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Comparative study of semiconductor power losses between CSI-based STATCOM and VSI-based STATCOM, both used for unbalance compensation

Abstract

In this paper, we present a detailed procedure to determine the semiconductor losses for both structures of a shunt STATCOM (Static Compensator), STATCOM based on Current Source Inverter (CSI) and STATCOM based on Voltage Source Inverter (VSI), both used for voltage unbalance compensation. As a first step, we study the VSI-based STATCOM and the CSI-based STATCOM used in high speed railway substations. Then we analyze the design and the sizing of the unbalance compensator in order to obtain an unbalance factor that does not exceed the limits imposed by the standards or by the energy provider. Following that, we compare the performances obtained with both structures VSI-STATCOM and CSI-STATCOM, after calculating the semiconductor power losses in the STATCOM converters. Finally, we validate our approach by simulation over real data of unbalance compensation caused by the new high-speed railway in Morocco. We use the tools MATLAB / Simulink/Simpowersys for performing our simulations.

Introduction

The flexible alternative current transmission system (FACTS) is used in the power grid in order to improve the quality of energy. In particular, the static shunt compensators with voltage source inverters are installed in high-speed railway substations to compensate the unbalance [1,2,3].

The railway operator is mainly interested in reducing the compensator size, cost, and the converter losses; this is from where comes our idea to propose a replacement of the voltage source inverter structure by the current source inverter structure. To validate this proposition, we show the performances obtained by a CSI-based STATCOM used in the unbalance compensation. The rest of this paper is organized as follows:

In the second section, we give an overview of the principle of electric power supply system for high-speed railways (HSR). The third section presents the analysis of voltage unbalance generated by the railway substation. In the fourth section, we present the STATCOM structure used for unbalance compensation. While in the fifth section, we present our sizing methodology and our control strategy, for both STATCOM structure VSI and CSI. The sixth section, we show the detailed calculation of the semiconductor power losses in the converters. Then in the seventh section, we compare and discuss the obtained results for both structures (VSI-based STATCOM and CSI- based STATCOM) using data coming from railway operator in Morocco about the HSR substation.

Principle of electrification of high-speed railway

The HSR are electrified by a tow-phases system 2*25KV − 50 Hz (Fig. 1), where the single-phase transformer of the substation is connected between two phases of the HV power grid.

Fig. 1
figure1

Power circuit of supply AC system (2*25KV-50 Hz) of the HSR substation

This system transmits the energy at 50 kV between the catenary and a complementary cable, called the “negative feeder”. A voltage of 25 kV between the catenary and the railis, is obtained by means of Mid-point autotransformer connected between the catenary, the rail, and the negative feeder. The first implementation of this solution was in 1981 on the HST South-East line in France [2].

Analysis of the unbalance caused by HSR

A three-phase system is balanced if the three currents or voltages have the same amplitude, the same frequency, as well as the difference between their phases is equal to 120°; otherwise the system is unbalanced. The HSR substations generate a significant unbalance in the high voltage lines with low short-circuit power (Scc), because they are more sensitive to the disruptions. Figure 2 shows the supply schema of a HSR substation by a three-phase line with line impedance (Zcc) [2].

Fig. 2
figure2

A power schema of a substation connection [2]

The apparent power and the unbalance factor for HSR substations:

$$ {T}_{iV}\left(\%\right)\approx 100\frac{S_{ss}}{S_{CC}} $$
(1)
$$ {S}_{ss}=U\cdotp {I}_{SS} $$
(2)

Compensation of the unbalance by STATCOM

Principle of the STATCOM

The static compensator (as shown in Fig. 3) is a three-phase sinusoidal AC current source that injects the negative sequence of currents to compensate the unbalance at the PCC point. This injection of current is made by the STATCOM which is based on power electronics converters [2,3,4, 5, 6].

Fig. 3
figure3

Diagram of an unbalance compensator

The STATCOM must be sized to control the unbalance around Tiv.max in the limit imposed by the energy provider. The currents injected at PCC have a negative sequence [7] (see Table 1).

