Application of Fractional Order-PID Control Scheme in Automatic Generation Control of a Deregulated Power System in the Presence of SMES Unit

: A fractional order PID (FOPID) control technique for automatic generation control (AGC) in a multi-area power system is presented in this study. To create a reliable controller, a variety of control strategies were used. The load frequency control (LFC) problem in a power system implementing different power transactions, such as bilateral and Poolco transactions, are investigated here. Because any control scheme’s performance is only as good as its parameters, the parameters of the designed control scheme were determined using the big bang big crunch (BBBC) algorithm. Furthermore, in this work, the effect of a superconductive magnetic energy storage (SMES) unit is addressed in the given test (two and four area) systems. When confronted with a ﬂuctuation in immediate load, the SMES unit is thought to follow the initial drop in frequency and tie-line power in order to increase LFC. It is evident that the performance of an FOPID control scheme is improved in the presence of an SMES unit and it provides frequency, tie-line power, change in generation with reduced oscillations and settling time.


Introduction
Load frequency control (LFC) is a mechanism that divides the load between generators and maintains a generally consistent frequency in an electric power system. The power system is a massive, complex technical system with multiple control zones. Tie-lines connect each control region to the next. As a result, maintaining the system's balance is a challenging task. Any interruption or change in load can cause a shift in system frequency and tie-line power, which may have severe effects such as the stalling of generators, etc., if not addressed properly [1].
The electrical sector's structure, working conditions and control parameters have all changed since deregulation was implemented. LFC's responsibilities have also increased as a result of this.
A detailed description of the restructuring LFC, including issues, modifications and changes, is presented in [2].
An optimal controller is termed as the heart of the LFC scheme. In the literature, several approaches, starting from classical to modern, as well as optimization-based, have been presented regarding designing an optimal controller [3]. For a very long time, controllers such as PID (proportional integral derivative) have been preferred among researchers due to their simple and convenient implementation [4]. LFC/AGC is a key factor in designing an electric power system with optimal considerations and aspects of quality and reliability in the electric power supply.
A sudden load perturbation leads to electromechanical oscillations. Therefore, a fastacting energy storage technology, i.e., SMES, battery and pump storage, is needed to offer fast response and minimum vibrations. A mismatch can lead to a complete system failure; therefore, a steady, fast and supremely correct controller design is ruled for constant desired frequency. It is reported that SMES improves load dynamics, controls real and reactive power, and is therefore widely used as an oscillation stabilizer in LFC problems [5,6]. The optimal installation of the number of SMES units was explained in [5], which states that it is not necessary to install an SMES unit in each control area. A single SMES unit can be used to control the frequency of other regions too, which works effectively [6].
Researchers are increasingly working on fractional order (FO) control schemes as an alternative to traditional control approaches. An FOPID control scheme is termed as an extension of PID and is used in a variety of fields such as design [7], stabilization [8] and automatic voltage controller (AVR) [9]. Various optimization approaches have been successfully implemented to obtain the parameters of FOPID parameters [10][11][12].
A good control approach must have optimal parameters in order to have optimal performance. There are several other algorithms particle swarm optimization (PSO), genetic algorithm (GA), imperialistic competition algorithm (ICA), harmony search (HS), are available in the literature. The authors used BBBC [13] to identify the best parameters of an FOPID controller, after comparing it to other search algorithms such as ICA and GA [14][15][16][17][18][19][20].
The power flow between control areas is regulated by load frequency control to keep the frequency constant. However, as a result of deregulation, a variety of power transactions have formed in the electrical sector, affecting power transfer between areas. Through the Disco participation matrix, any Disco can now have power contracts with Gencos of the same and other areas via bilateral transactions. Another type of power contract is the Poolco transaction.
Two and four area power systems were chosen as test systems to assess the performance of the designed control scheme. The designed control scheme was evaluated in terms of settling time, oscillations and other time-domain responses using a range of load disturbances and both (Poolco plus bilateral) power transactions. A comparison reveals that at steady state, the targeted parameters are settling to their desired levels.
Different simulation results were obtained using the FOPID controller at MATLAB/Simulink platform. It is observed that the FOPID controller gives increased performance with an SMES unit. It also establishes that the settling time of various responses is reduced significantly using the SMES unit.
Novelty: The use of FOPID-SMES control scheme for load frequency control of two and four-area power systems is provided in this paper. This study contributes by offering a complete performance investigation of a designed control scheme employing actual test system.
The main highlights of this paper are: (1) Two area thermal and four area hydro-thermal power systems are taken for the case study, and a simulation model of the two and four area power systems is modeled. (2) An FOPID control scheme modelled using BBBC is implemented.
(3) The performance and effectiveness of the designed control scheme are checked under different disturbance scenarios, with and without an SMES device. (4) It is observed that, in all cases, FOPID with SMES performs better, specifically in terms of settling time and oscillation. Figure 1 represents a graphical summary of the research presented in this study. The rest of the article is structured as follows: Section 2 introduces the modelling of test systems. The designed approach is presented in Section 3. The results and conclusion are discussed in Sections 4 and 5. Figure 1 represents a graphical summary of the research presented in this study. The rest of the article is structured as follows: Section 2 introduces the modelling of test systems. The designed approach is presented in Section 3. The results and conclusion are discussed in Sections 4 and 5.

