DE102007009302B4 - Method for determining pump flow without the use of traditional sensors - Google Patents

Abstract

A method of determining pump flow without using traditional sensors has steps and modules to create a calibrated performance curve with the valve closed at multiple speeds, to calculate coefficients from a normalized performance curve based on the performance ratio of a pump, and to solve a polynomial performance equation for the Flow at the current operating point. The calibrated performance curve can be created by increasing the pump speed from a minimum to a maximum value and by operating the pump with a closed outlet valve. This data is used to correct the published performance for the shutdown power and the optimal operating point at nominal speed in order to determine the performance ratio of the pump. They are also used to precisely determine the performance with the valve closed at the current operating speed. The performance ratio of the pump is determined according to the following equation: Pratio = Pshutoff @ 100% / PBEPcorr. For example, the polynomial power equation may include a 3rd order polynomial equation developed using coefficients from a normalized power versus flow curve, where corrections may be made in the polynomial power equation according to speed, hydraulic efficiency, and relative density . To solve the 3rd order polynomial equation, complex roots can be determined using either the Müller method or another suitable method, whereby the calculated actual flow rate can be determined for a specific operating point.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application also claims the benefit of a provisional patent application Serial No. 60 / 780,546, filed March 6, 2006, entitled "Method for Determining Pump Flow Without the Use of Traditional Sensors" (911-2.24-1 / 05GI003) to Patent Application Serial No. 11 / 601,373 filed November 17, 2006, entitled "Method and Apparatus for Pump Protection Without the Use of Traditional Sensors" (911-2.22-1 / 05GI002), and also relates to the provisional patent application under reference 60 / 780,547, filed March 8, 2006, entitled "Method for Optimizing Valve Position and Pump Speed in a PID Control Valve System Without the Use of External Sensors" (911-2.23-1 / 06GI001). All of these patent applications are incorporated herein by reference in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the invention

The present invention relates to a pump system including a pump including a centrifugal pump, more particularly to a method of determining pump flow without the use of traditional sensors.

2. Brief description of the related art

Pumping devices are known in the art and the associated methods and their disadvantages are as follows:
Pump governors are known to use pump affinity laws, which approximate how the performance (flow, head, power) of a centrifugal pump is affected by speed and impeller tuning. While the affinity laws are useful for general estimation, the power factoring coefficient often results in over- or underestimating the power based on the operating speed, size and specific speed of the pump. This inaccuracy has a direct impact on pump protection and flow prediction algorithms found in programmable logic controllers (PLC), distributed control systems (CS) and frequency converter drives (VFD).

Also, when creating pump maps, deviations of the actual performance of a pump from the standard performance curves significantly affect the accuracy of the flow and / or pump state estimation. This is usually accomplished by performing a pump performance test at multiple speeds to confirm accurate pump performance. However, this solution can be time consuming, application specific and quite expensive. In view of this, there is a need in the industry for a method that eliminates the error of the affinity laws.

US 6,715,996 B2 discloses a method for operating a centrifugal pump that senses closed-valve pump performance at two speeds, determines eddy current losses, and calculates adjusted power at other frequencies to determine if the pump is operating with the valve closed. However, methods such as this to correct closed valve performance begin to become inaccurate at speeds below 50% of the rated engine speed, which may limit the range of application. The method of interpolation between power values at other speeds is based in part on the affinity laws and is thus less accurate.

WO 2005/064167 A1 discloses a method that uses a calibrated curve for power / differential pressure versus flow and against speed. To determine the pump flow, the calibrated data is stored and compared to current values. This procedure requires a differential pressure transmitter and requires that calibration curves for power / Δ pressure vs. flow be stored in the analyzer. To maintain flow, this method is application-dependent, which reduces flexibility during installation on the plant. It is also not easy to adjust to compensate for wear.

US 6,591,697 B2 discloses a method of determining pump flow rates by measuring engine torque, which is the relationship of torque and speed to pump flow rate and explained the possibility of regulating the pump flow with a VFD to adjust the centrifugal pump speed. However, this method uses calibrated flow versus torque curves for multiple speeds that are application dependent, which reduces flexibility during installation on the plant. It is also not easy to adjust to compensate for wear.

US 6,464,464 B2 discloses an apparatus and method for controlling a pumping system based on a control and pump protection algorithm that uses a VFD to regulate the flow, pressure, or speed of a centrifugal pump. However, this method requires the use of auxiliary measuring instruments, but which make the drive system more complex, an additional possible source of error and unnecessarily increase the cost. However, it also uses calibrated TDH flow curves at multiple speeds, which are application-dependent, reducing flexibility during installation on the plant.

In addition, the following patents have been developed in a patentability research conducted in relation to the present invention. Below are summarized briefly:
US 4,358,821 A lays down a method and devices for the inclusion of fluctuating flow in the regulation of process variables, in which the flow is measured and the amount of material extracted by the process is determined by integration of the measurement results.

US 5,213,477 A discloses a device for controlling the pump delivery rate, in which the highest allowable flow is determined based on the relationship between the existing and the required holding pressure level (NPSH).

