Rule-Based Adaptive Frequency Regulation With Real Stochastic Model Intermittency in a Restructured Power System

The increased deployment of renewable energy in power networks makes it necessary to maintain equilibrium between generation and demand due to their intermittent behavior. However, numerous strategies, including load shedding, load shifting, and energy storage technologies, can also be utilized to meet the increasing demand for load. This article proposes a course of action based on demand response (DR), which prioritizes demand-side monitoring, within the automatic generation control paradigm. A rule-based fractional control scheme with a two-degree-of-freedom topology is developed for the frequency regulation of a deregulated identical hybrid two-area power system in a DR framework. A quasi-oppositional Harris Hawks optimization is investigated along with the proposed controller to tune the controller coefficients adaptively. A thorough examination of the preferred system, including the DR approach, significantly enhances the frequency regulation services and offers a significant improvement over conventional frequency regulation in terms of system dynamics. Research is further enhanced by considering natural random time delay in the DR framework to analyze the dynamic behavior of the system. An experimental evaluation using the OPAL-RT 5700 is presented to verify the practicality of the suggested technique for intermittent sources and loads.

Abstract-The increased deployment of renewable energy in power networks makes it necessary to maintain equilibrium between generation and demand due to their intermittent behavior.However, numerous strategies, including load shedding, load shifting, and energy storage technologies, can also be utilized to meet the increasing demand for load.This article proposes a course of action based on demand response (DR), which prioritizes demand-side monitoring, within the automatic generation control paradigm.A rule-based fractional control scheme with a two-degree-of-freedom topology is developed for the frequency regulation of a deregulated identical hybrid twoarea power system in a DR framework.A quasi-oppositional Harris Hawks optimization is investigated along with the proposed controller to tune the controller coefficients adaptively.A thorough examination of the preferred system, including the DR approach, significantly enhances the frequency regulation services and offers a significant improvement over conventional frequency regulation in terms of system dynamics.Research is further enhanced by considering natural random time delay in the DR framework to analyze the dynamic behavior of the system.An experimental evaluation using the OPAL-RT 5700 is presented to verify the practicality of the suggested technique for intermittent sources and loads.
Index Terms-Communication delay, degree of freedom (DOF), demand response (DR), rule-based fuzzy logic control (FLC), two-area power system.

I. INTRODUCTION
T HE main goal of grid frequency regulation (FR) is to maintain a consistent nominal frequency and tie-line power transmission between nearby areas with varying loads.To ensure the stability of the power system, it is necessary to manage both the load demand and the generation capability.The conventional approach to meet load demand is to enhance generation, which is expensive and time consuming [1].However, the more intelligent approach is to reduce the peak demand, which is known as demand response (DR).DR emerged as an eminent strategy for the future grid in the automatic generation control (AGC) framework that emphasizes demand-side monitoring (DSM).The analysis of FR performance has become significantly more essential as a result of the restructuring of the power system [2] with the integration of renewable energy sources (RES) [3] and the DR framework.DR is a constructive strategy in the energy market that improves the stability of the power system [4] and also collectively reduces the spinning reserve capacity.The traditional frequency control technique may not be adequate in the future to maintain uniform frequency.Consequently, the implication of the DR mechanism is progressively gaining attention in contemporary power grids [5], providing operational benefits to utility systems with improved regulation.To stabilize the frequency in the future modernized grid, the conventional FR scheme must be improved with the DR framework [6] and intelligent control approaches for sustainable operation [7].
Different model-based FR control approaches, such as sliding-mode control, Smith predictor, and linear matrix inequalities, provide the best performance when the integrated power system model is precise and free from uncertainties [8], [9], [10].However, model-free controllers, such as fuzzy logic control (FLC) [11], [12] and fractional-order control (FOC) [13], have added advantages against the randomness of the load and RES for FR services in the hybrid power system.Frequency variations imposed due to load and generation discrepancies can be effectively minimized by employing FLC against deformities and uncertainties in the grid.During instances of nonlinear loads and small/large signal interruptions in a multimicrogrid, FLC in [14] provides enhanced performance.Several studies demonstrate the extensive use of FLC in the electric power industry to address a variety of issues, including FR analysis [15], [16].At the same time, FOC can be utilized to improve grid dynamics, as it offers a higher degree of freedom (DOF) for controller coefficient design than that of conventional integer-order controllers [17].In addition, it promotes increased flexibility in adjusting control parameters, ultimately resulting in resilient operational performance.As described in [18], an FOC can also be employed in the majority of FR schemes to regulate the power exchange between regions.As a result, an FOC-based fuzzy controller is introduced in [19] that adapts the control parameters according to the operating point to address the aforementioned problems.Collectively, the effectiveness of the one-DOF fuzzy fractional-order (FFO) controller for an islanded microgrid is demonstrated in [20] to improve system performance with minimal computation and complexity.However, the one-DOF FFO controller has limited capability in terms of tracking set points and removing exterior distortions.One DOF with an extra DOF, i.e., two DOFs, fulfills the requirements of control action with minimal computation and lesser complexity to handle nonlinearities and uncertainty in the system efficiently.The distinctive applications of the two-DOF FFO controller in permanent magnet synchronous linear motors [21], temperature management of biological reactions [22], and power system stability [23] enable the utilization of this approach in the power system to improve FR services as well as to participate in the solution of practical system uncertainties and disruptions.
Based on the existing literature, few articles have admirably implemented the DR concept in FR modeling to improve system performance [24] but have emphasized only conventional generating units.RES and the FR-DR framework are combined in some research work [25] but not to interpret the real-time load and the implications of RES.There has been no investigation of the robustness of the supplementary DR control technique for physical restrictions of the grid [10].Furthermore, it is essential to take into account the unpredictable communication latency with real-time load profile, intermittent behavior of RES, and system nonlinear constraints to accurately assess the realistic impact of DR on grid frequency stability in AGC.Therefore, the motivation for examining the impact of DR on frequency stabilization with the intermittent characteristic in real time of RES and loads is as follows: 1) to introduce a novel control scheme, the two-DOF fuzzy fractional-order proportional-integral tilt derivative (FFO-PI-TD), that optimizes both the transient and steady-state responses for robust and precise control performance; 2) to evaluate the impact of DR control on the transient characteristics of the power system, taking into account the intermittent nature of real-time load and RES; 3) to utilize the quasi-oppositional Harris Hawks optimization (QOHHO) technique to optimize the integral time absolute error (ITAE) performance index, thereby significantly enhancing the overall performance and stability of the controller and system.Through the aforementioned investigation, this article brings the following original major contributions.
1) A novel approach, which integrates DR into the AGC framework, is introduced in this article.This approach shifts the focus from traditional generation-side adjustments to DSM for effective FR.
2) The impact of DR control on the transient characteristics of the test power system is comprehensively analyzed in the study.The intermittent nature of the real-time load and RES is taken into account, providing a more thorough analysis.3) A unique fuzzy-logic-rule-based fractional control scheme is proposed for a two-DOF FFO-PI-TD controller as part of the solution.The transient and steady-state responses are optimized by this innovative control strategy, ensuring robust and precise control performance.4) The uncommon QOHHO technique is employed in the research to optimize the ITAE performance index.The overall performance of the controller and the stability of the system are significantly improved by this optimization approach.The rest of this article is organized as follows.The investigated test system modeling is developed in Section II-A.A suggested controller and an optimization method are provided in Section II-B, whereas the FR mechanism with DR steady-state error and stability evaluations are provided in Section II-C.Simulation and experimental result analysis is presented in Section III.Finally, Section IV concludes this article.

