Control of Aggregated Virtual Synchronous Generators for PV Plants Considering Communication Delays

In this paper, a new method for the delay compensation when using an aggregation of virtual synchronous generators is proposed. Lack of inertia in power converters can potentially provoke stability issues that can be mitigated by the use of virtual inertia techniques. Among those, the Virtual Synchronous Generator (VSG) concept has received strong impulse in the last years. This paper is focused on the idea of using the distributed VSG concept in a renewable power plant, in which a single Synchronous Central Angle Controller (SCAC) is used for the power control exchange at the Point of Connection (PoC), while distribution control units are employed for the local inverter control. This idea, already discussed in the literature, is in here extended to consider the implementation on industrial string-level commercial power converters, recalling the importance of accessible measurements and communication delays. In order to validate the proposal, firstly communication delays are measured and modelled. Following, simulations with different SCAC operating modes are conducted, and finally experimental results validation of different operation modes with commercial converters are presented.


Control of Aggregated Virtual Synchronous Generators for PV Plants Considering Communication Delays
Daniel del Rivero , Graduate Student Member, IEEE, Pablo García , Senior Member, IEEE, Cristian Blanco , Senior Member, IEEE, and Ángel Navarro-Rodríguez , Member, IEEE Abstract-In this paper, a new method for the delay compensation when using an aggregation of virtual synchronous generators is proposed.Lack of inertia in power converters can potentially provoke stability issues that can be mitigated by the use of virtual inertia techniques.Among those, the Virtual Synchronous Generator (VSG) concept has received strong impulse in the last years.This paper is focused on the idea of using the distributed VSG concept in a renewable power plant, in which a single Synchronous Central Angle Controller (SCAC) is used for the power control exchange at the Point of Connection (PoC), while distribution control units are employed for the local inverter control.This idea, already discussed in the literature, is in here extended to consider the implementation on industrial string-level commercial power converters, recalling the importance of accessible measurements and communication delays.In order to validate the proposal, firstly communication delays are measured and modelled.Following, simulations with different SCAC operating modes are conducted, and finally experimental results validation of different operation modes with commercial converters are presented.Index Terms-Communication delay, real-time simulation, smith predictor, virtual synchronous generator.

