Wake Effect

The layout of wind turbines in a wind farm affects AEP of the array. As we discussed in Chapter 4, wind has spatial variability; therefore, if the farm is large enough, in some places wind energy is higher than other places. If variability of the available resource was the only reason, we could just locate wind turbines in places that have the highest energy. A more complicated issue is the interaction of a wind turbine with neighbouring turbines. Fig. 9.4 shows how turbines can be located in the wake of each other under particular wind conditions. The wind speed in the wake of a turbine is significantly lower than the undisturbed wind speed (in the absence of the upwind turbine). This reduction of speed adversely affects total AEP. It is possible to place turbines very far from each other to avoid wake effects, but this can lead increased cost of cabling, electrical connections between turbines, maintenance cost, and a larger leased area. Therefore, finding the optimum layout is an optimization problem.

Estimating the reduction of wind speed in the wake of a turbine can be achieved by simplified methods, based on the distance of the turbines, hub height, and radius of turbines (e.g. [5, 6]), or wakes can be more accurately simulated using CFD codes and high performance computing (e.g. [7, 8]).

Decision Variables

In micro-siting of offshore wind farms, the layout of the farm, which consists of several variables, needs to be optimized. The simplest case is when the number and the capacity of turbines are given, in which the locations of the turbines are the decision variables. More complicated cases involve more decision variables, such as the number, size, type, and hub-heights of turbines, in addition to the locations of the wind turbines.

Objective Functions

As mentioned before, a renewable energy system can be optimized by a single or multiple objective functions. The simplest objective function is AEP (maximize). This objective function does not take into account the cost associated with AEP, which is a major factor in the decision-making process. Referring to the concept of levelized cost of energy (LCOE) introduced in Chapter 1, the ratio of the cost of energy to electricity production can be minimized, which is a more practical objective function. This objective function takes into account the increased cost of electrical cables and other elements of the farm when turbine spacing is increased:

$\begin{array}{ll}\hfill \text{minimize}& \frac{C_{\mathrm{t}}}{E_{\mathrm{p}}}\hfill \\ \hfill \text{subject to}& \text{constraints}\hfill \end{array}$

where C_t can be chosen as the total cost of the project, and E_p is the total energy production during the lifetime of the project. Alternatively, the investment cost divided by AEP can be minimized, which does not take into account the interest rate, operation and maintenance cost, and the time value of money.

Constraints

Micro-siting is subject to several constraints. The most common constraint is the available area/plot for the farm (i.e. all turbines should be located inside the array). The minimum distance between turbines can also be a constraint due to technical issues or standards/regulations. Another constraint is the maximum available investment. Although a large project can produce reasonable and lower LCOE, the resources for financing a project are usually limited. The layout of a wind farm may be subjected to some constraints to reduce the visual impact or improve aesthetic design (e.g. Fig. 9.3B). Finally, forbidden areas in a farm can limit the search space. These areas may be excluded due to foundation issues, dedicated to electrical cable routes, etc.

Solution Techniques

Due to the complexity of the objective function and constraints of the wind farm optimization problem, classical optimization techniques that are often more suited to convex and continuous problems are less popular. Therefore, metaheuristic methods are more effective and common in this area. Metaheuristic approaches provide satisfactory solutions, but they do not necessarily find the theoretical optimum. Genetic algorithm, particle swarm optimization, the greedy algorithm, evolutionary algorithm, and ant colony are metaheuristic approaches applied in this area [5, 9].

