<= span lang=3DEN-GB style=3D'mso-fareast-font-family:Candara;mso-bidi-font-family:= Candara'>1&nb= sp; INTR= ODUCTION

Power System Stability holds gre= at importance when it comes to operation and planning of electric power systems (EPS). Small signal stability studies the electric system performance when = it is subjected to small variations [1], [2].

_______________________________<= /p>

* Correspondencia= :
E-mail: <= span lang=3DPT-BR style=3D'font-size:8.0pt;mso-bidi-font-size:10.0pt;font-family= :"Candara","sans-serif"; color:black;mso-ansi-language:PT-BR;text-decoration:none;text-underline:non= e'>cordero.lg@gmail.com

Therefore, oscillations with low frequencies play an important role.

If these oscillations lack of sufficient damping, it may cause the loss of power system synchronism and w= ith time, it may prevent the connection between neighbouring areas. Electromechanical low frequency oscillation under study are classified as l= ocal (0.8 to 2.0 Hz), inter-area (0.2 to 0.8 Hz), or intrap= lant (1.5 to 2.5 Hz) [3].

These oscillations may compromise EPS lines capacity and system stability. Most electrical power plants have dealt this problem palliative solutions such as PSS installation which inse= rts additional damping to local mode oscillations.

However, PSS installation does n= ot always offer proper solution to mitigate poor damping oscillation [4].

Studies shows that PSS operates = well to damp local mode oscillations but low performance to influence inter-area mode oscillations Thus, control strategies to da= mp these oscillations are necessary to maintain power system stability. Power System Stabilizer (PSS) and Power Oscillation Damping (POD) provide a supplementary damping to the local mode and inter-area oscillation modes, respectively [5].

FACTS stabilizers are usually installed at key points of transmission lines in a power system [6]. IPFC F= ACTS device is based on voltage source controller (VSC) which mainly compensate = and manage power flow (active and reactive) in multiple lines. As a result, vol= tage profile improves in the surrounding area of FACTS device installation [7]. =

The supplementary controller of power oscillation damping (POD) is used for IPFC to damp inter-area modes I= PFC structure consists of 2 VSC which provide series compensation and a common = DC connection that is able to transmit real power to another line. Therefore, = this device can supply reactive and real power compensation to alleviate overloa= ded lines. PSS and IPFC-POD controller design enhance low frequency electromechanical oscillations by proper parameter tuning [8] Recently, Optimization techniques like Bacterial Foraging Optimization Algorithm (BFO= ), the Particle Swarm Optimization (PSO) [8] and Genetic Algorithm (GA) [9] ha= ve been used for the problem of PSS and POD design in a coordinated way. In th= is paper, an Adaptive Genetic Algorithm [10] with Hyper-mutation [11] is used = for tuning PSS and IPFC-POD controllers in a coordinated way. Coding and simulations are completed in MatLab platform. Results show effectiveness of AGAH compared to GA. This work considers two areas 14 bus symmetrical system [2] and IPFC device which is modelled by a current injection Current.<= /o:p>

<= span lang=3DEN-GB style=3D'mso-fareast-font-family:Candara;mso-bidi-font-family:= Candara'>2&nb= sp; CURR= ENT SENTIVITY MODEL

The CSM is based on Kirchhoff’s current law which applies to all dynamic processes in the EPS along anytime. The CSM is a linear analysis tool for EPSs that preserves the external netw= ork and there is no need of an infinite bus [8]. What is more, CSM works very w= ell when it comes to adding new equipment such as FACTS devices (IPFC current injection model) to the EPS [12].

<= span lang=3DEN-GB style=3D'mso-fareast-font-family:Candara;mso-bidi-font-family:= Candara'>3&nb= sp; INTE= RLINE POWER FLOW CONTROLLER

This work considers a IPFC dev= ice with two Voltage Source Converter (VSC) technology, which addresses the pro= blem of compensating 2 transmission lines. These VSCs are connected through a co= mmon DC link in order to allow active power ﬂow between lines. This capability allows the IPFC to provide both reactive and active power. Therefore, proper adjustment can relieve overloaded lines and thereby optim= ize the utilization of the overall transmission system [12]. Figure 1 shows thr= ee buses i, j and k where IPFC get installed [2]. IPFC structure considers zero n= et power at the common dc terminals. Therefore, this ideal system losses zero active power [13]. According to active power invariance of IPFC, the equati= on is as follows (1).

= (1)

This work considers the VSC as= a complex vector which decomposes it into a quadrature component and in-phase component by equation (2) [14] where . By this way, power flow analysis with IPFC-PI control becomes a way easier to solve it out.

