3.4 Laboratory tests
3.4.2 Test results of the QH- and QP-curve-based estimation methods
In order to test the accuracy of theQH- andQP-curve-based estimation methods in the case of a radial flow centrifugal pump, test measurements were conducted with five different system curve shapes that were generated with control valves: the valves were adjusted so that the flow rates were approximately 50, 70, 100, 120 and 140 percent ofQBEP 28 l/s at 1450 rpm. With these valve settings, the pump was driven at rotational speeds ranging from 1080 rpm to 1560 rpm. The head and flow rate produced by the pump, the rotational speed and shaft torque of the motor, and the frequency converter estimates for the rotational speed and shaft power consumption (firmware parameters 1.02 and 1.06) were measured in each operating point.
Operating point locations were then estimated by applying the presented model-based methods.
In the case of the QH-curve-based estimation method, magnitude of the velocity head was determined from the initial estimation of the flow rate. After this, the flow rate estimate was determined using the sum of measured head and velocity head (i.e., the head estimate).
The results for the measuring sequence with the 100 % relative flow rate are shown in Fig. 3.11.
Separately determined efficiency curves of the pump have also been shown in the figure. In this case, the pump was operating very close to its BEP and in the steep region of the pump QP curve, allowing the model-based methods to provide correct results for the pump operating point location: with theQP-curve-based method, the estimation error of the flow rate is within
2.0 l/s (7 % of QBEP), and the estimation error of the head is within 0.5 m (3 % of HBEP) compared with the measured values. For theQH-curve-based estimation method, the estimation error of the flow rate is within 0.9 l/s (3 % ofQBEP), which can be regarded as an applicable accuracy even for control purposes.
10 15 20 25 30 35 40
0 5 10 15 20 25 30
Flow rate (l/s)
Head (m)
41 % 56 %
61 %
64 % 63 %
M easured QH curve est.
QP curve est.
Fig. 3.11: Test results for theQH- andQP-curve-based estimation methods in the case of a 100 % relative flow rate (i.e., 100 % ofQBEP). The estimation error of the flow rate is within 0.9 l/s (3 % ofQBEP) for the QH curve method and within 2.0 l/s (7 % ofQBEP) for theQP curve method, respectively.QH curves of the pump are drawn for the rotational speeds of 1000 rpm, 1450 rpm and 1600 rpm, respectively.
As discussed in Chapter 2, Hydraulic Institute’s guideline advises to use the pump in its preferred operating region, at the flow rates between 70 % and 120 % of theQBEP. Test results for these two relative flow rate values are shown in Fig. 3.12. In either case, the both estimation methods show that the pump is not operating as near its BEP as in the case of the 100 % relative flow rate. However, there is a systematic difference between the measured and QP-curve-estimated operating points, which is most likely caused by the difference between the corrected and measuredQP curve of the pump. In the case of 70 % relative flow rate, the estimation error of the flow rate is within 3.3 l/s (12 % ofQBEP), and the estimation error of the head is within 1.1 m (7 % ofHBEP) compared with the measured values. For theQH-curve-based estimation method, the estimation error of the flow rate is within 1.4 l/s (5 % ofQBEP). In the case of 120
% relative flow rate, the estimation error of theQP-curve-based method is within 3.0 l/s (11 % of QBEP) for the flow rate and within 1.1 m (7 % of HBEP) for the head, respectively. The estimation error of theQH-curve-based method is again notably smaller, within 0.6 l/s (2 % of QBEP) for the flow rate.
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Fig. 3.12: Test results for theQH- andQP-curve-based estimation methods, when the relative flow rate is (a) 70 % and (b) 120 % of theQBEP. The symbols applied are consistent with Fig. 3.11.
When the laboratory pump is driven away from the vicinity of the BEP, it may be prone to events that can alter the actual pump characteristic curves. In addition, the dP/dQ value of the laboratory pumpQP curve gets lower at very low and large relative flow rates, which decreases the accuracy of the QP-based estimation method. In Fig. 3.13, the test results for the measurement sequence with a 140 % relative flow rate are illustrated. In this case, the operating points are located in the far-right region of the published characteristic curves, where the dP/dQ of the published QP curve is at its minimum. For this reason, the QP-curve-based estimation method cannot provide as accurate results for the pump operating point location as in the recommendable operating region of the pump. At the rotational speeds of 1080–1260 rpm, the estimated flow rate values are negative, which is the reason why they are not visible in the figure. At the rotational speeds of 1320–1560 rpm, the estimation error of the flow rate is within 5.3 l/s (19 % ofQBEP), and the corresponding error of the head is within 2.1 m (13% ofHBEP), respectively. On the other hand, the QH-curve-based estimation method performs well also in this case, since there was neither cavitation nor other adverse phenomena that would have affected the pump performance in this measurement sequence. For the QH-curve-based estimation method, the estimation error of the flow rate is within 0.7 l/s (3 % ofQBEP).
