Portal de Periódicos da CAPES

Modified virtual inertia control method of VSG strategy with improved transient response and power‐supporting capability

2019; Institution of Engineering and Technology; Volume: 12; Issue: 12 Linguagem: Inglês

10.1049/iet-pel.2019.0099

1755-4543

Yawei Wang, Bangyin Liu, Shanxu Duan,

Smart Grid Energy Management

IET Power ElectronicsVolume 12, Issue 12 p. 3178-3184 Research ArticleFree Access Modified virtual inertia control method of VSG strategy with improved transient response and power-supporting capability Yawei Wang, State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 1037, Luoyv Road, Wuhan, People's Republic of ChinaSearch for more papers by this authorBangyin Liu, Corresponding Author lby@hust.edu.cn orcid.org/0000-0002-9137-4598 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 1037, Luoyv Road, Wuhan, People's Republic of ChinaSearch for more papers by this authorShanxu Duan, State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 1037, Luoyv Road, Wuhan, People's Republic of ChinaSearch for more papers by this author Yawei Wang, State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 1037, Luoyv Road, Wuhan, People's Republic of ChinaSearch for more papers by this authorBangyin Liu, Corresponding Author lby@hust.edu.cn orcid.org/0000-0002-9137-4598 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 1037, Luoyv Road, Wuhan, People's Republic of ChinaSearch for more papers by this authorShanxu Duan, State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 1037, Luoyv Road, Wuhan, People's Republic of ChinaSearch for more papers by this author First published: 11 September 2019 https://doi.org/10.1049/iet-pel.2019.0099Citations: 9AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract Virtual synchronous generator (VSG) controlled grid-tied converters could increase power overshoot and oscillation if real power reference disturbance (PRD) occurs. Existing VSG methods can mitigate the power oscillations, but they may reduce the supporting capability of grid contingency. To cope with the issue, a modified virtual inertia control method of VSG strategy is proposed. The proposed modified VSG method introduces two frequencies of point of common coupling into the virtual inertia control. The estimated frequency is used to mitigate the power oscillations and the measured frequency aims to provide extra power supporting. The formulated parameters design principles are given according to the transient characteristics. Stability analysis of power and frequency response is carried out to evaluate the proposed method. Besides, the transient power and frequency response of the PRD case and grid-frequency disturbance (GFD) case are studied. The power overshoot of the proposed modified VSG method decreases by 52.5% under the PRD case and the power support peak increases by 34.3% under the GFD case. Experimental results show that the transient performance of the proposed modified VSG controlled grid-tied converters is improved. 1 Introduction In recent years, the utilisation of distributed renewable energy has received extensive attention, and a large number of distributed renewable power sources are connected to the grid through grid-tied converters [1]. With the increase in the penetration of intermittent renewable energy, grid frequency stability is severely threatened. In combination with energy-storage devices, the issues of power fluctuation and grid frequency deviation are resolved [2]. However, compared with the synchronous generators, the equivalent inertia of grid-tied converters is small. As a result, it is difficult for these grid-tied converters to provide inertia support for high penetration grid. It is popular to introduce virtual inertia control into the grid-tied converters [3-5]. One of the virtual inertia emulation strategies is using the physical inertia of the DC-link capacitor of grid-tied converters. Various kinds of energy storage units can be employed as the DC power source of the virtual inertia control [6]. However, the implementation of this method needs the grid-tied converters to cooperate with the energy storage units, which increases system complexity. Another strategy is to emulate the swing equation