* Below is the math for F(x) = the probability capacity is available at x MW load. * generator i forced outage rate is FOR(i) and maximum capacity is Pmax(i) * initialize F(0)=1 and all other F(x>0)=0, F(0)=1 always * begin loop i to add the next i'th generator * begin loop x sweeping x from the largest x to 1 MW in 1 MW steps * j=x-Pmax(i) * if(j<0) j=0 * F(x)=(1-FOR(i))*F(j)+FOR(i)*F(x) * end loop x * end loop i Matlab and Octave--------------------------------------------------------------------------------- % Gene Preston's version of GNU Octave http://www.gnu.org/software/octave/ which should work in Matlab. % This program calculates the exact LOLP of 10 randomly outaged generators for a given MW load level ix. clear clc PMax = [5,10,13,22,43,57,101,198,248,276]; FOR = [0.15,0.10,0.09,0.07,0.06,0.05,0.04,0.04,0.04,0.0454]; F = zeros(1000); for i = 1:10 % generator i for ix = 1000:-1:1 % ix is the MW value on the x axis j = ix - PMax(i); if j > 0 F(ix) = (1.-FOR(i))*F(j) + FOR(i)*F(ix); else F(ix) = (1.-FOR(i)) + FOR(i)*F(ix); % F(j<1)=1 always! end end end fprintf(1,' 0 1.0000000000000000 0.0000000000000000\n') for i = 1:1000 fprintf(1,'%4d%20.16f%20.16f\n',i,F(i),1-F(i)); end fprintf('\n\n') fprintf('file OP contains the output report\n') fileID = fopen('OP','wt') fprintf(fileID,' MW F(X) LOLP = 1 - F(X)\n') fprintf(fileID,' 0 1.0000000000000000 0.0000000000000000\n') for i = 1:1000 fprintf(fileID,'%4d%20.16f%20.16f\n',i,F(i),1-F(i)); end fclose(fileID) fortran------------------------------------------------------------------------------------------- * This program calculates the LOLP of 10 randomly outaged generators for a given MW load level IX. CHARACTER A*1/' '/ INTEGER PMAX(10)/5,10,13,22,43,57,101,198,248,276/ REAL*8 F(0:1000)/1.D0,1000*0.D0/,FOR(10) & /.15D0,.10D0,.09D0,.07D0,.06D0,.05D0,.04D0,.04D0,.04D0,.0454D0/ DO 1 I=1,10 DO 1 IX=1000,1,-1 J=IX-PMAX(I) IF(J.LT.0) J=0 1 F(IX)=(1.-FOR(I))*F(J)+FOR(I)*F(IX) OPEN(3,FILE='OP') WRITE(3,*)' MW F(X) LOLP = 1 - F(X)' WRITE(3,'(I4,2F20.16)')(IX,F(IX),1.-F(IX),IX=0,1000) WRITE(*,*) 'FILE OP CONTAINS THE OUTPUT REPORT' WRITE(*,*) 'PRESS ENTER TO END THIS PROGRAM' READ(*,'(A1)') A STOP END python-------------------------------------------------------------------------------------------- # direct calculation LOLP example convolving ten randomly outaged generators # this Python version by Graham Palmer Nov 25, 2015, slightly revised by Gene Preston # note on precison - uses Python floats (double precision, 52 bits + 1 sign) IEEE 754 import sys, math from decimal import Decimal F = [] # initialise F and fill with zero probabilities before generators are added for i in range(0, 1001, 1): F.append(float(0)) F[0] = 1 # except the probability of 0 MW is always 1 with or without generation PMax = [0,5,10,13,22,43,57,101,198,248,276] # generator capacity (MW), added zero at start - not used FOR = [0,0.15,0.10,0.09,0.07,0.06,0.05,0.04,0.04,0.04,0.0454] # forced outage rate, added zero at start - not used for i in range(1,11): # count from 1 to 10, ignore PMax[0], FOR[0] for