Fractional Cascade LFC for Distributed Energy Sources via Advanced Optimization Technique Under High Renewable Shares

Unpredictable high renewable shares in a standalone microgrid (MG) system with stochastic load demands introduces an unavoidable mismatch among loads and sources. This mismatch directly impacts the system frequency, which can be mitigated via applying a suitable load frequency control (LFC) scheme. This brief proposes a maiden attempt of marine predator algorithm (MPA) assisted one plus proportional derivative with filter-fractional order proportional-integral ((1+PDF)-FOPI) controller to obtain the proper power flow management among loads and sources. The investigated MG system consists of a photovoltaic (PV) system, a wind turbine (WT) generator (WTG), and a diesel engine generator (DG) as the distributed energy sources, and an ultracapacitor (UC) and a flywheel are chosen as the energy storage elements (ESEs). Various system nonlinearities, such as governor dead-band (GDB) and generation rate constraint (GRC) are also considered to reflect the practical scenario. Five state-of-the-art optimization techniques and three traditional controllers, PID, FOPID, and PI-PD, are vividly compared to assess the proposed scheme’s performance. The parametric uncertainties are considered obtaining the robust performance of the proposed control scheme. An eigenvalues-based stability evaluation of the considered plant employing the proposed LFC scheme is also included in this work. In the worst situation, the maximum frequency deviation is obtained as −0.016 Hz, which is entirely satisfactory and under the range of the IEEE standard. Finally, a modified New England IEEE-39 test bus system is chosen to perform the real power system validation via MATLAB/Simulink.


I. INTRODUCTION A. BACKGROUND
Enhancing electricity demand requires employing hybrid generation units in standalone or interconnected power system networks. In the present era, renewable shares are The associate editor coordinating the review of this manuscript and approving it for publication was Okyay Kaynak . enhancing the existing power system network due to the high emission of greenhouse gases, galloping oil prices, and sustainable development. Renewable energy (RE) sources, considered economical and clean energy sources, are likely to be interconnected to the MG power systems [1], [2]. Solar and wind are the most critical RE sources among all the energy sources due to their abundant availability [3]. The critical drawback of RE sources is their highly unpredictable nature.
Due to the stochastic nature of RE sources, its efficacy is very low; with PV, the conversion efficacy is as low as it falls under the range of 7-19% [3]. Hence, in order to harvest the maximum obtainable power from the uninterrupted solar insolation, various maximum power point tracking (MPPT) schemes are employed [3], [4], [5]. The most commonly utilized MPPT schemes are perturbed & observe (P&O) and incremental conductance (IC) [5]. With wind energy conversion, the most common MPPTs are P&O and tip speed ratio [6]. In this investigated MG system, the maximum obtainable power from PV is harvested through the modified IC (MIC) MPPT scheme as presented in [7], and a nonlinear WTG modeling is employed to harvest maximum power from the stochastic wind speed. Due to the significant share of these RE sources in the MG system, the most interesting parameter of the power system, ''frequency,'' is affected [8]. The change in frequency deviation (CFD) severely affects the frequency-sensitive loads, and in the worst situation, a blackout may occur. To maintain the proper power flow management among loads and sources and to make CFD → 0, it is required to incorporate a supervisory LFC scheme in the MG system [9]. In other words, LFC allows the generating units to regulate their generations corresponding to load demands, resulting in a zero CFD under ideal situations. The system performance may undermine due to the improper design of LFC and also causing large oscillations in the system [10]. In order to the proper design of the LFC scheme, various meta-heuristics-based control approach is employed for various types of power system networks [7], [8]. The metaheuristics handle the optimal performance of the designed frequency control scheme.

