**1. Introduction**

Hydro and wind powers are promising renewables. However, due to the stochastic nature of the wind power, it is more efficient and reliable to combine it with another suitable energy system to provide a stable operation for large utility grid systems. Pumped hydro storage (PHS) is a suitable energy storage system that can be hybridized with wind power in order to overcome its variability and provide real-time load following. Hydro power makes up around 19% of electrical power generated worldwide [1]. It is one of the oldest methods of renewable energy generation [2]. Hydropower originates from the sun, as its water cycle is driven by solar radiation. Approximately 22% of incoming solar energy is captured to form precipitation, which is the source of hydropower [3]. Hydropower stations can be categorized based on their output power. They are classified as small, mini, or micro types when the maximum output power is 15 MW, 1 MW and 100 kW, respectively [4]. In this paper, the maximum output of the PHS exceeds the small type, therefore, a large type is added to the aforementioned category.

PHS plants are mainly used to serve demand during the peak load hours [3]. When wind generation exceeds demand, excess power can be stored by pumping water into the upper reservoir of the PHS system. Conversely, when the load exceeds the wind generation, the stored hydro energy can be used to supply the power deficit. In fact, PHS plants are considered to be one of the best utility-scale energy storage solutions due to their ability to supply power in just one to three minutes [3].

In the published literature, the operation of the grid-connected PHS, combined with wind power, has been extensively investigated. In [5], the authors suggested using pumped hydro storage as an operating reserve ancillary service in order to mitigate the problems related to wind farm integration with the grid. A probabilistic unit commitment using Lagrange relaxation was suggested to find the optimal scheduling of the thermal generators when wind power was integrated into the system while considering the uncertainty of the wind speed. It was found that pumped hydro storage could be e ffectively employed to reduce operating and flying reserve costs. In [6], PHS application in combination with a wind farm to increase profit in electricity markets was investigated. The results showed that the revenue was a function of the type of hydro storage used and market characteristics. The revenue increased by up to 11% by employing PHS. The authors in [7] proposed a deterministic, dynamic programming, long-term generation expansion model to find the optimal generation mix, total system cost, and total carbon dioxide emissions of a PHS system connected to a wind farm. It was found that in order to gain financial benefit from building the capital-intensive PHS, the exogenous market costs had to be very strong. In [8], a novel coordination strategy of a wind farm combined with PHS for a faster, reliable self-healing process in the grid restoration phase was proposed. The problem was formulated as a two-stage adaptive robust optimization and solved using the column-and-constraint generation (C&CG) decomposition algorithm. The results proved that the PHS could increase system reliability and reduce wind power curtailment. A combinatorial planning model in order to maximize wind power utilization and reduce wind energy curtailment was studied in [9]. A posterior multi-objective (MO) optimization approach was proposed to deal with wind energy curtailment cost and the total social cost. The obtained results introduced an optimization approach capability and e fficiency regarding the planning of renewable-based power systems. In [10], a sizing method for a wind–hydro system in the Canary Islands was proposed and its economic benefits for the island's electrical system were investigated. The contribution of this wind–hydro system to satisfying electricity demand was 29% higher than wind-only, and the electrical energy generation cost was reduced by 7.68 M€/year. In [11], the authors presented an improved probabilistic production simulation method to facilitate the cost–benefit analysis of PHS. A case study on the IEEERTS79 system, which was used to demonstrate the e ffectiveness of the proposed simulation method, helped the industry move toward high penetration of the integrated wind energy power system.

In order for sustainable power generation to become universally adopted so that its planetary benefits are realized, the economic and technical designs of these power plants must be locally appropriate and optimal. This paper addresses this fundamental challenge for design engineers and managerial decision-makers.

The scientific/technical problem that is addressed and solved in this case study is as follows. In order to solve the global warming and cost of energy problems contributed to by electric power generation, local renewable resources must be utilized, combined, and optimized in their overall system design. This paper addresses these technical problems in a case study of combining wind and hydro power generation in Jordan as a specific location. In addition, this paper investigates the financial, environmental, and technical feasibility of wind farming and pumped hydro energy storage in an oil-importing country to reduce the energy-producing burden. Three heuristic optimization techniques are used from the Matlab optimization toolbox to verify the system design. Results show that the proposed system may be notably beneficial for Jordan. The same methodology can be applied in countries where this is relevant, such as Panama, a country which one of the authors visited for this purpose.

