LQG-Based Virtual Inertial Control of Islanded Microgrid Load Frequency Control and DoS Attack Vulnerability Analysis

The load frequency control (LFC) in modern power system like microgrid has turned out to be significantly challenging due to the high penetration of renewable energy sources (RESs) and the consequent reduction of overall system inertia. The inverter-equipped RESs like solar and wind power generation units, besides the load variations can prompt sustained frequency fluctuations in microgrid and further lead to system instability, power outages, and even complete system blackout in the worst case. As a solution to the concerns of intermittent power source integration and resulting microgrid frequency instability, in this work, two robust LFC schemes using conventional linear quadratic gaussian (LQG) and modified LQG with linear quadratic integral (LQI) control schemes are proposed for secondary/battery energy storage system (BESS)-based auxiliary (virtual inertia (VI)) control of islanded/non-linear microgrid. The efficacy of the suggested control strategy is confirmed through MATLAB/SIMULINK simulations and by comparing with other different control schemes under various scenarios of distinct load and RES disturbance input profiles. The simulation results exhibited superior frequency regulation performance for the proposed control mechanisms over other types of control schemes. The proposed control schemes also ensure fast settling of frequency transients and help improve frequency stability under stochastic loads and random RES output power. In addition to the development of an effective robust controller, the vulnerability of the microgrid LFC system towards the denial of service (DoS) attack is analyzed for different control schemes. The vulnerability analysis is performed in the presence and absence of local auxiliary control loop and the remote secondary measurement communication channel is considered as the DoS attack point. The simulation results indicate that the local auxiliary control mechanism can not only help to improve frequency stability but also helps to add cyber-attack resilience to an extent when the secondary control loop is under attack.


I. INTRODUCTION
The challenge of abruptly increasing global power demand and the environmental concerns of climate change and inadequate fossil fuel reserves are currently anticipated by employing RESs-integrated modern power systems like microgrids [1]. The microgrid system permits the connection The associate editor coordinating the review of this manuscript and approving it for publication was Ruisheng Diao . of independent multiple generation units or distributed energy resources (DERs), controllable loads, and storage systems on a common platform with the use of appropriate power converter interfaces. The integration of converter-equipped non-dispatchable and intermittent RESs in microgrid can lead to low system inertia and result in high frequency and voltage fluctuations in microgrid compared to conventional power systems [2]. The RES random output power besides the stochastic loads, thus, insist for the deployment of appropriate secondary and energy storage system (ESS)-based auxiliary/VI LFC strategies. Even though the secondary and auxiliary LFC schemes of microgrid ensure system stability and guaranty electric power quality, it is vulnerable to cyber-attacks from the malicious adversary [3], [4], [5] due to the absence of multi-stage security detection, high number of entry points, and increased dependence on communication infrastructure [6]. Hence, performance of cyber-attack vulnerability analysis and development of attack resilient control methods and mitigation strategies are essential for the microgrid LFC systems.

A. LITERATURE REVIEW
One of the promising solutions to the concerns of microgrid LFC system frequency instability arising from the integration of intermittent RESs is to provide auxiliary control like VI control (based on rate of change of frequency (RoCoF)) in addition to secondary and primary LFCs [7], [8], [9], [10], [11], [12].
Various VI control strategies are proposed for microgrids in different literature. A derivative control-based VI control using ESS is introduced for an interconnected microgrid LFC system in [7]. A novel design of derivative-based VI control with the emulation of damping and inertia properties in an islanded microgrid is presented in [8]. In [7] and [8], the imitation of VI and virtual damping is employed for improving the system inertia and damping properties to satisfy frequency stabilization conditions. However, the performance can be further enhanced if an additional controller is used along with traditional VI methods. In [9], a robust H ∞ controller-based VI control mechanism and in [10] a similar VI control mechanism considering the effects of frequency measurements using phase-locked loop (PLL) is implemented for the LFC system of islanded microgrid. However, the robust controller is complex in design as design capabilities are needed to form the weighting functions for the system. Moreover, orderreduction of the H ∞ controller needs to be performed if the designed controller has order greater than that of the plant. Model predictive control (MPC) and Coefficient Diagram Method (CDM)-based VI control mechanisms are suggested for frequency control of microgrid system in [11] and [12] to improve robustness and frequency stability. The MPC provided optimal control signal to the VI control system while satisfying frequency and power constraints [11]. The MPC control design requires an accurate plant model and it has algorithmic complexity and high computational load. According to the system mathematical model equations provided in [9], [10], [11], and [12], the inertia power is generated using ESS with the help of RoCoF signal. However, for the frequency regulation and inertial power generation the rate of change of control signal from the designed controller is used, in contrary, to the concept of usage of RoCoF mentioned in VI power generation equation. Moreover, the VI control loop with derivative term can intensify measurement noise signals if frequency measurement noise is consid-ered. Further, fuzzy adaptive MPC [2], dynamic output feedback controller [5], modified java optimization-based adaptive controller [13], proportional integral derivative (PID)based secondary controller with Craziness-Based Particle Swarm Optimization (CRPSO) [14], a proportional integral (PI) controller using combined soft computing techniques like genetic algorithm (GA) and artificial neural network (ANN) [15], online tuned integral controllers [16], and balloon effect modulated java optimizer for a virtual rotor-based technique [17] are also proposed for microgrid LFC system. Stability analysis of microgrid LFC system with occasional large time-delays is performed in [18]. Linear LFC system model with switched delay is used to obtain the stability criterion in [18]. However, most of the works do not consider system non-linearities, communication time-delay, and measurement noise for the study.
The effect of DoS and distributed DoS attacks on conventional LFC systems are analyzed in previous research work and it mainly uses switched system models for the analysis [19], [20], [21], [22], [23]. A resilient control strategy is proposed for multi-area power systems with communication time-delay against aperiodic DoS attack in [20] and a resilient event-triggered communication scheme for multi-area power systems under energy-bound DoS attack is presented in [21]. In these studies, using the average dwell time approach, the exponential stability is obtained for the LFC system under attack. In [20], the authors also identify the difference between communication time-delay and DoS attack by considering a tolerable upper bound for time-delay and any input delay exceeding the upper bound is recognized as DoS attack. However, in this work, the system non-linearities and RES integration are not considered. DoS attack in the additional control loop and time-delay in the local PI loop of multi-area LFC system is considered in [24]. In [24], the system non-linearities like generator rate constraint (GRC), speed droop coefficient uncertainty and time-varying delay is considered for the system analysis. A defense method for DoS attack using the Deep auto-encoder Extreme Machine Learning (DALEM) algorithm is proposed in [19] and this prediction-based defense scheme supplements lost data due to attack and ensures normal system operation. The main advantage of using DALEM model technique provided in [19] is that it is not required to set large number of network parameters manually and the optimal solution is attained without altering network input weights and hidden layer bias. However, the impact of RESs is not evaluated in this work. The detection of DoS and false data injection attacks in the automatic generation control (AGC) of a deregulated three area low inertia power system using the area control error forecast data is proposed in [25]. In this work, the area control error (ACE) and frequency signals are assumed to be affected by attack. Since, the impact of attack on a multi-area system is more compared to a single area, the development of mitigation strategy is very significant in this case. The proposed detection and mitigation technique can also be used to detect stealthy cyber-attacks using a frequency correction multiplier. Hence, most of this research work does not consider the integration of RES and frequency control of microgrid for the cyber-attack analysis. To anticipate this knowledge gap, this work also analyzes the effect of DoS attack in the secondary measurement channel of islanded non-linear microgrid LFC system integrated with RESs.

