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Article

Communication-Less Power Sharing Strategy for Microgrids Using Oscillations Generated by Inertia-Enabled Power Sources

Department of Electrical and Mechanical Engineering, University Center for Exact and Engineering Sciences, University of Guadalajara, Guadalajara 44430, Mexico
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Authors to whom correspondence should be addressed.
Electricity 2025, 6(4), 59; https://doi.org/10.3390/electricity6040059
Submission received: 11 July 2025 / Revised: 3 October 2025 / Accepted: 9 October 2025 / Published: 16 October 2025

Abstract

Microgrids have extended their use when connected to or isolated from the grid, where decentralized control architectures are increasingly being used due to their inherent advantages. Among controllers, the non-communicated type allows the problems introduced by the use of communication systems to be avoided; however, these type of controllers are generally limited to performing first-level control actions, precisely due to the lack of information caused by the absence of a communication network. This work proposes an algorithm for a non-communicated controller to (a) identify which of the power sources are connected to a microgrid and (b) calculate the load power; both of these actions only require local measurements and allow the microgrid performance to be improved. The proposal aims at identifying the power sources by analyzing the electromechanical oscillations that occur in microgrids that are fed by inertia-enabled inverters and synchronous generators using droop controllers. This is used to automatically adjust the power sharing ratio between sources based on the generation capacity and load of a microgrid. Numerical simulations that clearly show the advantages are used to support the effectiveness of the proposal.

