Hybrid Offshore Wind Farm Wake Optimization with Multi-Type Wind Turbines

Abstract

Offshore wind power currently shows the trend of a larger wind turbine capacity and deep-sea wind farm sites. Traditional wind farms with single-type wind turbines can hardly accommodate the dual requirements of high-efficiency power generation and wake effect mitigation of wind farms. Moreover, the wind shear of fixed wind turbines and the platform motion of floating wind turbines result in insufficient adaptability to a hybrid wind farm with multi-type wind turbines. To address that issue, this paper takes offshore wind farms with a multi-type hybrid layout for wake optimization. Firstly, based on the wind shear model, the influence of hub height difference for fixed wind turbines is analyzed, and the platform motion of semi-submersible floating wind turbines is evaluated through MoorDyn. On this basis, the wake optimization strategy for maximizing the total power generation of a wind farm is proposed based on the Gaussian Curl Hybrid model, which realizes three-dimensional wake control by considering the hub height difference and floating platform motion of multi-type wind turbines. The case study demonstrates that the multi-type hybrid layout itself has inherent wake suppression and optimization potential. The fixed wind farm with a row–column hybrid layout achieves an average power generation efficiency of 65.25%, which is superior to the single-type layout. For the floating wind farm with an inner–outer hybrid layout, the displacement misalignment effect is significant, with a maximum offset of 21.66 m in surge and 10.32 m in sway, and the total power is increased by 6.87 MW. And a hierarchical wake control mode matching multi-type wind turbines is formed. It provides a novel wake regulation mechanism for the design and operation of hybrid offshore wind farms.

1. Introduction

The Global Wind Energy Council (GWEC) predicts that offshore wind will reach the installed capacity of 441 GW by the end of 2034. Offshore wind has advantages of abundant resources, high power generation efficiency, and status as a core flexible resource for smart integrated energy systems [1,2]. Meanwhile, efficient and predictable offshore wind power generation plays an increasingly critical role in ensuring the energy supply reliability of complex integrated energy systems under the uncertainties of renewable energies, load demands and system operations [3].

With the global acceleration of large-scale offshore wind power development, the traditional design mode of wind farms with a single turbine type can no longer accommodate key sets of demands. The first is the high-efficiency power generation demands of large offshore wind farms, and the second is the system-level flexible operation requirements supported by supply–demand side management. This limitation is making it imperative to explore wake optimization methods for hybrid offshore wind farms [4].

Current offshore wind power development is characterized by two major trends: the upsizing of wind turbine capacity and the advancement of wind farm sites to deep sea [5,6]. The capacity of single wind turbines has rapidly evolved from the early 5 MW to commercial 15 MW. And ultra-large units of 20 MW and above have gradually entered the engineering application stage. For fixed offshore wind farms, the core differences between different types of wind turbines are concentrated in key parameters such as hub height and rotor diameter. With the substantial increase in hub height and rotor diameter, the complexity of aerodynamic loads and wake effects has increased significantly [7,8]. Meanwhile, the surging demand for deep and deep-sea development has driven the rapid development of floating offshore wind power. This technology breaks through the water depth limitations of fixed wind turbines [9] and has become one of the mainstream directions for future offshore wind power. In addition, affected by the wind shear of the atmospheric boundary layer, different types of wind turbines correspond to different inflow wind speed conditions. These differences lead to variations in their wake influence range and evolution [10].

Regarding the design of multi-type hybrid offshore wind farms, there are a series of relevant studies. Feng et al. addressed the optimization of multi-type configuration, quantity, and site selection. Their work verified that hybrid design can reduce the levelized cost of electricity (LCOE) and demonstrates the economic advantages of multi-type hybrid layouts [11]. Sun et al. proposed a directional constraint method that considers wind direction effects and rotor diameter correlation, and they carried out layout optimization for multi-type wind farms. They further verified the applicability of this method at sites with dominant wind directions [12]. Similarly, Charhouni et al. found that optimal layout effects are more easily achieved by optimizing multi-type layouts [13]. Tao et al. proposed a multi-type hybrid layout optimization method for deep and far-sea boundary sites, with hybrid installation of 4 MW and 8 MW wind turbines. Their study verified the necessity of multi-type hybridization [14]. However, existing studies rarely link wind farm-level wake optimization to the broader operation context of integrated energy systems.

Furthermore, research on power optimization of hybrid wind farms has become an important direction of wake optimization, and relevant studies are still in the exploratory stage [15,16]. Huang et al. considered the wake effect of hybrid wind farms and adopted active yaw control to maximize the total power of the whole farm [17]. Li et al. compared three wake control methods, and they verified the power improvement effect of wind farms with hybrid layouts. They also found that hybrid wind farms are less sensitive to wind direction changes [18]. Q. Wang et al. proposed a coordinated optimization method for wind turbine start–stop, yaw, and position control, which is built on the three-dimensional wake model. They found that hybrid wind farms can effectively avoid wake superposition problems [19]. Tao et al. focused on wake optimization of hybrid offshore wind farms, confirming that active yaw control strategies can effectively mitigate wake effects. They also found that prioritizing the implementation of these strategies on small-capacity wind turbines in non-dominant wind directions can significantly increase the total power generation of the whole farm [20].

These studies have verified the advantages of multi-type hybrid layouts in improving power generation efficiency and optimizing wake effects. However, most existing work is limited to scenario evaluation and still lacks an exploration of the impact of floating wind turbine motion characteristics. Compared with fixed wind turbines, the wake evolution of floating wind turbines is significantly affected by the motion of floating platforms, resulting in more complex wake characteristics [21,22]. The steady-state motion of floating platforms causes clear offset of the wake center, directly changing the degree of wake impact on downstream wind turbines [23]. Moreover, floating wind turbines of different power levels exhibit significant differences in the horizontal motion range in surge and sway directions. These differences arise from variations in rotor swept area, platform structure, and mooring system configuration. The variable motion characteristics alter the relative spacing between wind turbines in the array, as well as wake overlap characteristics [24,25]. This phenomenon further affects the three-dimensional wake effect of wind farms; the multi-type wake control mechanism lacks systematic summarization, and the wake control strategies for hybrid wind farms still need to be improved.

To address the above research issues, this paper takes multi-type hybrid offshore wind farms as the research object. Firstly, it systematically analyzes the wind shear characteristics of different fixed wind turbines and the platform motion of different floating wind turbines. This analysis clarifies the core influence mechanism of turbine-type parameter differences on wake characteristics. Secondly, based on the Gaussian Curl Hybrid (GCH) model, a three-dimensional wake calculation model adapted to multi-type hybrid scenarios is constructed, fully considering the coupling effects of hub height difference and platform motion on wake evolution. Furthermore, based on a novel wake regulation mechanism adapted to multi-type wind turbines, the wake optimization model for hybrid wind farms for maximizing wind farm power is proposed. Finally, the effectiveness of the proposed method is verified through engineering cases of large fixed wind farms and regular array floating wind farms. The research can provide theoretical support and an engineering reference for the design and operation optimization of hybrid offshore wind farms.

