Design, Implementation, and Evaluation of an Output Prediction Model of the 10 MW Floating Offshore Wind Turbine for a Digital Twin

Abstract

Predicting the output power of wind generators is essential to improve grid flexibility, which is vulnerable to power supply variability and uncertainty. Digital twins can help predict the output of a wind turbine using a variety of environmental data generated by real-world systems. This paper dealt with the development of a physics-based output prediction model (P-bOPM) for a 10 MW floating offshore wind turbine (FOWT) for a digital twin. The wind power generator dealt with in this paper was modeled considering the NREL 5 MW standard wind turbine with a semi-submersible structure. A P-bOPM of a 10 MW FOWT for a digital twin was designed and simulated using ANSYS Twin Builder. By connecting the P-bOPM developed for the digital twin implementation with an external sensor through TCP/IP communication, it was possible to calculate the output of the wind turbine using real-time field data. As a result of evaluating the P-bOPM for various marine environments, it showed good accuracy. The digital twin equipped with the P-bOPM, which accurately reflects the variability of the offshore wind farm and can predict the output in real time, will be a great help in improving the flexibility of the power system in the future.

1. Introduction

According to the statistics of the International Energy Agency (IEA), the share of new and renewable energy consumption is steadily increasing, and wind power accounts for 36% of the total increase. It is growing much faster than other renewable power generations, such as solar power (27%), hydro (22%), and biomass (12%) [1,2]. In particular, there is an increasing proportion of offshore wind turbines that have better wind conditions and can mitigate problems such as noise pollution during operation. However, offshore wind turbines are exposed to harsher weather conditions than onshore due to sea salinity and strong winds [3,4,5]. With the recent rapid increase in variable renewable electricity (VRE), there are growing concerns about the deterioration of the flexibility of the electric power system [6]. Grid flexibility is the ability of a system to manage fluctuations and uncertainties in electricity supply and demand stably. The VRE will play an essential role in future energy systems, but integrating large-scale VREs into energy systems requires additional flexibility enhancement [7,8]. In order to respond cost-effectively to the spread of the VRE, it is necessary to develop an accurate prediction method for renewable energy generation along with strategies such as introducing energy storage systems and sector-coupling technologies [9].

In general, forecasted weather environment data can be used to predict the output of a wind turbine in advance. However, because offshore wind turbines are exposed to very variable weather conditions, such as rapid wind speed fluctuations and strong winds, tropical heat, hail, and snow, the current environment may differ from the predicted data. Furthermore, unlike stationary wind turbines that only consider wind data, the output of floating offshore wind power is immediately affected by waves, so the height and period of waves must also be considered. In the case of marine environment data, it is more accurate to predict the weather data one hour ago than one month ago, and it is more accurate to predict the weather data one minute ago. Therefore, it is necessary to develop a real-time prediction method that can effectively predict output using data predicted at a closer time. The output prediction of offshore wind turbines requires high-speed calculation time and accuracy. However, the existing simulation tools take a long calculation time and are difficult to calculate close to reality in consideration of the dynamics and control values of the wind turbine [10,11]. In particular, floating offshore wind turbines (FOWT) are exposed to harsher weather fluctuations than stationary ones, and the output of FOWT is affected by the complex dynamics related to moorings, floats, towers, and nacelles. For the optimization of these complex structures, a digital twin system can be an effective alternative.

A digital twin is a virtual model that accurately reflects a physical object. Digital twin utilizes IoT communication, AI-based machine learning, and real-time analytic software to implement virtual models to analyze the state of real systems and diagnose causality. In addition, the virtual models can predict outcomes by applying various input parameters that will occur in real systems in the near future [12,13,14,15,16,17,18,19]. In recent years, digital twins have been studied as an alternative and new method for predicting the output of wind turbines [20,21]. Recent studies on the digital twin technology of wind turbines contributed to the improvement of operational conditions by developing fault diagnosis, condition monitoring, and residual life prediction techniques for offshore fixed and floating wind turbines based on data collected from SCADA devices [22,23,24]. Among them, Fahim, M. et al. [24] used machine learning and SCADA data to develop a digital twin-based model capable of generator output prediction and real-time condition monitoring. When predicting the output of a wind turbine based on machine learning, once the model is trained, it is stable in prediction and inference. However, this modeling method has several drawbacks. Developing models with machine learning is quite tricky without long-term measured SCADA data. In addition, when the capacity, size, and controller of the wind turbine are changed, it is difficult to modify and verify the system [13]. Therefore, there is a need for a physics-based digital twin that can predict the output without the historical and SCADA data of the wind turbine. If a physics-based model is used, the digital twin can be developed without SCADA data.

