Equ 19.7 Investment calculation — existing plant

Present capitalised value method





подпись: where
For existing plant the question is often asked if an improvement of the plant can reduce the operational costs in such a way as to reduce the whole-life costs. According to the present capital­ised value method the summation of the savings during the ser­vice life will be expressed at today’s current value.

R|m = motor efficiency (decimal)

T|C = control efficiency (decimal)

R|A = other ancillary efficiencies

The flow control illustrated in Figure 19.3 takes into account the power losses which are caused as a direct result of the method of flow regulation.

P = qvxPF no

_ m3IsxPa •r|0 x1000

= flowrate (m3/s)

= system resistance (Pa)

BL =

Total savings during working life (currency)

^Dcap “

Capitalised reduction of operating costs (cur­


F =

Present capitalised value factor

Kd =

Annual operating cost reduction (currency/an­


K, =

Investment cost (currency)


Bl = where


K, = F

KD — K,

Equ 19.5


By investing Ј3,000 it is possible to reduce the annual costs for air movement by Ј1,000. The plant is designed to operate for 15 years and the estimated profits to be a minimum of 15%. How great are the savings during the service life of the plant at today’s currency value?

According to Figure 19.2 the present capitalised value factor F = 5.9 for n = 15 years and r = 15%.

BL = 5.9 • 1000-3000 = Ј2900

Over and above the repayment of investment, including esti­mated profits, an extra Ј2900 is obtained.

If several alternatives are available to achieve a similar techni­cal improvement, then it is normal to choose the alternative which produces the greatest savings.

Annuity method

The question as to how great the first year’s saving will be at to­day’s currency value is answered by using the annuity method.

The power used depends upon the useful air power required to maintain the specified flowrate in the ducting system and upon the efficiency of converting the electrical power (or other equiv­alent) into this useful air power.

This efficiency is usually called the overall efficiency and is de­fined as:

Tlo=-^ = ‘nF-Tlm-%Tlo’TlA

Equ 19.6







= overall fan efficiency factor (decimal) = required air power (kW)

= power absorbed (kW)

= fan efficiency (decimal)

= transmission efficiency (decimal)

Equ 19.7 Investment calculation - existing plant

M3/sxkPa m3/sxkPa


Equ 19.8


NF-nm-nj — nc-nA




It will be noted that if P is quoted in Watts then resistance pF should be quoted in Pascals Pa. If resistance is given in kilo — Pascals kPa then the power will be given in kiloWatts kW.

Flow regulation efficiency illustrated in Figure 19.3, takes into account the power losses which result directly from the method chosen to regulate the flow. Such power losses are caused by damper regulation in the discharge duct, by-pass duct or on-off control.

The expression for regulation efficiency for on-off control con­sists of the quotient of energy requirements. Whereas the oth­ers are represented by the quotient of power requirements.

The fan efficiency will obviously be determined for the actual operating point and not the rated duty point efficiency, maxi­mum flow point or any other arbitrary operational point. The


Throttle regulation


— P..


V’ =


——————— P„,


By-pass control





On-off control





1r =


Equ 19.7 Investment calculation - existing plant Equ 19.7 Investment calculation - existing plant Equ 19.7 Investment calculation - existing plant


подпись: 7p

X o


подпись: x o
o x



подпись: x

Power absorbed by any auxiliary systems, such as lubrication

Oil, seal oil or cooling water must be included in the overall fan efficiency.

The transmission efficiency represents losses in gears, cou­plings, vee belt drives and speed variators. It is important to consider the transmission efficiency when speed regulation is used. Losses in rectifiers, frequency inverters, regulation resis­tance, additional motor losses, etc., i. e. losses when utilising electrical methods of speed regulation, are traditionally calcu­lated as transmission losses.

The motor efficiency should be taken at the actual operating point. Acommon misconception is to assume that the motor ef­ficiency is still high even at part load. At part load the percent­age of reactive power is increased and this may be costed as a separate item. It is important to remember about the power ab­sorbed by separately driven cooling fans; this is an integral part of the motor efficiency.

