Hierarchical Model-Predictive Droop Control for Voltage and Frequency Restoration in AC Microgrids

The hierarchical control structure was introduced to allow the integration of power-electronics-based distributed generation into the microgrid in a smart and flexible manner. The main aim of the primary controller in such a structure is to achieve accurate active and reactive power sharing, whereas the secondary control aims to ensure voltage and frequency (V/f) stability. Generally, converter-level secondary controllers utilize classical nested loop control that suffer from a slow dynamic response and cumbersome parameter tuning. The existing-model-based and estimation-based secondary controllers are fast, but require complex design methodology, high communication bandwidth, and, consequently, higher data analysis and computational burden. This article presents a simple predictive-based secondary control for the ac microgrid that is fast and robust and has a low design complexity, low communication bandwidth, and no parameter tuning requirement in the secondary control layer. The proposed predictive control optimally restores voltage and frequency in the microgrid by predicting their trajectory deviations and leveraging the droop characteristic curves. Experimental tests performed with three parallel-connected grid-forming inverters in an islanded operation validate that the controller can accurately maintain V/f stability, while ensuring active and reactive power sharing.


I. INTRODUCTION
With the global community shifting toward the usage of more renewable power, the inclusion of a more diverse supply of energy to the utility grid is inevitable. With that regard, the microgrid (MG) is a geographically confined smart grid that aids such diverse power integration with smaller controllable elements known as distributed generators (DGs). The MG allows users to actively manage not only their energy consumption but also their generation, leading to a more reliable, interactive, intelligent, and efficient power system paradigm [1]. In the case of any disruption to the utility grid, the MG should disconnect itself and continue to regulate its own voltage and manage its loads autonomously in the islanded mode of operation. It is also vital that the transition between the two modes occurs seamlessly without disruption to power consumers [2], [3]. During the absence of the bulky rotating generators of the main utility grid, the MG faces challenges due to the lack of inertia in inverter-based resources. Virtual inertia emulation based on virtual synchronous generators and the use of power reserve are some of the techniques that have been used to compensate for the lack of inertia in MGs [4], [5]. In addition, the islanded renewable-energy-based MG faces stability, reliability, and resilience issues due to the sporadic characteristic of renewable energy sources and the lack of stable power generation units such as gas-powered plants [6].
The inverter-based distributed energy resources act as current-controlled inverters in grid-following mode. This happens when the DGs are connected to the grid, where the output current of the inverter is regulated. Inverters are operated as grid forming (GFM) when they behave as voltage source while regulating the output voltage of the inverter. The parallel connection of multiple GFM inverters under the decentralized control scheme is established in this article, where each of the GFM inverters is regulating its own voltage. The absence of a master inverter reduces the risk of single point of failure, which increases the reliability of the MG. The primary control objectives here are observed for the islanded MG operating in a decentralized manner, where the low or no use of communication between the DGs reduces the risk of communication latency, data losses, and cyberattacks.
The general hierarchical control structure of MGs usually consists of zero, primary, secondary, and tertiary layers of power management to ensure the accurate control of several factors including voltage, current, and frequency while maintaining high power quality and stability in the grid [1], [7]. Droop control can be used to achieve accurate power sharing between DGs in the MG without the use of communication systems in the primary control layer. Although droop-controlbased inverters are able to achieve accurate power sharing, they suffer from V/ f deviation at the primary level [8]. The droop characteristic curves determine the amount of deviation in V/ f in response to active and reactive power disturbances in the MG [9]. Therefore, many papers discuss the restoration of the deviated V/ f of the MG by estimating the deviation terms and adding them to the droop voltage reference, in the secondary control (SC) layer [10], [11], [12], [13], [14], [15], [16], [17].
