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Instance powerflow0009p

Optimal Power Flow problem modeled using trigonometric functions (polar coordinates)
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
5296.68620400 p1 ( gdx sol )
(infeas: 9e-15)
Other points (infeas > 1e-08)  
Dual Bounds
3560.23041600 (COUENNE)
2357.82828700 (LINDO)
4330.06770400 (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 NLP
#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 139
#Linear Constraints 85
#Quadratic Constraints 18
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 36
Operands in Gen. Nonlin. Functions cos mul sin sqr
Constraints curvature indefinite
#Nonzeros in Jacobian 361
#Nonlinear Nonzeros in Jacobian 180
#Nonzeros in (Upper-Left) Hessian of Lagrangian 147
#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 1.0000e+00
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
*        140       56       33       51        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
*        365      182      183        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,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
          ,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
          ,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140;


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

e2.. -17.0648464163823*x3*x6*sin(x48 - x51) + x10 =E= 0;

e3.. -17.0648464163823*x6*x3*sin(x51 - x48) + x11 =E= 0;

e4.. 1.61712247324614*x7*x8*cos(x52 - x53) - 1.61712247324614*sqr(x7) - 
     13.6979785969084*x7*x8*sin(x52 - x53) + x12 =E= 0;

e5.. 1.61712247324614*x8*x7*cos(x53 - x52) - 1.61712247324614*sqr(x8) - 
     13.6979785969084*x8*x7*sin(x53 - x52) + x13 =E= 0;

e6.. 1.28200913842411*x5*x6*cos(x50 - x51) - 1.28200913842411*sqr(x5) - 
     5.58824496236153*x5*x6*sin(x50 - x51) + x14 =E= 0;

e7.. 1.28200913842411*x6*x5*cos(x51 - x50) - 1.28200913842411*sqr(x6) - 
     5.58824496236153*x6*x5*sin(x51 - x50) + x15 =E= 0;

e8.. 1.1550874808901*x6*x7*cos(x51 - x52) - 1.1550874808901*sqr(x6) - 
     9.78427042636317*x6*x7*sin(x51 - x52) + x16 =E= 0;

e9.. 1.1550874808901*x7*x6*cos(x52 - x51) - 1.1550874808901*sqr(x7) - 
     9.78427042636317*x7*x6*sin(x52 - x51) + x17 =E= 0;

e10.. -16*x8*x2*sin(x53 - x47) + x18 =E= 0;

e11.. -16*x2*x8*sin(x47 - x53) + x19 =E= 0;

e12.. 1.94219124871473*x4*x5*cos(x49 - x50) - 1.94219124871473*sqr(x4) - 
      10.5106820518679*x4*x5*sin(x49 - x50) + x20 =E= 0;

e13.. 1.94219124871473*x5*x4*cos(x50 - x49) - 1.94219124871473*sqr(x5) - 
      10.5106820518679*x5*x4*sin(x50 - x49) + x21 =E= 0;

e14.. -17.3611111111111*x1*x4*sin(x46 - x49) + x22 =E= 0;

e15.. -17.3611111111111*x4*x1*sin(x49 - x46) + x23 =E= 0;

e16.. 1.36518771331058*x9*x4*cos(x54 - x49) - 1.36518771331058*sqr(x9) - 
      11.6040955631399*x9*x4*sin(x54 - x49) + x24 =E= 0;

e17.. 1.36518771331058*x4*x9*cos(x49 - x54) - 1.36518771331058*sqr(x4) - 
      11.6040955631399*x4*x9*sin(x49 - x54) + x25 =E= 0;

e18.. 1.18760437929115*x8*x9*cos(x53 - x54) - 1.18760437929115*sqr(x8) - 
      5.97513453330859*x8*x9*sin(x53 - x54) + x26 =E= 0;

e19.. 1.18760437929115*x9*x8*cos(x54 - x53) - 1.18760437929115*sqr(x9) - 
      5.97513453330859*x9*x8*sin(x54 - x53) + x27 =E= 0;

e20.. 17.0648464163823*x3*x6*cos(x48 - x51) - 17.0648464163823*sqr(x3) + x28
       =E= 0;

e21.. 17.0648464163823*x6*x3*cos(x51 - x48) - 17.0648464163823*sqr(x6) + x29
       =E= 0;

