1The 2-Wattmeter method re-visited! This is to illustrate the 2-Wattmeter method and its readings as observed in the lab. The circuit analyzed is the general one shown below. It is assumed that the voltages are balanced and the impedances are also balanced. The loads are of the form ZRjX=+ and the voltages (to neutral) are given by: 1230120120VVVVVV=∠=∠−=∠ Let θ be the angle of the impedance Z. Thus 1IIθ=∠− where VIZ=. Similarly, ()2120IIθ=∠−− and ()2120IIθ=∠−. When the wattmeters are connected as shown, their readings will be equal to: ()*1131RePVI= and ()*2232RePVI= . A program using Matlab is shown below where the value of the reactance is varied from 25to25−+ Ohm. clear;clf; v=10; % voltage to neutral r=5; % resistance X=-25:0.1:25; % reactance from –25 to +25 zero=zeros(size(X)); % x-axis R=r*(ones(size(X))); % constant R Z=R+j*X; % Impedance vector V1=v*(ones(size(X))); % three balanced voltages V2=v*(cos(2*pi/3)+j*sin(2*pi/3))*(ones(size(X))); V3=v*(cos(-2*pi/3)+j*sin(-2*pi/3))*(ones(size(X))); I1=V1./Z; % compute the three current vectors I2=V2./Z; I3=V3./Z; V13=V1-V3; % voltage on top wattmeter V23=V2-V3; % voltage on lower wattmeter P1=real(V13.*conj(I1)); % reading of top wattmeter P2=real(V23.*conj(I2)); % reading of lower wattmeter P=P1+P2; % the three phase power using 2 wattmetere Pp=3*real(V1.*conj(I1)); % computed three phase power plot(X,P1,X,P2,X,P,X,zero),grid %plot(X,Pp,'.') xlabel('X in Ohm'),ylabel('Power in Watt'), text(-20,0,'capacitive X'),text(15,0,'inductive X') Z ZZV1V2V3nnP1P2I1I2I32-25 -20 -15 -10 -5 0 5 10 15 20 25-100102030405060X in OhmPower in Wattcapacitive X inductive X The powers plotted are the reading of P1 in blue, the reading of P2 in green and the sum in red. Remarks: The powers of the wattmeters are equal only when 0X= and are unequal for all other values! Note also that for some values of X one of the two wattmeters can change the sign of its reading (this happens when 30θ =±o. The sum of the two wattmeter readings is still exactly equal to the three phase power. The two wattmeters would read exactly alike if the common voltage connections is to the neutral point, in which case each meter would read only one third of the total three-phase