The most widely used linear control method for such SC includes the proportional SC (P-SC)-and the proportional-integral SC (PI-SC)-based methods. The aforementioned methods scale the error between the measured and nominal values of V/ f to obtain the deviation terms [10], [27], [28]. Even though the P-SC is fast, it results in a high steady-state error [10]. The PI-SC resolves the steady-state error issue; however, the integral controller reduces the speed of the transient operation of the controller and results in incorrect levels of power sharing between the inverters [12]. Heydari et al. [17] and Zhang et al. [18] proposed a distributed PI-based secondary controller; however, it requires high-bandwidth communication and parameter tuning. In [13], a switched control scheme allowed the controller to switch between P-SC and PI-SC to balance the disadvantages of each approach. However, the dependence on the event detection scheme made the system less reliable, similar to the control proposed in [19]. Therefore, in [14], a small ac signal (SACS) SC approach was presented, which does not rely on event detection. Furthermore, it enabled PI-SC to be implemented without affecting the power sharing accuracy between GFM units. PI control was implemented to achieve frequency control, while an ac current signal was extracted from the voltage to produce the reference voltage with a fixed amplitude and variable frequency. However, the use of PI controllers posed the tedious task of tuning numerous variables and resulted in a slower restorative performance compared to nonlinear controllers.
The existing literature on SC based on nonlinear control techniques shows that the estimation-based and model-based techniques have been explored. A consensus-based approach was used in [20] where the reactive power of the system was communicated to all the neighboring DGs using a sparse low-bandwidth communication network. The deviation of the angular frequency was continually updated based on the estimated reactive power of adjacent DGs. This approach requires a much more complicated communication network as compared to the proposed method as the reactive power information of all the neighboring DGs need to be conveyed, whereas in the proposed method, the V/ f deviation from a single DG is communicated to the other DGs in a single control cycle. An unscented Kalman filter was implemented in [21] using a dynamic state estimation technique where the internal states of the available DGs in the MG were estimated. Gu et al. [23] discussed a nonlinear state estimation technique of the system's voltage for decentralized SC. Dehghanpour et al. [22], Haughton and Heydt [24], and Hashmi et al. [25] have introduced more state-estimation-based techniques.
Variations of predictive control have also been implemented for V/ f restoration. In [15], a linear generalized predictive control was implemented from the z-domain of the transfer function for the DG system. The state-space equations of the system model have been realized by utilizing the generalized predictive control model along with the controlled autoregressive moving average model, allowing the prediction of the future state variables of the system. The N-step-ahead predicted values were used in a cost function to obtain the system's frequency and voltage deviation. A model-predictive-based secondary V/ f control method was shown in [16], where the deviation of the restoration variables were obtained for a decentralized control system. An autoregressive model was used along with an exogenous variable model of the phase-locked loop (PLL) controller and the model-predictive controller (MPC) to obtain the state-space equations. Finally, the adopted cost function included the minimization of the difference between the predicted and nominal frequencies. An estimation-based predictive control technique was presented in [26], where a Kalman filter estimated the present state vector of the linear-time-invariant state-space model. The controller was demonstrated for secondary voltage restoration by using the deviation of the reactive power. Table 1 summarizes and distinguishes the advantages and  disadvantages of the proposed SC method from the existing techniques.
Although the above estimation-and model-based nonlinear control systems achieve secondary V/ f control, they involve substantial mathematical calculations that carry high computational burden, which could be problematic for realtime implementation. Furthermore, their complex structure makes the initial design stage more challenging. Therefore, the motivation behind this article is to present a simple realtime implementation of a predictive-based controller with low communication and computational burden. In this article, finite-control-set model-predictive control (FCS-MPC) is implemented in the primary layer, and consequently, the predicted powers resulting from the optimally selected switching states are used to obtain the V/ f deviations (δV, δ f ), which are the SC variables that are computed in a single DG and conveyed to other DGs of the MG, as seen in Fig. 1. This article presents extended experimental results and an enhancement on the controller presented in [29]. The main improvement includes the complete elimination of PI controllers.
This article presents the following unique contributions: 1) a multitime scale-predictive optimal control for voltage and frequency restoration in the ac MG; 2) computationally efficient predictive control leveraging droop characteristic curves for straightforward implementation with low design complexity where SC calculations are performed in only a single DG of the MG; 3) flexible power sharing (i.e., equal and unequal power sharing) to meet the desired dispatch, with virtual impedance control and no circulating reactive currents between the parallel GFM units; 4) robust predictive SC for GFM units with a fast-dynamic response for V/ f restoration with no parameter tuning and a low bandwidth for communication.

