METHOD OF CONTROLLING A WATER RESERVOIR SUPPLY PUMP ARRANGEMENT AND WATER RESERVOIR SUPPLY PUMP ARRANGEMENT

Abstract

A method of controlling a water reservoir supply pump arrangement determines a set value p, q, v, n of the pump arrangement based on an offset value p.sub.ref, q.sub.ref, n.sub.ref, v.sub.ref, G.sub.0 reduced by a component which is a function of a difference between an actual water level h and a predetermined water level h.sub.ref in a water reservoir. The difference is weighted by a proportional gain factor G. Further, a water reservoir supply pump arrangement is provided including at least one water pump and a control device for controlling the at least one pump.

Claims

1. A method of controlling a water reservoir supply pump arrangement, the method comprising the steps of: determining a set value of the pump arrangement based on an offset value reduced by a component which is a function of a difference between an actual water level and a predetermined water level in a water reservoir; weighting the difference by an automatically adjusted proportional gain factor; and adjusting the gain factor each time a predetermined water level in the reservoir is reached or a predetermined time interval has elapsed or both each time a predetermined water level in the reservoir is reached and a predetermined time interval has elapsed.

2. The method according to claim 1, wherein the set value and the offset value are one of pump reference pressure, reference pump flow, reference pump speed, reference number of switched-on pumps in the water reservoir supply pump arrangement.

3. The method according to claim 1, wherein the predetermined water level is a minimum water level.

4. The method according to claim 1, wherein the water level, when the gain factor is adjusted, is the maximum water level in the reservoir.

5. The method according to claim 1, wherein the gain factor or the offset value or both the gain factor and the offset value are adjusted such that the maximum water level measured over time is a fraction of a difference between a maximum and a minimum permissible water level.

6. The method according to claim 5, wherein the gain factor (G) is adjusted each time after the predetermined time interval has elapsed such that
G.sub.k+1=G.sub.k?K(h.sub.high*?h.sub.high)
where
h.sub.high*=?h.sub.max+(1??)h.sub.min and where k denotes the k.sup.th said time interval, ? denotes the fraction, h.sub.max denotes a maximum permissible level threshold, h.sub.min denotes a minimum permissible level threshold, h.sub.high is the maximum level measured over a given period of time, and K being a predetermined constant>0.

7. The method according to claim 1, wherein the water reservoir supply pump arrangement is switched on when the actual water level is below a predetermined minimum level and is switched off when the actual water level has reached a predetermined maximum water level.

8. The method according to claim 1, wherein the set value is flow, and a maximum set flow is decreased by a predetermined flow value if the pressure is higher than a predetermined maximum pressure value, and a minimum set flow is increased by a predetermined flow value as long as the pressure is lower than a predetermined minimum pressure value.

9. The method according to claim 1, wherein the set value is pressure, and a maximum set pressure is decreased by a predetermined pressure value if the flow is higher than a predetermined maximum flow value, and a minimum set pressure is increased by a predetermined pressure value if the flow is lower than a predetermined minimum flow value.

10. The method according to claim 1, wherein the gain and the offset value are adjusted such that variations of the water level over the time utilize a predefined water level band, where the water level band lies between a maximum and a minimum permissible water level.

11. The method according to claim 5, wherein the set value is one of pressure and flow, and the offset value is gain, and wherein the proportional gain factor and the offset value are adjusted each time the predetermined interval has lapsed, the proportional gain factor and the offset value being adjusted as
G.sub.1,k+1=G.sub.1,k?K.sub.1((h.sub.high*?h.sub.high)?(h.sub.low*?h.sub.low))
G.sub.0,k+1=G.sub.0,k+K.sub.0((h.sub.high*?h.sub.high)+(h.sub.low*?h.sub.low)) with G.sub.1, k+1 being the set value adjusted after the (k+1).sup.th time interval, G.sub.1, k being the set value adjusted after the k.sup.th time interval, G.sub.0, k+1 being the offset value adjusted after the (k+1).sup.th time interval, G.sub.0, k being the offset value adjusted after the k.sup.th time interval, and h.sub.high being the maximum level of the k.sup.th time interval, h.sub.low being the minimum level of the k.sup.th time interval, and
h.sub.high*=?h.sub.max+(1??)h.sub.min
h.sub.low*=(1??)h.sub.max+?h.sub.min where k denotes the k.sup.th said time period and ? denotes the fraction, ? denotes another fraction, h.sub.max denotes a maximum permissible level threshold, h.sub.min denotes a minimum permissible level threshold, h.sub.high is the maximum level over a given period of time, h.sub.min is a minimum level over a given period of time and K.sub.0 and K.sub.1 being predetermined constants>0.