  • For total compensation:

Table 1 Expression & diagram of injected currents
$$ \overline{I_{inj}^{-}}=\frac{\sqrt{3}}{3}\overline{I_{SS}}{e}^{j\frac{\pi }{6}} $$
(3)

The apparent power of STATCOM used for unbalance total compensation is: [7].

$$ {S}_{C. Total}=\sqrt{3}U{I}_{inj}^{-}=\sqrt{3}U\frac{\sqrt{3}}{3}{I}_{SS}=U{I}_{SS}={S}_{SS} $$
(4)
  • For partial compensation:

In order to size the STATCOM, in first step, it is necessary to determine the percentage of the limit RMS value of the current negative component to be injected:

$$ {I}_{inj}^{-}\left(\%\right)={T}_{iV.\mathit{\max}}\left(\%\right)\bullet \frac{S_{CC}}{\sqrt{3}U}\bullet \frac{1}{100} $$
(5)

The apparent power of STATCOM used for unbalance partial compensation is given by:

$$ {S}_{C. partial}=\frac{I_{inj}^{-}\left(\%\right)}{100}\bullet {S}_{ss} $$
(6)

Voltage source inverter based STATCOM (VSI-STATCOM)

A compensator STATCOM based on a VSI (see Fig. 4) is composed of several compensation cells coupled in parallel with the secondary of the three-phase transformer with Yy0 connection. Each cell contains an AC filter inductor (L), a VSI converter with sine-triangle PWM control, and a DC side voltage source made by a capacitor (Cdc). The VSI-STATCOM and the HSR substation (unbalanced load) are connected to the PCC bus

Fig. 4
figure4

One-Line Diagram of VSI-STATCOM

In general, the apparent power of the compensator (Sc) is equal to the number of cells (NVSI) multiplied by the power of each cell (Scel):

$$ {S}_C={N}_{VSI}\bullet {S}_{cel} $$
(7)

Current source inverter based STATCOM

A CSI-STATCOM (see Fig. 5) is composed of several compensation cells coupled in parallel to the secondary of the three-phase transformer with Yy0 connection. Each cell contains an AC LC filter, a CSI converter with sine-triangle PWM control, and a DC side current source realized by an inductor (Ldc). The CSI-STATCOM and the HSR substation (unbalanced load) are connected to the PCC bus.

Fig. 5
figure5

One-Line Diagram of CSI-STATCOM

In general, the apparent power of compensator (Sc.) is equal to the number of cells (NCSI) multiplied by the power of each cell (Scel):

$$ {S}_C={N}_{CSI}\bullet {S}_{cel} $$
(8)

Sizing and control strategy of STATCOM

Sizing of VSI-STATCOM cell

The power circuit of the VSI-STATCOM cell is composed of a six bidirectional current switch (IGBT with anti-parallel diode), a capacitive storage source in a DC side inverter, and a three-phase inductor filter connected between the AC side inverter (a’,b’,c’) and the transformer secondary (a,b,c). The IGBT switch is controlled by the PWM signal (see Fig. 6).

Fig. 6
figure6

Power circuit of VSI-STATCOM cell

The DC capacitor and the filter inductor are given by the flowing expressions [8,9,10]:

$$ {C}_{dc}=\frac{\sqrt{2}\bullet {S}_{cel}}{V_{DC. ref}\bullet \varDelta {V}_{DC}\left(\mathit{\max}\right)\bullet {\omega}_r} $$
(9)
$$ L=\frac{V_{DC. ref}}{12\bullet {f}_d\bullet \varDelta {I}_{inj}} $$
(10)

The voltage and current supported by IGBT are given by the flowing expressions [11]:

$$ {I}_{sw}\ge \sqrt{2}\bullet {I}_{inj} $$
(11)
$$ {V}_{sw}\ge {V}_{DC. ref} $$
(12)

The VSI_STATCOM cell apparent power is given by:

$$ {S}_{cel}=3\cdotp m{V}^{pcc}\cdotp {I}_{inj} $$
(13)

Sizing of the CSI-STATCOM cell

The power circuit of the CSI-STATCOM cell is composed of six unidirectional current switches (only IGBT or IGBT with anti-parallel diode and diode in series), an inductor storage source in the DC side inverter, and a three-phase L’C filter connected between the AC side inverter (a’,b’,c’) and the transformer secondary (a,b,c). The IGBT switches are controlled by the PWM signal (see Fig. 7).

