JP6534546B2 - Pump operation number control method and pump apparatus - Google Patents

Description

  The present invention relates to a pump operating number control method and a pump device in which a plurality of pumps are operated in parallel, and more particularly to a pump operating number control method and a pump device capable of realizing energy saving operation.

  Conventionally, pumping devices such as water intake pump devices for water supply, water supply and distribution pump devices, water supply pump devices, irrigation pump devices for agriculture, pumping pumps, pumping pumps for river water use, petroleum pipeline pumps, drainage pumps and the like It has been known. In such a pump device, in order to control the pressure and the flow rate smoothly, a plurality of identical performance pumps are arranged in parallel, and the plurality of pumps are often operated at the same characteristic parallel uniform velocity. Here, the same characteristic parallel all-speed operation means operating a plurality of pumps having the same performance in parallel at the same rotation speed. Then, in the pump device, control of the number of operating pumps is performed to increase or decrease the number of operating pumps arranged in accordance with the head and flow rate required at the water supply location.

  In the conventional control of the number of operating pumps, a set flow rate value serving as a trigger for switching the number of operating pumps is fixed. That is, when the flow rate of water required on the pump discharge side exceeds the set flow rate value, the number of operating pumps is increased, and when the flow rate of water decreases from the set flow rate value, the number of operating pumps is reduced. The

  When switching the number of operating pumps based on the fixed set flow rate value, if the discharge flow rate of the pump device increases or decreases more than the set flow rate value, even if the pump device can be operated with the number of operating pumps before switching The number of operating pumps will be switched. For example, when the number of operating pumps is one, if the discharge flow rate increases to the set flow value at which the number of operating pumps is switched to two, pump operation is automatically performed even if operation is possible with one pump. We will switch the number to two. Alternatively, if the number of operating pumps is two, if the discharge flow rate decreases to the set flow value at which the number of operating pumps is switched to one, pump operation is automatically performed even if operation is possible with two pumps. Switch the number to one.

  In the same characteristic parallel constant velocity operation, for example, when the number of operating pumps is switched from one to two, the discharge flow rate per one pump is halved. For this reason, the pump efficiency per pump may become low. Here, the pump efficiency is a ratio that can be converted from shaft power to water power. In this case, compared with the single pump operation, the two pump operation increases the total shaft power of the pump, which may be undesirable from the viewpoint of energy saving. That is, if switching of the number of operating pumps is performed based on the fixed set flow rate value, the number of operating pumps may be switched despite the energy saving of operating the pump apparatus with the number of operating pumps before switching. there were.

JP, 2010-276006, A

  The present invention has been made in view of the above-described conventional problems, and provides a pump operation number control method and a pump device capable of switching the number of operating pumps so that the total shaft power of the pump is reduced. To aim.

One aspect of the present invention for solving the above-mentioned problems is to increase the number of operating pumps operated at the same characteristic parallel constant velocity from n to n + 1 when the total discharge flow rate increases (from n to n + 1) Pump for switching n to 1 is a natural number of 1 or more) or a pump that switches from n to n-1 (when n is switched to n-1 a natural number of 2 or more) when the total discharge flow rate decreases In the method of controlling the number of operating units, it is confirmed that the total discharge flow rate before and after switching the number of operating units of the pump and the rotational speed of the pump are within a range where the number of operating units of the pump can be switched. The pump efficiency per pump during n operation and the pump efficiency per pump during operation with n + 1 units from the function with the discharge flow rate of the pump and the rotational speed of the pump as variables The pump efficiency per pump at the time of operating with pump n-1 is calculated, and from the calculated pump efficiency per pump, the axial power per pump during n unit operation and n + 1 units The axial power per pump at the time of operation or n-1 units of operation is calculated respectively, and the calculated axial power per unit of pump is multiplied by the number of pump operations, and the total axis at the time of n units of operation Power and total shaft power during n + 1 and n-1 operations are calculated, and total shaft power during n and n + 1 and n-1 operations is compared with total shaft power When calculating the pump efficiency per pump when the total shaft power is lower and the number of pump operation per unit of n-1 units is calculated, a predetermined set value is calculated from the calculated pump efficiency. N-1 unit operation based on the reduced pump efficiency A pump operation number control method characterized by calculating the shaft power of the pump per one.

A preferred aspect of the present invention is characterized in that control is performed while monitoring that the total discharge flow rate before and after switching the number of operating pumps and the rotational speed of the pump are within a range where the number of operating pumps can be switched. I assume.
Another aspect of the present invention is that when the total discharge flow rate is increased, the number of pumps operated at the same characteristic parallel uniform velocity is increased from n to n + 1 (where n is 1 when n is switched to n + 1). It is a pump operation number control method of switching from n units to n-1 units (n in the case of switching from n units to n-1 units is a natural number of 2 or more) when the total discharge flow rate decreases. Confirming that the total discharge flow rate before and after switching the number of operating pumps and the rotational speed of the pump are within a range where the number of operating pumps can be switched, and the discharge flow rate per pump and the pump From the function with the rotational speed as a variable, the pump efficiency per pump at n-unit operation and the pump efficiency per pump at n + 1-unit operation or pump n-1 unit Based on the calculated pump efficiency per pump, the axial power per pump during n operation and n + 1 operation or n-1 operation is calculated from the calculated pump efficiency per pump The axial power per pump at a time is calculated respectively, and the calculated axial power per pump is multiplied by the number of operating pumps to obtain the total axial power during n-unit operation, n + 1 unit operation or The total shaft power is calculated by calculating the total shaft power at n-1 vehicle operation and comparing the total shaft power at n vehicle operation with the total shaft power at n + 1 vehicle operation or n-1 vehicle operation. Determine the number of operating pumps and control the total discharge flow rate before and after switching the number of operating pumps and the rotational speed of the pump while monitoring that the number of operating pumps can be switched. Number of operating pumps featuring It is your way.

Yet another aspect of the present invention is to control a plurality of pumps operated at the same characteristic parallel uniform velocity, a flow meter for measuring the total discharge flow rate of the plurality of pumps, and control of the rotational speed and the number of operating pumps. A flow rate determining unit that determines whether the total discharge flow rate of the pump is increasing or decreasing, and the total discharge flow rate of the pump before and after switching the number of operating pumps And n from the function that uses as variables the discharge flow rate per pump and the rotational speed of the pump, and a region determination unit that checks whether or not the rotational speed is within an area where the number of operating pumps can be switched. The pump efficiency per pump at the time of operation and the pump per pump at the time of operation with pump n + 1 (when n is switched from n to n + 1, n is a natural number of 1 or more) Pump efficiency or pump efficiency per pump calculated when operating with pump n-1 units (where n is a natural number of 2 or more when switching from n units to n-1 units) per pump calculated The axial power per pump during n operation and the axial power per pump during n + 1 operation or n-1 operation are calculated from the pump efficiency of The axis power per unit is multiplied by the number of pump operation to calculate the total axis power at n unit operation and the total axis power at n + 1 unit operation or n−1 unit operation. and shaft power, by comparing the total shaft power of n + 1 units or n-1 units during operation during operation, a pump driving number determiner total shaft power to determine the lower pump number of operating, and have a The pump operation number determination unit is operated when the n-1 units are operated When calculating the pump efficiency per one pump, a predetermined set value is subtracted from the calculated pump efficiency, and based on the subtracted pump efficiency, the axis per pump at n-1 unit operation It is a pump device characterized by calculating power .

  According to the present invention, when it is determined whether to switch the number of operating pumps, the number of operating pump with the lower total shaft power is selected. Therefore, energy saving of the pump device can be achieved. Further, the pumps to be operated are always operated with the number of operating pumps at which the axial power becomes low (except for the hunting prevention amount (−Δη) at the time of switching from n to n−1). Therefore, since the load applied to the pump is small, the load applied to consumable parts such as the bearing of the pump can be reduced, and as a result, the service life of the pump can be extended.

