Compared with traditional power transformers, Hybrid Distribution Transformers (HDTs) generate higher power losses due to the application of power electronic converters. However, HDTs can apply reactive power compensation as well as three-phase load current unbalance compensation, which leads to line loss reduction of the distribution power grid. When comparing the power losses of HDTs and traditional transformers, it is necessary to comprehensively consider the operational power loss of HDTs and line losses of the distribution network reduced by its converter. This article proposes a comprehensive loss model for the application of HDTs in distribution networks and conducts theoretical calculations on HDT self-losses and distribution network line losses caused by reactive power and three-phase asymmetric load currents. The power losses on the transmission wire of the distribution power grid with the application of HDTs instead of traditional transformers are analyzed. The calculation and simulation results based on parameters such as reactive power, three-phase unbalanced current, and HDT comprehensive loss have verified the correctness of the theoretical analysis.

Topics
Transformer, Power electronics, Semiconductor devices, Energy consumption, Energy storage, Electrical grid, Power distribution systems, Electric currents, Electric measurements

With the construction of a new type of power system, the distributed solar power, generated wind power, various types of energy storage devices, and electric vehicle charging piles are connected to the power grid on a large scale, which brings problems such as high frequency harmonics and reactive power component injection as well as voltage fluctuations to the power grid.1,2 Due to the increasing need to promote the consumption of distributed power sources and carry new types of loads, the distribution network changes significantly in composition and structure, gradually transforming from a power network that simply receives and distributes electricity to users to a smart grid that integrates the source, grid, load, and storage, and is flexibly coupled with the higher-level power grid.

The distribution network connects the transmission network and the power, featuring a large number of complex power equipment pieces and power lines. It not only directly provides power to consumers as the terminal of the power grid but also undertakes distributed power generation and transmission networks, being responsible for the transmission efficiency and power quality of both upper and lower grids. In the distribution network, voltage fluctuations, low power factors, and unbalanced three-phase loads can increase line losses and reduce the power quality of the power terminals, which pose new challenges to flexible voltage regulation, harmonic control, reactive power compensation, as well as three-phase asymmetric load management. As the most commonly used power equipment in the distribution network, conventional distribution transformers have low power losses, high reliability, and low prices,3–5 but they are unable to regulate the input and output voltages and currents, which cannot meet the requirements of the distribution network transforming from a traditional “passive” one-way radiation network to an “active” two-way interactive system.

The Hybrid Distribution Transformer (HDT) integrates traditional transformers and modern power electronic devices. Aeloiza et al. combined traditional transformers with choppers to achieve stable regulation of the grid voltage.6,7 Bala et al. integrated rectifiers and inverters on traditional transformers to achieve adjustment of the secondary side voltage and primary side current, respectively.8,9 Therefore, the hybrid distribution transformer integrates several power electronic devices, such as active filters, dynamic voltage regulators, and power quality regulators, to achieve reactive power compensation, harmonic control, and voltage stabilization.3,4

The corresponding US standard requires the efficiency of oil-immersed distribution transformers to be no less than 99.5%.10 The national standard of China GB20052-2020 requires that the efficiency of dry-type transformers and oil-immersed transformers at the ultra-high-efficiency energy efficiency level is not less than 99.0%.11,12 The efficiency of the back-to-back converter equipped with HDTs based on fully-controlled power electronic devices is only 97%–98% at most.13,14 Taking the solid-state transformer of North Carolina State University as an example, its maximum efficiency is only 94%.15,16 Therefore, compared with conventional transformers, HDTs have lower efficiency, which restricts their large-scale renewal for the traditional power transformer.

However, the line loss of the distribution network will decrease with the enhanced function on voltage regulation, reactive power compensation, and three-phase unbalanced load current compensation of HDTs. Through reactive power compensation, HDTs can flexibly control the power factor of the distribution network, thereby compensating for the voltage drop on the power transmission line and reducing transmission line loss. When the three-phase load current is unbalanced, HDTs can inject negative sequence current into the distribution network to maintain the symmetrical three-phase load current, thus reducing the loss of the phase line and neutral line.

