ANALYZE THE EFFECT OF TIME DELAY ON THE STABILITY OF HYBRID ACTIVE POWER FILTER

ANALYZE THE EFFECT OF TIME DELAY ON THE STABILITY OF HYBRID ACTIVE POWER FILTER CHAU MINH THUYEN Faculty of Electrical Engineering & Technology, Industrial University of Ho Chi Minh Cit

ANALYZE THE EFFECT OF TIME DELAY ON THE STABILITY OF

HYBRID ACTIVE POWER FILTER

CHAU MINH THUYEN

Faculty of Electrical Engineering & Technology, Industrial University of Ho Chi Minh City;

chauminhthuyen@iuh.edu.vn

Abstract Hybrid Active Power Filter (HAPF) has highly effective in improving the power quality of power

system In this paper, a stable analysis of HAPF considering the time delay was made The mathematical model of HAPF with time delay has been established Based on that, the stable domain of the HAPF parameters was determined based on the Routh’s stability standard Simulation results based on Matlab software have shown that: time delay has a marked impact on the stability of the HAPF system This research has practical significance in the design and control of HAPF in real system

Keywords Passive power filter, hybrid active power filter, stability analysis, time delay

Nowadays, the power electronic devices are very popular, such as motor drives, converters in renewable, electric arc furnace, uninterruptible Power Supply, etc All of these devices are nonlinear loads The nonlinear loads are the sources of the harmonic distortion; it affect directly to grid and reduces power quality

of the power system There are many ways to solve this problem such as using a passive power filter (PPF), active power filter (APF) and hybrid active power filter (HAPF) The passive power filters are simple, low cost, ability to compensate reactive power and harmonic filter [1-3] However, they are many disadvantages such as resonance with supply system, no flexibility in harmonic filtering also reactive power compensation, instability in power system

A new harmonic filter method based on power electronic devices is an active power filter (APF) The APF

is connected parallel with nonlinear loads and harmonic elimination more flexibility than PPF However, APF is limited by high cost, small capacity, less life of power electronic devices and difficult connection with high voltage network [4-5] To solve these problems, hybrid active power filter is studied HAPF is a topology that is combined by passive power filter (PPF) and active power filter (APF) Hence the HAPF inherits the advantages of both passive power filter (PPF) and active power filter (APF) Hybrid active power filter (HAPF) flexibly eliminated harmonic, greatly reduced power rating of APF, avoided resonance with the supply system, connected with high voltage network [6-10] Therefore, studying about the hybrid active power filter is a necessary role to contribute energy saving, especially save energy at business, office, school, factory, etc Also improve power quality in power system

Determination of the exact parameters of the hybrid active power filter will decide its performance So far these parameters of hybrid active power filter are most determined based on experience but not considering stable system Moreover, researches [11-16] are not considering time delay In HAPF system, from harmonic current signal of load to compensation of current into the grid must through many elements such

as capacitors, coils, transformer, output filter, voltage source inverter, controller, etc All these elements created time delay at output The time delay affected the efficiency and stability of HAPF In this paper, the mathematical model of HAPF is established with considering time delay of system Since then, an analysis of the stability of the HAPF system is established to find a stable domain for parameters of HAPF This has practical significance for improving work efficiency of HAPF in the real system conditions

The topology of HAPF is shown in Figure 1

In Figure 1, Usand Zs are supply voltage and equivalent impedance of the grid CF, C1, L1, Cp, Lp, L0, C0 are the injection capacitor, fundamental resonance capacitor, fundamental resonance inductor, the capacitor and inductor of the passive power filters, the capacitor and inductor of the output filter A branch with CF - C1 - L1 is injected to reduce capacity of APF C1 and L1 resonate at the fundamental frequency and connect

in series with additional branch CF Nonlinear loads are considered as sources of harmonics Most high order harmonics will be reduced by the passive filter PPF In this paper, the passive filters eliminate the 11th

82 ANALYZE THE EFFECT OF TIME DELAY ON THE STABILITY OF HYBRID ACTIVE POWER FILTER

and 13th order harmonics Moreover, the APF also rejects some remaining low order harmonics Thus the capacity of PPF is reduced significantly

