MATPOWER - Power Systems Engineering Research Center
Contents
1. gt gt hel MPOP opt opt lp mpoption TION Used to set and retrieve a MATPOWER options vector mpoption returns the default options vector mpoption namel valuel name2 value2 11 returns the default options vector with new values for up to 7 options value Example opt mpoption opt op na namet is the name of an option tions mel val mpoption PF_ALG uel name2 value2 and value is the new 2 PF_TOL le 4 same as above except it uses the options vector opt as a base instead of the default options vector The currently defined options are as follows idx NAME default power flow options 1 PF_ALG 1 power flow algorithm 1 Newton s method 2 Fast Decoupled XB version 3 Fast Decoupled BX version 2 PF_TOL le 8 termination tolerance on per unit P amp Q mismatch 3 PF_MAX_IT 10 maximum number of iterations for Newton s method 4 PF_MAX_IT_FD 30 maximum number of iterations for fast decoupled method OPF options 11 OPF_ALG 0 algorithm to use for OPF see README for more info on formulations algorithms The algorithm code F 100 S 20 where F specifies one of the following OPF formulations 1 standard polynomial cost in obj fcn 2 CCV constrained cost variables S specifies one of the following solvers 0 constr from Optimization Toolbox 1 Dense LP b2. or if this is the first iteration go to step 3 otherwise go to step 4 Compute a decommitment index for each generator i as follows d f P heP where P is generator i s dispatch computed by the OPF f is the cost of operating at P and A is the Lagrange multiplier on the real power equality constraint at the bus where generator i is located Continue with step 5 Return to the previous commitment and set d to zero to eliminate it from consideration Find the generator k with the smallest decommitment index If d is negative shut down generator k and return to step 1 If d is positive stop 3 5 MATPOWER Options MATPOWER uses an options vector to control the many options available It is similar to the op tions vector produced by the foptions function in Matlab s Optimization Toolbox The primary difference is that modifications can be made by option name as opposed to having to remember the index of each option The default MATPOWER options vector is obtained by calling mpoption with no arguments So typing gt gt runopf case30 mpoption is another way to run the OPF solver with the all of the default options The MATPOWER options vector controls the following power flow algorithm power flow termination criterion OPF algorithm OPF default algorithms for different cost models OPF cost conversion parameters OPF termination criterion verbose level printing of results The details are given below
3. 4 Qd reactive power demand MVAR 5 Gs shunt conductance MW demanded at V 1 0 p u 6 Bs shunt susceptance MVAR injected at V 1 0 p u 7 area number 1 100 8 Vm voltage magnitude p u 9 Va voltage angle degrees bus name 10 baseKV base voltage kV 11 zone loss zone 1 999 12 maxVm maximum voltage magnitude p u 13 minVm minimum voltage magnitude p u Generator Data Format 1 bus number machine identifier 0 9 A Z Pg real power output MW Qg reactive power output MVAR Qmax maximum reactive power output MVAR Qmin minimum reactive power output MVAR Vg voltage magnitude setpoint p u remote controlled bus index mBase total MVA base of this machine defaults to baseMVA machine impedance p u on mBase step up transformer impedance p u on mBase step up transformer off nominal turns ratio 8 status 1 machine in service 0 machine out of service of total VARS to come from this gen in order to hold V at remote bus controlled by several generators Nos WN J 9 10 Pmax maximum real power output MW Pmin minimum real power output MW Branch Data Format 11 f from bus number t to bus number circuit identifier r resistance p u x reactance p u b total line charging susceptance p u rateA MVA rating A long term rating rateB MVA rating B short term rating rateC MVA rating C
