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“I enjoyed interacting with the Impact Lab team and on the technical side there was a real can-do attitude. Dan listened to the problems, listened to what was needed and came back with a good solution.”

Andrew MoinzadehDirector

The Project

Pumping stations play an essential role in moving and collecting water from one location to another. For example, removing sewage and placing into a drainage system to ensure a supply of clean and safe water. Devon-based small business, Thermancy provide water distribution companies with pump switching schedules based on their equipment’s measurement of the power efficiency of pumps. Thermancy’s measurements are used to predict the behaviour of the pumps and monitor changes in performance over their lifetime. 

The problem presented to the Impact Lab was to determine an appropriate combination of pumps and pump settings to achieve the desired flow at the minimum power consumption.  This is also in tandem with minimising switching and balancing the usage between the pumps over time. The output must enable a pump-room operator to choose a pump combination to suit given conditions and requirements within an appropriate time-frame (usually around 15 minutes).

The Approach

The system is governed by two sets of equations: one that describes the behaviour of the pipe network (which shows increasing flow as pressure increases); and one describing the behaviour of a pump (which shows decreasing flow as pressure against it increases), both shown in Figure 1. Flow and pressure found in the system is the intersection of these two lines.

When multiple pumps are in operations, the resulting flow at a given pressure is the sum of the flows generated by each of the two pumps at the pressure. A combined pump curve can be plotted, and it is the intersection of this combined pump curve with the system curve (shown in Figure 2) that determines the resulting pressure and flow in the system when more than one pump is in operation.

Sample problem parameters and data were provided, based on a ten-pump pumping station; six fixed-speed and four variable-speed, resulting in 420,000 possible combinations of pump settings. Suspecting that the computation was small enough to be able to complete a brute-force search of all possible combinations, a brute-force approach was adopted for the project. An implementation was built in the programming language Python.

Python was chosen because it has powerful language features for numerical analysis, a rich set of libraries for mathematical functions and optimisations, is open source and widely available and can be run from other languages so can be easily integrated into Thermancy’s existing infrastructure.

Figure 1

Pump 1 and the System Curve. This shows a System Curve, for which flow increases as pressure increases; and a typical pump, for which the generated flow decreases as resistance (pressure) increases. The resulting flow and pressure is the intersection of the two lines.

Figure 2

Combined Pump Curves. This graph takes the viable sections of the pump curves for pumps 1 and 7 and sums their flow to generate a combined curve describing the behaviour of the pumping station when both pumps are in operation. The intersection of the ‘Combined Pump Curve’ with the System Curve will determine the resulting pressure and flow in the combined pump and pipe network system.

The Results

The brute-force search of all possible pump combinations can be completed in around 20 minutes, finding 22,492 viable combinations, with the remaining combinations being unviable because the equilibrium point falls outside the operating range of at least one of the active pumps. 
A second script was created to process the results, loading previously-saved results from disk and providing the user with a small set of the combinations closest to a requested flow value. This runs fast enough (less time than can be measured using the computer’s built-in clock) to be run on-demand in real-time.

The density of combinations that achieve close to a given flow varies greatly with flow. If flow within 3% of the requested value is considered acceptable, the choice of combinations within that range varies from just 4 at the lower and upper extremes to over 4,000 at its maximum. The larger the number of combinations is available close to a given flow, the greater the chance of finding one that minimises power consumption and fulfils the pump constraints. This spread is illustrated in in Figure 3. A larger number of combinations greatly increases the chance of being able to fulfil all the pump constraints without incurring large excess power consumption.

Pump combinations also vary in their power consumption, even when generating similar flow. In some cases the most power-hungry combination uses nearly 70% more energy than the lowest-power combination delivering similar flow. Figure 4 shows the maximum potential waste in power consumption (the difference between the highest- and lowest-power combinations) as a proportion of the lowest. 

Figure 3

Number of combinations within 3% of flow requirement for a sample of flow requirements. This figure illustrates the much greater choice of combinations the user will have in the optimum region on the flow range (around 1,400 m3/hr in the test data) than at the upper or lower ends of the range.

Figure 4

Power Usage of combinations delivering within 3% of the required flow for a sample of flow requirements. The potential waste is the maximum proportion of power that could be considered ‘excess’ consumption with respect to the minimum possible.

A number of possible extensions may be possible, including optimisation of pump scheduling over a day, based on historical demand; optimisation over multiple pumping stations; and prediction of degradation in performance to enable predictive maintenance. Ongoing collaboration between Thermancy and the University of Exeter is being discussed in order to pursue these next steps.

Speaking of the project and working with the Impact Lab, Andrew Moinzadeh, Director of Thermancy said: “The Impact Lab seemed to be very switched on to what the company wants. They understood that timescales were really important to us.” He continued: “Dan Maxwell (Industrial Research Fellow) managed to speak to a lot of people, get good ideas and understand the problem to come up with a neat solution to break down the scheduling problem into neat chunks. He has come up with a nice technique and used clever optimisation functions in documentation which we can take on.” 

The Team


  • Andrew Moinzadeh, Director

Impact Lab:

  • Kathryn White, Innovation Manager, University of Exeter
  • Dr Daniel Maxwell, Industrial Research Fellow, University of Exeter
  • Dr Albert Chen, Centre for Water Systems, University of Exeter