Frequency Modulation Control of Hydraulic Wind Turbines Based on Ocean Used Wind Turbines and Energy Storage

Abstract

Based on the energy storage type of hydraulic wind turbines (HWTs) and in view of the unit frequency drop problem under high wind power proportion conditions, this paper proposes a method of primary frequency control under maximum power point tracking (MPPT). HWT power output is affected by wind speed randomness and volatility. In addition, traditional wind turbines do not have inertial adjustment ability, leading to a decrease in the frequency stability of the power system caused by the increase in wind power permeability. In the paper, a hydraulic energy storage system and synchronous generator are combined to carry out primary frequency modulation, and a mathematical model of the hydraulic energy storage system, the hydraulic main transmission system, and the generator active power regulation system after grid connection is established. By analyzing the load changing rules of power systems and frequency fluctuation caused by the power system load after the wind turbine is grid-connected, the variable parameter frequency modulation compensation control strategy of combined turbine-energy storage systems is established, and simulation verification under different load fluctuations is carried out, verifying the effectiveness of the frequency modulation control strategy, which achieves a good control effect for improving the frequency modulation ability of hydraulic wind turbines.

1. Introduction

Wind power generation has many advantages, such as low pollution and convenient use, and has become an important part of the new energy industry [1,2]. However, the inertia and anti-interference ability of a high wind power proportion system are poor, which seriously affects the stability and power quality of the power grid. As the research in [3] shows, if a variable speed constant frequency (VSCF) wind turbine has a frequency modulation capability, the frequency instability time of the power grid can be reduced from 81% to 53%. Therefore, grid standards in most countries require grid wind turbines to have the ability to participate in system frequency modulation [4]. When the wind turbine’s active power is more than 20% of the rated value or the frequency deviation is over a certain range (±0.2 Hz), regulations demand that wind turbines have the ability to adjust the frequency in order to support recovering the power system frequency [5].

The main types of conventional wind turbines include doubly fed wind turbines and direct drive wind turbines, and the related technologies are relatively mature. Both models are rigid transmissions [6] and are close to the grid by a rectifier inverter, with weak coupling to the power grid and unstable wind power output, leading to a high wind power proportion that will seriously affect the frequency stability and safe operation of the power grid. Hydraulic energy storage systems with advantages such as fast response speed, large power density, long storage time, and absorption of the pulse, which can quickly respond to the demand of the power grid, are widely used in various fields. Due to the complex nonlinear characteristics of the hydraulic servo actuator system, modeling and simulation analysis brings great difficulty. Reference [7] proposed two methods for modeling and simulation analysis of complex systems. The first one is to use a variable step size adjusted to the fastest processes in which the model is continuous, and the second one is to approximate fast processes by ideal instantaneous mode transitions, which is a hybrid. The continuous model is simpler since it is based on physical laws. In this paper, the hydraulic system model is established based on the three physical equations of flow, flow continuity, and force/torque balance, and the ideal instantaneous mode transition is used to approximate the fast process, which is convenient for the simulation analysis of subsequent frequency modulation control. Moreover, the hydraulic servo actuator system parameters cannot be accurately determined due to various uncertainties, the inability to measure some parameters, and disturbances [8]. Reference [8] proposed a data-driven optimal controller of the hydraulic servo with completely unknown dynamics, based on an adaptive dynamic programming framework, avoiding the knowledge of entire system dynamics. However, in some cases, we need to study internal disturbances and parameters, in this paper, based on dynamics research and a small signal processing method, the hydraulic servo system is simulated and analyzed. Hydraulic wind turbines adopt wrapping connector driving, cooperate with excitation synchronous generators, and omit the rectifier inverter, greatly reducing the weight of the wind turbine [9,10]. This avoids problems caused by traditional wind turbine rigid transmission and can help improve the frequency stability under a high wind power proportion [11].

With the integration of wind power, preserving the planned frequency limit is essential for active power balance in an area. Apart from that, the power systems may become unstable. Reference [12] proposed a new instantaneous slip frequency control (ISFC) method that improves rotor-speed stability of dual stator-winding induction generators (DWIG)-based wind turbines during a severe fault in the power system. Reference [13] proposed an improved frequency response analysis for fault detection, that can effectively measure the frequency failure of the system. Reference [14] discussed the problem of the asynchronous fault detection observer design for 2-D Markov jump systems expressed by a Roesser model. The designed strategy behaves with strong robustness against exogenous disturbances and sensitivity to faults. All of the research above solve problems after fault detection. This paper will discuss the frequency modulation control in the stage when the frequency starts to fluctuate.

The commonly used frequency modulation control methods for wind turbines are as follows: virtual inertial control, droop control, load shedding control, overspeed control, and compound control [15,16]. These methods to some extent meet the needs of wind power participating in frequency modulation but are greatly influenced by wind conditions and tend to cause the power grid frequency to drop again [17]. At present, many frequency modulation research scholars work on virtual inertia control. Reference [18] proposed combining energy storage with the wind turbine’s own frequency modulation capability. By taking advantage of their complementary advantages in response speed, available power, and energy, as well as the flexible control of energy storage, the wind turbine platform has the inertia response and frequency regulation ability similar to a traditional power supply with less energy storage capacity configuration, which improves the engineering applicability of wind turbines with energy storage system frequency modulation. The simulation experiment shows that the power and capacity required by frequency modulation are only 67% and 11.1% of the energy storage, respectively, which makes the wind farm have an inertia response and primary frequency modulation capability similar to traditional power supply, further improving the frequency characteristics of the power system under high wind power penetration, reducing the frequency change rate and maximum frequency deviation, and verifying the feasibility of energy storage participating in wind power frequency modulation. Reference [19] proposed a control method for wind turbines and flywheel energy storage systems to jointly participate in frequency modulation. By coordinating the regulation of the power reserves of the wind turbines and the flywheels to proceed with the primary frequency control, the method reduces the energy loss of the unit, and the system frequency is quickly restored to near the rated value, verifying the feasibility of the flywheel energy storage system participating in frequency regulation. In references [20,21], the frequency response of the system under different operation modes and different wind power proportions is analyzed. The proposed frequency processor, based on a dynamic dead zone, enhances the frequency response capability of wind turbines and has been verified in power systems with a wind power proportion of 60% [20,21]. Reference [22] proposed a controller based on the frequency droop method, which is applied to a robust droop controller in parallel connected inverters. With this controller, the frequency error is eliminated and the feasibility of drooping control in the frequency control of isolated island micro-grid is verified. However, in the system studied in this paper, the inverter is replaced by the hydraulic transmission system, so the frequency control method needs to be further explored. Reference [23] proposed a method based on low frequency response correction droop coefficient, through issuing the load shedding control instruction, which realized the frequency stability control and verified the feasibility of droop control and load shedding control in the power system frequency control. However, this method is only applicable to the rated wind speed, the method is not universal. Based on the feasibility analysis of the energy storage system to system frequency modulation, this paper will explore the further study of the frequency modulation control strategy of hydraulic wind turbines with energy storage.

