Stable equilibrium point (SEP) calculation apparatus of power system
View Patent ↗In the present invention, in a case where a stable equilibrium point calculation is not calculable by using a Newton method, a damping factor of a mechanical system differential equation of a generator is set to be greater than an actual value of the generator of the power system. By applying pseudo-transient simulation to the nonlinear differential algebraic equation of the power system including the mechanical system differential equation of the generator, in which the damping factor is set, a norm of a mechanical system equation is found. If the found norm meets a predetermined condition, variable values of the power system at a time when the norm is found are set as initial values of the nonlinear differential algebraic equation of the power system. A stable equilibrium point is determined by applying the Newton method to the nonlinear differential algebraic equation in which the initial values are set.
1. A stable equilibrium point calculation apparatus of a power system, comprising:
means for applying a pseudo-transient simulation method to a nonlinear differential algebraic equation of the power system including a mechanical system differential equation of a generator of the power system, in which a mechanical system damping factor of the generator in the power system is set to be greater, by a predetermined degree, than an actual mechanical system damping factor of the generator, thereby finding a norm ∥F(x,y)∥ of a mechanical system equation of the nonlinear differential algebraic equation of the power system including the mechanical system differential equation of the generator in which the mechanical system damping factor is set, wherein contingencies, on which an influence of virtual power system disturbances is reflected, is reflected as parameters of variables in the nonlinear differential algebraic equation of the power system;
means for determining whether the found norm meets a predetermined condition;
means for setting, when it is determined that the norm meets the predetermined condition, variable values of the nonlinear differential algebraic equation including the mechanical system differential equation of the generator at a time, when the norm that is determined to meet the predetermined condition is found, as initial values of the variables of the nonlinear differential algebraic equation of the power system; and
means for determining a stable equilibrium point (SEP) by applying a Newton method to the nonlinear differential algebraic equation of the power system, in which the initial values are set,
wherein F(x,y) is the mechanical system equation of the power system, and
x,y are variables of the nonlinear differential algebraic equation of the power system.
2. The stable equilibrium point calculation apparatus of a power system, according to claim 1 , wherein the nonlinear differential algebraic equation of the power system is expressed by the following formula:
{
x
.
=
F
(
x
,
y
)
G
(
x
,
y
)
=
0
where
G (x, y): a power flow equation of the power system.
3. The stable equilibrium point calculation apparatus of a power system, according to claim 1 , wherein the mechanical system differential equation of the generator is expressed by the following formula:
2
H
i
ω
0
ⅆ
2
δ
i
ⅆ
t
2
+
D
i
ω
0
ⅆ
δ
i
ⅆ
t
=
T
mi
-
T
ei
where
i: an i-th generator of the power system,
H: per unit inertia constant of the generator,
δ: internal angle of the generator,
ω0: rated angular velocity of the system,
D: damping factor,
Tm: mechanical input torque, and
Te: electrical torque.
4. The stable equilibrium point calculation apparatus of a power system, according to claim 1 , wherein the damping factor is set in a range of 1 to 10 times a rated angular velocity of the power system.
5. The stable equilibrium point calculation apparatus of a power system, according to claim 1 , wherein the predetermined condition is that the found norm is 20% or less of the mechanical system equation of the nonlinear differential algebraic equation of the power system in a sound state prior to occurrence of contingencies, and that a variation amount of the norm is 2 or less per one repetitive calculation of the pseudo-transient simulation method.
6. The stable equilibrium point calculation apparatus of a power system, according to claim 1 , wherein the means for determining the stable equilibrium point comprises means for determining whether the stable equilibrium point of the power system is calculable or not, by applying a Newton method to the nonlinear differential algebraic equation of the power system to determine the stable equilibrium point.