4. costs for reactive generation case30pwl m case30 m with a piece wise linear cost function Source files used by all algorithms bustypes m dSbus_dV m computes partial derivatives for Jacobian ext2int m idx_brch m idx_bus m idx_gen m int2ext m makeSbus m makeYbus m builds Ybus matrix mpoption m sets MATPOWER options printpf m prints output 14 Other source files used by PF Power Flow fdpf m newtonpf m pfsoln m runpf m makeB m implements fast decoupled power flow implements Newton s method power flow main program for running a power flow Other source files used by OPF Optimal Power Flow dAbr_dV m dSbr_dV m fg_names m fun ccv m fun_std m grad_ccv grad_std idx_area idx_cost opf m opfsoln m opf_form m opf_slvr m poly2pwl m pqcost m runopf m totcost m 3333 computes partial computes partial L derivatives of apparent power flows L derivatives of complex power flows computes obj fcn and constraints for CCV formulation computes obj fcn and constraints for standard formulation computes gradients for standard formulation computes gradients for standard formulation implements main OPF routine main program for running an optimal power flow computes cost The following are used only by the LP based OPF algorithms LPconstr m LPegslvr m LPrelax m LPsetup m Other source files used by UOPF Unit decommitment OPF all fil
5. performs worse than the const r based method even on small systems Fortunately there are LP solvers available from third parties which do exploit sparsity In general these yield much higher performance One in particular called bpmpd 7 actually a QP solver has proven to be robust and efficient It should be noted however that even with a good LP solver MATPOWER s LP based OPF solver unlike it s power flow solver is not suitable for very large scale problems Substantial im provements in performance may still be possible though they may require significantly more com plicated coding and possibly a custom LP solver On a Sun Ultra 2200 the LP based OPF solver using bpmpd solves a 30 bus system in under 4 seconds and a 118 bus case in under 25 seconds OPF Formulation The OPF problem solved by MATPOWER is a smooth OPF with no discrete variables or con trols The objective function is the total cost of real and or reactive generation These costs may be defined as polynomials or as piecewise linear functions of generator output The problem is for mulated as follows min 2 fy Pai f 04 such that P P P V 8 0 active power balance equations Q 0 Q V 0 0 reactive power balance equations Sf lt de Si apparent power flow limit of lines from side s lt S apparent power flow limit of lines to side VY lt V Sy bus voltage limits Pe SPP active power generation limits oe lt Q 5 Qa reactive p
6. LIM 1 control output of gen P limit info 42 OUT_OG_LIM 1 control output of gen Q limit info 43 OUT_RAW 0 print raw data for Perl database interface code Ooty 1 J 13 A typical usage of the options vector might be as follows Get the default options vector gt gt opt mpoption Use the fast decoupled method to solve power flow gt gt opt mpoption opt PF_ALG 2 Display only system summary and generator info gt gt opt mpoption opt OUT_BUS 0 OUT_BRANCH 0 OUT_GEN 1 Show all progress info gt gt opt mpoption opt VERBOSE 3 Now run a bunch of power flows using these settings gt gt runpf case57 opt gt gt runpf casell18 opt gt gt runpf case300 opt 3 6 Summary of the Files Documentation files README basic intro to MATPOWER CHANGES modification history of MATPOWER manual pdf PDF version of the MATPOWER User s Manual requires Adobe Acrobat Reader Input data files cdf2matp m a stand alone m file which reads IEEE CDF formatted data and outputs data in MATPOWER s case m format case m same as case9 m case9 m a 3 generator 9 bus case case30 m a 6 generator 30 bus case case57 m IEEE 57 Bus case Ccasel18 m IEEE 118 Bus case case300 m IEEE 300 Bus case case9Q m case9 m with costs for reactive generation case300 m Case30 m with
7. MATPOWER A MATLAB Y Power System Simulation Package Version 2 0 December 24 1997 User s Manual Ray D Zimmerman Deqiang David Gan rz10 cornell edu deqiang O ee cornell edu O 1997 Power Systems Engineering Research Center PSERC School of Electrical Engineering Cornell University Ithaca NY 14853 Table of Contents Tabl e Of CORtEtS aid A A E ASA A das 2 TANCIA A a a aaa 3 2 Getting Slar ld AA AAA EA AAA ARA AA 3 2 eS stem A A al a eet Aa ee eeu eae id ae tig 3 2 cP A A A 3 o 4 2 4 Running an Optimal Power El A ta A den 4 A O TO 4 3 PechniGal Reterence A ds 5 3 1 Data File Formation iii 5 E LENUS A E S E E TA 6 333 Optimal Power Flo Wiese iis cava ese eo a aN PAESE SA KEE Eiye O ERa 7 3 4 Unit D commntment Alo Mistica 10 3 3 MATPOWER Options sita rada ees 11 0 S mmary of the les ci 14 4 ACKNOWIEDSMCMUS weceececeiersctieilanestinedeacestaeuesavessMidesthesceerebibhiadosstindeadesswesscastaeens 15 B REED 16 Appendix A Notes on LP Solvers for Matlab sccsscccscccscccssccccsccsscccsccesscessceees 17 Appendix B Some General Matlab Performance Notes cccsccscsssscscsscscscsscsceees 17 1 Introduction What is MATPOWER MATPOWER is a package of Matlab m files for solving power flow and optimal power flow prob lems It is intended as a simulation tool for researchers and educators which will be easy to use and modify MATPOWER is designed to give the best performance possible while keeping the c