It is a systematic diagram of a pump device concerning one embodiment of the present invention. It is an operating characteristic curve figure (QH diagram) of the pump apparatus which concerns on embodiment shown in FIG. It is an example of the flow volume-rotational speed graph incorporated in the area | region determination part. It is an example of the driving | operation characteristic curve figure (QH diagram) in front of pump operation number switching. It is an example of the operating characteristic curve figure (QH diagram) immediately after pump driving | operation switching. Operating point a _{n / n} per pump operating number and operating point a _{n + 1 / n + 1} per pump when switching the number of operating pumps from n to _{n + 1} And is an example of the operating characteristic curve diagram (QH diagram). It is a driving | operation characteristic curve figure (QH diagram) when converting the driving | operation point B of 100% of rotational speed from the operating point A of rotational speed R% shown in FIG. It is an example of a driving | operation characteristic curve figure (QH diagram) at the time of determining whether the number of driving | operations of a pump switches from 1 unit driving | operation to 2 unit driving | operation. It is another example of a driving | running characteristic curve figure (QH diagram) at the time of determining whether the number of driving | operations of a pump switches from 1 unit driving | operation to 2 unit driving | operation. It is another example of the driving | operation characteristic curve figure (QH diagram) at the time of determining whether the number of driving | operation of a pump switches from 1 unit driving | operation to 2 unit driving | operation. It is an example of a driving | operation characteristic curve figure (QH diagram) at the time of determining whether the number of driving | operation of a pump switches from 2 unit driving | operation to 1 unit driving | running | working. It is another example of a driving | running characteristic curve figure (QH diagram) at the time of determining whether the number of driving | operation of a pump switches from 2 unit driving | operation to 1 unit driving | running | working. It is another example of the driving | operation characteristic curve figure (QH diagram) at the time of determining whether the number of driving | operation of a pump switches from 2 unit driving | operation to 1 unit driving | running | working.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1 is a system diagram of a pump device according to an embodiment of the present invention. As shown in FIG. 1, the pump device includes a pump 2 in communication with the suction water tank 1 and transferring the water in the suction water tank 1 to a water supply location 3 (for example, a water supply pipe network). In the embodiment, a plurality of pumps (for example, three) are originally disposed in parallel, but only one line is shown because the drawing becomes complicated. The plurality of pumps 2 are operated at the same characteristic parallel uniform velocity. That is, these pumps 2 have the same configuration and are operated at the same rotational speed. The number of operating pumps 2 to be operated is increased or decreased based on the flow rate of water transferred to the water supply location 3, the pump efficiency, and the axial power calculated using the lift. A plurality of (for example, three) branch suction pipes 5 ′ branched from one suction pipe 5 communicating with the suction water tank 1 are connected to a suction port of the pump 2. A branch discharge pipe 6 ′ is connected to the discharge port of the pump 2, and a plurality of (for example, three) branch discharge pipes 6 ′ are collected into one discharge pipe 6. The pump 2 transfers the water sucked from the suction water tank 1 through the suction pipe 5 and the branch suction pipe 5 ′ to the water supply location 3 through the branch discharge pipe 6 ′ and the discharge pipe 6.

  A water stop valve 11 is disposed in the branch suction pipe 5 '. The check valve 7 and the pump discharge valve 12 are disposed in the branch discharge piping 6 ', respectively. The check valve 7 is provided to prevent the backflow of water when the pump 2 is stopped. The pump discharge valve 12 is configured as a motor driven electric valve. The shutoff valves 13 are disposed downstream of the pump discharge valves 12 respectively. Furthermore, a pressure gauge 17 that measures the discharge pressure and a flow meter 18 that measures the discharge flow rate are disposed in the discharge pipe 6.

  A motor 15 for driving the pump 2 is connected to the pump 2. The motor 15 is connected to a speed control device 16 for increasing or decreasing the rotational speed of the motor 15. A controller 20 for controlling the speed controller 16 is connected to the speed controller 16 by a wire (not shown), and the rotational speed of the motor 15 is determined by the speed controller 16 receiving a command from the controller 20. . A pressure gauge 17 and a flow meter 18 are connected to the controller 20 by wiring (not shown), and measurement values obtained by the pressure gauge 17 and the flow meter 18 are sent to the controller 20. Although the speed control device 16 and the controller 20 are connected by wiring, illustration of the wiring is omitted because the drawing is complicated. Similarly, although the pressure gauge 17 and the flow meter 18 and the controller 20 are connected by wiring, illustration of the wiring is omitted because the drawing is complicated. The controller 20 also performs control of the number of operating pumps, which will be described later.

FIG. 2 is an operation characteristic curve diagram (Q-H diagram) of the pump device according to the embodiment shown in FIG. In FIG. 2, the horizontal axis is the total discharge flow rate of the pump device (ie, the flow rate measured by the flow meter 18), and the vertical axis is the discharge pressure of the pump device (or the head, ie, the pressure measured by the pressure gauge 17). . Curves N _x1 , N _x2 and N _x3 show the operating characteristics of the pump 2 with the rotational speed as a parameter. That is, the curve N _x1 represents the operating characteristic of one pump 2 during operation, the curve N _x2 represents the operating characteristic of two pumps 2 during operation, and the curve N _x3 represents the operating characteristic of three pumps 2 during operation. It represents. The pipeline resistance curve R is a pipeline resistance that changes according to the flow rate of water from the pump 2 to the water supply end. In the estimated terminal pressure constant control, the rotational speed of the pump 2 is controlled in consideration of the conduit resistance indicated by the conduit resistance curve R. That is, based on the measurement value obtained by the pressure gauge 17, the number of movements and the rotational speed of the pump 2 are controlled so that the discharge pressure of the pump 2 changes along the conduit resistance curve R.

  As shown in FIG. 2, the flow rate of water discharged from the pump device varies depending on the number of operating pumps 2. Specifically, the discharge flow rate increases in proportion to the number of operating pumps 2. Conventionally, when the discharge flow rate increases or decreases from a predetermined set flow rate value, the number of operating pumps 2 is increased or decreased.

For example, in FIG. 2, when the pump 2 is operating with one pump, the discharge flow rate increases, and when it exceeds 60 m ³ / min (operating point A in FIG. 2) which is the set flow rate value, the pump 2 The number of operating vehicles was switched to two. In this case, although the discharge flow rate is within the flow rate range achievable with one pump, the number of operating pumps 2 is automatically switched to two, and either one becomes the energy saving operation before and after switching. Was not considered. In the embodiment of the present invention, it is determined from the viewpoint of the energy consumption of the pump device whether the number of operating pumps 2 should be switched, and the number of operating pumps 2 is determined. Below, this pump operation number control method is demonstrated.

  As shown in FIG. 1, the controller 20 monitors the flow rate value measured by the flow meter 18, and includes a flow rate determination unit 21 that determines whether the flow rate value is increasing or decreasing. There is. Further, the controller 20 has a pump operation number determination unit 22. When the flow rate determination unit 21 determines that the flow rate is increasing, the pump operation number determination unit 22 determines whether to increase the number of operating pumps 2 and determines that the flow rate is decreasing. Determines whether the number of operating pumps 2 is to be reduced.

  The pump operation number determination unit 22 includes a region determination unit 23. Before the pump operation number determination unit 22 determines whether to switch the number of operation of the pump 2, the region determination unit 23 is configured so that the total discharge flow rate of the pump device and the rotational speed of the pump 2 before and after the operation number switch of the pump It is determined whether or not the number 2 operation is within the switchable area. The provision of the area determination unit 23 prevents the pump 2 from being operated in the cavitation generation area or the overload area.

FIG. 3 is an example of a flow rate-rotational speed graph built in the area determination unit 23. As shown in FIG. In FIG. 3, it is determined whether or not the total discharge flow rate of the pump device and the rotational speed of the pump 2 are within the range where the number of operating pumps 2 can be switched from one to two or from two to one. Boundary lines for drawing are drawn. In FIG. 3, the horizontal axis is the total pump discharge flow rate [m ³ / min], and the vertical axis is the rotational speed [%] of the pump 2.

The area determination unit 23 determines whether the total discharge flow rate and the rotational speed of the pump 2 are within the above-described area (the area in which the number of operating pumps 2 can be switched) using the following four equations. ing.
Maximum limited rotational speed Nn _{max. flow} = (α / n) × Q (1)
Minimum limited rotational speed Nn _{min. flow} = (β / n) × Q (2)
Lower limit rotational speed N _L = γ (3)
Upper limit rotational speed N _U = δ (4)
Here, n is the number of operating pumps 2 and Q is the total discharge flow rate of the pump device. α, β, γ, and δ are constants determined in advance from the performance of the pump 2 and the like, and differ depending on the pump 2. In the example shown in FIG. 3, α is 1.33, β is 4.17, γ is 60, and δ is 100.

As shown in FIG. 3, the upper limit and the lower limit of the rotational speed of the pump 2 are determined by the equations (3) and (4). The maximum limited rotational speed and the minimum limited rotational speed of the pump 2 are defined by the equations (1) and (2). An area surrounded by four straight lines expressed by the formulas (1) to (4) is an operable area of the pump 2 in the number of operation determined by n. In FIG. 3, according to the equations (1) and (2), the maximum limited rotational speed N1 _{max. The flow} is N1 _{max. It} draws with the straight line of _flow = 1.33Q, and the minimum limited rotation speed N1 _{min. flow} is N1 _min. It is drawn by the straight line of _flow = 4.17Q. Similarly, when the pump 2 is operated with two units, the maximum limited rotational speed N2 _{max. The flow} is N2 _{max. It} draws with the straight line of _flow = 0.67Q, and the minimum limited rotation speed N2 _{min. flow} is N2 _min. It is drawn by the straight line of _flow = 2.08Q.

