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FPPowerSystem3BusFunctions.c File Reference

Miscellaneous functions for the 3-bus power system model. More...

#include <stdio.h>
#include <stdlib.h>
#include <basic.h>
#include <math.h>
#include <arrayfunctions.h>
#include <physicalmodels/fppowersystem3bus.h>

Go to the source code of this file.

Functions

static void ComputeElectricalPower (double theta1, double theta2, void *p, double *Pe1, double *Pe2, double *Pe3)
 
int FPPowerSystem3BusDriftFunction (int dir, void *p, double *x, double t, double *drift)
 
int FPPowerSystem3BusDissipationFunction (int dir1, int dir2, void *p, double t, double *dissp)
 

Detailed Description

Miscellaneous functions for the 3-bus power system model.

Author
Debojyoti Ghosh

Definition in file FPPowerSystem3BusFunctions.c.

Function Documentation

static void ComputeElectricalPower ( double  theta1,
double  theta2,
void *  p,
double *  Pe1,
double *  Pe2,
double *  Pe3 
)
static

Compute the electrical power of each generator, given their phases and other system parameters

Parameters
theta1Phase of generator 1
theta2Phase of generator 2
pObject of type FPPowerSystem3Bus
Pe1Electrical power of generator 1
Pe2Electrical power of generator 2
Pe3Electrical power of generator 3

Definition at line 14 of file FPPowerSystem3BusFunctions.c.

22 {
23  FPPowerSystem3Bus *params = (FPPowerSystem3Bus*) p;
24 
25  double E1 = params->E1;
26  double E2 = params->E2;
27  double E3 = params->Eref;
28 
29  double *G = params->G;
30  double *B = params->B;
31 
32  double Eph[3][2];
33  Eph[0][0] = E1*cos(theta1); Eph[0][1] = E1*sin(theta1);
34  Eph[1][0] = E2*cos(theta2); Eph[1][1] = E2*sin(theta2);
35  Eph[2][0] = E3; Eph[2][1] = 0.0;
36 
37  double Y[3][3][2];
38  int i,j;
39  for (i=0; i<3; i++) {
40  for (j=0; j<3; j++) {
41  Y[i][j][0] = G[i*3+j];
42  Y[i][j][1] = B[i*3+j];
43  }
44  }
45 
46  double YEph[3][2];
47  YEph[0][0] = Y[0][0][0]*Eph[0][0] - Y[0][0][1]*Eph[0][1]
48  + Y[0][1][0]*Eph[1][0] - Y[0][1][1]*Eph[1][1]
49  + Y[0][2][0]*Eph[2][0] - Y[0][2][1]*Eph[2][1];
50  YEph[0][1] = Y[0][0][0]*Eph[0][1] + Y[0][0][1]*Eph[0][0]
51  + Y[0][1][0]*Eph[1][1] + Y[0][1][1]*Eph[1][0]
52  + Y[0][2][0]*Eph[2][1] + Y[0][2][1]*Eph[2][0];
53  YEph[1][0] = Y[1][0][0]*Eph[0][0] - Y[1][0][1]*Eph[0][1]
54  + Y[1][1][0]*Eph[1][0] - Y[1][1][1]*Eph[1][1]
55  + Y[1][2][0]*Eph[2][0] - Y[1][2][1]*Eph[2][1];
56  YEph[1][1] = Y[1][0][0]*Eph[0][1] + Y[1][0][1]*Eph[0][0]
57  + Y[1][1][0]*Eph[1][1] + Y[1][1][1]*Eph[1][0]
58  + Y[1][2][0]*Eph[2][1] + Y[1][2][1]*Eph[2][0];
59  YEph[2][0] = Y[2][0][0]*Eph[0][0] - Y[2][0][1]*Eph[0][1]
60  + Y[2][1][0]*Eph[1][0] - Y[2][1][1]*Eph[1][1]
61  + Y[2][2][0]*Eph[2][0] - Y[2][2][1]*Eph[2][1];
62  YEph[2][1] = Y[2][0][0]*Eph[0][1] + Y[2][0][1]*Eph[0][0]
63  + Y[2][1][0]*Eph[1][1] + Y[2][1][1]*Eph[1][0]
64  + Y[2][2][0]*Eph[2][1] + Y[2][2][1]*Eph[2][0];
65 
66  YEph[0][1] = - YEph[0][1];
67  YEph[1][1] = - YEph[1][1];
68  YEph[2][1] = - YEph[2][1];
69 
70  *Pe1 = Eph[0][0]*YEph[0][0] - Eph[0][1]*YEph[0][1];
71  *Pe2 = Eph[1][0]*YEph[1][0] - Eph[1][1]*YEph[1][1];
72  *Pe3 = Eph[2][0]*YEph[2][0] - Eph[2][1]*YEph[2][1];
73 }
FPPowerSystem3Bus
Structure containing variable and parameters specific to the 3-bus power system model. This structure contains the physical parameters and variables for the Fokker-Planck model for a 3-bus power system.
Definition: fppowersystem3bus.h:49
int FPPowerSystem3BusDriftFunction ( int  dir,
void *  p,
double *  x,
double  t,
double *  drift 
)