8. ased method 2 Sparse LP based method w relaxed constraints 3 Sparse LP based method w full constraints This yields the following 9 codes 0 choose appropriate default from OPF_ALG_ POLY or OPF_ALG _ PWL 100 standard formulation constr 120 standard formulation dense LP 140 standard formulation sparse LP relaxed 160 standard formulation sparse LP full 200 CCV formulation constr 220 CCV formulation dense LP 240 CCV formulation sparse LP relaxed 260 CCV formulation sparse LP full 12 OPF_ALG_ POLY 100 default OPF algorithm for use with polynomial cost functions 13 OPF_ALG_PWL 200 default OPF algorithm for use with piece wise linear cost functions 14 OPF_POLY2PWL_PTS 10 number of evaluation points to use when converting from polynomial to piece wise linear costs 15 OPF_NEQ 0 number of equality constraints 0 gt 2 nb set by program not a user option 16 OPF_VIOLATION 5e 6 constraint violation tolerance 17 CONSTR_TOL_X le 4 termination tol on x for constr description options 12 18 CONSTR_TOL_F le 4 termination tol on F for constr 19 CONSTR_MAX_IT 0 max number of iterations for constr 0 gt 2 nb 150 20 LPC_TOL GRAD 3e 3 terminati
9. ch that A Ax lt b A lt Ax lt A If this is rewritten as min ci Ax c Ax such that A Ax 4 Ax A Ax A Ax Sb A lt Ax lt A Where A 1s a square matrix Ax can be computed as Ax Ay b A Ax Substituting back in to the problem yields a new LP problem min c Ay Ait ch Ax such that A Ax A Ax b Az Ay b A Ax Ay Ax lt b A SAD b A Ax lt A A S Ax lt A This new LP problem is smaller than the original but it is no longer sparse As mentioned above to realize the full potential of the LP based OPF solvers it will be necessary to obtain a good LP solver such as bpmpd See Appendix A for more details 3 4 Unit Decommitment Algorithm The standard OPF formulation described in the previous section has no mechanism for completely shutting down generators which are very expensive to operate Instead they are simply dispatched at their minimum generation limits MATPOWER includes a unit decommitment algorithm which 10 allows it to shut down these expensive units The algorithm is based on a simplified version of the decommitment technique proposed in 6 The algorithm proceeds as follows Step 0 Step 1 Step 2 Step 3 Step 4 Step 5 Assume all generators are on line with all generator limits in place Solve a normal OPF If the OPF converged to a feasible solution and the objective function decreased from the previous iteration
10. emergency rating ratio transformer off nominal turns ratio 0 for lines taps at from bus impedance at to bus i e ratio Vf Vt angle transformer phase shift angle degrees Gf shunt conductance at from bus p u Bf shunt susceptance at from bus p u Gt shunt conductance at to bus p u Bt shunt susceptance at to bus p u initial branch status 1 in service 0 out of service E El Area Data Format a 2 i area number price_ref_bus reference bus for that area Generator Cost Data Format NOTE the If gen has n rows then the first n rows of gencost contain cost for active power produced by the corresponding generators If gencost has 2 n rows then rows n l to 2 n contain the reactive power costs in the same format 1 model 1 piecewise linear 2 polynomial 2 startup startup cost in US dollars 3 shutdown shutdown cost in US dollars 4 n number of cost coefficients to follow for polynomial or data points for piecewise linear total cost function 5 and following cost data piecewise linear data as x0 yO xl yl x2 y2 and polynomial data as e g EZ El 50 where the polynomial is c0 c1 P c2 P 2 3 2 Power Flow MATPOWER has three power flow solvers The default power flow solver is based on a standard Newton s method 11 using a full Jacobian updated at each iteration This method is described in detail in many textbooks The other two