The fundamental problem of global sustainable energy production is the optimal use of locally specific renewable energy sources, such as wind and hydro energy resources, as laid out in this paper. In other words, this global problem must be solved locally everywhere. This is an engineering design optimization, which usually requires hybrid power plants. This paper presents a detailed case study of how this engineering problem is solved. In the process, it also sheds light on our concept of local solutions to a global problem. This important concept is often lost on countries and companies that attempt to build sustainable power generation projects.

In this paper, the Matlab optimization toolbox was used to find the optimal solution in terms of technical, environmental, and economic considerations. Moreover, genetic algorithm (GA), simulated annealing (SA), and pattern search (PS) techniques were used from the above toolbox to solve the problem described in this paper. Furthermore, it was shown that the objective function, cost of energy, of the on-grid, which was penetrated by the hydro–wind system (COEPS) was optimally minimized. The economically feasible solution was considered to find detailed solutions. This work aims to help decision-makers find the best technical solutions before actual implementation of the proposed energy configuration.

### **2. Description of the Proposed System**

This paper discusses the combination of a wind and hydropower system (See Figure 1), which is integrated with the distribution grid in the country of Jordan, as a case study in an oil-importing country.

**Figure 1.** On-grid hydro–wind energy schematic.

The location was the same as one investigated in [12], where an on-grid wind power system was studied in Aqaba, Jordan. However, in this paper, an on-grid wind farm combined with a PHS station was investigated. Therefore, some data are the same, while others are updated for this more up-to-date study. The location was considered to be geographically suitable to construct a PHS station.

Artificial intelligence techniques (GA, SA, and PS) provided by the Matlab optimization toolbox were used to find the optimal solution of the objective function (COEPS). Then, based on the best fitness, many indicating corresponding functions were computed, such as the wind and hydro fraction (WHf), grid purchases, the footprint of the renewables, and carbon dioxide emissions (ECO2). This procedure aimed to help design engineers replicate the same criteria to find optimal solutions for other system configurations to be adopted based on these technical studies and negotiations between electric utilities and investors. Economic, technical, and environmental feasibility impacts were also studied.

### *2.1. PHS Station Data*

The information that was specified for the pumped hydro storage plant to be accurately modeled is shown in Table 1. First, the roundtrip efficiency referred to the ratio of the energy out to the energy in over a period of time [13]. It is difficult to separately measure the charging and discharging energies, therefore, manufacturers usually determine the round-trip efficiency and consider it to be the charging efficiency by assuming 100% discharging efficiency. Many authors have discussed this issue in the case of battery systems. Thus, the charging efficiency was set to be equal to the round-trip efficiency, and the discharging efficiency was assumed be in agreemen<sup>t</sup> in [14,15].


**Table 1.** Values of parameters used for the pumped hydro storage (PHS) station.

Second, the usable state of charge (SOC) [1] referred to the ratio of the usable energy that was taken to the total energy of the PHS. In other words, the usable SOC was the energy left in the upper reservoir compared with the amount of energy in a full reservoir. This gave an indication into how long the PHS station could provide energy before a refill. In this study, it was assumed that a minimum stored energy should remain, and this value was the complement of the usable SOC. The usable SOC was assumed to be the same as the round-trip e fficiency. Third, an initial PHS stored energy in the upper reservoir was assumed [18]. The aforementioned parameters helped to determine the PHS power generation capacity in kW, which could be used to supply the load as needed. This capacity value was sized using the GA, SA, and PS of the Matlab optimization toolbox. The capital cost of the PHS had an average value of 1651.04 \$/kW [16]. The operation and maintenance costs (OMC) were taken as percentages of the capital cost (CC) [16]. Table 1 shows the values that were assumed and considered for the PHS plant. These plant data were used to compute the hourly energy generated. There was an approximate ratio of ten between the rated power (in kW) and energy (in kWh) of the PHS station, as stated in [19].

### *2.2. Wind Speed and Probability Distribution Function*

Wind speed can change rapidly in any region. Its variation depends on several factors, such as the surface and the local weather. Appropriate predictions of wind speed in a specific area are necessary for wind power and energy estimations in that area. One of the models for characterizing the wind power is a cubic function of the wind speed. Therefore, a small error in the prediction of wind speed leads to huge variations in the wind energy estimation. Various methods are used to study the characteristics of wind speed. Weibull and Rayleigh distributions are the most preferred methods, as they are flexible and easy in terms of parameter determination.

