A Novel Hybrid Prairie Dog Optimization Algorithm - Marine Predator Algorithm for Tuning Parameters Power System Stabilizer

— The article presents the parameter tuning of the Power System Stabilizer (PSS) using the hybrid method. The hybrid methods proposed in this article are Praire Dog Optimization (PDO) and Marine Predator Algorithm (MPA). The proposed method can be called PDOMPA. In the PDOMPA method, the marine predator algorithm (MPA) is able to search around optimal individuals when updating population positions. MPA is used to make the exploration and exploitation stages of PDO more valid and accurate. PDO is an algorithm inspired by the life of prairie dogs. Prairie dogs are adapted to colonizing in burrows underground. Prairie dogs have daily habits of eating, observing for predators, establishing fresh burrows, or preserving existing ones. Meanwhile, MPA is a duplication of marine predator life which is modeled mathematically. In order to validate the performance of the PDOMPA method, this article presents a comparative simulation of the objective function and the transient response of PSS. This research uses validation by comparing with conventional methods, Whale Optimization Algorithm (WOA), Grasshopper Optimization Algorithm (GOA), Marine Predator Algorithm (MPA), and Praire Dog Optimization (PDO). Based on the simulation results, PDOMPA presents fast convergence in some cases and shows optimal results compared to competitive algorithms. From the simulation results using load variations, it was found that the proposed method has the ability to reduce the average undershoot and overshoot of speed by 42.2% and 85.37% compared to the PSS-Lead Lag method. Meanwhile the average settling time value of speed is 50.7%.


INTRODUCTION
The stability of the electricity network system is important.Technological developments increase the complexity of the electrical network which is increasingly playing an important role [1][2][3][4].Demand for electrical energy from consumers has increased rapidly [5] [6][7][8][9].In addition, the remote location of the plant and away from the load increases the complexity of the power system [10][11][12][13][14].The important keys in distributing electric power systems are stability and consistency [15][16][17][18][19][20][21].The ability of a system to recover after experiencing a shock is an important focus [22][23][24][25][26][27][28].Changes in loads and additions to loads that are well planned or sudden are things that worry the electric power system [29].This will cause a tremendous shock to the power plant, especially the generator.This causes the generator to experience a decrease or loss of synchronization which creates the need for a damping torque [30][31].This can be fulfilled by the power system stabilizer.
Power System Stabilizer (PSS) is an additional control on the generator.PSS is maintaining the frequency and terminal voltage locally or globally on each generator [32][33][34][35][36][37][38].An unreliable response can cause frequency oscillations over long periods [39].This can result in a reduction in power transfer strength.Over the decades, the development of methods for maintaining stability has increased significantly [40][41][42][43][44][45].This should be of particular concern in its application.Various methods and approaches to Power System Stabilizers have been presented in the popular literature as conventional PSS.It is known to have a simple structure.Besides that, it is easy to apply [46].The development of power systems that have different characteristics and are always changing.This demands an adaptive and established control.The existing control is a linear-based control so that it experiences problems when dealing with nonlinear systems that are often found in the industry [47] [48].
Although several studies have presented optimization approaches for power system stabilizers.Research on optimizing the power system stabilizer still has a lot of room to explore and is still popular.In this article, a hybrid method is presented, namely the Prairie Dog Optimization algorithm and the Marine Predator Algorithm to obtain the power system stabilizer parameter.MPA has the advantage of looking into exploitation and exploration, besides that it is also easier to go beyond the local optimum and find a global The article consists of methods and mathematical formulations in section 2. Section 3 is a presentation of the proposed method approach along with its pseudocode.Section 4 is a simulation and discussion.The last section contains the conclusions of the research.

A. Prairie Dog Optimization Algorithm (PDO)
Prairie Dog Optimization Algorithm adopts the behavior of prairie dogs in nature.The prairie dog (genus Cynomys) is a herbivorous rodent found mainly in the Great Plains and desert prairies of the southwestern US, Canada, and Mexico [67].In PDO, the optimization phase that characterizes the optimization method is exploration and exploitation using four activities of prairie dogs.Prairie dogs in small groups in one unit are called coterie.In one coterie, there are several numbers of prairie dogs.The cotere concept can be modeled mathematically in equation ( 1) to (6).
Where  is the j-th dimension of the i-th neighborhood in a herd.The location of the prairie dogs in the coterie is modeled in equation (2). is the th dimension of the th prairie dog in a coterie.Equations ( 3) and ( 4) are uniform distributions of the locations of the conteries and prairie dogs.The upper and lower bounds of the j-th matrix of the optimization problem are denoted by UB and LB. is a random value [0,1].The value of the fitness function of each prairie dog is a representation of the quality of food, new burrows and the accuracy of response to predators.this is evaluated by plugging into the fitness function in equation (7).

