Energy-cost optimisation in water-supply system.
Mahmood, Farrukh ; Ali, Haider
Households as well as community water-supply systems for
utilisation of underground aquifers are massive consumers of energy.
Prevailing energy crisis and focus of the government on demand-side
energy policies (i.e., energy conservation) in Pakistan raises need of
using energy efficient techniques in almost every aspect of life. This
paper analyses performance of community relative to household
water-supply system in connection with efficient energy utilisation.
Results suggest that total operational energy cost in case of community
(centralised) water supply system is lower than the cost incurred under
the household (individual) water pumping units. Besides, average fixed
cost under community water supply system is three times less than that
incurred under household water supply system.
JEL Classification: Q25, Q41, D24
Keywords: Water Supply, Energy, Cost Efficiency, Economies of Scale
1. INTRODUCTION
Water, being the basic requirement of life, is important to all
living organism, human health and food production. A positive
correlation between economic growth and rate of water utilisation has
also been observed in a growth model with water as a productive input
for private producers [Barbier (2004)]. In addition, high per-capita
consumption (PCC) of water is regarded as an indicator of the level of
economic development where per-capita water consumption is defined as
the average of water consumed by a person in a day. The declining
availability of water supply, mainly due to global climate change, is
one of the important issues faced by many developing countries at the
present time. It is estimated that nearly two third of nations across
the globe will experience water stress by 2025. (1) Thus, the safety and
availability of clean water is an on-going concern within the global
village.
In Pakistan, drinking water supplies are generally obtained from
either surface water sources (i.e. rivers, streams, lakes) or the
underground aquifers. Unfortunately, both sources are subject to
pollution due to anthropogenic activities. Water supply systems (WSS)
require energy in each of the stages of water production (pumping it
from underground) and distribution chain. A number of studies [i.e.,
Abdalla (1990); Nguyen, et al. (2009); Khan, et al. (2012)] have
analysed the economic and social cost of water degradation but a few
studies at international level [Feldman (2009)] and no study in case of
Pakistan, particularly after severe energy crisis, have analysed
energy-cost optimisation in a WSS.
The most important factor in the design of a WSS is the estimation
of water requirement for a community. The per-capita consumption of
water varies from place to place and is affected by various factors
i.e., climatic conditions, water pressure and quality, population size
etc. There is no common understanding on the minimum per-capita water
requirement for human health and economic and social development.
According to World Health Organisation (WHO), minimum level of
per-capita water consumption is twenty litre of water to take care of
basic hygiene needs and basic food hygiene. Laundering and cleaning
would require more water. Taking into account that average household
size of Pakistan is six; (2) a single unit of household requires a
minimum of 120 litre of water per day for basic hygiene needs.
Figure 1 shows different categories of water need of an individual
along with standard quantities of water requirement set by WHO to assess
the accuracy of the per capita consumption of water for domestic use.
Primarily, there are two types of water-pumping systems for
utilisation of underground aquifers. One is direct pumping system where
the instantaneous demand is met by pumping water with no elevation
storage provided. This direct pumping system is being phased out because
of the operating costs. Severe load-shedding due to recent energy crisis
is another reason why people are moving from this pumping system to
other economical options. The second type is an indirect system in which
the pumping station lifts water to an elevated storage tank which floats
on the water system and provides system pressure by gravity. These days,
majority of households (which utilise underground aquifers) use the
indirect pumping system in Pakistan and have elevated storage tanks as
this system does not require instantaneous energy supply for minute to
minute water demand.
The underground WSS can be categorised into household and community
water distribution system where the later implies a common elevated
storage tank which flows water by gravity to each customer on the
system. At household level, every household unit has to bear the fixed
cost along with the variable cost of electricity consumption.
Interestingly, the cost structure of the community WSS (capital
investment in water infrastructure (reservoir and pipes) and operating
and maintenance cost) is also not very different from that of household
but due to large scale of production, it seems that average cost of
producing water would be lower and all customers on community water
system would incur a lower cost than otherwise. Under community WSS,
number of customers and water pressure are negatively correlated. It
implies that customers of community WSS have to face some additional
cost to pump water from ground storage to elevated storage when lower
pressure does not elevate the water. On the contrary, heights of the
elevated-tank and water pressure are positively correlated.