The straight line γ = 60, the straight line δ = 100, the straight line N1 _{min. flow} = 4.17Q, and straight line N2 _min. An area surrounded by _flow = 2.08Q is defined as an area I. Straight line γ = 60, straight line δ = 100, straight line N2 _{min. flow} = 2.08 Q, and straight line N1 _max. A region surrounded by _flow = 1.33Q is defined as a region II. Straight line γ = 60, straight line δ = 100, straight line N1 _{max. flow} = 1.33Q, and straight line N2 _max. A region surrounded by _flow = 0.67Q is defined as a region III. The regions I and II defined as described above are regions in which the pump 2 can be operated by one unit. Regions II and III are regions in which two pumps 2 can operate. Therefore, the region II is a region where one or two pumps 2 can operate.

  Before determining whether to switch the number of operating pumps 2 from n to n + 1 or n−1, the region determining unit 23 determines that the total discharge flow rate of the pump device and the rotational speed of the pump 2 are n While confirming whether it exists in the drivable area | region, it is confirmed whether it exists in the drivable area | region by n + 1 unit or n-1 unit. For example, when determining whether to switch the number of operating pumps 2 from one to two, the region determining unit 23 can operate the total discharge flow rate of the pump device and the rotational speed of the pump 2 with one pump. Check if the vehicle is operating in the following areas I and II. At the same time, the region determination unit 23 confirms whether or not the total discharge flow rate of the pump device and the rotational speed of the pump 2 are operated in the regions II and III which can be operated by two pumps.

  After confirming that the total discharge flow rate of the pump device after switching the number of operating pumps 2 and the rotational speed of the pump 2 have entered the region where the number of operating pumps can be switched, the region determining unit 23 The operating number determination unit 22 determines the number of operating pumps so as to reduce the total shaft power of the pump device, according to a pump operating number determination algorithm described below. Hereinafter, a pump operating number determination algorithm for calculating the total shaft power of the pump device will be described.

In order to operate the pump apparatus with energy saving, it is necessary to reduce the energy consumed by the pump 2 as much as possible. The energy consumption of the pump 2 is expressed by shaft power. The axial power of the pump is the power required to rotate the pump impeller, and is expressed by the following equation.
L = 0.163 × Q × H / (η / 100) (5)
Here, L is shaft power [kW], Q is flow rate [m ³ / min], H is total head [m], η is pump efficiency [%]. The total head H [m] is a value obtained by subtracting the suction water level [m] from the discharge pressure P [m]. In the case of this example, the suction water level is 37.1 m. Therefore, assuming that the discharge pressure P is 70 m, the total lift H is 32.9 m.

The total shaft power of the pumps 2 arranged in a plurality of pumps in the pump apparatus calculates the shaft power per pump from the equation (5), and multiplies the obtained shaft power per pump by the number of operating pumps. It can be calculated by Therefore, the determination as to whether or not to switch the number of operating pumps 2 depends on the total operating shaft power L _n during n-unit operation, which is the actual number of operating pumps, and total shaft power L _{n + 1} or n-1 during n + 1-unit operation. The total shaft power L _n-1 at the time of operation is calculated based on the equation (5), and the pump 2 is obtained by comparing the total shaft power L _n with the total shaft power L _{n + 1} or the total shaft power L _n-1 Decide whether to switch the number of operating vehicles. Hereinafter, FIGS. 4 and 5 will be referred to for a method of determining the shaft power L in the case of determining whether to switch to the n + 1 operating number from the state where the operating number of pumps operated by the pump device is n. It explains, referring to it. Note that n is a natural number of 1 or more when determining whether to switch the number of operating pumps from n to n + 1.

  FIG. 4 is an operation characteristic curve diagram (Q-H diagram) immediately before the pump operation number switching, and FIG. 5 is an operation characteristic curve diagram (Q-H diagram) immediately after the pump operation switching. 4 and 5 show operating characteristic curves when the number of operating pumps 2 is switched from one to two, and in the lower part of each drawing, a curve representing the pump efficiency with respect to the discharge flow rate of the pump is drawn. It is done.

4, the operating point of the pump which is n stand operating _a ^{n *} are the coordinates ^{_{(Q an *, H an *}} , N an *) is represented by. Q _an ^* is the total discharge flow rate in m units of operation [m ³ / min], H _an ^* is the total head in n units of operation [m], and N _an ^* is the rotation of the pump in n units of operation It is speed [%]. In FIG. 5, the operating point a _{n + 1} ^* when the number of operating pumps is switched from n operation to n + 1 is represented by coordinates (Q _{an + 1} ^* , H _{an + 1} ^* , N _{an + 1} ^* ) Be done. Here, Q _{an + 1} ^* is the total discharge flow rate [m ³ / min] in the n + 1 vehicle operation, and H _{an + 1} ^* is the total head in the n + 1 vehicle operation [m], N _{an + 1} ^* Is the rotational speed [%] at the time of n + 1 vehicle operation. Note that coordinate values with “*” on the right shoulder indicate that they are known values or calculated solutions. For example, Q _an ^* and Q _{an + 1} ^* are measured values of the flow meter 18, and H _an ^* and H _{an + 1} ^* perform pressure terminal control of estimated end pressure in this embodiment. It is 17 measured values. If Q _an ^* and H _an ^* and Q _{an + 1} ^* and H _{an + 1} ^* are known, the controller 20 stores the QH diagram of the pump 2 for controlling the speed controller 16. So, N _an ^* and N _{an + 1} ^* can be obtained from this QH diagram.

Since the total discharge flow rate and the total head immediately after switching the pump operation number from n to n + 1 are equal to the total discharge flow rate and the total head just before the switching, the following equation is established.
Q _an ^* = Q _{an +1} ^* (6)
H _an ^* = H _{an + 1} ^* (7)

Here, FIG. 6, the operating point a _{n / n} per one operation number is at the n-stage operation of the pump, the operating point per one time of switching the pump operation number from n number (n + 1) units a It is an example of the operating characteristic curve figure (QH diagram) which showed _{n + 1 / n + 1} . In FIG. 6, an operating point a _1/1 per unit when one pump 2 of the pump unit is in operation and an operating point per unit when the pump 2 is switched to two units operation. a _2/2 is shown. As shown in FIG. 6, the operating point a _{n / n} per n-unit operation is _expressed by the coordinates (Q _{an / n} , H _{an / n} , N _{an / n} ). Similarly, when switching the number of pump operation from n to n + 1, the operating point a _{n + 1 / n + 1} per vehicle has coordinates (Q _{an + 1 / n + 1} , H _{an + 1 / n} It is represented by ₊₁ , _{Nan + 1 / n + 1} ). In this case, since the pump device of the present embodiment is operated at the same characteristic parallel uniform speed, the following equation is established.
Q _{an / n} = Q _an ^* / n (8)
H _{an / n} = H _an ^* (9)
N _{an / n} = N _an ^* (10)
Also, the following equation holds.
Q _{an + 1 / n + 1} = Q _{an + 1} ^* / (n + 1) (11)
H _{an + 1 / n + 1} = H _{an + 1} ^* (12)
N _{an + 1 / n + 1} = N _{an + 1} ^* (13)

Substituting the equation (6) into the equation (11) and substituting the equation (7) into the equation (12), the following equation is obtained.
Q _{an + 1 / n + 1} = Q _an ^* / (n + 1) (14)
H _{an + 1 / n + 1} = H _an ^* (15)

Here, in the pump operation characteristic curve diagram (Q-H diagram) as shown in FIG. 4 and FIG. 5, when one pump is operated at a rotational speed of 100%, the total head H is the discharge flow rate Q As expressed as a function of, the following relationship holds.
H ₁₀₀ ^* = f (Q ₁₀₀ ^* ) (16)
Here, H ₁₀₀ ^* represents the total head at 100% rotation speed, and Q ₁₀₀ ^* represents the discharge flow rate at 100% rotation speed. That is, equation (16) shows that the total head H ₁₀₀ ^* is obtained from the equation of the function f with the discharge flow rate Q ₁₀₀ ^* of the pump 2 as a variable. The equation of the function f plots a plurality of points determined from the total head H and the discharge flow rate Q obtained in the performance test of the pump 2 etc., and connects these plotted points by an approximate curve as a polynomial approximation You can get it. This polynomial approximation can be drawn, for example, as a quadratic curve. The polynomial approximation is predetermined and stored in the controller 20.

