SG_TOPOLOGY Generate random power grid topology using RT-nestedSmallWorld
[YOUTN, ZPR, LAMBDA2, L, A, INDX] = ...
SG_TOPOLOGY(N, N0, KS, LTC_K, TOPO_PARS, RWD_PARS, ZPR_PARS)
Inputs:
N - network size
N0 - island size; if this given '0', the program will compute it
ks - total number of islands
ltc_k - total number of lattice connections between neighboring islands
topo_pars - topology parameters
rwd_pars - rewiring parameters
Zpr_pars - line impedance parameters
Outputs:
youtN - actual network size;
Zpr - generated line impedances;
lambda2 - algebraic connectivity
L - the Laplacian
A - line admittance matrix;
indx - link index
model: (1) form islands limited by connectivity limits
(2) connect the islands with lattice connections0001 function [youtN, Zpr, lambda2, L, A, indx] = sg_topology(N, N0, ks, ltc_k, topo_pars, rwd_pars, Zpr_pars) 0002 %SG_TOPOLOGY Generate random power grid topology using RT-nestedSmallWorld 0003 %[YOUTN, ZPR, LAMBDA2, L, A, INDX] = ... 0004 % SG_TOPOLOGY(N, N0, KS, LTC_K, TOPO_PARS, RWD_PARS, ZPR_PARS) 0005 % 0006 % Inputs: 0007 % N - network size 0008 % N0 - island size; if this given '0', the program will compute it 0009 % ks - total number of islands 0010 % ltc_k - total number of lattice connections between neighboring islands 0011 % topo_pars - topology parameters 0012 % rwd_pars - rewiring parameters 0013 % Zpr_pars - line impedance parameters 0014 % 0015 % Outputs: 0016 % youtN - actual network size; 0017 % Zpr - generated line impedances; 0018 % lambda2 - algebraic connectivity 0019 % L - the Laplacian 0020 % A - line admittance matrix; 0021 % indx - link index 0022 % 0023 % model: (1) form islands limited by connectivity limits 0024 % (2) connect the islands with lattice connections 0025 0026 % SynGrid 0027 % Copyright (c) 2008-2018, Electric Power and Energy Systems (EPES) Research Lab 0028 % by Zhifang Wang, Virginia Commonwealth University 0029 % 0030 % This file is part of SynGrid. 0031 % Covered by the 3-clause BSD License (see LICENSE file for details). 0032 0033 % obtain the parameters 0034 degModel = topo_pars{1}; mdeg = topo_pars{2}; 0035 if(N0 == 0) 0036 N0 = round(3*exp(mdeg(1))); 0037 ks = ceil(N/N0); 0038 end 0039 % added to make youtN == N as given 0040 N0s = round(N/ks).*ones(1,ks); 0041 N0s(ks) = N-sum(N0s(1:ks-1)); 0042 if(N~=sum(N0s)) 0043 disp('error, youtN does not equal N as given!'); 0044 end 0045 N0=N0s(1); 0046 if(isempty(rwd_pars)) % if rewired_pars not given 0047 if(N0 <= 30) 0048 p_lrwd = 0.24; p_nrwd = 0.43; avg_clsts = 2.6; 0049 elseif(N0 <= 57) 0050 p_lrwd = 0.22; p_nrwd = 0.37; avg_clsts = 3.0; 0051 elseif(N0 <= 118) 0052 p_lrwd = 0.21; p_nrwd = 0.46; avg_clsts = 2.0; 0053 elseif(N0 <= 300) 0054 %p_lrwd = 0.367; p_nrwd = 0.67; avg_clsts = 4.22; % estimate from NYISO data 0055 %p_lrwd = 0.15; p_nrwd = 0.3; avg_clsts = 3; % for the clustreing coefficient 0056 p_lrwd = 0.1; p_nrwd = 0.1; avg_clsts = 3; 0057 else 0058 p_lrwd = 0.367; p_nrwd = 0.67; avg_clsts = 4.22; 0059 end 0060 else 0061 p_lrwd = rwd_pars(1); p_nrwd = rwd_pars(2); avg_clsts = rwd_pars(3); 0062 end 0063 bta = 1/avg_clsts; 0064 alph = bta*(p_nrwd/(1-p_nrwd)); 0065 0066 0067 if(ltc_k==0) % if lattice connection not specified 0068 % the number of links between neighboring islands, each side have ltc_k links. 0069 ltc_k = 2; 0070 end 0071 0072 % Form the topology 0073 indx =[]; 0074 youtNs =zeros(ks,1); 0075 lls = zeros(ks*ltc_k,1); % starting nodes of lattice links between islands 0076 llt = zeros(ks*ltc_k,1); % terminating nodes 0077 0078 for ni = 1:ks 0079 % the island with size of N0 0080 N0i=N0s(ni); 0081 [Ai,Mai,indxi,Mdi,lbd2i,youtNi,L] = nsw_cluster_smallworld(N0i,degModel,mdeg,p_lrwd,alph,bta); 0082 indx =[indx; 0083 indxi+sum(youtNs)]; % generate ks islands, update links of each island 0084 0085 % generate lattice links between islands 0086 lls( (ni-1)*ltc_k+1 : ni*ltc_k ) = randi([1,youtNi],ltc_k,1)+sum(youtNs); 0087 if(ni>1) 0088 llt( (ni-2)*ltc_k+1 : (ni-1)*ltc_k ) = randi([1,youtNi],ltc_k,1)+sum(youtNs); 0089 else 0090 llt( (ks-1)*ltc_k+1 : ks*ltc_k ) = randi([1,youtNi],ltc_k,1)+sum(youtNs); 0091 end 0092 % update island size 0093 youtNs(ni) = youtNi; 0094 end 0095 youtN = sum(youtNs); % total topology size 0096 if(ks>1) 0097 indx = [indx; [lls llt] ]; % all the links 0098 m3 = length(lls); 0099 else 0100 m3 =0; 0101 end 0102 m = length(indx(:,1)); 0103 m2 = round((m-m3)*p_lrwd); 0104 m1 = m-m2-m3; 0105 [lambda2,L,A]=nsw_conn_check(indx,youtN); 0106 0107 % Generate the line impedances 0108 Zpr = nsw_gen_Zpr(Zpr_pars, [m1 m2 m3]);