2. Model of Offshore Wind Farms with Multi-Type Wind Turbines

In offshore wind farms with a multi-type hybrid layout, there are significant differences in the structural dimensions and operational characteristics among different types of wind turbines, which directly affect the propagation and evolution of the wake behind the rotor plane of the wind turbine. To provide the basis for the operational performance evaluation for wake optimization, this chapter takes fixed wind turbines and mainstream semi-submersible floating wind turbines as the research objects, and analyzes the main characteristics related to the wake effects of different wind turbines.

2.1. Wind Shear Calculation for Fixed Wind Turbines with Different Hub Heights

Wind turbines with different design capacities usually correspond to different hub heights and rotor sizes, which directly leads to significant differences in the vertical distribution of wind speed on the rotor plane under the same incoming flow condition, and ultimately changes the effective wind speed and output power of wind turbines. To quantify this difference and provide the basis for the power calculation of hybrid offshore wind farms, the wind shear model is adopted in this section to describe the variation in wind speed with height, as shown in Figure 1.

The figure shows the wake region of the upstream wind turbine on downstream wind turbines with different hub heights, as well as the variation law of incoming wind speed with height. Among them, the curve on the right is the wind speed calculation considering the wind shear according to IEC 61400-3-1:2019, which represents the wind speed at height $z$, as shown in Equation (1):

$$V(\mathrm{z})=V_{hub}\cdot {(z/z_{hub})}^{shear}$$

(1)

where $V_{hub}$ is the wind speed at the hub height $z_{hub}$; and $shear$ is the wind shear exponent. For offshore wind farms located on flat sea surfaces, the surface roughness is extremely low, and the wind shear exponent is generally taken as 0.12. This value is a conventional and widely recognized setting for offshore wind farm simulation in general scenarios [26].

The above wind shear calculation is used to calculate the effective wind speed deviation of the rotor plane caused by the difference in hub height. As the core parameter for wake effect evaluation, the equivalent wind speed will further change the influence range and degree of the wake effect. In engineering applications, the measured wind speed $V_{ref}$ at the selected reference height $z_{ref}$ of the incoming wind can usually be obtained. Combined with Equation (1), the incoming wind speeds $V(z_{hub,i})$ and $V(z_{hub,j})$ of two wind turbines with different hub heights (wind turbine $i$ and wind turbine $j$) at their respective hub heights $z_{hub,i}$ and $z_{hub,j}$ can be calculated respectively. And the spatial distribution of the wake of different wind turbines can be calculated, as shown in Figure 2.

The front view and side view of the wake effect intuitively reflect the influence of wind shear on the wake effect. The wake distribution on the rotor plane and the wake superposition along the incoming flow direction comprehensively affect the effective wind speed of the downstream wind turbines. To accurately evaluate the influence of the hybrid wake on downstream wind turbines, it is necessary to focus on the overlap area between the wake region of the upstream wind turbine $i$ and the rotor plane $A_j$ of the downstream wind turbine $j$. Taking the representative green point in the overlap area in Figure 1 as example, the wind speed at the sampling point with the corresponding height $z_{hub,j}+\Delta z_{sort}$ is calculated as follows:

$$V(z_{hub,j}+\Delta z_{sort})=V_{ref}\cdot {\left({\displaystyle \frac{z_{hub,j}+\Delta z_{sort}}{z_{ref}}}\right)}^{shear}$$

(2)

The area $A_{overlap}$ of the wake overlap surface and the wind speed $V(z_{hub,j}+\Delta z_{sort})$ at each sampling point are the key indicators for evaluating the wake effect: $A_{overlap}$ determines the proportion of the wake covering the rotor of the downstream wind turbines, which directly affects the influence degree of the wake on the wind turbines’ power; $V(z_{hub,j}+\Delta z_{sort})$ is the wind speed in the overlap area, which is used to calculate the effective wind speed of the downstream wind turbines, thereby improving the calculation accuracy of the wake model.

It is worth noting that the relative positions in the lateral and streamwise directions jointly determine the initial coupling state between the wake effect and the rotor plane. For fixed wind turbines, the above spacing is a fixed value; meanwhile, for floating wind turbines, the floating platform will produce non-negligible motion during operation, leading to changes in the relative spacing between upstream and downstream wind turbines, and thus further changing the characteristics of the wake overlap area.

2.2. Floating Reposition for Floating Wind Turbines with Different Motion Ranges

The variation degree of the relative position of floating wind turbines directly depends on the amplitude of the floating platform motion, among which the motion displacement in the X and Y directions is the key factor affecting the wake region. The floating platform motion of floating wind turbines is mainly affected by wind loads. Different floating wind turbines have different platform structures, mooring configurations and overall turbine parameters, as shown in

Table 1. Core parameters of three semi-submersible floating offshore wind turbines.

Parameter	OC4	OO-Star Semi	UMaine VolturnUS-S
Rated Power	5 (MW)	10 (MW)	15 (MW)
Rated Wind Speed	11.4 (m/s)	11.4 (m/s)	10.59 (m/s)
Cut-in Wind Speed	3 (m/s)	4 (m/s)	3 (m/s)
Cut-out Wind Speed	25 (m/s)	25 (m/s)	25 (m/s)
Rotor Diameter	126 (m)	178.3 (m)	240 (m)
Hub Height	90 (m)	119 (m)	150 (m)
Generator Efficiency	94.4%	94.0%	96.55%
Maximum Power Factor	0.482	0.498	0.489
Mooring Line Length	835.5 (m)	703 (m)	850 (m)
Installation Water Depth	200 (m)	130 (m)	200 (m)
AP and FLP of Mooring Line 1	[−837.600, 0.000, −200.000], [−40.868, 0.000, −14.000].	[−691.000, 0.000, −130.000], [−44.000, 0.000, 9.500].	[−837.600, 0.000, −200.000], [−58.000, 0.000, −14.000].
AP and FLP of Mooring Line 2	[418.800, 725.383, −200.000], [20.434, 35.393, −14.000].	[345.500, 598.424, −130.000], [22.000, 38.105, 9.500].	[418.800, 725.383, −200.00], [29.000, 50.229, −14.000].
AP and FLP of Mooring Line 3	[418.800, −725.383, −200.000], [20.434, −35.393, −14.000].	[345.500, −598.424, −130.000], [22.000, −38.105, 9.500].	[418.800, −725.383, −200.00], [29.000, −50.229, −14.000].

. Their motion responses are significantly different, and the difference in motion range will directly affect the layout design and operation control of a wind farm [25].

