Cooperative control strategy for frequency regulation of wind-pumped storage system considering wind speed partition

Abstract

In order to solve the problem of system inertia reduction and frequency response degradation caused by large-scale wind power interconnection, a strategy is proposed. This strategy incorporates a joint system model composed of doubly-fed wind turbine (DFWT) and variable speed pumped storage (VSPS), utilizing a fuzzy controller to dynamically determine the virtual inertia coefficient of the wind-pumped storage system based on the frequency state of the system, and adjusts the frequency-regulation participation factor of the DFWT in real time according to the operating conditions of it. The simulation results show that the proposed strategy can not only significantly improve the frequency nadir, speed up the system frequency and each generating unit in the system to restore to steady state, but also avoid the second frequency drop (SFD) caused by the wind farm out of primary frequency regulation (PFR), and improve the stability of the system frequency.

Keywords

Frequency control variable speed pumped storage doubly-fed wind turbine adaptive virtual inertia wind speed division

Introduction

According to data released by British Petroleum (2022), wind and solar energy reach a 10.2% share of power generation in 2021, providing more than 10% of global electricity for the first time. Due to the weak inertia of the DFWT currently used mainly in wind farms, their replacement of conventional synchronous generators (SGs) makes the system inertia decrease and threatens the system frequency safety, so the latest grid guidelines (National Grid (Great Britain) Company, 2009; National Standardization Administration of the People’s Republic of China, 2021) released in several countries require grid-connected wind turbines to have a frequency active support capability similar to conventional SG.

The main methods for frequency active support of DFWT include rotor kinetic energy control (Altin et al., 2018; Hafiz and Abdennour, 2015; Morren et al., 2006), load reduction control (Morren et al., 2006; Wang and Tomsovic, 2018). Li et al. (2021) proposed a virtual inertia fuzzy adaptive control method for DFWT based on frequency response interval division to achieve a reasonable and optimal distribution of finite rotor kinetic energy of DFWT; Huang et al. (2017) proposed to introduce a damping control link in the conventional sag control loop to improve the system frequency stability and reduce the small disturbance stability issues. Courtecuisse et al. (2008) proposed a fuzzy logic based multivariable control strategy to determine in real time the generator power reference value to maintain a fixed minimum reserve without any wind speed measurement. However, the above references do not take into account the residual frequency-regulation capability of the DFWT, which may cause rotor speed of it to be too low resulting in it being forced out of regulation triggering the SFD.

In recent years, various forms of energy storage system (ESS) have been heavily used in power systems for providing short-term active frequency support due to their flexibility of control and rapid response. Torres et al. (2014) has considered the use of ESS to simulate synchronous machine characteristics for frequency control, but the power rating and capacity limitations of the ESS have not been considered. Waheed Kumar et al. (2023) has demonstrated that superconducting magnetic energy storage (SMES) operating in virtual synchronous generator (VSG) mode can enhance the damping ratios of inter-area oscillatory modes and improve system frequency response. Manzoor and Mufti (2020) has presented a genetically tuned fuzzy controller to make flywheel continuously control the system frequency and simultaneously satisfy the operational constraints of it. Peng et al. (2018) has designed a fuzzy controller embedded in the wind-storage control system to decide the total active power output of the wind-storage system and the frequency-regulation participation coefficient of the DFWT, which reduces the power shock generated by restoration of rotor speed of it. However, conventional ESSs have the problems of high operating costs and service life constrained by the depth of charge and discharge.

As a new form of energy storage that has been vigorously developed in recent years, pumped storage has received attention because of its large storage capacity, low operating cost, and long cycle life (Zhao et al., 2023), in which VSPS with doubly-fed induction machine is a hot spot for current research due to the advantages of flexible and adjustable unit speed and the hydraulic characteristics of the prime mover that do not directly affect the output power, etc. Currently, research on the application of VSPS to PFR has been conducted (Chen et al., 2023; Li et al., 2023; Sarasúa et al., 2015; Xu et al., 2023). However, the focus of the existing research is mainly on the modeling, frequency regulation performance evaluation and the design of the frequency control link of the doubly-fed pumped storage unit itself, while in fact, the VSPS can be used to improve the frequency regulation capability of the DFWT by forming a joint system with the DFWT under the power-first control mode, so that the wind-pumped storage system has the overall frequency response characteristics similar to that of SG. Figure 1 presents the conceptual schematic of the wind-pumped storage system. There are already operational wind-pumped storage systems in several countries (Ding, 2015; Papaefthymiou et al., 2010).