1. Introduction

In recent years, the inclusion of distributed generation sources (DGSs) based on renewable energy on the low-voltage side of electric power systems (EPSs) has changed the conventional structure of the electric network. This transition has caused distribution systems to acquire characteristics observed in generation and transmission systems, such as injection of power at different points, the occurrence of bidirectional power flows through the lines, the formation of clusters of DGSs and loads, and isolated operation of some regions of the distribution network, among others [1].
At this point, it is important to establish how these systems with DGSs operate. If DGSs and loads are individually controlled, this is classified as a distribution system with DGSs. However, if DGSs and loads are independently controlled and globally coordinated, the system becomes a microgrid (MG). These MGs can operate in on-line mode, that is, connected to an EPS, or in off-line mode if these are not connected to other networks [2].
Depending on the location, physical characteristics, and operating needs of a distribution system with DGSs, there are several control actions that must be covered to ensure a suitable and safe operation; these can be classified into three levels of control [3]. The first-level control actions are those related to the individual operation of DGSs, for example, to regulate the magnitude and frequency of the voltage and the power injected by each DGS or to synchronize each DGS with the grid at the point of connection. The second level comprises those actions related to the coordinated operation of all components, for example, to distribute the load power between DGSs and to regulate the magnitude and frequency of the voltage throughout the grid, as well as synchronization, load shedding functions, and off-line economical operation. This control level defines the system as an MG, as distribution systems with DGSs do not incorporate second-level control actions [2]. The third level manages the interaction of an MG with other MGs or EPSs, for example, to synchronize, connect, and regulate the power exchange of an MG with an EPS, as well as the economical operation of the MG. The third-level control actions are only present in MGs connected to an EPS or other MGs, as opposed to isolated MGs, such as those geographically distant, that do not perform third-level control actions.
The control system of an MG is designed according to three different architectures: centralized, decentralized, and hybrid or mixed; these can also be communicated or non-communicated [4,5]. In the centralized control architecture, a central control unit (CCU) coordinates the operation of all elements of an MG; the CCU can perform control actions at the three levels. This type of architecture requires communication links from the CCU to each component of an MG [5]. An example of this architecture that shows the kind of control actions achieved is the work of Karimi M. et al. [6], in which second-level control such as the balance between generation and load, frequency control, and load shedding are addressed. Another one is presented by Díaz N. L. et al. [7], that also performs second-level control actions such as coordinating and managing energy storage systems (ESSs) or regulating the voltage magnitude and frequency profiles of an MG. Or the one from Prasanna I. V. et al. [8], where the CCU performs first-, second-, and third-level control actions, such as regulation of voltage magnitude and frequency, load power distribution between DGSs, and coordination of the simultaneous operation of various MGs.
On the other hand, the decentralized control architecture has an individual control unit (ICU) in each element connected to an MG [5,9]. Controllers based on this architecture can be communicated, to coordinate the operation of the ICUs, or non-communicated, to perform control actions based on local measurements at each ICU; the levels of control action that can be achieved are dependent on the controller being communicated or non-communicated. Examples of this architecture that show the capabilities of communicated controllers are the work of He Y. et al. [10], which proposes a distributed controller based on multi-agent theory, where each ICU is considered an agent and all agents cooperate to perform second-level control actions to optimally use the resources of an MG; this controller also performs first-level control actions. Equally, the work of Hou X. et al. [11] presents a hierarchical controller that can perform actions at the three levels, such as regulating the magnitude and frequency of the MG voltage, controlling the power flow within the MG, connecting/disconnecting the MG to/from other EPSs, transitioning between different operating states, and regulating the power flow between the MG and an EPS. It is important to note that the droop controller, which is commonly used in non-communicated schemes, is also present in this kind of communicated architecture. An example of this architecture in a non-communicated approach is the work of Li L. et al. [12], that proposes a fully distributed controller to coordinate the operation of an MG with photovoltaic generation and ESSs; only local information is used to regulate the power injection and the magnitude and frequency of the voltage at each power source and coordinate the charge/discharge of ESSs. Additionally, in the work of Chunxia D. et al. [13], a two-level controller is proposed to optimally regulate the voltage magnitude and frequency, as well as the power dispatch.
The hybrid or mixed control architecture combines centralized and decentralized schemes, where an ICU is located in each element of the MG and a CCU coordinates all ICUs (master/slave scheme) [5,9]. Generally, ICUs perform first- and some second-level control actions, and the CCU performs third- and also some second-level control actions. This type of architecture requires communication links to connect each ICU to the CCU. An example of this master/slave hierarchical organization is presented by Brandao D. I. et al. [14] and performs second-level control actions to distribute the load power between DGSs and enhance the power quality at the point of common coupling; the ICUs are managed as slaves by the central CCU. Equally, in the work by Mathew P. et al. [15], the controller can operate based on both centralized and decentralized architectures while being able to perform control actions at the three levels, such as load shedding and power exchange between the MG and an EPS; to regulate the magnitude and frequency of the voltage at each DGS; to distribute the load power between DGSs; or to enhance power quality at the point of common coupling.
Despite the different architectures, the decentralized one is gaining relevance due to its advantages [16]. One of these is to distribute control actions among several ICUs instead of a single CCU, which represents a single failure point in the centralized architecture. With several ICUs, this drawback is partially mitigated in the hybrid architecture, but a failure in the CCU still compromises the critical functions of an MG. In the decentralized architecture, since there is no CCU, the risk of a generalized state of failure is greatly reduced, and even when an ICU fails, the operation can continue due to the fact that each DGS has a dedicated ICU; this makes the distributed architecture the most robust [16]. A very important feature of decentralized architectures is scalability; that is, elements can be added or removed from an MG and only moderate changes in the controllers are needed [16]. Finally, the communication network in the decentralized architecture tends to be less complex and hence less expensive than the one required in the centralized and hybrid architectures [17]; moreover, the decentralized architecture can be non-communicated, which makes its implementation even simpler and less expensive, for example, by using the droop controller, as presented by Sabzevari K et al. [18].