II. PROPOSED FR-DR STRATEGY
A two-area (region-1 and region-2) deregulated power system (DPS) is considered to implement the FR-DR strategy.For detailed analysis, the description of each system with appropriate modeling is provided in this section, along with a coordinated control approach.For such a control strategy, optimized coefficients and gains are necessary, which are covered by proposing an optimization technique with appropriate steady-state and stability analysis.Fig. 1 shows the DPS in a bilateral scenario, whereas Fig. 2 details its modeling by representing the momentary change in power and frequency information.

A. System Description and Modeling
Each area (r ∈ {r1, r2}, r1: region-1 and r2: region-2) of Fig. 1 has an installed capacity rated of 2000 MW, including RES such as parabolic trough solar thermal (PTST), wind turbines, and biogas plants with a generation rate constraint (GRC) of 20% each minute, i.e., 0.0033 p.u./s.However, the thermal plant has the governor dead band (GDB) (with Fourier coefficients 0.8 and −0.2/π), GRC of 0.0005 p.u./s, and boiler dynamics (BD) with a time delay of 0.1 s.The area control error (ACE) participation factor (APF) for thermal (α th,r ), biogas (α bg,r ), and PTST (α ptst,r ) is assumed to be 0.5, 0.3, and 0.2, respectively [2] to meet the constraint of α th,r + α bg,r + α ptst,r ≈ 1.As a result of multiplying the base load of 2000 MW by the APF, the installed rating of thermal, biogas, and PTST is 1000, 600, and 400 MW, respectively.At the same time, the optimal power transfer capability of a tie-line is considered to be 200 MW.Here, electric vehicles (EVs) are used as energy storage systems (ESSs) in both the areas to fuel and drain the power demand.
1) Generation Units: The modeling of the proposed FR scheme, mentioned in Fig. 2, requires individual system modeling, which is elaborated explicitly in the following.
Thermal plant: The linearized model of the thermal power plant of [2] is considered in this article, which comprises a governor and a reheat turbine model.As shown in Fig. 2, G th (s) (=u th /p th ) is the transfer function of the thermal power plant with input u th and change in power output pth .For a realistic evaluation of FR in the DPS, physical constraints, such as GRC of 3% per minute, GDB and BD are enforced in the thermal power unit.
Biogas power unit: The linearized modeling of this power plant is taken from [26], which contains the governor, input valve, fuel system, and turbine.The transfer function G bg (s) of the biogas power plant is the relationship between the input u bg and its fluctuated power output pbg , as mentioned in Fig. 2. Biodegradable waste from the agricultural sector and animal manure is used as combustible fuel for these power plants.
PTST power plant: A parabolic trough is a type of solar thermal collector that is straight in one dimension and parabolic in the other two.The PTST power plant makes use of the solar rays that arrive at a solar collector, which impels mirrors to focus the sunbeams on a receiver, and turns them into heat to generate steam.Later, the steam is converted to mechanical energy, which drives a turbine generator, producing useful electrical power.This power plant turbine with generating units can be modeled using [26].Now, the input signal u ptst and the fluctuated PTST power output pptst can be used to formulate the transfer function G ptst (s), as shown in Fig. 2.
Wind farm power generation: Wind power generation required wind turbines that convert the kinetic energy of the wind to electric energy.The confined mechanical output power of the wind turbine can be adequately modeled using [1].The transfer function G w (s) of the wind power plant can be obtained from the input signal u w and the fluctuated wind power output pw , as mentioned in Fig. 2.
EVs as ESSs: EVs are a potential choice for noncontracting electricity use with a charging and discharging capacity of 5-50 kW.EVs accommodate FR services if the state of charge (SoC) of the EV battery pack satisfies the required SoC level of 50-70% [27].The appropriate modeling of the EV transfer function G ev (s) and the change in the power output of the EV ( P max ev ) can be obtained from [28], where fr1 is the input to the EV control module.
2) Deregulated Scenario: In a deregulated market, Discos of any specific region can handle the available Gencos power either within the test region (unilateral agreement) or in some other areas (bilateral agreement).Consider y r ∈ {d1, d2} r as Disco units (d1: Disco-1 and d2: Disco-2) and x r ∈ {th,bg,ptst} r as Genco units (thermal, biogas, and PTST) for area r ∈ {r1, r2}.The contract participation factor (a x r y r ) is the demand contracted by the (y r )th Disco from the (x r )th Genco and represents the element of the Disco participation matrix (A) [2], which is used to visualize a Genco-Disco contract It should be noted that x r a x r y r = 1 should be fulfilled in A. Now, the contracted demand of the (x r )th Genco ( P g x r ) with Discos can be mathematically expressed as where P l y r is the net demand of the y r th Disco.For more clarity, the input (u x r ) to each Genco unit (x r ) of each area r ∈ {r1, r2} can be defined as where u c r represents the proposed controller output, which is detailed in the following subsection.It can be seen from the participation matrix A from (1) that the diagonal elements represent the unilateral agreement, while all the off-diagonal elements represent the bilateral agreement between interarea Gencos and Discos.This agreement can be achieved through the tie-line, and the scheduled tie-line power can be evaluated as [2] follows: Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where P l y r2 ←x r1 denotes the power demand of Discos existing in r2 from Gencos of r1, and P l y r1 ←x r2 is the power demand of Discos existing in r1 from Gencos of r2.Now, the tie-line power error can be derived as [2] follows: The tie-line power error decreases when the actual tie-line power ( P a tie ) approaches the scheduled power ( P s tie ) limit equilibrium.For the test regions r1 and r2, the relative ACE signal [28] can be calculated as follows: 6) where the bias coefficient B r has a value of 0.4312 p.u. MW/Hz with droop R r of 2.4 p.u. Hz/MW considering identical area.ξ r ∈ {ξ r1 , ξ r2 } represents the ACE signal, and B r ∈ {B r1 , B r2 } signifies biasing coefficient for region-1 and region-2, respectively.The coefficient α tie = −P cr1 /P cr2 is assigned for tie-line with P cr 1 and P cr 2 as the rated capacity of region-1 and region-2, respectively.

