A Systematic Load Frequency Regulation in Two Area Renewable Micro-grid Cluster Utilizing Bald Eagle Search Algorithm

This paper works on the systematic load frequency and tie-lie power transfer regulation within the prescribed limit. The proposed two area renewable energy based micro-grid cluster comprises of dish stirling solar generator, micro hydro turbine, biogas generator as energy generators in area 1. Also, wind turbine, tidal generator, biogas generator as energy generators in area 2. The Flywheel and battery act as mechanical and electrical energy storage devices in their respective areas. Moreover, to make the frequency oscillation die out quickly super magnetic storage devices are connected in the system. A comparison of performance of system with respect to objective function error is made to determine superior controller with minimum error and most stability. The controller parameters is adjusted with Bald eagle search optimizer, Black widow optimizer algorithm, Giza pyramid construction, Teaching learning based optimizer and Genetic algorithm. Lastly, best controller-algorithm i


Introduction
Renewable energy sources are the alternative to the fossil fuel based conventional sources.They help to meet the ever growing world energy demand.More than one renewable energy sources are connected to form micro-grid cluster as the energy generated by single source is not sufficient to meet the load requirement.The multi source multi area makes the cluster more reliable and resilient.Moreover, energy storage devices are connected to the energy sources to improve system performance and stability [1].The major advantages of renewable sources like safety, efficiency, less global warming, inexhaustibility, improved public health and economic benefits as stable energy prices outweigh its disadvantages like weather uncertainty and unpredictability of renewable sources.This has increased the generation of energy from non-conventional renewable sources [2].There are a large number of papers, elaborating creation of micro-grid with fossil fuel and renewable energy sources.In [3] describes conventional system consisting modeling of non-reheat thermal in real time simulation software OPAL-RT.This system performs well with 2 Degree Of Freedom TIDF tuned with whale optimization algorithm (WOA) with and without governor dead band.Also, [4][5][6] describes about multi area power system model with conventional energy sources like thermal-hydro-gas units.The impact of integration HVDC is demonstrated in [7].The detailed modeling of PV and wind sources with energy storage and load forming a stable system in discussed in [8,9].The extended modeling of integration of conventional and renewable sources in two area is given in [10].Thermal-hydro-gas are the component of conventional sources where as wind and solar energy made the renewable energy portion.An effort is also made to make the micro-grid more realistic with the inclusion of rate constraints, dead band, delays and uncertainties present in the system.
Penetration of multi renewable energy sources in the system results in large frequency and tie-line power overshoot.This deviation because of the energy imbalance is mitigated using frequency regulation controller.The fundamental frequency regulators are having the gain of proportional, integral and derivative.All other controllers are built with the combinations of the aforementioned controllers.In [11,26,27] authors has demonstrated stabilization of cluster of hydrothermal plant with wind/diesel generator/aqua electrolyser/fuel cell/battery as its components.Controller employed are PID with 2 or 3 degree of freedom, PIDF, FOPID, PI-PID, TID and CC-TID.FOPID is the controller which is explained by the concept of Oustaloup, Carlson, Matsuda, and continued fraction expansion for s-domain approximation as discussed in [12].In [13] purely renewable energy based stand alone micro-grid is evaluated with some of the derived complex controller namely PIDF-(1+I) PID, PIDF, and PIDF-(1+I).Furthermore, application of cascade multistage controller in hybrid micro-grid system with multi area units is presented in [14].Wind farm integrated with electric vehicle and system frequency is stabilized with 2 degree of freedom PID tuned with robust internal mode control (IMC) is provided in [9].Some other optimization techniques for example sliding mode control [16], Model predictive control [8,15], terminal sliding mode control [17], adaptive sliding mode control [18] and artificial neural network methods [19] help in improving the controller tuning and subsequently its performance.
After, an appropriate controller is sorted out; its gain parameters are tuned using advanced optimization techniques.A quest for newer and better optimization techniques is becoming an emerging field for the researches.Number of optimization algorithm is utilized for the frequency and tie-line power transfer management in MμS.Some of the present day intelligent algorithms developed are Modified sine cosine algorithm (MSCA) [20], Grasshopper algorithmic technique (GOA) [21] and Modified salp swarm algorithm (MSSA) [22] [25] and Equilibrium optimizer (EO) [6] in 2020 and 2019 respectively.The present work includes optimization algorithm namely Bald eagle search optimization (BESO) [24,28], Black widow optimizer algorithm (BWOA) [30], Giza pyramid construction (GPC) [29], Teaching learning based optimization (TLBO) [32] and Genetic algorithm (GA) [31].These algorithms are employed to adjust PID, PIDN, TIDF II and TI-TDF.The main benefits of algorithm optimization are accurate, rapid convergence rate and preventing local optimum solutions for the micro-grid clusters.Also, BESO is not being used to control load frequency in DS-SG/Micro-Hydro/Wind/Tidal/ Biogas Based Renewable Micro-grid Cluster with tilt order control.The major focus of this paper is made to select best optimization algorithm for the proposed controller with minimum objective function in the two area renewable energy micro-grid cluster.The remaining portion of the paper is organized as follows.The whole configuration description of the proposed system is provided in section 2. Moving further, controller design scheme and selection of objective function is elaborated in section 3. Also, section 4 gives details of the steps of the algorithms utilized to tune the controller parameter.After, this time based evaluation and result analysis is covered in section 5 and 6 respectively.Lastly, section 7 explains the conclusion and there after references.