Now, in general, as shown in FIGS. 4 and 5, in the flow rate-pump efficiency characteristic curve (Q-− curve) in which one pump is operated at a rotational speed of R%, the pump efficiency η is As expressed as a function of the discharge flow rate Q, the following relationship is established.
η _R = g (Q _R ) (17)
Here, η _R represents the pump efficiency at the rotational speed R%, and Q _R represents the discharge flow rate at the rotational speed R%. That is, equation (17) represents that the pump efficiency eta _R is obtained from the equation discharge flow rate Q _R of the variable function g. The equation of the function g plots a plurality of points determined from the pump efficiency η and the discharge flow rate Q obtained in the performance test of the pump 2 and the like, and a plurality of plotted points are connected by an approximation curve as a polynomial approximation You can get it. This polynomial approximation can be drawn, for example, as a cubic curve. The polynomial approximation is predetermined and stored in the controller 20.

FIG. 7 is an operating characteristic curve diagram (QH diagram) when converting the operating point B of 100% of rotational speed from the operating point A of rotational speed R% shown in FIG. As shown in FIG. 7, a point B (Q ₁₀₀ ^* , H ₁₀₀ ^* ) converted into 100% rotation speed obtained by the similarity law with respect to the operating point A of the rotation speed R% is a QH curve with 100% rotation speed It can be determined from the point of intersection of the quadratic curve H = α × Q ² passing through the point A. Here, α = H _{an / n} / (Q _{an / n} ) ² .

With respect to the flow rate Q ₁₀₀ ^* at the rotational speed 100%, the following equation (18) holds for the flow rate Q _R at the rotational speed R%, and the rotation for the full head H ₁₀₀ ^* at the rotational speed 100% relationship of the following formulas in the total head H _R when the rate R% (19) holds.
Q _R = (N _R / 100) × Q ₁₀₀ ^* (18)
H _R = (N _R / 100) ² × H ₁₀₀ ^* (19)
Here, N _R is the rotational speed. (The symbols differ for convenience, but both N _R and R represent the rotational speed [%])
From the equation (18), Q ₁₀₀ ^* = Q _R / (N _R / 100) (20)
From the equation (19), H ₁₀₀ ^* = H _R / (N _R / 100) ² (21)

Substituting equations (20) and (21) into equation (16), the following equation (22) is derived.
H _R / (N _R / 100) ² = f (Q _R / (N _R / 100))
Therefore, H _R = (N _R / 100) ² × f (Q _R / (N _R / 100)) (22)
Substituting equation (18) into equation (17), the following equation (23) is derived.
η _R = g ((N _R / 100) × Q ₁₀₀ ^* ) (23)
From the equation (23), the pump efficiency η _{an / n} per pump when n pumps are operated can be obtained by the following equation (24).
η _{an / n} = g ((N _{an / n} / 100) × Q ₁₀₀ ^* ) (24)
Substituting equation (10) into equation (24),
η _{an / n} = g ((N _an ^* / 100) × Q ₁₀₀ ^* ) (25)
From the equation (25), the pump efficiency _{an an / n} per pump can be calculated when _n pumps are in operation.

Similarly, the pump efficiency η _{an + 1 / n + 1} per pump at the time of pump n + 1 operation is obtained by the following equation (26).
η _{an + 1 / n + 1} = g ((N _{an + 1 / n +} 1/100) × Q ₁₀₀ ^* ) (26)
Substituting equation (13) into equation (26),
η _{an + 1 / n + 1} = g ((N _{an + 1} ^* / 100) × Q ₁₀₀ ^* ) (27)
From the equation (27), the pump efficiency _{+1 an + 1 / n + 1} can be calculated per pump at the time of operation of the pump _{n + 1} .

The pump shaft power can be determined by the equation (5) described above. From this equation (5), the pump shaft power L _{an / n} per pump at the time of operation of n pumps can be obtained by the following equation (28).
L _{an / n} = 0.163 × Q _{an / n} × H _{an / n} / (η _{an / n} / 100) (28)
By substituting the equations (8), (9) and (25) into the equation (28), the following equation (29) can be obtained.
L _{an / n} =
0.163 × (Q _an ^* / n) × H _an ^* /
(G ((N _an ^* / 100) x Q ₁₀₀ ^* ) / 100) ... (29)

Similarly, the pump shaft power L _{an + 1 / n + 1} per pump when the n + 1 pumps are operated can be obtained by the following equation (30).
L _{an + 1 / n + 1} = 0.163 × Q _{an + 1 / n + 1} × H _{an + 1 / n + 1} / (η _{an + 1 / n +} 1/100)
... (30)
By substituting Formula (11), Formula (12), and Formula (27) into Formula (30), the following Formula (31) can be obtained.
L _{an + 1 / n + 1} =
0.163 × (Q _{an + 1} ^* / (n + 1)) × H _{an + 1} ^* /
(G ((N _{an +1} ^* / 100) x Q ₁₀₀ ^* ) / 100))
... (31)

Since the equation (29) indicates the axial power L _{an / n} per pump during n pump operation, the total axial power L _n of the pump _n is the axial power L _{an /} per pump It can be obtained by multiplying _n by n.
Therefore,
L _n = L _{an / n} × n
= 0.163 x Q _an ^* x H _an ^* /
(G ((N _an ^* / 100) x Q ₁₀₀ ^* ) / 100) ... (32)

In equation (32), as noted above, Q _an ^* can be obtained from flow meter 18 and H _an ^* can be obtained from pressure gauge 17. If Q _an ^* and H _an ^* are obtained, N _an ^* can be obtained from the QH curve stored in the controller 20. Therefore, the pump operation number determination unit 22 of the controller 20 can calculate the total shaft power L _n at the time of n pump operation using Equation (32).

Similarly, since the equation (31) indicates the axial power L _{an + 1 / n + 1} per pump when the n + 1 pumps are operated, the total axial power L _{n + 1} of the pump _{n + 1} is one pump. It can be obtained by multiplying the axial power L _{an + 1 / n + 1} of the circumference by n + 1.
L _{n + 1} = L _{an + 1 / n + 1} × (n + 1)
= 0.163 × Q _{an + 1} ^* × H _{an + 1} ^* /
(G ((N _{an +1} ^* / 100) x Q ₁₀₀ ^* ) / 100)
... (33)
Substituting equations (6) and (7) into equation (33),
L _{n + 1} = 0.163 × Q _an ^* × H _an ^* /
(G ((N _{an +1} ^* / 100) x Q ₁₀₀ ^* ) / 100)
... (34)

In equation (34), as noted above, Q _an ^* can be obtained from flow meter 18 and H _an ^* can be obtained from pressure gauge 17. If Q _an ^* and H _an ^* are obtained, N _{an + 1} ^* can be obtained from the QH curve stored in the controller 20. Therefore, the pump operation number determination unit 22 of the controller 20 can calculate the total shaft power L _{n + 1} at the time of the pump n + 1 operation using the equation (34).

  So far, the method of calculating the total shaft power L in the case of determining whether to switch the number of operating pumps 2 from n to n + 1 has been described. Hereinafter, a method of calculating the total shaft power L in the case of determining whether to switch the number of operating pumps 2 from n to n−1 will be described. Note that n is a natural number of 2 or more when determining whether to switch the number of operating pumps from n to n-1.

The total shaft power L _n when the number of operating pumps 2 is n can be calculated by the above equation (32). When calculating the total shaft power L _n-1 when the number of operating pumps 2 is switched from n to n-1, the predetermined set value is derived from the pump efficiency per pump at the time of n-1 operation By subtracting Δη, shaft power per pump at n−1 operation is calculated based on the reduced pump efficiency. This is because, when the discharge flow rate of the pump 2 moves up and down in the vicinity of the pump operation number switching point, there is a possibility that the number of operation of the pump 2 may increase or decrease and hunting. Therefore, in order to prevent hunting, ΔQ, which is the difference in flow rate switching, is provided to switch from n units to n−1 units. As this means, by subtracting a predetermined set value Δη from the pump efficiency per pump, it is possible to prevent the number of operating pumps from switching back to n immediately after switching to n−1. The total shaft power is also used for determination when switching from n to n-1. However, since the subtraction of -Δη is included in the pump efficiency, the comparison of the total shaft power is strictly carried out It does not mean that The predetermined set value Δη is, for example, 5%.

