A Novel Control Strategy Based on -VSG for Inter-Face Converter in Hybrid Microgrid

Glossary/Nomenclature/Abbreviations

1  Introduction

The power system is establishing the “double high” development trend of “high proportion of renewable energy” and “high proportion of power electronic equipment” as a result of the growth of new energy generation and the evolution of “power electronics” of energy conversion equipment [1]. The use of HMG to address the issue of distributed energy consumption and absorption has grown in popularity to optimize the benefits of distributed power generation. HMG not only reduces the number of energy conversion devices but also has more flexibility than single-system MGs, which can be adapted to the actual needs and is an essential means to improve the utilization of resources in the context of “double-high” [2,3].

Many scholars have made significant contributions to the research of hybrid AC-DC microgrids. For example, literature [4] proposed a planning model to solve the optimal sizing problem of hybrid AC/DC microgrids by a novel GA/AC OPF algorithm, which provides a basis for designing bidirectional interface converters. In addition, research on toughness-driven modelling, operation, and evaluation of hybrid AC/DC microgrids is also of great significance, as it can help to cope better with extreme events and improve the toughness of microgrids [5]. In the HMG system, BIC coordinates the power between MGs, so the study and control of BIC is critical [6,7]. A new active sharing control based on droop control has been proposed to simulate the droop characteristics of a traditional synchronous generator, aiming to realize the power allocation and voltage and frequency regulation functions of the MG [8]. A normalized bidirectional droop control approach was presented for the power-sharing problem in HMGs. This method calculates the transmitted power flow by comparing the two normalized values [9,10]. A hierarchical control strategy for BICs is presented in the literature [11]. This strategy may maximize power interchange between the distribution grid and the MG while limiting the voltage variation brought on by droop control to a particular degree. However, the traditional droop control strategy can no longer actively provide inertia support for the system as distributed power sources become more prevalent in MGs. As a result, the dynamic characteristics of frequency and voltage deteriorate, endangering the stability of the HMG system and failing to fully utilize the potential of BIC to enhance the stability of the HMG system [12,13].

To solve the lack of inertia problem, the virtual synchronous generator (VSG) concept was developed [14]. The VSG technique gives inertia to the power electronic converter by simulating the equations of motion of a traditional synchronous generator’s rotor to enhance the system’s stability. Some scholars have used VSG control as the primary control scheme to improve the frequency transient performance. Usually, VSG control is employed to provide inertia for the AC bus frequency [15]. However, since the traditional VSG technique cannot realize the bidirectional flow of power, literature [16] also proposes an improved VSG control strategy for BICs, which establishes the relationship between VSG active power, voltage, and frequency. The previously mentioned control system disregards the dynamic properties of the DC voltage and only offers inertial support for the AC frequency. The BIC control must consider the stability of both the DC and AC sides to stabilize the MG system. A DC virtual voltage control approach based on VSG control was described in the literature [17] to support the DC bus voltage inertia and realize a bidirectional energy flow during rapid changes in load. However, the previously mentioned control approach aims to enhance one side of the converter’s transient performance by providing a steady source on the other side. Literature [18] proposes a virtual inertia control approach for BIC to limit the power transfer of BIC during the dynamic process, which can restrict the drastic fluctuations to one side of the subgrid, but it cannot play the role of inertia support for the opposite side of the MG. Literature [19] proposes an integrated inertia control approach to improve the dynamic characteristics of HMGs. Still, it relies too much on communication to realize decentralized control and needs to clarify the magnitude of inertia support between the two subgrids. In terms of improving the dynamic response of the BIC through virtual inertia parameters, in the literature [20], the traditional DC electric potential equation is generalized. In contrast, the dynamic response of the BIC is improved by adding a virtual inductor to provide inertia for the system. However, this approach is a current-based control and cannot provide sufficient voltage and frequency support to the HMG during islanding operation.

In conclusion, the control requirements for BICs face many new challenges. Table 1 lists the current mainstream control strategies for BICs. In view of the shortcomings of the above studies, this paper considers the inertia demand on both sides of the AC and DC and adopts π-VSG control to provide voltage and frequency support for the AC and DC buses and inertia for the AC and DC subgrids.