US Pat. No. 6,424,873 B1 discloses a method and system for limiting integrating components in a PID controller based on a method of excluding or integrating a component of a primary PID controller into a PID calculation.

US 6,546,295 B1 sets forth a method for tuning a process control loop in an industrial process in which plant equipment and process controls are fine-tuned by determining control parameters for the controllers that interact to produce a desired process variability.

US 6,554,198 B1 discloses an edge prediction controller and a variable volume air volume (VAV) PID controller in a pressure independent VAV temperature control system that rely on a method that includes calculating a deviation between an airflow setpoint and an airflow measured value.

US 2004/0267395 A1 sets forth a system and method for multi-objective dynamic optimization of the selection, integration, and use of machines based on a method of modifying the use of assets in an industrial automation system based on a function of analyzed diagnostic and machine data.

US 2005/0237021 A1 discloses a rotary driving device of construction machinery in the form of a method and apparatus for pumping a medium at a constant average flow rate.

None of the above-mentioned patents or publications teach or suggest the method of determining pump flow described herein without traditional sensors having the object of the present invention. The object is achieved by the method according to claim 1, and by the regulator and the pumping system of independent claims 18 and 35.

SUMMARY OF THE INVENTION

The present invention provides a new and unique method of determining flow in a centrifugal pump, a centrifugal mixer, a radial fan or a centrifugal compressor without the use of traditional sensors; it includes steps to create a calibrated performance curve with closed valve and multiple speeds; it calculates coefficients from a power versus flow curve based on the power ratio of a pump; and it solves a power equation for the flow at the current operating point.

The calibrated power curve can be created by increasing the pump speed from a minimum to a maximum value while operating the pump against a closed exhaust valve and detecting speed and performance data at multiple speeds. These data are used to correct the published performance for shutdown power and optimum operating point at rated speed to determine the power ratio of the pump. They also serve to accurately determine closed-valve performance at the current operating speed. This is necessary because the published performance data often differ from the actual data due to seal losses, wear, differences in castings, etc.

The power ratio of the pump is calculated according to the following equation: P _ratio = P _{shutoff @ 100%} / P _{BEP_corr} .

For example, the performance equation may include a 3rd order polynomial equation developed using coefficients from a normalized power versus flow curve, wherein corrections may be made in accordance with speed and hydraulic efficiency in the polynomial performance equation. In addition, complex roots can be determined either using the Muller's method or some other suitable method to solve the 3rd order polynomial equation, whereby the calculated actual flow can be determined for a specific operating point.

The steps of the method may be performed on a frequency converter drive (VFD) having one or more modules that implement the features illustrated herein, as well as on a programmable logic controller (PLC).

The present invention may also include a controller having one or more modules in a configuration for implementing the functional features illustrated herein and a pump system having such a controller.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings include the following illustrations:

is a block diagram of a simple pump system according to the present invention.

is a flowchart with the essential steps of the in shown regulator according to the present invention.

is a block diagram of an in shown regulator for performing the in shown essential steps.

is a graph of the error (HP) in% versus speed (RPM) using various methods such as cubic interpolation, method x and affinity laws.

is a plot of power (HP) versus closed-valve speed (RPM) for actual drive power, tuned power, and affinity methods.

is a graph of power (BHP) versus flow (GPM) for actual drive power, data published in Pricebook (with gasket), and corrected power adjusted data, also showing polynomial curve adjustments for each data set.

is a plot with normalized curves for% power (HP) vs.% flow (rpm) at 1700, 2200, 2800, 3570 RPM actual and calculated speed.

is a graph with normalized BHP versus flow (gallons per minute) for actual flow and calculated flow.

DETAILED DESCRIPTION OF THE INVENTION

shows the simple pump system, which according to the present invention with 2 is called and a controller 4 , a motor 6 and a pump 8th having. In operation and according to the present invention, the controller is used 4 to determine the pump flow rate without the use of traditional sensors based on a method of making a closed valve closed loop performance curve at multiple speeds, calculating coefficients from a power versus flow curve based on a pump power ratio, and a Power equation for the flow at the current operating point is solved, as shown and described here.

shows an example of a flowchart, which is generally with 10 is called and the essential steps 10a . 10b and 10c contains the algorithm for determining the pump flow, that of the controller 4 can be realized according to the present invention. The determined flow value can also be used as input to a PID loop to control flow without an external flow meter or traditional gauges. The algorithm for determining the flow rate may be embedded in a frequency converter drive or a programmable logic controller, as described above in terms of the regulator 4 shown.

In accordance with the present invention, the calibrated power curve may be established by increasing the pump speed from a minimum to a maximum value and operating the pump against a closed exhaust valve. These data are used to correct the published performance for shutdown power and optimum operating point at rated speed to determine the power ratio of the pump. They also serve to accurately determine closed-valve performance at the current operating speed.

The power ratio of the pump can be calculated according to the following equation: P _ratio = P _{shutoff @ 100%} / P _{BEP_corr} .

