Flexible Grid-Connected/Off-Grid Switching Control Strategy for Storage Inverter

Abstract

Taking a dual-mode grid-connected/off-grid storage inverter as the research subject, control models for both grid-connected and off-grid operation modes were established. For the grid-to-off-grid transition, an improved adaptive active frequency drift islanding detection algorithm was proposed, which employs a cubic power-based detection method when frequency deviation is small to reduce positive feedback speed, and a parabola-based detection method when frequency deviation is large to enhance positive feedback speed. Compared with the traditional active frequency drift islanding detection algorithm, the proposed method can ensure islanding detection speed while effectively reducing the current total harmonic distortion during grid-connected operation. Experiments conducted on a storage inverter prototype demonstrated stable operation in both grid-connected and off-grid modes. The results indicate that the proposed control strategy enables rapid identification of operating conditions and mode switching, significantly improving the stability and reliability of the inverter during transition, thus laying a foundation for the autonomous operation of dynamic microgrids.

1. Introduction

Against the backdrop of the escalating energy crisis and worsening environmental problems, renewable energy sources such as photovoltaic (PV) and wind power have been widely adopted, with the installed capacity of new energy power equipment registering steady annual growth [1]. Constructing a new power system dominated by new energy has become a crucial direction for the transformation and upgrading of power systems [2]. However, the output power of PV systems is constrained by factors including light intensity and temperature, exhibiting randomness and intermittency, which significantly impairs grid-connected stability [3,4,5]. In contrast, energy storage systems (ESSs) can effectively regulate output power, suppress PV power fluctuations [6], and enhance system stability. Therefore, ESS microgrids play a pivotal role in improving the reliability of PV power generation and the stability of grid connection.

Aiming at the off-grid and grid-connected control of inverters in ESS microgrids, this paper introduces the quasi-proportional resonant controller [7] and repetitive controller based on the internal model principle (IMP) to suppress disturbances and harmonics [8,9], as well as to improve the steady-state accuracy of the system. The ESS inverter with off-grid/grid-connected dual-mode operation is capable of switching between the two operating modes. When the inverter operating in grid-connected mode detects an islanding event caused by a grid power outage, it will switch to the off-grid mode. Islanding detection algorithms are mainly classified into three categories: passive, active, and hybrid types [10,11]. Passive algorithms mainly include overvoltage/undervoltage detection, overfrequency/underfrequency detection, and impedance detection for the system, which feature simple implementation but suffer from detection blind zones and are prone to maloperation under grid disturbances [12,13,14]. Active algorithms inject a disturbance term into the inverter’s output current, and the frequency will exceed the limit to trigger protection in the event of islanding. This method greatly reduces the detection blind zones but also degrades the power quality of the system. At present, active islanding detection methods based on signal injection strategies have been extensively investigated. References [15,16,17] all propose improved methods based on passive impedance detection, which realize islanding detection by analyzing the impedance characteristics before and after islanding through synchronous signal injection. However, these methods require injecting harmonics into the system, and the harmonic signals of multiple parallel-connected units are prone to mutual interference. Ref. [18] combines active and passive methods, taking both voltage and the rate of change of active power as the criteria for islanding detection, which can reduce the impact of active injected disturbances on power quality and avoid misjudgment in passive detection. However, this method is relatively complicated. Ref. [19] proposes a novel islanding detection method applicable to both grid-following and grid-forming inverters without additional communication. This method injects negative-sequence current into the grid and identifies islanding by detecting the voltage unbalance generated by the inverter at the point of common coupling, which is not suitable for single-phase inverters. Ref. [20] analyzes the output impedance characteristics of grid-connected inverters on the basis of the traditional active frequency drift (AFD) method, quantifies the interaction between AFD parameters and grid impedance, and proves that the system will become unstable due to insufficient phase margin after islanding occurs, so that the islanding state can be identified through frequency detection. However, the harmonic distortion of grid-connected current is still not taken into consideration. Ref. [21] puts forward an active islanding detection technology based on the mean absolute frequency deviation, which achieves effective islanding detection with low current distortion.

