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Questions and Answers
What is the value of $f(x(3))$?
What is the value of $f(x(3))$?
- 0.0145
- -0.236
- 0.0000906 (correct)
- 0.8554
What does $J(x(1))$ equal to?
What does $J(x(1))$ equal to?
- -1.788
- 0.212
- 8.199 (correct)
- -1.986
What is the result of $2.0 - 0.2$?
What is the result of $2.0 - 0.2$?
- 0.0145
- 0.0000906
- 0.8554
- -0.236 (correct)
What is the value of $10sin(-0.2)$?
What is the value of $10sin(-0.2)$?
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What is $f(x(2))$ equal to?
What is $f(x(2))$ equal to?
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In the given text, what is the value of $V(0)$?
In the given text, what is the value of $V(0)$?
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What is the result of $10sin(-0.2)$ in the given text?
What is the result of $10sin(-0.2)$ in the given text?
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What does $J(x(2))$ equal to in the given text?
What does $J(x(2))$ equal to in the given text?
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What is the value of $f(x(0))$ based on the given text?
What is the value of $f(x(0))$ based on the given text?
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According to the given text, what is the value of $x(3)$?
According to the given text, what is the value of $x(3)$?
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Study Notes
Two Bus Power System Example
- The two-bus power system consists of bus one (slack) and bus two (load) with a line impedance of 0.1j.
- Bus one has a voltage of 1.000 pu, and bus two has a load of 200 MW and 100 MVAR.
- The Y-bus matrix is given as:
[ -j10 j10 ]
[ j10 -j10 ]
Power Balance Equations
- The general power balance equations are:
- ∑[Vi Vk (Gik cosθik + Bik sinθik)] - PGi + PDi = 0
- ∑[Vi Vk (Gik sinθik - Bik cosθik)] - QGi + QDi = 0
- For bus two, the power balance equations are:
- V2 V1 (10sinθ2) + 2.0 = 0
- V2 V1 (-10cosθ2) + V2 (10) + 1.0 = 0
Jacobian Matrix
- The power flow Jacobian matrix is:
[ ∂P2/∂θ2 ∂P2/∂V2 ]
[ ∂Q2/∂θ2 ∂Q2/∂V2 ]
- The Jacobian matrix is calculated as:
[ 10sinθ2 10V2 cosθ2 ]
[ 10V2 sinθ2 -10cosθ2 + 20V2 ]
First Iteration
- The initial guess for x(0) is [θ2(0) = 0, V2(0) = 1].
- Calculate V2(0) (10sinθ2(0)) + 2.0 = 0.
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