Automatic Generation Control of Simplified Egyptian Power System Using Fractional Order PI Controller Based on PSO

: In this Paper, Fraction Order (FO) PI controller is tested in order to find the optimized gains for Automatic Generation Control (AGC) controller by Particle Swarm Optimization (PSO) algorithm to represent the Simplified Egyptian Power System (SEPS) to achieve the development of power grid for the sustainable growth of Egypt. The mission of AGC is to return primary frequency regulation capability, bring back the frequency to its predefined set point in addition to reduce power fluctuation due to unplanned tie-line power flows among nearby control zones. The suggested controller is built using actual statistical records of SEPS for minimum and maximum loading situations of the SEPS in Winter and Summer of 2019-2020


Introduction
Keeping the predefined produced megawatt of power plants in addition to assisting in controlling the frequency of the control zone is the main task of automatic Load Frequency Control (LFC). However, through the real process of the zone, there will be variances between forecasted and actual loads. Therefore, the task of LFC is to recompense the common load forecast difficulties. The typical structure method of a load-frequency controller uses the linear control theory to improve control rules on the basis of the linearized mathematical model. The controller design is usually based on Algebraic Riccati-Equation using state-feedback fixed-parameters controller as illustrated [1][2].
However, in the fact that the system parameters may be changed (or cannot be totally identified), the controller layout constructed on a static parameter model could not ensure the stability of the entire system if the real power station model differs from the suggested power station model. The system transient frequency variation cannot be competently adjusted. Likewise, the state feedback controller used depends on measuring signals from all the states which may be essentially difficult to achieve. The three major difficulties to implement load-frequency controller of power systems [3]: a) Non-linearity in the interactions b) Uncertainty in the parameters, and c) System parameter differences because of changes in Process conditions. The healthy load frequency controller design is studied in several methods [4]. The most popular technique to implement frequency control is primary frequency regulation (generator governor response) and LFC. The essential mission of LFC is to bring back primary frequency tuning capability, recovering again the frequency to its nominal set point and reducing unplanned tie-line energy flows between nearby control zones. From the approaches used to process the economics of this facility in other markets, competitive offers or common contracts be obvious [5]. The nominal speed will not reach the value as of the primary controller, and remaining offset. There is one technique to recover the frequency or speed to its predefined set point by modifying the integral controller. The integrator detects the mean error at a specific time so the offset will have vanished. This approach is achieved by Automatic Generation Control (AGC) or manually by Load Frequency Control (LFC) [6][7].
PSO is used to obtain a strong load frequency controller for SEPS. The suggested controller is obtained and considered on two dissimilar loading situations of the SEPS through the winter and summer of 2019-2020 [8]. Complete stability of the SEPS is achieved while the proposed controller is implemented to it for these four loading situations in the existence of all system constraint uncertainties and the GRC.
Alhelou et al. [9] provide a comprehensive survey on different challenges and viewpoints of AGC in both conventional and untraditional power stations and presents initially reviews the usage of AGC in the different configuration of the electric power system. Furthermore, the applications of various modern and intelligent control methods are reviewed. In-depth survey on dissimilar approaches for AGC systems by adding Battery Energy Storage Systems (BESSs) because of their high energy density regarding to BESS advantage is given [10]. These advantages are: fast response, ownership obligations, and cooperation with the national grid system. While Obaid et al. [11] many difficulties in the AGC of unconventional smart electric power systems are studied where various AGC approaches; integrating the BESS-based electrical vehicles (EVs); are considered. Wu et al [12] described the difficulties and application of diverse AGC systems in wind energy generation plants and the fact of the poor primary performance and low inertial of wind turbines which affect on the AGC regulations. Furthermore, the study investigated variable speed wind turbines and appropriate frequency control methods which can improve the frequency response. Bevrani and Hiyama [13] concentrated on several intelligent AGC systems and their application in distributed and renewable power energy schemes.
Shankar et al. [14] illustrate a complete analysis on AGC relating its distribution generation systems, conventional power systems, and a various structure of the micro-grid system. Additionally, the study also exposed the application of various energy storage devices, High Voltage Direct Current (HVDC), Flexible AC Transmission Systems (FACTS) devices and connects in the AGC scheme. Though, the study still suffers weak in several contemporary regulation structures and optimization methods for AGC. It's observed that the same approach relating the analysis on AGC is followed which illustrated several difficulties related with adding of FACTS devices, fast energy storage systems, photovoltaic (PV) systems, and wind-diesel power plant into the AGC systems [15].
The article is arranged as following: In Part II presents the SEPS power system grid and illustrated the entire arrangement for power production stations of SEPS in 2019-2020. Moreover, Part III presents the used MATLAB simulation model which used in this article, Part IV explained the used control algorithms such as Fractional Order PI and several forms of particle swarm optimization while Part V illustrates the simulation outcomes and discussion. Finally, Part VI finalize the conclusion. The entire mounted production capacity of SEPS in 2019 understudy was expanded to be 58353 MW as well as emergency and reserve power plants the total production approximately to 60000 MW [8,31] [16]. The NECC model is mainly designed for solving the difficulties of load shedding as well as studied the impact of primary reserve. The model is reconstructed with some modification based on Matlab / Simulink. The original model is adjusted by minor loop control with a simple integral controller to allow the addition of a secondary controller [16].

