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# Sensorless VFD driven pumping system

**Abstract**

Increasing energy efficiency is one of the key methods when aiming for sustainable energy use. Pumping systems are responsible for a significant part of the industrial electricity consumption, which has increased the interest in finding energy saving opportunities in the pumping applications. Usually, the greatest energy saving potential in pumping systems can be found by optimizing the system control. This is because increasing the efficiency of an individual component can seldom reduce the energy consumption as efficiently as setting the delivered output according to the process needs. Tapping this energy saving potential requires not only appropriate control methods, but also easily implementable and sufficient monitoring solutions. Rotational speed control with a VFD (variable frequency drive) has proved to be an energy efficient way to control the pumping system operation.

After implementing the rotational speed control with VFD to a pumping system, the optimization of the control procedure is usually left for the pump operator. In many cases, the information required to fulfill the pumping task in the most energy efficient way is not available or has to be gathered manually by startup measurements with separate metering equipment. For these reasons, full optimization of the pumping task is often neglected. As modern variable frequency drives are also able to monitor the output of the pumping system without additional metering, these monitoring data can be used in the drives system control to ensure optimal energy use.

This paper shows how VFD-driven pumps can monitor the energy efficiency of the pump and set the rotational speed according to the lowest specific energy consumption. The method does not require any additional start-up measurements or identification runs, excluding the pump performance curves required for sensorless pump monitoring. The operation of the VFD control strategy is presented and the operation of the strategy is validated by simulations and tests for an actual pumping system.

**Introduction**

The importance of energy efficiency both in industrial and municipal processes has increased the interest in finding energy saving solutions for pumping applications. Energy efficient operation in a pumping system is often accomplished by applying the rotational speed control of pumps with VFDs (variable frequency drives). In VFD-driven pumping processes, where precise flow adjustment is necessary, energy efficient pumping can be enabled by adjusting the rotational speed of the pump so that the pump performance varies according to the desired process output. In steady-state processes,the energy saving potential of the rotational speed control can be achieved even with an ON-OFF control scheme, if the rotational speed of pump is first optimized according to the VFD system characteristics.

Optimizing the energy use in VFD-driven pumping requires certain information on the pumping system. For instance, if the total head of the system as a function of flow rate is determined, the resulting operating points in variable speed operation can be calculated using the pump performance curves, and the most energy efficient operating conditions can be found. This information can be gathered by analyzing the system data available or by using separate start-up measurements, where the measurements are made for the system and the system is optimized once with these data. Optimization of the energy efficiency of a pump based on the monitored output and system data is described for instance, where the system is optimized by applying measurements of flow rate and head, respectively. However, the requirement of sufficient system data often limits the feasibility of the optimized control strategies: the pump operator is not necessary aware of the details of the system, or changes have been made to the system characteristics. In addition, real-time process information is often limited, since the direct measurement of the pump output is rarely available. To avoid direct metering in VFD-driven pumping, the pump operating point and the energy efficiency of the pumping can be determined using the pump performance curves and the variable frequency drive's internal estimates for the torque, rotational speed, and power. Moreover, these monitoring data can be used for control purposes, and the operating state of the pump can be optimized without startup measurements or detailed system data.

This study describes a method suitable for optimizing the operation of a VFD-controlled pumping system. The method calculates the specific energy consumption of the pump using the sensorless monitoring of the pump operating point available in modern variable frequency drives and determines the operating state with the lowest specific energy use. The only information required from the pump operator is the

*QH*and

*QP*characteristic curves of the pump. The simplified block diagram of the VFD-driven pumping method is illustrated in Fig 1. As the control algorithm is completely software based, the implementation of the method to the variable frequency drive controlled pumping systems is simple and inexpensive. The presented method can be applied especially in systems, where the pumping task is related to lifting a certain volume of liquid from one place to another without strict limitation for the duration. An example of such systems is a reservoir filling task, in which the main concern is typically related to sufficient fluid level in the inlet our outlet reservoir. In addition, the flow rate in such systems is not a direct reference for the control. However, the applicability can be limited if the pumping tasks has requirements for minimum pump output pressure or flow rate.