Figure 1.

Conceptual schematic of the wind-pumped storage system.

In order to optimize the system frequency response, this paper proposes a fuzzy control-based cooperative control strategy for the wind-pumped storage system. The main work of this paper is as follows.

(1) A multi-source frequency response model including conventional thermal power, hydro power and wind-pumped storage system is constructed, and the influence of the virtual inertia coefficient of the wind-pumped storage system on the stability is analyzed by system eigenvalues, and the range of the virtual inertia coefficient to make the system stable is determined.

(2) Based on the operational characteristics of the DFWT, the characteristics of different active power reference value calculation methods used when participating in PFR are analyzed, and appropriate control methods are determined based on the strategy needs of this paper.

(3) The wind speed is partitioned according to the frequency regulation capability of DFWT in different wind speed zones, and different frequency regulation strategies are formulated for different wind speed zones. Secondly, the adaptive virtual inertia control based on fuzzy control is used in the external control layer of wind-pumped storage system, and the frequency-regulation participation factor of the DFWT is dynamically decided in the internal scheduling layer according to the residual frequency-regulation capability of the DFWT using fuzzy controller.

Modeling and analysis of multi-source frequency response models for wind-pumped storage systems

Thermal power unit using reheat steam turbine unit, the transfer function of its frequency response model is given as (Prabha and Kimbark, 2001)

G_{H} (s) = - R_{T} R_{H} \frac{1}{R} \frac{1}{1 + s T_{G}} \frac{K_{m} (1 + s F_{HP} T_{RH})}{(1 + s T_{CH}) (1 + s T_{RH})}

(1)

where T_G is the governor time constant (s); F_HP is the turbine reheat time constant (s); T_RH is the reheat time constant (s); T_CH is the turbine time constant (s); K_m is the mechanical power gain coefficient; R is the regulation coefficient; R_T is the proportion of conventional unit capacity to the total installed capacity; R_H is the ratio of thermal unit capacity to conventional unit capacity.

In order to mitigate the adverse impact of water hammer effect in hydropower units, it is necessary to add a temporary rate of decline compensation to the governor, and transfer function of frequency model for hydropower units with temporary drop rate compensation can be represented by (Prabha and Kimbark, 2001)

G_{W} (s) = - \frac{R_{T} R_{W}}{R} \frac{1 + T_{Rs}}{1 + (R_{T} / R_{P}) T_{R s}} \frac{1}{1 + T_{G s}} \frac{1 - T_{WS}}{1 + 0.5 T_{W s}}

(2)

where T_R is the reset time (s); T_G is the main servo time constant (s); T_W is the water start time (s); R_T is the temporary rate of decline; R_P is the permanent rate of decline; R is the regulation coefficient; R_W is the ratio of hydropower unit capacity to conventional unit capacity.

The generator of both DFWT and VSPS is doubly-fed induction machine (DFIM), whose active power changes rapidly. The frequency response transfer function of the wind-pumped storage system with integrated inertia control participated in frequency regulation is

G_{N} (s) = \frac{Δ P_{N} (s)}{Δ f (s)} = R_{N} (k_{D} s + k_{P})

(3)

where k_D is the virtual inertia coefficient; k_P is the sag coefficient; R_N is the ratio of the sum of the capacities of DFWT and VSPS to the total installed capacity of the system.

The equation of motion of the system equivalent rotor is given by

(T_{J s} + D) Δ f (s) = Δ P_{H} (s) + P_{W} (s) + Δ P_{N} (s) - Δ P_{L} (s)

(4)

where T_J is the inertia constant of the system (s); D is the system damping.