B. Proposed Control Scheme and Optimization
1) Principle of the Proposed Control Scheme: The proposed control system initiates its operation by calculating the ACE, which quantifies the discrepancy between actual and scheduled power in the power grid.The ACE is essentially a frequency bias term that signifies the difference between expected and actual system frequency and ties.The further utilization of ACE brings forth the principles of the proposed FFO-PI-TD control scheme with two DOFs.This control scheme can be explained stepwise as follows.
Step 1: The calculated ACE (ξ r ) and its derivative ( ξr ) are fed to an FLC to generate an output signal u f r , as shown in Fig. 3.A triangular membership function (μ(ξ)) is used in the fuzzification process for the input ξ ∈ {ξ r , ξr } where {μ a , μ b , μ c } are the coordinate points to evaluate the slope and intercept of μ(ξ).The Mamdani interface engine [11] is chosen for fuzzy action to make decisions based on rules provided in Fig. 3 (indigo color), where five fuzzy linguistic variables are negative large (NLG), negative small (NSL), zero (ZE), positive small (PSL), and positive large (PLG).After decision making, the defuzzification process is involved to generate the u f r signal using the centroid technique, given a continuous membership function μ(ξ) The capacity to tune the coefficients and its accuracy and greater disturbance rejection capabilities are all advantages of the proposed rule-based FLC technique.Some restrictions of the FLC may include a slightly longer optimization run time for the control parameters.
Step 2: In conventional one-DOF controllers, optimizing the disturbance response often compromises the set-point response, and vice versa.The extra DOF in two-DOF control systems enables swift disturbance rejection and improved set-point tracking, resulting in reduced overshoot in the dynamic response of the plant.Although integer-order control [29] improves certain performance metrics, FOCs, such as fractional-order proportional integral (FO-PI) controllers, are favored for their resiliency, better tuning capabilities, superior performance in noninteger order dynamics, and improved transient and steadystate responses in complex control systems.Taking advantage of the noninteger order of the Laplace variable, the fractional integral differential operator S f can be expressed as [30] as follows: Re(σ r ) = 0 s −σ r , Re(σ r ) < 0 (10) where σ r is a fractional-order term and Re(σ r ) denotes the real part of σ r .According to Caputo's definition of fractional-order calculus [30], σ r : n − 1 < σ r < n, where n ∈ Z + .However, in this article, the coefficient σ r is optimized between 0 and 1 for better system dynamic performance.For practical implication, a fifth-order Oustaloup filter [31] in a band-limited frequency range (10 −3 , 10 +3 ) can be used for effective fitting of FO components.The output of the FLC is forwarded to a two-DOF FO-PI controller.Combining the inherent adaptability of FLC and the mathematical robustness of FO-PI yields the rule-based fuzzy fractional-order proportional integral (FFO-PI) approach, providing a more precise and flexible control method.When paired with the two-DOF structure, this FFO-PI approach can handle even more diverse operating conditions and system uncertainties.The FFO-PI controller governs the "Plant," here referred to as Gencos from a specified area r.The control actions from the FFO-PI controller are used to adjust the power generation of these Gencos to ensure grid stability and power balance.
Step 3: Finally, the output of the plant, i.e., fr , is feedback to the control system through tilt derivative (TD), facilitating dynamic adjustments in response to system changes or disturbances.This feedback mechanism is a crucial part of maintaining system stability and achieving desired performance, making it an integral part of the control system.TD control can provide incomparable performance as a traditional proportional-derivative control scheme with the exception that the proportional gain k pr is substituted with k tr s −1/Φ r , where Φ r ( = 0) is a tilt coefficient preferably kept between 2 and 3 [1].TD offers simpler tuning, a higher disturbance rejection ratio, and minimal effects of fluctuations in plant parameters.Now, the proposed two-DOF FFO-PI-TD controller output u c r can be written as where w pr denotes the weight of gain k pr .The parameters k ir , k tr , k dr , and N fr are the integral gain, tilt gain, derivative gain, and first-order filter coefficient for region-r controller, respectively.The rule-based FLC output u f r with control signals ξ r and fr can provide an accurate model of the proposed controller as (12) and can be confirmed from Fig. 3 where G CE (s) and G CY (s) are the feedforward and feedback components of the two-DOF controller, respectively, and G CF (s) is the transfer function of the feedback TD controller, which can be defined as follows: The proposed FFO-PI-TD controller with two DOFs enhances robustness against disturbances and model uncertainties, provides adaptability to various linear and nonlinear control applications through fractional computations, and improves reference trajectory tracking, and due to its ease of implementation and minimal computational requirements, it is well suited for realtime control applications.