In this section, semi-submersible floating wind turbines are taken as the research object to conduct a comparative analysis of the motion ranges of different floating wind turbines, which provides a basis for the subsequent research on the influence of wind turbine displacement on the wake region. To compare the differences in motion characteristics of different wind turbines, three representative semi-submersible wind turbines covering the mainstream power levels and design parameter ranges of current offshore wind power, namely OC4 5 MW [27], OO-Star semi 10 MW [28] and UMaine VolturnUS-S 15 MW [29], are selected as the test objects for the motion range, as shown in Figure 3.

For floating wind farms, the motion effect of the floating platform and the control actions of the wind turbines jointly affect the wind farm wake effect. Based on that, this paper analyzes the force characteristics of floating wind turbines, and derives the following simplified reposition equilibrium equation based on the iterative coupling relationship between control and motion:

$${\overrightarrow{F}}_{tension}(x,y,\delta )+{\overrightarrow{F}}_{thrust}(\gamma ,a;V_{eff})=0$$

(3)

where ${\overrightarrow{F}}_{tension}$ is the tension of the mooring system, which is related to the installation angle $\delta$ of the mooring system and the center position $(x,y)$ of the wind turbine; and ${\overrightarrow{F}}_{thurst}$ is the effective wind thrust under the effective wind speed $V_{eff}$ at the rotor plane, which can be adjusted through the wind turbine control actions $\gamma$ and $\alpha$.

To accurately compare the steady-state motion characteristics and ranges of different turbine types, motion simulation analysis is carried out for three floating wind turbines of different sizes based on the MoorDyn (Version 1.00.02F) mooring dynamics simulation software [30], to calculate the steady-state equilibrium positions and corresponding motion ranges of each turbine under wind loads. MoorDyn adopts the lumped-mass mooring line model widely used in floating offshore wind engineering design, which balances simulation accuracy, solution efficiency and convergence, and the hydrodynamic modeling settings in this study are fully consistent with the real project design conditions of the selected floating turbine benchmark cases. The key motion characteristic parameters of each turbine type are set according to the official test documents of the corresponding models, and the simulation settings and test process are consistent with the official conditions.

Furthermore, through the force analysis of the mooring lines, the mapping relationship between $(x,y,\delta )$ and ${\overrightarrow{F}}_{tension}$ on the horizontal plane for the three open-source floating wind turbines is obtained, which is used for the repositioning of the motion in surge along the longitudinal X-axis and sway along the lateral Y-axis under the operating conditions of the wind turbines. To compare the movability of different wind turbines, the maximum horizontal motion ranges corresponding to the motion of three wind turbines are shown in Figure 4.

The simulation results show that under the condition of similar mooring constraint strength, the maximum motion ranges of the three semi-submersible floating wind turbines increase step by step with the increase in rated power and rotor size: the innermost corresponds to the OC4 5 MW with a rotor diameter of 126 m, with X ∈ [−12.57 m, 9.30 m] and Y ∈ [−11.36 m, 11.39 m]; the middle corresponds to the OO-Star semi 10 MW with a rotor diameter of 178.3 m, with X ∈ [−33.61 m, 22.18 m] and Y ∈ [−29.82 m, 29.83 m]; the outermost corresponds to the UMaine VolturnUS-S 15 MW turbine with a rotor diameter of 240 m, with X ∈ [−39.00 m, 25.00 m] and Y ∈ [−34.65 m, 34.57 m]. It is worth noting that 5 MW and 15 MW with the same installation water depth and similar mooring configurations show significant differences in the overall motion range, which is worthy of further exploration of its optimization law in hybrid offshore wind farms. Overall, the differences in rated power, rotor diameter and mooring system are the core reasons for the difference in motion ranges of different turbine types. The horizontal motion range of floating wind turbines is jointly determined by the equivalent wind thrust and the stiffness of the mooring system, and the motion in the surge and sway directions also presents a three-way symmetry characteristic corresponding to the mooring system.

The floating platform displacement in the X and Y directions will directly change the relative positions of wind turbines in a wind farm, and also indirectly affect the wake overlap area and the intensity of the wake effect. Through the steady-state motion simulation of the three typical semi-submersible floating wind turbines, the mooring system tension ${\overrightarrow{F}}_{tension}(x,y,\delta )$ within the horizontal motion range of each turbine is obtained, which can be used to solve the floating platform motion under wind thrust in the reposition equilibrium equation, and also provides an evaluation basis for wake control and power optimization of hybrid offshore wind farms.

3. Wake Optimization for Hybrid Offshore Wind Farms

Based on the wind shear evaluation of fixed wind turbines and the platform motion range of floating wind turbines, this chapter focuses on the wake control and power optimization problems in multi-type hybrid offshore wind farms, and elaborates on the description of the hybrid power optimization problem, the coupling principle of the wake model, and the implementation method of three-dimensional wake control.

3.1. Description of Power Optimization Problem for Hybrid Offshore Wind Farms

To expand the universality of the optimization model for an offshore wind farm with multiple types of fixed wind turbines and floating wind turbines, this section adopts the power maximization problem with inequality constraints and equality constraints to describe the wake optimization problem of hybrid offshore wind farms.

For this high-dimensional non-linear optimization problem, the adaptive differential evolution strategy provides the theoretical basis for algorithm selection [31]. In consideration of the engineering design specifications of offshore wind farms, the optimization core of this model focuses on the wake control in the operation stage of the wind farm, and the Equilibrium Optimizer suitable for offshore wind farm optimization problems is adopted for this solution. The adopted EO algorithm is verified in high-dimensional wind farm optimization [32], which avoids local optima via an equilibrium pool mechanism. The optimization problem of the hybrid offshore wind farm is shown in Equation (4):

$$\begin{array}{l}\min f_{total}(\Theta )=-P_{\mathrm{s}um}=-{\displaystyle {\sum }_{i=1}^N{P}_i\left({\alpha }_i,{\gamma }_i;V_{eff,i}\right)}\\ s.t.\left\{\begin{array}{c}{P}_i\le P_{\max ,i}\\ {\gamma }_{\min }\le {\gamma }_i\le {\gamma }_{\max }\\ {\alpha }_{\min }\le {\alpha }_i\le {\alpha }_{\max ,i}\\ {\overrightarrow{F}}_{tension,i}(x_i,y_i,{\delta }_i)+{\overrightarrow{F}}_{thrust,i}({\gamma }_i,a_i;V_{eff,i})=0\end{array}\right.\end{array}$$

(4)

The constraint conditions of Equation (4) are composed of two parts: the operation control constraint of the wind farm and the reposition equilibrium constraint of floating wind turbines. Among them, the operation control constraint of the wind farm needs to be set differentially according to the design parameters of different wind turbine models, including the upper limit of rated power of a single wind turbine, the adjustment range of yaw angle $\gamma$, and the feasible interval of axial induction factor $\alpha$, to ensure that the wind turbines are always regulated within the safe operation range. For fixed wind turbines, the reposition equilibrium constraint of floating wind turbines is equivalent to being always valid without additional processing, while for floating wind turbines, it needs to be solved based on the force analysis of the floating platform in Equation (3).

