Cascade-I λ D μ N controller design for AGC of thermal and hydro-thermal power systems integrated with renewable energy sources

Expert, intelligent and robust automatic generation control (AGC) scheme is requisite for stable operation and control of power system (PS) integrated with renewable energy sources (RES) under sudden/random small load disturbances. Large frequency deviations appear if AGC capacity is inept to compensate for the imbalances of generation and demand. In this paper, a cascade-fractional order ID with ﬁlter (C-I λ D μ N) controller is proposed as an expert supplementary controller to promote AGC recital adequately in electric power systems incorporated with RES like solar, wind and fuel cells. The imperialist competitive algorithm is fruitfully exploited for optimizing the controller parameters. First, a 2-area reheat thermal system is examined critically and then to authorize the worth of the proposed controller, the study is protracted to a 2-area multi-source hydro-thermal system. The prominent beneﬁts of C-I λ D μ N controller with/without renewable energy sources consist of its great indolence to large load disturbances and superiority over various optimized classical/fuzzy controllers published recently. The sensitivity study validates the robustness of the recommended controller against ± 20% deviations in the system parameters and random step load perturbations.


INTRODUCTION
The generation control is progressively turning challenging due to the gradual enhancement in the power demands and depletion of power resources. The expanding power demands are posing severe dangers to the stable conduct of power system. The growing power demand causes sluggishness in turbine speed and hence, frequency in output voltage of the alternator decline undesirably. In an interconnected large-scale power system (PS), all the synchronously connected generation units perform with the common frequency. It is desirable to sustain frequency/scheduled tie power flows irrespective of load variations in control areas of interconnected PS during normal operating and small abrupt disturbance conditions. To carry out this, an efficient and intelligent automatic generation control (AGC) strategy is vital to spontaneously manipulate the operation of hydro or steam valves which regulates real output power of generators [1]. The PS is turning complicated day-by-day, because of upsurge in its dimension and mixing of renewable energy sources (RES). Because of the ongoing depletion of fossil fuels and the environmental hazards caused by them, the derivative-proportional integral derivative with double derivative filter (PDPID + DDF) [14], grey wolf optimization (GWO) optimized PI/PID [15], artificial bee colony algorithm (ABCA) optimized PI/PID [16], hybrid firefly algorithmpattern search (hFA-PS) technique optimized PI/PID [17], ICA optimized PID [18], jaya algorithm-invasive weed optimization (JA-IWO) optimized PID [19], bacterial swarm optimization (BSO) optimized PID/FOPID [20], optics inspired optimization (OIO) optimized PID [21], symbiotic organisms search (SOS) algorithm optimized PID/PIDN [22,23], quasioppositional differential search algorithm (QODSA) optimized PI/PID [24], hybrid IWO-PS (hIWO-PS) tuned 2DOF-PID [25] and whale optimization algorithm (WOA) optimized cascade PIDN-FOPD [26]. Since, the operating conditions of power system are liable to vary widely over the time due to wearing out of the components, the conventional controllers optimized for fixed operating condition might work inappropriately in changed operating condition. To overcome this difficulty and to get excellent control of generation/frequency/tie power in any interconnected PS, intelligent control system like fuzzy logic controller (FLC) is recommended over conventional one [5].
FLC can handle small deviation in system operating condition efficiently by automatically adjusting the controller parameters online. With the aid of FLC, diverse intelligent conventional controllers are proposed recently [5,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. The choice of FLC parameters like input/output scaling factors (SFs), control rules (CRs), membership functions (MFs) etc. is an intricate assignment. Classically, their selection depends on operator's experiential rules and usually are non-optimal. The inappropriate assortment of FLC parameters might impact the system results adversely. Hence, to overcome this problem, various intelligent optimization methods are applied fruitfully in different types of PSs for tuning the parameters of FLC having different configurations. The procedure of concurrent optimization of all FLC parameters might be a difficult, costly and time consuming task. Hence, prevalent trend of FLC optimization is the tuning/setting of input/output SFs only and MFs/CRs are kept fixed for dissimilar models as getting their values is simpler; and also they impact the system results to a great extent [5,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Recently, hybrid particle swarm optimization-pattern search (hPSO-PS) [27] and bacterial foraging optimization algorithm (BFOA) [28] techniques are adopted to tune input/output SFs and ICA [29] to tune output SFs of fuzzy PI (FPI) controller. But, FPI structure may probably show substandard performance due to its inherent integral action. To conquer this drawback, a derivative mode is attached in PI configuration to get FPID structured controller. To improve FPI performance, some researchers have implemented different optimization methods to tune FPID controller. BFOA [28]/hybrid PSO-levy flight algorithm (hPSO-LFA) [30]/hybrid harmony search-cuckoo optimization algorithm (hHS-COA) [31]/hybrid improved FA-PS (hIFA-PS) [32] and hybrid differential evolution-PSO (hDE-PSO) [33] are employed efficiently to tune input/output SFs of FPID controller for different types of systems. In FPID controller, since derivative block is affected by higher frequency noise in area control error (ACE) fed to FPID, a first order filter is employed in derivative block to attenuate higher frequency noise to get FPID with filter (FPIDN) controller. In the literature, some researchers have employed FPIDN controller with input/output SFs selected using hybrid local unimodal sampling-teaching learning based optimization (hLUS-TLBO) [34]/jaya algorithm (JA) [35] algorithm and it shows better performance than FPID controller.
Fractional order (FO) controllers are earning fame in the current years due to their extra flexibility and skill to handle control design specifications. FO controllers are verified to be superior than their integer order (IO) equivalents [36][37][38][39][40][41]. Recently, FO controllers are implemented in PS models and desirable results are observed. Further, the literature review indicates that the hybridization of fuzzy controller with FO controller shows enhanced performance compared to fuzzy hybridized with conventional controller. A FO fuzzy PID (FOFPID) controller tuned recently using ICA [36], BFOA [37,38] and quasioppositional harmony search algorithm (QOHSA) [39] displays healthier results compared to their conventional counterparts for different single/multi-area PSs. Further, some intelligent cascade controllers like SCA based FOPI-FOPID [6]/FOPI-FOPD [7], WOA optimized PIDN-FOPD [26] and ICA based FFOPI-FOPD [40]/FOPID [41] are appeared in the literature. However, the performance assessment of cascade fuzzy-FOIDN (C-I λ D μ N) structured controller has not been explored so far. Considering these facts, a C-I λ D μ N controller is recommended for 2-area PS models. Besides the controller construction, system performance also relies on the suitable choice of optimization technique to tune the controller parameters. Due to better convergence rate, scarcity in AGC applications, robust control performance of ICA against nonlinearities, constraints and parameters uncertainties, the optimal adjustment of C-I λ D μ N controller parameters is attained by adopting ICA.
Considering the above analysis, the novel contributions of this work are stated as follows: (i) To propose a novel ICA tuned C-I λ D μ N structured controller for AGC of interconnected 2-area RES penetrated RTS and MSHTS. (ii) To authenticate the strength of the proposed method compared to the various intelligent control strategies existing in the state-of-the-art literature. (iii) To exemplify the returns of RES penetration in RTS and MSHTS.

