Research on a power smoothing control strategy for energy storage hydraulic wind turbines

To solve the problem of large output power fluctuations in wind turbines and improve grid adaptability, a hydraulic energy storage system is introduced in traditional hydraulic wind turbines. Based on the working principle of energy storage hydraulic wind turbines, an energy storage hydraulic wind turbine state space model is established, and the feedback linearization method is introduced to solve the multiplication nonlinear problem in the modeling process. The output power is taken as the control output, and the torque compensation controller is established with the feedback linearization method. The displacement of the variable displacement pump motor is controlled to realize hydraulic energy storage system energy charging and discharging, and the wind turbine output power smoothing control is realized with the fluctuating wind speed. The power smoothing control strategy is verified with the 24 kW energy storage hydraulic wind turbines semi‐physical simulation experimental platform. The proposed control strategy lays the groundwork for the wide application of the energy storage hydraulic wind turbines.


| INTRODUCTION
As the proportion of wind turbines in the power grid continues to increase, the power grid has placed higher requirements on the power quality of wind turbines. However, the output power quality of wind turbines is poor, due to the randomness and volatility of wind energy, The energy storage hydraulic wind turbines (ESHWTs) may offer a better solution. 1,2 The concept of hydraulic wind turbine (HWT) was proposed about 30 years ago, but it was not feasible at that time due to low power transmission efficiency. 3 With the development of hydrostatic transmission techniques, the efficiency has been largely improved with the digital-displacement technique, 4 which made the HWT feasible in industry. [5][6][7][8][9][10] In HWT, the gearbox drivetrain between the rotor shaft and generator shaft of a conventional wind turbine is replaced by the hydrostatic transmission, aiming to provide continuously variable transmission ratio and reduce the maintenance costs by removing the troublesome gearbox and power converters with reduced wind turbine nacelle weight. [11][12][13][14][15][16] The hydraulic motor is installed on the ground through long hydraulic pipeline, and the generator is connected with hydraulic motor. Thus, the wind turbine nacelle weight can be reduced. 17 Hydrostatic transmission offers a significant reduction in operation & maintenance cost of up to 56% in comparison with traditional gearbox drivetrain. 8 At the same time, the efficiency of hydraulic accumulator is about 90%, and the hydraulic energy storage system (HESS) can realize seamless connection with the HWT, further improve the performance of the HWT and realize the smooth short-term power of the HWT in. 18 The efficiency comparison between hydraulic accumulator and other energy storage methods is shown in Table 1.
Current research on HWTs pays considerable attention to improve the power capture performances and electrical grid connection by applying advanced control strategies. [25][26][27] Some research are relevant to active power smoothing control by HWT. The 60 L hydraulic accumulator was added to a 50 kW HWT, and a control strategy proposed for the energy storage system to realize the power smooth control. 28,29 The proposed ESHWT as shown in Figure 1 is consistent with the ESHWT in this paper. However, the research on power smoothing control is only in the simulation stage, and the system nonlinear problem is not described.
A control strategy was proposed for the energy storage system to realize power smoothing control. An offshore HWT with an accumulator was proposed in Fan et al., 30 and a linear distributed control strategy was designed to balance the load and smooth the output power. The proposed ESHWT as shown in Figure 2 is inconsistent with the ESHWT in this paper, the main difference is that the hydraulic pump displacement is variable, the conversion link from wind energy to electric energy is open-loop, and the adjustment of the HESS energy and flow is not continuous.
An offshore HWT with a HESS was proposed in Lin et al., 1 an ESHWT frequency modulation control is realized, with controlling the swing angle of variable motor and HESS variable pump motor. The proposed ESHWT as shown in Figure 3 is inconsistent with the T A B L E 1 Comparison of efficiency between hydraulic accumulator and other energy storage methods