of synchronous generators. Some scholars proposed the concept of virtual synchronisation [7] and a variety of virtual synchronous generator (VSG) or virtual synchronous machine (VSM) strategies were presented [8-11]. Especially the voltage-type strategies not only provide power for standalone operation, but also enhance the frequency stability for grid-tied application [10, 11]. Besides, the equivalence of droop and VSG strategies was demonstrated to provide virtual inertia during load transitions [12, 13]. If the power reference disturbance (PRD) occurs, the rates of change of frequency (ROCOF) of droop and VSG are both slowed down. However, the introduction of virtual inertia upgrades the mathematical model order of power control. The real output power of VSG tends to have a larger power overshoot and oscillation, which degrades the transient power performance [13]. In addition, the power oscillation increases unnecessary power loss and decreases the lifetime of energy storages. In response to the issue of the transient real power optimisation (RPO), the existing research studies mainly include the following solutions. The inertia droop strategy was proposed to improve the transient power characteristics [14]. The choice of damping factor needs to balance the transient power performance and the high frequency gain of the inertia droop controller. The generalised droop strategy [13] is effective in improving the equivalent damping and enhancing the transient power performance. More parameters of the power controller yield better performance, but the parameters' design becomes more complicated. Alternative moment of inertia strategies were proposed in [15-17], which change the inertia constant and/or damping factor according to the frequency deviation and/or the ROCOF scheduled or adaptively. Modified droop coefficient strategies were proposed in [18, 19]. Both of these variable parameters could relieve the PRD oscillation issue, but the intrinsically non-linear characteristic may negatively influence the stability of the power system [6]. The band pass damping method was introduced in [20], which is similar to the damping method with integrated grid frequency [21]. It was beneficial to eliminate the problem of the damping power changing with the difference of grid frequency and the rated frequency (50/60 Hz), but the transient power performance of these methods is not improved apparently. Although these methods were able to optimise the power performance and some of them could relieve the issue of the transient power overshoot and oscillation, the grid-supporting capability of grid-frequency disturbance (GFD) is influenced. In the event of grid disturbances or faults, the grid frequency will change with the influence of the system inertia and damping. For the VSG-controlled grid-tied converters, extra power should be provided or absorbed according to the change of grid frequency. The existing transient RPO methods weakened the inertia support when the grid frequency changes. The methods of frequency feedforward of PCC voltage [22-25] are effective to provide virtual inertia power. The addition of extra virtual inertia could promote the grid-supporting capability. The virtual rotor strategies [26, 27] were proposed to increase the damping effect of the extra virtual inertia. However, fewer VSG methods considering the transient power optimisation and the grid-supporting capability for the voltage-controlled grid-tied converters were proposed. Besides, low-pass filter is usually used in the virtual inertia control to imitate the dynamic performance of storage devices. However, little consideration has been taken to investigate the damping effect of the filter time constant. In this paper, a modified VSG (VSG-MD) method for voltage-controlled grid-tied converters is proposed based on the estimated PCC frequency and the measured PCC frequency. A formulated parameters design method is proposed based on the transient performance, such as the maximum of the damping power, the transient frequency deviation and the pre-set phase margin. The proposed method not only provides enough inertia to suppress VSG frequency deviation of the PRD response, but also ensures suitable damping to decrease the power overshoot and oscillation. In addition, the grid-supporting capability of GFD response is greatly improved. The rest of this paper is organised as follows. The topology and strategy of VSG controlled grid-tied converters is introduced in Section 2. In Section 3, the modified VSG-MD strategy is proposed. In Section 4, the formulated parameters design method is proposed. Experimental results and conclusion are given in Sections 5 and 6, respectively. 