Aiming at the grid-connected/off-grid switching process of the inverter, to reduce the impact of islanding detection on grid-connected power quality while improving islanding detection performance, this paper proposes an improved positive feedback active frequency shift islanding detection algorithm, which adopts different positive feedback rates for different frequency deviation ranges. Compared with traditional islanding detection algorithms, such as positive feedback active frequency drift and impedance detection, this method can reduce the impact of islanding detection on grid-connected current harmonics without slowing down the islanding detection speed. In addition, it has lower complexity and is easier for engineering implementation than other detection methods. Experimental verification results demonstrate that this method achieves excellent performance in both reducing the impact of injected disturbances on power quality under grid-connected conditions and realizing fast islanding detection.

2. Structure and Control Strategy of ESS Inverter System

2.1. Structure of ESS Inverter System

The ESS inverter system investigated in this paper is shown in Figure 1. After inversion, electrical energy is fed into the power grid or supplied to the loads. In Figure 1, C₁ is the DC bus capacitor, L₁ is the filter inductor, and C₂ is the filter capacitor. i_in denotes the total current flowing into the DC capacitor and the inverter, i_dc is the current flowing into the inverter, i_L is the inductor current of the inverter, U_dc is the DC bus voltage, u_i is the bridge arm voltage of the inverter, u_o is the filter capacitor voltage, and u_g is the grid voltage. This paper mainly focuses on the grid-connected and off-grid operation control as well as the switching strategy of the ESS inverter. Therefore, only the mathematical modeling and control strategy of the inverter are investigated in this study.

2.2. Control Strategy of ESS Inverter

2.2.1. Control in Grid-Connected Mode

Based on Kirchhoff’s Voltage and Current Laws, wherein the current directions are defined as shown in Figure 1, the mathematical model of the inverter in grid-connected mode is derived as follows:

$$i_{\mathrm{in}}=i_{\mathrm{dc}}+C_1{\displaystyle \frac{\mathrm{d}{U}_{\mathrm{dc}}}{\mathrm{d}t}}$$

(1)

$$u_{\mathrm{i}}=u_{\mathrm{g}}+i_{\mathrm{L}}r+L_1{\displaystyle \frac{\mathrm{d}{i}_{\mathrm{L}}}{\mathrm{d}t}}$$

(2)

where r is the equivalent resistance of L₁. The control structure shown in Figure 2 is adopted for the inverter in grid-connected mode.

A PI controller is used in the outer voltage loop to realize the static-error-free tracking of the DC bus voltage U_dc to its reference value U_{* dc}, thus maintaining the stability of the DC bus voltage. The double-frequency component contained in U_dc needs to be filtered out by a notch filter. To suppress grid voltage interference, feedforward compensation of the grid voltage is added to the output of the inner loop controller. The inner current loop is required to realize the static-error-free tracking of the AC inductor current to its reference value $i_L^{*}$, and thus the quasi-proportional resonant (QPR) controller expressed in (3) is employed.

$$G_{\mathrm{QPR}}\left(s\right)=k_{\mathrm{p}}+{\displaystyle \frac{2k_{\mathrm{r}}{\omega }_{\mathrm{c}}s}{s^2+2{\omega }_{\mathrm{c}}s+{{\omega }_0}^2}}$$

(3)

where k_p is the proportional coefficient, k_r the resonant coefficient, ω_c the cut-off frequency, and ω₀ the resonant frequency. Considering the effects of control and modulation delays, the total delay is 1.5T_s, where T_s denotes the control cycle. The delay transfer function is given in (4):

$$delay\left(s\right)={\displaystyle \frac{1}{1+1.5s{T}_{\mathrm{s}}}}.$$

(4)

Thus, the open-loop transfer function G_i(s) of the current loop is given by:

$$G_i\left(s\right)={\displaystyle \frac{(k_{\mathrm{p}}{s}^2+2{\omega }_{\mathrm{c}}\left(k_{\mathrm{r}}+k_{\mathrm{p}}\right)s+k_{\mathrm{p}}{{\omega }_0}^2)\frac{k_{\mathrm{pwm}}}{1.5s{T}_{\mathrm{s}}+1}}{L_1{s}^3+\left(r+2{\omega }_{\mathrm{c}}{L}_1\right)s^2+\left({{\omega }_0}^2{L}_1+2{\omega }_{\mathrm{c}}r\right)s+r{{\omega }_0}^2}}$$