1) Exploration Phase
In the exploration phase, prairie dogs are foraging for food and digging nearby burrows.The optimization problem space is explored from foraging activities and building tunnels in the ground.These animals build tunnels in the ground around which there is a food source.The concept of these passages is that they will connect because these prairie dogs build tunnels in the ground at each new food source.On the other hand, this underground tunnel is used as a refuge from predators.New burrows will be dug depending on the quality of the food source.The position update for foraging in the exploration phase of our algorithm is given in equation ( 8) and the position update for the underground passage building is given in equation (9).
, =  , −   , + ∆ (11) Where  , is the optimal solution achieved. , represents the effect of the optimal solution.Signal indicating the source of food is symbolized by .The random combined effect on the herd of prairie dogs is symbolized by  , .() is the levy distribution.The ability to dig a herd is represented by .To ensure the exploration process used stochastic items symbolized by  with a value of -1 or 1.The difference between prairie dogs is represented by∆.

2) Exploitation Phase
This section describes the steppe dog exploitation phase.Prairie dogs have the ability to communicate among themselves by different signals or sounds when looking for food and avoiding predators.This is modeled in equations ( 13) and (14).The exploitation process aims to find promising spots as shown in (15).
Where  is a symbol of predatory effect. is the current iteration and   is the maximum number of iterations.
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B. Marine Predator Algorithm (MPA)
Marine Predator Algorithm (MPA) is an optimization method based on the behavior of marine predators in nature [68].This algorithm has three important steps in solving optimization problems, namely:

1) Step 1: High Speed
In this stage ( < 1 3 × max _), the prey is finding for feed and the predator is observing the mobility of the prey.The stage can be formulated in equations ( 16) and (17). ) The ⊗ is operation of element-wise multiplication.  ⃗⃗⃗⃗ is a random value.It is based on brownian motion with normal distribution. ⃗ ∈ [0, 1]. is uniform random value equal to 0.5.

2) Stage 2: Equal Speed
In this stage ( In the first population,   ⃗⃗⃗⃗ denotes random numbers based on the distribution.Prey movement is simulated by   ⃗⃗⃗⃗ Multiplication.While the second half of the population, the mathematical equation is as (20) to (22).

3) Stage 3: Low-Speed
In this last stage, the prey has a speed below the predator.When  > 2 3 × max _, the mathematical equation is as (23) and (24).
⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗  =  ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗  +  ×  ⊗ ℎ  ⃗⃗⃗⃗⃗⃗ One of the environmental issues that influence the attitude of marine ecosystems is Fish Aggregating Devices (FADs).The FADs modeling is as (25).
Where  is a uniform random variable.xmax is the upper limit and xmin is the lower limit.the optimization process is affected when the  is 0.2. is a binary vector.

C. Power System Stabilizer (PSS)
The addition of PSS will dampen generator rotor oscillations in the excitation system by supplying an additional feedback stabilization signal [69].The modeling scheme of PSS can be seen in Fig. 1.

III. PROPOSED HYBRID PDO-MPA
In improving the method, we propose a hybrid algorithm called Prairie Dog Optimization based on marine predator algorithm (PDOMPA.In the proposed PDOMPA, the marine predator algorithm (MPA) is applied to the PDO to sharpen the exploration and exploitation stages so that they are more valid and accurate as well as avoiding local optimal traps and preventing premature convergence.In this article, the PDO and MPA methods are integrated by replacing equation (11) with equation ( 16).The advantage of the PDOMPA hybrid algorithm is that the individuals in the top layer are not only affected by each individual in the PDO, but also have an effect on the global optimal solution.The Matlab/Simulink application is used to write the PDOMPA method code with a laptop with RAM specifications: 8 GB, CPU Intel I5-5200: 2.19GHZ 64 bit.The PDOMPA is applied to obtain the optimal power system stabilizer parameters.To determine the performance of the PDOMPA, a test of twenty-three benchmark functions was carried out.Benchmark function has three categories: unimodal (Fig. 2 (a)-(g)), multimodal (Fig, 2 (h)-(m)) and multimodal with fixed dimensions (Fig. 2 (m)-(w)).The three categories have their own characteristics.The unimodal function has one global ideal and no local optimal, making it a good candidate for benchmarking algorithm exploitation.The multi-modal function is particularly useful for assessing exploration and deducting the algorithm's local optima position since it has a large number of local optimum points.Multi-modal test functions that have been rotated, shifted, and biassed make up the composite function.PDOMPA was compared with the PDO, MPA, GWO, and WOA.For (i=1 to m) do 8: For (j=1 to n) do 9: Calculate of the fitness  10: Find the Best Solution so far 11: Update  12: Update  and  → Equation ( 12) and ( 15 Here, Fig. 2 displays a number of convergence graphs taken from each benchmark, demonstrating how all of the algorithms' convergence curves differ significantly from one another and can be quickly identified for purposes of analysis and interpretation.In comparison to other methods, the convergence speed of PDOMPA was examined.The algorithm has the highest rate of convergence, as seen by the curve's fastest decline towards the global minimum.PDOMPA has a satisfactory convergence rate, as seen in Fig. 2. On several benchmark functions, PDOMPA's convergence speed is a little bit slower than WOA's, but it is clear that PDOMPA can reach a more minimum global best objective fitness.
The proportional distribution to exploration and exploitation is primarily determined by the linear reduction of the weight vector's fluctuation range.Overall, PDOMPA's convergence speed is competitive, occasionally even outpacing that of all other comparable methods.These reasons lead to the conclusion that PDOMPA is a wellbehaved algorithm in terms of convergence rate.
Furthermore, the PDO-MPA performance was measured by applying to tune the PSS parameter.PDOMPA is used to obtain parameters that match the optimal output criteria.This article tests a single machine system owned by Heffron-Philips by conducting several case studies.The case study is to change the load on the system by 25%, 50% and 95%.The first step is to optimize the PSS parameter by using the integral of time multiplied absolute error (ITAE).ITAE is adopted as the objective function for the design problem.This can be seen in equation (26).

