MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance powerflow0009r

Optimal Power Flow problem modeled using quadratic functions (rectangular coordinates)
Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
5296.68620400 p1 ( gdx sol )
(infeas: 8e-15)
Other points (infeas > 1e-08)  
Dual Bounds
5296.15653500 (ANTIGONE)
5296.68458100 (BARON)
5296.65000000 (COUENNE)
5296.68280400 (GUROBI)
5154.91260300 (LINDO)
5296.68443000 (SCIP)
References Hijazi, H L, Coffrin, C, and Van Hentenryck, P, Convex Quadratic Relaxations of Nonlinear Programs in Power Systems, Tech. Rep. 2013-09, Optimization Online, 2013.
Application Electricity Networks
Added to library 18 Aug 2014
Problem type QCQP
#Variables 60
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 57
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 3
#Nonlinear Nonzeros in Objective 3
#Constraints 103
#Linear Constraints 31
#Quadratic Constraints 72
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 307
#Nonlinear Nonzeros in Jacobian 216
#Nonzeros in (Upper-Left) Hessian of Lagrangian 129
#Nonzeros in Diagonal of Hessian of Lagrangian 57
#Blocks in Hessian of Lagrangian 40
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 18
Average blocksize in Hessian of Lagrangian 1.425
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 5.7754e-01
Maximal coefficient 1.2250e+03
Infeasibility of initial point 1.25
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*        104       56       15       33        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         61       61        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        311       92      219        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
          ,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
          ,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
          ,x54,x55,x56,x57,x58,x59,x60,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
          ,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
          ,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
          ,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
          ,e104;


e1.. 1100*sqr(x55) + 500*x55 + 850*sqr(x56) + 120*x56 + 1225*sqr(x57) + 100*x57
      - objvar =E= -1085;

e2.. 8.53242320819113*x42*x48 - 8.53242320819113*x39*x51 + 8.53242320819113*x48
     *x42 - 8.53242320819113*x51*x39 + x1 =E= 0;

e3.. 8.53242320819113*x39*x51 - 8.53242320819113*x42*x48 - 8.53242320819113*x48
     *x42 + 8.53242320819113*x51*x39 + x2 =E= 0;

e4.. 0.808561236623068*x43*x44 - 1.61712247324614*sqr(x43) - 6.84898929845422*
     x43*x53 + 0.808561236623068*x44*x43 + 6.84898929845422*x44*x52 + 
     6.84898929845422*x52*x44 - 1.61712247324614*sqr(x52) + 0.808561236623068*
     x52*x53 - 6.84898929845422*x53*x43 + 0.808561236623068*x53*x52 + x3 =E= 0;

e5.. 0.808561236623068*x43*x44 + 6.84898929845422*x43*x53 + 0.808561236623068*
     x44*x43 - 1.61712247324614*sqr(x44) - 6.84898929845422*x44*x52 - 
     6.84898929845422*x52*x44 + 0.808561236623068*x52*x53 + 6.84898929845422*
     x53*x43 + 0.808561236623068*x53*x52 - 1.61712247324614*sqr(x53) + x4 =E= 0
     ;

e6.. 0.641004569212057*x41*x42 - 1.28200913842411*sqr(x41) - 2.79412248118076*
     x41*x51 + 0.641004569212057*x42*x41 + 2.79412248118076*x42*x50 + 
     2.79412248118076*x50*x42 - 1.28200913842411*sqr(x50) + 0.641004569212057*
     x50*x51 - 2.79412248118076*x51*x41 + 0.641004569212057*x51*x50 + x5 =E= 0;

e7.. 0.641004569212057*x41*x42 + 2.79412248118076*x41*x51 + 0.641004569212057*
     x42*x41 - 1.28200913842411*sqr(x42) - 2.79412248118076*x42*x50 - 
     2.79412248118076*x50*x42 + 0.641004569212057*x50*x51 + 2.79412248118076*
     x51*x41 + 0.641004569212057*x51*x50 - 1.28200913842411*sqr(x51) + x6 =E= 0
     ;

