Method of determining delivery flow or delivery head
A torque required to achieve the modulated reference speed or adjustment of a modulated torque and the actual speed of the centrifugal pump is determined. Then a model speed is calculated with the aid of a mathematical pump-motor model simulating the behavior of the centrifugal pump within a hydraulic system as well as a disturbance signal from a deviation of the model speed from the actual speed of the centrifugal pump. Then a correction signal is determined by integrating the product of the disturbance signal and a sine or cosine signal with a multiple of the excitation frequency over at least one period of the excitation signal. Finally, at least one model parameter of the pump-motor model is determined as a function of the correction signal and the flow rate and/or the head is calculated using the adapted pump-motor model.
1 . A method of determining the delivery flow rate and/or the delivery head of a speed-controlled centrifugal pump assembly arranged in a hydraulic pipeline network, the method comprising the steps of:
a. operating the centrifugal pump assembly in the hydraulic pipeline network at a reference rotational speed or a torque,
b. periodically exciting, by a control electronics, the hydraulic pipeline network by applying a periodic excitation signal of a specific excitation frequency to the reference rotational speed or to the torque to obtain a modulated torque or a modulated setpoint rotational speed, thereby modulating the actual rotational speed of the centrifugal pump assembly,
c. setting, by the control electronics, the modulated torque or determining and setting a torque required to achieve the modulated setpoint rotational speed,
d. determining, by the control electronics, the actual rotational speed of the centrifugal pump assembly,
e. calculating, by the control electronics, a model rotational speed with the aid of a mathematical pump-motor model simulating the behavior of the centrifugal pump assembly within the hydraulic pipeline network,
f. calculating, by the control electronics, at least one disturbance signal from a deviation of the model rotational speed from the actual rotational speed of the centrifugal pump assembly,
g. determining, by the control electronics, at least one correction signal by integrating the product of the disturbance signal and a sine or cosine signal with the single or a multiple of the excitation frequency over at least one period of the excitation signal,
h. adapting, by the control electronics, at least one model parameter of the pump-motor model as a function of the correction signal,
i. calculating, by the control electronics, the delivery flow rate and/or the delivery head using the adapted pump-motor model, and
j. setting, by the control electronics, the delivery head as a function of the delivery flow rate.
2 . The method according to claim 1 , wherein the pump-motor model comprises at least a first equation in integral form for calculating the delivery flow rate and a second equation in integral form for calculating the model rotational speed, and these two equations are repeatedly cyclically evaluated.
3 . The method of claim 2 , wherein the first equation is used in the following integral form:
Q
m
d
l
=
1
L
h
y
d
∫
0
t
(
(
a
ω
2
-
b
Q
m
d
l
ω
-
c
Q
m
d
l
2
)
-
R
h
y
d
Q
m
d
l
2
-
H
s
t
a
t
i
c
)
dt
or
Eq1
Q
m
d
l
(
k
+
1
)
=
Q
m
d
l
(
k
)
+
1
L
h
y
d
(
(
a
ω
2
(
k
)
-
b
Q
m
d
l
(
k
)
ω
(
k
)
-
c
Q
m
d
l
2
(
k
)
)
-
R
h
y
d
Q
m
d
l
2
(
k
)
-
H
s
t
a
t
i
c
(
k
)
)
·
Δ
t
Eq1
where
Q mdl is the delivery flow rate of the centrifugal pump assembly,
ω a is a rotational speed or rotational frequency of the centrifugal pump assembly,
a, b, c are parameters that describe the hydraulic pump performance characteristics by means of pump curves,
R hyd is the hydraulic resistance of the hydraulic pipeline network,
L hyd is the hydraulic inductance of the hydraulic pipeline network,
H static is a geodetic head,
k is a discrete point of time and
Δt is the time interval between one point of time k and the next point of time k+1.
4 . The method according to claim 2 wherein the first equation is used in the form of the following two partial equations that are calculated repeatedly one after the other:
H
m
d
l
=
a
ω
2
-
b
Q
m
d
l
ω
-
c
Q
m
d
l
2
Eq1a
Q
m
d
l
=
1
L
h
y
d
∫
0
t
(
H
m
d
l
-
R
h
y
d
Q
m
d
l
2
-
H
s
t
a
t
i
c
)
dt
or
Eq1b
H
m
d
l
(
k
)
=
a
ω
2
(
k
)
-
b
Q
m
d
l
(
k
)
ω
(
k
)
-
c
Q
m
d
l
2
(
k
)
Eq1a
Q
m
d
l
(
k
+
1
)
=
Q
m
d
l
(
k
)
+
1
L
h
y
d
(
H
m
d
l
(
k
)
-
R
h
y
d
Q
m
d
l
2
(
k
)
-
H
static
(
k
)
)
·
Δ
t
Eq1b
where
H mdl is the delivery head of the centrifugal pump assembly,
Q mdl is the delivery flow rate of the centrifugal pump assembly,
ω is a rotational speed or rotational frequency of the centrifugal pump assembly,
a, b, c are parameters that describe the hydraulic pump performance characteristics by means of pump curves,
R hyd is the hydraulic resistance of the hydraulic pipeline network,
L hyd is the hydraulic inductance of the hydraulic pipeline network,
H static is a geodetic head,
k is a discrete point of time and
Δt is the time interval between one point of time k and the next point of time k+1.