To address the bidirectional power transfer requirements, inertia deficit, and stability problems of HMGs, this paper improves the electric potential equation of a traditional DC motor and realizes power sharing and distribution using virtual resistors. For BIC, a π-VSG control is suggested. Inertia for both AC and DC subgrids, as well as voltage and frequency support for AC and DC buses, can be obtained using this control scheme. It successfully enhances the system’s anti-interference properties while lessening the effects of abrupt changes in load disturbances and enhancing the HMG’s stability.

This paper proposes a BIC control strategy based on π-VSG with the following main contributions:

(1) Innovative power allocation and bi-directional flow realization: The bi-directional power flow between subgrids is successfully realized by implementing virtual resistors for power sharing and allocation. Compared with other control techniques, this method only changes the external control loop of the converter without mode switching, which reduces the power loss and instability factors and effectively solves the deficiencies of the traditional control strategy in terms of the flexibility and stability of power allocation.

(2) Comprehensive voltage and frequency support and inertia provision: The proposed strategy can provide voltage and frequency support for the AC and DC buses and inertia for the AC and DC subgrids. This feature enables the AC/DC subgrid to share the disturbance effects by adjusting the virtual capacitance during sudden load changes, which improves the situation in which the traditional control strategy cannot consider the dynamic performance of both sides simultaneously.

(3) Improved dynamic response and anti-disturbance performance: Under load fluctuation, the π-VSG control effectively enhances the anti-disturbance of the AC frequency and DC voltage in the HMG system, improves system stability, meets the power-sharing control objective between the AC and DC subgrids, and overcomes the problem of the traditional control strategy’s poor dynamic response to load change.

To confirm the efficacy of this control approach, a standard HMG system was built using PSCAD/EMTDC simulation software for this research.

2  π-VSG Control

This paper mainly discusses the BIC control of HMG in island mode. Fig. 1 shows the structure of AC-DC HMG. In the HMG, the offsets of AC frequency and DC bus voltage are the main metrics reflecting the amount of active power inequality in AC and DC MGs, respectively.

Figure 1: Structure diagram of HMG

Droop control has been used in both AC and DC MGs to balance the distribution of AC and DC active loads [21]. Traditional droop control enables power sharing and provides voltage and frequency support in HMGs, but it suffers from fast response and lack of inertia [22]. Virtual resistors and inductors have been proposed in the literature [20] for power distribution and inertia control via BIC-based generalized DC motor electromotive force (G-DCEMF) control. In Fig. 2, the G-DCEMF control model is displayed.

Figure 2: G-DCEMF control model

The G-DCEMF control equations are as follows:

ΔUdc=RaΔI+LadΔIdt+KωΔω(1)

where Ra is the virtual resistance, Kω is the electromotive force coefficient, ΔUdc is the DC voltage deviation, Δω is the AC frequency deviation, and ΔI is the deviation of the current flowing through the BIC.

Neglecting the virtual inductance La, the power-sharing of the G-DCEMF control for the BIC can be expressed as

ΔU=RaΔI+KωΔω(2)

In (2), Kω can be determined by

Kω=MuMω(3)

The values of Mu and Mω represent the permissible ranges for fluctuations in Udc and ω, respectively.

The active power reference value Pref of BIC can be obtained by

Pref=(UdcN+ΔUdc)(I0+ΔIbic)≈UdcNΔUdc−KωΔωRa(4)

In the proposed G-DCEMF control, SN should be expressed as

SN=|Pref|max=UdcNMu+KωMωRa(5)

As a result, the BIC’s virtual resistance Ra can be calculated using

Ra=UdcN2MuSN=UdcN2KωMωSN(6)

Virtual capacitors are more suitable for voltage-based control, while virtual inductors used in G-DCEMF control are more suitable for current-based control. To realize sufficient voltage and frequency support for the HMG during islanding operation, virtual inductance in the G-DCEMF is converted to virtual capacitance, thus proposing π-VSG control.

2.1 Active Power Loop Control of BIC

The mechanical motion equation of VSG is shown in (7).

Jωdωdt=Pm−Pe(7)

where J is moment of inertia, Pm is mechanical power, and Pe is electromagnetic power.

