Comparative Study Between (CSI based STATCOM and VSI based STATCOM) Used For Current Unbalance Compensation

Comparative Study Between (CSI based STATCOM and VSI based STATCOM) Used For Current Unbalance Compensation

Anas Benslimane Laboratory of Electrical Engineering and Maintenance

Higher School of Technology Oujda, Morocco

Jamal Bouchnaif

Laboratory of Electrical Engineering and Maintenance

Higher School of Technology Oujda, Morocco

Mohamed Azizi Laboratory of Electrical Engineering and Maintenance

Higher School of Technology Oujda, Morocco

Abstract

The sub-stations of the high speed railway connected to the high voltage power system, are considered pollutant loads, and disrupting power grid. The major problem of these sub-stations is the current unbalance caused by the connection between two phases of high voltage power grid. In general case, the shunt STATCOMs used for current unbalanced compensation, are based on voltage source inverter (VSI). By using a current source inverter (CSI) we obtain important performances compared to the VSI structure.

In this paper, we presented a comparative study between the two structures of shunt STATCOM (VSI and CSI), in order to evaluate the current unbalance compensation performances and the sizing optimization.

1. Introduction

   A large DC inductor and a current control system, allow the CSI_STATCOM to offer very interesting performances. CSI topology offers a number of distinct advantages below compared to VSI, [1]:

   • Inverter power circuit size reduction;

   • Direct control of the injected current;

   • No risk of DC link source short-circuit, because it is a current source realized by an inductor;

   • High converter reliability, due to the unidirectional nature of the switches.

     The DC link inductor must be equipped by a protection circuit against overvoltage caused by the circuit opening [6]. This work shows that the current source inverter-based STATCOM (CSI) can be exploited to compensate the current unbalance with

     optimal sizing of the power circuit, on the other side the compensation performance are lower compared to of the voltage source inverter-based STATCOM (VSI). The classic structure of VSI_STATCOM used for unbalanced compensation is explained in the first part of this paper. Then, the power circuit and the current control loop for shunt CSI_STATCOM is studied. Finally, this study is applied to the future sub-station for a new high speed railway (HSR) in Morocco, and the model for each structure is simulated in MATLAB/Simulink environment.

2. Current unbalance caused by the high speed railway sub-stations

   Figure 1: The electrification system of high speed railway (2*25KV-50Hz)

   Usually, the single-phase transformer in a HSR sub- station is connected to two phases of high voltage power grid (Figure 1). In this case, the symmetrical components of current and current unbalance factor Ti obtained by the Fortescue transformation are as follows [2],[7]:

   I I

   Id

   3

   3 Iss.e

   • j 6

     I = I = 3 I

     inj i 3 ss

     (3)

     1 ss

     3 j I

     i

     i

     I2 Iss F Ii

     Iss.e 6

     and Ti 100% (1)

     With:

     I

     I

     0

     0

     3

     With:

     3 Id

     Io 0

     |X|: Rms value (with X is a voltage or current); The Inductor (L) is calculated by using the

     Iss: current consumed by the substation;

     Ii,Id,Io : symmetrical components of three-phase

     equation below [2]:

     L|

     100.m.Vdc

     (4)

     current, respectively negative, positive, and zero- sequence;

     F: Fortescue transformation matrix;

     With:

     With:

     2.12.fd.Iin(j

     %). Iinj

     min

     1 1 1

     F 1 1 a a2 and

     j 2

     a e 3

     (2)

     fd: Carrier frequency of the PWM control;

     Iinj(%) : Injected current ripple;

     3 1 a2 a

     The DC side voltage Vdc is calculated according to

     Note that the negative sequence of the current is very large, which generates unbalanced voltages at different points in the network. The shunt STATCOM used to compensate this unbalance is equivalent to an AC current source. It injects at the

     the maximum magnitude between the three phase- ground voltages AC side of inverter (VAC1, VAC2, VAC3), because these voltages are unbalanced [2]. For a voltage source inverter with PWM control, Vdc equal:

     connection point the negative sequence current Ii, in order to control the current unbalance factor Ti to a value 2% limited by the standards [2].

3. Classical structure of VSI_STATCOM

   The voltage structure of shunt STATCOM (Figure 2) is composed of a PWM voltage source inverter, a current filtering inductor L (with an

   Vdc = 2. 2.maxVAC1 , VAC2 , VAC3

   In the phase number i, we have:

   1

   1

   VACi mVi (R ' jL'r ) m Iinj,i

   With:

   (5)

   (6)

   internal resistance R), a coupling transformer with ratio (m), and an energy storage circuit often capacitive which represents a DC voltage source (Vdc)[2].