12. The method according to claim 5, wherein the set value is one of pressure and flow, and the offset value is gain, and wherein the proportional gain factor and the offset value are adjusted each time a predetermined interval has elapsed, the proportional gain factor and the offset value being adjusted as
G.sub.1,k+1=G.sub.1,k?K.sub.1((h.sub.high*?h.sub.high)?(h.sub.low*?h.sub.low))
G.sub.0,k+1=G.sub.0,k+K.sub.0G.sub.1,k+1((h.sub.high*?h.sub.high)+(h.sub.low*?h.sub.low)) with G.sub.1, k+1 being the set value adjusted after the (k+1).sup.th time interval, G.sub.1, k being the set value adjusted after the k.sup.th time interval, G.sub.0, k+1 being the offset value adjusted after the (k+1).sup.th time interval, G.sub.0, k being the offset value adjusted after the k.sup.th time interval, and h.sub.high being the maximum level of the k.sup.th time interval, h.sub.low being the minimum level of the k.sup.th time interval, and
h.sub.high*=?h.sub.max+(1??)h.sub.min
h.sub.low*=(1??)h.sub.max+?h.sub.min where k denotes the k.sup.th said time period, ? denotes the fraction, ? denotes another fraction, h.sub.max denotes a maximum level threshold, h.sub.min denotes a minimum level threshold, h.sub.high is the maximum level over a given period of time, h.sub.low is the minimum level over a given period of time and K.sub.0 and K.sub.1 being predetermined constants>0.

13. The method according to claim 1, wherein the set value is one of pressure and flow, and the offset value is gain, and wherein the offset value is updated each time the predetermined interval has elapsed and if the water level has dropped below the minimum permissible level (h.sub.min), the offset value being adjusted as $G_{0,t+1}=\{\begin{array}{cc}{G}_{0,t}& ,h?h_{\min }\\ G_{0,t}+K_2?\left(h_{\min }-h\right)& ,h<h_{\min }\end{array}$ with G.sub.0, t+1 being the offset value adjusted after the (t+1).sup.th time interval, G.sub.0, t being the offset value adjusted after the t.sup.th time interval, and K.sub.2 being a predetermined constant>0.

14. A method of controlling a plurality of water reservoir supply pump arrangements, the method comprising the steps of: supplying a same water reservoir with all pump arrangements; providing flow as a set value; determining each set value of each pump arrangement based on an offset value reduced by a component which is a function of a difference between an actual water level and a predetermined water level in said same water reservoir, and the respective set values being scaled according to the following formula:
q.sub.set,i=s.sub.iG.sub.0?s.sub.iG.sub.1(h?h.sub.min) with s.sub.i denoting a scaling coefficient adjusting the amount of water delivered by the i.sup.th pump arrangement, and i denoting the respective pump arrangement.

15. The method according to claim 14, wherein the proportional gain factor and the offset value are the same for all pump arrangements, and given by: $G_{0,t+1}^{\left(j\right)}=G_{0,t}^{\left(j\right)}+\frac{?}{.Math.U.Math.}.Math.\underset{i?U}{\overset{}{.Math.}}.Math.\left(G_{0,t}^{\left(i\right)}-G_{0,t}^{\left(j\right)}\right)$ $G_{1,t+1}^{\left(j\right)}=G_{1,t}^{\left(j\right)}+\frac{?}{.Math.U.Math.}.Math.\underset{i?U}{\overset{}{.Math.}}.Math.\left(G_{1,t}^{\left(i\right)}-G_{1,t}^{\left(j\right)}\right)$ with U being the number of switched on pumps, and ? being a predetermined gain convergence control factor.