The load of the rural power grid in China is scattered,16 the distance of distribution lines is long,17 and the problem of three-phase load current unbalance as well as low power factor is prominent. Meanwhile, the distribution network of industries and enterprises also faces the same problems due to long distribution lines, single-phase loads, and three-phase mixed loads.18,19 In addition, the single-phase traction load in railway transportation will also lead to a low power factor and three-phase asymmetric load current.20 When the HDT is applied to the distribution network mentioned above, its reactive power compensation and three-phase asymmetric current compensation lead to an effectively reduction on line loss. Therefore, under the ideal condition of unit power factor and symmetric three-phase load current, the operating loss of HDTs is higher than that of traditional transformers. With the increase in integration of distributed power sources, new energy storage, and various new loads, the application of HDTs can effectively solve the problems of high-frequency harmonics and reactive power component injection, as well as voltage fluctuations in the distribution network under the new situation, and effectively reduce the total power loss.

This paper proposes a comprehensive power loss analysis of hybrid distribution transformers in the distribution network and analyzes the reasons for using HDTs to reduce distribution line loss under non-unit power factor and three-phase unbalanced current conditions. Considering the loss of HDTs and conventional transformers, the conditions that should be met for the power factor and current balance when using HDTs to replace conventional transformers are determined to reduce overall loss. Finally, the validity of the model is verified through simulation.

Section II of this paper analyzes the system loss of HDTs. Section III analyzes the application of HDTs in the distribution power grid, reduces the line loss of the distribution power grid, and establishes a comprehensive power loss model of HDTs. Sec. IV conducts a sensitivity analysis, and Sec. V carries out simulation verification.

Figure 1 illustrates the schematic diagram of a hybrid distribution transformer, which includes a traditional distribution transformer and an HDT converter. The traditional transformer is applied to transmit power and convert voltage levels. The terminals of the HDT converter are connected in series and parallel with the distribution network, respectively, and can achieve reactive power compensation, three-phase unbalance compensation, and output voltage regulation for the distribution network.

FIG. 1.
Topology of the HDT.
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Topology of the HDT.

FIG. 1.
Topology of the HDT.
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Topology of the HDT.

Close modal

The HDT converter generally consists of a rectifier and inverter based on power electronic switching devices. Its current compensation winding and voltage compensation winding are, respectively, connected with the main transformer in parallel and series; hence, the power loss model can be simplified to the AC–DC–AC converter loss model.

When the reactive load or the unbalanced three-phase load causes a low power factor or three-phase load current unbalances, the converters of HDTs will provide three-phase load current unbalance compensation and reactive power compensation, and the output voltage and current of the converter can be given by
(1)
(2)
in which U and I represent the amplitude of the output voltage and current of the HDT converter, respectively.
The power electronic switching devices of the HDT converter are mainly an insulated-gate bipolar transistor (IGBT) and its body diode, and the duty cycle can be expressed as
(3)
(4)
in which Mod represents the modulation ratio.
Hence, the current of the IGBT and its body diode can be given by
(5)
(6)
(7)
(8)
in which IAV_IGBT and IAV_BD represent the average value of the current to the IGBT and its body diode, and IRMS_T and IRMS_BD represent the RMS value of the current to the IGBT and its body diode, respectively.
Hence, the conduction loss of the IGBT can be given by
(9)
The conduction loss of the body diode of the IGBT can be given by
(10)
in which UCE, UBD, Rr, and RBD represent the collector-emitter saturation voltage of the IGBT, the repetitive peak reverse voltage of the diode, the on state resistor of the IGBT, and the on state resistor of the body diode, respectively.
The switching losses of the IGBT and its body diode can be calculated as
(11)
(12)
in which ETon, EToff, EBDon, and EBDoff represent the turn-on and turn-off energy loss per pulse of the IGBT and its body diode, respectively, which can be found in the datasheet of the IGBT component, and fsw represents the switching frequency of the HDT converters.
According to China’s national standard GB 20052-2020, the minimum efficiency of a 500 kVA distribution transformer with electrical steel strip material, Dyn-11 connection, and three-level energy consumption is 98.92%. By setting the efficiency of the series winding and parallel winding of the traditional main transformer magnetic core of the HDT converter to ηcoil = 98.92% as well, the winding loss can be calculated as
(13)
in which PHDT represents the output power of HDT converters.
According to the derivation given above, the operating loss of the HDT can be given by
(14)
When there are both active and reactive power loads in the distribution power grid, the line loss of the transmission line can be given by
(15)
in which P represents the active power, R represents the resistor of the transmission line, and cos φ represents the power factor.
During the reactive power compensation, converters of the HDT generate reactive compensation current IQ, and the reduction of line loss can be given by
(16)
Because the capacity of the HDT converter is generally 10%–30% of the main transformer capacity, if the proportion is set to RHDT, the reactive compensation current and the three-phase unbalanced compensation current should both be less than RHDT times the rated current of the main transformer. Meanwhile, the compensation current IQ should be less than the maximum reactive compensation current IQmax when the HDT compensates the unit power factor with a power factor of cos φ, and the reactive compensation current will be constrained by
(17)

