# Energy Consumption Comparison of a Single Variable-Speed Pump and a System of Two Pumps: Variable-Speed and Fixed-Speed

^{1}

^{2}

^{*}

## Abstract

**:**

## Featured Application

**The presented results can be used to assess the energy-saving potential of various topologies of multi-pump pumping stations.**

## Abstract

## 1. Introduction

## 2. Structure of the Examined Pump Systems

- The pumping system with a single pump supplied with a VSD, the nominal power of 1500 W, and the nominal speed of 2900 rpm. Water supply is controlled by the speed control method;
- The multi-pump system with two parallel pumps, the nominal power of 750 W, and the nominal speed of 2900 rpm. The electric drive of the first pump is equipped with a VSD, and the second pump has an induction motor connected directly to a grid. The water supply is controlled by the VSD of the first pump and by throttling of the second pump.

_{100%}= 24 m

^{3}/h can be provided by the single pump with the rated power of 1.5 kW (Figure 2a). When using the pumps with the rated power of 750 W, two such pumps are required to provide Q

_{100%}= 24 m

^{3}/h (Figure 2b). The required mechanical power P

_{mech}can be calculated as H∙Q∙g∙ρ/η

_{pump}, where g = 9.81 m/s

^{2}is the gravitational acceleration; ρ = 1000 kg/m

^{3}is the water density; η

_{pump}is the pump efficiency. However, for calculations in this study, P

_{mech}is obtained from P

_{mech}(Q) dependences from the manufacturer’s catalogue (Figure 2c,d). The maximum required flowrates of both pumping systems were chosen to correspond to the flowrate of the pump Calpeda—B—40/12C/A at the best efficiency point (BEP) Q

_{100%}= Q

_{BEP}

_{1}= 24 m

^{3}/h (Figure 2e).

## 3. Operating Point Calculation for Pumps

_{1}and H

_{1}are the flowrate and the head of the variable speed controlled pump; Q

_{2}and H

_{2}are the flowrate and the head of the non-adjustable speed pump; a = −0.02903, b = 0.15655, and c = 18.284 are the coefficients of the interpolation polynomial obtained according to the Q-H characteristics of pump Calpeda—B—NM 32/12D at the rated rotational speed (Figure 2); s

_{1}and s

_{2}are the rotational speeds of the variable speed and non-adjustable speed pumps in relative units (s

_{1}= n

_{1}/n

_{rate}; s

_{2}= n

_{2}/n

_{rate}); n

_{1}and n

_{2}are the rotational speeds in absolute values; n

_{rate}= 2900 rpm; Q

_{req}and H

_{req}are the required values of the water supply and hydraulic head (hydraulic loads); H

_{st}and k are the static head and the hydraulic friction coefficient of the hydraulic system.

_{1}and Q

_{2}and the total flowrate of the pumping system Q

_{req}are related according to Equation (4) [8]:

_{max}= 16 m, Q

_{max}= 24 m

^{3}/h, H

_{st}= 0.5∙H

_{max}[25].

_{mech}at different rotational speeds, the affinity laws are applied [23]:

_{N}

_{1}, H

_{N}

_{1}and P

_{mechN}

_{1}are the flowrate, pump head, and power on the shaft at speed N

_{1}< n

_{rate}; Q

_{N}

_{2}, H

_{N}

_{2}and P

_{mech}are the flowrate, pump head, and power on the shaft at speed N

_{2}= n

_{rate}.

_{req}, Equation (3) determines the required value of the head H

_{req}. Since the pumps operate at different rotational speeds, to achieve the same head H

_{pump}

_{1}= H

_{pump}

_{2}= H

_{req}, the pump capacity in the absence of throttling should be different. The speed of the second pump with non-adjustable electric drive equals the rated speed (2900 rpm); therefore, s

_{2}= 1. According to Equations (2) and (4), the values of Q

_{2}and Q

_{1}are obtained as follows:

_{1}and Q

_{2}. This condition leads to an overload of the non-adjustable pump and underload of the variable speed pump, which is not acceptable in terms of the energy efficiency point of view (at Q

_{req}less 75% of Q

_{max}, Q

_{1}becomes negative) [8]. This article considers the parallel operation of the pumps by ensuring equal flowrates of the two pumps with the help of throttling by using throttle M3 for the non-adjustable pump. Flowrates Q

_{1}and Q

_{2}are calculated according (11):

_{req}/2 (points 1 and 2, Figure 5). The performance curve of the first pump (VSD) should cross point 1 with coordinates (Q

_{req}/2; H

_{req}). The rotational speed of the first pump is determined by equation (9). The regulation throttle of the second pump (non-adjustable) is controlled to maintain Q

_{2}= Q

_{req}/2.