16. The method according to claim 14, wherein one of the pump arrangements comprise a plurality of slave pump arrangements and respective sub-pump flows are calculated according to
q.sub.set,i=s.sub.iq.sub.set,1 with q.sub.set, i being the flow reference for the i.sup.th slave pump controller, q.sub.set, 1 being the flow of the master controller, and s.sub.i being a number that defines the distribution of the flow between the pump arrangements, in particular, between pump stations.

17. A water reservoir supply pump arrangement comprising: at least one water pump; and a control device configured to control the at least one pump by: determining a set value of the pump arrangement based on an offset value reduced by a component which is a function of a difference between an actual water level and a predetermined water level in a water reservoir; weighting the difference by an automatically adjusted proportional gain factor; and adjusting the gain factor each time a predetermined water level in the reservoir is reached or a predetermined time interval has elapsed or both each time a predetermined water level in the reservoir is reached and a predetermined time interval has elapsed.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0036] FIG. 1 is a schematic view for a setup of a water supply system according to prior art;

[0037] FIG. 2 is a further schematic view for a setup of a water supply system according to prior art;

[0038] FIG. 3 is a schematic view for a setup of a water supply system for buildings with roof top tanks;

[0039] FIG. 4 is a proportional pressure curve for a water reservoir supply pump arrangement according to an embodiment of the present invention;

[0040] FIG. 5 is a schematic illustration for the division between on/off control mode and continuous level control mode for controlling a pump according to an embodiment of the present invention;

[0041] FIG. 6 is a schematic view for a setup which is controlled according to an embodiment of the method according to the present invention;

[0042] FIG. 7 is a further schematic view for a setup which is controlled to a further embodiment of the method according to the present invention;

[0043] FIG. 8 is a diagram showing a level series for identifying a maximum level on a daily basis;

[0044] FIG. 9 is a schematic view for a setup which is controlled according to still a further embodiment of the method according to the present invention;

[0045] FIG. 10 is a schematic view for a setup which is controlled according to another embodiment of the method according to the present invention;

[0046] FIG. 11 is a diagram showing a pressure profile and a logged pressure profile for the use in case of a level sensor fault;

[0047] FIG. 12 is a diagram view of a control structure for controlling the limits for the flow according to an embodiment of the present invention;

[0048] FIG. 13 is a diagram view of a further control structure comprising an inlet pressure protection;

[0049] FIG. 14 is a proportional level curve, where a predefined water level band is utilized;

[0050] FIG. 15 is diagram showing a further level series identifying the maximum and minimum levels on a daily basis;

[0051] FIG. 16 is a diagram showing the control behaviour exemplified on the flow proportional curve;

[0052] FIG. 17 is a diagram showing the level behaviour over a period of a couple of days, where the actual water level has fallen below the minimum permissible water level threshold;

[0053] FIG. 18 is a schematic illustration of a system with elevated reservoir according to an embodiment of the present invention; and

[0054] FIG. 19 is a schematic illustration of a water supply system according to an embodiment of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0055] FIG. 1 shows a schematic view for a setup for a water supply system 1 according to prior art as it is typically used in America and Asia. The water supply system 1 comprises a water reservoir supply pump arrangement 2 with a pump 3 and a tank or reservoir 4 for supplying water to a plurality of houses 5. The reservoir 3, here, controls the pressure in the network connected by pipes 6 and serves as a disconnection reservoir between the end user flow q.sub.u and the pump flow q.sub.p. This enables an on/off control of the pump 3 or a plurality of pumps, whereby the water level h in water reservoir 4 is controlled by on/off controllers which start the pumps 3 when a low-level threshold is reached and stops the pumps when a high-level threshold is reached. Besides enabling on/of control, the reservoir 4 serves as an emergency reservoir. Moreover, the reservoir 4 may also function as a reactor for, for example, chlorine injection, since all the water in the water supply system 1 passes through the reservoir 4.

[0056] FIG. 2 shows a further schematic arrangement of a water supply system 1 according to prior art which commonly is used in Europe. The configuration shown basically corresponds to the one illustrated in FIG. 1. However, here the reservoir 4 is not able to function as reactor. A further disadvantage with this configuration is that it is difficult to ensure the age of the water is below a predefined value.