(5)

where k_pwm is the equivalent gain of the inverter and ω₀ = 100π. Since the allowable range of grid voltage frequency fluctuation is ±0.5 Hz, the value range of ω_c is 0~π rad/s, and 3 rad/s is selectable. In addition, the cut-off frequency ω_ioff of the inner current loop is set to 1/10f_s, and the phase margin is required to be greater than 45°, that is:

$$\left\{\begin{array}{c}\left|G_i\left(j{\omega }_{\mathrm{ioff}}\right)\right|=1\\ \angle G_i\left(j{\omega }_{\mathrm{ioff}}\right)+{180}^{\circ }>{45}^{\circ }\end{array}\right.$$

(6)

For (7), assuming that the power loss of the inverter switching devices is neglected, the power flowing into the inverter from the DC bus is equal to the inverter’s output power; thus, the following can be derived:

$$\begin{array}{ll}{U}_{\mathrm{dc}}^{*}{C}_{1}s{U}_{\mathrm{dc}}& =U_{\mathrm{dc}}^{*}{i}_{\mathrm{in}}-U_{\mathrm{dc}}^{*}{i}_{\mathrm{dc}}\\ & =p_{\mathrm{in}}-{\displaystyle \frac{1}{2}}{I}_{\mathrm{m}}{U}_{\mathrm{m}}\end{array}$$

(7)

where I_m and U_m are the peak values of the grid current and voltage, respectively, and p_in is the input power of the DC bus. Based on (7), the control structure of the outer DC bus voltage loop is shown in Figure 3.

The notch filter in (8) is used to filter out the second-order ripple in U_dc where ω_t = 2ω₀ and η = 0.707.

$$G\left(s\right)={\displaystyle \frac{s^2+{\omega }_{\mathrm{t}}^2}{s^2+2\eta {\omega }_{\mathrm{t}}s+{\omega }_{\mathrm{t}}^2}}.$$

(8)

The closed-loop transfer function G_uc(s) of the outer DC bus voltage loop is given by:

$$G_{\mathrm{uc}}\left(s\right)={\displaystyle \frac{k_{\mathrm{up}}s+k_{\mathrm{ui}}}{2C_1{U}_{\mathrm{dc}}^{*}{s}^2/U_{\mathrm{m}}+k_{\mathrm{up}}s+k_{\mathrm{ui}}}}.$$

(9)

It can be treated as a typical second-order element to configure k_up and k_ui, thus:

$$\left\{\begin{array}{c}{k}_{\mathrm{ui}}={\displaystyle \frac{{2\mathrm{C}}_1{U}_{\mathrm{dc}}^{*}{\ast \mathsf{\omega }}_{\mathrm{n}}^2}{U_{\mathrm{m}}}}\\ k_{\mathrm{up}}={\displaystyle \frac{2C_1{U}_{\mathrm{dc}}^{*}\ast 2\zeta {\omega }_{\mathrm{n}}}{U_{\mathrm{m}}}}\end{array}\right.$$

(10)

where ζ is the damping coefficient and ω_n is the natural oscillation angular frequency.

2.2.2. Control in Off-Grid Mode

The mathematical model of the inverter in off-grid mode is given by:

$$u_{\mathrm{o}}=u_{\mathrm{i}}-L_1{\displaystyle \frac{\mathrm{d}{i}_{\mathrm{L}}}{\mathrm{d}t}}-r{i}_{\mathrm{L}}$$

(11)

$$C_2{\displaystyle \frac{\mathrm{d}{u}_{\mathrm{o}}}{\mathrm{d}t}}=i_{\mathrm{L}}-i_{\mathrm{o}}$$

(12)

Figure 4 shows the off-grid control structure of the inverter, which adopts a dual closed-loop control strategy of voltage and current.