Modelling of Multiarea Power System in Deregulated Environment
Many traditional power system improvements occurred as a result of deregulation, and such a scenario becomes increasingly crucial in order to manage frequency control. In today environment, Disco (distribution company) has the option of selecting a power contract from a Genco (generation company) in their jurisdiction or forming their own. Bilateral trade is a method of power transmission that is implemented via DPM. The area control error is eliminated with the help of a controller and given by Equation (1).
Transactions such as Poolco and bilateral are used for electricity transmission in a deregulated system. Equation (2) shows the impact of bilateral trades on tie-line.
where n is total areas, Dij/Dji shows Discos' demands to Gencos, and i ΔPtie is tie-line power deviation. This variation in tie-line modifies the earlier ACE as presented using Equation (3).
Finally, the net generation of different Gencos is evaluated by Equation (4).
where D P is the total load demand. Figures 2 and 3 show an SMES unit and its control structure [7]. The detailed literature regarding SMES can be referred from [7,8]. The expression of DC voltage of an SMES unit can be written as

SMES and Its Control Strategy
where L E = DC voltage across the coil (kV), Vd0 = maximum circuit bridge voltage (kV), Rcm = equivalent commutating resistance (  ), IL = current through coil (kA) and c α is the firing angle (degrees). For an ith area, the expression for DC voltage is given in Equation (6)

Modelling of Multiarea Power System in Deregulated Environment
Many traditional power system improvements occurred as a result of deregulation, and such a scenario becomes increasingly crucial in order to manage frequency control. In today environment, Disco (distribution company) has the option of selecting a power contract from a Genco (generation company) in their jurisdiction or forming their own. Bilateral trade is a method of power transmission that is implemented via DPM. The area control error is eliminated with the help of a controller and given by Equation (1).
Transactions such as Poolco and bilateral are used for electricity transmission in a deregulated system. Equation (2) shows the impact of bilateral trades on tie-line.
where n is total areas, D ij /D ji shows Discos' demands to Gencos, and ∆Ptie i is tie-line power deviation. This variation in tie-line modifies the earlier ACE as presented using Equation (3).
Finally, the net generation of different Gencos is evaluated by Equation (4).
where P D is the total load demand. show an SMES unit and its control structure [7]. The detailed literature regarding SMES can be referred from [7,8]. The expression of DC voltage of an SMES unit can be written as

SMES and Its Control Strategy
where E L = DC voltage across the coil (kV), V d0 = maximum circuit bridge voltage (kV), R cm = equivalent commutating resistance (Ω), I L = current through coil (kA) and α c is the firing angle (degrees). For an ith area, the expression for DC voltage is given in Equation (6) ∆E L_i (s) = K SMES 1 + T dc_con_i ∆Error (6) where ∆E L = Change in converter voltage, T dc_con = time delay (s), K SMES = control loop gain and ∆Error = ACE. The ACE signal is defined in Equation (3). On placing the value of ACE from Equation (3) in Equation (6), convertor voltage can be modified as To respond to a load disturbance, the SMES control loop uses coil current deviation (∆I L ) as a feedback to provide the quick restoration. Therefore, Equation (7) can be modified as where K IL = Coil current deviation feedback loop gain (kV/kA). The deregulated LFC scheme with different transactions, incorporation of an SMES unit and a load deviation is shown in Figure 4.    The ACE signal is defined in Equation (3). On placing the value of ACE from tion (3) in Equation (6), convertor voltage can be modified as To respond to a load disturbance, the SMES control loop uses coil current d ( L ΔI ) as a feedback to provide the quick restoration. Therefore, Equation (7) can b ified as The deregulated LFC scheme with different transactions, incorporation of a unit and a load deviation is shown in Figure 4.   Figure 3. SMES Control Scheme. Bilateral transaction signals to Gencos of same area