For better integration with the G-DCEMF control, Eq. (7) can be transformed into

CωdUωdt=Pm−PeUω=Im−Ie(8)

where

Uω=KωωCω=J/Kω2(9)

where Uω is the virtual voltage of the AC frequency converted to the DC side, and Cω is the virtual capacitor on the AC side.

In traditional VSG control, the dynamic response of AC frequency is considered, but the oscillation of DC voltage has not been considered. Consequently, a DC voltage control mode similar to (8) is proposed as

CudUdcdt=Iin−Iout(10)

where Cu is the virtual capacitor on the DC side.

Likewise, taking into account the governing equation’s initial state, a π-VSG control model applied to BIC is proposed based on (2), (8), and (10), as shown in Fig. 3.

Figure 3: BIC π-VSG control model

Based on Fig. 3, Eq. (11) can be obtained.

ΔUdc=RaΔIbic+ΔUω

CudΔUdcdt=ΔIu−ΔIbic

CωdΔUωdt=ΔIbic−ΔIω(11)

where

ΔUω=KωΔω

ΔIu≈ΔIω≈ΔPbicUdcN=Pbic−P0UdcN(12)

Combining (11) and (12), Eq. (13) can be obtained via Laplace transform.

Cω2sΔUω−Cu2sΔUdc=ΔUdc−ΔUωRa−ΔPbicUdcN(13)

The BIC transmission power is expressed as Eq. (14), which consists of a steady state component and a transient component. The transient component is the actively transmitted inertial power ΔPvir. The frequency will fall below the rate when there is a sudden rise in the AC load without an additional power supply. To give the AC frequency priority support, the BIC sends the inertial power ΔPvir to the AC subgrid. When the DC load grows significantly and no more power input is available, the BIC transfers inertial power ΔPvir to the DC subgrid to offer prioritised DC voltage support.

Pbic=UdcN(ΔUdc−ΔUωRa⏟steady-state component+Cu2sΔUdc−Cω2sΔUω⏟transient component)ΔPvir=UdcN(Cu2sΔUdc−Cω2sΔUω)(14)

And because

ω=sθ(15)

where θ is the phase angle.

The control block diagram of the active loop of BIC can be obtained, as shown in Fig. 4.

Figure 4: BIC π-VSG active loop control model

2.2 Reactive Power Loop Control of BIC

The reactive power loop of the BIC adopts reactive power-voltage (Q-V) droop control, and Eq. (16) is the excitation control of VSG.

Em=1sKQ[Dq(Vn−V)+(Q0−Qbic)](16)

where Em is the AC voltage amplitude reference value, KQ is the reactive inertia coefficient, Dq is the droop coefficient of Q-V control, Vn and V are the AC voltage amplitude and actual values, respectively, and Q0 and Qbic are the BIC reactive power initial and actual values, respectively.

The frequency and phase signal output by the active loop and the voltage amplitude signal output by the reactive loop can be synthesized into the reference voltage eabc by

{ea=Emsin⁡θeb=Emsin⁡(θ−2π/3)ec=Em(sin⁡θ+2π/3)(17)

2.3 Voltage and Current Double Closed-Loop Control of BIC

Fig. 5 is the voltage-current double closed-loop control diagram. When the BIC needs to ensure the stability of the HMG, the actual value of the BIC power transmission and the DC side bus voltage are synthesized to obtain the voltage reference value after passing through the π-VSG control link together. After the voltage-current loop and SPWM control, the switching signal is obtained to realize the stabilization and control of the voltage and frequency of the HMG.

Figure 5: Voltage and current double closed-loop control model

The primary circuit, the π-VSG control, and the voltage-current double closed-loop control together form the overall π-VSG control model of the BIC. Fig. 6 is the π-VSG overall control block diagram of BIC in HMG.

Figure 6: BIC π-VSG overall control model

3  Stability Analysis

For the proposed π-VSG control, a small signal model is established, and the dynamic responses of the AC frequency and DC voltage as the load power varies are determined. Below is the active power loop small signal model analysis with a single BIC.

