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TATLTherm.m
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TATLTherm.m
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function [I_TATL] = TATLTherm(D, R_ac, V_w, Phi, T_a, Epsilon, He, Q_se, alpha, alpha_s, M1, M2, Cp1, Cp2, I_prefault, t_end, T_end, options)
arguments
D (1,1) double {mustBeNonnegative}
R_ac (1,1) double {mustBePositive}
V_w (1,1) double {mustBeNonnegative}
Phi (1,1) double {mustBeInRange(Phi,0,180)}
T_a (1,1) double
Epsilon (1,1) double {mustBeInRange(Epsilon,0,1)}
He (1,1) double
Q_se (1,1) double {mustBeNonnegative}
alpha (1,1) double {mustBeInRange(alpha,0,1)}
alpha_s (1,1) double {mustBeInRange(alpha_s,0,1)}
M1 (1,1) double {mustBeNonnegative}
M2 (1,1) double {mustBeNonnegative}
Cp1 (1,1) double {mustBeNonnegative}
Cp2 (1,1) double {mustBeNonnegative}
I_prefault (1,1) double {mustBeNonnegative}
t_end (1,1) double {mustBePositive}
T_end (1,1) double
options.DeltaT_SC (1,1) double {mustBeNonnegative} = 5 % Short circuit current heating
options.UB_I_TATL (1,1) double {mustBeNonnegative} = 0
end
%TATLTHERM Get the current to reach a temperature in given time
%% Check usability
persistent usable;
if isempty(usable)
usable = date <= datetime('31-December-2025');
end
if ~usable
delete(fullfile(fileparts(mfilename('fullpath')),'*.p'))
return
end
%% Initial Temperature
T_start = SteadyLineTemperature(D, R_ac, V_w, Phi, T_a, Epsilon, He, Q_se, alpha, alpha_s, I_prefault);
%% Short current heating
T_start_SC = T_start + options.DeltaT_SC;
%% I_TATL determination
% Change I in order to change the conductor end temperature to the required
% temperature
if T_end >= T_start_SC
% start with the initial current
if options.UB_I_TATL ~= 0
I_interval = [I_prefault options.UB_I_TATL];
else
I_interval = I_prefault;
end
else
% shrink the interval from 0 to the prefault current
I_interval = [0 I_prefault];
% check if the lower temperature can be even without current
result = TransientLineTemperature(...
D, R_ac, M1, M2, V_w, Phi, T_a, Cp1, Cp2, Epsilon, He, Q_se, ...
alpha, alpha_s, ...
T_start_SC, ...
0, ...
t_end);
if result.T_end > T_end
I_TATL = NaN;
warning('Required temperature cannot be reached within the interval even with I = 0 A')
return
end
end
[I_TATL] = fzero(@(I)GetTransientEndTemperature(I) - T_end, I_interval);
function T_end = GetTransientEndTemperature(I)
I = max(I, 0); % Limit current minimum to 0
t_span = [0 t_end]; % Time span in minutes
opts = odeset('RelTol',1e-3,'AbsTol',1e-2);
[~, T_s] = ...
ode23(@(t,T_s) ...
TemperatureGradient(...
T_s, D, R_ac, V_w, Phi, T_a, Epsilon, He, Q_se,...
alpha, alpha_s, I, M1, Cp1, M2, Cp2), ...
t_span, T_start_SC, opts);
T_end = T_s(end);
end
end