Simulation apparatus for motor-driven compressor system and the simulation method thereof
View Patent ↗With a simulation apparatus for a system including a motor-driven compressor, a compressor that does not suffer from a driving torque shortage and surging, but can operate at low costs, can be provided. A simulation apparatus for a motor-driven compressor system includes a simulation section in which a driving motor, a compressor driven by the driving motor, a suction throttle valve controlling the inlet flow rate of the compressor, and an anti-surge valve interposed between pipes for returning a part of gas discharged from the compressor to the inlet side of the compressor are translated into unit models and stored. The simulation apparatus further includes an input section through which designed specification data of the compressor is input, a data setting section storing the designed specification data, and a display section displaying unsteady-state Q-H characteristics and required driving torque obtained through simulation by the simulation section.
1. A simulation apparatus for a motor-driven compressor system including a driving motor, a compressor driven by the driving motor, a suction throttle valve controlling an inlet flow rate of the compressor, and an anti-surge valve interposed between pipes for returning a part of gas discharged from the compressor to a suction side of the compressor, the simulation apparatus comprising:
an input section through which designed specification data of the compressor is input;
a data setting section storing the designed specification data;
a simulation section capable of calculating Q-H characteristics and required driving torque of the compressor in an unsteady state based on the data stored in the data setting section; and
a display section displaying the resultant unsteady-state Q-H characteristics and required driving torque simulated by the simulation section;
the simulation section includes a driving motor unit model being a mathematical model of the driving motor, a compressor unit model being a mathematical model of the compressor, a suction throttle valve unit model being a unit model of the suction throttle valve, an anti-surge valve unit model being a mathematical model of the anti-surge valve, a heat exchanger unit model being a mathematical model of a heat exchanger disposed between the anti-surge valve and the suction side of the compressor, a suction throttle valve controller unit model being a mathematical model of a suction throttle valve controller controlling the suction throttle valve, and an anti-surge valve controller unit model being a mathematical model of an anti-surge valve controller controlling the anti-surge valve,
the compressor unit model calculates an operating point and required driving torque of the compressor in an unsteady state, and
the driving motor unit model calculates unsteady-state behavior of the compressor from a torque characteristic curve of the driving motor and the calculated required driving torque of the compressor;
wherein the compressor unit model in the simulation section includes mathematical models expressed by the following Equation 3 to Equation 6, the driving motor unit model includes a mathematical model expressed by the following Equation 7, the suction throttle valve unit model includes a mathematical model expressed by the following Equation 8, and the anti-surge valve unit model includes a mathematical model expressed by Equation 9:
[
Expression
1
]
H
pol
=
1
g
n
n
-
1
RT
1
[
(
p
2
p
1
)
n
-
1
n
-
1
]
Equation
3
H pol : polytropic head [m]
g: acceleration of gravity [m/s 2 ]
n: polytropic exponent
R: gas constant [J/kgK]
T: temperature [K]
p: pressure [Pa]
[
Expression
2
]
Q
s
(
N
)
=
N
N
R
f
Q
[
H
pol
(
N
)
(
N
R
N
)
2
]
Equation
4
Q s : inlet flow rate [m 3 /h]
N: rotational speed [rpm]
N R : rated speed [rpm]
f Q : function expressing inlet flow rate-polytropic head performance curve with the polytropic head
H pol : polytropic head [m]
[
Expression
3
]
η
pol
(
N
)
=
f
η
[
Q
s
(
N
)
N
R
N
]
Equation
5
η pol : polytropic efficiency
N: rotational speed [rpm]
f η : function expressing inlet flow rate-polytropic efficiency performance curve with the inlet flow rate
Q s : inlet flow rate [m 3 /h]
N R : rated speed [rpm]
[
Expression
4
]
L
C
=
m
.
s
gH
pol
1000
η
pol
Equation
6
L c : compressor shaft power [kW]
{dot over (m)} s : compressor suction mass flow rate [kg/s]
g: acceleration of gravity [m/s 2 ]
H pol : polytropic head [m]
η pol : polytropic efficiency
[
Expression
5
]
J
(
2
π
60
)
ⅆ
N
ⅆ
t
=
T
M
-
L
(
2
π
60
)
N
Equation
7
J: moment of inertia [kgm 2 ]
N: rotational speed [rpm]
t: time [s]
T M : motor torque [N-m]
L: compressor shaft torque
[Expression 6]
{dot over (m)}=CA √{square root over (2ρ( p 1 −p 2 ))} Equation 8
{dot over (m)}: mass flow rate [kg/s]
C: flow coefficient
A: cross-sectional area of flow path [m 2 ]
ρ: density [kg/m 3 ]
p: pressure [Pa]
[Expression 7]
Q=KA c ΔT Equation 9
Q: amount of heat transfer [W]
K: heat transfer coefficient [W/m 2 K]
A c : heating area [m 2 ]
ΔT: temperature difference [K]
Index 1 denotes an inlet, while index 2 denotes an outlet.
2. The simulation apparatus for a motor-driven compressor system according to claim 1 , wherein
the simulation section includes a determination section that calculates an operating point and required driving torque of the compressor at startup from the calculated unsteady-state behavior of the operating point and required driving torque of the compressor and determines whether a torque margin of the driving motor and a turndown of the compressor are equal to preset allowable values or lower.