Determining the delivery rate of a pump

Abstract

The invention relates to a method for determining the delivery rate of a pump. In this context, a value of the delivery level and a value of the power of the pump are determined. A probability density function is calculated for the delivery level and the power. A first probability density function of the delivery rate is calculated on the basis of a delivery level-delivery rate relationship and the probability density function of the delivery level. A second probability density function of the delivery rate is determined on the basis of a power-delivery rate relationship and the probability density function of the power. A combined probability density function of the delivery rate is determined on the basis of the first and second probability density functions. The delivery rate is determined on the basis of the combined probability density function.

Claims

1. A method for determining a current delivery flow of a motor-driven pump, comprising the acts of: determining by at least one of measurement and calculation a value for a current delivery head being generated by the pump and a value for a current shaft power of the pump used to generate the delivery head, calculating with an electronic evaluation unit a probability density function for the current delivery head and a probability density function for the current shaft power, determining with the electronic evaluation unit a first probability density function for the current delivery flow from the probability density function for the current delivery head and a delivery head-delivery flow relationship of the pump, determining with the electronic evaluation unit a second probability density function for the current delivery flow from the probability density function for the current shaft power and a power-delivery flow relationship of the pump, determining with the electronic evaluation unit a combined probability density function for the current delivery flow from the first probability density function for the current delivery flow and the second probability density function for the current delivery flow, determining the current delivery flow from the combined probability density function, updating, using the current delivery flow from the combined probability density function, one or both of the delivery head-delivery flow relationship of the pump and the power-delivery flow relationship of the pump, and using the updated one or both of the delivery head-delivery flow relationship and the power-delivery flow relationship, and one or both of further measurement and further calculation of one or more of the current delivery head and the current shaft power of the pump, to one or both of control the pump to obtain a predetermined amount of delivery flow and determine an amount of actual delivery flow from the pump over a predetermined time interval.

2. The method as claimed in claim 1, wherein the probability density function for the current delivery head and the probability density function for the current shaft power is calculated by the electronic evaluation unit as a Gaussian function.

3. The method as claimed in claim 2, wherein the probability density function for the current delivery head and the probability density function for the current shaft power are normalized.

4. The method as claimed in claim 3, wherein the act of determining the combined probability density function for the current delivery flow includes multiplying the first probability density function for the current delivery flow by the second probability density function for the current delivery flow.

5. The method as claimed in claim 4, wherein in the act of determining the current delivery flow on the basis of the combined probability density function, the current delivery flow is determined as an expected value of the combined probability density function.

6. The method as claimed in claim 5, wherein in the act of determining the current delivery flow on the basis of the combined probability density function, the current delivery flow is ascertained as a maximum of the combined probability density distribution.

7. The method as claimed in claim 1, wherein an offset correction based on a value of a shaft power at a known delivery flow is applied to the power-delivery flow relationship.

8. The method as claimed in claim 1, wherein the value of the current delivery head is determined from a pressure difference between a pressure side and a suction side of the pump.

9. The method as claimed in claim 1, wherein the value of the current shaft power is determined from an actuation frequency of the motor and an effective pump power.

10. An arrangement for determining a current delivery flow of a motor-driven pump, comprising: sensors for determining a pressure difference between a suction side and a pressure side of the pump; at least one pump power determination unit configured to determine a mechanical power of the pump; and at least one evaluation unit configured to: receive data from the sensors and the pump power determination unit, store a delivery head-delivery flow relationship and a power-delivery flow relationship of the pump, determine values for a current delivery head and a current shaft power from the received data and the stored relationships, calculate a probability density function for the current delivery head and a probability density function for the current shaft power, determine a first probability density function for the current delivery flow from the probability density function for the current delivery head and the stored delivery head-delivery flow relationship of the pump, determine a second probability density function for the current delivery flow from the probability density function for the current shaft power and the stored power-delivery flow relationship of the pump, determine a combined probability density function for the current delivery flow from the first probability density function for the current delivery flow and the second probability density function for the current delivery flow, and determine the current delivery flow from the combined probability density function, and update, using the current delivery flow from the combined probability density function, one or more of the delivery head-delivery flow relationship of the pump and the power-delivery flow relationship of the pump, and one or both of control the pump to obtain a predetermined amount of delivery flow and determine an amount of actual delivery flow from the pump over a predetermined time interval, using the updated one or both of the delivery head-delivery flow relationship and the power-delivery flow relationship, and one or both of further measurement and further calculation of one or more of the current delivery head and the current shaft power of the pump.

