Research on Torque Compensation Strategy of Wind Maneuver Model Experimental System by Increasing the Analog Multiple of Moment of Inertia

Abstract

Fan power generation, a form of new energy, has gained significant attention. However, as fan capacities grow, the challenges in the development process also increase. A wind maneuver model experiment system must be constructed to simulate the actual fan operation dynamics. The wind turbine simulator is essential for conducting experiments on wind turbines and advancing the research of wind power production technology. However, due to the insufficient moment of inertia in wind turbine simulators under laboratory conditions, physical compensation methods are challenging to implement. Therefore, most scholars rely on software compensation algorithms to realize the stability simulation of wind turbine simulators with small moments of inertia and actual wind turbines with large moments of inertia. Under this research background, this paper presents the existing moment of inertia compensation strategies based on current research hotspots. The theoretical foundation covers the mechanical dynamic models of both actual wind turbines and simulators along with an analysis of inertia compensation strategies, including high-order filters and feedforward bias suppression. Finally, the Simulink simulation platform is used to compare and validate the effectiveness of these strategies.

1. Introduction

Overreliance on non-renewable resources in traditional development has led to their depletion and to environmental degradation. To promote sustainable societal development, new energy generation technologies are increasingly coming into focus [1]. New energy encompasses wind, solar, and biomass energy and is characterized by renewability, cleanliness, and abundant reserves, offering vast development potential [2]. Compared with traditional energy, new energy has many advantages: Firstly, it is highly renewable, widely distributed, and poses no risk of depletion. Secondly, the use of new energy in the process is pollution-free, will not produce too many greenhouse gases, and is conducive to the development of the environment. Thirdly, China’s substantial new energy reserves also support the country’s traditional energy transition and societal development [3]. The meteorological department estimates that China’s wind energy, at 70 m height, can produce 5 billion kilowatts, with the richest wind resources concentrated in the “Three North” regions (Northeast, North, and Northwest China) and in coastal areas. These figures highlight the promising future of wind power technology in China [4].

In pursuit of its “dual carbon” goals, China has accelerated its promotion of new energy, with a 2020 survey showing new energy accounting for 73% of its energy system, ranking second globally [5]. As new energy technologies advance, China’s wind power technology continuously improves, with wind power capacity steadily increasing each year [6]. In 2022, China’s installed wind power capacity reached 365 million kilowatts, representing an 11.2% increase [7].

With the continuous increase in the capacity of single fans, the test demand in the development process is increasing, but field tests are challenging due to site and time limitations [8]. To address this problem, wind power enterprises build wind power model experiment systems to simulate the actual fan operation dynamics to meet the test requirements [9]. For example, in reference [10], a two-tier wind power time series model is proposed that takes into account daily weather variations and daily wind power fluctuations. In reference [11], the economic scheduling problem of wind power generation systems is discussed. A real power curve model is proposed, considering the normal distribution of wind speed data in each range in reference [12]. Reference [13] calculates the power curve distribution of wind farms. Wind turbine simulators reduce costs and enhance safety by replacing real turbines in research. At present, the wind power field has ushered in the wave of research and development of MW wind turbines, and different types of wind power models have been developed in response to different application scenarios [5]. The mean switching real-time model and detailed switching real-time model of the Opal-RT real-time simulator are presented in reference [14]. An error-based auto-disturbance rejection control strategy for a variable-speed wind power generation system is proposed in [15], which provides a novel and practical control structure. By using multi-agent reinforcement learning, reference [16] develops an efficient control system for wind farms composed of a new type of hydrostatic drive wind turbine. However, as turbines’ capacity grows, their moment of inertia also increases, and test benches with small inertia cannot meet the demands of MW turbines, making accurate mechanical and electrical simulations difficult [17]. Therefore, the research on the torque compensation strategy for the wind maneuver model test system with the increase in the analog multiple of the moment of inertia has become a key research focus [18].