[0057] FIG. 3 shows a schematic arrangement of a water supply system 1 for a building 7 with a roof top tank or reservoir 4 which are employed in cities in which it is mandatory to have water reservoirs inside the building 7 for firefighting. The water supply system 1 shown here also is similar to the one shown in FIG. 1, except that the tank or reservoir 4 is placed on the top 8 of the building 7.

[0058] In all water supply systems 1 described above, a controller controls the pump 3 or a plurality of pumps so as to stop and start the pump 3 or pumps in accordance with a water level h in the tank or reservoir 4. It is noted that in many large water supply systems 1, the pumps 3 are started at different water levels h which procedure approximates a proportional pressure control. However, according to prior art applications, it is not possible to adjust the proportional factor automatically so as to ensure a continuous flow.

[0059] FIG. 4 shows a proportional pressure curve for a water reservoir supply pump arrangement 2 according to an embodiment of the present invention. Here, a pressure set-point p.sub.set for a controller of a pump station or water reservoir supply pump arrangement 2 is a function of the water level h in the reservoir 4. In the diagram of FIG. 4, p.sub.ref indicates the maximum pressure set point for the pumping station controller, and the tank or reservoir water level h is controlled between a minimum water level setting h.sub.min of the reservoir 4 and a maximum water level setting h.sub.max of the reservoir 4 by using a proportional controller with a fixed offset term so that the water level h stays below p.sub.ref. The reason for this is that it ensures robustness against the control parameters design. That is, in addition to the other advantages already listed above, stability is always ensured in the water supply system 1.

[0060] In the on-periods, the pump station water reservoir supply pump arrangement 2 controls the pressure in accordance with the level h following the relation equation (1)

p.sub.set=p.sub.ref?G(h?h.sub.min)equation (1)

with p.sub.set being the actual pressure provided by the pump station water reservoir supply pump arrangement 2, p.sub.ref being the pressure reference of the pump station water reservoir supply pump arrangement 2 when running as an on/off controller, and G being the proportional factor. Further, h is the actual level in the tank or reservoir 4, and h.sub.min is the minimum permissible level threshold set by the user. The effect of this control is illustrated in FIG. 4. According to this approach, the pressure is used as a reference value or pump station reference. Instead, the flow could be used just as well, in which case the proportional control would be represented by equation (2):

q.sub.set=q.sub.max?G(h?h.sub.min)equation (2)

[0061] In the case of a water reservoir supply pump arrangement 2, which is controlled by a speed reference, the proportional control would be represented by equation (3):

n.sub.set=n.sub.ref?(h?h.sub.min)equation (3)

[0062] Finally, in the case where the water reservoir supply pump arrangement 2 comprises fixed speed pumps 3, the number of running pumps 3 can be controlled proportional to the level h. Let v denote the number of active pumps 3, then the proportional control would be represented by equation (4):

v.sub.set=ceil(v.sub.max?G(h?h.sub.min))equation (4)

where ceil is denoting that the smallest integer number bigger that the content of the bracket.

[0063] On the basis of FIG. 5 showing a schematic illustration for the division between on/off control mode 12 and continuous level control mode 13 for controlling a pump 3 according to an embodiment of the present invention, the adaptive adjustment of the gain factor G is explained. The adjustment of the gain factor G in the previous described level control strategy is in this approach adaptive. The adjustment strategy is divided into two levels following the division of the level control strategy.

[0064] The main control strategy is on/off control 12. This control ensures that the level h never exceeds the maximum level setting and never decrease below the minimum level setting. This is done by switching the complete pump station or water reservoir supply pump arrangement 2 on and off based on the level settings. When the pump station or water reservoir supply pump arrangement 2 is switched on, the continuous level control 13 adjusts the pump pressure and flow depending on the choice of control. This is done according to the control described in equations (1) to (4). The gain is adjusted both in the on/off control and in the continuous control and a reference output 14 is obtained. In the following, first the adjustment in the on/off control mode 12 is described followed by the adjustment in the continuous control mode 13.