The symmetric three-phase loads lead to symmetric three-phase load currents, as well as basically non-zero-sequence current that flows through the neutral line. The asymmetric three-phase loads lead to asymmetric three-phase load currents, as well as zero-sequence current that flows through the neutral line due to the unequal phase currents, which causes the line loss on the neutral line. The zero-sequence current compensation of the HDT under unbalanced load is essentially to control the converter to generate a current with the same amplitude and opposite phase and then offset the zero-sequence current to approximately zero, thus reducing the line loss on the neutral line.

When three-phase load currents are unbalanced, the neutral line current can be given by
(18)
in which iA, iB, and iC represent the phase current of phases A, B, and C, respectively, and can be calculated as
(19)
(20)
(21)
in which IA, IB, and IC represent the amplitudes of phase current.
The neutral line current formula can be modified as
(22)
Hence, the line loss, which is composed of a phase line and a neutral line, can be expressed as
(23)
The line loss reduced by offsetting the zero-sequence current is calculated as
(24)
in which IεA, IεB, and IεC are the unbalanced compensation currents generated by the HDT converters for phases A, B, and C, respectively.
The constraints of three-phase load unbalanced compensation current include not exceeding the average three-phase current and not exceeding the rated current of the HDT converter and is expressed as
(25)
in which Iε(A,B,C) and I(A,B,C) are the unbalanced compensation current and the unbalanced load current of any one of the three phases before compensation, respectively.
The unbalance degree of three-phase current is generally used as a reference to measure the degree of three-phase asymmetry, which is given by
(26)
in which I1 and I2 are the positive and negative sequence components of the three-phase current, respectively.
If the total system loss by applying the HDT for reactive power compensation or three-phase unbalance compensation is lower than that when only using traditional transformers, the line loss reduced by reactive power compensation should be greater than the loss of the HDT itself, or the line loss reduced by three-phase unbalance compensation is greater than the loss of the HDT itself, which can be expressed by the following formula:
(27)
(28)

Taking the 500 kVA 10 kV/400 V HDT prototype applied in the 10 kV distribution transformer in Ezhou, Hubei, China as an example, the HDT consists of a main transformer and an independent H-bridge converter. The main transformer applies a Dyn11 connection, and both the parallel winding and the series winding are installed at the 400 V side of the transformer. The converter of the HDT generates reactive current and asymmetric current through the parallel winding to achieve reactive power compensation as well as three-phase unbalance compensation and adjusts the load voltage through the series winding.

The HDT converter is composed of three single-phase back-to-back converters; the rated power of each phase is 16.67 kW (10% of the main transformer’s single-phase capacity), and the rated output current is 72.4 A. The converter module applies the IGBT model Infineon FF600R12ME4. According to the specifications of this model, for the full load HDT converter at 25 °C, the typical value of VCE is 1.2 V, turn-on loss is 50 mJ, turn-off loss is 41 mJ, both the switching and turn-off losses of the body diode are 17 mJ, and the conduction voltage drop is 1.1 V. The line voltage on the primary and secondary side of the traditional transformer of the HDT is 10 kV and 400 V, respectively, the rated power of each phase is 166.7 kW, and the maximum output current is 724 A. Assuming that the HDT accesses a 5 km long 10 kV LGJ-120 overhead line, the line impedance is calculated as 2.15 Ω based on 0.43 Ω/km.