Fan simulation test platforms for different electrical links need to configure different hardware and electrical structures for the experiment, so the fixed simulation test platform can simulate only a specific type of wind power generation system [19]. Currently, wind turbine simulators developed by scholars fall into two categories: those focusing on fault simulation and on wind turbine condition monitoring algorithm design. For example, an integrated method for anomaly detection and fault diagnosis of wind turbine is proposed in reference [20]. A fault detection method of loss data based on compressive sensing is proposed in reference [21] that is used for remote condition monitoring of wind turbines. An example of those focusing on wind turbine gas link and wind turbine access research is reference [22], which proposes a frequency safety constrained scheduling method that considers the frequency support and backup provided by wind farms. Reference [23] studies the dynamic and transient performance of a battery energy storage system connected to the output of a wind energy conversion system to smooth out short-term fluctuations in output power. In order to verify this concept and prove the practicability of power transmission, an engine simulator was constructed in the document reference [24]. This paper focuses on the third type of simulator, wind turbine servo control algorithm design and verification, which is modeled and analyzed [25]. A novel APC strategy combining rotor speed and pitch angle adjustment is proposed in reference [26]. Reference [27] describes the load reduction results achieved with trailing edge flaps in full-scale tests of a Vestas V27 wind turbine. The peak-to-peak graph of periodic sampling is used in reference [28] to characterize and distinguish different types of nonlinear responses under a hovering state.

The main idea of the servo control algorithm is to collect the position or speed signal of the motion axis of the prime mover, obtain the real-time acceleration of the motion axis of the prime mover through the differential algorithm, and use the acceleration feedback to compensate the dynamic torque [29]. An image-based adaptive visual servo algorithm is proposed by reference [30], which uses an uncalibrated camera to realize the visual shape control of a cable-driven soft robot arm. A global finite-time adaptive attitude control algorithm for a flexible spacecraft with a jitter structure under model uncertainty, external interference, and actuator failure is studied in reference [31]. In reference [29], a control strategy based on generalized learning systems is proposed and applied to a micro-robot system for the first time. Some researchers have found that even with a high-order filter, wind turbine simulators face instability when compensating torque under turbulent wind conditions [14].

Wind energy is a renewable and environmentally friendly resource, and the wind power generation technology in our country is becoming increasingly mature [8]. Reference [32] compares biomass power generation with wind and solar power generation in the case of load uncertainty and generation variation. As turbine capacities grow, small-inertia simulators struggle to accurately and stably simulate large-inertia turbines, driving deeper research into torque compensation strategies [9]. The current torque compensation strategies focus on control algorithm compensation, traditional moment of inertia compensation, moment of inertia compensation based on a first-order filter, and moment of inertia compensation based on a higher-order filter [33]. Despite advances in compensation strategies, challenges remain. Based on these issues, this study explores a feedforward deviation suppression-based torque compensation strategy for wind turbine simulators [5].

The primary objective of this paper is to explore the modeling methods for the wind maneuver model experiment system and to examine the moment of inertia compensation techniques. On this basis, the electromechanical dynamic mathematical model of the wind maneuver model experiment system is built based on the MATLAB/Simulink (Version number R2018b) simulation platform, and the moment of inertia compensation method is simulated and verified.

The main contributions of this paper are as follows: This research on moment of inertia compensation in wind power generation holds significant theoretical and practical value. Through the analysis and experimental verification of different compensation strategies, the limitations and potential risks of existing technologies are revealed. As turbine capacities increase, small-inertia simulators face growing challenges in accurately simulating large-inertia turbines. The proposed compensation strategy and improvements offer a novel solution to this technical challenge, advancing wind turbine simulation technology. Adaptive control and intelligent algorithms exemplify the future potential of modern control theory in wind power generation. These advancements enhance the flexibility and adaptability of compensation strategies, laying the groundwork for intelligent wind power system development. This study enriches theoretical research in wind power generation and provides crucial technical support for improving the efficiency and safety of wind energy utilization, with broad social and economic significance.