I. INTRODUCTION
T HE world's power generation is currently moving toward a more sustainable and environmentally friendly approach.This is due to the usage of Distributed Energy Generation (DEG) facilities based on Renewable Energy Sources (RES) has replaced fossil fuels because of their significant environmental The authors are with the Department Electrical Engineering, University of Oviedo, 33203 Gijón, Spain (e-mail: riverodaniel@uniovi.es; garciafpablo @uniovi.es;blancocristian@uniovi.es;navarroangel@uniovi.es).
Color versions of one or more figures in this article are available at https://doi.org/10.1109/TIA.2024.3377169.
Digital Object Identifier 10.1109/TIA.2024.3377169cost (greenhouse emissions, lack of source material, etc.).Additionally, the most widely used RES, like photovoltaic (PV) and wind power, are becoming more affordable, offering improved Levelized Cost of Electricity (LCOE) indices [1].However, the inclusion of this kind of generation systems provokes a weaker power system due to the inertia reduction currently provided by synchronous generators with rotating mass, to a power converter-based system with little to no inertia [1], [2], [3].
Since power converters lack both inertia and damping, this problem could affect the power grid's stability.It is currently understood that grid-forming and grid-supporting services must be taken into account in the design when significant penetration of DEG, with aggregated sizes comparable to traditional power plants [4], [5], [6].This is where the Virtual Synchronous Generator (VSG) approach arises.For the power electronics-based DEG/RES units, this control method enables the emulation of the dynamic characteristics of a real or arbitrary Synchronous Generator (SG) [2], [3].
SPC operates with inner current and outer voltage control loops, using a virtual admittance to establish a cascaded control loop.SPC is typically integrated into the local control of each inverter, offering frequency and voltage support at local PV collector connection points [5].However, for PV plants, grid support is ideally expected at the Point of Connection (PoC).With that motivation, a modification of the SPC designed to provide grid support at the PoC has been proposed, the Synchronous Central Angle Controller (SCAC) [4].
The SCAC technique suggests simultaneously driving several converters, emulating a unique SG in the PoC, giving rise to an aggregated VSG.This concept presents the idea of a single virtual rotor, emulated at the PoC, where the electromechanical model of the SG is considered (central control architecture).Hence, the SG inertia and damping response are emulated at the PoC.Regardless of the distances between the local converters, this control structure enables the system operator at the PoC to control the exchange of power (both active and reactive), allowing each converter to distribute the energy to be delivered under different operating modes (power and frequency support) on their own.A more detailed explanation can be found in the literature, where both, central and local control systems are detailed [7].
A concept for a structure with N converters is shown in Fig. 1, where a central controller handles the local controller references of each converter.In this system, it is possible to independently control the exchanged active and reactive power, as indicated in the dynamic model and control loops.In Fig. 1(a), a comprehensive connection diagram illustrates the interconnection of various converters.In Fig. 1(b), the control block diagram is depicted, with the global controller in green and the local controller for each power converter in orange.Each power converter requires a replicated local controller tailored to its specific characteristics.Further explanations for these blocks are provided below.The key control system is implemented in the central controller, where the inertia is emulated by the swing equation of a virtual synchronous generator (see ( 1) and ( 2)).
where δ sm is the power angle, Δω r is the angular speed deviation of the rotor, J is the SG inertia, P m is the mechanical power, P e is the electrical power, D is the damping constant and ω B is the base frequency.In [5], the electromechanical control has been studied, and a frequency analysis has been taken into account to obtain the power loop control H M (3).k p , k i , and K D have been designed, according to the required inertia constant and frequency droop slope, respectively.
In (3), H is the inertia constant, P max is the maximum active power of the converter, S N is the nominal power, ω n is the natural frequency and ξ is the damping factor.In this control system, the dynamic response is mainly supported by the inertia, while the frequency droop supports the steady state behavior.Based on the analysis presented in [4], [5], (4) shows the relationship between ΔP o and the frequency change Δω g .
The internal time-domain variables and control loops (current/voltage) of the converter are presumed to be accessible by this control system, though.However only active and reactive power set-points are normally externally accessible for commercial converters that have already been installed, typically via a communications link.So, a modification of this control is required for a wider applicability.Due to its wide adoption as the go-to solution in power plants, MODBUS TCP is proposed as the communication system [14].
In the following sections, the control system architecture is modified in accordance with the prior motivation using a communication-based implementation.In order to perform that implementation, the system communication delay is measured, the integration of the Smith predictor (SP) in the system is explained, and also a small stability analysis is performed.For validating the model, several working operations will be tested in local simulation and in real-time operation with commercial converters.Those working modes are: I) Active and reactive injection.II) Power support operation, taking into account grid operator requests.III) Frequency support operation by power management depending on frequency variations.IV) Phasejump in the grid voltage performance.V) Island operation.First, a local simulation is used to evaluate the control system, and following a real-time hardware controller with commercial converters is employed for the first three cases.The main article contribution is the proposal of using a distributed virtual synchronous generator in an industrial environment considering communication delays and their compensation.
This paper is based on the paper in [13] by the same authors, with extended analysis and results.The added content includes a stability analysis of the system considering the delay impact.Regarding the results, a variety of different operating conditions is included, considering Hardware-In-the-Loop (HIL) and Power-Hardware-In-the-Loop (PHIL) validation schemes.

II. PROPOSED CONTROL SYSTEM
Most of the VSG techniques integrate their controllers into each converter's firmware as an add-on.However, as it was already indicated, the SCAC technique requires having access to different control actions and sensor readings (current, voltages).This paper proposes a new control structure that can be applied to already-existing commercial converters, that only requires access to active and reactive powers set-points and measurements obtained by MODBUS TCP communications and the dictionary variables included in the SunSpec DER specification [15].The method does not require any additional measuring elements, such as extra voltage and current sensors, which would make implementation more complicated and expensive.Instead, it relies on the RMS voltage, frequency, and active and reactive power communication-based readings from each converter.Therefore, this approach is an appealing solution for the standardization of the VSG concept for a massive implementation in future and existing DEG's.However, it is important to acknowledge certain limitations when comparing the external implementation of the VSG concept in power converters to its internal counterpart.The external implementation focuses solely on the fundamental component for signal reconstruction in the time domain.Additionally, achieving a rapid response is constrained by communication delays and the necessary time for reconstruction, which