The 500 kVA main transformer core is made of electrical steel strip material and adopts a Dyn11 connection with a three-level energy consumption level. According to the relevant standards of GB 20052-2020, its no-load loss and full-load loss are 480 and 5410 W, respectively. Therefore, the no-load loss and full-load loss of the series winding and parallel winding of the HDT converter sharing the main transformer core can be set to 48 and 541 W, respectively, according to the corresponding capacity.

Theoretical calculations and Saber simulation software are used to calculate the loss of each module of the HDT converter. The operational power loss of the HDT for different components is calculated and listed in Table I.

TABLE I.

The operational power loss of the HDT.

Power modulePower loss with 50% load (W)Power loss with 100% load (W)
Converter 583 702 
Series and parallel winding 294.5 541 
Total power loss 877.5 1243 
Total efficiency 89.5% 92.5% 
Power modulePower loss with 50% load (W)Power loss with 100% load (W)
Converter 583 702 
Series and parallel winding 294.5 541 
Total power loss 877.5 1243 
Total efficiency 89.5% 92.5% 
View Large

Compared to the minimum efficiency of 99.5% for the traditional transformer, the total efficiency of the HDT is 89.2% and 92.3% at 50% load and 100% load, respectively, which is shown in Table I. Hence, the power loss will increase after the traditional transformer is replaced with the HDT under ideal operating conditions at three-phase balanced and pure resistive load. For the non-resistive and three-phase unbalance load, the HDT can achieve reactive power compensation and three-phase unbalanced current compensation, hence reducing the line loss and improving the comprehensive efficiency of the system.

When an HDT converter performs reactive power compensation, it can provide a reactive compensation current for each phase, thus correcting the power factor of the input current. Taking phase A as an example, its voltage and current are as shown in Fig. 2. From 0 to 0.6 s, due to the reactive power, the load current IO = 68.5 A lags behind the grid voltage US with the load power factor PF = 0.707, which can be seen in Fig. 2. After the reactive power compensation is activated at 0.6 s, the HDT converter injects capacitive compensation current Ic = 47 A into the grid, keeping the load current and grid voltage in the same phase, with the power factor PF = 0.99.

FIG. 2.
The phase voltage and current after reactive power compensation.
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The phase voltage and current after reactive power compensation.

FIG. 2.
The phase voltage and current after reactive power compensation.
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The phase voltage and current after reactive power compensation.

Close modal

The capability of the reactive compensation for the HDT converter is limited by its capacity (set to 10% of the main transformer capacity in this paper). The comprehensive loss reduction caused by the reduction of the HDT reactive compensation, shown in Fig. 3, considers the converter’s operational loss and the reduced line loss under different compensation currents. As can be seen from Fig. 3, when PF = 0.707, the HDT can improve the power factor through reactive compensation, hence reducing the comprehensive loss. When the main transformer is at 100% load, the power factor can be compensated to 0.759, reducing the comprehensive loss by 4.681 kW. When the main transformer is at 80% load, 50% load, and 10% load, the power factor can be compensated to 0.772, 0.813, and 0.96, and the comprehensive loss reduced is 3.406, 1.494, and −0.419 kW, respectively. The slopes of the curves under four different load rates in Fig. 3 show the effect of HDT reducing line loss through reactive compensation, indicating that the effect of reducing loss is better with a lower power factor and larger load.

FIG. 3.
The power loss reduction and power factor after the reactive power compensation.
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The power loss reduction and power factor after the reactive power compensation.

FIG. 3.
The power loss reduction and power factor after the reactive power compensation.
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The power loss reduction and power factor after the reactive power compensation.

Close modal

Taking into account the interaction between reactive compensation current and power factor, the loss reduction achieved by HDT reactive compensation is illustrated by the three-dimensional surface in Fig. 4. When the power factor is low, the effect of the HDT in reducing losses is more significant with the increase in reactive compensation current. However, when the power factor is high, the increase in reactive compensation current has a less effective impact on reducing losses.

FIG. 4.
The power loss reduction and power factor after the compensation.
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The power loss reduction and power factor after the compensation.

