Since the goals of carbon peaking and carbon neutrality and new-energy-oriented electric systems have been put forward, the power industry has established a new power system that treats renewable energy as the principal part of the reform goal in China. Since renewable energy’s output is uncertain, the change of the power system’s main source will further reduce its stability. The introduction of energy storage units into the power system shall not only improve the utilization rate of new energy but also actively carry out peak shaving and frequency modulation [1–4].

With the innovation of battery technology, large-capacity centralized energy storage power stations continue to be used as power sources to provide energy support for the grid [5–7], which are included in the grid-connected operation and auxiliary service management. Li et al. [8,9] concluded that the main functions of the energy storage power station are peak load regulation, long-term power supply, primary frequency regulation, stabilizing power fluctuation, standby power and tracking planned power generation.

According to Zhong [10], nowadays distributed generation system with the power electronic converter as the interface lacks the inertia and damping of the traditional synchronous generator (SG). In the wake of increasing new energy penetration rate and withdrawal of corresponding SGs, the system inertia level and primary frequency modulation resources gradually decrease. Under the disturbance of the same intensity, Delille et al. [11] had concluded that the reduction of the inertia level will worsen the maximum frequency offset and the maximum frequency change rate, so the power system is more vulnerable to power fluctuations and system failures.

Over the last decade, Zhong et al. [12,13] proposed a virtual synchronous generator (VSG), which gives power electronic converter of energy storage power station capacity to sustain inertia and damping of the electrified wire netting by imitating SG, and enhance its anti-interference ability, give a pledge to electrical grids’ safe and steady operation. In the distributed system described by Torres et al. [14], the converter takes an adaptive control of VSG, and relevant adaptive control rules are designed to optimize the inertia and damping coefficients to reduce the output power of energy storage devices. In addition, the anti-jamming capability of the system can also get improved by using a newly designed equation about frequency-dependent coefficient [15,16]. Such expositions are unsatisfactory because the above adaptive VSG control strategies need to accurately model the converter to get the best control.

On the other hand, fuzzy control uses a language method, which is easy to carry out human-computer interaction. The precise mathematical model does not need to be established in the control process. It has strong robustness and is suitable for solving the problems of nonlinearity, strong coupling, time-varying and delay in process control [17,18]. Ebrahimi et al. [19–23] used fuzzy adaptive VSG control to reduce frequency fluctuation.

Hu et al. [24] expound the essence of inertia in an energy storage system with the theory that inertia is a form of energy, and an equivalent inertia calculation method for a given energy storage system is came up. On this basis, Yuan et al. [25] established the physical constraints of the energy storage side on the virtual synchronous machine plus its operating boundary.

Chen et al. [26] proposed an adaptive control strategy to achieve SOC balance between several VSGs based on paralleled energy storage systems in a decentralized manner. With the proposed method, no matter what the difference between VSGs’ initial values and interference is, the SOC balance can be easily achieved without a communication network. The above research fails to consider that when the energy storage system shuts down at the minimum SOC, the output power of VSG will be greatly reduced in a short time, which will seriously affect the power grid.

To sum up, a VSG adaptive control strategy considering SOC feedback of energy storage battery is proposed. Firstly, this paper lists physical constraints based on the energy storage side, thus given VSG’s inertia, output power and change rate of the power have corresponding value ranges. Then divides the VSG parameter settings of inertia, damping, active and reactive reference values into three groups. Different control strategies are adopted under different SOC to realize parameter adaptive control, so as to smooth power fluctuations when VSG is off-grid while maintaining a certain frequency modulation performance. Finally, through the MATLAB platform, the validity of the above integrated control strategy is verified by simulation.