Fig. 1 Optimizing the rotational speed of the VFD-driven pump based on monitored specific energy consumption. The subscript 'est' denotes the estimated values.

The structure of the paper is as follows. First, the method of determining the operating point by applying a variable frequency drive and the criteria selected for energy efficient operation is reported in brief. After this, the method suitable for optimized specific energy consumption is introduced. The viability of the proposed method is demonstrated by laboratory measurements. The paper is concluded in the last section.

**Sensorless pump operating point estimation**

The output of the VFD-driven pumping system can be monitored by using sensorless operating point estimation with variable frequency drives. The estimation is based on the VFD estimates for the motor rotational speed and mechanical power, which are used as inputs to the estimation method. Pump characteristic curves, given as total head and pump power as a function off low rate (

*QH*curve and

*QP*curve), are used as a model of the pump, and the operating point is estimated with this model and the inputs. As the pump characteristic curves are usually given only for the nominal rotational speed, an approximation of the operation of the pump at other rotational speeds can be obtained by the affinity laws.

1) Q = (n/nwhere the subscript o denotes the values at the nominal rotational speed, n is the rotational speed, Q is the flow rate, H is the pump head, and P is the pump mechanical power. A graphical example of this estimation method is given in Fig 2._{o})Q_{o}

2) H = (n/n_{o})^{2}H_{o}

3) P = (n/n_{o})^{3}P_{o}

Fig. 2 Flow rate vs. head (QH) and flow rate vs. shaft power (QP) characteristic curves of a centrifugal pump; an example of the pump operating state determination with the shaft power estimate P

_{est}.

The sensorless operating point estimation can assess the output of the pump with sufficient accuracy in many cases. The accuracy of the estimation may decrease in situations where there is a substantial difference between the performance curves and actual operation of the pump in a system. In addition, the shape of the characteristic curves has a clear effect on estimation accuracy; for instance in the case of a flat QP curve, even a small error in the estimated power can result in a more significant error in the estimated flow rate value. The feasibility and accuracy of the operating point estimation methods applying a variable frequency drive.

**Minimum specific energy**

The total head of a pumping system can be divided into a static head and a dynamic head. The static head H

_{s}comprises the geodetic head and the pressure difference between the inlet and outlet sections of the system. The dynamic head H

_{d}consists of the difference in the velocity heads and the friction head. In open systems, the total head is usually referred to as the sum of the elevation difference and the friction head only, and is written

4) H = Hwhere H_{s}+ H_{d}= H_{geo}+ kQ^{2}

_{geo}refers to the geodetic head and k is the dynamic head coefficient depending on the liquid and the characteristics of the piping.

Specific energy consumption defines the amount of energy needed to pump a unit of liquid. It can be considered an appropriate criterion for energy efficiency in systems where the sole purpose of the pumping process is to transfer liquid to a higher level. Specific energy consumption E

_{s}can be calculated by

5) Ewhere E is the energy consumed by the pumped volume V._{s}= E/V = P/Q

In VFD-driven pumping, the minimum specific energy consumption for a pumping system, having a static head H

_{s}and a flow resistance coefficient k, can be determined at a single operating speed n of the pump. Correspondingly, if the dynamic flow resistance coefficient k remains constant, a higher static head results in a higher optimal rotational speed at which the minimum E

_{s}is found. Further, the required minimum E

_{s}increases with a higher static head, because the delivered output has to be lifted to a higher elevation. An example of the behavior of the specific energy consumption as a function of rotational speed at four different static head values is given in Fig 3.

Fig. 3 Specific energy as a function of rotational speed and static head for a system with a constant dynamic flow resistance k = 0.0143. The specific energy consumption is calculated for four different static heads.

The curves plotted in Fig 3 represent a series of operating points where the rotational speed of the pump is raised from zero to 1500 rpm. The pump can deliver flow only after overcoming the static head of the system. In this case, the rotational speed at which the pump starts to deliver flow is approximately 700 rpm for the static head of 5 m. The minimum E

_{s}for the pumping in the illustrated system case is ~29 Wh/m

^{3}when the static head is 5 m, and this operating state is achieved when the rotational speed of the pump is ~800 rpm. Correspondingly, if the static head of the system is 10 m,the minimum E

_{s}(52 Wh/m

^{3}) can be achieved at the rotational speed of 1150 rpm (Fig 3).

