A robust microgrid using an inverter with CCS-MPC control and resilient operation

Modern generation trend through renewable energy-based distributed energy resources has made microgrids an important part of the power system. Robust control of the inverter providing quality power has become an essential microgrid (MG) requirement. This paper proposes continuous control set model predictive control (CCS-MPC) on inverter for dynamic voltage regulation supplying reactive power to the load for a MG. The proposed method uses the terminal voltage magnitude, which reduces calculation time, sensor per phase, and the engagement burden of the controller. This paper applies a nonlinear VSI model and a series parallel structure nonlinear autoregressive exogenous (NARX) model of artificial neural network (ANN) to predict future output which CCS-MPC optimizes. The proposed VSI with CCS MPC is applied to a case study of a real system as a plug-and-play device. Simulation shows the satisfactory result of the proposed controller. The inverter control system has been made resilient to protect itself and automatically recover from faults on the DC and AC side, providing quality power to its local load when the fault has been removed.


INTRODUCTION
The layout of the modern power network is changing day by day, with microgrid (MG.) and smart grid (SG) emerging as the cornerstones of the new trends in power systems.MG primarily relies on renewable energy sources (RES) and empowers societies to decrease energy dependency on the conventional grid system.RES using photovoltaic (PV) energy conversion to electricity makes solar inverters inevitable in MGs.However, critical loads and the absence of inertia make a MG susceptible to instability.The voltage source inverter (VSI), being the principal element of the source in the MG, can be controlled to improve these issues.
In this paper, a grid-connected MG is described, having industrial consumers.This paper studies a case of a real-time system where voltage is controlled through on-load tap changers.This technique is inadequate for voltage profile control, resulting in voltage dip and fluctuations.Dropping the voltage level below the reference value hampers industrial production.A new control method is proposed in this paper for voltage regulation without disturbing the above existing system.A plug-and-play PV inverter is connected to the point of common coupling (PCC) to maintain the voltage profile at the reference value under extreme loading conditions.The inverter has battery backup during the absence of the sun.It also supplies reactive power to improve the voltage profile.Exchange of reactive power requires only magnitude difference between system bus and inverter bus.This paper uses only one inverter to demonstrate the above control Another problem with industrial processes is sudden power interruption due to faults.Here a faultresilient arrangement is proposed by which the system can overcome short-time power interruption.
Inverter installation in a system needs an associated circuit where the controller is the primary component.Conventional systems rely on classical proportional (P) and integral (I) control action for inverter control in this respect.The scheme using PI controllers for reference current extraction in the d-q axes has been proposed [1].A similar approach is observed in [2], [3].The PI controller needs to be tuned initially during installation and also if the operating condition changes.Therefore, particle swarm optimization (PSO) based techniques to determine controller gain constants are applied for three phases in [2].Therefore, the controllers need to find optimization of six parameters (Kp, Ki in all three phases) which imposes burden on the controller and also consumes time.Further, PSO can also be lost in a sub-optimal region producing vague results.To overcome this, blending ant colony optimization (ACO) and PSO is used to tune PI controllers [3].This meta-heuristic method guarantees an optimum result but takes long time because the controller needs to solve ACO and PSO simultaneously at the beginning.A grid-coupled inverter scheme with additional battery backup is proposed [4], which can also perform during grid disconnection.The scheme also uses a PI controller.The grid-tied inverter is modelled using its RLC parameters, leading to a linear 2 nd order transfer function.However, inverters use semiconductor devices and exhibit nonlinear characteristics in form of on-off, saturation, and dead zone.Thus, a simple linearized model leads to erroneous results.Several research on inverter control in the form of FACTS device are also reported in the literature to impose plugand-play features in inverters.A particular port-controlled Hamiltonian (PCH) system and an input-output linearization tracking control strategy have been proposed [5].It requires the realization of a storage function for the passivated system.The STATCOM structure has been modelled with PCH to apply the passivity theorem.However, authors first convert the system into an input affine system which may result in a weak minimum phase, making the system difficult to control.The sources in the microgrid are of small capacity and more susceptible to change than the conventional synchronous generators.Therefore, reactive power management is crucial.A fuzzy neural control algorithm is proposed [6] for active (P) and reactive (Q) power control during grid disruption.The power of neural networks for classification and pattern reorganization is used, which is not available with simple fuzzy logic.The adaptive neuro-fuzzy interference (ANFIS) technique is presented [7] for tuning PID controllers for active and reactive power compensation through solar-inverter.Four sets of proportional, integral and derivative control coefficients need to be tuned in voltage and current control loops, making the system cumbersome.An observer is the state model where available measurements are taken as inputs and estimates the states as outputs.Observer-perceived methods for grid-connected inverter operation are described [8], where L and R values for the state and disturbance observer need to be tuned, restricting the device for plug-and-play use.A maximum power point tracking (MPPT) controlled 1-phase grid-tied inverter design aspect is demonstrated [9] to transfer solar energy to the grid.The least mean mixed norm control algorithm for the VSI is described [10] for real power extraction from the photovoltaic panel and also reactive and harmonic demand compensation of the load.