2. Wind Turbine Simulator Modeling

The actual wind turbine system comprises three main components: the pneumatic part, the mechanical structure part, and the electromagnetic dynamic part, among which the mechanical structure part is the hub of the whole wind turbine, as shown in Figure 1. The pneumatic part mainly includes wind speed, turbine pneumatics, and pneumatic correction. The mechanical structure part mainly includes the transmission chain model and structure model; the electromagnetic dynamic part mainly includes the electromagnetic dynamic model of the generator and converter and the equivalent model of the power grid. Wind speed, pneumatic model, transmission chain model, and wind turbine controller constitute the mechanical dynamic mathematical model of a wind turbine.

The two key components of a wind turbine simulator system are the digital control system and the electromechanical servo system, as illustrated in Figure 2. The digital control system includes a digital analog system and wind turbine controller; the system is mainly used to simulate the natural wind and pneumatic model. The electromechanical servo system adopts the transmission chain part. The wind turbine simulator’s mechanical dynamics model mirrors that of a real turbine, with the main difference being the moment of inertia in the transmission chain model. The moment of inertia of the actual wind turbine is significantly larger than that of the wind turbine simulator.

Wind Turbine System Modeling

The mechanical dynamic mathematical model of a wind turbine simulator is composed of wind speed model, pneumatic model, transmission chain model, and wind turbine controller model, as shown in Figure 3. With wind speed as the input and generator rotor speed as the output, the mechanical dynamic mathematical model of the actual wind turbine is established.

Likewise, a dynamic model for the wind turbine simulator using traditional inertia compensation was developed, with wind speed as input and simulator speed as output, as shown in Figure 4.

In the output end of the simulator system, the deviation suppression strategy is designed; that is, the system speed is corrected, but in the actual physical system, the speed measured by the feedback loop is also the actual speed of the drive shaft, so the deviation suppression strategy cannot be redesigned in the output end of the model. In summary, the feedforward deviation suppressor is designed in the input part of the simulator.

Build a wind turbine simulator drive chain model with the same feedforward torque bias suppression strategy as the actual wind turbine drive chain:

$$H\left(k\right)=Z\left(k\right)•h\left(k\right)$$

where $Z\left(k\right)$ is the feedforward deviation suppressor and $h\left(k\right)$ is

$$h(k)={\displaystyle \frac{z^{k_0+1}-a_d}{J_s{z}^{k_0+1}-a_d{J}_t+J_t-J_s}}$$

Set $H\left(k\right)=1/J_t$; then, we obtain

$$Z(k)={\displaystyle \frac{\frac{J_s}{J_t}{z}^{k_0+1}-\frac{J_s}{J_t}+1-a_d}{z^{k_0+1}-a_d}}$$

where $a_d$ is the filter coefficient. Take the filter coefficient as the optimal value $a_d^{opt}$, and substitute it into the above formula to obtain

$$Z(k)={\displaystyle \frac{a_d^{opt}{z}^{k_0+1}}{z^{k_0+1}-a_d^{opt}}}$$

The wind turbine simulator based on the inertia compensation strategy of feedforward deviation suppression can better simulate the mechanical dynamics of wind turbines with large moments of inertia. Before the drive command is issued, the command value is scaled forward to avoid the acceleration impact caused by turbulent sudden wind speed change, so that the simulator continues to simulate the moment of inertia with a larger multiple under the influence of time delay.

The traditional inertia compensation strategy can simulate a moment of inertia less than twice its value under the step wind speed, but if it is more than twice its value, instability will occur. The improved first-order filter compensation strategy can simulate the moment of inertia more than twice its value stably, but the simulator will oscillate when there is a non-negligible communication delay in the system. With the communication delay taken into account, a high-order filter can simulate inertia up to 20 times its actual value under step wind speed. Under turbulent wind speeds, the simulator’s speed curve fluctuates along the real turbine’s curve. The enhanced feedforward deviation suppression strategy accurately simulates high inertia multiples under both step and turbulent wind conditions while mitigating communication delays. Thus, the traditional moment of inertia compensation, the compensation strategy based on the first-order filter, the compensation strategy of the higher-order filter considering the communication delay, and the compensation strategy of the feedforward deviation suppression are simulated, respectively. A comparative analysis is conducted by examining the similarity between the speed and acceleration curves of the actual wind turbine and those of the simulated system and by evaluating the rationale behind the compensated torque.

