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Copy pathdistrbution_transformer_random_load.m
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distrbution_transformer_random_load.m
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function [HST_max,TOT_max,AEQ,Energy_transfer,Current_ageing]=distrbution_transformer_random_load(PUL,AMB)
% This function calculates thermal mode for ONAN distrbution transformer based on IEC 60076-7
% Input data:
% PUL - loading of transformer in pu
% AMB - ambient temperature, degC
% Output data:
% HST_max - maximal hot-spot temerature of winding, degC
% TOT_max - maximal top-oil temperature, degC
% AEQ - ageing equivalent, pu relatve to normal ageing
% Energy_transfer - energy transfer
% Current_ageing - ageing at each moment
%
% Thermal characteristics of ONAN distrbution transformer
delta_theta_or = 55; % Top-oil (in tank) temperature rise in steady state at rated losses (no-load losses + load losses),K
delta_theta_hr = 23; % Hot-spot-to-top-oil (in tank) gradient at rated current, K
tao_0 = 180; % Average oil time constant, min
tao_w = 4; % Winding time constant, min
R = 5; % Ratio of load losses at rated current to no-load losses
x = 0.8; % Exponential power of total losses versus top-oil (in tank) temperature rise (oil exponent)
y = 1.6; % Exponential power of current versus winding temperature rise (winding exponent)
k11 = 1; % Thermal model constant
k21 = 1; % Thermal model constant
k22 = 2; % Thermal model constant
NPUL=length(PUL); % Finding the length of load data
NAMB=length(AMB); % Finding the length of ambient temperature data
% Checking that input data is in minute format
if NPUL==1440 && NAMB==1440 || NPUL==2880 && NAMB==2880
% do nothing
elseif NPUL==24 && NAMB==24
PUL=PUL_to_1min(PUL,60); % Convert loading data to minute format
AMB=PUL_to_1min(AMB,60); % Convert amb. temperature data to minute format
elseif NPUL==1440 && NAMB==24
AMB=PUL_to_1min(AMB,60); % Convert amb. temperature data to minute format
elseif NPUL==24 && NAMB==1440
PUL=PUL_to_1min(PUL,60); % Convert loading data to minute format
elseif NPUL==48 && NAMB==48
PUL=PUL_to_1min(PUL,30); % Convert loading data to minute format
AMB=PUL_to_1min(AMB,30); % Convert amb. temperature data to minute format
elseif NPUL==96 && NAMB==96
PUL=PUL_to_1min(PUL,15); % Convert loading data to minute format
AMB=PUL_to_1min(AMB,15); % Convert amb. temperature data to minute format
elseif NPUL==288 && NAMB==288
PUL=PUL_to_1min(PUL,5); % Convert loading data to minute format
AMB=PUL_to_1min(AMB,5); % Convert amb. temperature data to minute formatelse
else
PUL=PUL_to_1min(PUL,60); % Convert loading data to minute format
AMB=PUL_to_1min(AMB,60); % Convert amb. temperature data to minute format
% error('Check the length of input data')
end
% Change the variable
K=PUL;
theta_a=AMB;
% load('initial_data.mat','TIM')
Dt=1;% time step 1 minute
% Although the system may not strictly be in the steady state at the start of a calculation period,
% this is usually the best one can assume, and it has little effect on the result.
K_0=K(1);
theta_a_0=theta_a(1);
theta_0 = ((1+K_0.^2.*R)./(1+R)).^x.*delta_theta_or+theta_a_0; % top-oil temperature
delta_theta_h1 = k21*K_0.^y*delta_theta_hr; % Hot-spot-to-top-oil (in tank) gradient at start
delta_theta_h2 = (k21-1)*K_0.^y*delta_theta_hr; % Hot-spot-to-top-oil (in tank) gradient at start
Loss_of_life = 0;
% Create an array of hot-spot temperature and top-oil temperature
HST=NaN(length(K),1);
TOT=NaN(length(K),1);
% Solving difference (not differentiate) equations: iterative approach (see
% Annex C in IEC 60076-7 for equations)
for i=1:1:length(K)
D_theta_0 = (Dt./(k11.*tao_0)).*((((1+K(i).^2.*R)./(1+R)).^x).*(delta_theta_or)-(theta_0-theta_a(i)));
theta_0 = theta_0+D_theta_0;
D_delta_theta_h1 = Dt./(k22.*tao_w).*(k21.*delta_theta_hr.*K(i).^y-delta_theta_h1);
delta_theta_h1 = delta_theta_h1+D_delta_theta_h1;
D_delta_theta_h2 = Dt./(1./k22.*tao_0).*((k21-1).*delta_theta_hr.*K(i).^y-delta_theta_h2);
delta_theta_h2 = delta_theta_h2+D_delta_theta_h2;
delta_theta_h = delta_theta_h1-delta_theta_h2;
HST(i,:) = theta_0+delta_theta_h; % hot spot temperature
TOT(i,:)=theta_0; % top oil temperature
end
% Calculating ageing
DL=NaN(length(K),1);
for i=1:1:length(HST)
% DL(i,:) = (exp((15000./(110+273)-15000./(HST(i)+273)))).*Dt;
DL(i,:) = (2^((HST(i)-98)/6)).*Dt;
end
Loss_of_life = Loss_of_life+DL; % loss of insulation life
ASUM=sum(Loss_of_life); % cummulative loss of insulation life
Current_ageing=0;
for i=1:length(DL)
Current_ageing(i,1)=Current_ageing(end,1)+DL(i);
end
% Output
Current_ageing=Current_ageing/length(Current_ageing); % ageing at each time
AEQ=ASUM/length(K); % ageing equivalent, pu relatve to normal ageing
HST_max=max(HST); % Maximal hot spot temperature
TOT_max=max(TOT); % Maximal top oil temperature
Energy_transfer=sum(PUL); % energy transfer (NB: units are pu*min!!! not MWh)
end