III. DELAY COMPENSATION
Each converter control unit communicates with the central controller in the proposed renewable energy plant application using MODBUS TCP.The communication between the central controller and each of the distributed units may experience some delay since MODBUS TCP is not a real-time protocol, the delay depending on the number of components in the bus and the distance.The effectiveness of the closed-loop system is compromised by these delays, which have a direct impact on the control instructions transmitted from the central controller and the provided feedback information.
Considering that MODBUS TCP is not a real-time protocol, it is expected a variable delay distribution.Accordingly, the delay statistical distribution is modeled in this section and a compensating mechanism is discussed.

A. Delay Modelling
In the literature, there are several proposals to model random delays.One of them uses the Markov chain [17], [18] as its foundation.A stochastic model called a Markov chain discretely represents certain potential states or events (in this case delays).
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The probability of those potential outcomes is solely dependent on the outcome of the prior event.For this paper, to model the communication latency in the local network where the tests are going to be performed, the communication delays in a link using MODBUS TCP protocol are measured.A 30 kW bidirectional dc/dc converter (CNG) from Cinergia SL, similar to the one in Fig. 3, was employed as the PHIL system.This power supply features different emulation units, including batteries and solar panels, and may work as a voltage, current, and power source.Two of these power sources will be used in Section IV for the experimental validation.For performing the measurements, a HIL system (Speedgoat target machine) is used to act as a communication gateway between the converters and the control system in a real-time simulation.These components are also displayed in Fig. 3.
The delay measurement procedure is as follows: a digital square reference signal of 0.25 Hz has been supplied simultaneously to the current converter set-point, so it can be used as a trigger signal in an external scope that also captures the output current response.Both signals can be observed in Fig. 4(a).The delay distribution varies between a much wider range, as it can be seen in Fig. 4(b), with a mean value of around 68 ms and a mode of 45 ms.In Fig. 4(c), the time variation of the delay during all the experiments can be easily appreciated.The time variation of the delay throughout the entire experiment is seen in Fig. 4(c).For the delay modelling, a Poisson distribution with the form ( 5) is chosen, as proposed in queuing theory delay models for communication networks [19], [20].The Poisson distribution is obtained with the delay evolution from Fig. 4(b), with 795 number of events (k) and the mean (λ) value of 68 ms.That distribution is used as delay estimation for compensating the delays in the SP loop.For the real communication delay, the measured data is used.
By using the Poisson distribution, the distribution from Fig. 4(d) is obtained.

B. Delay Compensation. The Smith Predictor
Various methods for delay compensation have been explored, including the study of the Smith predictor (SP) and its modifications [21], [22], the investigation of the Scattering transformation [23], [24], the examination of the linear predictor [25], [26], and the consideration of predictive control [27], [28], among other strategies.The Scattering transformation serves as a method to passivate the control system, mitigating delay effects and contributing to stabilization.Similarly, the linear predictor, a commonly used model-free scheme, employs the linear extrapolation concept to predict future control variables.However, for the purposes of this paper, the SP has been chosen due to its simplicity and reliable operation [21].Ongoing research in this field aims to identify alternative delay compensation methods more suitable for the stochastic nature of communication-based delays.The SP achieves the removal of the delay component from the system's control loop by incorporating a model of the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.delay structure, along with a relatively precise modeling of the system plant [22].
In the SCAC system, the delay is presented in the control actions sent to the local converters.The SP compensates for the plant delay, through a plant model ( G p ) and an estimated delay ( e tps ).The plant model shall be the one between the control actions (δ m , ΔE) and the output (P out , Q out ) (see Fig. 5(a).Unfortunately, finding the transfer model for the proposed communications-based control system is not an easy task.The suggested approach is to run a replica of the local control for each converter in the central controller.As many replicas of the local control will be used as there are SCAC converters.It should also be clarified that the local control structure of each of the converters is the same in all of them, simply changing the value of the instantaneous values of each converter.Fig. 5(c) shows the simulated plant for SP which is considered as the affected plant by the delay.Besides, δ m and e i outputs of the emulated local model are used for computing the output power using the power (6).Finally, the error between the predicted active and reactive power and the values given by the local control units is used to compensate for the delay (see Fig. 5).
In order to demonstrate and validate the operation of the SP, the limit stability constant delay is firstly considered while the compensation method is applied.The system used for applying the delay with SP is the one shown in Fig. 5, and without compensation the one shown in Fig. 1.
To clarify this point, Fig. 6 shows the difference in behavior when using or not the SP under the limit stability delay condition.As it can be seen, by setting the limit delay (75 ms), the response with (d LSP ) and without SP (d LN SP ) are clearly different, where the additional overshot created by the delay is mostly removed by applying the SP.
It is also included a larger delay (d = 80 ms) to illustrate the instability condition above a certain delay level.In this case the unstable case is scaled for representation purposes.In the next subsection, a concise stability analysis is undertaken Fig. 6.System step response with a constant communication delay of d 3 = 75 ms (which is the stable limit regarding the delay), with (d LSP ) and without delay compensation (d LN SP ).Also, the unstable case (d UNS ) is represented for a case of d 2 = 80 ms.For representation, the unstable power is corrected by a factor of 0.005.R is the reference signal.
to complement the explanation and validate the importance of implementing a delay compensation method.