[0065] FIG. 6 shows a schematic view for a setup which is controlled according to an embodiment of the method according to the present invention, wherein a state machine 9 controls the level h and adjusts the gain factor G so as to ensure continuous operation of the pump station or water reservoir supply pump arrangement 2.

[0066] As described above, the problem with the use of a proportional tank filling control is to choose a good value for the gain factor G. Here, this problem is solved by adjusting the gain each time the maximum level is reached as this is an indication that the pressure is too high to obtain continuous pump operation. The state machine 9 illustrated in FIG. 6 acts on the level, starts and stops the pump 3 of the pump station or water reservoir supply pump arrangement 2. The state machine adjusts the gain factor G after each pump 3 is switched off, and at predefined time instants to obtain continuous pump operation.

[0067] FIG. 7 shows a further schematic view for a setup which is controlled to a further embodiment of the method according to the present invention. Here, the state machine 9 identifies the minimum and maximum control level and adjusts the gain factor G according to the on/off level control signal. This applies for cases in which the water supply system 1 is equipped with a level controller that sends an on/off signal to the pump controller. In these cases, this on/off signal can be used for identifying the minimum and maximum level and to adjust the gain factor G, as is done by the state machine 9 shown here.

[0068] FIG. 8 is a diagram for explaining the adjustment in the continuous control and showing a level series for identifying a maximum level on a daily basis. Here, the value of the maximum level decreases by increasing the gain factor G until the maximum level is below the value h*.sub.high

[0069] When the pump 3 is running continuously the gain G is adjusted such that the maximum valve of h is around 80% of the difference between the maximum and minimum level threshold (h.sub.max and h.sub.min). This is done by first identifying the highest level obtained over a given period according to equation (5):

[00003]$\begin{array}{cc}{h}_{\mathrm{high}}=\underset{t?T}{\max }.Math..Math.h?\left(t\right)& \mathrm{equation}.Math..Math.\left(5\right)\end{array}$

where h(t) is the level at time t and the term max searches for the maximum level over the time period ?, where ? preferably covers 1 day. The outcome of this search is the maximum level obtained during one day, here denoted as h.sub.high in this figure.

[0070] When the maximum level over the period ? is known then G is adjusted according to the following equation (6) once in each time period ?:

G.sub.k+1=G.sub.k?K(h.sub.high*?h.sub.high)equation (6)

where

h.sub.high*=?h.sub.max+(1??)h.sub.min

where k denotes the k time period ?, and 0<?<1 denotes the fraction between the maximum level h.sub.max and the minimum level h.sub.min that the level should reach in the period ?. The term ?h.sub.max(1??)h.sub.min here equals to h*.sub.high. Finally, ? is a gain constant that controls the adjustment rate. ? is the adaptation constant and should have a value larger than zero.

[0071] FIG. 9 shows a schematic view for a setup which is controlled according to still a further embodiment of the method according to the present invention. Here, a procedure or strategy for pump station control with forced water change in the tank or reservoir 4 and the water quality features are explained.

[0072] The age of the water in the reservoir 4 is a very important parameter for the quality of the water. To ensure the water quality, the average stay time of the water in the reservoir 4 must be limited, and the reservoir 4 has to be clean. With the control approach described in connection with this FIG. 9, the natural stay time of the water will increase in applications with a structure similar to the water supply system 1 shown in FIG. 2. Here, the water quality problem with the following two features.

[0073] In order to ensure water quality, an emptying procedure is initiated at predefined times, typically once a day or once a week. The state event machine 9 shown in this figure controls the emptying procedure. At the empty state, the pumping station or water reservoir supply pump arrangement 2 controls the pressure or flow according to a predefined pressure or flow set point that is low enough to empty the reservoir 4. Alternatively, the pumps 3 of the pump station or water reservoir supply pump arrangement 2 stop.

[0074] FIG. 10 shows a schematic view for a further setup which is controlled according to another embodiment of the method according to the present invention. Here, a strategy for pump station control for cleaning the tank or reservoir 4 will be explained, wherein cleaning means that the reservoir 4 is filled to its maximum ensuring that the whole reservoir 4 is flushed. The state event machine 9 illustrated here carries out such a cleaning procedure. The cleaning Level in the figure is the level that defines the top of the tank or reservoir 4 just before water flows over. Commonly, the cleaning procedure is run as the reservoir is already filled to its maximum, thereby ensuring the best possible change of the water.

