Neural adaptive control by state space system UPFC - IJSER.org

International Journal of Scientific & Engineering Research Volume 3, Issue 3, March -2012 ISS N 2229-5518

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Neural adaptive control by state space system UPFC (SSNN) for compensation of active And reactive power Bouanane Abdelkrim, Chaker Abdelkader, Addadi Zoubida, Amara Mohamed Abstract—in our present paper, we present the effectiv eness of the controller's electric al power flow Universal (unif ied power flow controller UPFC) w ith the choice of a control strategy. To evaluate the performance and robustness of the system, w e proposed a hybrid control combining the concept of neural networks with conventional regulators vis -à-vis the changes in characteristics of the transmission line in order to improve the stability of the electrical power network. Index Terms—UPFC system, adaptive control, neural netw orks, state space (SSNN).

——————————  ——————————

w

1 Introduction

ith the rapid development of the modern world, the demand for electricity is growing and electrical installations are continually enhanced to meet these requirements. The construction of new plants and new lines are necessary, but with FACTS devices, we can solve some problems while using the existing facilities. Having highlighted the need for rapid control of power flow in transmission line and the description of the new concept of "FACTS" that was born to meet the increasing difficulties in networks including control of the flow on the axes transport, we are interested in our work to the controller's electrical power flow universal [1], [2] (Unified Power Flow Controller UPFC). The UPFC consists of two switching converter, (series and shunt) (Fig. 1) and even this device is the union of a parallel compensator and a series compensator. It is capable of simultaneously and independently control the active power and reactive power. It can control the three parameters associated with power flow the line voltage, the impedance of the line and angle of transport.

2 Configuration Variable Universal Charges (UPFC): It is assume d that the UPFC [3] shown in Fig. 1 was plugge d into a simplifie d transmission system, the arrival of the transmission line (Rece iving End). The two voltage source inve rters constituting the UPFC are connecte d togethe r through a common DC circuit. Two transformers T1 and T2 are use d to connect the two inve rters,

———————————————— Boua na ne,, Addadi a nd Amara are teachers in the department of electrica l engineering a t the University Dr. MOULAY TAHER, in SAIDA, Algeria . ([email protected]) Cha ker is professor in the department of electrical engineering at the ENSET in ORAN , Algeria. ([email protected])

one

serial

and

one

paralle l

to

the

transmission

line .

Fig. 1 UPFC System Configuration

After all, this composition offers the UPFC's ability to control the active power and reactive power regardless of where: - The series inverter (2) "Inverter2" performs the principal function of the UPFC by injecting an AC voltage in series (AC) with an amplitude and a phase angle adjustable. - The parallel UPS (1) "Inverter1 'role is to provide or absorb the real power demanded by the inverter (2) to the connection (DC), as it can also produce or absorb reactive power according to demand, and provide independent shunt compensation transmission line. The series inverter (2) provides or absorbs the needed reactive power locally produced active power as a result of injecting a voltage in series.

3 Modelling O f the System UPFC: The simplified circuit of the control system and compensation of UPFC is shown in (Fig. 2) modeling of this circuit is based on simplifying assumptions in the form of ideal voltage sources then the dynamic equations of the UPFC are divided into three systems of equations: the equations of the series branch, the equations of parallel branch and those of the DC

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International Journal of Scientific & Engineering Research Volume 3, Issue 3, March -2012 ISS N 2229-5518

circuit. By applying Kirchhoff’s laws we will have the following equations. UPFC M odel of the line Is r

~

Ir

L

Lp rp

Vs

d

(Sending) End

d

d

~

dt

rp Lp

. i pb 

1 . v pb - v cb - v rb  Lp

(4)

di r 1  pc  - p .i  .  v - v - v  dt Lp pc Lp  pc cc rc 

di

rp 1  pd  ω . ipq .i   v - v - v  dt Lp pd Lp  pd cd rd 

Vr

d

Vp

~

-

With a transformation marke r d, q we have the syste m of equations (5):

~

Vc

di pb

2

ip

di pq dt

(Receiving) End

  . i pd -

rp

. i pq 

Lp

1   v - v - v  L p  pq cq rq 

(5)

The matrix form is give n as follows:    i d  1  v sd  v cd  v rd  d i pd   rp l p i       r l .i   . v  v  v  dt  pq   l  sq p p  q cq rq  p