Considering that the frequency modulation ability of wind turbines directly affects the power output quality, we need a better frequency controller to solve the frequency drop problem. Many scholars have studied the frequency stability of the system caused by the uncertain power generation generated by wind farms. In reference [24], a primary frequency modulation control model based on wind power plants was proposed for the uncertainty of the wind field side. In reference [25], a multi-area interconnected power system combined with wind farms was proposed. A method of load frequency control based on sliding mode control is proposed. There is little research on the control of frequency fluctuation caused by the load side. Therefore, the mechanism of the frequency drop by both the wind side and load side is analyzed in this study. When the energy storage hydraulic wind turbine supplies power to the load, due to the load disturbance of the power system, the electrical energy generated by the generator changes accordingly, resulting in the power imbalance of the rotor on both sides of the synchronous generator, and the rotor-speed changes. In order to maintain the stability of the system frequency, it is necessary to regulate the drive power transmitted to the synchronous generator. However, there is no change in the power input of the wind turbine, that is, the wind power value captured by the wind turbine remains constant, the swing angle of the variable displacement pump/motor does not deflect, and the accumulator does not store energy. At this time, the unit cannot provide additional energy to compensate or there is excess energy that is not needed. The supply and demand of active power on the network side of the unit will be unbalanced, which will cause the system frequency’s instability to go beyond the normal range, leading to off-network accidents and raising security issues.

The relationship between system power deficiency, output power change of frequency modulation unit, total inertia of the system, and power grid frequency change is shown in Formula (1) [26]

$$2H\frac{\partial \Delta f(t)}{\partial t}+D{D}^{ML}\Delta f(t)={\displaystyle \sum _{n\in N}\Delta P_n^E}-\Delta P^{loss}$$

(1)

where H is the total inertia of the system, Δf(t) is the frequency variation, D is the load damping coefficient, D^ML is the motor load, $\Delta P_n^E$ is the unit output variation that provides frequency modulation for the system, and $\Delta P^{loss}$ is the system power deficiency.

According to Formula (1), the adjustment of unit frequency is mainly through adjusting the active power of wind turbines, and then the matching of wind side and network side power is realized. Hence, in view of the problems existing in the mechanism analysis, a joint frequency modulation controller based on wind turbines and hydraulic energy storage systems is purposed to actively adjust the active power of the energy storage hydraulic unit, and verification and simulation experiments are carried out.

This article is structured as follows. In Section 2, the working principle of the system is introduced, and the mathematical model is established. In Section 3, the dynamic and static response characteristics of the energy storage hydraulic wind turbines are analyzed. In Section 4, the frequency modulation control strategy of the energy storage hydraulic wind turbine is designed, and the parameters are adjusted and analyzed. In Section 5, the effectiveness of the control strategy is verified by simulation analysis. In Section 6, the effectiveness of the control strategy is verified by experiment analysis. In Section 7, The results of the simulation and experiment are compared and analyzed and compared the results with other researchers. In Section 8, the conclusion of this paper is given.

2. Working Principle and Mathematics Model of Energy Storage Hydraulic Wind Turbine

2.1. Working Principle of The Hydraulic Wind Turbine

An energy storage hydraulic wind turbine is composed of a wind turbine, hydraulic transmission system, hydraulic energy storage system, synchronous generator, and a grid connection. The wind turbine captures the wind energy to drive the fixed displacement pump rotation. The hydraulic transmission system, through a fixed displacement pump and hydraulic motor, achieves the transformation of mechanical energy into hydraulic energy and then into mechanical energy. The hydraulic energy storage system realizes the storage of oil in the energy accumulator through the control of the variable displacement pump/motor swing angle and provides energy support for the frequency modulation of the unit. One end of the synchronous generator is coaxially connected with the variable displacement pump/motor to convert mechanical energy into electrical energy. The grid-connected system is used to monitor the grid side data and complete the connected. Due to the randomness and poor predictability of wind power generation, the load of wind power fluctuates greatly [27,28]. The instability and randomness of wind power will lead to frequency fluctuations in the electric energy released by the generator system. With the increase in wind power proportion, the inertia and anti-interference ability of the power system will be affected. This restricts the stability and power quality of the power grid [29,30]. To improve the power quality and ensure the stability of the power grid, frequency modulation control of hydraulic wind turbines is proposed.The diagram of the principle of operation of the hydraulic system for HWT is shown as Figure 1.

As shown in Figure 2, when the unit is in the partial power stage, can be grid-connected, and is capable of producing stable electric energy, the unit normally runs under the condition of MPPT, and the wind energy conversion rate is the maximum. At this stage, the unit is in the partial load area, and the output power does not reach the upper limit. Therefore, the kinetic energy released by the wind turbine/pump can be controlled by adjusting the motor displacement to respond to frequency fluctuations.

2.2. Wind Turbine Mathematical Model

The rotor captured wind energy is [9]

$$P_w=C_p\left(\lambda ,\beta \right)\frac{\rho A}{2}{v}^3=\frac{1}{2}\rho \pi R^2{v}^3{C}_p\left(\lambda ,\beta \right)$$

(2)

where P_w is the captured wind power, C_p is the wind power utilization coefficient, ρ is the air density, R is the leaf blade radius, β is the blade pitch angle, λ is the tip-speed ratio, i.e., $\lambda =R{w}_w/v$, v is the wind speed, and ω_w is the wind turbine speed.

2.3. Main Transmission Hydraulic System Mathematical Model

To analyze the mathematical model of the pump-motor closed speed control system, the following assumptions are made:

• The oil volume elastic modulus in the pipeline is a constant, that is, the flow compression is only related to the pressure;
• The low-pressure pipeline pressure is zero;
• When the rotor is working, the oil density, leakage coefficient, viscous damping, and transmission efficiency are considered to be constant;
• The fixed displacement pump is rigidly connected to the rotor, so the two speeds are considered to be equal.

2.3.1. The Model of The Fixed Displacement Pump

The fixed displacement pump flow continuity equation is [31]

$$Q_p=D_p{\omega }_p-C_{tp}{p}_{h1}$$

(3)

The fixed displacement pump torque balance equation is [32]

$$T_w-\frac{D_p{p}_{h1}}{{\eta }_p}=J_p\frac{d{\omega }_p}{dt}+B_p{\omega }_p+G_p{\theta }_p(G_p\approx 0)$$

(4)

where Q_p is the pump flow (amount of fluid passing through the pump per unit time), D_p is the pump displacement (volume of liquid discharged from the driving spindle of the pump per revolution), ω_p is the pump speed (number of turns per unit time), C_tp is the pump leakage coefficient (leakage flow coefficient due to pressure difference), p_h1 is the pump inlet and outlet pressure differential, T_w is the wind turbine torque, J_p is the moment of inertia of the rotor and pump, B_p is the pump damping coefficient (determined by the viscous force of the liquid), G_p is the pump load spring stiffness, θ_p is the pump angle, and η_p is the pump mechanical efficiency. In the hydraulic servo system with a hydraulic motor as the actuator, there is almost no elastic load.

The fixed displacement pump state equation is [32]

$$\frac{d{\omega }_p}{dt}=\frac{1}{J_p}\left(T_w-\frac{D_p{p}_{h1}}{{\eta }_p}-B_p{\omega }_p\right)$$

(5)

2.3.2. The Model of The Variable Displacement Motor

The variable displacement motor flow continuity equation is [31]

$$Q_m=K_m{\gamma }_1{\omega }_m+C_{tm}{p}_{h1}$$

(6)

The variable displacement motor torque balance equation is [9]

$$K_m{\gamma }_1{p}_{h1}{\eta }_m-T_h=J_m\frac{d{\omega }_m}{dt}+B_m{\omega }_m+G_m{\theta }_m(G_m\approx 0)$$

(7)

where Q_m is the motor flow (amount of fluid passing through the motor per unit time), K_m is the motor displacement (volume of liquid discharged from the driving spindle of the motor per revolution), ω_m is the motor speed (number of turns per unit time), C_tm is the motor leakage coefficient (leakage flow coefficient due to pressure difference), γ₁ is the non-dimensional displacement fraction ranging from 0 to 1, T_h is the electromagnetic torque acting on the motor, J_m is the moment of inertia of the motor, B_m is the motor damping coefficient (determined by the viscous force of the liquid), G_m is the motor load spring stiffness, θ_m is the motor angle, and η_p is the motor mechanical efficiency.