Specifically, the equation for calculating the pump efficiency per pump at the time of n-1 operation is expressed by the following equation corresponding to the above equation (27).
η _{an-1 / n -1} = g ((N _{an -1} ^* / 100) x Q ₁₀₀ ^* ) (35)
The pump efficiency value obtained by subtracting the predetermined set value Δη from the equation (35) is used in the following calculation as the pump efficiency value at the time of obtaining the pump shaft power.
That is, the pump shaft power _{Lan-1 / n-1} per pump when the pump _n-1 is in operation can be obtained by the following equation corresponding to the equation (31).
L _{an-1 / n-1} =
0.163 × (Q _an−1 ^* / (n−1)) × H _an−1 ^* /
((((N _an-1 ^* / 100) x Q ₁₀₀ ^* )-Δ)) / 100)
... (36)

Since Formula (36) has shown axial power L _{an-1 / n-1} per pump at the time of pump n-1 operation, total axial power L _n-1 of pump _n-1 is It can be obtained by multiplying the axial power L _{an-1 / n-1} per pump by n-1.
L _n−1 = L _{an−1 / n−1} × (n−1)
= 0.163 x Q _an-1 ^* x H _an-1 ^* /
((((N _an-1 ^* / 100) x Q ₁₀₀ ^* )-Δ)) / 100)
... (37)
Immediately after the number of operating pumps changes, the following equation holds.
Q _an ^* = Q _an-1 ^* (38)
H _an ^* = H _{an -1} ^* (39)
Therefore, Formula (38) and Formula (39) can be substituted to Formula (37), and the following Formula (40) can be obtained.
L _n−1 = 0.163 × Q _an ^* × H _an ^* /
((((N _an-1 ^* / 100) x Q ₁₀₀ ^* )-Δ)) / 100)
... (40)

In equation (40), as described above, Q _an ^* can be obtained from flow meter 18 and H _an ^* can be obtained from pressure gauge 17. If Q _an ^* and H _an ^* are obtained, N _an−1 ^* can be obtained from the QH curve stored in the controller 20. Therefore, the pump operation number determination unit 22 of the controller 20 can calculate the total shaft power L _n-1 when the pump n-1 is in operation using the equation (40).

More precisely, in the flow rate-pump efficiency characteristic curve (Q-η curve) in which one pump is operated at a rotational speed of R%, the pump efficiency η as a function of the discharge flow rate Q has the following relationship.
η _R = g (Q ₁₀₀ ^* ) (41)
Here, η _R represents the pump efficiency at the rotational speed R%, and Q ₁₀₀ ^* represents the discharge flow rate at the 100% rotational speed. That is, the equation (41) is a function that uses as a variable Q ₁₀₀ ^{* the} pump efficiency η _R at the discharge flow rate Q _R at R% rotational speed is converted to the discharge flow rate at 100% rotational speed with respect to Q _R It shows that it can be obtained from the equation of g. The equation of the function g plots a plurality of points determined from the pump efficiency η and the discharge flow rate Q at 100% rotational speed obtained in the performance test of the pump 2 etc., and connects the plotted plurality of points by an approximate curve It can be obtained as a polynomial approximation of time. This polynomial approximation can be drawn, for example, as a cubic curve. The polynomial approximation is predetermined and stored in the controller 20.

As described above, FIG. 7 is an operating characteristic curve diagram (QH diagram) when converting the operating point B of 100% of rotational speed from the operating point A of rotational speed R% shown in FIG. As shown in FIG. 7, a point B (Q ₁₀₀ ^* , H ₁₀₀ ^* ) converted into 100% rotation speed obtained by the similarity law with respect to the operating point A of the rotation speed R% is a QH curve with 100% rotation speed It can be determined from the point of intersection of the quadratic curve H = α × Q ² passing through the point A. Here, α = H _{an / n} / (Q _{an / n} ) ² .

With respect to the flow rate Q ₁₀₀ ^* at the rotational speed 100%, the above equation (18) holds for the flow rate Q _R at the rotational speed R%, and the rotation at the full head H ₁₀₀ ^* at the rotational speed 100%. relationship of the above equation is the total head H _R when the rate R% (19) holds. Formula (18) and Formula (19) are described again.
Q _R = (N _R / 100) × Q ₁₀₀ ^* (18)
H _R = (N _R / 100) ² × H ₁₀₀ ^* (19)
Here, N _R is the rotational speed. (The symbols differ for convenience, but both N _R and R represent the rotational speed [%])
The equation (20) and the equation (21) described above are obtained from the equation (18) and the equation (19). Formula (21) and Formula (21) are described again.
Q ₁₀₀ ^* = Q _R / (N _R / 100) (20)
H ₁₀₀ ^* = H _R / (N _R / 100) ² (21)

As described above, substituting the equations (20) and (21) into the equation (16) leads to the equation (22) described above. Formula (22) is described again.
H _R / (N _R / 100) ² = f (Q _R / (N _R / 100))
Therefore, H _R = (N _R / 100) ² × f (Q _R / (N _R / 100)) (22)
Substituting equation (20) into equation (41), the following equation (42) is derived.
η _R = g (Q _R / (N _R / 100)) (42)
From equation (42), the pump efficiency η _{an / n} per pump when n pumps are operated can be obtained by the following equation (43).
η _{an / n} = g (Q _{an / n} / (N _{an / n} / 100)) (43)
Substituting equation (8) and equation (10) above into equation (43),
η _{an / n} = g ((Q _an ^* / n) / (N _an ^* / 100)) (44)
From the equation (44), the pump efficiency _{an an / n} per pump can be calculated when _n pumps are in operation.

Similarly, the pump efficiency η _{an + 1 / n + 1} per pump at the time of operation of pump _{n + 1} is obtained by the following equation (45).
η _{an + 1 / n + 1} = g (Q _{an + 1 / n + 1} / (N _{an + 1 / n +} 1/100)) (45)
Substituting the equations (11) and (13) into the equation (45),
η _{an + 1 / n + 1} = g ((Q _{an + 1} ^* / (n + 1)) / (N _{an + 1} ^* / 100))
... (46)
From the equation (46), the pump efficiency η _{an + 1 / n + 1} can be calculated per pump at the time of operation of the pump _{n + 1} .

The pump shaft power can be obtained by the above-mentioned equation (5). From this equation (5), the pump shaft power _{Lan / n} per pump at the time of operation of n pumps can be obtained by the equation (28) described above. Formula (28) is described again.
L _{an / n} = 0.163 × Q _{an / n} × H _{an / n} / (η _{an / n} / 100) (28)
By substituting the equations (8), (9) and (44) into the equation (28), the following equation (47) can be obtained.
L _{an / n} =
0.163 × (Q _an ^* / n) × H _an ^* /
(G ((Q _an ^* / n) / (N _an ^* / 100)) / 100) ... (47)

Similarly, the pump shaft power L _{an + 1 / n + 1} per pump when the n + 1 pumps are operated can be obtained by the above-mentioned equation (30). Formula (30) is described again.
L _{an + 1 / n + 1} = 0.163 × Q _{an + 1 / n + 1} × H _{an + 1 / n + 1} / (η _{an + 1 / n +} 1/100)
... (30)
Formula (11), Formula (12), and Formula (46) can be substituted for Formula (30), and the following Formula (48) can be obtained.
L _{an + 1 / n + 1} =
0.163 × (Q _{an + 1} ^* / (n + 1)) × H _{an + 1} ^* /
(G ((( _{Qan + 1} ^* / (n + 1) / ( _{Nan + 1} ^* / 100)) / 100))
... (48)

Since Formula (47) shows axial power L _{an / n} per pump at the time of n pump operation, total axial power L _n of pump _n is axial power L _{an /} per pump It can be obtained by multiplying _n by n.
Therefore,
L _n = L _{an / n} × n
= 0.163 x Q _an ^* x H _an ^* /
(G (Q _an ^* / (N _an ^* / 100)) / 100) (49)

In equation (49), as noted above, Q _an ^* can be obtained from flow meter 18 and H _an ^* can be obtained from pressure gauge 17. If Q _an ^* and H _an ^* are obtained, N _an ^* can be obtained from the QH curve stored in the controller 20. Therefore, the pump operating number determination unit 22 of the controller 20 can calculate the total shaft power L _n at the time of n pumps using the equation (49).

Similarly, since equation (48) indicates the axial power L _{an + 1 / n + 1} per pump during operation of pump n + 1, the total axial power L _{n + 1} of pump _{n + 1} is one pump. It can be obtained by multiplying the axial power L _{an + 1 / n + 1} of the circumference by n + 1.
L _{n + 1} = L _{an + 1 / n + 1} × (n + 1)
= 0.163 × Q _{an + 1} ^* × H _{an + 1} ^* /
(G ((Q _{an + 1} ^* / (n 1)) / (N _{an +1} ^* / 100)) / 100)
... (50)
Substituting equations (6) and (7) into equation (50),
L _{n + 1} = 0.163 × Q _an ^* × H _an ^* /
(G ((Q _an ^* / (n + 1)) / (N _{an + 1} ^* / 100)) / 100)
... (51)

In equation (51), as noted above, Q _an ^* can be obtained from flow meter 18 and H _an ^* can be obtained from pressure gauge 17. If Q _an ^* and H _an ^* are obtained, N _{an + 1} ^* can be obtained from the QH curve stored in the controller 20. Therefore, the pump operation number determination unit 22 of the controller 20 can calculate the total shaft power L _{n + 1} at the time of the pump n + 1 operation using the equation (51).