The purpose of the proposed pump control algorithm is to find the optimal rotational speed by using only the sensorless VFD controlled pump operating point estimation methods and track the optimal rotational speed in systems where the system characteristics change over the pumping task, for example the static head changes during a reservoir filling task. The suggested control can be fitted according to the process requirements, for instance, if there is a certain time limit for the reservoir filling task. The minimum required output can also be included in the suggested control algorithm as a limiting factor to the rotational speed.

**Optimization method**

The specific energy optimization method is based on the sensorless operating point estimation and the option to control the pump rotational speed by the variable frequency drive. The rotational speed is changed in a stepwise manner, and the rotational speed with the minimum specific energy is selected as the optimal rotational speed. The algorithm that can accomplish this is presented in Fig 4. First, the pump is operated at the nominal rotational speed, and the specific energy consumption is estimated with this speed. Then, the rotational speed is reduced, and if this reduced rotational speed results in a lower specific energy consumption than the previous value, the rotational speed is reduced again. If the rotational speed reduction results in a higher specific energy consumption, the rotational speed is increased to see if the increased rotational speed will result in a lower specific energy consumption.The search for the optimal rotational speed is continued until the algorithm is stopped.

Fig. 4 Simplified flow chart of the algorithm that can be used to minimize the specific energy consumption of a pumping system. n-step refers to a rotational speed step, which is used in the search for the minimum specific energy.

As can be seen in Fig 4, the simplified flow chart has no stop state. Hence, the rotational speed will move constantly ± one n-step around the optimal rotational speed in this simplified example. The control can nevertheless be stabilized, because in many actual pumping applications stability of the pumping is preferred. For example, in systems where the system characteristics are constant the determined optimal rotational speed can be used as a constant rotational speed reference to eliminate the oscillation.

To demonstrate the behavior of the suggested control, the algorithm in Fig 4 was simulated with a system consisting of a 5 m static head and a dynamic flow resistance factor of 0.0143. The behavior of the rotational speed and the specific energy as a function of time is illustrated in Fig 5. The control procedure is started approximately at time 1 s. The rotational speed is decreased from 1450 rpm to795 rpm with 15 rpm steps. At this point, the algorithm detects that the specific energy consumption at810 rpm was lower than with 795 rpm and increases the rotational speed. At 825 rpm the algorithm again detects that the specific energy consumption at 810 rpm is lower than at 825 rpm and starts to reduce the rotational speed. This is continued until the simulation is stopped. The algorithm finds the optimal rotational speed within the accuracy of the rotational speed step, which is 15 rpm in this case, but the step can be fixed depending on the nominal rotational speed of the pump and the desired resolution. The selected control interval in the simulation is 0.5 s, but it can also be fixed to ensure steady operation between steps and to avoid rapid rotational speed changes of the pump.

Fig. 5 Behavior of the algorithm in a simulation where a pumping system has a 5 m static head and a dynamic flow resistance of 0.0143. The optimal rotational speed is approximately 810 rpm in this example, and it is found approximately at 15 s.

**Laboratory measurements**

The proposed control method was tested with a laboratory test setup consisting of a water container,various piping, and a Sulzer APP22-80 centrifugal pump driven by an ABB 11 kW induction motor and a Gozuk VFD equipped with a sensorless flow estimation method. The static head in the system was approximately 5 m and the dynamic flow resistance coefficient could be controlled with valves. The laboratory measurement setup is shown in Fig 6. The control interval was25 s and the rotational speed step was varied between 30 rpm and 60 rpm.

Fig. 6 Laboratory test setup comprises a water tank, various piping, a centrifugal pump, an induction motor, and a VFD.