5 . The method according to claim 2 , wherein the second equation is used in the following integral form:
ω
mdl
=
1
J
∫
0
t
(
T
m
o
t
-
(
a
t
Q
m
d
l
ω
-
b
t
Q
m
d
l
2
-
c
t
Q
m
d
l
3
ω
+
v
i
ω
2
+
v
s
ω
-
I
d
Q
d
t
)
+
T
D
)
dt
or
Eq2
ω
m
d
l
(
k
+
1
)
=
ω
m
d
l
(
k
)
+
1
J
(
T
m
o
t
(
k
)
-
(
a
t
Q
m
d
l
(
k
)
ω
(
k
)
-
b
t
Q
m
d
l
2
(
k
)
-
c
t
Q
m
d
l
3
(
k
)
ω
(
k
)
+
v
i
ω
2
(
k
)
+
v
s
ω
(
k
)
-
I
Q
(
k
)
-
Q
(
k
-
1
)
Δ
t
)
+
T
D
(
k
)
)
·
Δ
t
Eq2
where
T mot is the mechanical torque of a motor of the centrifugal pump assembly,
T D is the calculated disturbance signal in the form of a moment,
Q mdl is the delivery flow rate of the centrifugal pump assembly,
ω mdl is the model rotational speed or rotational frequency of the centrifugal pump assembly,
ω is a rotational speed or rotational frequency of the centrifugal pump assembly,
a t , b t , c t are parameters describing the static torque performance characteristics of the centrifugal pump assembly by means of torque curves,
v i is a quantity describing a friction between an impeller of the centrifugal pump assembly and a medium pumped by the centrifugal pump assembly,
v s is a quantity describing friction in bearings of the centrifugal pump assembly,
J is the mass inertia of rotating components of the centrifugal pump assembly,
I is the mass inertia of the pumped medium in the impeller,
k is a discrete point of time and
Δt is the time interval between one point of time k and the next point of time k+1.
6 . The method according to claim 2 wherein the second equation is used in the form of the following two partial equations that are calculated successively, cyclically repeated:
T
m
d
l
=
a
t
Q
m
d
l
ω
-
b
t
Q
m
d
l
2
-
c
t
Q
m
d
l
3
ω
+
v
i
ω
2
+
v
s
ω
-
I
d
Q
d
t
Eq2a
ω
m
d
l
=
1
J
∫
0
t
(
T
m
o
t
-
T
m
d
l
+
T
D
)
dt
or
Eq2b
T
m
d
l
(
k
)
=
a
t
Q
m
d
l
(
k
)
ω
(
k
)
-
b
t
Q
m
d
l
2
(
k
)
-
c
t
Q
m
d
l
3
(
k
)
ω
(
k
)
+
v
i
ω
2
(
k
)
+
v
s
ω
(
k
)
-
I
Q
(
k
)
-
Q
(
k
-
1
)
Δ
t
Eq2a
ω
m
d
l
(
k
+
1
)
=
ω
m
d
l
(
k
)
+
1
J
(
T
m
o
t
(
k
)
-
T
m
d
l
(
k
)
+
T
D
(
k
)
)
·
Δ
t
Eq2b
where
T mdl is a pump torque of the centrifugal pump assembly,
T mot is the mechanical torque of a motor of the centrifugal pump assembly,
T D is the calculated disturbance signal in the form of a moment,
Q mdl is the delivery flow rate of the centrifugal pump assembly,
ω mdl is the model rotational speed or rotational frequency of the centrifugal pump assembly,
ω is a rotational speed or rotational frequency of the centrifugal pump assembly,
a t , b t , c t are parameters describing the static torque performance characteristics of the centrifugal pump assembly by means of torque curves,
v i is a quantity describing friction between an impeller of the centrifugal pump assembly and a medium pumped by the centrifugal pump assembly,
v s is a quantity describing friction in bearings of the centrifugal pump assembly,
J is the mass inertia of rotating components of the centrifugal pump assembly,
I is the mass inertia of the pumped medium in the impeller,
k is a discrete point of time and
Δt is the time interval between one point of time k and the next point of time k+1.
7 . The method according to claim 5 or 6 , wherein the at least one model parameter is the parameter c t , and in step g the sine or cosine signal is in phase with the excitation signal.