2 Transient response of the traditional VSG method The diagram of VSG topology and control strategy is shown in Fig. 1. The power stage is a typical two-level three-phase converter. DC link voltage vDC, AC side output voltage vAB and vBC, AC side inductor current iLA and iLB and output current ioA and ioB are measured for voltage and power control. Fig. 1Open in figure viewerPowerPoint VSG topology and control strategy Instantaneous power calculation is based on decoupled voltage and current components in αβ frame. Although low-pass filters are added in the voltage and current measurement process, there are some low-frequency harmonic components in the result of power calculation. Thus, it is better to add a group of notch filters to improve the power-calculation accuracy. Virtual impedance is configured to decouple real power and reactive power instead of bulky physical inductor. Thus, a virtual output inductor with fixed gain is implemented in the decoupled αβ frame. LV denotes the virtual inductance. The inner voltage and the inner current controller are based on proportional resonance controllers [28]. Conventionally, VSG strategy is implemented based on the imitation of swing equation. VSG power controller is shown by (1), where J is the virtual moment of inertia and D is the damping factor. (1)Reactive power control is based on droop method. As shown in Fig. 1, vdref and vqref are the targets of phase voltages in the dq frame, respectively, E0 is the phase voltage base value, and kq is the coefficient of droop controller. Qref and qo are the reference and the instantaneous value of output reactive power, respectively. The small signal model of the simplified real power control loop is shown in Fig. 2. KP = 3EVcos(δ0)/X ≃ 3EV/X. E∠δ is the voltage phasor of grid-tied equivalent source. is the PCC voltage phasor. X = ωref (Lf + LV), which is the equivalent of output impedance. Fig. 2Open in figure viewerPowerPoint Small signal model of the simplified real power control diagram According to the small signal model shown in Fig. 2, the closed loop transfer functions (CLTFs) of power and frequency response are evaluated asfollows: (2)The PRD step responses of 0.125 p.u. rated capacity and the GFD step response of −0.628 rad/s are shown in Fig. 3, and the VSG parameters are shown in Table 1. It can be seen that the PRD power peak decreases with decreasing virtual inertia time constant τJ, as shown in Fig. 3a, and decreases with the increase in damping factor D, as shown in Fig. 3b. However, as shown in Fig. 3c, decreasing inertia time constant will contribute to a large VSG frequency oscillation peak and a further increase in PCC frequency oscillation. The influence of the increasing damping factor D on GFD power response is shown in Fig. 3d. A large damping factor contributes to the increase in the transient output power in response to the PCC frequency disturbance, which is beneficial to grid-supporting. Whereas, the power control steady error is greatly increased with the increase in damping factor, which in fact increases the VSG damping power (Table 1). Table 1. VSG parameters Symbol Quantity Value E, V AC voltage in RMS 220 V SR rated capacity 6 kVA ωref rated frequency 100π rad/s Lf filter inductance 0.05 p.u. LV virtual inductance 0.75 p.u. Lg grid impedance 0.1 p.u. kvp voltage proportional parameter 0.06978 kvr voltage resonant parameter 0.585 kip current proportional parameter 5.376 kir current resonant parameter 0.02 Fig. 3Open in figure viewerPowerPoint Power and frequency response of PRD and GFD, and τJ = Jωref / D (a) PRD power response (Cpp(s) in (2)) with various τJ, (b) PRD power response (Cpp(s) in (2)) with various D, (c) PRD frequency response (Cpω(s) in (2)) with various τJ, (d) GFD power response (Cωp(s) in (2)) with various D Based on the above analysis, increasing the damping factor D and reducing the time constant τJ are beneficial to promoting the VSG performance of PRD power response. However, a limited damping power reserve restricts the upper limit of the damping factor. Therefore, it is hard to use a larger virtual inertia constant to suppress the frequency variations. Above all, the PRD response of the traditional VSG method is coupled with the GFD response which is why it is hard to balance the transient characteristics by debugging the inertia time constant and the damping factor. 