For example, the performance equation may include a 3rd order polynomial equation developed using coefficients from a normalized power versus flow curve, wherein corrections may be made in accordance with speed and hydraulic efficiency in the polynomial performance equation. In addition, complex roots can be determined either using the Muller's method or some other suitable method to solve the 3rd order polynomial equation, whereby the calculated actual flow can be determined for a specific operating point.

An advantage of the present invention is that it eliminates the error of the affinity laws by sampling the power at different closed-valve speeds to produce an accurate power curve when turned off. By applying a proprietary cubic interpolation technique, it is then possible to accurately determine pump performance with a closed valve over a wide range of RPMs. See the graphs in the and ,

The performance obtained by using published pump performance curve data often deviates from actual performance due to pumping loss losses that vary linearly. The difference between the actual and the published power in the off state can be used to balance (adjust) the power from the published curve at the optimum operating point (BEP), since the seal losses are constant at a given speed. This approach eliminates the need for a particularly accurate pump performance curve (eg, factory testing) or a more complex calibration process on the equipment. This results in a more accurate estimate of PBEP and PSO at different speeds. This data can then be used to further model pump performance based on the minimum external data.

By doing that, the normalized power coefficients into a power equation 3 , In order to be integrated, it is not necessary to perform flow calibrations against parameters such as torque, power or pressure at various speeds, external transducers are unnecessary, and flexible application in plant setup becomes possible. With the present invention, wear compensation is possible by regularly carrying out the tuning process described in step A below.

Fig. 3: Controller 4

shows the main modules 4a . 4b . 4c and 4d of the regulator 4 , Many different types and types of regulators and control modules for controlling pumps are known in the art. One skilled in the art familiar with such controllers and control modules would be able to use control modules such as 4a . 4b and 4c and to configure to perform the functionality described herein, that is, to create a closed-valve calibrated closed-valve performance curve at multiple speeds, calculate a normalized power curve coefficient based on a pump power ratio, and a polynomial performance equation to solve for the flow at the current operating point, such as in shown and described above, according to the present invention. By way of example, the functionality of the modules 4a . 4b and 4c by hardware, software, firmware, or a combination thereof, although it is not intended to limit the scope of the invention to any particular embodiment thereof. In a typical software implementation, such a module would be one or more microprocessor-based architectures including a microprocessor, random access memory (RAM), read only memory (ROM), input / output devices and controller, and data and address buses to its connection. One skilled in the art would be able to program such a microprocessor-based implementation without undue experimentation to achieve the functionality described herein. It is not intended to limit the scope of the invention to any particular implementation using any known or otherwise developed technique.

The controller has additional control modules 4d known in the art, which are not part of the underlying invention and which are not described in detail herein.

engine 6 and pump 8th

engine 6 and pump 8th are known in the art and will not be described in detail here. In addition, it is not intended to limit the scope of the invention to any particular type or manner thereof which is either now known or will be developed in the future. Furthermore, the scope of the invention should also include the application of the method according to the present invention in relation to the regulation of the operation of a centrifugal pump, a centrifugal mixer, a radial fan or a centrifugal compressor.

realization

This method of flow calculation consists of two main steps:
In step A, a closed-valve calibrated performance curve is created at multiple speeds.

In step B, the coefficients of the normalized power curve are calculated based on the power ratio of a pump and a polynomial power equation 3 , Order for the flow at the current operating point solved.

Step A:

The function of the logic according to the present invention is to increase the pump speed from a predetermined minimum value (eg, 30% of the maximum speed) to another value (eg, 60% of the maximum speed) while the pump works with a closed outlet valve. The ratio of the speeds should be about 2: 1. The power is then measured at these speeds and at maximum speed of 100% and corrected by a relative density = 1.

The shutdown power at any speed can then be determined by a proprietary method of cubic interpolation:
The coefficients A to F are calculated as follows: A = (P _{SO_30%} ) / (N _30% ) B = (P _{SO_60%} - P _{SO_30%} ) / (N _60% - N _30% ) C = (B - A) / (N _60% - N _30% ) D = (P _{SO_100%} - P _{SO_60%} ) / (N _100% - N _60% ) E = (D - B) / ((N _100% - N _30% ) F = (E - C) / (N _100% )

The shutdown power at any speed is calculated as follows: P _{SO_N%} = A (N _ACT ) + C (N _ACT ) (N _{ACT -N 30%} ) + F (N _ACT ) (N _{ACT -N 30%} ) (N _{ACT -N 60%} ) in which
P _{SO_30%} = P _{Meas_30%} / SG is the measured _breaking capacity at 30% of rated motor speed corrected to a specific gravity = 1,
P _{SO_60%} = P _{Meas_60%} / SG is the measured shutdown power at 60% of rated motor speed corrected to a specific gravity = 1, and
P _{SO_100%} = P _{Meas_100%} / SG is the measured shutdown power at 100% of rated motor speed corrected to a specific gravity = 1.

It is noted that in some embodiments, such as sealless pumps, estimates of eddy current losses must be removed from readings at shutdown.