Fig. 2 Equivalent circuit of UPFC

3.1 The modelling of the UPFC seri es branch:

p

3.3 The modelling of the UPFC continues branch: The mathematical model is given by the following equations:



di sa  - r . i  1 v - v dt L sa L sa ca

v ra



disb r 1  - . i  . v - v - vrb dt L sb L sb cb







di sc  - r . i  1 . v - v - v dt L sc L sc cc rc

(1)



- sin (  t )

1 2 1 2 1 2

 sin (  t - 120 )  sin ( t  120 )

T



v

sd

-v

cd

-v

rd

e

 p ep 

pep = vpa ipa + vpb i pb + vpc ipc With: pe: active powe r consumption of the AC syste m

3 dc  dt 2Cv

dc

 v i  v pq i pq - v i - v cq i q  cd d  pd pd 

(7)

The UPFC se ries and shunt UPFC's are ide ntical in e very respe ct. The commands use d to se t the inve rte r are the same for the shunt inve rter.

4 Configuration Control Circuit:



r 1 . isq  vsq - vcq - vrq  dt L L The matrix form of the dq axis can be re writte n as follows :   . isd -

d i sd   r l    i sd  1  v sd  v cd  v rd  .   .    dt i sq      r l i sq  l  v sq  v cq  v rq  3.2 The modelling of the shunt branch: The mathematical mode l of the UPFC shunt is give n similarly by the following e quations : di r 1  pa  - p .i  .  v - v - v  dt Lp pa Lp  pa ca ra 

p

pe = vca isa + vcb isb + vccisc

dv

(3)

disq

C vc

Applying the Park transformation on equa tion (6) we obtain:

In our case, the component x0 is not seen as the power system is assumed to be symmetric. After the transformation of Park, equation (1) is expressed in the d q reference by the equations: sd   . i - r . i  1 sq L sd L dt



Pe p: active powe r injecte d by the shunt inve rte r AC syste m

x a    x b    x c 

Where x; can be a voltage or current.

di

dt

He nce

The transformation of Park aims to model this three-phase system (a, b, c) two-phase (d, q) as follows: (2) x d  cos (  t )    2  x q   3 cos (  t - 120 )    cos (  t  120 ) x o 

By passing on the principle of balance of powe r and ne glecting the losses of the converters. The DC voltage V dc by the following equation: dv (6) 1 c

The ore tically the UPFC should be treate d as a multivariable system because both se ries and shunt converte rs are connecte d from one side to the transmission line and the other side in continuous DC circuit and thus each has two inputs and two outputs. This for to facilitate the synthesis of se ttings, treatme nt of the two converte rs will be done se parate ly. The possibility of this se paration is justifie d by two main factors. First, the coupling be tween the two conve rters of the transmission line is quite small. Second, the dynamic variation of the voltage of DC side of the continuum is dominate d by the paralle l conve rter. Control of the converte r in paralle l UPFC is very similar to that of the compe nsator SVC. So to control the flow of active powe r in the transmission line , the controlle r of the UPFC series must adjust the angle of the phase of the compe nsation voltage V c while to adjust the flow of reactive powe r, the amplitude of the input voltage range must be controlle d. To e nsure syste m stability, a chain of control is imple mente d with PI control.

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International Journal of Scientific & Engineering Research Volume 3, Issue 3, March -2012 ISS N 2229-5518

Control of the se ries branch Control of paralle l branch and the game continues.

4.1 Description of the Control System of UPFC:

3

Zie gle r-Nichols, use d in the pre sent thesis is base d on a trial conducte d in close d loop with a simple analog proportional controlle r. The gain Kp of the regulator is gradually increase d until the stability limit, which is characterize d by a steady oscillation. Base d on the results obtaine d, the paramete rs of the PI controlle r give n by the analog transfer function.  K ( s )  Kp   1  

1   Ti s  

The active and reactive powe rs P and Q are give n by 3 the equations: P  3 V .i  V .i (8) Q  Vsd .isq  Vsq .isd sd sd sq sq

We can say in the conditions of the converter, the e xcess curre nts should be minimal. There fore , the introduction of a

Where

simple condition K i  (r L).k p . We obtain the transfer function

2





2





ird = isd + i pd

F(s)  k p k p  s of the form is first class with a time constant

irq = isq + i pq The re fere nce power and reactive P * and Q * of the desire d real powe rs P and Q are use d as input to the control syste m of UPFC. From equation (8) the re fe rence currents isd * and isq * can be calculate d as follows: (9) * *  *   *  2  P .Vsq  Q .Vsd i* q  3   

P .Vsq  Q .Vsd  i*  2  q  3     

   

