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We came across the following power flow equations in variables V 3 , 3 and 2 : f 1 (V 3 , 3, 2 ) = 10V 3 sin( 3 ) + 10.5V 3 sin( 3 2 ) + 2.
We came across the following power flow equations in variables V3, θ3 and θ2:
f1(V3, θ3, θ2) = 10V3 sin(θ3) + 10.5V3 sin(θ3 − θ2) + 2.8653,
f2(V3, θ3, θ2) = −10V3cos(θ3) − 10.5V3cos(θ3 − θ2) + 19.99V32 + 1.2244,
f3(V3, θ3, θ2) = 10.5 sin(θ2) + 10.5V3 sin(θ2 − θ3) − 0.6661.
Answer the following questions.
a) Find the Jacobian of the power flow.
b) The initial guesses for V3, θ3, and θ2 are V3[0] = 1 p.u, θ3[0] = 0.3 rad, θ2[0] = 0.1 rad. Using
Newton-Raphson method, find V3, θ3, and θ2 such that the power balance equations are satisfied
up to 0.001 p.u using MATLAB. Print and attach the MATLAB code that you write for solving
the power flow equations.
