PSS AND IPFC POD controllers coordinated tuning by an Adaptive Genetic Algorithm with Hyper-mutation

Flexible AC transmission systems (FACTS) are a modern technology to increase controllability in power systems. This work presents an analysis of Interline Power Flow Controller (IPFC) which is a FACTS device. This device control and manage power flow in transmission lines. Supplementary damping controller is installed on IPFC Proportional Integral (PI) control. Power Oscillation Damping (POD) and Power System Stabilizers (PSS) contribute to power system stability. This works represents the electric power system and Interline Power Flow Controller FACTS device by a current sensitivity model (CSM). This work focuses on small-signal stability studies using an Adaptive Genetic Algorithm and Hyper-mutation (AGAH) to design simultaneously controller parameters. Adaptive Genetic Algorithm aims to find optimal controller parameters to enhance greatly stability of the power system. This paper considers two areas 14 bus symmetrical system in order to assess proposed algorithm. Simulations are carried out in MatLab platform in order to compare genetic algorithm with proposed algorithm performance. Results show AGAH outweighed AG by time convergence and accuracy.


INTRODUCTION
Power System Stability holds great 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]. _______________________________ * Correspondencia: E-mail: 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 with time, it may prevent the connection between neighbouring areas. Electromechanical low frequency oscillation under study are classified as local (0.8 to 2.0 Hz), inter-area (0.2 to 0.8 Hz), or intraplant (1.5 to 2.5 Hz) [3]. However, PSS installation does not 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 damp 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 interarea oscillation modes, respectively [5].
FACTS stabilizers are usually installed at key points of transmission lines in a power system [6]. IPFC FACTS device is based on voltage source controller (VSC) which mainly compensate and manage power flow (active and reactive) in multiple lines. As a result, voltage 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 IPFC 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 overloaded 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] have been used for the problem of PSS and POD design in a coordinated way. In this paper, an Adaptive Genetic Algorithm [10] with Hypermutation [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.

CURRENT 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 network and there is no need of an infinite bus [8]. What is more, CSM works very well when it comes to adding new equipment such as FACTS devices (IPFC current injection model) to the EPS [12].

INTERLINE POWER FLOW CONTROLLER
This work considers a IPFC device with two Voltage Source Converter (VSC) technology, which addresses the problem of compensating 2 transmission lines. These VSCs are connected through a common 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 optimize the utilization of the overall transmission system [12]. Figure 1 shows three buses i, j and k where IPFC get installed [2]. IPFC structure considers zero net power at the common dc terminals. Therefore, this ideal system losses zero active power [13]. According to active power invariance of IPFC, the equation is as follows (1).
This work considers the VSC as a complex vector which decomposes it into a quadrature component and inphase component by equation (2) [14] where = , . By this way, power flow analysis with IPFC-PI control becomes a way easier to solve it out. 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 [14]. Differential Equations from (3) to (6) represents PI control. PI controllers gains are 1 , 2 and 3 in p.u and PI time constants are 1 , 2 and 3 in seconds..
Equation (3) and (4) relates to active power flow control at bus j. Where is a supplementary signal from the POD controller which modulates the quadrature component of the prime VSC converter in order to provide additional damping to ESP oscillations [8]. Equation (5) and (6) relates to reactive power flow control at bus j. Equation (7) and (8) relates to active power flow control at bus k.
, are the active and reactive power flow control 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.

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. 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].
= ( cos + sin ) = ( sin − cos ) Where represents − 1 and = , . Equation (12) and (13) are real and imaginary current injection at bus i. Similarly, equations (14) and (15) works similar to (16) And (17) which are real and imaginary current injection at bus j and k, respectively. Figure 3 shows PSS and POD control structures which are quite similar. They differ from each other because input and output signals. PSS input signal comes from generators speed (∆ ) 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 and POD washout time constants are and [12]. Phase lead-lag time constants are 1 , 2 , 3 e 4 . This paper considers = = 1 , 1 = 3 and 2 = 4 [1], [2] and [5]. Stabilizing gains are and .

DESIGN OF THE ADAPTIVE ALGORITHM GENETIC WITH HYPERMUTATION FOR TUNING PSS AND POD
The Adaptive GA operations consist of some key components such as genetic representation, population initialization, fitness function, selection scheme, diversity strategy population, crossover and mutation. Hyper-mutation intervenes selectively speeding up desired fitness 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).
Where ( ) represents Diversity rate, q is current generation and np is population size. In this paper, represents number of prospective individuals in the current population.
counts those individuals which meet equation (28).
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.

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]. Therefore, the chromosome is a vector with size equal to 9. Fig. 4 shows PSS1, PSS2 and POD parameter encoding. 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 different 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).
One parameter that stands out is ρ (ρ>>1). This work considers ρ=1000. 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. Block Diagram AGA with Hyper-mutation
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, they 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 crossover and mutation dynamic rates. Hyper-mutation level 1 begins at generation number 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 the 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. Mutation and Hyper-mutation do not overlap each other. Since mutation help generate new solution [11]. Hypermutation depends on population diversity and it gets activated when (maximum number of prospective individuals) 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.

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-PI 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]. What is more, table 1 shows that 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. Conventional solutions involve PSS installation but instability menace still remains because poor damping values. 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 AGA with Hyper-mutation which simultaneously tune PPS and POD parameters to achieve desired damping. Table 2 shows eigenvalues after controller coordinated tuning. This paper considers desired damping between 10 and 10.9 percent. It is worth mentioning that computational time becomes rather efficient if desired damping set a range between 10 and 15 or 10 and 30 percent of damping values. The more 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 also shows that AGAH error distance is 0.00720 p.u and it converges at generation 7 on average.  Figure 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.   Table 3 shows optimal parameters tuned by AGAH for PSS and POD to damp properly electromechanical oscillation.

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. to long time convergence. However, AGAH successfully performed getting a low time convergence and accurate results.  AGAH becomes a prominent tool for tuning controller parameters.

ACKNOWLEGMENT
This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES) -Finance Code 001.