the integrationdegree of static method and dynamic method. Realizations of the TJU power flowmethod using the SDF (Simple Defined Formulation) and QGS formulations aredesigned, respectively. TJU method combines the advantages of static method anddynamic method, such as good convergence property, near-by property, robust andfast computation speed.(5) In the algorithm aspect of TJU method, firstly, the principle for choosing thestatic method and dynamic method is investigated. In a typical construction, theNewton method and the Pseudo-Transient method are chosen as the static method anddynamic method, respectively. Subsequently, according to the employed integralscheme, the TJU basic power flow method and the TJU enhanced power flow methodare proposed. Finally, some factors to affect computational speed in TJU power flowmethod are analyzed using numerical simulations, which may lead to guidelines forselecting parameters. Numerical results show that TJU power flow method cansuccessfully compute power flow solutions for improperly initialized orill-conditioned cases, for which Newton method will diverge. In addition, resultsshow that the TJU method has a good convergence property and is computationallyefficient, which suggests its applicability to large-scale power systems. |
