# A Study of Energy Optimisation of Urban Water Distribution Systems Using Potential Elements

## Abstract

**:**

## 1. Introduction

^{3}/h) and suggest the installation of pumps in the supply pipes that act as micro-hydro turbines to generate electric power. These turbines may be used to provide pressure control instead of using pressure control valves.

## 2. Improving Energy Efficiency of Water Pumping

#### 2.1. A Brief Review of Previous Works

^{3}; Q is the pump discharge, in m

^{3}/s; H

_{p}is the pump head for the operating point, in m; η is the global efficiency of the pumping station; and T

_{p}is the operation period, in h.

_{p}of the pumps can be estimated as:

_{i}, H

_{i}, and η

_{i}are the pump characteristics in classical operation at the ith hour of a day; and ${\int}_{0}^{{T}_{p}}P\text{\hspace{0.17em}}\mathrm{d}t$ is the energy consumption during interval T

_{p}at discharges different from Q

_{i}.

- Bypassing part of the water flow rate.
- Introducing a supplementary pressure loss using a control valve [28] that can lead to higher energy efficiency of the water supply system when the nominal pump head is lower than the optimal value. Additionally, valves can be a source of emissions and suffer from corrosion, erosion, plugging, cavitation, and leakage.

_{1}and n

_{2}) on the fixed system curve H

_{r}. Pipe work curve H

_{r}start from point (0, H

_{g}), where H

_{g}is the geodesic head. The operating point F

_{2}corresponds to the reduced pump head H

_{F}

_{2}.

_{1}and n

_{2}, i.e., that the efficiency curve will only be shifted to the left in the case of speed reduction. The efficiency variation depending of the pump speed is provided by following analytical relationship [29]:

_{1}and n

_{2}are two different speeds and η

_{1}, η

_{2}are the corresponding efficiencies.

_{m}is the motor efficiency; η

_{VFD}is the efficiency of the VSD; and η

_{p}is the pump efficiency.

_{p}= n

_{c}+ n

_{v}number of pumps, where n

_{c}is the number of classical (fixed-speed) pumps (p

_{f}) and n

_{v}is the number of variable-speed pumps (p

_{v}).

#### 2.2. Case Study

^{3}.

_{p}) by applying throttling or rotational speed control and the classical control (start–stop). The system head curve H

_{r1}corresponds to the start–stop control. If the pumps are partially shut by valve control the system curve becomes H

_{r2}.

## 3. Energy Optimisation Methodology

#### 3.1. Pumped Storage Tanks

_{p}and pump heads H

_{pe,j}of external pumping stations is achieved as follows.

_{p}delivered by NP external pumping stations, a part Q

_{pn}is transported through the distribution mains of pressurised network, and another part Q

_{pa}is transported through transmission mains at NT buried storage tanks, according to the following equation:

_{pe,j}of the external pumping stations are decreased at the values h

_{pe,j}. The total pump station power P is computed using Equation (7) if the transmission mains are operated by gravity or using Equation (8) if the transmission mains operate by pumping:

_{pa,k}is the discharge of the pumped storage pump (internal pumping station) k; H

_{pi,k}is the pump head corresponding to the pressure zone served by the internal station k; and H

_{pa,k}is the pump head at the external station for water delivery through transmission mains at storage tank k.

_{pe,j}are much lower than pump heads H

_{pe,j}because the head losses are changing in proportion with the square of the ratio Q

_{pn,j}/Q

_{p,j}< 1. Thus, the power of the external pumping stations decreases by reducing the discharge as well as by reducing the pressure, and total power is decreased by:

_{i}) on a distribution main (Figure 4) is moved towards the upstream extreme of distribution main (i.e., towards larger and larger discharges), the power P

_{i}of the internal station SP

_{i}increases and the power P

_{e}of the external station SP

_{e}decreases greatly because the head losses in upstream segments of distribution main are reduced according to the Darcy–Weisbach formula [6].

