CA3096796A1 - System and method for control of pumps in a water distribution network - Google Patents

Abstract

Computer-implemented methods, and related computer systems and computer program products are provided for controlling operation of pumps according to "on/off' schedules. In one aspect, the method involves using pump performance curves for different "on/off' state combinations of pumps of a pumping station, to select one of the "on/off' state combinations and determine the duration for one or more of the pumps to be in an "on" state. In another aspect, the method involves detennining a new "on/off' schedule for operating a pump over a time horizon, by applying a rule set to a proposed "on/off' schedule for operating a pump over the same time horizon, and an old "on/off' schedule for operating the pump over an earlier time horizon. Output signals are generated for controlling operation of the pump according to the selected "on/off' state combination and the detennined "on" duration, and the new "on/off' schedule.

Description

SYSTEM AND METHOD FOR CONTROL OF PUMPS IN A WATER
DISTRIBUTION NETWORK
FIELD OF THE INVENTION
[0001] The present invention relates to computer-implemented methods and systems, and computer program products for controlling pumps in a water distribution network.
BACKGROUND OF THE INVENTION

[0002] A municipal potable water distribution network may include multiple pumps for pressurizing water from multiple sources to multiple demand points, interconnected by a complex pipe topology. The electrical energy for operating the pumps is a significant component of the network's operating cost. Conventionally, switching the pumps on and off is based on human decision-making or automated means, accounting for water levels and pressures, but not energy costs of operating the pumps. These conventional methods are suboptimal from the perspective of energy cost perspective, and do not respond optimally to the changing and future hydraulic state of the network. Accordingly, a need remains for technologies that automate real-time control of pumps in the network with a view to significantly improving the hydraulic control of the network and energy use.
SUMMARY OF THE INVENTION

[0003] In one aspect, the present invention comprises a first method for controlling operation of hydraulically connected pumps of a pumping station. The pumping station is operable in one of a plurality of different "on/off' state combinations, each corresponding to a Date Recue/Date Received 2020-10-22 different combination of one or more of the pumps being in an "on" state. The pumping station is subject to a pumping station flow demand, u,, and a corresponding pumping station output pressure demand, P,, that vary over a series of time steps. The method is performed by a processor and comprises the steps of:
(a) for each one of the time steps:
(i) for each one of the "on/off' state combinations, determining a pumping station output flow, Q0, for the pumping station output pressure demand, P,, based on a pump performance curve corresponding to the one of the "on/off' state combinations, wherein the pump performance curve is stored on a non-transitory computer readable medium and comprises a quantitative relationship between a pumping station output pressure, P and a pumping station flow, Q;
(ii) for each one of the "on/off' state combinations, determining a flow difference, 1 Q, - u, 1, between the determined pumping station output flow, Q0, and the pumping station flow demand, u0;
(iii) selecting one of the "on/off' state combinations, based on the determined flow difference for the one of the "on/off' state combinations being either less than the determined flow difference for at least one other one of the "on/off' state combinations, or less than a predetermined threshold flow difference;

Date Recue/Date Received 2020-10-22 (iv) for the selected one of the "on/off' state combinations, determining a duration for the corresponding combination of the one or more of the pumps being in the "on" state to be in the "on" state, for the determined pumping station output flow, Q0, to satisfy the pumping station flow demand, u0; and (b) generating at least one output signal for controlling operation of the pumps over the series of time steps, in accordance with the selected "on/off" state combinations and the determined durations.

[0004] In one embodiment of the first method, in step (a)(iii), selecting one of the "on/off"
state combinations, is based on the determined flow difference for the one of the "on/off" state combinations being less than the determined flow difference for at least one other one of the "on/off' state combinations.

[0005] In one embodiment of the first method, in step (a)(iii), selecting one of the "on/off"
state combinations, is based on the determined flow difference for the one of the "on/off" state combinations being less than the predetermined threshold flow difference.

[0006] In embodiments of the first method, step (a)(i) further comprises, for each one of the "on/off' state combinations, determining a pumping station efficiency, go, for the pumping station output pressure demand, P,, based on a pump efficiency curve corresponding to the one of the "on/off" state combinations. The pump efficiency curve is stored on the non-transitory computer readable medium and comprises a quantitative relationship between a pumping station output efficiency, ri, and a pumping station flow rate, Q. In one embodiment of such Date Recue/Date Received 2020-10-22 first method, in step (a)(iii), selecting one of the "on/off' state combinations, is further based on the determined pumping station efficiency, go, for the one of the "on/off' state combinations being greater than the determined pumping station efficiency, go, for at least one other one of the "on/off' state combinations. In another embodiment of such method, in step (a)(iii), .. selecting one of the "on/off' state combinations, is further based on the determined pumping station efficiency, rio, for the one of the "on/off' state combinations being greater than the determined pumping station efficiency, rio, for the selected one of the "on/off" state combinations for the time step preceding the one of the time steps.

[0007] In one embodiment of the first method, in step (a)(iv), for the selected one of the .. "on/off' state combinations, determining the duration is further based on a condition that the duration exceeds a predetermined threshold duration.

[0008] In another aspect, the present invention comprises a system for controlling operation of hydraulically connected pumps of the pumping station, as described above, subject to the pumping station flow demand, u0, and the corresponding pumping station output .. pressure demand, P,, that vary over the series of time steps, as described above. The system comprises a processor. The system further comprises a non-transitory computer readable medium operatively connected to the processor. The non-transitory computer readable medium stores a set of instructions executable by the processor to implement any one or more of the embodiments of the first method as described above, the pump performance curves used in the first method, and optionally, the pump efficiency curves used in embodiments of the first method.

Date Recue/Date Received 2020-10-22

[0009] In another aspect, the present invention comprises a computer program product for controlling operation of hydraulically connected pumps of the pumping station, as described above, subject to the pumping station flow demand, u,, and the corresponding pumping station output pressure demand, P,, that vary over a series of time steps, as described above. The computer program product comprises a non-transitory computer readable medium that stores a set of instructions executable by a processor to implement any one or more of the embodiments of the first method as described above, the pump performance curves used in the first method, and optionally, the pump efficiency curves used in embodiments of the first method.

[0010] In another aspect, the present invention comprises a second method for controlling operation of a pump based on an old "on/off' schedule for operating the pump over a first time horizon commencing at a first time instance, and a proposed "on/off' schedule for operating the pump over a second time horizon commencing at a second time instance subsequent to the first time instance, but within the first time horizon. The method is performed by a processor and comprises the steps of:
(a) determining a new "on/off' schedule for operating the pump over the second time horizon, wherein the determining is based on a rule set stored on a non-transitory computer readable medium, wherein the rule set comprises a rule to continue any portion of an old "on" period of the old "on/off' schedule that is after the second time instance to a proposed "on" period of the proposed "on/off' schedule", if a time elapsed from the old "on" period to the proposed "on" period is less than a predetermined threshold duration; and Date Recue/Date Received 2020-10-22 (b) generating at least one output signal for controlling operation of the pump over the second time horizon in accordance with the new "on/off' schedule.

[0011] In another aspect, the present invention comprises a system for controlling operation of the pump based on the old "on/off' schedule, and the proposed "on/off' schedule for operating, as described above. The system comprises a processor. The system further comprises a non-transitory computer readable medium operatively connected to the processor.
The non-transitory computer readable medium stores a set of instructions executable by the processor to implement the second method as described above.

[0012] In another aspect, the present invention comprises a computer program product for controlling operation of the pump based on the old "on/off' schedule, and the proposed "on/off' schedule, as described above. The computer program product comprises a non-transitory computer readable medium storing a set of instructions executable by a processor to implement the second method as described above.
BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In the drawings, which form part of the specification, like elements may be assigned like reference numerals. The drawings are not necessarily to scale, with the emphasis instead placed upon the principles of the present invention. Additionally, each of the embodiments depicted is but one of a number of possible arrangements utilizing the fundamental concepts of the present invention.

[0014] Figure lA is a schematic depiction of an embodiment of a water distribution network to which the present invention may be applied.

Date Recue/Date Received 2020-10-22

[0015] Figure 1B is a schematic depiction of an embodiment of one of the pumping stations of the water distribution network of Figure 1A.

[0016] Figure 2 is a block diagram of a pump control system of the present invention, in relation to a SCADA system and a water distribution network.

[0017] Figure 3 is a block diagram of an embodiment of the pump control system of the present invention.

[0018] Figure 4 is a flow chart of an embodiment of a pump control method of the present invention, as may be implemented by the pump control system of Figure 3.

[0019] Figure 5 is a table of an example of "on/off' state combinations for the pumps of the pumping station of Figure 1B, as may be used in the method of Figure 4.

[0020] Figures 6A, 6B and 6C are charts showing exemplary pump performance curves and combined pump efficiency curves for the "on/off' state combination "B" of Figure 5 (Figure 6A), combination "E" of Figure 5 (Figure 6B) and combination "F" of Figure 5 (Figure 6C), as may be used in the method of Figure 4.