C. Stability Analysis
In this section, a comparative stability study is conducted, considering both the system without considering communication delays and those that include them, leading to the system instability.This analysis is visually presented in Fig. 7, illustrating Bode diagrams for the different enumerated cases.
The stability response will be compared in two different scenarios: one where the system is operated without communication delays (d 1 = 0 ms) and another where communication delay is introduced at the stability boundary (d 2 = 75 ms).Those scenarios are introduced in Fig. 7, where Bode diagrams are depicted.Initially, the Bode diagram without communication delays was approximated using the Frequency Response Function (FRF) method, a frequency-based measurement function.It consists in a frequency-based measurement function that expresses the frequency domain relationship between an input and output of a system [29].In the Fig. 7, just the case without delay is included with this method.However, considering that the response at low frequencies closely resembles the transfer function obtained from the system in Fig. 8 (due to the inertia control system being slow and the rest being fast at low frequencies), the latter has been employed for the subsequent stability tests.The three first cases were analysed in the Bode by using the system from Fig. 8.  9 Fig. 7. Bode diagram of the SCAC system considering no delay (d 1 = 0 ms), the limit delay which makes unstable the system (d 2 = 75 ms), and the same delay but compensated with the SP method (SP ).Furthermore the Bode diagram extracted by FRF method is also presented (just for non delay case).(a) The amplitude Bode is presented.(b) Shows the phase evolution for the different cases, including the PMs.Notice the low-frequency ranges of the system (x-axis) due to the emulated system inertia (10 s).Table I shows the stability values of these cases.As observed in the Bode diagram of Fig. 7 and the data presented in Table I, system stability is evident in the absence of communication delays, with a Phase Margin (P M) of 143.44 and an infinite Gain Margin (GM ).When the limiting delay (d 2 ) is introduced, the system is positioned at the stability boundary, featuring a GM of 1.001 and a P M of 0.0038.Additionally, upon the introduction of the SP, the system regains its stability margin, displaying a GM of 6.86 and a P M of 97.7.
Taking advantage of the stability analysis conducted in the baseline case, a brief assessment of the system's stability sensitivity has been carried out.Critical parameters such as inertia (H), damping (τ ), and droop slope (K p ) were varied across three different scenarios: A) without delay, B) with a limiting delay, and C) limiting delay but employing SP as a compensation method.These variations are reflected in Fig. 9. Furthermore, the aim of this analysis is to emphasize the significance of certain elements in the control system, demonstrating how they influence the variation of stability margins.
Leveraging Fig. 9 and Table I, it can be observed that, in the case A) without delays, the modification of H values a) causes the system to become more underdamped but faster as its value decreases.Increasing the value of τ b) results in a more overdamped and slower system, while the variation of K p c) mainly affect to the position of the zeros, moving the root locus to the right, as K p is increasing.In case B), the system behaves similarly, but with eigenvalues shifted to the right.It is even noticeable that, by increasing H and decreasing τ , the dominant poles can lead the system to the stability margin, as detailed in Table I.In case C), after delay compensation with SP, the significant eigenvalues return to the negative semi-axis, ensuring system stability.