Power system models
The AGC models investigated are 2-area RTS displayed in Figure 5(a) [3,16,20,22,28,33] and 2-area MSHTS displayed in Figure 8 [15,17,28,29,34]. The systems consist of generating areas of equal sizes. The RTS consists of one single reheat type of turbine and MSHTS comprises of one non-reheat and one hydro turbines in each area. Both systems in area-1 embrace renewable energy sources (RES) based systems involving of 2 solar thermal generators (STGs), 3 wind turbine generators (WTGs), 1 aqua-electrolyser (AE) and 2 fuel cells (FCs). As this study is conducted in low frequency domain, the transfer functions (TFs) for these RES are denoted by first order lag [2][3][4][5]. The STG entails solar and thermal parts. The solar part comprises of parabolic collectors which targets the sunlight on to the thermal part to generate steam to run the turbine [3]. The AE is exploited to engage portion of the inconstant power produced by STGs and WTGs to generate hydrogen [3,5]. Analogous to STGs and WTGs, the FC is also characterized via first order lagbased TF having time constant obtained experimentally [3]. The detailed RES system is demonstrated in Figure 5(b) [3]. Every control area comprises its own speed governing system, turbine and generator. There are three inputs and two outputs for an area. The inputs are control input that is, ΔP C , change in load demand that is, ΔP D , and change in tie power that is, ΔPtie. One extra input in area-1 exists due to RES output that is, ΔP gRES . The outputs consist of change in area frequency (ΔF) and area control error (ACE). The test models are picked up from the literature stated above. The data used for the systems have been taken from the stated references and given in Appendix. The Nomenclature describes various symbols used.