Based on the classical second-order model of SG with polar logarithm of 1, the second-order VSG model is established. In order to meet the seamless switching and smooth transition between isolated island operation and grid connected operation of energy storage power station, a voltage source VSG mode is adopted in this paper, where Fig. 1 is its topology diagram, where mechanical and electromagnetic equations can broadly be defined as follows:

(1){Pm−Pe=Jωdωdt+D(ω−ω0)Lfdiabcdt=eabc−uabc−Rfiabc

In Eq. (1): P_m is the virtual machine power; P_e is the output active power; J is virtual inertia; ω is the real-time electric angular velocity generated by VSG; D is the damping coefficient; ω0 is the rated angular velocity of the power grid. Where in Fig. 1, U_dc is the DC side voltage; e_abc, u_abc and i_abc are the potential, terminal voltage and output current of VSG, respectively; R_f, L_f and C_f are the filter resistance, filter inductance and filter capacitance of AC side, respectively. R_g, and L_g are the equivalent resistance and inductance of power grid.

In this paper, the VSG control is primarily composed of active frequency control and reactive voltage control. P_m is made up of active power given reference value P_ref and frequency deviation response command value:

(2)Pm=Pref−Kf(ω−ω0)where K_f is the active frequency modulation coefficient of VSG.

VSG’s transient potential E consists of three parts: E₀, the no-load potential, represents the machine terminal voltage when the converter runs off-grid without load; the machine terminal voltage regulation amount and the reactive power regulation amount. In summary, the given output voltage amplitude expression is:

(3)E=E0+Kv(Uref−U)+Kq(Qref−Qe)

In Eq. (3), K_v is the voltage regulation coefficient of the VSG; U_ref means the rated value of the machine terminal voltage; U is the converter output port line voltage; K_q represents the reactive power regulation coefficient of the VSG; Q_ref indicates system’s reactive power command, Q_e indicates instantaneous reactive power output of machine terminal. From Eqs. (1)–(3), the VSG control scheme adopted in this paper is shown in Fig. 2.

The output modulation voltage is controlled by an inner loop of inductor current and an outer loop of capacitor voltage, and the output 6-pulse PWM signal is modulated by Space Vector Pulse Width Modulation (SVPWM), which is shown in Fig. 3. In the figure, L_v represents virtual impedance.

In practical energy storage projects, the storage capacity of VSG is usually fixed, and its size is limited by factors such as environment and investment. Therefore, to ensure that the inertia and damping of the VSG are always subject to the energy storage during the setting process and the corresponding response characteristics of the system during the transient process, the corresponding physical constraints index of the VSG are designed, namely, SOC, the charge rate and discharge rate, and power change rate.

During the normal shutdown of the conventional generator set, the load shall be gradually removed, the load switch shall be disconnected, and the generator shall be shut down after running at idle speed for 3–5 min. Since the capacity of the energy storage batteries is still very limited compared to the large grid, the energy storage power station will temporarily stop providing power grid support and frequency modulation services to prevent its energy storage units from discharging beyond the limit especially after one battery pack have been discharging to the power grid for a long period of time. Due to the discharge characteristics of the electric energy storage system, once the energy storage battery is disconnected from the energy storage converter, the energy storage converter AC output shall drop sharply, along with grid frequency becoming unstable, and VSG frequency modulation completely loses its energy support, which is a huge disturbance to the grid.

To test the correctness and effectiveness of the theory and strategy mentioned above, three VSG control methods, Common VSG control (C-VSG), Conventional adaptive VSG control (S-VSG) and Improved VSG (I-VSG) control, are compared with each other. Note that the J and D of the C-VSG are constant. In addition, C-VSG does not consider the physical constraints on the energy storage side, and only power off and shutdown at SOC_min. The grid-connected simulation model of the energy storage power station as proposed in Fig. 1 has been constructed on the MATLAB platform.

The energy storage converter takes a VSG control method just the same way as Fig. 2, and Table 4 shows the specific simulation parameters of VSG.

First, this paper verifies the influence of the discharge characteristics of the energy storage battery on the value range of J and D, as shown in Fig. 9.

Set the system with a 5 kW, 1 kvar load. In this simulation experiment, the maximum discharge power limit of the energy storage battery is 12 kW. and the change threshold of discharge power is 80 kW/s. In the beginning, VSG operates with P_ref = 4 kW and Q_ref = 1 kvar. After 0.8 s, the active power command value of the system increases to 10 kW.

