Please show all working out and methods clearly and legable

Please show all working out and methods clearly and legable.

Figure 2 shows a three bus bar transmission system. Assuming a 100 MVA base; determine: (a) The admittance matrix for the system. (b) Determine which types of busses in the system. (c) Determine the size of the Jacobian Matrix if the Full NR method is used. (d) Determine the sending apparent power of the generator, the unknown polar values of the voltages as well as the power flows via the Decoupled Method up to a tolerance of 0.01 pu. (e) Repeat the exercise using the DC power flow method. (f) As an exercise try solving the network using the full Newton Raphson method.

Solution

If we consider the above example, with V₁ is in per unit values and S_base = 100 MVA

In Bus 2:

The base is: -(100 + j50)/100 = -1 – j0.5 pu

à P₂

= - 1 Q₂ = - 0.5

In Bus 3:

The base us: -(150+j25)/100 = -1.5-j.25 pu

à P₃

= -1.5 Q₃=-0.25

2. formation of y bus

y12=1/z12=1/j0.1=j10

y23=1/z23=1/j0.08=j12.5

Y11=y12=j10

Y12=Y21=-y12=-j10

Y13=Y31=0

Y22=y12+y23=j10+j12.5=j22.5

Y23=Y32=-y23=-j12.5

Y33=y23=j12.5

Y-bus= [ j10 -j10 0

-j10 j22.5 -12.5

0 -j12.5 12.5]

b) Bus 1 Slack V1, 1 are given P1, Q1 are unknown

Bus 2 Load P2, Q2 are given |V2|, 2 are unknown

Bus 3 Load P3, Q3 are given   |V3|, 3   are unknown

c).The Jacobian matrix is a 3x3 matrix, so we need to find 9 partial derivatives.

In Bus 2:	The base is: -(100 + j50)/100 = -1 – j0.5 pu	à P2	= - 1 Q2 = - 0.5
In Bus 3:	The base us: -(150+j25)/100 = -1.5-j.25 pu	à P3	= -1.5 Q3=-0.25