3 Proposed VSG-MD control method Generally, the virtual inertia control method based on VSG frequency deviation (in Fig. 4b) is equivalent to the traditional VSG method (in Fig. 4a). The VSG frequency tends to be synchronous with the grid frequency and thus it reflects the change of the grid frequency indirectly. Therefore, in the proposed method, two frequencies are taken into consideration. One is the estimated PCC frequency ωPCC,e shown in (3), which is implemented by the low-pass-filtered VSG frequency. τω is the time constant of the low pass filter. The low pass filter helps to decrease the influence of the high frequency component of the VSG frequency and avoids unnecessary power oscillation. The other one is the measured PCC frequency ωPCC,m. The frequency deviation ΔωPCC,m in (4) reflects the change of grid frequency directly and helps to provide extra inertia power to support the system frequency stability. PCC frequency extraction can be implemented by many proven phase locked loop (PLL) or frequency locked loop (FLL) techniques [29]. The SRF PLL with P-type loop filter [30] is considered as the FLL of PCC frequency. The FLL delay is evaluated by (5). (3) (4) (5)The relationship between the virtual inertia power, the estimated grid frequency and the measured frequency deviation is shown in (6). If only the estimated PCC frequency ωPCC,e is considered, i.e. ΔωPCC,m = 0, the improvement of the proposed VSG-MD method is mainly concentrated on the RPO performance, and this simplified VSG method is named as the VSG-RPO method. Realisation of the digital differentiator is using the non-ideal generalised integrator (NIGI) [31] (6)The damping power in (7) is taken as the product of the damping factor and the frequency difference of the VSG frequency from the reference. The power balance equation is shown in (8). (7) (8)The diagram of the proposed VSG-MD method is shown in Fig. 4c and the small signal model is shown in Fig. 4d. Gpω(s) and Gωp(s) are the power controller and frequency feedforward compensator respectively, which are expressed as (9) and (10). (9) (10)To evaluate the performance of the proposed VSG-MD method, the open loop transfer function (OLTF) from power reference Pref to output power po is derived from Fig. 4d and expressed in (11). The Bode diagram of (11) with τω increasing is shown in Fig. 5, and the NIGI parameters are shown in Table 2. With the time constant τω increasing, the phase margin is increased (Table 2). (11)The locus of dominant zeros and poles of the power control CLTF Cpp(s) is shown in Fig. 6a. With the increase in the time constant τω, the dominant conjugate poles move from the position near the imaginary axis to the left and then become two negative real poles. The equivalent damping ratio increases with increasing τω. Therefore, no matter how the time constant τω changes, the VSG power control system remains stable. Table 2. NIGI parameters Symbol Quantity Value ωc cut-off frequency of NIGI differentiator 2000 rad/s ω′ resonant frequency of NIGI differentiator 2000 rad/s Fig. 4Open in figure viewerPowerPoint Control diagram of the VSG methods (a) Traditional VSG method, (b) equivalent model of traditional VSG method, (c) proposed VSG-MD method, (d) small signal model of the proposed VSG-MD method Fig. 5Open in figure viewerPowerPoint Bode diagram of Gpp(s) with τω increasing Fig. 6Open in figure viewerPowerPoint Locus of dominant zeros and poles of the power control CLTF Cpp(s) and the frequency response CLTF Cωp(s) (a) Locus of Cpp(s) with τω and τlp increases, (b) locus of Cωp(s) with τω and τlp increases The locus of dominant poles and zeros of the CLTF Cωp(s) are