Fig. 7
figure7

Power circuit of CSI_STATCOM cell

The DC inductor and the L’C filter are given by the flowing expressions: [12].

$$ {L}_{dc}=\frac{\sqrt{2}\bullet {S}_{cel}\left(1-\left(2\bullet C\bullet {\omega_r}^2\bullet L^{\prime}\right)\right)}{I_{DC. ref}\bullet \varDelta {I}_{DC}\left(\mathit{\max}\right)\bullet {\omega}_r} $$
(14)
$$ L^{\prime }=\frac{{\left({mV}^{pcc}\right)}^2}{3\bullet {S}_{cel}\bullet {\omega}_r} $$
(15)
$$ C=\frac{1}{L^{\prime}\bullet {\omega_0}^2} $$
(16)

The voltage and current supported by IGBT are given by the flowing expressions: [11].

$$ {I}_{sw}\ge {I}_{DC. ref} $$
(17)
$$ {V}_{sw}\ge \sqrt{2}\bullet {V}_C\left(\mathit{\max}\right) $$
(18)

The CSI-STATCOM cell apparent power is given by:

$$ {S}_{cel}=3\cdotp m{V}^{pcc}\cdotp {I}_{inj} $$
(19)

The fundamental component of the AC side current (IO) is given by: [12].

$$ {I}_{DC.r{{e}^{'}}f}=\sqrt{2}\bullet {I}_O\left(\mathit{\max}\right) $$
(20)
$$ \overline{I_O}=\overline{I_{inj}}\left(1-C.{L}^{\prime }.{\omega_r}^2\right)+j.C.{\omega}_r.m\overline{V^{pcc}} $$
(21)

Control of VSI_STATCOM cell

The shunt STATCOM must inject the negative sequence of the current consumed by the single-phase load (High speed railway substation) in the transformer’s secondary. According to equations of Table 1, the block diagram for the set-point generation of the injected currents is shown in Fig. 8 [9, 13].

Fig. 8
figure8

Obtaining the set-point currents to be injected

The VSI-STATCOM cell is controlled by two loops: The first loop controls the injected current (Iinj) in the d-q plan (park transformation) with PI controller RI(p) (see Fig. 9), the second loop regulates the DC bus voltage (Vdc) around its reference value with a proportional delay controller Ru(p) (see Fig. 10). The generation of three-phase PWM control signals from the corrected sinusoidal modulating signals (sine) is shown in Fig. 11.

Fig. 9
figure9

Diagram control blocks of the voltage VDC

Fig. 10
figure10

Diagram control blocks of the injected current negative sequence for VSI cell

Fig. 11
figure11

Generation of three-phase PWM signal

The transfer functions of controllers used in the control part are given by [9]:

$$ {R}_u(p)=\frac{K_v}{1+{\tau}_vp} $$
(22)
$$ {R}_I(p)={K}_I\frac{1+{\tau}_Ip}{\tau_Ip} $$
(23)

The transformation matrices (Park & Clark) are given by:

$$ C=\frac{1}{\sqrt{3}}\left[\begin{array}{ccc}0& \frac{\sqrt{3}}{\sqrt{2}}& \frac{-\sqrt{3}}{\sqrt{2}}\\ {}\sqrt{2}& \frac{-1}{\sqrt{2}}& \frac{-1}{\sqrt{2}}\end{array}\right] And\ {C}^{\prime }=\left[\begin{array}{cc}{V}_{\alpha }& {V}_{\beta}\\ {}-{V}_{\beta }& {V}_{\alpha}\end{array}\right] $$
(24)
$$ \left\{\begin{array}{c}{P}_k^{-}=\frac{1}{3}\left[\begin{array}{ccc}2\mathit{\sin}\left(-\theta \right)& 2\mathit{\sin}\left(-\theta -\frac{2\pi }{3}\right)& 2\mathit{\sin}\left(-\theta +\frac{2\pi }{3}\right)\\ {}2\mathit{\cos}\left(-\theta \right)& 2\mathit{\cos}\left(-\theta -\frac{2\pi }{3}\right)& 2\mathit{\cos}\left(-\theta +\frac{2\pi }{3}\right)\\ {}1& 1& 1\end{array}\right]\\ {}\theta ={\omega}_r\cdotp t\end{array}\right. $$
(25)

Control of CSI-STATCOM cell

The CSI-STATCOM cell is controlled by two loops: The first loop controls the injected current (Iinj) in the d-q plan (park transformation) with PID controller RI1(p) (see Fig. 12); the second loop regulates the DC bus current (IDC) around its reference value with a proportional delay controller RI2(p) (Fig. 13). We use the same block diagrams (Figs. 8 and 11) for the injection of set-point currents and the generation of three-phases PWM signals,

