This application claims priority under 35 U.S.C. §119 to European Patent Application No. 10153168.9 filed in Europe on Feb. 10, 2010, the entire content of which is hereby incorporated by reference in its entirety.
The present disclosure relates to a pump, such as estimating the output of a pump which is driven with a frequency converter and without additional sensors.
The operation point of a centrifugal pump can be estimated using a torque estimate (Test) and a rotational speed estimate (nest) from the frequency converter and the QH and QP characteristic curves provided by the pump manufacturer together with affinity laws. This method is referred to as QP calculation. The estimate of the operation point (volumetric flow Qv and head h) obtained with the calculation is most accurate at the nominal (i.e., best efficiency) operation point of the pump, and its accuracy becomes poorer when moving away from the nominal operation point. This limits the usability of the QP calculation in estimating the operation point of the pump. An alternative estimation method or improvement of the existing QP calculation algorithm is, therefore, required for the accurate estimation of the operation point of a centrifugal point, when the pump is operating outside/away from the nominal point.
One reason for the inaccuracy of QP calculation is that the slope of the QP curve gets lower when the efficiency of the pump decreases, which takes place when moving away from the nominal operating point. This causes errors in the estimation of the volumetric flow and head produced by the pump. Another reason for the inaccuracy is the fact that a notable change of the rotational speed can affect the efficiency of the pump. In addition, the amount of mechanical losses in the pump at different speeds may affect the accuracy of the affinity laws. These factors are not typically taken account in the affinity laws.
When the pump operates in a normal manner, the operation point is always situated at the intersection of QH curves of the pump and the process. This is illustrated in
An exemplary embodiment is directed to a method of estimating an operation point of a pump driven with a frequency converter when a QH characteristic curve of the pump is known. The method includes controlling the pump with the frequency converter, by estimating a process curve when a first operation point of the pump is in a nominal range, the process curve defining a head required by the process as a function of volumetric flow. The frequency converter further controls the pump by determining a rotational speed of the pump, converting the QH characteristic curve of the pump to a current rotational speed of the pump, and estimating a second operation point of the pump by determining the intersection point of the converted QH characteristic curve and the estimated process curve.
Another exemplary embodiment is directed to a frequency converter that estimates an operation point of a pump when a QH characteristic curve of the pump is known and the pump is adapted to be driven with the frequency converter. The frequency converter includes means for estimating a process curve when a first operation point of the pump is in a nominal range, the process curve defining a head as a function of volumetric flow means for determining a rotational speed of the pump, and means for converting, based on affinity laws, the QH characteristic curve of the pump to a current rotational speed of the pump. The frequency converter also includes means for estimating a second operation point of the pump by determining an intersection point of the converted QH characteristic curve and the estimated process curve.
In the following the disclosure will be described in greater detail by means of exemplary embodiments with reference to the accompanying drawings, in which
An object of an exemplary embodiment of the present disclosure is to provide a method and an apparatus for implementing the method so as to solve the above problem in the estimation of the operating point of the pump.
The disclosed exemplary embodiments are directed to estimating the process curve using QP calculation when the pump is operated in or close to the nominal operation area. The obtained process curve is then used for estimating the output of the pump by calculating the intersection point of the process curve and the QH curve of the pump, which is converted with affinity laws to the current rotational speed of the pump. This intersection calculation can be carried out if the pump is operated outside of its nominal operation area.
In an exemplary embodiment, the validity of the process curve is monitored using the intersection point calculation and QP calculation. The results of these two calculations are compared with each other to determine whether the process has changed.
The advantage of the exemplary method is that the estimation of the operation point is more accurate than with the other known methods that do not apply direct sensing of the head or the volumetric flow rate.
The disclosed exemplary embodiments also relate to a frequency converter which carries out the disclosed method. Such an apparatus can be used in estimating the operation point of the pump.
An exemplary method of the disclosure can be divided into separate entities. First, the process curve can be estimated. This estimation is carried out using QP calculation, as will be described later. After the process curve has been estimated, the operation point of the pump can be calculated using information on the rotational speed of the pump, the known pump QH characteristic curve, and the estimated process curve. According to an exemplary embodiment, the validity of the estimated process curve is monitored while the pump is being used.
In the above referred QP calculation, the operation point of the pump can be continuously estimated using a torque estimate and a rotational speed estimate, which are produced by the frequency converter that controls the pump. Further, the characteristic curves of the pump are required for the calculation.
in which ωest is the estimate of the angular speed of the motor.