[0021] Figure 7 is a schematic illustration of an example of two time horizons in respect to which certain steps of the method of Figure 4 are performed.

[0022] Figure 8 is a chart showing adjustment of a predicted energy price rate, as may be implemented in the method of Figure 4.

[0023] Figure 9 is a schematic illustration of an example of a proposed pump "on/off' schedule over a time horizon, as may be implemented in the method of Figure 4.

Date Recue/Date Received 2020-10-22

[0024] Figures 10A to 1OF are schematic illustrations of examples of determining new a pump "on/off' schedule for a time horizon, based on a proposed pump "on/off' schedule for the time horizon, and an old pump "on/off' schedule for a previous time horizon, as may be implemented in the method of Figure 4.
DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

[0025] Definitions.

[0026] The invention relates to a computer-implemented system and method, and a computer program product for controlling pumps in a water distribution network. Any term or expression not expressly defined herein shall have its commonly accepted definition understood by a person skilled in the art. As used herein, the following terms have the following meanings.

[0027] "Memory" refers to a non-transitory tangible medium for storing information in a format readable by a processor, and/or a set of instructions readable by a processor to implement an algorithm. Non-limiting types of memory include solid-state, optical, and magnetic computer readable media. A memory may comprise a plurality of operatively connected, physically discrete devices, despite use of the term in singular form. Instructions stored on a memory may be encoded or compiled from any suitable programming language known in the art, with non-limiting examples including Python, C, C++, Java, and MATLAB.

[0028] "Processor" refers to an electronic device that is capable of reading or processing data stored on a memory or provided in a data signal, and/or executing instructions stored on a memory to perform an algorithm. Non-limiting examples of processors include devices Date Recue/Date Received 2020-10-22 referred to as microprocessors, microcontrollers, central processing units (CPU), and digital signal processors. A processor may comprise a plurality of operatively connected, physically discrete devices, despite use of the term in singular form.

[0029] "Pump" refers to a mechanical device for pressurizing a fluid (e.g., a gas, a liquid, or a mixture of gas and liquid), which mechanical device is driven by an associated electromechanical motor that is controllable to switch the pump between an "off' state and an "on" state. In the "off" state, electrical power is not supplied to the motor.
In the "on" state, electrical power is supplied to the motor. In one embodiment, the motor may be controlled by an electrical switch or a variable frequency drive (VFD), as known in the art.

[0030] "Pumping station" refers to a plurality of pumps that are hydraulically connected together by pipework either in series and/or in parallel.

[0031] "Quantitative relationship" refers to a relationship, which can be used by a processor, to determine a value of a variable based on a value of at least one other variable.
"Based on", as used in the context, refers to determining the value of the variable either directly using the other variable (and possibly additional variables), or indirectly using a parameter derived from the other variable. Non-limiting forms of quantitative relationships include a mathematical function, a rule (e.g., in the form of a conditional "if-then-else" statement), a data point set (e.g., in the form of a lookup table or associative array), or a best-fit curve applied to a data point set. Irrespective of the form of the quantitative relationship, a quantitative relationship to determine the numeric value of a variable, )6, based on "n"
number of variables (a], az, ... an), may be symbolically represented herein by the notation: )6 =
f (al, a2,... an), where 'f denotes a function operator. The present invention is not limited by the manner in Date Recue/Date Received 2020-10-22 which a quantitative relationship is determined. For example, a quantitative relationship may be based on either one or a combination of a rational model according to theory, and empirical data.

[0032] Water distribution network.

[0033] Figure lA shows a schematic depiction of an embodiment of a potable water distribution network (100), to which the present invention may be applied. The present invention may be adapted for networks having a different topology and number of components, and different degree of complexity than shown in Figure 1A.

[0034] In this embodiment, network (100) includes sources (102, 104) and sinks (106, 108, .. 110, 112), interconnected by distribution lines (114, 116, 118) that include pumping stations (120a to 120g). Sources (102, 104) may be inputs from potable water plant or water bodies (e.g., oceans, lakes, or rivers). Sinks (106 to 112) may be spatially separated demands (e.g., residential and commercial building plumbing systems, or storage tanks or reservoirs).
Distribution lines (114 to 118) are pipes or other conduits for conveying water between the sources (102, 104) and sinks (106 to 112). Pumping stations (120a to 120g) pressurize water in distribution lines (114 to 118), and as an example, may be located at potable water plants and regional booster stations.

[0035] Each pumping station (120a to 120g) includes one or more pumps (122) (as an example, see Figure 1B discussed below) for pressurizing water in distribution lines (114 to 118). In embodiments of pumping stations (120a to 120g) having multiple pumps, the pumps (122) may be connected in series (i.e., with a common flow rate, and additive pressure) and/or Date Recue/Date Received 2020-10-22 in parallel (i.e., with an additive flow rate, and common pressure). The present invention is not limited by any particular number of pumping stations (120) or by the pumping stations (120) having any particular number or topology of pumps (122). Different pumping stations (120) may have the same or different numbers and/or topologies of pumps (122).

[0036] As a non-limiting example, Figure 1B shows a schematic depiction of pumping station (120a) shown in Figure 1A. In this example, pumping station (120a) includes three pumps (122a 122b, 122c) each of which is driven by an associated electromechanical motor (124a to 124c). Pumps (122a and 122b) are arranged in series in relation to each other, and in parallel in relation to pump (122c). Pumps (122a to 122c) may be the same or dissimilar in their performance characteristics.

[0037] Pump control system.

[0038] Figure 2 shows a block diagram of an embodiment of a computer-implemented pump control system (200) of the present invention in relation to a supervisory control and data acquisition (SCADA) system (150), and water distribution network (100).
Arrow lines indicate operative connections for communication of electronic signals and/or data, which may be implemented by wired and/or wireless data signal communication paths.
System (200) is not limited by physical proximity to the SCADA system (150) and network (100).
For example, the system (200) may be implemented by computers of a water utility operator, and/or computers operated by another party providing a remotely hosted software service delivered via a communications network including the Internet. In some embodiments, system (200) may comprise SCADA system (150) or parts thereof.

Date Recue/Date Received 2020-10-22

[0039] SCADA system (150) may include components such as sensors, remote terminal units (RTUs), programmable logic controllers (PLCs), and electronic data communication equipment, as known in the art. Components of SCADA system (150) are operatively connected to components of network (100) (e.g., valve controllers, switches, and VFDs of motors (124)). SCADA system (150) mediates sensor signals indicative of the operating state of the components of the network (100), and transmits them to system (200) as SCADA data.
For example, SCADA data may be indicative of flow rate and pressure of water through components of network (100), and operating speed and electrical power demand of motors (124) of pumps (122). In accordance with a method of the present invention, system (200) processes SCADA data and other data. In response thereto, system (200) generates output signal, mediated by the SCADA system (150), to control the switching of pumps (122) between their "on" and "off' states in accordance with an "on/off' schedule. Once the pump "on/off' schedule is determined as described below, the generation of such output signals is within the skill of the person of ordinary skill in the art, for a given SCADA system (150) of known specification.

[0040] In real-world implementation, network (100) behaves non-linearly due to phenomena such as pressure-dependent hydraulic losses in components of network (100), and speed-dependent electrical losses of motors (124). Further, network (100) may be subject to time-varying water supply at sources (102 to 104), time-varying demand at sinks (106 to 112), .. and operational constraints. Non-limiting examples of operational constraints include capacities of components of network (100), and permissible ranges of operating parameters such as minimum water pressure, minimum storage requirements at sinks (106 to 112), and minimum water quality measures such as water age, and residual chlorine content. Further still, Date Recue/Date Received 2020-10-22 electrical power for the motors (124) that drive pumps (122) may be supplied under "time-of-use" (TOU) pricing plans, wherein the price of electricity varies over time due to factors such as time of day, time of year, prevailing demand on an electrical grid, and generation sources of electricity. Given the complexity of network (100), computer implementation of the system (200) is essential for real-time automated switching of pumps (122) between their "on" and "off' states, by processing of SCADA data (and other data) and generation of control signals, without human intervention.

[0041] Figure 3 is a block diagram of system (200). System (200) includes a processor (202) and an operatively connected memory (204). As a non-limiting example, processor (202) may be a general purpose or specialized central processing unit (CPU) or server running an operating system (e.g., examples such as UnixTM, LinuxTM, or WindowsTm), and memory (204) may be a hard disk data storage device. Memory (204) stores data and instructions readable by processor (202) to execute a pump control method as described below.
Accordingly, processor (202) is specifically configured by instructions stored on memory (204) to implement the present invention. Memory (204) (i.e., a non-transitory computer readable medium) storing such instructions may be considered a computer program product of the present invention.

[0042] Optionally, system (200) includes one or more user input devices (206) (e.g., computer keyboard, mouse, or touch screen), which allow a human operator to interact with system (200) for purposes such as configuring parameters of the method implemented by the system (200). As non-limiting examples, these parameters may include aforementioned operational constraints on network (100).