II. SYSTEM DESIGN FOR ZERO-AND PRIMARY-LEVEL CONTROL A. MG SYSTEM
The general structure of the proposed MG system is shown in Fig. 1. The MG consists of multiple DGs connected in parallel at the point of common coupling (PCC) and feeding common resistive-inductive (RL) loads. Each DG's framework comprises a dc voltage source, a two-level three-phase inverter, an LCL filter, circuit breakers to individually connect the DGs to the load, and line impedances to account for the lengthy cables that connect DGs across long distances in a given area. The equivalent dc resistance of the inductors is considered in the filter models of the MG. Table 2 shows the rated values of the DGs, which have identical components. The 200-V dc voltage is selected due to the limitation of the available equipment for laboratory-based experimental testing.

B. PRIMARY-AND ZERO-LEVEL INVERSE DROOP AND FCS-MPC
The hierarchical control structure adopted in [1] is implemented in the proposed MG system. The lower levels of control include the zero, primary, and secondary controls, which are the focus of this article, while the tertiary level is out of the scope of this article. The main purpose of the lower levels of control in the proposed MG includes the following goals: 1) maintaining the MG voltage and frequency at the nominal ranges; and 2) accurate sharing of active and reactive power between the DGs.
The following sections will provide the detailed design and description of the zero-level FCS-MPC and the primary-level droop control.

1) MODELING OF FCS-MPC FOR VOLTAGE CONTROL MODE
FCS-MPC is utilized to ensure that the inverter is operated in the voltage control mode. The technique primarily involves developing a mathematical model of the DG, the prediction of control variables, and the optimization of a cost function. The measured signals include the input current (I i ), capacitor voltage (V c ), output current (I o ), and output voltage (V o ). a) Mathematical modeling of the LCL filter: First, the mathematical model of the LCL filter is used to develop the dynamic equations for the filter input inductor (L i ), filter capacitor (C), and filter output inductor (L o ). This is done by applying Kirchhoff's voltage and current laws. The state-space representation of these equations can be developed as follows to allow easy and efficient calculation in matrix form ⎡ where V i is the inverter output voltage, and a, b, and c are the matrices defined as follows, which are derived from (1): b) Prediction of control variables: To reduce the calculations from a 3-D space to a 2-D space, the Clarke transformation is used, where the measured three-phase currents and voltages (abc) are converted into the stationary reference frame (αβ). The discretized state-space model is developed using the Duhamel integral approach as given in [30]. The discretized equations are used to predict the control variables, as follows: ⎡ ⎢ ⎣ where the matrices A a , B b , and C c are defined as follows: where I 3x3 is an identity matrix and the inverse of matrix a is represented by a −1 . c) Optimization of cost function: The presence of the LCL filter poses some