Z S

F

C 1

L 1 0

L

0

C

C

380V

AC

inverter

Transformer

nonlinear loads

Rectifier

C 11

L 11

C 13

L 13

Figure 1: Topology of HAPF

The single phase equivalent circuit of HAPF is shown in Figure 2

IL

US

ZS

U L

Z

3

n2ZL0

CF

C1

L1

Figure 2: Single phase equivalent circuit of HAPF

Where:

The impedance of resonance at fundamental frequency branch 1 1

1

1L C L

The impedance of additional branch Z2 Z CF

The impedance of the PPFs is Z3 Where R11 – C11 – L11 branch and R13 – C13 – L13 branch are inner resistance of inductor, capacitor and inductor that tuned at the 11th and 13th harmonics In each passive filter branch, the impedance is





















1 3

1 3

1 3

1 1

1 1

1 1 13 11

L C R

L C R

Z Z Z Z

Z Z Z Z

The single phase equivalent circuit with the effect of harmonic source is shown in Figure 3 with output

current of APF is i apf

Z C 1 L 1

Z 2

Z 3

i Fh

Z sh

i Lh

i sh

U sh

i apf

i Ph i CFh

i 1

Figure 3: Single phase equivalent circuit with the effect of harmonic source

According to Figure 3, if we control to achieve the purpose I FhI Lh then we will obtain Ish = 0

With control strategy I apf = KI Lh is output current of APF According to Figure 3, equations are

established:







































3 1

1 1 2 3 1

Z I Z I Z I

U Z I Z I

I I I

I I I

I I I

Ph L C CFh

sh Ph

sh sh

CFh Ph Fh

CFh apf

Fh Lh sh

(1)

From (1), I sh is calculated as

sh sh

L C

Lh L C L C sh

Z Z Z Z Z Z

I Z KZ Z

Z I

3 3

1 1 2

3 1 1 1 1 2

) )(

(

) (











 (2) The equation (2) showed that if K is large enough, the harmonic current source components will gain a value of zero K is the coefficient control and depends on many elements such as control strategy, parameters, topology…

If only considering the response of the voltage source inverter, Us=0, iL=0 The single phase equivalent circuit is shown in Figure 4

Z 1

Z 2

Z 3

n 2 Z L0

nU inv

i Fh

Z s

i 2

i 3

i 1

i 0

Figure 4: Single phase equivalent circuit when only considering VSI

Where:

















































































s L R Z

s C Z

s C s L R s C n

s C s L R s C n s C

n s C s L R Z

n C Z Z

s L R Z

L F

C L

s s s

0 0 0 2

1 1 1 0

2

1 1 1 0 2

0 2

1 1 1 0 2 1 1 1

1

1

1

//

1 //

(3)

According Figure 4, equations are established:







































inv L

L s

Fh

inv L

L

s Fh L Fh

nU Z

n I Z I Z I

nU Z

n I Z I

Z I Z I

I I I

I I I

0 2 0 2 2 0 2 0 1 1

3 3

1 2 0

3 2

(4)

With IFh is compensation harmonic current that is controlled by VSI, VSI as a controlled voltage source From (4), IFh can be calculated as (5)

3 3 2 2 1 3 2 1 2

1 3 0 2

3 1

s s

s L

inv Fh

Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z n

Z Z nU I















84 ANALYZE THE EFFECT OF TIME DELAY ON THE STABILITY OF HYBRID ACTIVE POWER FILTER

The transfer function of compensation harmonic current IFh along the controlled voltage source U inv is

G out (s)

3 3 2 2 1 3 2 1 2

1 3 0 2

3 1

s s

s L

inv

Fh out

Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z n

Z Z n U

i s G

















There are two control strategies for U inv based on load harmonic current detection and source harmonic current detection In this paper, the control strategy is based on load harmonic current detection Here the load harmonic current detection is calculated based on ip-iq harmonic detection method [6], [10]

From the above analysis, we can see that the HAPF system has not time delay With time delay is constituted

by processes of the HAPF system, control block diagram of HAPF is shown in Figure 5 Where Gc(s) and Ginv(s) are transfer functions of the conventional PI controller and the VSI

Lh

I 1 G c (s) G inv (s) G out (s) es  I sh







Fh I

inv U

Figure 5: Control block diagram of HAPF

The transfer function of the conventional PI controller:















s T K s G

i p c

1

1 (7)

Where Kp is the proportional gain constant and Ti is the integral time

The transfer function of VSI is expressed:

 