The focus in this paper was on the Rayleigh distribution, which is a special form of the Weibull distribution with a shape factor that is always equal to two. In the Rayleigh distribution, the mean wind speed is su fficient to determine the wind characteristics. The Rayleigh distribution function (*fR(v)*) is given by Equation (1) [20,21].

$$f\_{\mathbb{R}}(\upsilon) = \left(\frac{\pi}{2}\right) \left(\frac{\upsilon}{\upsilon\_a^2}\right) \exp - \left[\frac{\pi}{4} \left(\frac{\upsilon}{\upsilon\_a}\right)^2\right] \tag{1}$$

where *va* is the average wind speed in a specific area in (m/s). The wind speed logarithmic law shown in Equation (2) was used to model the variation of wind speed due to the di fference in height between the anemometers of the metrological station and the hub of the proposed wind turbine. In addition, it considered the terrain roughness between two altitudes [12,22].

$$\frac{v}{v\_0} = \frac{\ln(H/z\_0)}{\ln(H\_0/z\_0)}\tag{2}$$

where *v*0 is the wind speed corresponding to the height ( *H*0) and *Z*0 is the roughness coe fficient. A case study was conducted in Aqaba, which is the free Trade Area in Jordan. The wind speed was measured in a specific location using anemometer installed at 45 m above ground level, in which the output data was taken on a monthly average basis. Then, Rayleigh distribution was used to obtain hourly data, as shown in Figure 2. The roughness factor of the logarithm used for this case was 0.03 to adjust for the wind speed of open terrain areas [22]. Also, the hub height of the proposed wind turbine was 80 m (Table 2) which was also considered in the logarithm. The wind speed-based Rayleigh distribution function in Aqaba for twelve months is shown in Figure 2.

**Figure 2.** Curves of Rayleigh distribution for all months.



Other information that was determined for the wind farm to be precisely sized is shown in Table 3. The financial input parameters were the same as the ones described in the wind-only investigation [12]. The project lifetime was assumed to be 50 years. Therefore, the wind turbine will be replaced twice, with a cost that was assumed the same as the capital cost.



The geographical area of the wind farm (*AWF*) was computed using Equation (3). *L* and *W* are the dimensions of the wind farm, which was considered to have a rectangular shape. For the row spacing (RS) and column spacing (CS) values shown in Table 3, Equations (4) and (5) were used to calculate *L* and *W*.

$$A\_{\rm MF} = L \times \mathcal{W} \tag{3}$$

$$L = C\_S(N\_{\alpha l} - 1) + D\_r \tag{4}$$

$$\mathcal{W} = R\_S (N\_{row} - 1) + D\_I \tag{5}$$

where *Dr*, *Nrow*, and *Ncol* are the rotor diameter, number of rows, and number of columns, respectively. These helped to compute the maximum and minimum wind areas, i.e., the *Amax* and *Amin*. A footprint cap limit of 20,000 Dunam was considered for the on-grid wind hydro energy system.

### *2.3. Load Demand Hourly Data*

The load demand hourly values of Aqaba, Jordan in 2017 were prepared after tailoring the supervisory control and data acquisition (SCADA) demand values in 2016 used in [12]. They were obtained from the National Control Center of the National Electric Power Company, Jordan. A percentage growth of 6% for a year is usually used in electric utilities in Jordan to obtain the annual load demand for the following year, therefore, in this paper, the hourly load values in 2017, as shown in Figure 3, were obtained by applying this percentage.

**Figure 3.** Load demand hourly values of the Aqaba Qasabah district in 2017.

The minimum, maximum, and mean load demand values were 27.295 MW, 132.270 MW, and 85.073 MW, respectively, as shown in Figure 3.

### **3. Mathematical System Formulation**

### *3.1. Modeling of the Hydro Station*

The priority was to satisfy the load from the wind farm. If the wind power was not su fficient, then energy deficit should be covered by the PHS station and, lastly, the energy purchased from the utility grid. The Matlab code had the target of satisfying the entire load. Three cases were considered. First, the load was satisfied by the wind farm, and if there was excess wind power and the reservoir was full, the generation of the hybrid renewable energy system came only from the wind power plant. Second, the load was satisfied by the wind farm, and there was excess wind power and the reservoir was not full. Thus, we computed the excess wind power that could charge the PHS plant by comparing the excess wind power value to the rated capacity of the PHS plant.

