Newton-Raphson Power Flow Analysis Quiz

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Questions and Answers

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

  • 0.212
  • -0.236
  • 0.279
  • 0.0145 (correct)

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

  • -1.988
  • 0.279
  • 8.82
  • -0.233 (correct)

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

  • 0.8554 (correct)
  • 0.0190
  • -0.2
  • -0.236

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

<p>-1.986 (C)</p> Signup and view all the answers

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

<p>-0.233 (C)</p> Signup and view all the answers

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

<p>2.864 (B)</p> Signup and view all the answers

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

<p>-0.236 (B)</p> Signup and view all the answers

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

<p>0.212 (D)</p> Signup and view all the answers

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

<p>-0.236 (D)</p> Signup and view all the answers

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

<p>-0.233 (A)</p> Signup and view all the answers

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

<p>0.279 (C)</p> Signup and view all the answers

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

<p>-0.236 (D)</p> Signup and view all the answers

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

<p>-0.233 (C)</p> Signup and view all the answers

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

<p>0.8586 (C)</p> Signup and view all the answers

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

<p>0.8554 (A)</p> Signup and view all the answers

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Study Notes

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 = ?

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