Login| Sign Up| Help| Contact|

Patent Searching and Data


Title:
WATER DISTRIBUTION
Document Type and Number:
WIPO Patent Application WO/2009/020402
Kind Code:
A1
Abstract:
The invention provides approaches for optimising pump usage within a water distribution system. One approach involves considering combinations of physical pumps as single logical pumps to simplify the pump scheduling optimisation problem. Another approach relates to selection of an operating speed for a variable speed drive pump that is used to distribute fluid within a fluid distribution system at a given head. Yet another approach predicts fluid demand by controlling the extent to which estimated demand deviates from actual demand of a fluid.

Inventors:
BUNN SIMON MICHAEL (NZ)
THORSTENSEN SARAH-JANE (NZ)
ATKINSON EVAN PETER HENRY (NZ)
PATEL SANJAY UNKA (NZ)
CLARK SARAH ELIZABETH (NZ)
PEGG STEPHANIE ANNE (NZ)
Application Number:
PCT/NZ2008/000192
Publication Date:
February 12, 2009
Filing Date:
July 31, 2008
Export Citation:
Click for automatic bibliography generation   Help
Assignee:
DERCETO LTD (NZ)
BUNN SIMON MICHAEL (NZ)
THORSTENSEN SARAH-JANE (NZ)
ATKINSON EVAN PETER HENRY (NZ)
PATEL SANJAY UNKA (NZ)
CLARK SARAH ELIZABETH (NZ)
PEGG STEPHANIE ANNE (NZ)
International Classes:
F04B49/08; F04D15/00
Foreign References:
GB2010959A1979-07-04
US3294023A1966-12-27
JP2002005075A2002-01-09
JPH0626466A1994-02-01
Other References:
PATENT ABSTRACTS OF JAPAN
PATENT ABSTRACTS OF JAPAN
Attorney, Agent or Firm:
BALDWINS (Wellesley StreetAuckland, 1141, NZ)
Download PDF:
Claims:
CLAIMS

1. A method of selecting which of a plurality of pumps to operate in a fluid distribution system to meet demand for the fluid, the method including: establishing predetermined pump combinations; for each pump combination, determining the operating characteristics thereof including the combined flow rate; comparing the hydraulic constraints and demand requirements of the distribution system with the operating characteristics of each pump combination; and selecting one of the pump combinations based on the comparison.

2. The method of claim 1 , wherein the pumps are configured to distribute the fluid across an operating range of flow rates and the step of establishing predetermined pump combinations includes: obtaining operating characteristics of each pump; and selecting pumps to combine to establish the predetermined pump combinations such that each pump combination is configured to provide the required flow rate for a portion of the operating range of flow rates.

3. The method of claim 2, wherein each portion of the operating range of flow rates is assigned to a particular pump combination to reduce undesirable switching between pump combinations and therefore physical pumps.

4. The method of claim 3, wherein undesirable switching between pumps is further reduced using hysteresis control.

5. The method of any one of the preceding claims, wherein the step of establishing the predetermined pump combinations is based in part on the determined operating characteristics of each pump combination.

6. The method of any one of the preceding claims, including repeating the step of establishing the predetermined pump combinations.

7. The method of claim 6, wherein said repeating is performed after a predetermined period of time, whereby different pump combinations are established to provide for pump duty rotation.

8. The method of any one of the preceding claims, wherein the hydraulic constraints and/or demand vary over time and the method further includes: receiving an indication of a change in the hydraulic constraints and/or demand requirements; and

repeating the steps of comparing the hydraulic constraints and demand requirements with the operating characteristics of each pump combination and selecting one of the pump combinations to account for the change in the hydraulic constraints and/or demand requirements,,. 9. The method of any one of the preceding claims, wherein each pump has substantially the same operating characteristics and the number of predetermined pump combinations is equal to (n + 1), where n is the total number of pumps and the predetermined pump combinations-include the combination of zero pumps operating.

10. The method of any one of the preceding claims, wherein each predetermined pump combination is represented as a single logical pump.

11. The method of claim 10, wherein the step of selecting is performed on the logical pumps.

12. A method of selecting an operating speed for a variable speed drive pump that is used to distribute fluid within a fluid distribution system, the method including: determining the efficiency of and head resulting from operating the pump at a plurality of flow rates and at a plurality of speeds; determining a first flow rate corresponding to a first pump efficiency at a first pump speed; determining the head when operating at the first flow rate and first speed; and determining the operating speed based on the given head, the determined head and the first speed, wherein the given head is the head used to distribute the fluid.