B. RESEARCH GAP AND MOTIVATION
In previous works like [2], [9], [11] the control algorithms used are complex in design and require high computational load. Moreover, derivative-based VI control strategy is used in the works [2], [9], [11], [12], [16], [17] have certain disadvantage of measurement channel noise amplification. According to authors' knowledge, a simple and computationally less complex optimal auxiliary control scheme like LQG/LQI control mechanism that is capable of taking care of Gaussian noise corrupted output measurements is not applied for a non-linear islanded microgrid LFC system. Moreover, with the usage of a simple auxiliary control loop equipped with ESS and an efficient auxiliary/additional controller that uses frequency deviation measurements instead of RoCoF, it is possible to supply additional power similar to that of a virtual synchronous generator and can achieve high system performance similar to RoCoF-based VI control mechanisms provided in [7], [8], [11], and [26]. Hence, an auxiliary control technique using frequency measurement (instead of RoCoF) can be also called as VI-based control scheme and a similar auxiliary control strategy is provided in this paper.
In [7], [8], [9], [11], [14], [16], and [17], an accurate information about the location of secondary and VI controllers are not provided for the considered microgrid framework. In many real-time scenarios, the secondary controller is implemented at the control center and primary/VI controllers are implemented locally [27], [28], [29], [30], [31], [32]. Then, the usage of same frequency measurement signals for both remote secondary and local auxiliary control loops, without considering the practical challenges like communication delay and difference in measurement noise, is a limitation. Further, the latest studies like [2], [5], [13], [15], [17] do not consider all the system non-linearities for the analysis. Hence, a non-linear microgrid frequency control system with different noise levels in secondary and auxiliary measurement channels are considered in this work.
Further concerning the cyber-attack studies of LFC system, works like [19], [20], [21], [22], and [23] mainly concentrate on conventional LFC system without RES integration and in some work system non-linearities are not considered. Hence, the field of cyber-attack and cyber-security of microgrid LFC system requires further research. Moreover, the influence of local control loops of microgrid LFC system in providing attack resilience is not considered according to authors' knowledge. Therefore, in this study, the DoS attack vulnerability of microgrid LFC system is explored both in the presence and absence of auxiliary control mechanisms.
Additionally, DoS attack is considered in this study as it can be easily implemented by adversaries with limited knowledge about the system and does not require disclosure capabilities compared to the data integrity attacks.

C. CONTRIBUTION
The key features of the proposed LFC controller are as follows: 1) Two BESS-based auxiliary control mechanisms based on conventional LQG controller and modified LQG controller with LQI tracker are proposed in this study to obtain the frequency stability of islanded microgrid with high RES integration. In the first case, the secondary control loop employs a PI controller along with LQG-based BESS auxiliary controller and the second case employs an LQI-based control scheme for both secondary and auxiliary control loops.
2) The LQG/LQI-based is capable of taking care of Gaussian noise corrupted output measurements and hence sensor noise of frequency measurement channel of microgrid LFC system is also considered. 3) System non-linearities like speed-governor dead band, valve position limits of the governor, generator rate constraints (GRC), and maximum power limits of BESS are included in the system dynamic model. 4) Sensor noise signals with different noise levels are considered for the secondary and auxiliary frequency measurement channels in the system model. Additionally, time-delay is included for the secondary communication channel for simulation. This would allow the controller implementation more practically realizable for the considered framework as the secondary and auxiliary controllers are assumed to be situated at remote and local locations, respectively, as mentioned in [33]. 5) Auxiliary controller based on the frequency measurement is considered in this work instead of RoCoF/derivative-based VI control. 6) The suggested control scheme is analyzed under several operating conditions such as constant loads, stochastic loads, random RES penetration, and under parameter uncertainty like system inertia variation to validate the performance and robustness and it is compared with various other control schemes. 7) The load sensitivity analysis of LQG and LQI auxiliary control schemes under constant and random load conditions is performed to further validate the controller performance. 8) The DoS attack vulnerability in the presence and absence of RES integration is also analyzed for the considered system model. 9) The vulnerability to DoS attack is also examined for microgrid LFC system with and without local auxiliary control mechanism. This helps to determine the impact of local additional controller-based auxiliary control mechanism in contributing cyber-attack resilience, when the remote secondary control loop is attacked by the DoS adversary.

D. PAPER ORGANIZATION
The remainder of the paper is as follows: Sections II and III describe the dynamic and state-space model of islanded microgrid considered for the study, respectively. The general control structure of LQG controller with and without LQI tracker is given in Section IV. Section V gives the details of the identification of attack points of microgrid LFC system and modeling of DoS attack. Section VI provides the simulation results of proposed control schemes and the impact of DoS attack. The conclusion and future scope of the work are provided in Section VII.