FIG. 4.
The power loss reduction and power factor after the compensation.
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The power loss reduction and power factor after the compensation.

Close modal

When the HDT converter performs three-phase unbalance compensation, if the theoretical compensation current is less than the rated current of the HDT converter, the HDT can achieve three-phase load current balance. When the theoretical compensation current is greater than the rated current of the HDT converter, the HDT converter is unable to achieve a three-phase load current balance; however, it outputs the rated current of the HDT converter for three-phase unbalanced compensation to reduce the unbalanced degree of the system and offsets the neutral line current, hence reducing the additional line loss caused by three-phase unbalance.

In the Saber simulation, unbalanced three-phase load currents are 434.4, 398.2, and 253.4 A, with 60%, 55%, and 40% of the rated current, respectively. The neutral line current is 165.9 A, and the three-phase unbalance degree is 15.28%. After 0.6 s, the HDT initiated three-phase unbalance compensation, with three-phase compensation currents of 72.4, 36.2, and 72.4 A. Since both phase A and phase B can be compensated to a balanced current of 362 A, the theoretical compensation current for phase C is 108.6 A, greater than the rated current of the HDT at 72.4 A. The three-phase currents after compensation are 362, 362, and 325.8 A. The neutral line current is reduced from 165.9 to 36.2 A, and the three-phase unbalance degree is reduced from 15.28% to 3.45%. The waveforms of three-phase currents and three-phase unbalanced compensation currents are shown in Fig. 5.

FIG. 5.
The voltage and current after 3-phase unbalance compensation.
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The voltage and current after 3-phase unbalance compensation.

FIG. 5.
The voltage and current after 3-phase unbalance compensation.
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The voltage and current after 3-phase unbalance compensation.

Close modal

The three-phase unbalance degrees are, respectively, 28%, 32.5%, 40%, and 47.5% at 50% load, and the reduction in the unbalance degree for three-phase current and the comprehensive loss reduction achieved by the three-phase unbalance compensation current (not exceeding 72.4 A) are illustrated in Fig. 6. The HDT can reduce the three-phase unbalance degree through three-phase unbalance compensation, thereby reducing line losses. The more serious the three-phase unbalance, the better the loss reduction effect.

FIG. 6.
The power loss reduction and 3-phase unbalance degree after the compensation.
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The power loss reduction and 3-phase unbalance degree after the compensation.

FIG. 6.
The power loss reduction and 3-phase unbalance degree after the compensation.
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The power loss reduction and 3-phase unbalance degree after the compensation.

Close modal

When the line lengths are 5, 10, and 15 km with 50% load (with a three-phase current of 1086 A), the comprehensive loss reduction achieved by the HDT converter three-phase unbalance compensation current (ranging from 0 to 72.4 A) under different three-phase unbalance degrees (ranging from 0.7 to 1.0) are shown as the three-dimensional surface in Fig. 7. The greater the three-phase unbalance degree and the longer the line, the larger reduction on the comprehensive loss.

FIG. 7.
The power loss reduction and 3-phase unbalance degree after the compensation.
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The power loss reduction and 3-phase unbalance degree after the compensation.

FIG. 7.
The power loss reduction and 3-phase unbalance degree after the compensation.
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The power loss reduction and 3-phase unbalance degree after the compensation.

Close modal

Due to the power electronic semiconductor devices, the power loss of the HDT is generally higher than that of traditional electromagnetic transformers, but the reactive power compensation and three-phase unbalance compensation of the HDT can reduce the loss of power distribution lines. This paper analyzes the comprehensive loss of the HDT based on its reactive power compensation and three-phase unbalance compensation functions and studies the loss of traditional transformers, the operational power loss of the HDT, the line loss that can be reduced by the reactive power compensation and three-phase unbalance compensation of HDT, and the comprehensive line loss reduction achieved by replacing traditional transformers with the HDT. Theoretical calculations and simulations show that replacing traditional transformers with the HDT can effectively reduce the overall system loss through reactive power compensation or three-phase unbalanced compensation with the low power factor or three-phase load current unbalanced situation and has broad application prospects in scenarios with low power factors and unbalanced three-phase loads.