2) Problem Formulation for Constraints Optimization: To attain the optimal values for the controller coefficients, the main objective is to minimize the dynamics of the system over a time horizon, such as tie-line power error deviation ( Ptie ) and the frequency deviation ( fr1 and fr2 ) in regions r1 and r2.The objective function J ψ in the following equation considers the performance index ITAE to minimize the frequency deviation and tie-line power change with the proposed controller: subject to −0.1 ≤ fr1 , fr2 ≤ 0.  (14).
3) Optimization Algorithm: Through Harris Hawks optimization (HHO) [32], the possibility of local optima entrapment delays the convergence process.By enhancing population diversity through balanced exploration and exploitation, QOHHO leads to faster convergence to the best possible solution at a lower computational burden with precise scheduling tools.The QOHHO process involves the following steps.
Step 1: Define the search space (x q ijr ): Consider that i ∈ {1, 2, . . .i n } is the population number with the maximum number of populations i n , and j ∈ {1, 2, . . ., j n } denotes the position in the controller coefficient vector y jr with the maximum dimension (j n ) in a single iteration.Let X r be the position matrix of the entire population.The initial position and the current position of each opposite population y o ijr can be denoted as x * ijr and x o ijr , respectively.Now, using the opposition-based learning algorithm, the position x o ijr of the opposite population can be calculated as follows: where y l jr and y u jr denote the lower bound and upper bound of the population position x o ijr , respectively.In addition, the elements of the quasi-opposite population position matrix (x q ijr ) can be determined as follows: where λ(LB,UB) denotes the random number in [LB: lower bound, UB: upper bound].
Step 2: Initialize the population: A population of candidate solutions is initialized randomly within the defined search space x q ijr , i.e., x * ijr .Each candidate solution is a set of values for the proposed two-DOF FFO-PI-TD controller parameters y jr .
Step 3: Evaluate fitness: Each candidate solution is evaluated by simulating the response of the system to a given reference signal using the proposed two-DOF FFO-PI-TD controller with the corresponding parameter values.The fitness of each candidate solution is then calculated based on a performance metric, such as ITAE from (14).
Step 4: Update the position of the hawks: In the HHO algorithm, the position of the hawks represents the candidate solutions.The position of the hawks is updated based on the fitness of each candidate solution.The best solution becomes the leader, and the other hawks follow the leader by adjusting their position using the Harris Hawks' hunting mechanism.Here, the evaluation of x q ijr depends on the escaping energy (E p ) and the jumping strength (J p ) of the prey to move from one iteration to the next, which can be evaluated in terms of the initial energy E * p (=2λ(0, 1) − 1) of the prey as where the escaping energy of the prey E p is a linear decaying function until E p → 0 over time considering τ as the iteration number and τ n as the maximum number of iterations.λ(0, 1) → λ() denotes the random number between 0 and 1.Now, |E| ≥ 1 shows prey's exploration, whereas |E| < 1 signifies the exploitation of prey.|E| ≥ 0.5 and |E| < 0.5 denote the stage of soft besiege and hard besiege, respectively, with λ() ≥ 0.5, i.e., the chances of prey exploration.With |E| < 1, λ() < 0.5 denotes a soft/hard besiege with a hasty plunge.Now, the next hawk's position x q ijr (τ + 1) can be obtained as (18) using the current position x q ijr (τ ) of the hawks' population where x shows the random position of the prey, x λ is the arbitrarily chosen hawks' position, xq ijr (=x − x q ijr ) is the difference in position between the prey and the hawk, and x m describes the average position of the population of the hawks and can be denoted as Step 5: Repeat steps 3 and 4: The fitness of each candidate solution is reevaluated based on the updated position of the hawks.The position of the hawks is then updated again, and the process is repeated until a stopping criterion is met, such as a maximum number of iterations or a satisfactory fitness value.
Step 6: Select the optimal solution: Once the algorithm is converged, the best candidate solution corresponds to the optimal proposed two-DOF FFO-PI-TD controller parameter values y jr .