The relationship between the mechanical power consumed by the pump and volumetric flow produced by the pump is shown in the QP curve, which is the lower plot in the example of
in which n is the used rotational speed, n0 is the rotational speed for which the curves are defined, P0 is the mechanical power at the original rotation speed, P is the power at the new rotational speed, Q0 is the volumetric flow at the original rotational speed, and Q is the volumetric flow at the new rotational speed. In
The head produced by the pump can be determined by the volumetric flow, which is determined from the mechanical power fed to the pump. The head is determined from the curve representing the head as a function of volumetric flow (QH curve), which is the upper plot in
in which H is the head produced by the new rotational speed and H0 is the original value of the head at the nominal rotational speed n0.
The coefficient of efficiency of the pump can be estimated from the hydraulic power produced by the pump and the mechanical power required by the pump. The hydraulic power Ph is defined as
Ph=ρgQvh (5)
in which ρ is the density of the pumped fluid and g is the gravitational constant. The coefficient of efficiency is defined as
Unlike the other quantities, the coefficient of efficiency does not have affinity laws. In theory, according to equations (2)-(6) the rotational speed of the pump should not have any influence on the efficiency of the pump. In practice, the decrease of the rotational speed decreases the Reynolds number of the flow and, therefore, also the hydraulic efficiency of the pump. Accordingly, the increase of the rotational speed increases the efficiency of the pump unless the pump starts to cavitate. Due to the above, the characteristic curves provided by the pump manufacturer, the affinity rules are only valid in a limited rotational speed range. Generally it can be considered that if the rotational speed of the pump differs less than 20% from the nominal speed, the co-efficient of efficiency does not change merely due to a change of the rotational speed in a manner that would lead to inaccurate QP calculation results.
The QP calculation can be considered to be most exact in the range close to the nominal operation point of the pump. In this range, the changes in the coefficient of efficiency are considerably small and QP curve has its steepest portion. In connection with a radial centrifugal pump, the preferred range of operation is about 80 to 120% of the nominal volumetric flow and of the nominal rotational speed. If needed, the preferred operation range can be defined more closely on the basis of the behavior of the steep portion of the QP curve and from the behavior of the coefficient of efficiency of the pump.
The estimation of a process curve includes a continuous or nearly continuous calculation of the operation point of the pump using the above QP calculation. Further, in the estimation of the process curve the measurement points are stored when the pump is operating near its nominal point. The measurement point is stored after the rotational speed of the pump has changed while still in the preferred range of operation. Further, the curve is fitted to the measured points. The estimation of a process curve is presented in the flow diagram of
In
After the QP calculation, it is checked if the values obtained with the QP calculation show that the pump is in its nominal operation range (174). If not, then the process returns to the start (175). If the values are in the nominal operation range, the values are stored (176).
After the values are stored, it is checked if there are five valid data points (177). If there are less than five data points stored, then the process returns to the start (178). If five data points are stored, it is checked (179) if hs of the process is known. If hs is not known, parameters k and hs are solved (1710) by minimizing equation (1) shown in
After step 1710 or 1711 it is checked if k and hs are positive (1712). If the values are not positive, the process returns to the start 1713. Once the values are positive, they are stored (1714). In the example of the flow chart of
The characteristic curve of the process, i.e. the process curve, can be of the format
h
process
=h
s
+kQ
v
2, (7)
in which hs is the static head and the term k represents the dynamic flow resistance. Both values depicting the shape of the process curve are normally positive hs,k≧0.
When the rotational speed of the pump changes and when the operation point of the pump is in the nominal range, the operation point of the pump is determined using a QP calculation. When the rotational speed changes, the operation point {circumflex over (Q)}v,i,ĥi estimated with the QP calculation is stored together with the present rotational speed nest,i, if the operation point is in the range or area near the nominal operation point. The nominal operation area is shown in
At least two operation points are required for estimating the process curve. In practice, however, the number of operation points should be higher in order to obtain a reliable estimate of the process curve. For example, five operation points are found to be a suitable number for obtaining reliable results. Further, the operation points should preferably be gathered in a large rotational speed range such that the shape of the process curve would be as correct as possible. For example, as illustrated in
If, at the beginning, the available measurement points are from a very low rotational speed range, for example under 10 rpm, and, for example, the static head of the process is not known, the process curve can be estimated to be mostly constructed from the static head, which is typical in the water distribution applications. Then, for example, in the nominal operation point
(h=hprocess)
h
s=0.75·hprocess, (8)
kQ
v
2=0.25·hprocess (9)
Further, the share of the static head could be approximated on the basis of the pumping application for this step. For the liquid transfer application between reservoirs, the share of the static head could be 50% of the total head (i.e., hprocess). However, in most of the pumping applications the change rate of the static head is very slow and the range of possible static head values can be estimated, or the static head can even be presumed to remain relatively constant. In addition, the dynamic head is usually small when compared to the static head in well-engineered applications. This leads to a process curve which is flat as a function of volumetric flow. Thus, the accurate estimation of the static head may be considered more important than the estimation of the dynamic head.