FOPID Control Scheme Using BBBC
For a successful LFC, a good control scheme is required. Researchers have devised a variety of control systems, but the fractional-order control scheme is presently in use because it has advantages over traditional control schemes in terms of reduced steady-state error, less oscillation and shortened settling time. The most frequent structure of a FOPID control scheme is shown in Figure 5. where -λ μ The Laplace form of Equation (9) is given in Equation (10).
where KP,KI, and KD = FOPID parameters and λ / μ is fractional integrator/differentiator. Equation (11) gives the fitness function, which is used to design the FOPID control scheme. • Steps to design FOPID using BBBC Step 1. The population of parameters is generated in this step.
Where x = FOPID parameters, k = total number of areas, i = total parameters, and j = total population size Step 2. The fitness function (11) is assessed for the population created in step 1 in this phase.

FOPID Control Scheme Using BBBC
For a successful LFC, a good control scheme is required. Researchers have devised a variety of control systems, but the fractional-order control scheme is presently in use because it has advantages over traditional control schemes in terms of reduced steady-state error, less oscillation and shortened settling time. The most frequent structure of a FOPID control scheme is shown in Figure 5. Genco Tie -Line

FOPID Control Scheme Using BBBC
For a successful LFC, a good control scheme is required. Researchers have devised a variety of control systems, but the fractional-order control scheme is presently in use because it has advantages over traditional control schemes in terms of reduced steady-state error, less oscillation and shortened settling time. The most frequent structure of a FOPID control scheme is shown in Figure 5. where -λ μ The Laplace form of Equation (9) is given in Equation (10).
Equation (11) gives the fitness function, which is used to design the FOPID control scheme. • Steps to design FOPID using BBBC Step 1. The population of parameters is generated in this step.
Where x = FOPID parameters, k = total number of areas, i = total parameters, and j = total population size Step 2. The fitness function (11) is assessed for the population created in step 1 in this phase. where u(t) = K P e r (t) + K I D −λ e r (t) + K D D µ e r (t) (9) The Laplace form of Equation (9) is given in Equation (10).
where K P ,K I , and K D = FOPID parameters and λ/µ is fractional integrator/differentiator. Equation (11) gives the fitness function, which is used to design the FOPID control scheme.
• Steps to design FOPID using BBBC Step 1. The population of parameters is generated in this step.
where x = FOPID parameters, k = total number of areas, i = total parameters, and j = total population size.
Step 2. The fitness function (11) is assessed for the population created in step 1 in this phase.
Step 3. This phase entails constructing the center of mass as shown in Equation (13).
Step 4. A new population is produced near the center of mass in this step.
where α = parameter limit the size, K = iteration number, r = random number.
Step 5. The following best parameters are generated in this step.
Step 6. The best fitness function and its related parameters are determined in this step. Figure 6 shows the flowchart of the BBBC algorithm.
Mathematics 2022, 10, x FOR PEER REVIEW 6 of 17 Step 3. This phase entails constructing the center of mass as shown in Equation (13).
Step 4. A new population is produced near the center of mass in this step.
where  = parameter limit the size, K = iteration number, r = random number.
Step 5. The following best parameters are generated in this step.
Step 6. The best fitness function and its related parameters are determined in this step. Figure 6 shows the flowchart of the BBBC algorithm.

Results and Discussion
The simulation was performed using the MATLAB Simulink platform. The Simulink models of both tests were modeled to discuss the LFC scheme with Poolco and Bilateral transactions. It is observed that system responses, i.e., frequency/tie-line power disturbed after a load perturbation. SMES has a role in reducing disturbances to a safe limit. After the SMES, common control elements take over to adjust the deviation.