Substituting (1), (2), (3) into (4), when the load varies in a step form, that is $Δ P_{L} (s) = Δ P_{L} / s$ , the system frequency deviation is obtained as

Δ f (s) = \frac{1}{s} \frac{- Δ P_{L}}{(T_{J} + R_{N} k_{D}) s + (D + R_{N} k_{P}) + G_{H} (s) + G_{W} (s)}

(5)

From the initial value theorem, the rate of change of the system frequency at the initial moment ${\frac{d f}{d t} |}_{t = 0}$ can be found as

{\frac{d f}{d t} |}_{t = 0} = lim_{s \to \infty} s Δ f (s) = \frac{- P_{L}}{T_{J} + R_{N} k D} = \frac{- P_{L}}{{T'}_{J}}

(6)

Analyzing (6), the following conclusions can be obtained: In the initial moment of frequency change, the virtual inertia coefficient k_D of the wind-pumped storage system can reduce the speed of frequency drop, thus reducing the transient frequency deviation of the system. Further analysis of the impact of the k_D of the wind-pumped storage system on the system frequency response from Figure 2 shows that: The larger the k_D (i.e. the larger $T'_{J}$ ), the slower the frequency drop and the higher the frequency nadir, but the excessive k_D will hinder the system frequency restoration, and the constant k_D outputs a negative frequency regulation power in the frequency restoration stage, which further inhibits the frequency restoration. Therefore, the flexible controllability of the virtual inertia coefficient of the wind-pumped storage system can be used to increase k_D in the frequency drop stage to prevent the system frequency from departing too quickly, while reducing k_D in the frequency restoration stage and taking the reverse value to speed up the frequency restoration, in order to obtain the ideal frequency response characteristics as shown in the red curve in Figure 2. Virtual inertia coefficient adjustment principle for different frequency response intervals is shown in Table 1.

Figure 2.

Frequency response curves corresponding to different k_D.

Table 1.

Virtual inertia coefficient adjustment principle for different frequency response intervals.

Δf	df/dt	k _D
>0	>0	<0
>0	<0	>0
<0	>0	>0
<0	<0	<0

The steady-state frequency deviation ${Δ f |}_{t \to \infty}$ can be obtained from the final value theorem as follows

\begin{matrix} {Δ f |}_{t \to \infty} = lim_{s \to 0} s Δ f (s) \\ = \frac{- P_{L}}{D + R_{N} k_{P} - (R_{T} R_{W}) / R - (K_{m} R_{H} R_{T}) / R} \end{matrix}

(7)

From (7), the wind-pumped storage system continuously outputs active power during the PFR, taking up part of the unbalanced power and reducing the system frequency steady-state deviation, but if there is no reasonable distribution of the system’s frequency regulation power within it, continuous participation of DFWT in frequency control will result in SFD.

Cooperative control strategy for wind-pumped storage system based on fuzzy logic and wind speed partition

Wind speed partition

A typical DFWT operation curve is shown in Figure 3 (Gagnon et al., 2005). When the wind speed is lower than 6 m/s, that is, before point B, the wind turbine does not have the capability of frequency regulation due to the low rotor kinetic energy, and the wind speed zone is defined as low wind speed zone. When the wind speed is higher than 13 m/s, that is, after point D, the DFWT does not have the capability of frequency regulation at this stage because the output power has reached the rated value and the power cannot be increased, and the wind speed zone is defined as high wind speed zone. The wind speed range between points B and D, that is, 6 m/s–13 m/s, is defined as the medium wind speed zone, and only in this zone the DFWT can participate in PFR by releasing rotor kinetic energy to generate additional power.

Figure 3.

Typical operation curve of DFWT.

Since both too high and too low wind speed limit the participation of wind turbines in frequency control, this paper develops different frequency regulation strategies for different wind speed intervals, so that the wind-pumped storage system has the capability to respond to changes in system frequency across the full range of wind speeds.

Cooperative control strategy for wind-pumped storage system

In order to improve the frequency regulation performance of the wind-pumped storage system, this paper determines the virtual inertia coefficient of the wind-pumped storage system based on the system frequency state, and determines the frequency-regulation participation factor of DFWT according to the operation state of it, so as to realize the flexible cooperation of frequency regulation characteristics between DFWT and VSPS.

Strategy for the external control layer

The system state space model is obtained by associating (1)−(4):

{\begin{matrix} x^{.} = A x + B u \\ y = C x + D u \end{matrix}

(8)

where A is the system state matrix, B is the control matrix, C is the output matrix, and D is the direct transfer matrix.