1





s T

K s G

inv

inv inv (8) Where Kinv is amplification factor of the VSI and Tinv is time delay of the VSI

The time delay of the entire system of HAPF is τ and can be represented as e-τs function To facilitate the analysis, may be simplified as follow

 

! 2 1

1

~ 1

2

s s e

e s s















 (9)

According to control block diagram of HAPF in Figure 5, the control transfer function with load current input signal ILh and source current output signal Ish of HAPF system with time delay e-τs is calculated

out inv c Lh

sh

e s G s G s G I

I s







)

( )

( )

( 1

1

(10)

There are many criteria used to assess the stability of a system of such: Routh criterion, Hurwitz criterion, the root locus, Bode plots, Nyquist plots, etc In this paper, Routh criterion used stability analysis

of HAPF To consider the stability of the system according to Routh criterion, first establishing Routh table

follows rules The elements in row i column j of Routh table (i ≥ 3) are calculated:

1 , 1 1

,

(11) Where

1 , 1

1 , 2







i

i

c

c



From (10), the characteristic equation of the control transfer function of HAPF system is determined

0 11

1 10

2 9

3 8

4 7

5 6

6 5

7 4

8 3

9 2

10 1

11 0

)

(12) Where the coefficients a0…a11 are coefficients of the characteristic equation (12) with the 11th degree, that

is the highest degree of the equation The coefficients are calculated:

2

a  i ; a1T i(2A12A2); a2T i(2A12A22A3);a3T i(2A22A32A4);

) 2

2

2

a  i     c F ; a5T i(2A42A52A62nK c C F B2);

) 2

2

2

a  i     c F ; a7T i(2A62A72A82nK c C F B4);

) 2

2

2

a  i     c F ; a9T i(2A82A922nK c C F B6);

) (

a  i   c F ; a112T i(1nK c C F)

Where:

p inv

K   ; n is the transfer ratio of the transformer and the expressions from A1 to A9 and B1 to B7 are determined by the Appendix

From the coefficients of the characteristic equation (12) can be established Routh table to survey of stability

of HAPF system To determine the HAPF is stable, then the all of elements at first column are positive Thus the stable domain of parameters of the HAPF system is determined as (13)































































0 0 0 0 0 0 0 0 0 0 0 0

121 111 101 91 81 71 61 51 41 31 21 11

c c c c c c c c c c c c

(13)

Where the coefficients from c11 to c121 are calculated in Appendix

To demonstrate the influence of time delay on the stability of the system HAPF, simulation results are implemented on a system HAPF 10kV-50Hz with parameters as in [5] and are listed as in Table 1 Nonlinear loads contain order harmonics such as such as 5th, 7th, 11th and 13th The dc-side voltage is 600V

Table 1: Parameters of system simulation

When τ=10-8s, Tinv=0.01ms, Kinv=1, Ti=10-6s, Kc=100 the elements in first column of Routh table c11, c21, c31, c41, c51, c61, c71, c81, c91, c101, c111 and c121 are determined in Table 2 All elements at first column are positive, that HAPF system is stable operation

Now, we change time delay of the HAPF system: τ=0.0095s, Tinv=0.01ms, Kinv=1, Ti=10-6s, Kc=100 Calculate the parameters of the Routh table we can see that the elements c51 and c111 at first column Table

3 change sign According to Routh criterion, the HAPF system with these parameters won’t be stabilize when it operate

To demonstrate the above analysis, the simulation results done in MATLAB software, the HAPF system with the parameters in the stable domain is shown in Figure 6 The HAPF system will be stabilize after the transitional period 0.01s

86 ANALYZE THE EFFECT OF TIME DELAY ON THE STABILITY OF HYBRID ACTIVE POWER FILTER

The grid current harmonic spectrum with the parameters in the stable domain is shown Figure 7 The total harmonic distortion THD of supply current in this case is 3.38%, satisfaction of IEEE Std 1547™ and IEEE 519-2014 Standard [17-18]

