ADAPTATION OF THE DELIVERY HEAD OF A CENTRIFUGAL PUMP TO A CHANGING VOLUMETRIC FLOW RATE

Abstract

The present invention relates to a method of operating an electric motor-driven centrifugal pump (3) in a hydraulic system (4) having at least one self-controlled load, where a gradient (dQ.sub.akt/dt) of the volumetric flow rate (Q.sub.akt) of the centrifugal pump (3) is determined and the current set-point delivery head (H.sub.soll) of the centrifugal pump (3) is calculated from a mathematical operation on the gradient (dQ.sub.akt/dt) weighted with a gain factor (K) and the last specified set-point delivery head (H.sub.soll,alt). The operation describes a positive feedback between the set-point delivery head (H.sub.soll) and the volumetric flow rate (Q.sub.akt). The gain factor (K) is determined from a calculation instruction that is modified dynamically during operation of the centrifugal pump (3) taking into consideration the current operating point of the centrifugal pump (3) and taking into consideration a current and/or at least one past state of the hydraulic system (4).

Claims

1. A method of operating an electric motor-driven centrifugal pump in a hydraulic system having at least one self-controlled load, the method comprising the steps of: determining a gradient of the volumetric flow rate of the centrifugal pump; calculating a current set-point delivery head of the centrifugal pump from a mathematical operation on the gradient weighted with a gain factor and the last specified set-point delivery head to describe a positive feedback between the set-point delivery head; determining the volumetric flow rate, and the gain factor a calculation instruction modified dynamically during operation of the centrifugal pump taking into consideration the current operating point of the centrifugal pump a current or at least one past state of the hydraulic system.

2. The method according to claim 1, wherein the mathematical operation is the addition of the gradient weighted with the gain factor to the last specified set-point delivery head.

3. The method according to claim 1, wherein the calculation instruction describes a functional relationship between the current operating point and a target point, and the current operating point of the centrifugal pump is determined and the gain factor is calculated from the functional relationship.

4. The method according to claim 3, wherein the a slope of a straight gauge line between the current operating point and the target point is determined and used as the gain factor.

5. The method according to claim 3, wherein the target point in the case of a positive gradient is an upper target point characterized by a volumetric flow rate greater than the volumetric flow rate of the current operating point.

6. The method according to claim 3, wherein the target point in the case of a negative gradient is a lower target point characterized by a volumetric flow rate lower than the volumetric flow rate of the current operating point.

7. The method according to claim 5, further comprising the steps of: determining a first gain factor corresponding to a slope of a first straight gauge line between the current operating point and the upper target point; determining a second gain factor corresponding to the slope of a second straight gauge line between the current operating point and the lower target point; and using the first gain factor used when the gradient is positive and the second gain factor is used when the gradient is negative.

8. The method according to claim 3, further comprising the steps of: determining a current and/or past system characteristic curve of the hydraulic system, and determining a point on this system characteristic curve that forms the upper target point.

9. The method according to claim 8, further comprising the steps of: determining an intersection between the current or past system characteristic curve and the maximum pump curve of the centrifugal pump; and using the determined intersection as the upper target point.

10. The method according to claim 3, wherein the past system characteristic curve is the one that is flattest within a past reference period.

11. The method according to claim 10, wherein the reference period is between 12 and 48 hours.

12. The method according to claim 3, wherein the upper target point or the lower target point lies on the minimum pump curve of the centrifugal pump.

13. The method according to claim 3, wherein the target point or the lower target point is an operating point that, when the volumetric flow rate is zero, lies on the minimum pump curve of the centrifugal pump.

14. The method according to claim 1, further comprising the step of: calculating the gain factor or the first gain factor in the case of a positive gradient according to the calculation instruction
K.sub.up=(H.sub.ZO−H.sub.akt)/Q.sub.ZO−Q.sub.akt) where K.sub.up is the gain factor or first gain factor, H.sub.ZO is the delivery head associated with the upper target point, H.sub.akt is the delivery head associated with the current operating point, Q.sub.ZO is the volumetric flow rate associated with the upper target point, and Q.sub.akt is the volumetric flow rate associated with the current operating point.

15. The method according to claim 7, further comprising the step of calculating the gain factor or the second gain factor is calculated in the case of a negative gradient according to the calculation instruction
K.sub.down=(H.sub.akt−H.sub.ZU)/(Q.sub.akt−Q.sub.ZU) where K.sub.down is the gain factor or second gain factor, H.sub.ZU is the delivery head associated with the lower target point, H.sub.akt is the delivery head associated with the current operating point, Q.sub.ZU is the volumetric flow rate associated with the lower target point, and Q.sub.akt is the volumetric flow rate associated with the current operating point.

16. The method according to claim 1, further comprising the step of: repeating the steps of determining a gradient, determining a set-point delivery head, and determining the volumetric flow rate cyclically in intervals between 3 seconds and 15 minutes.

17. The method according to claim 3, further comprising the step of: limiting the calculated gain factor to a maximum value corresponding to the slope of a straight line between a lower limit point and an upper limit point where the lower limit point lies on or below the minimum pump curve and the upper limit point lies on or above the maximum pump curve of the centrifugal pump.

18. The method according to claim 17, further comprising the step of: setting the upper limit point at an intersection between the maximum pump curve and the steepest system characteristic curve of the hydraulic system.

19. The method according to claim 17, wherein the upper limit point is defined by the maximum delivery head on the maximum pump curve and 10% to 20% of the maximum volumetric flow rate on the maximum pump curve.

20. The method according to claim 3, further comprising the step of: limiting the calculated gain factor to a minimum value of zero.

21. The method according to claim 3, further comprising the step of: setting the calculated gain factor to the last non-negative value if the calculated value of the gain factor is negative.

22. The method according to claim 1, further comprising the step of: determining the current volumetric flow rate in order to determine the current operating point, and resetting a newly determined volumetric flow rate value to the last determined volumetric flow rate value if the newly determined volumetric flow rate value is greater than the maximum volumetric flow rate on the maximum pump curve.

23. The method according to claim 1, wherein the gradient is calculated from a number of slidingly averaged volumetric flow rate values.

24. The method according to claim 1, wherein the gradient is determined slidingly via a certain number of values.

25. The method according to claim 1, further comprising the step of: raising the lower target point to a higher delivery head by 2% to 8% of the maximum delivery head on the maximum pump curve when the volumetric flow rate lies for a certain length of time below 0.1% of the maximum volumetric flow rate on the maximum pump curve.