  So far, the method of calculating the total shaft power L in the case of determining whether to switch the number of operating pumps 2 from n to n + 1 has been described. Hereinafter, a method of calculating the total shaft power L in the case of determining whether to switch the number of operating pumps 2 from n to n−1 will be described. Note that n is a natural number of 2 or more when determining whether to switch the number of operating pumps from n to n-1.

The total shaft power L _n when the number of operating pumps 2 is n can be calculated by the above equation (49). When calculating the total shaft power L _n-1 when the number of operating pumps 2 is switched from n to n-1, the predetermined set value is derived from the pump efficiency per pump at the time of n-1 operation By subtracting Δη, shaft power per pump at n−1 operation is calculated based on the reduced pump efficiency. This is because, when the discharge flow rate of the pump 2 moves up and down in the vicinity of the pump operation number switching point, there is a possibility that the number of operation of the pump 2 may increase or decrease and hunting. Therefore, in order to prevent hunting, ΔQ, which is the difference in flow rate switching, is provided to switch from n units to n−1 units. As this means, by subtracting a predetermined set value Δη from the pump efficiency per pump, it is possible to prevent the number of operating pumps from switching back to n immediately after switching to n−1. The total shaft power is also used for determination when switching from n to n-1. However, since the subtraction of -Δη is included in the pump efficiency, the comparison of the total shaft power is strictly carried out It does not mean that The predetermined set value Δη is, for example, 5%.

Specifically, the formula for calculating the pump efficiency per pump at the time of n-1 operation is expressed by the following formula corresponding to the above-mentioned formula (46).
η _{an-1 / n -1} = g ((Q _an-1 ^* / (n-1)) / (N _an-1 ^* / 100))
... (52)
The pump efficiency value obtained by subtracting the predetermined set value Δη from this equation (52) is used in the following calculation as the pump efficiency value when obtaining the pump shaft power.
That is, the pump shaft power _{Lan-1 / n-1} per pump when the pump _n-1 is in operation can be obtained by the following equation corresponding to the equation (48).
L _{an-1 / n-1} =
0.163 × (Q _an−1 ^* / (n−1)) × H _an−1 ^* /
((((Q ( _an-1 ^* / (n-1)) / ( _Nan-1 ^* / 100))-[Delta] [eta]) / 100)
... (53)

Since Formula (53) has shown axial power _{Lan-1 / n-1} per pump at the time of pump n-1 operation, total axial power Ln-1 of pump _n-1 is It can be obtained by multiplying the axial power L _{an-1 / n-1} per pump by n-1.
L _n−1 = L _{an−1 / n−1} × (n−1)
= 0.163 x Q _an-1 ^* x H _an-1 ^* /
((((Q ( _an-1 ^* / (n-1)) / ( _Nan-1 ^* / 100))-[Delta] [eta]) / 100)
... (54)
Immediately after the number of operating pumps is switched, the relationships of the above-mentioned equation (38) and equation (39) hold. Formula (38) and Formula (39) are described again.
Q _an ^* = Q _an-1 ^* (38)
H _an ^* = H _{an -1} ^* (39)
Therefore, Equation (38) and Equation (39) can be substituted into Equation (54) to obtain Equation (55) below.
L _n−1 = 0.163 × Q _an ^* × H _an ^* /
((((Q _an ^* / (n-1)) / (N _an-1 ^* / 100))-??) / 100)
... (55)

In equation (55), as noted above, Q _an ^* can be obtained from flow meter 18 and H _an ^* can be obtained from pressure gauge 17. If Q _an ^* and H _an ^* are obtained, N _an−1 ^* can be obtained from the QH curve stored in the controller 20. Therefore, the pump operation number determination unit 22 of the controller 20 can calculate the total shaft power L _n-1 when the pump n-1 is in operation, using Expression (55).

The pump operation number determination unit 22 of the controller 20 determines the total shaft power L _n during n-unit operation thus _calculated and the total shaft power L _{n + 1} or L _n during n + 1-unit operation or n-1-unit operation. Compare with _-1 to determine the number of pump operation with low total shaft power. Specifically, when L _{n + 1} is _{equal to} or less than L _n (L _n LL _{n + 1} ) when the total discharge flow rate of the pump device is increasing, the number of operating pumps 2 is increased to n + 1. When the total discharge flow rate of the pump device is _{increased, L n + 1} is greater than _{L n (L n <L n} + 1) cases, to keep the number of operating pumps 2 to n units. When L _n-1 is _{equal to} or less than L _n (L _n LL _n-1 ) when the total discharge flow rate of the pump device is decreasing, the number of operating pumps 2 is reduced to n-1. When the total discharge flow rate of the pump device is _{decreased, L n-1} is _{L n} greater than _(L n _{<L n-1)} case, to keep the number of operating pumps 2 to n units. The controller 20 operates the number of pumps 2 determined by the pump operation number determination unit 22.

  According to this embodiment, when it is determined whether or not to switch the number of operating pumps, the number of operating pump at which the total shaft power decreases is selected. Therefore, the pump device can be operated with energy saving. In addition, the pumps 2 to be operated are operated with the number of operating pumps at which the axial power becomes low (except for the hunting prevention (−ΔΔ) at the time of switching from n to n−1). Therefore, since the load applied to the pump 2 can be small, the load applied to the consumable parts such as the bearing of the pump can be reduced, and as a result, the life of the pump 2 can be extended.

  Specific pump operation number control will be described below with reference to FIGS. 8 to 13. FIG. 8 shows an example of an operating characteristic curve diagram (QH diagram) when deciding whether to switch the number of operating pumps 2 from one to two as the total discharge flow rate of the pump device increases. It is. As described above, before the pump operating number determining unit 22 of the controller 20 determines whether to switch the operating number of the pumps 2, the region determining unit 23 determines the total number of pump devices before and after the operating number switching of the pumps. It is determined whether the discharge flow rate and the rotational speed of the pump 2 are within the above region (a region where the number of operating pumps 2 can be switched). As described above, the region determination unit 23 stores three regions I, II, and III (see FIG. 3) defined according to Equations (1) to (4). The area determination unit 23 determines which one of the three areas I, II, and III the total discharge flow rate of the pump device and the rotational speed of the pump 2 are located. In the formulas (1) to (4), the constant α is selected to be 1.33, the constant β to be 4.17, the γ to be 60, and the δ to be 100, respectively. Further, the flow rate-pump efficiency characteristic curve (Q-) curve) shown in the lower part of FIG. 8 is represented by a polynomial approximation of the function g shown in the equation (17), and this polynomial approximation is It is predetermined and stored in the controller 20. The flow rate-pump efficiency characteristic curve (Q-η curve) shown in the lower part of FIGS. 9 to 13 described later is also represented by the polynomial approximation of the function g shown in the equation (17), and this polynomial approximation The equation is predetermined and stored in the controller 20.

First, the area determination unit 23 determines whether the total discharge flow rate of the pump device and the rotational speed of the pump 2 before and after switching of the number of operating pumps are within the above-described area. FIG. 8 shows an example where the area determination is performed when the pump 2 is operated at the operating point C. Point C is the operating point when the total discharge flow rate of the pump device is 36 m ³ / min. At this time, the pump 2 is operated by one unit, and the pump rotational speed is 86%. The total discharge flow rate of the pump device at the operating point C and the rotational speed of the pump 2 are in the region I in FIG. Therefore, at the operating point C, only one pump 2 is operated. When the number of operating pumps 2 is switched to two at this operating point C, the rotational speed of the pump 2 is 82%. The total discharge flow rate 36 m ³ / min and the rotational speed 82% of the pump 2 are in the region I. Therefore, the area determination unit 23 determines that the total discharge flow rate of the pump device and the rotational speed of the pump 2 do not fall within the area where the number of operating pumps 2 can be switched to two, and the pump operating number determination unit 22 determines Maintain the number 2 operation as one.

The total shaft power L _n at one operating point of the pump 2 at this operating point C is determined as follows. Because the pump efficiency _{an an / n} per pump is 77%, the flow rate Q _an ^* is 36 m ³ / min, and the discharge pressure P _an ^* is 78 m (total head H _an ^* is 40.9 m) From the equation (32) or (49), the total shaft power L _n is 311.7 kW. On the other hand, the total shaft power L _{n + 1} when the two pumps 2 are operating at the operating point C is obtained as follows. Pump efficiency _{an an + 1 / n + 1} per pump is 77%, flow rate Q _an ^* is 36 m ³ / min, discharge pressure P _an ^* is 78 m (total head H _an ^* is 40.9 m Therefore, from the equation (34) or (51), the total shaft power L _{n + 1} is 311.7 kW, which is equal to the total shaft power L _n when one pump is in operation. However, since the total discharge flow rate of the pump device at the operating point C and the rotational speed of the pump 2 do not exist in the region II and III where two pumps 2 can operate, the number of operating pumps 2 is one. Maintained.