Predictive control predicts the future output considering previous details of a system or process and forecasting future input.A predictive deadbeat-controlled inverter supplies a doubly fed induction generator as proposed in [11].Deadbeat controllers perform well without overshoot but are comparatively slower than model predictive control (MPC) [12].MPC is also popular in literature because of its ability to predict a system's dependent variable from the measure of independent variables.An observer-recognized (MPC) [13] is used for grid voltage measurement to reduce the offset.MPC is also an important method for operating gridconnected inverters [14].A droop-controller assisted with the MPC technique is proposed [15] to reduce voltage variation in the wind farm.A finite control set (FCS) MPC-driven grid-connected inverter switching is also presented [16], [17].FCS-MPC does not require any modulator, yet complex calculations lead to variable switching of the inverter.An increased number of switching states cause harmonic penetration in voltage and current waveform, leading to power loss, and audible noise.The authors use three-phase control, which needs tuning of coefficients of three phases [18].A continuous control set (CCS) MPC requires modulator but produce fixed switching frequency.A CCS-MPC based on a feedforward ANN controlled VSI is described in [19].Although a complex training method for the ANN is used to get the optimum voltage vector which is difficult in real-time, however the CCS MPC has a good performance in steady state operations [20].
This paper proposes a CCS MPC with sine pulse width modulation (SPWM) for better power quality.Inverter installation in an existing grid system is generally tied to several system factors.However, each inverter configuration must be independently programmed to minimize energy and time loss.Most of the research papers use three-phase control, which needs tuning of coefficients of three phases.This paper proposed an approach to optimize the controller setting for the VSI to achieve a plug-and-play feature in the MG.In this paper, a terminal voltage control method is used for the magnitude control of the voltage where a single variable needs to be controlled, which is more manageable and creates less burden on the controller.This method is friendly for the user, and no tuning arrangement of the controller is required here, unlike the PI Int J Pow Elec & Dri Syst ISSN: 2088-8694  A robust microgrid using an inverter with CCS-MPC control and resilient operation (Epsita Das) 2219 controllers [21], [22].PSO is used in [19] to determine PI controller gains, but this technique may be lost in the suboptimal region.Therefore, a backtracking line search algorithm is proposed with PSO for better results in [23].In this paper, a backtracking line search algorithm is used for optimized results by MPC.Moreover, in most research papers, inverter is modelled using RLC circuits neglecting the nonlinearity of semiconductor switches.This paper also includes the nonlinearity of switches in inverter modelling.Describing function method analysis of the modelled inverter guarantees stable operation.Moreover, a fault-resilient robust system is designed to overcome power interruption in the microgrid during the occurrence of a fault at the grid source.To demonstrate the above-mentioned characteristics, this paper models a real-time distribution network in MATLAB/Simulink, following the loading pattern of the network, to demonstrate controller potential in terms of power quality.An existing 11kV feeder (Elachi feeder) from a 33/11 kV sub-station at Narendrapur, belonging to West Bengal state electricity and distribution company limited (WBSEDCL), India is studied, where voltage control is only through the on-load tap changers of the power transformer (PTR1, 2, 3).The absence of dynamic voltage control causes fluctuation in the industrial loads which is detrimental to the plant, machinery and production.The salient features of the proposed work are as follows: − Terminal voltage magnitude method: The three-phase voltages are controlled using a single terminal voltage magnitude method in the proposed controller.− The nonlinearity of the inverter: The Inverter has nonlinear dynamics, which research articles neglect to achieve simplicity.This paper takes care of the nonlinear behaviour of the inverter.− Robustness: Resilient control action for the fault in the distribution feeder line and the external wires which connect the solar panel to the inverter are also taken care of to provide robustness to the MG.− Plug and play feature: The proposed inverter control can be attached to any point of the MG.network.
The paper is organized as follows: i) Proposed method with system architecture using proposed controller design is detailed in section 2; ii) The theoretical basis of the proposed method is described in section 3; iii) The design aspect and control circuit for the robust fault-resilient microgrid is explained in section 4; and iv) Simulation results are presented in section 5, and the paper is concluded in section 6.

