Bulk power systems are frequently operated by viewing them as composed of control regions connected to one another [1]. Load frequency control, or LFC, is the process of regulating the real power output of producing units within predetermined bounds in response to variations in system frequency and tie-line power interchange [2]. The power pool is significantly impacted by the automated load frequency control component of automatic generating control, which maintains scheduled system frequency and scheduled tie line power during regular operation and minor disturbances [3,4]. Every control area needs to supply the exchange power that is scheduled for it, as well as its own needs. By keeping an eye on frequency deviation, we can identify any discrepancy between the load and the generation [5]. The use of Automatic Generation Control (AGC) can accomplish this balance between generation and load.

Several forms of generation, including hydro, thermal, gas, solar, and so forth, may be present in each control area. A model in this study has been investigated that can be quite like real-world circumstances. Through the findings in [6], an attempt has been made to investigate the performance of AGC in a two-area system with thermal, hydro, and gas generators. Thus, we have thought about a load scenario that changes arbitrarily. Most past studies in the field of AGC only looked at utilising AI approaches to optimise additional control parameters. Few people look to the governor speed regulation parameter, or principal control loop parameter R, selection [7]. Reading literature makes it clear that significant control variables, such as B and R, have an effect on system performance. Sensitivity analysis is conducted by altering the loading situation and two system parameters, R (Governor Speed regulation) and B (Frequency Bias parameter), in order to test the stability and robustness of the suggested controller.

Most of the previous study is limited to hydrothermal systems; gas generation is not included, whereas in this work it has been considered. This study investigates the robustness of controllers for deviation in R and B parameters as well as modifying PID controller parameters for each thermal, hydro, and gas generation due to random changes in the load. The aim of this study is to investigate the AGC of power systems with thermal-hydro-gas generation in each region in an effective manner compared with the existing literature.

The thermal, hydro, gas power generating station & EV are the four components of the examined IHPS in this paper. Fig. 1 depicts the IHPS system under investigation. The system parameters of the studied IHPS are given in Appendix A. Eq. (1) gives the total power balance equation in the IHPS model. (1)ΔPIHPS=ΔPHD+ΔPGD+ΔPTPPD−ΔPD+ΔPtie+ΔPdc±ΔPEVDwhere, ΔPHD is the variation in the power output of the hydro power plant, ΔPTPPD is the variation in the power output of the TPP, ΔPGD is the variation in the power output of the Gas power plant (GPP), ΔPEVD is the variation in the power output of the EV. ΔPtie is the tie line power variation. ΔPIHPS is the total output variation of the IHPS model and ΔPD is the variation of the load disturbance.

Control Scheme of the System under Study

A single area system with hydro, thermal with reheat turbine, and gas units is taken into consideration initially while developing the controller for the system. As shown in Fig. 1, the linearized models of governors—gas turbines, hydro turbines, and reheat turbines—are used in the power system’s LFC analysis and simulation. Each unit provides a certain amount of the nominal loads, which is determined by its regulatory parameter and participation factor. Every control’s participation factor added should equal 1. The regulating parameters of each unit of the proposed IHPS model are, represented by the letters R1, R2, and R3 in Fig. 1. The control outputs for each unit of the proposed IHPS model are, respectively, UT, UH and UG. The participation factors of each unit of the proposed IHPS model are, respectively, KT, KH, and KG. TSG is the expression for a TPP’s speed governor time constant. The TPP’s time constant is expressed as TT. TW is the nominal starting time of water in penstock. The TPP’s reheat time constant is expressed as K_r. whereas Tr is TPP’s reheat time constant in seconds. The HPP’s speed governor reset time is measured in seconds TRS, the GPP’s speed governor lead time constant is measured in secondsTGS. Xc is the HPP’s speed governor main servo time constant and measured in seconds, cg is the GPP’s valve positioner, bg is the GPP’s constant of valve positioner, and Yc is the lag time constant of GPP’s speed governor in seconds. TPS is the power system time constant in seconds, ΔPD is the gradual shift in load variation, ΔF is the gradual shift in frequency variation, and KPS is the power system gain in Hz/puMW. The system’s nominal parameters are listed in reference.

The current challenge is formulated in a deregulated domain with an AGC perspective. To ensure the validity of the results, it is necessary to examine the effects of PID controllers. In light of this, the following three subsections have been discussed in this paper.