Proportional control is adopted for the current control of the off-grid inverter. Since the series resistance of the filter inductor is small, it is neglected. The closed-loop transfer function of the inner current loop control is given by:

$$G(s)={\displaystyle \frac{i_{\mathrm{L}}(s)}{i_{\mathrm{L}}^{*}(s)}}={\displaystyle \frac{1}{s{L}_1/(k_{\mathrm{pi}}{k}_{\mathrm{pwm}})+1}}={\displaystyle \frac{1}{{\tau }_{\mathrm{i}}s+1}}$$

(13)

where τ_i determines the bandwidth of the system and the control parameter k_pi is set as:

$$k_{\mathrm{pi}}={\displaystyle \frac{L}{{\tau }_{\mathrm{i}}{k}_{\mathrm{pwm}}}}$$

(14)

Since the inner current loop features a fast dynamic response, the closed-loop current structure can be equivalent to a unity gain. The outer voltage loop control adopts a combination of repetitive control and quasi-resonant control. The control structure of the outer voltage loop is shown in Figure 5.

Where Q(z) is the integral coefficient of the repetitive controller, C(z) is the compensator, K_r is the gain of the repetitive controller, z^k is the lead element for phase compensation, and S(z) is the filter. This controller calibrates the low- and mid-frequency gain of the controlled object to 1, which eliminates the resonant peak of the controlled object. In addition, it enhances the high-frequency attenuation characteristic of the forward channel and improves the stability and anti-interference ability of the system. G_v(z) is the quasi-resonant controller.

Q(z) can be set as a low-pass filter or a constant, and a constant is usually selected with a value range of 0.95–1. The closer the value of Q(z) is to 1, the higher the steady-state accuracy, but the system may oscillate. The filter S(z) consists of a notch filter for suppressing the resonant peak of the system and a second-order filter for filtering out high-frequency noise. A comb filter expressed in (15) is adopted for the notch filter, where m is the number of delay steps.

$$F(z)={\displaystyle \frac{z^m+a+z^{-m}}{2+a}}$$

(15)

When z = e^jθ, (15) can be turned into

$$F\left(\theta \right)={\displaystyle \frac{2\cos m\theta +a}{2+a}}.$$

(16)

where θ = ω/f_s, ω is the resonant frequency, and f_s is the switching frequency.

When a = 2 and F(θ) = 0, F(z) achieves the maximum attenuation at specific frequencies with zero phase shift; thus,

$$\cos (m\theta )=-1\Rightarrow m\theta =\pi +2k\pi ,k=0,1,2\dots$$

(17)

Let k = 0, then we have

$$m\theta =\pi \Rightarrow m=f_{\mathrm{s}}\pi /\omega$$

(18)

The second-order filter of the filter S(z) is used to provide high-frequency attenuation characteristics, whose resonant frequency can be selected as the cut-off frequency of the inverter, and the damping coefficient is chosen to be in the range of 0.707–1. In the design of the quasi-resonant controller, the influence of the repetitive controller part can be neglected initially, which renders the system a linear one and facilitates the design process.

3. Smooth and Flexible Grid-Connected/Off-Grid Transition Control Strategy for ESS Microgrid Inverters

3.1. Grid-Connected/Off-Grid Switching Strategy for ESS Inverters

The principle of the traditional Active Frequency Drift with Positive Feedback (AFDPF) method is to inject the slightly distorted current of the inverter into the main grid. When an islanding event occurs, the frequency of the voltage at the point of common coupling (PCC) is forced to shift upward or downward. An islanding event is detected once the frequency shift exceeds the threshold value. With the AFDPF method, the slightly distorted current output by a single-phase inverter has two types of shifts: upward and downward. This paper adopts the upward shift method, as shown in Figure 6, where the light blue curve is the reference for the slightly distorted current and the black dashed line is the desired current reference.

The truncation coefficient c_f is defined as follows:

$$c_f={\displaystyle \frac{t_{\mathrm{z}}}{T_{vk-1}}}.$$

(19)

The reference frequency f_i of the current with slight distortion is given by:

$$f_i={\displaystyle \frac{f_{vk-1}}{1-c_f}}$$

(20)

where f_vk−1 is the PCC voltage frequency at the previous sampling step. The calculation formula for the truncation coefficient of the traditional AFDPF is given by:

$$c_f=c_{f_0}+k\left(f-f_0\right)$$

(21)

where c_f0 is the initial truncation coefficient, k is the positive feedback coefficient, f is the real-time voltage frequency at the PCC, and f₀ is the standard grid voltage frequency.

