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]
where
H is the total inertia of the system, Δ
f(
t) is the frequency variation,
D is the load damping coefficient,
DML is the motor load,
is the unit output variation that provides frequency modulation for the system, and
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.
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]
where
JW is the total inertia of the rotor and the load,
ωw0 is the rotational speed under MPPT, and
ωw0 is the minimum operating speed of the wind turbine.
Taking a hydraulic wind turbine to a traditional synchronous wind turbine together by analogy yields
where
Jvir is regarded as the virtual inertia by analogy to a synchronous wind turbine and
ωs and
ωs1 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:
Due to
and
, the following is obtained:
In actual frequency fluctuation,
and
, which gives
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 Jvir1 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]
where
Va1 is the volume of the gas vessel before energy absorption of the accumulator and
Va2 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]
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]:
The swing angle of the variable displacement pump/motor is [
32]
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, and , and the frequency falls over the dead zone . The compensation power of virtual inertial control is , and the compensation power of virtual droop control is . 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, and , and the virtual droop control compensation power . The virtual inertial control compensation power of the method , so only droop control is used in the frequency recovery stage.
When the frequency rises, and ; 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, and , so droop control is used to respond to the change in frequency. Therefore, if , the integrated control method is used in the frequency regulation; if , 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
and variable pump/motor swing angle
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
where Δ
P1 is the power compensated by the virtual inertia control,
f is the system frequency deviation, and
Kdf 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
where Δ
P2 is the power compensated by the virtual droop control and
Kpf 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.
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
According to
Figure 6, the power-frequency model of the power system can be expressed as
After the introduction of frequency modulation control, Formula (48) can be expressed as
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
where
ft is the current frequency and
fref1 and
fref2 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
where Δ
Pt is the active power that the wind turbines need to compensate for and Δ
Pacc 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
According to Formula (52), the compensated power of the wind turbine is determined by the changing rate of frequency deviation and the virtual inertia coefficient Kdf.
The calculation formula of the additional active power output by the hydraulic energy storage system is
According to Formula (53), the compensated power of the hydraulic energy storage system is determined by the frequency deviation and the virtual droop coefficient Kpf.
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, Kdf and Kpf should be set according to the real-time state of the wind turbine and energy storage system to determine the values of ΔPt and ΔPacc.
Setting the virtual inertia coefficient of the wind turbine, the energy variation provided by the wind turbine in the process of frequency change is
where Δ
E1 is the change in wind turbine kinetic energy and Δ
E2 is the change in wind energy capture.
The change of wind turbine kinetic energy is
where
ωw0 is the initial speed of the wind turbine and
ωw1 is the speed when the wind turbine participates in frequency modulation.
The capture change in wind energy of wind turbines is
The virtual inertia time of the wind turbine can be expressed as
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,
When the frequency rises,
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
where
Kf 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
In Formula (61), V1 is the liquid chamber volume and Vtotal 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 Δ
f < 0 and Δ
f exceeds the dead zone, if the
SOC is large, the drop coefficient
Kpf 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
Kpf should be reduced appropriately to reserve energy for the next frequency modulation. Similarly, when Δ
f > 0 and Δ
f exceeds the dead zone, if the
SOC is small, it indicates that the accumulator has a large unfilled liquid volume. Then, the droop coefficient
Kpf 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
According to
Figure 10b and Equation (62),
Kpf can be expressed in the following two cases.
When the frequency drops,
When the frequency rises,
According to Equations (63) and (64), the virtual droop coefficient of the accumulator can be adaptively changed with its SOC state.
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.