Description

[0064] Other features and advantages of the method according to the present invention discussed below with reference to an embodiment. In the drawings,

[0065] FIG. 1 is a block diagram of the control according to the present invention with a metrological determination of the current operating point;

[0066] FIG. 2 is a block diagram of the control according to the present invention with a computational determination of the current operating point;

[0067] FIG. 3 shows a flow charge of the basic method sequence;

[0068] FIG. 4 shows an embodiment with calculation of the upper target point;

[0069] FIG. 5 shows a detail view of the determination of the ideal gain factor;

[0070] FIG. 6 shows a second embodiment with calculation of the upper target point and a detail view of the determination of the ideal gain factor;

[0071] FIG. 7 is an HQ diagram for depicting the method;

[0072] FIG. 8 is a flow chart for determining the upper target point;

[0073] FIG. 9 is an HQ diagram for depicting the upper target point on the flattest system characteristic curve;

[0074] FIG. 10 is an HQ diagram for depicting the upper limit of the gain factor; and

[0075] FIG. 11 is an HQ diagram for depicting the lower limit of the gain factor.

[0076] FIG. 1 is a block diagram of a control according to the present invention of an electric motor-driven centrifugal pump 3 in a hydraulic system 4. The hydraulic system 4 may be, for example, a heating system or a cooling system in which a heating or cooling medium is delivered by the centrifugal pump 3 from a central heat source or cooling machine to at least one, preferably, a plurality of self-controlled loads in the circuit. The loads may be, for example, heating elements and/or heating circuits of an underfloor heating system, or cooling zone of an overhead cooling system. Allocated to each one thereof is an actuator, in particular a thermostatic valve, an engine valve, or an electrothermal actuator that controls the volumetric flow rate through the corresponding load. Hereinafter, the actuators described below as valves.

[0077] Through the suction side and the pressure side thereof, the centrifugal pump 3 generates a differential pressure Δp, that is proportional to the delivery head H.sub.akt and generates a volumetric flow rate Q.sub.akt in the hydraulic system 4. Disturbances affect the state of the hydraulic system 4. This is understood to mean, in particular the valves that determine the hydraulic piping resistance of the system.

[0078] A controller 2 that specifies a certain rotational speed n in order to achieve a certain set-point delivery head H.sub.soll of the centrifugal pump 3 is allocated to the centrifugal pump 3. The rotational speed n is set in a manner known per se, by a frequency inverter (not shown) that controls the centrifugal pump 3. The controller 2 and the pump 3 form a control circuit with which the current set-point delivery head H.sub.akt is fed back to the controller input, so as to be taken out from the set-point delivery head H.sub.soll and so that the controller 2 corrects the rotational speed n in a manner corresponding to the resulting control deviation. The controller 2 may be configured as a P-, PI-, or PID-controller.

[0079] This assembly, which is widely known in the prior art, shall now be complemented by a dynamic controller 1 according to the present invention, which determines a delivery head set-point value H.sub.soll and specifies the rotational speed control in accordance with the current operating point B.sub.akt and the state of the hydraulic system 1. The current operating point B.sub.akt is described here by the current volumetric flow rate Q.sub.akt and the current delivery head H.sub.akt. These quantities are fed to the dynamic controller.

[0080] It should be noted that the current operating point and all of the other operating points mentioned below, as well as other points described with reference to the HQ diagram, may also be described by other physical quantities of the pump 3 or of the hydraulic system 4 without departing from the idea of the present invention. Thus, the current operating point and/or the other points may be described, for example, by the rotational speed, the torque, the power consumption, the voltage, and/or the current consumption of the centrifugal pump. This because this involves equivalent manners of description that would be readily familiar to a person skilled in the art. However, because the description on the basis of the known HQ diagram that describes the behavior of the delivery head H via the volumetric flow rate Q, is especially accessible and easy to understand, this means of description is used here.

[0081] It should also be noted that insofar as the delivery head is discussed here, the differential pressure of the pump is also meant, because these two quantities can be converted into one another in a closed system such as a heating system, through the proportional relationship H=Δp/(ρ×g), where ρ is the density of the delivered medium and g is gravitational acceleration, i.e. ρ and g are constants.

[0082] The current volumetric flow rate Q.sub.akt may be measured or calculated. In FIG. 1, the current volumetric flow rate Q.sub.akt and the delivery head H.sub.akt are measured by a volumetric flow rate sensor and by a differential pressure sensor, respectively, and fed to the dynamic controller 1. In contrast, FIG. 2 differs from FIG. 1 in that the current volumetric flow rate Q.sub.akt and the current delivery head H.sub.akt are determined computationally, here purely by way of example, through assessment of the current rotational speed n and the current power consumption P of the centrifugal pump 3. Because measurement generally cannot take place over the entire volumetric flow rate range without measurement errors, it is useful to combine measurement at higher volumetric flow rates and calculation at lower volumetric flow rates.

[0083] According to another embodiment that is not shown, it is also possible to determine only one of the two quantities of volumetric flow rate Q.sub.akt and delivery head H.sub.akt or differential pressure metrologically, and determine the other quantity computationally.

[0084] A calculation, if performed, may be done on the basis of at least one mathematical model, for example, a model of the electromotive and/or hydraulic part of the pump 3, optionally supplemented by a hydraulic mode of the hydraulic system 4. The electromotive part of the centrifugal pump 3 may be described, for example, by an electrical model and a mechanical model. It should be noted that calculation is also understood to mean estimation. Such an estimation may be based, for example, on an observer formed by a model of the electromotive pump 3 and optionally in combination with a model of the connected hydraulic system 4.

[0085] The embodiment according to FIG. 2 is provided with a calculator 5 that calculates the current delivery head H.sub.akt and the current volumetric flow rate Q.sub.akt from the current rotational speed n and the current power consumption P of the centrifugal pump 3. The values of these quantities are then fed to the dynamic controller 1 that assesses the current volumetric flow rate Q.sub.akt and specifies a new set-point delivery head H.sub.soll on the basis of the assessment. The method steps carried out by the dynamic controller 1 are shown, inter alia, in FIG. 3 that shows the basic flow of the method. The method proceeds from the current operating point B.sub.akt of the centrifugal pump 3 that is provided to the dynamic controller 1, step 20 in FIG. 3. Then, it is first assumed that the method has already been running for some time. When it is being initialized and started, different preparatory steps not shown here for the sake of simplicity take place. Inter alia, parameters and control variables are initialized and different parameters are preset with values. Furthermore, prior to step 20, some measurement values may be collected for possible averaging or smoothing.