## 4. Determination of Pump Characteristics and Mechanical Power during the Operation Cycle

_{mech}are calculated, for ten different operation modes shown in Figure 1. Table 1 represents the calculated characteristics of the single pump system at ten different water flowrates, according to Figure 1. In the case of the single-pump system with one variable speed pump, the working points of the pumping system move along the system curve and are defined as intersection points of Q-H pump characteristics at a certain rotation speed n and the hydraulic system curve.

_{1}+ Q

_{2}. The first pump has an adjustable speed drive, and the rotation speed of the second pump is constant.

- Water flowrate regulation in the range from 0 to 60% is achieved by speed variation of the variable speed pump. A non-adjustable pump in this range of flows is not switched on and is closed by a return valve to prevent water from flowing through it in the backward direction;
- Water flowrate regulation in the range from 60 to 100% is achieved by the operation of both pumps. Water is supplied by joint control of the rotational speed of the 1st pump according to the regulation law (10) and of throttling the 2nd pump. In a dynamic mode, this type of regulation can be achieved with the help of proportional-integral (PI) controllers.

_{req}decreases, the load difference will increase. If the flow rate is such that for a given speed n

_{1}the head H

_{2}approximately equals or is greater than the shut-off head of the adjustable pump, then the flowrate of a variable speed pump will be close to zero (deadheading), or even negative (reverse flow). The reduction of the total flow of pumps operating in parallel by increasing the reverse flow of one of the pumps is identical to bypass-control. However, continuous operation of the pump in such modes is unacceptable due to low energy efficiency and can lead to deterioration of the pump equipment [2]. To avoid these operation modes, it is necessary to reduce the pressure in the pipeline connected to a non-adjustable pump with the help of throttling.

_{req}/2 according to Equations (1)–(3). The working point of the pump with a non-adjustable drive is determined by the intersection of its Q-H characteristics and vertical line Q

_{req}/2. Table 2 represents the calculation results for these pumps operating in parallel for ten different modes of the cycle with the selected control method Q

_{1}= Q

_{2}. Figure 7 also shows the calculated working points of these parallel pumps in terms of Q-H axes.

_{mech}

_{1}is the mechanical power of the variable speed pump; P

_{mech}

_{2}is the mechanical power of the non-adjustable pump. As can be seen from Figure 7 and Table 2, when using the two pumps, the second parallel pump is used only at the required flow rate of 70% or more. Flow rates in the range of 0–60% can be provided by one of the lower power pumps. When both pumps are used, the equal distribution of the required flow rate Q

_{1}= Q

_{2}= Q

_{req}/2 between them is adopted. As mentioned above, this control law provides minimum power consumption in this case. The head values of the two pumps are not equal to each other, H

_{1}≠ H

_{2}, which is achieved by throttling the output of the second pump. The speed of the first pump n

_{1}is adjusted by the VSD. The rotational speed of the second pump powered directly from the mains is assumed to be constant, n

_{2}= 2900 rpm. The H

_{1}, H

_{2}, and n

_{1}values are calculated according to the method described in Section 3 (see Figure 5). The mechanical powers P

_{mech}

_{1}and P

_{mech}

_{2}are evaluated using the P

_{meh}(Q) dependence shown in Figure 2b. Figure 8 represents graphical dependencies of the total mechanical power of the two configurations of a pumping system on the water flowrate according to Table 1 and Table 2. It can be seen that during the variation of the flowrate up to Q

_{req}= 14.4 m

^{3}/h (60%), the multi-pump system demands less mechanical power. At higher Q

_{req}, however, it requires more mechanical power than a system with a single pump.

## 5. Assessment of Energy Consumption of the Two Considered Pump Systems

_{conv1}is the frequency converter efficiency of the multi-pump system for variable speed drive; η

_{motor2}is the efficiency of non-adjustable motor in multi-pump system.