_{M}and D

_{m}of the supply section A and terminal section O, respectively.

_{0}) by means of a transmission main located between section A and X

_{0}. A pumped storage (buried tank and SP

_{i}) is located in section X

_{0}. The head loss H(x) that occurs until a computing section X (Figure 4c) is evaluated with the following equation:

_{0}(x) is the specific (per unit length) hydraulic resistance [6,35] of the distribution main in section X; and β is an exponent with values in the range of 1.85 to 2.0, that depends on the Reynolds number and the relative pipe roughness [36].

_{0}(x) are estimated as:

_{0}, r

_{0}, and b are computed from the boundary conditions: x = 0, Q(0) = q

_{0}, ${R}_{0}(0)=8\mathsf{\lambda}/({\pi}^{2}g{D}_{m}^{5})$, and x = L, ${R}_{0}(L)=8\mathsf{\lambda}/({\pi}^{2}g{D}_{M}^{5})$ in which λ is the pipe friction factor, R

_{0}(x) is the hydraulic resistance per length unit of the pipe, and the parameters a and α are determined statistically [37] based on the discharge distribution along the distribution main.

_{i}is determined by the value of x

_{0}, for which the total power P expressed by Equation (Appendix A, A6) becomes minimum (Figure 4d):

_{0}… c

_{9}are the coefficients of the objective function depending on the parameters a, b, α, β, r

_{0}, q

_{0}, and L as shown in [38].

_{0}is the interpolation result.

#### 3.2. Intermediary Pumping Stations Integrated on the Distribution Mains

_{1}and repressed at a higher pressure p

_{2}, and the pump head is H

_{pi}= (p

_{2}–p

_{1})/γ.

_{e}) intermediary pump stations are directly serial-connected on a number of NA distribution mains, the total power in the system is:

_{p,j}and h

_{pe,j}are the discharge and pump head, respectively, for external pump station j, and Q

_{pak}and H

_{pi,k}are the discharge and pump head, respectively, for intermediary pump station k.

_{pe,j}<< H

_{pe,j}) and the discharges of the intermediary pump stations became equal to the local discharges of the distribution mains on which they are integrated, a power reduction $\Delta $P occurs according to Equation (9). As a result, electrical energy consumption in the system is reduced with $\Delta $W.

#### 3.3. Elevated Tanks

_{p}is the pumped discharge in the system; H

_{pe}is the maximum pump head (for a network supplied by one-sided pumping from the exterior); T

_{p}is the pumping time; and η is the efficiency of the pump station.

_{1}, and e

_{2}are the estimated electric energy tariffs during peak hours and base hours, respectively.

#### 3.4. Economic Indicators

_{e}is the annual operation cost for the reference system with the network supplied by one-sided pumping from the exterior; C

_{i}is the annual operation cost for the system with internal potential elements; and RT

_{n}is the normal recovery time of 10–12 years.

_{we}for the reference system and the energy cost C

_{wi}for the optimised system and r is the repair, maintenance and periodic testing rate for the distribution system.

## 4. Case Studies

#### 4.1. Potential Characteristics Influence of the Elevated Tanks on Distribution Energy Balance

_{d}and α

_{p}, and cumulative per cents Σα

_{d}and Σα

_{p}). Starting from this table, the compensatory function will be analysed for two types of elevated tanks: taper tank optimised, with generatrix angle of inclination 45° from the horizontal line, diameters of 36 m and 16 m, and maximum height of 10 m, and a rectangular (flat) tank with a height of 2 m. These water towers are located in the distribution system of a large urban centre from Romania and have an average hourly load equal to the maximum-day discharge Q

_{d}

_{max}= 3.59 m

^{3}/s = 301,536 m

^{3}/day.

_{v}·Q

_{d}

_{max}/100 and total compensatory capacity is defined as α

_{v}

_{max}·Q

_{d}

_{max}/100. The water height h was computed every hour for both types of tanks, as shown in Figure 6. On this basis, the comparative values of electricity consumption for both types of elevated tanks are reported in Table 3.

