- #1

David J

Gold Member

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## Homework Statement

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This question was raised on the 11th January 2015 but that thread appears to be no longer active now. There are 2 parts to the question (a) and (b). Initially I am only trying to work on (a)

Figure shows a 50 Hz, high-voltage, transmission line. The relationships between the sending and receiving end voltages and currents are given by the complex ABCD equations:

where 'S' stands for sending-end and 'R' stands for receiving-end

(a) Given the parameter values in TABLE C and an open-circuit received voltage measured as 88.9 kV, calculate the values of

The Table C values are :-

##A_1=0.8698##

##A_2=0.03542##

##B_1=47.94\Omega##

##B_2=180.8\Omega##

##C_1=0 S##

##C_2=0.001349 S##

##D_1=0.8698##

##D_2=0.03542##

## Homework Equations

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##V_s=V_R\left(A_1+jA_2\right)+I_R\left(B_1+jB_2\right)##

##I_s=V_R\left(C_1+jC_2\right)+I_R\left(D_1+jD_2\right)##

## The Attempt at a Solution

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##V_s=V_R\left(A_1+jA_2\right)+I_R\left(B_1+jB_2\right)##

The receiving end is open circuit so there cannot be any current flow so ##I_R=0##

##V_s=88900\left(0.8698+j0.03542\right)+0\left(47.94\Omega+j180.8\Omega\right)##

##V_s=\left(77325.22+j3148.84\right)+0##

So ##V_S=77325.22+j3148.84## or ##77389.31\angle2.33^0##

##I_s=V_R\left(C_1+jC_2\right)+I_R\left(D_1+jD_2\right)##

##I_s=88900\left(0+j0.001349\right)+0\left(0.8698+j0.03542\right)##

So ##I_s=j119.93##

To find the absorbed power

##P_{SO}=V_SI_S##

So ##\left(77325.22+j3148.84\right)\left(j119.93\right)##

So ##P_{SO}=-377640.38+j9273613.63##

In the post from 2015 this same calculation was made and I have shown it below

Now the power should be calculated by

P=Real{VsIs*}

P=Real{(77325.22+j3148.84)(j119.93)}

P=377565w

In the earlier post answer they only included the real value (P=377565w) which I suppose is ok so my calculation, in that case, is pretty close apart from the fact that my value is negative.

The question is asking for a value of power in watts so do I just assume that even though the calculation appears negative it is actually positive ??

My question is why is my value different ?? Have I made a mistake somewhere with this calculation ??

Appreciated as always