The core calculation unit of the optimization objective function is the output power of a single wind turbine. Based on the blade element momentum theory, the steady output power of different types of wind turbines can be uniformly described by a piecewise function, as shown in Equation (5):

$$P_i=\left\{\begin{array}{cc}0,& V_i<V_{\mathrm{cutin},i},V_i>V_{\mathrm{cutout},i}\\ {\displaystyle \frac{1}{2}}\rho A_i{C}_p\left({\alpha }_i,{\gamma }_i\right)V_i^3,& V_{\mathrm{cutin},i}\le V_i\le V_{rated,i}\\ P_{\max ,i},& V_{rated,i}\le V_i\le V_{\mathrm{cutout},i}\end{array}\right.$$

(5)

where $\rho$ is the air density; $A_i$ is the rotor area of the wind turbine $i$; $C_p\left({\alpha }_i,{\gamma }_i\right)$ is the power coefficient of the wind turbine, which is a function of the axial induction factor $\alpha$ and yaw angle $\gamma$; $V_i$ is the effective wind speed; and $V_{\mathrm{cutin},i}$, $V_{rated,i}$ and $V_{\mathrm{cutout},i}$ are the cut-in wind speed, rated wind speed and cut-out wind speed of the corresponding wind turbine type, respectively.

Similarly, according to the equivalent wind load on the rotor plane, combined with the thrust coefficient $C_T$, the equivalent wind thrust $F_{thrust}$ is obtained, as shown in Equation (6):

$$F_{thrust}=\left\{\begin{array}{cc}0,& V_i<V_{\mathrm{cutin},i},V_i>V_{\mathrm{cutout},i}\\ {\displaystyle \frac{1}{2}}\rho A_i{C}_T\left({\alpha }_i,{\gamma }_i\right)V_i^2,& V_{\mathrm{cutin},i}\le V_i\le V_{\mathrm{cutout},i}\end{array}\right.$$

(6)

For hybrid multi-type offshore wind farms, the cut-in wind speed and cut-out wind speed of different types of wind turbines are usually in a similar range, but the rated wind speed needs to be differentially designed according to the blade airfoil and power coefficient curve of different wind turbines, which often has a significant gap. This difference will directly affect the power generation performance and wake characteristics of wind turbines under different incoming wind conditions. Meanwhile, there are differences in rotor diameter, hub height, and feasible interval of the axial induction factor among different turbine types, which will directly affect the calculation of the wake overlap area of downstream wind turbines and the solution of effective wind speed, and which need to be targeted for processing in the subsequent construction of the wake model.

3.2. The Gaussian Curl Hybrid Wake Model for Multi-Type Wind Turbines

Commonly used wake models for wind farms include the Jensen model, multi-zone model, conventional Gaussian model, Gaussian Curl Hybrid (GCH) model, and high-fidelity CFD. The Jensen model is oversimplified and cannot characterize 3D wake characteristics or the effects of platform motion. The multi-zone model struggles to capture wake curl and deflection. The conventional Gaussian model ignores the helical features of real wakes. CFD achieves high accuracy but involves a prohibitive computational cost.

Therefore, the GCH wake model is adopted, which strikes a good balance between accuracy and efficiency for farm-level optimization [33]. The basic parameter settings and calibration framework of the model refer to the mature and widely verified system of FLORIS (Version 4.5.1), which provides a solid basis for the model application [10]. Based on the classical self-similar Gaussian wake model, this model supplements the correction of the curl effect caused by yaw control on wake evolution. The mathematical expression and physical meaning of sub-models are as follows.

To accurately describe the wake characteristics of wind farms in multi-type hybrid scenarios, the complete evolution process of the wake is divided into multiple sub-models including wake deficit and expansion, and wake deflection and wake superposition, as shown in Figure 5. Aiming at the correction logic and mathematical expression for hybrid scenarios, the basic principles of each sub-model are elaborated in detail as follows.

Firstly, to consider the hub height difference and rotor diameter difference in different turbine types, and characterize the spatial misalignment characteristics between the wake of upstream wind turbines and the rotor plane of downstream wind turbines, the GCH model adopts Gaussian distribution to describe the wake deficit and expansion during the downwind propagation process, as shown in Equation (7):

$${\displaystyle \frac{V_G(\mathrm{x},\mathrm{y},\mathrm{z})}{V_{\infty }}}=1-C{e}^{-{(\mathrm{y}-\theta )}^2/2{\sigma }_y^2-{(\mathrm{z}-{\mathrm{z}}_{\mathrm{h}})}^2/2{\sigma }_z^2}$$

(7)

where $V_{\infty }$ is the inflow wind speed; $C$ is the velocity deficit at the wake center, calculated according to the thrust coefficient $C_T$; $\theta$ is the wake steering angle; $z_h$ is the hub height of the wind turbine; ${\sigma }_z$ is the wake width in the Z direction, which is related to the rotor diameter $D$; and ${\sigma }_y$ is the wake width in the Y direction, whose initial value is related to the cosine of the yaw angle $\cos (\gamma )$. ${\sigma }_y$ and ${\sigma }_z$ are used to jointly determine the expansion degree of different wake cross-sections.

Figure 5 shows the calculation framework of the wake-power full process for hybrid multi-type offshore wind farms.

Secondly, since the adjustment of yaw angle $\gamma$ and axial induction factor $\alpha$ will change the wake propagation direction, to describe the offset effect of the active control action of the wind turbine on the wake centerline, the wake deflection distance calculated by the initial deflection and expansion deflection is used, as shown in Equation (8):

$$\delta =x_0\tan \left({\displaystyle \frac{0.3\gamma }{\cos \gamma }}(1-\sqrt{1-C_T(\alpha )\cos \gamma })\right)+{\displaystyle \frac{\gamma E_0\nu \left({\sigma }_{\mathrm{y}},{\sigma }_z\right)}{5.2}}\sqrt{{\displaystyle \frac{{\sigma }_{y0}{\sigma }_{z0}}{k_y{k}_z{M}_0}}}$$

(8)

where $x_0$ is the near-wake length, generally three times the rotor diameter; $E_0$ is the initial parameter related to $C_T$; and $M_0$ is the intermediate parameter. The initial value of the deflection distance is determined by the wind turbine control action, and then dynamically changes with the downwind position of the wake cross-section; the rest are model parameters and intermediate calculation parameters related to the wake width.

It is worth noting that the core feature of the GCH model that distinguishes it from the traditional Gaussian model is that it supplements the correction of the reverse curl effect caused by yaw control on wake deflection, as well as the equivalent yaw angle correction of the upstream wind turbine wake on the downstream wind turbine wake, which is called secondary steering. This core correction mechanism is calibrated for multi-type hybrid layouts: for scenarios with different hub heights of turbines, the equivalent yaw angle correction is adapted to the spatial misalignment between the upstream wake and the downstream rotor plane; for mixed fixed-floating configurations, the reverse curl effect correction is optimized to match the dynamic wake deflection caused by floating platform motion. The specific principles are as follows.