11. es from OPF uopf m runuopf m except runopf m implements decommitment heuristic main program for running OPF with decommitment algorithm Files for use with the bpmpd LP QP solver bpmpd lp m replacement for bpmpd gqp m replacement for 4 Acknowledgments Optimization Toolbox lp m Optimization Toolbox qp m used by constr m The authors would like to acknowledge contributions from several people Thanks to Carlos Murillo Sanchez for suggesting the CCV formulation for handling piecewise linear costs in the OPF for his help on the decommitment algorithm and for creating the Matlab MEX interface to the bpmpd LP and QP solver Thanks to Chris DeMarco one of our PSERC associates at the Univer sity of Wisconsin for the technique for building the Jacobian matrix Our appreciation to Bruce Wollenberg for all of his suggestions for improvements to version 1 The enhanced output function ality in version 2 0 are primarily due to his input Thanks also to Andrew Ward for code which helped us verify and test the ability of the OPF to optimize reactive power costs Last but not least we d like to acknowledge the input of Bob Thomas throughout the of development of MATPOWER here at PSERC Cornell 15 5 References Ls Dn w 10 11 R van Amerongen A General Purpose Version of the Fast Decoupled Loadflow IEEE Transactions on Power Systems Vol 4 No 2 May 1989 pp 760 770 O Alsac J Bright M P
12. include and LP solver 1p m which is based on it s QP solver gp m For large sparse problems these routines are very slow Fortunately there are some third party LP and QP solvers for MATLAB with much better performance Several LP and QP solvers have been tested for use in the context of an LP based OPF Some of them we were unable to get to compile on our architecture of choice Sun Ultra running Solaris 2 5 1 and others proved to be less than robust in an OPF context Here is a list of the solvers we ve attempted to use e bpmpd QP solver from http www sztaki hu meszaros bpmpd 100 Matlab MEX interface by Carlos Murillo lt cem14 cornell edu gt e lpm LP solver included with Optimization Toolbox from MathWorks e lp_solve LP solver from ftp ftp ics ele tue nl pub lp_solve free e logo LP solver from http www princeton edu rvdb free e sol_qps m LP solver developed at U of Wisconsin not publicly available Of all of the packages tested the bpmpd solver has been the only one which worked reliably for us It has proven to be very robust and has exceptional performance The distribution includes two files 1p m and qp m in the bpmpd directory If bpmpd is installed and these two files are included in your Matlab path before the Optimization Toolbox routines they will be used in place of the 1p m and qp min the Toolbox More information about free optimizers is available in Decision Tree for Optimiza
13. n power flow on the default 9 bus system specified in the file case m with the default algorithm options at the Matlab prompt type gt gt runpf To run a power flow on the 118 bus system whose data is in case118 m type gt gt runpf casel18 2 4 Running an Optimal Power Flow To run an optimal power flow on the default 9 bus system specified in the file case m with the default algorithm options at the Matlab prompt type gt gt runopf To run an optimal power flow on the 30 bus system whose data is in case30 m type gt gt runopf case30 To run an optimal power flow on the same system but with the option for MATPOWER to shut down decommit expensive generators type gt gt runuopf case30 2 5 Getting Help As with Matlab s built in functions and toolbox routines you can type help followed by the name of a command or m file to get help on that particular function Nearly all of MATPOWER s m files have such documentation For example the help for runopf looks like gt gt help runopf RUNOPF Runs an optimal power flow baseMVA bus gen gencost branch f success et runopf casename mpopt fname Runs an optimal power flow where casename is the name of the m file without the m extension containing the opf data and mpopt is a MATPOWER options vector see help mpoption for details Uses default options if 2nd parameter is not given and case if lst parameter is not given The resul