#### 4.2. Energy–Economic Efficiency of Optimisation Solutions

_{e}at the water plant (direct pumping), which delivers a maximum-hour discharge Q

_{h}

_{max}= 4.30 m

^{3}/s and an average pump head H

_{pe}= 60 m. Taking into account the schedule of the hourly pumped discharge (Figure 8), the daily energy consumption W is determined.

_{e}supplies buried tanks R

_{k}(k = 1 ... 7) of pumped storage through a low pressure looped transmission network (Figure 9). In this way, outside of the peak energy consumption hours, the maximum-day discharge Q

_{d}

_{max}= 3.94 m

^{3}/s and the average pump head h

_{pe}= 15 m are continuously assured. The pumped storage pump stations generate via the buried tanks the hourly discharge Q, according to the pumping schedule from Figure 10, and the required pressure for the pressure zones.

_{k}with the elevated tanks C

_{k}(k = 1 ... 7) with smaller levels of fluctuation, which ensures a gravitational distribution in the respective zones. The discharge Q

_{d}

_{max}= 3.94 m

^{3}/s is pumped from external pump station SP

_{e}with an average pump head h

_{pe}= 49 m, according to the pumping schedule presented in Table 2, which sets a reduced pumping during peak hours of electricity consumption.

_{i1}and SP

_{i2}(Figure 7), assuming that the service pipes are connected immediately downstream of these stations. The intermediary pump stations are integrated on water mains M

_{1}and M

_{2}. External pump station SP

_{e}delivers discharge Q

_{h}

_{max}= 4.30 m

^{3}/s, with an average pumping head h

_{pe}= 40.5 m, and intermediary pump stations equipped with two sets of three parallel-connected pumps operating with discharges of 0.94 m

^{3}/s and 1.78 m

^{3}/s, for average pump heads H

_{pi,}

_{1}= 13.0 m and H

_{pi,}

_{2}= 11.4 m, respectively.

## 5. Results and Discussion

_{1}= 0.23 €/kWh, e

_{2}= 0.11 €/kWh.

## 6. Conclusions

## Conflicts of Interest

## Appendix A

_{0}is obtained:

_{0}, the discharge equation can be written under a simple form:

_{e}+ P

_{i}can be expressed as:

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**Figure 3.**Characteristic curves H-Q, η-Q and the operating points for different parallel-connected pumps.

**Figure 4.**Optimal location of a pumped storage tank. (

**a**) Schematic of the distribution main; (

**b**) Discharge distribution; (

**c**) Head loss variation; (

**d**) Power variation of the external and internal pump stations.

Adjustment Method | Period (h) | Number of Operating Pumps | Pumped Flow Q (m^{3}/s) | Pump Head H_{p} (m) | Absorbed Power P (kW) | Consumed Energy W (kWh/Day) | Specific Energy Consumption w (%) |
---|---|---|---|---|---|---|---|