[0086] The current operating point B.sub.akt necessary for carrying out the method is defined by the current volumetric flow rate Q.sub.akt and the current delivery head H.sub.akt, where only the current volumetric flow rate Q.sub.akt is of importance at the beginning of the method. Therefore, it would suffice to take only the current volumetric flow rate Q.sub.akt into consideration in step 20.

[0087] According to the present invention, first a gradient the volumetric flow rate Q.sub.akt of the centrifugal pump 3 is determined, step 30 in FIG. 3. The gradient dQ.sub.akt/dt is the time derivative of the volumetric flow rate Q.sub.akt, with the sign thereof setting forth the direction and the value thereof setting forth the magnitude of the current volumetric flow rate change, i.e. a trend. If the gradient dQ.sub.akt/dt is positive, of course at least one valve of the hydraulic system 4 opens, as a result of which the volumetric flow rate Q.sub.akt increases. If the gradient dQ.sub.akt/dt is negative, however, of course at least one valve closes, as a result of which the volumetric flow rate Q.sub.akt decreases.

[0088] The gradient dQ.sub.akt/dt may be calculated in a time-continuous or time-discrete manner. It should be noted here that, in any event, the entire method may be run either in a time-continuous manner or on the basis of discrete sample values, or even partially time-continuously and partially discretely. In the case of a time-discrete calculation, the gradient dQ.sub.akt/dt may be determined from the differential quotients of two successive volumetric flow rate values Q.sub.akt(t.sub.1), Q.sub.akt(t.sub.2), and the differential of these two values is divided by the sampling interval.

[0089] The sampling interval may be, for example, between 3 s and 30 s. It preferably corresponds to the interval according to which the method is repeated over and over. This means that at the end of every interval, there is a new delivery head set-point value H.sub.soll, i.e. the last delivery head set-point value H.sub.soll is valid for the duration of one interval and is set by the differential pressure controller 2 in the centrifugal pump 3. In each interval, thus, the delivery head set-point value H.sub.soll determined by the dynamic controller 1 is kept constant.

[0090] In order to suppress measuring noise, the gradient dQ.sub.akt/dt may be smoothed. For example, the gradient dQ.sub.akt/dt may be calculated from a number of slidingly determined volumetric flow rate values Q.sub.akt. Alternatively or additionally, the calculated gradient dQ.sub.akt/dt may itself be determined slidingly over a certain number of values. The number may be, ideally, 4 to 16 values each. Sliding average means that an average value is determined via the group formed by the certain number of values and the oldest value of each current group is replaced by a new value once the new value is available. It can be readily understood that a sufficient number of values must be available in order for sliding averaging to be possible. Therefore, a sufficient number of measurement values must be connected at the beginning of the method. In this respect, it may be provided that step 30 is then first run only if there are sufficiently many values available.

[0091] In step 50, at least one ideal gain factor K that is required in the following step 60 for adapting the set-point delivery head H.sub.soll is calculated. The adaptation is done in accordance with the calculated volumetric flow rate gradient dQ.sub.akt/dt and the calculated gain factor K. At the end of the method, then, the new set-point delivery head H.sub.soll is available, see step 70. The method is then repeated, the repetition being cyclical, here every 30 seconds by way of example. There is then a new set-point delivery head H.sub.soll that is again ascertained on the basis of the now new current operating point B.sub.akt.

[0092] Different embodiments are possible for the method sequence. The volumetric flow rate gradient dQ.sub.akt/dt must be calculated in every case for the adaptation of the set-point delivery head H.sub.soll in step 60. It need not necessarily be used in any of the previous steps. For this reason, in one embodiment, the sequence of the steps 30 and 50 may be interchangeable, or the steps 30 and 50 may be implemented simultaneously.

[0093] FIGS. 4 and 5 illustrate an embodiment of the method in step 50 that embodies the calculation of the gain factor K. Therein, the calculation is made from the current operating point B.sub.akt and an upper target point Z.sub.O(Q.sub.O,H.sub.O) or from the current operating point B.sub.akt and a lower target point Z.sub.U(Q.sub.U,H.sub.U).

[0094] The upper target point Z.sub.O lies above the current operating point B.sub.akt in the HQ diagram. The upper target point is defined by a volumetric flow rate Q.sub.ZO greater than the current volumetric flow rate Q.sub.akt, preferably but not necessarily also by a delivery head H.sub.ZO greater than the current delivery head H.sub.akt.

[0095] The lower target point Z.sub.U lies below the current operating point B.sub.akt. The lower target point is defined by a volumetric flow rate Q.sub.ZU lesser than the current volumetric flow rate Q.sub.akt, preferably but not necessarily also by a delivery head H.sub.ZU greater than the current delivery head H.sub.akt. Thus, the current operating point B.sub.akt always lies between the upper and lower target points Z.sub.O, Z.sub.U.

[0096] The lower target point Z.sub.U(Q.sub.U, H.sub.U) is specified first and therefore need not be determined at first. It is required in order to calculate an ideal gain factor K=K.sub.down in the case of a negative gradient dQ.sub.akt/dt. This is checked in step 51 in FIG. 5, where the query there of dQ.sub.akt/dt>0 would accordingly lead to the no-branch in this case. The case-specific gain factor K=K.sub.down is then determined in step 54 from the calculation instruction

K.sub.down=(H.sub.akt−H.sub.ZU)/(Q.sub.akt−Q.sub.ZU)

This describes the slope of a straight gauge line between the current operating point B.sub.akt that is characterized by the current volumetric flow rate Q.sub.akt and the current delivery head H.sub.akt, and the lower target point Z.sub.U that is characterized by a corresponding volumetric flow rate Q.sub.ZU associated with the lower target point and by a corresponding delivery head H.sub.ZU. In step 55, this case-specific gain factor K.sub.down is set as a general gain factor K that is used for calculating the set-point delivery head H.sub.soll in step 60. Steps 54 and 55 may also be combined, however, and the general gain factor K is immediately calculated then with the calculation instruction.