With   V 2  V 2 sq sd

T  1 k p .He nce

F(s) 

(10)

1 1  s.T

Thus, de termining the time constant de pe nds on the maximum allowable change of control variable s and V cd V cq for controlle r se ries and the same for the shunt converte r. So according to the method of Zie gle r-Nichols, the critical gain Kpc and the pe riod Tc of the oscillations is measure d by the choice of the table as follows: Kp =0,45 kp c e t Ti =0,83 Tc avec Td=0

UPFC (Série)

The re fere nce powe r and reactive P * and Q * of the desire d real powe rs P and Q are use d as input to the control syste m of UPFC. From equation (8) the re fe rence currents isd*and isq * can be calculate d as follows. The refe re nce curre nts I rdref I rqref and are calculate d according to equations (8). These re fe rence values and I rdref I rqref are the n compare d with actual line curre nts from the re ce iver. The outputs of the PI e ditors provide the curre nt value s of control voltages V sd and V cq. The goal is to have active and reactive power at the finish line (Rece iving End) ide ntical to those instructions (P *, Q *) by forcing the line curre nts (I sd , I sq) to monitor properly the ir refe re nces. The re fere nce curre nts calculate d (8) compare d to the actual line curre nts and afte r a correction to the curre nt one e nds control voltages (UPFC se ries) and V cd Vcq re prese nting the re fe re nce voltage control circuit (PWM) of the inve rter in Fig. 3.

* isd

* isq

v cd

PI

+

+ + +  - + +



+ -

PI

v cq

+

+

1

isd

S+r/l



-

+

 1 S+r/l

+

isq

Fig. 3 Block Diagram of the UPFC Control (series)

-

4.2 Simulation Results with PI-D UPFC:

4.2 Decoupled PI Controller

(a)

According to the system of e quations (3) or (5), one can have the system contains a coupling be twee n the reactive and active curre nt Id Iq. The inte raction betwee n curre nt loops cause d by the coupling term (ω) (Fig. 3). This e xplains the deviation of reactive powe r with respect to the re fere nce . To re duce the inte raction be twee n the active and reactive power, a decoupling of the two curre nt loops is nee de d.The function of decoupling is to remove the product ωL and I q controlle r along the axis d and adding the product te rm ωL I d and the controller along the axis q. The design of the control system must be gin with the se lection of variables to adjust and the n that of the control variables and the ir association with variables se t. There is various adjustment te chniques we ll suite d to the PI controlle r. The re are two we ll-known e mpirical approaches propose d by Zie gle r and Tit for de termining the optimal paramete rs of the PI controller. The method IJSER © 2012 http://www.ijser.org

(b)

International Journal of Scientific & Engineering Research Volume 3, Issue 3, March -2012 ISS N 2229-5518

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Fig. 5 Answers Powers to Change the Reactance of 30%

Fig. 4 (a), (b). Answers of Pow ers with PI-D.

Figures (4-a, b) illustrates the behaviour of active and reactive powe r, whe re we see that the control system has a fast dynamic re sponse to the forces reach the ir steady states after a change in the re fe rence values. We also note the presence of the interaction be twee n the two compone nts (d and q). These influe nces are cause d by the PWM inve rter is unable to produce continuous signals nee de d by the decoupling, thus increasing the e rror in the PI -D controlle rs. To test robustness, we teste d for a variation of the reactance XL to 30% and I had variations on the output powe r following Following the se changes, the active and reactive powe r (Fig. 5) unde rgo large deviations more or less with an ove rflow at times of great change instructions (Pre f, Qref), which means the pe rformance de gradation of the PI controlle r, interpre te d by the loss of system stability We simulate d this time by introducing perturbation (Fig. 6) duration of 25 ms and amplitude 1.5 to test again its robustness and stability of the system. The response of active and reactive powe r at 30% of XI could be de tecte d; the e rror message give n by "MATLAB command" indicate d the saturation of the orde r at infinity in the spike s of the re fe re nce signals. We can check the response of the se rvo not only continue d but also regulation by adding a disturbance

Fig.6. UPFC System Perturbed to Test Stability

5 Adaptive Neural Controls: The inte rest in adaptive control [4] appears mainly at the le ve l of parame tric pe rturbations, ie act on the characte ristics of the process to be controlle d, disturbance acting on the variable s to control or order. In this pape r we present the metho d of adjustme nt propose d for the UPFC, e mphasizing the classical approach base d on ne ural ne tworks.