Once a physics-based model is created for the digital twin, it is easy to analyze and validate a variety of input data and compute complex systems such as wind turbines in near real-time as a reduced order model (ROM). The ROM system uses the correlation of input and output data to simplify various models in full 3D simulations, system simulations, and characteristics of historical data and is effective in implementing them as close to real-time as possible. The mechanism of ROM is similar to that of artificial neural networks, but it is more advantageous to analyze the correlation between input and output within an operational wind speed range [25]. It is possible to calculate the output of a wind turbine using real-time field data through an IoT sensor connected to a physics-based model with ROM or to predict the output of a generator using weather forecast data.

This paper is the first attempt to implement and evaluate a physics-based output prediction model (P-bOPM) for digital twin construction on a 10 MW FOWT. A P-bOPM of 10 MW was implemented, and its performance was confirmed through a comparative evaluation of the reduced model test results and the developed digital twin system. The P-bOPM for a digital twin was designed considering the geographical characteristic of Korea and simulated using ANSYS Twin Builder. The wind turbine was scaled by considering the DTU 10 MW and the national renewable energy laboratory (NREL) 5 MW standard wind turbine equipped with a semi-submersible type platform for the marine environment of Korea. The average wind speed of the site was 8.5 m/s, and the rated wind speed of the wind turbine was 11.3 m/s. The blade pitch and nacelle yaw control systems of the 10 MW FOWT were designed taking into account the operating characteristics of the wind turbine simulator developed by NREL called the fatigue, aerodynamics, structures, and turbulence code (FAST). Since the motion of the floater in the offshore wind turbine continuously changes the output power and the control value, the six degrees of freedom (6-dof) of the FOWT were implemented using the ROM for real-time status updating. Through the FAST simulation, the correlation of the 6-dof of floater in various marine environments was analyzed and applied to learning the ROM system. The wind speed and sea level were used as input data, and 6-dof was generated as output data for the ROM system. In the equation of the output power of 10 MW FOWT, the wind speed was replaced by the effective wind speed determined by the motion equation of the 6-dof. In the P-bOPM proposed in this paper, the output power was predicted by calculating the effective wind speed reflecting the dynamic ROM system. Additionally, for verification of the P-bOPM of the 10 MW FOWT, the reduced model test was conducted by the Korea Research Institute of Ships and Ocean Engineering (KRISO). As a result, the testing of the 1/35 reduced model was performed with a variable marine environment and showed good accuracy with the P-bOPM of the 10 MW FOWT. The error occurred in the output power due to the error of the developed ROM system for the real-time prediction of 6-dof, and the accuracy was 92% when comparing the result of the reduced model test and the P-bOPM for the digital twin. Through this, the accuracy and reliability of the P-bOPM were confirmed. The digital twin integrated with P-dOPM, considering the offshore wind farm’s variability, can greatly help improve the power system’s flexibility.

2. Description and Modeling of a 10 MW FOWT

2.1. Description of a 10 MW FOWT

The weight of the FOWT has a significant influence on the dynamic characteristics of the floater and the effective wind speed of the turbine. The wind turbine covered in this paper was scaled by considering the DTU 10 MW and the NREL 5 MW standard wind turbine equipped with a semi-submersible type platform taken into account in the Korean offshore environment. The mass of the FOWT was calculated by referring to the 10 MW wind turbine of the IEA fixed offshore wind turbine [26]. According to the rated power, wind speed, and driven type, the weight of the wind turbine was calculated using the scaling method from NREL [27]. The ratio of scaling up of the rotor was 1.414 compared to the 5 MW NREL wind turbine. The blade lengths of the 5 MW and 10 MW wind turbines were 63 m and 89.1 m, respectively. The distances of the rotor axis to the blade root of the 5 MW and 10 MW wind turbines were 1.5 m and 2.12 m, respectively. The height of the hub takes into account 50 years of extreme waves and safety margins. The height of the 50-year extreme wave was 34.38 m in the marine environment considering the installation site in Korea. The calculated height of the hub was 119.0 m. In

Table 1. Dimensions and weights of the 10 MW FOWT system.