13. The method of claim 12, wherein the step of determining the operating speed, RPM 2 , is calculated using the equation: where RPM- \ is the first pump speed, Head^ is the determined head and Head 2 is the given head.

14. The method of claim 12. or claim 13, wherein the first pump efficiency is substantially equal to the maximum pump efficiency at the first pump speed.

15. The method of any one of claims 12 to 14, wherein the step of determining the operating speed is further based on a cost of operating the pump.

16. The method of claim 15, including determining the cost of operating the pump using piecewise linear approximations to the cost of operating the pump at the given head.

17. The method of claim 16, wherein the step of determining the cost includes: determining minimum and maximum operating flow rates for the pump and at least one flow rate therebetween; determining the pump speed required to obtain each of the plurality of flow rates; determining the cost of operating the pump at each of the plurality of flow rates; and determining the cost of operating the pump at the operating speed by interpolating between adjacent flow rates for the which the costs have been determined.

18. The method of claim 17, wherein at least one flow rate between the minimum and maximum flow rates substantially corresponds to ' the most efficient flow rate for the pump. 19. A method of predicting demand for a fluid in a fluid distribution system, wherein data is available providing an estimated demand for the fluid in predetermined time intervals, the method including; monitoring actual demand for the fluid over successive said time intervals, the most recent interval being the previous interval; and comparing the actual demand to the estimated demand for at least the previous interval.

20. The method of claim 19, wherein the step of comparing further includes comparing the actual demand to the estimated demand for at least the interval immediately preceding the previous interval.

21. The method of claim 19 or claim 20, including using a Loess algorithm to predict water demand.

22. The method of any one of claims 19 to 21 , wherein weights are used to place greater emphasis on the values of demand in the most recent intervals.

23. The method of claim 22, wherein an exponential distribution of weights is used to weight demand values for at least a subset of the most recent intervals, the weight for each interval being:

(N - MaxDemandAdaptPeriods) ,

\K.1 H )

Weight® = N

M<xDen , a n u da P , per , ods ^ _ MaxDemcindAdciptPeriods) , ,

( *1 + ^ ) wherein MaxDemandAdaptPeriods determines how many past intervals preceding the current period are used to predict future demand, K1 is a constant and N is a predetermined number of prior intervals and is greater than MaxDemandAdaptPeriods. 24. The method of claim 23, wherein K1 is 1.075.

25. The method of claim 23 or claim 24, including summing the weighted previous demand values for each of the MaxDemandAdaptPeriods.

26. The method of claim 25, including comparing the sum of weighted previous demand values to a sum of corresponding weighted estimated demand values to determine a scale factor for future predictions of demand.

27. The method of claim 26, including applying the scale factor to estimated demand values to determine and/or adjust future- predictions of demand.

28. The method of any one of the preceding claims, including repeating one or more of the steps thereof. 29. The method of claim 8 or claim 28, wherein the repeating occurs at least every hour or at least every 30 minutes or at least every 15 minutes.

30. A method of operating a fluid distribution system including the steps of: any one of claims 1 to 11 ; and/or any one of claims 12 to 18; and/or any one of claims 19 to 27.

31. The method of any one of the preceding claims, configured to operate substantially in or near real time.

32. The method of any one of the preceding claims, configured to operate automatically, substantially without human intervention. 33. The method of any one of the preceding claims, configured to reduce energy use and/or costs of distributing the fluid around the fluid distribution system.

34. The method of any one of the preceding claims, wherein the fluid distribution system is a water distribution system.

35. Use of the method of any one of the preceding claims, to simplify or reduce calculation time of scheduling in a pumping system.

36 A set of computer readable instructions which when executed on a suitably enabled computing device implement the method of any one of claim 1 to 34.

37. An apparatus for controlling a fluid distribution system, the apparatus including a processor configured to implement the method of any one of claims 1 to 34. 38. The apparatus of claim 37, including or communicatively coupled to one or more sensors for monitoring actual demand for the fluid.

39. The apparatus of claim 37 or claim 38, including or communicatively coupled to means for controlling operation of one or more pumps within the fluid distribution system.

40. A fluid distribution system including the apparatus of any one of claims 37 to 39.

Description:

WATER DISTRIBUTION

FIELD OF THE INVENTION

This invention relates to distribution of water such as by water utilities. More particularly, the invention relates to control of the distribution of water so as to provide for efficient, or more efficient distribution.