[0097] Thus, if the gradient dQ.sub.akt/dt is negative in step 51, then no other calculation needs to be performed in step 50. The gradient calculation in step 30 in FIG. 4 could then immediately transition into step 50, and step 50 into step 60, as is shown also in FIG. 3.

[0098] If, however, the gradient dQ.sub.akt/dt is positive, then a second case-specific ideal gain factor K=K.sub.up is calculated according to the present invention, see step 52. The calculation instruction used therefor reads

K.sub.up=(H.sub.ZO−H.sub.akt)/(Q.sub.ZO−Q.sub.akt)

and describes the slope of a straight gauge line between the current operating point B.sub.akt that is characterized by the current volumetric flow rate Q.sub.akt and the current delivery head H.sub.akt, and the upper target point Z.sub.O that is characterized by a corresponding volumetric flow rate Q.sub.ZO associated with the upper target point and by a corresponding delivery head H.sub.ZO. In step 53, this case-specific gain factor K.sub.up is set as a general gain factor K that is used for calculating the set-point delivery head H.sub.soll in step 60. Steps 52 and 53 may also be combined, however, and the general gain factor K is immediately calculated then with the calculation instruction.

[0099] Consequently, the upper target point Z.sub.O(Q.sub.O, H.sub.O) is required for the second case-specific gain factor K.sub.up. It must therefore be known before the second case-specific gain factor K.sub.up is calculated. The determination thereof takes place in step 40, i.e. at least before step 52. However, different positions may be useful for the actual implementation of step 40.

[0100] FIG. 4 shows an embodiment where the determination of the upper target point Z.sub.O(Q.sub.O, H.sub.O) takes place outside of step 50. This is advantageous in that the case distinction in step 51 may be forgone in step 50. Then, both case-specific gain factors K.sub.up, K.sub.down are calculated in step 50. Only when the set-point delivery head H.sub.soll is adapted does the query (step 51) of the sign of the gradient dQ.sub.akt/dt take place, and therewith the decision of which of the two ideal gain factors K.sub.up, K.sub.down should be used. In this case, the determination of the gradient dQ.sub.akt/dt may take place in step 30, in contrast to FIG. 4, behind step 40 or step 50. If the case distinction in step 51 takes place within step 50, however, then the calculation of the gradient dQ.sub.akt/dt necessarily must come before.

[0101] FIG. 6 shows an alternative embodiment to those of FIGS. 4 and 5. It differs from the variant in FIGS. 4 and 5 in that the determination of the upper target point Z.sub.O(Q.sub.O,H.sub.O) comes immediately before the calculation of the second case-specific gain factor K.sub.up, i.e. here only after it has been ascertained that the gradient dQ.sub.akt/dt is positive. For this reason, step 40 in FIG. 6 follows after the case distinction in step 51 in the yes-branch. The upper target point is thus only calculated or recalculated if also actually needed. It is, however, not calculated if the gradient dQ.sub.akt/dt in the current cycle is negative.

[0102] Moreover, FIG. 6 summarizes the steps 52, 53, 54, and 55, respectively. Thus, there is namely no distinction made between two different gain factors, even though two different gain factors K are calculated in the flow chart in FIG. 6. Finally, in each cycle, only one single gain factor K, which is then used for calculating the new set-point delivery head, is calculated. Following the calculation of one of the gain factors, a new current set-point delivery head H.sub.soll is then determined in step 60. This is done in accordance with the gradient dQ.sub.akt/dt, here in accordance with the magnitude and sign of the gradient dQ.sub.akt/dt, and the set-point delivery head H.sub.soll is calculated from a mathematical operation of the gradient dQ.sub.akt/dt, having been weighted with the calculated gain factor K, and the last specified set-point delivery head H.sub.soll,alt.

[0103] The mathematical operation achieves a positive feedback between the volumetric flow rate change dQ.sub.akt/dt and the set-point delivery head H.sub.soll. Then, the set-point delivery head H.sub.soll is increased if the volumetric flow rate Q is rising, i.e. the gradient dQ.sub.akt/dt is positive, and the set-point delivery head H.sub.soll is reduced if the volumetric flow rate Q is decreasing, i.e. the gradient dQ.sub.akt/dt is negative. The positive feedback between the delivery flow change dQ.sub.akt/dt and the delivery head H ensures a rapid response of the set-point delivery head H.sub.soll to the system-induced change in the delivered volumetric flow rate Q.sub.akt, for example if the thermostatic valves in the heating system 4 open or close quickly.

[0104] This positive feedback is achieved in such a manner that a positive feedback value M, which is positive if the gradient dQ.sub.akt/dt is positive and is negative if the dQ.sub.akt/dt is negative, is added to the last specified set-point delivery head H.sub.soll,alt. The new set-point delivery head H.sub.soll consequently arises from the old value H.sub.soll,alt plus the positive feedback value M according to the equation

H.sub.soll=H.sub.soll,alt+M.

[0105] In terms of control, this is an integrator. The positive feedback value M is calculated dynamically during operation of the centrifugal pump 3. It corresponds to the volumetric flow rate gradient dQ.sub.akt/dt having been weighted with a gain factor K. The gain factor K is, consequently, a positive variable in this case. In the present example, thus, the mathematical operation is the addition of the gradient dQ.sub.akt/dt, having been weighted with the gain factor K, to the last specified set-point delivery head H.sub.soll,alt.

[0106] Suitably, the positive feedback value M may additionally include a normalization factor with which the product of the gain factor K and the gradient dQ.sub.akt/dt is multiplied in order to achieve normalization of the positive feedback value W and an adaptation of the dimension thereof to the dimension of the set-point delivery head H.sub.soll. This normalization factor may be, for example, the sampling interval T. Thus, the equation will be

M=K×dQ/dt×T.

[0107] With the calculation of the new set-point delivery head H.sub.soll in step 60, the main part of the method according to the present invention is finished. The new set-point delivery head H.sub.soll is provided by the dynamic controller 1 in system 70 to the constant pressure controller 2 that then adjusts this via the rotational speed n.

[0108] It is therefore proposed, with the method according to the present invention, to determine the current operating point B.sub.akt of the centrifugal pump 3 and calculate the current ideal gain factor K from a functional relationship between the current operating point B.sub.akt and a target point Z.sub.O, Z.sub.U that lies either above or below the current operating point. This is described below with reference to the HQ diagram in FIG. 7.