Items	Value
Rated power	10.63 MW
Hub height	119 m
Rotor diameter	178.3 m
Number of blades	3 ea
Single blade mass	32.5 ton
Rotor mass	198.0 ton
Nacelle mass	414.0 ton
Tower mass	559.0 ton

, the dimensions and weights of the 10 MW FOWT are shown. The floater was designed based on the OC4 semi-submersible type [28], and the scale-up ratio was calculated using the upper structure’s weight ratio.

2.2. Design Parameters of a 10 MW FOWT

In

Table 2. Specifications of the 10 MW FOWT.

Items	Value
Rated power	10.63 MW
Type of the generator	PMSG
Rated line-to-line voltage	6.6 kV
Rated armature current	930 A
Rotating speed at rated wind speed	9.6 rpm
Rated torque	10.57 MN·m
Number of poles	250
Cut-in wind speed	5 m/s
Cut-out wind speed	25 m/s
Rated wind speed	11.3 m/s
Length of rotor blades	89.1 m
Inertia	$\mathrm{305,147,058} \mathrm{kg}·$m2
Rated frequency	20 Hz
Stator winding resistance	6.4 mΩ
d-axis stator inductance	1.8 mH
q-axis stator inductance	1.8 mH
Power coefficient	0.48
Optimal tip speed ratio	7.92
Average wind speed of the site of installation	8.5 m/s

, the specifications of the 10 MW FOWT are shown. The advantages of the direct-driven type wind generator can be removing the gearbox and improving the reliability of a turbine, as well as reducing the maintenance and repair costs. Therefore, the direct-driven permanent magnet synchronous generator (PMSG) was used for the 10 MW FOWT in this paper. The 10 MW FOWT was modeled using ANSYS Twin Builder. Considering the offshore environment of Korea, when the rated wind speed of 11.3 m/s was applied, the rotor speed, the tip speed ratio ($\mathsf{\lambda }$), and the maximum power coefficient ($C_p$) of the turbine were designed at 9.6 rpm, 7.92, and 0.48, respectively. The configuration of the 10 MW FOWT is illustrated in Figure 1.

The detailed model of the wind turbine includes the mechanical components of the wind power system and the back-to-back (B2B) converter. The B2B converter is composed of the DC-link capacitor, grid-side converter, and generator-side converter. The grid-side converter was used to maintain the DC-link voltage and to control the active power given to the grid. The generator-side converter was used to control the power coefficient for maximum power point tracking (MPPT). The frequency of the wind generator was selected at 20 Hz, considering the operating range of the conventional inverter, the number of poles, and the rated rotational speed of the wind turbine.

The following equations were applied to the wind turbine system (1)–(5):

$$P=0.5\rho \pi R^2{V}^3{C}_p\left(\lambda ,\beta \right),$$

(1)

$$\lambda =wR/v,$$

(2)

$$C_p\left(\lambda ,\beta \right)=c_1\left(\frac{c_2}{{\lambda }_i}-c_3\beta -c_4{\beta }^{c_5}-c_6\right)e^{\frac{c_7}{{\lambda }_i}},$$

(3)

$$\frac{1}{{\lambda }_i}=\frac{1}{\lambda -c_8\beta }-\frac{0.008}{{\beta }^3+1},$$

(4)

$$J\frac{d\omega }{dt}=Tm-Te$$

(5)

where $P$ is the output power of the wind turbine (W), $\rho$ is the air density (kg/m³), R is the rotor radius (m), $\lambda$ is the tip speed ratio, ${\lambda }_i$ is the optimal tip speed ratio, $\beta$ is the blade pitch angle of the turbine blade (°), $C_p\left(\lambda ,\beta \right)$ is the power coefficient of the wind turbine, $J$ is the inertia of the wind turbine, $\omega$ is the angular speed of the rotor (rad/s), T_m is the mechanical torque, and T_e is the electrical torque. In

Table 3. Constants of the power coefficient.