Efficiency (%) Reference
Pumped hydroelectric storage 75-85 [19] Compressed air energy storage 50-89 [19] Flywheel energy storage 93-95 [19] Gravity energy storage 80-90 [20] Flow battery energy storage 85 [21] Lithium battery energy storage 97 [21] Hydrogen-based energy storage 35-40 [22] Superconducting magnetic energy storage 95-98 [23] Supercapacitor energy storage 90-95 [19] Hydraulic energy storage system 90 [24] F I G U R E 1 An energy storage hydraulic wind turbine principle in Dutta 28 and Howlader et al. 29 F I G U R E 2 An energy storage hydraulic wind turbine principle in Fan et al. 30 F I G U R E 3 An energy storage hydraulic wind turbine principle in Lin et al. 1 ESHWT in this paper. A variable displacement pumpfixed displacement motor closed transmission system is adopted, the control variables are different, and the HESS medium is sea water.
A new type of compressed air energy storage system modeling and control method for HWTs was proposed in Li et al. 31 and Li 32 and a nonlinear controller was designed to realize maximum power point tracking (MPPT) and to absorb the power fluctuations in hydraulic pipes. The proposed ESHWT as shown in Figure 4 is inconsistent with the ESHWT in this paper. A variable displacement pump-variable displacement motor closed transmission system is adopted, the control variables and the HESS are different.
However, the above-mentioned papers only consider the HESS to smooth the output power, without deeply considering the HESS nonlinear problem. At the same time, the simulation research are only carried out in above research, without the experimental research. Therefore, it is necessary to further study the ESHWTs power stable output control strategy with experiments.
The present paper aims to investigate the ESHWTs power smoothing control strategy with the HESS nonlinear problem. The feedback linearization method can overcome the limitation of small signal linearization and realize the analysis and synthesis of the system in a large range. 33 A power smoothing control strategy is proposed with the method, the simulation and experiment results indicate that the proposed control scheme is a promising solution for ESHWTs to improve power quality.
The contents of this paper are organized as follows. Section 2 describes the composition of the ESHWT and wind condition analysis. Section 3 presents the corresponding mathematical models and characteristics. Section 4 shows the proposed controller design process. Section 5 presents the simulation results and the corresponding analysis. Section 6 presents the experimental results plus the corresponding analysis. Some conclusions are given in Section 7.

| ESHWT working principles
The proposed ESHWT structural principles are shown in Figure 5. The energy storage device (hydraulic accumulator) can be easily coupled to the hydraulic system transmission of wind turbine and the HWT is connected to the grid via synchronous generator without power converters. 1,17 And the HESS consists of a hydraulic displacement pump/motor and an accumulator.
The fixed displacement pump is connected to the rotor with a stiff shaft, and the variable hydraulic motor and the variable displacement pump motor are also connected to the synchronous generator with stiff shafts. The rotor captured power is used to drive the fixed displacement pump to output high-pressure oil, and the hydraulic motor is driven to rotate through the high-pressure pipeline. The variable displacement pump motor and the synchronous generator rotate under coaxial action to generate electricity. The working state of the hydraulic variable displacement motor is affected by the wind power fluctuation and the rotor acceleration or deceleration. Although the motor speed is constant (1500 r/min) in the grid-connected state, the hydraulic motor output torque fluctuates. The F I G U R E 4 An energy storage hydraulic wind turbine principle in Li et al. 31 and Li 32 F I G U R E 5 Schematic diagram of an energy storage hydraulic wind turbine displacement of the HESS variable displacement pump motor is adjusted by detecting the output torque fluctuation of the motor. Therefore, HESS charging or discharging is controlled to output compensating torque to realize a power stable output.

| Rotor aerodynamic model
The power and torque of the rotor can be expressed as 34 (1) where P r is the rotor captured power, ρ is the air density, R is the rotor radius, v is the effective average wind speed, C p (λ, β) is the rotor wind energy utilization coefficient, λ is the tip speed ratio, λ = Rω r /v, β is the rotor pitch angle, T r is the rotor aerodynamic torque, and ω r is the rotor speed.