14. ode simple to understand and modify The MATPOWER home page can be found at http www pserc cornell edu matpower matpower html Where did it come from MATPOWER was developed by Ray Zimmerman and Deqiang Gan of PSERC at Cornell Univer sity http www pserc cornell edu under the direction of Robert Thomas The initial need for Matlab based power flow and optimal power flow code was born out of the computational require ments of the PowerWeb project see http www pserc cornell edu powerweb Who can use it MATPOWER is free Anyone may use it Anyone may modify it for their own use as long as the original copyright notices remain in place Please don t distribute modified versions of MATPOWER without written permission from us 2 Getting Started 2 1 System Requirements To use MATPOWER you will need a Mac UNIX machine or PC with e Matlab 4 or higher available from The MathWorks e Matlab Optimization Toolbox available from The MathWorks 2 2 Installation Step 1 Goto the MATPOWER home page and follow the download instructions Step 2 Unpack the archive using the appropriate software for your machine StuffIt Expander for Mac gunzip and tar for UNIX pkzip WinZip etc for PC Step 3 Copy all of the m files in the MATPOWER distribution to a location in your Matlab path See http www mathworks com http www pserc cornell edu matpower matpower html 2 3 Running a Power Flow To run a simple Newto
15. on criteria is outlined below L d 7 4 A lt tolerance g x lt tolerance Ax lt tolerance Here A is the vector of Lagrange multipliers of the LP problem The first condition pertains to the size of the gradient the second to the violation of constraints and the third to the step size More detail can be found in 4 Quite frequently the value of x given by step 1 is infeasible and could result in an infeasible LP problem In such cases a slack variable is added for each violated constraint These slack vari ables must be zero at the optimal solution The LPconstr function implements the following three methods e sparse formulation with full set of inequality constraints e sparse formulation with relaxed constraints ICS Iterative Constraint Search e dense formulation with relaxed constraints ICS 10 These three methods are specified using algorithm codes 160 140 and 120 respectively for sys tems with polynomial costs and 260 240 and 220 respectively for systems with piecewise linear costs As with the constr based method selecting one of the 2xx algorithms for a system with polynomial cost will cause the cost to be replaced by a piecewise linear approximation In the dense formulation some of the variables x and the equality constraints g are eliminated from the problem before posing the LP sub problem This procedure is outlined below Suppose the LP sub problem is given by min c Ax su
16. on tolerance on gradient for LPconstr 21 LPC_TOL_X 5e 3 termination tolerance on x min step size for LPconstr 22 LPC_MAX_IT 1000 maximum number of iterations for LPconstr 23 LPC_ MAX RESTART 5 maximum number of restarts for LPconstr output options 31 VERBOSE 1 amount of progress info printed 0 print no progress info 1 print a little progress info 2 print a lot of progress info 3 print all progress info 32 OUT_ALL 1 controls printing of results 1 individual flags control what prints 0 don t print anything overrides individual flags except OUT_RAW 1 print everything overrides individual flags except OUT_RAW 33 OUT_SYS_SUM 1 print system summary 0 or 1 34 OUT_AREA SUM 0 print area summaries O or 1 35 OUT_BUS 1 print bus detail 0 or 1 36 OUT_BRANCH 1 print branch detail Qo ct 37 OUT_GEN 0 print generator detail 0 or 1 OUT_BUS also includes gen info 38 OUT_ALL LIM 1 control constraint info output 1 individual flags control what constraint info prints 0 no constraint info overrides individual flags 1 binding constraint info overrides individual flags 2 all constraint info overrides individual flags 39 OUT_V_LIM 1 control output of voltage limit info 0 don t print 1 print binding constraints only 2 print all constraints same options for OUT_LINE_LIM OUT_PG_LIM OUT_QG_LIM 40 OUT_LINE_LIM 1 control output of line limit info 41 OUT_PG_