The 2009 EMEC guide the assessment of tidal energy resources [10] recommends that the lateral spacing between devices (the distance between axes) should be two-and-a-half times the rotor diameter (2.5D), and the downstream spacing should be 10D—both based on the assumption of horizontal axis turbines. Further, the EMEC guide states that devices should be positioned in an alternating downstream (i.e. staggered) arrangement (Fig. 9.5). Although the exact details of device spacings is device-specific and can be debated (and indeed no justification is given for the values 2.5D and 10D, although we can assume that such guidance has propagated through from the wind industry), the reasoning behind the spacings is introduced here. Each tidal stream device will generate a wake—a relatively narrow turbulent region downstream of the device where the velocity is below ambient. Clearly, placement of a subsequent device within this wake zone would lead to suboptimal device performance (e.g. increased turbulence), and so not exploiting the resource to its full potential (because the velocity in this region is below ambient). Therefore, the guidance of spacing devices 10D in the longitudinal direction is designed to minimize the wake effect. In addition, by staggering the devices, this will further prevent a device positioned downstream of another device from operating in its wake (Fig. 9.5). Myers and Bahaj [11] investigated the impact of lateral device spacing. They found that for very close lateral turbine spacings (0.5D measured between the innermost edges of the actuator disks, which is equivalent to 1.5D in the EMEC guidelines; based on flume experiments where the turbine rotors were represented by porous disks), the individual wakes generated by each of two devices merged by around 4D downstream. At increased lateral spacings (1.5D), a region of around 1D width accelerated flow between the two disks resulted, indicated by a negative velocity deficit¹ in Fig. 9.6. Therefore, for a final experiment, Myers and Bahaj [11] placed a third ‘turbine’ 3D downstream of the first row of disks in an attempt to exploit this region of accelerated flow. Although they did not perceive any significant negative changes to the efficiency of this third device, they found that the far wake region of the array had a relatively high velocity deficit due to the combined wakes, and so a third row of devices would need to be installed at a considerably increased longitudinal spacing to enable interception of flow speeds comparable to the first row. Of course, flume experiments such as this are unidirectional, and so bidirectional (tidal) flows will require further consideration, for example, the ‘first’ row during the flood phase of the tidal cycle will become the ‘last’ row during the ebb.

Apart from potentially making use of regions of accelerated flow to strategically site devices (as discussed above), it is clearly advantageous, from both economic and practical perspectives, to minimize lateral and longitudinal extents of tidal energy arrays. Many leased tidal energy sites are situated in relatively narrow straits, where the principal flow dimension is much greater than the lateral channel dimension. Therefore, due to physical and navigational constraints, a more compact lateral array configuration (and hence spacing) is desirable. Excessive longitudinal spacing will significantly increase subsea cable lengths (e.g. the range of 5D–15D longitudinal spacing to avoid wake effects equates to 100–300 m for a 20 m diameter turbine), but such potentially increased cabling costs would depend on the design of the subsea connections and cable route between the devices and the substation (e.g. [12]).

Blockage

The theoretical upper limit to power extraction by a wind turbine is constrained by the Betz limit (C_p = 0.59), where C_p is the rotor power coefficient (see Section 3.13.1). However, in wind energy conversion, the cross-sectional area (CSA) of the turbine is very small in comparison to the CSA of the wind resource. By contrast, when tidal turbines are placed in a tidal channel, the turbine blockage ratio² increases, resulting in a theoretical C_p that can considerably exceed the Betz limit for array scales/configurations that are characterized by high blockage ratios [13]. However, the situation is complicated by the fact that by increasing the blockage ratio of a channel, there will be a corresponding reduction in the free-stream flow due to the increased drag resulting from tidal energy conversion. In other words, placing too many turbines in a tidal channel will merely block the flow.

To maximize turbine efficiency (i.e. the power available per turbine), tidal arrays should occupy the largest possible fraction of a channel’s CSA [14]. However, practical constraints, such as navigation and the passage of marine life, will require gaps between the turbines in an array. In such a scenario, energy is dissipated in the wakes, and so the turbines are less effective than if they were deployed in a fence that spans the entire channel³ [15].

An interesting extension of the work on simple tidal channels (e.g. [15]) is application to split channels [16]. Split channels are fairly common amongst tidal energy sites—for example, the Bay of Fundy, Puget Sound, and the Pentland Firth. How, for example, would large-scale tidal energy extraction in the Inner Sound influence the tidal energy resource within the Pentland Firth itself (Fig. 9.7)? In addition, for scenarios where there is a fairly equal channel division, devices could be strategically installed on one side of an island, leaving the opposite side clear for navigation [16]. Polagye and Malte [17] simulated a range of channel networks, including a split tidal channel (which they call a multiple-connected network). They found that transport in the impeded channel reduced, at maximum power, to around 50% of its magnitude compared with its undisturbed state. This is agreement with Cummins [18], who found, using an electric circuit analogue, that the transport in the impeded channel was reduced to 50–71%: a similar range to the much reported 58% calculated by Garrett and Cummins [19] for a single channel in the resistive limit. Polagye and Malte [17] found that maximum dissipation (P_max) was 20% higher when extraction was evenly distributed between the two branches (Fig. 9.8), and that an even distribution minimizes far-field impacts. However, such an optimal arrangement may be neither desirable (e.g. it would preclude the dedicated navigational channel mentioned earlier) nor attainable (e.g. natural flow asymmetry between the two channel branches).