3.1 Small Signal Analysis

In the closed-loop control system of the BIC, the underlying voltage-current dual closed-loop control responds very rapidly with negligible response time compared to the response time of the π-VSG control. Therefore, only the real-time tracking performance of the voltage-current double closed-loop on the voltage and current reference values are considered in the small-signal modelling, as shown in Fig. 5, the BIC takes udref and uqref. As input, and finally realizes the control of converter output voltage ud and uq. That is, ud = udref and uq = uqref always hold during fast tracking, so the transfer function of the voltage-current double-closed loop can be viewed as a constant 1.

The BIC is comparable to a voltage source in series with an output impedance, whose reactance value is generally much greater than the resistance value. Thus, the BIC’s active power output may be expressed as

Pbic=3EUXsin⁡δ=KPδsin⁡δ(18)

where KPδ is a constant coefficient, U is the output voltage amplitude, E is the amplitude of the output electromotive force of BIC, X is BIC equivalent output impedance, and δ, be expressed by (19), is the phase difference between the output electromotive force and the output voltage.

δ=∫(ω−ωg)dt(19)

where ωg is the angular frequency of the output voltage.

The small signal model is formulated based on (13), (18), and (19) and eliminates the steady-state quantity. Due to sin δ ≈ δ and cos δ ≈ 1, the small signal model can be gotten as

Cω2sKω(ω∧−ωN∧)−Cu2s(Udc∧−UdcN∧)=(Udc∧−UdcN∧)−Kω(ω∧−ωN∧)Ra−Pbic∧−P0∧UdcN

Pbic∧=KPδδ∧

ω∧−ωg∧=sδ∧(20)

In the DC subgrid, ignoring the small signal disturbance of the DC load, Eq. (21) can be obtained as

Pbic∧=−kdcUdc∧(21)

where kdc is the P-U droop coefficient of the DC subgrid.

According to (20) and (21), the active loop small signal model of BIC π-VSG control can be derived, as shown in Fig. 7.

Figure 7: Active loop small signal model of BIC π-VSG control

In the small signal model, the small signal disturbances of UdcN, ωN and ωg can be set to 0, and then the closed-loop transfer function of active power can be obtained as

Pbic∧(s)P0∧(s)=kdcUdcNCωKωkdc2KPδs2+(Cu2+KωkdcRaKPδ)s+(1Ra+kdcUdcN)(22)

Assuming the denominator is zero, Eq. (22) can be transformed into

Cu12sCωKωkdc2KPδs2+KωkdcRaKPδs+1Ra+kdcUdcN=−1(23)

The left side of (18) can be regarded as the equivalent open-loop transfer function, where Cu is the root locus gain. When 1/Cω ranges from 0 to infinity, the pole distribution of the equivalent open-loop transfer function on the s plane is displayed in Fig. 8. It is clear that regardless of the value of Cω, the pole of the open-loop transfer function is always on the left half axis of the s plane. Beginning at the pole of the open-loop transfer function and ending at zero is the root locus of the closed-loop transfer function. There is a root locus that ends at negative infinity since the equivalent open-loop transfer function has two poles and one zero with a value of 0. In the s plane, the pole distribution of the Cu closed-loop transfer function from 0 to infinity is displayed in Fig. 9 for Cω values of 0.1, 1, and 10. So, in the π-VSG control strategy’s small signal model, the closed-loop root locus of active power is always in the left half plane, regardless of the values of Cω and Cu. This suggests that the control system is always stable under small disturbances and that variations in Cu and Cω only impact the small signal system’s damping state.

Figure 8: The pole distribution of the equivalent open-loop transfer function on the s plane

Figure 9: The pole distribution of the closed-loop transfer function on the s plane

3.2 Dynamic Response of AC Frequency and DC Voltage

In HMG, the load power variation ΔPL satisfies (24).

ΔPL=−kacΔωac_L−kdcΔUdc_L(24)

where kac is the P-ω droop coefficient of the AC subgrid, Δωac_L and ΔUdc_L are AC frequency variation and DC voltage variation caused by ΔPL, respectively.

The load power variation in the AC subgrid ΔPLac satisfies (25).

ΔPLac=−kacΔωac_Lac+ΔPbic_Lac=−kacΔωac_Lac−kdcΔUdc_Lac(25)

where ΔPi_Lac is the BIC power variation caused by ΔPLac.