5.1Choi x a Neural Network: In this paper the Elman ne twork [5] said hidde n layer ne twork is a recurre nt ne twork, and there fore be tter suite d for mode lling dynamic systems. His choice in the ne ural control by state space is justifie d by the fact that, in particular, the ne twork can be inte rpre te d as a state space mode l nonlinear. Learning by back propagation algorithm standard is the law use d for the ide ntification of the UPFC.

5.2State Space Adaptive Neural Control« SSNN»: The inte gration of these two approaches (ne ural adaptive control) [6] in a single hybrid structure, that each be nefits from the othe r, but to change the dynamic be haviour of the UPFC system was adde d against a reaction calculate d from the state vector (state space ) (Fig. 7).

E (t) + IJSER © 2012 http://www.ijser.org

U (t)

Process’s UPFC

Y (t)

International Journal of Scientific & Engineering Research Volume 3, Issue 3, March -2012 ISS N 2229-5518

K

x (t)

Fig. 7 Block Diagram of Feedback Control State of the UPFC.

The state fee dback control is to conside r the process mode l in the form of an e quation of state : X‫( ٭‬t) = A x (t) + B u (t) (11) And observation e quation: Y (t) = C x (t) +D u (t) (12) Where u(t) is the control vector, x (t) the state vector, and y (t) the output vector of dime nsion for a discre te syste m to the sampling process parame ters Te at times of Te sample k are formalize d as follows : x(t+1) = Ad x(t) + B ud(t) (14) Y(t) = C d x(t) + Dd u(t) (15) The transfer function G (s) = Y (s) / U (s) of our process UPFC can be writte n as:

5

hidde n laye r and output laye r. The laye rs of input and output inte rfere with the e xternal e nvironme nt, which is not the case for the interme diate laye r calle d hidde n laye r ie the network input is the command U (t) and its output is Y (t). The state vector X (t) from the hidde n laye r is inje cte d into the input laye r. We de duce the following e quations: X (t) = W r X (t-1) + W h U (t-1) ( 21) Y(t) = W o X (t) (22) Where , Wh ; Wr e t Wo are the we ight matrices. Equations are standard de scriptions of the state space of dynamical systems. The orde r of the syste m de pe nds on the number of states e quals the numbe r of hidde n laye rs. Whe n an input-output data is prese nte d to the network at ite ration k square d error at the output of the ne twork is de fine d as 1 2 (23) E t  y d ( t )  y( t )  2 For all data u (t), y d (t) de t = 1,2,….. N, the sum of square d e rrors N is: (24) E   Et t 1

G s  

(16)

1 sr L

The we ights are modifie d at each ite ration, for W 0 we have : E t y( t )  y d ( t )  y( t )  W0 W0  y d (t )  y(t ).x T (t )

We de duce the e quations of state re presentation of the UPFC:  * r  x   L .x  u     y  x  

(17)

E t y( t ) x ( t ) . . y( t ) x ( t ) Wh

(19)

Our syste m is describe d in matrix form in the state space : (20)

x *  A.x  B.u    y  C.x  D.u 

(26)

E t E t y( t ) x i ( t )  . . Wri y( t ) x i ( t ) Wri

(18)

The dynamics of the process correcte d by state space is prese nte d base d on the characte ristic e quation of the matrix [Ad - B d K], whe re K is the matrix state space controlle d process.

 v cd    u   v cq   



 y d (t )  y(t ).W0T .u(t )

Y (t) = C d x (t)

 r    L   A      r  L  

For Wh e t Wr, we re : E t Wh

With: U (t)=e (t) –k x (t) Le t: X (t +1) = [Ad – K B d] x (t) + B d e (t)

Where :

(25)

 y d ( t )  y( t ) .W0i

x i ( t ) Wri

(27)

x i x ( t  1)  X T ( t  1)  Wri . i  W Wri r The latter we obtain:

(28)

The variation of the we ight matrix base d on the learning gain is writte n as: W  . E t W

1 L B  0 

 0    1 L 

i sd    y  i sq   

(29) Elman network

1 0  C    0 1

x  i sd

W 0 , W h et W r

0 0   D    0 0

i sq 

e (t)= i *sd

T

V(t)= id

+

G(s)

u(t)=Vc d

UP FC in system the state space

5.3 Identification Based Network Elman: Process ide ntifie d [7] [8] will be characte rize d by the mode l structure (Fig. 8), of his orde r and paramete r values. It is there fore , a corollary of the simulation process for which using a mode l and a set of coe fficie nts to pre dict the response of the system. The Elman network consists of three laye rs: an input layer,

K

X

Estimated state vector

Fig. 8 Netw ork ELMAN and State Space.