The SEPS Power System Grid Under Study
The Simplified Egyptian Power System (SEPS) developed is enhanced by adding the DFIG model to signify the wind generation stations as displayed in 2017 report of EPS [17][18].
The SEPS model is achieved and presented in Matlab/Simulink® program. The block diagram of DFIG model is given in Figure 1 [19].
The SEPS composed of seven strongly linked areas [16], the interconnection specifics among the various zones were neglected and the proposal is accomplished relying on a single zone (area) power system scheme. The scheme has been tested via two various loading situation scenarios with outage or tripping of the biggest generation power unit (650 MW) in the SEPS [17].

Simulation Scheme for SEPS Power System
The LFC scheme of the SEPS block diagram in addition to the DFIG scheme without including the combined cycle and non-reheat turbines as presented by Matlab Simulink in Figure 2 [18]. Due to increasing of load change of EPS or tripping of power generation unit, the turbine speed will be dropped earlier the turbine governors make correction modification to regulate the steam input to new load value therefore it's important to implement of robust LFC controller with optimized gains.

Proposed Control Algorithms
The Proportional Integral controller enhance the performance of the closed loop system in addition to can dealing with nonlinearly systems with any changes in system parameter or in operating point through online upgrading the PI controller parameters [18]. a) Particle Swarm Optimization Particle Swarm Optimization (PSO) is considered as one of stochastic Evolutionary Computation algorithms which depend on intelligence and motion of swarms. In contrast with GA which it the highest advantage of PSO algorithm, PSO doesn't have genetic processes like crossover and mutation. Particles velocity is interiorly updated by particles themselves and fast converge to the best (optimum) solution [20].
The major change among PSO and other ECs demonstrated in the methodology of particles can alter the population/swarm from the iteration to the next iteration in the search space through the iteration run, while in EA, the particles are altered in every iteration [21]. The coordinates of every particle in PSO display a promising result via two vectors, the velocity ( ) with every particle i there are the two vectors associated.
A swarm contained of feasible solutions "or a number of particles" that fly (advance) over the possible solution space to discover optimal solutions. Every particle informs its location according to its hold best search; best swarm whole experience, and its earlier velocity vector based on the following model [22]. Equations (1) and (2) define the PSO. 1 1  [20].
The inertia weight w is beginning with large weight at starting of the searching then proportionally reduced when iteration progressed relating to Equation This is termed Time Varying Inertia Weight (TVIW-PSO), but occasionally it suffers from local optimal which means swarm doesn't getting a solution [23].
The PSO flow chart is clarified in Figure 3, as presented in [20,22,25]. b) Constrictive Particle Swarm Optimization The highest advantage of Constrictive Particle Swarm Optimization (C-PSO) is to enhance the convergence of PSO in primarily iterations of search and assists to escape from local optimal point then the convergence of PSO technique will enhanced [23]. By setting Constrictive factor (K) multiply by Equation (2) according to constrictive factor (K) Equation [24]: Where C = 1 c) Adaptive Acceleration Coefficients Particle Swarm Adaptive Acceleration Coefficients Particle Swarm (AAC-PSO) is known by the acceleration coefficients 1 C and 2 C are updated linearly with time that the cognitive. Component is decreased whereas social component is increased as search iteration progress.
The AAC-PSO updates the acceleration coefficients exponentially with time based on their minimum and maximum values. The reason of using exponential function to decrease or increase speed of such function to accelerate the convergence procedure to get better search.