8 . The method according to claim 5 or 6 wherein the model parameter is the parameter c t , and in step g the sine or cosine signal is in phase with the excitation signal, and in step fa first disturbance signal and a second disturbance signal are determined by supplying the difference between the model rotational speed and the actual rotational speed to a controller containing at least one integral component, and an output signal of this controller forms the first disturbance signal and the second disturbance signal is formed by multiplying the output signal of this controller by the actual rotational speed, and wherein the parameter c t is adjusted in dependence of a first correction signal formed from the first disturbance signal.
9 . The method according to claim 1 , wherein in step f:
a. the difference between the model rotational speed and the actual rotational speed is fed to a controller containing at least one integral component, an output signal of this controller forming the disturbance signal or the disturbance signal being formed by multiplying the output signal of this controller by the actual rotational speed.
10 . The method according to claim 1 , wherein in step f. a first disturbance signal and a second disturbance signal are determined by supplying the difference between the model rotational speed and the actual rotational speed to a controller containing at least one integral component, and an output signal of this controller forms the first disturbance signal and the second disturbance signal is formed by multiplying the output signal of this controller by the actual rotational speed.
11 . The method according to claim 10 , wherein the model parameter is the hydraulic resistance of the hydraulic pipeline network, and in step g. the sine or cosine signal is in phase with the excitation signal, and the hydraulic resistance is adjusted in dependence of a first correction signal formed from the second disturbance signal.
12 . The method according to claim 10 , wherein the model parameter is the mass inertia of the centrifugal pump assembly or the hydraulic inductance of the pipeline network and in step g. the sine or cosine signal is phase-shifted 90° to the excitation signal and wherein the mass inertia of the centrifugal pump assembly is adjusted in dependence of a second correction signal formed from the second disturbance signal, and/or the hydraulic inductance of the pipeline network is adjusted in dependence of a second correction signal formed from the first disturbance signal.
13 . The method according to claim 1 , wherein two or more correction signals are determined from the disturbance signal or from each of the disturbance signals, and each correction signal is used to adapt in each case a specific model parameter of the pump-motor model.
14 . The method according to claim 1 , wherein the model parameter is the hydraulic resistance of the pipeline network, and in step g. the sine or cosine signal is in phase with the excitation signal.
15 . The method according to claim 1 , wherein the model parameter is the mass inertia of the centrifugal pump assembly or the hydraulic inductance of the pipeline network and in step g. the sine or cosine signal is phase-shifted 90° to the excitation signal.
16 . The method according to claim 1 , further comprising the step of adapting the model parameter by means of a controller containing an integral component by:
supplying the correction signal to the controller; and
multiplying an output signal of the controller with an initial value for the model parameter to obtain the adapted model parameter.
17 . A centrifugal pump assembly having a centrifugal pump, an electric motor driving it and control electronics for controlling the electric motor with or without feedback, wherein the control electronics is adapted to perform the method according to claim 1 .
18 . A system comprising:
a centrifugal pump;
a motor adapted to drive the centrifugal pump; and
a control electronics adapted to perform operations comprising:
a. operating the centrifugal pump assembly in a hydraulic pipeline network at a reference rotational speed or a torque;
b. periodically exciting the hydraulic pipeline network by applying a periodic excitation signal of a specific excitation frequency to the reference rotational speed or to the torque to obtain a modulated torque or a modulated setpoint rotational speed, thereby modulating the actual rotational speed of the centrifugal pump assembly;
c. setting the modulated torque or determining and setting a torque required to achieve the modulated setpoint rotational speed,
d. determining the actual rotational speed of the centrifugal pump assembly;
e. calculating a model rotational speed with the aid of a mathematical pump-motor model simulating the behavior of the centrifugal pump assembly within the hydraulic pipeline network;
f. calculating at least one disturbance signal from a deviation of the model rotational speed from the actual rotational speed of the centrifugal pump assembly;
g. determining at least one correction signal by integrating the product of the disturbance signal and a sine or cosine signal with the single or a multiple of the excitation frequency over at least one period of the excitation signal;
h. adapting at least one model parameter of the pump-motor model as a function of the correction signal;
i. calculating the delivery flow rate and/or the delivery head using the adapted pump-motor model; and
j. setting the delivery head as a function of the delivery flow rate.
19 . The system of claim 18 , wherein the operations further comprise:
determining that the correction signal falls below a predetermined limit value; and
in response to determining that the correction signal falls below the predetermined limit value: issuing one of an error message, a warning, or a maintenance notice based on the correction signal.
20 . The system of claim 18 , wherein the operations further comprise:
detecting a condition of the centrifugal pump assembly based on a plurality of adjustments of the at least one model parameter over a period of time; and
determining a maintenance requirement of the centrifugal pump assembly based on the determined condition.