ECE576_Spring2014_Lect20

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Read Chapter 7
Homework 6 is due on Tuesday April 15

Simultaneous Implicit

The other major solution approach is the simultaneous implicit in

Simultaneous Implicit

Recalling the first lecture, we covered two common implicit integration

Nonlinear Trapezoidal

We can use Newton's method to solve with the trapezoidal
We

Nonlinear Trapezoidal using Newton's Method

The full solution would be at each time

Infinite Bus GENCLS Implicit Solution

Assume a solid three phase fault is

Infinite Bus GENCLS Implicit Solution

The initial conditions are
Let Δt =

Infinite Bus GENCLS Implicit Solution

Then calculate the initial mismatch
With x(0.02)(0) =

Infinite Bus GENCLS Implicit Solution

Repeating for the next iteration
Hence we have

Infinite Bus GENCLS Implicit Solution

Iteration continues until t = Tclear, assumed

Infinite Bus GENCLS Implicit Solution

With the change in f(x) the Jacobian

Computational Considerations

As presented for a large system most of the computation

Two Bus Results

The below graph shows the generator angle for varying

Adding the Algebraic Constraints

Since the classical model can be formulated with

Adding the Algebraic Constraints

The network equations are as before

Classical Model Coupling of x and y

In the simultaneous implicit method

Classical Model Coupling of x and y

The in the state equations

Variables and Mismatch Equations

In solving the Newton algorithm the variables now

Jacobian Matrix

Since the h(x,y) and g(x,y) are coupled, the Jacobian is
With

Jacobian Matrix Entries

The dependence of the Norton current injections on δ

Jacobian Matrix Entries

The dependence of the swing equation on the generator

Two Bus, Two Gen GENCLS Example

We'll reconsider the two bus, two

Two Bus, Two Gen GENCLS Example

Initial terminal voltages are

Two Bus, Two Gen Initial Jacobian

Results Comparison

The below graph compares the angle for the generator at

Four Bus Comparison