The vortex generated when the wind turbine adopts active yaw control will further change the spatial distribution of the wake. Its vortex intensity can be expressed as a function of the yaw angle $\gamma$, as shown in Equation (9):

$$\Gamma (\gamma )={\displaystyle \frac{\pi }{8}}\rho D{U}_{\infty }{C}_T\sin \gamma \cos {\gamma }^2$$

(9)

Based on this vortex intensity, the vertical velocity additional term $W\left(\Gamma (\gamma )\right)$ caused by the curl effect can be further obtained, to realize the accurate description of the three-dimensional wake velocity distribution behind the wind turbine, as shown in Equation (10):

$$V(\mathrm{x},\mathrm{y},\mathrm{z})=V_G(\mathrm{x},\mathrm{y},\mathrm{z})+{\displaystyle \frac{W\left(\Gamma (\gamma )\right)(x-x_0)(y-y_0)}{\pi ({\alpha }_r(x-x_0)+\frac{D}{2})}}$$

(10)

where ${\alpha }_r$ is an adjustment parameter for the influence degree on wake recovery.

Then, the equivalent yaw angle ${\gamma }_{eff}$ is used to describe the influence of the upstream wind turbine vortex on the downstream wind turbine wake, which is used to calculate the total yaw angle ${\gamma }_{wake}$ of the lateral deflection of the downstream wind turbine wake, as shown in Equation (11):

$${\gamma }_{wake}=\gamma +{\gamma }_{eff}$$

(11)

On the basis of the velocity distribution of the Gaussian wake, through additional velocity correction and equivalent yaw correction, the wake deflection characteristics under active yaw control can be evaluated more accurately, especially the wake effect under the coupling of floating wind turbine motion and control actions. In the coupling calculation of hub-height wind shear and wake evolution, the inflow wind field adopts the steady uniform shear wind model suitable for general offshore scenarios, which is the mainstream setting for wind farm wake simulation in engineering applications.

Finally, for downstream wind turbines in the wind farm, their inflow wind speed will be simultaneously affected by the coupling of the wakes of multiple upstream wind turbines. Therefore, the sum of squares method is used to calculate the equivalent wind speed affected by wake superposition, as shown in Equation (12):

$$V_j=V_{\infty }-\sqrt{{\displaystyle {\sum }_{i=1}^{j-1}{(V_i-V_{i,j})}^2}}$$

(12)

where $V_{i,j}$ is the single wake velocity of the wind turbine $j$ affected by the wake effect of the upstream wind turbines, which can be calculated by multiple sampling points on the wake overlap surface according to Equation (2), especially in FOWFs, where it is also necessary to solve the floating platform reposition.

3.3. Wake Regulation Considering Hub Height and Platform Motion

For hybrid multi-type offshore wind farms, it is necessary to calculate the overlap area $A_{overlap}$ between the wake of the upstream wind turbine and the rotor of the downstream wind turbine in combination with the inherent differences in hub height $z_{hub}$ and rotor diameter $D$ of upstream and downstream wind turbines, and calculate the equivalent wind speed of the downstream wind turbine through the wind speed at sampling points. For mixed fixed-floating configurations, the model is further calibrated by introducing the floating platform motion offset into the wake overlap area calculation, to adapt to the change in the wake–rotor spatial coupling relationship caused by platform motion.

In the coupling process of hub-height wind shear and floating platform motion, the main assumptions and simplifications adopted in this study are as follows: (1) For the wind shear effect, the steady uniform shear wind model is adopted, and the random fluctuation characteristics of the incoming wind field are not considered in the current coupling framework. (2) For the floating platform motion, the static equilibrium position of the platform under a steady wind load is used to characterize the motion offset, and the dynamic response characteristics of the platform under unsteady loads are not further analyzed in the wake coupling calculation.

Considering fixed and floating wind turbines, the wake evolution and control mechanism of the hybrid offshore wind farm are shown in Figure 6.

Four groups of typical scenarios are set from two core dimensions: turbine parameter difference and active control action, which fully present the wake evolution law of the hybrid multi-type wind farm and the spatial coupling relationship with the downstream rotor. The dotted line is used to mark the influence of the motion of a floating wind turbine in the surge and sway directions on the wake overlap surface. The description of each scenario is as follows:

(a) Benchmark scenario with the same turbine type and no control: The upstream and downstream wind turbines satisfy $D_i=D_j$ and $z_{hub,i}=z_{hub,j}$, no active control action is taken, the wake naturally expands and attenuates along the downwind direction according to Equation (7), and the wake center is aligned with the hub center of the wind turbine, which is the initial wake distribution of the wind farm with the same turbine type;

(b) Active control scenario with the same turbine type: The parameters of upstream and downstream wind turbines are the same as those in scenario (a), $\gamma$ and $\alpha$ are actively adjusted, the lateral wake deflection $\delta$ is realized based on Equation (8), and the adjustment of the wake overlap surface $A_{overlap}$ is realized, which is the implementation method of wake control for the wind farm with the same turbine type;

(c) Hybrid benchmark scenario with multi-type turbines and no control: The upstream and downstream wind turbines satisfy $D_i\ne D_j$ and $z_{hub,i}\ne z_{hub,j}$; no active control action is taken; combined with the wind shear effect in Equation (1), there is a greater spatial misalignment between the wake and the downstream rotor; and $A_{overlap}$ changes significantly with the difference in turbine type parameters, which is the initial wake distribution of the hybrid multi-type wind farm;

(d) Fully coupled optimization scenario with multi-type turbines: The parameters of upstream and downstream wind turbines are the same as those in scenario (c), superimposed with multi-type parameter differences, and active control of $\gamma$ and $\alpha$, and due to the coupling of motion and control of floating wind turbines, it is necessary to further consider the influence of the plane displacement of floating wind turbines under the constraint of Equation (3) and the secondary steering correction of the equivalent yaw angle in Equation (11), which is the core adaptation scenario and optimization control method of the hybrid multi-type wind farm.

It can be seen from the above wake control mechanism that the wake propagation process of the hybrid multi-type offshore wind farm can change the influence degree of the wake overlap $A_{overlap}$ on the wind speed distribution of the downstream wind turbine rotor plane by adjusting the velocity $V(x,y,z)$ of the wake cross-section ${\sigma }_{\mathrm{y}}$${\sigma }_z$, the wake center offset distance $\delta$ and the motion of the floating wind turbine, so as to realize the three-dimensional wake control for hybrid turbine types.