Figure 4 shows the eigenvalues of the system state matrix A corresponding to different virtual inertia coefficients k_D for a sudden increase in load of 0.1 pu.

Figure 4.

Eigenvalue of simulation system.

From Figure 4, it can be obtained that when k_D is less than −14, the characteristic root of the system lies in the right half-plane and the system is destabilized. When the value of k_D is taken in the range of [−14,37], the initial value of the characteristic root is −0.0184 ± 0.3931i, which corresponds to an oscillation mode with a damping ratio of 0.047 and an oscillation frequency of 0.0626 Hz, and the system damping ratio increases continuously with the increase of k_D until it is smooth. The final determination of the stable set of values of k_D is in the range of [−12,36].

The sag control has a continuous improvement on the dynamic process of frequency response. To make the wind-pumped storage system smoothly exit from PFR, high-pass filtering is introduced to make it work only for frequency dynamic changes. The sag coefficient k_P is taken as a constant value of 20 with reference to the thermal unit’s regulation coefficient.

Based on the above analysis, this paper proposes the fuzzy virtual inertia control for the external control layer of the wind-pumped storage system, and the control structure is shown in Figure 5.

Figure 5.

Control structure diagram of wind-pumped storage system.

As shown in Figure 5, at the external control layer of the wind-pumped storage system, the fuzzy logic controller FC1 is used to dynamically adjust the virtual inertia coefficient k_D to change the system equivalent inertia $T'_{J}$ , which takes frequency deviation Δf (−0.8 to 0.8 Hz) and rate of change of frequency df/dt (−0.5 to 0.5 Hz/s) as input variables and the adjustment factor γ_D (−0.4 to 1.2) of the k_D as output variables. Input and output membership function of fuzzy controller FC1 is shown in Figure A1 in the Appendix. γ_D is multiplied with the virtual inertia coefficient base value k_D0 to obtain the actual value, and k_D0 is taken as 30. The frequency-regulation active power increment for wind-pumped storage system is

Δ P_{total} = - k_{P} Δ f - γ_{D k D 0} \frac{d f}{d t}

(9)

According to the principles of virtual inertia adjustment in different frequency fluctuation intervals in Table 1, the fuzzy logic rule of FC1 is determined with the goal of damping the system frequency deviation too fast and speeding up the system frequency restoration: increase k_D as much as possible in the system frequency drop stage to increase the system equivalent inertia $T'_{J}$ and raise the system frequency nadir; reduce k_D as much as possible in the system frequency restoration stage and take reverse value, in order to reduce the system equivalent inertia, speed up the system frequency restoration. Based on the above inference principles, the fuzzy control rules are designed as shown in Table A1 in the Appendix and the fuzzy control inference result are shown in Figure 6.

Figure 6.

Fuzzy inference result of FC1.

Strategy for the internal scheduling layer

In order to fully adapt to the frequency regulation capability of the DFWT to prevent the excessive release of rotor kinetic energy from causing the rotor speed to be too low and off-grid, the fuzzy controller FC2 is used at the scheduling layer within the wind-pumped storage system to determine the frequency-regulation participation factor γ_W of the DFWT, and the specific control structure is shown in Figure 5. The input variable of FC2 is the rotor speed ω_W (0.72 pu–1.2 pu) of the DFWT and the current active power output P_W (0.2 pu–1.0 pu) of the DFWT, and the output variable is γ_W (0–1). Input and output membership function of fuzzy controller FC2 is shown in Figure A2 in the Appendix.

The inference principle of FC2 is: if ω_W is larger and P_W is smaller, then the output γ_W is larger; if ω_W is very small or P_W is very large, then γ_W is as small as possible. Based on the above inference principles, the fuzzy control rules of FC2 shown in Table A2 in the Appendix are designed, and the fuzzy control inference result are shown in Figure 7.

Figure 7.

Fuzzy inference result of FC2.

Analysis of active power reference value calculation method of DFWT converter

There are two ways to calculate the active power reference value of DFWT converter during PFR. Method 1 is the initial value of the active power of the DFWT added with the frequency-regulation power, as shown in (10), and the corresponding trajectory is A-B-C-D-A; Method 2 is the MPPT power added with the frequency-regulation power, as shown in (11), and the corresponding trajectory is A-B-C′-D′-A.