   Figure 2: Classical structure of VSI_STATCOM

   1. Power circuit of VSI_STATCOM

      The injected current rms value Iinj depends on the current sub-station [2]:

      Vi: Phase-to-ground voltage at the connection point to the power grid;

      r: Pulsation of the power grid voltage (r=2..fr);

      The Vdc voltage must be maintained at a constant value, using one of both following techniques:

      • Additions of a voltage control loop of Vdc

        in the inverter control;

      • The state feedback control of VSI_STATCOM, with Vdc is a state variable of the system.

        The power switches for a voltage source inverter must support a voltage Vsw and a current Isw [3]:

        Isw 2*(1/m)*|Iinj| and Vsw Vdc (7)

   2. Injected current control in the VSI topology

   The principle of this control (Figure 3) is to find the current to be injected using the sub-station current Iss [2]:

   With:

   m. Vdc G' 2

   R '.Vp max

   The response time of the system is:

   3.|

   Tr I

   bI.K'.G'

   (10)

   Figure 3: Calculation technique of currents to be injected.

   K is given by the expression below using the response time Tr:

   With:

   bI : Gain of the current sensor;

   3.| K' = I

   bI .Tr .G'

   (11)

   Iinj.c : Currents to be injected;

   F-1: Fortescue inverse transformation matrix.

   The current controller is a proportional integral with the transfer function:

   I

   I

   1 (| .p) R| (p) K|. I

4. General structure of CSI_STATCOM The current structure of the shunt STATCOM (Figure 5) is composed of, a PWM current source inverter, a second order filter (RLC), a coupling transformer with the same characteristic of the VSI_STATCOM, and a DC current source Idc often

   i

   (8)

   | .p

   made by an inductive energy storage circuit [4].

   The injected current control loop for VSI_STATCOM is below:

   Figure 4: Structure of the current control loop.

   With:

   Vdc

   VSI(p) = 2 : Transfer function of the VSI;

   Vpmax

   Figure 5: General structure of CSI_STATCOM.

   m

   R' : Transfer function of (filtering

   1 + ( L' .p) R'

   inductor + coupling transformer);

   Vpmax : Magnitude of the PWM carrier;

   Vréf : The sinusoidal reference o PWM voltage source inverter;

   The time constant of the PI controller is maintained to the value (I=L/R), so the expression of the closed loop transfer function of the system is

   1. Power circuit of CSI_STATCOM

      The rms value of the injected current is the same as the VSI structure (Equation 3).

      1. RLC filter

         The (Figure 6) , presents the single-phase schema of second order filter (RLC) between the coupling transformer secondary and AC side of the current source inverter.

         T (p) 1 1

         (9)

         b

         b

         BF

         I

         |

         1 I .p bI.K'.G'

         Figure 6: Single-phase schema of RLC filter.

         With:

         IAC: AC side current of the CSI;

         Vc, Ic: Respectively voltage and current in the filter capacitor;

         (1/m)Iinj: Injected current at the coupling transformer secondary.

         The transfer function of the RLC filter is as follows:

         1 I (p)

         With:

         Figure 7: Symmetrical components of CSI_STATCOM.

         F(p)

         m inj

         m (12)

         With:

         IAC (p) CpmV(p) (1 2 p 1 p2 )

         2

         2

         0 0

         Xi,Xd,Xo : Symmetrical components of X, respectively negative, positive, and zero-sequence (with X is a three-phases voltages or three-phases currents);

         2

         2

         LC 1

         0

         And RC 2

         0

         If the AC side current harmonics are neglected relative to the fundamental, the symmetrical components of VC voltages and IAC currents are:

         0: Natural pulsation of the RLC filter;

         : Damping factor of the RLC filter.

         VCd mVd

         1

         VCd

         Z

         Z

         I

         I

         ACd

         C

         V 1

         This filter introduces the LC oscillations with a

         VCi

         .Ii.ZRL

         And

         IACi Ci

         .Ii

         (15)

         low damping factor, because the value of R is small. These oscillations disrupt the system stability. For this reason, the natural pulsation should be superior to the network voltage pulsation

         m

         VCO 0

         ZC m

         IACo 0

         (0>r) [4].