BACKGROUND

Energy costs for pumping are typically one of the largest expenses in a water utility's operations budget and may be more than US$ 5 million per annum. The significance of the scale of this expenditure means that improvements in energy efficiency and consumption reduction can have a substantial effect. In general, water utilities have significant flexibility in how they operate their water distribution system even taking into account strict constraints on minimum fire-fighting storage and water quality requirements. Many utilities practice the strategy of filling storage tanks overnight to cope with the morning demand, and then refill them before the evening peak. Such practice may necessitate pumping during high tariff afternoon hours. If a water utility can accurately predict the water usage profile and manipulate the substantial storage prevalent in the water distribution industry, then there are numerous opportunities to be smarter in the time at which you choose to use this energy, and which pumps you choose to run. The amount of energy consumed by these pumps is considerable, and the ability to control when this energy is consumed can have a significant impact on electricity costs.

SUMMARY OF THE INVENTION It is an object to provide a system and / or method that at least mitigates one of the aforementioned problems.

Alternatively, it is an object of the invention to provide the public with at least a useful choice.

To achieve consistent savings in energy, an automatic pump scheduling system can be added on top of an existing SCADA (Supervisory Control And Data Acquisition) and telemetry system to control the starting and stopping of pumps in response to electricity tariff schedules as well as system production demands, operational constraints and predicted water usage.

Factors taken into account when looking at the optimization of pump and valve control may include:

o Differences in efficiency between pumps at a pump station (which can vary during the day depending on conditions); o Time of use energy tariffs, where the energy price is dependent on the time of use; o The changing efficiency of variable speed drive pumps, with speed set point; o Monthly maximum electrical demand charges, which affect the strategy for optimum selection of pumps at each station; o Multiple possible paths for- directing water throughout a network, some of which will be more efficient than others; o Physical constraints in the network such as storage volumes, min and max flow limitations and min/max pressure requirements; and o Comparison of alternatives including gas, diesel and hydro powered pumps to electrically driven pumps.

According to preferred embodiments of the invention, the problem is approached by providing an automatic pump scheduling system, preferably software embodied, which sits on top of the utility company's SCADA system, and reads in all flows and reservoir levels to calculate and store the current water usage. This information provides the basis for predictions of water usage throughout a predetermined time period, preferably, the coming 48 hours.

This demand prediction is used to generate optimized schedules for all pumps and valves in the network to meet the water demand at minimum cost, while meeting all physical constraints of the distribution network. The schedule is then taken and implemented directly and automatically, setting the status of the pumps and valves utilizing the SCADA system.

Most conventional arrangements solve this problem once per day and provide a printed schedule which operations staff use as a guide for that entire day. A key point of difference between the invention and these conventional arrangements is that the invention provides a real time, or near real time, automated optimizer. Data may be read in, say, every 10 minutes and a new solution produced, say, at least every 30 minutes, with the updated schedules being implemented automatically. This real time or near real time approach means that it is possible to more quickly adapt to changing demand, equipment failure and automated or more fully automated operation is enabled. While 30 minutes is a preferred time interval, the invention is not limited thereto. The presently preferred range is from 15 minutes to an hour but the selected range will depend on parameters of the system to which the invention is applied.

To create optimized pumping schedules, it is necessary to first model each pump in the network, so as to provide estimates of flow and pressure when each pump is turned on. At a pump station with numerous parallel pumps, there are a number of different possible pumping

combinations. As the combining of pumps is a non-linear relationship (meaning that running two identical pumps simultaneously does not result in twice the flow i.e., it is not possible to simply sum the individual flows of each of a plurality of pumps in order to determine the total combined flow), the number of distinct pumping combinations has the following relationship with the number of pumps at the station:

"n\ n\ j* J r\(n — τ)\ where n is the number of pumps in the station, and r is the number of pumps you want to run. For example, if there are 4 pumps at a station (n), for the number of pumps to run options (r) are (0,1,2,3,4 pumps). The number of combinations given by this formula are (1 ,4,6,4,1), with respect to the number of pumps r, making a total of 16 possible pump combinations. More generally, the relationship between the number of different combinations and the number of pumps in a pump station is governed by the equation:

Number of Pumping Combinations = 2"

This relationship produces a rapid increase in complexity as the size of the station increases and makes the mathematical problem very difficult to optimize.