P'_{Wind, ref} = P_{Wind, ref 0 +} Δ P_{Wind}

(10)

P''_{Wind, ref} = P_{MPPT +} Δ P_{Wind}

(11)

When the DFWT generates additional power to participate in frequency control, the decrease in rotor speed leads to a reduction in MPPT power, so the actual increase in power in Method 2 is less than the given frequency-regulation power, which weakens the frequency-regulation effect to some extent. And as the rotor speed of DFWT decreases, the MPPT power decreases continuously, so that the active reference value of the DFWT may be less than the active power initial output P₀, and in Figure 8, the DFWT has lost the frequency support effect when the rotor speed is lower than ω₃. Compared with Method 2, Method 1 releases more rotor kinetic energy when the frequency-regulation participation time is certain, and the frequency support effect is better. However, when DFWT exits the frequency control, the power shock induced by using Method 1 is greater than that of Method 2, as is the depth of SFD.

Figure 8.

Schematic diagram of frequency regulation process for DFWT.

The VSPS can compensate for the deficiencies of Method 1 by its rapid response to changes in active power commands when combined with DFWT to form a joint system. Therefore, Method 1 is used to calculate the active power reference value of DFWT converter to obtain better frequency support capability.

Frequency-regulation strategies for wind-pumped storage systems with different wind speeds

In this paper, different frequency-regulation strategies are designed in different wind speed zones according to the frequency regulation capability of DFWT, and the control flow chart is shown in Figure 9.

(1) When the system frequency monitoring device detects that the system frequency deviation exceeds 0.033 Hz, the wind-pumped storage system starts frequency regulating. Firstly, γ_D in the current frequency state is calculated by FC1 of the external control layer, after which the total frequency-regulation power $Δ P_{total}$ that the wind-pumped storage system should bear is calculated by (9); if the system frequency deviation is within 0.033 Hz, the DFWT operates normally in MPPT mode.

(2) If the current wind speed is in the medium wind speed zone, when the rotor speed of the DFWT ω_W is higher than the minimum speed allowed ω_W,min, the FC2 of the internal scheduling layer calculates the γ_W of the DFWT, and then obtains the frequency-regulation power increment of the DFWT and the VSPS; when ω_W is lower than the ω_W,min or the frequency-regulation participation time reaches 20 seconds, the DFWT enters the speed restoration mode. After that, the VSPS will make up for the power shortage caused by the DFWT restoring rotor speed and continue to complete the task of system frequency restoration.

(3) When located in the high wind speed zone or low wind speed zone, the DFWT cannot participate in frequency control at this time, so the VSPS will assume the task of frequency regulation in this wind speed zone.

Figure 9.

Flow chart of cooperative control strategy for wind-pumped storage system.

Example analysis

To verify the effectiveness of the control strategy proposed in this paper, a multi-source frequency regulation simulation system containing a wind-pumped storage system is established based on actual grid data in a region of China, where the installed capacities of thermal power and hydropower are 500 MW and 370 MW respectively, while the installed capacities of wind power and pumped storage are 300 MW and 280 MW respectively. The following simulation scenarios have a sudden increase in load of 0.1 pu at 100 seconds.

Comparison of active power reference values of DFWT’s converters

As can be seen from Figure 10(a), when $Δ P_{wind}$ is the same, the DFWT output power P_Wind calculated in Method 1 is greater than that calculated in Method 2, and as the rotor speed ω_W of the DFWT decreases, the difference between the two power gradually becomes larger, so the frequency support effect of Method 1 is better than Method 2, and its frequency nadir increases by 0.03 Hz, and the more significant the difference in frequency-regulation effect with PFR. At 117 seconds, the P_Wind calculated by Method 2 starts to fall below the initial value, at which point the DFWT has lost its role in supporting the system frequency. At 120 seconds, the rotor speed of DFWT begins to restore, causing a power drop of 0.06 pu, resulting in a SFD of 0.11 Hz, after which the rotor speed gradually restores. As can be seen from Figure 10(b), the speed drop is faster because Method 1 is more “aggressive” in calculating the P_Wind. At 118 seconds the ω_W drops to 0.72 pu triggering the speed protection thus DFWT is forced out of the frequency control, causing a power drop of 0.19 pu and a SFD of 0.38 Hz, which exceeds the depth of primary frequency drop.