20 25 30 35 40 45 50
Fig. 3.13: Test results for theQH- andQP-curve-based estimation methods, when the relative flow rate is 140 %. The symbols applied are consistent with Fig. 3.11.
The estimation methods were also tested with the 50 % relative flow rate, which describes a system with an oversized radial flow centrifugal pump. In this case, the operating points are in the allowable operating region of the pump, and the shape of theQP curve is steeper than at the 140 % flow rate. The test results are shown in Fig. 3.14. Compared with the 140 % relative flow rate, the estimates provided by theQP-curve-based method are now more accurate. However, at rotational speeds over 1450 rpm, there is a notable difference between the measured and estimated operating points. For this reason, the estimation error of the flow rate is within 3.5 l/s (12 % ofQBEP), and the estimation error of the head is within 0.9 m (5 % ofHBEP) for the QP-curve-based estimation method. The estimation error of the QH-curve based method is within 2.0 l/s (7 % ofQBEP), which is most likely caused by the effect of the flat QH curve shape on the estimation accuracy.
0 5 10 15 20 25 30
5 10 15 20 25 30
Flow rate (l/s)
Head (m)
27 % 41 %
56 % 61 % 1600 rp m
1450 rp m
1000 rp m
Fig. 3.14: Test results for theQH- andQP-curve-based estimation methods, when the relative flow rate is 50 %. The symbols applied are consistent with Fig. 3.11.
For the comparison of the QH- and QP-curve-based estimation methods, test results are gathered in Table 3.1. Based on the test results, both theQH- andQP-curve-based estimation method are applicable to the laboratory pumping system, if the available pump characteristic curves are accurate enough to describe the pump operation, and the flow estimation accuracy of 2–19 % of QBEP is acceptable. For the laboratory pumping system, the estimation accuracy of the QH andQP curve methods can be considered sufficient for the diagnosis purposes, as the methods provide correct information on the operating point location, that is, when it is in the recommendable operating region of the pump. According to the test results, methods are able to inform the user when the actual operating point location of the laboratory pump is outside the recommendable operating region, and the pump operates with a lower efficiency. In practice, however, this cannot be expected with all centrifugal pumps, as the mixed flow centrifugal pumps can have a flat QP curve near the pump BEP. The actual characteristic curves of the pump may also be more inaccurate than with the laboratory pumping system, leading presumably to a lower estimation accuracy. It should also be noted that theQH- and QP-curve-based methods may provide erroneous results, if the pump is actually operating in the region where cavitation or other events may affect the pump characteristic curves. Consequently, the shown test results most likely hold true only for other pumping systems having a radial flow centrifugal pump (nq 30), water as the pumped fluid, good characteristics against the occurrence of cavitation and an option to determine the accuracy of the pumpQP curve.
According to the test results for the laboratory pumping system, theQH-curve-based estimation method could be considered accurate enough for the control purposes of a radial flow centrifugal pump, if this is allowed by the accuracy of the pump characteristic curves. This can also be the situation with other centrifugal pump types and industrial pumping systems, if the actual pump QH curve is known, there are no unstable operating regions and curves are not affected by the mechanical wear of the pump or fluid characteristics. On the other hand, the QP-curve-based estimation method cannot be recommended for applications where strict estimation accuracy is required or the pump is typically operating at the flat parts of published characteristic curves (i.e., a small |dP/dQ|)): in such a case, estimated operating points can be clearly unrealistic, or they may lead to false analysis results concerning the pump operational state. Thus, the use ofQP-curve-based estimation method is limited to pumping systems, where theQP curve shape allows the use estimation method for unambiguous results (i.e., radial flow and axial flow centrifugal pumps), and the accuracy of the pump QP curve could be checked somehow. In addition, limitations could be added to the model-based methods, so they would not produce unrealistic results for the pump operating point location.
Table 3.1: Relative estimation errors of theQH- andQP-curve-based estimation methods compared with the measured values at different relative flow rates at the rotational speeds of 1080–1560 rpm. At the relative flow rate of 140 % and at the rotational speeds of 1080–1260 rpm, the estimated flow rates provided by theQP-curve-based method have been negative and hence inapplicable.