In practical systems, the grid voltage exhibits a certain degree of frequency fluctuation. Consequently, the positive feedback attaches the error fluctuation of the frequency deviation to the disturbance, which impairs the power quality of the grid-connected current. To address this problem, this paper improves the traditional AFDPF method and proposes a variable positive feedback coefficient method for islanding detection. This method adopts a piecewise algorithm expressed in (22), which employs a cubic power-based detection method when the frequency deviation is small and a parabola-based detection method when the frequency deviation is large. Since the frequency fluctuation range of normal grid voltage is within 0.2 Hz, the piecewise threshold is set to 0.2 Hz.

$$c_f=\left\{\begin{array}{ll}{c}_{f_0}+k{\left(\Delta f\right)}^3& ,\left|\Delta f\right|\le \overline{\left|\Delta f_{\mathrm{e}}\right|}\\ c_{f_0}+k\mathrm{sign}\left(\Delta f\right)\sqrt{\mathrm{abs}\left(\Delta f\right)}& ,\left|\Delta f\right|>\overline{\left|\Delta f_{\mathrm{e}}\right|}\end{array}\right.$$

(22)

where Δf = f − f₀.

This method enables a small positive feedback coefficient when the frequency deviation is small, which reduces the interference of grid voltage frequency fluctuations on islanding detection and the impact on power quality. When the frequency deviation is large, a large positive feedback coefficient is adopted to amplify the current disturbance, accelerate the frequency offset of the inverter’s output voltage, and ensure the rapid realization of islanding detection. This method can not only realize the timely and rapid response to islanding but also avoid the distortion of grid-connected current under normal grid conditions.

3.2. Non-Detection Zone Analysis of Islanding Detection Method

To evaluate the non-detection zone (NDZ) of islanding detection methods, it is necessary to reduce the dimension and complexity while accurately describing the NDZ characteristics. Therefore, the Q_f0 × C_norm space of the load parameter coordinate system is selected to characterize the NDZ distribution, which can reflect the relationship between the quality factor and the success or failure of islanding detection. The parameters are defined as follows:

$$Q_{f0}={\displaystyle \frac{R}{{\omega }_{0}L}}$$

(23)

$$C_{norm}={\displaystyle \frac{C}{C_{res}}}$$

(24)

$$C_{res}={\displaystyle \frac{1}{L{\omega }_0^2}}$$

(25)

where R, L, and C represent the resistance, inductance, and capacitance of the local load respectively, and denotes the grid angular frequency.

According to [22], the boundary formula of the NDZ for the active frequency drift method can be expressed as

$$\arctan \left[Q_{f0}{\omega }_0{{\displaystyle \frac{{(\frac{\Delta \omega }{{\omega }_0})}^2+\frac{2\Delta \omega }{{\omega }_0}+\Delta C\left(1+\frac{\Delta \omega }{{\omega }_0}\right)}{{\omega }_0+\Delta \omega }}}^2\right]={\displaystyle \frac{\pi }{2}}{c}_f$$

(26)

Here, ∆ω = ω − ω₀, ∆C = Cnorm − 1, where C = (1 + ∆C)Cres.

Since ∆ω is negligible compared to the ω itself, (21) can be expressed as

$$\arctan \left[Q_{f0}\left({\displaystyle \frac{2\Delta \omega }{{\omega }_0}}+\Delta C\right)\right]={\displaystyle \frac{\pi }{2}}{c}_f$$

(27)

Further derivation leads to the following expression:

$$\Delta C={\displaystyle \frac{\tan \left(\frac{\pi }{2}{c}_f\right)}{Q_{f0}}}-{\displaystyle \frac{2\Delta \omega }{{\omega }_0}}$$

(28)

