Program Design and Application of Calculating Generator Rocking Curve by Improved Euler Method

The sway of the generator (<5-0 curve is one of the important basis for analyzing the transient stability of the power system and the time to cut the fault limit. The essence of the rocking curve is to solve the rotor motion equation of the generator, and improve the Euler The method is a rotor motion equation solving method that is very suitable for computer operations.

2 Improve the principle of Euler's method The numerical solution of the initial value problem of ordinary differential equations used in bookmark2 computer is that for the first-order differential equations = not directly to find the analytical solution, but from the known initial value, discretely Finding the corresponding time point by point is generally taken as an equal step, that is, =h 2-/,=h... Of course, the step size can also be changed. When the step size is chosen enough, the calculation results are accurate enough. If the calculation method used is calculated by 知, and then X2 is calculated by X, the function value of each time is calculated recursively, which is called single-step method. The improved Euler method is a single-step Euler method. Its specific steps are as follows: (assuming it is known. X, seeking .v*+,)) The rate of change of X when calculating. v*=) It is assumed that T increases by the rate of change L in the interval t4/+|, and is 11.1, +|. 1: preliminary estimate i ten value (3) according to the preliminary estimate; when calculating / * + :: c change rate (4); +1 and the average to calculate ~ + |. Further estimate of t (5) Calculate r*+ according to the rate of change (6) of the calculation and the average of L+I(l), and further estimate of x is calculated by this rule until two estimates before and after The value satisfies the error requirement.

In practical applications, the step size should be selected according to the objective number of the computer's effective number of bits, calculation speed, etc., generally in the stable calculation / / take about 0.01s.

3 Using the improved Euler method to obtain a simple power system shakebook3 For a simple power system, the generator rotor motion equation is a system of equations containing two first-order differential equations. Just solve the calculation for K at the same time. After the short-circuit fault occurs, the equation of motion of the generator rotor is: the maximum power of the generator at fault = l; 5 = < 50, the rotor motion equation after the short-circuit fault is the maximum power of the generator after the fault is removed: Starting condition: / given cut-off time, A, % is the J sum corresponding to the time L. A program flow chart for calculating a simple system rocking curve using the modified Euler method.

4J——/Curve Application in System Transient Stability Analysis When the above equations (1) are solved to obtain 5——/curves, the limit cut-off time corresponding to the cut-off angle can be found by the curve. If you know the fault removal time to judge the stability of the system, you can solve the equation (1) from time to time, and then solve the equation (2) to get the J——/curve at L time, and then pass J through time. The change of f judges the transient stability of the system.

In general, the system is stable if it is not exceeded during the calculation of a few seconds, and the amplitude is getting smaller and smaller, or if the system is calculated without the damping, the system is stable.

For example, a power system (assuming no damping) stable operation = 8. After a sudden short circuit, Aw = standard value) can be obtained by the above method design procedure to obtain five different cut-off time corresponding to the 5- / curve. The partial program (VB) code is as follows: the definition and declaration of variables and constants are slightly. The rate of change of A at the beginning of a certain period of time Q01=V00 is calculated according to the normal operation mode: judge whether the system has disturbance at this time, and select according to the disturbance condition. Power characteristic curve (Pi for short circuit, Pm after cutting) Whether the printing is greater than i. The average rate of change of the system swing curve program S w is improved by the modified Euler method. Q111 *h The value at the end of this period is used as the next period. The calculated initial value W00=W1Q00=Q1 ​​can be used to intuitively judge the transient stability of the system: when the fault is 0.2s, the corresponding J is rapidly increased by more than 180, and the system must be unstable: the other two curves are basically within 5s. It is a constant amplitude oscillation. Because the solution curve is under the condition that the system is undamped, and the actual running system has damping, the actual curve amplitude will be smaller and smaller, and the system is transiently stable.

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