# A Cost–Benefit Based, Parametric Procedure to Screen Existing Irrigation and Municipal Supply Reservoirs for Wind Energy Storage

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}emissions. The evaluation exercise is carried out parametrically, i.e., looking at a large number of combinations of the four parameters, in order to explore a wide range of possible plant configurations and to identify optimal ones under different locational conditions. A sensitivity analysis performed on models’ parameters points out the sensitivity of results to benefit, rather than cost-related, input parameters, such as the efficiency of the generating and pumping system and the opportunity cost of energy.

## 1. Introduction

^{2}and a population of over 5,000,000, Sicily is the largest and most populated island in the Mediterranean, and is energetically independent from the mainland. While conventional thermo-electric plants account for more than 90% of the energy produced in the island, RES, especially wind power, have been booming in Sicily in the last ten years, although bottlenecks in the grid and its overall obsolescence hinder a better exploitation of these type of resources. Sicily features 58 reservoirs, with a potential capacity of 2360 Mm

^{3}. In Italy there are 538 dams recorded at the Italian Register of Dams, and 187 of them are in the South.

## 2. Materials and Methods

#### 2.1. Estimation of Wind Power Production Data

#### 2.2. Load Data

#### 2.3. The Evaluation Model

_{j}is the initial hour of the j-th surplus event. Figure 2 depicts the characteristics of the surplus events in terms of duration and magnitude for years 2011–2013 separately. The elbow shape of these relationships is the consequence of the highly skewed distribution of hourly wind speeds, and gives rise to a considerable scope for optimization when defining the design variables (first of all, storage capacity and installed power) of the PHS plants. These aspects are however better analyzed through a simple model of the storage–release process, illustrated in the following section.

#### 2.3.1. Modelling the Storage–Release Process

_{t}is the pumped water from the lower reservoir in the t-th hour (Q

_{t}> 0 only during a surplus event), K is upper reservoir’s active capacity, and R

_{t}is the release from the upper reservoir. R

_{t}> 0 only outside surplus events, so that R

_{t}× Q

_{t}= 0. All quantities are in m

^{3}.

_{p}, is set equal to 0.85; g (in ms

^{−2}) is the acceleration of gravity, w

_{t}is the available energy surplus (in MW), ΔY (in m) is friction loss along the pipes, and ${\mathrm{Q}}_{\mathrm{max}}^{*}$ is the maximum volume conveyable in a hour by n independent pipes, each of diameter D (in m). In Equation (4), L (in m) is the length of the pipes connecting bidirectionally the upper and the lower reservoir, D is the pipes’ diameter (assumed constant for all pipes), and β is Darcy’s friction factor for steel pipes (Equation (4a)).

_{t}= R

_{max}, unless water in the reservoir is not sufficient, in which case R

_{t}= S

_{t}. According to Equation (6), R

_{max}is given by the flow that can be conveyed at the maximum admissible velocity v

_{max}by the n pipes connecting bidirectionally the upper and lower reservoir, each having an internal section of ω (in m

^{2}). Although both n, D (and hence ω), and v

_{max}could be selected by an optimization study, we rather adopted the following reference values for D and v

_{max}: D = 2 m, v

_{max}= 4 m/s. We then obtained n, recalling that the maximum flow that can be pumped by a pump system with installed power P is:

_{max}= 4Q

_{max}/(π × v

_{max}), and subsequently

_{max}/D)

^{2}

_{t}(including w

_{t}= 0 when production is less than demand) for the 26,304 h of triennium 2011–2013 can be routed through Equations (2)–(6), and for each time step energy production may be evaluated:

_{turb}is the efficiency of the power generation system (the turbines), set equal to 0.90. From Equation (10), the overall energy produced during the three year period can be assessed as