II. DYNAMIC MODEL OF ISLANDED MICROGRID
The islanded multi-source microgrid model considered in this work includes a 20 MW non-reheat small thermal power plant [12], [34], solar power generation unit (PV panels) of 5 MW, and wind turbine power generation unit of 8 MW.
The thermal power plant represents the conventional synchronous generator-based power generation and it provides both primary and secondary controls. The consumers of the power generation include industrial loads and residential loads with capacities of 10 MW and 5 MW, respectively. The system base is 20 MW and the nominal frequency is 50 Hz.
To deal with the issues of parameter uncertainties like system inertia reduction, and high RES penetration, auxiliary control scheme using BESS of 6 MW capacity is equipped in the islanded microgrid. The power produced from solar power plants and wind farms is non-dispatchable and highly dependent on existing weather conditions like solar irradiation, air density, and wind speed. Hence, they are exempted from the ancillary services like secondary frequency control and considered as disturbance inputs that inject power into the microgrid. The dynamical model of the non-linear islanded microgrid LFC system is provided in Fig. 1. For obtaining the accurate microgrid LFC system realization, the inherent non-linearities like speedgovernor dead band, valve position limits of governor, GRC, and maximum power capacity limits of BESS are taken into account. The steam turbine governor dead band has a maximum value of 0.05 pu [11], [13]. GRC of 12%puMW/min (δ U = 0.002 puMW/s and δ L = −0.002 puMW/s) is considered for the system analysis.
Auxiliary Control Mechanism: In this study, instead of using conventional derivative-based VI control strategy, an additional controller-based BESS is utilized to provide additional virtual power for acquiring required frequency regulation performance. The schematic of auxiliary control mechanism is provided in Fig. 2. The traditional VI control strategy basically utilizes a control topology and inverter-based ESS to emulate the dynamic behavior of synchronous generator to deliver additional active power to microgrid for enhancing frequency stability [12] and a function based on RoCoF is utilized for VI emulation. However, it is also possible to deliver similar additional active power with the help of an efficient additional controller and BESS by using frequency measurement signal instead of RoCoF as given in Fig. 2. The additional controller produces control signal based on the noise corrupted frequency measurement in order to reduce the system frequency variation to zero and improves the frequency stability of system.

III. STATE-SPACE MODELING OF ISLANDED MICROGRID
This section provides the linear state-space model of islanded microgrid considering primary (governor action), secondary (LFC), and auxiliary VI control loop. In this work, the power variation of wind input signal ( P wind ), power variation of solar radiation ( P solar ), and variation in load ( P L ) are regarded as disturbance input signals. The dynamic relation between the mismatch power deviation and frequency deviation of generator-load is expressed as: The linear turbine and governor dynamics can be expressed as: where P c1 (t) is the secondary control signal. The BESSbased auxiliary control dynamics can be described as: where P c2 (t) is the control signal from the additional controller. Here, P m (t) is the mechanical output power change of thermal power generation unit, P g (t) is the deviation in the valve position of governor, P pv (t) is the variation in power generation from the solar unit, P w (t) is the variation in power generation from the wind turbine generation unit, and P L (t) represents the total load deviation from industrial and residential loads. Further details of load model, solar and wind power generation models are provided in Appendix. Table 1 provides the dynamic model parameter values of considered islanded microgrid LFC system.  [9], [10], [33].
The linearized state-space model of the islanded microgrid can be obtained as the following equations: where , and u(t) represent the state vector, disturbance input vector, and control input vector, respectively. v 1 (t) and v 2 (t) represent the measurement noise signals of the secondary and auxiliary measurement channels, respectively, and they have different noise covariances. y 1 (t) and y 2 (t) denote the noise corrupted frequency measurements of the secondary and auxiliary control loops, respectively. The state, control input, and disturbance vectors are provided as follows: The matrices A, B, E, and C are given as: VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.

IV. GENERAL FORM OF CONVENTIONAL LQG AND MODIFIED LQG CONTROLLER WITH LQI TRACKER
LQG is an optimal control scheme that is capable of taking care of Gaussian noise corrupted output measurements and can be used to control perturbed non-linear systems [35]. It is simple in design and easy to implement as it requires less number of design parameters. Further, it is computationally and algorithmically less complex because it basically solves a minimizing quadratic cost function to determine an optimal state feedback law. LQG is an optimal stochastic control design problem that incorporates the concepts of both linear quadratic regulator (LQR) and Kalman filter for full state feedback and state estimation. The application of separation principle for LQG control design makes the implementation easy as the state estimator and feedback controller can be designed independently. The fundamental step of the LQG design problem is to individually design or obtain the optimal state feedback (K lqr ) and state estimation (K se ) gains of LQR and Kalman filter upon the satisfaction of the controllability (stabilizability) and observability (detectability) criteria [36]. The satisfaction of criteria is essential for the existence of solutions of Riccati equations of optimal state feedback and state estimation gains. If some of the system states are unobservable, as in the control design scenarios of real-world problems, Kalman filter could be utilized for full state estimation if the accessible measurements of the system sustain essential information concerned with the system states. Kalman filter basically acts as a low pass filter and it is effective in rejecting system disturbance. The control input and system output are the prime inputs to the Kalman filter [37].
The open-loop state-space equations of a general system for LQG design problem is provided by: where x(t) ∈ R n , u(t) ∈ R m , and y(t) ∈ R p represent the state, control input, and measured output vector, respectively, and w(t) and v(t) denote the zero mean uncorrelated process and measurement stochastic white noises associated with the system. The linear quadratic cost function of LQG optimal control problem can be expressed as [37] and [38]: where Q and R are the constant weighting matrices that could be chosen based on the trial and error approach and the weighting matrices define the trade off between control effort and regulation performance [37] where Q is symmetric positive semi-definite state weighting matrix and R is symmetric positive definite control weighting matrix [37]. The optimal control input that minimizes the cost function can be provided as u(t) = −K lqr x(t) for the system (6), where K lqr = R −1 B T P and P is obtained by solving the control algebraic Riccati equation, PA + A T P − PBR −1 B T P + Q = 0. The state estimation process of Kalman filter of LQG controller can be expressed as [38]: where The optimal Kalman filter gain K se is provided as K se = P 0 C T V −1 and P 0 is a positive semi-definite matrix obtained as the solution of filter algebraic Riccati equation, where W and V are the noise covariances of w(t) and v(t), respectively [37], [38].
The mentioned conventional LQG control scheme does not provide reference signal tracking and in order to guarantee the pursuit of the reference signal on the controlled system. Thus, the conventional LQG control mechanism is modified with the addition of an integrator having a distinct gain. The schematic diagram of modified LQG controller with LQI tracker for the secondary and auxiliary control of islanded microgrid LFC system is provided in Fig. 3.
In the case of LQG with LQI tracker, the optimal Kalman gain is achieved using the same procedure as in (8). However, the optimal state feedback gain matrix is obtained as K lqi = −K lqr − K i using the complete closed-loop system model formed by augmenting the tracking error,q(t), to the state of the plant. The tracking error can be given as: and the complete closed-loop system model [37] can be obtained as , where, Hence, the modified optimal state feedback matrix can be obtained in a similar manner as that of the conventional LQG controller, by replacing matrices A and B by A q and B q , respectively [37]. In addition, Theoretically, the optimal control gains K lqr and K i can be attained by solving the Riccati equation for state-space model (11) and K lqi is obtained as K lqi = R −1 B T q P where P is obtained by solving the control algebraic Riccati equation, The prominent features of the proposed control techniques for LFC problem in the case of islanded microgrid with high RES penetration are: 1) LQG/LQI-based frequency control mechanism is designed to ensure fast settling of frequency transients. 2) LQG/LQI-based auxiliary control loop using BESS helps to improve microgrid frequency stability under stochastic loads and random output power of RESs. 3) LQG/LQI controller allows the estimation of all state variables with the help of Kalman state estimator.

