2.1. Critical Period Approach
Service reservoir and associated pump station, which deliver water into the reservoir when energy from the energy power system is used, are usually designed according to deterministic guidelines that specify minimal water service reservoir and optimal pump system capacity. The required capacity of the reservoir and pumping system is determined according to daily consumer demand for water in design period VWS(i) and hourly demand QWS(i) in the day of maximum demand, the critical demand period. Design period tb is usually the period with the highest consumption of water during the planning year. However, the design period can be longer: two or more days, up to a maximum of one week.
The size of the reservoir depends on the regime of water consumption in a settlement, and on the planned work of the pumping station. The work of pumping station, supplied with electric energy from the regional power system, can be continuous for 24 hours or more intense during the night when electricity is cheaper. Various combinations are possible that seek to optimize the operation of the pumping system, its capacity QPS and reservoir capacity Vop. The capacity of such a reservoir increases for fire and emergency storage, in accordance with the respective norms. Such guidelines have to accommodate a large range of possible conditions, meaning that systems are potentially overdesigned, but reliable.
In the case when PV electric energy is used, the design is more complex, because the available energy for pump system operation is variable throughout the year and during the day, depending on daily insolation. In this case, the designer must determine the PV generator power Pel,PV that will provide enough electricity for re-pumping water into the reservoir during the entire planning period (planning year), according to daily water consumption in a settlement VWS(i). In addition, the duration of sunshine TS(i) determines the period of operation of the pumping station. In this case, the critical energy supply period, or the period for calculation of the PV generator power, is one in which the relationship between hydraulic energy required for re-pumping water EH(i) and the available solar radiation ES(i) is the smallest.
Consequently, the critical period for calculating the capacity of the pumping station QPS(i) is the one in which the relationship between the daily consumption of water in a settlement VWS(i) and the period of active insolation TS(i) is the greatest.
If the design period tb is longer than one day, the impact of one extreme day of low insolation (usually due to cloudiness) on the capacity of the PV generator decreases, so that lower power of the PV generator is required and thereby lower costs. With a longer design period, the impact of extremely low insolation on calculation results will be smaller, so the solution will be safer and more rational. In this case they are longer critical periods.
In this paper we used the approach based on critical design period. This approach includes design elements of the solution: PV generator, pump station and service reservoir based on the critical period of operation of each one. It is a deterministic approach which accommodates a large range of possible conditions. It is a conservative approach, meaning that the elements of the solution are potentially overdesigned. However, such an approach provides a reliable solution and a required level of reliability, necessary for the functioning of water supply systems. The reliability of the bulk water supply system can be defined in terms of reliability of its storage reservoir/tank, as consumers will only notice a service interruption if the storage tank has failed (i.e., run dry).
Optimization of the possible solution is based on economic and other criteria in the function of a balancing period. The balancing period of water pumping and service reservoir water balance in the urban water supply system is at least one day and may be several days, usually no more than five, (tb = 1–5 days). A longer balance period reduces the uncertainty of solar irradiation and increases the reliability of the solution. With a longer balancing period, the system is more cost-effective from the perspective of solar energy harvesting, because the sum of overall available solar radiation is greater when the balancing period is longer. This means that the required water volume can be pumped with lower installed PV generator power. Normally, with a longer balancing period, the storage capacity of the reservoir will be higher. Therefore, regardless the fact that the daily output of water from the storage does not change significantly from day to day, due to uneven influx of water into the reservoir, it will generally be higher. The relationship between Pel,PV and Vop depends on climate characteristics of the location, or on daily variability of solar radiation. With lower variability the impact on the required storage volume and the PV generator power is smaller and vice versa.
In the critical period approach, the estimate is mainly carried out in the following steps:
- •
Collecting all necessary data for estimation of water demand in the planning period, QWS(i), and determining the daily water usage pattern;
- •
Collecting climate and other necessary data for the design of PV generator;
- •
Selecting the number of days for system water usage balance, i.e., balancing (design) period, tb = 1, 2, 3, 4 and 5 days;
- •
Selecting the most critical periods for the determination of the required power of the PV generator Pel,PV from available time series of solar radiation ES(i) and water demand VWS(i) in accordance with the selected balancing period tb;
- •
Determining the required power of PV generator
Pel,PV, according to the selected critical daily balancing period
tb [
10,
11];
- •
Determining the capacity
QPS and power
PPS of the main pumping station (MPS) for each balancing period
tb for every day
i of the year [
12]. The largest obtained capacity
QPS(i) and power
PPS(i) is selected;
- •
For the selected balancing period tb, determining the required operative reservoir volume Vop for the selected PV generator power Pel,PV and the period of its work during the day (inflow), according to the foreseen regime of hourly water consumption in a settlement (outflow) for each balancing period tb, for every day i of the year. The largest obtained volume Vop(i) is selected;
- •
Determining the cell area
APV (m
2), for each balancing period
tb [
10];
- •
Analysis and ranking of obtained solutions of PV generator power Pel,PV, operative reservoir volume Vop and total power PPS of MPS of different balancing period tb.