Since a renewable energy converter absorbs energy from its surrounding environment, the total available resource is reduced for neighbouring energy converters [20]. For a wave energy converter (WEC) array, the ‘park effect’ Q can be represented as the ratio of the power of the full array (P_tot) to the sum of the power for each isolated WEC (P_isolated)

$\begin{array}{l}\hfill Q=\frac{P_{\mathrm{tot}}}{\sum _{j=1}^N{P}_j^{(\mathrm{isolated})}}\end{array}$

where N is the number of WECs in the array [21]. Although it is theoretically possible for some WEC array configurations to result in constructive wave interactions (i.e. Q > 1), in general Q < 1, and array designs tend to focus on limiting destructive interferences [20]. As the number of devices in a WEC array increases, the mean power per WEC reduces (Fig. 9.9B); but it is possible to minimize such destructive interferences through optimization of various parameters such as array geometry and device spacing.

Smoothing Power Fluctuations

Wave energy comes in pulses, and so is unsuitable for direct conversion and transmission to the electricity grid [22]. The addition of devices to an array reduces the variance in power (Fig. 9.9A); however, at the expense of reduced average power per WEC due to the park effect (Fig. 9.9B). In sea trials with WECs, Rahm et al. [22] found that there was an 80% reduction in the standard deviation of electrical power output from three WECs, compared with the standard deviation from a single WEC. Based on model simulations of a larger number of WECs [21], normalized variance of power $\frac{Var}{{\overline{P}}^2}$ (where variance V ar = σ² and σ is the standard deviation) reduced from ∼0.9 to ∼0.4 for 4 to 64 WECs, respectively (Fig. 9.9A).

Geometry of WEC Layout

It is possible to further smooth power fluctuations through careful consideration of the geometric WEC layout [22, 23]. It has been shown that ‘global’ array layouts can increase power by 5% or reduce power by 30% [24]. Göteman et al. [25] simulated four global geometries, each with the same number of WECs (Fig. 9.10). Device spacings for the different configurations varied within the range 20–55 m, other than for the ‘random’ layout, where the minimal device spacing was set to 6 m. Because the incident waves propagate in the x-direction, clearly those devices at the rear of each array (increasing x coordinate) absorbed less power. However, it was not always the first row that absorbed the most power; for the rectangular configuration, it was the third row that absorbed most power, demonstrating a positive interference effect from the other WECs in the array. All four configurations resulted in similar energy absorption (Fig. 9.11A); however, power variance differed significantly between the four cases: ‘rectangular’ and ‘random’ layouts led to the highest and lowest variance, respectively (Fig. 9.11B). Engström et al. [26] investigated WEC array layouts that were only slightly randomized, that is, to represent uncertainty in mooring positions and temporal drift, again finding a reduction of variance in these more realistic ‘randomized’ layouts. This could be explained by considering regular WEC layouts that are aligned with the dominant wave direction (e.g. Fig. 9.10B). In this case, the electricity produced by all of the WECs distributed along the wave crest will generally be in phase for each WEC row. Staggering the devices slightly in the direction of wave propagation would introduce more phase diversity into the array, leading to more stable (less variable) aggregated power output. Minimizing the lateral dimension of the WEC array, and maximizing the longitudinal dimension, will have a similar effect, provided the longitudinal spacing is considered, in conjunction with the expected wavelengths. For example, a WEC array of 4 × 5 has lower variance if there are five rows along the direction of wave propagation, as compared to four [21].

Device Spacing

The spacing between individual devices within a WEC array has been shown to influence variance in power output. As summarized by Göteman et al. [21], a 3 × 3 square wave array covering an area of 400 m² (10 m device spacing) has considerably lower variance than an array that covers 1600 m² (20 m device spacing). A relatively closely spaced WEC array, provided the ‘park effect’ is minimized, will have the added advantage of lower cabling costs, that is similar to cabling issues associated with the longitudinal and lateral spacing of tidal energy devices (Section 9.2.2). In a further study of a 3 × 3 array of point absorbers, Göteman et al. [25] found a localized peak in power variance associated with 18 m device spacing. Although this exact value is unique to this particular device, it demonstrates that careful design is required to avoid nonoptimal device spacings.

