A Fractional Order Tilt Integral Controller Based Load Frequency Control with Dispersed Generation and Electric Vehicle

Fractional


░ 1. INTRODUCTION
The fundamental goal of electrical power system is to maintain the balance between total power output and total demand including losses.It is the responsibility of auxiliary controller to control the load Frequency depending on optimal value to assure the trait of the power supply [1][2].This process of stabilizing the frequency is called load frequency control.According to [3][4] it is the most significant control challenge in power system design & operation.Authors in [3][4] also discussed that the role of LFC is to maintain zero steady state error for frequency, reducing the number of unplanned power transfers between adjacent control zones, maintaining solid handle on load needs and disruptions, minimizing overshoot and settling time on interconnecting power frequency.
Global attention has been drawn to environmental issues such as increasing carbon emissions due to fast growth of economy, carbon dioxide emission are caused by the burning of fossil fuels for generating power.For carbon free power generation huge intermittent non-conventional energy is already being incorporated into power system networks globally [5][6].Over time, the usage of green energy has become more wide spread as a means of reducing the energy shortages.In recent years, advancement in technology has allowed wind forms to create more electrical energy.When it comes to generating electricity for its customers, power industry is investing more on wind power.Wind mills are now being integrated in to the actual power system in order to extend grid connectivity.However due to frequency variations, the wind mills connected to current electricity grid gives certain problems.The major concerns in operating wind power plants are issues in MPPT, synchronizing problems, complexity in parameter calculation [7][8][9].Grid integrated wind mills must meet the same LFC requirements as traditional power stations under any circumstances.There are several research gaps devoted to the combination of wind and thermal power in hybrid power system [10].
In present situation, the number of EVs has steadily increased and they have become a significant burden on the power grid, which cannot be neglected.It is known that EVs and the power grid encounter in a complex way, for example in [11,12] the design of EV and their involvement in frequency control is discussed.The addition advantage obtained by deploying V2G application is economical by enabling bidirectional power flow [11].Increasing in uncertainty in load demands and incorporation of dispersed power sources causing huge frequency variations in the system.This laid the researches to concentrate on putting EVs to regulate the frequency [13][14] However wind mills & EVs interconnection to grid is suffering from major problems like, frequency instability due to low inertia system and dynamic charging discharging of electric vehicles.Traditionally the normal LFC system is also suffering from non-linearity, load disturbances, mismatch uncertainty.
The control approaches have been utilized for LFC discussed in [15][16][17][18] lacking from system parameters uncertainty is becoming more and more prevalent.Power system models are estimated as linear models around an operational point in traditional LFC design, without addressing generator dynamics.For years, PID control has been widely used as a general frequency control approach.A simple design and implementation of PID controller [19][20][21] makes easy to use, but the performance of their controllers are efficient under fixed power system parameters, but when the system parameters changes then such traditional controllers will fail to trace the output.
Under these situations it is important to implement the controllers which are tenacious and adaptable [22][23].A fraction order controller is therefore a new idea where the basic principle in this control structure is to expand integer order terms of integration which is differentiating the fractional order operator.So, these control law has more degrees of freedom when compared with integral order control.Hence, fractional controller can achieve good performance in perspective of low settle seek and %Mp than IOC.In [24][25] FOC is implemented but direct implementation of FOC is not straight forward and it is also evident that selection of  is much sensitive and sometime under dynamic situation it leads to instability.This problem can be solved using a sliding mode control (SMC) method.We choose it as a result of its ability to withstand load disruptions and parameter changes.The criteria described in [26][27] were used to build the SMC scheme for LFC in interconnected power system.However, in order to remove the matching external disruption signal, the sliding mode control will come across chattering problem which is not addressed in above literature.The linear model of two area system with EVs and wind power plant is presented in paper.This paper presents a new fractional order tilt integral control of LFC for multi area system.This controller has benefits of TID and FOPID.The results obtained from FOTID are compared with PID, FOPID and SMC controllers in terms of Settling time, peak overshoot, number of peaks, the final results have proved the effectiveness and sensitivity of controller gains towards parameter variations.