B. LITERATURE REVIEW
The apropos literature has witnessed various works on the novel controller design. Some of the recently published literature incorporates PI/PID structured controllers are dragonfly search algorithm [11], bacterial foraging optimization algorithm (BFOA) [12], particle swarm optimization (PSO) and hybrid BFOA (PSO-hBFOA) algorithm [13], lozi map-based chaotic algorithm [14], fire-fly algorithm tuned PI controller [15], PIDD2 control approach [16], ant colony optimization for hydrothermal power plant [17], flower pollination algorithm tuned PI-PD cascade control [18], genetic algorithm (GA)/differential evolution (DE) [19], bat algorithm tuned PD-PID cascade control approach [20], improved stochastic fractal search (SFS) algorithm [21], sine cosine algorithm based PI controller [22], DE tuned PI/PID [23], biogeography based optimization tuned I/PI/PIDF [24], teaching learning based optimization algorithm based 2-degree of freedom (DOF) PID (2DOF-PID) [25], disrupted oppositional based gravitational search algorithm -pattern search based PID [26], symbiotic organism search algorithm tuned PID [27], hybrid SFS -local unimodal sampling (hSFS-LUS) based multistage PDF-(1+PI) [28] and imperialist competition algorithm tuned PID controller for PV-thermal and hydrothermal based interconnected power system [29]. A GA-based LFC scheme with stability evaluation under solar, DG, and batterybased distributed energy sources is demonstrated in [7]. A (1+PD)-PID-based cascade control approach for the interconnected power system under RE contributions is briefed in [11]. Kumar and Hote [16] designed a robust PIDD2 controller to mitigate the frequency deviations in the interconnected power system. The authors have chosen Kharitonov's theorem-based worst-case plant section model design. A sliding mode control approach is implemented to design a robust controller [16]. In order to improve the performance of the control scheme, other advanced control approaches based on H-infinity [30], sliding modes [31], fuzzy logic control [32], [33], artificial neural network-based [34], adaptive neuro-fuzzy inference system [35], disturbance observer-based fractional control [36], nonlinear disturbance observer [37], modified tilted control approach [38], delaydependent control approach including electric vehicles, and constant and varying loads [39], [46] and fractional control approach [40] are discussed. In [33], an intelligent LFC scheme for a standalone MG system is demonstrated. In this, the authors have used an improved IC MPPT scheme to harvest power from PV, and a fuzzy observer-based control approach is chosen for the wind energy conversion system. The obtained results revealed the superior performance of the proposed controller over other considered control approaches. A double-stage controller design is proposed for a hybrid ocean-wind-based maritime MG system [47]. A grasshopper algorithm is used to tune the proposed PI-(1+PD) controller, and the obtained results revealed the enhanced performance of the proposed controller over PID and PID with filter-type controllers. A novel performance index criterion termed a hybrid peak area for the automatic generation control of two area power systems is revealed in [45], and the obtained results are compared with the existing performance indices. A lightning search tuned variable structure control approach for the frequency control of load following a nuclear reactor power system is briefed in [48], and the results are compared with a GA-based variable structure control scheme. An improved gray wolf optimizationbased control approach for vision system-based autonomous vehicles is revealed in [49]. A PID controller design for two area power systems via an artificial bee colony is proposed in [50]. A black widow optimization algorithm-based PIDF -(1+I) cascade control approach for the LFC of the MG system is investigated in [51]. This P&O MPPT algorithm is used to harvest maximum obtainable power from PV, and the real-time benchmarking is performed via a modified New England IEEE 39 test bus system. A tilt integral derivative controller for the multi-MG system considering the electric vehicle is presented in [52]. Sensitivity analysis of the proposed control scheme is performed under ±30% of parametric uncertainties. The investigated system performances due to cascade control approaches are worth-appreciating control action in interest. Moreover, selecting an appropriate optimization approach for the LFC design is also challenging for VOLUME 10, 2022 researchers in this field. However, according to the authors' best knowledge, the system responses depicted in these works have space for further enhancement considering time-domain specifications.

