% East Induction Motor (High Efficiency)
% Carlton Cross 25 Feb 10 Updated 4 May 2021
% E2016 XRI HVK213TTFW6026BP L
% 7.5 HP, 5.6 kW, 1765 rpm, 208-230 Vrms, pf = 0.8
% IEC 34-1 IEC 34-5 IP 43
% DC resistance test 25 Feb 10 cec
% 5.0 A 1.95 V line-to-line
clear; close all; DataID = ['East Machine (Logan, Rivas, Carrigan)'];
R1 = (0.5*1.95/5.0);
f = 60; np = 4; Nph = 3; rpm = 1765;
Prated = 7.5*745.7; wmrated = rpm*2*pi/60; % W
taurated = Prated/wmrated;
mass = 7.65; % kg calibration mass
d = 0.260; % m moment arm
g = 9.81; % m/s^2 acceleration of gravity
Vcal = -2.08; % V load cell voltage
Tscale = -mass*g*d/Vcal; % Nm/V torque scale factor
data = [
% Vl-ln, V I, A P, kW Q, kVAR Nm, rpm Vcell, V
144.8 8.8 0 3.5 1800 -0.178 % Unexplained offset
145 8.9 0.5 3.5 1798 0.0911
141 9.2 1.1 3.5 1795 0.442
141 9.7 1.6 3.6 1791 0.676
144 10.6 2.2 3.6 1790 1.025
144 11.5 2.7 3.7 1788 1.296
146 12.8 3.3 3.8 1786 1.615
150 13.2 3.8 3.9 1784 1.892
144 15.0 4.4 4.1 1781 2.192
150 16.4 4.9 4.3 1778 2.505
141 17.7 5.5 4.4 1776 2.764
146 19.4 6.1 4.7 1772 3.106];
Vphase = mean(data(:,1)); % Vrms
Iline = data(:,2); % Arms
P = 1000*data(:,3); % W
Q = 1000*data(:,4); % VAR
Nm = data(:,5); % rpm
tau = Tscale*(data(:,6)-data(1,6)); % Nm (with offset correction)
% Model Parameters
Pcore = P(2) - 3*R1*Iline(2)^2; % Idle power less resistive losses
Rc = 5*(Vphase^2)/(Pcore/Nph); % per phase
R2 = 0.71*R1; % Adjusted for best power-torque fit
Xm = 0.95*(Vphase^2)/(Q(1)/Nph); % Most significant at low power
Qdiff = Q(end) - Q(1); % Increase from rotor inductance
X1X2 = (Qdiff/Nph)/Iline(end)^2; % X1X2 is really X1+X2
X1 = 0.7*X1X2; % Adjusted for best pf fit
X2 = 1.21*X1X2; % Adjusted for high-load reactive power
% Performance from data
Ns = 120*f/np; wm = 2*pi*Nm/60; s = (Ns - Nm)/Ns;
Pout = wm.*tau; eta = 100*Pout./P; pf = cos(atan(Q./P));
% Peformance from model
npts = 200; smin = 1/1800; smax = (Ns - 1)/Ns;
smodel = linspace(smin,smax,npts)';
ws = 2*pi*Ns/60; wshaft = (1-smodel)*ws; Nshaft = wshaft*30/pi;
z1 = R1+j*X1; y1 = 1/z1; z2 = R2./smodel + j*X2; y2 = (1./z2);
yc = 1/Rc + 1/(j*Xm);
Ea = Vphase*y1./(y1 + yc + y2); Ia = y2.*Ea;
Pomodel = 3*R2*(abs(Ia).^2).*(1-smodel)./smodel;
taumodel = Pomodel./wshaft;
ze = z1 + R2 + j*X2; % Approximate impedance at under load
sp = R2/(R2 + abs(ze)); % Slip at max power
sb = R2/(sqrt(R1^2 + (X1+X2)^2)); % Slip at max torque
figure(1); hold on;
plot(Nshaft,taumodel, Nm,tau,'xr', 'linewidth',1.5)
axs = axis;
plot([(1-sb) (1-sb)]*Ns, axs(3:4),':r','linewidth',1.5)
plot([(1-sp) (1-sp)]*Ns, axs(3:4),'--c','linewidth',1.5)
plot(axs(1:2), [taurated taurated],':k');
hold off
title('\fontsize{14}Induction Motor Load Characteristic')
ylabel('Torque, Nm'); xlabel('Mechanical Speed, rpm');
legend('Model','Test Data','Max Torque','Max Power','location','north')
grid
text(400,50, DataID, 'backgroundcolor','white')
text(200,1.05*taurated,['Rated Torque'])
fmt1 = 'R_1 = %5.3f X_1 = %5.3f'; S1 = sprintf(fmt1,R1,X1);
fmt2 = 'R_2 = %5.3f X_2 = %5.3f'; S2 = sprintf(fmt2,R2,X2);
fmt3 = 'R_c = %5.0f X_m = %5.1f'; S3 = sprintf(fmt3,Rc,Xm);
text(400,40,{S1 S2 S3},'BackgroundColor','white')
% Place a caption under the graph box
AxesPos = get(gca,'Position');
CapStr = ['From file ...\\' mfilename '.m plotted ' date '. Carlton Cross'];
annotation('textbox',[AxesPos(1) 0 .99 .04],'string',CapStr,...
'FitBoxToText','on', 'LineStyle','none', 'BackgroundColor','white');
% % Peformance from model (over data segment)
npts = 200; smin = 0; smax = (Ns - Nm(end))/Ns;
smodel = linspace(smin,smax,npts)';
ws = 2*pi*Ns/60; wshaft = (1-smodel)*ws; Nshaft = wshaft*30/pi;
z1 = R1+j*X1; z2 = R2./smodel + j*X2;
Ea = Vphase./((1/z1 + 1/Rc + 1/(j*Xm) + 1./z2)*z1);
Ia = Ea./z2; Ic = Ea*(1/Rc + 1/(j*Xm)); I1 = Ia + Ic;
Smodel = 3*Vphase*conj(I1);
Pinmodel = real(Smodel);
Qinmodel = imag(Smodel);
pfmodel = cos(angle(Smodel));
Pomodel = 3*R2*(abs(Ia).^2).*(1-smodel)./smodel;
taumodel = Pomodel./wshaft;
Effmodel = 100*Pomodel./Pinmodel;
