## Modeling, Optimization & Control of Hydraulic Networks

Publication: Research › Ph.D. thesis

### Abstract

Water supply systems consist of a number of pumping stations, which deliver water to the customers via pipeline networks and elevated reservoirs. A huge amount of drinking water is lost before it reaches to end-users due to the leakage in pipe networks. A cost effective solution to reduce leakage in water network is pressure management. By reducing the pressure in the water network, the leakage can be reduced significantly. Also it reduces the amount of energy consumption in water networks.

The primary purpose of this work is to develop control algorithms for pressure control in water supply systems. To have better understanding of water leakage, to control pressure and leakage effectively and for optimal design of water supply system, suitable modeling is an important prerequisite. Therefore a model with the main objective of pressure control and consequently leakage reduction is presented. The nonlinear network model is derived based on the circuit theory. A suitable projection is used to reduce the state vector and to express the model in standard state-space form. Then, the controllability of

nonlinear nonaffine hydraulic networks is studied. The Lie algebra-based controllability matrix is used to check if the network is controllable.

Afterward the pressure control problem in water supply systems is formulated as an optimal control problem. The goal is to minimize the power consumption in pumps and also to regulate the pressure drop at the end-users to a desired value. The formulated optimal control problem is non-convex. To solve the nonlinear optimal control problem, first the maximum principle is used. Subsequently the toolbox ICLOCS is used to solve the optimal control problem. In ICLOCS the nonlinear problem solver IPOPT is used.

The IPOPT uses the interior point optimization method to solve nonlinear optimal control problems. In the water supply system model, the hydraulic resistance of the valve is estimated by real data and it is considered to be a disturbance. The disturbance in our system is updated every 24 hours based on the amount of water usage by consumers every day. Model Predictive Control can handle disturbances much better compared with the other control

strategies. Therefore the pressure control problem is formulated within model predictive control framework. Because of nonlinearity which we have in both cost function and constraints, the model predictive control method could only solve the problem for a short time frame (three hours).

Solving model predictive control and optimal control problems for large-scale, nonlinear, non-convex systems generally is not trivial. There are a lot of computational prob-lems and issues such as sensitivity, feasibility and computational burden which one has to face with. To cope with these problems a static approximation is used. The steady state model of water network is derived by removing all dynamics in the system. The problem of pressure management in new system is presented in the form of nonlinear non-convex

optimization problem. The toolbox IPOPT is used to solve this optimization problem.

Water supply companies are dividing their networks into pressure zones to enable better control of leakages in their networks. Dividing the network into different pressure zones in the optimal way is a non-trivial task. The problem of dividing the pressure zones in an optimal way is studied in the last part of this Ph.D. study. To this end, the problem is formulated as an optimization problem, which minimizes the power consumption in all pumping stations and maintains the pressure at end-users bigger than some specific

values. The defined optimization problem is solved for all possible pump positions in the network and an optimal place of an extra pumping station is found.

The primary purpose of this work is to develop control algorithms for pressure control in water supply systems. To have better understanding of water leakage, to control pressure and leakage effectively and for optimal design of water supply system, suitable modeling is an important prerequisite. Therefore a model with the main objective of pressure control and consequently leakage reduction is presented. The nonlinear network model is derived based on the circuit theory. A suitable projection is used to reduce the state vector and to express the model in standard state-space form. Then, the controllability of

nonlinear nonaffine hydraulic networks is studied. The Lie algebra-based controllability matrix is used to check if the network is controllable.

Afterward the pressure control problem in water supply systems is formulated as an optimal control problem. The goal is to minimize the power consumption in pumps and also to regulate the pressure drop at the end-users to a desired value. The formulated optimal control problem is non-convex. To solve the nonlinear optimal control problem, first the maximum principle is used. Subsequently the toolbox ICLOCS is used to solve the optimal control problem. In ICLOCS the nonlinear problem solver IPOPT is used.

The IPOPT uses the interior point optimization method to solve nonlinear optimal control problems. In the water supply system model, the hydraulic resistance of the valve is estimated by real data and it is considered to be a disturbance. The disturbance in our system is updated every 24 hours based on the amount of water usage by consumers every day. Model Predictive Control can handle disturbances much better compared with the other control

strategies. Therefore the pressure control problem is formulated within model predictive control framework. Because of nonlinearity which we have in both cost function and constraints, the model predictive control method could only solve the problem for a short time frame (three hours).

Solving model predictive control and optimal control problems for large-scale, nonlinear, non-convex systems generally is not trivial. There are a lot of computational prob-lems and issues such as sensitivity, feasibility and computational burden which one has to face with. To cope with these problems a static approximation is used. The steady state model of water network is derived by removing all dynamics in the system. The problem of pressure management in new system is presented in the form of nonlinear non-convex

optimization problem. The toolbox IPOPT is used to solve this optimization problem.

Water supply companies are dividing their networks into pressure zones to enable better control of leakages in their networks. Dividing the network into different pressure zones in the optimal way is a non-trivial task. The problem of dividing the pressure zones in an optimal way is studied in the last part of this Ph.D. study. To this end, the problem is formulated as an optimization problem, which minimizes the power consumption in all pumping stations and maintains the pressure at end-users bigger than some specific

values. The defined optimization problem is solved for all possible pump positions in the network and an optimal place of an extra pumping station is found.