C. Stability Analysis and Steady-State Error
1) Demand Aggregator: In the power market, demand aggregators appear as mediators between the utility and the customers.Aggregators play a significant action in DR, ensuring the installation of communication and controlling devices (such as smart meters) at the consumer end.Each aggregator monitors a sort of specified load demand in the DR power market.Aggregators have eloquent functioning in DR, and they can negotiate with the customers productively and provide incentives on account of insignificant load shed.It would be admirable that/if aggregators are market players.
2) Distinctive Demand Controllers' Action Plan: When a region's frequency (f r ) drops underneath the critical frequency (f c r ), the controller deactivates trivial loads to prevent the frequency deviation from becoming too severe.If the frequency deviation (Δf r ) is monitored, the system is given a time delay (t d ) to safeguard the devices.The controller will turn ON the DR load again after t d has completed and the frequency f r exceeds the critical frequency f c r .The maximum frequency variations Δf max r and t d in both the regions are considered to be 0.5 Hz and 10 s in the studied system.
3) Assessing Dynamic Performance With DR: In the twoarea power system, the primary frequency regulation offers an inherent quick response.It is, however, poor at reducing frequency variation to zero at a steady state.Therefore, additional secondary regulation (SR) support is required for proper control operation [25].Fig. 2 illustrates the detailed modeling of the suggested FR scheme.A DR regulation loop has been introduced in the test setting to improve dynamic behavior [4].As a result, the impact of the DR control unit on system performance must be investigated in an equilibrium state.
When an area frequency (f r ∈ {f r1 , f r2 }) drops below the critical frequency (f c r ) of the area r, the controller deactivates insignificant loads to maintain the frequency deviation by introducing a time delay (t d ≈10 s) to safeguard the devices.The fifth-order communication latency can be modeled using Pade's approximation as follows [10]: where c 1 = 30240, c 2 = 15120, c 3 = 3360, c 4 = 420, and c 5 = 30 are the coefficients of the delay transfer function G r (s).
The control center specifies a frequency deviation (−0.1 ≤ fr ∈ { fr1 , fr2 } ≤ 0.5) limit, i.e., f max r = 0.5 Hz and f min r = −0.1 Hz.The amount of demand participating in DR (P d,r ) during such a period that can be turned OFF can be calculated as [10] where P max d,r denotes the maximum available load that participates in DR and is taken as 0.1 p.u., that is, 10% DR support.The tie-line coefficient for area r (ξ r ) needs to be optimized, while the DR frequency coefficient (j d,r ) can be calculated as Here, the value of j d,r is fixed due to the utilization of the maximum value of frequency deviation and participation of DR.From Fig. 2, the system frequency fluctuation in the rth region of a multiarea power system can be stated as where G p r (s) = (2H r s + D r ) −1 is the transfer function of the power system with inertia H r and damping D r .Furthermore, the tie-line power error Ptie (s) can be ruled out in terms of frequency deviation as where T tie is the tie-line synchronizing coefficient with value of 0.0866.With the sudden step load demand Pl,r (s) (= Pl,r /s), fr (s) can be further simplified as (25).With P e Θ,r (s) (= Pth,r (s) + Pbg,r (s) + Pptst,r (s) + Pw,r (s)) and its governor/turbine dynamics H Θ,r (s) (=H th,r (s) + H bg,r (s) Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
+ H ptst,r (s) + H w,r (s)), (23) can be further simplified to where ς r (s) = 2H r s + D r + R −1 r H Θ,r (s) is the denominator.The steady-state response of the system's frequency fluctuations can be derived using the final value theorem as The steady-state error for the dynamics stabilization of the rth region will never be nullified until the DR regulatory loop, SR, EV, and tie-line participation exist, as shown in (23).If power from an adjacent area is not needed, i.e., P tie = 0, no intervention from the EV, i.e.P ev = 0, and zero DR assistance at a steady point, then the steady-state error would retain a null value.Furthermore, SR will provide the required supervision to keep supply and consumption in balance.Therefore, the SR share ( P ss ε,r ) and DR participation ( P ss d,r ) control attempt (Ω) can be characterized as follows: P ss ε,r = δΩ and P ss d,r = (1 − δ)Ω (28) where the value of regulatory participation (δ) ranges from 0 to 1 and reflects the cooperation of the traditional regulatory operation.