The variable displacement motor state equation is [32]

$$\frac{d{\omega }_m}{dt}=\frac{1}{J_m}\left(K_m{\gamma }_1{p}_{h1}{\eta }_m-B_m{\omega }_m-T_h\right)$$

(8)

2.3.3. The Model of The Energy Storage System

The Model of The Bag Type Accumulator

The accumulator charging and discharging oil responding to the changing frequency is fast, which can be regarded as an adiabatic process.

The bag type accumulator force balance equation is [33]

$$p_{\mathrm{a}}-p_{\mathrm{l}}=L\frac{d{q}_{\mathrm{l}}}{dt}+R{q}_{\mathrm{l}}$$

(9)

where p_l is the line pressure, which is equal to the pressure, q_l is the line flow, L is the liquid inductance of the liquid in the accumulator, i.e., $L=\rho \frac{4l_{\mathrm{a}}}{\mathsf{\pi }{d}_{\mathrm{a}}{}^2}$, R is the fluidic resistor of the liquid in the accumulator, i.e., $R=\frac{128\mu l_{\mathrm{a}}}{\mathsf{\pi }{d}_{\mathrm{a}}^4}$, l_a is the length of the line, d_a is the diameter of the line, ρ is the oil density, and μ is the oil kinetic viscosity.

The accumulator state equation is [33]

$$\frac{d{q}_{\mathrm{l}}}{dt}=\frac{1}{L}(-R{q}_l-p_l+p_a)$$

(10)

The Model of The Variable Displacement Pump/Motor

The variable displacement pump/motor torque balance equation is [9]

$$T_h+p_l{K}_{mp}{\gamma }_2{\eta }_{mp}=T_L+J_{mp}\frac{d{\omega }_m}{dt}+B_{mp}{\omega }_m+G_{mp}{\theta }_{mp}(G_{mp}\approx 0)$$

(11)

where K_mp is the pump/motor displacement, ω_m is the motor speed, and γ₂ is the non-dimensional displacement fraction ranging from −1 to 1; −1 to 0 is under the pump condition and 0 to 1 is under the motor condition. η_mp is the pump/motor mechanical efficiency, T_L is the loading torque acting on the motor, J_mp is the moment of inertia of the pump/motor, B_mp is the pump/motor damping coefficient, G_mp is the pump/motor load spring stiffness, and θ_mp is the pump/motor angle. In the hydraulic servo system with a hydraulic motor as the actuator, there is almost no elastic load.

The variable displacement pump/motor flow continuity equation is [9]

$$q_l=K_{mp}{\gamma }_2{\omega }_m+C_{tmp}{p}_l+\frac{V_1}{{\beta }_e}\frac{d{p}_l}{dt}$$

(12)

where C_tmp is the pump/motor leakage coefficient, V₁ is the volume of the hydraulic energy storage system pipeline, and β_e is the effective bulk modulus of elasticity.

The variable displacement pump/motor power balance equation is [9]

$$P_{G1}+p_l{K}_{mp}{\omega }_m{\gamma }_2{\eta }_{mp}=P_{G2}+J_{mp}{\omega }_m\frac{d{\omega }_m}{dt}+B_{mp}{\omega }_m^2$$

(13)

where P_G2 is the load power of the pump/motor.

The variable displacement pump/motor state equation is [9]

$$\frac{\mathrm{d}{p}_l}{\mathrm{d}t}=\frac{{\beta }_e}{V_1}(-K_{mp}{\gamma }_2{\omega }_m-C_{tmp}{p}_l+q_l)$$

(14)

2.4. The Model of The Synchronous Generator

The power balance equation of the synchronous generator after grid connection is [33]

$$P_m=P_{\Omega }+P_{Fe}+P_{Cu}+P_2$$

(15)

where P_m is the power input into the synchronous generator by the variable displacement motor and energy storage system, P_Ω, P_Fe, and P_Cu are the mechanical loss, iron loss, and copper loss, respectively, and P₂ is the power supplied to the grid by the synchronous motor.

The generator torque equation is [33]

$$T_m=T_0+T_e$$

(16)

where T_m is the generator driving torque, i.e., $T_m=P_m/{\omega }_0$, T_e is the electromagnetic torque, i.e., $T_e=P_e/{\omega }_0$, and T₀ is the no-load torque, i.e., $T_0=(P_{Fe}+P_{\Omega })/{\omega }_0$.

The equations of the generator rotor in an unbalanced state between the mechanical torque and electromagnetic torque are [33]

$$J_f\frac{d{\omega }_g}{dt}=T_m-T_e-T_D$$

(17)

$${\omega }_e=p{\omega }_g$$

(18)

$$\frac{d{\omega }_e}{dt}=\frac{d\theta }{dt}=\frac{d({\omega }_{e}t+\delta )}{dt}$$

(19)

where J_f is the moment of inertia of the generator, ω_g is the generator mechanical speed, ω_e is the generator electrical speed, T_D is the damping torque, p is the generator pole logarithm, and δ is the phase difference between the exciting magnetic potential and the terminal voltage.

3. Dynamic and Static Response Characteristics of the Energy Storage Hydraulic Wind Turbine

The frequency of the power system can be regarded as the balance between the generated power and the electricity load. When the frequency is in a stable state, it indicates that the power of the power supply side and the load demand side are matched. When the frequency increases gradually, it indicates that the power supply on the grid side exceeds the load demand; the contrary indicates that the power supply on the grid side is insufficient to meet the load demand.

3.1. Power-Frequency Static Characteristic of The Electric System

The load power of the power system is [30]

$$P_L=P_D(f)=a_0{P}_{DN}+a_1{P}_{DN}(\frac{f}{f_N})$$

(20)

The power-frequency static characteristics of the load are shown in Figure 3.

As shown in Figure 3, at the rated frequency f_N, the load power is P_DN, and with the change in frequency, the load power will also change. Its variation value is determined by angle a, and its tangent value is called the power-frequency characteristic coefficient of load, expressed as

$$K_L=\tan \alpha =\frac{\Delta P_L}{\Delta f}$$

(21)

The unit value of power-frequency characteristic coefficient K_L is

$$K_L{}^{*}=\tan \alpha =\frac{\Delta P_L{}^{*}}{\Delta f^{*}}$$

(22)

When the load power increases abruptly, the load power-frequency static characteristic curve jumps from l₁ to l₂, and the active power load changes from equilibrium point A to B. When the load suddenly increases, the frequency will decrease. According to Equation (19), the load will decrease with decreasing frequency, and its power will decrease from point B along l₂ until it reaches a new equilibrium point. The characteristic of the load sliding from A to B along l₂ is called load regulation.

3.2. Power-Frequency Static Characteristic of The Generator

The power-frequency static characteristics of the generator are shown in Figure 4, which indicates that in the system at the rated frequency f_N, the generator that produces the active power is P_GN. If the system frequency fluctuates, the active power generated by the generator will increase or decrease with the fluctuation of the frequency.