V. ATTACK POINT IDENTIFICATION AND DoS ATTACK IN ISLANDED MICROGRID
The coherent operation of the microgrid is ensured by microgrid control center (MGCC) through the realization of proper control strategies [31]. The AGC or secondary LFC technique is one of the most significant functionalities of MGCC and it is implemented by acquiring frequency deviation measurements from phasor measurement units (PMUs) and based on the frequency measurements, control signals are sent to respective power generation units for the production level adjustment and consequent correction of frequency variation [27], [28], [29], [32]. In this work, the microgrid framework has its MGCC, assumed to be, located away from the generation system as mentioned in [33] and MGCC utilizes communication infrastructure for performing the control and monitoring operations of microgrid. A similar framework is also observed in the case of Robben Island microgrid, South Africa and it has its operations center located remotely in Cape Town and uses wireless communication for monitoring and controlling operations.
In this work, microgrid LFC system operating in islanded mode is considered, as the functionality of energy management and secondary LFC is extremely challenging in the case of islanded mode compared to that of the grid-connected mode [31]. In islanded mode, the power imbalance and system parameter regulations are directly handled by the microgrid itself with the help of MGCC-based secondary controllers and local controllers. The frequency measurement signals and control signals are updated on a more frequent basis among MGCC, PMUs, and respective power generation units with the help of low bandwidth communication network [8], [10], [31], [32], [39]. This further adds the potential risk of cyber-attacks as the secondary measurement/control signals can be maliciously exploited by attackers [3], [31], [32], [39]. The communication channels of microgrid LFC system are the attack points of malicious adversaries like DoS and data integrity attacks when the MGCC with secondary controller is remotely located. The block diagram of islanded microgrid LFC system with attack points is provided in Fig. 4.
The islanded microgrid frequency control follows a hierarchical control scheme consisting of control levels like primary and secondary. The primary control level utilizes local controllers and local measurement information for implementing the required control action [30]. While the secondary control level requires extensive communication between MGCC and controlled units as the required calculations and determination of control action is performed at the MGCC located remotely [40]. Thus, the secondary communication channels can be attacked by adversaries and in this work, the measurement channel of secondary LFC is regarded as the attack point of DoS adversary as the secondary control requires the transmission of frequency measurements to MGCC at respective control cycles. The primary control schemes like governor control and auxiliary control using BESS are considered to be implemented locally and hence no attack is considered for these local control loops. The novelty of the work is that the consideration of attacked secondary control loop and un-attacked auxiliary control loop allows examining the resilience added by local control loops against the cyber-attack.
Modeling of DoS Attack: DoS attack is modeled as an on/off switching event of frequency measurement, ( f ) in the secondary control loop. The secondary LFC controller is assumed to be provided with a zero-order hold such that in the presence of DoS attack the previous or last updated frequency measurements will be available to the controller and in the absence of DoS attack, the current frequency measurement will be accessible to the controller. The DoS attack at the k th time instant can be modeled as: where, S 1 indicates the closed position of the switch in Fig. 1, implying the availability of measurements and S 2 indicates the open position of the switch in Fig. 1, implying the unavailability of measurements due to DoS attack. The control input will be updated to the thermal power generation actuation system based on the available frequency measurement, i.e. P c1 will be a function of f (k). The implementation of DoS in the concerned microgrid system is provided in Fig. 1.

VI. SIMULATION RESULTS
The microgrid LFC system model provided in Fig. 1 is tested using MATLAB/SIMULINK software to demonstrate the efficacy of presented LQG and LQG with LQI tracker control strategies and verify the vulnerability of the given system towards the DoS attacks. The implementation and performance analysis of different controllers is described in Section VI-A and the impact analysis of DoS attacks is provided in Section VI-B. According to the operating standards of frequency, the admissible microgrid frequency deviation range considered for the study is 49-51 Hz (±1Hz) during the generation or load occurrence and 49.5 -50.5 Hz (i.e. ±0.5 Hz) in the absence of any contingency. These are the acceptable frequency deviation ranges used in the power systems of Australia and Nordic countries [10].

A. CONTROLLER IMPLEMENTATION AND ANALYSIS
The five different controller combinations are implemented for the secondary and BESS-based auxiliary control loops and they are tested with and without RES integration for the performance evaluation. The controller combinations considered for the study include: (1) PI secondary control without BESS-based auxiliary control loop, (2) PI secondary control with BESS-based auxiliary control (without considering additional controller), (3) PI secondary control with PI-based BESS auxiliary control, (4) PI secondary control with LQG-based BESS auxiliary control, and (5) LQI-based secondary and BESS auxiliary control. The frequency measurement channel of the LFC system is considered to be affected by a random measurement noise with zero mean and low variance, for all the control schemes. Different noise signals are considered for the secondary and auxiliary measurement channels as the secondary and auxiliary controllers are implemented in two different locations. Random noise signals with zero mean and noise levels of ±2.5 mHz and ±1.5 mHz are considered for the secondary and auxiliary measurement channels, respectively. Moreover, for the simulation a practical limit of ±0.25 pu is applied for the secondary control signal [41] in order to avoid attaining very high values. Additionally, a time-delay of 3 s is also considered in the secondary communication channel.
The optimum gain values of the secondary PI controller of schemes (1), (2), (3) and (4) (5) is again modified to incorporate the PI controller dynamics as state as given in [42] and through the proper selection of Q and R matrices, the optimal LQR gain is In order to obtain the estimator gain values of LQI scheme, the different covariances of secondary and auxiliary measurement channel noises are applied for the Kalman filters of secondary and auxiliary control loops. Then, Q and R matrices are chosen by trial and error method to obtain optimal control gain values ensuring required system performance. Finally, the optimal control and estimator gain values of LQI scheme is obtained as: shown in the equation at the bottom of the next page, using the lqi() command of MATLAB. Q and R matrices are chosen satisfying the positive definiteness and positive semi-definiteness conditions of matrices. The control gain K bess of auxiliary control loop is also tuned manually by trial and error approach to get the best system response as mentioned in [7] and [11]. In this work, four different test scenarios are considered for the examination of microgrid VOLUME 11, 2023 frequency stability and the performance analysis results of all four scenarios are provided in Table 3.