The efficiency of other components takes into consideration losses for phase compensation and protection against supply disturbances, power requirements for supplementary ventila­tion and other environmental power consuming arrangements which can be directly associated with energy conversion in the ventilation plant when working.

It is extremely important to remember that it is the overall fan ef­ficiency factor and not the efficiency of isolated components which is the characteristic unit for energy conversion efficiency. If all the component efficiencies are high at the actual operating point then a high overall fan efficiency factor will obviously be obtained. However, it only requires one of the component effi­ciencies to be low to cause a poor overall efficiency.


Determine the overall fan efficiency factor for a flow of 70% of maximum flow for the installation shown in Figure 19.4, for (I) speed regulation and (II) throttle regulation.

Using estimated component efficiency values:

Case I

Case II

T|F = 0.75 (estimated)

TlF =



R|T = 0.75 (estimated)

M =



R|m = 0.90 (estimated)

^m ~



R)c = 1 (not included)

Tic =


(not included)

Tio = 0.51

TlO =


Flow, for 75 % of the time. During 30% of the time the fan is then at rest. In this case higher duct losses are obtained during the time the fan operates and the efficiency factor becomes:

R|0 = 0.75 x 1 X 0.90 x 0.60 = 0.41

For multi-fan systems the efficiency factor can be determined in asimilarway. Here again, it is only the total efficiency for the ac­tual flow and not the maximum efficiency of individual compo­nents which is characteristic for energy conversion efficiency. For on-off control of multi-fan systems there are a number of significant operating points. The efficiencies for these flows are greatly influenced by the sizes and designs of the fans se­lected.

An example of this is shown in Figure 19.5. In the case of three identical fans having maximum efficiency at Qmax, poor part load efficiencies, shown as circles on the graph, are obtained. By choosing larger fans, with r|max at a somewhat higher Q value, better part load efficiencies can be obtained, shown as crosses on the graph. Only by choosing three different sizes of fan can the highest efficiency be achieved for all three operating points. Three different fans, however, involve the stocking of additional spare parts and more expensive maintenance, and the fans cannot be used as stand-bys for each other.

The basic fan efficiency is very important. Fan efficiency is greatly influenced by size, design and choice of fan. Informa­tion on fan efficiencies is given in Chapter 1, but it is also worth again noting that efficiency increases with fan size in a homoge­nous series.

Equ 19.7 Investment calculation - existing plant

The efficiency factor for on-off control becomes evident, if it is assumed, for example, that the fan operates at full flow, 100%

Equ 19.7 Investment calculation - existing plant

I____ I

подпись: i i Equ 19.7 Investment calculation - existing plant



Equ 19.7 Investment calculation - existing plant


подпись: ipO o o

Figure 19.5 Example of overall fan efficiency for three fans connected in parallel

Pay-off method

The pay-off method uses an imaginary “repayment time” de­fined by the relationship

TD = —Equ 19.9



Tp = pay-off time (decimal)

K| = investment cost (currency)

KD = annual operating cost reduction (currency/an­


The shorterthe pay-off time the more profitable the investment. By comparing with equation 19.5 it is found that for BL = 0 then Tp = F, i. e. the pay-off time and present capitalised value factor have the same numerical value when the total saving is equal to zero.

Investment grant

Grants for energy saving investment may apply. For up to date information it is best to seek the advice of the relevant local or central government authority.

Whilst writing this book, the most relevant schemes would seem to be:

Enhanced Capital Allowances (ECA). ECAs enable a busi­ness to claim 100% first-year capital allowances on their spend­ing on qualifying plant and machinery. There are three schemes for ECAs:

— Energy-saving plant and machinery

— Low carbon dioxide emission cars and natural gas and hydrogen refuelling infrastructure

— Water conservation plant and machinery

Businesses can write off the whole of the capital cost of their in­vestment in these technologies against their taxable profits of the period during which they make the investment.

This can deliver a helpful cash flow boost and a shortened pay­back period.

The Market Transformation Programme (MTP) is a DEFRA initiative that develops policy strategies for improving the re­source efficiency of traded goods and services in the UK.