depicted in Fig. 6b. With increasing τω, the dominant conjugate poles p1 and p2 move to the left, which means that the performance of the output power in response to the PCC frequency disturbance is influenced. Therefore, it is not appropriate to use an excessive time constant τω. The measured PCC frequency feedforward adds a zero z2 and a pole p3 at the negative real axis. With the increase in the time constant τlp, the added pole moves closer to the imaginary axis. To achieve a better response of frequency support, it is better that the time constant τlp is just a little larger than τω. In this way, high frequency oscillation of VSG frequency is avoided. 4 Parameters design If the NIGI differentiator is replaced with a pure differentiator, the OLTF Gpp(s) can be given as (12). Where τS = τJ + τω and τp is the time constant of the power sampling delay. (12)The whole frequency domain can be divided into four regions, which are denoted as Region I (0+, 1/τS), Region II (1/τS, 1/τω), Region III (1/τω, 1/τp) and Region IV (1/τp, + ∞). 4.1 Frequency region II In this region, the frequency characteristic of (12) is little affected by the high-frequency pole 1/τp, thus this pole is omitted. (13)Assuming τJ = aτω (a > 0), (14)The geometric midpoint of the pole 1/τS and the zero 1/τω is ωa (). If τω is much less than τS, Gpp1(s) in (13) is simplified as (15) in region (), where it can be considered as the traditional VSG method. (15)The Bode diagram of transform function (13) and (15) are shown in Fig. 7a. With increasing τω, the difference of the phase of Gpp2(s) and Gpp1(s) becomes larger, which makes the approximation of (15) questionable. Thus, the upper limit of τω is set by (16). (16)If the maximum of the grid frequency steady-state deviation is Δωmax and the maximum of the VSG damping power is pdmax, the maximum of the damping factor is limited by (17). (17)According to (15), the PRD step response of Cpω(s) in time domain is shown in (18). (18)where, and . Fig. 7Open in figure viewerPowerPoint Bode diagram of Gpp1(s), Gpp2(s) and Gpp3(s) (a) Bode diagram of Gpp2(s) and Gpp1(s) in region II, (b) bode diagram of Gpp3(s) and Gpp1(s) in region III If the transient frequency deviation of the PRD response is not greater than ɛ (rad/s), i.e. ω(tp) ≤ ɛ, the inertia constant is not less than (19), where tp is the peak time of ω(t). (19) 4.2 Frequency region III In this region, the low frequency pole 1/τS is close to origin and (20) is established. (20)Assuming τω = bτp (0 ≤ b ≤ 1), (12) can be simplified as (21). (21)The geometric midpoint of the pole 1/τp and the zero 1/τS is ωb (). If the high frequency pole 1/τp is omitted, the OLTF (12) is simplified as (22) in region (ωa, ωb). (22)The Bode diagram of the Gpp1(s) and Gpp3(s) are shown in Fig. 7b. Similarly, the increase in τω will result in the increase in the difference of the phase of Gpp3(s) and Gpp1(s). The parameter selection in (16) restricts the error of the transfer function approximation. Thus the simplification of the transfer function Gpp3(s) in (22) is reasonable, and Gpp3(s) has a similar phase margin with system Gpp1(s) in (12). If the pre-set phase margin of (22) is configured as γ, the relation between phase margin γ and time constant τω can be given, (23)Combining (16) with (23), the parameter τω is formulated by (24). (24)Equation (24) is the key formula of parameter τω designing, which shows that the time constant τω is related to the damping factor D, the phase margin γ and the time constant τS. The graphical depiction is shown in Fig. 8 and the related parameters are shown in Table 3. The upper limit line is confined by (16) and the mesh zone is defined by (23). The maximal damping factor Dmax and time constant τSmin is chosen based on (17) and (19). The intersection of the above two ranges is the feasible domain of constant τω. Based on Fig. 8, it can be seen that a larger inertia time constant or a small damping factor yields a larger phase margin. Table 3. VSG-MD parameters Symbol Quantity Value Δωmax maximum of grid frequency steady-state deviation ± 1.257 rad/s pdmax maximum of VSG damping power ± 0.083 p.u. Γ pre-set phase margin 30° Ε transient frequency deviation maximum of PRD response 0.34 rad/s τJ time constant