CONTROLLER STRUCTURE
The major intentions of a controller designed for an AGC system are to force frequency, generation and tie power variations to zero with least over/under shoots as swiftly as possible under sudden/step load perturbation (SLP). Under SLP, the resultant area control error (ACE) is employed to call upon the controller action to curtail ACE to zero in possible minimum time in each area. Conventional PID controller is favoured in the majority of PS industry due its simple design, robust performance, inexpensive and effective potential for use in the engineering disciplines. Though, because of the inherent intricacy of the extended PS, presence of nonlinearities, uncertainties and their combined impacts, PID controllers become comparably ineffectual to provide a desired level of resilience and outcome in changing operating situations of large scale PS. On the other hand, PID with fuzzy logic (FL) has demonstrated better flexibility and performance to achieve the challenges in PS control. The FL combined with PI/PID/PIDN/FOPID controller is recommended in majority of the recently appeared AGC literature [5,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. But, cascade type of fuzzy controller has not been discussed more. Hence, in this paper, a cascade fuzzy FOIDN (C-I λ D μ N) controller is recommended for AGC of multi-area PSs as an expert, robust and intelligent controller. The controller construction is exposed in Figure 1. It consists of a FPIDN and I λ D μ N controllers connected in cascade. The FPIDN has area control area (ACE) and derivative of ACE as two inputs. The area-1 (ACE 1 ) and area-2 (ACE 2 ) ACEs are given by where, B i is the frequency bias, ΔF i is area frequency deviation, ΔPtie ij is tie flow deviation, α 12 is the control area rating ratio. The FLC output y performances as the input to PIDN controller. The output of C-I λ D μ N controller is the control input ΔP C for the PS as represented by Equation (2).
Fractional calculus (FC) is expansion of the nth order continuous differentiation/integration of an arbitrary function with a real value order. The notions of FO controller connect with differential equations employing FC. The FOPID/FOPIDN controller is the expansion of the integer order (IO) PID/PIDN controller with fractional choice of integral-differential orders along with the IO PID/PIDN controller gains. The transfer function (TF) portrayal of FOPID (PI λ D μ )/FOIDN (I λ D μ N) controller is given as: In Equations (2) and (4), N and N1 denote coefficients of filter. The N/N1 curtails the impact of high frequency noise that appears because of regular switching of loads. In this work a well-known approximation termed as CRONE approximation, proposed by Oustaloup is utilized [6]. CRONE practices a recursive dispersal of A poles and A zeros leading to a TF inside a pre-specified frequency limit [ω L , ω H ]. For computer simulations, the considered ω L , ω H and A are 0.01 rad/s, 100 rad/s and 6, in order. For further details of FO controllers, [6,7,20,26,[36][37][38][39][40][41] can be referred.
The controller gains of C-I λ D μ N controller are to be selected via an appropriate method. Here, seven membership functions (MFs) are adopted for each inputs/output. The innermost five MFs have triangular shapes and the outer two have trapezoidal shapes as showcased in Figure 2 [29]. The rule base is utilized from [29]. In Figure 2, the fuzzy linguistic variables L, N, M, S, Z and P signify large, negative, medium, small, zero and positive, in order. The unfuzzified output of FLC is decided via center of  Handling two subsequent processes gives the notion of cascade control (CC). CC can advance control system outcome compared to single-loop control. CC is effective in fast disturbance rejection and provides fast/enhanced system response [6,41]. The basic CC system includes two control loops as revealed in Figure 3. In Figure 3, primary/master/outer controller C 1 (s) is FPIDN and secondary/slave/inner controller C 2 (s) is FOIDN. The primary process is termed as G 1 (s) and the complete process is exposed to load disturbance d 1 (s) creating Y(s) output. The input to G 1 (s) is U 1 (s), which is the inner process output. Y(s) is organized in reference to R(s). U 2 (s) is the input to the secondary loop process G 2 (s). The major purpose of the secondary loop is to bound the result of secondary process gain deviations on the control system outcome [6,7]. These gain changes might originate from variations in operating conditions.