Third, when the generation of wind farm was less than what was required by the load demand, we checked the availability of the PHS plant for this power deficit. Moreover, the PHS minimum energy storage capacity was set, which was not exceeded during the discharge.

Once the rated power of the hydro station, *Prated*, in kW was optimized, the energy in kWh, *Wrated*, was estimated based on the assumption made in Section 2.1. Then, the potential energy (in J/m3), *WJ*, and (in kWh/m3), *WkWh*, of water in the upper reservoir were computed using Equation (6) and Equation (7), respectively.

$$\mathcal{W}\_{\mathcal{I}} = \rho\_{water} \mathcal{g} H \tag{6}$$

$$\mathcal{W}\_{\text{kWh}} = 2.78 \times 10^{-7} \mathcal{W}\_{\text{J}} \tag{7}$$

where ρ*water* is the density of water (1000 kg/m3), *g* is the gravitational acceleration (9.81 m/s2), and *H* is the actual head of the PHS station [12].

Then, the volume of the water in the upper reservoir (in m3), *Vwater,* was computed using Equation (8). At this point, the area required for the PHS station, *APHS*, was computed using Equation (9) for a given mean depth, *D* [12]. Furthermore, Equation (10) was used to compute the water flow (*Fwater*) in the pipeline in (m<sup>3</sup>/s) [23].

$$V\_{water} = \frac{E\_{rated}}{\eta \mathcal{W}\_{kWh}} \tag{8}$$

$$A\_{PHS} = \frac{V\_{water}}{D} \tag{9}$$

$$F\_{\text{water}} = \frac{P\_{\text{rated}}}{\eta Hg} \tag{10}$$

### *3.2. Modeling of the Wind Turbine Power Curve*

The wind turbine output power model can be typically presented in two main regions. Region 1 exists between the cut-in speed [1] and the rated wind speed ( *VR*), while Region 2 exists between *V*R and the cut-out wind speed [6], as shown in Figure 4. This shows the ideal model representation of a wind turbine and the corresponding main regions.

To convert the hourly wind speed values, obtained before using Rayleigh distribution, into hourly output wind turbine values, the mathematical model in Equation (11) is used to model Region 1 shown in Figure 4. *PR* is the rated power generated by a wind turbine. Further, the corresponding A, B and C parameters are given in Equations (12)–(14) [9,24,25]. This model is di fferent from the ones described in [12]. The output power in Region 1 runs smoothly between *VI* and *VR* with no protrusions at the cut-in value, as shown in the models described in [12], see Figure 5. This will result in an accurate computation of the output power extracted from the wind farm. This leads to precise computations in the output wind power and energy and thus in the number of units sizing, geographical footprint, economic and environmental indicators.

$$P(\upsilon) = \left\{ \begin{array}{ll} P\_R \langle A + B\upsilon + \mathbb{C}\upsilon^2 \rangle, & V\_I \le \upsilon \le V\_R \\ P\_{R\_{\upsilon}} & V\_R \le \upsilon \le V\_{\upsilon} \end{array} \right\} \tag{11}$$

$$A = \frac{1}{\left(V\_I - V\_R\right)^2} \left[ V\_I (V\_I + V\_R) - 4V\_I V\_R \left(\frac{V\_I + V\_R}{2V\_R}\right)^3 \right] \tag{12}$$

$$B = \frac{1}{\left(V\_I - V\_R\right)^2} \left[ 4(V\_I + V\_R) \left(\frac{V\_I + V\_R}{2V\_R}\right)^3 - \left(3V\_I + V\_R\right) \right] \tag{13}$$

$$C = \frac{1}{\left(V\_I - V\_R\right)^2} \left[2 - 4\left(\frac{V\_I + V\_R}{2V\_R}\right)^3\right] \tag{14}$$

Wind Velocity(݉/ݏ݁ܿ(

**Figure 4.** Schematic of wind turbine output power model.

**Figure 5.** Output wind power of a C96–2.50 MW wind turbine.