| Hydraulic main transmission system mathematical model and characteristics
To establish the state space model of the hydraulic transmission system, the following assumptions is ① The low-pressure pipeline is connected with the oil tank, so the low-pressure pipeline pressure is zero, ② The leakage coefficient, viscous damping coefficient and bulk modulus will have small changes with the working conditions and environment, and these small changes will have a certain impact on the control accuracy. Thus these soft parameters are assumed as constant, ③ The pressure loss in the hydraulic lines is existed, and the pressure loss is about 0.5 MPa. Thus, the pressure loss in the hydraulic lines is ignored. The fixed displacement pump flow continuity equation is expressed as where, Q p is the pump flow rate (m 3 /s), D p is the pump displacement (m 3 /rad), ω p is the pump speed (rad/s), C t1 is the pump leakage coefficient (m 3 /[s·Pa]), and p h is the high pressure (Pa).
The fixed displacement pump torque balance equation is expressed as The variable hydraulic motor flow continuity equation is expressed as where, γ 1 is the motor swing angle, K m is the motor displacement gradient (m 3 /rad), Q m is the motor flow rate (m 3 /s), ω m is the motor speed (rad/s), and C t2 is the motor leakage coefficient (m 3 /[s·Pa]). The hydraulic variable displacement motor torque balance equation is 35 θ m is the motor angle (rad), and G m is the motor load spring stiffness (N·m/rad). The flow in the pipeline between the pump and motor is expressed as where, Q c is the flow caused by oil compression (m 3 /s), V is the pressure-affected oil volume (m 3 ), β e is the effective oil bulk modulus including a correction for pipeline expansion, and p h is the oil pressure in the high-pressure pipeline (pa). The flow between the pump and the motor is also expressed as where, C t is the total leakage coefficient (m 3 /[s·Pa]), and Then, the equation of state of the high pressure is Under random wind speeds, the torque and speed of the rotor are bound to fluctuate, and the pressure and flow in the hydraulic system also fluctuate. However, because the synchronous generator is pulled by the infinite power in the grid connection state, the generator speed is constant at 1500 r/min. Thus, the HWT can increase or reduce the torque with a constant rotation speed to achieve a change in power generation, as shown in Figure 6.
At the rated wind speed, the rotor output power is expressed as where, P t is the rotor output power (W), T m,rate is the motor rated output torque (N.m), and ω md is the rated speed of the motor (rad/s). A pressure change is caused by the random wind speed, and this pressure change results in a torque change in the variable hydraulic motor. Then, the total power generation is expressed as where T Δ is the motor output torque ripple (N.m), P rate is the motor rated output power (W), and P Δ is the motor output power fluctuation value (W).
The power that needs to be smoothed by the HESS is expressed as m md acc (12) where P acc is the power that needs to be smoothed by the HESS (W).
(2) HESS mathematical model The thermodynamic equation of the hydraulic accumulator is expressed as Equation (13) is expanded with a Taylor series at the stable operating point p V ( , ) 0 0 , and the high-order infinitesimals are ignored. The working pressure change rate of the hydraulic accumulator is expressed as where p 0 is the preinflated pressure of the hydraulic accumulator (pa), V 0 is the gas volume of the hydraulic accumulator under the preinflated body pressure (m 3 ), p 1 is the minimum working pressure of the hydraulic accumulator (pa), V 1 is the gas volume of the hydraulic accumulator at the lowest working pressure (m 3 ), p a is the working pressure of the hydraulic accumulator at any time (pa), V a is the gas volume of the working pressure of the hydraulic accumulator at any time (m 3 ), and k is the gas index, which is generally taken as k = 1.4 during the adiabatic process. The flow of the hydraulic accumulator is expressed as The force balance equation of the hydraulic accumulator is expressed as ac ac ac ac ac (16) where q a is the hydraulic accumulator flow (m 3 /s), p 2 is the pressure from the pump motor to the accumulator (pa), A ac is the cross-sectional area of the hydraulic accumulator oil chamber (m 2 ), m ac is the mass of oil in the pipes and accumulators (g), and B ac is the viscous damping coefficient of the hydraulic accumulator (N/[m/s]). The hydraulic variable displacement pump-motor displacement equation is expressed as where, D mp is the hydraulic pump-motor displacement (m 3 / rad), K mp is the hydraulic pump-motor displacement gradient, and γ 2 is the hydraulic pump-motor swing angle. The flow equation of the hydraulic variable displacement pump motor used as the variable displacement motor is expressed as F I G U R E 6 Power flow of a wind turbine with an energy storage system where Q am is the input flow of the hydraulic pump motor (motor condition) (m 3 /s), C tmp is the HESS total leakage coefficient (m 3 /[s·Pa]), V ta is the total volume of the HESS oil chamber, and V ta = V 0 + V a . The flow equation of the variable displacement pump motor used as the variable displacement pump is expressed as where, s is the variable in the complex field. The variable displacement pump-motor output/input torque is expressed as where Q ap is the output of the pump motor (pump condition), T Δ ac is the HESS torque output or input, and p Δ 2 is the pressure change in hydraulic pipeline.
The HESS requires that the hydraulic pump motor output different torques to compensate for the torque fluctuation value of the hydraulic transmission system.
The HESS state space model can be obtained by joining Equations (13), (15), (16), (18), and (19). When the hydraulic pump motor is operating under motor conditions, the state space model is expressed as When the hydraulic pump motor is operating under pump conditions, the state space model is expressed as Equation (23) is simplified into a single input single output affine nonlinear standard form.
The input is γ 2 , and the output is the output power of the hydraulic energy storage subsystem.