         With ZRL and ZC are the RLC filter impedances:

      2. ZRL

   R2 (L )2 .e

   r

   r

   • jArc tan( Lr )

     R

     Sizing the CSI power switches

     The switches characteristics are obtained using the DC current Idc, and the capacitor voltage VC. In the case of PWM current source inverter, the DC

     ZC

     r

     r

     1 j

     e 2

     C.r

     (16)

     current Idc is linked to the fundamental rms value of inverter AC side current |IAC|, by the following equation [3]:

     Idc=2.|IAC| (13)

     We assume that the voltages at the power grid

     Note that the currents IAC and the voltages VC in the inverter output contain an additional component, which means that they are unbalanced. The DC link current Idc must be calculated according to the maximum rms value between the three currents IAC. IAC are given by the Fortescue inverse transformation:

     connection point are balanced with positive sequence. The injected currents are balanced with

     I

     I

     ACd

     VCd

     Z

     negative sequence. We take V

     as reference phases. C

     IAC1 IACd IACi

     1 I

     VCi 1 I F1 I

     a2 .I

     • a.I

   (17)

   By applying the Fortescue transformation on the

   ACi

   Z m i

   AC2 ACd ACi

   power grid voltages and injected currents; the C

   I a.I

   • a2 .I

     following symmetrical components are obtained:

     IACo 0

     AC3 ACd ACi

     Vd V1

     Iinj,d 0

     So :

     V 0

     And I I I

     (14)

     i inj,i inj,1 i Idc = 2*max {|IAC1|, |IAC2|, IAC3|} (18)

     V 0 I 0

     O

     inj,o

     The DC current source Idc is generally made by an inductive circuit (Ldc) with an internal resistance (Rdc). The Idc average current must be maintained at a constant value. Regulation of this average current in the energy storage inductor is obtained

     by using the equation of active power balance between the inverter DC side and the power grid AC side [4], or by the state feedback control, in which Idc is one of the system state variables [5].

     The three-phase voltages VC across C are given in functions of their symmetrical components:

     4.2.2 Choice of injected current controller From the equation (12) and (23), the structure of the injected current control loop is given below:

     VCd mVd

     V V V

     1

     C1 Cd Ci

     V I .Z

     F1 V a2.V a.V

     (19)

     Figure 8: Structure of the injected current control

     Ci m i RL C2 Cd Ci

     V

     a.V

   • a2.V

   loop

   VCo 0

   C3 Cd Ci

   The transfer function of the CSI_STATCOM direct

   The power switches for a current source inverter must support a voltage Vsw and a current Isw [3]:

   chain without controller (Ri(p)=1) is:

   (1 + 1 p)

   Isw Idc and Vsw 2*max {|VC1|, |VC2|, |VC3|} (20)

   T (p) =

   3 m

   Idc

   3.r

   1 (24)

   pmax d

   pmax d

   D 2 V (1 + T p) LCp2 + RCp + 1

   4.2 Injected current control in the CSI topology

   The injected current set-point in the phases is the same as for VSI_STATCOM. The current control loop imposes the instantaneous value of the injected current. The choice of the current controller is according to the regulation objectives

   To compensate the phase shift introduced by the current source inverter and to improve the control performances. A controller composed of a mixed PID multiplied by a phase delay controller is proposed.

   1+ p 1 + p + ( . )p2

   and the output filter order.

   4.2.1 Modelling the PWM current source inverter

   With:

   Ri (p) = Kp I I d

   1 + (r.p) Ip

   (25)

   The PWM carrier frequency is greater than network frequency (fd>>fr). This allows to neglect the first six harmonics in comparison to the current fundamental (IAC) of the inverter. The CSI introduces a phase shift of /6 between the sinusoidal reference of PWM block (Iref) and the AC side current fundamental (IAC):

   r

   r

   I (t) = sin( t) PWM_CSI I (t) = Idc sin( t + ) (21)

   I.d = LC; I = RC; = Td, r=3 (26)

   Kp is increased to have an optimal response time.

5. Comparative study and simulation

   To evaluate the possibilities of the unbalance compensation, in cost viewpoint, we must compare the voltage and current values supported by each switch for both structures (VSI and CSI). We must

   compare the current unbalance factor Ti(%) and

   réf r AC

   Vpmax 6

   total harmonic current distortion THD(%) obtained by both structures, in order to evaluate the

   The transfer function of this inverter is given by

   the following equation:

   unbalance compensation quality.

   This study is applied to the future sub-station

   CSI(p) = IAC (p) =

   3 Idc

   (1+

   1 p)

   (22)

   expected for the high speed railway Tangier-

   Iréf (p) 2 Vpmax

   3.r

   Kenitra in Morocco.

   A delay time that corresponds to carrier period (Td=1/fd) is introduced, so:

   1

   This sub-station has the following electrical characteristics:

   • Nominal apparent power Sss,n = 60MVA ;

     (1 +

     3 I

     p)

     3.