The efficient operation of WSS is not just a technical issue.
Prevailing energy crisis and focus of the government on demand-side
energy policies (i.e., energy conservation) in Pakistan raises the need
of using energy efficient techniques in every aspect of real life. Water
supply systems are massive consumers of energy. Besides, the main
life-cycle cost of a water pump is related to the energy spent in
pumping, with the rest being purchase and maintenance cost of the
equipments. Any optimisation in the energy efficiency of the water pump
results in a considerable reduction of the total operational cost.
Feldman (2009) asserts that energy efficiency can be achieved by;
installing new technology, improving system design, installing variable
speed of pump and reducing leakages.
Household WSS (individual unit) and community WSS (aggregate unit)
are two major types of water systems in urban areas of Pakistan [Haydar,
et al. (2009)]. This paper will examine whether community WSS relative
to household WSS is more energy efficient or not. In other words, a
single community WSS (assuming it consists of 'H' number of
household units) face less operational costs (energy consumption) than
total operational cost faced by 'H 'number of households when
they work as individual entities. Besides, this study will determine the
optimal threshold number of consumers under a single community elevated
storage tank. This will allow determining the minimum number of
customers required to make the option of building a given community WSS
feasible.
The remainder of this paper is organised as follows. Section 2
contains the analytical framework and a brief description on data and
variables. Section 4 includes discussion on the results of cost-benefit
analysis of household and community water-supply systems. Finally,
Section 4 concludes this study.
2. ANALYTICAL FRAMEWORK, DATA AND VARIABLES
Following Kim (1987), the theoretical framework to examine
cost-structure of WSS is represented by:
[C.sub.i] = [C.sub.i] (p,y), ... ... ... ... ... ... ... (1)
where [C.sub.i] is cost of producing water supply, i = 1,2 index
refers to household and community WSS, p is the vector of strictly
positive input prices and y is the output. Thus, the cost function is
given by:
[C.sub.i] (p,y) = min p.x, x [member of] v(y), ... ... ... ... ...
... ... (2)
where x is a vector of inputs and v(y) is the input requirement
set. From the cost function, it is possible to derive the cost
minimising factor demand equations using Shephard's Lemma [Chambers
(1989)].
[partial derivative]c(p,y)/[partial derivative][p.sub.i]=
[X.sub.i](p,y). ... ... ... ... ... ... ... (3)
Scale economies (returns to scale) are important measurements for
examining the potential for amalgamation and/or separation of (water)
production units in view of the economic benefits. If there are
economies of scale, larger firm (community WSS) can produce at lower
average cost than smaller ones (household WSS). Scale economies are
defined as the relative increase in output as a result of a
proportionate increase in all inputs. In a nutshell, scale economies are
measured by the relationship between average and marginal cost. Returns
to scale ([theta]) are the inverse of the elasticity of output
[[epsilon].sub.cy].
[theta] = [c(p,y)]/[MC x y] = [1/[[epsilon].sub.cy]] (4)
Where [[epsilon].sub.cy]] = [partial derivative]lnC/[partial
derivative][lny.sub.i] and [MC.sub.i] is the marginal cost [MC.sub.i] =
C/[Y.sub.i] x [[epsilon].sub.cy]. Economies of scale exist if [theta]
> 1, constant returns to scale exist if 0 - 1 and decreasing returns
to scale exist if [theta] < 1. The important implication of this is
that marginal cost pricing is not sufficient to recover costs for
industries with economies of scale.
Total cost of installing a WSS consists of fixed cost and variable
cost where the later varies with the level of output. Fixed cost of
household WSS includes cost of tank, cost of motor, cost of water pipes,
boring (drilling) cost, cost of wire, cost of joints for pipe and some
miscellaneous expenses (i.e. cost of grease, cost of making holes in
outer pipe etc.). Drilling cost depends positively on depth as well as
radius of the earth bore while motor cost depends directly on the
capacity (horse power) of the motor and indirectly on the depth of the
bore (Data on prices of all variables used are given in Appendix 1). It
is important to explain, here, that water-tank cost in case of
individual household is taken for water-tank of three hundred gallon
capacity (300 * 3.78 = 1134 1134 litres) that is minimum size of tank
available in the market. One rational is that this study pivots around
WHO daily per-capita water requirements that vary from 120 litres
(minimum) to 420 litres (maximum) per household.