IMPERIALIST COMPETITIVE ALGORITHM (ICA)
ICA, a meta-heuristic evolutionary algorithm stimulated by socio-political practices of imperialistic competition of people in the physical world was established by Atashpaz-Gargari and Lucas [42]. It establishes abundant recital both in convergence rate and global optimal solution achievement. It commences with early population of countries segregated into two groups; imperialists having the best/lowest values of fitness/cost function and other countries with less power named as colonies of the imperialists and all together constitute few initial empires. In the initial population, the colonies attached with the imperialists based on imperialists' powers so that the imperialist with extra power has extra colonies. The empire's power depends on the powers of the imperialist and its colonies. The colonies begin to vary their societies as per relevant imperialist. Here, colonies start moving regarding their relevant imperialist and this process is called assimilation. In it, the colony having more power may swap the imperialist with less power and vice versa.
During the imperialistic competition among the empires; the powerful empires try to boost their powers. The empires which are not powerful enough to compete and not able to raise their power will crumble. The competition will slightly enhance the power of powerful empires and decrease the power of lesspowerful empires. Due to this, during imperialistic competition, feeble empires will gradually lose their powers and breakdown at last. At the completion of competition, countries converge to a condition where there exists only one empire, all countries act as colonies of this empire and these colonies occupy the equivalent position/power as the imperialist.
The main steps concerned with the decision regarding the optimal controller parameters via ICA are specified as follows.

Initialize the empires
In this step, an array of variables (country) to be optimized is decided as: where, p i are variables to be tuned. The country's cost is determined as: To shape the early empires, the colonies are distributed among imperialist evenly using the imperialist's normalized cost Shifting of a colony to its related imperialist [37] described as: here, C n is the nth imperialist's cost and C n denotes its normalized cost. The normalized power of each imperialist is obtained as: here, N imp denotes the powerful countries to be imperialists to constitute empires. The nth empire's colonies can be given as: here, N × C n denotes nth empire's preliminary colonies and N col is the total number of colonies.

Assimilation
The colonies of every imperialist are assimilated regarding their particular imperialist as: here, x old col depicts colony's old position, β denotes assimilation factor and x is a random variable with even distribution. X imp , X new col are the imperialist's position and colony's new position, in order. Figure 4 displays the drive of a colony near its related imperialist. The progress is explained via x (distance) and α (angle) chosen randomly with even distribution (11)(12).
where β > 1, d denotes the distance between colony-imperialist and η is a limit angle for adjusting departure from the original direction [42].

Switching positions
During drive in the direction of the imperialist, a colony may arrive at a station having lesser cost value compared to the imperialist. In this case, the position of imperialist and colony are interchanged and then colonies commence moving near this new location.

Total cost of empires
An empire comprises of the imperialists and colonies. Hence, the cost of an empire is given as: here, T × C n is the nth empire's total cost and ξ is a positive number < 1. A small value of ξ implies that the empire's power is due to only the imperialist. However, a high value of ξ implies that the empire's total power is due to mainly the colonies.

Imperialist competition
In imperialist competition (IC), the power of frailer empires gradually decreases and that of powerful ones increases. This practice embraces the competition between imperialists to snatch colonies associated with other imperialists and this is performed by choosing the weakest colony from the weakest empire and creating a competition among all empires to own this colony. The most dominant empire conquers the selected colony. To initialize the IC, primary, the possession probability (PP) of every empire is calculated on the basis of its total power. The normalized cost of nth empire is computed by here NT × C n is the nth empire's normalized cost. The PP of every empire is calculated as: After computing the PP vector, additional vector termed D having the equal size is expressed by subtracting R (a random vector) from the PP vector (D = P − R), the possessed colony owns the highest value of D.

Revolution
In each iteration, in addition to assimilation, the revolution process is utilized to shift the colony positions. Few weakest colonies are selected and replaced with new colonies, haphazardly. Revolution is a sudden change, which improves the exploitation and exploration processes. It creates variety during searching of solution space. Comparable to the mutation process in GA, revolution advances the global convergence and thwart ICA from being trapped in local minimum. The number of colonies presumed to be interchanged with the equal number of new colonies is: (16) here N RC denotes revolutionary colonies and P revolution is the revolution rate. Prior the movement of each colony, a random number having constant distribution [0,1] is originated and matched with P revolution . If this number is less than P revolution , revolution process is adopted and the recent colony will substitute with the previous one.