| POWER SMOOTHING CONTROL STRATEGY
From Equation (20), the nonlinearity is mainly reflected in the displacement and pressure. Thus the feedback linear method is adopted to solve the nonlinearity problem, and the controller is proposed to achieve the power smoothing.
To characterize the smoothness of wind power generation, the smoothness coefficient S is defined at 0-t.
where, S is the power smoothing coefficient.

| HESS control strategy operating at motor conditions
The solution idea of power smoothing control strategy based on feedback linearization is shown in Figure 7.
(1) System control output determination The HESS power is the control output when the hydraulic pump motor works under motor conditions. The control output is expressed as (2) Correspondence relationship between system relative order and system order According to Equation (25), the relative order is expressed as Because the relative order of the HESS (motor operating conditions) is 1 < 2, the design state feedback control is more complicated at this time, and it is difficult to implement in engineering practice.
(3) Zero dynamic design Thus, only a part of the linearization can meet the engineering requirements and simplify the control function. It is necessary to perform zero dynamic design of nonlinear systems. 36 General system behavior dynamics are divided into external and internal parts. Zero dynamic design requires the external dynamics to be stable and to be of good quality. This is necessary for the internal dynamics to be stable.
From Equation (26), the control system cannot be linearized for full state linearization, so it is necessary to transform the coordinate system. Select the functional relationship The transformation relationship between z i and x i can be expressed as follows.
(4) Verify the rationality of coordinate transformation Thus, the Jacobian matrix of the vector function φ This is nonsingular at x = x 0 , so the coordinate transformation is valid.
The expression of the original system mapped to the standard form (28) is Then, the inverse mapping of z = φ(x) is x = φ-1(z). Therefore, x can be expressed as a function of z.
From (30) and (31), the energy storage system (motor operating conditions) can be finally expressed as (6) Zero dynamic stability verification The dynamic deviation of the actual output is always zero at any time, that is, z z =̇= 0 1 1 . At this time, the energy storage system is expressed as From expression (33), the system is progressively stable, so the entire system must be stable with the control function, and the output remains unchanged under any interference. 37 (7) Constructing pseudo linear systems ż1 must satisfy the equation z v = * 1 , and when the HESS operates at the motor conditions, the system can be linearized as Thus, the zero dynamics are asymptotically stable, so the whole system is asymptotically stable. That is, the selected coordinate transformation can be used to determine the control function, and the system is in a stable state under the control function. At this time, the HESS control function of the energy storage system is The tracking error is defined as where, y d is the demand value for HESS output power.
The bounded tracking principle is used to determine v * because there are tracking errors in the changes in certain parameters in actual engineering. To eliminate this error, the integral term is added.
where the controller parameters k 1 = 0.0267, k 2 = 2. From Equations (34) to (37), the final HESS control function is expressed as

| HESS control strategy for operating under pump conditions
Similarly, the final HESS control function can be obtained under pump working conditions.