IV. RESULTS
In this section some results are presented to validate the proposed compensation method, presenting different working modes of the system.Those operations are tested in both local Simulink simulations and real-time experimental proofs through Speedgoat emulator.Real-time tests are based on Fig. 3, where two 30 kW bidirectional dc/dc converters (CNG) from Cinergia S.L are used.In this case, CNG-2 has three strings working as power sources to emulate the power demand from the control system, which will receive the commands from the simulation . Those setpoints are sent and written in CNG-2 through MODBUS TCP.The energy computed by the control system will be obtained from CNG-1, which works as a battery emulator in each string, which is running in battery emulation mode to replicate the SCAC idea.As it was stated in Section III, a HIL system is used for real-time simulation.
For the case of communication delays between the central controller and the local units, the same variable time delay used in the local simulations (computed in Section III) are used for experimental tests.However, due to the CNG converter's internal delay in the processing of the power references and integration windows used for the calculation of the active and reactive power, additional delays are added to the control system (20 ms for active power and 400 ms for reactive power).These delays are also included in the model used by the Smith predictor to achieve better results.This is a critical step, as the Smith predictor will also tackle the additional delays present in a real implementation.
For these tests, grid, and VSG models are taken from [4], where the SCAC idea was first published.In this case, the model includes three DEGs connected to a grid and considers a battery locally connected per converter, which is the element that provides/absorbs energy for frequency support.In this case,

TABLE II SCAC PARAMETERS AND SET-POINTS FOR THE SIMULATION
feeder impedance is considered, demonstrating that the system could work in a real implementation with real feeders.Fig. 10 shows an overview of the different tests that are going to be evaluated, showing several operation modes to be validated.Going from a simple active and reactive power reference tracking to a power support operation mode, depending on the grid operator requirements modifying the power exchange with the grid.Besides frequency support capability, by injecting/absorbing energy through an ESS, validating the disturbance rejection capability, which is one of the main purposes of the system.Also the phase-jump reaction of the system and the islanding mode operation are analysed in this paper, to show other extra operations of the system.The cases I, II and III can be seen in Fig. 11, but in terms of power signals in the form of a complete simulation.Fig. 11(a) shows I, II, and III working modes in terms of active power.Fig. 11(b) depicts the behavior in Case I, injecting the required power by the global controller.Fig. 11(c), depicts Case II, for active power management.Besides, Fig. 11(d) and (e) show Case III, which is the injected power when a frequency drop appears in the grid, trying to reduce the frequency variation.These working operations will be explained in more detail in the following subsections.Worth noting that power is oddly shared among the three converters in the next section, providing a distribution shown in Fig. 12, for each DEG.Simulation parameters are given in Table II.
Previous simulation is performed by using an ideal grid.However, in order to validate and demonstrate how the SCAC system works, the following simulations will be performed by using a weak grid formed by a simple synchronous generator (with real frequency variations), with a limited power (300 kW) and inertia (0.116 kgm 2 ).In these simulations, the five cases from Fig. 10 are validated: I) active and reactive power injection, II) supporting frequency changes, III) grid operator active power reference tracking, IV) phase angle jump and V) islanding operation.

A. Case I
Considering what is accounted in Figs.10(b) and 11, active and reactive power setpoints are established in order to control the power exchange with the grid.This principle is the basis for the other two working modes, showing how the SCAC can manage the required power by the global controller.This operation is tested by a simple local simulation, and also by a real-time simulation.Besides, these power injections are varied by adjusting the virtual admittance in control as Fig. 12 shows, where the unit admittance is divided in 3, and it varies during time.
1) Local Simulation: As it can be seen in Fig. 13(a), the power setpoint is reached, sharing the energy among the DEGs, regarding the power distribution between the DEGs shown in Fig. 12.The same happens with the reactive power in b).
2) Real-Time Experimental Test: As it was aforementioned, the control system is tested in real-time by using the Speedgoat simulator and CNG converters.The experimental results are presented in Fig. 14.As it can be seen active and reactive power are tracked perfectly, quite similar to local results.It is important to note that there is a different delay between active and reactive power, which has to do with the integration window from each variable in the power converter used in the HIL system [13].In case of c), the different steps that appear in the read power are directly the delay of the integration window for active power.Nevertheless, those delays are tackled by the Smith predictor making the system controllable and stable.The difference in the ripple between the local simulation and the real-time is because Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