e22.. 13.6979785969084*x7*x8*cos(x52 - x53) - 13.6234785969084*sqr(x7) + 
      1.61712247324614*x7*x8*sin(x52 - x53) + x30 =E= 0;

e23.. 13.6979785969084*x8*x7*cos(x53 - x52) - 13.6234785969084*sqr(x8) + 
      1.61712247324614*x8*x7*sin(x53 - x52) + x31 =E= 0;

e24.. 5.58824496236153*x5*x6*cos(x50 - x51) - 5.40924496236153*sqr(x5) + 
      1.28200913842411*x5*x6*sin(x50 - x51) + x32 =E= 0;

e25.. 5.58824496236153*x6*x5*cos(x51 - x50) - 5.40924496236153*sqr(x6) + 
      1.28200913842411*x6*x5*sin(x51 - x50) + x33 =E= 0;

e26.. 9.78427042636317*x6*x7*cos(x51 - x52) - 9.67977042636317*sqr(x6) + 
      1.1550874808901*x6*x7*sin(x51 - x52) + x34 =E= 0;

e27.. 9.78427042636317*x7*x6*cos(x52 - x51) - 9.67977042636317*sqr(x7) + 
      1.1550874808901*x7*x6*sin(x52 - x51) + x35 =E= 0;

e28.. 16*x8*x2*cos(x53 - x47) - 16*sqr(x8) + x36 =E= 0;

e29.. 16*x2*x8*cos(x47 - x53) - 16*sqr(x2) + x37 =E= 0;

e30.. 10.5106820518679*x4*x5*cos(x49 - x50) - 10.4316820518679*sqr(x4) + 
      1.94219124871473*x4*x5*sin(x49 - x50) + x38 =E= 0;

e31.. 10.5106820518679*x5*x4*cos(x50 - x49) - 10.4316820518679*sqr(x5) + 
      1.94219124871473*x5*x4*sin(x50 - x49) + x39 =E= 0;

e32.. 17.3611111111111*x1*x4*cos(x46 - x49) - 17.3611111111111*sqr(x1) + x40
       =E= 0;

e33.. 17.3611111111111*x4*x1*cos(x49 - x46) - 17.3611111111111*sqr(x4) + x41
       =E= 0;

e34.. 11.6040955631399*x9*x4*cos(x54 - x49) - 11.5160955631399*sqr(x9) + 
      1.36518771331058*x9*x4*sin(x54 - x49) + x42 =E= 0;

e35.. 11.6040955631399*x4*x9*cos(x49 - x54) - 11.5160955631399*sqr(x4) + 
      1.36518771331058*x4*x9*sin(x49 - x54) + x43 =E= 0;

e36.. 5.97513453330859*x8*x9*cos(x53 - x54) - 5.82213453330859*sqr(x8) + 
      1.18760437929115*x8*x9*sin(x53 - x54) + x44 =E= 0;

e37.. 5.97513453330859*x9*x8*cos(x54 - x53) - 5.82213453330859*sqr(x9) + 
      1.18760437929115*x9*x8*sin(x54 - x53) + x45 =E= 0;

e38.. sqr(x10) + sqr(x28) =L= 9;

e39.. sqr(x11) + sqr(x29) =L= 9;

e40.. sqr(x12) + sqr(x30) =L= 6.25;

e41.. sqr(x13) + sqr(x31) =L= 6.25;

e42.. sqr(x14) + sqr(x32) =L= 2.25;

e43.. sqr(x15) + sqr(x33) =L= 2.25;

e44.. sqr(x16) + sqr(x34) =L= 2.25;

e45.. sqr(x17) + sqr(x35) =L= 2.25;

e46.. sqr(x18) + sqr(x36) =L= 6.25;

e47.. sqr(x19) + sqr(x37) =L= 6.25;

e48.. sqr(x20) + sqr(x38) =L= 6.25;

e49.. sqr(x21) + sqr(x39) =L= 6.25;

e50.. sqr(x22) + sqr(x40) =L= 6.25;

e51.. sqr(x23) + sqr(x41) =L= 6.25;

e52.. sqr(x24) + sqr(x42) =L= 6.25;