In combination with (13) and (25), the AC frequency variation Δωac_Lac and the DC voltage variation ΔUdc_Lac caused by ΔPLac can be expressed as

Δωac_Lac=−bω0s+bω1+kdc/UdcNa0s+a1ΔPLac

ΔUdc_Lac=−bu0s+bu1a0s+a1ΔPLac(26)

where

a0=(Cukac+CωKωkdc)/2

a1=(kac+Kωkdc)/Ra+kackdc/UdcN

bω0=Cu/2,bω1=1/Ra

bu0=CωKω/2,bu1=Kω/Ra(27)

Similarly, the load power variation in the DC subgrid ΔPLdc satisfies (28).

ΔPLdc=−ΔPbic_Ldc−kdcΔUdc_Ldc=−kacΔωac_Ldc−kdcΔUdc_Ldc(28)

where ΔPbic_Ldc is the BIC power variation caused by ΔPLdc.

Hence, the AC frequency variation Δωac_Ldc and DC voltage variation ΔUdc_Ldc caused by ΔPLdc are

Δωac_Ldc=−bω0s+bω1a0s+a1ΔPLdc

ΔUdc_Ldc=−bu0s+bu1+kac/UdcNa0s+a1ΔPLdc(29)

As shown, the values of Cω and Cu only influence the dynamic response, but the value of Ra influences the steady-state values of AC frequency and DC voltage, which are established by (6).

Ignoring the different terms between (26) and (29), the analysis can be simplified to

Δωac_L=−(bω0a0+−a1bω0/a0+bω1a0s+a1)ΔPL

ΔUdc_L=−(bu0a0+−a1bu0/a0+bu1a0s+a1)ΔPL(30)

It is evident from (30) that in the event of a sudden change in the load power, both the AC frequency and the DC voltage will likewise change quickly. However, these changes will eventually recover to the new steady-state operation point. The increase of Cu will lead to the rise of bω0/a0 and the decrease of bu0/a0, which means that the sudden change of AC frequency will increase and the sudden change of DC voltage will decrease. When Cω increases, the AC frequency mutation decreases, and the DC voltage mutation increases. When Cu is 0, the AC frequency will change slowly, similar to the traditional VSG control. However, the sudden change of DC voltage reaches the maximum, which means that the DC bus voltage entirely bears the impact of the load power fluctuation. The proposed π-VSG control can make AC frequency and DC voltage jointly withstand load disruptions. The whole HMG will react when a load disturbance occurs in a single subgrid, enhancing that subgrid’s anti-interference capabilities.

According to Fig. 7, the closed-loop transfer function between Δω and Pbic can be obtained.

ΔωPbic=2KPδsUdcNCωKωs2+(2UdcNKω/Ra)s+1(31)

According to Fig. 7, the closed-loop transfer function between ΔUdc and Pbic can be obtained.

ΔUdcPbic=−1UdcNCωKωkdc2KPδs2+(Cu2+KωkdcRaKPδ)s+(1Ra+kdcUdcN)(32)

Fig. 10 gives the output power step response curves caused by the change of virtual capacitance on the AC and DC sides. As shown in Fig. 10a, when the virtual capacitance Cu on the DC side is kept constant, as Cω increases, it will bring some inertia to the system, but at the cost of an increase in the system’s overshoot; Fig. 10b shows that, by fixing the value of the virtual capacitance Cω on the AC side, the DC voltage overshoot will decrease as Cu increases, and at the same time accelerates the system back to a steady state.

Figure 10: Step response curve of output power Pbic varying with control parameters

Furthermore, Mω0 and Mu0 are the maximum allowable fluctuation ranges of Udc and ω, respectively. The inequalities between Cu and Cω should be

bω0a0ΔPL≤bω0a0kacMω≤Mω0

bu0a0ΔPL≤bu0a0kdcMu≤Mu0(33)

If both AC frequency and DC voltage change rate must satisfy the conditions listed in (34) correspondingly.

|dωacdt|≤Mω′

|dUdcdt|≤Mu′(34)

where Mω′ and Mu′ are the maximum AC frequency and DC voltage change rate values, respectively.