Fig. 12
figure12

Diagram control blocks of the injected current negative sequence for CSI cell

Fig. 13
figure13

Diagram control blocks of the voltage IDC

The transfer functions of controllers used in the control part are given by [12]:

$$ {R}_{I1}(p)={K}_I^{\prime}\frac{1+{\tau}_I^{\prime }p+{\tau}_I^{\prime }{\tau}_d{p}^2}{\tau_I^{\prime }p} $$
(26)
$$ {R}_{I2}(p)=\frac{K_{IDC}}{1+{\tau}_{IDC}s} $$
(27)

The transfer functions of the physical system for CSI-STATCOM in dq plan are given by [12]:

$$ {H}_1(p)=\frac{\frac{m}{1-\frac{{\omega_r}^2}{{\omega_0}^2}}}{\left(1+\frac{\frac{R^{\prime }}{L^{\prime }}}{{\omega_0}^2-{\omega_r}^2}p+\frac{1}{{\omega_0}^2-{\omega_r}^2}{p}^2\right)} $$
(28)
$$ {H}_2(p)=\frac{\left(R^{\prime }C{\omega}_r+\left(L^{\prime }C\cdotp 2{\omega}_rp\right)\right)\frac{1}{1-\frac{{\omega_r}^2}{{\omega_0}^2}}}{\left(1+\frac{\frac{R^{\prime }}{L^{\prime }}}{{\omega_0}^2-{\omega_r}^2}p+\frac{1}{{\omega_0}^2-{\omega_r}^2}{p}^2\right)} $$
(29)

Calculation of power losses in semiconductors

Analytical expressions of power losses in semiconductors

The IGBT module is a bidirectional current switching device. It is composed of a bipolar transistor with an insulated gate and an anti-parallel diode which allows bidirectional current (VSI cell case) (Fig. 14 (a)). The IGBT combines the advantages of a bipolar transistor (high voltage, high intensity) and a MOSFET (fast switching).

Fig. 14
figure14

a The module of an IGBT with anti-parallel diode. b The module of the diode in series used in CSI case

The diode module added in series with the IGBT module ensures the unidirectional current circulation (CSI cell case) (Fig. 14 (b)).

Conduction losses

The equivalent model of an IGBT transistor (Fig. 15 (a)) and the diode (Fig. 15 (b)) during conduction is presented in the following figure:

Fig. 15
figure15

a IGBT model in conduction. b Diode model in conduction

The analytical expression of the conduction losses can also be expressed in an alternative way in the case when the transistor is in conduction: [2, 14, 15].

$$ {P}_{cond. IGBT}=\left({V}_{CE. sat}\bullet {I}_{C. AVG}\right)+\left({r}_{on. IGBT}\bullet {I_{C. rms}}^2\right) $$
(30)

In the same way, the conduction diode losses are expressed as follows: [2, 14, 15].

$$ {P}_{cond.D}=\left({V}_F\bullet {I}_{FAV. AVG}\right)+\left({r}_{on.D}\bullet {I_{FAV. rms}}^2\right) $$
(31)

Switching losses:

The analytical expressions of the switching losses for IGBT are expressed by [2, 14, 15]:

$$ {\mathrm{P}}_{\mathrm{c}\mathrm{omm}.\mathrm{IGBT}}={\mathrm{f}}_{\mathrm{d}}\bullet \frac{{\mathrm{V}}_{\mathrm{C}\mathrm{E}}}{{\mathrm{V}}_{\mathrm{C}\mathrm{E}.\mathrm{r}}}\bullet \left(\left({\mathrm{a}}_{\mathrm{on}}+{\mathrm{a}}_{\mathrm{off}}\right)\frac{{{\mathrm{I}}_{\mathrm{C}.\mathrm{peak}}}^2}{4}+\left({\mathrm{b}}_{\mathrm{on}}+{\mathrm{b}}_{\mathrm{off}}\right)\frac{{\mathrm{I}}_{\mathrm{C}.\mathrm{peak}}}{\uppi}+\left({\mathrm{c}}_{\mathrm{on}}+{\mathrm{c}}_{\mathrm{off}}\right)\frac{1}{2}\right) $$
(32)

In the same way, the switching losses of the diode are expressed by: [2, 14, 15].