e8.. 0.577543740445048*x42*x43 - 1.1550874808901*sqr(x42) - 4.89213521318159*
     x42*x52 + 0.577543740445048*x43*x42 + 4.89213521318159*x43*x51 + 
     4.89213521318159*x51*x43 - 1.1550874808901*sqr(x51) + 0.577543740445048*
     x51*x52 - 4.89213521318159*x52*x42 + 0.577543740445048*x52*x51 + x7 =E= 0;

e9.. 0.577543740445048*x42*x43 + 4.89213521318159*x42*x52 + 0.577543740445048*
     x43*x42 - 1.1550874808901*sqr(x43) - 4.89213521318159*x43*x51 - 
     4.89213521318159*x51*x43 + 0.577543740445048*x51*x52 + 4.89213521318159*
     x52*x42 + 0.577543740445048*x52*x51 - 1.1550874808901*sqr(x52) + x8 =E= 0;

e10.. 8*x38*x53 - 8*x44*x47 - 8*x47*x44 + 8*x53*x38 + x9 =E= 0;

e11.. 8*x44*x47 - 8*x38*x53 + 8*x47*x44 - 8*x53*x38 + x10 =E= 0;

e12.. 0.971095624357363*x40*x41 - 1.94219124871473*sqr(x40) - 5.25534102593397*
      x40*x50 + 0.971095624357363*x41*x40 + 5.25534102593397*x41*x49 + 
      5.25534102593397*x49*x41 - 1.94219124871473*sqr(x49) + 0.971095624357363*
      x49*x50 - 5.25534102593397*x50*x40 + 0.971095624357363*x50*x49 + x11
       =E= 0;

e13.. 0.971095624357363*x40*x41 + 5.25534102593397*x40*x50 + 0.971095624357363*
      x41*x40 - 1.94219124871473*sqr(x41) - 5.25534102593397*x41*x49 - 
      5.25534102593397*x49*x41 + 0.971095624357363*x49*x50 + 5.25534102593397*
      x50*x40 + 0.971095624357363*x50*x49 - 1.94219124871473*sqr(x50) + x12
       =E= 0;

e14.. 8.68055555555556*x40*x46 - 8.68055555555556*x37*x49 + 8.68055555555556*
      x46*x40 - 8.68055555555556*x49*x37 + x13 =E= 0;

e15.. 8.68055555555556*x37*x49 - 8.68055555555556*x40*x46 - 8.68055555555556*
      x46*x40 + 8.68055555555556*x49*x37 + x14 =E= 0;

e16.. 0.68259385665529*x40*x45 + 5.80204778156997*x40*x54 + 0.68259385665529*
      x45*x40 - 1.36518771331058*sqr(x45) - 5.80204778156997*x45*x49 - 
      5.80204778156997*x49*x45 + 0.68259385665529*x49*x54 + 5.80204778156997*
      x54*x40 + 0.68259385665529*x54*x49 - 1.36518771331058*sqr(x54) + x15
       =E= 0;

e17.. 0.68259385665529*x40*x45 - 1.36518771331058*sqr(x40) - 5.80204778156997*
      x40*x54 + 0.68259385665529*x45*x40 + 5.80204778156997*x45*x49 + 
      5.80204778156997*x49*x45 - 1.36518771331058*sqr(x49) + 0.68259385665529*
      x49*x54 - 5.80204778156997*x54*x40 + 0.68259385665529*x54*x49 + x16 =E= 0
      ;

e18.. 0.593802189645574*x44*x45 - 1.18760437929115*sqr(x44) - 2.9875672666543*
      x44*x54 + 0.593802189645574*x45*x44 + 2.9875672666543*x45*x53 + 
      2.9875672666543*x53*x45 - 1.18760437929115*sqr(x53) + 0.593802189645574*
      x53*x54 - 2.9875672666543*x54*x44 + 0.593802189645574*x54*x53 + x17 =E= 0
      ;