Table 2: The elements of the Routh table with τ=10-8s

6.9612E-55

c 12 = 1.4061E-38

c 13 = 6.71E-28

c 14 = 2.88E-20

c 15 = 2.85E-13

c 16 = 1.63E-07

1.40E-46

c 22 = 1.3941E-32

c 23 = 6.52E-22

c 24 = 1.81E-14

c 25 = 1.22E-07

c 26 = 1.19E-02

1.40E-38

c 32 = 6.68E-28

c 33 = 2.87E-20

c 34 = 2.84E-13

c 35 = 1.63E-07

1.39E-32

c 42 = 6.52E-22

c 43 = 1.81E-14

c 44 = 1.22E-07

c 45 = 1.19E-02

1.32E-29

c 52 = 1.05E-20

c 53 = 1.61E-13

c 54 = 1.51E-07

6.41E-22

c 62 = 1.79E-14

c 63 = 1.22E-07

c 64 = 1.19E-02

1.01E-20

c 72 = 1.59E-13

c 73 = 1.51E-07

7.87E-15

c 82 = 1.13E-07

c 83 = 1.19E-02

1.38E-14

c 92 = 1.36E-07

3.52E-08

c 102 = 1.19E-02

1.31E-07

1.19E-02

Table 3: The elements of the Routh table with τ=0.0095s

6.28252E-35

c 12 = 2.4509E-27

c 13 = 2.75E-20

c 14 = 1.23E-13

c 15 = 3.17E-08

c 16 = 2.12E-03

1.62E-31

c 22 = 3.0786E-24

c 23 = 3.57E-17

c 24 = 1.19E-10

c 25 = 1.30E-05

c 26 = 2.00E-01

1.26E-27

c 32 = 1.37E-20

c 33 = 7.68E-14

c 34 = 2.66E-08

c 35 = 2.04E-03

1.31E-24

c 42 = 2.58E-17

c 43 = 1.15E-10

c 44 = 1.28E-05

c 45 = 2.00E-01

-1.11E-20

c 52 = -3.38E-14

c 53 = 1.43E-08

c 54 = 1.85E-03

2.18E-17

c 62 = 1.17E-10

c 63 = 1.30E-05

c 64 = 2.00E-01

2.56E-14

c 72 = 2.09E-08

c 73 = 1.95E-03

9.91E-11

c 82 = 1.13E-05

c 83 = 2.00E-01

1.80E-08

c 92 = 1.90E-03

9.06E-07

c 102 = 2.00E-01

-2.08E-03

2.00E-01

Simulation results of the HAPF system with the parameter τ changed is shown Figure 8 These parameters

of HAPF are set outside of stable domain with time delay τ = 0.0095s, Tinv = 0.01ms, Kinv= 1, Ti = 0.1s, Kc

= 100.The HAPF system will be destabilized from 0.0095s to 0.2s The supply current increases to 1600A and the current error is 1500A

The supply current harmonic spectrum with the parameters outside of stable domain is shown Figure 9 The total harmonic distortion THD of supply current in this case is 379.21% The individual harmonic components almost increase higher than in case the parameters of in the stable domain, not satisfying power quality standards in power system [17-18]

Figure 6: Response of HAPF with the parameters in the stable domain

Figure 7: The supply current harmonic spectrum with the parameters in the stable domain

Figure 8: Response of HAPF with the parameters outside of stable domain

-1

0

1x 10

4

-500

0

500

-500

0

500

-500

0

500

Time (s)

-200

0

200

Selected signal: 10 cycles FFT window (in red): 9 cycles

Time (s)

0 20 40 60 80 100

Harmonic order

Fundamental (50Hz) = 232.7 , THD= 3.38%

-1

0

1x 10

4

-500

0

500

-2000

0

2000

-2000

0

2000

Time (s)

88 ANALYZE THE EFFECT OF TIME DELAY ON THE STABILITY OF HYBRID ACTIVE POWER FILTER

Figure 9: Grid current harmonic spectrum with the parameters outside of stable domain

According to the obtained simulation results, in the case of parameters of HAPF outside of stable domains cannot be stabilized for the filtering as well as the power system network that the filtering is connected In this case, the total harmonic distortion and individual harmonic will be raised much more than in the case

of parameters in stable domain Thus, with time delay highly increases will result in adverse impacts, loss

of stability of HAPF Power quality of the power system will become very poor and unachievable standards for connecting to the grid

The paper has built the mathematical model of HAPF considering the time delay and analyzed the impact

of the time delay on the stability of the system HAPF When the time delay becomes smaller, the stability

of HAPF is higher, and vice versa The parameters of filtering outside of stable domain and longer time delay are unstable with HAPF system as well as power system that the filtering is connected Thus power quality will not achieve international standards with requirements becoming more and more stringent The results of this study can serve as a basis for choice parameters of HAPF in considering time delay, and also ensure stability and more efficient operation of HAPF system