(2)

Figure 1 IPFC Installation at Buses i, j and k

Management power flow strategy= used for the IPFC is based on PI controllers. PI controllers are powerful tools = for power flow control by boosting voltage levels and small-signal stability [1= 4]. Differential Equations from (3) to (6) represents PI control. PI controllers gains are , and in p.u and PI time constants are , and in seconds..

	(3)
	(4)
	(5)
	(6)
	(7)
	(8)

Equation (3) and (4) relates to active power flow control= at bus j. Where is a supplementa= ry signal from the POD controller which modulates the quadrature component of the prime VSC converter in order to p= rovide additional damping to ESP oscillations [8]. Equation (5) and (6) relates to reactive power flow cont= rol at bus j. Equation (7) and (8) relates to active power flow control at bus k. , are the active and reactive power flow c= ontrol set-points for one transmission line. is the active= power flow control set-point for the other line [14]. represents inherent delay of the control device which varies between 1 to 10 ms.

Equations (9)-(11) are the controlled flows at bus j and k ( , and ).

	(9)
	(10)
	(11)

A. IPFC Current Injection Model

IPFC current injection model at buses i, j and k are described by equations (12) -(17). Figure 2 shows current injection at buses i, j and k.

Figure 2 IPFC current injection at buses i, j and k=

&= nbsp;

These equations do not depend = on voltage series converter parameters but quadrature and in-phase components = of VSC which is a way easier to use them [12].

	(12)
	(13)
	(14)
	(15)
	(16)
	(17)

Where represents and n=3Dj,k . Equation (12) and (13) are real and imaginary current injection at bus i. Similarly, equations (14) and (1= 5) works similar to (16) And (17) which are real and imaginary current injectio= n at bus j and k, respectively.

<= span lang=3DEN-GB style=3D'mso-fareast-font-family:Candara;mso-bidi-font-family:= Candara'>4&nb= sp; PSS AND POD CONTROLLER STRUCTURE

Figure 3 shows PSS and POD con= trol structures which are quite similar. They differ from each other because inp= ut and output signals. PSS input signal comes from generators speed (∆<= span style=3D'font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambr= ia Math"; mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-sty= le: normal'>= ωk ) and its output signal links to AVR voltage reference. IPFC-POD input signal uses active power ﬂow ( ) which has an impact over inter-are= mode and its output signal links IPFC-PI voltage quadrature component [8]. PSS a= nd POD washout time constants are and [12]. Phase lead-lag time constants are = , , e . This paper considers , and [1], [2] and [5]. Stabilizing gains are = and .

Stabilizing gain

Washout filter

Lead-Lag Phase Block

<= /o:p>

Figure 3 PSS and POD Dynamic Model

Equations that describe PSS an= d POD dynamic control upon supplementary damping signals are show in (18) – (26).=

<= span style=3D'mso-spacerun:yes'> (18)

(19)

= (20)

(21)

(22)

= (23)

= (24)

= (= 26)

represents ﬁeld voltage, <= !--[if gte msEquation 12]>∆= Vk represents terminal voltage and is voltage reference at k-th generator at equation (21). represents active power variation in a s= teady state operation.

<= span lang=3DEN-GB style=3D'mso-fareast-font-family:Candara;mso-bidi-font-family:= Candara'>5&nb= sp; DESIGN OF THE ADAPTIVE ALGORITHM GENETIC WITH HYPERMUTATION FOR TUNING PSS AND POD

The Adaptive GA operations con= sist of some key components such as genetic representation, population initializ= ation, fitness function, selection scheme, diversity strategy population, crossover and mutation. Hyper-mutation intervenes selectively speeding up desired fit= ness at specific generation.

A. Adaptive Genetic Algorithm

This algorithm has mutation and crossover rates which dynamically calibrates by = each generation [10]. Diversity rate are ruled as follows in equation (27).=

= (27)

Where represents Diversity rate, q is current generation and np is population size. In this pap= er, represents number of prospective individ= uals in the current population. = counts those individuals which meet equation (28).

= (28)

= (29)

DFD means Distance Fitness Deviation in equation (28) and (29). Crossover and mutation rate depend on . Equation that relate to them are in (30) and (31) where = and = are crossover rate and mutation rate, respectively.

	(30)
	(31)

B. Chromosome Encoding

PSS1 and PSS2 installation takes places at generator 2 and 3 in the two area symmetrical system [2], [8]. IPFC-POD get installed at bus 7 [12]. Therefor= e, the chromosome is a vector with size equal to 9. Fig. 4 shows PSS1, PSS2 and POD parameter encoding.