B. Case II
This case aims to demonstrate the main operation mode of the SCAC system.As it was above-mentioned, SCAC system  adds virtual inertia capabilities, helping to reduce any frequency disturbance in the grid.Two frequency variations (see Fig. 15(a)) are induced by forcing some abrupt load changes (8.5 kW at 12 and −12 kW 18 s) to observe the dynamic behavior of the control system.
1) Local Simulation: In Fig. 15, the response of the system is demonstrated, when a frequency variation is forced due to Fig. 13.Simulation validation: (a) Active power reference tracking injected to the grid, taking into account the power-sharing between DEGs.(b) Reactive power reference tracking injected to the grid, taking into account the power-sharing between DEGs.G 1 , G 2 and G 3 is the designation of each power converter.DEG is the power developed by the power plant, as Fig. 10 shows.R is the reference power.a load-step change.Fig. 15(a) shows the frequency variation by using the SCAC system connected to the grid (showing the frequency with and without SCAC system).With SCAC system, the frequencies that appears are for two different rated power of the SCAC system.So frequency is forced to change at 12 s.In case of using the SCAC system, the ESS will inject active power (Fig. 13(a)) to the system in order to help the grid to increase its frequency, as it can be seen in b).On the other hand, if a suddenly frequency increase appears, as it can be seen at 18 s, the ESS-SCAC will absorb power from the system to decrease the frequency.Therefore, the power injection/absorption by the 15.Simulation: (a) Frequency variation of a weak grid due to a power change demand (with and without SCAC), modifying the installed power in the power plant.The higher power the lower frequency variation (f 0 is for the case without SCAC, f 1 is for the case with SCAC and S n = 6 kVA, and f 2 is for the case with SCAC and S n = 10 kVA.(b) Power injected by each DEG, to mitigate the frequency variation from the case f 1 of b).G 1 , G 2 and G 3 are the designations of each power converter and DEG is the power of the total power plant, as Fig. 10 shows.
SCAC system will depend on the inertia emulated and also the power installed in their ESS.It can be concluded from [13], the more power installed in the system, the lower the frequency variation will be.
2) Real-Time Experimental Test: In the case of real-time simulation, the SCAC system has been emulated by using the battery module from CNG.Those results are presented in Fig. 16.As it can be seen it works as the local simulation, when a frequency dip appears (Fig. 18(a)), DEGs inject power trying to reduce the frequency variation, respecting the power-sharing between converters (Fig. 18(b)).In this case, as a battery emulator is used, the SOC state of each battery is presented in c), showing how the battery is charged or discharged.

C. Case III
This operation mode is controlled by the DEG operator (central controller), in order to reduce or increase the power injected by the power plant, depending on the grid requirements, as long as the ratings of the power plant are not exceeded.This means that if a power change is requested by the grid operator, the power injected will vary, taking into account that the RES are working normally at their maximum power point (MPP), and the excess or lack of power regarding the new power command will be managed by the SCAC-ESS.Once the grid operator's setpoint returns to normal state, the storage system would stop absorbing energy, returning to zero power if there are not frequency changes.Another possible scenario is that the storage system reaches its maximum capacity and it cannot absorb more energy.This would mean that the PV string has to be taken out of its maximum power point to comply with the conditions of the grid operator.
1) Local Simulation: The aforementioned effect can be observed in Fig. 17, where at t = 40 s, grid operator active power reference varies (P DEG , as shown in Fig. 15(a), forcing to inject less power from the DEG system.In this situation, either an Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Fig. 16.Experimental validation: (a) Frequency variation of a weak grid due to a power change demand (with and without SCAC), modifying the installed power in the power plant.The higher power the lower frequency variation (f 0 is for the case without SCAC, f 1 is for the case with SCAC and S n = 6 kVA, and f 2 is for the case with SCAC and S n = 10 kVA.The same legends than Fig. 15 are used in this plot.(b) Power injected by each DEG, to mitigate the frequency variation from the case f 1 of (a).The same legends as Fig. 15 are used in this plot.(c) State of Charge (SOC) of each ESS-SCAC emulated in CNG.The same legends than Fig. 15 are used in this plot.For SOC information, colors match.Fig. 17.Simulation: (a) Power injected to the grid.At 40 s, the required grid power changes to 2.4 kW.R is the power reference, DEG is the total power injected by the power plant, and P V is the power developed by the PV array.(b) ESS-SCAC power absorption to obtain the required 2.4 kW power demand by the PoC.G 1 , G 2 and G 3 is the designation of each power converter, as Fig. 10 shows.
inverter curtailment or a charging of the ESS is required.In this case, the power set-point has been reduced by 2.4 kW, and as the PV system is working at its MPP, the ESS-SCAC will absorb the energy difference.However, in case the ESS-SCAC reach their maximum capacity, the PV arrays will have to be moved out of their maximum power point, in order to comply with TSO requirements.
2) Real-Time Experimental Test: The same results are obtained in real-time simulations as can be seen in Fig. 18.When  there is a power setpoint requirement by the global controller, the ESS-SCAC absorbs the extra power, charging the batteries as can be seen in c).If the opposite were the case, the batteries would be discharged.