C. MOTIVATION AND CONTRIBUTIONS
Enticed by the structural simplicity of PI and PID controllers and the magnificent performance of cascade and fractional controllers suggested in [11], [40], and [51], the present study preconceives a new fractional cascade controller named (1+PDF)-FOPI, whose performance evaluation has not been investigated so far. The proposed controller has both the property of cascade and fractional order control. As per the literature inspection, many nature-inspired optimizations have been employed for LFC studies. For the optimized search performance, exploitation and exploration are the two vital indices expected to be balanced for the meta-heuristics [15]. A perfect trade-off between exploitation and exploration is obtained with MPA for global optimization. MPA was recently invented metaheuristic proposed by Faramarzi et al. [41]. The proposed MPA technique has proved the superior performance over various meta-heuristics such as GA, PSO, cuckoo search (CS), salp swarm algorithm (SSA), gravitational search algorithm (GSA) for various engineering problems such as welded beam design, pressure vessel design, operating fan schedule for demand-controlled ventilation, tension/compression spring design and building energy performance [41]. Hence, tempted by the enhanced performance of the MPA technique, a maiden attempt has been performed to employ it for the LFC of the considered MG system. Moreover, a stability evaluation of the proposed fractional cascade LFC of the MG system is also performed. The stability assessment approximates the fractional order into its respective entire order using the stability boundary locus (SBL) method [53]. The critical contributions of the work are summarized as follows: • Design and implement MPA-assisted (1+PDF)-FOPI fractional cascade control scheme for the LFC of renewable-rich MG system.
• To scrutinize the performance of the proposed LFC scheme, five state-of-the-art optimization techniques and PI, FOPID, and PI-PD controllers are considered.
• Eigenvalues-based stability evaluation of the considered MG system employing MPA:(1+PDF)-FOPI controller is performed.
• A New England IEEE-39 test bus system is chosen for the real power system assessment of the proposed controller.

II. SYSTEM DESCRIPTION AND MODELING
A 1.5 MW (1 pu) MG system is considered in this proposed work, as shown in Fig. 1. The power obtained from DG, PV, and WTG are 450 kW, 100 kW, and 750 kW, respectively, whereas UC and flywheel provide 50 kW and 150 kW, respectively.

A. MODELING OF WTG
The rated wind speed (V w ) plays a critical role in the power production from WTG (P w ), and the V w is dependent on base wind speed (V wb ), ramp speed (V wr ), gust speed V wg and noise component of wind (V wn ) [42]: The wind model inculcates its essential components as base fluctuation and randomness, which are represented as [43]: The V wb is a constant, and its presence is detected when WTG is in operation. Randomness of V wb is expressed by the Heaviside step function as [42]: In order to consider the practical scenario, variations in V w is chosen from 2.5 m/s to 12.5 m/s. Moreover, the noise component of V w is revealed as [43]: where, ω i = i − 1 2 ω and ϕ i ≈ U (0, 2π). The noise variation is σ 2 and spectral density critical factor is ω. The spectral density component S v (ω i ) is given as [38]: where, k n µ and F denote surface drag coefficient, reference height, and base V w at turbulence measure. A nonlinear WTG model is considered to harvest the power from unpredictable wind speed. The wind power generation modeling is revealed as [33]: where WT angular speed and power output are ω m and P W Swept area of the rotor is A T , air density is ρ, and rotor blade coefficient is C p that revealed as follows [33]: where, C 1 to C 7 are WT's coefficients for fixed and variable speed, the pitch angle is β, and the optimal tip speed ratio is λ T that demonstrated as [33]: where the radius of the rotor blade is r T and λ I is the intermittent tip speed ratio briefed as [33]:

B. MODELING OF PV SYSTEM
The governing relation of I-V for PV is as follows [44]: where, The output power of the PV system is briefed as [38]: where η is conversion efficacy, S is the measured surface area, φ is input insolation on the surface area, and T a = 25 • C is atmospheric temperature. The solar insolation φ is expressed as the heavy step function as [38]: where, φ n is in the range (-0.1, 0.1). In this proposed work, the actual PV power through the MIC MPPT scheme is injected into the investigated MG system at the insolation level varying from 400 W/m 2 to 1000 W/m 2 in a ramp variation form. Hence all the nonlinearities of the system are already considered. The obtained maximum power from PV is shown in Fig. 7. The simulation parameters of the PV system are depicted in Table 1.