The variable cost is basically the operational cost and is sum of
cost of energy consumption and cost of wear and tear of capital.'
Energy (mainly electricity in our study) cost is a product of units
consumed times tariff rate whereas consumption of energy units depends
on the (horse) power of motor and total time duration when motor works.
In community WSS, only fixed cost structure is a little different
as it includes all those expenses incurred in household WSS plus
compensation of water-supply staff. It is important to note that in the
long run, the households can change the level of water consumption.
Since acquiring a WSS is a decision of long-run planning horizon,
households have to make decision either they should use independent or
the community WSS.
Primary data on five community and fifty households WSS have been
taken randomly for cost-benefit analysis from Islamabad/Rawalpindi
district as it mainly consists of well-planned Government and private
housing societies. Data on variables of cost of water tank, cost of
motor, cost of water pipes and cost of joints for pipes have been taken
from whole sellers and retail sellers while data on boring cost is taken
from private contractors. Data of electricity tariff are taken from
Islamabad Electricity Supply Corporation (IESCO). Data are taken on
market prices of water tank installed per gallon, capacity of motor
(Horse Power), billing cost (price times units consumed) and cost of
boring, water pipes and wire per feet. Same variables are also observed
for elevated water supply system including construction rate of elevated
water supply system.
3. RESULTS AND DISCUSSION
All variables are explained in three scenarios where the cost is
estimated for depth of 150, 200 and 300 feet of earth bore. Household
WSS usually has bore of 150 feet while community WSS can have either 200
or 300 feet earth bore. Descriptive statistics for the data on fixed
variables are shown in Table 1.
It can be seen from Table 1 that all variables depend positively on
the depth of earth bore. One anomaly is seen in case of wire per feet
where increased depth of earth bore reduces the length of wire. It is
because increased depth of bore needs high-power motor for water suction
(which simultaneously pumps water from underground aquifer and throw it
into the system), that precludes need of a separate water pump.
Therefore, wire is required just to connect the motor with electricity
source. Sum of market values of all these above variables along with
water-motor cost, drilling (boring) cost, water-tank cost and working
staff (in case of only community WSS) yield total fixed cost for
community and household water supply systems. Table 2 below presents a
brief picture of total fixed cost for both WSS.
The major difference in fixed cost of both systems is primarily due
to construction cost of elevated water tank in case of community WSS.
Fixed cost of community WSS includes cost of elevated water tank of 8000
gallon (8000*3.78 = 30240 litres) capacity. This construction cost alone
is higher than total cost of a single household WSS under 150 bore depth
(See Appendix). Besides, the motor cost of community WSS is also much
higher than the cost of motor used in household WSS. But, this huge
fixed cost of community WSS can be divided among customers of this
system to bring the per-head cost down to the fixed cost faced by an
individual in case of 150 bore depth (as household usually utilises
water up to 150 bore depth). The diagram below shows how average fixed
cost responds to increase in number of customers.
[FIGURE 2 OMITTED]
The depth of boring for individual household cannot go beyond 150
feet due to the low capability of the machine used in household WSS
while, for community WSS, it can be 300 feet as the machines used in
this system is highly powerful. It can be deduced from Table 2 that it
is not beneficial to develop community WSS unless number of houses
exceed 25 (2232.500/88.812 = 25.137). Interestingly, a community WSS can
serve much greater number of households than just twenty five and, in
that case, average fixed cost would be even further lower. If we take
420 litres of daily water consumption by a housing unit (WHO standard);
a community WSS, in this case, can serve seventy two household units
with average fixed cost that is one-third of total fixed cost incurred
under household water supply system.
The remaining part of total cost is variable cost which includes
operational cost of a WSS whereas daily operational hours of motor
depend on the daily water requirement of a household. Table 3 below
presents electricity units consumed and energy cost for WHO's
established hierarchy of minimum water requirement under both household
and community WSS.