of virtual inertia 1.132 s τω time constant of low pass filter 0.118 s D damping factor 16.7 p.u. τFLL FLL equivalent time constant 0.120 s Fig. 8Open in figure viewerPowerPoint Visualised parameter τω feasible domain (a) Domain with fixed D, (b) domain with fixed τS 5 Experimental results To verify the proposed VSG-MD method and parameters design principles, an experimental platform has been built. The traditional VSG method, the proposed VSG-RPO method and the VSG-MD method are evaluated and compared. The proposed VSG-MD control parameters are shown in Table 3. Two cases are studied to compare these VSG methods: the PRD response of positive 0.125 p.u. rated capacity and the GFD response of negative 0.628 rad/s. Grid-tied experimental waveforms of the proposed VSG-MD method with 0.125 p.u. real output power is shown in Fig. 9. Fig. 9Open in figure viewerPowerPoint Grid-tied experimental waveform of the proposed VSG-MD method 5.1 Traditional VSG method Fig. 10 shows the characteristic of the traditional VSG method. In the case of the PRD step increase, the transient power peak is about 1.216 kW with an overshoot of 72.7%. The VSG frequency oscillation peak is 314.511 rad/s with a maximal frequency deviation of 0.352 rad/s, which is a little larger than the transient frequency deviation maximum of 0.34 rad/s in Table 3. In the case of the GFD step decrease, the VSG output power peak 1.056 kW is much larger than the steady-state damping power of 0.204 kW. The existence of virtual inertia makes the output power to be greatly increased in a short period of time to assist in supporting the grid frequency. Fig. 10Open in figure viewerPowerPoint Response characteristic of the traditional VSG method (a) PRD positive step response, (b) GFD negative step response 5.2 Proposed VSG-RPO method Fig. 11 shows the characteristic of the proposed VSG-RPO method. It can be seen that the transient power peak is much lower than that of the traditional VSG method. Compared with the traditional method, the power overshoot of the VSG-RPO method is decreased to 35.5% with a reduction of about 55.4%. Thus, the transient power overshoot of PRD is effectively relieved by the damping effect of time constant τω. Besides, the VSG transient frequency deviation is lower than that of the traditional VSG method, which is decreased to 0.327 rad/s with a reduction of about 7.1% and less than the transient frequency deviation maximum. In the case of GFD, the power oscillation peak is decreased to 0.800 kW, as shown in Fig. 11b, which has a little contribution to grid supporting. Fig. 11Open in figure viewerPowerPoint Response characteristic of the proposed VSG-RPO method (a) PRD positive step response, (b) GFD negative step response 5.3 Proposed VSG-MD method Fig. 12 shows the characteristic of the proposed VSG-MD method. It can be seen that the power peak is similar to that of the VSG-RPO method. Compared with the traditional method, the power overshoot of the proposed VSG-MD method is decreased to 37.8% with a reduction of about 52.5%. As a result, the PRD power overshoot is relieved. Compared with the VSG-RPO method, the PRD power response of the proposed VSG-MD method is slightly larger, but it does not change the potential of the RPO performance improvement. Besides, the VSG maximal frequency deviation of the VSG-RPO method and that of the proposed VSG-MD method are almost the same and less than the transient frequency deviation maximum. Fig. 12Open in figure viewerPowerPoint Response characteristic of the proposed VSG-MD method (a) PRD positive step response, (b) GFD negative step response In the case of GFD, the VSG output power peak of the proposed VSG-MD method is significantly improved, compared to other control methods. The VSG real output power is 1.408 kW, as shown in Fig. 12b, which is even higher than that of the traditional VSG method (increased by 34.3%) and shows greater supporting characteristics due to the feedforward of the actual PCC frequency. From the experimental results it can be seen that the proposed VSG-MD method can provide better RPO performance and stronger supporting capability compared with other two methods. Moreover, the VSG-RPO method and the VSG-MD method can effectively reduce the duration period of the transient process. 