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Intercluster voltage balancing control of a delta connected modular multilevel cascaded converter under unbalanced grid voltage
Protection and Control of Modern Power Systems volume 6, Article number: 23 (2021)
Abstract
A new intercluster DC capacitor voltage balancing scheme for a delta connected modular multilevel cascaded converter (MMCC)based static synchronous compensator (STATCOM) is presented. A detailed power flow analysis of applying negative sequence current (NSC) and zerosequence current (ZSC) injection methods in addressing the issue of intercluster DC voltage imbalance under unbalance grid voltage is carried out. A control scheme is proposed which integrates both intercluster methods using a quantification factor Q_{F}. This is used to achieve the sharing of the intercluster active power between the NSC and ZSC injection methods. An accurate method of determining the quantification factor is also presented. The proposed method offers better submodule DC capacitor voltage balancing and prevents converter overcurrent. The influence of unbalanced grid voltage on the delta connected MMCCbased STATCOM rating using this integrated cluster balancing technique is investigated. The control scheme is verified with a 5 kV 1.2MVA MMCCSTATCOM using 3level bridge submodules, and the results show the advantages of the proposed method over other intercluster methods.
1 Introduction
Grid voltage unbalance can be caused by remote faults, uneven distribution of loads such as singlephase traction drives, open wye and delta transformer banks, asymmetric transmission impedances, and so on [1]. The increasing connection of renewable source generators to the utility network exacerbates the situation because of the use of power electronic converters for grid interface and the unpredictable power generation [2]. As a consequence, all gridtied power electronic converters are required to operate under normal and abnormal grid voltage conditions, and support the grid voltage during transient grid faults.
The modular multilevelcascaded converter (MMCC) is attractive for medium and high voltage applications for a battery energy storage system (BESS), reactive power compensation and harmonic mitigation of a power system network [3,4,5,6,7,8]. The modular structure of this converter offers the merits of scalability, i.e. scaling up to any desired voltage level, thus eliminating the use of stepup transformers. This also helps achieve good waveform quality with low total harmonic distortion of the output voltage while only using low switching frequency leading to reduced power losses [8, 9].
MMCCbased STATCOM has been studied to adequately provide reactive power support to the grid under balanced conditions [4, 10]. However, under an unbalanced grid voltage condition, it faces a challenge of active power imbalance across the converter phases [11, 12]. This unequal converter phase active power leads to intercluster voltage imbalance and causes submodule DC capacitor voltage imbalance. If this intercluster voltage imbalance is not properly managed, distorted currents are injected into the grid via the MMCCSTATCOM. In addition, excessive drift of submodule capacitor voltages may overstress the MMCC semiconductor switches and potentially damage the devices [13].
In [14,15,16,17], intercluster DC capacitor voltage balancing is achieved under an unbalanced load condition by injecting a zerosequence current (ZSC) to circulate the three phases of the single delta bridge converter (SDBC). However, this injection method can lead to currents exceeding their rated limit and damaging converter switches. The use of a negative sequence current (NSC) injection method has not been analyzed and applied to this topology. In addition, the influence of zero sequence current and negative sequence current injection techniques on the voltage and current rating requirements of the delta connected MMCC STATCOM under grid voltage fault conditions has not been investigated.
This paper proposes a new control scheme for phasecluster voltage imbalance and overcurrent of deltaconnected MMCCSTATCOM operating under unbalanced voltage conditions. Different from conventional methods, the new scheme incorporates both methods to overcome the overcurrent problem. In applying this scheme, a quantification factor Q_{F} is determined based on the maximum allowable converter current. A detailed power flow analysis of deltaconnected MMCC operating under unbalanced voltage condition is carried out, and the influence of an unbalanced voltage level on the voltage and current ratings of this configuration is investigated. The MMCC submodule considered in this paper is the 3level Hbridge (3 LHB), though the scheme presented can also be applied to a 5level flying capacitor Hbridge (5 LFC) [16, 18]. Digital simulation test results are presented to validate the proposed method.