[0075] FIG. 11 is a diagram showing a pressure profile and a logged pressure profile for the use in case of a level sensor fault on the basis of which several safety strategies are described. For a level sensor fault, the following applies.

[0076] The level sensor (not shown) is transmitted from the reservoir 4 to the pump station or water reservoir supply pump arrangement 2 which typically are separated by several kilometres so that a sophisticated strategy for controlling the pump station or water reservoir supply pump arrangement 2 in the case of a level sensor fault is very important. When a level sensor fault appears, the pump station or water reservoir supply pump arrangement 2 operates with the pressure values that have been provided to the system at the same time of the day the day before. This is done by setting up a profile of pressure values from the day before, or an average of the pressure from a number of days in the past. This is exemplified in this where the average pressure for each hour is logged, and used for the next day control in the case of a level sensor fault.

[0077] FIG. 12 shows a control structure 10 for controlling the limits for the flow according to an embodiment of the present invention. The control structure 10 comprise two controllers 11 and 11 which here are embodied as PI controllers and which control the limits for the flow in order to ensure that the pressure is kept in accordance to the constraints p.sub.max and p.sub.min, with p.sub.max>p.sub.min.

[0078] In the case where the flow s is chosen as the control variable (control as represented in equation (2) there is a risk of the pressure becoming too high or too low for the water supply system 1, if the connection to the tank or reservoir 4 is closed (for example due to cleaning). To avoid the pressure being too high or too low, variable constraints are set on the flow. This is accomplished by the controller configuration shown in this FIG. 12. In this configuration, the controller 11 decreases the upper limit of the flow if the pressure is higher than the maximum pressure, and the controller 11 increases the lower limit of the flow if the pressure is lower than the minimum pressure requirement. The middle controller 11 is the level proportional controller described with respect to FIG. 11.

[0079] FIG. 13 shows a further control structure 10 comprising an inlet pressure protection, which control structure 10 is available for both pressure control mode and flow control mode. In the following, flow protection in case of flow control mode is described.

[0080] In the case where the pressure p is chosen as the control variable (control procedure represented by equation (1), there is a risk that the flow becomes too high or too low for the water supply system 1. In order to avoid the flow being too high or too low, variable constraints are set on the pressure. This is accomplished in a similar way as it was described with respect to FIG. 12 as to pressure protection. Especially, high flow protection is an important feature as this can be part of a protection scheme that protects the water resource from which the pump station or water reservoir supply pump arrangement 2 is supplied.

[0081] With respect to inlet pressure protection, the following is noted. In many water supply systems, it is very important to protect the water reservoir at the inlet side of the pump station or water reservoir supply pump arrangement 2. Often the inlet pressure indicates the amount of water available in this reservoir 4. Therefore, an inlet pressure protection is designed for the pump controller 11. This protection has the same form as the protection function described above, except that it uses the inlet pressure measurement for the control, and its control architecture is shown in this figure.

[0082] FIG. 14 is a diagram showing a proportional level curve in which both the offset and the gain terms are adjusted. If the largest possible variations in the level and thereby the largest possible exchange of water during the day should be ensured, both the gain G.sub.1 and the offset term q.sub.max=G.sub.0 must be adjusted, wherein the adjustment of both the gain and the offset is illustrated in FIG. 14. With respect to the flow control case, the expression proportional level curve is given by equation (7):

q.sub.set=G.sub.0?G.sub.1(h?h.sub.ref)equation (7)

where

[00004]$h_{\mathrm{ref}}=\frac{h_{\max }+h_{\min }}{2}$

[0083] In this case, both a value for the gain G.sub.1 and a value for the offset G.sub.0 have to be identified automatically. The same approach as before is used. That is, as can be seen in FIG. 15, the maximum value of the level obtained during a predefined time frame T, typically a day, is used. The only difference is that both the maximum and minimum levels during the time frame T are used. These values are obtained by equations (8) and (9):