The conventional solution of modelling every pump individually directly suffers from the massive escalation of problem complexity and corresponding solution time, especially when stations have a large number of pumps. The rapid increase in combinations of pumps, can be seen in Table 1. As noted above, the relationship for the number of combinations, is 2".

Table 1 - Variation of Pump Combinations with No. of Pumps using Prior Art Methods

Particularly in the situation where pumps are of similar if not identical size, the Applicant has surprisingly found that, in practice, treating every pump as distinct and separate, leads to undesirable behaviour from an operational point of view. When there are pumps of near identical size, their separate solution options match very closely. In these situations, it is not uncommon for conventional solutions to swap between these similar sized pumps, as slight changes in cost calculations create small differences in cost. This results in "flip/flopping"

between running pumps of the same size, which while achieving small cost savings, creates additional operational nuisance.

According to a first aspect of the invention, physical pumps within a network are combined, preferably in real time, into logical pumps so as to simplify the pump scheduling optimization problem.

More particularly, physical pump combinations (i.e., combinations of 2 or more pumps) are modelled as individual "Logical Pumps". Thus, according to the invention two or more physical pumps may be combined together to form a new, single logical pump, with performance properties equal to the operation of all pumps together. Taking a simple example of a pump station having 4 pumps of identical or "near" identical size, it is possible to reduce the number of possible combinations from 16 using conventional approaches to only 5 pump combinations using combined Logical Pumps as illustrated in Figure 1. While specific reference is made to pumps having the same or similar size, the invention is not limited thereto and also covers combinations of pumps having different sizes. Thus, according to the first aspect, the problem of determining which pumps to run is simplified by limiting to selection between a plurality of single logical pumps, thereby greatly reducing the complexity of the problem. While each combination of pumps may be predetermined, according to preferred embodiments, the combinations may be varied so as to achieve proper pump duty rotation and better match the run hours for each pump. The substitution of one pump for another is most easily performed when multiple pumps are provided of the same or similar size but those skilled in the art will be aware that such cycling of pumps may also be applied to systems having differently sized pumps, particularly where one or more of the pumps is a variable speed pump.

The first aspect of the invention may be embodied in systems and/or methods, or additionally or alternatively, an apparatus, such as a processing apparatus for determining which pump(s) should be run and which may be included within systems of the invention.

According to a second aspect of the invention, there is provided modelling of variable speed drive pumps using best efficiency point linear approximations for the simplification of the pump scheduling optimization problem. This aspect may also be embodied in systems and/or methods, or additionally or alternatively, an apparatus, such as a processing apparatus.

Variable speed pumps, can be run at any chosen speed within their speed ranges. From a mathematical perspective, this provides an unlimited number of speed options, each with their own pump efficiency and power curves. The way in which the changing speeds of a pump are modelled is via the pump affinity laws listed below.

Power > Affinity Law 3

When put into practice, these equations show how the pump performance will change while varying the speed at which the drive is running. One such plot is provided in Figure 2.

The affinity laws may be used to translate points of one curve onto points of another curve, where the different curves are defined by the speed at which the pump is running. For example, taking a point on the curve marked "100% speed" of Figure 2 (100% speed, 1200 rpm), with Flow = 5 MGD and Head = 180 ft, the curve marked "80% speed" (80% speed, 960rpm) is created by translating the points of the 100% speed curve using the affinity laws as illustrated below.

From Affinity Law 1 :

From Affinity Law 2:

HeQd 1 = 180 [ ^L ] = 180 (0.8) 2 = 18θ (θ.64)= 115 .2 feet

Therefore the point (5,180) translates to (4,115.2) when the pump is slowed to 80% speed.

One approach to this problem involves using a pressure set point for the pump while trimming the flow range of the VSD (Variable Speed Drive), using settings such as minimum and maximum flow at desired head. These settings may be combined with the knowledge of the head across the pump to calculate cost points for the minimum and maximum flow points.

A linear approximation of flow and cost may be used by the solver to select any desired flow..

Using the pump affinity rules, the speed at which the desired flow is produced is then calculated and returned for use as a set-point of the VSD pump. While this works effectively,

there are a number of shortcomings. As Figure 3 depicts, there can be a significant difference between the actual running cost and the linear approximation of the running cost. Due to the nature of linear programming, as there is no cost incentive for the solver to operate this pump at the point of maximum efficiency "B" (due to the linear approximation of cost), the solver will choose the operating speed based upon a desired flow only "A".