e19.. 0.593802189645574*x44*x45 + 2.9875672666543*x44*x54 + 0.593802189645574*
      x45*x44 - 1.18760437929115*sqr(x45) - 2.9875672666543*x45*x53 - 
      2.9875672666543*x53*x45 + 0.593802189645574*x53*x54 + 2.9875672666543*x54
      *x44 + 0.593802189645574*x54*x53 - 1.18760437929115*sqr(x54) + x18 =E= 0;

e20.. 8.53242320819113*x39*x42 - 17.0648464163823*sqr(x39) + 8.53242320819113*
      x42*x39 - 17.0648464163823*sqr(x48) + 8.53242320819113*x48*x51 + 
      8.53242320819113*x51*x48 + x19 =E= 0;

e21.. 8.53242320819113*x39*x42 + 8.53242320819113*x42*x39 - 17.0648464163823*
      sqr(x42) + 8.53242320819113*x48*x51 + 8.53242320819113*x51*x48 - 
      17.0648464163823*sqr(x51) + x20 =E= 0;

e22.. 6.84898929845422*x43*x44 - 13.6234785969084*sqr(x43) + 0.808561236623068*
      x43*x53 + 6.84898929845422*x44*x43 - 0.808561236623068*x44*x52 - 
      0.808561236623068*x52*x44 - 13.6234785969084*sqr(x52) + 6.84898929845422*
      x52*x53 + 0.808561236623068*x53*x43 + 6.84898929845422*x53*x52 + x21
       =E= 0;

e23.. 6.84898929845422*x43*x44 - 0.808561236623068*x43*x53 + 6.84898929845422*
      x44*x43 - 13.6234785969084*sqr(x44) + 0.808561236623068*x44*x52 + 
      0.808561236623068*x52*x44 + 6.84898929845422*x52*x53 - 0.808561236623068*
      x53*x43 + 6.84898929845422*x53*x52 - 13.6234785969084*sqr(x53) + x22
       =E= 0;

e24.. 2.79412248118076*x41*x42 - 5.40924496236153*sqr(x41) + 0.641004569212057*
      x41*x51 + 2.79412248118076*x42*x41 - 0.641004569212057*x42*x50 - 
      0.641004569212057*x50*x42 - 5.40924496236153*sqr(x50) + 2.79412248118076*
      x50*x51 + 0.641004569212057*x51*x41 + 2.79412248118076*x51*x50 + x23
       =E= 0;

e25.. 2.79412248118076*x41*x42 - 0.641004569212057*x41*x51 + 2.79412248118076*
      x42*x41 - 5.40924496236153*sqr(x42) + 0.641004569212057*x42*x50 + 
      0.641004569212057*x50*x42 + 2.79412248118076*x50*x51 - 0.641004569212057*
      x51*x41 + 2.79412248118076*x51*x50 - 5.40924496236153*sqr(x51) + x24
       =E= 0;

e26.. 4.89213521318159*x42*x43 - 9.67977042636317*sqr(x42) + 0.577543740445048*
      x42*x52 + 4.89213521318159*x43*x42 - 0.577543740445048*x43*x51 - 
      0.577543740445048*x51*x43 - 9.67977042636317*sqr(x51) + 4.89213521318159*
      x51*x52 + 0.577543740445048*x52*x42 + 4.89213521318159*x52*x51 + x25
       =E= 0;

e27.. 4.89213521318159*x42*x43 - 0.577543740445048*x42*x52 + 4.89213521318159*
      x43*x42 - 9.67977042636317*sqr(x43) + 0.577543740445048*x43*x51 + 
      0.577543740445048*x51*x43 + 4.89213521318159*x51*x52 - 0.577543740445048*
      x52*x42 + 4.89213521318159*x52*x51 - 9.67977042636317*sqr(x52) + x26
       =E= 0;