#### 2.3.2. Assessing the Economic Indicators of the Plant

- 1)
- NPV of the plant:$$\mathrm{NPV}=-{\mathrm{C}}_{0}+{\displaystyle \sum}_{\mathrm{y}=1}^{\mathrm{N}}\left({\mathrm{B}}_{\mathrm{y}}-{\mathrm{C}}_{\mathrm{y}}\right)/{\left(1+\mathrm{r}\right)}^{\mathrm{y}}$$
_{0}is the investment cost, assumed concentrated in year 0, B_{y}is the benefit in year y, C_{y}is the cost in year y and r is the social discount rate (SDR), set equal to 3.5% [30]. The methodology to obtain costs is illustrated in 2.3.3, and benefit estimation is reported at 2.3.4. After N years, at the end of the planning period, a residual value of the existing infrastructure should be considered. In addition, depending on N, the cost for equipment renewal should be concentrated in some year distant from the first one (say the 20th or the 30th). In this analysis, the planning horizon was set equal to 25 years so to avoid considering renewal costs, while residual value was conservatively omitted.

- 2)
- IRR of the plant: the discount rate that makes NPV = 0.
- 3)
- B/C: the ratio between actualized benefits and costs:$$\mathrm{B}/\mathrm{C}={\displaystyle \sum}_{\mathrm{y}=1}^{\mathrm{N}}[{\mathrm{B}}_{\mathrm{y}}\times {\left(1+\mathrm{r}\right)}^{\mathrm{y}}]/\left\{\mathrm{Co}+{\displaystyle \sum}_{\mathrm{y}=1}^{\mathrm{N}}[{\mathrm{C}}_{\mathrm{y}}\times {\left(1+\mathrm{r}\right)}^{\mathrm{y}}]\right\}$$
- 4)
- LCOE, the levelized cost of energy:$$\mathrm{LCOE}={{\displaystyle \sum}}_{\mathrm{y}=1}^{\mathrm{N}}[({\mathrm{IC}}_{\mathrm{y}}+{\mathrm{M}}_{\mathrm{y}}+{\mathrm{F}}_{\mathrm{y}})/{\left(1+\mathrm{r}\right)}^{\mathrm{y}}]/{{\displaystyle \sum}}_{\mathrm{y}=1}^{\mathrm{N}}[{\mathrm{Erel}}_{\mathrm{y}}/{\left(1+\mathrm{r}\right)}^{\mathrm{y}}]$$
_{y}, M_{y}and F_{y}respectively represent investment, operation and maintenance costs (O&M), and fuel expenditures in year y. LCOE has the dimension of a price and is similar to B/C ratio, except that benefits are not quantified explicitly.

- 5)
- Eff = Erel
_{tot}/Eabs_{tot}Finally, a saturation index may be defined, as the ratio between energy produced and the total energy surplus: - 6)
- Sat = Erel
_{tot}/W_{tot}The first three indicators require an explicit assessment of both costs and benefits of the plant.

#### 2.3.3. Cost Assessment

_{K}= 23% (with a standard deviation SD of 2.8%), C

_{pipes}= 15% (SD = 7.8%), C

_{turb}+ C

_{pump}= 40% (SD = 5.2%), CTE = 9% (SD = 0.2%), and 13.2% for all the other cost items of Table 2 (SD = 1.5%). Overall, the small value of SD for the various cost typologies indicates that the average cost breakdown is quite representative of a wide class of investments, with the cost of the new reservoir weighing on total investments for 23%. The high standard deviation of C

_{acc_res}is due to the fact that the optimal plants selected to assess this average cost breakdown refer to different values of parameter L, ranging from 1000 m to 10,000 m.

#### 2.3.4. Benefits Assessment

_{2}emissions. To assess this external effect, released energy was first turned into avoided tons of CO

_{2}using an emission coefficient of 433.2 CO

_{2}tons/GWh, according to Italian technical standard UNI/TS 11300-4; the economic value of avoided CO

_{2}tons was then attributed using the reference tables of the European Commission [29], which provide for each year of application (from 2010 to 2050) a range of values (lower–central–upper, in €/CO

_{2}tons) for the avoided emissions. For this application, the central value, spanning from 25 €/CO

_{2}ton in 2010 to 85 €/CO

_{2}ton in 2050, was used.