D. Case IV
The conducted simulation aims to illustrate the operation of the SCAC system in the presence of a phase-jump in the grid voltage.In this specific test, a phase jump of 50 deg.Has been triggered.Variable delay from Fig. 4 has been considered for this test.Fig. 19 visually depicts this event.As observed, when the event occurs at 6 s (see Fig. 19(a)), there is a decrease in the frequency detected by the converter (see b).In response to this variation, the inertia emulation system takes the task of injecting active power, as it can be seen in c), to actively mitigate the disturbance, working towards reducing the discrepancy until the event completely dissipates.This detailed assessment not only provides a deeper understanding of the SCAC system's behavior under specific conditions but also emphasizes the effectiveness of the implemented strategy in maintaining stability and the continuity of electrical supply in the face of network disturbances.

E. Case V
In case V, the objective is to showcase the functionality of the SCAC control system in island mode, demonstrating its ability to create a proper grid, thus providing power to the loads connected to that grid.The converters will power the loads assuming different weights to their power injection (0.6 for G 1 , 0.1 for G 2 , and 0.3 for G 3 ).As it can be seen in Fig. 20(a) the grid is created, starting to feed the connected loads by the VSG converter (see b).The delivered power (see Fig. 20(c)) will vary with the load connected to the microgrid.For this case, the reactive power control loop depicted in Fig. 1(c) is employed, in order to add grid forming features to the system.To achieve this, a proportional (P) gain of 0.05 has been utilized, alongside a Proportional-Integral (PI) controller with a P value of 0.27 and an I value of 8.This case has been tested with a constant delay of 75 ms.This scenario underscores the robustness of the SCAC system when operating autonomously, ensuring the stability of the electrical supply even in instances of disconnection from the main grid.The efficient management of loads, considering the distinct characteristics of each converter, highlights the versatility and effectiveness of the system in varied environments.

V. CONCLUSION
This paper proposed a method for the implementation of the aggregated VSG concept in industrial converters by removing access to internal instantaneous variables (current/voltage) and replacing them with a reconstruction technique from RMS values obtained by communications.Considering communications, the effect of a stochastic delay has been addressed, measuring the magnitude of the delay in a MODBUS TCP communication protocol and then employing a delay compensation mechanism to mitigate its effect on the control system performance.Besides, the stability of the system with constant communication delays has been studied, showing that the system remains stable up to 75 ms, although it does not have good dynamics, but the response is significantly improved using the Smith predictor compensation.Furthermore, simulation and experimental results show a satisfactory response with the considered constant and variable delay, in which the effect of internal computational delay and integration windows have been also considered.For that, different scenarios were considered, to test different operation modes, such as Case I, II and III, and they were validated in local and in real-time simulations.In case of Case IV and V, just local simulations.Both reference tracking and disturbance rejection mechanisms have been considered for the system's overall performance evaluation.

Fig. 1 .
Fig. 1.(a) SCAC scheme for n-converters.(b) Simplified Local control scheme.The light green control loop is implemented in the central controller.The orange control loop is implemented in the local controller [13].(c) Added AVG Control for grid forming capabilities [2].