difficulties in modeling FCS-MPC in the islanded MG, where the output voltage is the main control objective. The coupling of the input inductor current derivative (dI i /dt) with the capacitor voltage (dV c /dt) affects the output inductor current of the DG. Therefore, the dynamics of the output inductor current needs to be taken into consideration. Typical linear controllers based on cascaded dual loops are usually employed to secure the stability of the system under this scenario. To ensure accurate power delivery from the DG, not only the voltage but also current requires to be regulated precisely. Therefore, the multiobjective optimization capability of the MPC algorithm is designed to control both the output voltage (V o ) and the input current (I i ) from the converter side to their respective references as presented in the cost function g shown in (5). The prediction can be obtained for an N-step horizon. A two-step horizon is implemented in this article to compensate for the time delay that arises when operating at high sampling and control frequencies, especially for finite-time predictive controllers that have a large amount of calculations to complete within one control cycle [31]. Large delays between the measurement and the actuation can cause significant problems if such delay compensations are not considered in the design of the controller. It is assumed that the reference variables remain constant during two steps of prediction where λ i and λ v are the weighting factors for the control on the input current and output voltage, respectively. The discretized state-space equation generates the predicted capacitor voltage and not the predicted output voltage as it is needed in (5). The dynamic equation of L o is, therefore, used as presented in (6) to obtain the predicted output voltage. Consequently, the optimization is conducted as traditionally done for the discretized FCS-MPC controller as presented in [32]  Another important aspect to consider at this stage is the significant voltage drop caused by line impedance across the cables that connect the ends of the DGs to the loads. This can lead to inaccurate power sharing between the DGs. Therefore, and as explained in [33], in order to achieve accurate power sharing without the need of communication and extra sensors, virtual impedance in the control is added to adjust the output impedance that the inverter sees at the PCC. The cable line impedance Z line consists of a resistive impedance R line and inductive impedance X line . The virtual impedance voltage V Zv is calculated based on the virtual impedance, measured output current I o , and MG frequency ω as follows: where R v and L v are the virtual resistance and virtual inductance, respectively. The estimation of the input reference current, I i,ref , requires the calculation of the output current reference. I o,ref can be calculated in the αβ frame by using the measured powers P(k), Q(k), and the reference output voltage V o,ref .
Similar to the case with L o , the dynamic equation of the filter capacitor C is used, as shown in the following equation, to estimate the predicted input current reference:

2) DROOP CONTROL FOR POWER SHARING
Droop control is a technique extensively used for achieving decentralized active and reactive power sharing between multiple DGs. The conventional droop method is typically used for systems with highly inductive line impedances at the output of the inverter, while the inverse droop is used for systems with highly resistive line impedances [34]. Numerous literature works for low-voltage MGs use the inverse droop control because the low-voltage line parameters are predominantly resistive [35]. The low-voltage grid has a highly resistive network, requiring the use of inverse droop control in the primary controllers. The inverse droop control has a Q-f and P-V relationship, as illustrated in (9). The variables P and Q are the actual powers, which are calculated using the measured voltage (V o,abc ) and current (I o,abc ) at the output of the filter, as shown in Fig. 2. The invariant quantities are the nominal frequency ( f n ), the nominal RMS voltage (V n ), and the droop gains k p and k q

III. SECONDARY-LEVEL PREDICTIVE-BASED CONTROL
Power sharing in the primary control level is achieved as a consequence of drooping the voltage magnitude and frequency, as depicted in the previous section. The droop of active and reactive power levels results in a variation in the V/ f of the system, creating steady-state deviations from the nominal values and consequently affecting the stability and power quality of the entire system. Therefore, the secondary controller is required to restore such deviations and bring the system's V/ f back to their nominal values. However, this should be realized without affecting the power sharing established in the primary layer. To achieve this task, a widely used technique includes detecting the V/ f deviation values, δV and δ f , and adding them to the droop equations [10], [11], [12], [13], [14], [15], [16]. This is generally achieved by applying a vertical shift to the Q-f and P-V droop equations at a magnitude equal to the calculated deviation terms. As seen in Fig. 3, when active or reactive loads are added, the primary controller shifts the operation of the DG from point 1 to point 2. This creates a deviation of V/ f from the nominal values. Therefore, this deviation is estimated and added as a vertical shift to the droop lines, changing the operation from The calculation of δV and δ f is usually obtained by measuring the error between the measured and reference V/ f , followed by a PI controller to drive the error to zero. In this article, the deviation restoration is obtained using MPC without the use of PI controllers. The proposed method is also devoid of the requirement of measured RMS voltage or frequency in the SC level. Therefore, this layer no longer requires PLL control, which is used to obtain the frequency of the MG. The flowchart in Fig. 4 describes the proposed FCS-MPC algorithm, where the output includes the predicted powers in addition to the optimal switching sequence. Compared to the traditional FCS-MPC algorithm, the predicted values of the optimally selected output voltage and current from the DG, V g,opt (k + N ) and I g,opt (k + N ), are utilized to calculate the predicted powers of the upcoming control cycle. Correspondingly, the optimal predicted values are used to obtain P(k + N ) and Q(k + N ) with the help of (10). The optimal values are selected after the optimization of the cost function g, as depicted in Fig. 4. Thereupon, the inverse droop equations (9) are rearranged to obtain the general deviations δV and δ f , with the application of the predicted powers according to (11). It is clear that the V/ f deviations are based on the predicted powers and the inverse droop gains; hence, they are obtained in a straightforward manner.
Following that, a delay (D) allows the predicted active and reactive powers to be utilized within the same control cycle. It is assumed in this controller that δ f (k + N ) can be equal to δ f (k) for small values of N, as the sampling time is small enough for the approximation to be valid. Finally, as shown in Fig. 5, the restorative terms are incorporated with the droop control terms to form the reference voltage to the inner control layer. This method of SC reduces the deviation of V/ f by a significant amount, as shown in Section IV. It is possible to achieve precise secondary restoration with this approach as the predicted output voltage and current are a compelling indication of the power required from the DG in the upcoming cycle of control and can consequently represent the antici- Furthermore, the droop equations show that the deviation terms δ f and δV are not dependent on the droop constants (or the rating of the DG) even during unequal load sharing conditions. To prove this, variables k q , k p , Q, and P can be defined according to (12) and (13) based on the highest allowed deviation of V/ f from the nominal values (5% and 2%, respectively), required by the international IEEE 1547 standard [36]. The values of P load and Q load are assumed to be the amount of load power at a given instance, while P total and Q total are the total active and reactive power generation capacities of the MG based on the individual rated capacities of the DGs. The general equations for the deviation terms, presented in (14), can be calculated by substituting (12) and (13) into the droop equations (9). This proof shows that at any given instance, δ f and δV are independent of the droop constants and are mainly dependent on the load requirement of the MG, allowing them to be used globally within the system. The resilience of the secondary controller in the case of a failure to any of the DGs is an important aspect to consider. The deviation variables for the SC layer are determined in the largest DG unit that dominates the power contribution. Therefore, in the case that a failure is detected in this unit, the SC calculations need to be initiated in the controller with the next largest unit and communicated to the smaller DGs. This would require a prior knowledge of the maximum capacity of each DG in order to decide which of the available units would take over the calculation of the deviation variables. In the case that a failure occurs in any of the other smaller DGs, there need not be any particular action as this DG will be disconnected from the MG