Thus, according to preferred embodiments, a piecewise linear approximation method is adopted. More particularly, a number of piecewise linear approximations to the cost function of running a VSD pump at fixed head are used. The same min - max range of flows are used, but a specified number of additional points are included, for which are entered into the solver, the pump and efficiency curves for each point. The example in Figure 4 is based on using 5 ppints. Inside the solver, constraints are enforced which means that the solver must choose an operating speed which lies on one of the straight lines between the points entered into the solver. This greatly increases the accuracy of the approximation to the actual cost function.

According to another preferred feature in the modelling of VSD pumps, given the current head across the VSD pump, through calculation, it is possible to establish the speed at which the particular VSD pump will run at its highest efficiency (i.e., best efficiency point).

In order to find the optimal pump schedule, a prediction of the water demand must be obtained. The closer these predictions are to reality, the better the quality of the pump schedule solution. According to preferred embodiments, the Demand Prediction Algorithm is a process that is carried out every half hour throughout the day, thereby continually adapting to changing historically recorded demand readings. The average standard demand curve is input which contains the average water usage for each half hour period for the zone for each particular day type (i.e., day of the week, whether the day is a public holiday, etc) along with the operator entered estimated total system demand for the day. According to another aspect, there is provided a LOESS Adapted Demand Prediction

Algorithm. The algorithm may be incorporated in a method and/or a system and/or an apparatus (e.g. a controller/processor) for controlling distribution, particularly of water. The LOESS algorithm is defined as a locally weighted polynomial regression. The idea is generic and can be applied to a range of cases. The Applicant has created a surprising new technique as a branch off from this LOESS algorithm to predict water demand. 1 A step by step approach explaining components of the algorithm and what makes it so unique is explained herein below.

Further aspects of the invention, which should be considered in all its novel aspects, will become apparent to those skilled in the art upon reading the following description which provides at least one example of a practical application of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more embodiments of the invention will be described below by way of example only and without intending to be limiting with reference to the following drawings, in which:

Figure 1 is a schematic view of an embodiment of the invention;

Figure 2 charts variable speed pump operating variation;

Figure 3 charts variable speed drive costing based on a linear approximation;

Figure 4 charts variable speed drive costing using best efficiency point analysis;

Figure 5 charts variable speed pump and efficiency curves;

Figure 6 charts minimum and maximum flows for a variable speed drive pump; FFiigguurree 77 charts scaling of a standard demand curve;

Figures 8-10 are charts showing demand prediction according to one method;

Figure 11 charts scaling of the average standard demand curve;

Figures 12-14 are charts showing demand prediction according to another method;

Figure 15 provides a graphical depiction of the demand prediction parameters of the second method;

Figure 16 illustrates a method according to one embodiment of the invention; and

Figure 17 is a schematic representation of a system according to an embodiment.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS As shown in Figure 1 , the complexity of the problem of selecting pumps to run is greatly reduced by limiting the decision to be between logical pumps which represent one or more real pumps, rather than leaving open the decision as to which combinations of pumps should be considered. In the example shown in Figure 1 , the 16 possible combinations of 4 real pumps are reduced such that the selection may be made between 5 logical pumps, which represent 0, 1 , 2, 3 or 4 real pumps running at any one time.

Thus, in order to achieve the reduction in decision variables and calculation time, the solver is limited to selecting from a combination of these new Combined Logical Pumps. The new constraint is as follows:

Number of logical pumps running at this Station ≤ 1 This new approach greatly reduces the number of pump combinations. The size and performance properties of each logical pump is determined by which pumps are linked together. To define how pumps are combined, the concept of a pump sequencing order is used, as illustrated below.

This sequencing means that if any pumps are running, Pump#3 must be running and Pump#1 will only run if all other pumps are on. Thus, it is preferable to frequently reorder the sequence to balance the run hours on each pump without modifying the logical pumps.

The pump curves which define the performance of the logical pump combinations, are generated using the sequence order described above, to determine which pump curves will make up the logical pump curve. This combination is most easily undertaken as a one-off exercise, and this is generally sufficient when all pumps are near identical, or where the sequence doesn't change.

The pump sequencing, can be fixed, but in most systems, it is preferable to have this sequence order dynamically altered from within the client SCADA system, so as to achieve proper pump duty rotation and cycling to match the run hours for each pump. It may also be necessary to change the pump sequence due to pump servicing and outages. As this sequence changes dynamically, to maintain the accuracy of the logical pump model, it is also necessary to dynamically alter the pump curve of the logical pump.

