Function MPReduction does modified Ward reduction to the full system model given in the MATPOWER case file (mpc) based the external buses (ExBusOrig)defined by the user. [mpcreduced,Link,BCIRCr]=MPReduction(mpc,ExBusOrig,Pf_flag) INPUT DATA: mpc: struct, includes the full model in MATPOWER case format ExBusOrig: n*1 vector, include the bus numbers of buses to be eliminated Pf_flag: scalar, indicate if dc power flow needed to solve (=1) or not (=0) in the load redistribution subroutine OUTPUT DATA: mpcreduced: struct, includes the reduced model in MATPOWER case format Link: n*2 matrix, includes the generator mapping info, showing how external generators are moved: The first column includes generator bus numbers in full model and the second column includes generator bus nubmers where the external generators are moved to. BCIRCr: n*1 vector, includes branch circuit numbers. This vector can be used to identify parallel branches and equivalent lines generated by the network reduction process. If a branch number is higher than 1 and less then it indicate this branch is parallel to one of the branch in the full model. If a branch circuit number is 99 then it indicate this branch is an equivalent branch. Note: The reduction is based on dc assumption which means all resistance, reactive power components will be ignored. And the reduced model is only good for solving dc power flow or dc opf. If the input full model case file includes dclines, it is assumed that no dc terminal is to be eliminated, otherwise the function will return error. If Pf_flag = 1 which means dc power flow need to be solved during the load redistribution process, user must make sure that MATPOWER toolbox is installed.

- BuildYMat Subroutine BuildYMat construct the addmittance matrix and store it in a
- DoReduction Subroutine DoReduction create the reduced network based on input network
- Initiation Subroutine Initiation read in the input full model data and convert the
- LoadRedistribution Subroutine LoadRedistribution moves loads in reduced model in order to
- MapBus Subroutine MapBus convert bus indices from oldbusnum to newbusnum. The
- MoveExGen Subroutine MoveExGen moves generators on external buses to internal buses
- PreProcessData Subroutine PreProcess do following tasks to input model:

- Example_9bus Example_9bus

0001 function [mpcreduced,Link,BCIRCr]=MPReduction(mpc,ExBusOrig,Pf_flag) 0002 % Function MPReduction does modified Ward reduction to the full system 0003 % model given in the MATPOWER case file (mpc) based the external buses 0004 % (ExBusOrig)defined by the user. 0005 % 0006 % [mpcreduced,Link,BCIRCr]=MPReduction(mpc,ExBusOrig,Pf_flag) 0007 % 0008 % INPUT DATA: 0009 % mpc: struct, includes the full model in MATPOWER case format 0010 % ExBusOrig: n*1 vector, include the bus numbers of buses to be 0011 % eliminated 0012 % Pf_flag: scalar, indicate if dc power flow needed to solve (=1) or not 0013 % (=0) in the load redistribution subroutine 0014 % 0015 % OUTPUT DATA: 0016 % mpcreduced: struct, includes the reduced model in MATPOWER case format 0017 % Link: n*2 matrix, includes the generator mapping info, showing how 0018 % external generators are moved: The first column includes generator bus 0019 % numbers in full model and the second column includes generator bus 0020 % nubmers where the external generators are moved to. 0021 % BCIRCr: n*1 vector, includes branch circuit numbers. This vector can be 0022 % used to identify parallel branches and equivalent lines generated by 0023 % the network reduction process. If a branch number is higher than 1 and 0024 % less then it indicate this branch is parallel to one of the branch in 0025 % the full model. If a branch circuit number is 99 then it indicate this 0026 % branch is an equivalent branch. 0027 % 0028 % Note: The reduction is based on dc assumption which means all resistance, 0029 % reactive power components will be ignored. And the reduced model is only 0030 % good for solving dc power flow or dc opf. If the input full model case 0031 % file includes dclines, it is assumed that no dc terminal is to be 0032 % eliminated, otherwise the function will return error. If Pf_flag = 1 0033 % which means dc power flow need to be solved during the load 0034 % redistribution process, user must make sure that MATPOWER toolbox is 0035 % installed. 0036 0037 % MATPOWER 0038 % Copyright (c) 2014-2016, Power Systems Engineering Research Center (PSERC) 0039 % by Yujia Zhu, PSERC ASU 0040 % 0041 % This file is part of MATPOWER. 0042 % Covered by the 3-clause BSD License (see LICENSE file for details). 0043 % See http://www.pserc.cornell.edu/matpower/ for more info. 0044 0045 fprintf('%n Reduction process start'); 0046 fprintf('%n Preprocess data')'; 0047 [mpc,ExBusOrig]=PreProcessData(mpc,ExBusOrig); 0048 dim = size(mpc.bus,1); 0049 %% Modeling 0050 % check if dc terminals are external 0051 if isfield(mpc,'dcline') 0052 tf1 = ismember(mpc.dcline(:,1),ExBusOrig); 0053 tf2 = ismember(mpc.dcline(:,2),ExBusOrig); 0054 if (sum(tf1)+sum(tf2))>0 0055 error('not able to eliminate HVDC line terminals'); 0056 end 0057 end 0058 ExBusOrig = ExBusOrig'; 0059 if ~isempty(ExBusOrig) 0060 fprintf('\nConvert input data model'); 0061 [NFROM,NTO,BraNum,LineB,ShuntB,BCIRC,BusNum,NUMB,SelfB,mpc,ExBus,newbusnum,oldbusnum] = Initiation(mpc,ExBusOrig); % ExBus with internal numbering 0062 %% Create data structure 0063 fprintf('\nCreating Y matrix of input full model'); 0064 [CIndx,ERP,DataB]=BuildYMat(NFROM,NTO,BraNum,LineB,BCIRC,BusNum,NUMB,SelfB); 0065 %% Do Reduction 0066 fprintf('\nDo first round reduction eliminating all external buses'); 0067 [mpcreduced,BCIRCr,ExBusr] = DoReduction(DataB,ERP,CIndx,ExBus,NUMB,dim,BCIRC,newbusnum,oldbusnum,mpc); % ExBusr with original numbering 0068 %% Generate the second reduction with all retained buses and all generator 0069 %% buses mpcreduced_gen 0070 % Create the ExBus_Gen to create the reduced model with all gens 0071 tf = ismember(ExBus,mpc.gen(:,1)); 0072 ExBusGen = ExBus; 0073 ExBusGen(tf==1)=[]; % delete all external buses with generators 0074 tf=ismember(mpc.gen(:,1),ExBus); 0075 fprintf('\n%d external generators are to be placed',length(tf(tf==1))); 0076 if ~isempty(ExBusGen) 0077 fprintf('\nDo second round reduction eliminating all external non-generator buses'); 0078 [mpcreduced_gen,BCIRC_gen,ExBusGen] = DoReduction(DataB,ERP,CIndx,ExBusGen,NUMB,dim,BCIRC,newbusnum,oldbusnum,mpc); 0079 else 0080 mpcreduced_gen = mpc; 0081 mpcreduced_gen=MapBus(mpcreduced_gen,newbusnum,oldbusnum); 0082 BCIRC_gen = BCIRC; 0083 end 0084 %% Move Generators 0085 fprintf('\nPlacing External generators'); 0086 [NewGenBus,Link]=MoveExGen(mpcreduced_gen,ExBusOrig,ExBusGen,BCIRC_gen,0); 0087 mpcreduced.gen(:,1)=NewGenBus; % move all external generators 0088 %% Do Inverse PowerFlow 0089 fprintf('\nRedistribute loads'); 0090 mpc=MapBus(mpc,newbusnum,oldbusnum); 0091 [mpcreduced,BCIRCr]=LoadRedistribution(mpc,mpcreduced,BCIRCr,Pf_flag); 0092 else 0093 mpcreduced = mpc; 0094 warning('No external buses, reduced model is same as full model'); 0095 end 0096 %% Delete large reactance equivalent branches 0097 ind=find(abs(mpcreduced.branch(:,4))>=max(mpc.branch(:,4))*10); 0098 mpcreduced.branch(ind,:)=[]; 0099 BCIRCr(ind)=[]; 0100 %% Print Results 0101 fprintf('\n**********Reduction Summary****************'); 0102 fprintf('\n%d buses in reduced model',size(mpcreduced.bus,1)); 0103 fprintf('\n%d branches in reduced model, including %d equivalent lines',size(mpcreduced.branch,1),length(BCIRCr(BCIRCr==max(BCIRCr)))); 0104 fprintf('\n%d generators in reduced model',size(mpcreduced.gen,1)); 0105 if isfield(mpcreduced,'dcline') 0106 fprintf('\n%d HVDC lines in reduced mode,',size(mpcreduced.dcline,1)); 0107 end 0108 fprintf('\n**********Generator Placement Results**************'); 0109 for i=1:size(Link,1) 0110 if Link(i,2)-Link(i,1)~=0 0111 fprintf('\nExternal generator on bus %d is moved to %d',Link(i,1),Link(i,2)); 0112 end 0113 end 0114 fprintf('\n'); 0115 0116 end

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