## 3. Results and Discussion

^{3}, but smaller capacities can be also appropriate, albeit for a limited, selected number of other locational and installed power scenarios. The interplay among the four parameters can be investigated by plotting one of the selected economic indicators against one parameter, e.g., capacity, for different values of the other design parameter, e.g., installed power, for each combination of the locational parameters H and L. As an example, Figure 5a–h shows these plots for H = 200 m and L = 3000 m, but the comments apply comprehensively to all the different combinations plotted.

_{tot}and Eabs

_{tot}exhibited decreasing marginal values with K, i.e., they grew steadily for low K values, but they tended towards an asymptotic value, faster the smaller the power capacity, as should be expected. Saturation showed a similar pattern, while efficiency showed a minimum for K values where Eabs

_{tot}has an elbow. For low values of the installed power, the economic indicators all exhibited a maximum storage capacity, while for larger installed powers this maximum was not directly detectable, as it probably fell outside the K domain adopted in this study. For large installed power, however, a decreasing marginal value for these indicators was recognizable, pointing out that increasing storage capacity leads to benefits that are bound to be outweighed by investment costs. For all (H, L) pairs, plots like those of Figure 5 were analyzed in order to find the pairs (K, P) that maximized a given economic indicator. This search process was performed on the IRR rather than on the NPV because, like the B/C ratio, it is a dimensionless indicator and allows comparison with other storage technologies or different investment projects. As a result, functions P* = f(K*):(P*, K*) = arg

_{max}(IRR | H, L) were developed. Figure 6 shows such relationships for different H and L combinations, from the less advantageous (H small, L large), to the most favorable ones.

_{turb}, the overall efficiency of the generation system, which ranked first as sensitive parameter in 100% of cases. After η

_{turb}, the opportunity cost of energy ranked second for importance (in 96% of cases), and η

_{pump}ranked third (in 92% of cases). In concluding, the ranking of parameters according to their impact on NPV, IRR and B/C is reported in Table 5, together with the average values of elasticities. The table shows that the five most sensitive parameters were the same regardless the PI used to assess elasticity.

_{NPV}, η

_{turb}with H, L, P and K. The figures reported the average value of the elasticity of the NPV to η

_{turb}, together with an upper and lower confidence level built with the standard deviation of the elasticity. According to Figure 7, this elasticity was almost insensitive to capacity (K). Average elasticity (blue line), and consequently uncertainty, seemed to grow in the direction where conditions become less favorable for a PHS plant (small Hs and Ps, large distances Ls between reservoirs).

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Location of wind farms in Sicily and wind metering stations used to reconstruct wind power production. The colored areas cover clusters of wind farms of which production is assessed using data from the same wind gauge station.

**Figure 2.**(

**a**) Distribution of the duration of events of wind power surplus for years 2011–2013; (

**b**) magnitude of wind power surpluses for the same period.

**Figure 3.**Design scheme for the new, upper reservoir. Dimensions are in m and refer to K = 0.2 Mm

^{3}.