Constants of the Power Coefficient	C1	C2	C3	C4	C5	C6	C7	C8
50% or more	1.13	151	0.2	0.002	2.9	13.2	20.9	−0.002

, the constants of the power coefficient are shown.

Figure 2 shows the characteristics of power and control of the 10 MW FOWT system studied in this paper. Figure 2a shows the peak power extraction curves of a wind turbine as a function of the rotational speed at different absolute wind speeds. The generator side converter was operated to control the MPPT according to the rotation speed variance caused by the torque mismatch between the turbine and the generator load. Figure 2b shows the power coefficient curves with blade angle variation. The $C_p$ for the modeled wind turbine is 0.48. The variation in the blade angle is expressed by Equations (3) and (4). The blade pitch control value at a fixed wind speed was checked for modeling the same control value as the blade pitch control of the FAST simulator. In

Table 4. Blade pitch angle value according to the wind speed.

Wind Speed	11.4 m/s	13 m/s	15 m/s	18 m/s	21 m/s	25 m/s
Pitch angle	1.1°	10.4°	14.3°	17.2°	19.3°	20.8°

, the blade pitch angle values according to the wind speed are shown.

2.3. Effective Wind Speed and 6-Dof in the 10 MW FOWT

Unlike the conventional fixed wind turbine, the total FOWT output power is affected by not only wind conditions but also ocean waves. The offshore wind turbines, including floating platforms, freely move in three-dimensional space, which is referred to as 6-dof. A rigid body of an offshore wind turbine freely changes position in three perpendicular axes with surge and roll motion in the normal axis, heave, and yaw motion in the transverse axis, and sway and pitch motion in the longitudinal axis. The coordinate system that describes the wind turbine movements is depicted in Figure 3. The x-axis is aligned with the water surface, and its direction is the same as the wind direction. The z-axis points upward. The y-axis is perpendicular to the x-axis and z-axis, as shown in Figure 3. The origin is placed in the static equilibrium position. As FOWT is free to change position in 6-dof, the use of full 6-dof could increase the complexity of the turbine modeling, which would pose a significant impact on the computational burden. Thus, the 6-dof representation of FOWT is reduced to 4-dof, which has the most significant impacts on the total output power, which are surge, heave, pitch, and yaw. The effective wind speed at the nacelle is different from the absolute wind velocity, as given by Equations (6)–(8).

$$V_e=V-\Delta V,$$

(6)

$$V=V_0{\left(\frac{{\xi }_{heave}}{h_T}\right)}^{0.143}·\cos \left({\xi }_{yaw}\right),$$

(7)

$$\Delta V=\frac{d\left({\xi }_{surge}+h_{T}tan\left({\xi }_{pitch}\right)\right)}{dt},$$

(8)

where $V_e$ is the effective wind speed, $V_0$ is the absolute wind speed at the rotor hub, $\Delta V$ is the variation in wind speed at the rotor hub due to the structure movement, $h_T$ is the turbine hub height, ${\xi }_{surge}$ is dynamic response of the surge, ${\xi }_{heave}$ is dynamic response of the heave, ${\xi }_{pitch}$ is dynamic response of the pitch, and ${\xi }_{yaw}$ is the dynamic response of the yaw.

3. Development of a P-bOPM of a 10 MW FOWT

3.1. Configuration of the P-bOPM

Figure 4 shows the P-bOPM configuration of the 10 MW FOWT model. The P-bOPM uses external marine environment data such as wind and waves as input. In the ROM, the 4-dof of the floating body is calculated in real time by inputting the marine environmental data and the blade pitch angle of the wind turbine as inputs. The wind turbine’s output is calculated using the equation of the relative wind speed calculated at 4-dof and the actual wind speed measured on an anemoscope. Effective wind speed was calculated using Equation (6), and output values such as power, blade pitch angle, rotational speed, torque, voltage, and current of the wind power generator were simulated using Figure 1 and Equation (1). The ROM was used for real-time calculation of 4-dof, and the ROM learning was performed under various marine environments using the correlation between the 4-dof of floater and the environment.