Figure 10.

Simulation results of different active power reference calculation methods: (a) active power of DFWT, (b) rotor speed of DFWT, and (c) system frequency.

Validation of cooperative control strategy for frequency regulation of wind-pumped storage system

Since the proposed control strategy deals with the low and high wind speed zones in a similar manner, the scenarios of medium and high wind speed zones are selected to test the application of the proposed strategy.

Simulation results in high wind speed zone

When the wind speed reaches 14 m/s, the wind-pumped storage system is operating in the high wind speed zone. At this stage, the DFWT cannot participate in frequency control alone, and according to the cooperative control strategy proposed in section “Frequency-regulation strategies for wind-pumped storage systems with different wind speeds”, the active power output of the VSPS is changed to respond to the frequency fluctuation, so that the wind-pumped storage system also has the short-term frequency response capability at high wind speed.

This section verifies the effectiveness of the Wind-pumped storage system external control layer strategy by analyzing the system frequency response in the following three scenarios in high wind speed zone:

case1: VSPS does not participate in frequency control.

case2: VSPS uses conventional integrated inertia control to participate in frequency control.

case3: VSPS uses fuzzy adaptive inertia control to participate in frequency control.

Figure 11 compares the frequency response curves after a sudden increase in load for different control methods. From Figure 11(a), it can be seen that the frequency nadir increases significantly after the VSPS participates in frequency control compared with that without frequency control, where the frequency nadir increases by 0.18 Hz with the conventional control and by 0.27 Hz with the strategy proposed in this paper. The frequency drop speed is case1, case2, and case3 in order from fast to slow, and the frequency restoration speed is case3, case2, and case1 in order from fast to slow, and the proposed control strategy greatly reduces the oscillation amplitude during the frequency restoration process, so that the system returns to the steady state faster. As can be seen from Figure 11(b) and (c), the differential link of the conventional control has a negative active power increment during the frequency restoration stage, which makes the output power of the DFWT lower than the initial value, resulting in the loss of the DFWT’s frequency support capability and affecting the frequency restoration. Combined with Figure 11(d), under the proposed strategy, the γ_D increases with the frequency deviation during the frequency drop stage to damp the rapid frequency decrease, and the reverse value is taken during the frequency restoration stage to make the differential term output positive active power to speed up the frequency restoration.

Figure 11.

Dynamic response waveform of the system after a sudden increase in load in high wind speed zone: (a) system frequency, (b) differential term frequency regulation power, (c) active-power variation of VSPS, and (d) adjustment factors for virtual inertia coefficient.

As can be seen in Figure 12, compared with the conventional control, it takes less time for the VSPS to return to the steady state under the proposed strategy, although the speed of that varies more. Moreover, in the pump mode, the conventional control has overshoot phenomenon, while the proposed strategy avoids this problem very well.

Figure 12.

Rotor speed of VSPS in high wind speed zone: (a) turbine mode and (b) pump mode.

From Figure 13, it can be seen that VSPS shares part of the frequency-regulation power after participating in frequency control, which reduces the frequency-regulation pressure of the conventional unit. Compared with the conventional control strategy, the active power variation of the conventional unit under the proposed control strategy is smaller, which reduces the consumption of fossil fuel, and the power oscillation amplitude is smaller and the time required to enter the steady state is shorter.

Figure 13.

Active-power variation of conventional units in high wind speed zone.

Simulation results in medium wind speed zone

The simulated wind speed is taken as 9 m/s, and the system is operating in the medium wind speed zone at this time. According to the proposed strategy, at this stage the fuzzy controller FC2 calculates the frequency-regulation participation factor γ_W of the DFWT based on the rotor speed ω_W and the active power output P_W to prevent the DFWT from being forced out of frequency control due to excessive rotor kinetic energy release triggering speed protection and resulting in SFD. The VSPS is used as a supplement to the DFWT to participate in frequency control, the proposed control strategy in this wind speed zone aims to reduce the power shock to reduce the depth of SFD through the fast response of VSPS to the power change command.

This section verifies the effectiveness of the Wind-pumped storage system internal scheduling layer strategy by analyzing the system frequency response in the following three scenarios in medium wind speed zone:

Case4: VSPS does not participate in frequency control.