The MTP quantifies current thinking on how the daily use of products, systems and services impacts on the environment. MTP uses market projections and policy scenarios to explore alternative future developments.

The Energy Saving Trust (EST) was set up by the UK Govern­ment following the 1992 Rio Earth Summit and is one of the UK’s leading organisations addressing the damaging effects of climate change. The Energy Saving Trust’s goal is to achieve the sustainable and efficient use of energy, and to cut carbon di­oxide emissions, one of the key contributors to climate change. The Energy Saving Trust is a non-profit organisation funded by the Government and the private sector.

Estimated profits and service life

Estimated profits

Profit estimates should, in principle, correspond to the interest on capital which would otherwise be realised from an alterna­tive investment. It is a measure of a company’s profitability and is higher than the current bank rate. The profit estimate in­creases with reduced capital resources, since it is necessary to be more particular when investment capital is limited. Profit es­timates are rarely considered at less than 15%.

The methods of calculation previously reviewed assume that the annual operating cost reductions are of the same magni­tude from year to year. The majority and largest savings on the operational side are achieved by reducing energy consump­tion. Energy costs, currency per kWh, can also be expected to rise more quickly than other costs, which mean that energy sav­ings will become more profitable with time.

One way of considering energy cost increase when making economic calculations is to use corrected profit estimation.

Rk=r-e + i Equ19.10


Rk = corrected profit estimate (percentage)

R = uncorrected profit estimate (percentage)

E = rate of increase of energy (percentage)

I = general inflation rate (percentage)

A more rapid rate of increase of energy costs can in this way be transferred to a reduced profit estimation requirement for en­ergy saving investment.

Service life

The economic service life is determined by factors such as write-off rules, the technical service life of components and the planned period of use of the plant. As with other parameters for fans, the economic service life is dependent upon the size and type of industry.

As an approximation with the exception of small plant the fol­lowing applies:


40 years

Ducting, underground

50 years

Other ducting

20 years


15 years

Control equipment

10 years


10 years

The service life of control equipment and instrumentation may be taken as 10 years for financial planning. The rate of change within the electronics industry is very rapid. Control systems and instrumentation should be reviewed every 5 years using the “Present capitalised value” method, to see if improved equipment or improved control strategies could reduce existing operating costs and hence reduce whole-life costs.

Energy costs

Energy costs depend upon the amount of energy consumed the prevailing energy price scale and fixed costs for the supply in­stallation. Premiums may be levied if the “maximum demand” is exceeded. In the most usual cases of electric motor operation, energy prices are determined by the relevant electricity tariff.


The basis of most forms of tariff is a fixed charge dependent upon the “maximum demand” taken by the consumer and de­signed to cover:

• the costs dependent upon maximum demand, e. g. interest and depreciation of generating plant, rates, taxes, insur­ance, salaries,

• the costs incurred for each consumer, e. g. transformers, meters, meter reading labour, service cabling. And a run­ning charge depending on the energy supplied e. g. fuel, losses and maintenance of the supply plant, equipment, etc.

For industrial consumption two-part tariffs are usual with the fixed charge proportional to maximum kW or maximum kVAde — mand; and a running cost kWh, which may be dependent upon the time of day and/or year, i. e. peak and off-peak periods, and also include for example, a fuel cost variation clause. A kVA maximum demand is preferable since it takes into account the effect of low power factor. It involves, however, more expensive metering equipment. The cost of metering maximum demand makes it uneconomic, in any case, for loads of less that 20 to 50 kW.

If supplies are taken at a high voltage instead of the usual

415V/380V for distribution, the maximum demand charge may

Be less since the consumer then has the option to provide his own transformer.

Annual energy cost

The energy costs are a product of energy consumption and cost per unit. The annual energy cost will therefore be:

KE=keE Equ 19.11


KE = annual energy cost (currency)

Ke = energy cost (currency per unit)

E = annual energy consumption (units)

Or capitalised for the service life of the fan station.

KEcaP=FkeE Equ 19.12

Posted in Fans Ventilation A Practical Guide