IV. EXPERIMENTAL AND SIMULATION STUDIES
The validation of the implemented control technique has been carried out experimentally to observe the steady-state and transient responses of the controller with varying levels of RL loads for similar rated and differently rated DGs. This allows the observation of the MG controllers for equal power sharing and unequal power sharing between the DGs. In addition, the robustness of the controller to model parameter variations has been investigated. The weighting factors have been heuristically tuned to be at unity to balance the control of voltage at the nominal level and the current to prevent reactive power circulation and maintain accurate power levels. The controller has been validated using the test bed shown in Fig. 6, and Fig. 7 shows the detailed schematic diagram. The power stage for each DG includes an EA PSI 9750-12 dc power supply with constant 200-V dc voltage. The inverters are built using insulated gate bipolar transistor switches and rated to handle up to a maximum of 6.1 kW. The parameters used in the LCL filter and output line impedances are the same parameters as mentioned in Table 2. Three identical DGs have been constructed and connected in parallel at the PCC. The controllers are implemented on OPAL-RT simulators, where DG1 and DG2 are controlled by the OP5600 and DG3 is controlled by the OP5700. The requirement for two OPAL-RT controllers arises due to the limitations on the number of analog inputs available in a single controller. The low power load consists of a series-connected resistor with 45 and inductor with 30 mH per phase, with a power rating of 300 W and 18 VAR and is connected at the PCC. The high power load similarly consists of 9 and 1-mH power rating of 1500 W and 30 VAR. The high load switch enables the parallel connection and disconnection of the high power load to the MG.
The following sequence of events is followed to power up the entire MG.
1) Initially, DG1 is connected to the low power load (CB 1 of Fig. 1 is turned ON) and operating in droop control mode. DG2 and DG3 are in the voltage tracking mode and synchronized to the MG voltage but not physically connected to it. 2) Next, the circuit breaker switch of DG2 (CB 2 in Fig. 1) is turned ON to physically connect DG2, while the controller is simultaneously switched from the synchronization mode to the droop control mode. This is done by changing the voltage reference from the PCC voltage to the droop voltage. 3) Consequently, DG3 is similarly connected via CB 3 . 4) Finally, the high power load is connected to test the MG for step changes in load power. To observe the transient and steady-state responses of the secondary controller, two tests are captured during two consecutive transients, first while enabling the secondary restoration controller and next while changing the load power, as depicted in Figs. 8 and 10, for equal and unequal load power sharing scenarios. The transients are designed to monitor not only the restoration of V/ f , but also the ability to maintain

A. CASE 1: EQUAL LOAD POWER SHARING
The amount of the total load handled by each DG is decided based on the decentralized droop controller, specifically the droop constants. The droop constants include the rating of the DGs to obtain equal load sharing. Each DG is rated at 1 kW and 100 VAR. As illustrated in Fig. 8(a), initially only primary control is enabled. The zoomed windows in Fig. 8(b) and (c) show that the RMS voltage has deviated by 8%, while the frequency has risen by 0.14% to enable accurate power sharing as dictated by the inverse droop laws. The total load connected is 1800 W and 48 VAR. Each DG equally supplies 600 W and 16 VAR to the combined common load. During the first transient, as V/ f restoration is enabled, it is observed that the voltage error reduces to 2.6% and the frequency error to 0.01%, while each DG maintains sharing the same amount of power. The minor rise in active and reactive power by a few units is due to the overall increase of the system voltage. During the second transient, the total active and reactive load reduces by 84% and 47%, respectively. The frequency is maintained at 60 Hz, and the voltage error is slightly reduced as the total load is very low. As presented in Fig. 9, the total harmonic distortion (THD) of the voltage and current are 1.3% and well within the ranges imposed by the IEEE 1547 standards [36].

B. CASE 2: UNEQUAL LOAD POWER SHARING
To test for unequal load power sharing, DG1 is rated the same as before, but the ratings of DG2 and DG3 are reduced by half. Therefore, they individually supply half of the power supplied by DG1 at all times, as seen in Fig. 10(a). Thus, the DGs cover the total load in a 2:1:1 ratio. Fig. 10(b) and (c) shows that the average deviation leads to a steady-state voltage error of 7%, while the frequency rises by an average of 0.2%. DG1 supplies 900 W and 24 VAR, while DG2 and DG3 each supply half of that. During the first transient as V/ f restoration is enabled, it is observed that the average voltage error reduces to 2.7 V and the average frequency error to 0.03 Hz, while each DG maintains accurate power sharing. During the second transient, the frequency is maintained close to 60 Hz with 0.01% error and the average voltage error remains low at 2.5%, while the power sharing ratios stay unaffected.

