Use of Genetic Algorithms for Optimal Control Of Bulk Water Supply
S.I.Rodin
Department of Material Science and Mechanics

 A genetic algorithm approach is used for optimization of a pump scheduling system so as to minimize the cost of pumping over a 24-hour period. Island ring topology is used to achieve solution.

A pump scheduling system has N different pumps delivering water to a reservoir from an assumed infinite water source (Figure 1). Each pump may have its own characteristics.

The pumps can only be switched on or off.

Figure 1. City water supply.

Figure 2. Electricity tariffs through 24 hours.                          Figure 3. Water consumption through 24 hours.             

The constraint is that the reservoir level (or its capacity) L may only vary between max and min levels with given initial water level and the desired level after 24 hours.

 The objective is to minimize the cost of pumping (i.e. cost of electricity) over a 24-hour period, with pump switching changes being at hourly intervals (i.e. may only change 24 times in the 24 hour period).

Boundary conditions of the task are shown on Fig.4.

Figure 4. Boundary conditions.

 The result of the solution is the pumps scheduling program for 24 hours (or it may be any time interval) with minimum cost of pumping.

 The fitness function determines the "goodness" of a given solution based on a weighted combination of full cost of pumping and fulfillment of boundary conditions:

fitness = f (cost) * f (boundary) ,

where

f (cost) - cost of pumping;
f (boundary) - fulfillment of boundary conditions.

This solution and program for Windows may be used daily on base of real initial conditions of reservoir (sure predictions and reality may vary).

In the example is given:

1. A pump scheduling system has 4 pumps delivering water to a reservoir. Total reservoir capacity is 2500 cu m.

2. Electricity tariffs are 2.86p for peak tariff 0800 - 0200 through the day and 1.2p for off peak tariff 0200 - 0800 through the night (Fig.2).

3. Pumping capacities of the fixed speed pumps

(amount of water pumped in one hour, cu m/
 amount of electricity used in one hour, kWh):

The pumps can only be ON or OFF with pump switching changes being at hourly intervals (program also minimizes number of switches).

4.Hourly demand is shown on Fig.3.

The objective is to minimize the cost of pumping over a 24-hour period.

The results for optimal solutions with different boundary conditions are shown on Fig.5, 6, 7 (sign “$” means only currency unit and in this case it is a penny).

Results are relative to the chosen Standard = 100%(Fig.8).

Intermediate results for final solution 1 (Fig.5) during optimization process are shown on Fig.9.

Figure 5. Optimal solution 1.                                        Figure 6. Optimal solution 2.

Figure 7. Optimal solution 3.                                        Figure 8. Standard.