All participating generators’ participation factors add up to unity. The market operator establishes that the following expression [42] must be met by the participation factor: (2)∑i=1niβni=1

For secondary frequency regulation, the participation factor’s value ranges from 0≤βni≤1. ΔPD,i and ΔPEVD,i denote load disturbance and change in EV’s behavior that must be compensated by the AGC loop, respectively.

The ith unit regulation parameter is denoted by Ri and the equivalent regulation parameter of that ith area, Req,i is necessary to express the frequency bias parameter, Bi using the following equation [43]: (3)Bi=Di+1Reqwhere, Di is the load damping factor of ith area and can be found by the following equation (4)1Req=∑i=1ni1Ri

The area control error (ACE) is computed from the linear combination of the tie line power flow deviations and frequency deviations and it’s given as: (5)ACEi=BiΔωi+∑jεNiTij1S(Δωi−ai) (6)ΔPtie,i,j=∑jεNiTij1S(Δωi−ai)where, Tij = Synchronizing torque coefficients

ai = Area interface signal

From the above equation it can be easily mentioned that if ACEi is minimized to zero, then the tie line power flow and frequency deviation are regulated.

Thus, the frequency deviation dynamics in the kth region of the interconnected power system depicted in Fig. 2 accept the following expression: (7)Δfk=12HkS+Dk(ΔPth,k+ΔPhd,k+ΔPg,k−ΔPD(Load),k+ΔPtie,k±ΔPevd,k)where, (7a)ΔPth,k=11+STtg,k(ΔPth,k) (7b)ΔPhd,k=−Tw,kS+11+S0.5Tw,k(ΔPhd,k) (7c)ΔPg,k=11+STcd,k(ΔPg,k)where, Hk is the inertia constant and is the damping constant in the k-th area. ΔPth,k, ΔPhd,k and ΔPg,k are the thermal, hydro and gas’s incremental power in k-th area, respectively. Ttg, Tw, and Tcd are the different time constants of thermal, hydro and gas power plants in k-th area. ΔPevd,k is representing the charging and discharging of EV system. In contrast to conventional power generation, which modifies its output in response to frequency fluctuations, electric vehicle (EV) systems exchange electricity with the grid based on fluctuating system frequencies.

The steady state error, which is provided by the following equation, is decreased in order to adjust the PID controller parameters. (8)J=∫0t(|ACE1|+|ACE2|+|ACE3|)dt

Thus, the proposed controller receives the reference value of ACEi, the area control error ACEi, and the load perturbation ΔPD1 as inputs in order to generate the control signal output. All of the ACEi reference values need to be set to zero. In order to minimize the quantity of performance matrices, such as overshoot, undershoot, and settling time for various signals, the objective function is built. The objective function for minimizing frequency deviation by optional PID parameter adjustment is as follows [43]: (9)minJ=∫ACE(ΔF1,ΔF2,ΔPtie−i)

Fig. 2 shows kth area HVDC links, represented in the model by Pdc,k from the main transfer function block diagram of Fig. 1

The control center sends an incremental change in power set-point, Ps,k, to maintain system frequency and power tie-line at the scheduled values. Through participation factor βev,k, control signal Psev,k is sent to regulate the power output of the generating units and EVs, respectively. EVs can contribute to the LFC control as a power plant by using their power capacity, and the bidirectional power electronic devices enable them to pump energy into the grid. All EV data is gathered by the aggregator and sent to the control center. Furthermore, the control center sends the power set-point to the aggregator, which distributes it among the scattered EVs. An EV fleet is represented using a first-order model with time constant Tev,k and gain Kev,k [44,45]. According to Fig. 2, the output power deviation of EVs is (10)PEVD,k(S)=Kev,kTev,k×S+1Psev,k(S)

Using the supplemental HVDC PID controller, HVDC lines can be integrated into LFC. With a time constant Tdc,k, the HVDC control signal Kdc,k determines the HVDC power interchange, Pdc,k, of k-th area [46]. The difference between frequency deviations of k-th area and l-th is used to calculate the Kdc. l=1,2,……,N,l≠k with a HVDC gain Kdc. So, Pdc,k can be expressed as follows. (11)Pdc,k(S)=Kdc,k(S)Tdc×S+1where, (11a)Kdc,k(S)=∑l=1,l≠kNKkl(fk(s)−fl(s))

Kkl=0 wthen there is no HVDC link between areas k and l.