Dish Stirling solar generating unit (DS-SG)
DS-SG is an electrical energy producing unit which comprises up of a concave parabolic dish, cavity receiver and stirling heat engine with generating unit.The solar dish rotates in such a direction so as to throw back the optimal amount of sun ray to the receiver.This results in increasing the temperature of receiver as well as engine.The piston attached to engine converts the energy of working gas such as hydrogen or helium into electrical energy.The description of DS-SG transfer function is given in equation (1), where, K DS-SG , T DS-SG is DS-SG valve gain and valve time constant whose values are 1 and 5 respectively.Micro hydro unit generates the electrical energy from the kinetic flow of the water.The standard power generated from MHT is of 5-100 KW capacity [35].The linearized MHT transfer function description is given in equation ( 2), where, K MHT , T MHT , K PH , T PH , T W are MHT governor gain and time constant, penstock gain and time constant, turbine time constant whose values are 0.5, 0.2, 5, 28.75 and 1 respectively.

Energy storage devices area 1-flywheel energy storage devices (FESD)
In case of malfunctioning of generating sources, energy storage devices are connected in the system as a secondary energy producing unit.In the present work, flywheel is interconnected in area 1 of microgrid.The linearized mathematical description of function FESD is expressed as in equation (3), where, T C , T CM , T DM are flywheel converter time constant , command measurement time constant and delay measurement time constant whose values are 0.1, 0.001 and 0.1 respectively.