  • Anti-parallel diode:

$$ {\mathrm{P}}_{\mathrm{c}\mathrm{omm}.\mathrm{D}}={\mathrm{f}}_{\mathrm{d}}\bullet \frac{{\mathrm{V}}_{\mathrm{RRM}}}{{\mathrm{V}}_{\mathrm{RRM}.\mathrm{r}}}\bullet \left({\mathrm{a}}_{\mathrm{rec}}\frac{{{\mathrm{I}}_{\mathrm{FAV}.\mathrm{peak}}}^2}{4}+{\mathrm{b}}_{\mathrm{rec}}\frac{{\mathrm{I}}_{\mathrm{FAV}.\mathrm{peak}}}{\uppi}+{\mathrm{c}}_{\mathrm{rec}}\frac{1}{2}\right) $$
(33)
  • Serial diode (for CSI):

$$ {\mathrm{P}}_{\mathrm{comm}.\mathrm{D}}={\mathrm{f}}_{\mathrm{d}}\bullet {\mathrm{V}}_{\mathrm{r}}\bullet {\mathrm{Q}}_{\mathrm{r}\mathrm{r}} $$
(34)

Power losses calculation for VSI cell

If we take a single-phase AC side of the VSI cell as an example, the both power switches (IGBT module) in the arm (TOP and BOTTOM), switches in a complementary way, and they have the same losses. The Fig. 16 shows the waveform of the current in the IGBT transistor and its anti-parallel diode.

Fig. 16
figure16

IGBT and anti-parallel diode currents waveform with sine-triangle PWM modulation

The modulating signal and the injected current for one phase in the VSI cell are expressed as follows:

$$ {r}_{a\prime }(t)={r}_{a\prime, \mathit{\max}}\bullet \mathit{\sin}\left({\omega}_rt\right) $$
(35)

With a’ is a phase reference.

The collector current of IGBT is:

$$ {I}_C(t)={I}_{inj}(t)=\sqrt{2}\bullet {I}_{inj}\bullet \mathit{\sin}\left({\omega}_rt+\varphi \right) $$
(36)

The IGBT transistor is conducting in the interval [φ;φ + π], while the antiparallel diode is conducting in the interval [φ + π; φ + 2π]. Therefore, the expressions of the peak, RMS, and AVG values of the IGBT currents and the ant parallel diode current are [11] (see Table 2):

Table 2 Expression of Peak, RMS, and AVG value of IGBT and antiparallel diode current and voltage (VSI cell)

Power losses calculation for the CSI cell

In the same way as for the VSI cell, expressions of the peak, RMS, and AVG values of the IGBT currents and the series diode current for CSI cell are illustrated in Table 3 [11]:

Table 3 Expressions of Peak, RMS, and AVG value of IGBT and antiparallel diode current and voltage (CSI cell)

Application and simulation (case study)

The simulation has been performed with the real parameters of the IGBT module of the manufacturer ABB (VCE.r = 4.5KV / IC.r = 1.2KA, ref.: 5SNA1200G450300) and the diode module of the manufacturer SEMIKRON (VRRM.r = 2.2KV / IFAV.r = 1.37KA, ref.: SKKE 1200/22 H4). The Table 4 presents the characteristics of these semiconductors.

Table 4 STATCOM Semiconductors characteristics

We choose one substation among others of the new Moroccan HSR as a study case (see Fig. 17). This substation has the following characteristics (see Table 5) [16]. The unbalance (see Fig. 18) caused by this substation exceeds the limit of 2% imposed by the standard NF EN50160 [17]. Soit is interesting to install an unbalance compensator in this substation.

Table 5 Substation characteristics of study case
Fig. 17
figure17

Distribution schematic of HSR

Fig. 18
figure18

Unbalance factor and substation power in function of daily railway traffic without STATCOM [16]

Sizing of the unbalance compensators substation (PK100)

In this subsection, we calculate the compensator power with a total unbalance compensation for each type of the converter (VSI and CSI). The calculation results are presented in the Table 6.

Table 6 Sizing results for unbalance compensator

Table 7 shows the values of the parameters calculated for the power circuit of each cell (VSI and CSI):

Table 7 STATCOM power circuit parameters

Table 8 depicts the values of the controller parameters used for control of each cell (VSI and CSI):

Table 8 Controller parameters

Simulation of unbalance compensation

Figures 19 and 20 show the simulation results of the unbalance factor obtained using static compensators (VSI and CSI):

Fig. 19
figure19

Unbalance factor in function of daily railway traffic caused by substation Pk100 with VSI_STATCOM

Fig. 20
figure20

Unbalance factor in function of daily railway traffic caused by substation Pk100 with CSI-STATCOM

Calculating of power losses in full load

The Table 9 presents the conduction and switching power losses for each structure of STATCOM (VSI and CSI):

Table 9 Power losses converter STATCOM

If considering the active power losses in the AC side filters, and in the DC side storage circuit, the Table 10 presents the global power losses for STATCOM:

Table 10 Global power losses for STATCOM

Simulation of power losses in dynamic power variation

Figure 21 shows the dynamic evolution of the global power losses according to the variation of the power consumed by the substation during railway traffic.