SG

= relative Dichte,

N_30%

= Drehzahl bei 30% der Motornenndrehzahl,

N_60%

= Drehzahl bei 60% der Motornenndrehzahl,

N_100%

= Drehzahl bei 100% der Motornenndrehzahl.

It should also be noted that to increase the accuracy for some embodiments, such as low power pumps used for liquids having a specific gravity not equal to 1.0, mechanical losses (for example, seals and bearings) in the above turn-off power equations are compensated as follows can be: P _{SO_N} = [(P _{Meas_N%} - (Mech Loss × N _Act / N _Rated )) / SG] + (Mech Loss × N _Act / N _Rated ), in which

SG

= relative density,

N _30%

= Speed at 30% of rated motor speed,

N _60%

= Speed at 60% of rated motor speed,

N _100%

= Speed at 100% of the rated motor speed.

FIG. 12 is a graph of the matched power versus speed curve vs. power correction according to the closed valve affinity laws (shutdown state) versus actual power. FIG.

For higher power pumps, it is necessary to limit the speed when tuning to prevent overheating the pump. In this case, the power can be calculated at a speed of 100% from: P _{SO_100%} = (N _100% / N _60% ) ^KSO × P _{SO_60%} , where KSO is usually a shutdown exponent with a value of 3.0.

wobei

P_SO

= Pumpenleistung bei Abschaltung bei 100% Drehzahl von der publizierten Kurve und

P_BEP

= Pumpenleistung am BEP bei 100% Drehzahl aus der publizierten Kurve.

In the final step of the logic according to the present invention, the power is estimated at the optimum operating point (BEP). This function relies on the observation that although the actual values of PBEP and PSO at any pump may differ greatly from the published power curve, the slope of the power curve remains relatively constant.

in which

P _SO

= Pump power at shutdown at 100% speed of the published curve and

P _BEP

= Pump power at the BEP at 100% speed from the published curve.

, Figure 4 is a graphical representation of the relationship of the matched curve for power versus flow to the published Pricebook curve. Note that both curves have the same slope.

P_so1

= gemessene Abschaltleistung bei Drehzahl N₁ und

P_so2

= gemessene Abschaltleistung bei Drehzahl N₂.

Other, less accurate approximations can also be made to obtain a decomposition coefficient "K _SO " which can be estimated using the ratio of the natural logarithm of the power ratio to the speed ratio, as follows: KSO = LN (P _SO1 / _SO2 P) / LN (N ₁ / N _2), in which

P _so1

= measured shutdown power at speed N ₁ and

P _so2

= measured breaking capacity at speed N ₂ .

P_SOxrpm

= Abschaltleistung bei Drehzahl N_xrpm und

P_SOyrpm

= Abschaltleistung bei Drehzahl N_yrpm.

The shutdown power at any speed can then be determined by: P _SOxrpm = P _SOyrpm × ( _Nxrpm / _Nyrpm ) ^KSO , in which

P _SOxrpm

= Shutdown power at speed N _xrpm and

P _SOyrpm

= Shutdown power at speed N _yrpm .

Step B:

To determine a calculated flow rate, normalized power curves are calculated based on the power ratio of the pump,
in which P _Ratio = P _{SO_100%} / P _BEPcorr .

The normalization curves are characteristic of the power ratio and the specific speed of a pump.

The specific speed is a numerical value related to the hydraulic power of a centrifugal pump.

Figure 4 is a graph of normalization curves as examples plotted for multiple speeds of a 2 × 3-13 axial aspirator with P _ratio = 0.45 and a specific speed of 836.

The following table shows the actual versus normalized flow and power test data of the 2 × 3-13 pump at 3570 rpm. Flow, GPM Normalis., Flow Performance, HP Normalis., Performance 0 0.00 79.8 0.45 188 0.24 102.7 0.58 398 0.51 129.2 0.73 590 0.76 154.5 0.87 Flow 775 BEP 1.00 177.2 HP BEP 1.00 960 1.24 198.7 1.12

A 3rd order polynomial performance equation was developed using the coefficients from the normalized power versus flow curve. Corrections of the speed and the hydraulic efficiency are made in the power equation.

The coefficients a, b and c of the normalized power vs. flow curve define the shape of the normalized curve as follows: 0 = [(P _BEPCORR (a)) / ((Q _BEP ) ³ (η _{HBEP_CORR} ))] (Q _Act ) ³ + [((N _Act ) (P _BEPCORR ) (b)) / ((N _Rated ) ( Q _BEP ) ² (η _{HBEP_CORR} ))] (Q _Act ) ² + [((N _Act ) ² (P _BEPCORR ) (C)) / ((N _Rated ) ² (Q _BEP ) (η _{HBEP_CORR} ))] (Q _ACt ) + (P _{SO_N%} - (P _ACT / SG)), in which
P _BEPCORR = corrected pump power at the BEP, as determined from the curve of the tuned power at rated speed,
Q _BEP = pump flow at the BEP at rated speed,
η _{HBEP_CORR} = correction of hydraulic efficiency,
η _{HBEP_CORR} ≅ 1 - 0.8 / QBEP ^0.25 published values usually range from 0.7 to 0.95,
N _act = actual operating speed,
N _Rated = rated speed,
P _{SO_N%} = _{pump shutdown power} at actual operating speed (determined from the curve of the tuned power),
P _ACT = actual pump power,
SG = relative density and
Q _Act = calculated actual flow at current operating speed.