e28.. 8*x38*x44 + 8*x44*x38 - 16*sqr(x44) + 8*x47*x53 + 8*x53*x47 - 16*sqr(x53)
       + x27 =E= 0;

e29.. 8*x38*x44 - 16*sqr(x38) + 8*x44*x38 - 16*sqr(x47) + 8*x47*x53 + 8*x53*x47
       + x28 =E= 0;

e30.. 5.25534102593397*x40*x41 - 10.4316820518679*sqr(x40) + 0.971095624357363*
      x40*x50 + 5.25534102593397*x41*x40 - 0.971095624357363*x41*x49 - 
      0.971095624357363*x49*x41 - 10.4316820518679*sqr(x49) + 5.25534102593397*
      x49*x50 + 0.971095624357363*x50*x40 + 5.25534102593397*x50*x49 + x29
       =E= 0;

e31.. 5.25534102593397*x40*x41 - 0.971095624357363*x40*x50 + 5.25534102593397*
      x41*x40 - 10.4316820518679*sqr(x41) + 0.971095624357363*x41*x49 + 
      0.971095624357363*x49*x41 + 5.25534102593397*x49*x50 - 0.971095624357363*
      x50*x40 + 5.25534102593397*x50*x49 - 10.4316820518679*sqr(x50) + x30
       =E= 0;

e32.. 8.68055555555556*x37*x40 - 17.3611111111111*sqr(x37) + 8.68055555555556*
      x40*x37 - 17.3611111111111*sqr(x46) + 8.68055555555556*x46*x49 + 
      8.68055555555556*x49*x46 + x31 =E= 0;

e33.. 8.68055555555556*x37*x40 + 8.68055555555556*x40*x37 - 17.3611111111111*
      sqr(x40) + 8.68055555555556*x46*x49 + 8.68055555555556*x49*x46 - 
      17.3611111111111*sqr(x49) + x32 =E= 0;

e34.. 5.80204778156997*x40*x45 - 0.68259385665529*x40*x54 + 5.80204778156997*
      x45*x40 - 11.5160955631399*sqr(x45) + 0.68259385665529*x45*x49 + 
      0.68259385665529*x49*x45 + 5.80204778156997*x49*x54 - 0.68259385665529*
      x54*x40 + 5.80204778156997*x54*x49 - 11.5160955631399*sqr(x54) + x33
       =E= 0;

e35.. 5.80204778156997*x40*x45 - 11.5160955631399*sqr(x40) + 0.68259385665529*
      x40*x54 + 5.80204778156997*x45*x40 - 0.68259385665529*x45*x49 - 
      0.68259385665529*x49*x45 - 11.5160955631399*sqr(x49) + 5.80204778156997*
      x49*x54 + 0.68259385665529*x54*x40 + 5.80204778156997*x54*x49 + x34 =E= 0
      ;

e36.. 2.9875672666543*x44*x45 - 5.82213453330859*sqr(x44) + 0.593802189645574*
      x44*x54 + 2.9875672666543*x45*x44 - 0.593802189645574*x45*x53 - 
      0.593802189645574*x53*x45 - 5.82213453330859*sqr(x53) + 2.9875672666543*
      x53*x54 + 0.593802189645574*x54*x44 + 2.9875672666543*x54*x53 + x35 =E= 0
      ;

e37.. 2.9875672666543*x44*x45 - 0.593802189645574*x44*x54 + 2.9875672666543*x45
      *x44 - 5.82213453330859*sqr(x45) + 0.593802189645574*x45*x53 + 
      0.593802189645574*x53*x45 + 2.9875672666543*x53*x54 - 0.593802189645574*
      x54*x44 + 2.9875672666543*x54*x53 - 5.82213453330859*sqr(x54) + x36 =E= 0
      ;

e38.. sqr(x1) + sqr(x19) =L= 9;

e39.. sqr(x2) + sqr(x20) =L= 9;