Eliminating powerless empires
In the imperialist competition, feeble empires will breakdown and colonies associated with them will be allocated among remaining empires. An empire is expected to downfall when it drops all of its colonies.

Convergence
The preceding steps are replicated till the criterion decided for convergence is attained. At the convergence point all empires breakdown except the utmost powerful one. In this condition, all colonies occupy identical positions and costs; competition ends and ICA stops. For more detail please refer [18,42]. The parameters used in ICA are taken from [29].

OPTIMIZATION CONSTRICTIONS AND OBJECTIVE FUNCTION
To tune the parameters of a controller utilizing an optimization algorithm, an objective/cost function is needed. A cost function (J) is designed based on the desired provisions and limitations. Some of the industry-linked cost functions are integral time absolute error (ITAE), integral square error (ISE), integral time square error (ITSE) and integral absolute error (IAE) [3,6,14,28,29,36,38,40,41]. However, in this paper, ISE is utilized because of its better performance [28, 29, 36-38, 40, 41].  Other performance criteria are utilized to display an effective comparison of the system results. The structure for ISE is given in Equation (17) and other cost functions (J S ) are expressed by Equations (18)- (20).
The results of the systems are attained with the controller parameters acquired for smallest value of Equation (17) using ICA. J S in Equations (18)- (20) are also computed for comparison purpose. The parameters to be tuned for the proposed C-I λ D μ N controller are 9 (K P /K I /K D /N/K I1 /λ/K D1 /μ/N1) and for outer loop FPIDN are 4 (K P /K I /K D /N) parameters. Both controllers are tuned using ICA to get smallest value of (17) in the presence of the following restraints: The min/max in Equation (21) represents minimum/maximum values of the concerned parameter.

Implementation of ICA based control strategy
The models of the systems under examination shown in  Table 1 for 2-area RTS and 2-area MSHTS PS models under study.

2-area reheat thermal system
Primarily, the study is conducted on a more pragmatic 2-area reheat thermal system (RTS) integrated with renewable energy sources (RES) in area-1 ( Figure 5(a)). The details of RES are   [29] represented in Figure 5(b). The system dynamic results of change in area-1 frequency (∆F 1 ), change in area-2 frequency (∆F 2 ) and change in tie power (∆Ptie 12 ) with the proposed method are obtained by directing a step load perturbation (SLP) of 0.01 puMW in area-1 at time t = 0 s. Additionally, a SLP of 0.001 puMW for each STG and 0.002 puMW for each WTG at time t = 0 s are considered. The results are exposed in Figure 6(a-c). To reveal the contribution of C-I λ D μ N controller, its outcomes are matched with various existing and the best claimed intelligent controllers like sine-cosine algorithm (SCA) tuned cascade PDN-PIDN (C-PDN-PIDN) [14], artificial bee colony (ABC) tuned PID [16], bacterial swarm optimization (BSO) tuned fractional order PID (FOPID) [20], SOS algorithm tuned PIDN [22], hybrid differential evolution-PSO (hDE-PSO) tuned FPID [33] and jaya algorithm (JA) tuned FPIDN [35] controllers. The inspection of Figure 6(a-c) divulges that the C-I λ D μ N controller significantly displays superiority over other controllers in concerning swift responses, no oscillations and negligible settling times (T S )/peak undershoots (U S )/overshoots (O S ) in ∆F 1 /∆F 2 /∆Ptie 12 results.
To inspect the outcome of the C-I λ D μ N controller further, the numerical values of ISE/ITSE/IAE/ITAE defined via Equations (17)- (20), T S , U S and O S are calculated through simulations and shown in Table 2. Error criteria ISE/ITSE/IAE/ITAE are obtained via simulating the models for 15 s and T S are obtained for a tolerance band of ±0.0005. Table 2 also demonstrates the advantage of ICA tuned C-I λ D μ N controller over SCA C-PDN-PIDN [14], ABC PID [16], BSO FOPID [20], SOS PIDN [22], hDE-PSO FPID [33] and JA FPIDN [35] [3] and hence, it establishes a literature gap. It is plainly perceived that C-I λ D μ N controller is competent in alleviating the oscillations in the system responses. Hence, the disturbance rejection characteristic of C-I λ D μ N is reasonably appropriate for the AGC compared to other methods.
To check the stability of the proposed ICA based controller, a comparative statistical investigation is performed. The statistical data of minimum, average, maximum and standard deviation (SD) of ISE objective function values achieved in 50 independent runs with the proposed controller (with/without RES) are summarized in Table 3. From the analysis Table 3, it is vibrant that minimum objective function value is attained with the proposed C-I λ D μ N controller in the presence of RES (ISE = 3.31 × 10 −8 ) compared to C-I λ D μ N controller (ISE = 1.07 × 10 −7 ). It is also clear from Table 3 that C-I λ D μ N (RES) outperforms C-I λ D μ N technique in terms of average, maximum and standard deviation values obtained. It can be stated that the proposed controller is stable and superior specifically with RES for an AGC problem.