e53.. sqr(x25) + sqr(x43) =L= 6.25;

e54.. sqr(x26) + sqr(x44) =L= 6.25;

e55.. sqr(x27) + sqr(x45) =L= 6.25;

e56..    x55 =L= 2.5;

e57..    x56 =L= 3;

e58..    x57 =L= 2.7;

e59..    x55 =G= 0.1;

e60..    x56 =G= 0.1;

e61..    x57 =G= 0.1;

e62..    x58 =L= 3;

e63..    x59 =L= 3;

e64..    x60 =L= 3;

e65..    x58 =G= -3;

e66..    x59 =G= -3;

e67..    x60 =G= -3;

e68..    x1 =L= 1.1;

e69..    x2 =L= 1.1;

e70..    x3 =L= 1.1;

e71..    x4 =L= 1.1;

e72..    x5 =L= 1.1;

e73..    x6 =L= 1.1;

e74..    x7 =L= 1.1;

e75..    x8 =L= 1.1;

e76..    x9 =L= 1.1;

e77..    x1 =G= 0.9;

e78..    x2 =G= 0.9;

e79..    x3 =G= 0.9;

e80..    x4 =G= 0.9;

e81..    x5 =G= 0.9;

e82..    x6 =G= 0.9;

e83..    x7 =G= 0.9;

e84..    x8 =G= 0.9;

e85..    x9 =G= 0.9;

e86..    x48 - x51 =G= -0.26;

e87..  - x48 + x51 =G= -0.26;

e88..    x52 - x53 =G= -0.26;

e89..  - x52 + x53 =G= -0.26;

e90..    x50 - x51 =G= -0.26;

e91..  - x50 + x51 =G= -0.26;

e92..    x51 - x52 =G= -0.26;

e93..  - x51 + x52 =G= -0.26;

e94..  - x47 + x53 =G= -0.26;

e95..    x47 - x53 =G= -0.26;

e96..    x49 - x50 =G= -0.26;

e97..  - x49 + x50 =G= -0.26;

e98..    x46 - x49 =G= -0.26;

e99..  - x46 + x49 =G= -0.26;

e100..  - x49 + x54 =G= -0.26;

e101..    x49 - x54 =G= -0.26;

e102..    x53 - x54 =G= -0.26;

e103..  - x53 + x54 =G= -0.26;

e104..    x48 - x51 =L= 0.26;

e105..  - x48 + x51 =L= 0.26;

e106..    x52 - x53 =L= 0.26;

e107..  - x52 + x53 =L= 0.26;

e108..    x50 - x51 =L= 0.26;

e109..  - x50 + x51 =L= 0.26;

e110..    x51 - x52 =L= 0.26;

e111..  - x51 + x52 =L= 0.26;

e112..  - x47 + x53 =L= 0.26;

e113..    x47 - x53 =L= 0.26;

e114..    x49 - x50 =L= 0.26;

e115..  - x49 + x50 =L= 0.26;

e116..    x46 - x49 =L= 0.26;

e117..  - x46 + x49 =L= 0.26;

e118..  - x49 + x54 =L= 0.26;

e119..    x49 - x54 =L= 0.26;

e120..    x53 - x54 =L= 0.26;

e121..  - x53 + x54 =L= 0.26;

e122..    x46 =E= 0;

e123..    x22 - x55 =E= 0;

e124..    x19 - x56 =E= 0;

e125..    x10 - x57 =E= 0;

e126..    x40 - x58 =E= 0;

e127..    x37 - x59 =E= 0;

e128..    x28 - x60 =E= 0;

e129..    x20 + x23 + x25 =E= 0;

e130..    x14 + x21 =E= -0.9;

e131..    x11 + x15 + x16 =E= 0;

e132..    x12 + x17 =E= -1;

e133..    x13 + x18 + x26 =E= 0;

e134..    x24 + x27 =E= -1.25;

e135..    x38 + x41 + x43 =E= 0;

e136..    x32 + x39 =E= -0.3;

e137..    x29 + x33 + x34 =E= 0;

e138..    x30 + x35 =E= -0.35;

e139..    x31 + x36 + x44 =E= 0;

e140..    x42 + x45 =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: 2022-08-11 Git hash: f176bd52
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