Wind turbine generating unit (WT)
The generating power from wind plants is considered one of the fully grown and promptly developing renewable energy sources [14].The mechanical power derived from WT i.e.P MWT can be articulated as equation ( 4), where, C P is turbine power conversion coefficient of WT which is the function of tip to speed ratio λ and pitch angle β, ρ is air density in kg per cubic meter, A B is blade swept area in meter square and ν is wind speed in meter per second.The key factor in deciding the amount of mechanical power is wind speed which is summation of base wind speed, gust wind speed, ramp wind speed and noisy wind speed.The transfer function for the WT is expressed as equation ( 5), where, K WT , T WT are WT gain and time constant whose values are 1, 1.5 respectively.
2.5 Tidal generating unit (TG) An on-seashore TG is an upcoming renewable energy source.Its working principle and control techniques are identical to WT [37].The mechanical output from TG i.e.P MTG can be presented as equation ( 6), where, ρ W is water density in kg per cubic meter, r is the turbine blade radius, ν T is tidal speed in meter per second, C TG is turbine power conversion coefficient, Φ is tip to speed ratio and β is the pitch angle.The transfer function of TG is as follows, equation (7), where, K TG , T TG are TG gain and time constant whose values are 1, 0.08 respectively.
2.6 Energy storage devices area 2 -battery energy storage devices (BESD) BESD is a type of ESD which stores electrical energy in the form of chemical energy.It confers the reserved energy to minimize the mismatch in power generation and load demand [36].Thus, act as assistance to the prime generating sources at the time of necessity.The linearized transfer function of BESD is indicated in equation (8), where, T C , T CM , T DM are flywheel converter time constant, command measurement time constant and delay measurement time constant whose values are 0.1, 0.001 and 0.1 respectively.
2.7 Biogas turbine generating unit (BgT) BgT is the renewable bio-degradable energy source which utilizes human and animal wastes.The anaerobic fermentation of bio-degradable wastes results in the production of biogas.These produced biogas mainly consist of carbon dioxide, methane, hydrogen sulphide, siloxanes and moistures.The oxidation of biogas ingredients releases heat and energy which can be utilized as fuel in BgT [38,39].The major components of BgT are fuel system and combustor, valve actuator, speed governor and turbine.The output power from BgT is proportional to the input fuel valve so, the transfer function of the BgT can be approximated as equation (9), where, X C , Y C , b B , T CR , T BG and T BT are Lead time.Lag time, valve actuator, combustion reaction time constant, biogas time constant and turbine time constant whose values are 0.6, 1, 0.05, 0.01, 0.23, and 0.2 respectively.

( )( )
2.8 Super Magnetic Energy Storage Device (SMESD) SMESD is a super fastly acting energy storage device connected in the system.It is made up of superconducting inductor storing energy in the form of magnetic energy [40].Compared to other ESD, it supports to damp out the system deviation quickly.The mathematical description of SMESD is given by equation (10), where, T S1 , T S2 , T S3 , T S4 , K SMESD , T SMESD are time constant of device compensator, SMESD's gain and time constant whose values are 0.121, 0.8, 0.011, 0.148, 0.297, 0.03 respectively.
2.9 System dynamic load (SDL) The mismatch in overall power generated and gross load requirement leads to fluctuation in frequency and tie-line power transfer [41].The power balance equations of two area proposed system is given by equation ( 11) and ( 12) respectively.ΔP =ΔP +ΔP +ΔP ±ΔP ±ΔP -ΔP -ΔP (12) where, ΔP G1 , ΔP s, ΔP MT, ΔP BG, ΔP FS , ΔP SM1, ΔP L1, ΔP 12, ΔP G2 , ΔP W, ΔP T, ΔP SM2, ΔP L2, ΔP 21 are power generated in area 1, power generated from DS-SG, power generated from MHT, power generated from BgT, power stored in FESD, power stored in SMESD in area 1, load demand in area 1, tie-line power transferin area 1 and 2, power generated in area 2, power generated from WT, power generated from TG, power stored in BESD, power stored in SMESD in area 2, load demand in area 2, tie-line power transferin area 2 and 1 respectively.The comprehensive transfer function of the rotating mass dynamics i.e.G RMD can be expressed as equation (13), where, D, M are Damping factor and inertia constant whose values are 0.012, 0.2 respectively.

Sensitive load (SL)
In both the area, SL is a step changing load whose magnitude is taken as 0.04 pu for 0 to 100 seconds and increases from 0.04 to 0.05 pu at 100 seconds.It remains at 0.05 pu for the rest of the simulation period of 200 seconds.