3. Simulation of the Moment of Inertia Compensation Strategy and Comparison of Results

Figure 5 and Figure 6 illustrate the experimental simulation platform based on Simulink. The pneumatic module receives the wind speed as input and the pneumatic torque as output, which connect the transmission chain module. The transmission chain module outputs the speed, which serves as the feedback of the pneumatic module and the input of the control system module. The control system module outputs the electromagnetic torque as the feedback of the transmission chain module. The compensation strategy mainly compensates the feedback in the transmission chain module, forming a closed-loop system.

In the wind turbine performance test, 600S turbulent wind speed is typically selected for dynamic simulation. The wind speed characteristics of the turbulent wind speed model are presented in

Table 1. Turbulent wind speed model parameters.

Average Wind Speed	Turbulence Intensity	Integral Scale
9 m/s	Class C	250

, and the wind speed curve is shown in Figure 7.

The fan model adopts the CART 3 model designed and developed by NREL, with the parameters shown in

Table 2. Fan model parameters.

Parameter	Value
R: Wind wheel radius (m)	20
ρ: Air density (kg/m3)	1.225
ν: Cutting wind speed (m/s)	8
$k_{opt}$: Optimal torque gain (Nm/rpm2)	0.002
${\omega }_g$: Rated generator speed (rpm)	1780
${\omega }_t$: Rated speed of wind turbine (rad/s)	3.64
$n_g$: Gearbox change ratio	43.165
λ: Optimum tip ratio	5.8
$C_{p max}$: Maximum wind energy utilization factor	0.467
$J_g$: Rotor moment of inertia (kg·m2)	5.492 × 105
$J_r$: Generator moment of inertia (kg·m2)	34.4
$P_a$: Rated power (kW)	600

below.

4. Waveform and Result of Simulation Experiment

4.1. Traditional Inertia Compensation Strategy

Figure 8 presents the waveform diagram of the simulation of the moment of inertia less than twice its actual value using the conventional moment of inertia compensation strategy. Figure 8a shows that the speed of the wind turbine simulator gradually converges after a certain time and approaches the actual wind turbine speed until it is stable. The compensating torque in Figure 8b, after some time of oscillations, is also beginning to converge; in Figure 8c, the oscillation of the acceleration of the wind turbine simulator changes from violent to stable.

This demonstrates that the wind turbine simulator system using the traditional inertia compensation strategy can simulate only a moment of inertia up to twice its actual value, otherwise the system will be unstable and cannot accurately simulate the moment of inertia of the actual wind turbine.

4.2. Moment of Inertia Compensation Strategy Based on First-Order Filter

Figure 9 is a simulation waveform diagram with an improved moment of inertia compensation strategy based on a first-order filter. With step wind speed as input, the simulation models three times the actual inertia with a filter parameter of 0.9. Figure 9a is a comparison diagram of the speed of the wind turbine simulator and the actual wind turbine. Compared with the traditional moment of inertia, the speed of Figure 9a is basically consistent with the speed curve of the actual wind turbine, although it still oscillates slightly during the rise. In Figure 9b, the compensated torque waveform of the wind turbine simulator tends to flatten rapidly after a small oscillation; Figure 9c shows that the acceleration curves of both the actual wind turbine and the wind turbine simulator approach 0. Using a first-order filter, the simulator can accurately simulate inertia greater than twice its actual value, resulting in a relatively stable mechanical dynamic process.

4.3. Rotational Inertia Compensation Strategy Based on High-Order Filter

Figure 10 shows the simulation results of the high-order filter-based inertia compensation strategy with communication delay. In Figure 10a, the simulator’s speed closely matches the real turbine’s speed. Figure 10b shows reduced torque oscillation compared with the first-order filter, and Figure 10c shows the simulator’s acceleration stabilizing after minor oscillations.

It can be seen that the wind turbine simulator system using the first-order filter has a failure phenomenon when simulating a moment of inertia of less than a higher multiple and does not consider the communication delay, so it cannot accurately simulate the moment of inertia of the actual wind turbine. The high-order filter, with communication delay considered, eliminates deviation and ensures normal operation of the simulator.

