-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathlosses_partial_transients.m
94 lines (77 loc) · 3.87 KB
/
losses_partial_transients.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
function [Theta_ct,Theta_Et,Alpha]=losses_partial_transients(I)
%% Function input/output
% INPUT
% I - current step, A
% OUTPUT
% Theta_ct - cable partial transient,K
% Theta_Et - cable environment partial transient, K
% Alpha - conductor to cable surface attainment factor, pu
global R_AC90_eval Ta Tb TA TB a b Lambda1 Lambda2 t De Diff_sol Depth
global Rho_sol Wd
%% Losses estimation
% p27 IEC60287-1-1
% 2.4.2.1 Single-core lead-sheathed cables – steel wire armour, bonded to
% sheath at both ends
% Wc is the power loss per unit length (W/m)in a conductor or an equivalent
% conductor based on the maximum conductor temperature attained.
% The power loss is assumed to be constant during the transient.
Wc=3*I^2*R_AC90_eval; % or Wc=I^2*R_AC90_eval (without multiplication by 3);
% total I^2*R (ohmic) power loss of each cable
WI=Wc*(1+Lambda1+Lambda2); % excluding Wd
% WI=Wc*(1+Lambda1+Lambda2)+3*Wd; % including Wd
% But (p12 Nielsen, Applied Sciences 2019)says that WI includes Wd...
% Total internal cable losses WI, including dielectric, sheath and armour
% losses
%% 4.2.3 Calculation of cable partial transient (p 33 IEC 60853-2)
Theta_ct=Wc.*(Ta.*(1-exp(-a.*t))+Tb.*(1-exp(-b.*t)));
% Theta_ct=3*Wc.*(Ta.*(1-exp(-a.*t))+Tb.*(1-exp(-b.*t)));
% Where t is a time from start of application of heating, a general symbol
% for time, usually in seconds (t = 3 600i)
% The conductor to cable surface attainment factor Alpha is then obtained
% Alpha=Theta_ct/(Wc*(TA+TB)); % iniial formula with Wc but see next
% However, if I==0 then Wc==0 therefore Alpha would turn to NaN since Wc
% is the denominator of alpha (i.e. dividing by 0). Hence,we suggest to
% avoid using Wc in alpha as follows:
Alpha=(Ta.*(1-exp(-a.*t))+Tb.*(1-exp(-b.*t)))./(TA+TB);
%% 4.2.4 Calculation of cable environment partial transient (p33 IEC853-2)
% argument of the first integral exponential
X=(De^2)./(16.*Diff_sol.*t);
% argument of the second integral exponential
Y=(Depth^2)./(Diff_sol.*t);
% NOTES TO FIGURES 6 AND 7 "SCALES FOR EXPONENTIAL INTEGRAL"(p101 IEC853-2)
% preallocation of X_1 and Y_1 to increase the speed
% X_1=NaN(length(X),1);
% Y_1=NaN(length(Y),1);
% for i=1:length(X)
% if (X(i)>=0 && X(i)<=1)
% X_1(i)=-0.5772-log(X(i))+X(i)-0.2499*X(i)^2+0.0552*X(i)^3+...
% 0.0098*X(i)^4+0.0011*X(i)^5; % contradiction between IEC 853-2 (+0.0098*X^4) p101 and Dorison (-0.0098*X^4) p142
% elseif (X(i)>1 && X(i)<8) % contradiction between IEC 853-2 (x>8, E=formula) p101 and Dorison (x>=8, E=formula) p142
% X_1(i)=1/(X(i)*exp(X(i)))*((X(i)^2+2.3347*X(i)+0.2506)/(X(i)^2+...
% 3.3307*X(i)+1.6815));
% elseif (X(i)<0.01)
% X_1(i)=-log(X(i))-0.5772;
% else
% X_1(i)=0;
% end
%
% if (Y(i)>=0 && Y(i)<=1)
% Y_1(i)=-0.5772-log(Y(i))+Y(i)-0.2499*Y(i)^2+0.0552*Y(i)^3+...
% 0.0098*Y(i)^4+0.0011*Y(i)^5; % contradiction between IEC 853-2 (+0.0098*X^4) p101 and Dorison (-0.0098*X^4) p142
% elseif (Y(i)>1 && Y(i)<8) % contradiction between IEC 853-2 (x>8, E=formula) p101 and Dorison (x>=8, E=formula) p142
% Y_1(i)=1/(Y(i)*exp(Y(i)))*((Y(i)^2+2.3347*Y(i)+0.2506)/(Y(i)^2+...
% 3.3307*Y(i)+1.6815));
% elseif (Y(i)<0.01)
% Y_1(i)=-log(Y(i))-0.5772;
% else
% Y_1(i)=0;
% end
% end
%
% % cable environment partial transient
% Theta_Et=((WI*Rho_sol)/(4*pi))*(X_1-Y_1);
X_1=expint(X);
Y_1=expint(Y);
% cable environment partial transient
Theta_Et=((WI*Rho_sol)/(4*pi))*(X_1-Y_1);
end