1) SCENARIO A1: FULL SYSTEM INERTIA AND SUDDEN LOAD VARIATION
In the first scenario, the behavior of the proposed control schemes along with various other controllers are examined under the nominal operating condition with 100% system inertia (H = 0.083 puMW·s) for a step load variation ( P L = 0.1 pu) and without considering RES integration. The simulation result of Scenario A1 is shown in Fig. 5 and from the performance parameter values provided in Table 3, the best system performance is attained by LQG-based auxiliary control implementation methods. It has better transient performance and very low peak overshoots in the presence of sudden load change. In the case of no auxiliary control, the maximum frequency deviation is around ±4.168 Hz and oscillates within a value of ±0.5 Hz after approximately 110 s. Here, the frequency deviation goes beyond the permissible limit of 1 Hz due to the load occurrence. In the case of BESS-based auxiliary control and PI-based BESS auxiliary control, the frequency performance is significantly enhanced to ±0.02724 Hz and ±0.01884 Hz, respectively, and these values are below the allowable limit of 1 Hz. In comparison to all the above cases, LQG and LQI-based cases have significant frequency performance (±0.01190 Hz and ±0.009233 Hz), respectively. All the control schemes

2) SCENARIO A2: LOW SYSTEM INERTIA, CONSTANT LOAD DISTURBANCE
This scenario evaluates the frequency stability of microgrid under a step load change of 0.1 pu and when there is parameter uncertainty. The parameter uncertainty is assessed by drastically reducing the system parameters of microgrid. Here, the system inertia is reduced to 15 % of the nominal value i.e. H = 0.01245 puMW·s, to account the parameter uncertainty. The frequency deviation induced by microgrid LFC system for different controllers of Scenario A2 is illustrated in Fig. 6 and from the results of Table 3, it is observed that LQG controller-based microgrid system has the highest capability to perform frequency regulation when there is a high reduction in system inertia and under no RES integration.
In the case of without BESS auxiliary control, the system has a frequency deviation of ±5.906 Hz and oscillates within a value of ±0. 45 Hz after approximately 65 s. Similar to Scenario A1, the transient peak frequency deviation raised above the admissible level of 1 Hz during the sudden load change and compared to Scenario A1 a higher peak in frequency deviation occurred due to system inertia reduction. The high settling time and oscillatory behavior observed for without auxiliary control are due to the time-delay, system non-linearities and low values of system inertia and damping of microgrid compared to the traditional LFC system. The low frequency performance of this control scheme can be mitigated by providing an auxiliary control. In the cases of BESS auxiliary control/ PI-based BESS auxiliary control, there is an increase in the frequency deviation to values ±0.06499 Hz and ±0.04588 Hz, respectively as compared to the frequency deviation values of Scenario A1. While the LQG and LQI controller schemes have the least frequency deviations of ±0.01190 Hz and ±0.02109 Hz, respectively as provided in Table 3. All the control mechanisms with auxiliary control had a frequency deviation much lower than the limit of 1 Hz during sudden load deviation and in the absence of any contingencies the system frequency is maintained within 0.5 Hz for all control schemes. The LQG and LQI-based controllers are also implemented for the islanded microgrid LFC system model of [9] under and the frequency performance is compared with the robust H ∞based VI control method of [9]. The proposed controllers provided better frequency performance compared to the robust H ∞ -based VI control method of [9] and the frequency deviation is given in Fig. 7. The frequency deviations produced by LQG and LQI-based auxiliary controllers are ±0.003949 Hz and ± 0.004079 Hz, respectively, for the scenario with 10% load change and 100% nominal system inertia (H = 0.083 puMW·s), and ± 0.004031 Hz and ±0.004127 Hz, respectively, for the scenario with 10% load change and 50% nominal system inertia (H = 0.0415 puMW·s). However, FIGURE 7. Frequency deviation of system model [9] with LQG and LQI-based auxiliary controllers under 10% constant step load change.  according to [9], the H ∞ -based method produced a frequency deviation within the range of ±0.04 Hz and ±0.05 Hz, respectively, for 100% and 50% system inertia cases.
The simulation is also performed for the considered system model with RES integration and it is provided in Scenarios B1 and B2. In Scenarios B1 and B2, the islanded non-linear microgrid is tested under low solar power penetration (2 MW), high wind power penetration (5.9 MW), low residential load fluctuation, and high industrial load fluctuation as provided in Fig. 8 and 9. The test operating conditions of the considered microgrid LFC system is mentioned in Table 2. The maximum frequency deviation of various controller implementations for Scenarios B1 and B2 are also provided in Table 3. The summary of the pros and cons of all controller implementations is provided in Table 4.

3) SCENARIO B1: FULL SYSTEM INERTIA AND OPERATING CONDITIONS AS IN TABLE 2
In Scenario B1, the different operating conditions provided in Table 2 are implemented for microgrid system under nominal or 100% of system inertia i.e., H = 0.083 puMW·s. The frequency response of the microgrid LFC system with  different controller implementations for Scenario B1 is provided in Fig. 10. The frequency deviation is the highest ( f = ±8.603 Hz) in the case of the system without auxiliary control loop. The very low values of H and D microgrid parameters, time-delay, presence of system non-linearities and absence of auxiliary power compensation from BESS auxiliary con- In comparison to the first three controller cases, the LQG and LQI-based auxiliary controllers are superior in frequency stabilization and have frequency variations of ±0.02181 Hz and ±0.01627 Hz, respectively. Except without auxiliary control, all the controllers were able to maintain the transient frequency deviation within 1 Hz during load occurrence/RES integration and in the absence of any contingency the system frequency is kept within 0.5 Hz.