2-area multi-source hydro-thermal system
To examine the competence of the C-I λ D μ N controller to deal with different AGC systems, the study is also widened to a 2area multi-source hydro-thermal system (MSHTS) whose TF model is displayed in Figure 8. In an area, two units that is, one non-reheat thermal and one mechanical governor outfitted hydro are available. Additionally, RES are integrated in area-1 [3]. The symbols used in the figure are explained in Nomenclature and their values are specified in Appendix. The simulation outcomes of the system at SLP = 0.015 puMW due to the C-I λ D μ N/fuzzy-PIDN (FPIDN) controllers developed in the study and various other prevalent controllers like grey wolf optimization (GWO) [15]/hFA-PS [17]/JA-IWO [19]/optics inspired optimization (OIO) [21]/quasi oppositional differential search algorithm (QODSA) [24] optimized PID and BFOA optimized FPI/FPID/FOPID [28,38] are displayed in Figure 9(a-c) and Table 4. It is obvious from Figure 9(a-c) and Table 4 [21] based PID and BFOA based FPI/FPID/FOPID [28,38] controllers. However, performance of the recommended C-I λ D μ N controller is additionally advanced in the company of RES as clearly indicated in Figure 9(a-c) and Table 4. The generation results in area-1 (ΔP gArea-1 ) and area-2 (ΔP gArea-2 ) are exposed in Figure 10(a,b). The generated powers by STGs, WTGs, FCs, RES, area-1 thermal and area-1 hydro are ∆P gSTG = 0.0036 puMW, ∆P gWTG = 0.006 puMW, ∆P gFC = 1.536 × 10 −7 puMW, ∆P gRES = 0.00576 puMW, ∆P gThermal-1 = 0.004622 puMW, ∆P gHydro-1 = 0.004618 puMW, respectively. The total power generation in area-1 that is, ∆P g1 (= ∆P gRES + ∆P gThermal-1 + ∆P gHydro-1 ) = 0.015 puMW, which is equal to the demand in area-1 that is, ∆P D1 . However, in area-2, as ∆P D2 = 0 puMW, ∆P gThermal-2 = 0 puMW, ∆P gHydro-2 = 0 puMW and ∆P g2 = (∆P gThermal-2 + ∆P gHydro-2 ) = 0 puMW. Next, in practical scenario, the power outputs of STG and WTG renewable sources are highly unpredictable and variable due to their dependence on environmental factors like solar irradiation and wind speed. Consequently, the deviations in their power outputs are inspected in the existence of random powers (P sol ) and (P W ) caused due to solar insolation and wind speed respectively varying abruptly with time as shown in Figure 11(a). However, SLP in area-1 remains the same. With the proposed controller, the simulation results of generations in area-1 that is ∆P gSTG , ∆P gWTG , ∆P gFC , ∆P gRES , ∆P gThermal-1 , ∆P gHydro-1 and ∆P g1 are shown in Figure 11(b). It is observed from Figure 11(b) that the generations are changing randomly in contrast to Figure 10