Case5: DFWT and VSPS use integrated inertia control to independently participate in frequency control.

Case6: Wind-pumped storage system uses cooperative control strategy to participate in frequency control.

Figure 14 shows the frequency curve of the multi-source power system operating at medium wind speed. The frequency nadir under the proposed strategy in this paper is improved by 0.36 Hz compared to no control and by 0.05 Hz compared to conventional control.

Figure 14.

System frequency in medium wind speed zone.

From Figure 15(a) and (b), it can be seen that the DFWT under conventional control is forced out of frequency control at 118 seconds when the speed is reduced to 0.72 pu, whose output active power drop from 0.35 pu to 0.16 pu, resulting in a SFD of 0.38 Hz. While the proposed control in this paper takes the residual frequency-regulation capability of the DFWT into full consideration, Figure 15(d) shows that the γ_W decreases as that decreases, so the output power of DFWT under the proposed control is lower compared with the conventional control, and the output power of VSPS as a supplement to the frequency regulation of DFWT is higher than that under the conventional control. The power drop caused by DFWT at 120 seconds is only 0.06 pu. The VSPS quickly responds to the power change command to replenish this power deficit, but there is still a small SFD due to communication delays and the limited control performance of the converter.

Figure 15.

Dynamic response waveform of the system after a sudden increase in load in medium wind speed zone: (a) active power of DFWT, (b) rotor speed of DFWT, (c) active-power variation of VSPS, and (d) frequency-regulation participation factor of DFWT.

Figure 16 demonstrates the simulation results for the rotor speed of VSPS. When VSPS is in turbine mode, the rotor kinetic energy extracted under the proposed control is about four times higher than that of the conventional control, but the time for the rotor speed to restore to steady state is basically the same for both control strategies. When VSPS is in pump mode, the rotor kinetic energy extracted under the proposed control is about nine times that of the conventional control, and the time required for rotor speed to restore to steady state is only 1.5 times that of the conventional control.

Figure 16.

Rotor speed of VSPS in medium wind speed zone: (a) turbine mode and (b) pump mode.

Conclusion

In this paper, a fuzzy control-based cooperative control strategy for wind-pumped storage system is proposed for high wind power penetration power system, so that the joint system has frequency regulation capability at all wind speeds, and the specific conclusions are as follows:

(1) Calculating the active reference value of converter of DFWT by adding the initial value of power output to the frequency-regulation power can significantly improve the frequency support capability of the DFWT, but at the same time can exacerbate the SFD.

(2) The virtual inertia coefficient of wind-pumped storage system is dynamically adjusted by fuzzy control at different frequency response stages to achieve rationalized distribution of the joint system frequency-regulation energy, which not only effectively reduces the speed of system frequency drop and transient frequency deviation, but also speeds up the system frequency restore.

(3) The reasonable distribution of frequency-regulation power in the Wind-pumped storage system according to the residual frequency-regulation capacity of DFWT greatly reduces the depth of SFD, makes up for the deficiencies in the calculation of the active reference value of the converter of DFWT, and speeds up the restore to steady state of each unit in the power system.

The short-term frequency support energy of VSPS comes from its rotor kinetic energy. How to take the speed constraint of VSPS into account in the frequency regulation strategy to avoid the speed of VSPS out of the allowed range is a question that will be further explored.

Footnotes

Appendix

Table A2.

Fuzzy control rules for FC2.

$γ W$		$ω W$
$γ W$		VS	MS	S	M	L	ML	VL
P _W	VS	VS	MS	S	M	L	ML	VL
	MS	VS	MS	S	M	L	ML	VL
	S	VS	MS	S	M	M	L	ML
	M	VS	MS	MS	S	M	L	L
	L	VS	MS	MS	S	S	M	L
	ML	VS	VS	MS	MS	S	M	M
	VL	VS	VS	MS	MS	MS	S	S

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Scientific Research Project of Jilin Provincial Department of Education (JJKH20230123KJ).

ORCID iD

Yang Feng

References

Altin

Hansen

Barlas

, et al. (2018) Optimization of short-term overproduction response of variable speed wind turbines. IEEE Transactions on Sustainable Energy 9(4): 1732–1739.