4) SCENARIO B2: LOW SYSTEM INERTIA AND OPERATING CONDITIONS AS IN TABLE 2
This scenario verifies the frequency stability of microgrid under extreme operating conditions i.e at high RES penetration and massive deduction of system inertia (i.e., H = 15 % of total inertia = 0.01245 puMW·s). Fig. 11 provides the frequency performance of non-linear microgrid for Scenario B2 under critical operating conditions as mentioned in Table 2 and when there is a high reduction in system inertia. As observed in Scenario B1, there is a high frequency deviation ( f = ±11.88 Hz) beyond the allowable grid code in the case of no auxiliary control. Noticeably, LQG and LQI-based VI controllers could robustly bring down frequency variations to the least values (±0.02182 Hz and ±0.03769 Hz). While the frequency deviations of BESS-based and PI-based BESS auxiliary controllers are ±0.1159 Hz and ±0.08188 Hz, respectively. The frequency deviation surges for all the control schemes in Scenario B2 compared to B1, as provided in Table 3. However, the least rise in frequency deviation is observed in the case of proposed controller schemes and all the control schemes except without auxiliary control kept the transient frequency deviation within 1 Hz during load change/RES integration and within 0.5 Hz in the absence of any contingencies.
The LQG and LQI-based controllers are also implemented for the microgrid LFC system of [9] under similar RES disturbance conditions and random load fluctuations to compare the frequency performance of the robust H ∞ -based VI control method of [9] with the proposed controllers. The frequency deviations produced by LQG and LQI-based auxiliary controllers are ±0.02288 Hz and ±0.01379 Hz, respectively, for the scenario with 95% nominal system inertia (H = 0.07885 puMW·s) and ±0.03605 Hz and ±0.01837 Hz, respectively, for the scenario with 45% nominal system inertia (H = 0.03735 puMW·s). However, the H ∞ -based method had a frequency deviation within the range of ±0.025 Hz and ± 0.03 Hz, respectively, for 95% and 45% system inertia cases. The frequency deviation produced by the system model of [9] with LQG and LQI controllers and under random load and high RES penetration is provided in Fig. 12.
Hence, from the results of Scenarios A1, A2, B1, and B2, superior performance against system inertia parameter variation is observed for LQG and LQI-based BESS auxiliary control schemes compared to other analyzed controllers.

5) LOAD SENSITIVITY ANALYSIS
In order to further explore the robustness and validity of proposed controllers, the load sensitivity analysis is also  conducted for LQG and LQI-based BESS auxiliary control schemes, apart from the system inertia sensitivity analysis of Scenarios A1, A2, B1, and B2.
The load sensitivity analysis is performed by varying constant and random operating loads from their nominal values in steps of 25% for the range −50% to +50%. The results of load variation of LQG and LQI-based BESS auxiliary control schemes are provided in Fig. 13 and 14, respectively. The LQG-based BESS auxiliary control scheme has a maximum frequency deviation of ±0.01767 Hz,  ±0.01478 Hz, ±0.009024 Hz, and ±0.006153 Hz, respectively, for +50%, +25%, −25%, and −50% of nominal constant loads. Further, for +50%, +25%, −25%, and −50% of nominal random loads, the maximum frequency variation obtained are ±0.04595 Hz, ±0.02264 Hz, ±0.02255 Hz, and ±0.02342 Hz, respectively. In the case of LQI-based BESS auxiliary control scheme, the maximum frequency deviation observed for +50%, +25%, −25%, and −50% of nominal constant loads are ±0.01366 Hz, ±0.01145 Hz, ±0.007017 Hz, and ±0.004808 Hz, respectively. Additionally, the maximum frequency deviations observed in the cases of +50%, +25%, −25%, and −50% of nominal random loads are ±0.03932 Hz, ±0.01761 Hz, ±0.01634 Hz, and ±0.03206 Hz, respectively. A slight increase in the frequency deviation is observed in the case of -50% of nominal random loads for both LQG and LQI-based auxiliary controllers. This is due to the sudden peak occurring in the applied random RES disturbance signal obtained after 50% percent reduction. However, both of the controllers are capable of maintaining the system frequency deviation very less than the allowable grid code range (0.5 Hz) under various load conditions and hence, robustness to the load variation is validated.

B. IMPLEMENTATION OF DoS ATTACK AND ANALYSIS
The DoS adversary is modeled as mentioned in Section V and two periodic DoS attack signals with frequencies 0.05 Hz and 0.06 Hz are implemented with different attack periods (6 s and 12 s) to evaluate the vulnerability and impact of DoS attacks in the measurement communication channel of secondary control loop of the LFC system. Four test scenarios: Case 1: DoS attack in high inertia (H = 0.083 puMW·s) microgrid LFC system under sudden load deviation of 0.1 pu with no RES integration, Case 2: DoS attack in low inertia (H = 0.01245 puMW·s) microgrid LFC system under sudden load deviation of 0.1 pu with no RES integration, Case 3: DoS attack in high inertia (H = 0.083 puMW·s) microgrid LFC system for operating conditions as provided in Table 2, and Case 4: DoS attack in low inertia (H = 0.01245 puMW·s) microgrid LFC system for operating conditions as provided in Table 2 are considered for the analysis. The simulation results of Cases 1, 2, 3, and 4 are provided in Fig. 15, 16, 17, and 18, respectively, and the frequency performance values are provided in Table 5.
In this work, DoS attack is applied after transient settling of frequency response, i.e., after 300s of simulation time for Cases 1 and 2. This allows to analyze the effect of adversary in the absence of frequency transients due to load change. Further, for Cases 3 and 4, the DoS attack is applied after 100 s as practically, the adversaries attack the system after starting time. The impact of DoS adversary in the given system depends on the attack period (AP), attack frequency (AF), and the supply of auxiliary power compensation from the BESS control loop.