Results and Discussion
The simulation was performed using the MATLAB Simulink platform. The Simulink models of both tests were modeled to discuss the LFC scheme with Poolco and Bilateral transactions. It is observed that system responses, i.e., frequency/tie-line power disturbed after a load perturbation. SMES has a role in reducing disturbances to a safe limit. After the SMES, common control elements take over to adjust the deviation.

Two-Area System (Bilateral + Poolco Transactions)
In this section, the performance of the FOPID control scheme in two area power systems (with and without an SMES unit) is discussed. The LFC scheme for two area systems is developed on the basis of Figure 4. Non-reheat turbine units are taken in both area cases. In every area, 2-Gencos and 2-Discos are considered. The developed controller is examined in every area when load disturbances of 0.2 pu is applied. It is considered that the SMES unit is presumed only in area-1 and engages in every Genco LFC scheme. It is assumed that Gencos have fixed participation factors, which are given as pf 1 = 0for Genco1 pf 2 = 1 for Genco2 area − 1 and pf 3 = 0.5 for Genco3 pf 4 = 0.5 for Genco4 area − 2 A given DPM is used for bilateral transactions. A load of 0.2 pu is employed to check the effectiveness of the designed control scheme. The responses of both areas' frequency were disturbed after this load perturbation. To bring back these frequencies to their desired values, LFC makes a change in Genco generation and restores frequencies of both areas to their scheduled values. The SMES unit takes care of the initial dampening in the frequency deviation response. The variation in frequencies is substantially more significant in magnitude in the absence of the SMES unit, as seen in Figure 7. The frequency variations in area-1 and area-2 abruptly vanish, resulting in reduced oscillation when the SMES system is used.

Two-Area System (Bilateral + Poolco Transactions)
In this section, the performance of the FOPID control scheme in two area power systems (with and without an SMES unit) is discussed. The LFC scheme for two area systems is developed on the basis of Figure 4. Non-reheat turbine units are taken in both area cases. In every area, 2-Gencos and 2-Discos are considered. The developed controller is examined in every area when load disturbances of 0.2 pu is applied. It is considered that the SMES unit is presumed only in area-1 and engages in every Genco LFC scheme. It is assumed that Gencos have fixed participation factors, which are given as A load of 0.2 pu is employed to check the effectiveness of the designed control scheme. The responses of both areas' frequency were disturbed after this load perturbation. To bring back these frequencies to their desired values, LFC makes a change in Genco generation and restores frequencies of both areas to their scheduled values. The SMES unit takes care of the initial dampening in the frequency deviation response. The variation in frequencies is substantially more significant in magnitude in the absence of the SMES unit, as seen in Figure 7. The frequency variations in area-1 and area-2 abruptly vanish, resulting in reduced oscillation when the SMES system is used. In order to compensate for these deviations in frequency, the Gencos of each area regulate their generation as per Equation (4), which can be written as In order to compensate for these deviations in frequency, the Gencos of each area regulate their generation as per Equation (4), which can be written as It is observed that after the settlement of bilateral contracts, a power requirement of 0.025 pu is still needed. This is where participation factors of Gencos come into the picture. This additional power is supplied by the Gencos as per their participation factors and can be represented as (∆P G(area−1) ) net = (0 .085) bi +(0) pf = 0.085 pu (∆P G (area−1) ) net = (0 .04) bi +(0 .025) pf = 0.065 pu The net generation change in Gencos of area-1 is depicted in Figure 8. It is clear that Gencos are settling to their generation as per the requirement. It is observed that after the settlement of bilateral contracts, a power requirement of 0.025 pu is still needed. This is where participation factors of Gencos come into the picture. This additional power is supplied by the Gencos as per their participation factors and can be represented as The net generation change in Gencos of area-1 is depicted in Figure 8. It is clear that Gencos are settling to their generation as per the requirement. Area-2: as it is seen from DPM, G3 has bilateral contracts with Discos of both areas; therefore, in order to bring the frequency back, G3 changes its generation to supply 0.025 pu to D2 (area-1), 0.1 pu to D3 (area-2) and 0.07 pu to D4 (area-2). G4 of area-2 has bilateral contracts with Discos of area-1 only. It changes its output to supply 0.03 pu to D1 (area-1) and 0.025 pu to D2 (area-1).
The total output of Gencos of area-2 is given in Figure 9. Area-2: as it is seen from DPM, G3 has bilateral contracts with Discos of both areas; therefore, in order to bring the frequency back, G3 changes its generation to supply 0.025 pu to D2 (area-1), 0.1 pu to D3 (area-2) and 0.07 pu to D4 (area-2). G4 of area-2 has bilateral contracts with Discos of area-1 only. It changes its output to supply 0.03 pu to D1 (area-1) and 0.025 pu to D2 (area-1).
The total output of Gencos of area-2 is given in Figure 9. Equation (16) shows the change in tie-line power, which has a dependency on bilateral transactions. It is evident that load perturbation also affects net power. Due to the effect of bilateral transactions, power is settled to −0.05 pu, given in Figure 10.  Equation (16) shows the change in tie-line power, which has a dependency on bilateral transactions. It is evident that load perturbation also affects net power. Due to the effect of bilateral transactions, power is settled to −0.05 pu, given in Figure 10. (16) (a) Change in generation in Genco-G3 (b) Change in generation in Genco-G4 Equation (16) shows the change in tie-line power, which has a dependency on bilateral transactions. It is evident that load perturbation also affects net power. Due to the effect of bilateral transactions, power is settled to −0.05 pu, given in Figure 10. From the above analysis, one can easily verify that FOPID with SMES results in better performance than FOPID without SMES. Table 1 shows a comparison of the performance, and demonstrates that the FOPID controller with an SMES unit provides better dynamic response.  From the above analysis, one can easily verify that FOPID with SMES results in better performance than FOPID without SMES. Table 1 shows a comparison of the performance, and demonstrates that the FOPID controller with an SMES unit provides better dynamic response.

