Optimum Design of Power System Stabilizer based on Improved Ant Colony Optimization Algorithm

T his paper presents an improved technique on Ant Colony Optimization (ACO) algorithm. The procedure is applied on Single Machine with Infinite Bus (SMIB) system with power system stabilizer (PSS) at three different loading regimes. The simulations are made by using MATLAB software. The results show that by using Improved Ant Colony Optimization (IACO) the system will give better performance with less number of iterations as it compared with a previous modification on ACO. In addition, the probability of selecting the arc depends on the best ant performance and the evaporation rate.


INTRODUCTION
In the last years, much effort has been invested in improving the damping performance of power systems using Power system stabilizers (PSS). PSS provides a supplementary excitations control signal that enhances the damping capabilities of synchronous machines. The choice of parameters for the PSS is important as it affects the overall dynamic performance of the power system, there are various forms of PSS controllers, and the famous types are lead-lag compensator (i.e., classical PSS) and PID. Kundur, 1993, illustrated the construction, function, and operation of a PSS that uses auxiliary stabilizing signals to control the excitation system so as to improve power system dynamic performance. Commonly used input signals to the power system stabilizer are shaft speed, terminal frequency, and power. PSS will add a component of electrical torque in phase with the rotor speed. A robust PID stabilizer was proposed by Otaru, et al., 2004. The authors used a genetic algorithm to enhance the performance of the considered system which is a synchronous generator connected to an infinite bus, this model is sufficient for low-frequency oscillations studies, the PID stabilizer gains are designed optimally using Genetic Algorithm (GA) to arrive at the optimal setting of the controller. Another PID-PSS was proposed by Hosseini, et al., 2007, where the gain setting of PID-PSS is optimized by minimizing an objective function using GA. The dynamic response was compared with other two stabilizers named FUZZY-PSS and LQR-PSS. The authors revealed that their stabilizer gave better performance. They applied the proposed stabilizer on single machine infinite bus (SMIB) system and the simulations were made in MATLAB. Abdul-Ghaffar, et al., 2013, used hybrid particle swarm bacteria foraging optimization (PSO-BFA) in tuning the PID parameters. This research considers the stabilization of a synchronous machine connected to an infinite bus via a PID. Simulation results were presented with and without the proposed controller then compared with the classical PID. They applied the controller to SMIB system. The results showed that using of hybrid control gave better performance. Duman and Ozturk, 2010, presented a Real Coded Genetic Algorithm (RCGA) based PID controller to improve power system dynamic stability applied on (SMIB). Different controllers' structures are presented; conventional power system stabilizer (CPSS), optimized PSS and RCGAPID are used to improve the stability. Two performance indexes; integral absolute error (IAE) and integral squared error (ISE) were used as objective functions. Different loading conditions were studied. The results show that the ISE is better than IAE for the optimization problem. A Harmony Search Algorithm (HSA) approach is presented by Abdul Hameed, et al., 2014, for the robust and optimal design of PID controller to PSS for damping low-frequency power oscillation. Also, they applied their technique to infinite bus single machine system, Eigenvalue analysis by using genetic algorithm based PSS (GAPSS) under different operating conditions reveals that under-damped and lightly damped oscillation modes are shifted to a specific stable zone in the S-Plane. Boroujeni, et al., 2011, demonstrated a different type of stabilizers to generate supplementary damping control signals for the excitation system to damp the low frequency oscillation of the electric power system, they applied a new optimal technique PID type PSS based on (PSO-PSS) to a typical single machine infinite bus power system. The simulation results demonstrated that these design is showing the guarantee of the robust stability and robust performance of the power system to some conditions. A new technique in designing a power system stabilizer PSS was presented by Mahmoud and Soliman, 2012, based on a combination of Particle Swarm Optimization (PSO) and Linear Matrix Inequality (LMI) in order to eliminate the number of variables. They applied their idea on (SMIB) using MATLAB environment. Finally, they concluded that their method was effective and convergence as the system confirms better performance under different loading conditions. Soliman, et al., 2008, demonstrated another type of PSS that minimizes the maximum overshoot in order to alleviate the generator shaft fatigue. They used PSO algorithm in order to fix the gain of the PSS and lead time compensator. They applied their stabilizer to SMIB system at different loading conditions, the results showed the effectiveness and robustness of the proposed technique. The rest of this paper is organized as follows: the mathematical model is illustrated in the next section. Ant colony optimization and its' modifications are demonstrated in the third section while the fourth section contains the results and discussion. Finally, a conclusion is demonstrated in the last section.

MATHEMATICAL MODEL
In this section, the mathematical model of the system with PSS and finding the transfer function are described.

SMIB
A synchronous machine with infinite bus system was taken in this research as a test system, as shown in Fig Table 1.

Power System Stabilizer (PSS)
The transfer function of power system stabilizer is = 1< Ki < 50

Modified Ant Colony Optimization (MACO) Algorithm
The flowchart of this method is shown in Fig.4. A modification was made by Mathiyalagan, et al., 2010, that deal with the process of updating the pheromone. This equation is illustrated in the flowchart of Fig.4, as one can see there the new pheromone depends on the pheromone evaporation rate (). In addition to this, the initial pheromone is entered in a random way with a dependency on the pheromone evaporation rate.

Improved Ant Colony Optimization (IACO) Algorithm
The proposed ACO algorithm in this research work is represented by a new improvement through modifying the updating pheromone equation; by adding the pheromone deposited by the best ant (*fbest / fworst) multiplied by (k) in case more than one ant take the best path. The flowchart of this process is illustrated in Fig. 5.

RESULTS AND DISCUSSION
The results of this research are simulated by MATLAB R2013 environment executed on the core (TM) i5, 2.5GHz and 4 RAM system. 8 overall proper transfer functions (SMIB with PSS) were taken for 3 loading regimes (heavy load, nominal load, and light load). 4 design variables were taken; T1, T2, TW, and gain of PSS. Two different methods of optimization were taken; modified ant colony optimization (MACO) introduced by Mathiyalagan, et al., 2010, and proposed improved ant colony optimization (IACO), 4 ants were taken for each variable and two evaporation rate ( = 0.5 and 0.2). Table 1, shows the results; the system alone, the system with PSS applying MACO and the system with PSS applying IACO at =0.5. In spite of getting the same results sometimes, IACO algorithm is better than the MACO algorithm that because of two reasons; the number of iterations in the first method (MACO) is between 10-500 iterations while it is between 1-15 iterations in the second method (IACO). This means the second method is faster.
The second reason deals with the process of updating the pheromone that affects the probability of selecting the arc.
It is clear from the 1 st equation that the last term (1j ) is constant while the last term in the 2 nd equation takes the effect of the best ant that makes the probability of selecting the arc closer to the optimal solution then the number of iteration will be less

CONCLUSIONS
Many researchers studied the stability problem of power system with the existence of PSS, and many methods were taken in order to analyze the system performance. One of these methods is ACO, an additional improvement to a previous modification of ACO algorithm is proposed in this paper. It is clear from the results that the system gives better performance when using IACO than when using MACO. That because the number of iterations is less and the simulation process will be faster. The process of updating the pheromone depends on the effect of the best ant.
Finally, follow the same procedure as described above but this time on program 3. The difference is the analysis is done according to our fitness equation.