Size of WECs in an Array

One final issue in WEC array optimization is the size of individual devices within an array. Consider Fig. 9.10, for example, where larger WEC devices would be more suited to the ‘front’ of the array, and smaller devices to the ‘rear’. Blending WEC sizes within an array can lead to higher power output for the array [21] and, it could be assumed, lead to more efficient use of each WEC within the array. Indeed, a concert of wave energy devices within a single array, each exploiting different parts of the wave energy spectrum, could be achieved, but only as a result of detailed knowledge of the wave climate, and extensive optimization.

Simulation

Assume that you have designed a configuration for a hybrid renewable energy system. This system has several components such as one or several wind turbines, a storage system (e.g. batteries, hydrogen tank), and diesel generators (for hybrid systems). HOMER simulates the performance of the system every hour for the duration of a year. It calculates the energy produced and compares it with electricity demand. The hourly time series of demand should be provided as an input to the model. HOMER calculates the surplus or deficit at each time step, and tries to address these differences by storing energy during surplus periods, and using stored energy, diesel generators, or grid imports, in times of deficit. Several criteria can be imposed by the user as constraints to determine whether the performance of a system/configuration is acceptable; for example, minimum percent of the time that energy demand should be met, the share of the power supplied by renewable energy (in a hybrid system), and a limit on the emissions can be imposed. In the simulation phase, HOMER also calculates total net present cost of the system (i.e. all future costs are discounted to the present by a discount/interest rate). The costs include initial capital cost, the O&M cost during the lifetime of the project, fuel, and power purchased from the grid. The revenue from selling the power is then subtracted from the total cost to compute the net present cost. LCOE can also be computed given total cost and energy produced during a year.

Optimization

Finding the best configuration of a renewable energy system is the objective of the optimization step. HOMER simulates the performance of several configurations. It selects those that meet the constraints (demand, and minimum percentage of renewable energy contribution in a hybrid system). The best configuration is a solution/configuration that has minimum net present cost. Sample independent (decision) variables that can be changed by HOMER include the number and type/size of wind turbines, the size of the storage system (number of batteries), and the size of diesel generators. A search space that contains all possible scenarios for a component (e.g. various battery sizes) is provided by the user.

Sensitivity Analysis

An optimized system is calculated based on certain assumptions about a number of uncertain parameters; examples are fuel price, grid power price, discount rate, life time of the project, and demand. By performing sensitivity analysis on these variables, a user can deal with uncertainty and understand how/if the optimized system changes with these parameters. For instance, what is the minimum lifetime for a project? What interest rates are feasible for a renewable energy system?

HOMER has been applied in several studies to find the optimum energy system. For instance, in a case study in a remote village in India, four energy sources (hydropower, solar, wind, and bio-diesel generators) were combined [37]. The optimal off-grid system was identified and compared with the alternative of grid extension. This study showed that the hybrid off-grid system is cost-effective, compared with grid extension.

Some studies have optimized energy systems at much larger scales. As an example, Budischak et al. [38] considered a large grid in the eastern United States (Fig. 9.21) with a capacity of 72 GW (PJM Interconnection; www.pjm.com). By combining several renewable energy resources distributed across the region (onshore wind, offshore wind, and solar), and storage systems (batteries and fuel cells), an alternative system based on renewable energy was simulated and optimized. This study proposed an energy system that can meet the electricity demand of this large region based on 90% to 99.99% renewable sources, and with a cost comparable to conventional energy systems by 2030. Notably, Budischak et al. [38] recommended excessive energy production as the least cost option; the renewable system should produce almost three times the electricity demand, on average, to compensate for intermittency, and to avoid high costs associated with energy storage. Offshore wind energy had nearly the same contribution as onshore wind in the energy mix for the 99.99% renewable case in 2030. Both HOMER and another tool RREEOM (Regional Renewable Electricity Economic Optimization Model) were used, whilst PREEOM was recommended for larger grids like PJM.