PROPOSED METHOD
The proposed control on the grid-tied PV inverter for plug-and-play operation is discussed in this section.The system architecture is modelled from a real-time system shown with blue dashed lines in Figure 1.The applied Simulink model is shown in the red dashed line where the inverter is installed.

System architecture
In this article, Elechi feeder of Narendrapur substation in West Bengal is modelled in MATLAB/Simulink.The architecture of the MG is depicted in Figure 1.It has two distinct portions.The red dotted line on the right-hand side indicates the architecture of the MG.The left-hand part, surrounded by green dotted lines, shows the 33/11 kV Narendrapur Substation of West Bengal State Electricity Distribution Company Limited (WBSEDCL).Sources of the substation are two incoming feeders (INC), 33 kV INC-1 (from Sonarpur) and 33 kV INC-2 (from Mahinagar).These feeders supply the 33 kV bus at Narendrapur and then further step down to 11 kV.This 11 kV bus is the source of the Elachi feeder.This is a mixed feeder with most industrial loading and some households.Table 1 reveals the load characteristic of this feeder system.Following the loading pattern, a system is modelled in MATLAB/Simulink.A 100 kVA, 11/0.433kV distribution transformer is supplying microgrid loads.The loads are simulated with induction motors and resistive and inductive loads in Simulink.The system configuration block diagram in Figure 2 comprises the MG connected to the main grid.A microgrid may have several distributed energies resources (DERs) connected within it.Here a single inverter control is presented to illustrate the operation of the inverters within the microgrid.As the microgrid is spread over a small area, the IGBT based VSI with CCS-MPC control is assumed to be connected to the point of common coupling (PCC).Terminal voltage magnitude (Vt) is calculated from the three-phase voltages at the PCC end and fed back to the MPC.A second order closed-loop transfer function with an on-off nonlinearity has been found as a suitable model for the VSI system and used to train the ANN [24].A non-linear autoregressive exogenous (NARX) series parallel based ANN is used to predict the plant output.The prediction horizon refers to the number of future control intervals the MPC controller evaluates by prediction at any instant.Optimization occurs based on the control horizon, but only the first variable, the modulation index (m), is applied to the system.Figure 3 shows the typical highest loading pattern of the year for the 11 kV Elachi feeder and Narendrapur 33/11 kV substation as the study time is the month of June.The loading pattern considered for simulation is from 23.00 hours of 06 June 2021 (day1) to 06.00 hours of 07 June 2021 (day2), as marked in Figure 3.