2 Circuit configuration of delta MMCCbased STATCOM
Figure 1 shows the system configuration of the deltaconnected MMCC STATCOM. Each cluster consists of N threelevel Hbridge (3 LHB) submodules connected in series. The filter reactors are connected between the SDBC phases to handle their voltage difference between phase clusters and limit the current circulating inside the converter. The DC capacitor submodule voltages, V_{dcmn}, (where m = ab, bc, ca; n = 1, 2,…N) in each phase cluster of the MMCC need to be regulated to keep their desired values even under a grid voltage unbalanced condition. The converter voltages and currents are expressed in (1) and (2), where k = 0, 1, 2. Superscripts + and , and subscript 0 represent the positive, negative and zero sequence components. V_{+}, V_{−}, I_{+} and I_{−} represent the positive and negative sequence voltage and current magnitude. I_{0} is the magnitude of the zerosequence current. φ_{V+}, φ_{V}, φ_{I+}, and φ_{I} are the phase angles of the positive and negative sequence voltages and currents, respectively, while φ_{I0} is the phase angle of the zero sequence current.
3 Delta connected MMCCSTATCOM power flow analysis
The intercluster DC capacitor voltage balancing control of the deltaconnected MMCC submodules is the main focus of this paper. The intercluster power flow of the system is analyzed, while multiplying (1) and (2) gives the instantaneous and average power across each phase of the delta MMCCSTATCOM. The average cluster powers are expressed as:
where q = 1, − 2, 1 and r = + 1, 0, − 1 for m = ab, bc, ca phases, respectively.
The overall average active power P_{T}^{++} and P_{T}^{−−} are solely determined by P_{Cm}^{++} and P_{Cm}^{−−} while the sum of the other power terms is zero, i.e.:
The zero sequence current active power P_{Cm}^{+ 0} and P_{Cm}^{− 0} do not contribute to the overall active power of the converter, as seen in (4). Thus, the zero sequence current does not influence the overall average active power control, and the overall average active power in (4) is equally provided by the individual converter phases.
The phase average active power for the delta MMCC is defined in (6).
The total average reactive power injected to the grid based on instantaneous power theory [19] is given as:
Three possible ways of regulating the deltaconfigured MMCC are available based on (6), i.e., the positive, negative and zero sequence currents. The positive sequence current is applied in providing the total average active and reactive power control. Thus, only the negative and zero sequence currents are the control terms available for intercluster active power balancing control.
4 Control scheme
The block diagram of the MMCC STATCOM control is shown in Fig. 2. The converter control is divided into three sections of overall power control, intercluster average active power control and individual control. The overall controller regulates the total average active and reactive power requirements of the converter by controlling the overall DC capacitor voltages of the deltaconfigured MMCC and the positive sequence currents (I_{+}cosφ_{I+}, I_{+}sinφ_{I+}), while the negative and zero sequence currents are the control terms that influence the regulation of the intercluster average power controller.
4.1 Overall average active and reactive power control
This controller is used to provide the active power required to compensate for power losses and maintain the MMCCSTATCOM overall DC capacitor voltages to their required values, while controlling the reactive power to be injected by the converter. This active power required by the DC capacitors is determined through a PI regulator as shown in Fig. 3. The direct component of the positive sequence current is:
where k_{p_dc} and k_{i_dc} are the controller proportional and integral gain constants, and V_{dc}^{*} and V_{dc_avg} are the reference and average values of all the submodule voltages, respectively.
The reactive current applied in the regulation of average reactive power injection is given as:
Where V_{d}^{+} and Q_{ref} are the direct component of the positive sequence voltage and the reactive power reference, respectively. To prevent excessive injection of converter current under a grid unbalanced fault condition, a fixed reactive current is applied.
4.2 Intercluster average active power balancing control
The unbalanced average active phase power of the MMCC in an unbalanced grid voltage condition results in unequal interphase submodule capacitor voltages. The cluster average active power of the converter is given as:
From (8), the average cluster active power comprises positive, negative and zero sequence current components. As the overall average active and reactive power control uses the positive sequence current, the two remaining control freedoms of negative and zero sequence currents are thus employed to regulate the intercluster control. A quantification factor Q_{F} is used to harness the two methods in controlling the average active cluster power. This is done by effectively sharing the intercluster power between P_{Cm}^{−+} and P_{Cm}^{0} methods. The 3phase cluster power is transformed into an αβ form as:
Equation (9) is further expressed using Q_{F} as:
where m = α, β phases.
Simplifying (10), the zero and negative sequence currents are given in (20).
The control scheme of the proposed interphase average active power balancing method is shown in Fig. 4. The output of the PI regulators P_{Cm}^{*} is subtracted from the positive sequence current active power P_{Cm}^{−+}, and is then used along with the quantification factor in determining the appropriate values of the negative and zero sequence currents.
The active power across each submodule is regulated using the individual DC capacitor voltage controller as:
Where V_{inmn} is the individual control signal for each submodule across a particular phase, and k_{p_in} and k_{i_in} are the proportional and integral gains of the individual DC capacitor voltage controller. As illustrated in Fig. 2, the negative sequence current is fed into the current controller to synthesize the converter reference voltage. The zero sequence current calculated from Fig. 4 is converted into a voltage command V_{A} through a proportional controller as:
This voltage command is added to the output of the predictive current controller v_{mref} to form the new converter voltage reference v_{m0ref}, which is applied to phaseshifted PWM (PSPWM) [20,21,22] to generate the converter gate signals.
4.3 Quantification factor determination
The value of the quantification factor Q_{F} is determined by ensuring that the converterrated current is not exceeded and submodule capacitor voltage deviations are within ±10% of their rated values. Among the two intercluster balancing methods, the zerosequence current method is superior to the negative sequence current technique in the determination of the Q_{F} value. This is because injecting negative sequence current into the grid in attaining intercluster voltage balancing disrupts the improvement of power quality.
The zero sequence current method is solely used to achieve intercluster control if the maximum converter current I_{max} is less than or equal to the converterrated current I_{Rated}, i.e.:
Where i_{ab}, i_{bc}, i_{ca} are the magnitudes of the threephase converter phase currents.
For conditions when the maximum converter phase current may be higher than the rated current (i.e. I_{max} > I_{Rated}), to ensure overcurrent management, a new value of Q_{F} is determined by equating the maximum current through the deltaconfigured MMCC as given in (14). The quantification factor Q_{F} is determined by equating the magnitude of the current components as:
Where
A flowchart for quantification factor Q_{F} determination is shown in Fig. 5.
5 Deltaconnected MMCC ratings under unbalanced voltage conditions
The operating range and ratings of delta MMCC are analyzed in a voltage unbalanced condition. These analyses are based on the integration of both intercluster balancing control methods of zero sequence and negative sequence currents using the quantification factor Q_{F} in sharing the intercluster phase active power. This quantification factor has a value of 0 ≤ Q_{F} ≤ 1. From (10), when Q_{F} = 0, P_{Cm}^{+ − *} = 0 and P_{Cm}^{0*} = P_{Cm}^{*} P_{Cm}^{−+}. When Q_{F} = 1, P_{Cm}^{+ − *} = P_{Cm}^{*}  P_{Cm}^{−+} and P_{Cm}^{0*} = 0. For 0 ˂ Q_{F} ˂ 1, P_{Cm}^{+ − *} = Q_{F} (P_{Cm}^{*}  P_{Cm}^{−+}) and P_{Cm}^{0*} = (1 Q_{F})(P_{Cm}^{*}  P_{Cm}. The degree of voltage imbalance K_{vr} = V_{n}/V_{p} is used in this investigation. In determining the DC capacitor voltage V_{dc_rated} and current rating I_{Rated}, the influence of both intercluster balancing methods are considered. Equations (16)–(19) found in [14] are applied for this investigation.
where V_{dc} is the submodule capacitor voltage, and N is the number of submodules per cluster. V_{f} represents the voltage drop across the converter filter, i_{mo} is the cluster current, and i_{+}, i_{−} and i_{0} are the positive, negative and zero sequence currents. Q_{F} values of 0, 0.5 and 1 are applied across the MMCCSTATCOM for this analysis. For Q_{F} = 0 and 1, only zerosequence current and negative sequence current methods are applied, respectively. While for Q_{F} = 0.5, the zero and negative sequence current methods are shared equally.