░ 2. CONFIGURATION OF PROPOSED SYSTEM
The above figure 1 shows the abridged model of grid connected system which consist of conventional thermal power plant dispersed generation like wind power plant, EVs and stepped loads.In conventional power grids the frequency control mainly depends on equivalence between power generated and demand.In case any imbalance occurs the control of frequency can be done in three different ways first one is primary control in which frequency control achieved by various speed regulation constant.In secondary control an auxiliary controllers is employed to stabilize the frequency, finally in inertia control the inertia offered by synchronous generator will take care of speed according to change in power demand [28].This explains us clearly that the dispersed generating systems which involve in regular grid connected system must have inertia, so from figure 1 the EVs which involving in the system is accompanied with inertia.

░ 3. SMALL SIGNAL MODELING INVESTIGATED SYSTEM
The power system under consideration in this article is a multiarea linked network with conventional TPP, a wind turbine generator and inertia based electric vehicle in both the areas.A tie-line connects both the locations for power exchange.

Modeling of Electric Vehicle
In conventional power system frequency control is based on the balance between generated power and load.Where as in the event of frequency variation caused by a power imbalance the alternators automatically accelerate/decelerate in line with the actual frequency.In simple words the kinetic energy (KE) stored in rotational mass of alternator will regulating the imbalanced power between generation load and so maintain frequency within the limits through this action.However, in current electric grids, inclusion of dispersed generating systems can considerably reduce the total system inertia owing to lack of rotating mass [29].The stability and dependability will be jeopardized when inertia decreases.
By investigating the inertia-based power response in traditional systems which are generally accommodated by KE of rotating mass.The KE of rotating mass and rotating load is represented as (2) From the dynamics of rotor of generator, the inertia constant (H) defined as ratio of KE to base power [30] Where Sb = base complex power The behavior of rotor of alternator can be easily explained by swing equation From equation ( 4) it is evident that the inertia power mainly depends on the time derivative of frequency [31].As a result to mimic the inertia in RES the first derivative of frequency must be estimated.This concept of derivative of frequency will emulate a change in overall inertia, eventually it will stabilize the frequency in low inertia system.Mathematically it can be represented as Where Hev and Dev are EV inertia and damping constant.

Figure 3: Block Diagram of EV Model
Figure 3 shows EV mode with inertia, however the major concern is with the frequency measuring devices which will create noise while measuring hence a low pass filter is deployed to minimize the effect of noise then,

Modeling of Wind Turbine
Mathematically the power generated from wind turbine generator is given as [32]   =  3      However, the power coefficient of rotor blades is complete dependent of pitch angle C, and tip speed ration , mathematically it can be expressed as  [33] As per swing equation we can write If Ta -Tg = C then equation ( 17) can be written as  =     ̈+     ̇+     (13) The transfer function of wind turbine system can be given as In this paper generate time constant (Tg) is considered as constant than Pw = Tgr so the output power can be controlled by wind speed (b)

Mathematical Model of Fractional Order Control
It is essential to know the fractional order calculus prior to define the FOPID controller.Those certain operators' mathematical information is available here included in [34][35][36].
Introduction to obtain FO calculus is described below.To consummate control of MFGII with help of fractional integral sliding surface FSMC is designated later.

Mathematical model of TID Controller
The TID controller's tilt component is derived from noninteger order calculus, whereas the FOPID controller's integral and derivative terms are derived from non -integer order operators.FOPID and TID controllers have high amounts of flexibility than IOCs.As a result, they can increase the effectiveness of control systems which are linked with a broad range of dynamics.In this two-region, there is one Tilted integral derivative controller per area (TID).When running in a wide range of conditions, a traditional PID controller with fixed gains will fail [37][38][39].As a result, researchers consider using a TID controller to improve a system's performance standards.TID's proportional element is replaced by a Tilted element, which is identical with that of a Conventional PID controller.Tilted components are represented using Fractional Integrators, such as 1/s (1/n) for example.This controller differs from others in that it has a simple design approach and can be tuned quickly and easily.

