DAE - Differential Algebraic Equations
DMA - Distinct Metered Area - small areas (1k to 3k houses)
PDAES - Partial Differential Algebraic Equations
Phenomenological - relating to observations
PID controller - proportional-integral-derivative controller
PMA - Pressure Management Areas (smaller subnetworks of larger water networks)
PRV - Pressure Reducing Valve
Friday, 18 May 2007
Wednesday, 16 May 2007
Dynamic Modelling of pressure reducing valves
No generally accepted representation of a Pressure Reducing Valve (PRV).
Pressure control reduces background leakage/pipe bursts.
Single feed = ease of control but loss of feed if fail.
Multi feed = increase security but less well understood/easy to model.
Differential algebraic equation or PDAE (Partial DAE) describe water network dynamics.
4 models in this paper
1. Detailed phenomenological model - constructed from applying physical laws to individual elements in PRV. Model is accurate but complex - solution in larger networks/linked to transient pipe is difficult. Basis for simpler models and gold standard to compare by.
2. Simplified version of phenomological model.
3. Behavioural model formed by observations of PRV on a test rig. Simplest model - very easy to solve. Reduction in accuracy.
4. Linear model - linearise the phenomenological model about its steady state. Model independant of needle setting in PRV.
PRV - valve operated by a control loop via orifice, pilot valve and needle valve connecting loop to the control space.
Actual Outlet Pressure > Required Outlet Pressure - pilot valve closes causing increase in T-junction pressure. Control space pressure increases causing main valve to close. Reduces outlet pressure.
Inlet Pressure < Required Outlet Pressure - PRV opens and acts as a short pipe.
Outlet Pressure > Inlet Pressure - completely closes to prevent reverse flow.
PRV = system of DAEs to solve. Ease depends on size of network, type of pipe model and choice of PRV model.
Pressure control reduces background leakage/pipe bursts.
Single feed = ease of control but loss of feed if fail.
Multi feed = increase security but less well understood/easy to model.
Differential algebraic equation or PDAE (Partial DAE) describe water network dynamics.
4 models in this paper
1. Detailed phenomenological model - constructed from applying physical laws to individual elements in PRV. Model is accurate but complex - solution in larger networks/linked to transient pipe is difficult. Basis for simpler models and gold standard to compare by.
2. Simplified version of phenomological model.
3. Behavioural model formed by observations of PRV on a test rig. Simplest model - very easy to solve. Reduction in accuracy.
4. Linear model - linearise the phenomenological model about its steady state. Model independant of needle setting in PRV.
PRV - valve operated by a control loop via orifice, pilot valve and needle valve connecting loop to the control space.
Actual Outlet Pressure > Required Outlet Pressure - pilot valve closes causing increase in T-junction pressure. Control space pressure increases causing main valve to close. Reduces outlet pressure.
Inlet Pressure < Required Outlet Pressure - PRV opens and acts as a short pipe.
Outlet Pressure > Inlet Pressure - completely closes to prevent reverse flow.
PRV = system of DAEs to solve. Ease depends on size of network, type of pipe model and choice of PRV model.
Benchmarks for water network modelling
Water network, consisting of a series of nodes (connection points) takes inputs:-
Control schedules - pump, valve, source schedules.
Demands - people using water
Initial conditions - reservoir levels.
Output - heads at nodes (I presume that means how much water is in each node), flows in elements (water flow?) and of course operating costs.
Several eqns describe behaviour of water network.
Topology - connection between nodes (i.e. shape of network). Equivalent to electric circuit with one-way resistors.
Network data - value of parameters in network. Equations represent physical operation of the model. Water network equivalent to an electrical network of non-linear monotonic (one way) resistors.
Non-linear differential algebraic equation (DAE). Describes component, mass balance and energy balance equation. Jacobian of these 3 eqns is non-singular (i.e. it has an inverse)
General Data Format - standard file format for modelling packages (inc. EPANET).
Larger networks more difficult to model. Difficulty index 0-10, determines how difficult it will be to model network.
Control schedules - pump, valve, source schedules.
Demands - people using water
Initial conditions - reservoir levels.
Output - heads at nodes (I presume that means how much water is in each node), flows in elements (water flow?) and of course operating costs.
Several eqns describe behaviour of water network.
Topology - connection between nodes (i.e. shape of network). Equivalent to electric circuit with one-way resistors.
Network data - value of parameters in network. Equations represent physical operation of the model. Water network equivalent to an electrical network of non-linear monotonic (one way) resistors.
Non-linear differential algebraic equation (DAE). Describes component, mass balance and energy balance equation. Jacobian of these 3 eqns is non-singular (i.e. it has an inverse)
General Data Format - standard file format for modelling packages (inc. EPANET).
Larger networks more difficult to model. Difficulty index 0-10, determines how difficult it will be to model network.
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