First, the control algorithm was tested with a valve setting, which was selected so that the flow rate produced at the pump nominal speed was 90 % of the nominal flow rate. The results for the rotational speed and the estimated and measured specific energy consumption as a function of time can be seen in Fig 7. The figure shows that the optimization method control reduces the pump rotational speed as long as the monitored specific energy consumption keeps decreasing (0−240 s). When the pump rotational speed is decreased to 720 rpm at 240 s, the specific energy starts to increase, as a result of which the rotational speed reference is increased in the next control round. The rotational speed varies from 720 to 900 rpm between 240 and 500 s as the control tries to determine the optimal rotational speed based on the minimum Es.

Fig. 7 Rotational speed, estimated and measured specific energies as a function of time. The minimum specific energy is more accurately determined after 500 s when the rotational speed step size is reduced from 60 to 30 rpm.

To determine the optimal rotational speed more accurately, the rotational speed step was changed from 60 rpm to 30 rpm at 500 s. Hence, the rotational speed starts to fluctuate between 780 rpm and900 rpm (500−900 s). In this region, there is only a small variation in the measured and calculated E

_{s}values. The minimum value for E

_{s}in this measuring sequence is ~35 Wh/m

^{3}, and it is achieved when the pump is operated at approximately 810−840 rpm (Fig 7).

The results of the same measuring sequence can also be seen in Fig 8, where the estimated and measured specific energies are shown as a function of rotational speed changed by VFD. It can be seen from Fig 8 that the E

_{s}values when operating between 780 rpm and 900 rpm are very close to each other, which suggests that this region is the most energy efficient speed region in terms of specific energy consumption. Fig 8 also shows that there is a notable difference between the estimated and measured E

_{s}in certain operating points, which is mainly caused by a divergence between the estimated and measured flow rate. Despite this, the region where the minimum E

_{s}is obtained is found in the same rotational speed region.

Fig. 8 Measured and estimated specific energies as a function of rotational speed in the 90% relative flow region. The minimum specific energy is found when the pump is operated at 810−840 rpm.

Similar results were obtained in a measuring sequence in which the pump was operated in the 100% relative flow region. The rotational speed step used in this sequence was 30 rpm. The resulting specific energy consumption as a function of rotational speed is depicted in Fig 9. Similar to the previous sequence, the control algorithm varies the rotational speed of the VFD-controlled pump and determines the rotational speed at which the estimated E

_{s}is at the minimum level according to both the measured and estimates values. Fig 9 shows that both the estimated and measured E

_{s}are at lowest when the pump is operated approximately at 840 rpm.

Fig. 9 Estimated and measured specific energies as a function of rotational speed in the 100 % relative flow region. The minimum specific energy is found when the pump is operated at 840 rpm.

The results show that the suggested control method is able to determine a rotational speed range in which the E

_{s}is at lowest. When the pump is operated near the minimum Es, the changes in the specific energy consumption after each control step can be so small that the optimal rotational speed is difficult to define accurately. According to the tests, the optimal rotational speed with the minimum E

_{s}was demanding to determine even with the measuring equipment, since the value for the measured minimum E

_{s}was not always the same. In addition, because of the inaccuracies in the flow estimation, the algorithm cannot always determine a single optimal rotational speed, but varies the speed of the pump with two to three steps near the optimal E

_{s}value. As shown in Fig 7, the selected rotational speed step also has a strong influence on the determination of the optimal rotational speed.

**Conclusion**

In this paper, a method was presented to optimize the specific energy consumption of a VFD-driven pumping system without sensors. The method uses the well-known model-based estimation for pump flow rate to assess the specific energy consumption of the pumping system, and by stepwise control of the rotational speed of the pump, the method finds the minimum specific energy consumption.

The laboratory measurements show that the algorithm is able to find the optimal rotational speed to minimize the specific energy consumption. According to the results, the absolute values of the estimated and measured specific energy consumption differ from each other. However, determination of the optimal rotational speed with the suggested method is based on the change in the estimated specific energy consumption according to the rotational speed. Hence, the exact accuracy for the E

_{s}values is somewhat irrelevant and the rotational speed for the minimum E

_{s}can be determined. The suggested control can be seen as an appropriate method to increase energy efficiency for instance in reservoir filling pumping tasks, where there are no strict time limits for the pumping.

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