ix in range(1000, -1, -1): # must count down from 1000 to 0 if ix <= round(PMax[i]): F[ix] = F[ix] * FOR[i] + (1 - FOR[i]) else: F[ix] = F[int(ix - PMax[i])] * (1 - FOR[i]) + F[ix] * FOR[i] print ' MW F(x) LOLP = 1 - F(x)' for ix in range(0,1001,1): print '{:4.0f}{:20.16f}{:20.16f}'.format(ix, F[ix], (1 - F[ix])) matlab-------------------------------------------------------------------------------------------- Bruce F. Wollenberg, Professor University of Minnesota Electrical and Computer Engineering Department Keller Hall, Room 4-174 200 Union Street SE Minneapolis MN 55455 Phone: (612) 626-7192 FAX: (612) 625-4583 E-mail: wollenbe@umn.edu %This program calculates the LOLP of 10 randomly outaged generators for a given MW load level IX. clear clc PMax = [5,10,13,22,43,57,101,198,248,276] FOR = [0.15,0.10,0.09,0.07,0.06,0.05,0.04,0.04,0.04,0.0454] MW = zeros(1001); F = zeros(1001); F(1) = 1; % Note that Matlab cannot use a negative or zero index. % F(0) is stored in F(1), F(1) is stored in F(2), etc and F(1000) is % stored in F(1001) %Build MW table with MW(1) = 0 for i = 1:1001 MW(i) = i-1; end for i = 1:10 for ix = 1001:-1:1 j = ix - PMax(i); if j<0 j = 0; end %F index is offset by 1 F(ix+1) = (1.0 - FOR(i))*F(j+1) + FOR(i)*F(ix+1); end end fprintf(' MW F(X) LOLP = 1 - F(X)\n') for i = 1:1001 fprintf(1,' %4d %20.16f %20.16f \n', MW(i), F(i), 1-F(i) ) end % write the same information to a file called OP.dat fprintf('\n\n\n') fprintf('FILE OP.txt CONTAINS THE OUTPUT REPORT\n') fileID = fopen('OP.txt','wt'); % write output to file called OP.txt fprintf(fileID, ' MW F(X) LOLP = 1 - F(X)\n'); for i = 1:1001 fprintf(fileID,' %4d %20.16f %20.16f \n', MW(i), F(i), 1-F(i) ); end fclose(fileID); matlab-------------------------------------------------------------------------------------------- Seyed Mahdi Mazhari PhD Student; Amirkabir University of Technology, Tehran, Iran Supervisor, Research Laboratory of Power System Operation and Planning Srudies, University of Tehran, Tehran, Iran. https://scholar.google.com/citations?user=YTO_g1YAAAAJ&hl=en note from Gene: Seyed also sent the full output to me as I requested. clear all; clc; format short g; %% Initialization PMAX = [5,10,13,22,43,57,101,198,248,276]; % generator capacity (MW) FOR = [0.15 0.1 0.09 0.07 0.06 0.05 0.04 0.04 0.04 0.0454]; % forced outage rate F = zeros(1000,1); % the probability capacity F(1,1) = 1; % initialize F(0)=1 and all other F(x>0)=0, F(0)=1 always %% Main for ii = 1 : 10 for jj = 1000 : -1 : 1 kk = jj - PMAX(ii); if (kk <= 0) kk = 1; end F(jj,1) = (1 - FOR(1,ii)) * F(kk,1) + FOR(1,ii) * F(jj,1); end end %% Output OUTPUT = zeros(1000,3); % 5he output: 1. MW 2. F(x) 3. LOLP = 1 - F(x) for ii = 1 : 1000 OUTPUT(ii,:) = [ii-1 F(ii,1) (1 - F(ii,1))]; end disp(' MW F(x) LOLP = 1 - F(x)') disp(OUTPUT); save all; matlab-------------------------------------------------------------------------------------------- Yi Liu F = zeros(1001); F(1) = 1; % except the probability of 0 MW is always 1 with or without generation PMax = [0,5,10,13,22,43,57,101,198,248,276]; % generator capacity (MW), added zero at start - not used FOR = [0,0.15,0.10,0.09,0.07,0.06,0.05,0.04,0.04,0.04,0.0454]; % forced outage rate, added zero at start - not used for i = 2 : 11 % count from 2 to 11, ignore PMax(1), FOR(1) for ix = 1001 : -1 : 1 % must count down from 1000 to 1 if ix <= round(PMax(i)) F(ix) = F(ix) * FOR(i) + (1 - FOR(i)); else F(ix) = F(int16(ix - PMax(i))) * (1 - FOR(i)) + F(ix) * FOR(i); end end end disp( ' MW F(x) LOLP = 1 - F(x)'); for ix = 1 : 1001 disp(sprintf('%4.0f\t%20.16f\t%20.16f', ix - 1, F(ix), (1 - F(ix)))); end matlab-------------------------------------------------------------------------------------------- % This program calculates the LOLP of 10 randomly outaged generators % for a given MW load level IX % By Prof. Jose Rubens Macedo Jr, Ph.D. - Federal University of Uberlandia - Brazil clc; clear variables; F = zeros (1001,1); F(1) = 1; MW(1) = 0; for k = 2:1:1001; MW(k) = MW(k-1) + 1; end MW = MW'; PMAX = [0 5 10 13 22 43 57 101 198 248 276]; FOR = [0 0.15 0.10 0.09 0.07 0.06 0.05 0.04 0.04 0.04 0.0454]; for i = 2:11 for ix = 1001:-1:1 if ix <= round(PMAX(i)); F(ix) = F(ix)*FOR(i) + (1-FOR(i)); else F(ix) = F(round(ix-PMAX(i))) * (1-FOR(i)) + F(ix) * FOR(i); end end end disp('------------------------------------------------------------------------'); disp('MW F(X) LOLP = 1 - F(X)'); disp('------------------------------------------------------------------------'); for x = 1:1:1001 disp([num2str(MW(x), '%10.0f'),' ',num2str(F(x), '%10.16f'),' ',num2str((1 - F(x)), '%10.16f')]); end matlab-------------------------------------------------------------------------------------------- Rishabh Jain Doctoral Student, FREEDM Systems Center, NC State University URL: www.linkedin.com/in/risjain/ % Below is the math for F(x) = the probability capacity is available at x MW load. % generator i forced outage rate is FOR(i) and maximum capacity is Pmax(i) % initialize F(0)=1 and all other F(x>0)=0, F(0)=1 always % begin loop i to add the next i'th generator % begin loop x sweeping x from the largest x to 1 MW in 1 MW steps % j=x-Pmax(i) % if(j<0) j=0 % F(x)=(1-FOR(i))*F(j)+FOR(i)*F(x) % end loop x % end loop i F = zeros(1,1001); % initialise F and fill with zero probabilities before generators are added F(1) = 1; %except the probability of 0 MW is always 1 with or without generation PMax = [0,5,10,13,22,43,57,101,198,248,276]; %generator capacity (MW), added zero at start - not used FOR = [0,0.15,0.10,0.09,0.07,0.06,0.05,0.04,0.04,0.04,0.0454]; %forced outage rate, added zero at start - not used for i = 2:1:size(PMax,2) %count from 2 to 11, ignore PMax(1), FOR(1) for ix = 1001:-1:1 %must count down from 1000 to 0 if ix <= round(PMax(i)) F(ix) = F(ix) * FOR(i) + (1 - FOR(i)); else F(ix) = F(ix - PMax(i)) * (1 - FOR(i)) + F(ix) * FOR(i); end end end disp(' MW F(x) LOLP = 1 - F(x)') for ix = 1:1:1001 disp([num2str(ix-1,'%4.0f'),' ',num2str(F(ix),'%20.16f'),' ',num2str(1 - F(ix),'%20.16f')]); end matlab-------------------------------------------------------------------------------------------- anandini