CLIAMS:1. A method for optimization of water-flow in an entity water network, the method comprising:
obtaining a model of the entity water network having multiple water distribution networks, wherein each of the multiple water distribution networks comprises a set of nodes coupled through a set of pipes for flow of water of multiple water-grades, wherein the set of nodes comprises an inlet node, at least one sewage treatment node and at least one demand node, wherein each pipe of the set of pipes couples one node to another node for flow of water of one of the multiple water-grades, and wherein the inlet node is coupled to a super source node through an inlet pipe to receive water of an intake water-grade h;
determining, by a computing device, an entity water network cost function based on a water distribution network cost function for each of the multiple water distribution networks and based on an intake water cost function for each inlet pipe, wherein the water distribution network cost function is based on a cost of flow of fg(e) volume of water of a respective water-grade g through a respective pipe e for the set of pipes in the respective water distribution network, and wherein the intake water cost function is based on a cost of flow of fh(s) volume of water of the intake water-grade h through a respective inlet pipe s; and
computing, by the computing device, a value of fg(e) volume of water for each pipe in each water distribution network and a value of fh(s) volume of water for each inlet pipe to control water-flow in the each pipe in the each water distribution network based on the value of fg(e) volume of water for the respective pipe and in the each inlet pipe based on the value of fh(s) volume of water for the respective inlet pipe, wherein the computing is by minimizing the entity water network cost function.

2. The method as claimed in claim 1, wherein the entity water network cost function is minimized using a predefined linear programming solver and by subjecting the entity water network cost function to node water-flow constraints for the set of nodes in each water distribution network, wherein a node water-flow constraint for a respective node indicates that a total water-inflow across water-grades in the respective node is equal to a sum of a total water-outflow across the water-grades from the respective node, and water demands and water losses across the water-grades at the respective node.

3. The method as claimed in claim 1, wherein the entity water network cost function is minimized using a predefined linear programming solver and by subjecting the entity water network cost function to node demand constraints for the set of nodes for the multiple water-grades in each water distribution network, wherein a node demand constraint for a respective node and for a respective water-grade indicates that a water demand of the respective water-grade at the respective node is met, wherein the water demand of the respective water grade is met by water of a water-grade equivalent or higher than water of the respective water-grade.

4. The method as claimed in claim 1, wherein the entity water network cost function is minimized using a predefined linear programming solver and by subjecting the entity water network cost function to node capacity constraints for the set of nodes in each water distribution network, wherein a node capacity constraint for a respective node indicates that a total water-inflow across water-grades in the respective node is less than or equal to a total water capacity of the respective node.

5. The method as claimed in claim 1, wherein the entity water network cost function is minimized using a predefined linear programming solver and by subjecting the entity water network cost function to a water intake constraint, wherein the water intake constraint indicates that a total flow of water of the intake water-grade h in inlet pipes from the super source node to the multiple water distribution networks is less than or equal to a total water intake of the intake water-grade h for the multiple water distribution networks.

6. The method as claimed in claim 5 further comprising obtaining the total water intake of the intake water-grade h for the multiple water distribution networks, wherein the total water-intake of the intake water-grade is based on a water intake objective of an entity.

7. The method as claimed in claim 1 further comprising obtaining:
a water demand of water of each water-grade at each node in each water distribution network;
a water loss of water of each water-grade at each node in each water distribution network; and
a total water capacity of each node in each water distribution network.

8. The method as claimed in claim 1 further comprising:
obtaining a cost of flow of a unit volume of water of a respective water-grade through each pipe in each water distribution network;
obtaining a cost of flow of a unit volume of water of the intake water-grade through each inlet pipe;
formulating the water distribution network cost function for a respective water distribution network based on linear function modeling of the cost of flow of a unit volume of water through the each pipe in the respective water distribution network; and
formulating the intake water cost function for a respective inlet pipe based on linear function modeling of the cost of flow of a unit volume of water through the respective inlet pipe.

9. The method as claimed in claim 8, wherein the cost of flow of a unit volume of water through the each pipe and the each inlet pipe is an energy cost, wherein the energy cost is indicative of energy consumed in making a unit volume of water flow through the each pipe and the each inlet pipe, respectively.

10. The method as claimed in claim 8, wherein the cost of flow of a unit volume of water through the each pipe and the each inlet pipe is a carbon cost, wherein the carbon cost is indicative of carbon emission in flowing of a unit volume of water through the each pipe and the each inlet pipe, respectively.

11. The method as claimed in claim 8, wherein the cost of flow of a unit volume of water through the each pipe and the each inlet pipe is a monetary cost, wherein the monetary cost is indicative of money spent in flowing of a unit volume of water through the each pipe and the each inlet pipe, respectively.

12. A water-flow optimization system (100) comprising:
a processor (102);
entity water network modeler (112) coupled to, and executable by, the processor (102) to obtain a model of the entity water network having multiple water distribution networks, wherein each of the multiple water distribution networks comprises a set of nodes coupled through a set of pipes for flow of water of multiple water-grades, wherein the set of nodes comprises an inlet node, at least one sewage treatment node and at least one demand node, wherein each pipe of the set of pipes couples one node to another node for flow of water of one of the multiple water-grades, wherein the inlet node is coupled to a super source node through an inlet pipe to receive water of an intake water-grade h;
a cost function modeler (114) coupled to, and executable by, the processor (102) to determine an entity water network cost function based on a water distribution network cost function for each of the multiple water distribution networks and based on an intake water cost function for each inlet pipe, wherein the water distribution network cost function is based on a cost of flow of fg(e) volume of water of a respective water-grade g through a respective pipe e for the set of pipes in the respective water distribution network, and wherein the intake water cost function is based on a cost of flow of fh(s) volume of water of the intake water-grade h through a respective inlet pipe s; and
an operating point computing module (118) coupled to, and executable by, the processor (102) to compute a value of fg(e) volume of water for each pipe in each water distribution network and a value of fh(s) volume of water for each inlet pipe by minimizing the entity water network cost function, for controlling water-flow in the each pipe in the each water distribution network based on the value of fg(e) volume of water for the respective pipe and in the each inlet pipe based on the value of fh(s) volume of water for the respective inlet pipe.