Using the mathematical functions for sine and cosine, which are described in detail in [8], SCA is a chaotic population-based optimization technique that produces fresh, updated solutions. Based on the sine and cosine functions, it uses a mathematical model. In the beginning, potential solutions are thrown into the solution space at random. Additionally, candidate solutions are updated frequently. Updated individuals move in the direction of the global optimal solution or away from it. Once the algorithm has determined the optimal answer, it is preserved and never lost. With an increase in iterations, the sine and function range are updated. Exploitation is guaranteed in this instance. When the uttermost number of iterations allowed by the method is reached, the optimizations process ends. The SCA optimization procedure consists of two phases. There are two steps in the SCA optimizations process. High reconnaissance and avoiding the local optimum are guaranteed by SCA. Additionally, the fastest time to the result is found.

The position updating equations listed below are suggested for both stages in this work by Eq. (18) according to [19] (18)xit+1=xit+r1xsin⁡(r2)x|r3Pit−xit|r4<0.5xit+1=xit+r1xcos⁡(r2)x|r3Pit−xit|r4≤0.5}where, i is the size and t is the present iteration number. xit is the ith size value of the agent at the tth iteration and Pit is the ith size value of the uttermost individual at the tth iteration. The arbitrary integers r1, r2, r3 and r4 have values in the interval [0, 1]. To strike a balance between exploration and exploitation, r1 is determined using the Eq. (19) as per [19] (19)r1=α−t∝Twhere, T is the uttermost number of iterations and ∝ is constant values (taken as 2).

This section describes the application of the innovative QOSCA to adjust the various gains of the PID controller, which have been employed one at a time in the studies of the IHPS model, shown in Fig. 1. Here in this work, controller I connects to the governor of the thermal unit, while controller II regulates the pitch angle of the hydro unit and controller III connects to the Gas unit.

PID Model IHPS of Fig. 1: In this model, the dynamic performances of the studied IHPS model have been considered by controllers I, II, and III, which are regarded as PID controllers. Dynamic performance (settling time (ts(s)), maximum overshoot (Hz/V/pu) and maximum undershoot (Hz/V/pu)) comparison is done in different scenarios in this paper, which are explained below.

In this work, three cases have been studied, and they are as follows: In Case 1, the applications of the PID controllers are considered for performance assessments and their comparison which results in the two situations that are outlined as Scenario 1 (With SCA optimization technique) and Scenario 2 (With proposed QOSCA optimization technique). In Case 2, effects of the PID controllers have been checked for simplifying the IHPS system. Finally, in Case 3, the system’s robustness has been checked along with proposed optimization algorithm.

Assessment of Performance

This section analyses the dynamic performance of the IHPS controller models in the time domain. Next, two scenarios of change of tuning process of required parameters have been examined for the three PID controller-based models. The optimization techniques have been compared under various conditions in order to improve performance in the IHPS model under consideration. The innovative SCA and QOSCA have been employed for controller parameter tuning and optimization with the aim of suppressing the frequency deviation of the investigated IHPS model. Requirement of PID controllers have been checked. In accordance with all of this the system’s robustness has been checked by varying the load at area 1.

Case 1

Here, the necessary parameters have been tuned using SCA & QOSCA optimization techniques to examine the dynamic behavior of the suggested IHPS model: TPP, HPP, GPP, and EV (area 1) and TPP, HPP, and GPP (area 2). The comparison of the dynamic characteristics of the suggested IHPS model followed by two scenarios has been shown in Fig. 4. Further, Table 1 displays comparison in two scenarios with respect to settling time (ts(s)), maximum overshoot (Hz/V/pu) and maximum undershoot (Hz/V/pu)of the proposed models under study.