FIG. 9 is an operating characteristic curve diagram (QH diagram) when determining whether the total discharge flow rate of the pump device increases and the number of operating pumps 2 is switched from one to two. Another example of First, it is first determined in which of the three regions I, II, and III the total discharge flow rate of the pump apparatus and the rotational speed of the pump 2 are located before and after switching of the number of operating pumps. FIG. 9 shows an example where the area determination is performed when the pump 2 is operated at the operating point D. The point D is the operating point when the total discharge flow rate of the pump device is 63 m ³ / min. At this time, the pump 2 is operated by one unit, and the pump rotational speed is 98%. The total discharge flow rate of the pump device at the operating point D and the rotational speed of the pump 2 are in the region II in FIG. Therefore, the pump 2 can be operated by one unit. When the number of operating pumps 2 is switched to two at this operating point D, the rotational speed of the pump 2 is 85%. The total discharge flow rate 63 m ³ / min and the rotational speed 85% of the pump 2 are in the region II. Therefore, the area determination unit 23 determines that the total discharge flow rate of the pump device and the rotational speed of the pump 2 are in an area where the number of operating pumps 2 can be switched to two.

In this case, the pump operation number determination unit 22 determines the number of pump operations so that the total shaft power of the pump device becomes smaller, according to the pump operation number determination algorithm described above. The total shaft power L _n when one pump 2 is in operation at this operation point D can be obtained as follows. Since the pump efficiency _{an an / n} per pump is 78%, the flow rate Q _an ^* is 63 m ³ / min, and the discharge pressure P _an ^* is 79 m (total lift H _an ^* is 41.9 m) From (32) or Formula (49), the total shaft power L _n when one pump 2 is in operation is 551.6 kW. On the other hand, the total shaft power L _{n + 1} when the two pumps 2 are operating at this operating point D is determined as follows. Pump efficiency _{an an + 1 / n + 1} per pump is 79%, flow rate Q _an ^* is 63 m ³ / min, discharge pressure P _an ^* is 79 m (total head H _an ^* is 41.9 m Therefore, from equation (34) or equation (51), the total shaft power L _{n + 1} when the two pumps 2 are operating is 544.6 kW, which is smaller than the total shaft power L _n when one pump is operating. Therefore, the pump operating number determination unit 22 issues a command to switch the number of operating pumps to two, and the controller 20 operates the two pumps 2.

FIG. 10 is an operating characteristic curve diagram (Q-H diagram) when determining whether the total discharge flow rate of the pump device increases and the number of operating pumps 2 is switched from one to two. Yet another example of First, it is determined in which of the three regions I, II and III the total discharge flow rate of the pump apparatus and the rotational speed of the pump 2 are located before and after the operation number switch of the pump. FIG. 10 shows an example in which the area determination is performed when the pump 2 is operated at the operating point E. Point E is an operating point when the total discharge flow rate of the pump device is 66 m ³ / min. When the pump 2 is operated at one operating point E, the pump rotational speed is 100%. The total discharge flow rate of the pump device and the rotational speed of the pump 2 at the operating point E at this time are in the region II in FIG. However, the rotational speed of the pump 2 has reached the upper limit rotational speed N _U (= δ = 100) shown by the equation (4). If the number of operating pumps 2 is switched to two at this operating point E, the rotational speed of the pump 2 is 85%. The total discharge flow rate 66 m ³ / min and the rotational speed 85% of the pump 2 are in the region III. Therefore, the pump operation number determination unit 22 determines to switch the operation number of the pumps 2 from one to two, and the controller 20 operates the two pumps 2.

The total shaft power L _n when one pump 2 is in operation at this operating point E can be obtained as follows. Since the pump efficiency _{an an / n} per pump is 82%, the flow rate Q _an ^* is 66 m ³ / min, and the discharge pressure P _an ^* is 80 m (total lift H _an ^* is 42.9 m) From (32) or Formula (49), the total shaft power L _n when one pump 2 is in operation is 562.8 kW. On the other hand, the total shaft power L _{n + 1} when the two pumps 2 are operating at this operating point E is obtained as follows. The pump efficiency _{an an + 1 / n + 1} per pump is 72%, the flow rate Q _an ^* is 66 m ³ / min, the discharge pressure P _an ^* is 80 m (total head H _an ^* is 42.9 m Therefore, from equation (34) or (51), the total shaft power L _{n + 1} when the two pumps 2 are in operation is 641.0 kW, and the total shaft power is one that was operated by one pump 2 It becomes smaller. However, the total discharge flow rate of the pump device and the pump 2 after the rotational speed of the pump 2 reaches the upper limit rotational speed N _U (= δ = 100) shown by the equation (4) and switching the number of operating pumps. The number of operating pumps 2 is switched to two because the rotational speed of the motor is in the regions II and III.

  FIG. 11 is an example of an operating characteristic curve diagram (QH diagram) when determining whether the total discharge flow rate of the pump device decreases and the number of operating pumps 2 is switched from two to one. It is. First, it is determined in which one of the three regions I, II, and III the total discharge flow rate of the pump apparatus and the rotational speed of the pump 2 are located before and after switching of the number of operating pumps.

FIG. 11 shows an example in which the area determination is performed when the pump 2 is operated at the operating point F. Point F is an operating point when the total discharge flow rate of the pump device is 39 m ³ / min. When two pumps 2 are operated at the operating point F, the pump rotational speed is 82%. The total discharge flow rate of the pump device at this operating point F and the rotational speed of the pump 2 are in the region I in FIG. Also, assuming that the number of operating pumps 2 is switched to one at this operating point F, the rotational speed of the pump 2 is 86%. The total discharge flow rate 39 m ³ / min and the rotational speed 86% of the pump 2 are in the region I. Therefore, the area determination unit 23 determines that the total discharge flow rate of the pump device and the rotational speed of the pump 2 are not in the area that can be operated by two pumps but in the area that can be operated by one pump. Then, the pump operation number determination unit 22 determines to switch the operation number of the pumps 2 from two to one, and the controller 20 operates one pump 2.

The total shaft power L _n at the time of operation of two pumps 2 at this operating point F is determined as follows. Since the pump efficiency _{an an / n} per pump is 77%, the flow rate Q _an ^* is 39 m ³ / min, and the discharge pressure P _an ^* is 78 m (total head H _an ^* is 40.9 m) From (32) or Formula (49), the total shaft power L _n when the two pumps 2 are in operation is 337.7 kW. On the other hand, the total shaft power L _n−1 when one pump 2 is operating at this operating point F is obtained as follows. Pump efficiency _{an an-1 / n-1} per pump is 77%, flow rate Q _an ^* is 39 m ³ / min, discharge pressure P _an ^* is 78 m (total head H _an ^* is 40.9 m Since the set value Δη is 5%, the total axial power L _n−1 when one pump 2 is in operation is 361.1 kW from the equation (40) or (55). The total shaft power L is smaller when operating with two units. However, the total discharge flow rate of the pump device after the total discharge flow rate of the pump device and the rotational speed of the pump 2 are out of the range II and III where the number of operating pumps can be operated by two and the number of operating pumps is switched Since the rotational speed of the pump 2 is in the regions II and I, the number of operating pumps 2 is switched from two to one.

  FIG. 12 is an operating characteristic curve diagram (Q-H diagram) when determining whether the total discharge flow rate of the pump device decreases and whether to switch the number of operating the pumps 2 from the two-unit operation to the one-unit operation Another example of First, it is determined in which of the three regions I, II and III the total discharge flow rate of the pump apparatus and the rotational speed of the pump 2 are located before and after switching the number of operating pumps.

FIG. 12 shows an example in which the region determination is performed when the pump 2 is operated at the operating point G. Point G is an operating point when the total discharge flow rate of the pump device is 57 m ³ / min. At this operating point G, two pumps 2 are operated, and the pump rotational speed is 85%. The total discharge flow rate of the pump device and the rotational speed of the pump 2 at this operating point G are in the region II in FIG. Assuming that the number of operating pumps 2 is switched to one at this operating point G, the rotational speed of the pump 2 is 96%. The total discharge flow rate 57 m ³ / min and the rotational speed 96% of the pump 2 are in the region II. Therefore, the area determination unit 23 determines that the total discharge flow rate of the pump device and the rotational speed of the pump 2 are in an area where the number of operating pumps 2 can be switched.