3.2. Design and Performance Verification of the ROM

In this paper, the physical structure motion of the 10 MW FOWT was modeled with ROM for implementing the 4-dof. The ROM is an effective scheme that reduces the computational complexity and storage requirements of computer models while maintaining expected fidelity within acceptable error limits. Figure 5 shows the design and implementation procedures of the FAST simulation-based ROM presented in this paper.

Specifically, it consists of the following processes. (1) Input data (wind speed and sea sur-face level) were selected for the 4-dof calculation of the floater. (2) Simulation steps (5, 7, 10, 11.3, 13, 17, 22 and 25 m/s) for learning the ROM system were determined. If the simula-tion results for all cases under which the ROM is operated are used for learning, the accu-racy of the ROM system will increase, but simulation considering all states is practically difficult. Therefore, the simulation was performed by selecting the range of input variable values that the designed 10 MW FOWT can face and dividing it into several steps. (3) The 4-dof was calculated with the mooring and floating body dynamics using the FAST sim-ulator for each simulation step. The 4-dof results according to wind speed and sea level input data were saved for later ROM learning. (4) The ROM system was learned using the simulation results, and the input data for learning consisted of wind speed, sea level, surge, heave, pitch, and yaw. The ROM system was learned by Dynamic ROM Builder [29] of ANSYS Twin Builder and can be developed simply by setting input and output data and error rate for learning. (5) As a result of verifying the ROM using field data, it was con-firmed that the output for variable input data can be calculated within 1 s. Therefore, the ROM can be used for a real-time output prediction, and this is the very reason why the ROM is used in this paper.

3.3. Prediction of the 4-dof for the 10 MW FOWT Using the ROM System

The P-bOPM of the 10 MW FOWT for the digital twin is operated using the real-time or predicted data of the offshore environment to compare and diagnose the condition. The effective wind speed of the wind turbine according to the offshore environment and motion of the floater is necessary rather than calculating the output power of the FOWT only with the simplified wind speed data. Since the expression of 4-dof consists of a complex matrix function as Equation (9), it is difficult to apply to real-time analysis due to its complex and long computation time.

$$\xi \left(\omega \right)=\frac{{\mathit{F}}_{\omega }}{-\left(\mathit{M}+{\mathit{A}}_{\omega }\right){\omega }^2+i\left(\mathit{B}+{\mathit{B}}_{\omega }\right)\omega +\mathit{K}}$$

(9)

where ξ(ω) is the response for the 4-dof, ${\mathit{F}}_{\omega }$ is a vector of excitation forces and moments in the frequency domain, ${\mathit{A}}_{\omega }$ is the hydrodynamic added mass and inertia matrix, $\mathit{B}$ is the hydrodynamic linear damping matrix, ${\mathit{B}}_{\omega }$ is a damping matrix, $\mathit{K}$ is the restoring matrix, ${\mathit{F}}_{\omega }$ is a vector of excitation forces and moments in the frequency domain, $\mathit{M}$ is the structure mass and inertia matrix of whole FOWT systems, and ω is the angular frequency. In this paper, a ROM system was implemented using 4-dof for a real-time status update of floating motion, and its effectiveness was demonstrated. For the ROM learning, the 4-dof calculated by Equation (9) that affects the FOWT output under the conditions of wind speed of 5 m/s~25 m/s and sea level of 2.18 m~12.47 m was simulated using FAST. In

Table 5. FAST simulation results of the surge and heave according to the marine environment.

Environment		Surge [m]		Heave [m]
Average Wind Speed [m/s]	Amplitude of Sea Surface [m]	Average Value	Range	Average Value	RANGE
5	2.18	4.98	−0.56~9.58	−0.004	−0.046~0.033
7	2.62	8.26	−1.06~15.96	−0.010	−0.087~0.068
10	3.46	14.67	−1.39~27.29	−0.028	−0.142~0.091
11.3	3.93	15.42	−1.49~29.02	−0.039	−0.191~0.148
13	4.53	13.33	−0.57~26.46	−0.020	−0.266~0.264
17	6.45	11.69	2.03~20.39	−0.008	−0.548~0.533
22	9.56	11.85	−4.12~26.73	0.029	−1.767~2.049
25	12.47	12.21	−2.03~26.92	0.041	−2.045~2.606

and

Table 6. FAST simulation results of the pitch and yaw according to the marine environment.