C. MODELING OF DG
In this proposed work, first order governor model is chosen and revealed as [33]: where power output and time constant of the governor are P G and T g respectively, the control signal is u, and the droop coefficient is R d . Moreover, the first-order turbine model is chosen and revealed as [33]: where power output and time constant of DG are P DG and T t respectively. The overall open loop transfer function (OLTF) of DG and WTG by assuming other inputs as zero are revealed by (16) and (17) as: f where WTG's time constant is T WT , the inertia constant is H, and the MG system's damping coefficient is D.

E. CONSIDERED MICROGRID (MG) MODELING
The description of dynamic modeling of MG system or onearea LFC is revealed in the state space equation model as [46]: where, while considering no tie-line power exchange in MG and β as frequency bias factor, the ACE is as: and Equations (21) and (22) reveal the integral of CFD → 0 at a steady state. The linearized model of governor valve position due to ACE delay is as: where, d (t) denotes the system's delay, which is neglected in the present study. In summarized form, (18) is written as: where, where f is frequency deviation, P v is valve position and P d is the change in load demand. The dynamics of the MG system's frequency are demonstrated as [33], [45]: The (18) is written in the ''s'' domain and revealed as: where power error P e = P s − P d ± P FW ± P UC , and P s = P PV + P WTG + P DG The power output of the PV, WTG, and DG, respectively. The ±P FW and ±P UC reveal the power provided and absorbed by the flywheel and UC, respectively.

F. CONTROL STRATEGY
This section reveals the design consideration of the proposed (1+PDF)-FOPI cascade controller used for the droop control in the considered MG system. The output of the (1+PDF) controller is working as the input of the FOPI controller in a series manner; hence, it is considered the cascade control approach. The structure of the (1+PDF)-FOPI controller is shown in Fig. 1 and revealed as: where, k 1 − k 5 and λ are the parameters of the (1+PDF)-FOPI controller, and u is the controller's output. The total tuning parameters of the proposed controller are six. This is the optimization problem and can be reduced by minimizing the objective function (J s ). The different types of objective functions that are used in the LFC of the power system are IAE, ITAE, ISE, and ITSE. The ISE tuned controller reduces significant errors very fast, but the minor errors remain for a long duration [45]. The IAE tuned controller gives a slow dynamic response, and significant deviations remain compared to ISE [45]. The controller tuned via ITAE and ITSE give a dynamic response with less settling time (ST) [45]. The critical shortcoming of ITAE and ITSE is that the initial dynamic response is slow [45]. Hence, to ramp up the dynamic and steady-state performance (faster convergence with lesser divergence from the final value), an excellent combination is ISE and ITAE, which is considered in this work and given as: where, t s is simulation time, w 1 and w 2 are the weights and chosen as 50% each. The critical aim of this work is to reduce J s via MPA because reduced J s provides excellent performance of (1+PDF)-FOPI cascade controller for LFC of considered MG system. Minimize J s subject to:

III. PROPOSED MPA FOR LFC OF CONSIDERED MG SYSTEM
This is a population-based algorithm in which the solution is uniformly distributed as follows [41]: where the lower and upper bounds of variables are X max and X min and rand[0, 1]. The fittest predates are in the form of a matrix and searches for prey according to the prey's positional VOLUME 10, 2022   information as [41]:  (32) where, X l presents the top predator, which replicates n several times to make Elite matrix, search agents, and dimensions are n and d. Elite is updated if a better predator replaces the top predator. The Prey matrix is the same as Elite and represented as [41]: When prey and predator move in the same search space, they search for their food. This scenario presents the immediate phase of optimization and exploration that tries to convert into exploitation. Hence, half of the population is designated for exploration, and half is designated for exploitation. In this technique, it is considered that the movement of prey is Lévy and the movement of predator are Brownian. The various phases of MPA are revealed in Fig. 3 and presented as: For the first half of the population: where, − → R L is a vector-based on Lévy distribution presenting Lévy movement. For the second half of the population, the assumption is as follows [41]: Max_Iter is an adaptive parameter to control predator movement's step size. The multiplication of − → R B furthermore, Elite imitates the Brownian movement of the predator, while the updating of the position of prey is based on the predator's Brownian motion.
The last phase of optimization occurs when the movement of a predator is faster than prey and is associated with high exploitation capability. This is represented as: Multiplication of − → R L and Elite imitates the predator's movement in Lévy type while adding step size to Elite position imitates the predator's movement for updating of prey position. Another critical factor that affects the MPA is environmental impacts such as fish aggregating devices (FADs) effects. FADs are considered local-optimal points, and there is a chance to trap these points. The FADs effect is mathematically presented as [41]: where FADs = 0.2 is the impact of FADs on optimization. Binary vector is − → U Including an array with one and zero. Vectors containing maximum and minimum bounds are − → X max and − → X min . Random indexes of the Prey matrix is r 1 and r 2 . The flowchart of the MPA is depicted in Fig. 4.

A. CONSTANT LOAD CONDITION
The convergence rate of the proposed MPA:(1+PDF)-FOPI controller is shown in Fig. 5. From Fig. 5, the minimum J s is obtained as 0.000789, and the final convergence is obtained in 60 iterations. In order to investigate the performance of all the applied optimization schemes on the (1+PDF)-FOPI controller, a step load perturbation (SLP) of 45% is given as a load at constant wind speed and constant solar insolation. Hence, an SLP of 45% and without δ 1 (uncertainty in the wind) and δ 2 (uncertainty in solar insolation), The performance of the designed PSO, CS, GSA, SSA and MPA tuned (1+PDF)-FOPI controllers is depicted in Fig. 6 and tabulated in Table 2.
By observing Fig. 6 and Table 2, it can be noted that the maximum f is obtained as -0.   Table 2, it can be concluded that the error rates are minimum for the proposed controller as IAE(0.000137), ITAE (0.001439), ISE (4.21 × 10 −9 ) and ITSE (1.32 × 10 −9 ). So, in this considered state performance, the MPA:(1+PDF)-FOPI controller is superior to other control schemes.
The controller's performance in more practical scenarios by applying a constant SLP of 55% with δ 1 and δ 2 is considered for further analysis. The considered δ 1 is in between 400 W/m 2 -1000 W/m 2 , and the harvested MPP via MIC MPPT is depicted in Fig. 7. Which shows that the maximum obtained power is 100 kW (0.067 pu) at the maximum insolation of 1000 W/m 2 .
The considered δ 2 is in between 2.5 m/s-12.5 m/s, and the extracted MPP via the nonlinear WTG model is depicted in Figs. 8(a)&(b) respectively, the maximum obtained WTG power is 750 kW (0.5 pu). The CFD response of the controllers PSO, CS, GSA, SSA, and MPA tuned (1+PDF)-FOPI is revealed in Figs. 9(a)-(e) respectively. The controller's performance is summarized in Table 3, and from Table 3, the maximum f appeared with PSO as −0.  (2.701×10 −8 ). In this considered test case, the contribution of all the distributed energy sources with load demand is in Fig. 13(a). Moreover, PID, FOPID, and cascade PI-PD controllers are chosen to assess the proposed controller's superior performance over other traditional controllers, as depicted in Fig. 10. From Fig. 10 and Table 3   compared to the proposed control scheme. Hence, it can be concluded that the proposed controller surpasses the other designed controller for the considered test case.
To assess the robustness performance of the proposed controller, parametric variations are considered. The various components of parametric uncertainties will primarily affect the parameters of the MG system. Hence, a large perturbation order of 300% change in 2H and 300% change in D is considered for the robustness evaluation of the proposed controller. In this scenario, the controller's performance in terms of the error rates is summarized in Table 4, which is reasonably satisfactory. In order to investigate the robustness analysis of the proposed controller in a harsh situation, a rigorous load variation is also considered, as depicted in Fig. 14(a), and the performance of the MPA:(1+PDF)-FOPI controller is revealed in Fig. 14(b). Considering the challenging scenario, the performance of the proposed controller is entirely satisfactory, with a maximum CFD of −0.014 Hz, which is under the permissible limit of the IEEE standard.