As shown in Figure 4, as the active power changes, the frequency f will change in reverse. tanβ is the slope of the generator’s active power-frequency change, also known as the power-frequency characteristic coefficient of the generator, expressed as

$$K_G=tan\beta =-\frac{\Delta P_G}{\Delta f}$$

(23)

The unit value of power-frequency characteristic coefficient K_G is

$$K_G{}^{*}=tan\beta =\frac{\Delta P_G{}^{*}}{\Delta f^{*}}$$

(24)

The static adjustment coefficient of the generator can be expressed as

$$\delta =\frac{1}{K_G}=-\frac{\Delta f}{\Delta P_G}$$

(25)

In Formula (24), “$-$” means that the frequency is contrary to the increase or decrease of the generator’s active power.

3.3. Integrated Power-Frequency Static Characteristic of The Electric System

Combining Figure 3 and Figure 4, the integrated power-frequency characteristics are obtained, as shown in Figure 5. l₁ and l₂ are load curves, and G1 is the generator curve. The power system runs smoothly at position A, and its corresponding frequency is f₁. The active power generated by the generator and the active power of the load are recorded as P₁. When the load suddenly increases ΔP_L, the system state changes from point A to point B and then to point C, and the frequency decreases from f₁ to f₂. The generator will produce more active power ΔP_G. When the active power of the generator and the active power of the load are the same again, the system will be stabilized again at point C in the figure.

Combining Figure 4 and Figure 5, the active power increment of the generator is

$$\Delta P_G=-K_G\Delta f=-K_G(f_2-f_1)$$

(26)

After a sudden increase in load, the active power change is

$$\Delta P^{\prime }{}_L=K_L\Delta f=K_L(f_2-f_1)$$

(27)

The actual increment of the load power is

$$\Delta P_L+\Delta P_L{}^{\prime }=\Delta P_L+K_L\Delta f$$

(28)

Through the balance between generator output and load active power, the following can be obtained:

$$\Delta P_L=-(K_G+K_L)\Delta f=-K\Delta f$$

(29)

The relationship between the actual load active power increment and the actual frequency increment is

$$\Delta P_L=-(K_G+K_L)\Delta f=-K\Delta f$$

(30)

In Equation (29), “$-$” means that the frequency is contrary to the increase or decrease of the generator active power, and the integrated power-frequency characteristic coefficient K is the sum of the generator power-frequency characteristic coefficient and load power-frequency characteristic coefficient. Within the normal operating range of the frequency, the larger K is, the greater the load fluctuation of the power system. When ΔP_L is too large, the frequency fluctuation will exceed the normal range, and the system will need to be adjusted.

3.4. Power-Frequency Model of The Electric System

The generator power balance equation is [30]

$$P_{\omega }=P_m-P_e-P_D=J{\omega }_m\frac{d{\omega }_m}{dt}$$

(31)

The frequency fluctuation response of the synchronous generator is [30]

$$E_k={\displaystyle \int P_{\omega }dt}=\frac{1}{2}J{\omega }_m^2$$

(32)

Bringing in the inertia time constant to represent the inertia of the synchronous generator, that is, the needed time after adding the rated torque to the rotating shaft, the time rotor accelerates from the stopped state to the rated speed [34]. It is calculated by the ratio of the kinetic energy and rated capacity of the synchronous generator at synchronous speed as follows: [35]

$$H=\frac{E_0}{S_n}=\frac{J{\omega }_0^2}{2S_n}$$

(33)

Combining with Equation (32), transforming into a dimensionless unit value and considering the unit value of damped power P_D, i.e., $P_D{}^{*}=D\cdot {\omega }_e^{*}({\omega }_e^{*}-1)$, ${\omega }_e^{*}\approx 1$, the following is obtained:

$$P_{\omega }{}^{*}=P_m{}^{*}-P_e{}^{*}-D({\omega }_e^{*}-1)=2H\frac{d{\omega }_e^{*}}{dt}$$

(34)

If the power of the generator’s supply-demand side does not match, the power change is

$$\Delta P_{\omega }=P_m-P_e-D\Delta f=2H\frac{d\Delta f}{dt}$$

(35)

According to Equation (34), the power-frequency model of the power system is shown in Figure 6.

H is the inertia coefficient of the system, and D is the damping coefficient of the system. Figure 6 shows that the greater H and D, the more system is able to resist the change in frequency.

4. Methodology

The generator and the power grid are coupled, so the rotor of the motor can provide inertial support for the frequency when the power grid frequency fluctuates. However, due to the increase in wind power permeability, the system becomes difficult to stabilize, so it is not enough to adjust the frequency only by the inertia of the synchronous generator. Both the wind turbine and the synchronous generator contain rotational kinetic energy. However, since the wind turbine of this unit is not directly connected with the synchronous generator coaxially, the wind turbine cannot provide inertial support when the frequency fluctuates. When the frequency fluctuates, if the kinetic energy of the wind turbine can be released through additional frequency control links to meet the demand of frequency modulation, it can be considered that the wind turbine will also have the inertial support of frequency. So we define the virtual inertia of the wind turbine as the energy provided by the kinetic energy of the wind turbine rotor for the inertial response of the system. After the hydraulic energy storage system is introduced into the wind turbine, it can be improved by the accumulator to solve the power imbalance at the wind motor networking side. In the hydraulic energy storage system, the pressure stored by the accumulator can be transmitted to the generator through the rotating shaft of the variable displacement pump/motor. Therefore, a comprehensive control method combining virtual inertial control and virtual droop control is selected.

4.1. Frequency Modulation Control Analysis of The Wind Turbine and Energy Storage System

The kinetic energy provided by the rotor in the frequency modulation is [33]

$$\Delta E=\frac{1}{2}{J}_w({\omega }_{w1}^2-{\omega }_{w0}^2)$$

(36)

where J_W is the total inertia of the rotor and the load, ω_w0 is the rotational speed under MPPT, and ω_w0 is the minimum operating speed of the wind turbine.

Taking a hydraulic wind turbine to a traditional synchronous wind turbine together by analogy yields

$$\Delta E=\frac{1}{2}{J}_{vir1}({\omega }_{s1}^2-{\omega }_s^2)$$

(37)

where J_vir is regarded as the virtual inertia by analogy to a synchronous wind turbine and ω_s and ω_s1 represent the synchronous speed and the speed of the synchronous generator after the frequency modulation requirement is met.

In combination with Equations (35) and (36), the following is obtained:

$$J_{vir1}=\frac{J_w({\omega }_{w1}^2-{\omega }_{w0}^2)}{({\omega }_{s1}^2-{\omega }_s^2)}$$

(38)

Due to ${\omega }_{w1}={\omega }_{w0}+\Delta {\omega }_w$ and ${\omega }_{s1}={\omega }_s+\Delta {\omega }_s$, the following is obtained:

$$J_{vir1}=\frac{J_w(2{\omega }_{w0}\Delta {\omega }_w+\Delta {\omega }_w^2)}{(2{\omega }_{s0}\Delta {\omega }_s+\Delta {\omega }_s^2)}$$

(39)

In actual frequency fluctuation, $\Delta {\omega }_w\ll {\omega }_{w0}$ and $\Delta {\omega }_s\ll {\omega }_s$, which gives

$$J_{vir1}=\frac{J_w{\omega }_{w0}\Delta {\omega }_w}{{\omega }_s\Delta {\omega }_s}=K_1\frac{J_w{\omega }_{w0}}{{\omega }_s}$$

(40)

According to Equation (39), after adding the additional frequency control link, the wind turbine can be regarded as a synchronous generator with a moment of inertia of J_vir1 for the inertial response.

The power stored in the accumulator can be transferred to the generator through the rotating shaft of the variable displacement pump/motor to improve the power imbalance of the grid side.