Date Recue/Date Received 2020-10-22

[0043] Optionally, system (200) includes one or more display devices (208) (e.g., a computer monitor) to provide output readable by a human operator, for purposes such as monitoring the method implemented by system (200). As a non-limiting example, under control of processor (202), display device (208) may show a graphical depiction of network (100) indicating the operational "on"/"off' state of pumps (122), and pump "on/off' schedules determined in accordance with the method of the present invention.

[0044] In Figure 3, hardware components (i.e., processor (202) and memory (204)) and software components (i.e., the instructions stored on memory (204)) are conceptualized as operatively connected functional modules (209 to 222), which implement aspects of the method of the present invention as described below in relation to the method of the present invention.

[0045] Pump control method.

[0046] Figure 4 shows a flow chart of an embodiment of a pump control method (400) of the present invention that is implemented by system (200).

[0047] Step (401).

[0048] Step (401) is performed to initiate system (200). At step (401), pump model module (209) stores, in memory (204), for each of the pumping stations (120) of network (100), a set of pump performance curves and pump efficiency curves. Within each set, different pump performance curves and different efficiency curves are associated with different "on/off' state combinations of the constituent pumps of the pumping station. The present invention is not limited by the manner in which the pump performance and efficiency curves are determined.

Date Recue/Date Received 2020-10-22 For example, they may be determined based on empirical data, or a rational model, or a combination of them.

[0049] To provide an illustrative example, consider the embodiment of network (100) shown in Figure 1A. Network (100) has five pumping stations (120a to 120g).
Accordingly, five different sets of pump performance curves and pump efficiency curves are stored in memory (204), with each of the sets associated with a different one of the pumping stations (120a to 120g).

[0050] Now, consider the embodiment of pumping station (120a) shown in Figure 1B. In this example, each of pumps (122a to 122c) may be selectively switched between "off' and "on" states, independently of each other. The table of Figure 5 summarizes all the different possible "on/off' state combinations of pumps (122a to 122c). In this table, "1" denotes the pump (122) is "on" (i.e., power is supplied to its associated motor (124) to drive the pump (122)). In this table, "0" denotes that the pump (122) is "off' (i.e., power is not supplied to its associated motor (124) to drive the pump (122)). In general, for a pumping station (120) having 'n' number of pumps (122), the total number of possible combinations of on/off states is equal to (2") including the null combination in which all pumps (122) are in their "off' state. It will be appreciated, however, that any "on/off' state combination that is undesirable or impractical for any reason may be excluded from consideration. Accordingly, it will be understood that an "on/off' state combination" refers to a selection of pump(s) (122) of a pumping station (120) being in the "on" state, with any remaining pump(s) (122) of the pumping station (120) being in the "off' state.
Date Recue/Date Received 2020-10-22

[0051] Now, consider the "on/off' state combination "B" of Figure 5, in which pump (122a) is in the "on" state, while pumps (122b, 122c) are in the "off' state.
Figure 6A shows the pump performance curve (600) and pump efficiency curve (602) associated with this "on/off' state combination. The pump performance curve (600) relates the output pressure (P) (also referred to as "head") to the output flow rate (Q) of pump (122a). The pump efficiency curve (602) relates the efficiency (II) of pump (122a) to the output flow rate (Q) of pump (122b). As known in the art, pump efficiency (g) refers to the ratio of output waterpower of the pump to the input power to the pump. As known in the art, for a real (i.e., non-ideal) pump, the pump performance curve and pump efficiency curve are typically non-linear.
A best efficiency point (604) correlates to a combination of output flow rate (Q) and output pressure (P) denoted by point (606) on the pump performance curve.

[0052] Further, consider the "on/off' state combination "E" of Figure 5, in which series connected pumps (122a, 122b) are in the "on" state, while pump (122c) is in the "off' state.
Figure 6B shows the combined pump performance curve (610) and combined pump efficiency curve (612) associated with this "on/off' state combination. (Figures 6A and 6B are drawn at a common scale to permit comparison between them.) At a given pump flow rate (Q), combined pump output pressure (P) of pump performance curve (610) will be greater than that of pump performance curve (600) due to the additive pump output pressures of series connected pumps (122a, 122b). Further, combined pump efficiency curve (612) may have a different profile than pump efficiency curve (602).

[0053] Further still, consider the "on/off' state combination "F" of Figure 5, in which parallel connected pumps (122a, 122c) are in the "on" state, while pump (122b) is in the "off' Date Recue/Date Received 2020-10-22 state. Figure 6C shows the combined pump performance curve (620) and combined pump efficiency curve (622) associated with this "on/off' state combination.
(Figures 6A and 6C are drawn at a common scale to permit comparison between them.) At a given pump output pressure (P), the combined pump flow rate (Q) of pump performance curve (622) will be greater than that of pump performance curve (600) due to the additive pump flow rates of parallel connected pumps (122a, 122c). Further, combined pump efficiency curve (622) may have a different profile than pump efficiency curve (602).

[0054] In like manner, pump performance and efficiency curves associated with other "on/off' state combinations in the table of Figure 5 may be considered.
Further, in like manner, pump performance and efficiency curves associated with "on/off" state combinations for each of pumping stations (120b to 120g) may be considered.

[0055] The plurality of pump performance and efficiency curves are stored as quantitative relationships in the memory (204). For example, let the pump performance curve P = f(Q) and pump efficiency curve n = iof any single pump (122) of a pumping station (120) be .. denoted as follows:
P,= fj,(Q) and i=f(Q) Where: i is an ordinal of any of pumps 1 to N.

[0056] For two pumps, "i" and 7" operated in combination, the combined pump performance curves P = f(Q) and combined efficiency curves n = J(Q) may be noted as follows:

Date Recue/Date Received 2020-10-22 Py= f,(Q); and rbi =fi(Q) for i.NE. j , Where: "i.NE.j" denotes the condition that "i" is not equal to 7").

[0057] For three pumps "i", "j", and "k" operated in combination, the combined pump performance curves P = f,(Q) and combined efficiency curves ri = J(Q) may be noted as follows:
P,k=f(Q); and rbik =f7(Q) for i.NE.j.NE.k, k>j>i.

[0058] In general, the above notation may be expanded to any number of pumps operated in combination.

[0059] Step (402).

[0060] Step (402) is also performed to initiate system (200). At step (402), hydraulic model module (210) stores, in memory (204), a mathematical hydraulic model of network (100).
Method (400) is not limited by any particular hydraulic modelling methodology.
Minimally, however, the hydraulic model should model the hydraulic effect of operating pumping stations (120) in different "on/off' state combinations on the flow rate and pressure of water in network (100). The hydraulic model may be implemented using hydraulic simulators known in the art.
Non-limiting examples of suitable hydraulic simulators include EPANETTm (U.S.
Environmental Protection Agency), InfoWaterTM (Innovyze, Inc.); MIKE URBAN
(DHI
Water & Environment, Inc.), and WaterCADTM and WaterGEMSTm (Bentley Systems, Inc.).

Date Recue/Date Received 2020-10-22 Parameters of hydraulic model may be either "hard-coded", or re-configurable by input by a human operator using a user input device (206).

[0061] Steps (404) to (414) in general.

[0062] An object of steps (404) to (414) is to control switching of pumps (122) within each pumping station (120) in accordance with a pump "on/off' schedule, with a view to minimizing the cost of electrical energy to power the motors (124). The factors affecting the operation of pumping stations (120) are time varying. Therefore, steps (404) to (414) are performed in respect to successive "time horizons" beginning at "time instances." As an example, Figure 7 shows a schematic illustration of two successive time horizons. The upper time line shows .. 'Time Horizon no. l' beginning at 'Time Instance no. l' of 8:00 am on January 1, 2020, and ending 24 hours later at 8:00 am on January 2, 2021. The lower time line shows 'Time Horizon no. 2' beginning at 'Time Instance no. 2' of 4:00 pm on January 1, 2021, and ending 24 hours later at 4:00 pm on January 2, 2021. Steps (404) to (414) are performed in respect to the 'Time Horizon no. l', then repeated in respect to 'Time Horizon no. 2', and then repeated in respect to further time horizons (not shown) in the future. Method (400) is not limited by any particular duration of the time horizon. As non-limiting examples, the duration of the time horizon may be about 24 hours, 26 hours, 48 hours or 72 hours. The time instances may be separated by regular or irregular time intervals. Method (400) is not limited by any particular time duration between successive time instances, which may practically be limited only by the data .. processing and signal generation capabilities of system (200). As non-limiting examples, the time interval between successive time instances may be about 2 hours, or about 8 hours.

Date Recue/Date Received 2020-10-22

[0063] Step (404).