This method takes the wind farm layout and turbine type parameters as the basic input, and synchronously covers the core characteristics such as hub height difference in multi-type turbines, wind shear characteristics, and movability of floating wind turbines. Through the collaborative control of the yaw angle $\gamma$ and axial induction factor $\alpha$ of each wind turbine, it is extended to the calculation of the wake superposition effect and effective wind speed of multiple wind turbines, and finally realizes the power optimization of each wind turbine in the whole wind farm.

4. Case Study

4.1. Case Design and Parameter Description

To verify the applicability and effectiveness of the proposed optimization method in offshore wind farms with different scales, types, and multi-type hybrid layouts, two categories of five comparative cases are designed in this paper, which are analyzed for large-scale fixed offshore wind farms and regular array floating wind farms, respectively.

Case scenarios and parameter description are shown in

Table 2. Case scenarios and parameter description.

	Wind Farm Conditions			Wind Condition			Algorithm Settings
Case	Wind Farm Type	Wind Farm Scale	Wind Farm Layout Selection	Wind Shear	Wind Direction	Wind Speed	Maximum Iterations	Population Size
Case H1 (Initial)	Large-Scale Fixed	175 wind turbines referring to London Array Wind Farm	All 5 MW/All 10 MW/Hybrid Alternating	0.12	All Wind Directions	10 m/s (90 m)	--	--
Case H2 (Optimization)	Large-Scale Fixed	175 wind turbines referring to London Array Wind Farm	All 5 MW/All 10 MW/Hybrid Alternating	0.12	0°	10 m/s (90 m)	200	175
Case I1 (Distribution)	Regular Floating	5 × 5 = 25 wind turbines with Shared Mooring	Outer 5 MW, Inner 15 MW	0.12	Measured Wind Rose Distribution of Sea Area (100 m)		--	--
Case I2 (Wind Shear)	Regular Floating	5 × 5 = 25 floating wind turbines with Shared Mooring	Outer 5 MW, Inner 15 MW	0/0.12	0°	11.4 m/s (90 m)	--	--
Case I3 (Optimization)	Regular Floating	5 × 5 = 25 floating wind turbines with Shared Mooring	Outer 5 MW, Inner 15 MW	0.12	0°	10.69 m/s (150 m)	200	25

. Among them, for the large-scale fixed wind farm, the representative London Array wind farm is referred to [34], a globally recognized research benchmark with complete public data, to ensure the reliability and comparability of our quantitative analysis. To highlight the impact of different single-unit capacities on the overall power generation efficiency of the wind farm, while ensuring the consistency and comparability of simulation conditions, 5 MW and 10 MW wind turbines with the same rated wind speed are selected. For the regular array floating wind farm, a regular array with anchor point connection is adopted to avoid mooring line crossing problems, with a scale of 5 × 5 = 25 wind turbines, and 5 MW and 15 MW wind turbines with the same anchor point water depth are used. This capacity gradient matches the mainstream commercial offshore turbine models widely used in global projects, and the hybrid layout assumption fully aligns with the near-future development trend of large-scale offshore wind farms. The condition setting of the floating case adopts the conventional normal sea state in engineering design, which focus on the wind load.

In the simulation process, the wind shear exponent commonly used in offshore wind farms is adopted for both fixed and floating cases. The large-scale fixed wind farm uniformly adopts an inflow wind speed of 10 m/s and covers all wind directions; the floating wind farm adopts the measured wind rose data of a certain sea area as the wind condition [35]. Systematic convergence tests are carried out for population size and iteration number, verifying the stable convergence and robustness of the algorithm. The optimization algorithm parameters are set as follows: the maximum number of iterations is 200 for all cases, the population size is consistent with the number of wind turbines, the adjustment range of the optimization variable $\alpha$ is [0, 0.333], and the adjustment range of the optimization variable $\gamma$ is [−30°, 30°].

4.2. Case A: Large-Scale Fixed Wind Farm with 175 Wind Turbines

Case H refers to the layout of the London Array wind farm, including 175 wind turbines, with three turbine configuration settings. Among them, the hybrid scenario is shown in Figure 7, which consists of 89 wind turbines with 5 MW and 86 wind turbines with 10 MW arranged in a group alternating form. This study focuses on the wake control performance under normal wind conditions in the sea state.

To comprehensively evaluate the power generation performance of the offshore wind farm in different scenarios, this study conducts wake calculation for each wind direction, obtains the power generation and power generation efficiency of the wind farm under each wind direction, and presents the radar chart of its all-wind-direction distribution characteristics intuitively, as shown in Figure 8.

From the all-wind-direction distribution characteristics, the variation laws of power and efficiency with wind direction of the three scenarios are highly consistent, and all show significant periodic fluctuations with the change in incoming wind direction, reflecting the impact of wake distribution differences under different incoming flow directions on the power generation performance of the wind farm. In terms of power generation, the all-wind-direction output power of the all-10 MW scenario is the highest overall, the hybrid 5 MW and 10 MW scenario is stably between the all-10 MW and all-5 MW scenarios, and the power level of the all-5 MW scenario is the lowest overall. In terms of power generation efficiency, the efficiency curve of the hybrid 5 MW and 10 MW scenario is better than that of the all-10 MW and all-5 MW scenarios under most wind directions, showing an overall higher power generation efficiency in all wind directions. This is because the hybrid turbine type adopts a combination of wind turbines with different hub heights and rotor sizes, and its own structural difference is conducive to weakening the wake interference between wind turbines, which can reduce wake loss without optimization, thus maintaining higher initial power and efficiency.

To quantitatively evaluate the comprehensive power generation performance of the three scenarios under all working conditions, further calculation shows that the all-wind-direction average total power levels of the all-5 MW, all-10 MW, and hybrid 5 MW and 10 MW scenarios are 536.72 MW, 1131.01 MW, and 851.47 MW, respectively, and the total power generation increases step by step with the increase in single-unit rated capacity. The corresponding all-wind-direction average power generation efficiencies of the scenarios are 61.34%, 64.63%, and 65.25%, respectively. While the total power of the hybrid 5 MW and 10 MW scenario is significantly higher than that of the all-5 MW scenario, it also obtains a higher power generation efficiency than the all-5 MW scenario. Even compared with the all-10 MW scenario with an overall higher hub height, the wake reduction effect brought by the difference in hub height and rotor size of different wind turbines in the hybrid 5 MW and 10 MW scenario is still better than that of the all-10 MW scenario with a completely consistent hub height, achieving an improvement in power generation efficiency and becoming the initial scheme with the best comprehensive performance.

In addition, to study the wake optimization potential of different turbine configurations, according to the influence degree and symmetry relationship of the wake effect, the 0° wind direction is selected to carry out wake optimization for the three scenarios: all-5 MW, all-10 MW, and hybrid 5 MW and 10 MW. The comparison of the initial and optimized power generation performance levels is shown in

Table 3. Comparison of power generation performance of wind farms with different turbine configurations before and after optimization.