[0109] The HQ diagram shows the pump characteristic diagram that is delimited from below by the minimum pump curve 10 and from above by the maximum pump curve. The minimum pump curve 10 describes the dependence of the delivery H on the volumetric flow rate at a minimum rotational speed n.sub.min of the centrifugal pump, and the maximum pump curve 11 describes the dependence of the delivery head H on the volumetric flow rate at a maximum rotational speed n.sub.max of the centrifugal pump. The rotational speed n of the centrifugal pump 3 is consequently constant along a pump curve 10, 11 The operating points of the centrifugal pump 3 lie between the minimum pump curve and the maximum pump curve. It should be noted at this point that with the pump 3, a power limitation may be implemented that makes it possible to specify a lower maximum rotational speed that deviates from the maximum pump curve 11 in the range of the greatest power during operation.

[0110] The current operating point B.sub.akt of the centrifugal pump 3 is described here by the current volumetric flow rate Q.sub.akt and the current delivery head H.sub.akt. It is on a current pump curve that, by way of example, is located between the minimum and maximum pump curves 10, 11 in FIG. 7. At the same time, the current operating point B.sub.akt is on a system characteristic curve 14 that describes the current state of the hydraulic system. This system characteristic curve 14, also called a piping parabola, is described here by way of example by a parabola of the form H.sub.a=k×Q.sup.2, where k is the slope of the parabola. A check valve is not taken into consideration here, for the sake of simplicity. The slope is, at the same time, a measure of the hydraulic resistance of the system 4. The farther the valves close and/or the more valves there are that close, the greater k will be, i.e. the steeper the slope of the system characteristic curve will be. The farther the valves open and/or the more valves there are that open, the smaller k will be, i.e. the flatter the slope of the system characteristic curve will be.

[0111] The pump curves 10, 11 make it clear that the centrifugal pump 3 can, at any rotational speed n, achieve a maximum delivery head and a maximum volumetric flow rate on the maximum pump curve associated with the rotational speed. This depends on the location of the system characteristic curve 14. The theoretically maximum delivery head on the maximum pump curve 11 is designated with H.sub.max,Max, and the theoretically maximum volumetric flow rate on the maximum pump curve 11 is designated with Q.sub.max,Max. Correspondingly, the theoretically maximum delivery head on the minimum pump curve 11 is designated with H.sub.max,Min, and the theoretically maximum volumetric flow rate on the minimum pump curve 11 is designated with Q.sub.max,Min.

[0112] In the embodiment according to FIG. 7, the lower target point Z.sub.U is fixed, at least at the start of the method. There may be adaptation, however, if a check valve is present and recognized in the hydraulic system. The lower target point Z.sub.U is placed in FIG. 7 on the operating point of the maximum delivery head H.sub.max,Min on the minimum pump curve 10. At this point, the volumetric flow rate is zero.

[0113] As indicated by the embodiment in FIG. 7, an upper target point Z.sub.O that lies above the current operating point B.sub.akt is defined. It is characterized by a delivery head H.sub.ZO and a volumetric flow rate Q.sub.ZO. The upper target point Z.sub.O may also be fixed, for example, may lie in the operating point of maximum power of the centrifugal pump 3. For better dynamic adaptation of the gain factor K, however, it is advantageous to keep the upper target point Z.sub.O variable.

[0114] In FIG. 7, the upper target point is selected so as to lie on the maximum pump curve 11. This, however, need not necessarily be the case. If, for example, the centrifugal pump 3 is oversized for the hydraulic system 4, the centrifugal pump will never reach an operating point on the maximum pump curve 11. In this case, the upper target point Z.sub.O may lie on the pump curve that belongs to the highest rotational speed n that the centrifugal pump 3 is driven during operation in the hydraulic system 4. This highest rotational speed may be monitored, recorded, and repeatedly corrected if driven still higher than the currently recorded highest rotational speed. If the rotational speed is corrected upward, preferably the upper target point Z.sub.O can also be corrected upward, so as to remain lying on the pump curve associated with the highest rotational speed.

[0115] Another case, where the upper target point need not lie on the maximum pump curve 11, exists then when a power limitation of the pump 3 is acting. This is because in this case the rotational speed is reduced relative to the maximum rotational speed on the maximum pump curve 11, in order not to exceed a certain power limit. This causes the maximum pump curve to be flattened and form approximately a straight line in the range exceeding the power limit. The upper target point then lies on a curve that is described outside of the power limit by the maximum pump curve and inside of the power limit by this straight line.

[0116] FIG. 7 assumes, however, that the centrifugal pump 3 has been adapted to the hydraulic system in terms of power, i.e. is not oversized and also does not enact a power limitation. The pump characteristic diagram is limited therefore by the maximum pump curve, so that the upper target point lies usefully on this maximum pump curve.

[0117] Ideally, the upper target point is calculated from the past states of the hydraulic system 4, as described below. This may be done in addition to or as an alternative to the taking into consideration of the highest rotational speed.

[0118] As shown in steps 52 and 54 of FIGS. 5 and 6, the gain factor K is determined from the slope of a straight line, starting from the current operating point. As illustrated in FIG. 7, a straight gauge line 15, 16 between the current operating point B.sub.akt and one of the target points Z.sub.O, Z.sub.U is used, and the slope of this straight gauge line 15, 16 is used as the gain factor K.

[0119] The basic idea of the present invention is thus to use a reference point Z.sub.O or Z.sub.U and set same in relation to the current operating point B.sub.akt. This reference point Z.sub.O, Z.sub.U is targeted in a certain manner, which can be seen in the HQ diagram starting from the current operating point B.sub.akt, in the form of the straight lines 15, 16 linking the current one and the reference point Z.sub.O, Z.sub.U. Therefore, the reference points Z.sub.O, Z.sub.U are also referred to as target points. The slope, then, of one of the straight gauge lines 15, 16 is calculated and used as the gain factor K.

[0120] Already, due to the use of the current operating point B.sub.akt to calculate the gain factor K, the calculation instruction will always be a different one, and changes dynamically during operation of the centrifugal pump 3. As illustrated in the HQ diagram, the slope of the straight gauge line 15, 16, and, therewith, of the gain factor K, already changes as a result of the change of the current operating point B.sub.akt. Additionally, the slope changes if the target point is also changed. This achieves optimal adaptation of the pump 3 to the load state of the hydraulic system 4 on the one hand, and broadly prevents positive feedback-related oscillations in the hydraulic system 4 on the other hand.