Fig. 21
figure21

Global power losses in function of daily railway traffic

Discussion and evaluation of the results

In sizing terms, the calculation results in Table 10 show that the unbalance compensator with a voltage source inverter (VSI) needs up to 24 converter cells, but the one with a current source inverter (CSI) needs only up to 9 converter cells. This is the advantage of STATCOM with CSI cells; which is the congestion in the railway substation, and the reduced costs.

Figures 19 and 20 show that the STATCOM with VSI cell or CSI cell allow to control the unbalance factor according to the standards (Tiv < 2%).

In terms of power losses and efficiency, the calculation results in (Table 10) show that, the compensator based on CSI (4.75 MW, 92.56%) is more optimal than the one based on VSI (14.52 MW, 80.51%), in steady state with full load condition. In addition, Fig. 21 demonstrates that the STATCOM with CSI cells has less loss than the one with VSI in dynamic daily railway traffic. Thus, we conclude that the unbalance compensation with CSI cells is an optimal solution for railway operator.

Conclusion

According to the sizing procedure described in this paper, the use of STATCOM compensator is much more required when daily railway traffic reaches a certain value, especially in rush hours. This compensator implies a big investment for the railway operator. For this reason, the designer engineering office tries to choose the optimal solution in terms of cost and efficiency. The obtained results show that the VSI-STATCOM has lower efficiency then the CSI-STATCOM (80,51% VS 92.65%) with full load (rated conditions). The CSI-STATCOM presents a reduced number of converter cells compared to the VSI-STATCOM which reduces the size and the cost of the compensator while keeping the unbalance factor lower than the limit of 2% imposed by the standard. We conclude so that the STATCOM based on CSI is an optimal solution in high power compensation.

The experimental validation for this comparative study makes the objective of a second paper.

Nomenclatures

a, b, c phase indexes

+, −positive and negative sequence indexes

ScCompensator apparent power

SccShort-circuit apparent power

SssApparent power consumed by substation

Sc.totalApparent power for total compensation

Sc.partialApparent power for partial compensation

Scellconverter cell apparent power

PcondConduction losses

PcommSwitching losses

V HVline-ground rated voltages

VpccHV line-ground voltages in PCC

UHV line-line RMS voltage

VDC.refDC voltage set-point for VSI

ΔVDCvoltage ripple in DC side for VSI

VCEIGBT collector-emitter voltage

VFDiode forward voltage

VLine-ground in filter capacity for CSI

Isw and Vswcurrent and voltage of the semiconductor switch

ITCurrent consumed by train

iReturn current to substation

IssCurrent consumed by substation

IHV line phase current

Iinjinjected current by compensator

ICIGBT collector current

IFAVdiode current

ΔIinjinjected current ripple in AC side inverter for VSI

Tivvoltage unbalance factor

mtransformer ratio

NVSInumber of voltage source inverter cell

NCSInumber of current source inverter cell

fdswitching frequency

ω0Natural frequency of RLC filter for CSI

ωrpower grid pulsation

ZccLine impedance in PCC

rondynamic resistance diode

Availability of data and materials

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful and constructive comments that greatly contributed to improving the final version of the paper. They would also like to thank the Editors for their generous comments and support during the review process.

Funding

The work is not supported by any funding agency. This is the authors own research work.

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Contributions

AB, and JB performed the detailed design of the compensator cell sizing (VSI and CSI), as well as the calculation of the semiconductors power losses. ME, BH, and LE corresponding, engaged in modifying the paper and submitted it to the PCMP. SM, MT and YM checked the grammar and writing of the paper. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Anas Benslimane.

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The authors declare that they have no competing interests.

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Benslimane, A., Bouchnaif, J., Essoufi, M. et al. Comparative study of semiconductor power losses between CSI-based STATCOM and VSI-based STATCOM, both used for unbalance compensation. Prot Control Mod Power Syst 5, 4 (2020). https://doi.org/10.1186/s41601-019-0150-4

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Keywords

  • Power losses
  • VSI
  • CSI
  • STATCOM
  • Unbalance compensation
  • Railway