4) Random Delay (RD) in the DR Framework:
In analyzing the stability and synthesis of a nonlinear multiarea power system, it is often possible to linearize the dynamics of the system frequency by making minor modifications when subjected to small changes in load.This allows us to focus on an equilibrium point for analysis purposes.The block diagram representation in Fig. 1 showcases a multiarea load frequency control (LFC) model incorporating RDs in the DR strategy.Fig. 2 depicts the significant contribution of DR reserves, represented as Pd,r , in the context of FR.In situations where there is a negative (or positive) frequency variation, it becomes necessary to deactivate (or activate) a share of the loads .As a result, the following power equilibrium equation within the frequency band provides the linearized LFC model incorporating DR: Pth,r + Pbg,r + Pptst,r + Pw,r ± Pev,r − Pl,r − Pd,r The received command signal enables swift adjustments to be made to the DR mechanism.The performance of the power grid's LFC is primarily affected by RD, which serves as the sole obstacle for effective implementation of DR [5].The sharing rate of DR, denoted as δ, is established by regional transmission organizations and independent system operators in accordance with real-time electricity market conditions.While analyzing an impact of RD in the DR framework for δ = 0.7, i.e., 30% DR regulation, a random waveform generator is employed to produce RD at each sampling instant with a sampling rate of 0.2 s, and a seed value of 1 is chosen for signal generation [11].The minimum and maximum bounds of the random signal are set to 0.01 and 0.3, respectively, representing the limits for the random signal.This article examines three distinct cases, each characterized by a performance cycle duration (T s ) falling within specific ranges: [0.01, 0.03] s, [0.01, 0.05] s, and [0.05, 0.3] s.

5) Impact Assessment of DR on Stability:
By performing a linear analysis with the proposed control algorithm, the stability of the two-area power system, shown in Fig. 1, is evaluated in a bilateral scenario.In this instance, two cases are considered to measure the relative stability of the test system.Initially, the system stability is analyzed for conventional frequency regulation (CFR), δ = 1 (no DR regulation), and then, for CFR with the DR framework, δ = 0.3.For the evaluation of the relative stability of the test system for CFR and CFR with DR regulation, stability analysis has been performed through the Bode diagram, the pole zero plot, and the Nyquist plot.Each of these plots offers distinctive insights into the stability of the system.The Bode diagrams shown in Fig. 4 prove to be effective in determining both the gain and phase margins (PMs).Meanwhile, the pole-zero plots in Fig. 5 illustrate the specific location of the poles in the complex plane.Finally, the Nyquist plots presented in Fig. 6 allow the determination of the number of encirclement of the (−1, j0) point in the plot.An infinite PM  was observed in both the cases, with a gain margin (GM) of 69.5 and 77.1 dB for δ = 1 and δ 0.3, respectively.As the GM and PM increase, the comparative stability of the system reflecting a more stable system.Figs.4-6 demonstrate the GM and PM of the system that increase significantly by accounting DR regulation in CFR to enhance the stability of the test power system.

A. Test System Description With the HIL Platform
In order to analyze the dynamics of the test system while taking into account the actual load profile and RES intermittency [33], a multiregion DPS is adopted as a test power system.The test system shown in Fig. 1 incorporates real-time RES power fluctuations and the actual load data profile of BSES Rajdhani Power Limited (BRPL), New Delhi, India.To make the study more realistic, physical constraints, such as GDB, GRC, and BD, are taken into account.The control area of the test system is divided into two regions, and each test region comprises three Gencos (thermal, biogas, and PTST) and two Discos.The capacity of each tested region is 2000 MW with a 50-Hz-rated frequency.The optimum power transfer proficiency of the tie-line is considered to be 200 MW.
The practical implementation and reliability of the proposed control scheme are evaluated through hardware-in-the-loop (HIL) analysis.Though the real-time digital simulator provides efficient HIL analysis, its high cost makes it less attractive.Conversely, the dSPACE MicroLabBox falls short in supporting high-fidelity models due to its low sampling rate and limited processing capabilities.To reconcile these issues, this article opts for HIL validation using the OPAL-RT 5700 platform, which encompasses both the digital signal processor and the field-programmable gate array processor, meeting our computational resource requirements.This platform operates on RT-LAB software, based on SimPowerSystems of MATLAB/Simulink, noted for its ability to advance model-based design in electric power systems [19].The real-time experimental framework for the test system is shown in Fig. 7. Investigations carried out considering bilateral transactions for different scenarios are illustrated in the following subsection.