[0121] If the gradient dQ.sub.akt/dt is positive, a straight gauge line 15 from the current operating point B.sub.akt to the upper operating point Z.sub.O is used. The slope of this first straight gauge line 15 results, then, from the ratio of the lengths of the two sides of a right triangle placed against the first straight gauge line. This slope is selected as the gain factor K or first gain factor K.sub.up, so that the following equation applies

K=K.sub.up=(H.sub.ZO−H.sub.akt/(Q.sub.ZO−Q.sub.akt)

where K is the gain factor in general, K.sub.up is the first gain factor for an increasing volumetric flow rate, H.sub.ZO is the delivery head associated with the upper target point Z.sub.O, H.sub.akt is the delivery head associated with the current operating point B.sub.akt, Q.sub.ZO is the volumetric flow rate associated with the upper target point Z.sub.O, and Q.sub.akt is the volumetric flow rate associated with the current operating point B.sub.akt.

[0122] If the gradient is negative, a straight gauge line 16 from the current operating point B.sub.akt to the lower operating point Z.sub.U is used. The slope of this second straight gauge line 16 results, then, from the ratio of the lengths of the two sides of a right triangle placed against the second straight gauge line 16. This slope is selected as the new gain factor K or first gain factor K.sub.down so that the following equation applies

K=K.sub.down=(H.sub.akt−H.sub.ZU)/(Q.sub.akt−Q.sub.ZU)

where K is the gain factor in general, K.sub.down is the second gain factor, H.sub.ZU is the delivery head associated with the lower operating point B.sub.akt, H.sub.akt is the delivery head associated with the current operating point B.sub.akt, Q.sub.ZU is the volumetric flow rate associated with the lower operating point, and Q.sub.akt is the delivery flow associated with the current operating point. Because, in the embodiment in FIG. 7, the lower target point Z.sub.U lies on the minimum pump curve 10 with a volumetric flow rate of zero and maximum delivery head H.sub.max,Min, the following equation applies:

K=K.sub.down=(H.sub.akt−H.sub.min,Max)/Q.sub.akt

[0123] The use of different gain factors K.sub.up, K.sub.down for increasing and decreasing volumetric flow rates Q is advantageous in that there can be a response with different speeds to the different state changes in the system, i.e. to opening or closing valves. If, in contrast, the two gain factors K.sub.up, K.sub.down are the same, then the first and second straight gauge lines 15, 16 form a common, kink-free straight line.

[0124] The centrifugal pump 3 runs mostly in partial-load operation, i.e. in a system state with partially opened and partially closed valves, or with some opened valves and some closed valves. For this reason, the selection of the lower target point Z.sub.U on the minimum pump curve 10 and the upper target point Z.sub.O on the maximum pump curve 11 causes the gain factor K.sub.up to be greater with increasing volumetric flow rates Q than with decreasing volumetric flow rates Q. Thus, for example, in the case of a heating system, there can be a quickly response to a heating request where valves open, and the volumetric flow rate required for the heat transport can be made available. A slow response, meanwhile, would result in higher latencies until the heat arrives at the load, so that the corresponding room is heated more slowly and the comfort of the user is affected.

[0125] In contrast, in the reverse case of closing valves, a slow response may suffice and even be advantageous. In this case, the centrifugal pump 3 would indeed run energy-inefficiently for some time, but this would not lead to adversely affected comfort for the user. Rather, the pump 3 can slowly find an operating state in which it consumes less energy and yet still provides the necessary thermal energy, and the pump is in a sort of “standby” state on the way to quickly changing back to higher volumetric flow rates, because it has not yet achieved the optimal-energy operation that may possibly be far away from the previous operating point.

[0126] FIG. 8 represents method steps of an embodiment for ascertaining a suitable upper target point Z.sub.O. In this variant, the upper target point Z.sub.O is calculated from past states of the hydraulic system 4. It is then the objective for the dynamic controller 1 to set the upper target point Z.sub.O to where the pump 3 is operated with full load. In particular it should be set to where the pump 3 delivers the greatest volumetric flow rate Q at the highest rotational speed n. This is done in the embodiment according to FIG. 8 by selection of a target point Z.sub.O on the maximum pump curve 11 by the dynamic controller 1. This is done by determining the flattest system characteristic curve 13 and setting the intersection thereof with the maximum pump curve 11 as the upper target point Z.sub.O. This is illustrated in FIG. 9.

[0127] For this purpose, the current system characteristic curve 14 is determined in a first step 41. The system characteristic curve mathematically describes the functional relationship between the delivery head H and volumetric flow rate Q of the piping network forming the hydraulic system 4, inclusive of the connected loads and the controlling adjusting means thereof. This relationship is, at its simplest, quadratic, according to H.sub.a(Q)=k×Q.sup.2+c.sub.x, so that the system characteristic curve may also be considered a piping parabola of which the slope is defined by the value of the parameter k. The parameter c.sub.x sets forth, in terms of delivery head value, the differential pressure that must be overcome in order to open a check valve. Provided that the hydraulic system 4 does not have a check valve, c.sub.x can be set to zero. The current system characteristic curve 14 is determined by determining the parameter(s) k, c.sub.x of the piping parabola. The intersection between the system characteristic curve 14 and the maximum pump curve 11 is then determined in step 42. The intersection may be found by equating the mathematical equations for the system characteristic curve 14 and the maximum pump curve 11.

[0128] The calculation of the current system characteristic curve 14 is repeated with every cycle of the method, so that it is known at every point in time that past system curves existed. Every intersection with the maximum pump curve 11 is characterized by a certain volumetric flow rate and a certain delivery head. The cyclic determination of the system characteristic curve 14 and the intersection consequently produces a set of volumetric flow rates. This is followed by ascertainment of which of all of the specific intersections is the one with the greatest volumetric flow rate Q.sub.max,T. Consequently, the greatest volumetric flow rate Q.sub.max,T is determined from the set of volumetric flow rates. This greatest volumetric flow rate Q.sub.max,T lies on the system characteristic curve 13 that is the flattest. Should a new volumetric flow rate value of a new intersection that is even greater than all of the previous values be added to the set, then this new value is set as the greatest volumetric flow rate value Q.sub.max,T, because an even flatter system characteristic curve has obviously occurred in the hydraulic system 4.