Figure 11 depicts the mechanical dynamic process of a wind turbine simulator simulating 2–20 times the moment of inertia at the same step wind speed, requiring adjustment of the fifth-order filter parameters based on the analog multiple. As shown in the figure, the higher the inertia compensation multiple, the slower the simulator’s speed rise, torque stabilization, and acceleration smoothness. After the dynamic process, wind turbine simulators with different times of inertia compensation can reach the same stable state.

Figure 12 displays the stability verification waveform of torque deviation. Figure 12a,b, respectively, illustrate the application of fourth-order filters to simulate rotational speeds with 50× and 100× inertia compensations under step wind conditions. The rotational speed of the simulator with larger inertia is noticeably less sensitive than that of the smaller inertia simulator, and it fails to closely approximate the real turbine’s rotational speed.

Figure 12c,d compare rotational speeds under turbulent wind conditions by applying 4th and 8th-order filters to simulate 100 times the rotational inertia compensation strategy, respectively. It can be seen from the figure that the simulator under turbulent wind speed oscillates up and down along the actual wind turbine speed curve.

4.4. Moment of Inertia Compensation Strategy Based on Feedforward Torque Deviation Suppression

Figure 13 presents a simulation diagram of a wind turbine simulator using a feedforward deviation suppressor, with a communication delay of 8 and an inertia multiple of 100. As depicted in Figure 13a, the wind simulator can accurately and stably simulate the mechanical dynamics of the actual wind turbine under both step wind speed and turbulent wind speed without any abnormal fluctuations. Figure 13b,c further confirm the accuracy and stability of the simulation, showing results that closely match the actual conditions.

From the comparative analysis of the above compensation strategies, it can be seen that the traditional inertia compensation strategy can simulate the moment of inertia less than twice its value under the step wind speed, while instability will occur if the moment of inertia is greater than twice of its value.

A wind turbine simulator is an important tool to carry out wind turbine experiments and further study wind power generation technology. However, due to the insufficient moment of inertia in wind turbine simulators under laboratory conditions, physical compensation methods are challenging to implement, so the software compensation algorithm is adopted to realize the stability simulation of the wind turbine with a small moment of inertia and the actual wind turbine with a large moment of inertia. Although it can reflect the characteristics of the algorithm to a certain extent, the limitation of this paper is that it cannot complete the test under practical conditions.

5. Conclusions

Fan power generation is a new energy generation that is conducive to the sustainable development of human society. However, with the continuous increase in fan capacity, the difficulties in the development process are also increasing. It is necessary to use a wind turbine simulator with a small moment of inertia to simulate the stability of a real wind turbine with a large moment of inertia, and the improvement of the moment of inertia compensation strategy has become a current research hotspot.

This paper first introduces the components of the mechanical dynamic mathematical model of the wind turbine and wind turbine simulator and then introduces in detail the current moment of inertia compensation strategies, mainly from the two aspects of their design principles and existing problems, and summarizes the improvement reasons for each compensation strategy. Finally, the wind turbine simulator simulation platform was built by MATLAB/Simulink software, and various strategies were experimentally verified and compared.

From the comparative analysis of the above compensation strategies, it can be seen that the traditional inertia compensation strategy can simulate a moment of inertia less than twice its value under step wind speed, while instability will occur if the moment of inertia is greater than twice its value. The improved first-order filter compensation strategy can simulate a moment of inertia more than twice its value stably, but the simulator will oscillate when there is a non-negligible communication delay in the system. Considering the communication delay, the high-order filter can accurately calculate the moment of inertia of the simulator at a step wind speed of nearly 20 times its value. When the simulator is in the turbulent wind speed, its speed curve will oscillate up and down along the actual wind turbine curve. The improved feedforward torque deviation suppressor can accurately simulate the high multiple moment of inertia under step wind speed and turbulent wind speed and perfectly suppress the communication delay in the system.

In the simulation process, it is found that the current compensation strategy can simulate the moment of inertia of a higher multiple in the simulation platform, but the filter coefficient will increase with it, almost reaching the theoretical value boundary, and there is a risk of failure.