[0064] At step (404), water demand module (212) determines a predicted time-varying water demand over a time horizon at various locations within network (100), such as sinks (106 to 112). Step (404) is not limited by any particular method of determining the predicted water demand. As a non-limiting example, system (200) may determine predicted water demand based on stored quantitative relationships relating predicted water demand to variables such as historical and/or real time water demand, weather (e.g., temperature and precipitation), time of day, and water usage statistics. Data for these factors may be either received from SCADA data or other data sources, either via a communications network or input from user input device (206). The determination of the predicted water demand is within the skill of persons of ordinary skill in the art.

[0065] Step (406).

[0066] At step (406), energy price module (214) determines a predicted time-varying energy price rate over the time horizon, for energy to be supplied to motors (124) of pumps (122). Step (406) is not limited by any particular method of determining the predicted energy price rate. As a non-limiting example, system (200) may determine predicted energy price rates based on stored quantitative relationships that define energy price rates at various times of day.
As another non-limiting example, system (200) may use real-time energy price rates received from sources such as a regulating agency, which data may be received via a communications network or input from user input device (206). The determination of the predicted energy price rate is within the skill of persons of ordinary skill in the art.
Date Recue/Date Received 2020-10-22

[0067]
It is advantageous to minimize the error between the actual energy price rates, and predicted energy price rates. Accordingly, in one exemplary embodiment, step (406) involves the following sub-steps. First, step (406) determines an error between actual and predicted energy price rates at a "first time" during the time horizon. Second, step (406) determines whether the error exceeds a predetermined threshold. Third, if the error exceeds the predetermined threshold, step (406) adjusts the predicted price rate for a later "second time"
during the time horizon. This may help reduce the error in the energy price rate for the "second time" during the time horizon, when there is known to be a significant error between actual and predicted rates at the earlier "first time" during the time horizon.

[0068] Figure 8 illustrates an example of this approach. The values (ral) and (rl) are the actual and predicted energy price rates, respectively, for when step (406) is performed ¨ i.e., the "first time". The value (ra0) is the actual energy price rate at one hour before the first time.
The values (r2) and (r3) are the predicted energy price rates at 1 hour and 2 hours, respectively, in the future from the first time¨ i.e., the "second time" and the "third time".

[0069] The following conditions are evaluated to determine whether the error between the actual energy price rate (ral) and the predicted energy price rate (rl) at the "first time" exceeds predetermined thresholds, A max and A% max. (As used herein, operator "I"
denotes division.) Is 1 rl ¨ ral 1> A max? AND
(Cnd. 1) Is 1 rl ¨ ral 1/ ral > A% max?
(Cnd. 2) where:
A max is a predetermined threshold, as an absolute value; and A% max is a predetermined threshold, as a percentage value.

Date Recue/Date Received 2020-10-22

[0070]
The values of A max and A% max may be selected for an acceptable degree of error.
As a non-limiting example, A% max may be set to 10%. As a non-limiting example, A max may be set to 15 cents.

[0071]
If both conditions no. 1 and 2 (above) are 'true', then the values of (rl) and (r2) are adjusted to (rl i) and (r2 i), respectively, based on the following equations.
(As used herein, operator "*" denotes multiplication.) rl i = ral (Eqn. 1) r2 i = 4*a + 2*b + c (Eqn. 2) where:
a = (r3 -3*ral + 2*ra0)/6 (Eqn. 3) b = (9*ral ¨ 8*ra0 ¨ r3)/6 (Eqn. 4) c = ra0 (Eqn. 5)

[0072]
The values (r2 i ) and (r3 i ) are used as the determined predicted energy price rates at 1 hour, and 2 hours, respectively, from the "first time".

[0073] Step (408).

[0074]
Returning to Figure 4, at step (408) pumping station head flow optimization module (216) determines, over the time horizon, the optimal pumping station flow demand vector fi(t) and pumping station output pressure vector, P(t), required to satisfy the predicted water demand (step (404)) over the time horizon. The flow demand vector and output pressure vector are "optimal" in the sense that they correspond to a minimized total energy cost for operating Date Recue/Date Received 2020-10-22 the pumping stations (120) during the time horizon, based on the predicted energy price rates in step (406)), and based on the hydraulic model (see step (402)).

[0075]
In one embodiment, flow demand vector, 11(t), and pumping station output pressure demand vector, P (t), are determined at discrete "time steps" ¨ i.e., time intervals that make up the time horizon. Method (400) is not limited by any particular time duration of the time steps.
As a non-limiting example, each "time step" may be 15 minutes in length. Thus, if the time horizon commences at 4:00 pm (e.g., as in the case of 'Time Horizon no. 2' in Figure 4), then vectors rt(t) and P (t) may be evaluated at 4:00 pm, 4:15 pm, 4:30 pm, 4:45 pm, 5:00 pm, and so forth, until the end of the time horizon.

[0076] The pumping station flow demand vector rt(t) is a vector of water flow through each pumping station (120) over the time horizon. The components of the flow demand vector may be expressed in terms of volume, or normalized by the duration of the time step, so as to be expressed in terms of flow rate. The latter is assumed herein for convenience of discussion.
The pumping station flow demand vector rt(t) can be expressed by the following notation.
/1(0 = [u/(t) u2(t) u,(t)... ttN(t)]T
(Eqn. 6) where:
N is the number of pumping stations;
i is an ordinal of any of pumping stations 1 to N;
ui(t) is the water flow through pumping station "i" varying with time (t) over the time horizon; and T is a vector transpose operator.

Date Recue/Date Received 2020-10-22

[0077]
The value /JP) is a continuous variable, which may be subject to constraints of a minimum value u11111 and a maximum value ui , dictated by the hydraulic model.
Ili mm < < Ili max (Eqn. 7)

[0078]
The pumping station output pressure demand vector P (t) is a vector of output pressures at each pumping station (120a to 120g) over the time horizon. The pumping station flow vector P (t) may be expressed by the following notation.
P (t) = [P i(t) P2(t) . . . P ,(1) P N(1)]
(Eqn. 8) where:
N is the number of pumping stations;
i is an ordinal of any of pumping stations 1 to N;
P is the output pressure at pumping station "i" varying with time (t) over the time horizon; and T is a vector transpose operator.

[0079]
The person of ordinary skill in the art will be able to determine quantitative relationships that relate the overall energy cost of operating the pumping stations (120) to the pumping station flow demand vector, WO , and output pressure demand vector, P
(t). For example, the energy requirement for operating a particular pumping station (120) over the time horizon can be related to the flow demand vector WO and the output pressure demand vector 13(t) by a notional pump efficiency curve for the pumping station (120) in question. In this regard, it will be noted that the "on/off' state combination of the pumping station has yet to be determined; it will be subsequently determined in step (410). Therefore, as a non-limiting example, the notional pump efficiency curve for the pumping station in question may be based Date Recue/Date Received 2020-10-22 on a weighted average of a pump efficiency curves for different "on/off' state combinations, or some other aggregated basis of the constituent pumps of the pumping station. The energy cost of operating each pumping station (120) over the time step may be determined by multiplying the energy requirement by the predicted (and optionally, adjusted) energy price rate (step (406)) as well as other cost parameters such as demand charges. The overall energy cost of operating all the pumping stations may be determined by summation of their individual energy costs of each pumping station (120).

[0080] Further, the person of ordinary skill in the art will be able to apply appropriate algorithms for determining the optimal pumping station flow demand vector, fi(t), and output pressure demand vector, P(t), with a view to minimizing the overall energy cost of operating all the pumping stations during the time horizon, subject to the hydraulic model. Solvers (i.e., mathematical software) for non-linear optimization problems are known in the art. Non-limiting examples of suitable solvers include the COIN-OR Linear Program Solver (CLP) TM
and the COIN-OR Interior Point Optimizer (IPOPT) TM solver (COIN-OR
Foundation), used in conjunction with matrix solvers. Step (408) is not limited by the use of any particular solver.

[0081] Step (410).

[0082] The pumping station flow demand vector, fi(t), and the output pressure demand vector, P(t), are optimized to minimize the total overall energy cost of operating the pumping stations (120) during the time horizon. Further, the optimization is based on use of notional pump efficiency curves for the pumping stations (120). In actuality, however, the output pressure and flow rate of each pumping station (120) are interrelated and constrained by its Date Recue/Date Received 2020-10-22 pump performance curve, P = f,(Q), which depends on the "on/off' state combination of the constituent pumps (122), as discussed above in respect to step (401). As such, in respect to each pumping station (120), there may be a deviation between the pumping station's optimal flow demand vector and output pressure demand vector values [ui(t), Pi(t)]
resulting from step (408), and the pump performance curves P = f,(Q) , as discussed in respect to step (401).