| Simulation platform
The overall control block diagram of power smoothing is shown in Figure 8. The power smoothing control of HESS is focused on. The HESS control block diagram is built with the MATLAB/Simulink@ simulation platform, as shown in Figure 9, and the parameters are shown in Table 2.
Based on the feedback linearization method, the power smoothing control strategy is proposed with the hydraulic torque as the control output. The torque difference between the hydraulic main drive system and the generator is demand, and the hydraulic torque is taken as the control output. The flow, flow rate change rate, pressure, pressure change rate in the HESSs are collected into the controller. The HESS swing angle of the variable pump/motor is adjusted, and then the HESS output torque is adjusted. The power smooth control of ESHWT is realized.
F I G U R E 8 Overall control block diagram of power smoothing

| Power smoothing at step wind speed
The system states under stepped wind speeds of 8-9-7 m/ s are shown in Figure 10.
The wind speed changes are shown in Figure 10A; the wind speed changes from 8 to 9 m/s at 50 s, from 9 to 8 m/s at 100 s, from 8 to 7 m/s at 150 s, and from 7 to 8 m/ s at 200 s.
From Figure 10B, the hydraulic motor power trend is the same as that of the wind speed. Oscillations occur only at the rising steps and the falling steps. When the wind speed changes, the main transmission system pressure changes more quickly and more obviously, which leads to hydraulic motor power oscillation. The hydraulic motor power increases more than it decreases due to the relationship between the wind power and the wind speed.
From Figure 10C, the swing angle of the hydraulic pump motor increases at 50 s. At this time, the HESS works under pump conditions, absorbs energy, and stores the energy in the accumulator. The swing angle of the hydraulic pump motor decreases and becomes negative at 150 s. At this time, the HESS works under motor conditions and releases energy by hydraulic pump-motor torque. The above process realizes a cycle from pump working F I G U R E 9 Hydraulic energy storage system control block diagram conditions to motor working conditions, that is, the process of HESS energy storage and release is realized. The response time of internal variable mechanism of variable displacement pump/motor is 3 s.
From Figure 10D, the HESS output torque is positive under pump working conditions, and the excess energy is absorbed. When the HESS output torque is negative under motor working conditions, the excess energy is released. From Figure 10E, the energy storage system capacity is not zero after 200 s, which indicates that there is still some capacity in the accumulator at this time.
Comparing Figure 10F with Figure 10B, the generated power is significantly smoothed, but the power oscillation spike caused by the sudden wind speed change is not eliminated. It is necessary to improve the energy storage and response ability of the HESS and the anti-interference ability of the control strategy to further smooth the power fluctuation caused by the sudden change of wind speed.
From Figure 10G, the magnitude of the inflation pressure can affect the HESS response speed. When the pressure is greater, the output torque is greater in a short time, similar to Figure 8.
From Figure 10H, when the hydraulic motor power suddenly increases at 50 and 200 s, the hydraulic accumulator needs to absorb the corresponding excess power to generate stable power. However, the accumulator energy change is slightly slow because the charging pressure of the accumulator changes slowly.
The hydraulic motor power suddenly drops at 100 s and 150 s. Similarly, the hydraulic accumulator should release power to achieve smooth generator power.

| Power smoothing at random wind speeds
The hydraulic motor state, the HESS state, and the generator power change under a random wind speed of 8 m/s are shown in Figure 11.  Figure 11A is the power change of the hydraulic motor. The power fluctuation range is approximately 5-2 kW. Figure 11B is the power smoothing output coefficient of the hydraulic main transmission system. The system power fluctuates greatly from the slope. Figure 11C shows the HESS torque change, and its fluctuation trend is consistent with the hydraulic motor power trend. That is, the HESS can control the output according to the hydraulic motor power fluctuation value to achieve peak clipping and valley filling. Figure 11D is the HESS charge state. Overall, the charge state is increasing, which indicates that more energy is stored than the released. That is, the average wind power at the random wind speed of 8 m/s is slightly greater than the wind power with the constant wind speed of 8 m/s, this phenomenon is also caused by the relationship of the wind speed and wind power. Figure 11E shows the ESHWT output power after smoothing, which is significantly smoother than that in Figure 10A. At this time, the power generation increases 7.7%. Figure 11F is the smoothing output coefficient of the generator output power after the HESS. Compared with that in Figure 11B, THE smoothing level is 74.6% higher.