This research was funded in part by the State Grid Hubei Electric Power Company Science and Technology Project (Grant No. 521538230007).

The authors have no conflicts to disclose.

Zixia Sang: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Supervision (lead); Validation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Xu Zheng: Data curation (equal); Formal analysis (equal); Funding acquisition (equal). He Lei: Funding acquisition (equal); Investigation (equal); Methodology (equal). Jiong Yan: Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal). Jie Cai: Project administration (equal); Resources (equal); Software (equal). Rengcun Fang: Supervision (equal); Validation (equal); Visualization (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
L.
Deliang
,
L.
Yibin
,
K.
Peng
,
C.
Shengliang
,
Z.
Kun
, and
Z.
Mingkang
,“
Analysis of development trend for intelligent distribution transformer
,”
Automation Electr. Power Syst.
44
(
7
),
1
–
14
(
2020
), available at http://www.aeps-info.com/aeps/article/abstract/20190507007.
Google Scholar
 
2.
Y.
Shenhang
,
S.
Ying
,
N.
Xiaona
, and
Z.
Chuanhui
, “
Energy internet system based on distributed renewable energy generation
,”
Electr. Power Automation Equip.
30
(
5
),
104
–
108
(
2010
), available at https://www.epae.cn/dlzdhsb/ch/reader/view_abstract.aspx?file_no=201005158&flag=1.
Google Scholar
 
3.
J.
Wang
,
L.
Jinyuan
, and
X.
Layuan
, “
Scheme of arcless onload voltage regulation for distribution transformer using high power electronic switch
,”
Automation Electr. Power Syst.
30
(
15
),
97
–
102
(
2006
), available at http://www.aeps-info.com/aeps/article/abstract/d061523.
Google Scholar
 
4.
J.
Wang
,
S.
Wanxing
,
H.
Yang
 et al, “
Analysis on technical performance of amorphous core distribution transformer
,”
Power Syst. Technol.
34
(
10
),
32
–
37
(
2010
), available at http://www.dwjs.com.cn/AQUK5_3pRSOsawpq799vlW7_0pIwd34jrV_ln3jvi%2Bg%3D?encrypt=1.
Google Scholar
 
5.
J.
Wang
,
S.
Wanxing
,
H.
Fang
 et al, “
Design of a self-adaptive distribution transformer
,”
Automation Electr. Power Syst.
38
(
18
),
86
–
92
(
2014
).
https://doi.org/10.7500/AEPS20140208002
Google Scholar
 
6.
J.
Burkard
 and
J.
Biela
, “
Evaluation of topologies and optimal design of a hybrid distribution transformer
,” in
2015 17th European Conference on Power Electronics and Applications (EPE'15 ECCE-Europe)
(
IEEE
,
Geneva, Switzerland
,
2015
), pp.
1
–
10
.
https://doi.org/10.1109/EPE.2015.7309097
Google Scholar
Crossref
Search ADS
 
7.
S.
Bala
,
D.
Das
,
E.
Aeloiza
 et al, “
Hybrid distribution transformer: Concept development and field demonstration
,” in
2012 IEEE Energy Conversion Congress and Exposition (ECCE)
(
IEEE
,
Raleigh, NC
,
2012
), pp.
4061
–
4068
.
Google Scholar
Crossref
Search ADS
 
8.
H.
Zhang
,
C.
Sun
,
L.
Zhixin
 et al, “
Voltage vector error fault diagnosis for open-circuit faults of three-phase four-wire active power filters
,”
IEEE Trans. Power Electron.
32
(
3
),
2215
–
2226
(
2019
).
https://doi.org/10.1109/TPEL.2016.2555583
Google Scholar
Crossref
Search ADS
 
9.
A.
Javadi
,
A.
Hamadi
,
L.
Woodward
 et al, “
Experimental investigation on a hybrid series active power compensator to improve power quality of typical households
,”
IEEE Trans. Ind. Electron.
63
(
8
),
4849
–
4859
(
2016
).
https://doi.org/10.1109/TIE.2016.2546848
Google Scholar
Crossref
Search ADS
 