[0083] Accordingly, at step (410), pump scheduling module (218) selects, for each pumping station (120), the "on/off' state combination of the constituent pumps (122) that has an associated pump performance curve, P = f,(Q), that most "closely matches"
the optimal flow demand vector and output pressure demand vector values [ui(t), P i(t)]
resulting from step (408). It will be recalled that in one embodiment the pumping station flow demand vector, fi(t), and pumping station output pressure demand vector, P(t), are determined at discrete time steps of the time horizon. Thus, the selection of the "on/off' state combinations may be performed in respect to each time step, at which the flow demand and output pressure demand are denoted as ['to, P0]. In this context, the selection of the pump performance curve that most "closely matches" ['to, P0], may be based on minimizing the difference between u0 and Qo (as determined from the pump performance curve), or based on this difference being within a set tolerance, at the optimal value of P0.

[0084] For example, referring to Figures 6A to 6C, the pumping station's optimal flow demand vector and output pressure demand vector values for a given time step are shown by the point labelled ['to, P0]. The pumping station's flow rate at output pressure P0, is denoted by QoA,,QoB, and Qoc, for pump performance curves (600, 610, 620), respectively.
The differences between uo, and Qo, at the optimal value of Po, are shown by AA, AB, and AC, for pump Date Recue/Date Received 2020-10-22 performance curves (600, 610, 620), respectively. In this example,1AAlis smaller than AB, and lAc. As such, the "on/off' state combination associated with pump performance curve (600) may be selected in preference to the "on/off' state combinations associated with pump performance curves (610, 620). Alternatively, if IAAlis smaller than the set tolerance, while IAB1 and lAc l are larger than the set tolerance, then the "on/off' state combination associated with pump performance curve (600) may be selected in preference to the "on/off' state combinations associated with pump performance curves (610, 620).

[0085] If the values IAA, IAB, and lAc l do not allow for discrimination on the foregoing bases, then the selected "on/off' state combination may correspond to that combination having the highest pump efficiency (q%), at the optimal value of P0. Alternatively, the pump efficiency may be a factor in selecting the "on/off' state combination, that is additional to IAA, IAB, and lAc. For example, suppose thatIABlis approximately equal to Ac, but the efficiency (qc%) for pump efficiency curve (622) is greater than the efficiency (qB%) for pump efficiency curve (612), at the optimal value of P,. In that case, then the "on/off' state combination associated with pump performance efficiency curve (622) may be selected in preference to the "on/off' state combination associated with pump efficiency curve (612).

[0086] In one embodiment, the selection of the "on/off' state combination may be conditional on its efficiency relative to the efficiency of the "on/off' state combination that was selected for the previous time horizon. For example, suppose that "on/off' state combination "X" is to be selected based on the foregoing criteria, and that "on/off' state combination "Y" was selected for the previous time horizon. If the efficiencies of the two "on/off' state combinations "X" and "Y" are similar (i.e., within a set tolerance), then "on/off' Date Recue/Date Received 2020-10-22 state combination "Y" may be selected instead of "on/off' state combination "X". In this manner, a greater degree of continuity in pumping station operation may be provided.

[0087] Step (411).
1L0088_1 lAt step (411), pump scheduling module (218) determines a proposed "on/off' schedule for pumps of each pumping station (120) over the time horizon, based on the "on/off' state combinations selected in step (410) for the time horizon. The "on/off' schedule is nominally referred to being as "proposed" because it is subject to revision in step (412), as described below. As used herein "on/off schedule" refers to a schedule of start time(s) and stop time(s) for each of the pump(s) (122) of the pumping station (120) that are selected to be in the "on" state. As an illustrative example, suppose that the selected "on/off"
state combination for pumping station (120a) is combination "E" of Figure 5, in which pumps (122a and 122b) are selected to be in their "on" state, while pump (122c) is selected to be in its "off' state. The proposed "on/off' schedule would determine a start time for switching pumps (122a and 122b) from their "off' states to their "on" states, and stop time for switching pumps (122a and 122b) .. to their "off' states. However, pump (122c) would invariably remain in its "off' state as defined by the "on/off' state combination.
[0089] Figure 9 is a schematic illustration of an example of a proposed "on/off' schedule for a pump over a time horizon. In this example, the time horizon in question corresponds to 'Time Horizon no. 2', as shown in the lower time line of Figure 7.
[0090] In Figure 9, the times labelled 'Proposed ON', are times at which the pump is proposed to be switched "on." The times labelled 'Proposed OFF' are times at which the pump Date Recue/Date Received 2020-10-22 is proposed to be switched "off". In the example of Figure 9, the pumps are switched "on" at the time denoted 'Proposed OW until the time denoted 'Proposed Hi'. At that time, the pump is switched "off' until the time denoted 'Proposed _0N2'. At that time, the selected pump is switched "on" until the time denoted 'Proposed OFF2'.
[0091] In general, the determination of 'Proposed ON' and 'Proposed OFF' are determined to satisfy the flow requirements of the optimal flow demand vector values, ui(t). However, in one embodiment of step (411), the determination of 'Proposed ON' and 'Proposed OFF' are subject to additional conditions of 'MIN ON TIME' and 'MIN OFF TIIVIE' as described in the below examples.
[0092] Referring to Figure 9, suppose that the value of 'Proposed 01\11' is determined by the flow requirements of the optimal flow demand vector values, ui(t). For example, that the u,(t) is null until 4:30 pm, and becomes non-null at that time. Thus, 'Proposed 01\11' is set to 4:30 pm.
[0093]
The value of 'Proposed OFF can be determined to satisfy the requirements of the optimal flow demand vector values, ui(t), but subject to condition no. 3 of 'MIN ON TIIVIE' as below.
If lu0/Q0]1* At' >= 'MIN ON TIME':
(Cnd. 3) then: 'Proposed OFF1' = 'Proposed 01\11' + [u0/Q0]i * At;
(Eqn. 9a) else: 'Proposed OFF1' = 'Proposed 01\11' + 'MIN ON TIIVIE' (Eqn. 9b) Where:

Date Recue/Date Received 2020-10-22 Q, is the pump flow rate determined from the pump performance curve, P =f(Q) at the optimal value of P, for the selected "on/off' state combination; and At is the duration of the time step of the time horizon.
[0094] The parameter 'MIN ON TIME' is a predetermined minimum time duration that the pump must remain "on" before being switched "off'. This parameter prevents the pump from being switched "off' too soon after being switched "on". This avoids abrupt transitions that may damage the pump or other components of network (100). As a non-limiting example, 'MIN ON TIME' may be set to 30 minutes.
[0095] It will be appreciated that the quantity lu0/Q0] * At' in condition 3 (above) corresponds to the duration required to provide the required flow demand volume, u0, over the time step of the time horizon. It will be noted that the quantity Tu0/Q0] *
At' will be less than the duration of the time step, At, if Q, > u0, such as shown in the Example of Figure 6A.
Conversely, the quantity Tu0/Q0] * At' will be greater than the duration of the time step, At, if Q, <u0. In this latter case, any deficiency in the flow volume for a particular time step of the time horizon is added to the next time step of the time horizon. If condition no. 3 evaluates 'true', then equation no. 9a adds this duration to the proposed start time 'Proposed ON1'.
Conversely, if condition no. 3 evaluates 'false', then equation no. 9b adds 'MIN ON TIME' to the proposed start time 'Proposed ON1'. In either case, the above approach enforces the condition 'Proposed OFF1' - 'Proposed ONi' >= 'MIN ON TIME".
Date Recue/Date Received 2020-10-22 [0096]
It will also be noted that the quantity luo/Q0]i * At' is a continuous quantity. That is, the quantity may take on any multiple or fractional value of 'At', without the multiple or fractional value being restricted to an integer. It follows that switching the pumps "on" and "off' is not restricted to discrete time instances, even though the flow demand vector, WO, and pumping station output pressure vector, P(t), may have been evaluated in respect to discrete time instances. Accordingly, the present invention advantageously allows for control of the pumps over a continuous time domain.
[0097]
Continuing with the example, suppose that 'Proposed Hi' is determined to be 5:20 pm. The value of 'Proposed _0N2' is determined by the flow requirements of the of the optimal flow vector values, /JP), but subject to condition no. 4 of 'MIN OFF
TEVIE' as below.
'Proposed 0N2' >= 'Proposed OM + 'MIN OFF TEVIE' (Cnd. 4) [0098]
The parameter 'MIN OFF TEVIE' is a predetermined minimum time duration that the pump must remain "off' before being switched "on". This parameter prevents the pump from being switched "on" too soon after being switched "off'. This avoids abrupt transitions that may damage the pump or other components of network (100). As a non-limiting example, 'MIN OFF TEVIE' may be set to 30 minutes. The values of 'MIN OFF TEVIE' and 'MIN ON TEVIE' may be the same as or different from each other.
[0099]
Continuing with the example, let one suppose that the flow requirements of the optimal flow demand vector values, /JP) require 'Proposed _0N2' to be 5:30 pm.
Condition no.
4 above, however, requires 'Proposed _0N2' to be at least 'MIN OFF TEVIE' (30 minutes) past Date Recue/Date Received 2020-10-22 5:20 pm. Thus, step (411) may determine 'Proposed _0N2' to be 5:50 pm, and may then advance 'Proposed 0N2' to the next time step at 6:00 pm, as shown in Figure 9.
[00100] The value of the 'Proposed OFF2' can then be determined with reference to 'Proposed 0N2' in an analogous manner, with respect to condition no. 3 and equations 9a or .. 9b, as above, but applied in respect to the optimal flow demand vector and output pressure demand vector values at the applicable time step, lu,, P0]2' . Let one suppose that the flow requirements of the optimal flow demand vector value require 'Proposed OFF2' to be 5:45 pm.
Condition no. 3 above, however, requires 'Proposed OFF2' to be at least 'MIN
ON TEVIE' (30 minutes) after 'Proposed _0N2' (6:00 pm). Thus, step (411) determines 'Proposed OFF2' to be 6:30 pm, as shown in Figure 9. Further proposed "on" and "off' times, if any, of each pump can be determined in the above manner.
[00101] Step (412).
[00102] The proposed pump "on/off' schedule resulting from step (411) is determined with respect to a finite time horizon. In one embodiment, the time horizon overlaps with the time horizon with a previous iteration of steps (404) to (414). Referring to Figure 7, for example, it will be noted that 'Time Horizon no. 2' commences within 'Time Horizon no. F.
[00103] It is possible that the proposed pump "on/off' schedule for 'Time Horizon no. 2' is inconsistent with the "old" pump "on/off' schedule previous 'Time Horizon no.
1." For example, the proposed "on/off' schedule may require the pump to be "on", even though an .. "old" pump "on/off' schedule determined for 'Time Horizon no. l', by previous performance of steps (404) to (414) required the pump to be "off', or vice versa. In a pumping station (120) Date Recue/Date Received 2020-10-22 with multiple pumps (122), simultaneously turning "on" or "off' multiple pumps (122) at the beginning of the 'Time Horizon no. 2', can result in an abrupt physical transition that may damage the pumping station (120) or components of network (100).
[00104] To address this problem, at optional step (412), pump schedule transitioning module (220) determines a "new" pump schedule. This determination is based on the "old"
pump schedule determined at a previous performance of steps (404) to (414) for a previous time horizon, the "proposed" pump schedule determined at the present iteration of step (411) for the current time horizon under consideration, and a rules set. This transitioning may help to "mesh" the proposed "on/off' schedule and the old "on/off', and thus help to avoid abrupt changes to the water distribution network caused by switching "on" or "off' a large number of pumps simultaneously at the beginning of the time horizon.
[00105] Figures 10A to 10E illustrate an exemplary application of the rule set to determine the "new" pump schedule. These examples continue the example of Figure 7. For each of these Figures, the horizontal axes indicate progress of time from left to right. The rectangular bars indicate the extent of an "on" period of a pump "on/off' schedule.
[00106] The topmost "on/off' schedule, labelled "OLD", is determined by a previous iteration of steps (404 to 414) for the earlier time horizon 'Time Horizon no.
F. The pump is switched "off' according to this old "on/off' schedule at the time denoted 'Old OFF'.
[00107] The middle "on/off' schedule, labelled 'PROPOSED', is determined by the current iteration of step (411) for 'Time Horizon no. 2' under consideration. The 'Acceptance time' is Date Recue/Date Received 2020-10-22 the beginning of this time horizon (e.g., 4:00 pm). The pump is proposed to be switched "on"
and "off' at the times denoted 'Proposed ON' and 'Proposed OFF', respectively.
[00108] The lowermost "on/off' schedule, labelled "NEW, is determined in step (412), based on the old "on/off' schedule, the proposed "on/off' schedule, and parameter '% of MIN OFF TIIVIE.' The parameter '% of MIN OFF TIIVIE' is a predetermined threshold duration that is used to avoid an excessively short time gap between when a pump would turn "off' in accordance with the old "on/off' schedule, and when the pump would turn "on" in accordance with the proposed "on/off' schedule. (The application of '% of MIN
OFF TIIVIE' to this effect is illustrated in the example of Figure 10B, below.) In this example '% of MIN OFF TIME' is set to a percentage of the parameter 'MIN OFF TIME' used in step (411).
As a non-limiting example, if 'MIN OFF TIME' is 30 minutes, '% of MIN OFF
TIME' may be set to 50 % of this value, or 15 minutes. In other embodiments, the predetermined threshold time duration used in step (412) may be pre-determined independently of 'MIN
OFF TIIVIE' used in step (411).
[00109] Figure 10A illustrates the case where the 'Old OFF' time is later than the 'Proposed ON' time. In this case, the rule set determines the "on" period of the new schedule by continuing the "on" period of the "old" pump schedule to the end of the "on" period of the "proposed" pump schedule.
[00110] Figures 10B and 10C illustrate cases where the 'Old OFF' time is later than the 'Acceptance time', but earlier than the 'Proposed ON' time.

Date Recue/Date Received 2020-10-22 [00111] In the case of Figure 10B, the difference between the 'Proposed ON' time and the 'Old OFF' time is less than or equal to "% of MIN OFF TIIVIE' (e.g., 15 minutes). In order to avoid turning the pump off for this short period of time, the rule set determines the "on" period of the new schedule to continue the "on" period of the old schedule until the end of the "on"
period of the proposed schedule.
[00112] In the case of Figure 10C, the difference between the 'Proposed ON' time and the 'Old OFF' time is greater than "% of MIN OFF TIME' (e.g., 15 minutes), and as such, there is no concern about turning the pump "off' for this period of time. Thus, the rule set determines the "on" period for the new schedule by two parts. The first part is the "on"
period under the "old" pump schedule truncated to the 'Acceptance time'. The second part is the "on" period of the "proposed" pump schedule. In effect, the "proposed" "on/off' schedule take precedence over the "old" pump schedule.
[00113] Figures 10D, 10E, and 1OF illustrate cases where the 'Old OFF' time is earlier than the 'Acceptance time', and thus necessarily earlier than the 'Proposed ON' time'.
[00114] In the case of Figure 10D, the time difference between the 'Proposed ON' time and the 'Acceptance time' is greater than '% of MIN OFF TIIVIE'. Thus, the rule set determines the "on" period for the "new" schedule by two parts. The first part is the "on"
period under the old pump schedule extended to the 'Acceptance time'. (In actuality, however, there is no practical consequence, because the pump should already switch "off' under the old schedule. The new schedule will generate a redundant signal to switch the pump "off' at the 'Acceptance time'.) The second part is the "on" period of the proposed schedule.
Date Recue/Date Received 2020-10-22 [00115] In the case of Figure 10E, the time difference between the 'Proposed ON' time and the 'Old OFF' time is greater than '% of MIN OFF TEVIE'. Thus, the rule set determines the "on" period for the new pump schedule is made of two parts. The first part is the "on" period under the old pump schedule without modification. The second part is the "on"
period of the proposed pump schedule without modification.
[00116] In the case of Figure 10F, the time difference between the 'Proposed ON' time and the 'Old OFF' time is less than or equal to '% of MIN OFF TEVIE'. In this case, the rule set allows the "off' time of the pump to be less than '% of MIN OFF TEVIE'. Thus, the rule set determines the "on" period for the new pump schedule is made of two parts. The first part is the "on" period under the old pump schedule without modification. The second part is the "on"
period of the proposed pump schedule without modification.
[00117] In some embodiments of the method, step (412) may require a human operator to accept the "new" pump schedule before the method continues to any subsequent step of the method. As a non-limiting example, the method may cause a display device (208) to display a graphical depiction of the "new" pump schedule, and display a graphical user interface with selectable "buttons" for the human operator to provide an indication of whether the human operator declines or accepts the "new" pump schedule. If the method receives an indication that the human operator accepts the "new" pump schedule, then the method continues to step (414). Otherwise, the method may provide an alternate process for determining the "new"
pump schedule, and then continue to step (414). As non-limiting examples, the alternate process may continue using the "old" pump schedule, or allow the human operator to input information that defines the "new" pump schedule, and then continue to step (414).