Controller design scheme
The controller employed in order to optimize DS-SG/MHT/WT/TG/Biogas based two area renewable energy micro-grid cluster are PID, PIDN, TIDF II [28] and TI-TDF [35].The proposed main controller TI-TDF is a 7 variable controller whose transfer is given by equation ( 14), The mathematical description of other aforementioned controllers is tabulated in table 1.The section is dedicated to select an appropriate, well organized and efficient controller strategy.This will result in stabilization of the frequency and tie-line transfer power limit within the prescribed range.The controller parameters are tuned with BESO, BWOA, GPC, TLBO and GA within the constraints of objective function, upper and lower bounds.The values of the parameter with the corresponding lower-upper boundary conditions for PID, PIDN, TIDF II and TI-TDF thus obtained is provided in table 2, table 3, table 4 and table 5 respectively.
The performance of these controllers after tuning is evaluated with the objective function formulation.The appropriate selection of objective function is very much necessary for minimizing the transient and steady state response of the system.The objective function family consists up of integral square error (ISE), integral time square error (ITSE), internal absolute error (IAE) and integral time absolute error (ITAE).Table 6 depicts the comparison of controller with regard to predefined objective functions.It has been noted from table 6, that all the controller shows minimum error for ISE.Also, among the controller TI-TDF gives minimal error for ISE objective functions.Thus, the system stabilization with BESO based TI-TDF controller gives improved results than other controller-algorithm combinations.where, the constants are defined as a ∈ [5,10] dictates the corner between search points, R θ(i)=a*π*rand , r(i)=θ(i)+R*rand , ( ) * * i a rand θ π = and ( ) ( ) . Also, some factors are calculated by and 1 r(i)*sinh(q(i)) x (i)= max( r(i)*sinh(q(i)) ) .
It is necessary to have a proper selection of controller tuning algorithms to provide efficient, fast parameter calculating and less time consuming optimization procedure.The proposed renewable energy system is stabilized in two area micro-grid cluster with BESO [28], BWOA [30], GPC [29], TLBO [32] and GA [31].The convergence curve of the mentioned algorithm obtained with 5 search agent and maximum iteration of 100 is provided by figure 2.
Table 7. Algorithms parameters The essential parameters, maximum iteration, population size and simulation time period utilized for optimization are outlined in Table 7.It has been observed from Fig 2 .that the execution of BESO is step ahead from other optimization algorithms.Moreover, different case studies that have been implemented with the help of BESO optimization approach also justifies the superiority of BESO.An effort is made to analyse the various cases that may arise in different situations in the system and explained in this section.In normal cases, all the generating sources like DS-SG, MHT, BgT of area1 and WT, TG, BgT of area 2 are perfectly working and supplying adequate power to the system dynamic as well as sensitive load.Fig 3 and 4 plots power from DS-SG as P S , MHT as P MT , BgT as P BG , WT as P W , TG as P T , FESD as P FS , BESD as P BS , SMESD as P SM , DL as P L , frequency variations i.e. f 1 and f 2 and tie-line power P 12 response for area 1 and area 2 respectively.Initially, for area1, when generating units are about to generate power and taking as SDL = 0.04 pu till 100 seconds.All the required power is given by FESD and SMESD till the BgT starts to supply the load.It results in initial downward transients in the frequency and tie-line power response which varies around zero after sometime as shown in Fig 3.
Later on, when P S is fluctuating around 0.05 pu thus supply the SDL and P BG , P FS , P SM reduces to zero till 100 seconds.The frequency and tie-line power transferresponse just vary around zero.At 100 seconds, when there is sudden rise in SDL from 0.04 pu to 0.05 pu, there is a mismatch in generation and demand.To minimize this mismatch storage devices and BgT supplies the remaining required power requirement.Furthermore, after 120 seconds when SDL is the same but P S is decreasing, the P BG gradually increases to meet the load demand till the end of 200 seconds as in Fig 6.
Similarly, for area 2, P W and P T are gradually increased during 0 to 50 seconds.SDL is 0.04 pu during this phase, so BESD, SMESD and BgT are providing power to the SDL.Later on, during the peak generation period, P BS , P , P BG reduces to zero and all the power requirement is provided by combination of P and P T .After 100 seconds, there is increase in SDL, decrease in W , P T , so BgT provides the required power.The f 2 shows an initial dip in the initial phase after that it varies around zero for the rest of the simulation period as shown in Fig 4.  The improper functioning of DS-SG and WT occurs at night and due to non-availability of wind respectively.Also, abnormality in hydrological cycle can lead to non-functioning of MHT and TG.The system response in such situation is depicted in Fig 7 and 8.The increase in SDL is endowed by ESD initially and later on energy is solely provided by BgT in both the area.The dip in frequency observed during increase in DL which is under permissible limits and settle down after few cycles.Case 4: Presence of all sources with random load changing This last situation is considered to the sensitivity of the system towards the random changing load.It will give us information about the robustness of the controller towards the changing disturbance of the system.In this condition, all the generating sources are available in both the areas.The major difference between case 1 and case 4 is that the DL is step changing load in former whereas in later, the SDL is a random changing pattern which is shown in Fig 9 and 10.The power demanded by load is mainly supplied by DS-SG (for area 1) and WT (area 2).The unused excess power generated is stored in the ESD which is used during peak load demand.It has also been observed from frequency and tieline power transferresponse settles down quickly in both areas due to robust nature of the controller.

