Newton-Raphson Power Flow Analysis Quiz

What is the value of x(3) according to the given calculations?

What is the value of f(x) at x(2)?

What does V2 equal to, according to the given calculations?

What is the value of J(x) at x(1)?

What is the result of 0.9(10sin(-0.2)) + 2.0?

According to the given calculations, what does 0.9(10sin(-0.2)) + 2.0 equal to?

What is the value of J(x) at x(2) based on the given equations?

What is the result of 10sin(-0.2) according to the given calculations?

Solve for x(1) in the given equations: 2.0 / 1.0 = x - (10sin(-0.2)). What is the value of x(1)?

According to the given calculations, what does 10sin(-0.2) - 1.788 equal to?

What is the result of $f(x(0))$ based on the given equations?

What is the value of $J(x(2))$ according to the given equations?

According to the given calculations, what does $0.9(10sin(-0.2)) + 2.0$ equal to?

What is the value of $x(1)$ based on the given equations?

What does $V2$ equal to, according to the given calculations?

Power System Dynamics and Stability

The power system dynamics and stability analysis is performed on a two-bus system with a slack bus (Bus 1) and a load bus (Bus 2).

Two Bus Newton-Raphson Example

The two-bus power system has a line impedance of Z = 0.1j and a base power of SBase = 100 MVA.
Bus 1 has a voltage magnitude and angle of 1.000 pu, and a real power and reactive power of 200 MW and 100 MVR, respectively.
The unknown variables are the voltage magnitude and angle at Bus 2, which are represented by x = [θ2, V2].

Power Balance Equations

The general power balance equations for the two-bus system are:
Real power balance: ∑n Vk (Gik cosθik + Bik sinθik) - PGi + PDi = 0
Reactive power balance: ∑n Vk (Gik sinθik - Bik cosθik) - QGi + QDi = 0
For Bus 2, the power balance equations are:
Real power balance: V2 V1 (10sinθ2) + 2.0 = 0
Reactive power balance: V2 V1 (-10cosθ2) + V2 (10) + 1.0 = 0

Power Flow Analysis

The power flow equations are rewritten in terms of the unknown variables x = [θ2, V2]:
P2(x) + 2.0 = V2 (10sinθ2) + 2.0
Q2(x) + 1.0 = V2 (-10cosθ2) + V2 (10) + 1.0
The power flow Jacobian is calculated as:
J(x) = [[∂P2/∂θ2, ∂P2/∂V2], [∂Q2/∂θ2, ∂Q2/∂V2]]

Jacobian Matrix

The Jacobian matrix is:
J(x) = [[10 V2 cosθ2, 10 V2 sinθ2], [10 V2 sinθ2, -10 V2 cosθ2 + 20 V2]]

First Iteration

The initial guess for x(0) is [θ2(0), V2(0)] = [0, 1].
The power flow equations are calculated using the initial guess:
V2(0) (10sinθ2(0)) + 2.0 = ?
V2(0) (-10cosθ2(0)) + V2(0) (10) + 1.0 = ?

Test your knowledge of power system dynamics and stability through a two bus Newton-Raphson power flow analysis example. Determine the voltage magnitude and angle at bus two based on given parameters and Ybus matrix.