Its simple mathematics (part 3): subject – calculus & the Affinity Laws
Technology is the third variable in IPAT. It can be good and it can be bad. Technology allows things to be made for a much lower price on one hand, meaning that a lot more people have the ease of financial access to the products. On the other hand, technology allows more efficient use of resources, so environmental degradation is reduced by a percentage factor.
An example of the benefits of technological efficiency is found in the Affinity Laws and their application to motors. The International Energy Agency has estimated that 45% of global electricity consumption is by motors. It is estimated that 20% of global electricity consumption is by the motors that drive pumps (Pump Lifecycle Costs: A Guide to LCC Analysis for Pumping Systems, Europump and Hydraulic Institute, 2001).
The basis of the Affinity Laws is that pump and fan flow rates are related to pressure and power consumption. The calculus is as follows (assuming the impeller diameter remains constant):
Law 1a Flow is proportional to shaft speed:
Law 1b Pressure or Head is proportional to the square of shaft speed:
Law 1c Power is proportional to the cube of shaft speed:
To make the maths simple, I will explain what the key points to understand out of the above formulae:
If you reduce the speed of a pump or fan by 10%, you will use approximately 25% less power. If you reduce the pump or fan speed by 20% you will halve the amount of power consumed.
But how do you control the motor speed. Easy, with capacitors incorporated into variable frequency technology (VFD’s). Their connection to a motor is like giving the motor an accelerator pedal, allowing them to back off the gas as appropriate. VFDs are like big buckets of electric charge. The charge comes into the bucket as an alternating current at 50 or 60 hertz (depending on the country you are in). In Australia it is 50 hertz. The VFD deals out the power at the hertz rate necessary to maximise motor operational efficiency. Sensors are often connected to the VFD telling it:
“Hey mate, the motor doesn’t need to be running at maximum speed at the moment, so back off”.
Now for some rough estimates of the potential benefits of VFDs applied on a mass basis. Say there is an opportunity to reduce the electricity consumption of half the pumps and fans in the world by an average of 25% from their current consumption (by slowing their speed by 10%). This is a conservative estimate that incorporates situations where the pump has to run at 100% capacity, where VFDs are already in operation and finally, it presumes only a 10% reduction in speed. The estimate means that total global power consumption of motors could be brought down from 20% of total electricity consumption to 17.5% of the total. Given the total electricity consumption from fossil fuels will be approximately 16 TWH in 2014 (based on estimates derived from 2011 data of the International Energy Agency), then there is the opportunity here to reduce fossil fuel generated electricity consumption by 400,000 MWh in that year. Given that each MWH generated from fossil fuels causes the emission of approximately one tonne of CO-2e, the emission reduction would be of the order of 400,000 tonnes of CO2-e in 2014.
Going back to consider the algebraic consequences in IPAT, carbon emissions make up a significant part of the calculations of the ecological footprint (approximately half). Therefore, if VFD technology is introduced on a mass scale EPM/WTB estimates there will be a noticeable reduction in per capita global gha.
Finally, a specific example of the benefits of VFDs. David Bartush, the aquatics facilities manager for the Blue Mountains City Council, near Sydney, introduced VFDs to the two x 15 kWh pumps to the Springwood leisure pool. The pump power consumption has reduced by 56 MWh per annum since.
In following newsletters we will look at other ways of reducing motor power consumption with more efficient motors, correct pump and pipe sizing and power factor correction.