APPENDIX

1

2

11 T A

c  i ;c12T i(2A12A22A3)c13T i(2A32A42A52nK c C F B1)

) 2

2

2

c  i     c F ; c15T i(2A72A82A92nK c C F B5)

) (

) 2

c  i   ;c22T i(2A22A32A4)c23T i(2A42A52A62nK c C F B2)

) 2

2

2

c  i     c F ; c25T i(2A82A922nK c C F B6)c262T i(1nK c C F)

























) 2

( ) 2

2

2 2 1 1 2

3 2 2 1

A A T

A T A

A A

T

i

i











) 2

2 2 ( ) 2

(

) 2

2

2

(

2 6

2 5 4 2

2 1

1 2

1 5

2 4 3

32

B C nK A A A T A A

T

A T

B C nK A A A

T

c

F c i

i

i

F c i



































) 2

2 2 ( ) 2

(

) 2

2

2

(

4 8

2 7 6 2

2 1

1 2

3 7

2 6 5

33

B C nK A A A T A A

T

A T

B C nK A A A

T

c

F c i

i

i

F c i



































-1000

0

1000

Time (s)

0 50 100

150

200

250

Harmonic order

Fundamental (50Hz) = 231.9 , THD= 379.21%

) 2

2 2 ( ) 2

(

) 2

2

2

(

6 2

9 8 2

2 1

1 2

5 9

2 8 7

34

B C nK A

A T A A

T

A T

B C nK A A A

T

c

F c i

i

i

F c i



































) 1

( 2 ) 2

( ) (

2

2 2 1 1 2

7 2

9

i

i F

c

A A T

A T B

C nK A

T























32

4 2 3 2 2

2 1 1 2

3 2 2 1

2 2 1 4

2 3 2

41

) 2

2 ( ) 2

( ) 2

2

(

) 2

(

) 2

2

(

c A A A T A A T

A T A

A A

T

A A T

A A A

T

c

i i

i i

i

i





























































33

4 2 3 2 2

2 1 1 2

3 2 2 1

2 2 1

2 6

2 5 4

42

) 2

2 ( ) 2

( ) 2

2

(

) 2

(

) 2

2

2

(

c A A A T A A T

A T A

A A

T

A A T

B C nK A A A

T

c

i i

i i

i

F c i































































34 31

2 2 1 4

8 2 7 6

43

) 2

( ) 2

2

2

c

A A T B C nK A A A

T

35

4 2 3 2 2

2 1 1 2

3 2 2 1

2 2 1 6 2

9 8

44

) 2

2 ( ) 2

( ) 2

2

(

) 2

(

) 2

2

2

(

c A A A T A A T

A T A

A A

T

A A T

B C nK A

A

T

c

i i

i i

i

F c i





























































) 1

(

2

42 41

31 2 6

2 5 4 2

2 1

1 2

1 5

2 4 3

51

) 2

2 2 ( ) 2

(

) 2

2

2

(

c c

c B C nK A A A T A A

T

A T

B C nK A A A

T

c

F c i

i

i

F c i





































43 41

31 4 8

2 7 6 2

2 1

1 2

3 7

2 6 5

52

) 2

2 2 ( ) 2

(

) 2

2

2

(

c c

c B C nK A A A T A A

T

A T

B C nK A A A

T

c

F c i

i

i

F c i





































44 41

31 6 2

9 8 2

2 1

1 2

5 9

2 8 7

53

) 2

2 2 ( ) 2

(

) 2

2

2

(

c c

c B C nK A

A T A A

T

A T

B C nK A A A

T

c

F c i

i

i

F c i





































45 41 31

2 2 1 1 2

7 2

9

) 2

( ) (

c

c C nK T

A A T

A T B

C nK A

T

i

i F

c























52 51

41

42

c

c

c

51

41 43

c

c c

51

41 44

c

c c

c   , c64c45; 62

61

51 52

c

c c

61

51 53

c

c c

c   ;