11. The arrangement as claimed in claim 10, wherein at least one pump power determination unit includes a frequency converter configured to supply an actuation frequency and effective power to a motor of the pump.

12. The arrangement as claimed in claim 11, wherein the shaft power is determined from the actuation frequency of the motor and the effective power.

13. The arrangement as claimed in claim 10, wherein the current shaft power is determined from a shaft power measuring device.

14. The arrangement as claimed in claim 13, wherein the shaft power measuring device is a torque hub.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows a schematic illustration of the processing of individual parameters in accordance with an embodiment of the present invention,

(2) FIG. 2A shows a transfer of the probability density function for the delivery head in accordance with an embodiment of the present invention,

(3) FIG. 2B shows a transfer of the probability density function for the power in accordance with an embodiment of the present invention, and

(4) FIG. 2C shows a combination of the probability density functions for the delivery flows in accordance with an embodiment of the present invention.

DETAILED DESCRIPTION

(5) The sensors, which are not depicted in FIG. 1, ascertain a pressure p.sub.2 on the pressure side, in particular in the pressure connector, of a centrifugal pump and a pressure p.sub.1 on the suction side, in particular in the suction connector, of the centrifugal pump. A reduced delivery head H.sub.red is calculated from the pressures p.sub.1 and p.sub.2 in a step 1.

(6) The delivery head H calculation is known to a person skilled in the art. In this application, a reduced delivery head H.sub.red is understood to mean a delivery head in which the velocity term (v.sub.2.sup.2v.sub.1.sup.2)/2 g (where v.sub.2: pressure-side speed, v.sub.1: suction-side speed, g: gravitational acceleration) is omitted. When measuring the differential pressure p=p.sub.2p.sub.1, the measurement positions are configured in such a way that the pressure losses between the measurement positions are negligible. In the exemplary embodiment, a liquid with a largely constant density is delivered.

(7) Therefore, the reduced delivery head H.sub.red is available for the current rotational speed of the pump. Since the characteristics of the pump generally apply to the rated rotational speed, the reduced delivery head H.sub.red is converted to the rated rotational speed, and so H.sub.red,n.N. emerges. This calculation is likewise known to a person skilled in the art [Kreiselpumpenlexikon, KSB, 4.sup.th edition, 2009 ISBN 978-3-00-029711-3].

(8) In the exemplary embodiment, an actuation frequency f and an effective power P.sub.wirk of the motor are ascertained by a frequency converter. In a step 2, the shaft power P and the rotational speed n are ascertained from the actuation frequency f and the effective power P.sub.wirk by a motor model.

(9) Alternatively, the shaft power may also be ascertained directly by a measuring device, for example a torque measuring hub.

(10) In a step 3, the shaft power P.sub.nN at the rated rotational speed is calculated from the current shaft power P and the rotational speed n since the P(Q) characteristic of the pump is generally specified at the rated rotational speed. The conversion of the shaft power to the rated rotational speed is known to a person skilled in the art [Kreiselpumpenlexikon, KSB, 4.sup.th edition, 2009, ISBN 978-3-00-029711-3].

(11) In a step 4, an offset correction of the P(Q) characteristic is carried out. To this end, the power P.sub.n.N. determined for a delivery flow of Q=0 is compared to the value in the P(Q) characteristic created by the producer. The deviation is then removed in the style of a one-point calibration.