In this case, the pump operation number determination unit 22 determines the number of pump operations so that the total shaft power of the pump device becomes smaller, according to the pump operation number determination algorithm described above. The total shaft power L _n at the time of operation of two pumps 2 at this operating point G is determined as follows. Since the pump efficiency _{an an / n} per pump is 76%, the flow rate Q _an ^* is 57 m ³ / min, and the discharge pressure P _an ^* is 79 m (total lift H _an ^* is 41.9 m) From (32) or Formula (49), the total shaft power L _n when the two pumps 2 are in operation is 512.2 kW. On the other hand, the total shaft power L _n−1 when one pump 2 is in operation at this operating point G is determined as follows. Pump efficiency _{an an-1 / n-1} per pump is 82%, flow rate Q _an ^* is 57 m ³ / min, discharge pressure P _an ^* is 79 m (total head H _an ^* is 41.9 m ), and and the setting value Δη is 5%, the formula (40) or the equation (55), the total shaft power _{L n-1} is 506.0kW, and the total shaft power _{L n} during two pumps operating It becomes smaller. Therefore, the pump operating number determination unit 22 determines to switch the number of operating pumps from two to one, and the controller 20 operates one pump 2.

  FIG. 13 is an operating characteristic curve diagram (QH diagram) when determining whether the total discharge flow rate of the pump device decreases and whether to switch the number of operation of the pump 2 from 2 operation to 1 operation. Yet another example of First, it is determined in which one of the three regions I, II, and III the total discharge flow rate of the pump apparatus and the rotational speed of the pump 2 are located before and after switching of the number of operating pumps.

FIG. 13 shows an example where the area determination is performed when the pump 2 is operated at the operating point H. Point H is an operating point when the total discharge flow rate of the pump device is 54 m ³ / min. At this operating point H, two pumps 2 are operated, and the pump rotational speed is 84%. The total discharge flow rate of the pump device and the rotational speed of the pump 2 at this operating point H are in the region II in FIG. Assuming that the number of operating pumps 2 is switched to one at this operating point H, the rotational speed of the pump 2 is 94%. The total discharge flow rate 54 m ³ / min and the rotational speed 94% of the pump 2 are in the region I. Therefore, the area determination unit 23 determines that the total discharge flow rate of the pump device and the rotational speed of the pump 2 after switching the number of operating pumps are within the area where the number of operating pumps 2 can be switched.

In this case, the pump operation number determination unit 22 determines the number of pump operations so that the total shaft power of the pump device becomes smaller, according to the pump operation number determination algorithm described above. The total shaft power L _n when the two pumps 2 are operating at this operating point H can be obtained as follows. Since the pump efficiency _{an an / n} per pump is 82%, the flow rate Q _an ^* is 54 m ³ / min, and the discharge pressure P _an ^* is 78 m (total lift H _an ^* is 40.9 m) From (32) or Formula (49), the total shaft power L _n when the two pumps 2 are in operation is 439.0 kW. On the other hand, the total shaft power L _n-1 when one pump 2 is in operation at this operating point H is determined as follows. Pump efficiency _{an an-1 / n-1} per pump is 68%, flow rate Q _an ^* is 54 m ³ / min, discharge pressure P _an ^* is 78 m (total head H _an ^* is 40.9 m ), and and the setting value Δη is 5%, the formula (40) or the equation (55), the total shaft power _{L n-1} is 571.4kW, and the total shaft power _{L n} during two pumps operating It becomes bigger than. Therefore, the pump operating number determination unit 22 determines to maintain the number of operating pumps at two, and the controller 20 operates the two pumps 2.

  So far, the case where the number of operating pumps 2 is switched from one to two and the case where it is switched from two to one have been described as the simplest examples using FIGS. 8 to 13. Further, the same method can be applied to the case where the number of operating pumps changes from two to three and the case where the number of operating pumps changes from three to two. Similarly, the same method can be applied when the number of operating pumps changes from n to n + 1, or from n to n-1.

  Although the embodiment of the present invention has been described above, the present invention is not limited to the above embodiment, and various modifications may be made within the scope of the claims and the technical idea described in the specification and the drawings. It is possible.

DESCRIPTION OF SYMBOLS 1 suction water tank 2 pump 3 water supply place 5 suction piping 5 'branch suction piping 6 discharge piping 6' branch discharge piping 7 check valve 11 water stop valve 12 pump discharge valve 13 water stop valve 15 motor 16 speed control device 17 pressure gauge 18 Flow meter 20 Controller 21 Flow rate judgment unit 22 Pump operation number decision unit 23 Region decision unit

Claims (4)

When the total discharge flow rate increases, the number of pumps operated at the same characteristic parallel uniform speed increases from n to n + 1 (where n is a natural number of 1 or more when switching from n to n + 1), or total discharge It is a pump operation number control method which switches from n units to n-1 units (n in the case of switching from n units to n-1 units is a natural number of 2 or more) when the flow rate decreases,
It is confirmed that the total discharge flow rate before and after switching of the number of operating pumps and the rotational speed of the pump are within a range where the number of operating pumps can be switched.
From the function that uses the discharge flow rate per pump and the rotational speed of the pump as a variable, the pump efficiency per pump during n unit operation and the pump efficiency per pump when operating with n + 1 units or Calculate pump efficiency per pump when operating with pump n-1;
From the calculated pump efficiency per pump, the axial power per pump during n operation and the axial power per pump during n + 1 operation or n-1 operation are calculated respectively. ,
Calculate the total shaft power at n-unit operation and the total shaft power at n + 1-unit operation or n-1-unit operation by multiplying the calculated axial power per pump by the number of operating pumps.
Determine the number of pump operating units with lower total shaft power by comparing the total shaft power during n units with the total shaft power during n + 1 or n-1 units ,
When calculating the pump efficiency per pump when the n-1 unit operation is performed, the predetermined set value is subtracted from the calculated pump efficiency, and the n-1 unit operation is performed based on the subtracted pump efficiency A method of controlling the number of operating pumps, which comprises calculating axial power per pump at one time . According to claim 1, the rotational speed of the total discharge flow rate and the pump before and after the number of operating switching of the pump, and controlling while monitoring to be within the region capable of switching the operation number of the pump How to control the number of operating pumps.   When the total discharge flow rate increases, the number of pumps operated at the same characteristic parallel uniform speed increases from n to n + 1 (where n is a natural number of 1 or more when switching from n to n + 1), or total discharge It is a pump operation number control method which switches from n units to n-1 units (n in the case of switching from n units to n-1 units is a natural number of 2 or more) when the flow rate decreases,
  It is confirmed that the total discharge flow rate before and after switching of the number of operating pumps and the rotational speed of the pump are within a range where the number of operating pumps can be switched.
  From the function that uses the discharge flow rate per pump and the rotational speed of the pump as a variable, the pump efficiency per pump during n unit operation and the pump efficiency per pump when operating with n + 1 units or Calculate pump efficiency per pump when operating with pump n-1;
  From the calculated pump efficiency per pump, the axial power per pump during n operation and the axial power per pump during n + 1 operation or n-1 operation are calculated respectively. ,
  Calculate the total shaft power at n-unit operation and the total shaft power at n + 1-unit operation or n-1-unit operation by multiplying the calculated axial power per pump by the number of operating pumps.
  Determine the number of pump operating units with lower total shaft power by comparing the total shaft power during n units with the total shaft power during n + 1 or n-1 units,
  A method of controlling the number of operating pumps according to claim 1, wherein the total discharge flow rate before and after switching the number of operating pumps and the rotational speed of the pump are monitored while being in a region where the number of operating pumps can be switched. . A plurality of pumps operated at the same characteristic parallel uniform speed;
A flow meter for measuring the total discharge flow rate of the plurality of pumps;
A controller for controlling the rotational speed and the number of operating pumps of the pump;
The controller
A flow rate determining unit that determines whether the total discharge flow rate of the pump is increasing or decreasing;
An area determination unit that confirms whether or not the total discharge flow rate and rotational speed of the pump before and after switching of the number of operating pumps are within a range where the number of operating pumps can be switched;
When the pump efficiency per pump during n unit operation and the pump n + 1 unit operation (from n units to n + 1 units) based on a function using the discharge flow rate per pump and the rotational speed of the pump as variables N is 1 or more natural numbers) pump efficiency per pump or when operating with pump n-1 (n is 2 or more natural numbers when switching from n to n-1) per pump Based on the calculated pump efficiency per pump, the axial power per pump during n unit operation and per pump during n + 1 unit operation or n-1 unit operation are calculated. The axial power of each is calculated, and the axial power per pump calculated is multiplied by the number of operating pumps, and the total axial power during n operation and n + 1 operation or n-1 operation Total axial motion of The pump operation that determines the lower number of pump operating units by comparing the total shaft power during n unit operation with the total shaft power during n + 1 unit operation or n-1 unit operation and the number determining unit, and have a,
When calculating the pump efficiency per pump when the n-1 units are operated, the pump operation number determination unit subtracts a predetermined set value from the calculated pump efficiency, and the pump efficiency is subtracted. The pump apparatus characterized by calculating axial power per pump at the time of n-1 operation based on .

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