Compute the drift (advection) coefficients for the 3-bus power system

Parameters
dirSpatial dimension (not used)
pObject of type FPPowerSystem3Bus
xSpatial coordinates
tCurrent simulation time
driftArray to hold the drift velocities

Definition at line 76 of file FPPowerSystem3BusFunctions.c.

83 {
84  FPPowerSystem3Bus *params = (FPPowerSystem3Bus*) p;
85 
86  double theta1 = x[0];
87  double theta2 = x[1];
88  double Omega1 = x[2];
89  double Omega2 = x[3];
90 
91  double omegaB = params->omegaB;
92  double Pm1_avg = params->Pm1_avg;
93  double Pm2_avg = params->Pm2_avg;
94  double Pmref_avg = params->Pmref_avg;
95  double H1 = params->H1;
96  double H2 = params->H2;
97  double Href = params->Href;
98  double gamma = params->gamma;
99 
100  double Pe1, Pe2, Peref;
101  ComputeElectricalPower(theta1,theta2,params,&Pe1,&Pe2,&Peref);
102 
103  double F1 = Pm1_avg / (2*H1) - Pmref_avg / (2*Href);
104  double F2 = Pm2_avg / (2*H2) - Pmref_avg / (2*Href);
105  double S1 = Pe1 / (2*H1) - Peref / (2*Href);
106  double S2 = Pe2 / (2*H2) - Peref / (2*Href);
107 
108  drift[0] = omegaB * Omega1;
109  drift[1] = omegaB * Omega2;
110  drift[2] = F1 - gamma*Omega1 - S1;
111  drift[3] = F2 - gamma*Omega2 - S2;
112 
113  return(0);
114 }
drift
#define drift(x)
Definition: fpdoublewell.h:31
ComputeElectricalPower
static void ComputeElectricalPower(double theta1, double theta2, void *p, double *Pe1, double *Pe2, double *Pe3)
Definition: FPPowerSystem3BusFunctions.c:14
FPPowerSystem3Bus
Structure containing variable and parameters specific to the 3-bus power system model. This structure contains the physical parameters and variables for the Fokker-Planck model for a 3-bus power system.
Definition: fppowersystem3bus.h:49
int FPPowerSystem3BusDissipationFunction ( int  dir1,
int  dir2,
void *  p,
double  t,
double *  dissp 
)

Compute the dissipation coefficient for the 3-bus power system

Parameters
dir1First spatial dimension for the dissipation coefficient
dir2Second spatial dimension for the dissipation coefficient
pObject of type FPPowerSystem3Bus
tCurrent simulation time
disspMatrix of size ndims*ndims to hold the dissipation coefficients (row-major format)

Definition at line 117 of file FPPowerSystem3BusFunctions.c.

