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Finite-Difference Hyperbolic-Parabolic PDE Solver on Cartesian Grids
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fppowersystem.h
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1 /*
2 
3  Fokker-Planck Model for Power Systems
4 
5 Reference:
6 + Wang P., Tartakovsky A.M., Abhyankar S., Smith B.F.,
7  Huang Z., "Probabilistic Density Function Method for
8  Stochastic ODEs of Power Systems with Uncertain
9  Power Input", Preprint
10 
11  dp d[mu(x,y)p] d[nu(x,y)p] d^2 p
12  -- + ----------- + ----------- = f(t) -----
13  dt dx dy dy^2
14 
15  mu(x,y) = O_s(y-1)
16  nu(x,y) = (1/2H)[Pm - Pmax sin(x) - D(y-1)]
17  f(t) = (1/2H)^2 (l^2 q)/(lr+1) (1 - exp[-(r+1/l)t])
18 
19  where
20  r = D/2H
21 
22  [ EV/g1; t < tf
23  Pmax = [ 0 ; tf < t < tcl
24  [ EV/g2; tcl < t
25 
26  Physical Parameters:
27 
28  O_s Synchronous Speed
29  H Inertia constant
30  D Damping constant
31  l Correlation time
32  q Noise strength
33  Pm Mean mechanical power input
34  Pmax Maximum power output
35  E Internal voltage
36  V Terminal voltage
37  tf Fault incident time
38  tcl Clearing time
39  g1 Pre-fault impedance
40  g2 Post-clearing impedance
41 
42 */
43 
44 #define _FP_POWER_SYSTEM_ "fp-power-system"
45 
46 /* define ndims and nvars for this model */
47 #undef _MODEL_NDIMS_
48 #undef _MODEL_NVARS_
49 #define _MODEL_NDIMS_ 2
50 #define _MODEL_NVARS_ 1
51 
52 typedef struct fp_power_system_parameters {
53 
54  /* input parameters */
55  double O_s;
56  double H;
57  double E;
58  double V;
59  double g1,g2;
60  double D;
61  double Pm;
62  double l;
63  double q;
64  double tf, tcl;
65 
66  /* computed/constant parameters */
67  double Pmax;
68 
69  double pdf_integral; /* not an input */
71 
72 int FPPowerSystemInitialize (void*,void*);
73 int FPPowerSystemCleanup (void*);
double pdf_integral
Definition: fppowersystem.h:69
int FPPowerSystemInitialize(void *, void *)
int FPPowerSystemCleanup(void *)