     • Reactive power compensated cos1;

   CSI(p) = dc r

   (23)

   • Connection between two phases on a

     2 Vpmax

     (1 + Tdp)

     225KV power grid;

     • The short-circuit power at the connection point equal Scc = 800MVA.

   High voltage power grid which supplis this sub-station has the following electrical characteristics:

   • The limit of the voltage harmonic level is

     5%;

   • The limit of the voltage unbalance factor is 2%;

   • The characteristics of the power grid line are :

     Rline(/Km)=0.129; Lline(mH/Km)=1.366; Cline(nF/Km)=9.1

     The variation of the apparent power consumed by the sub-station depends on the high speed train traffic movement. The mean value of the apparent power consumed by the sub-station is presented in Figure (9). This mean value is calculated for 10min period:

     Figure 9: Sub-station apparent power for a daily railway traffic.

     The sizing of the CSI and VSI power circuit is based on the sub-station nominal apparent power. The rms value of the nominal injected current is

     |Iinj|=154A.

     For both structures (CSI and VSI):

   • PWM carrier frequency fd = 10Khz;

   • Coupling transformer ratio m=0.1;

   • Current sensor gain bi=4.6*10-3 V/A;

   1. Sizing CSI_STATCOM parameters

      The natural pulsation of the output filter is 0=3.5*r=2..fr=1099,56 rad/s, and the damping factor is very low = 0.013, we obtain the RLC filter values:

      R=0.15, L=5mH, C=167µF

      The calculation of voltage and current supported by the power switches is:

      ISW Idc = 3KA, VSW 21.5KV

      The controller parameters Ri(p) are:

      I = 50.01µs, d=16.66ms, Kp = 35, =100µs

   2. Sizing VSI_STATCOM parameters

      The ripple level of the injected currents

      Iinj(%)=10. The value of the filter inductor is:

      L=41,31mH with (R=0,8)

      The calculation of voltage and current supported by the power switches is:

      ISW 2.17KA, VSW Vdc = 90KV

      The controller parameters Ri(p) are:

      'I = 51.66ms, K = 60

   3. Simulation

      The simulation is performed on the MATLAB / Simulink blocks using simulink and simpowersys libraries. The current unbalance factor Ti and the total harmonic current distortion THD, for the three-phase current in the power grid connection point are in functions of daily railway traffic. The Ti, and THD obtained by both structures are presented in the following figures:

      Figure 10: Current unbalance factor Ti (%).

      Figure 11: Total harmonic current distortion THD (%).

   4. Comparison and results interpretation

      • In the paragraphs (5.1) and (5.2), the calculation of the voltage and current supported by the switches shows that, the CSI structure is optimum in sizing terms (ie reduction of cost), because the voltage supported by the switch Vsw in the CSI case is reduced of 76%. The following table summarizes the values found for Vsw and Isw :

        Table 1. The voltage and current value supported by the power switches

        	Vsw	Isw
        CSI Structure	21.5KV	3 KA
        VSI Structure	90KV	2.17KA

      • The figures (10) and (11) show that, for each change of power consumption level, we note that, an exceeding of the Ti and the THD, during transient regime. This exceeding is due to the response time of the injected current control loop. The VSI structure provides an exceeding reduced compared to the CSI structure.

      • The exceeding of current unbalance factor and total harmonic current distortion obtain by CSI, is due to oscillations introduced by the RLC filter, because its natural pulsation chosen is not very much greater than that of the power grid

        (0=3.5*r) and its damping factor is low ( = 0.013). But if 0 increases too much, filtering quality decreases and the THD exceeds the standard value.

      • In the transient regime, the both structures (VSI and CSI) allow to control the current unbalance factor and the total harmonic current distortion in the standards (Ti2% THD8%). But the VSI structure allows to obtain a current unbalance factor more stable and lower than that obtained by the CSI structure

6. Conclusion

   In this paper, a comparative study between both structures (VSI and CSI) of a shunt STATCOM used for current unbalance compensation caused by the sub-stations a high-speed railway was presented. The application of this study about the future sub-station planned for the high speed railway Tanger-Kenitra in Morocco, shows that the CSI structure is optimal in sizing terms, because it allows to have a switch voltage reduction of 76%. The results obtained in the simulation of this application, shows that the control loop of the injected current for both structures allows to have, a current unbalance factor and total harmonic current distortion in the standards, but a VSI structure gives a Ti and THD more stable compared to the CSI structure.

7. References

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