bharadwaj clc; clear all; F=zeros(1001,1); F(1)=1; Pmax = [0,5,10,13,22,43,57,101,198,248,276]; FOR = [0,0.15,0.10,0.09,0.07,0.06,0.05,0.04,0.04,0.04,0.0454]; for i=2:11 for ix=1001:-1:2 j=ix-Pmax(i); if (j<0 || ix==Pmax(i)) j=1; F(ix)=(1-FOR(i))*F(j)+FOR(i)*F(ix); else F(ix)=(1-FOR(i))*F(j)+FOR(i)*F(ix); end end end format long F LOPL=1-F matlab-------------------------------------------------------------------------------------------- %Rajendra Adhikari %Virginia Tech %Adapted from python code at: http://www.egpreston.com/dc.txt %Program to Calculate LOLP %% INPUT PMax = [0,5,10,13,22,43,57,101,198,248,276]; % generator capacity (MW) FOR = [0,0.15,0.10,0.09,0.07,0.06,0.05,0.04,0.04,0.04,0.0454]; % forced outage rate %% F = zeros(sum(PMax)+10,1); F(1) = 1; for i = 2:length(PMax) for x = length(F)-1:-1:0 if x <= PMax(i) F(x+1) = F(x+1)*FOR(i) + (1-FOR(i)); else F(x+1) = F(round(x - PMax(i))+1)*(1-FOR(i))+F(x+1)*FOR(i); end end end display(sprintf('MW F(X) LOLP')); for k=0:length(F)-1 display(sprintf('%d %d %d',k,F(k+1),1-F(k+1))) end matlab-------------------------------------------------------------------------------------------- Ilias Dimoulkas clear clc F = zeros(1001,1); F(1) = 1; PMax = [5 10 13 22 43 57 101 198 248 276]'; FORT = [0.15 0.10 0.09 0.07 0.06 0.05 0.04 0.04 0.04 0.0454]'; for i = 1:10 for ix = 1001:-1:1 j = ix - PMax(i); if j <= 0 j = 1; end F(ix) = (1 - FORT(i))*F(j) + FORT(i)*F(ix); end end LOLP = 1 - F; % Create output file X = 0:1000; O = [X; F'; LOLP']; fileID = fopen('output.txt','w'); fprintf(fileID,'%4s %12s %27s\r\n','MW','F(X)','LOLP = 1 - F(X)'); fprintf(fileID,'%4.0f %1.16f %1.16f\r\n',O); fclose(fileID); matlab-------------------------------------------------------------------------------------------- %% This program calculates the LOLP of 10 randomly outaged generators for a given MW load level IX %% MATLAB version by Krishnanand K.R., National University of Singapore (12-March-2016) %% Original program by Eugene G. Preston at http://www.egpreston.com/dc.txt %% Note: MATLAB's default is double-precision data type according to IEEEr Standard 754 clear; clc; %% Clear MATLAB Workspace and Command-Window % Initialise F and fill with zero probabilities before generators are added % except the probability of 0 MW is always 1 with or without generation F=[1,zeros(1,1000)]; PMax=[5,10,13,22,43,57,101,198,248,276]; % generator capacity (MW) FOR=[0.15,0.10,0.09,0.07,0.06,0.05,0.04,0.04,0.04,0.0454]; % forced outage rate for i=1:length(PMax) % count from 1st to last of PMax for IX=length(F):-1:1 % count down the level of load till IX is 1MW J=max( 1, IX-PMax(i) ); % max(...) is a built-in MATLAB function F(IX)=(1-FOR(i))*F(J) + FOR(i)*F(IX); end end disp(' MW F(X) LOLP = 1 - F(X)'); for IX=1:length(F) fprintf('%4.0f%20.16f%20.16f\n',IX-1, F(IX), (1 - F(IX))); end output-------------------------------------------------------------------------------------------- MW F(X) LOLP = 1 - F(X) 0 1.0000000000000000 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