POD Parameters

PSS2 Parameters

PSS1 Parameters

Figure 4 Chromosome encoding PSS and POD

POD tuning happen= to set first, behavioural population shows that POD tuning is quite decisive to find PSS proper tuning. PSS1 and PSS2 installation takes place in two diffe= rent areas. IPFC-POD locates strategically at bus 7 which connects a long line transmission that impacts on inter-area oscillations [12].

C. Fitness Function

Fitness function is comprised of the objective function, where f calculates eigenvalues ( ) distance from a desired eigenvalue at specific generation, represents best solution at generation g. = This fitness function considers infeasibility, where h calculates damping ( ) error between the desired value and the current value at generation g. Equation are written in (32) -(34).

(32)

(33)

(34)

One parameter that stands out is ρ (ρ>>1). This work considers ρ=3D1000. By doing so, it places importance over damping values. This fitness function search for the minimum value or in another words, they move closer to the desired damping.

D.&n= bsp; Block Diagram AGA with Hyper-mutation

<= /p>

Fig. 5a describes coding procedure for the AGAH which solve out the problem in this work. First step generates ten individuals as an initial population in a random way, th= ey go through CSM that considers IPFC-POD and PSS. Second step assesses prospective eigenvalues by the fitness function. Third step begins in ‘while loop’ condition. Diversity rate starts running and as a consequence crossov= er and mutation dynamic rates. Hyper-mutation level 1 begins at generation num= ber two in order to boost prospective individuals. An agent searches for desired damping values in the population even though they get spread out in other individuals. This procedure speeds up convergence because it increases the chance an individual mutates with desired damping. Then for the next step t= he best configurations keep alive for the next generation by means of minimum fitness and it continues until it reaches the stop criterion.

E. Hyper-mutation

Convergence becomes a big problem for GA due to its constant pace which may lead to long time convergence. On top of that, it substantially depends on initial population. Increasing diversity of prospective individuals speed up convergence. Hyper-mutation enables GA to cope with stagnated fitness. Muta= tion and Hyper-mutation do not overlap each other. Since mutation help generate = new solution [11]. Hyper-mutation depends on population diversity and it gets activated when (maximum number of prospective individua= ls) keep constant as shown at Fig. 5b. One thing to point out is that the chromosome encoding allows to hyper-mutate PSS genes and POD genes.<= span lang=3DEN-GB style=3D'font-family:"Candara","sans-serif";mso-fareast-langua= ge:ES-PE'>

(a)

(b)

Figure 5a Block Diagram = of AGA with Hyper-mutation and Figure 5b Hyper-mutation block diagram

<= span lang=3DEN-GB style=3D'mso-fareast-font-family:Candara;mso-bidi-font-family:= Candara'>6&nb= sp; VARIABLES CONSTRAINTS

The AGAH aims to adjust simultaneously the PSS = and POD controllers. Lead-lag time constants and stabilizers gains works within= a range which is shown in equation (35) and (36).

0.05≤T_{1_PSS}≤1, 0.05X= 04;T_{2_PSS}≤1, 1≤K_PSS≤5 (35)

0.05≤T_{1_POD}≤1, 0.05X= 04;T_{2_POD}≤1, 0.05≤K_POD≤5 (36)

IPFC-PI parameters keep fixed [13]: , , = (in seconds), and , , . These parameters may change and they depend on the system under study.

<= span lang=3DEN-GB style=3D'mso-fareast-font-family:Candara;mso-bidi-font-family:= Candara'>7&nb= sp; SIMULATIONS AND RESULTS

This work uses the two areas 14 bus symmetrical system which has a long line interconnection between bus 7 and 8. This system has 2 shunt compensation at buses 7 and 8 but it is not enough to enhance voltage drop at bus 7. IPFC-P= I installation solved voltage drop out and it also alleviated power flow at buses 7 and 8. This system has 2 local modes and 1 inter-are mode. PSS1, PPS2 and POD get installed at generator 2 and 3 and at bus 7,

respectively [12].<= /span>

Figure 6 Two areas 14 bus symmetrical system

What is more, table 1 shows th= at this system has a negative damping value which makes it unstable. Which may undermine system stability if a small power variation or a disturbance takes place at some point in time.