Considering that the frequency fluctuation range does not exceed 0.5 Hz, it can be obtained that

$${\displaystyle \frac{\tan \left(\frac{\pi }{2}{c}_f\right)}{Q_{f0}}}-{\displaystyle \frac{1}{f_0}}+1<C_{norm}<{\displaystyle \frac{\tan \left(\frac{\pi }{2}{c}_f\right)}{Q_{f0}}}+{\displaystyle \frac{1}{f_0}}+1$$

(29)

According to (21), the non-detection zone expression of AFDPF with fixed positive feedback gain is

$${\displaystyle \frac{\tan \left(\frac{\pi }{2}{c}_{f0}+\frac{0.5\pi }{2}k\right)}{Q_{f0}}}-{\displaystyle \frac{1}{f_0}}+1<C_{norm}<{\displaystyle \frac{\tan \left(\frac{\pi }{2}{c}_{f0}-\frac{0.5\pi }{2}k\right)}{Q_{f0}}}+{\displaystyle \frac{1}{f_0}}+1$$

(30)

Similarly, according to (22), the non-detection zone expression of the method proposed in this paper is obtained as follows:

$${\displaystyle \frac{\tan \left(\frac{\pi }{2}{c}_{f0}+\frac{\sqrt{0.5}\pi }{2}k\right)}{Q_{f0}}}-{\displaystyle \frac{1}{f_0}}+1<C_{norm}<{\displaystyle \frac{\tan \left(\frac{\pi }{2}{c}_{f0}-\frac{\sqrt{0.5}\pi }{2}k\right)}{Q_{f0}}}+{\displaystyle \frac{1}{f_0}}+1$$

(31)

Based on the formulations in (30) and (31), the non-detection zone (NDZ) distributions of the two methods can be mapped separately with different k, and the c_f0 is equal to 0.005.

As shown in Figure 7 and Figure 8, increasing the value of k helps reduce the non-detection zone. Under the same value of k, the proposed method exhibits a smaller non-detection zone than the method with fixed positive feedback gain.

4. Simulation Verification

4.1. Islanding Detection Algorithm Verification

To verify the performance of the proposed islanding detection algorithm and compare it with the conventional active frequency drift algorithm with fixed positive feedback gain, simulations are conducted under the grid condition with a short-circuit ratio (SCR) of 10 in the presence of grid frequency fluctuations. At 0.3 s, the grid frequency steps abruptly from 50 Hz to 50.1 Hz. The load is selected as the RLC type. The value of c_f is set to 0.005, and the value of k is set to 0.01.

Combined with Figure 9 and Figure 10, it can be concluded that both algorithms are capable of detecting the islanding condition after its occurrence. However, comparing the injected frequency perturbations of the two algorithms after the frequency disturbance in Figure 11a and Figure 12a, it can be observed that the conventional AFDPF with fixed positive feedback gain exhibits a continuous and significant increase in the injected frequency perturbation following the frequency step. In contrast, the proposed method only shows a minor increase. This indicates that the proposed method has a certain level of immunity to normal grid frequency fluctuations. It can be observed from Figure 11b and Figure 12b that the two algorithms achieve nearly the same detection speed.

By comparing Figure 13a,b, it can be found that under normal grid-connected conditions, the grid-connected current harmonic content of the proposed method is nearly 1% lower than that of the conventional method. The proposed method effectively reduces the harmonic injection caused by islanding detection.

It can be seen from

Table 1. Comparison of the two methods.

Comparison Category	Traditional AFDPF	Proposed AFDPF
THD of current	3.98%	3.07%
NDZ	larger	smaller
Detection time	47 ms	45 ms

that the proposed method possesses obvious advantages over the conventional method, especially in terms of the non-detection zone and harmonic performance.

4.2. Inverter Control in Off-Grid Mode

To verify the anti-disturbance capability and dynamic response performance of the proposed control strategy in the off-grid mode, simulations are carried out under the working conditions of sudden load switching, nonlinear load access, and DC bus voltage fluctuation.