B. Test Scenarios
The following five different test scenarios are investigated to establish the robustness of the proposed controller: 1) Scenario I: the dynamic response of the system during 1% step-load disturbance while RES fluctuation; 2) Scenario II: performance assessment during real-time intermittency in RES and load fluctuations; 3) Scenario III: the effect of various nonlinearities on the DPS dynamics; 4) Scenario IV: the robustness of the controller against parametric variations; 5) Scenario V: the assessment of marginal stochastic transmission delay in the DR framework.
Both regions r 1 and r 2 share 0.5% of the total disturbance of the region load of 1%, i.e., pl d = 0.005 p.u.According to (30), the power fluctuation in Genco is calculated and represented in Table I.Fig. 8 illustrates the dynamic response of the system with and without DR.Analysis shows that DR effectively improves FR services and system performance.The QOHHO-optimized designed controller coefficients are listed in Table II.In steady state, the scheduled tie-line power can be calculated from (4) as follows:   P a tie = P e tie + P s tie = 0.The theoretical value of P a tie can be calculated using (5), and its corresponding simulated response shown in Fig. 8(d).The theoretical power fluctuations of all Gencos are calculated in Table I, and its simulated response is shown in Fig. 9.Moreover, an improvement in the dynamics of the system with DR regulation is presented by a bar chart in Fig. 10.
2) Scenario II: This scenario evaluates the dynamic response of the DPS during the real-time in the of the RES power.The DPS dynamics shown in Fig. 11   wind farms in southeast Australia.In general, these data have a resolution of 5 min (288 samples for one day).Up to 10% of the total generation capacity in the region is scaled using power fluctuations from wind and solar power plants.Scaled data with a 5-min resolution to a 1-s resolution are employed to assess the proposed methodology.The transient behavior of the evaluated DPS model shown in Fig. 11(a)-(c) for various values of δ (0.3, 0.7, 0.9, and 1) shows that the better dynamics are characterized for δ = 0.3 with 0.7 DR regulation.
3) Scenario III: In this scenario, each physical constraint, such as GRC, GDB, and BD, is assessed separately to investigate their detrimental impact on the dynamics of the DPS.Moreover, generators are more prone to chase strong transient disturbances when there is a lack of GRC, which is not advantageous.As a result, the GRC must be taken into account as part of a comprehensive AGC evaluation.The ideal allowable GRC rates considered for the thermal unit and the biogas unit are 3% and 20%, respectively [2].The dead band of the thermal speed governor allows for a change in the position of the valve before the speed increases or decreases for a certain position of the governor control valves.The system response may be significantly affected by the dead band of the speed governor.As a limiting number for the dead band, 0.06% is adopted.In the presence of the dead band and GRC, since the system becomes extremely nonlinear even for minute changes in load, the optimal control problem becomes fairly difficult.Owing to the increased complexity of interconnected restructured power systems, BD and communication time delays have a major effect on AGC performance.In view of this consideration, the area control output signal is delayed by 0.1 s in each region.The consequences of each physical constraint on the test system are illustrated using Scenario I.The dynamic response significantly degrades when GDB, GRC, and BD are examined collectively for real-time analysis, and the inclusion of time delay makes the performance inferior.The variance assessed in the frequency response of r1 under various physical constraints is shown in Fig. 13.The optimal gain coefficients of the suggested controller using the suggested algorithm are shown in Table III for each case.
4) Scenario IV: Sensitivity analysis is carried out in this scenario to ensure that the suggested controller will remain functional, even though the DPS parameters and loading are severely varied in Scenario II.Furthermore, in an actual power system, factors such as damping coefficients (D) and the inertia constant (H) are difficult to accurately assess.As a result, it is assumed that D and H have a ±25% indeterminacy with respect to their rated values.For analysis, the DPS is evaluated against 25% variations in D and H taken separately one at a time for the 30% DR regulation support in r 1 with the δ = 0.7 and the 10% DR regulation support in r 2 with δ = 0.9.The evaluated Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.dynamic response of the DPS is shown in Fig. 14, which illustrates the durability of the recommended control algorithm with massive changes in the entity of the system.Observations reveal that the suggested controller operates steadily and is remarkably effective in varying system parameters with substantial fluctuations in the DPS.5) Scenario V: Typically, stochastic communication time delays are present in the DR process when establishing two-way communication between DR devices and the control center for activating DR signals.Consequently, to demonstrate the impact of these delays on system response, the dynamic performance of regional frequencies is analyzed.Fig. 15 illustrates the plotted results, utilizing the same dataset employed in Scenario II.
By analyzing the dynamic response, it is evident that the occurrences of dips/peaks in fr1 and fr2 are comparatively lower for stochastic random delay τ rd [0.01, 0.03] s indicated by the brown line, where 0.01 and 0.03 are the minimum and maximum ranges for the applied stochastic delay in a DR regulation, respectively.In contrast, a higher margin of τ rd [0.05, 0.3] s indicated by the green line leads to more pronounced deviations.This observation highlights the significant impact of communication time delay in the DR on system frequency response.Consequently, it becomes evident that a faster and more efficient communication infrastructure is essential to effectively aggregate and transmit real-time information between the control center and the smart meters installed on DR appliances.Such an infrastructure would enable a timely and accurate response to frequency fluctuations, ensuring the reliable operation of the power system.
Based on the analysis presented in Fig. 15, it is shown that the responses of fr1 and fr2 exhibit excellent performance in the case of CFR integrated with DR regulation and no transmission delays.However, as stochastic transmission delays are introduced, the responses of regional frequencies begin to deviate.Notably, the maximum deviation is observed within the range of τ rd = [0.05,0.3] s.Furthermore, if we expand the range of τ rd , the response would deteriorate, becoming worse than that of the CFR alone.Therefore, in the context of the test DPS, an analysis is conducted by considering a value of δ = 0.3, and it is determined that the marginal delay range for τ rd lies within [0.05, 0.3] s.