| Experimental platform
The experimental platform mainly consists of four parts: a wind turbine simulation system, hydraulic F I G U R E 12 The energy storage hydraulic wind turbine schematic diagram F I G U R E 13 The 24 kW semiphysical simulation platform main transmission system, HESS, grid-connected generation system, and control system. The ESHWT schematic diagram is shown in Figure 12, and the hydraulic main transmission system is shown in Figure 13.

| Power smoothing control effect under stepped wind speed
The ESHWT states under stepped wind speeds of 6-7-5 m/s are shown in Figure 14. The wind speed changes are shown in Figure 14A. The wind speed changes from 6 to 7 m/s at 50 s, from 7 to 6 m/s at 100 s, from 6 to 5 m/s at 150 s, and from 5 to 6 m/s at 200 s.
From Figure 14B, the demand speed curve and the experimental speed curve basically coincide.
From Figure 14C, the hydraulic main transmission system pressure changes with the wind speed. The system pressure has a large overshoot at the wind speed step point, and the pressure recovery changes slowly.
The power change of the synchronous generator is shown in Figure 14D. The hydraulic motor power fluctuation is caused by the pressure fluctuation. After the action of HESS peak storage and valley filling, the power is transmitted to the generator. From Figure 14D, the experimental and simulation curves exhibit relatively good correspondence, and the HESS has stable output characteristics. The fluctuation range is about 9% with the proposed control strategy, which is within the allowable fluctuation range. 38 Figure 14E,F are the HESS working states, and the sign of the swing angle γ 2 represents the switching of the pump and motor operating conditions. From the SOC value of the hydraulic accumulator, the hydraulic accumulator charging process is slower than the discharging process. This phenomenon may be related to the actual gas change index of the accumulator and the accumulator inflation pressure. In the last 50 s, the SOC value is not zero, which indicates that the hydraulic accumulator absorbs more energy and releases less energy in the early stage. This phenomenon is also caused by the relationship between the wind speed and wind power. The effectiveness of the HESS is further verified by Figure 14F. Figure 14G is the power smoothing output coefficient. The ESHWT power smoothing coefficient is about 20%.

| Power smoothing control effect under random wind speed
The response characteristics of the ESHWT under a random wind speed of 6 ± 2 m/s are shown in Figure 15.
From Figure 15A, the system input wind speed is random with an average of 6 m/s. Figure 15B is the hydraulic motor power change value. Due to wind speed fluctuations, the hydraulic motor output power fluctuates. The fluctuation value is large and has a large impact on the power quality and frequency of the ESHWT. Figure 15C is the generator power, and the fluctuating power is passed through the HESS and then to the generator. The fluctuation range is about 10% with the proposed control strategy, which is within the allowable fluctuation range. 38 Figure 15D shows the hydraulic accumulator working state. The simulation value and the measured value show similar trends. and the error between the simulation and the experiment is 0-0.25. A comparison of the hydraulic motor power with the synchronous generator power shows that the generation power is smoother due to the HESS. The HESS plays a certain role in the steady smooth power output process; the validity and feasibility of the ESHWT power smoothing controller with the energy storage system are verified. Figure 15E is the power smoothing output coefficient. The ESHWT power smoothing coefficient is about 18%.

| CONCLUSION
The ESHWT is taken as the research object, and combined with the feedback linearization method and HESS, power smoothing control of wind turbines is realized. The main research work and conclusions are as follows: (1) The ESHWT working principle is explained, and the ESHWT mathematical model is established.
(2) For the multiplication nonlinear problem existing in the hydraulic main transmission system and the HESS, the feedback linearization method is used. (3) The feedback linearization method is also introduced to realize power stability control, with the system transmission power as the control output. The smoothness is increased by 74.6%.
In this paper, based on the ESHWT power stable output control research, the time-varying of hydraulic parameters is not considered. At the same time, the accuracy of the control strategy depends on the model parameters, which still has some limitations. Therefore, it is necessary to conduct a comprehensive study on the anti-interference ability and robustness of the control strategy.