From Fig. 4a and Table 1, it is clear that, in the case of the frequency vs. time deviation analysis, the suggested QOSCA strategy is outperforming the SCA approach in terms of settling time, peak overshoot, and peak undershoot findings. Same thing is going on in case of Δf₂ vs. time and ΔP_tie vs. time. So, from Fig. 4a–c and Table 1, it can easily be seen that the result of proposed QOSCA optimization techniques provide better dynamic responses than the studied optimization techniques (SCA technique) as mentioned in literature survey [14]. In case of controllers with different types of optimization techniques, this work is also proving the better settling time, peak overshoot and peak undershoot rather than the work mentioned in literature survey [16]. The objective functions and other dynamic responses are also better than that of other QOBL based optimization techniques as mentioned in literature survey [23–26]. Table 2 depicts the QOSCA based optimization technique better controller gains, objective function values and performance indices than the SCA based approach. So, it may infer that using the suggested QOSCA method consistently produces a superior dynamic behavior than the SCA approach.

After seeing Fig. 5, it is very easy to say that the application of proposed QOSCA algorithm gives always the faster result than the traditional SCA optimization technique. From this convergence curve it also can be noticed that the QOSCA gives the better result of objective function rather than the SCA approach.

Case 2

As demonstrated by the analysis of case 1, the QOSCA technique outperforms the SCA technique in our suggested system when it comes to adjusting the controllers’ necessary parameters to obtain improved dynamic performance.

Now under case 2, the IHPS model needs to be simplified in such a manner that no such great change will be introduced in the system; thus, the physical behavior of the system will not be hugely distorted. Table 2 shows the modified values of the different PID controller parameters when three PID controllers are used in a region with the QOSCA technique (a metaheuristic optimization tactic). On the other hand, Table 3 displays the adjusted values of the PID controller gains, objective function values and performance indices for the two area systems using the same optimization method when there is only one PID controller is used against an area. Table 4 shows settling time (ts(s)), peak overshoot (Hz/V/pu) and peak undershoot (Hz/V/pu) of the proposed models under study in Case 2.

Based on Tables 2 and 3, three outputs of QOSCA have been shown in Fig. 6a–c as follows:

In this instance the QOSCA optimization technique has only been followed for checking the dynamic response of our proposed IHPS system by considering area wise one PID controller as well as three PID controllers. Fig. 6a–c shows the significant dynamic characteristic curves; the bold line indicates how one PID controller responds to each area, while the dashed line indicates how three PID controllers respond to each area. In case of study of each case, the characteristic curves look similar. Comparing Tables 1 and 4, it can be easily justified that the dynamic responses of the proposed system (settling time (ts(s)), peak overshoot (Hz/V/pu) and peak undershoot (Hz/V/pu)) under study in both of two cases are just similar to each other. Within this range of time limits of dynamic response of the system, rather than using three PID controllers we can use one PID controller only against each area safely. The QOSCA optimization method improves the dynamic response of the system effectively in such a manner that helps to simplify the interconnected system by reducing the number of PID controllers. Consequently, our interconnected model will become simpler than the last proposed model (as shown in Fig. 1) and the proposed model shown in Fig. 7 can be considered. This kind of approach of reduction of number of controllers is rarely discussed by researchers.

Case 3

The system dynamic responses of the sensitivity analysis carried out on the system model by altering operating load circumstances and the system parameters, R (governor speed regulation) and B (frequency bias parameter), as shown in Fig. 8. Results are shown in Figs. 9–12. To show how resilient the suggested QOSCA-optimized PID controller is to parameter uncertainties, parametric variations were added to the system model. The system reactions caused by the suggested control method in the system model were then examined. The robustness of the power system to large changes in the system parameters was examined by simultaneously varying the frequency bias parameter, B, and the governor speed regulation parameter, R, of both control areas in steps of 10%, one at a time, from their nominal values in the range of +25% to −25%. The dynamic system performance or behavior with the QOSCA optimized PID controller for 1% step load perturbations in area 1 for variation in the aforementioned parameters is shown in Figs. 9–12. The findings of sensitivity analysis make it clear that changing the operational load situation and system parameters little affects the system’s dynamic performances. The suggested optimized PID controller provides a satisfactory degree of robustness and stability at nominal parameters, as demonstrated by Figs. 9–12. These ideal controller parameter values do not need to be reset for notable changes in the system parameters or system loads. The suggested controller has effectively shown its efficacy and resilience to parametric uncertainty since changes in several system parameters have no discernible impact on control performance.

