The Numerical Integration Algorithm Of Transient Stability Calculation Based On Different Factorization Paths

Transient stability calculation is one of the most important issues in the power system analysis. The advanced technique such as dynamic security analysis online, emergency control of security and stability, intelligent scheduling require to conduct the transient stability simulation rapidly, accurately, credibly. Therefore, it is very necessary for us to improve the simulation speed.The main purpose of the paper is to decrease the calculation amount in the transient stability calculation process.The paper states the ideas as follows to achieve the goal:On one hand, optimizing the nodes ordering algorithm.First, the paper introduces several heuristic algorithms such as T-2, MD-ML, MD-A1, MD-MNP and states the theory of every heuristic algorithm from the aspect of graph theory and text the effectiveness on five different classical power systems. Then, because the heuristic algorithms search the optimization step by step, they can’t get the globally optimal solution. To overcome this weakness of heuristic algorithms, the paper provides Particle Swarm Optimization (which is shorted as PSO) to achieve the globally optimal solution.At last, the paper puts forward an algorithm named as MD-MNP-SG. In the process of transient stability calculation, the order of non-zero elements in the sparse vector are the same as the wanted solutions in the solution vector. To take advantage of this characteristic, the algorithm here aims to arrange those non-zero elements close to the root node so as to shorten the average path length of those non-zero elements. The paper provides the algorithm flow chart and simulation results.On the other hand, when solving the network equation YV=I, the iterative process of transient stability calculation would be different under different load models. The paper focuses on the motor model. Because the dummy current of motors keeps the same during one integration step, the node voltage of some motors will also remain the same during this integration step. Therefore, it’s unnecessary to solve these node voltage.Given this point, the paper comes up with an algorithm which sets three graph paths for the back substitution process to avoid redundant calculation amount.