Embodiments of the invention preferably incorporate the technique of numerically combining the physical pump curves every time the scheduling problem is solved with the latest sequence settings. This curve generation greatly increases the accuracy of the logical pumps and enables the linking together of pumps which are of non-equal size to simplify the pump scheduling optimization problem.

According to another aspect of the invention, in the modelling of VSD pumps, given the current head across the VSD pump, through calculation, the speed at which a particular VSD pump will run at its highest efficiency (i.e., best efficiency point) is established as follows:

Best Efficiency Point Example

Using the data from Figure 5: o Find the flow point corresponding to maximum efficiency at 100% speed. On the 100% speed curve, Maximum Efficiency 88% occurs at a flow of 6.77 MGD o Calculate head produced when running at this value of flow at 100% speed. On the 100% speed curve, 6.77MGD is achieved against a head of 155ft o Use the initial prediction of pump head and affinity law 2 to calculate the speed which will translate the maximum efficiency operation at the current head experienced by the pump.

> Affinity Law 2 If Head: = 155ft, if the current estimate of head (Head 2 ) = 100ft, and the RPM at 100% speed, RPM 1 = 1200rpm, then the new speed can be calculated as follows:

According to preferred embodiments, the "Best Efficiency Point" of operation is explicitly calculated on the fly, given the current Head across the pump, for every variable speed pump. This new operating speed is entered into the solver as one of the choice of operating points. By placing this point in the solution directly, the solver is actively encouraged to run at optimum efficiency where possible. A worked example is provided below of the process used to calculate the values of the points which are entered into the solver of the invention to model the cost of running a VSD pump at any chosen flow rate. The invention is not limited to this specific example and may be applied to pumps having different parameters operating in the same or other conditions.

Worked Example o Take the current estimate of head across the pump Example Head of 100ft

o Calculate the current minimum operating speed possible given this head This includes the following considerations

- Fixed Min Flow requirement of the pump

- Fixed Min Speed requirement of the pump - Fixed Min Efficiency requirement of the pump

Example of Min Flow = 0 5, Min Speed = 50%, Min Efficiency = 20% @100ft, Min Flow (0.5MGD) achieved at 68% speed @100ft, Min Efficiency (20%) achieved at 70% speed therefore, Min Speed = 70% (the highest of these speeds) o Calculate the maximum speed possible to run This includes the following considerations

- Max Speed

- Min Efficiency Setting

Example of Max Flow = 10, Max Speed = 100%, Min Efficiency = 20% @100ft, Max Flow (0.5MGD) achieved at 110% speed

@100ft, Min Efficiency (20%) achieved at 130% speed therefore, Max Speed = 100% (The smallest of these speeds)

Figure 6 shows minimum and maximum flows for a VSD pump, together with efficiency, o Calculate the Best Efficiency Speed From 100% speed curve, Max efficiency at 6.71 MGD

From 100% speed curve, 6.71 MGD achieved against 155ft of Head Using affinity laws, this 155 point is translated to current head 100ft at 80% speed. @ 80% speed curve, using affinity laws, 6.71 MGD is translated to a flow of 5.37MGD o Split any remaining points in between min and max speeds. In a four point model, the additional point would be entered at 85%, half way between min

(70%) and Max(100%) o For each speed setting listed, calculate the following properties

- Flow (given speed and head)

- Efficiency (given speed and flow) - Power (given flow, head and efficiency)

- Cost of running the pump (given power, and tariff, time spent running) for example, taking the maximum speed point (100%)

Flow (100%, 100ft) = 8.93 MGD from interpolating pump curve Efficiency (100%, 8.93MGD) = 73.6% from interpolating efficiency curve

Power (8.9MGD, 100ft, 73.6%eff) = 8.69kW by calculation Cost(8.69kW) = x depending on the tariff.

Note: When making the calculations for the other points, the flow, head and power values are scaled using the affinity laws. o Enter this operating point (cost and flow) into the solver o Apply Constraints

Apply constraints into the solver to limit the solutions to those which are a combination of two consecutive points (meaning that the solution lies on one of the straight lines between these points). o Calculate Final Solution Speed Properties

Once the solution has selected the flow for the pump, back calculate the following properties

- Speed (given flow and head)

- Efficiency (given flow and speed)

- Power (given flow, head, efficiency) - Cost (given power and tariff)

Final costs are calculated in the same manner as above but with the final speed settings.