6 Conclusions A modified VSG method for voltage-controlled grid-tied converters proposed in this paper. It can not only relieve the low-frequency power oscillation, but also ensure strong power-supporting capability and the parameters design principles are given out. The influence of the time constant of the low-pass filter is also analysed, and it is found that it has a larger impact on transient power performance: a larger time constant yields more damping effect. The effectiveness of the proposed VSG method is verified by experimental results. Compared with the traditional VSG method, the power overshoot of the proposed VSG-MD method is decreased by 52.5% under a PRD case and the power response peak is increased by 34.3% under a GFD case. 7 Acknowledgments This work is supported by the National Key R&D Program of China (grant no. 2016YFB0900400) and the National Natural Science Foundation of China (grant no. 51777084). 8 References 1Rocabert J., Luna A., and Blaabjerg F. et al.: ' Control of power converters in AC microgrids', IEEE Trans. Power Electron., 2012, 27, (11), pp. 4734– 4749CrossrefWeb of Science®Google Scholar 2Han Y., Li H., and Shen P. et al.: ' Review of active and reactive power sharing strategies in hierarchical controlled microgrids', IEEE Trans. Power Electron., 2017, 32, (3), pp. 2427– 2451CrossrefWeb of Science®Google Scholar 3Hirase Y., Sugimoto K., and Sakimoto K. et al.: ' Analysis of resonance in microgrids and effects of system frequency stabilization using a virtual synchronous generator', IEEE J. Emerging Sel. Topics Power Electron., 2016, 4, (4), pp. 1287– 1298CrossrefWeb of Science®Google Scholar 4Wu W., Chen Y., and Zhou L. et al.: ' Sequence impedance modelling and stability comparative analysis of voltage-controlled VSGs and current-controlled VSGs', IEEE Trans. Ind. Electron., 2019, 66, (8), pp. 6460– 6472CrossrefWeb of Science®Google Scholar 5Hirase Y., Abe K., and Sugimoto K. et al.: ' A novel control approach for virtual synchronous generators to suppress frequency and voltage fluctuations in microgrids', Appl. Energy, 2018, 210, pp. 699– 710CrossrefWeb of Science®Google Scholar 6Fang J., Li H., and Tang Y. et al.: ' On the inertia of future more-electronics power systems', IEEE J. Emerging Sel. Topics Power Electron., 2018, (early access, doi: 10.1109/JESTPE.2018.2877766) Web of Science®Google Scholar 7Driesen J., and Visscher K.: ' Virtual synchronous generators'. IEEE Power and Energy Society General Meeting, Pittsburgh, PA, USA, August 2008, pp. 1323– 1325CrossrefGoogle Scholar 8Visscher K., and De Haan S.W.H.: ' Virtual synchronous machines (VSG's) for frequency stabilisation in future grids with a significant share of decentralized generation'. CIRED Seminar 2008: Smart Grids for Distribution, Frankfurt, Germany, August 2008, pp. 1– 4Google Scholar 9Chen Y., Hesse R., and Turschner D. et al.: ' Improving the grid power quality using virtual synchronous machines'. Int. Conf. on Power Engineering, Energy and Electrical Drives, Malaga, Spain, May 2011, pp. 1– 6CrossrefGoogle Scholar 10Zhong Q., and Weiss G.: ' Synchronverters: inverters that mimic synchronous generators', IEEE Trans. Ind. Electron., 2011, 58, (4), pp. 1259– 1267CrossrefWeb of Science®Google Scholar 11Chen Y., Hesse R., and Turschner D. et al.: ' Comparison of methods for implementing virtual synchronous machine on inverters'. Int. Conf. on Renewable Energies and Power Quality, Santiago de Compostela, Spain, March 2012, pp. 1– 6Google Scholar 12D'Arco S., and Suul J.A.: ' Equivalence of virtual synchronous machines and frequency-droops for converter-based microgrids', IEEE Trans. Smart Grid, 2014, 5, (1), pp. 394– 395CrossrefWeb of Science®Google Scholar 13Meng X., Liu J., and Liu Z.: ' A generalized droop control for grid-supporting inverter based on comparison between traditional droop control and virtual synchronous generator control', IEEE Trans. Power Electron., 2019, 34, (6), pp. 5416– 5438CrossrefWeb of Science®Google Scholar 14Liu J., Miura Y., and Ise T.: ' Comparison of dynamic characteristics between virtual synchronous generator and droop control in inverter-based distributed generators', IEEE Trans. Power Electron., 2016, 