13. The water-flow optimization system (100) as claimed in claim 12 further comprising a constraint modeler (116) coupled to, and executable by, the processor to formulate node water-flow constraints for the set of nodes in each water distribution network, wherein a node water-flow constraint for a respective node indicates that a total water-inflow across water-grades in the respective node is equal to a sum of a total water-outflow across the water-grades from the respective node, and water demands and water losses across the water-grades at the respective node, and wherein the entity water network cost function is minimized using a predefined linear programming solver and by subjecting the entity water network cost function to the mode water-flow constraints.

14. The water-flow optimization system (100) as claimed in claim 12 further comprising a constraint modeler (116) coupled to, and executable by, the processor to formulate node demand constraints for the set of nodes for the multiple water-grades in each water distribution network, wherein a node demand constraint for a respective node and for a respective water-grade indicates that a water demand of the respective water-grade at the respective node is met, wherein the water demand of the respective water grade is met by water of a water-grade equivalent or higher than water of the respective water-grade, and herein the entity water network cost function is minimized using a predefined linear programming solver and by subjecting the entity water network cost function to the node demand constraints.

15. The water-flow optimization system (100) as claimed in claim 12 further comprising a constraint modeler (116) coupled to, and executable by, the processor to formulate node capacity constraints for the set of nodes in each water distribution network, wherein a node capacity constraint for a respective node indicates that a total water-inflow across water-grades in the respective node is less than or equal to a total water capacity of the respective node, and wherein the entity water network cost function is minimized using a predefined linear programming solver and by subjecting the entity water network cost function to the node capacity constraints.

16. The water-flow optimization system (100) as claimed in claim 12 further comprising a constraint modeler (116) coupled to, and executable by, the processor to formulate a water intake constraint, wherein the water intake constraint indicates that a total flow of water of the intake water-grade h in inlet pipes from the super source node to the multiple water distribution networks is less than or equal to a total water intake of the intake water-grade h for the multiple water distribution networks, and wherein the entity water network cost function is minimized using a predefined linear programming solver and by subjecting the entity water network cost function to the water intake constraint.

17. The water-flow optimization system (100) as claimed in claim 16, wherein the entity water network modeler (112) obtains the total water intake of the intake water-grade h for the multiple water distribution networks, wherein the total water-intake of the intake water-grade is based on a water intake objective of an entity.

18. The water-flow optimization system (100) as claimed in claim 12, wherein the cost function modeler (114)
obtains a cost of flow of a unit volume of water of a respective water-grade through each pipe in each water distribution network;
obtains a cost of flow of a unit volume of water of the intake water-grade through each inlet pipe;
formulates the water distribution network cost function for a respective water distribution network based on linear function modeling of the cost of flow of a unit volume of water through the each pipe in the respective water distribution network; and
formulates the intake water cost function for a respective inlet pipe based on linear function modeling of the cost of flow of a unit volume of water through the respective inlet pipe.

19. The water-flow optimization system (100) as claimed in claim 18, wherein the cost of flow of a unit volume of water through the each pipe and the each inlet pipe is one of
an energy cost indicative of energy consumed in making a unit volume of water flow through the each pipe and the each inlet pipe, respectively;
a carbon cost indicative of carbon emission in flowing a unit volume of water through the each pipe and the each inlet pipe, respectively; and
a monetary cost indicative of money spent in flowing a unit volume of water through the each pipe and the each inlet pipe, respectively.

20. A non-transitory computer-readable medium comprising instructions executable by a processor to:
obtain a model of an entity water network having multiple water distribution networks, wherein each of the multiple water distribution networks comprises a set of nodes coupled through a set of pipes for flow of water of multiple water-grades, wherein the set of nodes comprises an inlet node, at least one sewage treatment node and at least one demand node, wherein each pipe of the set of pipes couples one node to another node for flow of water of one of the multiple water-grades, wherein the inlet node is coupled to a super source node through an inlet pipe to receive water of an intake water-grade h;
determine an entity water network cost function based on a water distribution network cost function for each of the multiple water distribution networks and based on an intake water cost function for each inlet pipe, wherein the water distribution network cost function is based on a cost of flow of fg(e) volume of water of a respective water-grade g through a respective pipe e for the set of pipes in the respective water distribution network, and wherein the intake water cost function is based on a cost of flow of fh(s) volume of water of the intake water-grade h through a respective inlet pipe s; and
compute a value of fg(e) volume of water for each pipe in each water distribution network and a value of fh(s) volume of water for each inlet pipe to control water-flow in the each pipe in the each water distribution network based on the value of fg(e) volume of water for the respective pipe and in the each inlet pipe based on the value of fh(s) volume of water for the respective inlet pipe, wherein the value of fg(e) and the value of fh(s) are computed by minimizing the entity water network cost function.
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