Note that the performance of the ide ntification is bette r whe n the input signal is sufficie ntly high in freque ncy to e xcite the differe nt

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International Journal of Scientific & Engineering Research Volume 3, Issue 3, March -2012 ISS N 2229-5518

modes of process. The three we ights Wo, Wr and Wh which are re spective ly the matrices of the equation of state of the process system (UPFC) [CA and B] became stable afte r a rough time t = 0.3s and se veral ite rations (fig. 9). Note: For the Elman network ne uron type is assume d through the vector is zero (D = 0). In online learning Elman ne twork, the task of ide ntifying and correcting same synthesis are one afte r the other. Or correction of the numerical values of the parame ters is done re peate dly so the estimation error (Fig. 10) take s about almost a second (t = 1s) to conve rge to zero ie re gulation in pursuit.

Fig. 10 Estimation Error

To check the robustness to the controller, two tests were pe rforme d. For each test we varie d the parame te rs of the transmission line but the controller remains unchange d. It can be see n that the variation of the reactance (± 25%) has almost no influe nce on the output characte ristics of the UPFC syste m (Fig. 11).To compare the responses of active and reactive powe r of UPFC syste m, we gave the three cases (Fig. 11) Where (a) and (c) are the responses to changes (± 25%) and (b) is the response of the system without any change in reactance .

(c)

6

Conclusion

The ide ntification process will be characterize d by the mode l structure , its orde r and paramete r values. It is the re fore a corollary of the simulation process which uses a mode l and a set of coe fficie nts to pre dict the response of the syste m. The use of more advance d low-ide ntification ne ural ne twork can be de pe ndable in the calculation algorithm of the orde r.

Ne ural adaptive control by state fee dbac k (SSNN: state space ne ural ne twork)) is a hybrid control base d on the re prese ntation of system status UPFC was teste d. The pe rformance of the latter are slightly de grade d, this is may be due to the de lay cause d by the algorithm, it can't be re duce d at wil l, or it may due to the choice of the gain K of the close d loop.

5.4 Robustness Test:

(b)

Fig. 11 Neural Adaptive Control (SSNN) Pow ers P, Q And at (± 25% XL)

In this pape r we use d for the ide ntification of system paramete rs a ne uron ne twork said Elman ne twork with three laye rs. As we have already see n. Note that the performance of the ide ntification is be tte r whe n the input signal is sufficie ntly high in fre que ncy to e xcite the diffe re nt modes of process.

Fig. 9 Changing Weight

(a)

6

Finally, the ide ntification process base d on learning of Elman ne ural ne twork, provide s the dynamic be havior of the process and to estimate the syste m output as its state vector base d on the information that are control signal and the measure d output.

7 [1]

References

I. Papic, P. Zunko, D. Povh, M. Weinhold, ‚Basic control of unified power flow controller‛. IEEE Trans. Power Syst., vol. 12, no. 4, pp. 1734–1739, 1997. [2] Y. H. song and A .T. Johns,’ flexible AC transmission systems (FACTS).’ IEE power and Energy series 30.1999. [3] Gyugyi L.: unified power flow control concept for flexible AC transmission systems. IEE Proc. 139 (1992) 323-331 [4] O. pages ‘étude de comparaison de différentes struc tures de commande multi- contrôleurs application à un axe robotise.’ thèse 2001. (LAMII/CESALP).université de S avoie. [5] Xiang Li, Guanrong C., Zengqian C., and Z. Yuan ‘Chaotifying Linear Elman Networks’ IEEE transaction neural networks. vo1, 3. 5 September 2002. [6] M. A. Denaï, T. Allaoui, ‚Adaptive fuzzy Decoupling of UPFCPower Flow Compensation‛, 37th UPEC2002, 9-11 September 2002, S traffordshires University UK. [7] S. zebirate, A.chaker,O.traiaia , ‘commande addaptative decouple neuronale d’un compensateur de flux de puissance UPFC’reference480.laboratoire LAAS.CCECE 03-CCGEI 2003.Montreal.IEEE May 2003. IJSER © 2012 http://www.ijser.org

International Journal of Scientific & Engineering Research Volume 3, Issue 3, March -2012 ISS N 2229-5518

[8] S. zebirate, A.c haker, ‘commande addaptative decouple neuronale d’un UPFC (unified power flow control)’, JCGE Saint Nazaire ,Juin 2003.

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