Then, the values of Cu and Cω should also meet (35).

d|ΔUdc|dt|t=0=a1a0|−bu0a0+bu1a1|ΔPL≤|a0bu1−a1bu0|a02kdcMu≤Mu′

d|Δωac|dt|t=0=a1a0|−bω0a0+bω1a1|ΔPL≤|a0bω1−a1bω0|a02kacMω≤Mω′(35)

It can be seen from the previous analysis that the values of Cu and Cω not only provide inertia for the system but also affect the sudden change of AC frequency and DC voltage caused by ΔPL. The increase in Cu will lead to the sudden growth of the abrupt value of AC frequency and the sudden decrease of the abrupt value of DC voltage. The increase in Cω will lead to the sudden decrease of the abrupt value of AC frequency and the sudden increase of DC voltage. In general, the sudden change of DC bus voltage often has less impact on the subgrid than that of AC bus frequency.

4  Simulation Results

To test the efficacy of π-VSG control, an AC/DC HMG simulation model for island operation is constructed using PSCAD/EMTDC simulation software. Fig. 6 displays the BIC control model, and the DC and AC subgrids use P -U and P-ω droop control, respectively. The simulation parameters are listed in Table 2.

According to the former analysis, when Cu = 0 and Cω = 0, the BIC is under bidirectional droop control. Therefore, to compare different control modes more intuitively and keep other parameters unchanged in this paper, bidirectional droop control is simulated by setting Cu and Cω to 0. In the proposed π-VSG control, Cu is set to 0.3F, and Cω is set to 1F.

1) Inverter mode

At t = 2 s, the AC-side load increases by 100 kW; at t = 4 s, the AC-side load decreases by 100 kW. Fig. 11 shows the AC load change simulation diagrams containing the DC voltage, AC frequency, and transmitted active power, as well as the transmitted virtual inertia power waveforms under the bidirectional droop control and the π-VSG control. The blue line indicates that the bidirectional droop control strategy lacks inertia, has no inertial power transfer, responds quickly, and immediately affects the DC-side voltage with significant sudden changes. The red line represents the π-VSG control strategy, which increases the AC frequency and DC voltage inertia and actively transmits the inertial power ΔPvir during the abrupt load change. This is achieved by introducing the virtual parameters Cω and Cu, which improve the dynamic response characteristics of the AC and DC sides. Fig. 11 shows that the system’s steady-state values are the same for both controls, indicating that the π-VSG control exhibits the droop characteristic when it reaches the steady state. However, compared to the bidirectional droop control, the π-VSG control has minor AC frequency and DC voltage fluctuations, and the response is slower with the inertia. Combined with Table 3, it can be seen that the π-VSG control suppresses the overshooting of power, voltage and frequency and actively transfers the inertial power. This means that sudden large fluctuations in power can be avoided during system operation. Meanwhile, its power adjustment time increase possesses corresponding inertia, and the adjustment process is smooth. It does not cause system oscillation or instability, providing a reliable power conversion process.

Figure 11: DC bus voltage, BIC active power, AC bus angular frequency waveforms, and virtual inertia power waveforms transferred between subgrids when 100 kW AC load input to the AC subgrid

2) Rectifier mode

Similarly, at t = 2 s, the DC-side load increases by 100 kW; at t = 4 s, the DC-side load decreases by 100 kW. Fig. 12 shows the DC load change simulation diagrams containing the DC voltage, AC frequency, and transmitted active power, as well as the transmitted virtual inertia power waveforms under the bi-directional droop control and π-VSG control. The maximum fluctuation of AC frequency and DC voltage is about 1 rad/s and 20 V during the dynamic process under bidirectional droop control. However, when using the π-VSG control, the voltage and frequency adjust dynamically throughout 0.4 and 0.3 s to reach a new steady state, which is slower than the dynamic response of bidirectional droop control. The AC frequency gradually decreases in the dynamic process, and the fluctuation in the dynamic process is smaller than using bidirectional droop control. The inverter and rectifier simulations show that when the BIC is controlled with π-VSG, the whole HMG can still distribute the power shortfall of any subgrid. Combined with Table 4, it can be seen that the π-VSG control in the rectifier mode can still suppress the power, voltage and frequency overshoots, actively transfer the inertia power, and fully utilize the potential of the BIC to stabilize the HMG system.