Table 1Benchmark System eigenvalues before and after controller installation

Initial	Eigenvalues without PI, PSS and POD
Mode
	-0.362 j6.292	0.0575	1.003
	-0.265 j5.884	0.0450	0.937
	-0.060 j4.457	-0.0135	0.709

Table 2 Benchmark System eigenvalues after controllers tuning

Final	Eigenvalues without PI, PSS and POD
Mode
	-0.692 j6.426	0.1072	1.028
	-0.613 j6.024	0.1013	0.963
	-0.478 j4.544	0.1048	0.727

Conventional solutions involve= PSS installation but instability menace still remains because poor damping valu= es. IPFC-POD installations comes up as a novel solution to cope with poor inter= -area mode oscillations. This section mainly presents simulation results of the A= GA with Hyper-mutation which simultaneously tune PPS and POD parameters to ach= ieve desired damping. Table 2 shows eigenvalues after controller coordinated tun= ing. This paper considers desired damping between 10 and 10.9 percent. It is wor= th mentioning that computational time becomes rather efficient if desired damp= ing set a range between 10 and 15 or 10 and 30 percent of damping values. The m= ore it reduces damping range, the more time consuming. AGAH and AG perform a hundred tests to assess time convergence, error distance and generation convergence compared to desired damping.

Table 3 shows that AGAH enhanc= es time convergence

which is on average 14.66 seco= nds. On the other hand, GA takes 23.51 seconds on average to converge and genera= tion increases to attain a desired value. Moreover, calculated damping are that accurate than AG. Minimum time convergence observed was 6.227 seconds and a maximum 22.9 seconds.

Table 3Time Consuming AGA with Hyper-mutation and AG

Avgs<= span lang=3DEN-GB style=3D'font-size:7.0pt;color:black;mso-themecolor:text1; mso-fareast-language:ES-PE;mso-bidi-font-weight:bold'><= /p>

Min

Max

Avgs<= span lang=3DEN-GB style=3D'font-size:7.0pt;color:black;mso-themecolor:text1; mso-fareast-language:ES-PE;mso-bidi-font-weight:bold'><= /p>

Min

Max

0.10<ξmin

14.66

6.21

22.92

0.00720

0.00163

0.01365

0.10<ξmin

23.50

6.03

39.57

0.01112

0.00308

0.01453

Table 3 also shows that AGAH e= rror distance is 0.00720 p.u and it converges at generation 7 on average.

Figure 7 Crossover and Mutation rates by generations

Figure 7 depicts changing rates along generation from 1 to 4. The first two generations work with high crossover rate (cross symbol) and it starts to change dynamically as to ada= pt by generations. High Mutation rate (diamond symbol) happened at generation 3 and 4.

(a)

(b)

Figure 8 (a) Best fitness and (b) Damping convergence

Figure 8 (a) depicts how best fitness behaves along four generations until it reaches a desired value. Fi= gure 8 (b) describes best damping at each generation and how it evolves along generations and it seems to become closer around a desired value by each generation. The desired damping is greater than 10 percent but less than 11 percent for local and inter-are modes.

Figure 9 Eigenvalues without and with PSS and POD

Figure 9 describes how initial eigenvalues (asterisk symbol) move toward 10 percent damping region. Final eigenvalues (triangle symbol) get on the desired region with 10 percent of damping as minimum value.

Table 4 PSS1, PSS2 and POD optimal parameters

PSS and POD parameters	mi= n
PSS G2	PSS G3	POD
(s) 0.652	0.767	0.832
(s) 0.520	0.651	0.264
(p.u)	2.514	1.913	2.525

Table 3 shows optimal paramete= rs tuned by AGAH for PSS and POD to damp properly electromechanical oscillatio= n.

<= span lang=3DEN-GB style=3D'mso-fareast-font-family:Candara;mso-bidi-font-family:= Candara'>8&nb= sp; CONCLUSION

In this paper, AGA with Hyper-mutation is used for tuning simultaneously PSS and POD controllers. Significant results obtained from simulations are as follows.

·&nb= sp; The solutions achieved for 100 testes of optimizing objective function for PSS = and POD parameters show that AGA with Hyper-mutation yields more accurate dampi= ng value than GA.

·&nb= sp; AGA with Hyper-mutation time convergence outweighs GA.

·&nb= sp; Solutions obtained from AGA with Hyper-mutation have small standard error deviations.=

·&nb= sp; AGA with Hyper-mutation tuned successfully PSS and POD which allows to operate = with a desired damping value.

·&nb= sp; Desired Damping had a narrow range between 10 and 11 percent which may lead to long time convergence. However, AGAH successfully performed getting a low time convergence and accurate results.

·&nb= sp; AGAH becomes a prominent tool for tuning controller parameters.

<= span lang=3DEN-GB style=3D'mso-fareast-font-family:Candara;mso-bidi-font-family:= Candara'>9&nb= sp; ACKNOWLEGMENT

This study was financed in part by the Coordenaçăo d= e Aperfeiçoamento de Pessoal de Nível Superior - Brasil (= CAPES) - Finance Code 001.

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&= nbsp;

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