Since the process curves are case-dependent, the probable variation of hs could alternatively be given to the procedure, if more accuracy is required in the case of a small rotational speed range. When more measurement points are achieved, maybe also from a larger range, the shape of the process curve can be corrected by re-calculating new estimates for the static head hs and the dynamic flow resistance k of the process without the assumptions of equations (8) and (9).
When the data has been gathered, a method of least squares can be used for forming the process curve. In the method of least squares, equation
is minimized. The equation is at its smallest when hs and k form a process curve which corresponds to the measurement points as closely as possible. The minimum of S and the parameters of the process curves can be solved numerically or iteratively using, for example, a simplex-method.
Once the process curve has been determined, the operation point of the pump can be determined by solving the intersection point between the process curve (equation (7)) and the QH curve that has been converted to the current rotational speed (equations (3) and (4)). The intersection point can be solved by using numerical interpolation according to
If the rotational speed and the volumetric flow are outside the nominal region, it is checked (185) if parameters for the process curve are valid. If the parameters are valid, the intersection point calculation is used (186) for estimating the output of the pump. If the parameters for the process curve are not valid, the values of the QP calculation in (182) are used as the output of the pump (187).
According to an exemplary embodiment, the validity of the process curve is monitored. When the operation point is estimated using both the QP calculation and the calculation of the intersection point, the difference between the results obtained with these two can be used to estimate if the calculated process curve is correct. If the process remains unchanged, the operational points obtained with the QP calculation and the intersection point calculation should remain the same. The comparison between the results can be carried out, for example, by subtracting the results obtained with one from the other. That is, by subtracting the volumetric flow estimates obtained with differing methods from one another and similarly subtracting the estimates of the head produced by the pump obtained with differing methods from one another. These error terms ΔQ, Δh (equations (11), (12)) should stay the same at the same rotational speed points (for example 1300, 1350, . . . , 1500 rpm) if the process is unchanged
ΔQ=Qv,QP−Qv,intersection (11)
Δh=hQP−hintersection (12)
Once the process changes, the operation point of the pump moves, affecting the power consumption of the pump. This affects the results of the QP calculation and the magnitude of the error terms of equations (11) and (12). When it is noticed that the error terms have been changed at the constant speed points, it can be assumed that the process has changed and new values should be calculated for the parameters of the process curve. This means that the process curve should be estimated again using the above described procedure. The estimation of validity is presented in the flowchart of
At the beginning of the flowchart of
In addition to the change of the process, the error terms may also change due to normal wear of the pump, a malfunction of the pump, or some other factor disturbing the normal operation of the pump. Usually all the above factors can be noticed with condition monitoring measurements. Further, these factors disturb the operation of the pump quite seldom, and it is more likely that the changes in the error terms are due to changes in the process.
In the following, exemplary embodiments of the disclosure are described in connection with actual measurements.
As shown in
Additionally,
If, in the formation of a process curve, erroneous operation point estimates are also used (points from the QP calculation in the range 1500 to 1600 rpm, for example), the shape of the process curve can change considerably, as seen in
For the estimation of the process curve, at least two operation points measured at different rotational speeds can be obtained. In practice this number should be higher, preferably three or more, for example five, in order to obtain reliable results. Further, the rotational speed range from which the operational points are gathered should be wide so that the shape of the estimated process curve would correspond to the actual curve.
When the process curve is estimated from three or more points, the influence of erroneous points from the estimated process curve is decreased due to averaging of the measured results.
The speed range from which the operational points are estimated using QP calculation should be as wide as possible. If the points are close to each other, the estimated process curve can have a shape that does not correspond to the actual shape of the curve. Thus, the rotational speed range from which the samples are gathered should be at least 125 rpm and preferably at least 150 rpm or even 250 rpm. If the rotational speed range is wider, the process curve will be more accurate.
It will be obvious to a person skilled in the art that, as the technology advances, the inventive concept can be implemented in various ways. The disclosure and its embodiments are not limited to the examples described above but may vary within the scope of the claims.
Thus, it will be appreciated by those skilled in the art that the present invention can be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The presently disclosed embodiments are therefore considered in all respects to be illustrative and not restricted. The scope of the invention is indicated by the appended claims rather than the foregoing description and all changes that come within the meaning and range and equivalence thereof are intended to be embraced therein.
Number | Date | Country | Kind |
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10153168.9 | Feb 2010 | EP | regional |