The energy absorbed by the accumulator can be expressed as [33]

$$E={\displaystyle {\int }_{V_{a1}}^{V_{a2}}{p}_{a}dV=}{\displaystyle {\int }_{V_{a1}}^{V_{a2}}{p}_{a0}{(\frac{V_{a0}}{V})}^{1.4}dV=}\frac{p_{a0}{V}_{a0}^{1.4}}{0.4}(V_{a1}^{-0.4}-V_{a2}^{-0.4})$$

(41)

where V_a1 is the volume of the gas vessel before energy absorption of the accumulator and V_a2 is the volume of the gas vessel after energy absorption of the accumulator. It can be determined from the equation that the gas or liquid vessel volume of the accumulator can be directly controlled to balance the power.

When the wind energy utilization coefficient is the maximum, the optimal speed of the fixed displacement pump (wind turbine) is [9]

$${\omega }_p=\frac{\lambda (C_{p\max })v}{R}$$

(42)

The reference value of the swing angle of the variable displacement motor can be obtained from the conservation of pump–motor flow in the transmission system [32]:

$${\gamma }_{10}=\frac{D_p{\omega }_p}{K_m{\omega }_m}=\frac{D_p\lambda (C_{p\max })v}{R{K}_m{\omega }_m}$$

(43)

The swing angle of the variable displacement pump/motor is [32]

$${\gamma }_{20}=\frac{\Delta P_L}{p_a{K}_m{\omega }_m}$$

(44)

4.2. Coordinated Control Strategy of Wind Turbine and Energy Storage Joint Frequency Modulation

By studying and analyzing the characteristics of frequency fluctuations, we suggest methods of frequency modulation control in different fluctuation stages. Schematic diagram of the frequency fluctuation is shown in Figure 7.

When the frequency drops, $\Delta f<0$ and $d\Delta f/dt<0$, and the frequency falls over the dead zone $f_{\min }$. The compensation power of virtual inertial control is $\Delta P_1=-K_{df}(d\Delta f/dt)>0$, and the compensation power of virtual droop control is $\Delta P_2=-K_{pf}\Delta f>0$. Combining the methods above can provide compensation power to a great extent. Virtual inertia control can slow down the frequency variation, slowing the rate of frequency drop, and virtual droop control can reduce the frequency deviation and frequency drop depth.

When the frequency recovers in an upturn, $\Delta f<0$ and $d\Delta f/dt>0$, and the virtual droop control compensation power $\Delta P_2>0$. The virtual inertial control compensation power of the method $\Delta P_1<0$, so only droop control is used in the frequency recovery stage.

When the frequency rises, $\Delta f>0$ and $d\Delta f/dt>0$; when this occurs, the integrated control method of virtual inertial control and virtual droop control responds to the change in frequency.

When the frequency decreases, $\Delta f>0$ and $d\Delta f/dt<0$, so droop control is used to respond to the change in frequency. Therefore, if $\Delta f\cdot (d\Delta f/dt)\ge 0$, the integrated control method is used in the frequency regulation; if $\Delta f\cdot (d\Delta f/dt)<0$, only the droop control method is used for the frequency regulation.

The control idea is shown in Figure 8. First, the frequency fluctuation state is judged to determine the frequency modulation control method. Virtual droop control is used to calculate the compensation active power of the system’s frequency difference, and virtual inertia control is used to calculate the compensation active power of the system’s frequency difference change rate. The positive or negative of the product of the frequency difference and frequency difference change rate is judged, the corresponding control link is selected, and according to the corresponding power controller, the variable motor swing angle $\Delta {\gamma }_1$ and variable pump/motor swing angle $\Delta {\gamma }_2$ are calculated. The purpose of compensating power is achieved, the system frequency is constantly adjusted, and stability is restored.

In summary, the unit will adopt the united virtual inertia /virtual droop control of the integrated control method.

4.2.1. Virtual Inertia Control

According to the virtual inertia control link, the active power of the unit to compensate for frequency fluctuation is

$$\Delta P_1=-K_{df}\frac{d\Delta f}{dt}$$

(45)

where ΔP₁ is the power compensated by the virtual inertia control, f is the system frequency deviation, and K_df is the virtual inertia coefficient. At the beginning of frequency fluctuation, adding a virtual inertia link can compensate for the active power quickly.

4.2.2. Virtual Droop Control

Compared with the droop characteristic of the generator, the frequency variable is introduced to respond to the system frequency change. The compensated active power of the virtual droop control link is

$$\Delta P_2=-K_{pf}\Delta f$$

(46)

where ΔP₂ is the power compensated by the virtual droop control and K_pf is the virtual droop coefficient.

4.2.3. Integrated Control

Combining the power compensated by virtual droop control and virtual inertia control, the power compensated by the integrated control method is obtained.

$$\Delta P=\Delta P_1+\Delta P_2=-K_{df}\frac{d\Delta f}{dt}-K_{pf}\Delta f$$

(47)

When the frequency fluctuation exceeds the range of the frequency modulation dead zone, the system’s additional active power output based on the integrated control method is

$$\Delta P=\Delta P_1+\Delta P_2=-K_{df}\frac{d\Delta f}{dt}-K_{pf}\Delta f$$

(48)

According to Figure 6, the power-frequency model of the power system can be expressed as

$$\Delta P_m-\Delta P_L=2H\frac{d\Delta f}{dt}+D\Delta f$$

(49)

After the introduction of frequency modulation control, Formula (48) can be expressed as

$$\Delta P_m-\Delta P_L-K_{df}\frac{d\Delta f}{dt}-K_{pf}\Delta f=2H\frac{d\Delta f}{dt}+D\Delta f$$

(50)

The frequency anti-jamming capability of the power system is measured by the inertia coefficient and damping coefficient. The combined wind turbine and energy storage system is introduced to control the frequency of the system, which increases the damping coefficient and enhances the frequency anti-interference ability of the unit.

4.3. Setting The Frequency Modulation Control Parameters

The relationship between the compensated power and the frequency change is

$$\{\begin{array}{l}\Delta P=-K_{df}\frac{d(f_t-f_{ref1})}{dt}-K_{pf}(f_t-f_{ref1}),f_t\ge f_{ref1}\\ \Delta P=0,f_{ref2}\le f_t\le f_{ref1}\\ \Delta P=K_{df}\frac{d(f_t-f_{ref2})}{dt}+K_{pf}(f_t-f_{ref2}),f_t\le f_{ref2}\end{array}$$

(51)

where f_t is the current frequency and f_ref1 and f_ref2 are the upper and lower limits of the frequency modulation dead zones. Compared with thermal power generation, the size of the wind power frequency modulation dead zone is set to ±0.033 Hz.

The compensated power provided by the wind turbine and energy storage system is

$$\Delta P=\Delta P_t+\Delta P_{acc}$$

(52)

where ΔP_t is the active power that the wind turbines need to compensate for and ΔP_acc is the active power that the hydraulic energy storage system needs to compensate for.

The calculation formula of the additional active power output by the wind turbine is

$$\Delta P_t=-K_{df}\frac{d\Delta f}{dt}$$

(53)

According to Formula (52), the compensated power of the wind turbine is determined by the changing rate of frequency deviation $d\Delta f/dt$ and the virtual inertia coefficient K_df.

The calculation formula of the additional active power output by the hydraulic energy storage system is

$$\Delta P_{acc}=-K_{pf}\Delta f$$

(54)

According to Formula (53), the compensated power of the hydraulic energy storage system is determined by the frequency deviation $\Delta f$ and the virtual droop coefficient K_pf.