C. STABILITY EVALUATION
In order to boost the dynamic performance of an LFC technique, it is required to have enough stability. Various schemes FIGURE 15. Modified New England IEEE-39 bus system [44].
are available to assess the stability of a system and the eigenvalues-based stability approach is one of them. To obtain the eigenvalues, first, the fractional order term is converted into an absolute order term using the stability boundary locus (SBL) scheme [53]. The controller TF is revealed as: where, s 0.6 = 34470s 4 +56770s 3 +12680s 2 +405.6s+1 6300s 4 +5493s 3 +38800s 2 +4074s+52.66 . The complete closed loop TF of the considered MG system employing the proposed fractional cascade LFC is evaluated using [54] and revealed by as in (42)   standard IEEE-39 bus system [45]. In this work, out of three areas, only one area, i.e., area 1, is chosen to assess the proposed control scheme. The modification is done in area 1, where one conventional generator is replaced by the solar and wind as generating units and a flywheel as a storage unit. The considered modified IEEE-39 bus system is depicted in Fig. 15. The related simulation parameters are given in Table 1.
The effect of GRC nonlinearity is also incorporated in this study. The frequency response, supply, and demand power for SLP 65% pu are depicted in Fig. 16 (a) and (b).
Maximum f is obtained in the order of -0.148 Hz, which is reasonably satisfactory and within the permissible range. The performance is tested by employing the varying power demand of SLP 80%, 30%, and 65%, and responses are depicted in Figs. 17(a) and (b); with varying power demand, the maximum obtained f is +0.169 Hz, which is in the permissible frequency range. The idea of the proposed MG system may be implemented for the places which are not accessible to the conventional grid but enriched with RE sources, for rural electrification, hospitals, agricultural fields, etc. The proposed control scheme may be applied to control interconnected power systems and hybrid electric vehicles.

V. CONCLUSION
The study made in this paper has been directed toward a novel MPA:(1+PDF)-FOPI fractional cascade LFC for a 1.5 MW standalone MG system. The maximum PV power is successfully harvested via a modified IC MPPT technique, and the optimal power is extracted from the wind via a designed nonlinear WTG model. The results of the proposed controller are vividly compared with four state-of-the-art optimization techniques, PSO, CS, GSA, SSA, and three controllers, PID, FOPID, and cascade PI-PD. The obtained performance indices and maximum CFD show the effectiveness and superiority of the proposed LFC scheme over the other designed control schemes. For the robustness assessment of the proposed LFC scheme, huge parametric uncertainties are considered in the MG system's parameters, and rigorous load demand in triangular format is also considered. Under the worst situation, the maximum frequency deviation is −0.016 Hz, which is under the permissible limit. The controller has performed well, and CFD is under the permissible limit of the IEEE standard. Eigenvalues-based stability analysis shows the stable performance of the proposed control scheme. Finally, a modified New England IEEE-39 test bus system is successfully implemented to assess the proposed control scheme's actual power system implementation in an off-line scenario. This work's future scope may focus on designing of intelligent control scheme for renewable-rich multi-area power systems.