Scenario	Initial Power	Optimized Power	Initial Efficiency	Optimized Efficiency
All 5 MW	526.38 MW	553.17 MW	60.16%	63.22%
All 10 MW	1151.50 MW	1198.25 MW	65.80%	68.47%
Hybrid	859.54 MW	904.26 MW	65.87%	69.29%

.

In terms of power gain, the all-10 MW scenario has the largest initial power base, with a power increase of 46.75 MW after optimization, which is the scenario with the highest power gain. The power increase in the hybrid scenario is close to it at 44.72 MW, while the power increase of the all-5 MW scenario is only 26.79 MW. In terms of efficiency gain, the initial efficiency of the hybrid scenario is 65.87%, which is slightly higher than 65.80% of the all-10 MW scenario and significantly higher than 60.16% of the all-5 MW turbine type. After wake optimization, the optimized efficiency of the hybrid scenario reaches 69.29%, which is not only higher than 63.22% of the all-5 MW turbine type and 68.47% of the all-10 MW turbine type but also has a larger efficiency improvement range. The efficiency of the hybrid turbine type is increased by 3.42 percentage points, the all-10 MW turbine type by 2.67 percentage points, and the all-5 MW turbine type by 3.06 percentage points. The optimized results further amplify the advantages of the hybrid turbine-type scenario, achieving a more stable and significant improvement in efficiency optimization.

In summary, all three turbine configuration scenarios under the 0° wind direction can achieve a power generation performance improvement through wake optimization, but the hybrid turbine type is significantly better than the all-5 MW scenario and the all-10 MW scenario by virtue of its better optimized efficiency performance and comprehensive gain effect of power and efficiency. The hybrid 5 MW and 10 MW scenario combines the power generation scale advantage of large-capacity units and the wake loss mitigation effect of heterogeneous parameter layout, realizing the joint optimization of power generation and power generation efficiency. Therefore, the differences in hub height and rotor size of wind turbines with different capacities enable wake control to more fully weaken the wake effect, providing a feasible path for wake optimization of offshore wind farms that takes into account both scale and efficiency. The hybrid layout optimization law verified in this case is not limited to the 5 MW and 10 MW capacity combination, but has universal applicability for current mainstream commercial turbine models and near-future 15 MW+ ultra-large turbine projects, fully aligning with the development trend of global large-scale hybrid offshore wind farms.

4.3. Case B: Regular Array Floating Wind Farm with 5 × 5 Wind Turbines

Case I adopts a five-row and five-column wind farm connected by a regular array, which consists of 16 NREL 5 MW wind turbines with an OC4 semi-submersible platform and 9 IEA 15 MW wind turbines with a UMaine VolturnUS-S semi-submersible platform, arranged in an inner and outer layer distribution, as shown in Figure 9a. Figure 9b is the wind rose of a real sea area, corresponding to the joint distribution probability of 12 wind directions and 12 wind speeds.

(1) Power Characteristic Analysis Under Wind Rose Distribution

Based on the wind rose data, the power generation of the hybrid wind farm is calculated, and the three-dimensional distribution of wind speed–wind direction–power is obtained, as shown in Figure 10. From the wind direction dimension analysis, the power generation contribution of the 0° wind direction and its nearby interval in the full wind speed range is at a low level in all wind directions, which does not match the occurrence probability of wind resources in this wind direction. This is because the wake of the upstream wind turbines will directly act on all wind turbines in the same downstream row, eventually leading to the largest wake deficit and significantly low power generation efficiency in this wind direction, and there is a large wake optimization space in this part.

Based on the joint probability weight of wind speed and wind direction of the wind rose, the weighted sum of the power generation under all wind conditions is ascertained, and the contribution values of different wind speed sections to the annual energy production (AEP) of the wind farm are calculated: the core contribution is highly concentrated in the wind speed range of 9~13 m/s: the contribution ratio of 9 m/s wind speed is 17.43%, that of 11 m/s wind speed is 23.09%, and that of 13 m/s wind speed is 20.27%. The cumulative contribution ratio of these three wind speed sections alone exceeds 60.80% of the total AEP of the wind farm, which is the absolute core interval of power generation.

This distribution characteristic is jointly determined by the dual characteristics of wind turbine power generation efficiency and wind resource distribution: the rated wind speed of the NREL 5 MW wind turbine adopted in this case is 11.4 m/s, and that of the IEA 15 MW wind turbine is 10.69 m/s, and their rated working intervals are within the wind speed range of 9~13 m/s. In this wind speed range, both types of wind turbines can reach or approach the rated power, and the wind energy capture efficiency is at the highest level in the full wind speed range. At the same time, combined with the wind rose distribution characteristics, the probability of the 9~13 m/s wind speed range is much higher than that of the extremely low wind speed section below the cut-in wind speed and the extremely high wind speed section near the cut-out wind speed. With the dual characteristics of “high power generation efficiency + high distribution probability”, it has the highest contribution ratio to AEP.

(2) Comparison of the Effect of Wind Shear Under Rated Wind Speed

The rated wind speed of 11.4 m/s of the NREL 5 MW wind turbine is adopted as the wind speed condition, and the wind shear exponents are set to 0 and 0.12 respectively, to compare the power generation performance of the wind turbines in the hybrid array, as shown in Figure 11.

Under the uniform inflow wind speed of 11.4 m/s without considering wind shear, even if there is the wake effect of upstream wind turbines on downstream wind turbines, the most upstream 5 MW wind turbines and the downstream 15 MW wind turbines can still achieve full power generation at the same time. This phenomenon breaks through the traditional cognition that the rear row units in the same capacity array will inevitably have significant power generation loss, and the reason is the differentiated matching of turbine types in the hybrid array: the rated wind speed of the IEA 15 MW wind turbine is 10.69 m/s, which is lower than the inflow wind speed, and its hub height is higher than that of the front-row NREL 5 MW wind turbines. Even if the downstream wind turbines are affected by the wake of upstream wind turbines and wind speed attenuation occurs, the equivalent wind speed of their rotor plane can still reach above their rated wind speed, for example, 10.75 m/s for the second-row IEA 15 MW wind turbines.

When comparing the scenario results and considering wind shear, it can be seen that wind shear further amplifies the power generation advantage of the hybrid turbine-type array. The downstream high-hub IEA 15 MW wind turbines can directly use the higher wind speed at higher altitudes, which not only fully retains the characteristic of “simultaneous full power generation of front- and rear-row units” but also further improves the power generation of the more downstream units. Wind shear provides better inflow conditions for downstream high-hub units than uniform inflow, the hub height difference reduces the degree of wake coupling between wind turbines, and the resulting equivalent wind speed gain can partially offset the wind speed attenuation caused by the wake of upstream wind turbines.