░ 4. FOTID CONTROLLER GAIN CALCULATION USING INTEGRAL ERROR METHOD
The control design of FOPID controller using integral error method is explained.The main objective is to calculate controller gains like kP, kI,  and  at constant kD.This work uses non-reheat turbine of first order is used and the gains used are kp = kI = kD Tg, TI, TL, R. The Controller transfer function c(s) is given as Now the characteristic equations are given by 1+G(s)C(s) = 0 The system will converge when the roots of eq. ( 23) lies on the left half of s-plane.But the roots calculated from eq. ( 23) will has real roots and complex roots.However, a boundary can be formed after calculation, but system will converge only if real boundary intersects with complex boundary RB = R(s, kp, kI, kD, ,) = 0 for   (0,),CB = R(s, kp, kI, kD, ,) = 0 for u  (0, ).To get real boundary (RB) sub s = 0 then kI = 0 and to obtain complex boundary (CB) sub s = j To obtain the value of kp, ki & kD it is required to assume kD any arbitrary value and then solve eq.( 25) and eq.( 26) for boundaries  €(0,1), µ€(0,1).Here in this way we have fixed kd = 0.84 and then need to solve eq.( 25) and eq.( 26).These two equations are completely depending on the  & µ value so if , & µ is varied between (0-1) and  = (0 -) the curve kp Vs kI is called complex boundary.The intersection obtained from CB & RB is called global stability.For largest stability margin  & µ are varied between (0-1) to get many kp & kI values.The optimized values of kp = 2 kI = 3 are obtained at  = 0.005, µ = 0.8 which is done on the basis of integral area method () = 2 + 3  0.005 + 0.84 0.8

FOTID Controller Gain Calculation Using Integral Error Method
The control design of FOTID controller using integral error method is explained.The main objective is to calculate controller gain like kT, kI,  and  at constant kD is to be calculated.The stability investigation is done by using frequency response analysis is also carried out in this section.A linked two-area power system can be considered to investigate the dynamic effectiveness of the proposed controller with in AGC loop, Both the areas consist of TPP, wind farm, and Electric Vehicle.To investigate the efficiency of proposed controller the complete simulation studies are carried out for eight different cases and graphical results are presented for all the cases with tabulated Time domain specifications.The pursuance of envisaged controller is compared with PID, SMC and FOPID Controllers.The variable ambiguity is a key concern in today's sophisticated power systems.As a result, it is critical that the control technique used to regulate the LFC be resistant to the system's parameter uncertainties.The power system model is treated as an unpredictable system to examine the resilience of the controller, for this, a 50% minimum and maximum limit uncertainty in plant parameters is assumed, throughout the simulation a step load of 200MW disturbance is applied.Because the major goal of the LFC is to regulate frequency variations in the power system even though the system parameters are not consistent, this characteristic of the FOPID controller makes it extremely appropriate for the LFC.From the table-1 it is very much obvious that the settling time (Ts=7s) obtained for FOPID controller is far much less than the PID, SMC, FOPID controllers.From the table 1 it is evident that peak overshoot for positive and negative values obtained for FOTID (%Mp = 5.8, -1.9) controller are very less compared to other proposed controllers.This indicates the robustness of proposed FOTID controller.However, the number of peaks (Np = 2) obtained with proposed controller is less, which indicates the capability of FOTID Controller in damping the frequency oscillations.The RMS value obtained by using FOTID controller is optimal compared to other controllers.In this case the response of two area system with all controllers by considering the wind mill generating 24MW is presented.
The wind mill proposed is not a LFC based power generating system but it is involving in the frequency regulation.From the figures 8 & 9 it is also clear that the fluctuations obtained are very less with the FOTID controller compared to other controllers.In this case also the settling time offered is 11.1s which is minimum with respect to other controllers.The number of peaks obtained, peak over shoot and RMS value are also optimal in comparison with other controllers which is depicted in table-2.The sensitivity of FOTID controller towards uncertainties in parameters of power system is considered in this case.Specifically, the turbine constant Tt was considered as 0.4s in the regular model but to create perturbation the turbine time constant is increased by 50% of its original value.Theoretically when turbine time constant is increased then it will reflect in the speed of generator in thermal power plant which directly affects the system frequency, but the proposed robust FOTID controller gains are designed based on the integral error methods is effectively damping out the frequency oscillations, which can be observed from figures 12 & 13.From table -4 it is evident that the settling time, peak overshot and number of peaks are very less under ambiguity in turbine time constant, which can be also observed from the Table-IV