Design of the gain Controller Based on Particle Swarm Optimization Techniques
The proposed controller gains will be implemented based on the set-a parameters (Nominal parameters). Assume a process which has the transfer function is GP(s). A measure of the robust stability of the closed loop system can be represented as: Classical value for the maximum sensitivity Ms, is in the range of 1.4 to 2 [29]. Assume λi presents the real part of the poorly damped electromechnical mode eigenvalue of the system and identify the eigenvalue-based objective function as i J = min{maxλ } (14) In this case study, it is intended to minimize the objective function (performance index J) as given in Equation (14)  In this article, the controller gain is chosen between [0, 100]. It's clear that it is a nonlinear optimization problem. The input to the gain controller is the system frequency deviation and its output is the corrective control signal. It's cleared that the PSO using the multi-objective (Cost) function which PSO tries to minimize the Overshoot, Settling Time, Rise Time and the Error which in this case is frequency deviation (∆f)) as shown in following Fitness Function (FF) Equation (15): w h e r e [30].

Simulation Results and Discussion
Two different scenarios are considered based on the improved dynamic MATLAB-Simulink model of the National Energy Control Center (NECC) as illustrated in Figure 4, based on the Static and Operation Parameters of SEPS.
Frist scenario: tripping (outage) of the biggest power generation unit (Kuriemat 650 MW) at highest load of SEPS in July 2019 and monitoring the frequency response with Proportional integral controller.
Second scenario: tripping (outage) of the biggest power generation unit (Kuriemat 650 MW) at lowest load of SEPS in December 2019 and monitoring the frequency response with proportional integral controller.
These two scenarios are applied using Fractional Order Proportional Integral controller (FO-PI) based on PSO optimization techniques and compared with the performance of Proportional Integral (PI) controller based on PSO Techniques.
Four techniques of PSO are discussed and compared according to their performance in each scenario (Max or Min) loading conditions with both (FO-PI) and (PI) controllers.
The model parameters are divided into two groups. The first group of parameters is not depending on system operating conditions which are displayed in Table 1. These parameters values are evaluated by [16]. The second group parameters are updated with time corresponding to the SEPS operating conditions. The desired data to define the changing parameters are involved with the data of each generator including: status (on or off), unit rating (MW), type of unit (Reheat, Non-Reheat, or Hydro); unit production (MW) for the operating condition under case study; inertia of the unit and the spinning reserve of the unit in percentage of the unit rating [8]. The Simulink model take into consideration the difference between the Generating Rate Constraints (GRC) for various generating units. The simulated values for GRC are MW/min.1 pu and 0.2 pu 0 MW/min. for reheat turbines and non-reheat turbines, correspondingly. The GRC of hydro plants is disregarded as its actual value is much greater contrasted to the time periods of actual disturbances.
The Two SEPS loading conditions are simulated to design the PSO-based Controller gain. These two loading conditions stated the highest and lowest loads in two daily load curves of the SEPS in 2019-2020 [8].
Seven excel files are combined to calculate the changing parameters of the Simulink model. Every excel file contains the seven parameters values for each of the 304 generating units installed in 2019. The first parameter indicates the capacity (rating) of the unit, whereas the second parameter denotes the maximum operating MW. The third one shows maximum reserve power and the fourth for minimum operating MW of the unit. The fifth represents minimum reserve power of the unit and the sixth shows the unit inertia, while the seventh represents the unit's type [31]. Table 2 illustrates the calculated parameters produced from these seven files for the two operating conditions.