10.
Y.
Chen
,
M.
Wen
,
X.
Yin
 et al, “
Principle and design of the cascaded STATCOM integrated with distribution transformer
,”
Trans. China Electrotech. Soc.
33
(
12
),
2861
–
2872
(
2018
).
https://doi.org/10.19595/j.cnki.1000-6753.tces.170531
Google Scholar
 
11.
C.
Fu
,
Z.
Gao
,
Y.
Sun
 et al, “
Hybrid modular direct current solid state transformer II: Dynamic characteristic and rapid response control
,”
Trans. China Electrotech. Soc.
34
(
14
),
2980
–
2989
(
2019
).
https://doi.org/10.1109/TPEL.2019.2935029
Google Scholar
Crossref
Search ADS
 
12.
J.
Rodriguez
,
S.
Bernet
,
B.
Wu
,
J. O.
Pontt
, and
S.
Kouro
, “
Multilevel voltage-source-converter topologies for industrial medium-voltage drives
,”
IEEE Trans. Ind. Electron.
54
(
6
),
2930
–
2945
(
2007
).
https://doi.org/10.1109/tie.2007.907044
Google Scholar
Crossref
Search ADS
 
13.
G.
Kalcon
 et al, “
Analytical efficiency evaluation of two and three level VSC-HVDC transmission links
,”
Int. J. Electr. Power Energy Syst.
44
(
1
),
1
–
6
(
2013
).
https://doi.org/10.1016/j.ijepes.2012.07.018
Google Scholar
Crossref
Search ADS
 
14.
P.
Tatcho
,
H.
Li
,
Y.
Jiang
, and
L.
Qi
, “
A novel hierarchical section protection based on the solid state transformer for the future renewable electric energy delivery and management (FREEDM) system
,”
IEEE Trans. Smart Grid
4
(
2
),
1096
–
1104
(
2013
).
https://doi.org/10.1109/tsg.2012.2207412
Google Scholar
Crossref
Search ADS
 
15.
X.
She
,
S.
Lukic
,
A. Q.
Huang
,
S.
Bhattacharya
, and
M.
Baran
, “
Performance evaluation of solid state transformer based microgrid in FREEDM systems
,” in
IEEE 26th Annual Applied Power Electronics Conference and Exposition
(
IEEE
,
2011
), pp.
182
–
188
.
Google Scholar
Crossref
Search ADS
 
16.
E.
Li
 et al, “
Combined compensation strategies based on instantaneous reactive power theory for reactive power compensation and load balancing
,” in
2011 International Conference on Electrical and Control Engineering
(
IEEE
,
2011
), pp.
5788
–
5791
.
https://doi.org/10.1109/ICECENG.2011.6057765
Google Scholar
Crossref
Search ADS
 
17.
Y.
Wang
,
W.
Wang
, and
X.
He
, “
Research on the problem of rural distribution grid reconstruction to meet the demand of intelligent power distribution
,” in
2012 China International Conference on Electricity Distribution
(
IEEE
,
2012
), pp.
1
–
6
.
https://doi.org/10.1109/CICED.2012.6508582
Google Scholar
Crossref
Search ADS
 
18.
K.
Lee
,
G.
Venkataramanan
, and
T. M.
Jahns
, “
Modeling effects of voltage unbalances in industrial distribution systems with adjustable-speed drives
,”
IEEE Trans. Ind. Appl.
44
(
5
),
1322
–
1332
(
2008
).
https://doi.org/10.1109/tia.2008.2002277
Google Scholar
Crossref
Search ADS
 
19.
H.
Li
,
A. T.
Eseye
,
J.
Zhang
, and
D.
Zheng
, “
Optimal energy management for industrial microgrids with high-penetration renewables
,”
Prot. Control Mod. Power Syst.
2
(
1
),
12
–
28
(
2017
).
https://doi.org/10.1186/s41601-017-0040-6
Google Scholar
Crossref
Search ADS
 
20.
W.
Qingzhu
,
W.
Mingli
,
C.
Jianye
, and
Z.
Guiping
, “
Model for optimal balancing single-phase traction load based on Steinmetz’s method
,” in
IEEE Energy Conversion Congress and Exposition
(
IEEE
,
2010
), pp.
1565
–
1569
.
Google Scholar
Crossref
Search ADS
 
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