The Network Synthesis Framework

Scope of the study in this area includes

i) To develop the principles of transients control using synthesis approach and to develop criteria for network controllability.

ii) To develop methodologies using optimization principles for the control of pressure surges (slow transients) by valve operations in networks using synthesis approach.

iii) To develop the methodology for transient system components design and show applications for the design of surge tanks and valve operations.

iv) To show usefulness of the developed methodologies for the control of pressure surges in controlling rapid transients in the network by valve operations.

The full accomplishment of these objectives implies the solution of various sub-tasks along the way leading to the development of reliable and efficient tools for network steady state simulation, control of pressure surges, rapid transients and transient system component design.

At all levels potential of network synthesis approach has been shown in viewing different types of network problems encountered in practice from a coherent perspective and in providing their solutions.

2.3 The Network Synthesis Framework

The framework of network synthesis approach has been derived by viewing pipe networks from system-oriented-approach. To elaborate this approach, it is necessary, first, to define the

entities related to a network system. From system-oriented-approach, a pipe network can be described in terms of components, constraints and objectives.

Components consist of pipes, hydraulic devices such as pumps, valves, surge tanks etc., reservoirs and consumer demands. Every component has a unique characteristic, which is described by a relationship between head loss and flow through it.

Constraints include the restrictions imposed on the system because of the physical construction of the components and hydraulic performance requirement. Hydraulic performance requires restrictions on pressures and flows.

Objectives encompass the distribution of source supplies to consumers as safely, securely and as economically as possible. Requirement of safety implies restriction on maximum or minimum pressures and velocities or simply minimisation of pressure and velocity changes.

Security means an assurance to meet the demands. Objective of economy is to obtain a cost optimum design or operation. This implies optimisation to ensure the best compromise between these conflicting objectives.

An arbitrary network is composed of large number of mutually interacting components.

Mathematically, all components and constraints are different kinds of boundary conditions that are bonded together and are mutually interacting. These boundary conditions may be static or time-invariant as in the case of steady state or these may be dynamic or time varying as in the case of unsteady state.

To understand the hydraulic behaviour of a network, it is necessary first to understand the relationships between physical and topological properties of these mutually interacting boundary conditions.

In a network system, some boundary conditions are known and some are unknown. Known boundary conditions are related to the known inputs in the system and the desired hydraulic behaviour. These known boundary conditions are called decision parameters or decision variables or simply specifications. Unknown boundary conditions are those, which are to be designed and are called design parameters or design variables. These unknown boundary conditions are to be designed to meet the specifications. Design of unknown boundary conditions to meet the known boundary conditions is called network synthesis.

A large and complex pipe network consists of arbitrarily distributed different kinds of known and unknown boundary conditions. Mathematical modelling of such systems in a comprehensive and physically meaningful way is neither apparent nor straightforward. The problem of solvability of these models is dependent on the manner in which design parameters and corresponding boundary specifications are distributed over the network. In other words, design parameters and decision parameters can not be put arbitrarily in a network. Distribution of these parameters must follow certain rules to guarantee a unique solution. Determination of such rules is necessary and a prerequisite for the effective modelling of these systems. Otherwise, mathematical models become ill determined.

Obviously, solvability rules are dependent upon the relationships between physical and topological properties of different kinds of boundary conditions in a network.

The first step of network synthesis approach is to develop network model for the known network data, specifications and unknown boundary conditions (see Fig. 2.1). This requires categorisation of different boundary conditions.

Second step is to check problem solvability that demands development of network solvability rules.

Third step is the mathematical formulation of a network problem and development of efficient methodologies required for the solution of a problem. Methodology may use only analysis or optimization tools or a combination of both depending upon the problem objectives. Methodology provides desired design parameters.

This study is an attempt to develop network synthesis approach for the solution of various types of network problems. Not all kinds of problems related to network analysis, design, and operation have been considered within the scope of this study. Much attention is given to steady state analysis, control of pressure surges and transient system component design.

However, application of the developed network synthesis approach has been shown in viewing the different problems from the same perspective.

This study shows that network synthesis approach finds applications not only in other water resource systems but also in other branches of engineering.

Specifications

Network Data

Network Model

Optimizer

Design of

Boundary Yes Problem No

Conditions Solvable

?

Analyser

Fig. 2.1 Framework of network synthesis

Remodelling