High Loading Scenario
The results of simulation are presented in Table 4, It displays the dropping in the SEPS frequency response in terms of Minimum frequency values (Nadir values) and Rate Of Change of Frequency (ROCOF) till the tuned PI controller take the action to vanish the frequency deviation. Table 4 illustrate performance evaluation for PI controller obtained by various types of PSO Techniques in case of High Loading Scenario (HLS).  Figure 5 illustrates the comparisons between 4 gains (as displayed in Table 3) for Frequency Deviation in High Loading Scenario (HLS).
For facilitating calculation of ROCOF and Nadir point, a zoom in the curve is described in Figure 6.

Figure 5. Comparisons between 4 gains for Frequency Deviation in HLS.
From Figure 5 and Table 4; It is noticeable that without control the system can't returned back to its nominal frequency value so the need of PI control is apparent. The MAAPSO gain offering acceptable maximum overshoot value (0.01413) but it also gives the highest (worst) Nadir point which it's not preferable it power system grid while the PSOC gain gives second highest Nadir point but also gives highest maximum overshoot compared with other gains. Although the PSO gain presents the lowest (best) ROCOF but its performance regarding to other parameters don't gives the best performance at all.
The AAPSO gain shows the best obtained gain performance compared with other gains regarding to parameters like Nadir point, maximum overshoot and settling time.
It's clear that through run the iterations of every type of PSO separately, the best objective function index were gained are: PSOC, PSO, AAPSO respectively while the highest Objective function index was MAAPSO gain.
Although the PSOC gives best objective function index (also fast time to getting a solution) but shows highest settling time compared with other gains (according to ±2% of steady state of nominal frequency value); as given in Table 4.
It is obvious and interesting in Table 4, the value of ROCOF doesn't have substantial difference between the four obtained gains because it's presents the strength of the SEPS grid in case of disturbance happened.
Low Loading Scenario Table 5 illustrates the performance evaluation for the PI controller obtained by various types of PSO in case of optimized low loading condition.  Figure 7 clarifies the comparisons between 4 gains for Frequency Deviation in case of low loading scenario.
As apparent in Figure 7 that without controller gain, the frequency deviation (error) will be inherent because of the PI controller is not actuated in the system yet.
For clarifying the calculation of ROCOF and Nadir point in lowest loading scenario, a zoom for the curve is presented in Figure 8.  As presented in Figure 7, 8 and the results in table 5, the power system frequency response suffering from inherent frequency deviation (error) when not controller in system so the frequency deviation can't return back to zero.
Although the PSO gain offers the lowest (best) maximum overshoot value compared with other obtained gains but it shows highest (worst) Nadir Point value and value which mean highly deterioration in frequency of SEPS also it take along settling time (11.502 Sec) until frequency deviation vanished.
The AAPSO gain presents the highest (worst) maximum overshoot value and longest (worst) settling time compared to the other gains even though it shows good performance related to Nadir point and ROCOF values. The PSOC gain indicates the lowest (best) settling time value and gives 2 nd lowest values for both the maximum overshoot and ROCOF compared with other gains.
The MAAPSO gain denotes the lowest values (best) for both Nadir point and ROCOF and 2 nd lowest value for settling time overall gains and displays good performance related to maximum overshoot value.
It is noticeable that during run the iterations of each type of PSO individually, the best objective function index were gained are: MAAPSO, AAPSO, PSOC, respectively whereas the highest Objective function index was gain PSO.