1) CASE 1
In this case, DoS attack signals of different APs (6 s and 12 s) and AFs (0.05 Hz and 0.06 Hz) are considered and the attack is applied after 300 s of simulation time. As per the obtained results provided in Fig. 15 and Table 5, in the case of without BESS auxiliary control, the variation in system frequency reaches a maximum value of ±1.222 Hz from ±0.5042 Hz under DoS attacks with various APs and AFs. As far as the BESS-based auxiliary control is concerned, the maximum frequency variation increases to a value of ±0.004250 Hz from ±0.002444 Hz under DoS attacks with various APs and AFs. For both the cases, the frequency deviation amplitude is enhanced and the response turned more oscillatory with the increase in APs and AFs. However, the frequency variation is kept within the permissible limits with the help of auxiliary control action for BESS-based auxiliary control. The admissible frequency deviation in the absence of any load occurrence/RES integration is 0.5 Hz. While, the PI-based BESS control case has no high variation in frequency as the auxiliary control dominates the secondary control by providing more auxiliary power compensation. However, the variation in frequency is increased to a maximum value of ±0.003272 Hz compared to the unattacked frequency deviation of ±0.002607 Hz. A rise in the frequency deviation to values ±0.002840 Hz and ±0.0001958 Hz are observed for LQG and LQI-based BESS auxiliary control schemes under DoS attacks of various APs and AFs. The frequency deviation obtained for unattacked case of LQG and LQI auxiliary control schemes is ±0.001172 Hz and ±0.001905 Hz, respectively. Among the proposed controller schemes, LQIbased BESS auxiliary control mechanism remained least affected by the adversary due to the high performance of the auxiliary controller. In few cases like PI-based, LQG-based, and LQI-based BESS auxiliary control a slight decrease in absolute system frequency variation is observed for higher APs and AFs of DoS attack compared to lower APs and AFs. In such scenarios, the effect of DoS attack is observed as an increase in either peak overshoot or peak undershoot of frequency response. For instance, in the case of PI-based BESS auxiliary control, peak undershoot is increased from  is supplemented to the system when the secondary control loop is under attack.

2) CASE 2
The Case 2 examines the impact of DoS adversary on the frequency performance of the RES isolated microgrid LFC system with reduced system inertia and the result is provided in Fig. 16 and Table 5. In this case, the maximum frequency deviation obtained for without auxiliary control, BESS-based auxiliary control, PI-based BESS auxiliary control, LQGbased BESS auxiliary control and LQI-based BESS auxiliary control are ±0.9984 Hz, ±0.003543 Hz, ±0.003145 Hz, ±0.002827 Hz, and ±0.002325 Hz, respectively, for DoS attacks with various APs and AFs. An increase in the peak overshoot from ±0.3014 Hz to ±0.3038 Hz is observed in the case of without auxiliary control, with the increase in the DoS AP and AF. The overall absolute frequency deviation rises from 0.002524 Hz to 0.003543 Hz, 0.002703 Hz to 0.003145 Hz, 0.001165 Hz to 0.002827 Hz, and 0.002200 Hz to 0.002325 Hz, for BESS-based auxiliary control, PI-based BESS auxiliary control, LQG-based BESS auxiliary control, and LQI-based BESS auxiliary control, respectively, under various DoS attacks. However, the absolute frequency deviation either decreases or remains the same in some of the DoS attacks for control schemes such as without auxiliary control, PI-based BESS auxiliary control, and in LQI-based BESS auxiliary control. In such cases, either the peak overshoot or undershoot increases or the response turns more oscillatory. For instance, a higher oscillatory response is observed for without auxiliary control for DoS attack with AP = 6 s and AF = 0.05 Hz, compared to unattacked case even if the net frequency deviation is remaining almost same. Similarly, rise in the peak undershoot is observed for DoS attack AP = 6 s and AF = 0.06 Hz in the case of LQI-based control scheme, even if the net frequency deviation decreases. However, among all the control schemes, the controllers with auxiliary control scheme has least deterioration in the system stability. A higher frequency deviation due to system inertia reduction may not be expected for Case 2 compared to Case 1, similar to the Scenarios A1 and A2 of Section VI-A. This is due to the fact that the impact of system inertia reduction due to load change appears as increased frequency transient peak overshoots/undershoots before settling and in this case the DoS attack is applied after transient settling. Here, the variation in system frequency after transient settling is solely due to DoS attack.

3) CASE 3
In Case 3, the impact of DoS adversary on the frequency performance of high inertia microgrid LFC system is analyzed in the presence of high RES penetration. The results are provided in Fig. 17 and Table 5 and it show that RES integration can increase the impact of DoS attack, when the auxiliary control loop is absent or when the power compensation from the auxiliary control loop reaches the maximum limit. In this case, the frequency deviation of without auxiliary control, BESS-based auxiliary control, PI-based BESS auxiliary control, LQG-based BESS auxiliary control and LQI-based BESS auxiliary control rises to a maximum value of ±9 Hz, ±0.05079 Hz, ±0.03277 Hz, ±0.02194 Hz, and ±5.074 Hz, from ±8.603 Hz, ±0.04733 Hz, ±0.02929 Hz, ±0.02181 Hz, and ±0.01628 Hz, respectively, under DoS attacks of various APs and AFs. The BESS-based auxiliary control, PI-based BESS auxiliary control, and LQG-based BESS auxiliary control are able to maintain system frequency least affected under DoS attack. The observed high frequency deviation of LQI control scheme is due to the absence of secondary control action during the attack interval and due to the attainment of maximum power capacity limit of BESS in the auxiliary control loop. During the attack period, as the secondary control loop produces a control signal based on the previously available measurements, the auxiliary control loop tries to provide maximum power compensation. However, once the maximum limits of power capacity are attained no extra auxiliary power will be supplemented to nullify the additional frequency deviation caused by the RES integration and DoS attack. Hence, the system frequency goes beyond the allowable limits. For control schemes such as without auxiliary control, BESS-based auxiliary control, PI-based BESS auxiliary control, and LQG-based BESS auxiliary control the maximum peak value of frequency deviation decreases than unattacked case under some attacks. However, in such cases, the lower peaks of frequency response shows more deviation that of unattacked case as shown in the magnified images of Fig. 17.