[00005]$\begin{array}{cc}{h}_{\mathrm{high}}=\underset{t?T}{\max }.Math..Math.h?\left(t\right)& \mathrm{equation}.Math..Math.\left(8\right)\\ h_{\mathrm{low}}=\underset{t?T}{\min }.Math..Math.h?\left(t\right)& \mathrm{equation}.Math..Math.\left(9\right)\end{array}$

[0084] References for the maximum and minimum levels can be defined by equations (10) and (11):

h.sub.high*=?h.sub.max+(1??)h.sub.minequation (10)

h.sub.low*=(1??)h.sub.max+?h.sub.minequation (11)

where ? and ? are numbers between 0 and 1 which define the distance between the maximum acceptable level and the maximum level to be controlled, and similar for the minimum level. As can be seen in FIG. 15 which shows a level series identifying the maximum and minimum level for every day, the difference between the real maximum and minimum levels and the reference levels decreases each day by adjusting the gain and offset factors G.sub.1 and G.sub.0.

[0085] The update laws for the gain and offset terms are represented by the following equations (12) and (13):

G.sub.1,k+1=G.sub.1,k?K.sub.1((h.sub.high*?h.sub.high)?(h.sub.low*?h.sub.low))equation (12)

G.sub.0,k+1=G.sub.0,k+K.sub.0((h.sub.high*?h.sub.high)+h.sub.low*?h.sub.low))equation (13)

[0086] To obtain a better convergence behaviour, it may be beneficial to scale the update law for the offset term by the estimated gain according to equation (14):

G.sub.0,k+1=G.sub.0,k+K.sub.0G.sub.1,k+1((h.sub.high*?h.sub.high)+h.sub.low*?h.sub.low))equation (14)

[0087] As in the previous case, the algorithm can be used for both pressure and flow controlled pump stations or water reservoir supply pump arrangements 2. In the case of a pressure controlled pumping station, the proportional level control can be defined by equation (15):

p.sub.set=G.sub.0?G.sub.1(h?h.sub.min)equation (15)

with update laws for G.sub.0 and G.sub.1 that are similar in their structure and in the flow controlled pump station or water reservoir supply pump arrangement 2, just with other numerical values for the gain terms.

[0088] FIG. 16 is a diagram showing the control behaviour exemplified on the flow proportional curve for explaining safety control on the level. With the approach where both G.sub.0 and G.sub.1 are adjusted to fulfil requirements on both the average level and the variation of the level in the reservoir 4, it is no longer possible to guarantee that the output pressure or flow is at its maximum when the minimum level is reached. This can cause the level to decrease below the acceptable minimum level in case of changes in the demand. To solve this problem the flow/pressure set point is increased with the level by adjusting the offset term G.sub.0. This is done each time a predetermined time period T has elapsed in accordance with the following update law represented by equation (16):

[00006]$\begin{array}{cc}{G}_{0,t+1}=\{\begin{array}{cc}{G}_{0,t}& ,h?h_{\min }\\ G_{0,t}+K_2?\left(h_{\min }-h\right)& ,h<h_{\min }\end{array}& \mathrm{equation}.Math..Math.\left(16\right)\end{array}$

where t denotes the t.sup.th time period T the sampling time typically lies in the range of seconds

[0089] This implies that each time the level becomes lower than the minimum level h.sub.min, the following algorithm according to equation (17) is running

G.sub.0,k+1=G.sub.0,k+K.sub.2(h.sub.min?h), h<h.sub.minequation (17)

where ?.sub.2 is an update gain. This behaviour is illustrated in FIG. 16 for a case of levels below the minimum level.

[0090] FIG. 17 is a diagram showing the level behaviour over a period of a couple of days, with an active control as described above in connection with FIG. 16. At day 2 the water level becomes lower than the minimum level h.sub.min, equation (17) becomes active and G.sub.0 is updated.