[0129] It should be noted that a set of volumetric flow rate values of the intersections need not necessarily be formed. Rather, the greatest volumetric flow rate may be stored and replaced again and again by an even higher volumetric flow rate, as soon as one is detected. At the start of the calculation, then, the first determined volumetric flow rate is simply set as the greatest volumetric flow rate.

[0130] If, however, the formation of the set of volumetric flow rates is used, then it is advisable not to allow this set to be infinitely large, but rather to limit same to a reference period T. Due to the periodic recurrence of certain load states occurring in a heating system as a result of the user habits, it is useful to set the reference period to 24 hours, because the heat curve repeats daily due to the user habits. This applies at least for the days of the week. This is because the characteristic load states of the hydraulic system, for example, heating up in the morning and evening when one is at home or enters or leaves the office, or the reduced temperature at night, repeat daily. A shorter reference period T may also be used, however, for example, 12 hours, in order to determine a highest volumetric flow rate Q.sub.max,T for day operation and night operation, respectively, or a multiple of 24 hours in order to determine a highest volumetric flow rate Q.sub.max,T over two or more days.

[0131] The reference period T may preferably be used as a sliding time window. This means that the highest volumetric flow rate of the set gradually becomes older and, if no new highest volumetric flow rate is determined, is dropped from the set after an age corresponding to the duration of the reference period T, with the second-highest volumetric flow rate of the set then becoming the highest volumetric flow rate. The sliding time window thus has a regenerative effect.

[0132] As an alternative to the sliding time window, the set of volumetric flow rates or, in any case, the highest determined volumetric flow rate may be deleted and re-formed after a certain reference period T. FIG. 9 shows that the current system characteristic curve 14 is steeper than the flattest system characteristic curve 13 (dashed line) that has occurred in the system since the beginning of the current reference period T. If the valves of the loads open, the current system characteristic curve 14 moves in the direction of the flattest system characteristic curve 13.

[0133] Once the greatest volumetric flow rate Q.sub.max,T is known, the related delivery head H.sub.max,T can be determined, step 44, for example, by entering the greatest volumetric flow rate Q.sub.max,T into the equation for the system characteristic curve 14 or the equation for the maximum pump curve. The two determined values Q.sub.max,T and H.sub.max,T are then set as the upper target point Z.sub.O, step 45, which is then used for the other method steps. These values produce, for the mathematical calculation instruction in step 52, the equation

K=K.sub.down=(H.sub.max,T−H.sub.akt)/(Q.sub.max,T−Q.sub.akt).

[0134] As an alternative to repeated calculation of the system characteristic curve 14 and the intersection and the subsequent determination of the highest volumetric flow rate Q.sub.max,T, the slope k of the respectively determined current system characteristic curve 14 may be used to determine the flattest system characteristic curve. This is because the flattest system characteristic curve is the one with the smallest parameter k. The determination of the current system characteristic curve 14 in step 41 from FIG. 8 may therefore be followed by a step in which the flattest system characteristic curve is determined directly. This may, analogously to the approach above, be done either by determining the slope k of each determined system characteristic curve, collecting the slopes into a set of slopes, and then determining the smallest slope k.sub.min from this set, or by checking at each determination of the slope k for whether this is smaller than a previously ascertained smallest slope k.sub.min. In the mentioned second case, the slope of the first determined system characteristic curve should be stored as the smallest slope k.sub.min only at the beginning of the method.

[0135] If the smallest slope k.sub.min is known, the flattest system characteristic curve is also available. Then, in a subsequent step, the intersection of the flattest system characteristic curve with the maximum pump curve or the volumetric flow rate Q.sub.max,T defining this intersection and the defining delivery head H.sub.max,T may be determined and used as the upper target point.

[0136] With this alternative variant, thus, the intersection with the maximum pump curve 11 and, therefrom, the flattest system characteristic curve are not determined at every cycle; rather, first the system characteristic curve is determined, and then the intersection therefrom.

[0137] With the described alternative variant, too, the smallest slope k.sub.min may be determined for a certain reference period T, i.e. after the end of the reference period, the smallest determined slope k.sub.min is deleted again and re-determined. The same properties as previously discussed apply to the reference period T.

[0138] The method described is illustrated by FIG. 9. The pursued ideal gain factor K is selected according to the present invention so as to be equal in amount to the slope of the first straight gauge line 15 for a positive gradient dQ.sub.akt/dt and equal to the slope of the second straight gauge line 16 for a negative gradient dQ.sub.akt/dt. The gain factor K is thus determined according to a different mathematical rule when there is a volumetric flow rate increase, i.e. a positive gradient dQ.sub.akt/dt>0 (step 52) than when there is a volumetric flow rate decrease, i.e. a negative gradient dQ.sub.akt/dt<0 (step 54). In summary, the following calculation instruction applies therefor, with consideration given to the upper and lower target points Z.sub.O, Z.sub.U shown in FIG. 9:

[00001]$K=\left\{\begin{array}{cc}{K}_{\mathrm{up}}=\left(H_{\max ,T}-H_{\mathrm{akt}}\right)/\left(Q_{\max ,T}-Q_{\mathrm{akt}}\right)& \mathrm{for}.Math..Math.\mathrm{dQ}/\mathrm{dt}>0\\ K_{\mathrm{down}}=H_{\mathrm{akt}}-H_{\max ,\mathrm{Min}})/Q_{\mathrm{akt}}& \mathrm{for}.Math..Math.\mathrm{dQ}/\mathrm{dt}<0\end{array}\right\}$

[0139] For the sake of mathematical completeness, it should be noted that the gain factor K for dQ.sub.akt/dt<0 may be set to equal zero, because in this case there is no need to adapt the set-point delivery head H.sub.soll.

[0140] As a security measure, different limit value considerations may be carried out to make the method especially robust and more failsafe. They are illustrated in FIGS. 10 and 11.