31, (5), pp. 3600– 3611CrossrefWeb of Science®Google Scholar 15Alipoor J., Miura Y., and Ise T.: ' Power system stabilization using virtual synchronous generator with alternating moment of inertia', IEEE J. Emerging Sel. Topics Power Electron., 2015, 3, (2), pp. 451– 458CrossrefWeb of Science®Google Scholar 16Li D., Zhu Q., and Lin S. et al.: ' A self-adaptive inertia and damping combination control of VSG to support frequency stability', IEEE Trans. Energy Convers., 2017, 32, (1), pp. 397– 398CrossrefWeb of Science®Google Scholar 17Wang F., Zhang L., and Feng X. et al.: ' An adaptive control strategy for virtual synchronous generator', IEEE Trans. Ind. Appl., 2018, 54, (5), pp. 5124– 5133CrossrefWeb of Science®Google Scholar 18Soni N., Doolla S., and Chandorkar M.C.: ' Improvement of transient response in microgrids using virtual inertia', IEEE Trans. Power Deliv., 2013, 28, (3), pp. 1830– 1838CrossrefWeb of Science®Google Scholar 19Soni N., Doolla S., and Chandorkar M.C.: ' Inertia design methods for islanded microgrids having static and rotating energy sources', IEEE Trans. Ind. Appl., 2016, 52, (6), pp. 5165– 5174CrossrefWeb of Science®Google Scholar 20Suul J.A., D'Arco S., and Guidi G.: ' Virtual synchronous machine-based control of a single-phase bi-directional battery charger for providing vehicle-to-grid services', IEEE Trans. Ind. Appl., 2016, 52, (4), pp. 3234– 3244CrossrefCASWeb of Science®Google Scholar 21Huang L., Xin H., and Wang Z.: ' Damping low-frequency oscillations through VSC-HVDC stations operated as virtual synchronous machines', IEEE Trans. Power Electron., 2019, 34, (6), pp. 5803– 5818CrossrefWeb of Science®Google Scholar 22Kayikçi M., and Milanovic J. V.: ' Dynamic contribution of DFIG-based wind plants to system frequency disturbances', IEEE Trans. Power Syst., 2009, 24, (2), pp. 859– 867CrossrefWeb of Science®Google Scholar 23Fang J., Zhang R., and Li H. et al.: ' Frequency derivative-based inertia enhancement by grid-connected power converters with a frequency-locked-loop', IEEE Trans. Smart Grid, 2018, (early access, doi: 10.1109/TSG.2018.2871085) Web of Science®Google Scholar 24Xiong L., Li P., and Wu F. et al.: ' Stability enhancement of power systems with high DFIG-wind turbine penetration via virtual inertia planning', IEEE Trans. Power Syst., 2019, 34, (2), pp. 1352– 1361CrossrefWeb of Science®Google Scholar 25Pérez J.R., Suul J.A., and D'Arco S. et al.: ' Virtual synchronous machine control of VSC HVDC for power system oscillation damping'. IECON 2018-44th Annual Conf. of the IEEE Industrial Electronics Society, Washington D.C., United States of America, October 2018, pp. 6026– 6031CrossrefGoogle Scholar 26Kerdphol T., Rahman F.S., and Watanabe M. et al.: ' Enhanced virtual inertia control based on derivative technique to emulate simultaneous inertia and damping properties for microgrid frequency regulation', IEEE. Access., 2019, 7, pp. 14422– 14433CrossrefWeb of Science®Google Scholar 27Asrari A., Mustafa M., and Ansari M. et al.: ' Impedance analysis of virtual synchronous generator-based vector controlled converters for weak AC grid integration', IEEE Trans. Sustain. Energy, 2019, 10, (3), pp. 1481– 1490CrossrefWeb of Science®Google Scholar 28Zou C., Liu B., and Duan S. et al.: ' Stationary frame equivalent model of proportional-integral controller in dq synchronous frame', IEEE Trans. Power Electron., 2014, 29, (9), pp. 4461– 4465CrossrefWeb of Science®Google Scholar 29Ali Z., Christofides N.G., and Hadjidemetriou L. et al.: ' Three-phase phase-locked loop synchronization algorithms for grid-connected renewable energy systems: A review', Renew. Sustain. Energy Rev., 2018, 90, pp. 434– 452CrossrefWeb of Science®Google Scholar 30Wen B., Boroyevich D., and Burgos R. et al.: ' Analysis of D-Q small-signal impedance of grid-tied inverters', IEEE Trans. Power Electron., 2016, 31, (1), pp. 675– 687CrossrefWeb of Science®Google Scholar 31Xin Z., Wang X., and Loh P.C. et al.: ' Realization of digital differentiator using generalized integrator for power converters', IEEE Trans. Power Electron., 2015, 30, (12), pp. 6520– 6523CrossrefWeb of Science®Google Scholar Citing Literature Volume12, Issue12October 2019Pages 3178-3184 FiguresReferencesRelatedInformation