Proposed controller design
A CCS-MPC is applied in this research article to maintain the voltage regulation of the ac bus.MPC has a wider aspect as a controller.CCS MPC provides fixed switching frequency and maintains good response in steady state operation.In the proposed control scheme, the ANN represents a plant model for output prediction by the MPC.NARX model in series-parallel architecture is used in this paper.Auto regressive model is used to represent the time varying parameters of the power network as shown in Table 1.Auto regressive values predict future values from past observations.The proposed control avoids tuning of PI controllers in multiple loops.The nonlinearity of the semiconductor switches has also been adopted in the system model to minimize error.Describing function is applied for the stability of the designed nonlinear VSI model, which is a method for frequency response of nonlinear system.The nonlinear VSI model is illustrated in Figure 4.The nonlinearity is modelled using on-off, as shown in Figure 4(a), where vo is the voltage coming out from the circuit, and ve is the driving voltage of the semiconductor switch.The linear portion of the inverter is represented here as a 2 nd order transfer function (G(s)).G(s) and nonlinear describing function (Nf(A,ω)) with on-off nonlinearity is shown in Figure 4(b).
The neural network model is developed as a time series model.The terminal voltage magnitude is used as input to the plant.The input and output from the plant are fed to the neural network.The plant model generates output following the step response of a 2 nd order slightly underdamped system.The inverter model is discussed in the next section.The output from the plant transfer function with on-off nonlinearity block in series are simulated with normalized value of applied voltage.The output is considered as modulation index, m.Finally, the input voltage and m are applied to the neural network model.The ANN model is designed using a nonlinear auto-regressive exogenous series-parallel model [25].This architecture is employed because the model is stable and a good predictor of time series value.Further, it has a purely feedforward construction.Input and target variables are set for training.Bus voltage at PCC and bus loading factor time series values are taken simulating the MG system for different loading condition.These are taken as input data.Target values are obtained from the inverter model as m.Now, ANN is trained first, and the performance as well as regression values are checked.The training process is repeated until the regression values for training, validation, and testing are all nearly equal to 1.After the training, the network is used for output prediction.ANN predicts the future value of m, which is then fed to the optimization block.
MPC optimizes the value of output based on the ANN system model.It minimizes the cost function over a receding horizon using the modelled output.This minimization of cost function demands optimization algorithm.Here it has been considered that the degree of optimization problem remains the same throughout different operating points and a linear adaptive MPC is implemented as it would be able to identify the single global optimum of the convex optimization issue.