Environment		Pitch [deg]		Yaw [deg]
Average Wind Speed [m/s]	Amplitude of Sea Surface [m]	Average Value	Range	Average Value	Range
5	2.18	0.81	0.26~1.60	−0.18	−2.65~2.16
7	2.62	1.45	0.56~2.94	−0.15	−3.51~2.75
10	3.46	2.71	0.85~5.25	0.14	−6.49~6.87
11.3	3.93	3.05	0.92~5.86	0.11	−7.61~7.91
13	4.53	2.27	-0.40~4.01	−0.18	−4.81~5.27
17	6.45	1.66	-0.04~3.09	−0.31	−4.30~4.62
22	9.56	1.37	-0.13~2.99	−0.64	−5.09~5.84
25	12.47	1.21	-0.60~3.24	−0.88	−5.42~5.89

, the 4-dof dynamic characteristics of the 10 MW FOWT according to the wind speed and sea level are given.

The average value of pitch and yaw increases proportionally with wind speed, but after the rated wind speed, the surface area of the blades subjected to wind decreases by blade pitch control, so it is inversely proportional. The mean value of the surge is affected by the wind speed, the amplitude of the sea level, and the surface area of the blades subjected to the wind. The amplitude of the heave is proportionally increased according to the amplitude of the sea surface.

Figure 6 shows the comparison of the simulation results of the FAST and prediction results of the ROM according to the variable offshore environment. As shown in Figure 6, the accuracy of 4-dof was measured to be over 90%. The ROM results of 4-dof show sufficient accuracy compared to the detailed FAST simulation models.

4. Development of an Integrated Digital Twin System of the 10 MW FOWT

4.1. Integrated Digital Twin System of the 10 MW FOWT

In order to build a physical model-based digital twin system, it is necessary to receive data from an external sensor and perform real-time simulations. The data connector in Ansys Twin builder sends the real values from the sensor to the model over the network using TCP/IP communication.

Figure 7 shows the 10 MW FOWT model for real-time simulation by using a data connector and the ROM. The real-time digital simulator (RTDS) plays the role of an environment sensor and transmits signals through TCP/IP communication with the P-dOPM using python code. The wind speed and sea level data transmitted from the data connector to the P-bOPM and the output power and blade pitch control of the 10 MW FOWT are calculated in near real-time. The calculated output power of the wind turbine is saved as one csv file every 10 min, such as SCADA data.

4.2. Reduced Model Test of the 10 MW FOWT

In this paper, a reduced model test was conducted to verify the P-bOPM for a digital twin. The 10 MW FOWT was modeled with a 1/35 scale ratio in KRISO. In

Table 7. Comparison of the full-scale model and reduced model of the 10 MW FOWT.

Parameter	Full-Scale Model of the 10 MW FOWT (1:1)	Reduced Model of the 10 MW FOWT (1:35)
Model ratio	1	35
Water depth [m]	150	4.286
Draft [m]	15.0	0.429
Radius center to outer column [m]	47.0	1.34
Radius center bottom plate [m]	9.6	0.27
Displacement [ton]	11,277.663	0.263
GMT [m]	19.25	0.55
GML [m]	19.25	0.55
CoG (x,y,z) [m] based on free surface	(0, 0, 4.45)	(0, 0, 0.13)

, the specifications of the 10 MW FOWT are shown.

When the floater was in a stable state without waves and wind, the center of gravity (CoG) of the full-scale model and reduced model of the floater was 4.45 m and 0.13 m based on the sea water level. Since the semi-submersible type floater is constructed symmetrically, the transverse metacentric height (GM_T) and longitudinal metacentric height (GM_L) of the floater are the same value.

Table 8. Comparison of the reduced model test and the simulation results of the 10 MW FOWT motion natural period.