17. ower generation limits Here f and f are the costs of active and reactive power generation respectively for generator i at a given dispatch point Both f and f are assumed to be a polynomial or piecewise linear func tions The problem can be written more compactly in the following form min f x such that g x lt 0 where f and g are non linear functions Optimization Toolbox Based OPF Solver constr The first of the two OPF solvers in MATPOWER is based on the constr non linear constrained optimization function in Matlab s Optimization Toolbox The constr function and the algorithms it uses are covered in the Optimization Toolbox manual 5 MATPOWER provides constr with two m files which it uses during for the optimization One computes the objective function f and the constraint violations g at a given point x and the other computes their gradients df dx and d2 0x MATPOWER has two versions of these m files One set is used to solve systems with polynomial cost functions In this formulation the cost functions are included in a straightforward way into the objective function The other set is used to solve systems with piecewise linear costs Piecewise linear cost functions are handled by introducing a cost variable for each piecewise linear cost func tion The objective function is simply the sum of these cost variables which are then constrained to lie above each of the linear functions which make up the piece
18. power flow solvers are variations of the fast decoupled method 9 MATPOWER implements the XB and BX variations as described in 1 Currently MATPOWER s power flow solvers do not include any transformer tap changing or feasibility checking capabilities Performance of the power flow solvers should be excellent even on very large scale power sys tems since the algorithms and implementation take advantage of Matlab s built in sparse matrix handling On a Sun Ultra 2200 MATPOWER solves a 9600 bus test case in about 10 seconds and a 38400 bus case in about 50 seconds 3 3 Optimal Power Flow MATPOWER includes two solvers for the optimal power flow OPF problem The first is based on the constr function included in Matlab s Optimization Toolbox which uses a successive quadratic programming technique with a quasi Newton approximation for the Hessian matrix The second approach is based on linear programming It can use the LP solver in the Optimization Toolbox or other Matlab LP solvers available from third parties The performance of MATPOWER s OPF solvers depends on several factors First the constr function uses an algorithm which does not exploit or preserve sparsity so it is inherently limited to small power systems The LP based algorithm on the other hand does preserve sparsity How ever the LP solver included in the Optimization Toolbox does not exploit this sparsity In fact the LP based method with the default LP solver
19. rais B Stott Further Developments in LP based Optimal Power Flow IEEE Transactions on Power Systems Vol 5 No 3 Aug 1990 pp 697 711 R Fletcher Practical Methods of Optimization 2nd Edition John Wiley amp Sons p 96 P E Gill W Murry M H Wright Practical Optimization Academic Press London 1981 A Grace Optimization Toolbox The MathWorks Inc Natick MA 1995 C Li R B Johnson A J Svoboda A New Unit Commitment Method IEEE Transactions on Power Systems Vol 12 No 1 Feb 1997 pp 113 119 C M szaros The efficient implementation of interior point methods for linear programming and their applications Ph D Thesis E tv s Lor nd University of Sciences 1996 B Stott Review of Load Flow Calculation Methods Proceedings of the IEEE Vol 62 No 7 July 1974 pp 916 929 B Stott and O Alsac Fast decoupled load flow IEEE Transactions on Power Apparatus and Systems Vol PAS 93 June 1974 pp 859 869 B Stott J L Marino O Alsac Review of Linear Programming Applied to Power System Re scheduling 1979 PICA pp 142 154 W F Tinney and C E Hart Power Flow Solution by Newton s Method IEEE Transac tions on Power Apparatus and Systems Vol PAS 86 No 11 Nov 1967 pp 1449 1460 16 Appendix A Notes on LP Solvers for Matlab The MATPOWER distribution does not include an LP solver however the Matlab Optimization Toolbox does