C. CASE 3: ROBUSTNESS TO PARAMETER MISMATCH
MPC in the primary control layer involves model-based control and, therefore, uses the rated values of the LCL filter components to perform calculations during the control sequence. In reality, the actual inductances and capacitances deviate from the rated values due to heat and operating points. To observe the robustness of the controller to such variations, the values of each component are varied in the control algorithm, while the physical system is kept unchanged. Four tests are performed, where the first three involve the deviation of one of the components, L i , C, or L o , to values ranging from −20% to +20% of its rated value. The fourth test involves the variation of all three parameters together. The effect of parameter mismatch is observed for: 1) the percentage absolute reference tracking error (ARTE) of the variables in the cost function, i.e., %e Vo and %e I i ; 2) the THD of the output voltage and output current of each DG, i.e., THD Vo and THD Io . The ARTE is calculated according to the following equation, as explained in [37]: where x is the observed variable. Fig. 11 shows that the error is maintained well below 2% for the given range of parameter mismatch, while the THD is maintained under 5%. This proves that the entire controller, complete with primary and SC, shows a high range of robustness against parameter variations.

D. CASE 4: COMPARISON WITH LINEAR CONTROL
A comparison with the well-established PI-based secondary controller is highlighted in Fig. 12, where the connection and disconnection of an RL load has been simulated at time instances 3 and 4 s, respectively. The results indicate that while the overshoot in both the controllers is similar, the predictivebased controller has a shorter settling time. The absence of integral control allows the predictive controller to perform faster and reach a steady state more swiftly. Furthermore, an assessment of power sharing shows that the predictive-based controller shares the power at correct ratios, while the PIbased controller has a 20% error in its power sharing ratios.

E. CASE 5: TUNING OF WEIGHTING FACTORS FOR ZERO-LEVEL CONTROL
The multiobjective cost function of the MPC controller has two weighting coefficients, as seen in (5). The selection of optimal values for each parameter is significant in keeping the operations of the controller within stable limits at different operating points. Owing to the absence of the utility grid, the regulation of the MG voltage falls upon the inverters, and therefore, the output voltage is considered an essential control variable. Therefore, its weighting factor (λ v ) is kept at unity, while the current weighting coefficient (λ i ) is tuned for an optimal value below and above unity. Initially, the value of λ i is kept at unity; then, step increases were imposed. It is seen in Fig. 13(a) that, as λ i increases, the voltage gradually deviates from the nominal value. When reaching a λ i of 5, the voltage control loses stable operation. This occurs since current tracking supersedes voltage tracking, leading to system instability. Furthermore, the controller was tested for lower values of λ i . Fig. 13(b) shows that the controller maintains stability until the current control no longer exists at a null value of λ i . Without current control, accurate power sharing between DGs is not possible, which leads to voltage collapse and loss of stability. Therefore, a unity weighting factor is selected for both control variables in order to enable the optimal operation of the MG.
The experimental tests performed above prove that the proposed predictive-based secondary controller is able to restore voltage and frequency to nominal values while maintaining power sharing levels between parallel-connected inverters. It presents a faster dynamic response to transient changes and has a stable operation in the steady state despite large load changes. The controller has a low design complexity and low tuning requirement and is robust to system parameter variations. For future studies of the proposed predictive-based SC, some important aspects to analyze are the effects of nonlinear loads, unbalanced loads, and mismatched feeder impedance on the effectiveness of the secondary controller. Stability analysis to study the practical limitations of the controller, along with the controller's susceptibility to communication failure, will be topics for future research.

V. CONCLUSION
This article discussed a multitime scale-predictive control for voltage and frequency restoration in an ac islanded MG with multiple inverse-droop-based, parallel-connected, GFM inverters. Droop constants along with the optimally selected predicted powers are leveraged to estimate the voltage and frequency trajectory of the next time step. Therefore, the key advantages of the proposed method, in addition to the absence of parameter tuning in the SC layer, are a noncomplex design concept that is straightforward to implement and nonreliant on computationally intensive model-based calculations or complex-estimation-based techniques. The design of the hierarchical control layers presents a system that is completely devoid of PI controllers. Simulation and experimental results were conducted for the controller and, compared to the PI-based controller, showed significantly better response and operation. It has been proven that the controller is robust, has a fast dynamic feedback, and is able to restore voltage and frequency, while accurately maintaining active and reactive load power sharing between the distributed generation units.