It should again be noted that to increase the accuracy for some embodiments, such as low power pumps used for liquids having a specific gravity not equal to 1.0, mechanical losses (for example, seals and bearings) in the above performance equation by adjusting can be compensated by PACT as follows: P _ACTCORR = [((P _ACT - (Mech Loss × N _Act / N _Rated )) / SG) + (Mech Loss × N _Act / N _Rated )].

It is also pointed out that in some embodiments, such as sealless pumps, estimates of eddy current losses need to be removed from actual power readings in the power equation above.

Then, complex roots are determined to solve the 3rd order polynomial equation using the Muller's method or other equivalent methods. The calculated actual flow is then determined for the specific operating point. FIG. 12 is a graph of the calculated power vs flow curve plotted for the 3rd order polynomial power equation versus the actual flow data obtained by reading the flow meter. FIG.

Since the pump wear will affect the pump's power requirements and thus reduce the flow accuracy, the power calculations can be periodically balanced by periodically performing a further calibration as outlined in step A.

OTHER APPLICATIONS

There are at least the following additional uses:

Pump Load Monitors - Pump Load Monitors rely on accurate modeling of the pump performance curve to detect the minimum flow and shutdown conditions. While most load monitors only monitor power at one speed, this logic would allow more accurate load monitors in variable speed operation.

Sensorless Flow Calculations - Sensorless flow estimates rely on accurate performance curves to estimate pump flow. The application of simple affinity laws can affect flow accuracy as the RPM increases. This is especially true for smaller pumps, where losses, for example, through seals and bearings play a greater role and are disregarded in accordance with the Affinitätsgesetzen.

Pump Protection Algorithms - Sensorless flow measurements can provide a reliable indication of operating conditions: spill conditions (flow rate too high), operation below the pump's minimum flow rate (flow rate too low), or operation against a closed discharge valve.

It should be understood that unless otherwise stated herein, any of the features, characteristics, alternatives, or modifications described with respect to a particular embodiment set forth herein are also applied to any other embodiment described herein or can be included therein. In addition, the drawings in this document are not to scale.

Although the invention has been described and illustrated with respect to exemplary embodiments thereof, the foregoing or various other additions and omissions may be made thereto without departing from the spirit and scope of the present invention.

Claims (51)

Method for determining the pump flow in a centrifugal pump, a centrifugal mixer, a radial fan or a centrifugal compressor, comprising the steps of: - creating a calibrated closed-valve performance curve at multiple speeds, including a shut-off state of the pump; - wherein the calibrated power curve is established by increasing the speed of the pump from a minimum to a maximum value while operating the pump against a closed exhaust valve and detecting speed and power data at multiple speeds; Calculating power curve coefficients from a power versus flow curve based on the power ratio of a pump, wherein the power ratio of the pump is the power in the shutdown state divided by the power at the optimum operating point (BEP) at maximum speed corrected for the difference between actual and published power is off-line; and - Solving a polynomial power equation for the flow at the current operating point, which is developed by means of coefficients from the curve for power versus flow. The method of claim 1, wherein the closed valve performance data is corrected to a specific gravity of one. A method according to any one of the preceding claims, wherein for low power pumps used for non-1.0 specific gravity fluids, mechanical losses (e.g., seals and bearings) in the closed valve power readings can be compensated as follows: P _{SO_N} = [(P _{Meas_N%} - (Mech Loss × N _Act / N _Rated )) / SG] + (Mech Loss × N _Act / N _Rated ) where SG = relative density. A method as claimed in any one of the preceding claims, wherein for sealless pumps, estimates of eddy current losses must be removed from the actual closed valve readings. Method according to one of the preceding claims, in which, in order to minimize the heating of the pumped liquid in pumps with higher power, the breaking capacity at 100% rotational speed can be calculated according to the following equation: P _{SO_100%} = (N _100% / N _60% ) ^KSO × P _{SO_60%} , where KSO is usually a shutdown exponent with a value of 3.0. Method according to one of the preceding claims, in which the closed-valve performance at any speed can be determined precisely by the following cubic interpolation method: A = (P _{SO_30%} ) / (N _30% ), B = (P _{SO_60%} - P _{SO_30%} ) / (N _60% - N _30% ), C = (B - A) / (N _60% - N _30% ) D = (P _{SO_100%} - P _{SO_60%} ) / (N _100% - N _60% ) E = (D - B) / ((N _100% - N _30% ) and F = (E - C) / (N _100% ) wherein the breaking capacity at any speed is calculated as follows: P _{SO_N%} = A (N _ACT ) + C (N _ACT ) (N _{ACT -N 30%} ) + F (N _ACT ) (N _{ACT -N 30%} ) (N _{ACT -N 60%} ) where P _{SO_30%} = P _{Meas_30%} / SG is the measured cutoff power at 30% of the rated motor speed corrected to a _specific gravity = 1, P _{SO_60%} = P _{Meas_60%} / SG is the measured cutoff power at 60% of the rated motor speed, corrected to one relative density = 1, and P _{SO_100%} = P _{Meas_100%} / SG is the measured shutdown power at 100% of rated motor speed corrected to a specific gravity = 1. Method according to one of the preceding claims, in which the published power is corrected at the optimum operating point at rated speed on the basis of the actual closed-valve performance data. Method according to one of the preceding claims, in which the published power is corrected at the optimum operating point according to the following equation:

where P _SO = pump power at shutdown at 100% speed from the published curve, P _BEP = pump power at the optimum operating point BEP at 100% speed from the published curve and