The input data for the analysis are: climate data (daily average air temperature, daily average solar irradiation, average number of hours of daily insolation), water supply system configuration (water intake, pump station, service reservoir), daily and hourly water demand and fluctuation during the day. It is also necessary to determine the constraints related to the construction of a PV generator, pump station and service reservoir, as well as legal, environmental, social and other requirements.
At the beginning of the analysis it is necessary to define the daily quantity of water in a settlement VWS (m3/day), according to settlement characteristics and water consumption regime throughout the years of the planning period.
After this, the daily water usage pattern in a settlement VWS,t (m3/h) in the period of t = 1,…, 24 hours is determined (diurnal pattern). The same pattern is used for each day i.
Based on the obtained values, the minimum required size of the PV generator is determined, which provides the necessary inflow of water in the critical period. This procedure is simple, because the relation between Pel,PV and VPS is linear.
Based on the selected/calculated initial values,
Pel,PV and
VPS, which satisfy water demand
VWS in the planning period, the minimum required
Pel,PV is determined from established differences
∆Vtb,i:
The critical day/period
for PV generator design is determined by the minimum daily difference:
where
∆Vtb,i is an acceptable difference in practice application.
When the balancing period tb > 1 day, calculation series of tb days are performed, where series are formed with calculation step always ∆i = 1 day, i = 1, 2,…, 365. If the sum does not end with the last member of the observed series, the process ends with the next member of the same series.
Available insolation ES, i.e., electric energy Pel,PV determines the period of the pumping station operation TS with uniform rate during daily work period.
The required operation volume of service reservoir
Vop is obtained by standard procedure, using a mass diagram with cumulative pumping curve plotted on it [
12], by using of Excel ©2007 (Microsoft). Time step for calculation is one hour,
t = 1,…, 24 hours. The size of service reservoir has been calculated for each day
i in accordance with each balancing period
tb in the year. In general, the critical day/period for the design of volume reservoir
is the day with maximum water demand, providing that on day available insolation
ES(i) is sufficiently high. It should be noted that the fire and emergency volumes are not taken into account for this case. These volumes are more or less constant, while the operation volume is variable during the day. In accordance with the respective norms and particular situations, influence of fire and emergency volumes on operation volume analysis may be neglected [
12]. However, the total required volume of service reservoir is the sum of operation, fire and emergency volumes.
The required volume
for each alternative
tb is:
2.2. The Choice of a Compromise Solution
The general objective of the system design is finding the power of the PV power plant that will, in the best manner possible, meet all consumer needs for water, with minimal construction and operation costs of the system. The requested result of the optimization process is the best compromise solution between the pairs of
Pel,PV and
Vop and also the pump station power
PPS that best meets the set objectives. The optimal combination
x of PV generator power
(
f1), operating service reservoir volume
(
f2) and power
(
f3) of MPS is sought for the selected alternatives
X:
DR means to apply the appropriate decision rule(s) and to find the best-compromise solution
x* from the set of alternatives
X. The standard trade-off method could, among other, be used for the selection of a compromise solution [
13]. In this case, the economic criterion is dominant. However, the problem can be analyzed by extending the number of criteria, of which the reliability of water supply is the most important one.
General sustainable objectives are related to economic, social and environmental aspects of the problem. Most of the environmental objectives are fulfilled by using green energy instead of traditional. Social objectives relate to basic water service price as measurable criteria and sustainable green city environment as general commensurate criteria. The fulfillment of both sustainable objectives is closely related to economical characteristics of the solution. Nowadays, the economic criteria are still dominant and for this reason good economic analysis of the problem is the basis for the solution and alternative evaluation.
The economical approach, according to the concept of Life Cycle Cost
LCC (€) [
8,
9], is developed to be the best indicator of economic profitability of the system cost analysis.
LCC takes into account the initial capital cost
Ccapital, present value of replacement cost
Creplacement and present value of maintenance cost
Cmaintenance:
In the case of urban water supply systems, the economic objective is to minimize possible economic losses that occur due to not using conventional energy sources which are still cheaper than green sources. These losses are expected to decrease over the time, because PV generators are becoming cheaper and conventional energy more expensive [
14,
15].
In this paper we will simplify the economic analysis, providing sufficient information for understanding the problem characteristics.