[0091] FIG. 18 is a schematic illustration of a system with elevated reservoir according to an embodiment of the present invention with a filling from multiple pump stations or water reservoir supply pump arrangements 2. In the case where the reservoir 4 is supplied from multiple sources, the control of the individual pump station or water reservoir supply pump arrangement 2 should share the load (the flow) between the units in accordance with predefined settings. A water supply system 1 where two pump stations or water reservoir supply pump arrangements 2 supply water to the reservoir 4 is shown in this figure. Here, each of the pumps 3 runs the same control loop represented by equation (18):

q.sub.set,i=s.sub.iG.sub.0?s.sub.iG.sub.1(h?h.sub.min)equation (18)

[0092] Here, s is a scaling coefficient that adjusts the amount of water delivered by the different pumping stations or water reservoir supply pump arrangements 2. That is, if s.sub.i=s.sub.j then the i.sup.th and j.sup.th pump station or water reservoir supply pump arrangement 2 delivers the same flow, and if s.sub.i?s.sub.j, then the i.sup.th and j.sup.th pump station or water reservoir supply pump arrangement 2 delivers flow accordingly. In this embodiment, s.sub.i i=1, . . . , n is chosen by the users.

[0093] The update laws for G.sub.0 and G.sub.1 are the same for all the pump stations or water reservoir supply pump arrangements 2 and a consensus algorithm ensures that the individual pump stations match the values. The consensus updates are performed with a higher sampling rate than the update law described by equations (12) and (13). The sampling time of the update law is typically 24 hours and for the consensus algorithm below 1 hour. The consensus updates are controlled by the following update law described by equations (19) and (20):

[00007]$\begin{array}{cc}{G}_{0,k+1}^{\left(j\right)}=G_{0,k}^{\left(j\right)}+\frac{?}{.Math.U.Math.}.Math.\underset{i?U}{\overset{}{.Math.}}.Math.\left(G_{0,k}^{\left(i\right)}-G_{0,k}^{\left(j\right)}\right)& \mathrm{equation}.Math..Math.\left(19\right)\\ G_{1,k+1}^{\left(j\right)}=G_{1,k}^{\left(j\right)}+\frac{?}{.Math.U.Math.}.Math.\underset{i?U}{\overset{}{.Math.}}.Math.\left(G_{1,k}^{\left(i\right)}-G_{1,k}^{\left(j\right)}\right)& \mathrm{equation}.Math..Math.\left(20\right)\end{array}$

where k denotes the k.sup.th sampling time. The sampling time typically lies in the range of 10-60 minutes.
where U is the set of active units (the units that have communicated their values of G.sub.0 and G.sub.1 to the j.sup.th unit), |U| is the number of units that have communicated their values, and ? is a gain factor that controls the convergence of the agreement between the units.

[0094] FIG. 19 is a schematic illustration of a further water supply system 1 according to an embodiment of the present invention wherein filling is carried out by multiple pump stations or water reservoir supply pump arrangements 2. In the case shown here, more than one pump station or water reservoir supply pump arrangements 2 share the flow between them in accordance with user defined rules. This is done by defining one of the pump stations or water reservoir supply pump arrangements 2 as the master station 2, and then letting this master pump station 2 communicate flow references to the remaining slave pump station 2 in accordance with the predefined rule as can be seen from this figure.

[0095] Thereby, the slave pump station 2 is controlled to a reference flow which is calculated based on the flow of the master pump station 2 according to equation (21):

q.sub.set,i=s.sub.iq.sub.set,1equation (21)

where q.sub.set,i is the flow reference for the i.sub.th slave pump controller, q.sub.set,1 is the flow of the master pump controller, and s.sub.i is a number that defined the distribution of the flow between the pump stations 2, 2.

[0096] Finally, some alternative applications are mentioned. The proposed control approach can also be used for filling large reservoirs such as big ponds for raw water for water supply. Also, emptying reservoirs can be accomplished by a control that controls the flow proportional to the level. In this case, the flow should be controlled in accordance to the level following the rule represented by equation (22):

q.sub.set=q.sub.max?G(h.sub.max?h)equation (22)

[0097] Besides this, the approach is similar to the embodiments described above.

[0098] While specific embodiments of the invention have been shown and described in detail to illustrate the application of the principles of the invention, it will be understood that the invention may be embodied otherwise without departing from such principles.