Fig. 3 .
Fig. 3. Setup for HIL and PIL experimental tests.The control design is made on Matlab and executed in the real-time Speedgoat target.The converters are controlled by writing/reading published MODBUS/TCP variables [13].

Fig. 4 .
Fig. 4. (a) Instantaneous delay measurement in the lab (PWM is the sent reference signal and I is the actual current the converter develops).(b) Time variation of delay.(c) Delay histogram from experimental tests.(d) Probability density function of the measured communication delay (M.D) in comparison to Poisson distribution (P.D) with λ of 68 ms.

Fig. 5 .
Fig. 5. (a) Global SP architecture for n-converters (light green block for global control and orange for local control) [17].(b) Local model for each converter (blue blocks) emulated in the global controller.(c) Basic Smith predictor structure.

Fig. 9 .
Fig. 9. Root locus of control system.Base case parameters shown in Table II.(a) Z-P map without delay.(b) Z-P map with delay.(c) Z-P map with SP compensation delay.In the first row of the figure (a), the inertia (H) is varied.In (b) the damping (τ ), and in (c) the droop slope (K p ).In Table I the improved values are bold.

Fig. 10 .
Fig. 10.(a) Power system scheme with three DEGs, showing global and local controllers, battery (SCAC) and PV panels.(b) Working mode I: Active and reactive power setpoints by each DEG, controlled by the SCAC.(c) Working mode II: Power support operation, taking into account grid operator requests.(d) Working mode III: Frequency support operation by power management depending on frequency variations.(e) Working mode IV: Voltage angle stepchange.(f) Working mode V: Islanding mode.

Fig. 11 .
Fig. 11.(a) Active power management for all working modes in each DEG, taking into account the power-sharing between them.Legend G 1 is the first power converter, G 2 is the second power converter, G 3 is the third power converter, DEG is the total power injected by the power plant and R is the power reference.Case I shows the Active and reactive power setpoints by each generator, controlled by the SCAC.Case II shows the power support operation.Case III shows the frequency of support operation.(b) Zoom of case I for active power injection.(c) Zoom of Case II for active power management.(d) Grid frequency variation.(e) Zoom of Case III for Battery power injection for compensating frequency change.

Fig. 12 .
Fig. 12. Virtual admittance variation for Case I and Case II from this section, in order to modify the output power of each converter.G 1 , G 2 and G 3 is the designation of each power converter, as in Fig. 10.

Fig. 14 .
Fig. 14.Experimental validation: (a) Active power command, total power injected to grid and power injected by each converter.(b) Reactive power injected to the grid, showing the command and the actual reactive power.The same legends as Fig. 13 are used in this plot.(c) and (d) Zoomed active and reactive power values and sent references.Actual is the power read by MODBUS TCP.Sent is the power sent by MODBUS TCP to the converter.

Fig. 18 .
Fig. 18.Experimental validation: (a) Power injected to the grid, where at 40 s, the power required by the grid changes to 2.4 kW.(b) Power absorbed by the ESS-SCAC emulated with CNG to obtain the required power.c) ESS-SCAC state of charge (SOC) increases due to the power absorbed by the SCAC system.The same legends than Fig. 17 are used in this plot.For SOC information, the colors match with the number of generators from Fig.17.
Fig. 18.Experimental validation: (a) Power injected to the grid, where at 40 s, the power required by the grid changes to 2.4 kW.(b) Power absorbed by the ESS-SCAC emulated with CNG to obtain the required power.c) ESS-SCAC state of charge (SOC) increases due to the power absorbed by the SCAC system.The same legends than Fig. 17 are used in this plot.For SOC information, the colors match with the number of generators from Fig.17.

Fig. 19 .
Fig. 19.(a) Grid voltage evolution with angle-step at 6 s.(b) Frequency evolution due to the voltage angle-step.(c) Power injection caused for the frequency variation.

Fig. 20 .
Fig. 20.(a) Grid voltage creation and evolution with different load changes.(b) Feeding current by SCAC converter in islanding mode.(c) Power injected by SCAC with some load variations.

TABLE I STABILITY
VALUES FOR THE DIFFERENT CASES FROM FIG.