**Figure 4.**Percentage of economically worthwhile plants classified by head (

**a**), distance between reservoirs (

**b**), installed power (

**c**), and active storage capacity (

**d**).

**Figure 5.**(

**a**) NPV, (

**b**) IRR, (

**c**) B/C, (

**d**) LCOE, (

**e**) Eabs

_{tot}, (

**f**) Erel

_{tot}, (

**g**) efficiency and (

**h**) saturation as a function of storage capacity for different power capacities. H = 200 m and L = 3000 m.

**Figure 6.**Plots of (P, K) pairs that maximize IRR for (

**a**) L = 1000 m, H = 100 m; (

**b**) L = 1000 m, H = 400 m; (

**c**) L = 3000 m, H = 100 m; (

**d**) L = 3000 m, H = 400 m; (

**e**) L = 5000 m, H = 150 m; (

**f**) L = 10,000 m, H = 200 m.

**Figure 7.**NPV sensitivity to η

_{turb}as a function of the head (

**a**), distance between reservoirs (

**b**), installed power (

**c**), and upper reservoir’s active capacity (

**d**). Dotted lines indicate average elasticity value ± elasticity standard deviation.

**Table 1.**Values of the four locational (H and L) and design (P and K) parameters used in the parametric analysis.

H (m) | L (km) | P (MW) | K (Mm^{3}) |
---|---|---|---|

50 | 1 | 5 | 0.02 |

100 | 3 | 10 | 0.05 |

150 | 5 | 20 | 0.10 |

200 | 10 | 50 | 0.50 |

300 | 100 | 1.00 | |

400 | 150 | 1.50 | |

2.00 | |||

2.50 | |||

3.00 | |||

3.50 | |||

4.00 | |||

5.00 |

**Table 2.**Cost items, parametric investment cost models, and maintenance costs considered in the analysis.

Symbol | Cost Item | Parametric Investment Cost Model | Maintenance Costs (€/year) |
---|---|---|---|

C_{K} | Upper reservoir | C_{k} = K × 0.0038 × (K)^{−0.35}/1.275 K (m^{3}) | 0.0025 × C_{K} |

C_{pipes} | Pipelines | C_{pipes} = 0.0375 × (D)^{1.4562} × N_{T} × L D (mm) L (m) | 0.0015 × C_{pipes} |

C_{turb} | Power Generation (Turbines and equipment) | C_{turb} = 1.1948 × (P)^{0.7634} × N_{turb} × 0.82234 × 10^{6} P(MW) | 0.0030 × C_{turb} |

C_{pump} | Pumping System | 0.5 × C_{turb} | 0.0040 × C_{pump} |

C_{acc_res} | Reservoir ancillary works (fencing, lighting, access roads etc.) | 0.15 × C_{res} | 0.0030 × C_{acc_res} |

C_{acc_turb} | Pumping and generation ancillary works (power and pump house, keeper’s house, services etc.) | 0.05 × C_{turb} | 0.0040 × C_{acc-turb} |

C_{Land} | Land | 0.005 × (C_{res} + C_{pipes} + C_{turb} + C_{pump}) | |

C_{S} | Electric substation and connection to AC grid | 0.20 × (C_{turb} + C_{pump}) | |

C_{TE} | Technical expenditures | 0.1 × (C_{res} + C_{pipes} + C_{turb} + C_{pump}+ C_{acc_res} + C_{acc_turb} + C_{Land} + C_{s}) |

**Table 3.**Parameters considered in the sensitivity analysis and parameter range (%s are on the central value).

No | Parameter | Parameter Range | |||
---|---|---|---|---|---|

Lower Value | Central Value | Upper Value | |||

1 | Reservoir cost | C_{K} | 90% | 100% | 110% |

2 | Generation equipment cost | C_{turb} | 90% | 100% | 110% |

3 | Pumping system cost | C_{pump} | 90% | 100% | 110% |

4 | Pipelines cost | C_{pipes} | 90% | 100% | 110% |

5 | Total operation cost | C_{gtot} | 90% | 100% | 110% |

6 | Economic value of avoided energy production from the present mix | PUN | 90% | 100% | 110% |

7 | Value of avoided CO_{2} emissions | CO_{2} | 90% | 100% | 110% |

8 | Efficiency of the generation system | η_{t} | 0.80 | 0.85 | 0.90 |

9 | Efficiency of the pumping system | η_{p} | 0.75 | 0.80 | 0.85 |

10 | Maximum water velocity in the pipelines | v | 3 m/s | 4 m/s | 5 m/s |

**Table 4.**Importance matrix of the parameters analyzed. The elements of the matrix indicate the frequency (on the sample of the plants with IRR ≥ 7%) with which a parameter ranks first to second…tenth, by order of importance.