In traditional wind turbines, the values of the virtual inertia coefficient and virtual droop coefficient are usually fixed, which limits the best performance of wind turbines. Therefore, K_df and K_pf should be set according to the real-time state of the wind turbine and energy storage system to determine the values of ΔP_t and ΔP_acc.

Setting the virtual inertia coefficient of the wind turbine, the energy variation provided by the wind turbine in the process of frequency change is

$$\Delta E_t=\Delta E_1+\Delta E_2$$

(55)

where ΔE₁ is the change in wind turbine kinetic energy and ΔE₂ is the change in wind energy capture.

The change of wind turbine kinetic energy is

$$\Delta E_1=\frac{1}{2}{J}_w({\omega }_{w0}^2-{\omega }_{w1}^2),{\omega }_{w\min }\le {\omega }_1\le {\omega }_{w\max }$$

(56)

where ω_w0 is the initial speed of the wind turbine and ω_w1 is the speed when the wind turbine participates in frequency modulation.

The capture change in wind energy of wind turbines is

$$\Delta E_2={\displaystyle \int (P_w(t)-P_{w0}})dt$$

(57)

The virtual inertia time of the wind turbine can be expressed as

$$H_{vir}=\frac{\Delta E_t}{S_n}$$

(58)

The curve of virtual inertia changing with the speed is shown in Figure 9.

The inertia time constant is related to the variation in the wind turbine’s own speed and load and can be expressed in the following two cases.

When the frequency drops,

$$H_{vir}=\{\begin{array}{l}0, {\omega }_w\le {\omega }_{w\min }\\ \frac{1}{2}\frac{J_w({\omega }_{w1}^2-{\omega }_{w\min }^2)}{S_n}-\frac{\pi \rho R^2{v}^3}{2}\frac{{\displaystyle \int (C_{p\max }-C_{p1}})dt}{S_n},{\omega }_{w\min }<{\omega }_w<{\omega }_{w\max }\\ 0,{\omega }_w\ge {\omega }_{w\max }\end{array}$$

(59)

When the frequency rises,

$$H_{vir}=\{\begin{array}{l}0,{\omega }_w\le {\omega }_{w\min }\\ \frac{1}{2}\frac{J_w({\omega }_{w\max }^2-{\omega }_{w1}^2)}{S_n}-\frac{\pi \rho R^2{v}^3}{2}\frac{{\displaystyle \int (C_{p\max }-C_{p1}})dt}{S_n},{\omega }_{w\min }<{\omega }_w<{\omega }_{w\max }\\ 0,{\omega }_w\ge {\omega }_{w\max }\end{array}$$

(60)

At different wind turbine speeds, the virtual inertia time constant of the wind turbine can be adapted to the wind turbine speed. The inertia coefficient of the wind turbine can be set as

$$K_{df}=K_{f}H$$

(61)

where K_f is the proportional inertia coefficient.

Setting the virtual droop coefficient of the energy storage system, the frequency regulation capacity of the hydraulic energy storage system is measured by the state of charge (SOC), and the SOC of the accumulator is expressed as

$$SOC=\frac{V_l}{V_l+V_a}=\frac{V_l}{V_{total}}$$

(62)

In Formula (61), V₁ is the liquid chamber volume and V_total is the total accumulator volume. When the volume of the liquid cavity is large, the SOC is also large, and the frequency support capability is strong. As the volume of the liquid cavity decreases, the SOC decreases, and the support capacity for frequency gradually weakens.

When Δf < 0 and Δf exceeds the dead zone, if the SOC is large, the drop coefficient K_pf is set as the value that enables the accumulator to release oil at the fastest speed to recover the decreased frequency. With the gradual decrease in SOC, the droop coefficient K_pf should be reduced appropriately to reserve energy for the next frequency modulation. Similarly, when Δf > 0 and Δf exceeds the dead zone, if the SOC is small, it indicates that the accumulator has a large unfilled liquid volume. Then, the droop coefficient K_pf is set as the value to accelerate the oil absorption of the energy storage system. With the gradual increase in SOC, the droop coefficient should be appropriately reduced. Therefore, the set accumulator limit volume range is (0.2,0.8) p.u., the synchronous motor adjustment coefficient δ% is 4~7%, and the synchronous generator droop coefficient is 14.29~25. The active power output control of the energy storage system is used to simulate the frequency modulation droop control of the traditional generator. Therefore, the maximum droop coefficient of the output compensation power of the energy storage system is set to 25, and the minimum value is set to 14.29. The virtual droop coefficient of the accumulator is shown in Figure 10a.

Combined with the sigmoid growth curve, the curve changing with the effective volume of the accumulator can be regarded as an “S” curve, as shown in Figure 10b.

The sigmoid curve function is expressed as

$$S(x)=\frac{1}{1+e^{-x}}$$

(63)

According to Figure 10b and Equation (62), K_pf can be expressed in the following two cases.

When the frequency drops,

$$K_{pf}=\{\begin{array}{cc}\frac{14.29}{1+\exp [-(V_w-0.1)/0.01428)]}& 0<V_w\le 0.2\\ 14.29+\frac{10.71}{1+\exp [-(V_w-0.3)/0.01428)]}& 0.2<V_w\le 0.4\\ 25& 0.4<V_w\le 1\end{array}$$

(64)

When the frequency rises,

$$K_{pf}=\{\begin{array}{cc}25& 0<V_w\le 0.6\\ 25-\frac{10.71}{1+\exp [-(V_w-0.7)/0.01428)]}& 0.6\le V_w\le 0.8\\ 14.29-\frac{14.29}{1+\exp [-(V_w-0.9)/0.01428)]}& 0.8<V_w<1.0\end{array}$$

(65)

According to Equations (63) and (64), the virtual droop coefficient of the accumulator can be adaptively changed with its SOC state.

5. Simulation Research Results

5.1. Simulation Platform

The simulation platform is composed of a hydraulic wind turbine and a power system. The simulation platform is shown in Figure 11.

In the power system module simulation, a single-area two-unit power system simulation model is built, as shown in Figure 12.

According to reference [9] and the experiment platform, the relevant parameters mainly used in the model are shown in

Table 1. Simulation parameter list.

Num	Variable Symbol	Value and Unit
1	total inertia of the rotor and constant displacement pump Jp	$400 \mathrm{kg}\cdot {\mathrm{m}}^2$
2	constant displacement pump displacement Dp	$6.3\times {10}^{-5} {\mathrm{m}}^3/\mathrm{rpm}$
3	variable displacement motor displacement gradient Km	$4.0\times {10}^{-5} {\mathrm{m}}^3/\mathrm{rpm}$
4	effective bulk modulus of elasticity βe	$7.43\times {10}^8$ Pa
5	high-pressure pipeline cavity volume V0	$2.8\times {10}^{-3} {\mathrm{m}}^3$
6	hydraulic transmission system leakage coefficient Ct	$2.8\times {10}^{-11} {\mathrm{m}}^3/(\mathrm{s}\cdot \mathrm{Pa})$
7	variable displacement motor speed ωmd	$157 \mathrm{rad}/\mathrm{s}$
8	constant displacement pump viscous damping coefficient Bp	$0.4 \mathrm{m}\times \mathrm{s}/\mathrm{rad}$
9	energy storage system pipeline length la	$1.5 \mathrm{m}$
10	pipeline sectional area A	$4.9\times {10}^{-4} {\mathrm{m}}^2$
11	oil dynamic viscosity $\mu$	$1.1725\times {10}^{-2} \mathrm{kg}/\left(\mathrm{m}\cdot \mathrm{s}\right)$
12	energy storage system pipe diameter da	$0.025 \mathrm{m}$
13	accumulator initial pressure $p_0$	$5\times {10}^6$ Pa
14	accumulator initial liquid volume $V_0$	$0.01 {\mathrm{m}}^3$
15	variable displacement pump/motor gradient Kmp	$4.0\times {10}^{-5} {\mathrm{m}}^3/\mathrm{rpm}$
16	variable displacement pump/motor leakage coefficient Ctmp	$1.2\times {10}^{-11} {\mathrm{m}}^3/(\mathrm{s}\cdot \mathrm{Pa})$
17	variable displacement motor viscous damping coefficient Bm	$0.0345 \mathrm{N}\cdot \mathrm{m}\cdot \mathrm{s}/\mathrm{rad}$
18	variable displacement motor inertia Jm	$0.462 \mathrm{kg}\cdot {\mathrm{m}}^2$
19	oil density $\rho$	$860 \mathrm{kg}/{\mathrm{m}}^3$
20	accumulator effective volume Vacc	$0.02 {\mathrm{m}}^3$
21	viscous damping coefficient Bmp	$0.0345 \mathrm{N}\cdot \mathrm{m}\cdot \mathrm{s}/\mathrm{rad}$
22	variable displacement pump/motor generator inertia Jmp	$0.462 \mathrm{kg}\cdot {\mathrm{m}}^2$
23	stator leakage reactance Ls	0.063 p.u.
24	excitation leakage reactance Lf	0.1381 p.u.