Date Recue/Date Received 2020-10-22 [00118] Step (414).
[00119] Returning to Figure 4, at step (414), control signal module (222) generates an output signal to SCADA system (150) for controlling the pumps. The output signal is configured to cause the SCADA system (150) to control (e.g., by electrical switching) the electromechanical motors (124) so that their respective pumps (122) operate in accordance with the new pump "on/off' schedule as determined in step (412).
[00120] After completion of step (414), method (400) returns to step (404) and repeats step (404) to step (414) at a subsequent time, in respect to a subsequent time horizon.
[00121] Interpretation.
[00122] Aspects of the present invention may be described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions.
These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.
[00123] The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer Date Recue/Date Received 2020-10-22 program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures.
For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved.
It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
[00124] The corresponding structures, materials, acts, and equivalents of all means or steps plus function elements in the claims appended to this specification are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed.
[00125] References in the specification to "one embodiment", "an embodiment", etc., indicate that the embodiment described may include a particular aspect, feature, structure, or characteristic, but not every embodiment necessarily includes that aspect, feature, structure, or characteristic. Moreover, such phrases may, but do not necessarily, refer to the same embodiment referred to in other portions of the specification. Further, when a particular aspect, feature, structure, or characteristic is described in connection with an embodiment, it is within the knowledge of one skilled in the art to affect or connect such module, aspect, feature, Date Recue/Date Received 2020-10-22 structure, or characteristic with other embodiments, whether or not explicitly described. In other words, any module, element or feature may be combined with any other element or feature in different embodiments, unless there is an obvious or inherent incompatibility, or it is specifically excluded.
[00126] It is further noted that the claims may be drafted to exclude any optional element.
As such, this statement is intended to serve as antecedent basis for the use of exclusive terminology, such as "solely," "only," and the like, in connection with the recitation of claim elements or use of a "negative" limitation. The terms "preferably,"
"preferred," "prefer,"
"optionally," "may," and similar terms are used to indicate that an item, condition or step being referred to is an optional (not required) feature of the invention.
[00127] The singular forms "a," "an," and "the" include the plural reference unless the context clearly dictates otherwise. The term "and/or" means any one of the items, any combination of the items, or all of the items with which this term is associated. The phrase "one or more" is readily understood by one of skill in the art, particularly when read in context of its usage.
[00128] The term "about" can refer to a variation of 5%, 10%, 20%, or 25% of the value specified. For example, "about 50" percent can in some embodiments carry a variation from 45 to 55 percent. For integer ranges, the term "about" can include one or two integers greater than and/or less than a recited integer at each end of the range.
Unless indicated otherwise herein, the term "about" is intended to include values and ranges proximate to the recited range that are equivalent in terms of the functionality of the composition, or the embodiment.

Date Recue/Date Received 2020-10-22 [00129] As will be understood by one skilled in the art, for any and all purposes, particularly in terms of providing a written description, all ranges recited herein also encompass any and all possible sub-ranges and combinations of sub-ranges thereof, as well as the individual values making up the range, particularly integer values. A recited range includes each specific value, integer, decimal, or identity within the range. Any listed range can be easily recognized as sufficiently describing and enabling the same range being broken down into at least equal halves, thirds, quarters, fifths, or tenths. As a non-limiting example, each range discussed herein can be readily broken down into a lower third, middle third and upper third, etc.
[00130] As will also be understood by one skilled in the art, all language such as "up to", "at least", "greater than", "less than", "more than", "or more", and the like, include the number recited and such terms refer to ranges that can be subsequently broken down into sub-ranges as discussed above. In the same manner, all ratios recited herein also include all sub-ratios falling within the broader ratio.
REFERENCES
[00131] The following references are indicative of the level of skill of one skilled in the art.
[00132] Blaszczyk, J & Karbowski, Andrzej & Krawczyk, K & Malinowski, Krzysztof &
Allidina, A. (2012). Optimal pump scheduling for large scale water transmission system by linear programming. 2012. 91-96.
[00133] Blaszczyk, J., Malinowski, K., and Allidina, A. (2013). Optimal pump scheduling by non-linear programming for large scale water transmission system. In Callaos, N., Gill, T., and Sanchez, B., editors, Proceedings of The International Conference on Complexity, Date Recue/Date Received 2020-10-22 Cybernetics, and Informing Science and Engineering (CCISE 2013), June 30 -July 6, 2013, Porto, Portugal, pages 7-12, Winter Garden, Florida, U.S.A. International Institute of Informatics and Systemics (IIIS), Member of the International Federation for System Research (IFSR).
[00134] Blaszczyk, Jacek & Malinowski, Krzysztof & Allidina, Alnoor. (2014).
Optimal Pump Scheduling By NLP For Large Scale Water Transmission System. Proceedings -28th European Conference on Modelling and Simulation, ECMS 2014. 501-507.
10.7148/2014-0501 .

Date Recue/Date Received 2020-10-22

Claims (21)

The claimed invention is:

1. A method for controlling operation of hydraulically connected pumps of a pumping station, wherein the pumping station is operable in one of a plurality of different "on/off' state combinations, each corresponding to a different combination of one or more of the pumps being in an "on" state, and wherein the pumping station is subject to a pumping station flow demand, u0, and a corresponding pumping station output pressure demand, P,, that vary over a series of time steps, the method performed by a processor and comprising the steps of:
(a) for each one of the time steps:
(i) for each one of the "on/off' state combinations, determining a pumping station output flow, Q0, for the pumping station output pressure demand, P,, based on a pump perfomiance curve corresponding to the one of the "on/off' state combinations, wherein the pump performance curve is stored on a non-transitory computer readable medium and comprises a quantitative relationship between a pumping station output pressure, P, and a pumping station flow, Q;
(ii) for each one of the "on/off' state combinations, determining a flow difference, 1Q, - u01, between the determined pumping station output flow, Q0, and the pumping station flow demand, u0;

Date Recue/Date Received 2020-10-22 (iii) selecting one of the "on/off" state combinations, based on the determined flow difference for the one of the "on/off' state combinations being either less than the determined flow difference for at least one other one of the "on/off' state combinations, or less than a predetermined threshold flow difference;
(iv) for the selected one of the "on/off' state combinations, determining a duration for the corresponding combination of the one or more of the pumps being in the "on" state to be in the "on" state, for the determined pumping station output flow, Q0, to satisfy the pumping station flow demand, u0; and (b) generating at least one output signal for controlling operation of the pumps over the series of time steps, in accordance with the selected "on/off' state combinations and the determined durations.

2. The method of claim 1, wherein in step (a)(iii), selecting one of the "on/off' state combinations, is based on the determined flow difference for the one of the "on/off' state combinations being less than the determined flow difference for at least one other one of the "on/off' state combinations.

3. The method of claim 1, wherein in step (a)(iii), selecting one of the "on/off' state combinations, is based on the determined flow difference for the one of the "on/off' state combinations being less than the predetermined threshold flow difference.

Date Recue/Date Received 2020-10-22

4. The method of claim 1, wherein:
step (a)(i) further comprises, for each one of the "on/off' state combinations, determining a pumping station efficiency, Igo, for the pumping station output pressure demand, P,, based on a pump efficiency curve corresponding to the one of the "on/off' state combinations, wherein the pump efficiency curve is stored on the non-transitory computer readable medium and comprises a quantitative relationship between a pumping station output efficiency, r 1, and a pumping station flow rate, Q;
and in step (a)(iii), selecting one of the "on/off' state combinations, is further based on the determined pumping station efficiency, Igo, for the one of the "on/off' state combinations being greater than the determined pumping station efficiency, Igo, for at least one other one of the "on/off' state combinations.

5. The method of claim 1, wherein:
step (a)(i) further comprises, for each one of the "on/off' state combinations, determining a pumping station efficiency, Igo, for the pumping station output pressure demand, P,, based on a pump efficiency curve corresponding to the one of the "on/off' state combinations, wherein the pump efficiency curve is stored on the non-transitory computer readable medium and comprises a quantitative relationship between a pumping station output efficiency, g , and a pumping station flow rate, Q;
and Date Recue/Date Received 2020-10-22 in step (a)(iii), selecting one of the "on/off" state combinations, is further based on the determined pumping station efficiency, Igo, for the one of the "on/off" state combinations being greater than the determined pumping station efficiency, Igo, for the selected one of the "on/off' state combinations for the time step preceding the one of the time steps.

6. The method of claim 1, wherein in step (a)(iv), for the selected one of the "on/off' state combinations, determining the duration is further based on a condition that the duration exceeds a predetermined threshold duration.

7. A system for controlling operation of hydraulically connected pumps of a pumping station, wherein the pumping station is operable in one of a plurality of different "on/off' state combinations, each corresponding to a different combination of one or more of the pumps being in an "on" state, and wherein the pumping station is subject to a pumping station flow demand, u,, and a corresponding pumping station output pressure demand, P,, that vary over a series of time steps, the system comprising a processor; and a non-transitory computer readable medium operatively connected to the processor, and storing a set of instructions executable by the processor to implement a method comprising the steps of:
(a) for each one of the time steps:
Date Recue/Date Received 2020-10-22 (i) for each one of the "on/off' state combinations, determining a pumping station output flow, Q0, for the pumping station output pressure demand, Po, based on a pump performance curve corresponding to the one of the "on/off' state combinations, wherein the pump performance curve is stored on a non-transitory computer readable medium and comprises a quantitative relationship between a pumping station output pressure, P, and a pumping station flow, Q;
(ii) for each one of the "on/off' state combinations, determining a flow difference,1 Q, - u, 1, between the determined pumping station output flow, Q0, and the pumping station flow demand, u0;
(iii) selecting one of the "on/off' state combinations, based on the determined flow difference for the one of the "on/off' state combinations being either less than the determined flow difference for at least one other one of the "on/off' state combinations, or less than a predetermined threshold flow difference;
(iv) for the selected one of the "on/off' state combinations, determining a duration for the corresponding combination of the one or more of the pumps being in the "on" state to be in the "on" state, for the determined pumping station output flow, Q0, to satisfy the pumping station flow demand, u0; and Date Recue/Date Received 2020-10-22 (b) generating at least one output signal for controlling operation of the pumps over the series of time steps, in accordance with the selected "on/off" state combinations and the determined durations.