_{1}), daily electricity consumption (E

_{day}), annual electricity consumption (E

_{year}), total amount of annual electricity costs (C

_{year}), and annual cost savings (S

_{year}) for the multi-pump system with low-power pumps in comparison with the single-pump system:

_{mech}, and η

_{motor}are the mechanical power and efficiency of m-th electrical motor in the i-th operation mode; η

_{conv.}is the efficiency of m-th frequency converter in the i-th operation mode; t

_{∑}is the 24 h cycle time; t

_{i}is the duration of the i-th operation mode; GT = 0.2036 €/kWh is the electrical energy costs in Germany in the second quarter of 2019 for 1 kW∙h for industrial applications [31]; C

_{year}

_{1}and C

_{year}

_{2}are the total annual energy costs of the multi-pump system (two pumps) and single-pump (one pump) system configurations.

## 6. Conclusions

- The single-pump system is equipped with a single variable speed drive. The multi-pump system is equipped with one variable speed drive that is fed by a frequency converter and a non-adjustable drive connected directly to a grid;
- The comparison of energy consumption for both pump system configurations shows that the usage of a multi-pump system supplied with two low-power pumps instead of a high-power pump in the single-pump system can lead to 29.8% energy savings;
- The energy savings are achieved due to the application of pumps and variable speed drives with a lower rated power and, therefore, with low losses in the operation modes in which the flowrate can be provided by one of the two pumps.
- Despite a rather low efficiency of the multi-pump system at high flowrates, the gain in the efficiency at the most frequent low flowrates results in an increase in the overall efficiency and energy saving.
- In future works, the optimization of the energy consumption of the considered configurations of multi-pump systems will be presented using mathematical optimization methods, considering the characteristics of motors and frequency converters.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Flowrate-time dependence. Q, % is the percentage of the flow; t, % is the percentage of the time.

**Figure 2.**Pump characteristics [1] (

**a**) model 1, Q-H curve; (

**b**) model 2, Q-H curve; (

**c**) model 1, mechanical power versus flowrate; (

**d**) model 2, mechanical power versus flowrate; (

**e**) model 1, efficiency versus flowrate; (

**f**) model 2, efficiency versus flowrate.

**Figure 3.**Pumping system structure: (

**a**) single-pump, power 1500 W; (

**b**) multi-pump, each of the pump has a nominal power of 750 W.

**Figure 6.**(

**a**) Q-H characteristics of pump performance and system curve; (

**b**) hydraulic power curves of the pump at different rotational speeds.

Q_{req}, % | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
---|---|---|---|---|---|---|---|---|---|---|

n, rpm | 1918 | 1940 | 1991 | 2068.7 | 2181.4 | 2288 | 2424 | 2572 | 2731 | 2900 |

Q_{req}, m^{3}/h | 2.4 | 4.8 | 7.2 | 9.6 | 12 | 14.4 | 16.8 | 19.2 | 21.6 | 24 |

H, m | 8.07 | 8.28 | 8.63 | 9.13 | 9.89 | 10.53 | 12.39 | 12.51 | 13.7 | 15 |

P_{mech}, W | 234 | 290 | 356 | 437 | 547 | 663 | 817 | 1002 | 12,223 | 14,856 |

Q_{req}, % | Q_{req}, m^{3}/h | Q_{1}, m^{3}/h | Q_{2}, m^{3}/h | H_{1}, m | H_{2}, m | P_{mech1}, W | P_{mech2}, W | P_{mech} = P_{mech1} + P_{mech2}, W | n_{1}, rpm | n_{2}, rpm |
---|---|---|---|---|---|---|---|---|---|---|