Parameter	Reduced Model Test	Simulation	Error [%]
Surge natural period [s]	15.429	16.109	4.2%
Heave natural period [s]	2.787	2.806	0.7%
Pitch natural period [s]	3.926	3.955	0.7%

shows the comparison results of the reduced model test and the simulation results for the free-decay motion of the 10 MW FOWT, and it can be seen that the errors for surge, heave, and pitch are less than 5%.

Figure 8 shows the flow chart of the model-in-loop simulation for a real-time model test with a FAST simulator. The reduced model test of the 10 MW FOWT was conducted in the water tank at KRISO.

The wind maker implemented the wind speed and direction, and the wave maker generated the waves and currents in the water tank. When the 6-dof occurs in the floater due to wind and waves, the 6-dof motion is captured in the qualisys system on the top of the floater. The qualisys system can perform the 6-dof capture of data in real-time from the movement of the object. The nacelle velocity and effective wind speed were calculated from the qualisys system, and these values were replaced instead of the mooring, platform, tower, and nacelle dynamics in the structure of the FAST simulator. The thrust and output power of the actual 10 MW FOWT system was analyzed with calculated effective wind speed. The thrust of the actual size turbine was converted back into the thrust corresponding to the model in the accelerometer composed of the duct fan at the top of the test model. Through the model-in-the-loop simulation, the results of the motion, output, and thrust of the 10 MW FOWT model were fed back repeatedly.

4.3. Comparison of the Digital Twin System and the Reduced Model Test of the 10 MW FOWT

Figure 9 compares the results of the reduced model test and the P-dOPM results of the digital twin of the 10 MW FOWT with the same offshore environment. The input wind speed was an average value of 11.3 m/s, close to the rating, and the wave height was amplitude between −1.9 m and 1.8 m.

$$MAPE=\frac{100}{n}\sum \frac{\left|Prediction-Actual\right|}{Actual}$$

(10)

The accuracy of the P-bOPM was evaluated using the mean absolute percentage error (MAPE), which is one of the methods to evaluate the accuracy of time series data. The results of the P-bOPM on the predicted data and the results of the reduced model test on the actual data were compared. As a result of calculating the MAPE using Equation (10), the error and accuracy were 7.7% and 92.3%, respectively. Although it is difficult to compare the effective wind speed directly between the reduced model test and the P-bOPM, it was confirmed that the error of the output power of the wind turbine was affected by the accuracy of the 4-dof produced from the ROM system. The accuracy of more than 90% was targeted by considering the level of response to the impact of weather conditions and large fluctuations in grid power, and it was confirmed that the results were well matched when the results of the reduced model test and P-bOPM of the 10 MW FOWT.

5. Conclusions

This paper dealt with the development of a P-bOPM of a 10 MW FOWT for a digital twin. The 10 MW wind turbine system was modeled taking into account the offshore environment of Korea, and the volume and weight of the turbine and floater were calculated using the scaling method from NREL. A direct-driven PMSG was modeled for the 10 MW FOWT. In order to confirm the dynamic characteristics of the floater affecting the output power, the 4-dof according to the wind speed and sea level was analyzed using the FAST. Based on these data, the ROM was designed, and it is used to predict the dynamic characteristics of the floater according to the offshore environmental conditions. As a result, the ROM accuracy of the pitch was the lowest at 93.1%, and the ROM accuracy of the yaw was the highest at 98.9%.

The P-bOPM of a 10 MW FOWT for a digital twin was implemented, and its performance was confirmed through a comparative evaluation of the reduced model test results and the developed digital twin system. The RTDS plays the role of an environment sensor and transmits signals through TCP/IP communication with the P-dOPM using python code. The wind speed and sea level data transmitted to the P-bOPM and the output power and blade pitch control of the 10 MW FOWT are calculated in near real-time. Through the model test, the 6-dof motion of the floater was captured and linked with the FAST simulator to analyze the output power and thrust of the wind turbine. The output power of the 10 MW FOWT, considering the effective wind speed by the thrust and the motion of the floater, was calculated close to real-time. The accuracy of the digital twin equipped with P-bOPM of 10 MW FOWT was 92.3%, showing satisfactory results with the target accuracy of 90% or more. The digital twin integrated with P-dOPM, considering the variability of the offshore wind farm, can be of great help in improving the flexibility of the power system.