8. The system of claim 7, wherein in step (a)(iii), selecting one of the "on/off" state combinations, is based on the determined flow difference for the one of the "on/off"
state combinations being less than the determined flow difference for at least one other one of the "on/off" state combinations.

9. The system of claim 7, wherein in step (a)(iii), selecting one of the "on/off" state combinations, is based on the determined flow difference for the one of the "on/off"
state combinations being less than the predetermined threshold flow difference.

10. The system of claim 7, wherein:
step (a)(i) further comprises, for each one of the "on/off' state combinations, determining a pumping station efficiency, rio, for the pumping station output pressure demand, Po, based on a pump efficiency curve corresponding to the one of the "on/off' state combinations, wherein the pump efficiency curve is stored on the non-transitory computer readable medium and comprises a quantitative relationship between a pumping station output efficiency, ri, and a pumping station flow rate, Q;
and in step (a)(iii), selecting one of the "on/off" state combinations, is further based on the determined pumping station efficiency, rio, for the one of the "on/off" state Date Recue/Date Received 2020-10-22 combinations being greater than the determined pumping station efficiency, Igo, for at least one other one of the "on/off' state combinations.

11. The system of claim 7, wherein:
step (a)(i) further comprises, for each one of the "on/off' state combinations, determining a pumping station efficiency, Igo, for the pumping station output pressure demand, P,, based on a pump efficiency curve corresponding to the one of the "on/off' state combinations, wherein the pump efficiency curve is stored on the non-transitory computer readable medium and comprises a quantitative relationship between a pumping station output efficiency, II, and a pumping station flow rate, Q;
and in step (a)(iii), selecting one of the "on/off' state combinations, is further based on the determined pumping station efficiency, Igo, for the one of the "on/off' state combinations being greater than the determined pumping station efficiency, Igo, for the selected one of the "on/off' state combinations for the time step preceding the one of the time steps.

12. The system of claim 7, wherein in step (a)(iv), for the selected one of the "on/off' state combinations, determining the duration is further based on a condition that the duration exceeds a predetermined threshold duration.

13. A computer program product for controlling operation of hydraulically connected pumps of a pumping station, wherein the pumping station is operable in one of a plurality of different "on/off' state combinations, each corresponding to a different Date Recue/Date Received 2020-10-22 combination of one or more of the pumps being in an "on" state, and wherein the pumping station is subject to a pumping station flow demand, u0, and a corresponding pumping station output pressure demand, P,, that vary over a series of time steps, the computer program product comprising a non-transitory computer readable medium storing a set of instructions executable by a processor to implement a method comprising the steps of:
(a) for each one of the time steps:
(i) for each one of the "on/off' state combinations, determining a pumping station output flow, Q0, for the pumping station output pressure demand, P,, based on a pump perfomiance curve corresponding to the one of the "on/off' state combinations, wherein the pump performance curve is stored on the non-transitory computer readable medium and comprises a quantitative relationship between a pumping station output pressure, P, and a pumping station flow, Q;
(ii) for each one of the "on/off' state combinations, determining a flow difference,1Q, - u01, between the determined pumping station output flow, Q0, and the pumping station flow demand, u0;
(iii) selecting one of the "on/off' state combinations, based on the determined flow difference for the one of the "on/off' state combinations being either less than the determined flow difference for Date Recue/Date Received 2020-10-22 at least one other one of the "on/off' state combinations, or less than a predetermined threshold flow difference;
(iv) for the selected one of the "on/off' state combinations, determining a duration for the corresponding combination of the one or more of the pumps being in the "on" state to be in the "on" state, for the determined pumping station output flow, Q0, to satisfy the pumping station flow demand, u0; and (b) generating at least one output signal for controlling operation of the pumps over the series of time steps, in accordance with the selected "on/off' state combinations and the determined durations.

14. The computer program product of claim 13, wherein in step (a)(iii), selecting one of the "on/off' state combinations, is based on the determined flow difference for the one of the "on/off' state combinations being less than the determined flow difference for at least one other one of the "on/off' state combinations.

15. The computer program product of claim 13, wherein in step (a)(iii), selecting one of the "on/off' state combinations, is based on the determined flow difference for the one of the "on/off' state combinations being less than the predetermined threshold flow difference.
Date Recue/Date Received 2020-10-22

16. The computer program product of claim 13, wherein:
step (a)(i) further comprises, for each one of the "on/off' state combinations, determining a pumping station efficiency, Igo, for the pumping station output pressure demand, P,, based on a pump efficiency curve corresponding to the one of the "on/off' state combinations, wherein the pump efficiency curve is stored on the non-transitory computer readable medium and comprises a quantitative relationship between a pumping station output efficiency, r 1, and a pumping station flow rate, Q;
and in step (a)(iii), selecting one of the "on/off' state combinations, is further based on the determined pumping station efficiency, Igo, for the one of the "on/off' state combinations being greater than the determined pumping station efficiency, Igo, for at least one other one of the "on/off' state combinations.

17. The computer program product of claim 13, wherein:
step (a)(i) further comprises, for each one of the "on/off' state combinations, determining a pumping station efficiency, Igo, for the pumping station output pressure demand, P,, based on a pump efficiency curve corresponding to the one of the "on/off' state combinations, wherein the pump efficiency curve is stored on the non-transitory computer readable medium and comprises a quantitative relationship between a pumping station output efficiency, g , and a pumping station flow rate, Q;
and Date Recue/Date Received 2020-10-22 in step (a)(iii), selecting one of the "on/off" state combinations, is further based on the determined pumping station efficiency, Igo, for the one of the "on/off" state combinations being greater than the determined pumping station efficiency, 17,, for the selected one of the "on/off' state combinations for the time step preceding the one of the time steps.

18. The computer program product of claim 13, wherein in step (a)(iv), for the selected one of the "on/off' state combinations, determining the duration is further based on a condition that the duration exceeds a predetermined threshold duration.

19. A method for controlling operation of a pump based on an old "on/off' schedule for operating the pump over a first time horizon commencing at a first time instance, and a proposed "on/off' schedule for operating the pump over a second time horizon commencing at a second time instance subsequent to the first time instance, but within the first time horizon, the method performed by a processor and comprising the steps of:
(a) determining a new "on/off' schedule for operating the pump over the second time horizon, wherein the determining is based on a rule set stored on a non-transitory computer readable medium, wherein the rule set comprises a rule to continue any portion of an old "on" period of the old "on/off' schedule that is after the second time instance to a proposed "on" period of the proposed "on/off' schedule", if a time elapsed from the old "on" period to the proposed "on" period is less than a predetermined threshold duration; and Date Recue/Date Received 2020-10-22 (b) generating at least one output signal for controlling operation of the pump over the second time horizon in accordance with the new "on/off' schedule.

20. A system for controlling operation of a pump based on an old "on/off' schedule for operating the pump over a first time horizon commencing at a first time instance, and a proposed "on/off' schedule for operating the pump over a second time horizon commencing at a second time instance subsequent to the first time instance, but within the first time horizon, the system comprising:
a processor; and a non-transitory computer-readable medium storing a set of instructions readable by the processor to implement a method comprising the steps of:
(a) detennining a new "on/off' schedule for operating the pump over the second time horizon, wherein the determining is based on a rule set stored in the non-transitory computer readable medium, wherein the rule set comprises a rule to continue any portion of an old "on" period of the old "on/off' schedule that is after the second time instance to a proposed "on" period of the proposed "on/off' schedule", if a time elapsed from the old "on" period to the proposed "on" period is less than a predetermined threshold duration; and (b) generating at least one output signal for controlling operation of the pump over the second time horizon in accordance with the new "on/off' schedule.

Date Recue/Date Received 2020-10-22

21. A computer program product for controlling operation of a pump based on an old "on/off' schedule for operating the pump over a first time horizon commencing at a first time instance, and a proposed "on/off' schedule for operating the pump over a second time horizon commencing at a second time instance subsequent to the first time instance, but within the first time horizon, the computer program product comprising a non-transitory computer readable medium storing a set of instructions executable by a processor to implement a method comprising the steps of:
(a) detennining a new "on/off' schedule for operating the pump over the second time horizon, wherein the determining is based on a rule set stored on the non-transitory computer readable medium, the rule set comprising a first rule to continue any portion of an old "on" period of the old "on/off' schedule that is after the second time instance to a proposed "on" period of the proposed "on/off' schedule", if a time elapsed from the old "on" period to the proposed "on" period is less than a predetermined threshold duration; and (b) generating at least one control signal for operating the pump over the second time horizon in accordance with the new "on/off' schedule.

Date Recue/Date Received 2020-10-22