Figure 12: DC bus voltage, BIC active power, AC bus angular frequency waveforms, and virtual inertia power waveforms transferred between subgrids when 100 kW DC load input to the DC subgrid

3) Mode transition

At t = 2 s, a DC load of 50 kW is input to the DC subgrid. At t = 3 s, a 100 kW AC load is input to the AC subgrid. At 2~3 s, the BIC operates in rectifier mode, and the HMG shares the sudden DC load disturbance through the BIC. At 3~4.5 s, the AC subgrid is heavily loaded, and the BIC operates in inverter mode. The improvement in AC frequency and DC voltage inertia can also be realized during the mode-switching process. At t = 4.5 s, the AC and DC loads are removed, and after about 0.5 s, the system returns to the rated state, and the power transfer is 0. According to Fig. 13, it can be seen that the BIC can flexibly adjust the operation mode according to the changes of HMG measured loads to satisfy the requirement of the BIC’s power bidirectional transfer.

Figure 13: BIC mode transition simulation diagram

4) Power distribution

Meanwhile, to verify the power distribution ability of bidirectional virtual inertia augmentation control, it is known that the power transfer of BIC is related to virtual resistance. Setting the virtual resistance value ratio as R1:R2:R3 = 1:2:3, a 100 kW DC load is put in at t = 2 s to verify the power waveforms at different virtual resistance values. Set the ratio of virtual resistance values as R1:R2:R3 = 1:2:3, and at t = 2 s, put in 100 kW AC load to verify the power waveforms at different virtual resistance values. From Fig. 14, the BIC transmission power ratio is 3:2:1, and a flexible proportional transmission power distribution is realized.

Figure 14: BIC power distribution simulation diagram

In summary, the proposed BIC π-VSG control can provide inertia for HMG to reduce the impact of sudden load changes on the system’s stable operation. The virtual resistors enable flexible power distribution for BICs. The virtual inertia parameters Cω and Cu do not influence the steady-state performance and only optimize the transient performance. The transfer of virtual inertial power through BIC provides inertial support for the DC voltage and AC frequency, improving the HMG system’s immunity performance.

5  Conclusion

The transfer of virtual inertia between subgrids is a way to improve the stability of the HMG system by balancing the individual subgrids through BIC control. This approach enables and improves the transient performance on both sides of the system. So, in this paper, the π-VSG control method of BIC in HMG is proposed, and the following conclusions are obtained through example simulations:

(1) BIC’s power-sharing can be flexibly controlled by using virtual resistance, which facilitates the optimization of power transfer in the islanded HMG system.

(2) The π-VSG control can actively transfer inertial power to improve the dynamic response of AC frequency and DC voltage and adjust the power flow according to the load fluctuation of AC and DC subgrids, improving immunity and stability compared with the droop control.

(3) The power distribution and dynamic response of the BIC can be adapted to different operating modes. The virtual inertia parameters Cω and Cu provide inertial support for AC and DC subgrids without affecting the steady-state values of the control system.

Meanwhile, future work and research directions are as follows:

(1) Parameter optimization research: further explore the optimization methods of virtual capacitance Cω and Cu, virtual resistance Ra to adapt to more complex operating conditions.

(2) Research on parallel operation of multiple machines: for parallel operation of multiple machines, in-depth research on their interaction and coordination control methods to ensure the stability and reliability of the system in large-scale applications.

(3) Combination with other control strategies: Consider combining the π-VSG control strategy with other advanced control technologies (e.g., model predictive control, distributed cooperative control, etc.) to give full play to their respective advantages.

Acknowledgement: None.

Funding Statement: This research was funded by “The Fourth Phase of 2022 Advantage Discipline Engineering-Control Science and Engineering”, grant number 4013000063.

Author Contributions: The authors confirm their contribution to the paper as follows: study conception and design: Dongyang Yang; data collection: Kai Shi; analysis and interpretation of results: Dongyang Yang, Kai Shi; draft manuscript preparation: Dongyang Yang. All authors reviewed the results and approved the final version of the manuscript.

Availability of Data and Materials: The authors confirm that the data used in this study are available on request.

Ethics Approval: Not applicable.

Conflicts of Interest: The authors declare no conflicts of interest to report regarding the present study.

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