QH curve method QP curve method
Relative flow rate Q/QBEP| H/HBEP| Q/QBEP| H/HBEP|
50 % 7 % – 12 % 5 %
70 % 5 % – 12 % 7 %
100 % 3 % – 7 % 3 %
120 % 2 % – 11 % 7 %
140 % 3 % –
19 % (at 1320–
1560 rpm)
13 % (at 1320–
1560 rpm) 3.4.3 Test results of the system-curve-based estimation method
The system-curve-based estimation method was tested with the measurement data introduced in the previous chapter. The system curve parameters were calculated for each measurement sequence based on the expected operating point location and the amount of the estimated static head at 1450 rpm. Since the system conditions stayed relatively constant during the measurement sequence, the system-curve-based estimation should provide correct estimates for the pump operating point location.
Firstly, the system-curve-based method was tested with the 100 % relative flow rate sequence of measurements. The test results are shown in Fig. 3.15. In this case, the estimation error of the flow rate is within 1.0 l/s (4 % ofQBEP), and the estimation error of the head is within 0.2 m (1
% ofHBEP), respectively. The difference between the measured and estimated operating points is mainly caused by the inaccuracy of the system curve parameters.
10 15 20 25 30 35 40
Fig. 3.15: Test results for the system-curve-based estimation methods in the case of a 100 % relative flow rate (i.e., 100 % ofQBEP). The QH curves of the pump are drawn for the rotational speeds of 1000 rpm, 1450 rpm and 1600 rpm, respectively.
In Fig. 3.16, test results are shown for the 70 % and 120 % relative flow rates. Also in this case the estimation results provided by the system-curve-based method are comparable with the QH-curve-based method. In either case, the estimation error of the flow rate is within 0.9 l/s (3 % QBEP), and the estimation error of the head is within 0.3 m (2 % ofHBEP) compared with the measured values. In this case also, the accuracy of the estimation methods could be improved with more accurate system curve parameters.
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Fig. 3.16: Test results for the system-curve-based estimation methods, when the relative flow rate is (a) 70 % and (b) 120 % of theQBEP. The symbols applied in the figure are consistent with Fig. 3.15.
In the case of 140 % relative flow rate, the estimation accuracy of theQP-curve-based method was affected by the small dP/dQ value of theQP curve. For the system-curve-based method, operation in the far-right region of the pumpQH curve should not pose a problem, since there were no signs of cavitation that would have affected the pump performance. The test results are shown in Fig. 3.17. In this case, the estimation error of the flow rate is within 1.3 l/s (5 % of QBEP), and the estimation error of the head is within 0.4 m (2 % of HBEP), respectively.
Compared with Fig. 3.13, the estimation error of the system curve method is somewhat larger than the error of theQH-curve-based estimation method, but otherwise the system-curve-based estimation method provides correct information on the pump operating point location.
However, also in this case the estimation accuracy could be improved by using more accurate values for the determination of the system curve parameters. If the measured operating point location and the measured amount of static head were applied to determine the system curve shape, the estimation error of the flow rate would be within 0.7 l/s (2 % of QBEP), and the estimation error of the head would be within 0.3 m (2 % ofHBEP), respectively.
20 25 30 35 40 45 50
5 10 15 20
Flow rate (l/s)
Head (m)
41 %
61 %
64 % 63 %
58 % 55 %
50 %
Fig. 3.17: Test results for the system-curve-based estimation method, when the relative flow rate is 140
%. The symbols applied here are consistent with Fig. 3.15.
The system-curve-based estimation method was also tested with the 50 % relative flow rate, and the results are shown in Fig. 3.18. In this case, good accuracy of the pump and system QH curves has resulted in accurate estimation results. The estimation error of the flow rate is within 0.3 l/s (1 % of QBEP) and the estimation error of the head is within 0.3 m (2 % of HBEP), respectively.
0 5 10 15 20 25 30
5 10 15 20 25 30
Flow rate (l/s)
Head (m)
27 % 41 %
56 % 61 %
1000 rp m 1450 rp m 1600 rp m
Fig. 3.18: Test results for the system-curve-based estimation methods, when the relative flow rate is 50
%. The symbols applied are consistent with Fig. 3.15.