Table 3 explains that electricity cost is positively correlated
with daily water requirement as well as depth of earth bore. An increase
in daily water requirement increases operational time of the motor
required filling the tank; hence, resulting in higher billing cost. An
increase in depth of bore raises operational cost in two ways. First, it
reduces the suction rate of the pump, hence, increasing the time of
motor working (for details on suction rate and bore; see, Table A2 in
Appendix). Second, increased bore depth requires more energy to pump
water from underground aquifer and throw it into the system; that in
turn requires water motor of higher capacity (which bears higher cost).
That is why billing cost of community WSS is lower than billing cost of
individual WSS. On the other hand, the billing cost of household WSS is
much higher than that of community WSS.
To compare the operational (variable) cost between the two systems,
it is realistic to compare billing cost of household WSS at 150 earth
bore with billing cost of community WSS at 300 earth bore. Billing cost
of community WSS is then divided among 25 households (for the reason
discussed above that a community WSS can only be built if there are at
least 25 households to share its total fixed cost) for a better
appraisal of average household cost under community WSS. This will give
correct apportionment of the difference of energy cost (and, hence,
energy consumption) between the two WSS. Besides, this analysis will
also be extended for 72 household units as it has been estimated that a
community water tank of 8000 gallon capacity can serve 72 households for
daily water requirement of 420 litres.
Figure 2 below depicts trends in billing cost with respect to daily
water requirements for both water supply systems whereas trend in cost
of community WSS is shown for an average unit under community WSS; first
assuming it has 25 customers and, then, by assuming it has 72.
[FIGURE 3 OMITTED]
Figure 2 shows that household WSS is a massive consumer of
electricity as compared to community WSS. Besides, the gap is increasing
at increasing rate with increase in demand of water for daily
requirements (that depends on household size and water-consuming
habits). The operational cost under community WSS gets further lower in
case of increased units of households (72 units). One of the possible
reasons of this lower operational cost under community WSS is economies
of scale where a centralised system with greater scale of production can
utilise better inputs resulting in decreasing cost. These results
suggest that building of community WSS (if and only if there are, at
least, more than twenty five housing units) not only reduces fixed cost
but also results in lower operational cost of water system. In addition,
community system supplies cleaner drinkable water relative to individual
water system as the former sucks water 300 feet under the earth surface.
4. CONCLUSION
Recent energy crisis in all most all developing countries and
particularly in Pakistan forced government agencies to focus on
demand-side energy policies, especially energy conservation, as a
short-term solution. This study presents a view on how individual water
supply systems are bulk consumers of electricity while community water
supply systems can provide daily water requirements at much lower
consumption rate of electricity; hence, resulting in twofold benefit of
lower consumption of electricity and lower total cost (in monetary
terms) of per-capita water.
This study also reveals that a minimum of twenty five households
are required to bear the fixed cost of building a community water supply
system. If the number of customers in community water supply system
rises to seventy two, this fixed cost comes down to almost one-third of
the cost an individual household incurred for developing his own water
system. Besides, the results show that average billing cost goes down to
less than hundred if community water supply system includes seventy
housing units. In addition, community system supplies cleaner drinkable
water relative to individual water system as the former sucks water 300
feet under the earth surface. Based on these results, it is suggested
that community water system should be made compulsory for developing
housing colonies. Municipal authorities of Islamabad/Rawalpindi region
can develop community water systems in those sectors where tube wells
are supplying water but elevated tanks are not constructed. This will
incur less operational cost to each household due to less consumption of
electricity as elevated tank precludes electricity requirement for
throwing water from ground tank to elevated tank.
APPENDIX
Table A1
Market Price of Inputs for Household and Community WSS
Price (Rs)/Unit
Household Community
Variable Unit WSS WSS
Inner Pipe Feet 12 950
Outer Pipe " 235 950
Rope " 10 --
Wire " 25 200
Drilling Cost " 100 120
Joints No. 230 1250
Motor Cost 2 Horse Power 20000 --
5 Horse Power 70000 --
20 Horse Power 350000 350000
Plastic Tank Cost 300 Gallon 6000 --
400 Gallon 8000 --
Cement Tank Cubic Feet -- 120 *
Working Staff Rs -- 6000
* Cost of building an elevated water tank of 8000 Gallon capacity at
this rate requires (on average) 1.2 Million Rupees.