1) Case 1: 25% Of Load
The first test by giving a light load of 25% on the system.The output of system gives a different transient response for each algorithm.The output graph of the speed and rotor angle can be seen in Fig. 3 and Fig. 4. The transient response of the worst undershoot speed is owned by MPA.MPA was only able to reduce undershoot speed from PSS-lead lag by 13.11%.Meanwhile, the worst overshoot of speed was owned by WOA which was only able to reduce pss-lead lag by 68.82%.The application of PDOMPA is able to reduce the undershoot and overshoot values of the PSS-lead lag speed by 42.14% and 85.37%.In the transient response of the angel rotor, the undershoot value of PDOMPA is better than the PSS-Lead Lag of 78.26%.The details of case study 1 can be seen in Table I.

2) Case 2: 50% Of Load
The second case study by increasing the loading by 25%.The total load is 50%.The graphs of the second case study can be seen in Fig. 5 and Fig. 6.Details of case study 2 can be seen in Table 3.In the second case study, pdompa applied to pss was able to reduce the undershoot and overshoot speed of pss-lead lag by 42.21% and 85% .42%.Meanwhile, the undershoot value of the rotor angle PDOMPA is better than PSS-Lead lag by 78.25 %.Table II is detail of case study 2.

3) Case 3: 95% Of Load
The third case study is by 95% of load.With maximal load, PDOMPA-optimized PSS gives good transient Widi Aribowo, A Novel Hybrid Prairie Dog Optimization Algorithm -Marine Predator Algorithm for Tuning Parameters Power System Stabilizer response.The graphs of the second case study can be seen in Fig. 7 and Fig. 8.The undershoot and overshoot values of speed with the pdompa method are better by 42.26% and 85.53% than the PSS-Lead Lag method.speed in 95 % load in Fig. 9, speed in 50 % load in Fig. 10, rotor angle in 95 % load in Fig. 11.Meanwhile, the settling time value is better than the PSS-Lead Lag of 48%.The details of case study 3 can be seen in Table III.

V. CONCLUSION
PDOMPA is a method that combines the PDO and MPA methods.PDO is an algorithm inspired by the life of prairie dogs in nature.Meanwhile, MPA is inspired by the life of marine predators.MPA is used to accelerate convergence and improve PDO performance.In this article PDOMPA is applied to get the best PSS parameters.The PSS transient response using the PDOMPA method was measured and compared using the PSS-Lead Lag, PSS-WOA, PSS-GOA, PSS-MPA and PSS-PDO methods.Testing uses 3 loading case studies.The test results show that PDOMPA applied to PSS has the ability to reduce undershoot, overshoot and speed timing.From the simulation results using load variations, it is known that the proposed method has the ability to reduce the average undershoot and overshoot speeds by 42.2% and 85.37% compared to the PSS-Lead Lag method.Meanwhile, the average value of speed settling time is 50.7%.On the rotor angle side, PDOMPA has a longer settling time than other methods but has the best undershoot.
The PDOMPA method is a combination of the PDO and MPA methods.The application for binary and complex systems needs to be studied again to obtain more optimal exploration and exploitation performance.

Fig. 8 .Fig. 9 .Fig. 10 .
Fig. 8. Rotor Angle in 25 % Load Journal of Robotics and Control (JRC) ISSN: 2715-5072 693 Widi Aribowo, A Novel Hybrid Prairie Dog Optimization Algorithm -Marine Predator Algorithm for Tuning Parameters Power System Stabilizer ) Widi Aribowo, A Novel Hybrid Prairie Dog Optimization Algorithm -Marine Predator Algorithm for Tuning Parameters Power System Stabilizer

TABLE I .
CASE 1: 25 % OF LOAD