SOLUTION OF SWING EQUATION USING STEP BY STEP METHOD
The step by step method used for hand calculation is better and simpler than the methods used for the computers in this method of the hand calculation the angular position of the rotor is changed during the short interval of time and is computed using some assumptions and these assumptions are-:
- Accelerating power Pa which is doesnot change at the initial interval, which is the proceeding interval from the middle to middle of that interval.
- Throughout any interval angular velocity is constant at a value computed from the middle of the interval
But the above assumptions are not accurate because delta is changing continuously and both Pa and w are functions of delta. As the time interval is decreased the computed swing curve tends to accuracy.
SWING EQUATION SOLUTION USING MODIFIED EULER METHOD
Before we discuss the application of Euler’s method for solving the swing equations we should know the basic Euler’s method of numerical integration so the general form of the equation is –
Y’ = f (x,y) Y(xo)= yo
Where x is independent and y is dependent quantities whereas xo and yo
Is the initial value of x and y respective here the independent axis that is the x-axis is divided to intervals of length ‘h’ so that the discrete points on the independent axis will be xo, xo + h, xo + 2h, etc.
Our task is to calculate the values y1, y2, corresponding to the x co-ordinates after these values are calculated the curve representing the solution of differential equation given in equation can be plotted.
In this method the y1, y2, values are calculated in two steps predictor and corrector and then it is determined.
SWING EQUATION SOLUTION BY RANGE KUTTA METHOD
In this method we consider two equation –
And set the count k=0 and assume solution in terms of x1^0 and x2^0
QUESTIONS AND ANSWERS
- What are the advantages of the per unit system?
Ans- It yields important information about the relative magnitudes, identifies the error data.
- Why the transmission stability is lower that the steady state stability?
Ans- this is because the maximum power flow in transient stability is less that the maximum power flow in steady state stability.