Calculate weight of wire based on transmission voltage and losses

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Hello friends and colleagues, 

If you need to calculate the weight of wire based on transmission voltage, use the math lab model that I created. All what you have to do is: 

  1.  Enter the amount of power you need to transmit (red text “enter power”) 
  2. The allowable percentage power losses (it is 2% in the code below, and you can change that by typing different values) 
  3. The wire length  

 Copy and paste the code below in math lab, and you should be good to go. 

 Start of the code: 

% Calculate weight of wire based on transmission voltage 
clc 
clear 

p = “enter power“; % watts 
res_cu = 1.7e-8; %ohms 
res_al = 2.8e-8; 
rho_cu = 8940; %kg/m^3 
rho_al = 2700; 
rho_ins = 860; %kg/m^3 for ethylene polypropylene rubber 
l = “enter wire distance“; % length, meters 

lossVec = [0.02];% total wire losses (percentage of the power) 

for i = 1:length(lossVec) 
loss = lossVec(i); 
V = 400:100:3000; %line-line voltages, rms 
%V = V*(sqrt(3)); 
% AC 
I = p./(sqrt(3)*V); % RMS current in each line 
Vdrop = loss*V; %voltage drop across the wire for each phase 

thick_ins_AC = .0254*(8.1e-6*(V*sqrt(2)) + .057); %thickness in meters 
thick_ins_DC = .0254*(8.1e-6*V + .057); %thickness in meters 

A_al = res_al * l * I ./ Vdrop; %cross sectional area 
for k = 1:length(V) 
if A_al(k) < 1.33e-6 
A_al(k) = 1.33e-6; 
end 
end 
m_al = A_al*l*rho_al; % total mass for one wire(one phase) 
m_ins_al = (pi*((sqrt(A_al/pi)+thick_ins_AC).^2)-A_al)*l*rho_ins; 
m_al_tot = 3*(m_al + m_ins_al); % model using 3x mass_al +3x mass_ins, 

A_cu = res_cu * l * I ./ Vdrop; 
m_cu = 1*A_cu*l*rho_cu; 
m_ins_cu = (pi*((sqrt(A_cu/pi)+thick_ins_AC).^2)-A_cu)*l*rho_ins; 
m_cu_tot = 3*(m_cu + m_ins_cu); 

% DC 
Idc = p./V; %DC voltage 

Adc_cu = res_cu * (2*l) * Idc./ Vdrop; %cross sectional area, for one wires 
mdc_cu = Adc_cu*l*rho_cu; % total mass for one wires 
Rdc_cu = res_cu*l./Adc_cu; % resistance per wire 
mdc_ins_cu = (pi*((sqrt(Adc_cu/pi)+thick_ins_DC).^2)-Adc_cu)*l*rho_ins; 
mdc_cu_tot = 2*(mdc_cu + mdc_ins_cu); 

Adc_al = res_al * (2*l) * Idc./ Vdrop; %cross sectional area, for two wires 
for n = 1:length(V) 
if Adc_al(n) < 1.33e-6 %assumes that limit for aluminum is AWG 6 
Adc_al(n) = 1.33e-6; 
end 
end 
mdc_al = 1*Adc_al*l*rho_al; % total mass for one wire 
Rdc_al = res_al*l./Adc_al; 
mdc_ins_al = (pi*((sqrt(Adc_al/pi)+thick_ins_DC).^2)-Adc_al)*l*rho_ins; 
mdc_al_tot = 2*(mdc_al + mdc_ins_al); 

%figure 
%plot(V,m_al,V,m_ins_al,V,m_al_tot) 
%legend(‘Aluminum’,’Insulation’,’Total’) 
%title(‘Weight Composition for AC Aluminum Cables’) 
%xlabel(‘Line-line Voltage [V]’) 
%ylabel(‘Conductor weight [kg]’) 
%grid on 

%figure 
%plot(V,m_cu,V,m_ins_cu,V,m_cu_tot) 
%legend(‘Copper’,’Insulation’,’Total’) 
%title(‘Weight Composition for AC Copper Cables’) 
%xlabel(‘Line-line Voltage [V]’) 
%ylabel(‘Conductor weight [kg]’) 
%grid on 

%figure 
%plot(V,mdc_cu,V,mdc_ins_cu,V,mdc_cu_tot) 
%legend(‘Copper’,’Insulation’,’Total’) 
%title(‘Weight Composition for DC Copper Cables’) 
%xlabel(‘Line-line Voltage [V]’) 
%ylabel(‘Conductor weight [kg]’) 
%grid on 

%figure 
%plot(V,mdc_al,V,mdc_ins_al,V,mdc_al_tot) 
%legend(‘Aluminum’,’Insulation’,’Total’) 
%title(‘Weight Composition for DC Aluminum Cables’) 
%xlabel(‘Line-line Voltage [V]’) 
%ylabel(‘Conductor weight [kg]’) 
%grid on 

figure 
%semilogy(V,m_cu_tot,V,m_al_tot,V,mdc_cu_tot,V,mdc_al_tot) 
plot(V,m_cu_tot,V,m_al_tot,V,mdc_cu_tot,V,mdc_al_tot) 
legend(‘AC Cu’,’AC Al’,’DC Cu’,’DC Al’) 
title(‘Weight Comparison with 2% losses’) 
xlabel(‘Line-line Voltage [V]’) 
ylabel(‘Conductor weight [kg]’) 
grid on 
end