20. system voltage magnitudes and angles and x contains the generator real and reactive power outputs and corresponding cost variables for the CCV formulation This is a general non linear programming problem with the additional assumption that the equality con straints can be used to solve for x given a value for x The LP based OPF solver is implemented with a function LPconstr which is similar to constr in that it uses the same m files for computing the objective function constraints and their respective gradients In addition a third m file lpeqslvr m is needed to solve for x from the equality con straints given a value for x This architecture makes it relatively simple to modify the formulation of the problem and still be able to use both the constr based and LP based solvers The algorithm proceeds as follows where the superscripts denote iteration number Step 0 Set iteration counter k lt 0 and choose an appropriate initial value call it x for x Step 1 Solve the equality constraint power flow equations 2 x x4 0 for x Step 2 Linearize the problem around x solve the resulting LP for Ax min Y La Ax L Ax ys such that o E Lars e x ed ee A lt Ax lt A Step 3 Set k k 1 update current solution xi axl Ax Step 4 Ifx meets termination criteria stop otherwise go to step 5 Step 5 Adjust step size limit A based on the trust region algorithm in 3 go to step 1 The terminati
21. tion Software maintained by Mittenlmonn Hans and P Spellucci at http plato la asu edu guide html Appendix B Some General Matlab Performance Notes The performance bottlenecks in Matlab are different for Matlab 4 and Matlab 5 Here are two ob servations from our testing e Matlab 4 is slow at executing case m for large files Matlab 5 is not e Matlab 5 is slow at selecting rows of a large sparse matrix Matlab 4 is not Note when using constr in Matlab 5 it doesn t seem to find the bpmpd replacement for gp m although this seems to work fine under Matlab 4 17
22. ts may optionally be printed to a file appended if the file exists whose name is given in fname in addition to printing to STDOUT Optionally returns the final values of baseMVA bus gen gencost branch f success and et MATPOWER also has many options which control the algorithms and the output Type gt gt help mpoption and see Section 3 5 for more information on MATPOWER s options 3 Technical Reference 3 1 Data File Format The data files used by MATPOWER are simply Matlab m files which define and return the vari ables base MVA bus branch gen area and gencost The bus branch and gen variables are ma trices Each row in the matrix corresponds to a single bus branch or generator respectively The columns are similar to the columns in the standard IEEE and PTI formats The details of the speci fication of the MATPOWER case file can be found in the help for case m gt gt help case CASE Defines the power flow data in a format similar to PTI baseMVA bus gen branch area gencost case The format for the data is similar to PTI format except where noted An item marked with indicates that it is included in this data but is not part of the PTI format An item marked with is one that is in the PTI format but is not included here Bus Data Format I bus number 1 to 29997 2 bus type PQ bus PV bus reference bus isolated bus AUNE 3 Pd real power demand MW
23. wise linear cost function Clearly this method works only for convex cost functions In the MATPOWER documentation this will be referred to as a constrained cost variable CCV formulation The algorithm codes 100 and 200 respectively are used to identify the constr based solver for polynomial and piecewise linear cost functions If algorithm 200 is chosen for a system with poly nomial cost function the cost function will be approximated by a piecewise linear function by evaluating the polynomial at a fixed number of points determined by the options vector see Sec tion 3 5 for more details on the MATPOWER options It should be noted that the constr based method can also benefit from a superior QP solver such as bpmpd See Appendix A for more information on LP and QP solvers LP Based OPF Solver LPconstr Linear programming based OPF methods are in wide use today in the industry However the LP based algorithm included in MATPOWER is much simpler than the algorithms used in production grade software The LP based methods in MATPOWER use the same problem formulation as the const r based methods including the CCV formulation for the case of piecewise linear costs The compact form of the OPF problem can be rewritten to partition ginto equality and inequality constraints and to partition the variable x as follows min f x such that g x x 0 equality constraints gx x lt 0 inequality constraints where x contains the
Download Pdf Manuals
Related Search