.

5.2. Simulation of The System Response under Load Disturbance

Assuming that the wind speed during this period of simulation is relatively stable, a wind speed of 9 m/s is used. After the wind turbine is connected to the power system and runs smoothly, the initial frequency of the system is 50 Hz. When t = 5 s, different load amplitudes are set to disturb the system, and the system response characteristics are studied under the load disturbance.

5.2.1. Simulation of The System Response to A Sudden Load Increase

When the initial load suddenly increases to 6 kW, 9 kW, 10.5 kW, and 12 kW in 5 s, the simulation curve of the system response characteristics is shown in Figure 13.

Figure 13a shows the demand surge curve of the load power. Figure 13b shows that when the load power surges, the system frequency drops. When the load surges by 6 kW, the frequency drops to the deepest point of 49.63 Hz at 5.8 s and then recovers. In 12 s, the frequency basically recovered to 50 Hz and remained stable. During this process, the maximum frequency deviation was 0.37 Hz. In the sudden increase of 9 kW, the frequency dropped to the deepest point of 49.45 Hz at 5.8 s and then recovered. In 12 s, the frequency basically recovered to 50 Hz and remained stable. During this process, the maximum frequency deviation was 0.55 Hz. When the load suddenly increased by 10.5 kW, the frequency dropped to the deepest point of 49.37 Hz at 5.9 s and gradually recovered to 50 Hz at 17 s, during which the maximum frequency deviation was 0.63 Hz. As the load suddenly increases, the depth of the frequency drops increases, the time of frequency recovery increases, and the power system becomes more unstable. Due to the inertia of the synchronous generator, the initial decreasing velocity of the frequency is consistent. When the load increases by 12 kW, the frequency of the system continues to drop, and the amplitude of the drop has exceeded the maximum limit allowed by the power grid. At this time, the power grid is in a fault state. Figure 13c,d show the speed curves of the traditional generator and the rotor. Since both adopt synchronous generators and are connected to the same bus, the response curves of the two are basically the same, and the synchronous speed is linearly correlated with the system frequency, so the trends of the curves in Figure 13b–d are basically the same.

5.2.2. Simulation of The System Response to A Sudden Load Decrease

When the initial load suddenly decreases by 6 kW, 9 kW, 10.5 kW, and 12 kW at 5 s, a simulation curve of the system response characteristics is generated, which is shown in Figure 14.

Figure 14a shows the demand sudden reduction curve of the load power. Figure 14b shows that during the sudden reduction of the load power, the system frequency rises. In the case of a sudden reduction of 6 kW, the frequency rises to the highest point of 50.35 Hz in 5.7 s and then recovers. After 13 s, the frequency basically recovered and stabilized. In the sudden decrease of 9 kW, the frequency rises to the highest point of 50.51 Hz at 5.7 s and then recovers. After 13 s, the frequency basically recovered and stabilized. In this process, the maximum frequency deviation is 0.51 Hz. In the case of a sudden decrease of 10.5 kW, the frequency rises to the highest point of 50.60 Hz at 5.8 s and then gradually recovers at 13 s, during which the maximum frequency deviation is 0.60 Hz. In the sudden decrease of 12 kW, the frequency rises to the highest point of 50.71 Hz at 5.8 s and then gradually recovers at 13 s, during which the maximum frequency deviation is 0.71 Hz. The greater that the load suddenly decreases, the higher the frequency rises. Due to the function of the frequency modulator, the frequency recovery time is basically the same. When the load decreases, the output of the unit only needs to be reduced, and there is no lack of frequency modulation capacity.

5.2.3. Simulation of The Combined Rotor and Energy Storage Frequency Modulation Control

• Simulation of The System Response Characteristics Under a Load Surge.

When the load increases suddenly by 10.5 kW, a system frequency response curve is generated and is shown in Figure 15.

After the combined wind turbine and energy storage frequency modulation control strategy is introduced, the maximum frequency deviation of the system is reduced, and the frequency adjustment time is shortened. For the maximum frequency deviation value, the minimum frequency drop point is increased from 49.37 Hz to 49.58 Hz, and the maximum frequency deviation of the system is reduced from 0.63 Hz to 0.42 Hz when fixed parameter control is adopted. When variable parameter control is adopted, the lowest frequency point of the system is further increased to 49.66 The maximum frequency deviation of the system is reduced from 0.63 Hz to 0.34 Hz. For frequency regulation time, the fixed parameter control is basically consistent with the variable parameter control, which reduces from 12 s to 3 s compared with non-frequency modulation control. Compared with fixed parameter control, variable parameter control has a great improvement in frequency drop amplitude and frequency recovery overshoot.

When the load increases suddenly by 12 kW, the system frequency response curve is shown in Figure 16.

After the combined wind turbine and energy storage frequency modulation control strategy is introduced, the system frequency changes from a continuous falling state to a recoverable state. In the case of fixed parameter control, the frequency reaches the lowest point of 49.52 Hz, and the maximum frequency deviation is 0.48 Hz with frequency modulation control at 5.7 s. At 9.6 s, it recovers to the stable state, which is stable at 49.92 Hz, and the steady-state frequency deviation is 0.08 Hz. Under variable parameter control, the lowest frequency of 49.60 Hz at 5.5 s is reached, and the maximum frequency deviation is 0.40 Hz. Stability is recovered at 49.95 Hz at 8 s, and the steady-state frequency deviation is 0.05 Hz. The response time, maximum frequency deviation, and steady-state error are reduced compared with the fixed parameter frequency control.

When the load increases by 10.5 kW and 12 kW respectively, the simulation curve of the rotor, hydraulic transmission system, and hydraulic energy storage system is shown in Figure 17.

After the combined wind turbine and energy storage frequency modulation control strategy is introduced, the rotor adopts the method of reducing the rotational kinetic energy to provide energy for the generator, and the energy change caused by the change in rotor speed is reflected in the output power of the transmission system. The speed of the rotor starts to change at 5 s, and the output power of the transmission system increases. And the output power decreases at 11.2 s and 8 s. The insufficient energy from the rotor is compensated by the hydraulic energy storage system, as shown in Figure 17c. The final mechanical power input to the generator is shown in Figure 17d.

2.

Simulation of The System Response Characteristics with A Load Reduction.