Figure 16 shows a method of predicting demand which has several unfavourable characteristics in terms of accuracy and essentially involves scaling up or down a curve of standard water usage (standard demand curve) by comparing demand recorded previously in the day with this standard demand curve and scaling future predictions of demand based on the difference.

Inputs and Outputs according to One Method

The initial. step involves scaling the demand curve as shown in Figure 7 based on the estimated operator entered total system demand. Figures 8 and 9 show demand predictions generated at two different points during a day based on the difference between the scaled curve and the observed values. The predictions do not reflect the current trend and do not adapt quickly to changing demand throughout the day. Figure 10 shows that this method is not very accurate at predicting demand in the current half hour periods (shown by divergence of the dotted and dashed lines of Actual and Predicted demand). Systems using this approach may be slow to adapt to changes in demand. Thus, embodiments of the invention provide for a more accurate prediction of the half hourly demand values for up to 24 hours, preferably by manipulating an adjusted standard demand curve to predict future demands by using recent historically recorded half hour demands. This is outlined in the following.

Inputs and Outputs according to Another Method

After the inputs have been obtained, the first step is to adjust the average Standard Demand. As an example, for a particular day, the average system wide demand was 106MG. The operator entered value for the estimated total system demand was 114MG. As a starting point for predicting demand, the standard curve is scaled up as shown in Figure 11.

The output of the algorithm is shown in Figures 12 to 14. At different solve times, different predicted demands are generated based on the most recent historically recorded values. As the prediction gets further into the future, the predictions tend towards the operator scaled standard demand curve - one of the novel approaches being adopted according to preferred embodiments. Preferably, there are five applicable parameters (specified herein below) which determine:

• the length of time for predictions in the future to converge to the operator specified scaled standard demand

• the amount the predictions can stray from the scaled standard curve ' the number of previous half hour historical demand readings to use to for future predictions

In Figure 12, the most recent half hour historical demand readings stray from the scaled standard curve, hence immediate predictions after the solve time are separated from the scaled standard. In Figure 13, however, the most recent half hour historical demand readings are very ' close to the scaled standard which causes the predicted values to lie closer. Figure 14 shows final predictions at each half hour at the end of the day compared with historical demand.

According to another aspect, a Loess algorithm is used to predict water demand. For each demand prediction, one or more of the following specified fixed parameters are used:

• MaxDemandChange - This determines how far the predicted demand can stray from the standard demand curve • MaxDemandAdaptPeriods - This determines how many past periods, immediately preceding the current period, are used to predict the future expectations

• ScaleFactorSlope - This determines the effect that the scale factor has on points beyond two periods into the future. The calculated scale factor is used to scale the first two points after which the value of the scale factor approaches 1 as we predict further into the future. This parameter determines the slope at which it approaches 1

• PrevPeriodsToCompareSF - Number of previous periods over which to compare the scale factor to allow increases in the MaxDemandChange parameter

• SteplnMaxDemandChange - This is the amount per unit that the MaxDemandChange parameter is allowed to increase.

The importance of these parameters is shown graphically in Figure 15. The inputs for each particular demand prediction are as follows:

• Estimated daily total system demand is used as a starting point

Standard Demand Curve o Using historical data, typical average demand curves are preferably generated which give a water prediction usage for each half hour in the day. Demand curves are calculated and stored for each season and each day type. The Standard Demand Curve is scaled up or down depending on the estimated daily total system demand compared to average

• Historical Demand Readings o Historical half hour demand readings up to 24 hours prior to the current time, are used

Preferably, a series of weights are used to determine the importance of the recent half hour historical data. An Exponential Distribution for the weights is used for all instances of this algorithm. There are Max Demand AdaptPeriods number of weights where each value corresponds to the (MaxDemandAdaptPeriods - (/+1)th most recent half hour demand value) where:

yyeight{l) where K1 is a constant. It has been found that the algorithm performs well across a range of conditions if K1 is set to 1.075.

For example, if MaxDemandAdaptPeriods = 8 and if you are currently at period x:

Demand Period x - 8 x - 7 x - 6 x - 5 x -4 x - 3 x - 2 x - 1 i 1 2 3 4 5 6 7 8

Weight(i) 0.005 0.010 0.019 0.036 0.069 0.131 0.251 0.479

The algorithm uses a weighted sum of x previous points (x = MaxDemandAdaptPeriods) from the corresponding standard curve for the day and a weighted sum of the same points for the actual curve. A scale factor is determined by dividing these sums and is used to scale the future standard curve points to obtain an estimate for the rest of the day.