Four-Area System (Bilateral + Poolco Power Transactions)
A 75-bus Indian power system given in Table 2 is also considered to check the proposed control scheme. To implement the Poolco transaction, participant factors of Gencos (Table 3) and Discos (Table 4) in all four-areas are chosen on the basis of a bidding process, which includes price and capacity.   A load change of 50 MW each (area-1 to area-3), and 100 MW (area-4) is employed to simulate evaluated results of FOPID with/without an SMES unit. Following bilateral transactions are taken in different areas.
Additional power is needed in different areas when bilateral contracts of different areas are considered as follows: Area-1/45 MW, Area-2/35 MW and Area-4/70 MW. In order to achieve the demand, Poolco transactions are utilized by the ISO.
In area-1: There is a total load demand of 50 MW. In order to meet this load demand, Gencos with bilateral and Poolco contracts with area-1 begin regulating their generation. Genco G1 changes to 30 MW (0.6667 * 45) to response to this load demand, as it has a participation factor of 0.6667. Because it has a participation factor of 0.111; (0.111 * 45), Genco G2 regulates its output by 5 MW. Because of its participation factor of 0.2222, Disco D1 reduces its load by 10 MW ((0.2222 * 45). The remaining 5 MW of load demand is met by Genco G5 of area-2, which has a bilateral contract with area-1 for 10% of total load demand. As a result, Gencos G1, G2 and Disco D1 provide 45 MW of area-1 power based on their participation factors, while Genco G2 provides 5 MW through a bilateral contract. Figure 11 depicts changes in the power output of area-1. In area-2: Area-2 encounters a total load demand of 50MW. Gencos with bilateral and Poolco transactions participate and manage their generation to meet this demand. G4 and G5 are involved in the bilateral transaction. G6 and G8 are involved in Poolco. To meet bilateral transactions of area-2, G4 reduces its effective power by 5MW. G5 increases its output by 15 MW to meet 10% of area-1 load and 10% of area-4 load. Bilateral transactions provide 30% of the demand for area-2 load. As a result, G6 and G8 split the remaining In area-2: Area-2 encounters a total load demand of 50 MW. Gencos with bilateral and Poolco transactions participate and manage their generation to meet this demand. G4 and G5 are involved in the bilateral transaction. G6 and G8 are involved in Poolco. To meet bilateral transactions of area-2, G4 reduces its effective power by 5 MW. G5 increases its output by 15 MW to meet 10% of area-1 load and 10% of area-4 load. Bilateral transactions provide 30% of the demand for area-2 load. As a result, G6 and G8 split the remaining demand (35 MW) according to their participation parameters. G6 changes to 5 W and G8 to 25 MW. The load on D6 is reduced by 5 MW. The change in the generation is shown in Figure 12.
In area-2: Area-2 encounters a total load demand of 50MW. Gencos with bilateral and Poolco transactions participate and manage their generation to meet this demand. G4 and G5 are involved in the bilateral transaction. G6 and G8 are involved in Poolco. To meet bilateral transactions of area-2, G4 reduces its effective power by 5MW. G5 increases its output by 15 MW to meet 10% of area-1 load and 10% of area-4 load. Bilateral transactions provide 30% of the demand for area-2 load. As a result, G6 and G8 split the remaining demand (35MW) according to their participation parameters. G6 changes to 5W and G8 to 25MW. The load on D6 is reduced by 5MW. The change in the generation is shown in Figure 12. In area-3: Due to the absence of bilateral transaction, for better performance G9 and G10 participate to meet the load requirement of area-3. G9 regulates 15MW of real power and G10 increases up to 35MW. Figure 13 depicts changes in the real power output of area-3 in Gencos. In area-3: Due to the absence of bilateral transaction, for better performance G9 and G10 participate to meet the load requirement of area-3. G9 regulates 15 MW of real power and G10 increases up to 35 MW. Figure 13 depicts changes in the real power output of area-3 in Gencos.