10 | 2.4 | 2.4 | - | 8.1 | - | 136 | - | 136 | 1918 | - |

20 | 4.8 | 4.8 | - | 8.3 | - | 181 | - | 181 | 1975 | - |

30 | 7.2 | 7.2 | - | 8.7 | - | 247 | - | 247 | 2081 | - |

40 | 9.6 | 9.6 | - | 9.3 | - | 338 | - | 338 | 2229 | - |

50 | 12 | 12 | - | 10.0 | - | 463 | - | 463 | 2409 | - |

60 | 14.4 | 14.4 | - | 10.9 | - | 628 | - | 628 | 2615 | - |

70 | 16.8 | 8.4 | 8.4 | 11.9 | 17.6 | 394 | 616 | 1010 | 2433 | 2900 |

80 | 19.2 | 9.6 | 9.6 | 13.1 | 17.1 | 486 | 654 | 1140 | 2579 | 2900 |

90 | 21.6 | 10.8 | 10.8 | 14.5 | 16.6 | 598 | 691 | 1289 | 2736 | 2900 |

100 | 24 | 12 | 12 | 16.0 | 16.0 | 730 | 729 | 1460 | 2901 | 2900 |

Operation Point | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

n, % | 90 | 50 | 90 | 50 | 25 | 50 | 25 |

T, % | 100 | 100 | 50 | 50 | 100 | 25 | 25 |

η_{motor} IM-1.5 kW | 0.853 | 0.728 | 0.865 | 0.819 | 0.533 | 0.822 | 0.772 |

η_{motor} IM-750 W | 0.830 | 0.768 | 0.809 | 0.749 | 0.645 | 0.653 | 0.523 |

η_{conv.} FC-1.5 kW | 0.965 | 0.947 | 0.952 | 0.925 | 0.905 | 0.888 | 0.784 |

η_{conv.} FC-750 W | 0.937 | 0.906 | 0.898 | 0.849 | 0.857 | 0.771 | 0.686 |

Q_{req}, % | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | |
---|---|---|---|---|---|---|---|---|---|---|---|

Q_{req}, m^{3}/h | 2.40 | 4.80 | 7.20 | 9.60 | 12.0 | 14.4 | 16.8 | 19.2 | 21.6 | 24.0 | |

System with one pump (FC-IM) | η_{motor} | 0.431 | 0.507 | 0.580 | 0.651 | 0.723 | 0.783 | 0.838 | 0.874 | 0.879 | 0.834 |

η_{conv.} | 0.939 | 0.944 | 0.950 | 0.955 | 0.960 | 0.963 | 0.964 | 0.961 | 0.957 | 0.952 | |

Two parallel pumps (FC-IM1) + IM2 | η_{motor1} | 0.699 | 0.734 | 0.778 | 0.816 | 0.840 | 0.831 | 0.818 | 0.826 | 0.819 | 0.792 |

η_{motor2} | - | - | - | - | - | - | 0.796 | 0.797 | 0.796 | 0.792 | |

η_{conv.1} | 0.431 | 0.507 | 0.580 | 0.651 | 0.723 | 0.783 | 0.838 | 0.874 | 0.879 | 0.834 |

Q_{req}, % | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | |
---|---|---|---|---|---|---|---|---|---|---|---|

Q_{req}, m^{3}/h | 2.40 | 4.80 | 7.20 | 9.60 | 12.0 | 14.4 | 16.8 | 19.2 | 21.6 | 24.0 | |

P_{1}, W | Two parallel pumps | 213 | 272 | 347 | 453 | 599 | 812 | 1300 | 1465 | 1668 | 1928 |

One pump | 580 | 605 | 646 | 704 | 788 | 880 | 1012 | 1192 | 1454 | 1872 |

Pump System | E_{day}, kWh | E_{year}, kWh | C_{year}, € | S_{year}, % | S_{year}, € |
---|---|---|---|---|---|

Two parallel pumps (FC-IM1) + IM2 | 12.37 | 4516 | 919 | 29.8 | 391.1 |

System with one pump (FC-IM) | 17.63 | 6437 | 1310 | - | - |

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**MDPI and ACS Style**

Oshurbekov, S.; Kazakbaev, V.; Prakht, V.; Dmitrievskii, V.; Gevorkov, L.
Energy Consumption Comparison of a Single Variable-Speed Pump and a System of Two Pumps: Variable-Speed and Fixed-Speed. *Appl. Sci.* **2020**, *10*, 8820.
https://doi.org/10.3390/app10248820

**AMA Style**

Oshurbekov S, Kazakbaev V, Prakht V, Dmitrievskii V, Gevorkov L.
Energy Consumption Comparison of a Single Variable-Speed Pump and a System of Two Pumps: Variable-Speed and Fixed-Speed. *Applied Sciences*. 2020; 10(24):8820.
https://doi.org/10.3390/app10248820

**Chicago/Turabian Style**

Oshurbekov, Safarbek, Vadim Kazakbaev, Vladimir Prakht, Vladimir Dmitrievskii, and Levon Gevorkov.
2020. "Energy Consumption Comparison of a Single Variable-Speed Pump and a System of Two Pumps: Variable-Speed and Fixed-Speed" *Applied Sciences* 10, no. 24: 8820.
https://doi.org/10.3390/app10248820