The influence of the quantification factor Q_{F} and the degree of voltage unbalanced (0 ≤ Q_{F} ≤ 0.9) on the current and voltage rating requirements for deltaconnected STATCOM is shown in Fig. 6a–c. From Fig. 6a, the voltage and current ratings at K_{vr} = 0.8 are 1pu and 3.3pu for Q_{F} = 0, respectively. For Q_{F} = 0.5 as illustrated in Fig. 6b, where K_{vr} = 0.8, the voltage and current ratings are 1pu and 2.5pu, respectively. Figure 6c shows that the voltage and current ratings using negative sequence current method for Q_{F} = 1 are 1pu and 1.8pu, respectively.
From this analysis, the current requirement of the zero sequence current injection method is improved by combining it with the negative sequence current technique. Thus, employing equal power sharing between both methods reduces the current rating requirement of the deltaconnected MMCCbased STATCOM by 0.9pu. These ratings have a direct implication for the switching devices and DC capacitor current handling capabilities.
6 Results and discussion
Figure 1 shows the system configuration, where 4 threelevel Hbridges are cascaded in a single delta configuration. The proposed control scheme as illustrated in Fig. 2 is implemented using MATLAB / SIMULINK. The system and control parameters are shown in Tables 1 and 2, respectively. The control parameters are selected based on the cutoff frequency and phase margin of 10 Hz and 60^{0}, respectively.
The positive sequence active and reactive current references I_{d}^{+*} and I_{q}^{+*} are synthesized by the overall active and reactive power controller. The intercluster balancing techniques are tested under 100% phase A voltage sag as shown in Fig. 7.
The rated STATCOM phase current is I_{rated} = 65A and the converter reference DC capacitor voltage V_{dcref} is fixed at 2.5 kV. To validate the effectiveness of the proposed method, the zerosequence current and negative sequence current methods with respective quantification factors of Q_{F} = 0 and 1 are subjected to this unbalanced condition.
Figure 8 shows the results of using the zerosequence current technique for intercluster active power balancing control. The zerosequence average active power is applied in compensating for the phase cluster power which generates the zero sequence current as illustrated in Fig. 8a. The MMCCSTATCOM output voltages are wellmodulated as highlighted in Fig. 8b. The zerosequence current of 20A circulating in the deltaconfigured MMCCSTATCOM results in the submodule DC capacitor voltages fluctuating within ±10% of their reference voltages as illustrated in Fig. 8c. The maximum total STATCOM phase current is greater than the converter current rating as illustrated in Fig. 8d, while Fig. 8e shows that the currents injected into the grid do not have negative sequence current.
Figure 9 shows the test results with negative sequence current intercluster active power balancing control. The negative sequence average active power compensates for the phase cluster power using the negative sequence current as shown in Fig. 9a, while the maximum current is 80A (1.231 of I_{rated}) as indicated in Fig. 9a. This excessive current could result in semiconductor switch thermal breakdown. Figure 9b shows that the converter output voltages are not overmodulated, while Fig. 9c shows that the submodule capacitor voltages are maintained within ±7% of their reference values. Figure 9d shows that no zero sequence current is required with this technique. However, the degree of current imbalance injected to the grid is 50% as seen in Fig. 9e, and this could result in more imbalance in the grid.
Figure 10 shows the results of the proposed technique for the intercluster active power balancing control. To overcome the problems posed by zero sequence current and negative sequence current methods, the proposed method determines the quantification factor using (15) as Q_{F} = 0.381, i.e. sharing the intercluster unbalanced active powers between zerosequence current and negative sequence current in proportions of 61.9% and 38.1%, respectively.
Comparing Figs. 8a and 10a, the magnitude of the zero sequence current for the proposed method is less than the value for the zerosequence current injection technique. The maximum current injected into the grid is seen to be equal to the rated current as illustrated in Fig. 10b, and this is lower than the case of NSC and ZSC injection methods shown in Figs. 8d and 9a, respectively. Figure 10c shows that the converter output voltages are also wellmodulated. The proposed method maintains the submodule DC capacitor voltages ripple to be less than ±3% as seen in Fig. 10d. Figure 10e shows that the level of current imbalance injected into the grid by the proposed method is less than with the NSC method.
Table 3 compares the proposed method against the other two intercluster techniques. The following metrics are considered:

The maximum current flowing in the converter: this is the sum of all the current components as expressed in (18). Only the proposed method operates within the rated current of the converter while the others have higher current flowing in the converter.

The maximum current flowing from the converter to the grid: since the zerosequence current only flows within the converter clusters, this quantity is the sum of both positive and negative sequence grid currents. The NSC method injects a higher current to the grid than the proposed and ZSC methods.

Degree of unbalanced current injected to the grid K_{ir}: this is the ratio of negative sequence current to positive sequence current. The proposed method injects less unbalanced current to the grid than the NSC method, while the ZSC offers no unbalanced current to the grid.

Switching power losses P_{S}: this is calculated as:
where f_{SON} and f_{SOFF} are the switching energy functions for turnon and turnoff energies. T_{j_T} and T_{j_D} are the respective junction temperatures of IGBT and diode, while V_{CE_Ref}, V_{F_Ref} are the reference voltages for defining the IGBT and diode switching losses [20]. Since all the methods are subject to the same operating condition including modulation techniques, the only varying parameter is the current. Therefore, the switching power losses are simply expressed as a function of current as P_{S} = f (i(t)). The proposed method offers the lowest power losses of the three methods.

Maximum submodule capacitor voltage variation: this is the ratio of the change in submodule capacitor voltage to the reference capacitor voltage. From Table 3, the proposed method has the least variation of the three intercluster power balancing methods.
From the results, the proposed method is superior to the zero and negative sequence current methods.
7 Conclusion
The intercluster active power balancing control of the deltaconnected STATCOM in an unbalanced voltage condition is of serious concern. This paper has proposed an intercluster active power balancing method to address the challenges posed by both zero sequence current and negative sequence current injection methods which result in submodule DC capacitor voltages drift and overcurrent, respectively. The relationship between the active power flow and intercluster DC capacitor voltages are discussed, while the power flow analysis and the proposed method are presented in detail. The effectiveness of the proposed method is achieved by determining the optimum quantification factor Q_{F} value which integrates zero sequence current and negative sequence current in the correct proportion in addressing the problems of the two methods. The influence of Q_{F} as the degree of unbalanced voltage k_{vr} increases on the voltage and current ratings of the deltaconnected MMCC STATCOM is also investigated. The simulation results using the proposed method show that:

the submodule DC capacitor voltage fluctuations are maintained within ±3% of the reference voltage;

the maximum current is within the rated value;

converter switching power losses are reduced;

less unbalance current is injected into the grid than with the NSC method.
Availability of data and materials
The research was carried out using MATLAB SIMULINK.
Abbreviations
 ZSC:

Zero sequence current
 NSC:

Negative sequence current
 SDBC:

Single delta bridge converter
 LVRT:

Low voltage ride through
 STATCOM:

Static synchronous compensator
 MMCC:

Modular multilevel cascaded converter
 BESS:

Battery energy storage system
 3 LHB:

3level Hbridge
 5 LFC:

5level Flying capacitor
References
Oghorada, O. J. K., Nwobu, C. J., & Zhang, L. (2016). Control of a singlestar flying capacitor converter modular multilevel cascaded converter (SSFCCMMCC) STATCOM for unbalanced load compensation, (pp. 1–6).
Oghorada, O. J. K., & Zhang, L. (2016). Control of a Modular Multilevel Converter STATCOM for low voltage ridethrough condition. In IECON 201642nd Annual Conference of the IEEE Industrial Electronics Society, (pp. 3691–3696). IEEE.
Akagi, H. (2011). Classification, terminology, and application of the modular multilevel cascade converter (MMCC). IEEE Transactions on Power Electronics, 26(11), 3119–3130. https://doi.org/10.1109/TPEL.2011.2143431.
Sano, K., & Takasaki, M. (2012). A transformer less DSTATCOM based on a multivoltage cascade converter requiring no DC sources. IEEE Transactions on Power Electronics, 27(6), 2783–2795.
Hagiwara, M., Maeda, R., & Akagi, H. (2011). Application of a Modular Multilevel Cascade Converter (MMCCSDBC) to a STATCOM. IEEE Transactions on Industry Applications, 131(12), 1433–1441. https://doi.org/10.1541/ieejias.131.1433.
Nwobu, C., Oghorada, O. J. K., et al. (2015). A modular multilevel flying capacitor converterbased STATCOM for reactive power control in distribution systems. In Power Electronics and Applications (EPE’15), 17th European Conference on.
Gultekin, B., & Ermis, M. (2013). Cascaded multilevel converter based transmission STATCOM: system design methodology and development of a 12 kV ±12 MVAr power stage. IEEE Transactions on Power Electronics, 28(11), 4930–4950.
Akagi, H., Inoue, S., & Yoshii, T. (2007). Control and performance of a transformer less cascade PWM STATCOM with star configuration. IEEE Transactions on Industry Applications, 43(4), 1041–1049.
Zhang, J., Xu, S., Din, Z., & Hu, X. (2019). Hybrid multilevel converters: Topologies, evolutions and verifications. Energies, 12(4), 615. https://doi.org/10.3390/en12040615.
Huang, H., Oghorada, O. J. K., Zhang, L., & Chong, B. V. P. (2017). Active harmonic current elimination and reactive power compensation using modular multilevel cascaded converter. In 2017 19th European Conference on Power Electronics and Applications (EPE’17 ECCE Europe), (p. 1). IEEE.
Lee, C., Wang, B. S., Chen, S. W., Chou, S. F., Huang, J. L., Cheng, P. T., … Barbosa, P. (2014). Average power balancing control of a STATCOM based on the cascaded Hbridge PWM converter with star configuration. IEEE Transactions on Industry Applications, 50(6), 3893–3901. https://doi.org/10.1109/TIA.2014.2312618.
Sochor, P., & Akagi, H. (2016). Theoretical comparison in energybalancing capability between star and deltaconfigured modular multilevel cascade inverters for utilityscale photovoltaic systems. IEEE Transactions on Power Electronics, 31(3), 1980–1992. https://doi.org/10.1109/TPEL.2015.2442261.
Oghorada, O. J. K., & Zhang, L. (2018). Analysis of star and delta connected modular multilevel cascaded converterbased STATCOM for load unbalanced compensation. International Journal of Electrical Power & Energy Systems, 95, 341–352. https://doi.org/10.1016/j.ijepes.2017.08.034.
Oghorada, O. J. K., & Zhang, L. (2019). Unbalanced and reactive load compensation using MMCCbased SATCOMs with thirdharmonic injection. IEEE Transactions on Industrial Electronics, 66(4), 2891–2902. https://doi.org/10.1109/TIE.2018.2849962.
Wu, P., Chen, H., Chang, Y., & Cheng, P. (2017). Deltaconnected cascaded Hbridge converter application in unbalanced load compensation. IEEE Transactions on Industry Applications, 53(2), 1254–1262. https://doi.org/10.1109/TIA.2016.2633945.
Oghorada, O. J. K. (2017). Modular multilevel cascaded flying capacitor STATCOM for balanced and unbalanced load compensation. PhD. School of Electronic/Electrical Engineering, University of Leeds.
Lee, C., Chen, H., Wang, C., Wu, P., Yang, C., & Cheng, P. (2014). A peak current limit control technique in lowvoltage ride through operation of the starconnected cascaded Hbridges converter. In 2014 IEEE Energy Conversion Congress and Exposition (ECCE), Pittsburgh, PA, (pp. 505–512).
Oghorada, O. J. K., Zhang, L., Efika, I. B., & Nwobu, C. J. (2018). Control of modular multilevel converters using an overlapping multihexagon space vector modulation scheme. IEEE Journal of Emerging and Selected Topics in Power Electronics, 7(1), 381–391.
Akagi, H., Watanabe, E. H., & Aredes, M. (2017). Instantaneous power theory and applications to power conditioning. Wiley.
Oghorada, O. J. K., Zhang, L., Esan, B. A., & Dickson, E. (2019). Carrierbased sinusoidal pulsewidth modulation techniques for flying capacitor modular multilevel cascaded converter. Heliyon, 5(12), e03022.
Huang, H., Zhang, L., Oghorada, O., & Mao, M. (2021). Analysis and control of a modular multilevel cascaded converterbased unified power flow controller. IEEE Transactions on Industry Applications, 57(3), 3202–3213. https://doi.org/10.1109/TIA.2020.3029546.
Oghorada, O., Zhang, L., Esan, A., Egbune, D., & Uwagboe, J. (2020). Intercluster voltage balancing control of modular multilevel cascaded converter under unbalanced grid voltage. Journal of Modern Power Systems and Clean Energy.
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Oghorada, O.J.K., Zhang, L., Han, H. et al. Intercluster voltage balancing control of a delta connected modular multilevel cascaded converter under unbalanced grid voltage. Prot Control Mod Power Syst 6, 23 (2021). https://doi.org/10.1186/s41601021002030
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DOI: https://doi.org/10.1186/s41601021002030