The scale factor is capped by the MaxDemandChange parameter. There are instances where the original MaxDemandChange is no longer large enough. This would occur when demand picks up or drops off throughout the day and the standard curve is limited by how much it can move due to MaxDemandChange and therefore cannot get high enough / low

enough to accurately predict future demand. This is dealt with by using the parameters PrevPeriodsToCompareSF and SteplnMaxDemandChange. PrevPeriodsToCompareSF is the number of previous periods to compare the scale factor that would have been used in that particular period. A count is performed of any scale factors that are above and another count of any scale factors that are below the limits that MaxDemandChange imposes. These counts are then used to shift the allowable range beyond the MaxDemandChange for the Scale Factor. This allows for a larger scale factor to be used where required without the detrimental effects that a spike in the demand would cause.

Not all the future points on the standard demand curve are scaled by the same amount. The first two predicted values (current period plus the next) are the standard values scaled by multiplying by the Scale Factor (capped by the adjusted MaxDemandChange parameter). However the remaining standard values are scaled by a lesser amount. The parameter ScaleFactorSlope determines the amount per period that the Scale Factor after the first two predicted demand periods decreases / increases towards 1 for remaining periods of the day. For example, if the calculated Scale Factor = 1.20, ScaleFactorSlope = 0.05 and it is currently period x, the factor for each half hour period until the end of the day is as shown:

Demand Period x x + 1 x + 2 x + 3 x + 4 x + 5 x + 6 x + 7 x + 8

Factor to Multiply

Standard Demand 1.20 1.20 1.15 1.10 1.05 1.00 1.00 1.00 1.00 1.00 for period

According to preferred embodiments, for Each Demand Prediction Zone, the following steps are performed: o Scale the standard demand curve for the zone by the estimated total system demand o Create the exponential weighting function based on MaxDemandAdaptPeriods o Calculate the Current Scale Factor by dividing the weighted sum of actual demand by weighted sum of standard demand o Loop from Current Solve Period-1 back to Current Solve Peήoό-PrevPeriodsToCompareSF Calculate the Scale Factor for each of these periods as though each period was the current solve period

Check each Scale Factor against limits imposed by MaxDemandChange and keep a count of the number (a) that fall above and the number (b) that fall below this limit

End Loop o lf a > b then:

New Upper Limit = 1 + (MaxDemandChange + abs(a - b) * SteplnMaxDemandChange) Else if b > a'

New Lower Limit = 1 - (MaxDemandChange + abs(a - b) * SteplnMaxDemandChange) Endif o Cap the Current Scale Factor using the New upper and lower limits o Determine the Scale Factor Vector that will be used to scale each future standard demand point:

The first two Scale Factor vector elements are the capped Current Scale Factor. The ScaleFactorSlope is used to slope the scale factor towards 1 for the remaining vector elements up to period 48. The minimum / maximum = 1 o Scale Each Standard Demand Point for the current period to period 48 to determine the predicted Demand.

Figure 17 is a schematic representation of a system, generally marked 170, according to the invention. System 170 includes reservoir or other water source 171, pumps 172 fluidly coupled to reservoir 171 , optional holding tank or reservoir 173 for receiving water from reservoir 171 through operation of pumps 172, demand points 174 for receiving water from reservoir 171 (via holding tank 173, where applicable) and outputting water depending on consumer demand, and control station 175. Control station 175 is communicatively coupled to pumps 172 so as to enable monitoring and control thereof. As would be apparent to one of skill in the art, system 170 includes a number of elements not shown in Figure 17. For example, while one reservoir 171 is shown, system 170 may include a plurality of reservoirs and control station 175 is preferably communicatively coupled to a plurality of sensors (e.g. pressure sensors) positioned around system 170 so as to enable monitoring of additional parameters of the system. Preferably, control station 175 is configured to include the novel functionality of one or more of the aforementioned aspects of the invention. Control station 175 may include or be coupled to the SCADA of a conventional water distribution system.

While having been described with reference to specific examples, the invention is not limited thereto and may readily be applied to other scenarios by one of ordinary skill in the art. Moreover, while described in relation to the pumping of water within a water distribution system, the invention may be applied to systems pumping other fluids, including gases.

Although the invention has been described by way of example and with reference to possible embodiments thereof, it is to be understood that modifications or improvements may be made thereto without departing from the spirit and scope of the invention.