Studies Of Continuation Power Flow Theory And Its Expanded Applications

There exists a contradictory relationship between the economy of Power network operation and the power system security and stability. Overinvestment in the development of power network will lead to waste of money, on the other hand, the power system security and stability may be threatened due to underinvestment of network construction. For scientific and technological workers, it becomes the top priority to calculate and evaluate power network maximum transmission power, which is an important part of power system steady state voltage stability analysis. The power flow calculation is so powerfull that it could not be replaced for the analysis of power systems. It is an indispensable tool in modern power system analysis. However, Newton iteration method is needed in solving power flow problems due to the nonlinearity of the power flow equations. The iterative method has more stringent requirements in numerical conditions. Power flow iterative calculation may be difficult to or even impossible to converge in some special cases. Continuation algorithm is a large-scale convergence algorithm which is an important branch of the field of numerical analysis. Since the1990s, it is introduced in power flow calculation to solve above morbid numerical problem, resulting in the so-called continuation power flow. The continuation power flow equations are parametric equations, in which the load parameter is introduced. A predictor and corrector method is used to track the solution curve of the parametric equations. PV curves which describe the trend that load voltage changes due to the change of load power, as well as the critical point of steady state voltage stability, are obtained. The aim of this paper is to analyse and improve continuation method related problems in the power system analysis and present more practical solutions. The specific research works are as follows:(1) Perfecting the algorithm of continuation power flow:The principle and core thought of continuation method are summerized and discussed. From the aspects of numerical theory and performance, this paper analyses the character of the turning point of the continuation power flow solution curve and the reason why the computation of continuous power flow encounter convergence problem in iterative correction process when calculating close to the turning point. In order to improve the robustness of continuation power flow, a new approach is presented where the predictor tangent vector is normalized and its direction is checked. Then, based on the normalized predictor tangent vector, this paper presents an improved parameter selection strategy of local parameter method, which can reduce the possibility that local parameterization may be forced to convert local parameter. At the same time, in order to solve the problem that some initial parameters should be confirmed by testing computation in engineering applications, this paper advances an automatic variable step size controlling algorithm using correction iterative number of times as its main parameter. With the automacitc step size controlling algorithm, the step size increases automatically at the beginning which is benefit for the calculation speed and it decreases at the end automatically for the computation accuracy. Based on the improvement for the robustness and speed, the continuation power flow becomes more perfect and utility. Simulations of IEEE39buses system and Shandong Power Grid typical operation ways in the winter of2010verify the effectiveness of the improving method, and show good result.(2) Continuation power flow calculation considering change of transmission line resistance:In the conventional continuation power flow model, resistances of transmission lines are set to be invariable which do not change in the whole calculation process. It does not correspond to the real situation. The reason is that line resistance would be changed in terms of the temperature with the varying of the environment around and the power distribution. With this background, continuation power flow simulates a gradual varying process, in which the heat balance about line resistance, temperature and current must be considered to have practical significance. In order to analyze the influence on continuation power flow calculation by change of line resistance, this paper presents the electro-thermal power flow model and electro-thermal continuation power flow model in which the line resistance is considered as state variable of power grid. In the models, line resistances are calculated and corrected for the consideration of electro-thermal coupling. In the case studies on the2bus test system, the conventional continuation power flow and electro-thermal coupling continuation power flow are respectively for the calculation of PV curves and static voltage stability margin. The results show that it will produce some outstanding error when ignoring the electro-thermal coupling. In the case study on IEEE14bus system, the conventional continuation power flow and electro-thermal coupling continuation power flow are used respectively to analyze the power transfer limit where the system security constrain and static voltage stability constrain are both considered. The results show that the influence of electro-thermal coupling for the calculation is significant. Based on the above analysis, the electro-thermal coupling continuation power flow presented in this paper is in more accordance with the operation of the real power system, so it has higher application value and should be paid more attention to.(3) Complex utility of continuaton power flow and optimization method:The continuation power flow method and simulated annealing particle swarm optimization method are improved respectively in order to form a hybrid algorithm. A minimum load margin model on static voltage stability constraint is established and it is solved by the hybrid optimization algorithm. In the optimization model, the power increment direction is constrained by the extent of load power factor to have more practical significance. For continuation power flow calculation, based on the change of determinat of Jacobin matrix on PV-PQ converting, a fast and efficient method to identify limit induced bifurcation is presented. An improved method based on adaptive step control strategy is presented considering generator reactive power limit to improve the calculation accuracy of limit induced bifurcation point. The impact on load margin by reactive power device is taken into account and the node admittance maxtrix is corrected automatically. For particle swarm optimization, this paper adopts variable weight coefficient and variable learning factor strategies. Based on the included angle of vectors, a new criterion of precocious is presented. When the calculation is precocious, the particles vary in a certain probability conditions. The simulated annealing process is involved. All the improvements are beneficial to prevent falling into trap of local optimization. Above all, imporved continuation power flow is good at recongnition of bifurcations and consideration of reactive power equipment; improved particle swarm optimization method is good at goloble optimization and preventation of local optimization. With the programs in which multithreaded parallel technology is used, calculation results of IEEE5bus and IEEE30bus test system demonstrate the good effectiveness of the algorithm.(4) The continuation power flow is used in analysis of static voltage stability for a real power system:The aim, task, emphasis and difficulty for power system static voltage stability analysis are discussed. Based on the real data and operation model of Shandong power system, the power increment direction of continuation power flow is determined. For2010winter peak load mode of Shandong power system, the load margins of each area are calculated. The steady state voltage stability of Shandong power system is analyzed and evaluated for the power system planning and operation, meantime, the improved algorithm for continuation power flow method presented in this paper continuous are applied to practical project.