(3) Wake Distribution and Wind Turbine State After Optimization

Furthermore, wake optimization is carried out for the hybrid FOWF, and the wake distribution section at the hub height of 90 m for 5 MW wind turbines and the wake distribution section at the hub height of 150 m for 15 MW wind turbines are obtained, as shown in Figure 12 and Figure 13, respectively.

The wake optimization strategy brings a significant power increase to the hybrid wind farm, with the total power of the whole farm increasing from the initial 144.42 MW to about 151.29 MW, among which the 15 MW wind turbines contribute the main power increment. Due to the large relative distance between wind turbines, the control action is dominated by yaw adjustment. There are clear differences in wake distribution at different hub heights: the wake effect is relatively serious at the 90 m hub height of 5 MW wind turbines, so the upstream 5 MW wind turbines adopt a large yaw angle to reduce the impact on the rear 15 MW wind turbines; at the 150 m hub height of 15 MW wind turbines, the wake effect of 5 MW wind turbines is significantly weakened, and the wake control of 15 MW wind turbines focuses on collaborative control between the same types of wind turbines.

Specifically, for the first-row wind turbine array, which are all 5 MW wind turbines, the yaw angles of the upstream wind turbines numbered 1–4 are between 15.35° and 20.84°, and the floating platform displacements in the surge and sway directions are (7.99, 3.43), (7.36, 2.55), (6.87, 2.43) and (6.86, 2.55), respectively. The motion amplitude is close and relatively small, and the wake effect between upstream and downstream wind turbines cannot produce clear misalignment. The most downstream 5 MW wind turbine is affected by the superposition of the wake of upstream wind turbines, but does not affect other wind turbines, so it adopts a small yaw angle, which is also the yaw action characteristic of the last row of wind turbines.

For the second-row wind turbine array mixing 5 MW wind turbines and 15 MW wind turbines, the 5 MW wind turbine numbered 6 adopts the maximum yaw angle of 30°, and its floating platform displacement is (6.49, 3.68), which is clearly misaligned with the displacement (28.15, 14.00) of the 15 MW wind turbine numbered 7, which effectively reduces the wake impact on the rear 15 MW wind turbines. The yaw actions of the 15 MW wind turbines numbered 7–8 are similar to those of the 5 MW wind turbines numbered 1–4. The wind turbine numbered 9 is the penultimate wind turbine, but also the last 15 MW wind turbine in the second row and the last 5 MW wind turbine numbered 10 both adopt small yaw angles consistent with the yaw action characteristics of the last row of wind turbines. Combined with the control actions and floating body displacements of the 25 wind turbines in the whole farm, it can be seen that the wind turbine motion and yaw actions of the hybrid turbine-type FOWF present hierarchical characteristics related to the turbine type, which provides a new control idea for wake optimization of hybrid offshore wind farms.

5. Conclusions

This study systematically verifies the effectiveness of a multi-type hybrid layout in the wake optimization of fixed and floating offshore wind farms. Combined with the wind shear characteristics of fixed wind turbines (wind turbines) and the floating platform motion characteristics of floating wind turbines, it provides a feasible technical path for the application of hybrid offshore wind farms. Based on the simulation analysis and case verification in this paper, the following conclusions can be drawn:

(1)

Compared with the single-type layout, the multi-type hybrid layout already has a wake suppression effect and power generation efficiency advantage without active optimal control. In the large-scale fixed wind farm with 175 wind turbines based on the London Array prototype, the all-wind-direction average power generation efficiency of the hybrid alternating layout of 5 MW and 10 MW wind turbines reaches 65.25%, which is 3.91 and 0.62 percentage points higher than those of the all-5 MW and all-10 MW single-type layouts, respectively. The spatial misalignment of the wake is formed through the difference in turbine-type parameters, which reduces the wake superposition effect from the layout level and realizes the comprehensive improvement of power generation scale and utilization efficiency.

(2)

The wind farm with a multi-type hybrid layout has better wake optimization potential, and the improvement range of power generation performance after active optimization is significantly better than that of the single-type layout. After being solved by the optimization method, the power generation efficiency of the hybrid fixed wind farm increases from 65.87% to 69.29%, with an improvement range of 3.42 percentage points, which is 0.36 and 0.75 percentage points higher than those of the all-5 MW and all-10 MW single-type layouts, respectively. Meanwhile, the total power of the whole farm is increased by 44.72 MW, achieving a significant performance gain on the basis of the dominant initial efficiency.

(3)

The multi-type hybrid layout can fully match the wind shear characteristics, and break through the power generation limitation of the traditional same-type array in the FOWF scenario. In the 5 × 5 regular array FOWF with a hybrid layout of 5 MW and 15 MW wind turbines, over 60.80% of the annual energy production is contributed by the 9–13 m/s wind speed range, which is highly consistent with the rated wind speeds of 11.4 m/s (5 MW) and 10.69 m/s (15 MW). The simultaneous full power generation of front- and rear-row units can be realized by using wind shear and turbine-type parameter differences. The total power generation of the whole farm increases from 144.42 MW to 151.29 MW, with an increase of 6.87 MW.

(4)

Significant findings from Case B further demonstrate the superiority of the hybrid layout. Even when affected by upstream wakes, the equivalent wind speed of downstream 15 MW turbines can reach 10.75 m/s to maintain full power generation. Yaw control is adopted as the main optimization method, in which upstream 5 MW turbines apply relatively large yaw angles to mitigate the wake impact on downstream units. The upstream 5 MW turbines adopt yaw angles of 15.35–20.84°, and the first 5 MW turbine uses a maximum yaw angle of 30° for wake suppression, while 15 MW turbines contribute the main power increment after optimization. The combination of preference control and displacement misalignment presents hierarchical characteristics related to turbine types, which provides a new idea for multi-scale wake control of hybrid wind farms.

Notably, to focus on revealing the core wake suppression mechanism of multi-type hybrid layouts, this study sets clear research boundaries and has the following main limitations: steady uniform shear wind inflow and floating platform static equilibrium hypothesis are adopted, only conventional sea conditions are considered, and systematic sensitivity analysis of key parameters is not carried out; the optimization framework does not include dynamic operation constraints such as turbine load limits, grid code requirements and controller constraints; the quantitative trade-off between energy gain, mechanical load, and O&M complexity is not analyzed; and targeted verification for 20 MW+ ultra-large turbines is not carried out.

Future research will further expand the coverage of turbine types and carry out research on the hybrid layout characteristics of ultra-large units of 20 MW and above, as well as different types of floating wind turbines, such as barge-type and Spar-type. At the same time, combined with the full life cycle levelized cost of energy (LCOE) of the wind farm, the multi-objective joint optimization of array layout planning and operation control will be carried out. Furthermore, the unsteady wake coupling characteristics and real-time collaborative control strategy under the combined action of wind, wave and current will be explored, to provide more comprehensive theoretical and technical support for the efficient development of deep and far-sea hybrid wind farms.