Ex-6 – COMPLEX NUMBERS – PHASOR SUM – POWER FACTOR

\[\text{Do the following activities:}\ \hspace{25cm}\]

\[1.\ \hspace{1cm}\ \text{The representation of apparent power as phasor sum of}\ \hspace{14cm}\\ \text{active power and reactive power is given by}\ \hspace{16cm}\\ \text{S = 550 + 952.63j.}\ \hspace{10cm}\]

\[i.\ \hspace{1cm}\ \text{To draw the phasor diagram of the system}\ \hspace{12cm}\]

\[ii.\ \hspace{1cm}\ \text{Find the numerical value of the apparent power,}\ \hspace{11cm}\\ \hspace{1cm}\ \text{also calculate the phase angel and}\ \hspace{12cm}\\ \hspace{1cm}\ \text{power factor of the system}\ \hspace{10cm}\]

\[2.\ \hspace{1cm}\ \text{A machine takes 10KW (real power, P) at a power factor of}\ \hspace{14cm}\\ \text{0.6 from 400 V supply.}\ \hspace{10cm}\]

\[i.\ \hspace{1cm}\ \text{Calculate the total load in KVA (apparent power, S) and}\ \hspace{11cm}\\ \hspace{1cm}\ \text{KVAR (reactive power, R) represent the apparent power}\ \hspace{12cm}\\ \hspace{1cm}\ \text{as a phasor sum of active power and reactive power}\ \hspace{10cm}\]

\[\color{green}{Step\ 1:}\ \text{Open Geogebra classic 5 (by double clicking on the icon)}\ \hspace{18cm}\]

\[\color{green}{Step\ 2:}\ \text{To the representation of apparent power as phasor sum of active power and}\ \hspace{15cm}\\ \text{reactive power is given by by S = 550 + 952.63j using the input bar to type S = 550 + 952.63i}\ \hspace{10cm}\\ \text{and press the Enter key. change x axis (Min:0 to Max:1000) and change y axis (Min:0 to Max:1000)}\ \hspace{10cm}\]

\[\color{green}{Step\ 3:}\ \text{To plot the points O and P by using the input bar to type O=(0,0) and P=(550,0)}\ \hspace{15cm}\]

\[\color{green}{Step\ 4:}\ \text{To calculate the numerical value of the Apparenpower}\ \hspace{19cm}\\ \text{by using the input bar to type Apparentpower= segment (O, S)}\ \hspace{12cm}\\ \text{and press the Enter key}\ \hspace{16cm}\]

\[\color{green}{Step\ 4:}\ \text{To calculate the value of the Activepower}\ \hspace{19cm}\\ \text{by using the input bar to type Activepower= segment (O, P)}\ \hspace{12cm}\\ \text{and press the Enter key}\ \hspace{16cm}\]

\[\color{green}{Step\ 6:}\ \text{To calculate the value of the Reactivepower}\ \hspace{19cm}\\ \text{by using the input bar to type Reactivepower= segment (S, P)}\ \hspace{12cm}\\ \text{and press the Enter key}\ \hspace{16cm}\]

\[\color{green}{Step\ 7:}\ \text{To calculate the phase angle POS}\ \hspace{19cm}\\ \text{by using the input command Angle(P,O,S)}\ \text{and press the Enter key}\ \hspace{12cm}\]

\[\color{green}{Step\ 8:}\ \text{To calculate the power factor}\ \hspace{20cm}\\ \text{by using the input bar to type cos(α)}\ \text{and press the Enter key}\ \hspace{12cm}\]

\[\color{green}{Step\ 9:}\ \text{Open Geogebra classic 5 new Window}\ \hspace{19cm}\]

\[\color{green}{Step\ 10:}\ \text{By using input bar to type P =10 and F = 0.6}\ \hspace{19cm}\]

\[\color{green}{Step\ 11:}\ \text{To calculate the phase angel}\ \hspace{20cm}\\ \text{by using the input bar to type α = arccos(F)}\ \text{and press the Enter key}\ \hspace{12cm}\]

\[\color{green}{Step\ 12:}\ \text{By using input bar to type V = 400}\ \hspace{19cm}\]

\[\color{green}{Step\ 13:}\ \text{To calculate the value of current}\ \hspace{20cm}\\ \text{by using the input bar to type I=P /(V cos(α))}\ \text{and press the Enter key}\ \hspace{12cm}\]

\[\color{green}{Step\ 14:}\ \text{To calculate the reactive power (imaginary power)}\ \hspace{20cm}\\ \text{by using the input bar to type R = V I sin(α)}\ \text{and press the Enter key}\ \hspace{12cm}\]

\[\color{green}{Step\ 15:}\ \text{To plot the phasor representation}\ \hspace{20cm}\\ \text{by using the input bar to type S = P + Ri}\ \text{and press the Enter key}\ \hspace{12cm}\]

\[\color{green}{Step\ 16:}\ \text{To plot the points O and}\ P_1\ \text{by using the input bar to type O=(0,0) and}\ P_1\ =\ (10,0)\ \hspace{15cm}\]

\[\color{green}{Step\ 17:}\ \text{To calculate the numerical values of the three power components}\ \hspace{15cm}\\ \text{by using the input bar to type ApparentPower = Segment(O,S)}\ \text{and press the Enter key}\ \hspace{10cm}\]

\[\color{green}{Step\ 18:}\ \text{Similarly, by using the input bar to type}\ ActivePower\ =\ Segment(O,\ P_1)\ \hspace{15cm}\]

\[\color{green}{Step\ 19:}\ \text{Similarly, by using the input bar to type}\ ReactivePower\ =\ Segment(S,\ P_1)\ \hspace{15cm}\]