Inverter model
The equivalent circuit of an inverter can be represented as an LC circuit, as shown in Figure 4(c), with vx considered as step voltage [26].A standard 2 nd order transfer function is chosen to model the inverter.A standard second-order closed loop system transfer function, G(s), is given as (1).
Where k= DC gain; ζ= damping ratio; ωn= un-damped natural frequency of oscillation; RLC circuit can be modeled as 2 nd order differential in (2).
Where L= inductor value, R= resistance, C= the capacitance value, i= circuit current, and vx= step voltage in the equivalent circuit shown in Figure 4(c).Thus, the transfer function (TF) is given as (3).
Comparing it with (1),  = √1/ and  = (/2)√/ the (1)-( 3) are used in modeling the linear part of the inverter.Nonlinear dynamics of the inverter output voltage are described using the following describing function (DF), which implies the application of deadtime, hysteresis and relay [27].It is a method for analyzing any nonlinear system with the best-suited linear time-invariant (LTI) function.Thus, using the nonlinearity as mentioned earlier, describing the function for the inverter is modeled as (4).Where Vd denotes battery voltage, A is the peak value of sinusoidal current, r is the threshold voltage of semiconductor switch.In this work, threshold voltage of semiconductor switch is ignored in modeling for the sake of simplicity.Thus, the final describing function leads to (5).
The ( 4) leads to a model of an on-off nonlinearity.In Figure 5, ΓG is the representation of the Nyquist plot of G(s) while Γ N is used for the polar plot of {-1/[Nf(A,ω)]}.The (3) and ( 5) indicates the linear transfer function and nonlinear describing function of the modelled inverter respectively.Figure 5 presents the of stability analysis of inverter model using Nyquist plot for linear transfer function and polar plot for describing function.
As ΓG and ΓN of the modeled inverter do not intersect therefore the modeled inverter design is stable [28].It means any oscillation that may occur in the system output due to disturbance dies out and no sustained oscillation exists at a steady state.The objective of any feedback control system is to maintain the system goal, and it is done by measuring the output variable and permitting the actuating signal to achieve the desired system performance.The voltage at PCC is fed back to the control circuit of VSI.The three-phase instantaneous voltages are converted to the magnitude of terminal voltage, and the following transformation gives Vt: where u is the control inputs, d signifies the time delay, and y is the output from the plant model.After initializing the parameters as mentioned above, the neural network is ready for training.This training process optimizes the network performance.mean square error (MSE) governs the performance function.
Where ei = error between the network output (ŷ) and target output (y).The neural network is trained in batch mode.Levenberg-Marquardt (LM) algorithm is used here for backpropagation training for the minimization of cost function J(θ) [29].For any fitting problem, the aim is to minimize the error between output data and the fitting function.The rule for LM is as in (9).
Where hlm is the gradient vector (J T e), H is the approximated Hessian matrix (J TJ ), I is the identity matrix, and μis the learning parameter.After repeated training, the regression response is shown in Figure 6(b).Mean normalization is applied to convert the input (u) and target data to be better applicable for training, as mentioned before (10).
Here M is the mean of all feature values, and s is the standard deviation.After training, validation is done using the validation data set.

Receding horizon control
Receding horizon control (RHC) is also known as moving horizon control (MHC).The principle of the receding horizon controller is shown in Figure 7.As per the principle of this technique, the future output is predicted over the future time step N, which is known as the future horizon.The current time, k, and current state xk at k optimal control problem is solved over the future horizon, [k, k+N-1] [30].Though the whole future control trajectory is calculated, it only applies to the first-time step in the calculated optimal result.Next, the measure is taken at time k+1.This same procedure repeats itself in the next sampling instants over a fixed future horizon, i.e., between [k+1, k+N] at the current state [xk+1].The optimization process determines the control signal to minimize the cost function, J, over the setout horizon.
Where N1, N2, Nu describes the horizons over which the tracking error and the control increments are evaluated, and uʹ describes the tentative control variable.W is the reference, and ŷ is the predicted output.The value of ρ determines the contribution of the sum of squares of the control increments on the performance index, J.The model predictive control performs an optimization procedure repeatedly to determine the best input condition within a specified horizon to meet the desired output response while maintaining the constraints.Here prediction horizon of N2 = 7 and a control horizon of̴̴ ̴̴ Nu = 2 with control weight ρ = 0.05 is used.The controller action performs optimization over and over again as follows:

Online optimizer
The optimization algorithm presented here uses a multilayer prescribed time horizon.The neural network reciprocates the plant dynamics, which has to be controlled.This ANN-based plant model estimates future responses based on control signals.An optimization routine is then set to optimize the control inputs for the original plant for effective output responses maintaining the constraints over the input and following the prescribed path while moving towards the reference set value.The cost function is differentiable in nature.The optimizer determines uʹ to minimize the cost function.Then the optimal input is fed to the plant.The computation of αk is called the line search.The procedure for line search is as follows: i) Step I: choosing of initial state x0, putting k = 0 ii) Step II: till convergence of xk: a) Search direction of ρk from xk calculation considering where g k is Lipshitz continuous gradient b) Calculation of   > 0such that c) Setting However, the challenge here is to get a good αk to avoid step lengths from becoming too long or too short.Therefore, a backtracking line search algorithm is applied in this proposed controller.Backtracking line search starts with a relatively larger step size but decreases the step size as required to obtain optimized target.This paper uses a search parameter of 0.1 for applying the backtracking line search algorithm to reach the Armijo-Goldstein inequality condition.Backtracking line search algorithm i) Given  () > 0, let  0 =  () and  = 0