Result analysis
The DS-SG/MHT/WT/TG/biogas turbine based two area renewable energy micro-grid system is executed in MATLAB 2016 software for a 200 seconds simulation time period.The system is stabilized using PID, PIDN, TIDF-II and TI-TDF.The parameters of these controllers are optimized with BESO, BWOA, GPC, TLBO and GA with the five number of search agent and 100 as maximum iteration.The lower bound constraints for tuning the controller are 0 for all the controller parameters whereas upper bound is 1 for tilt parameter and 300 for the remaining.Following observations were made for the system regarding its performance -  8, that the minimum in frequency profile for the system is given by BESO tuned TI-TDF controller.Also, the maximum and minimum shoot for BESO tuned TI-TDF in frequency profile is 4.467 x10 -2 and 1.142 x10 -2 respectively.(v) The minimal shoot in tie-line power transfer for the system is given by BESO tuned TI-TDF controller as supported by figure 10(c) and table 8. Also, the maximum and minimum shoot for BESO tuned TI-TDF in tie-line power profile is 2.137 x10 -3 and 5.687 x10 -4 respectively.

Conclusion
The paper studies the collaborative load frequency regulation in two area micro-grid systems consisting up of DS-SG, MHT, WT, TG and BgT as the renewable energy generators.Also, FESD, BESD, and SMESD are included in the proposed system as energy storage devices.Initially, efforts have been made to select the superior algorithm from convergence curve.Next step is to determine effective control strategy and its parameter is tuned with BESO, BWOA, GPC, TLBO and GA.From different case studies and study of system frequency as well as tie-line power profile, it is has been concluded that BESO tuned TI-TDF controller is superior to other controllers.This work can be further on extended to employment of weighted objective function, incorporation of communication time delays, generation rate constraints and generation band constraints with recent controllers and algorithms combinations to the previous works.

Fig 1 .
Fig 1.Schematic diagram of proposed two area system 2.2 Micro hydro turbine generating unit (MHT)Micro hydro unit generates the electrical energy from the kinetic flow of the water.The standard power generated from MHT is of 5-100 KW capacity[35].The linearized MHT transfer function description is given in equation (2), where, K MHT , T MHT , K PH , T PH , T W are MHT governor gain and time constant, penstock gain and time constant, turbine time constant whose values are 0.5, 0.2, 5, 28.75 and 1 respectively.