4) CASE 4
The Case 4 analyzes the system frequency response of low inertia RES integrated microgrid under DoS attack and the frequency deviation results are given in Fig. 18 and Table 5. Here, the system inertia reduction along with adversarial attack can worsen the system stability if the power supplemented from auxiliary control mechanism becomes insufficient. In this case, BESS-based auxiliary control and LQG-based BESS auxiliary control schemes are least affected by the attack and the maximum frequency deviation observed in the presence of DoS attack is ±0.1185 Hz and ±0.02192 Hz, respectively, where the unattacked frequency deviation is ±0.1158 Hz and ±0.02182 Hz, respectively. Here, the power supplementation from auxiliary control loop was within the maximum power limit of BESS. For without auxiliary control, the absolute frequency deviation remained same for AP = 6 s and AFs = 0.05 Hz and 0.06 Hz. However, a slight increase in deviation is observed for various other parts of the frequency response, as shown in the magnified image of Fig. 18. In the case of BESS-based auxiliary control and LQG-based BESS auxiliary control with DoS attacks of AP = 6s and AF = 0.05 Hz, even though the highest peak frequency deviation under attack is lower than the unattacked case, the system response has higher amplitude for lower peaks of frequency response. The without auxiliary control scheme had the system frequency beyond the admissible grid code and frequency response even worsened to ±12.99 Hz under DoS attack of AP = 12s and AF = 0.06 s. Under DoS attack, the system frequency deviation of PI-based auxiliary control increased from ±0.07301 Hz to ±0.08120 Hz for AP= 6 s and AF = 0.05 Hz, ±0.08133 Hz for AP= 6 s and AF = 0.06 Hz, and ±0.4684 Hz for AP= 12 s and AF = 0.06 Hz. However, the frequency response of LQI-based control scheme produced a maximum frequency deviation of ±6.649 Hz under DoS attack and shows the insufficiency of auxiliary control mechanism even though it produced better performance for analysis of Section VI-A. The instability in LQI-based BESS auxiliary control scheme is due to the attainment of maximum power limit of BESS.
From all the cases, it is observed that the auxiliary control loops can improve cyber-attack resilience to certain level if the physical limits of auxiliary control loop components are not restricting the supply of auxiliary compensating power when the secondary communication channel is under attack. Further, in many cases the absolute frequency deviation rises with the increase in APs and AFs. In some cases, the effect of attack is also observed as the increase in either peak overshoot or peak undershoot values of system frequency, or the frequency response also turns more oscillatory with the rise in AP or AF, while the absolute frequency response values remain unaffected or decreased. Hence, the effect of attack not only depends on APs and AFs but also on the amount of auxiliary power compensation received when the secondary control loop is under attack.

VII. CONCLUSION
In this work, the conventional and modified LQG-based BESS auxiliary control techniques are proposed for non-linear islanded microgrid LFC system with measurement noise in the secondary and auxiliary measurement channels.
The performance of proposed controllers are also compared with several other control schemes and the vulnerability to DoS attack is analyzed for microgrid LFC system with and without auxiliary control loop. According to the obtained results, the following remarks can be summarized: 1) The LQG and LQI controller-based auxiliary controllers showed superior frequency regulation performance and could ensure fast settling of frequency transients under stochastic loads and random RES output powers, over other types of controllers. 2) In general, the BESS-based auxiliary, PI-based BESS auxiliary, LQG-based BESS auxiliary, and LQI-based BESS auxiliary controllers could maintain the system frequency deviation within permissible grid code even under high RES penetration and critical system inertia reduction with the help of additional power compensation provided by the auxiliary control mechanism. 3) In the case of without auxiliary control scheme, the frequency instability during high RES integration is due to the lack of power anticipation from the BESS-based auxiliary control loop, existence of system non-linearities and time-delay, and reduced system inertia of the microgrid system. 4) From the results of DoS attack vulnerability analysis, it is observed that the frequency performance of microgrid LFC system deteriorates in the presence of DoS adversary. Moreover, during the attack interval, secondary controller will be using previously available frequency measurements for control signal generation. Thus, higher power compensation from auxiliary control loop is required to maintain the system frequency stability. 5) Vulnerability analysis also shows that the auxiliary control can not only help to improve the frequency stability but also helps to add resilience against adversaries to an extent, when the communication channels of secondary control loop is under DoS attack. The un-attacked local auxiliary control loop provides additional power compensation during the attack interval of DoS attack and aids maintaining frequency stability to an extent. However, the maximum power capacity limits of auxiliary power component like BESS can limit the auxiliary power supplemented and can affect the frequency regulation in the presence of DoS attacks, when there is higher power compensation requirement due to RES integration and random loads. Hence, it is essential to develop suitable detection and mitigation measures for microgrid frequency control system to deal with the frequency instability due to cyber-attack. 6) The impact of DoS attacks in the microgrid LFC system depends on APs, AFs, and maximum power capacity limits of auxiliary control scheme.
Future Scope: 1) The results of vulnerability analysis shows the need of suitable detection and mitigation measures for micro- grid frequency control system to deal with the frequency instability due to cyber-attack and it is considered as the future work. 2) Apart from DoS attacks, the impact analysis and development of mitigation methods of data integrity attacks can be considered.
3) The proposed control schemes and DoS attack vulnerability analysis can be extended to low-inertia multi-area microgrid LFC systems. 4) Optimization algorithms can be used for the selection of Q and R matrices in future.

A. RANDOM LOAD MODEL
The MATLAB/SIMULINK model of random load used in this study is provided in Fig. 19 and more details about the model is mentioned in [11] and [16]. The power fluctuation of LFC system load is found by considering load fluctuation from an initial value. The real-time/actual random power deviation of LFC load is simulated by multiplying the standard deviation with a white noise derived random output fluctuation. In this model, the load deviation is simulated close to an actual load change by the following function: P Load = P L = 0.6 P Load−initial (A-1)

B. SOLAR POWER GENERATION MODEL
The solar power generation is irregular and non-dispatchable due to the dependence on the weather conditions and power fluctuation in the solar power generation can be obtained using MATLAB/SIMULINK model as given in Fig. 20.
In this model, the random output power fluctuation is generated using white noise block and it is multiplied by standard deviation to obtain the actual power change of solar generation system. The solar power deviation is simulated close to an actual solar power change by the following function [16]: P pv = 0.6 P solar−initial (A-2)

C. WIND POWER GENERATION MODEL
The MATLAB/SIMULINK wind power generation model considered in this study is provided in Fig. 21. The power VOLUME 11, 2023   Nominal parameters values of wind turbine generation system [44], [45].
extracted from wind is expressed as P w = 1 2 ρC P (λ, β)AV 3 w , where ρ, A, V w , and C P represent air density (Kg/m 3 ), blade swept area (m 2 ), wind speed (m/s), and rotor power coefficient (C P (λ, β)), respectively [44], [45]. The rotor power coefficient defines rotor power efficiency and it is expressed in terms of pitch angle (β), optimal tip speed ratio (λ T ), intermittent tip speed ratio (λ I ), and turbine coefficients (C 1 −C 7 ) by the following equation: λ I + C 7 λ T , where λ T = ω T r T /V w and the relation between λ I and λ T is provided as: Here, ω T is the rotor angular speed (rad/s) and r T is the rotor radius (m). The nominal parameter values of the wind turbine generation system is provided in 6.

DECLARATION OF COMPETING INTEREST
The authors declare no conflicts of interest concerning this work.