SENSITIVITY STUDY
A sensitivity study is performed to check the robustness of the recommended C-I λ D μ N controller for extensive deviations in the system operating conditions. To illustrate the robustness,  Figure 12(a,b) demonstrates ΔF 1 results under nominal and ±20% variations in parameters for 2-area reheat thermal system and multi-source hydro-thermal system, in order with/without RES. Here, ΔF 2 and ΔPtie 12 responses are not provided to save the space. The inspection of Figure 12(a,b) evidently reveals that all results with/without RES are stable and they do not deviate much from the nominal responses. However, controller outperforms in the continuation of RES. The several performance indices that is, T S and J S for nominal parameters and ±20% of nominal parameter variation cases for reheat thermal system (with/without RES) and multi-source hydro-thermal system (with/without RES) are given in Table 5 for ΔF 1 , ΔF 2 and ΔPtie 12 responses. It can be perceived from Table 5 that settling time, ISE, ITSE, IAE and  ITAE values diverge within tolerable ranges and are more or less  equal to the corresponding values attained with nominal system parameters. Therefore, it can be established that the proposed controller is robust and executes suitably when system nominal parameters deviate in the range ±20%. Additionally, the robustness study of the C-I λ D μ N controller is performed out under the existence of random load perturbations (RLPs) of high magnitudes in both control areas of 2-area reheat thermal system. Dissimilar RLPs in all control areas represent a much more realistic power system environment. At higher SLP/RLP scenario, the power system will become unbalanced if the designed controller is non-robust. Figure 13(a) shows RLPs of different magnitudes applied in areas 1 and 2 at t = 2 s of reheat thermal system. Figure 13(b,c) show ΔF 1 and ΔPtie 12 responses with parameters of the C-I λ D μ N Reheat thermal system (C-I λ D μ N (RES) (Figure 12(a) Multi-source hydro-thermal system (C-I λ D μ N) (Figure 12(b) Multi-source hydro-thermal system (C-I λ D μ N (RES) (Figure 12(b) controller optimized at area-1 SLP of 0.01 puMW (given in Table 1) and RLPs in areas 1-2. The optimized controller parameters obtained at this SLP produce ISE = 9.47 × 10 −5 /ITSE = 5.10 × 10 −3 /IAE = 0.0551/ITAE = 2.8890 and ISE = 3.26 × 10 −5 /ITSE = 1.76 × 10 −3 /IAE = 0.0372/ITAE = 1.9520 (with RES), which are greater than their corresponding values given in Table 2. This means that the controller with RES produces better performance regarding J S and results shown in Figure 13 Figure 13(c) evidently discloses that both the responses are stable. However, system responses and J S obtained at parameters optimized with RLPs are superior. Thus, the stable performance of the system at dissimilar operating conditions authorizes the robustness of ICA optimized C-I λ D μ N controller.

CONCLUSION
A novel ICA tuned C-I λ D μ N controller is suggested for AGC of 2-area electric PSs penetrated with RES. Initially, a 2-area RTS is scrutinized in the presence of 1% SLP in control area-1. The simulation results due to the proposed controller are compared with the existing ABC tuned PID, BSO tuned FOPID, SOS tuned PIDN, hDE-PSO tuned FPID and JA tuned FPIDN controllers. It is noted that significant development regarding oscillation free results with smallest values of T S /U S /O S /J S are obtained due to the suggested ICA tuned C-I λ D μ N controller over other controllers. However, further enhanced results are acquired in the presence of RES integrated in area-1. To further validate the capability, extensibility and advantage of the method for other systems, the work is also protracted to a 2-area MSHTS. The asset of C-I λ D μ N controller is established over ICA based FPIDN and intelligent JA-IWO/QODSA/GWO/hFA-PS/OIO tuned PID and BFOA tuned FPI/FPID/FOPID controllers prevailing in the literature. The worth of RES addition is validated via enhanced system outcome with the C-I λ D μ N controller. The sensitivity analysis validates the robustness of the C-I λ D μ N controller with/without RES under ±20% deviations in the system's parameters and random load perturbations (RLPs) created in both areas of reheat thermal system. It is observed that the proposed controller designed at nominal condition is robust and shows stable performance at extensive changes in the parameters of the systems and RLPs. Additionally, RES integration is suggested in PSs to get reliable, better quality, and environmentally-friendly electrical power. Hence, after analysis and discussion done above, it is assured that the suggested ICA optimized C-I λ D μ N controller may be an appropriate controller for solving more intricate engineering problems in isolated/multi-area interconnected traditional as well as modern restructured AGC systems with/without RES integration.