Fraction Order PI controller (FO-PI) Case
In this section, the FO-PI controller is used for tuning the frequency deviation of SEPS in both loading scenario and compared the performance with PI controller which illustrated last section.
As mentioned previously in table 3, the gain values of FO-PI and PI controllers which obtained by different PSO types were presented in both High (maximum) and Low (minimum) loading conditions.
High Loading Scenario Table 6 illustrate the performance evaluation for FO-PO controller optimized by various types of PSO in case of HLS. Figure 9 denote the comparisons between 4 gains for Frequency Deviation in high loading scenario in case of FO-PI controller.
For simplifying calculation of Nadir point and ROCOF, a zoom in for the curves is displayed in Figure 10. As presented in Figure 9 it is clear that the system without any controller can't resolve or handle with frequency deviation occurred by the disturbance load and error be inherent in the frequency system response. Although the PSO gain present the lowest (best) maximum overshoot value but it shows the 2 nd highest values for other parameters like Nadir point, ROCOF and Settling time values respectively compared with other gains. PSOC gain displays good performance which it was 2 nd lowest (best) Nadir point and ROCOF values overall gains.
MAAPSO gain display highest (worst) values for all parameters like Nadir, Maximum overshoot, ROCOF and Settling time which mean worst performance overall gains while AAPSO gain shows the lowest (best) values for all parameters and presents the best performance compared with other gains.
The best objective function index were gained during the run of iterations for each type of PSO individually are: PSO, AAPSO, PSOC, respectively while the highest Objective function index (which mean longer time to getting a solution) was gain MAAPSO.   Low Loading Scenario Table 7 clarifies performance evaluation for FO-PO controller gained through different types of PSO in case of low loading condition. Figure 11 denoted the comparisons between 4 gains for Frequency Deviation in low loading scenario in case of FO-PI controller. For simplifying calculation of Nadir point and ROCOF, a zoom for the curves is displayed in Figure 12.  As illustrated in Figure 11; it is obvious that the error (frequency deviation) is inherent in the frequency system response due to the occurred disturbance load which mean that the system by itself without controller can't resolve the disturbance. Despite the AAPSO gain shows the lowest (best) values for both the maximum overshoot and settling time but it presents highest (worst) values for both the Nadir point and ROCOF compared with other gains while in contrast the MAAPSO appears the lowest (best) values for both Nadir point and ROCOF whilst offering the highest (worst) values for both maximum overshoot and settling time compared with other gains.
PSO gain indicates moderated and good performance gives 2 nd lowest (best) values for all compared parameters like Nadir point, maximum overshoot, ROCOF compared with other gains while PSOC shows 3 rd best values for same parameters.
The best objective function index were gained during the run of iterations for each type of PSO individually are: MAAPSO, AAPSO, PSOC, respectively while the highest Objective function index (which mean longer time to obtain acceptable solution) was gain PSO.

Conclusion
The suggested PSO-based FO-PI and PI controllers is studied for the three major issues of the SEPS: a) System parameter variations as a result of changes in operating condition, b) Non-linearity in the interactions. These studies are completed firstly, by applying the Proportional Integral controller on two SEPS loading situations representing highest (Maximum) and lowest (Minimum) peak load of the SEPS separately and studding the effect of tripping of biggest unit in SEPS (K-650 MW) then apply same two loading situations on Fraction Order -PI controller to compare the performance of both controller.
The model used in this paper was developed and built on the dynamic model of the National Energy Control Center (NECC) by updating Combined Cycle units in addition to Wind units models to original model of (NECC) which is formed in 1992 to contain the new conventional power stations statistics till 2019-2020. Then using various types of suggested PSO algorithms to acquire the controller gain to annihilate the frequency deviation (error) caused by the disturbance (outage load) occurred in both two loading situations, which could be generalized to any loading situation.
The application of the suggested FO-PI controllers based on PSO present enhancement in the dynamic frequency response performance of the SEPS according to ROCOF, Settling Time, Maximum Overshoot, Nadir and well damping in a wide range of operating conditions. Even in the existence of Generating Rate Constraints (GRC), which confirms its strength. The achieved results are promising in this field.