Fig. 8 shows the random SLP (ΔPD) in per unit (p.u.) vs. time in seconds. The SLP changes from 0 to 0.1 p.u. at 1-s intervals from 1.2 to 20 s, then remains at 0.15 p.u. from 20 to 60 s. Subsequently, it drops to 0.1 p.u. at 60 s and remains same up to 80 s. At 80 s again it drops to 0.05 p.u. and remains there until 98 s. Further, it decreases to −0.1 p.u. at 98 s and remains constant until 140 s. Finally, it returns to −0.05 p.u. at 140 s and remains there until 160 s.

Tables 5–7 display settling time (ts(s)), peak overshoot (Hz/V/pu) and peak undershoot (Hz/V/pu) of the proposed models under study in Case 3. It can be seen from the different dynamic results of Figs. 9–12 (as shown in Tables 5 and 6) that the values are quite similar to the values shown in Table 4, despite a wide range of EV operating conditions. There is no significant change in the responses when compared to the nominal values. The system’s resilience is thus highlighted since it is not necessary to reset the parameters that were established at the nominal condition to a wide range of system loading fluctuations.

From Fig. 10, the three charts are clearlly shown the robustness of the system with proposed optimisation technique under different loading conditions. In Table 6, the optimised PID controller parameters, objective function values and and performance indices with respect to frequency bias parameter B has been shown under different loading condition. These results are quit similar to Table 3. Therefore, it can be said that QOSCA optimisation technique finally gives the robustness of the system in such a large scale variation of load.

Similarly from Fig. 9, the three charts are clearlly shown the robustness of the system with proposed optimisation technique under different loading conditions. The results, which has been shown in Table 8 by considering speed regulation parameter R, are quite similar to Table 3. So, through this approach it can be shown clearlly the effectiveness of QOSCA algorithm on this model model.

To verify the stability and robustness of the proposed controller, sensitivity analysis is carried out by varying the loading scenario and two system parameters, R (Governor Speed regulation) and B (Frequency Bias parameter). This approach rarely has been addressed in other works. The robustness of the system along with the proposed QOSCA optimization technique has been checked successfully in this work.

In this study, we propose the load frequency control analysis of a multi-unit source power system with several power generation sources, such as hydro, thermal, and gas power plants. PID controllers have been employed to regulate both the power and the frequency changes in this two-area interconnected system. In order to improve the dynamic response of our suggested system in a short amount of time, the necessary controller parameters have been adjusted using the metaheuristic hybrid optimization technique QOSCA and traditional SCA. In the case of QOSCA, the main performance indices (i.e., ITAE) are 8.1463, whereas the SCA-based approach gives the result of ITAE 27.430. Based on the results, it is evident that, for our analysis, the suggested QOSCA technique performs better than the standard SCA technique. This paper is unique because it applies to the QOSCA optimization technique, which has only been demonstrated in this work in the context of an LFC investigation so far.

An attempt has been made to simplify the circuit by reducing the number of PID controllers without hampering any dynamic response or other circuitry properties of the main circuit. It has been observed that the ITAE is 7.9683 when we are applying one PID controller only against one area, which is just the same as the IATE value (81,463) along with three PID controllers against one area. In addition to this, the dynamic responses (i.e., settling times, peak overshoots, and peak undershoots) of frequency variations and tie line power variations are similar. So, the application of one PID controller against one area can be an alternative to the application of three PID controllers against that particular area. Thus, it is possible to simplify the proposed system by using one PID controller in place of three PID controllers. This type of approach, which is considered to simplify the circuit configuration, is one more unique approach of this paper. After the reduction of the circuit by applying the QOSCA optimization technique and varying the load, the sensitivity of the proposed system has been checked. The redesigned interconnected model’s dynamic characteristic has been verified. The robustness of the system demonstrates that the controller is stable for a wide range of load changes. The EV system (Electrical Load) variation is followed by ±10% and ±25%. The ITAE values are 7.8714, 7.8607, 7.9043 and 7.9401 against the +10%, −10%, +25% and −25% load variation respectively which are quite similar to IATE of the zero load variation (i.e., 7.9683). The result analysis also shows that the dynamic responses are similar both under zero-load variation and under several cases of load variation. Thus, the robustness of the system has been checked in this work for a large range of load variations.

In future studies, more work can be done by enhancing and modifying the interconnected area, as well as including more detailed functions of the EV system, and with grid interconnection.