When the load decreases suddenly by 6 kW, the system frequency response curve is shown in Figure 18.

It can be seen from Figure 18b that when frequency modulation control with fixed parameters is adopted, the frequency rises to the highest point of 50.23 Hz at 5.5 s. When variable parameter control is adopted, the frequency rises to 50.19 Hz at 5.5 s. However, after a load disturbance for 3 s, the frequency basically recovered to become stable. Compared with no frequency modulation control, the introduction of frequency modulation control has a significant effect on reducing the maximum frequency deviation and frequency adjustment time. For the maximum frequency deviation, the fixed parameter control reduces the frequency from 50.35 Hz to 50.23 Hz, and the variable parameter control reduces the frequency from 50.35 Hz to 50.19 Hz. The frequency rise time is shortened from 5.7 s to 5.5 s. The frequency adjustment time is reduced from 8 s to 3 s. Frequency modulation control with fixed parameters can reduce the maximum frequency deviation and the frequency adjustment time. Compared with fixed parameter frequency modulation control, variable parameter control can greatly improve the frequency rise amplitude and frequency overshoot after recovery.

When the load decreases suddenly by 6 kW, the simulation curve of the rotor, hydraulic transmission system, and hydraulic energy storage system is shown in Figure 19.

After the combined wind turbine and energy storage frequency modulation control strategy is introduced, the rotor adopts the method of increasing the rotational kinetic energy to reduce the energy for the generator, and the energy change caused by the change in rotor speed is reflected in the output power of the transmission system. The speed of the rotor starts to increase at 5 s, and the output power of the transmission system decreases accordingly. At 8.6 s, the variation trend of output power turns to increase. The insufficient energy from the rotor is absorbed and compensated by the hydraulic energy storage system, as shown in Figure 18c. The final mechanical power input to the generator is shown in Figure 18d.

6. Experimental Research Results

6.1. Experimental Platform

The experimental platform mainly consists of four parts: a wind turbine simulation system, hydraulic main transmission system, grid-connected generation system, and control system. The hydraulic wind turbine semi-physical simulation experiment platform schematic diagram is shown in Figure 10, and the hydraulic main transmission system is shown in Figure 11, the corresponding parameters are shown in Table 1.

The speed and torque sensor between the rotor and the hydraulic pump measures the rotor speed (hydraulic pump speed) and the rotor output torque (hydraulic pump input torque). The pressure sensors measure the pressure of the high-pressure pipeline and the pressure of the low-pressure pipeline respectively, and the flow sensor measures the system flow. The speed torque sensor between the hydraulic motor and the generator measures the hydraulic motor speed (generator speed) and the hydraulic motor output torque (generator input torque). The grid-connected system measures the frequency of the power grid and the active power output by the generator et al. The above information data is input into the power tracking controller in the form of analog to participate in the closed-loop control.The schematic diagram of HWT semi-physical simulation experiment platform is shown as Figure 20 and hydraulic transmission system equipment drawing is shown as Figure 21.

6.2. Simulation Accuracy of Power Grid Frequency Characteristics

During the experiment, data collection was performed on the output of the power grid simulator, and the experimental results obtained are shown in Figure 22.

From the above experimental results in Figure 22, it can be seen that when the three-phase output voltages and currents of the power grid simulator are displaced by approximately 120°, the error is less than 0.5%; if the output frequency is approximately 50 Hz, the error is less than 0.5%; if the effective value of the output voltage is approximately 220, the error is less than 0.2%. In summary, the power grid simulator basically realizes the accurate simulation of the normal power grid, and its output characteristics meet the relevant parameter requirements of the grid.

After the wind turbine is successfully connected to the grid, the power control experiment of the turbine is carried out below. Since there is no energy storage system installed on the test bench, power control is only carried out by adjusting the swing angle of the variable displacement motor of the transmission system. When the wind turbine runs at a constant speed and stably, we changed the given load power of the wind turbine and the experimental response curve of power control of the system is shown in Figure 23.

As shown in Figure 23, Figure 23a is the speed curve of the motor (generator). It can be seen from the curve that, although the speed of the unit is stable at around 1500 r/min after grid connection, the speed fluctuates due to disturbance. Figure 23b shows the power control response curve of the unit under the motor speed fluctuation in a small range. Compared with the simulation curve above, although the power control does not achieve the simulation effect, the response characteristics of the unit are consistent with the simulation, and the power control is realized. Figure 23c,d show the response curves of generator driving torque and high pressure of the transmission system with the change of motor swing angle during power control. The active power output of the unit changes with the change of high pressure and driving torque. Figure 23 illustrates the effectiveness of power control, which can control the output power of the unit from the angle of adjusting the motor swing angle. The frequency instability of the power system is caused by the imbalance of power supply and demand on the grid side. This experiment can achieve power control on the supply side of the grid side, which indirectly indicates that the frequency is controllable and frequency stability can be achieved by adjusting the power.

7. Discussion

In this paper, based on the method of combined wind turbine and energy storage system frequency modulation control, the problem of insufficient frequency modulation capacity of power systems under high wind power proportion is solved and frequency modulation control of energy storage hydraulic wind turbines is realized. By establishing the control model of wind turbine and energy storage, the problem of voltage frequency drop caused by a load fluctuation is observed and solved, and frequency control under the condition of variable load disturbance is realized. However, fixed parameter frequency modulation control has difficulty achieving the optimal frequency modulation state of the system, while the variable parameter control method can greatly improve the system frequency regulation effect and achieve the purpose of optimal control of the system frequency. Therefore, a reasonable frequency modulation control method based on different frequency fluctuation stages is proposed.

Meanwhile, according to the response curve of the power, the response time of the power is 20 s, while that of the system under the simulation condition is 3 s. China’s National Standard requires that the primary frequency modulation power must reach the maximum value within 20 s. Although the response time is obviously slow under experimental conditions, the response time meets the requirements of national standards [34].

There is little research on the frequency control of hydraulic wind turbines. Some scholars from the University of Warwick, UK, carried out simulation research on frequency control of hydraulic wind turbines [36]. By controlling the pitch angle of the wind turbine, the swing angle of the variable displacement motor, and the swing angle of the variable displacement pump/motor of the hydraulic energy storage system, the power response time is about 3 s, which is basically consistent with the research results in this paper.

Due to the experimental conditions, the hydraulic energy storage system was not introduced into the wind turbine, and it will be further improved after the hydraulic energy storage is introduced into the experimental system. The study of this paper has not considered the influence of hydraulic parameters’ time variability on the unit frequency modulation control effect, which will be considered in the following research process.

8. Conclusions

We can draw some conclusions below from the analysis.

(1)

When the load of the system increases suddenly by 10.5 kW, the maximum frequency deviation of the system can be reduced by 33.3% when using fixed parameter frequency control and 46% when using variable parameter control, and the frequency adjustment time can be reduced by 75% compared with the control without frequency modulation.

(2)

When the system load increases by 12 kW, the system frequency changes from a continuous falling state to a recoverable state. When the load is suddenly reduced by 6 kW, the frequency deviation can be reduced by 34% with fixed parameter frequency control and 45.7% with variable parameter frequency control. The frequency rise time can be reduced by 3.5%.

(3)

When the load power of the network side changes, the active power response time of the unit is 20 s, which basically meets the demand of the active power response time of the wind turbine in the primary frequency modulation process.

The results show that the combined wind turbine and energy storage system frequency modulation control strategy can reduce the maximum frequency deviation, shorten the frequency fluctuation adjustment time, and improve the unit performance, and the frequency control effect is significant.