British Petroleum (2022) bp Statistical review of world energy. Available at: https://www.bp.com/en/global/corporate/energy-economics/statistical-review-of-world-energy.html (accessed 15 May 2023).

Chen

Liu

, et al. (2023) Small-signal system frequency stability analysis of the power grid integrated with type-II doubly-fed variable speed pumped storage. IEEE Transactions on Energy Conversion 38(1): 611–623.

Courtecuisse

Robyns

Francois

, et al. (2008) Variable speed wind generators participation in primary frequency control. Wind Engineering 32(3): 299–318.

Ding

(2015) Wind power and pumped storage joint optimization technology gets breakthrough. State Grid News, 25 June, 1.

Gagnon

Sybille

Bernard

, et al. (2005) Modeling and real-time simulation of a doubly-fed induction generator driven by a wind turbine. In: International Conference on Power Systems Transients (IPST’05), Montreal, Canada, 19–23 June 2005.

Hafiz

Abdennour

(2015) Optimal use of kinetic energy for the inertial support from variable speed wind turbines. Renewable Energy 80: 629–643.

Huang

Xin

Zhang

, et al. (2017) Synchronization and frequency regulation of DFIG-based wind turbine generators with synchronized control. IEEE Transactions on Energy Conversion 32(3): 1251–1262.

Cao

, et al. (2023) Performance assessment for primary frequency regulation of variable-speed pumped storage plant in isolated power systems. Energies 16(3): 1238.

10.

Wang

Zhang

, et al. (2021) Fuzzy adaptive virtual inertia control strategy of wind turbines based on system frequency response interval division. Power System Technology 45(5): 1658–1665.

11.

Manzoor

Mufti

(2020) Genetically tuned fuzzy controlled flywheel powered micro-grid for improved frequency control. Wind Engineering 45(3): 710–726.

12.

Morren

de Haan

SWH

Kling

, et al. (2006) Wind turbines emulating inertia and supporting primary frequency control. IEEE Transactions on Power Systems 21(1): 433–434.

13.

National Grid (Great Britain) Company (2009) The Grid Code. London: National Grid (Great Britain) Company.

14.

National Standardization Administration of the People’s Republic of China (2021) Technical specification for connecting wind farm to power system-part l: On shore wind power: GB/T 19963.1-2021. Beijng: General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China.

15.

Papaefthymiou

Karamanou

Papathanassiou

, et al. (2010) A wind-hydro-pumped storage station leading to high RES penetration in the autonomous island system of Ikaria. IEEE Transactions on Sustainable Energy 1(3): 163–172.

16.

Peng

Zhang

Liang

(2018) Coordinated control strategy for short-term frequency response of wind-energy storage system considering wind speed partition. Automation of Electric Power Systems 42(08): 57–65.

17.

Prabha

Kimbark

(2001) Power System Stability and Control. Beijing: China Electric Power Press.

18.

Sarasúa

Pérez-Díaz

Torres Vara

(2015) On the implementation of variable speed in pump-turbine units providing primary and secondary load-frequency control in generating mode. Energies 8(12): 13559–13575.

19.

Torres

Lopes

Moran

, et al. (2014) Self-tuning virtual synchronous machine: A control strategy for energy storage systems to support dynamic frequency control. IEEE Transactions on Energy Conversion 29(4): 833–840.

20.

Waheed Kumar

Din Mufti

Yaqoob Zargar

(2023) Utilization of superconducting magnetic energy storage and doubly fed induction generator for enhancing stability of interconnected power system. International Journal of Circuit Theory and Applications. Epub ahead of print 14 June 2023. DOI: 10.1002/cta.3699.

21.

Wang

Tomsovic

(2018) A novel active power control framework for wind turbine generators to improve frequency response. IEEE Transactions on Power Systems 33(6): 6579–6589.

22.

Deng

Yang

(2023) Flexibility of variable-speed pumped-storage unit during primary frequency control and corresponding assessment method. International Journal of Electrical Power & Energy Systems 145: 108691. DOI: 10.1016/j.ijepes.2022.108691.

23.

Zhao

Zhou

, et al. (2023) The primary frequency regulation method of wind power and pumped storage in the microgrid considering random wind speed. Power System and Clean Energy 39(01): 111–119.