125 {
126  FPPowerSystem3Bus *params = (FPPowerSystem3Bus*) p;
127  _ArraySetValue_(dissp,_MODEL_NDIMS_*_MODEL_NDIMS_,0.0);
128 
129  double sigma11 = params->sigma[0][0];
130  double sigma12 = params->sigma[0][1];
131  double sigma21 = params->sigma[1][0];
132  double sigma22 = params->sigma[1][1];
133 
134  double lambda11 = params->lambda[0][0];
135  double lambda12 = params->lambda[0][1];
136  double lambda21 = params->lambda[1][0];
137  double lambda22 = params->lambda[1][1];
138 
139  double gamma = params->gamma;
140  double omegaB = params->omegaB;
141 
142 #if 0
143  /* steady state coefficients */
144  dissp[2*_MODEL_NDIMS_+0] = sigma11*sigma11*lambda11*lambda11*omegaB;
145  dissp[2*_MODEL_NDIMS_+1] = sigma12*sigma12*lambda12*lambda12*omegaB;
146  dissp[3*_MODEL_NDIMS_+0] = sigma21*sigma21*lambda21*lambda21*omegaB;
147  dissp[3*_MODEL_NDIMS_+1] = sigma22*sigma22*lambda22*lambda22*omegaB;
148 
149  dissp[2*_MODEL_NDIMS_+2] = sigma11*sigma11*lambda11*(1.0-gamma*lambda11);
150  dissp[2*_MODEL_NDIMS_+3] = sigma12*sigma12*lambda12*(1.0-gamma*lambda12);
151  dissp[3*_MODEL_NDIMS_+2] = sigma21*sigma21*lambda21*(1.0-gamma*lambda21);
152  dissp[3*_MODEL_NDIMS_+3] = sigma22*sigma22*lambda22*(1.0-gamma*lambda22);
153 #endif
154 
155  /* time-dependent coefficients */
156  dissp[2*_MODEL_NDIMS_+0] = sigma11*sigma11*lambda11*omegaB*(lambda11*(1-exp(-t/lambda11))-t*exp(-t/lambda11));
157  dissp[2*_MODEL_NDIMS_+1] = sigma12*sigma12*lambda12*omegaB*(lambda12*(1-exp(-t/lambda12))-t*exp(-t/lambda12));
158  dissp[3*_MODEL_NDIMS_+0] = sigma21*sigma21*lambda21*omegaB*(lambda21*(1-exp(-t/lambda21))-t*exp(-t/lambda21));
159  dissp[3*_MODEL_NDIMS_+1] = sigma22*sigma22*lambda22*omegaB*(lambda22*(1-exp(-t/lambda22))-t*exp(-t/lambda22));
160 
161  dissp[2*_MODEL_NDIMS_+2] = sigma11*sigma11*(lambda11*(1-exp(-t/lambda11))+gamma*lambda11*(t*exp(-t/lambda11)-lambda11*(1-exp(-t/lambda11))));
162  dissp[2*_MODEL_NDIMS_+3] = sigma12*sigma12*(lambda12*(1-exp(-t/lambda12))+gamma*lambda12*(t*exp(-t/lambda12)-lambda12*(1-exp(-t/lambda12))));
163  dissp[3*_MODEL_NDIMS_+2] = sigma21*sigma21*(lambda21*(1-exp(-t/lambda21))+gamma*lambda21*(t*exp(-t/lambda21)-lambda21*(1-exp(-t/lambda21))));
164  dissp[3*_MODEL_NDIMS_+3] = sigma22*sigma22*(lambda22*(1-exp(-t/lambda22))+gamma*lambda22*(t*exp(-t/lambda22)-lambda22*(1-exp(-t/lambda22))));
165 
166  return(0);
167 }
_ArraySetValue_
#define _ArraySetValue_(x, size, value)
Definition: arrayfunctions.h:169
_MODEL_NDIMS_
#define _MODEL_NDIMS_
Definition: euler1d.h:56
FPPowerSystem3Bus
Structure containing variable and parameters specific to the 3-bus power system model. This structure contains the physical parameters and variables for the Fokker-Planck model for a 3-bus power system.
Definition: fppowersystem3bus.h:49