C. Comparative Analysis
This analysis evaluates the resilient performance of the proposed controller to changes in controller characteristics in the DPS under conditions of unrestricted RD in the DR regulation.It should be noted that Scenario II ignores an RD in the DR framework.From Fig. 11, it is clear that the suggested control algorithm responds better to the frequency and tie-line oscillations for δ = 0.3, considering 70% DR regulation.Therefore, in this case study, the characteristic of the proposed controller against unconfined RD in the DR loop with δ = 0.3 is assessed with the PI-TD [1], Fuzzy PI [25], FO-PI [29], and FO-PD [13] control methodology.While evaluating the comparative performance of the control algorithm, overshoots and undershoots are critical parameters to demonstrate the efficacy of controllers.Fig. 16 compares the effectiveness and adaptability of the proposed control scheme with the existing control strategies and shows that the proposed strategy performs better in terms of improving the secondary frequency control mechanism and is more resistant to the occurrence of RD oscillation than the other robust scheme in the DPS.

IV. CONCLUSION
This article delivered several original contributions, focusing primarily on integrating DR into AGC, transitioning from traditional generation adjustments to the DSM for efficient FR.It conducted a comprehensive analysis of DR control's impact on the test power system's transient characteristics, taking into account the intermittent nature of the real-time load and RES.A unique fuzzy-logic-rule-based fractional control scheme was proposed for a two-DOF FFO-PI-TD controller, optimizing both the transient and steady-state responses, which resulted in robust and precise control performance.The research employed the efficient QOHHO technique to enhance the ITAE performance index, significantly improving the controller's overall performance and system stability.As renewable energy became increasingly deployed in power networks, an effective approach was proposed to maintain the equilibrium between generation and demand.Natural random time delay within the DR framework was considered to further analyze the system's dynamic behavior.This article also provided an experimental evaluation using the OPAL-RT 5700 platform, affirming the practicality of the proposed technique for intermittent sources and loads.

1 )
Scenario I: In this scenario, a bilateral transaction framework is evaluated where the Discos have the freedom to make a power agreement with the Gencos of any test region for the dynamic response of the system.Each Disco is expected to have a step load demand of 0.005 p.u., and the bilateral agreement between Gencos and Discos can be represented, according to the Disco participation matrix (1), as follows:

Fig. 8 .
Fig. 8. Dynamic performances for Scenario I. (a) Frequency deviation in r 1 .(b) Frequency deviation in r 2 .(c) Deviation in tie-line power error.d) Deviation in actual tie-line power.
(a)-(c) corresponding to actual load fluctuation presented in Fig.However, the fluctuations of wind, photovoltaic, EV power in real time, and the SoC of EV are shown Fig. 12(a)-(d), respectively.In this the operational status of the test system is taken into account for FR with the DR framework in the event that there are variations in the load and RES-dependent generation.To determine the practicality of the suggested system, real-time load data are taken from the New Delhi State Load dispatch Center for dynamics evaluation.Solar and wind power fluctuation data are acquired from open data from IEEE and 22

Fig. 12 .
Fig. 12. Response based on power fluctuations in load, WP, and PV for distinct δ values.(a) Stochastic WP profile.(b) PV power variations.(c) Power change in EV response.(d) % SOC of EV in r 1 and r 2 .

Fig. 15 .
Fig. 15.DPS frequency response associated with different stochastic delays in the DR framework.(a) Frequency deviation in r 1 .(b) Frequency deviation in r 2 .

Fig. 16 .
Fig. 16.Comparative dynamic response of the test system with the real-time power fluctuations in WP, PV, and load disturbance.(a) Frequency deviation in r 1 .(b) Frequency deviation in r 2 .(c) Tie-line power fluctuation between r 1 and r 2 .(d) Random delay in the DR communication network.

Fig. 16
Fig.16illustrates the real-time HIL analysis of Scenario II with actual load and RES fluctuation to assess the effectiveness of the proposed control operation with random communication delay.It should be noted that Scenario II ignores an RD in the DR framework.From Fig.11, it is clear that the suggested control algorithm responds better to the frequency and tie-line oscillations for δ = 0.3, considering 70% DR regulation.Therefore, in this case study, the characteristic of the proposed controller against unconfined RD in the DR loop with δ = 0.3 is assessed with the PI-TD[1], Fuzzy PI[25], FO-PI[29], and FO-PD[13] control methodology.While evaluating the comparative performance of the control algorithm, overshoots and undershoots are critical parameters to demonstrate the efficacy of controllers.Fig.16compares the effectiveness and adaptability of the proposed control scheme with the existing control strategies and shows that the proposed strategy performs better in terms of improving the secondary frequency control mechanism and is more resistant to the occurrence of RD oscillation than the other robust scheme in the DPS.
Rule-Based Adaptive Frequency Regulation With Real Stochastic Model Intermittency in a Restructured Power System Abhishek Saxena , Graduate Student Member, IEEE, Ravi Shankar , Omar Al Zaabi , Member, IEEE, Khalifa Al Hosani , Senior Member, IEEE, and Utkal Ranjan Muduli , Senior Member, IEEE ∈ {g 1 , g 2 , g 3 , g 4 , g 5 , g 6 } denotes Genco units and d ∈ {d 1 , d 2 , d 3 , d 4 } is the Disco units.The term pl d represents the load perturbation of respective Disco in a region.In steady state, P s tie = 0 and P e tie = 0, which results P a tie to be zero, i.e., (31))where g Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE II OPTIMIZED
PARAMETERS FOR SCENARIO I