1. Classical (start–stop) | 0:00–4:00 | 3 p_{f} | 1.47 | 38.6 | 696.3 | 31,705.6 | 100 |

4:00–10:00 | 6 p_{f} | 2.48 | 49.8 | 1730.8 | |||

10:00–14:00 | 4 p_{f} | 1.91 | 42.5 | 995.4 | |||

14:00–17:00 | 5 p_{f} | 2.18 | 45.7 | 1303.1 | |||

17:00–22:00 | 6 p_{f} | 2.48 | 49.8 | 1730.8 | |||

22:00–24:00 | 4 p_{f} | 1.91 | 42.5 | 995.4 | |||

2. Throttle valve control | 0:00–5:00 | 3 p_{f} | 1.47 | 38.6 | 696.3 | 27,970.5 | 88 |

5:00–6:00 | 6 p_{f} | 2.25 | 53.0 | 1424.0 | |||

6:00–7:00 | 6 p_{f} | 2.48 | 49.8 | 1730.8 | |||

7:00–8:00 | 6 p_{f} | 2.25 | 53.0 | 1424.0 | |||

8:00–10:00 | 5 p_{f} | 2.08 | 47.5 | 1138.2 | |||

10:00–12:00 | 4 p_{f} | 1.91 | 42.5 | 995.4 | |||

12:00–13:00 | 5 p_{f} | 1.81 | 56.0 | 1181.6 | |||

13:00–15:00 | 4 p_{f} | 1.91 | 42.5 | 995.4 | |||

15:00–16:00 | 6 p_{f} | 2.08 | 47.5 | 1138.2 | |||

16:00–20:00 | 6 p_{f} | 2.25 | 53.0 | 1424.0 | |||

20:00–23:00 | 6 p_{f} | 2.46 | 50.0 | 1544.1 | |||

23:00–24:00 | 4 p_{f} | 1.81 | 43.0 | 1122.6 | |||

3. Rotational speed control | 0:00–5:00 | 2p_{f} + 1p_{v} | 1.42 | 37.6 | 655.2 | 25,375.5 | 80 |

5:00–6:00 | 5p_{f} + 1p_{v} | 2.25 | 45.5 | 1222.5 | |||

6:00–7:00 | 6 p_{f} | 2.48 | 49.8 | 1730.8 | |||

7:00–8:00 | 5p_{f} + 1p_{v} | 2.25 | 45.5 | 1222.5 | |||

8:00–10:00 | 5 p_{f} | 2.08 | 43.0 | 1030.3 | |||

10:00–12:00 | 4 p_{f} | 1.91 | 42.5 | 995.4 | |||

12:00–1:00 | 3p_{f} + 1p_{v} | 1.81 | 40.0 | 708.9 | |||

13:00–15:00 | 4 p_{f} | 1.91 | 42.5 | 995.4 | |||

15:00–16:00 | 5p_{f} | 2.08 | 43.0 | 1030.3 | |||

16:00–20:00 | 5p_{f} + 1p_{v} | 2.25 | 45.5 | 1222.5 | |||

20:00–23:00 | 5p_{f} + 1p_{v} | 2.46 | 49.6 | 1534.5 | |||

23:00–24:00 | 3p_{f} + 1p_{v} | 1.81 | 40.0 | 708.9 | |||

Energy saving, ΔW_{2-1} | (MWh/year) | 1345.0 | |||||

(%) | 11.6 | ||||||

Energy saving, ΔW_{3-1} | (MWh/year) | 2280.0 | |||||

(%) | 20 | ||||||

Energy saving, ΔW_{3-2} | (MWh/year) | 935.0 | |||||

(%) | 8.4 |

Period (h) | Demand Percentage, (%) | Pumping Percentage, (%) | Compensation Percentage, (%) | Compensatory Volume, (%) | |||
---|---|---|---|---|---|---|---|