Fig 2 .
Fig 2. Comparison of convergence curve of BESO, BWOA, GPC, TLBO and GA algorithm.5. Case studies Case 1: Normal conditionAn effort is made to analyse the various cases that may arise in different situations in the system and explained in this section.In normal cases, all the generating sources like DS-SG, MHT, BgT of area1 and WT, TG, BgT of area 2 are perfectly working and supplying adequate power to the system dynamic as well as sensitive load.Fig3 and 4plots power from DS-SG as P S , MHT as P MT , BgT as P BG , WT as P W , TG as P T , FESD as P FS , BESD as P BS , SMESD as P SM , DL as P L , frequency variations i.e. f 1 and f 2 and tie-line power P 12 response for area 1 and area 2 respectively.Initially, for area1, when generating units are about to generate power and taking as SDL = 0.04 pu till 100 seconds.All the required power is given by FESD and SMESD till the BgT starts to supply the load.It results in initial downward transients in the frequency and tie-line power response which varies around zero after sometime as shown in Fig3.Later on, when P S is fluctuating around 0.05 pu thus supply the SDL and P BG , P FS , P SM reduces to zero till 100 seconds.The frequency and tie-line power transferresponse just vary around zero.At 100 seconds, when there is sudden rise in SDL from 0.04 pu to 0.05 pu, there is a mismatch in generation and demand.To minimize this mismatch storage devices and BgT supplies the remaining required power requirement.Furthermore, after 120 seconds when SDL is the same but P S is decreasing, the P BG gradually increases to meet the load demand till the end of 200 seconds as in Fig6.Similarly, for area 2, P W and P T are gradually increased during 0 to 50 seconds.SDL is 0.04 pu during this phase, so BESD, SMESD and BgT are providing power to the SDL.Later on, during the peak generation period, P BS , P , P BG reduces to zero and all the power requirement is provided by combination of P and P T .After 100 seconds, there is increase in SDL, decrease in W , P T , so BgT provides the required power.The f 2 shows an initial dip in the initial phase after that it varies around zero for the rest of the simulation period as shown inFig 4.

Fig 3 . 1 Fig 4 . 2 Case 2 :
Fig 3. Response of change in input power generation, load, frequency and tie-line power transfer for area 1

Fig 5 . 1 Fig 6 . 2 Case 3 :
Fig 5. Response of change in input power generation, load, frequency and tie-line power transfer for area 1

Fig 7 . 1 Fig 8 .
Fig 7. Response of change in input power generation, load, frequency and tie-line power transfer for area 1

Fig 9 . 1 Fig 10 .
Fig 9. Response of change in input power generation, load, frequency and tie-line power transfer for area 1 (a) Frequency profile area 1 (b) Frequency profile area 2 (c) Tie-line power transfer profile Fig 11.Micro-grid cluster profile of BESO tuned PID, PIDN, TIDF II and TI-TDF controller in proposed system (i) Table 6 showing comparison of objective function with BESO, it has been noted that the maximum error in objective function is 39.89 for PIDN with ITAE and minimum is 0.001520 for TI-TDF with ISE.Moreover, ISE is showing minimal value of error for all the controller among the family of objective function.(ii) The superior controller is selected based on the minimum error in steady state and transient parameters as depicted in table 2, 3, 4, 5 and 8. So, it is concluded that TI-TDF when tuned with BESO gives superior performance compared to other proposed controllers.(iii) The algorithm's convergence curve as well as from frequency and tie-line power profile as per figure 10 helps in deciding the efficient and less time consuming algorithm for the controller.It is observed that proposed algorithm is providing best result in all the proposed controller.(iv) It has been observed from figure 11(a) & (b) and table

Table 1 .
Proposed controllers mathematical description

Table 2 .
PID controller tuned gain and J ISE

Table 6 .
Analysis of objective functions for proposed controller tuned with BESO Bald Eagle Search optimisation Algorithm abbreviated as BESO is an advanced algorithm developed by H. A. Alsattar et al in 2019.This meta heuristic algorithm is a based on the natural hunting methodology of raptor Bald eagle.The entire hunting techniques of the eagle can be classified into three parts which includes locating appropriate space full of food in the nearby area, searching for best swooping for particular prey by spirally above in the sky and lastly, accelerating towards the prey from best location.The detailed steps and equations involved for the BESO algorithm are as follows -

Table 8 .
Comparison of transient parameters of frequency and tie-line power transfer