e40.. sqr(x3) + sqr(x21) =L= 6.25;

e41.. sqr(x4) + sqr(x22) =L= 6.25;

e42.. sqr(x5) + sqr(x23) =L= 2.25;

e43.. sqr(x6) + sqr(x24) =L= 2.25;

e44.. sqr(x7) + sqr(x25) =L= 2.25;

e45.. sqr(x8) + sqr(x26) =L= 2.25;

e46.. sqr(x9) + sqr(x27) =L= 6.25;

e47.. sqr(x10) + sqr(x28) =L= 6.25;

e48.. sqr(x11) + sqr(x29) =L= 6.25;

e49.. sqr(x12) + sqr(x30) =L= 6.25;

e50.. sqr(x13) + sqr(x31) =L= 6.25;

e51.. sqr(x14) + sqr(x32) =L= 6.25;

e52.. sqr(x15) + sqr(x33) =L= 6.25;

e53.. sqr(x16) + sqr(x34) =L= 6.25;

e54.. sqr(x17) + sqr(x35) =L= 6.25;

e55.. sqr(x18) + sqr(x36) =L= 6.25;

e56.. sqr(x37) + sqr(x46) =L= 1.21;

e57.. sqr(x38) + sqr(x47) =L= 1.21;

e58.. sqr(x39) + sqr(x48) =L= 1.21;

e59.. sqr(x40) + sqr(x49) =L= 1.21;

e60.. sqr(x41) + sqr(x50) =L= 1.21;

e61.. sqr(x42) + sqr(x51) =L= 1.21;

e62.. sqr(x43) + sqr(x52) =L= 1.21;

e63.. sqr(x44) + sqr(x53) =L= 1.21;

e64.. sqr(x45) + sqr(x54) =L= 1.21;

e65.. sqr(x37) + sqr(x46) =G= 0.81;

e66.. sqr(x38) + sqr(x47) =G= 0.81;

e67.. sqr(x39) + sqr(x48) =G= 0.81;

e68.. sqr(x40) + sqr(x49) =G= 0.81;

e69.. sqr(x41) + sqr(x50) =G= 0.81;

e70.. sqr(x42) + sqr(x51) =G= 0.81;

e71.. sqr(x43) + sqr(x52) =G= 0.81;

e72.. sqr(x44) + sqr(x53) =G= 0.81;

e73.. sqr(x45) + sqr(x54) =G= 0.81;

e74..    x55 =L= 2.5;

e75..    x56 =L= 3;

e76..    x57 =L= 2.7;

e77..    x55 =G= 0.1;

e78..    x56 =G= 0.1;

e79..    x57 =G= 0.1;

e80..    x58 =L= 3;

e81..    x59 =L= 3;

e82..    x60 =L= 3;

e83..    x58 =G= -3;

e84..    x59 =G= -3;

e85..    x60 =G= -3;

e86..    x46 =E= 0;

e87..    x13 - x55 =E= 0;

e88..    x10 - x56 =E= 0;

e89..    x1 - x57 =E= 0;

e90..    x31 - x58 =E= 0;

e91..    x28 - x59 =E= 0;

e92..    x19 - x60 =E= 0;

e93..    x11 + x14 + x16 =E= 0;

e94..    x5 + x12 =E= -0.9;

e95..    x2 + x6 + x7 =E= 0;

e96..    x3 + x8 =E= -1;

e97..    x4 + x9 + x17 =E= 0;

e98..    x15 + x18 =E= -1.25;

e99..    x29 + x32 + x34 =E= 0;

e100..    x23 + x30 =E= -0.3;

e101..    x20 + x24 + x25 =E= 0;

e102..    x21 + x26 =E= -0.35;

e103..    x22 + x27 + x35 =E= 0;

e104..    x33 + x36 =E= -0.5;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;


Last updated: 2022-05-24 Git hash: 1198c186
Imprint / Privacy Policy / License: CC-BY 4.0