As shown in Fig. 9, when the system power command changes, the system shows different response characteristics under different control parameters. The peak value of the active power change and its area surrounding the time axis is the required energy storage margin at this time.

In Figs. 9a, 9c, when J = 1.5, D = 14 and J = 0.5, D = 3, the power fluctuation is large, the overshoot time is long, the maximum value exceeds the power limit, so the system response exceeds the capacity range of the energy storage unit.

As shown in Fig. 9b, when J = 0.1 and D = 14, the maximum power change rate is80.164 kW/s, which is greater than the physical limit of the power change rate, exceeding its performance accessibility, so it cannot be achieved.

If J = 0.5 and D = 14, as shown in Figs. 9a, 9b, when the active power command changes, its power change rate is up to 73.85 kW/s and is far from the limit value of the power change rate, so the system operates normally and safely. At this time, VSG is under damping control.

If J = 0.5 and D = 30, it can be seen that when VSG implements over-damping control, both power and power change rate meet operation constraints, and only the adjustment time is slightly extended. Therefore, the over-damping control can be adopted when the SOC is low. Since large system interference will not occur in a short time, the over-damping control with fixed parameters can maximize and weaken the adverse impact on the power grid when the output power drops.

Then, this paper verifies the function of the VSG fuzzy adaptive control module, as shown in Fig. 10. In this comparative experiment, it is assumed that SOC is in the normal working zone, and compares three different VSG control modes.

Constant parameter VSG, C-VSG: J = 0.5, D = 14;

The conventional adaptive control strategy as the control group is shown in Eqs. (22) and (23):

(22)J={J0Δω⋅dωdt≤0J0|dωdt|≤KJJ0+a|dωdt|Δω⋅dωdt>0∩|dωdt|>KJ

(23)D={D0|Δω|≤KDD0+b|Δω||Δω|>KDwherein, J₀ and D₀ are respectively the moments of inertia and damping coefficient of the VSG during stable operation; a and b are the adjustment coefficients of the moment of inertia and damping coefficient, respectively; K_J and K_D are change thresholds. The collaborative adaptive control flow chart is shown in Fig. 11, where K_J = 2.5, K_D = 0.1, a = 0.05, and b = 5.

Fig. 10 shows the output comparison of the VSG under different control strategies. The initial SOC of VSG under each control strategy is 50%. The simulation duration is 5 s, the load active power is 5 kW, and the reactive power is 1 kvar. The load is increased by 5 kW in 2 s, and the set value is restored in 4 s.

It can be seen from Fig. 10a that VSG under parameter adaptive control consumes significantly less power. Fig. 10b shows the response curves of the VSG output active power under different control strategies. When the load power suddenly increases by 5 kw at 2 s, the active power of C-VSG, S-VSG and I-VSG drops to 100,830 kW, 100,826 W and 101,077 W, respectively, and recovers to the rated output in 2.41, 2.43 and 2.39 s, respectively.

Fig. 10c shows that the adaptive change has a significant impact on the frequency change rate. When the frequency is subject to the initial load disturbance, the buffer effect of C-VSG control on the disturbance is general, and the maximum overshoot is 0.33 Hz; S-VSG control can better buffer frequency fluctuation, and the maximum overshoot is 0.25 Hz; The fuzzy adaptive VSG control has the best buffering effect on frequency fluctuation, and the maximum overshoot is 0.22 Hz.

When the load power suddenly increases, the frequency deviation of C-VSG exceeds 0.1 Hz, and the oscillation duration is about 0.6 s. As for S-VSG, its maximum frequency deviation is reduced to 0.093 Hz, and the adjustment time is reduced to 0.51 s. When I-VSG is used, the maximum frequency deviation is reduced to 0.086 Hz, and the adjustment time is reduced to 0.42 s. When the frequency deviation exceeds 0.1 Hz, the adaptive increase of D can significantly restrain the frequency deviation. Moreover, when the disturbance is eliminated, the fuzzy adaptive VSG control strategy can restore the frequency to stability as quickly as possible.