Figure 1 :
Figure 1: Configuration of proposed systemThe governing equation for frequency control in the i th area;

Figure 2 :
Figure 2: Small signal model of envisaged system 0167 − 0.44) − ( − 3).0184 (8) Where  =     b are speed of blade and R is radius of rotor The torque of wind turbine generator (HTG) is given as   =     Where,   =     =      3  (9) When Tw is applied the wind turbine wire revolve at the rate with b.Assuming that Tg & TL are the generator torques applied by gear box torque and load torques, the shaft of generator wire also revolve at r [34].There are few equations that are often used to describe turbine and generator dynamics   −   =     ̈+     ̇+     (10)   −   =     ̈+     ̇+     (11)     ̇=     ̇ Where J1 D & K are inertia constant damping constant & shaft stiffness facts and r, s indicates stator and rotor subscripts

16 )Figure 4 :Figure 4
Figure 4: Schematic diagram of FOPID Controller Figure 4 shows the block diagram of FOPID controller, where kI, kp, kD are the variable integral, proportional, and differential gains  and  are adjustable fractional order operators within the range of (0,1)

Figure 5 :Figure 5
Figure 5: Schematic diagram of FOTID Controller Here KP, KD, KI denote proportional gain, derivative gain, and integral gain, and n denotes a non-zero real number.Tilted element is registered in such a way that it imbues a frequency feedback gain that concocts itself in relation to the frequency of a traditional recompense unit.TID controller is now in transfer function model is written as

( 29 ) 3 𝐶Figure. 6 . 2 Figure 7 :
Figure. 6. Frequency deviation of Area-1 & Area-2 The results consist of Area-I & II frequency variations and Tie-Line power in pu.The case-I considers Two Area System without Wind power source and Electric Vehicle (Controlled and Uncontrolled Case with all Proposed Controllers) presented in the work.From figure 7 & 8 it is clearly observed that, using all controllers inside the AGC loop reduces variations in the frequency and tie-line power.Furthermore, within all controllers, the FOTID controller clearly outperforms the others in dampening the oscillations of all signals.Table 1 compares and lists the dynamic Indices of all signals and controllers, such as Settling time (TS), percentage Peak overshoot in positive and negative, Undershoot, Number of Peaks and RMS value of signal.

Case:Figure 8 : 9 :
Figure 8: Tie Line Power of two area system in pu, MW Figure 9: Frequency deviation of Area-1 & Area-2

░ 6 .
CONCLUSIONThe Drastic increase in load demand and subsequently involvement of distributed power sources like wind, solar power systems in to Conventional grid leads to lot of perturbation in load frequency.This work presents a LFC model which includes Electric vehicles and wind power plant.In this work Fractional order based tilt angle derivative controller is presented for two area system.Furthermore to evaluate the robustness of proposed controller the results are compared with other controllers like PID, SMC & FOPID in terms of settling time, %Mp, number of peaks, Undershoot and RMS value.The values obtained from different controllers are tabulated for easy comparison.From all the tabular data FOTID controller is giving noticeable performance under dynamic conditions.The sensitivity of controller towards parameter uncertainties like (Turbine time constant (Tt), Governor Time constant (Tg), and synchronizing power coefficient is also investigated with all controllers.Finally with clear observation FOTID controller is giving efficient performance with considered complicated model.

Table 3
This case presents two area system with wind mill and electric vehicle participating in the load frequency regulation.The EV model presented in this work is a virtual inertia based electric vehicle model where the virtual inertia is created based on the conventional TPP model.The results obtained in this case is shown in figure 10 & 11 are clearly indicating the good dynamic efficacy of FOTID controller in terms of time domain indices.Table-3 shows the complete details of all controllers from that we can justify that FOTID offers settling time, over shoot, number of peaks.In this case particularly FOPID controller also approaching similar response to the FOTID.