64 61

51

54

c

c

c

71

61 62

c

c c

71

61 63

c

c c

c   ; c83c64

82 81

71

72

c

c

c

81

71 73

c

c c

91

81 82

c

c c

c   ; c102c83; 102

101

91 92

c

c c

c   ; c121c102

The expressions from A1 to A9 and B1 to B7 are expressed:

90 ANALYZE THE EFFECT OF TIME DELAY ON THE STABILITY OF HYBRID ACTIVE POWER FILTER

2

1

2 0 2 1 5 0 2 4

3 1

1

2 T L C C f T f T n L f f n L f

5 0 2 4 3 1 1 9

0

2

8 0 2 7

0 2 13

11 13 11 3

1 1 6

1

1

3

f L n f f C C L f

C

L

n

T

f L L n T f R L n T C L C C L L T f C C R T f

C

L

T

A

F F

inv

s inv s

inv F s inv

F inv inv





















9 0 2 8 0 2 7 0 2 13

11 13 11 3 1

1

6

1

1

12 0 2 11 0 2 8

0 2 3

6 1 1 10

1

1

4

f C L n f L L n f R L n C L C C L L f C C

R

f

C

L

f C L n T f L L n T f R L n T f C T f C R T f

C

L

T

A

F s

s F

s F

F inv s

inv s

inv F

inv inv

inv



























12 0 2 11 0 2 8 0 2 3 6 1 1

10

1

1

15 0 2 14

0 2 11 0 2 6

10 1 1 13

1

1

5

f C L n f L L n f R L n f C f C

R

f

C

L

f C L n T f L L n T f R L n T f T f C R T f

C

L

T

A

F s

s F

F inv s

inv s

inv inv

inv inv



























15 0 2 14 0 2 11 0 2 6

10

1

1

13 1 1 17 0 2 14

0 2 10

13 1 1 16

1

1

6

f C L n f L L n f R L n f

f

C

R

f C L f C L n T f R L n T f T f C R T f

C

L

T

A

F s

s

F inv s

inv inv

inv inv

























17 0 2 14

0

2

10 13 1 1 16 1 1 18 0 2 13

16 1 1 1

1

7

f C L n

f

R

L

n

f f C R f C L f L n T f T f C R T

C

L

T

A

F s

inv inv

inv inv





















18 0 2 13 16 1 1 1 1

19

s inv R C R C C R C R C C R

T

A9  1 1 11 13  11 11 13 13

13 11 13

11

1

1

B  i

13 11

1

1

13 11 1 1 13

11

13

11

11 13 13 11 13 11 1 1 11 11 13 13 13 11 13 11

1

1

3

C C L L C R L R L R C C C L C

C

L

L

T

L R L R C C C R T C L C L C C R R

C

L

T

B

i

i i





















13

11

1

1

11 11 13 13 13 11 13 11 1 1 11 13 13

11

13

11

11 11 13 13 13 11 13 11 1 1 13 13 11 11

1

1

4

C C L L L R L R

C

C

C

R

C L C L C C R R C L L R L

R

C

C

T

C L C L C C R R C R T C R C

R

C

L

T

B

i

i i































1

1

11 11 13 13 13 11 13 11 13

13 11 11 1 1 1

1

5

L R L R C C C L C L C C R R C R C R C

R

C

L

C L C L C C R R T C R C R C R T

C

L

T





























 11 131 111 13 11131113 13111311 1 1 1 1 11 11 13 13

6

C L C L C

C

R

R

C R C R C R C L C R C R T

C

R

T





















 11 11 13 13 1

1

Where:

1 1 13

11

13

11

1

1

s R L R L C C L R

C

C

L

L

f3 11 13 11 13  11 13 13 11 11 13

F

s C L C C

L

L

C

R

f4 1 1 11 13 11 13

 11 13 13 11

13

11

1

1

13 11 13 11 1 13 11 11 13 13 11 1 13 11 13 11

1

1

13 11 13 11 1 1 13

11 13 11 1 13 11 13 11 1

1

5

L R L R C

C

C

L

C

C C L L R C C C L R L R C C L C C L L

C

L

C

L

C C R R C L C L C C L L C C R C C L L C

L

C

R

f

F

F F

s F

s

F s F

s F

s





























F

s F

s

L C L C L C

C

R

R

C

R C C L R L R C C C L L L C C

L

L

f

11 11 13 13 13 11

13

11

13 11 11 13 13 11 13

11 13 11 13 11 13

11

6



















1

1