(e) Change in generation in Genco-G8 In area-3: Due to the absence of bilateral transaction, for better performance G9 and G10 participate to meet the load requirement of area-3. G9 regulates 15MW of real power and G10 increases up to 35MW. Figure 13 depicts changes in the real power output of area-3 in Gencos. In area-4: Genco G11 supplies 20% of 2-area load demand of 50MW. Through bilateral transaction, 30% of the load demand of area-4 is provided. G12 (area-4) changes its generation to supply 20% of area-4 load. A total of 10% of area-4 load is supplied by G5 In area-4: Genco G11 supplies 20% of 2-area load demand of 50 MW. Through bilateral transaction, 30% of the load demand of area-4 is provided. G12 (area-4) changes its generation to supply 20% of area-4 load. A total of 10% of area-4 load is supplied by G5 (area-2). The demand of 70 MW is to be fulfilled by Gencos G11, G13, G15 and D11 of area-4. G11 considers 20% of area-2 load demand. G12 of area-4 modifies by 20 MW to supply 20% of area-4 load, and G5 of area-2 supplies 10% of area-4 load through bilateral exchanges. G11 regulates its power by 25 MW, G13 by 10 MW and G15 by 25 MW. D1 lowers its load by 10 MW. Figure 14 depicts the changes in Gencos of area-4.       As shown in Figure 16, the frequency of different areas settled faster to its target value using the SMES unit. As shown in Figure 16, the frequency of different areas settled faster to its target value using the SMES unit. As shown in Figure 16, the frequency of different areas settled faster to its target value using the SMES unit. The curtailment in Discos (D1, D2, D4) is shown in Figure 17, respectively.   Table 5 shows the type of contracts for different Gencos/Discos. Table 6 compares the performance of FOPID controllers with and without the SMES unit in terms of maximum overshoot/undershoot and settling time of area-1 and area-4 frequency deviations. Table  7 shows the parameters for FOPID controllers with SMES unit.

Discussion
From the results obtained for two area and four area power systems, it is evident that the performance of an FOPID control scheme is improved in the presence of an SMES device, in terms of settling time and oscillations. The SMES device dampens the system quickly and helps to minimize deviations in the minimum time as given in various tables.

Conclusions
In this paper, a frequency-related issue in the presence of SMES units in a restructured multi-area power system is investigated. Two area and four area power systems incorporating bilateral and Poolco transactions are employed to simulate different cases to check the performance of the designed control scheme. A FOPID control scheme optimally tuned using BBBC is utilized in this paper. It is evident that the FOPID control scheme gives better results and improves its performance in the presence of an SMES unit. The SMES helps to dampen the response quickly when a sudden load disturbance occurs. At steady state, the frequency error is seen to be zero in all circumstances. Furthermore, the simulation confirms that the proposed control scheme is successful and produces better outcomes, such as shorter settling times, less overshoot and faster damping, because the FOPID controller performs better in the presence of an SMES unit.