ROBUST FAULT RESILIENT SYSTEM DESIGN
Robust fault-resilient system is implemented in the MG network for line-to-ground fault at the grid end and at the outdoor near the solar panel.The block diagram of the control circuit for the fault-immune system is shown in Figure 8.A fault-resilient system is designed to maintain power during a fault at the end of supply transformer.The inverter is connected at the PCC of the MG.network and maintains the voltage profile.A feedback loop between the source and inverter intimates the VSI of the required action.This feedback interrupts the fault at the grid source end as the circuit breaker disconnects the faulty section.This work includes a control approach to maintaining communication during link failure, as illustrated in Figure 8(a).Additional arrangement from the neighbourhood transformer of a parallel feeder is connected via a relay arrangement.If the fault occurs at the feeding source of the MG., the control signal from transformer T1, i.e., VT1, becomes zero.This situation operates the relay, and neighbouring transformer T2 supplies the MG.Fault at exposed solar panel circuits and feeding wires may occur as it is placed outside.In this situation, the control circuit switches to the battery source for uninterrupted power, as shown in Figure 8(b).

RESULTS AND DISCUSSION
This section describes the results in detail.Results are arranged in two subsections to justify the proposed method.The first section explains the inverter controller action with load variations, and the other section analyzes the arrangements during system faults.

1. Load variation
In this paper, the loading pattern of a distribution system is simulated, as mentioned earlier.The simulation parameters are mentioned in the Table 2 are for the reference.The condition of the simulated system with a change in the loading condition is shown in Figure 9.The variation of load in terms of active power is given in Figure 9(a).In the simulation, a 4 kW squirrel cage induction motor and a 2 kW resistive load gets disconnected at 1.2 sec and 1.5 sec, respectively.Figure 9(b) shows the three-phase voltages during the entire period with the solar-fed inverter connected to a microgrid.Figure 10 compares the terminal voltage profile with and without the inverter connected to the microgrid system.Figure 10(a) depicts that since the grid-connected microgrid operates initially at peak load conditions without any inverter attached at PCC, the voltage at PCC drops from the reference value (433 V).It has been mentioned initially that a real-time system is modelled in Simulink as a microgrid which has voltage control through only an online tap changer.
Therefore, during maximum loading conditions, the system is not able to maintain the voltage profile, and the voltage goes below the reference value.However, the inverter equipped with the proposed controller can instantly maintain the voltage profile at the reference value, supplying reactive power to the grid without any tuning process, as shown in Figure 10(b).The proposed ANN-MPC method controls the modulation index m.A phase-locked-loop (PLL) is used to create the phase angle ωt, m, and ωt is used for a 50 Hz sinusoidal signal.A 5 kHz triangular carrier signal is compared with the modulating signal for gate pulse generation for the VSI. Figure 11 describes the voltage profile of the PCC when an induction motor (IM) starts during peak load conditions with the inverter connected to the system.Figure 11(a) shows that an induction motor is switched on at 0.05 sec, but the PCC voltage before and after switching displays a satisfactory result, with the other loads connected at PCC remaining unaffected.Figure 11(b) shows the magnitude of terminal voltage (Vt) during and after the switching of the induction motor.It indicates that after a drop at the switching instant, the terminal voltage again attains the reference value within 0.1 sec.The modelled VSI is a 2 nd order underdamped system which has overshoot in response.MPC controller is fast but susceptible to overshoot.However, an optimized model design and an appropriate number of control variables resulted in no overshoot in the simulation.