The test results are gathered in Table 3.2. They show the applicability of the system-curve-based estimation method with the laboratory pumping system, where the pump and systemQH
curves are accurate, water or a corresponding Newtonian fluid is pumped, and the process conditions can remain constant during the estimation. If these criteria can be met, the system-curve-based estimation method could also be utilised for diagnosis purposes of other pumping systems and centrifugal pump types, if there is no possibility for unstable operation of the pump. The method might also be applicable for control purposes of a pumping system, if the system curve is not affected by valves or other process devices, or the changes in the system characteristics could be taken into account.
In practice, the applicability of this method may however be very limited, as the system characteristics generally change during the pump operation and this change may remain unknown without additional measurements. For this reason, the results shown in Table 3.2 cannot be applied as a general example of the feasibility and accuracy of the system curve method. Therefore, this method can be recommended only for applications where the pump and system characteristics are accurately known or known to remain constant.
Table 3.2: Relative estimation errors of the system-curve-based estimation method compared with the measured values at different relative flow rates at the rotational speeds of 1080–1560 rpm. Compared with the results shown in Table 3.1, the resulting accuracy of the system curve method is comparable with the QH-curve-based estimation method.
System curve method Relative flow rate Q/QBEP| H/HBEP|
50 % 1 % 2 %
70 % 3 % 2 %
100 % 4 % 1 %
120 % 3 % 2 %
140 % 5 % 2 %
3.5 Pilot tests with theQP-curve-based estimation method
Besides laboratory tests, theQP-curve-based estimation method has been applied to determine typical operating point locations of two pumping system in a paper mill. The operation of a primary water pump and a pulp pump was monitored by a frequency converter and a measurement computer for the time period of six months. In this section, estimation results are introduced as an example of how model-based estimation can provide additional information for the analysis of the pump operation.
The primary water pumping system consists of an Ahlström P-X80X-1 vertical wet pit (i.e., axial flow) pump, a Strömberg 550 kW induction motor and an ABB ACS 800 frequency converter. The nominal values of the vertical wet pit pump are 1.85 m3/s for the flow rate, 22 m for the head, 85 % for the efficiency and 740 rpm for the rotational speed, respectively. The water pump transfers cold water from the water station further to the mill, allowing the use of original pump characteristic curves for the analysis. The accuracy of the pump QH curve has been previously ensured by a test measurement run, but this has not been carried out for the pumpQP curve, possibly affecting the estimation accuracy of theQP-curve-based method. The rotational speed of the primary water pump is controlled according to the pressure measurement located away from the pump and a typical pressure reference value of 135 kPa. In practice, the reference pressure value and the pump head can differ from each other because of the varying head losses and water consumption before the pressure measurement in the steam power plant.
The pulp pumping system shown in Fig. 3.19 comprises a Sulzer ARP 54-400 centrifugal pump, an ABB 400 kW induction motor and an ABB ACS 600 frequency converter. The nominal operating values of the pulp pump are 675 l/s, 24 m, 85 % and 990 rpm, respectively.
The pumped fluid consists of water and wood fibres. However, the fluid consistency is only 1.5
% and it has the same density as water, which enables the use of the original characteristic curves for the analysis also in this case. The pulp pump is located next to the paper machine 3, and it transfers the pulp from a reservoir to the tanks near the paper machine. Also in this case, the rotational speed of the pump is controlled according to the pressure measurement and a typical reference value of 285 kPa. Different from the primary water pump, the location of the pressure measurement is closer to the pump, and there are no valves between the pump and the measurement location.
Fig. 3.19: Pulp pumping system in a paper mill. The pulp pump is located next to the paper machine 3, and it transfers the fluid from a reservoir to the tanks near the paper machine.
For both cases, estimations of the pump operating point locations were carried for a period of six months to ensure inclusion of the most typical operational states for the analysis. The rotational speed and shaft power estimates provided by the frequency converter were fetched and stored every five minutes to a personal computer, which was connected to the frequency converter. For both cases, approximately 50000 estimations were carried out during the measurement period. In both cases, a pre-filtered shaft power estimate (parameter 1.06, -3dB cut-off frequencyFc = 1.6 Hz; ABB, 2009) was used in the estimations. The rotational speed of the primary water pump was determined with the converter parameter 2.17, which is the unfiltered estimate of the motor rotational speed (ABB, 2009). For the pulp pump, a pre-filtered estimate of the rotational speed (parameter 1.02,Fc = 0.3 Hz) was used.
The estimation results for the primary water pumping system were analysed and then divided into two separate time periods based on the pump rotational speed and the resulting operating
The estimation results for the primary water pumping system were analysed and then divided into two separate time periods based on the pump rotational speed and the resulting operating