α_{d} | Σα_{d} | α_{p} | Σα_{p} | α_{c} = α_{p} − α_{d} | Σα_{c} | α_{v} | |

0:00–1:00 | 3.30 | 3.30 | 4.50 | 4.50 | 1.20 | 1.20 | 2.80 |

1:00–2:00 | 3.25 | 6.55 | 4.50 | 9.00 | 1.25 | 2.45 | 4.05 |

2:00–3:00 | 3.25 | 9.80 | 4.50 | 13.50 | 1.25 | 3.70 | 5.30 |

3:00–4:00 | 3.25 | 13.05 | 4.50 | 18.00 | 1.25 | 4.95 | 6.55 |

4:00–5:00 | 3.40 | 16.45 | 4.50 | 22.50 | 1.10 | 6.05 | 7.65 |

5:00–6:00 | 3.95 | 20.40 | 4.50 | 27.00 | 0.55 | 6.60 (max) | 8.20 (max) |

6:00–7:00 | 4.80 | 25.20 | 4.50 | 31.50 | −0.30 | 6.30 | 7.90 |

7:00–8:00 | 5.25 | 30.40 | 2.50 | 34.00 | −2.70 | 3.60 | 5.20 |

8:00–9:00 | 4.55 | 34.95 | 3.00 | 37.00 | −1.55 | 2.05 | 3.65 |

9:00–10:00 | 4.55 | 39.50 | 4.50 | 40.50 | −0.05 | 2.00 | 3.60 |

10:00–11:00 | 4.60 | 44.10 | 5.50 | 47.00 | 0.90 | 2.90 | 4.50 |

11:00–12:00 | 4.50 | 48.60 | 5.20 | 52.50 | 1.00 | 3.90 | 5.50 |

12:00–13:00 | 4.75 | 53.35 | 5.25 | 57.75 | 0.50 | 4.40 | 6.00 |

13:00–14:00 | 4.50 | 57.85 | 5.25 | 63.00 | 0.75 | 5.15 | 6.75 |

14:00–15:00 | 4.30 | 62.15 | 5.00 | 68.00 | 0.70 | 5.85 | 7.45 |

15:00–16:00 | 4.25 | 66.40 | 4.50 | 72.50 | 0.25 | 6.10 | 7.70 |

16:00–17:00 | 4.20 | 70.60 | 4.25 | 76.75 | 0.05 | 6.15 | 7.75 |

17:00–18:00 | 4.10 | 74.70 | 2.50 | 79.25 | −1.60 | 4.55 | 6.15 |

18:00–19:00 | 4.20 | 78.90 | 2.50 | 81.75 | −1.70 | 2.85 | 4.45 |

19:00–20:00 | 4.30 | 83.10 | 2.85 | 84.60 | −1.45 | 1.40 | 3.00 |

20:00–21:00 | 5.00 | 88.20 | 3.00 | 87.75 | −2.00 | −0.45 | 1.15 |

21:00–22:00 | 4.80 | 93.00 | 3.65 | 91.40 | −1.15 | −1.60 (min) | 0.00 |

22:00–23:00 | 3.60 | 96.60 | 4.25 | 95.50 | 0.65 | −1.10 | 0.50 |

23:00–24:00 | 3.40 | 100.00 | 4.50 | 100.00 | 1.10 | 0.00 | 1.60 |

Period (h) | Pumping | Taper Tank | Rectangular Tank | |||||
---|---|---|---|---|---|---|---|---|

α_{p} (%) | Q_{p} (m^{3}/s) | H_{p} (m) | P (kW) | W (kWh/Day) | H_{p} (m) | P (kW) | W (kWh/Day) | |