[0141] Thus, FIG. 10 shows limiting the gain factor K through a maximum value K.sub.max corresponding through the slope of a straight line 12 between a lower limit point and an upper limit point. The lower limit point lies here on the minimum pump curve 10 when the volumetric flow rate is zero. It thus corresponds, for example, to the lower target point Z.sub.U. The upper limit point lies above the maximum pump curve 11. It is defined by the maximum delivery head H.sub.max,Max on the maximum pump curve 11 and the maximum volumetric flow rate Q.sub.max,Max on the maximum pump curve 11, having been weighted with a factor F.sub.flow. The factor F.sub.flow is based on the maximum rate of change in the rotational speed of the centrifugal pump 3, and lies here between 10% and 20%. The upper limit point also ideally lies on the steepest system characteristic curve 17 of the hydraulic system 4. The maximum value K.sub.max may be calculated from

K.sub.max=(H.sub.max,Max−H.sub.max,Min)F.sub.flowQ.sub.max,Max

If the result of the calculation according to the above calculation instruction is that the gain factor K attains a value greater than the described maximum value K.sub.max, the gain factor K is limited to this maximum value K.sub.max. The calculation done through this maximum value ensures that a system characteristic curve can always still be calculated, even in the case of very low volumetric flow rates or in the case of a volumetric flow rate of zero. In addition, overreactions are avoided.

[0142] FIG. 11 shows a case where the gain factor K.sub.up calculated for a positive gradient is negative. Here, the flattest system characteristic curve 18 is deeper than the one in FIG. 9.

[0143] At this point, it should be noted that this shows that in FIG. 9, either the reference period T has not yet ended and the flattest system characteristic curve 18 is still occurring, as in FIG. 11, but is not yet known to the dynamic controller, or the state of the hydraulic system 4 with which the flattest system characteristic curve from FIG. 11 is associated simply does not occur in the reference period T observed in FIG. 9. This shows that the flattest system characteristic curve 13 in FIG. 9 is a relative, reference period-relevant flattest system characteristic curve, whereas the flattest system characteristic curve 18 in FIG. 11 is the absolutely flattest system characteristic curve.

[0144] At the current operating point B.sub.akt according to FIG. 11, the current delivery head H.sub.akt is greater than the delivery head H.sub.max,T associated with the upper target point Z.sub.O. It thus is higher, as a result of which the straight gauge line 15 falls to the upper target point Z.sub.O. The slope of the straight gauge line 15 and the calculated gain factor are thus negative.

[0145] The same may happen for the other straight gauge line 16 when, namely, the current delivery head H.sub.akt is smaller than the delivery head H.sub.max,Min associated with the lower target point Z.sub.U at the current operating point B.sub.akt. It thus is deeper, as a result of which the other straight gauge line 16 rises to the lower target point Z.sub.O. Thus the slope of the straight gauge line 15 is positive and the calculated gain factor K.sub.down is negative.

[0146] Because the positive feedback in these cases is converted into a negative feedback, the calculated gain factor K.sub.up, K.sub.down is limited to a minimum value K.sub.min. This amounts to zero if the gain factor gradually decreases to below zero. This means that the delivery head set-point value H.sub.soll in this case is not changed, i.e. the pump 3 is controlled on the same Δp-c characteristic curve for the next cycle. If, however, the calculated gain factor K.sub.up jumps from a positive value to a value below zero, it is then set to the last non-negative value. Negative values for the gain factor K.sub.up also arise when the operating point of the centrifugal pump 3 moves on the maximum pump curve 11.

[0147] A test for whether the calculated gain factor K is under the minimum value or exceeds the maximum value, including correction thereof, may be performed after step 50, but, in particular immediately after step 52 or 54.

[0148] In addition or as an alternative, it may be provided in the method according to the present invention to prohibit an upper target point Z.sub.O that, in terms of the delivery head H.sub.ZO=H.sub.max,T thereof, lies below the delivery head H.sub.max,Min associated with the lower target point Z.sub.U. Therefore, step 44 may be directly followed by a query of whether this condition is met. If the answer is affirmative, the delivery head H.sub.ZO for the upper target point is equated with the delivery head associated with the lower target point Z.sub.U, H.sub.ZU=H.sub.max,Min. If the answer is negative, the determined delivery head H.sub.ZO remains unchanged.

[0149] As a further security measure, it may be provided to reset a newly measured volumetric flow rate value Q.sub.akt to the last-measured volumetric flow rate value Q.sub.akt if the new volumetric flow rate value Q.sub.akt is greater than the maximum volumetric flow rate value Q.sub.max,Max on the maximum pump curve 11. This is because this is not plausible. Such a measurement value may arise with faulty measurement, and may severely disrupt the method. The correction of the volumetric flow rate value Q.sub.akt may directly follow step 20.

[0150] Furthermore, as another security measure, it may be provided, as a result, to check the system characteristic curve 14 determined in step 41 for whether the steepness exceeds a maximum value K.sub.max. This results when the one that passes through the upper limit point is allowed as the steepest system characteristic curve 17. The maximum slope value then arises from

K.sub.max=(H.sub.max,Max)/(F.sub.flowQ.sub.max,Max).sup.2

[0151] Thus, step 41 may be immediately followed by a query of whether the slope K determined with the current system characteristic curve 14 exceeds the maximum value K.sub.max. If this is the case, the slope is limited to this maximum value K.sub.max.

[0152] As previously mentioned, the lower operating point may be changed, in particular raised, during operation of the centrifugal pump 3. This is necessary if the hydraulic system 4 contains a check valve for which the opening pressure lies above the delivery head H.sub.ZU associated with the lower target point Z.sub.U. If the operating point B.sub.akt of the centrifugal pump 3 reaches the lower target point Z.sub.U, the delivery head or the differential pressure built up by the pump 3 at this delivery head lies below the opening pressure of the check valve. This would then close and never reopen. In order to prevent this, the lower target point Z.sub.U is raised, for example, by 5% of the maximum delivery head H.sub.max,Max on the maximum pump curve 11. Then, H.sub.ZU=H.sub.ZU.sub._.sub.old+0.05×H.sub.max,Max applies.

[0153] The raising may then be done when the volumetric flow rate Q.sub.akt lies below a predetermined limit value for a certain length of time. The existence of the check valve is tested for by this limit value. The limit value may be 1% of the maximum volumetric flow rate Q.sub.max,Max on the maximum pump curve, and the length of time may be 30 minutes.

[0154] With the method described here, any electric motor-driven centrifugal pump, in particular a heating pump, can be operated with the use of positive feedback between volumetric flow rate changes and the set-point delivery head with a gain factor that is optimal in every load state.