= actual closed valve performance at 100% speed. Method according to one of the preceding claims, in which the power ratio of the pump is determined according to the following equation: P _ratio = P _{shutoff @ 100%} / P _{BEP_corr} . Method according to one of the preceding claims, in which the polynomial performance equation is: 0 = [(P _BEPCORR (a)) / ((Q _BEP ) ³ (η _{HBEP_CORR} ))] (Q _Act ) ³ + [(N _Act ) (P _BEPCORR ) (b)) / ((N _Rated ) (QBEP ) ² (η _{HBEP_CORR} ))] (Q _Act ) ² + [((N _Act ) ² (P _BEPCORR ) (c)) / ((N _Rated ) ² (Q _BEP ) (η _{HBEP_CORR} ))] (Q _Act ) + (P _{SO_N%} - (P _ACT / SG)), where P _BEPCORR = corrected pump power at the optimum operating point BEP as determined from the rated power curve at rated speed, the power curve being a normalized power curve, Q _BEP = pump flow at the optimum operating point BEP at rated speed, η _{HBEP_CORR} = hydraulic efficiency correction, η _HBEP ≅ 1 - 0.8 / Q _BEP ^0.20 published values usually range from 0.7 to 0.95, N _Act = actual operating speed, N _Rated = rated speed, P _{SO_N%} = _{pump shutdown power} at actual operating speed (determined from the curve tuned power), P _ACT = actual pump power, SG = relative density, and Q _Act = calculated actual flow at current operating speed. The method of claim 10, wherein the accuracy for low power pumps used for liquids of specific gravity not equal to 1.0 is compensated for by compensating the mechanical losses (for example, seals and bearings) in the polynomial power equation by adjusting the actual pump power P _ACT can be made as follows: P _ACTCORR = [((P _ACT - (Mech Loss × N _Act / N _Rated )) / SG) + (Mech Loss × N _Act / N _Rated )]. The method of claim 10, wherein for sealless pumps, estimates of eddy current losses are removed from the actual power measurement in the polynomial performance equation. Method according to one of the preceding claims, wherein corrections for speed, hydraulic efficiency and relative density are made in the polynomial power equation. The method of claim 13, wherein complex roots are determined to solve the polynomial equation either by the Muller method or another suitable method. The method of claim 14, wherein the calculated actual flow is determined for a specific operating point. Method according to one of the preceding claims, in which the steps of the method are carried out on a frequency converter drive (VFD) or a programmable logic controller (PLC). Method according to one of the preceding claims, in which the determined flow value can be used as an input value in a PID controller for controlling the flow, without the need for a flow meter or other external measuring instruments. Regulator for determining the pump flow in a centrifugal pump, a centrifugal mixer, a radial fan or a centrifugal compressor, with A module configured to create a calibrated closed-valve power curve at multiple speeds, including a pump shut-off state at maximum speed; - wherein the calibrated power curve is established by increasing the speed of the pump from a minimum to a maximum value while operating the pump against a closed exhaust valve and detecting speed and power data at multiple speeds; A module configured to calculate coefficients of the power curve from a power versus flow curve based on the power ratio of a pump, the power ratio being formed from the difference between actual and published power of the pump in the off state; and A module configured to solve a polynomial power equation for flow at the current operating point developed using coefficients from the power versus flow curve. A regulator according to claim 18, wherein the closed valve performance data is corrected to a specific gravity of one. A regulator according to either of claims 18 or 19, wherein for low power pumps used for liquids of specific gravity not equal to 1.0, mechanical losses (for example, seals and bearings) in the closed valve power readings are compensated as follows can: P _{SO_N} = [(P _{Meas_N%} - (Mech Loss × N _Act / N _Rated )) / SG) + (Mech Loss × N _Act / N _Rated ), where SG = relative density. A regulator as claimed in any one of claims 18-20, wherein, for sealless pumps, estimates of eddy current losses are removed from the actual closed valve readings. A regulator according to any one of claims 18-21 wherein, in order to minimize heating of the pumped liquid in higher power pumps, the cut-off power at 100% speed can be calculated from the equation: P _{SO_100%} = (N _100% / N _60% ) ^KSO × P _{SO_60%} , where KSO is usually a shutdown exponent with a value of 3.0. A regulator according to any one of claims 18-22, wherein closed-valve performance at any speed can be accurately determined by the following method of cubic interpolation: A = (P _{SO_30%} ) / (N30%), B = (P _{SO_60%} - P _{SO_30%} ) / (N _60% - N _30% ) C = (B - A) / (N _60% - N _30% ) D = (P _{SO_100%} - P _{SO_60%} ) / (N _100% - N _60% ), E = (D - B) / ((N _100% - N _30% ) and F = (E - C) / (N _100% ) wherein the breaking capacity at any speed is calculated as follows: P _{SO_N%} = A (N _ACT ) + C (N _ACT ) (N _{ACT -N 30%} ) + F (N _ACT ) (N _{ACT -N 30%} ) (N _{ACT -N 60%} ) where P _{SO_30%} = P _{Meas_30%} / SG: Measured turn-off power at 30% rated motor speed, corrected to a _specific gravity = 1, P _{SO_60%} = P _{Meas_60%} / SG: Measured turn-off power at 60% rated motor speed, corrected to a relative density = 1 , and P _{SO_100%} = P _{Meas_100%} / SG: Measured turn-off power at 100% rated motor speed, corrected to a specific gravity = 1 A regulator according to any one of claims 18-23, wherein the published power is corrected at the optimum operating point at rated speed on the basis of the actual closed-valve performance data. A regulator according to any one of claims 18-24, wherein the published power is corrected at the optimum operating point according to the following equation:

where P _SO = pump power at shutdown at 100% speed from the published curve, P _BEP = pump power at the optimum operating point BEP at 100% speed from the published curve and

= actual closed valve performance at 100% speed. A regulator according to any of claims 18-25, wherein the power ratio of the pump is determined according to the following equation: P _ratio = P _{shutoff @ 100%} / P _{BEP_corr} . A regulator according to any of claims 18-26, wherein the polynomial performance equation is: 0 = [(P _BEPCORR (a)) / (Q _BEP ) ³ (η _{HBEP_CORR} ))] (Q _Act ) ³ + [((N _Act ) (P _BEPCORR (b)) / ((N _Rated ) (Q _BEP ) ² (η _{HBEP_CORR} ))] (Q _Act ) ² + [((N _Act ) ² (P _BEPCORR ) (c)) / ((N _Rated ) ² (Q _BEP ) (η _{HBEP_CORR} ))] (Ω _Act ) + (P _{SO_N%} - (P _ACT / SG)), where P _BEPCORR = corrected pump power at the optimal operating point BEP as determined from the rated power curve at rated speed, Q _BEP = pump flow at the optimum operating point BEP at rated speed, η _{HBEP_CORR} = hydraulic efficiency correction, η _HBEP 1 - 0.8 / Q _BEP ^0.25 published values usually range from 0.7 to 0.95, N _act = actual operating speed, N _rated speed, P _{SO_N%} = _{pump shutdown power} at actual operating speed (determined from the tuned power curve), P _ACT = actual Pump power, SG = relative density and Q _ACT = calculated actual flow at current operating speed. A regulator according to any one of claims 18-27, wherein the accuracy for low power pumps used for liquids of specific gravity not equal to 1.0 is compensated for by compensating the mechanical losses (for example, seals and bearings) in the polynomial performance equation of P _ACT can be prepared as follows: P _ACTCORR = [((P _ACT - (Mech Loss × N _Act / N _Rated )) / SG) + (Mech Loss × N _Act / N _Rated )]. A regulator according to any one of claims 18-28, wherein for sealless pumps, estimates of eddy current losses are removed from the actual power measurement in the polynomial performance equation. A regulator as claimed in any of claims 18-29, wherein corrections for speed, hydraulic efficiency and relative density are made in the polynomial power equation. A controller as claimed in any of claims 18-30, wherein complex roots are determined to solve the polynomial equation, either by the Muller method or another suitable method. A regulator according to any of claims 18-31, wherein the calculated actual flow rate is determined for a specific operating point. A regulator according to any of claims 18-32, wherein the regulator comprises or is part of a frequency converter drive (VFD) or a programmable logic controller (PLC). A regulator according to any one of claims 18-33, wherein the determined flow value can be used as an input to a PID controller to control flow without the need for a flow meter or other external measuring instrument. A system having a regulator for determining pump flow in a centrifugal pump, a centrifugal mixer, a radial fan or a centrifugal compressor, the controller comprising: A module configured to create a calibrated closed-valve performance curve at multiple speeds, including a pump shut-off state at maximum speed; - wherein the calibrated power curve is established by increasing the speed of the pump from a minimum to a maximum value while operating the pump against a closed exhaust valve and detecting speed and power data at multiple speeds; A module configured to calculate coefficients of the power curve from a power versus flow curve based on the power ratio of a pump, wherein the power ratio is formed from the difference of actual and published power of the pump in the power down state; and A module configured to solve a polynomial power equation for the flow at the current operating point, which is developed using coefficients from the power versus flow curve. The pump system of claim 35, wherein the closed valve performance data is corrected to a specific gravity of one. A pump system according to any one of claims 35 or 36, wherein for low power pumps used for liquids of specific gravity not equal to 1.0, mechanical losses (for example, seals and bearings) in the closed valve power readings are compensated as follows can: P _{SO_N} = [(P _{Meas_N} % - (Mech Loss × N _Act / N _Rated )) / SG] + (Mech Loss × N _Act / N _Rated ), where SG = relative density. A pump system according to any of claims 35-37, wherein for sealless pumps, estimates of eddy current losses are removed from the actual closed valve readings. A pump system according to any one of claims 35-38, wherein in order to minimize heating of the pumped liquid in higher power pumps, the 100% speed cut-off power can be calculated from the equation: P _{SO_100%} = (N _100% / N _60% ) ^KSO × P _{SO_60%} , where KSO is usually a shutdown exponent with a value of 3.0. A pump system according to any one of claims 35-39, wherein closed-valve performance at any speed can be accurately determined by the following method of cubic interpolation: A = (P _{SO_30%} ) / (N30%), B = (P _{SO_60%} - P _{SO_30%} ) / (N _60% - N _30% ), C = (B - A) / (N _60% - N _30% ), D = (P _{SO_100%} - P _{SO_60%} ) / (N _100% - N _60% ) E = (D - B) / ((N _100% - N _30% ) and F = (E - C) / (N _100% ) wherein the breaking capacity at any speed is calculated as follows: P _{SO_N%} = A (N _ACT ) + C (N _ACT ) (N _{ACT -N 30%} ) + F (N _ACT ) (N _{ACT -N 30%} ) (N _{ACT -N 60%} ) where P _{SO_30%} = P _{Meas_30%} / SG: measured turn-off power at 30% rated motor speed, corrected to a relative density = 1, P _{SO_60%} = P _{Meas_60%} / SG: measured turn-off power at 60% rated motor speed, corrected to a specific gravity 1, and P _{SO_100%} = P _{Meas_100%} / SG: Measured turn-off power at 100% rated motor speed, corrected to a relative density = 1. A pumping system according to any one of claims 35-40, wherein the published power is corrected at the optimum operating point at rated speed based on the actual closed-valve performance data. A pump system according to any one of claims 35-41, wherein the published power is corrected at the optimum operating point according to the following equation:

where P _SO = pump power at shutdown at 100% speed from the published curve, P _BEP = pump power at the optimum operating point BEP at 100% speed from the published curve and

= actual closed valve performance at 100% speed. A pump system according to any of claims 35-42, wherein the power ratio of the pump is determined according to the following equation: P _ratio = P _{shutoff @ 100%} / P _{BEP_corr} . A pump system according to any of claims 35-43, wherein the polynomial performance equation is: 0 = [(P _BEPCORR (a)) / ((Q _BEP ) ³ (η _{HBEP_CORR} ))] (Q _Act ) ³ + [((N _Act ) (P _BEPCORR ) (b)) / ((N _Rated ) ( Q _BEP ) ² (η _{HBEP_CORR} ))] (Q _Act ) ² + [((N _Act ) ² (P _BEPCORR ) (c)) / ((N _Rated ) ² (Q _BEP ) (η _{HBEP_CORR} ))] (Q _Act ) + (P _{SO_N%} - (P _ACT / SG)), where P _BEPCORR = corrected pump power at the optimum operating point BEP, as determined from the rated power curve at rated speed, Q _BEP = pump flow at the optimum operating point BEP at rated speed, η _{HBEP_CORR} = hydraulic efficiency correction, η _HBEP ≅ 1 - 0.8 / Q _BEP ^0.25 published values usually range from 0.7 to 0.95, N _act = actual operating speed, N _rated speed, P _{SO_N%} = _{pump shutdown power} at actual operating speed (determined from the tuned power curve), P _ACT = actual pump power, SG = relative density and Q _Act = calculated actual flow at current operating speed. A pump system according to any one of claims 35-44, wherein the accuracy for low power pumps used for liquids having a specific gravity not equal to 1.0 is compensated for by compensating the mechanical losses (for example, seals and bearings) in the polynomial performance equation of P _ACT can be prepared as follows: P _ACTCORR = [((P _ACT - (Mech Loss × N _Act / N _Rated )) / SG) + (Mech Loss × N _Act / N _Rated )]. A pump system according to any one of claims 35-45, wherein for sealless pumps, estimates of eddy current losses are removed from the actual power measurement in the polynomial performance equation. A pump system according to any of claims 35-46, wherein corrections for speed, hydraulic efficiency and relative density are made in the polynomial power equation. A pump system according to any one of claims 35-47, wherein complex roots are determined to solve the polynomial equation, either by the Muller method or another suitable method. A pump system according to any of claims 35-48, wherein the calculated actual flow is determined for a specific operating point. A pump system according to any of claims 35-49, wherein the controller comprises or is part of a frequency converter drive (VFD) or one of the regulators comprises a frequency converter drive (VFD) or a programmable logic controller (PLC). A pump system as claimed in any one of claims 35-50, wherein the determined flow value may be used as an input to one of the determined flow values as input to a PID controller for controlling the flow without the need for a flow meter or other external measuring instrument.

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