Fault resilient system
A temporary line-to-ground (L-G) fault is simulated near the grid source.Due to this fault, the circuit breaker operates and cuts off all three phases of the faulty section from the other part.The fault exists between 0.2 sec to 0.3 sec.Industrial processes experience huge losses due to sudden power interruptions.Therefore, an arrangement is proposed in which a fault near the AC source does not interrupt industrial processes in the MG.The control arrangement from the neighboring feeder transformer maintains the supply of MG during temporary power disruption at the source end. Figure 12 presents the voltage profile at PCC and source end during fault.The second diagram in Figure 12 clearly indicates that the feeder has no supply during the simulated fault between 0.2 sec to 0.3 sec, but the load connected at PCC is getting power.The DC bus voltage is shown in Figure 13.Output from the solar panel feds the inverter during the daytime and charges the battery.If a power interruption occurs during the daytime, battery takes control to provide uninterrupted power.Figure 14 shows that due to a fault at 0.015 sec, the battery provides DC power for the VSI.The application of the inverter in the system deteriorates power quality, and voltage at PCC can be affected.However, in the proposed system, the PCC voltage shows total harmonic distortion (THD) within the limit.It indicates that the controller eliminates oscillations, thus reducing THD, indicating good quality power as in Figure 15.

CONCLUSION
This paper proposes an ANN-CCS-MPC controlled inverter connected at PCC in a grid-connected MG to improve the ac bus voltage profile.This MG has been configured following the loading pattern of a real-life system.The proposed ANN-CCS-MPC controller regulates the inverter operation which improves the voltage profile by supplying the reactive power demanded by the system.The single variable magnitude of the terminal voltage technique in linear adaptive MPC avoids the interaction of multiple loops in conventional PI controllers or complex adaptive weight calculations of the three phases in other adaptive techniques for auto-configuration.The controller uses a nonlinear model of the inverter as the system and a series-parallel NARX model for the ANN for future output prediction.The advantage of the applied method is that it has small numbers of hardware and sensors compared to the three-phase variables for voltage regulation.The inverter model introduces on-off nonlinearity to include real-time semiconductor switch characteristics.The proposed control can introduce the VSI anywhere in the microgrid as plug-and play device.Simulation results of CCS-MPC control algorithm for the inverter establishes a satisfactory result.MPC tends to overshoot, but in this system, the VSI model and the number of control variables chosen restrict the overshoot.A fault-resilient arrangement is made in the microgrid to protect the loads connected to the source transformer in case a fault occurs at the source transformer.The control circuit automatically

Figure 1 .
Figure 1.The architecture of the MG network

Figure 4 .Figure 5 .
Figure 4. Inverter model with (a) on-off nonlinearity, (b) system structure represented by linear transfer function and nonlinear describing function, and (c) linear equivalent circuit of inverter Int J Pow Elec & Dri Syst ISSN: 2088-8694  A robust microgrid using an inverter with CCS-MPC control and resilient operation (Epsita Das)

Figure 6 .
Figure 6.Series Parallel NARX model (a) structure and (b) regression response after training

Figure 8 .
Figure 8. Fault resilient control circuit for (a) fault near grid source and (b) fault at environment exposed circuit of the solar panel

Table 2 .Figure 9 .Figure 10 .
Figure 9. Modelled system under simulation with solar fed inverter connected with the MG network (a) load variation and (b) System line voltages Va, Vb, Vc

Figure 11 .Figure 12 .Figure 14 .
Figure 11.Voltage profile of PCC at the time of induction motor starting (a) voltage profile at the PCC during motor load switching at MG and (b) magnitude of terminal voltage at PCC during switching

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ISSN: 2088-8694 Int J Pow Elec & Dri Syst, Vol.14, No. 4, December 2023: 2217-2229 2228 switches the source feeder in case of a fault at the grid source end.The MG operation also takes care of a fault at the incoming lines from the solar panel to maintain constant power flow.