Parameter | Cardinality of the Order of Importance | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1° | 2° | 3° | 4° | 5° | 6° | 7° | 8° | 9° | 10° | |

C_{K} | 0.00 | 0.00 | 0.00 | 0.44 | 0.40 | 0.09 | 0.04 | 0.01 | 0.00 | 0.00 |

C_{pipes} | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.21 | 0.14 | 0.06 | 0.34 | 0.19 |

C_{turb} | 0.00 | 0.00 | 0.05 | 0.50 | 0.44 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |

C_{pump} | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.46 | 0.32 | 0.15 | 0.04 | 0.00 |

C_{gtot} | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.27 | 0.70 |

PUN | 0.00 | 0.97 | 0.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

CO_{2} | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.26 | 0.52 | 0.18 | 0.00 |

η_{p} | 0.00 | 0.03 | 0.92 | 0.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

η_{t} | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

v | 0.00 | 0.00 | 0.00 | 0.01 | 0.05 | 0.18 | 0.24 | 0.23 | 0.18 | 0.12 |

Order of Importance | 1° | 2° | 3° | 4° | 5° | 6° | 7° | 8° | 9° | 10° |
---|---|---|---|---|---|---|---|---|---|---|

Parameters ordered by importance—NPV | ${\mathsf{\eta}}_{\mathrm{t}}$ | PUN | ${\mathsf{\eta}}_{\mathrm{p}}$ | C_{turb} | C_{k} | CO_{2} | C_{pump} | C_{k} | C_{gtot} | v |

Average elasticity value (over the 225 plants)—NPV | 2.56 | 2.22 | 1.79 | −0.51 | −0.52 | 0.35 | −0.25 | −0.20 | −0.15 | −0.06 |

Parameters ordered by importance—IRR | ${\mathsf{\eta}}_{\mathrm{t}}$ | PUN | ${\mathsf{\eta}}_{\mathrm{p}}$ | C_{turb} | C_{k} | C_{pump} | CO_{2} | v | C_{k} | C_{gtot} |

Average elasticity value (over the 225 plants)—IRR | 1.40 | 1.23 | 0.98 | −0.48 | −0.48 | 0.23 | 0.18 | 0.16 | 0.17 | −0.08 |

Parameters ordered by importance—B/C | ${\mathsf{\eta}}_{\mathrm{t}}$ | PUN | ${\mathsf{\eta}}_{\mathrm{p}}$ | C_{turb} | C_{k} | C_{pump} | CO_{2} | v | C_{gtot} | C_{k} |

Average elasticity value (over the 225 plants)—B/C | 1.00 | 0.86 | 0.70 | −0.34 | 0.33 | −0.16 | 0.14 | 0.07 | −0.09 | 0.11 |

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**MDPI and ACS Style**

Arena, C.; Genco, M.; Lombardo, A.; Meli, I.; Mazzola, M.R.
A Cost–Benefit Based, Parametric Procedure to Screen Existing Irrigation and Municipal Supply Reservoirs for Wind Energy Storage. *Water* **2018**, *10*, 1813.
https://doi.org/10.3390/w10121813

**AMA Style**

Arena C, Genco M, Lombardo A, Meli I, Mazzola MR.
A Cost–Benefit Based, Parametric Procedure to Screen Existing Irrigation and Municipal Supply Reservoirs for Wind Energy Storage. *Water*. 2018; 10(12):1813.
https://doi.org/10.3390/w10121813

**Chicago/Turabian Style**

Arena, Claudio, Mario Genco, Alessio Lombardo, Ignazio Meli, and Mario Rosario Mazzola.
2018. "A Cost–Benefit Based, Parametric Procedure to Screen Existing Irrigation and Municipal Supply Reservoirs for Wind Energy Storage" *Water* 10, no. 12: 1813.
https://doi.org/10.3390/w10121813