(12) In a step 5, the data fusion according to the invention takes place. This step is described in detail in FIGS. 2a, 2b and 2c. The delivery flow for the rated rotational speed Q.sub.est.nN determined therefrom is then converted into the delivery flow Q.sub.est of the pump in a step 6. The conversion of the delivery flow from the rated rotational speed to the current rotational speed is known to a person skilled in the art [Kreiselpumpenlexikon, KSB, 4.sup.th edition, 2009 ISBN 978-3-00-029711-3].

(13) The calculations may be carried out in one or more electronic evaluation units. In the exemplary embodiment, the calculation of the mechanical power from the actuation frequency of the motor and the effective power is carried out in a first unit, which is assigned to a frequency converter. The data are then transferred to a second unit in which the pump characteristics are stored. The second unit carries out the data fusion according to the invention for determining the delivery flow.

(14) The delivery head-delivery flow relationships or power-delivery flow relationships may be stored as nodes, with the unit carrying out an interpolation and/or extrapolation. Alternatively, the delivery head-delivery flow relationships or power-delivery flow relationships may also be stored as a function, for example in the form of a polynomial.

(15) FIG. 2a shows three related diagrams. The upper left diagram depicts the probability density function .sub.Hred for the reduced delivery head. The probability density function .sub.Hred emerges from the following formula:

(16) ${}_{\mathrm{Hred}}=\frac{1}{\sqrt{2}}\exp \left(-\frac{1}{2}{\left(\frac{H_{\mathrm{red}}-H_{\mathrm{red}.\mathrm{mess}}}{}\right)}^2\right)$

(17) Here the value for the reduced delivery head H.sub.red.mess ascertained from the measured pressures forms the expected value. The standard deviation , which describes the width of the probability density function, approximately corresponds to the expected measurement errors. In the exemplary embodiment, the expected measurement errors are +/3% EOS.

(18) In FIG. 2a, the top right diagram shows the characteristic H.sub.red(Q). Each delivery flow value Q is assigned a probability density .sub.Hred by way of the pump characteristic H.sub.red(Q). The result .sub.Hred (H.sub.red (Q)) is normalized (diagram bottom right, FIG. 2a). Hence, a first probability density function .sub.Q1(Q) arises, for which, as a result of the normalization, the following applies: .sub.Q1(Q)dQ=1.

(19) Top left, FIG. 2b shows a probability density function .sub.p of the shaft power P. This function is calculated according to the following formula:

(20) ${}_P=\frac{1}{\sqrt{2}}\exp \left(-\frac{1}{2}{\left(\frac{P-P_{\mathrm{mess}}}{}\right)}^2\right)$

(21) Here, the current shaft power forms the expected value. The standard deviation , which describes the width of the probability density function, approximately corresponds to the expected measurement errors. In the exemplary embodiment, these are approximately +/3% EOS.

(22) The top right diagram in accordance with FIG. 2b plots the pump characteristic P(Q), in which the shaft power is represented depending on the delivery flow. Each discrete delivery flow value Q is assigned a probability density .sub.p by way of the pump characteristic P(Q). The result .sub.p(P(Q)) is normalized (bottom right diagram, FIG. 2b). Hence, a second probability density function .sub.Q2(Q) arises, for which, as a result of the normalization, the following applies: .sub.Q2(Q)dQ=1.

(23) FIG. 2c shows a diagram in which the product of the probability density functions .sub.Q2(Q) and .sub.Q1(Q) is plotted depending on the delivery flow. The upper curve shows the non-normalized values. The lower curve shows the normalized values. Said curve is the combined probability density function .sub.Qk(Q) of the delivery flow and is subsequently used for determining the delivery.

(24) The delivery flow emerges as the expected value of the combined probability density function .sub.Qk(Q) of the delivery flow (Q.sub.est in FIG. 2c). Alternatively, the maximum value of the curve may also be used as delivery flow. The delivery flow as expected value is calculated according to the following equation:
E(X)=.sub..sup.xf(x)dx.

(25) The foregoing disclosure has been set forth merely to illustrate the invention and is not intended to be limiting. Since modifications of the disclosed embodiments incorporating the spirit and substance of the invention may occur to persons skilled in the art, the invention should be construed to include everything within the scope of the appended claims and equivalents thereof.