### Details

Water supply systems consist of a number of pumping stations, which deliver water to the customers via pipeline networks and elevated reservoirs. A huge amount of drinking water is lost before it reaches to end-users due to the leakage in pipe networks. A cost effective solution to reduce leakage in water network is pressure management. By reducing the pressure in the water network, the leakage can be reduced significantly. Also it reduces the amount of energy consumption in water networks.

The primary purpose of this work is to develop control algorithms for pressure control in water supply systems. To have better understanding of water leakage, to control pressure and leakage effectively and for optimal design of water supply system, suitable modeling is an important prerequisite. Therefore a model with the main objective of pressure control and consequently leakage reduction is presented. The nonlinear network model is derived based on the circuit theory. A suitable projection is used to reduce the state vector and to express the model in standard state-space form. Then, the controllability of

nonlinear nonaffine hydraulic networks is studied. The Lie algebra-based controllability matrix is used to check if the network is controllable.

Afterward the pressure control problem in water supply systems is formulated as an optimal control problem. The goal is to minimize the power consumption in pumps and also to regulate the pressure drop at the end-users to a desired value. The formulated optimal control problem is non-convex. To solve the nonlinear optimal control problem, first the maximum principle is used. Subsequently the toolbox ICLOCS is used to solve the optimal control problem. In ICLOCS the nonlinear problem solver IPOPT is used.

The IPOPT uses the interior point optimization method to solve nonlinear optimal control problems. In the water supply system model, the hydraulic resistance of the valve is estimated by real data and it is considered to be a disturbance. The disturbance in our system is updated every 24 hours based on the amount of water usage by consumers every day. Model Predictive Control can handle disturbances much better compared with the other control

strategies. Therefore the pressure control problem is formulated within model predictive control framework. Because of nonlinearity which we have in both cost function and constraints, the model predictive control method could only solve the problem for a short time frame (three hours).

Solving model predictive control and optimal control problems for large-scale, nonlinear, non-convex systems generally is not trivial. There are a lot of computational prob-lems and issues such as sensitivity, feasibility and computational burden which one has to face with. To cope with these problems a static approximation is used. The steady state model of water network is derived by removing all dynamics in the system. The problem of pressure management in new system is presented in the form of nonlinear non-convex

optimization problem. The toolbox IPOPT is used to solve this optimization problem.

Water supply companies are dividing their networks into pressure zones to enable better control of leakages in their networks. Dividing the network into different pressure zones in the optimal way is a non-trivial task. The problem of dividing the pressure zones in an optimal way is studied in the last part of this Ph.D. study. To this end, the problem is formulated as an optimization problem, which minimizes the power consumption in all pumping stations and maintains the pressure at end-users bigger than some specific

values. The defined optimization problem is solved for all possible pump positions in the network and an optimal place of an extra pumping station is found.

The primary purpose of this work is to develop control algorithms for pressure control in water supply systems. To have better understanding of water leakage, to control pressure and leakage effectively and for optimal design of water supply system, suitable modeling is an important prerequisite. Therefore a model with the main objective of pressure control and consequently leakage reduction is presented. The nonlinear network model is derived based on the circuit theory. A suitable projection is used to reduce the state vector and to express the model in standard state-space form. Then, the controllability of

nonlinear nonaffine hydraulic networks is studied. The Lie algebra-based controllability matrix is used to check if the network is controllable.

Afterward the pressure control problem in water supply systems is formulated as an optimal control problem. The goal is to minimize the power consumption in pumps and also to regulate the pressure drop at the end-users to a desired value. The formulated optimal control problem is non-convex. To solve the nonlinear optimal control problem, first the maximum principle is used. Subsequently the toolbox ICLOCS is used to solve the optimal control problem. In ICLOCS the nonlinear problem solver IPOPT is used.

The IPOPT uses the interior point optimization method to solve nonlinear optimal control problems. In the water supply system model, the hydraulic resistance of the valve is estimated by real data and it is considered to be a disturbance. The disturbance in our system is updated every 24 hours based on the amount of water usage by consumers every day. Model Predictive Control can handle disturbances much better compared with the other control

strategies. Therefore the pressure control problem is formulated within model predictive control framework. Because of nonlinearity which we have in both cost function and constraints, the model predictive control method could only solve the problem for a short time frame (three hours).

Solving model predictive control and optimal control problems for large-scale, nonlinear, non-convex systems generally is not trivial. There are a lot of computational prob-lems and issues such as sensitivity, feasibility and computational burden which one has to face with. To cope with these problems a static approximation is used. The steady state model of water network is derived by removing all dynamics in the system. The problem of pressure management in new system is presented in the form of nonlinear non-convex

optimization problem. The toolbox IPOPT is used to solve this optimization problem.

Water supply companies are dividing their networks into pressure zones to enable better control of leakages in their networks. Dividing the network into different pressure zones in the optimal way is a non-trivial task. The problem of dividing the pressure zones in an optimal way is studied in the last part of this Ph.D. study. To this end, the problem is formulated as an optimization problem, which minimizes the power consumption in all pumping stations and maintains the pressure at end-users bigger than some specific

values. The defined optimization problem is solved for all possible pump positions in the network and an optimal place of an extra pumping station is found.

Original language | English |
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Number of pages | 101 |
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ISBN (print) | 978-87-7152-050-7 |

State | Published - 2014 |