The range of RoCoF is also specified in Fig.10d to ensure the system stability; the absolute maximum RoCoF with C-VSG method is 4.27 Hz/s. Using S-VSG and I-VSG control method, the maximum RoCoF becomes 3.50 and 4.00 Hz/s, respectively. Note that, using adaptive control, the maximum RoCoF has decreased by 6%~18%, which improves the system frequency stability.

Figs. 10e, 10f show the changes of J and D under S-VSG control and I-VSG control. In Fig. 10e, there are sharp spikes of the J waveform of S-VSG, which is caused by the uneven frequency change of the virtual rotor, sudden changes of dω/dt at the frequency inflection point.

Finally, this paper verifies the hierarchical power reduction control strategy when the SOC of the battery is in the buffer zone, as shown in Fig. 12.

The system is initially loaded with a 3 kW load. In the beginning, VSG operates withP_ref = 16 kW and Q_ref = 0 var. At 10 s, the system frequency suddenly increases by 0.2 Hz, and the frequency is recovered at 13 s.

To obtain a more obvious battery SOC curve, small capacity batteries are selected as the power supply in this test, and the graded power reduction operation strategy is started when the SOC reaches 7% and 6%, respectively.

By observing Fig. 12a, it can be found that the SOC of C-VSG control reaches the minimum value at 27.37 s, then the battery system is in a limited discharge state and stops discharging and actively disconnects from the converter, and from Fig. 12c we can see its output power drops sharply to a negative value, which means at that time, the energy storage converter did not supply power to the power grid, but consumed power from the power grid. The connection between the converter and the power grid should be immediately disconnected to reduce power loss. In practice, when the converter is going to stop power transmission, it should first disconnect the connection with the power grid side, then disconnect the DC input switch, and finally, the energy storage device can disconnect the interaction with the outside system.

More so, as shown in Fig. 12b, from 27.37 s C-VSG’s frequency management loses energy support, and the grid frequency is no longer maintained near the rated value.

Also, it can be seen from Fig. 12c that the I-VSG control starts active power reduction operation at 5.326 s and reduces its output power again at 23.075 s. At 49.594 s, the SOC reaches the lowest value that can VSG be operated, and the battery is disconnected from the converter. Due to different control strategies, I-VSG markedly prolongs the discharge working time. Thus, the power shortage in unit time is reduced, and the impact of VSG shutdown on the power grid is reduced.

Due to the use of overdamping control, the system output power under the I-VSG control strategy does not overshoot, and its power change rate is smaller, as shown in Fig. 12d. So the requirement for battery energy storage margin is smaller. The improved VSG control strategy effectively smoothes the short-term power fluctuation caused by the disconnection of the ionization network of the battery and retains sufficient frequency modulation capability during a sudden change in system frequency.

In the actual design of an energy storage power station, the capacity of the energy storage battery pack is far greater than 1Ah, and normally the installed capacity varies from 1 to 100 MW. Therefore, it is not only necessary to reasonably design the value of SOC_b1 and SOC_b2, so that the operation time of each level of power reduction is about 30 s, but also to add multiple buffer zones when necessary, so as to limit the change rate of the active power of the energy storage plant to a reasonable range.

This article is based on fuzzy control theory, energy storage converter model and fuzzy adaptive control strategy of VSG, this paper studies the rationality of VSG control parameter selection when the energy storage unit is in a safe working state, and analyzes the relationship between two parameters, inertia and damping, and dynamic performance of the energy storage converter, so as to realize the adaptive VSG control strategy of the energy storage converter. The following conclusions are obtained through simulation analysis of a grid-connected model of an energy storage power station:

Considering the physical constraints of energy storage, the output power and its power change rate of VSG are always within the allowable range of battery performance. This control strategy sacrifices the dynamic regulation performance of the energy storage converter, thus ensuring the overall dynamic response capability of the whole energy storage system. Therefore, the energy storage battery will not have over-discharge and other adverse phenomena, which protects the safety and service life of the battery. In the actual construction of energy storage power stations, batteries with large capacity, high discharge rate and large threshold of power change rate should be selected as the power supply to cut down the negative impact on the output performance of the energy storage system.