Figure 14 shows the inverter output waveforms when the load suddenly increases from 2500 W to 5000 W. It indicates that the inverter can quickly adapt to load variations and maintain a stable output voltage even under sudden load step changes. Figure 15 presents the operating performance of the inverter under nonlinear load conditions. In this paper, an uncontrolled rectifier bridge is adopted as the nonlinear load. It can be seen that the output voltage of the inverter is smooth with a low distortion rate. Figure 16 indicates that even when the DC bus voltage suddenly drops by 40 V, it has only a slight impact on the output voltage of the inverter. In addition, i_o, u_o, and u_load represent the output current of the inverter, the output voltage of the inverter, and the voltage across the resistive load on the output side of the uncontrolled rectifier, respectively.

According to the above simulation results, the controller in off-grid mode can well adapt to various disturbances and exhibits excellent anti-disturbance capability and dynamic response performance.

5. Experimental Verification

Based on a self-developed single-phase ESS microgrid inverter, the proposed grid-connected/off-grid dual-mode control and switching strategy is verified and analyzed. Table 1 presents the main parameters of the system. In the experiment, the inverter adopts SPWM modulation. The energy storage side is simulated by a DC power supply (IT6018C-1500-30, ITECH Electronics Co., Ltd., Nanjing, Jiangsu, China), and the controller is implemented based on the DSP chip TMS320F28069. A resistive load is adopted on the test platform. The nominal accuracy of the current sensor and the voltage sampling circuit are ±0.95% and 0.5%. The main parameters of the system are listed in

Table 2. Main parameters of the system.

Parameter	Value
AC filter inductor/mH	1.12
AC filter capacitor/μF	4.7
DC bus capacitor/μF	2250
DC bus voltage/V	380
Grid voltage (RMS)/V	220
Rated power/W	5000
Sampling frequency/kHz	20
Switching frequency/kHz	20
$\mathrm{Dead}\mathrm{time}/\mathsf{\mu }\mathrm{s}$	1.2

.

5.1. Grid-Connected Mode Operation

In the grid-connected mode, the grid-connected waveforms of the ESS inverter are presented in Figure 17. It can be observed that the inverter operates in the unity power factor mode with a stable system performance. The grid-connected current waveforms are smooth with low harmonic content, yielding high power quality. In addition, reference power adjustment tests under grid-connected mode were conducted. As can be seen from Figure 18, the grid-connected current varies smoothly without sudden changes.

5.2. Off-Grid Mode Operation

In off-grid mode, a resistive load is applied, and the corresponding operating waveforms are shown in Figure 19. It can be observed that the load voltage u_load and load current i_load are distortion-free with low harmonic content and maintain the same phase. In addition, Figure 19 also shows the loading test under off-grid mode. There is no current impact during the loading process, and the test proceeds very smoothly.

5.3. Flexible Grid-Connected/Off-Grid Mode Switching

This paper verifies the operation performance of the energy storage system (ESS) inverter during the grid-connected to off-grid switching process. The grid-connected/off-grid switching waveforms shown in Figure 20 demonstrate that the inverter can rapidly detect the occurrence of islanding under grid faults and initiate the grid-connected to off-grid switching, with no voltage or current overshoot during the entire process. The time from grid-connected shutdown to off-grid startup is 13 ms. Due to the adoption of the active frequency drift method, voltage and current distortion appear during the grid-connected to off-grid transition. However, the fast transient switching does not affect the normal operation of the inverter.

6. Conclusions

This paper designs corresponding control strategies for the grid-connected and off-grid modes of the inverter in energy storage microgrids, and proposes an improved mode switching algorithm. Simulation results demonstrate that the improved AFDPF strategy proposed in this paper has a smaller non-detection zone and lower current THD compared with the conventional AFDPF strategy, while its detection speed is not inferior to that of the traditional method with fixed positive feedback gain. Experimental results show that the energy storage inverter can operate stably in both grid-connected and off-grid modes, and the grid-connected/off-grid switching process is accurate and rapid, which verifies the effectiveness of the proposed control and flexible mode switching strategies for energy storage inverters. However, the applicability of the proposed method in multi-inverter scenarios has not been accurately verified yet. Further research is needed to improve the algorithm by considering the effect of the dilution effect in multi-inverter applications.