Table A2
Water Suction (Litre per Hour) Capability of the Motor
Motor Capacity (Horse Power)
Depth of Bore (Feet) 2 HP 20 HP
150 8327.902 189270.5
200 3028.328 83279.02
300 378.541 26497.87
Source: Pakistan Engineering Council, Islamabad.
Table A3
Tariff Rate for Electricity
Bracket Unit Tariff (Rs)
I 1-50 2.00
II 51-100 5.79
III 101-300 8.11
IV 301-700 12.33
V Above 700 15.07
Source: IESCO (2013).
REFERENCES
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Kim, H. Y. (1987) Economies of Scale in Multi-Product Firms: An
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(1) United Nations Environment Programme Report (2002).
(2) For check this if missing footnote..
(3) We are assuming a zero wear and tear cost to keep our analysis
simple. This assumption does not invalidate our results.
(2) Pakistan Statistical Bureau (2012).
Farrukh Mahmood <farrukhmahmod_501@yahoo.com> is MPhil
Student, Department of Economics and Finance, Pakistan Institute of
Development Economics, Islamabad. Haider Ali <haider@pide.org.pk>
is Lecturer, Department of Economics, Pakistan Institute of Development
Economics, Islamabad.
Table 1
Descriptive Statistics (Fixed Cost Variables)
Variables (Feet) Bore Depth Minimum Maximum
Inner Pipe 150 165 170
200 200 220
300 300 320
Outer Pipe 150 150 155
200 200 205
300 300 305
No. of Joints 150 15 16
200 20 21
300 30 31
Rope 150 155 160
200 205 210
300 310 320
Electric Wire 150 160 170
200 10 20
300 10 20
Miscellaneous Expenses (Rs) 150 600 800
200 11000 12000
300 17000 18000
Variables (Feet) Average S.D
Inner Pipe 167.5 3.53
210 14.14
310 14.14
Outer Pipe 152.5 3.53
202.5 3.53
302.5 3.53
No. of Joints 15.5 0.70
20.5 0.70
30.5 0.70
Rope 157.5 3.53
207.5 3.53
315 7.07
Electric Wire 165 7.07
15 7.07
15 7.07
Miscellaneous Expenses (Rs) 700 141.42
11500 707.10
17500 707.11
Table 2
Total Fixed Cost (Thousand Rs) of Water Supply Systems
Bore Depth (Feet) Household WSS Community WSS
150 88.812 1651.225
200 154.373 1732.000
300 472.848 2232.500
Table 3
Variable (Operational) Cost of Water Supply Systems
Households Daily Water
Requirement (Litres)
Bore Depth 120 180 240
Electricity Units Consumed
Household 150 51.874 77.811 103.748
200 142.653 213.979 285.306
300 1141.224 1711.836 2282.448
Community 150 22.824 34.237 45.649
200 51.874 77.811 103.748
300 163.032 244.548 326.064
Billing Cost (Rs)
Household 150 300.349 450.524 841.393
200 1156.916 2638.367 3517.822
300 17198.243 25797.364 34396.485
Community 150 132.154 198.231 370.213
200 420.697 631.045 841.393
300 2010.184 3015.276 4020.368
Households Daily Water
Requirement (Litres)
Bore Depth 360 420
Electricity Units Consumed
Household 150 155.621 181.558
200 427.959 499.285
300 3423.671 3994.283
Community 150 68.473 79.886
200 155.621 181.558
300 489.096 570.612
Billing Cost (Rs)
Household 150 1262.090 1472.438
200 5276.734 6156.189
300 51594.728 60193.850
Community 150 555.320 647.873
200 1918.812 2238.614
300 6030.553 7035.645
Fig. 1. Hierarchy of Minimum Water Requirements for Domestic Uses
10L Drink
20L Cooking
30L Personal Washing
40L Washing Clothes
50L Cleaning Home
60L Gardening/Growing Food (Domestic Use)
70L Water Disposal (Sanitation)
Source: World Health Organisation Report (2006).
Note: Table made from bar graph.