0:00–1:00 | 4.50 | 4.25 | 53.6 | 2980 | 67,375.0 | 43.7 | 2710 | 59,980.0 |

1:00–2:00 | 4.50 | 4.25 | 54.4 | 3025 | 48.8 | 2715 | ||

2:00–3:00 | 4.50 | 4.25 | 53.6 | 2980 | 48.7 | 2710 | ||

3:00–4:00 | 4.50 | 4.25 | 56.8 | 3160 | 49.0 | 2725 | ||

4:00–5:00 | 4.50 | 4.25 | 57.2 | 3180 | 49.5 | 2750 | ||

5:00–6:00 | 4.50 | 4.25 | 57.7 | 3205 | 49.8 | 2770 | ||

6:00–7:00 | 4.50 | 4.25 | 56.8 | 3155 | 49.8 | 2770 | ||

7:00–8:00 | 2.50 | 2.36 | 56.4 | 1740 | 49.3 | 1520 | ||

8:00–9:00 | 3.00 | 2.83 | 56.3 | 2085 | 48.9 | 1810 | ||

9:00–10:00 | 4.50 | 4.25 | 54.0 | 3000 | 48.8 | 2710 | ||

10:00–11:00 | 5.50 | 5.20 | 54.5 | 3705 | 49.0 | 3330 | ||

11:00–12:00 | 5.20 | 4.91 | 55.7 | 3580 | 49.2 | 3160 | ||

12:00–13:00 | 5.25 | 4.96 | 56.2 | 3645 | 49.3 | 3200 | ||

13:00–14:00 | 5.25 | 4.96 | 56.7 | 3680 | 49.4 | 3205 | ||

14:00–15:00 | 5.00 | 4.73 | 56.8 | 3515 | 49.5 | 3060 | ||

15:00–16:00 | 4.50 | 4.25 | 56.9 | 3160 | 49.9 | 2775 | ||

16:00–17:00 | 4.25 | 4.02 | 56.8 | 2985 | 49.7 | 2615 | ||

17:00–18:00 | 2.50 | 2.36 | 56.5 | 1745 | 49.6 | 1530 | ||

18:00–19:00 | 2.50 | 2.36 | 55.3 | 1705 | 49.3 | 1520 | ||

19:00–20:00 | 2.85 | 2.03 | 54.2 | 1440 | 48.9 | 1300 | ||

20:00–21:00 | 3.00 | 2.83 | 53.8 | 1990 | 48.4 | 1790 | ||

21:00–22:00 | 3.50 | 3.30 | 49.4 | 2130 | 48.1 | 2075 | ||

22:00–23:00 | 4.25 | 4.02 | 50.4 | 2650 | 48.1 | 2530 | ||

23:00–24:00 | 4.50 | 4.25 | 52.8 | 2935 | 46.8 | 2700 | ||

Energy saving, ΔW | (MWh/year) | 2662 | ||||||

(%) | 11 |

No. | Indicator | Solution | |||
---|---|---|---|---|---|

(1) | (2) | (3) | (4) | ||

1 | Additional investment, 10^{−3}ΔI [€] | ||||

– transmissions mains | – | 1240 | 1240 | – | |

– tanks | – | 157 | 625 | – | |

– pump stations | – | 52 | – | 63 | |

Total | – | 1449 | 1865 | 63 | |

2 | Average pump head, H_{p} [m] | ||||

– external pump station | 60 | 15 | 49 | 40.5 | |

– internal pump stations | – | 35 | – | 12 | |

3 | Consumed energy, W [MWh/year] | ||||

– external pump station | 25,300 | 6600 | 21,600 | 19,600 | |

– internal pump stations | – | 13,400 | – | 3600 | |

Total | 25,300 | 20,000 | 21,600 | 23,200 | |

Peak | 7300 | 2700 | 3400 | 5400 | |

4 | Operation cost, 10^{−3}C_{w} [€/year] | ||||

–energy cost difference, 10^{−3}ΔC_{w} | – | 170 | 135 | 67 | |

–pay-off rate, 10^{−3}rΔI | – | 29 | 38 | 1 | |

Costs difference, 10^{−3}(ΔC_{w} − pΔI) | – | 141 | 97 | 66 | |

5 | SPBT [years] | – | 10 | 19 | 1 |

6 | Energy saving, ΔW | (MWh/year) | 5300 | 3700 | 2100 |

(%) | 21 | 15 | 8 |

© 2016 by the author; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Sarbu, I.
A Study of Energy Optimisation of Urban Water Distribution Systems Using Potential Elements. *Water* **2016**, *8*, 593.
https://doi.org/10.3390/w8120593

**AMA Style**

Sarbu I.
A Study of Energy Optimisation of Urban Water Distribution Systems Using Potential Elements. *Water*. 2016; 8(12):593.
https://doi.org/10.3390/w8120593

**Chicago/Turabian Style**

Sarbu, Ioan.
2016. "A Study of Energy Optimisation of Urban Water Distribution Systems Using Potential Elements" *Water* 8, no. 12: 593.
https://doi.org/10.3390/w8120593