Regarding decentralized communicated and non-communicated architectures, the former present different drawbacks [17,19,20,21,22,23,24]—for example, the latency of the communication systems negatively affects the performance of controllers, especially in the first-level control actions; the bandwidth of a communication link is directly related to the performance of the controllers to provide suitable transient responses, and communication systems with high bandwidth tend to be expensive; and the loss of information packets, as well as the uncertainty, adversely affects the performance of the controllers. Another undesirable effect is the noise that can be captured by communication systems that affects measurements and ultimately control actions. Additionally, communication networks are prone to cyber-attacks (e.g., false data injection, denial of service, abnormal delays, or data tampering) and should be protected, which also increases their cost. Furthermore, MGs installed in marginalized, rural, and geographically isolated communities are expected to be as inexpensive and need as little maintenance as possible.
For the decentralized non-communicated architecture, the most researched and implemented scheme is the droop controller, which has been taken as a base for almost all ICUs due to its advantages [12,13]. It was originally designed to operate SGs in large EPSs without communication links [25]; however, with the advent of DGSs, it was adapted to be used in MGs, where it has become very popular for its simple structure and low computational complexity [26,27]. Due to the lack of information inherent to non-communicated controllers, these have been limited to first-level control actions such as regulating the voltage magnitude and frequency of each DGS and, in a limited way, second-level control actions such as distributing the load power among DGSs of an MG according to their rated capacities or global regulation of the voltage magnitude and frequency [27,28].
One of the variants of the droop controller is the synchronverter, which was proposed due to problems caused by the lack of inertia present in MGs predominantly fed by inverters [28,29]. The lack of inertia can be considered an advantage because of fast transient responses; however, it can also produce several operating drawbacks such as large values for the rate of change in the frequency during variations in the generation and load power, dynamic and frequency instability during severe disturbances, extremely fast transient responses that compromise the performance due to the reduced time available for controls and protections to respond, or the need for global signaling for synchronization of the DGSs, among others [30,31]. In addition, electric networks with low or null inertia lack the short-term energy reserve to carry out the primary regulatory actions over the parameters after a disturbance occurs [30,31]. All of the aforementioned problems can lead to risky operation of an MG and even to a generalized state of failure [30,31].
The synchronverter controller combines the droop controller’s features with the emulation of inertia allowed by using an ESS, hence making inverters respond as if they were synchronous generators (SGs). Therefore, different techniques originally used to coordinate and control the operation of large EPSs fed by SGs can be applied to MGs fed by inverters or a combination of inverters and SGs. From this, it follows that synchronverter-based ICUs maintain compatibility with other droop-based controllers for SGs [28,29].
The synchronverter is part of the virtual synchronous generator concept that was proposed to enable converters to mimic inertia. However, as opposed to other schemes, the synchronverter includes the electromagnetic transient behavior of an SG. In addition to the synchronverter, there are other inertia-enabled algorithms that have been proposed—for example, the virtual synchronous machine, the current-controlled virtual synchronous generator, or variants that can even adapt their inertial response [32,33,34,35]. All of these controllers can mimic inertia and can be used in conjunction with that proposed here. The synchronverter controller was selected in this work because of three advantages: (a) it can mimic inertia, which has been reported (virtual or physical inertia) to help MGs improve stability and avoid sudden changes in voltage magnitude and frequency after a disturbance [36]; (b) the virtual inertia of the controller can be set to generate a specific oscillation frequency, hence allowing a given DGS of an MG to have a distinctive and measurable signature; and (c) it can work without communication channels along other sources that also use droop controllers.
Considering the decentralized non-communicated architecture using DGSs based on synchronverters in an MG, the third-level and some of the second-level control actions cannot usually be performed due to the null exchange of information between ICUs. To solve this drawback, several schemes have been proposed; for example, Díaz N. L. et al. [37] propose a method for performing some second-level control actions to change the mode in which the inverters operate with ESSs. The method is based on bus signaling through the recognition of patterns in the voltage and frequency waveforms after a change in the operating conditions of an MG. The patterns are established according to thresholds that define the ranges of frequency and voltage magnitude that characterize the changes that occurred in the MG; however, because the trend patterns of the voltage are based on the charge and discharge characteristics of ESSs, the degradation of the storage elements can introduce uncertainties when determining the control actions. Another example is where Rey J. M. et al. [38] present a controller that adjusts the set-points of the output power of DGSs of an MG according to the voltage magnitude and frequency deviations observed after a change in load/generation; however, this approach manages the generation considering only power quality factors and dismisses others such as economic constraints and environmental objectives. The work of Khayat Y. et al. [39] presents an optimization-based control system based on a linear quadratic regulator; the control focuses on enhancing power quality, however, only for frequency regulation. The work of Serban E. et al. [40] presents a control strategy for MGs based on droop characteristics that uses the intentional variation in the frequency of the system as a communication agent; however, other phenomena that cause frequency deviations can introduce uncertainties into the information obtained. Equally, the work of Belgana S. et al. [41] proposes an adaptive neural network droop control strategy and particle swarm optimization to generate optimal voltage references that compensate for line effects and load variations; however, the results do not consider whether a DGS is connected or disconnected from the MG.
This work addresses the decentralized non-communicated architecture for MGs with ICUs based on the synchronverter controller for inverter-based DGSs. Among the disadvantages of not having communication links in non-communicated architectures is the inability of the ICUs to be aware of which DGSs are connected to an MG at a given time. Therefore, this work proposes
  • Avoiding communication links when controlling an MG due to their known disadvantages;
  • Identifying the DGSs that are connected to an MG using only local measurements that contain the electromechanical oscillations generated by each DGS after a disturbance;
  • Computing the load power of an MG using an (off-line-trained) ANN fed by only local measurements;
  • Finally adjusting the slope coefficients of the droop controller in each DGS and enhancing the power sharing ratio of an MG.
The main contribution of this work is a non-communicated method that detects which DGSs are connected or disconnected to an MG using a specific electromechanical oscillation frequency related to a specific DGS, to be able to modify the droop controller coefficients. The advantages are
  • The oscillation frequency of each synchronverter-based DGS in an MG can be fixed to a desired value. This allows a different oscillation frequency to be selected for each DGS to prevent them from being near one another, effectively having a distinctive and identifiable frequency fingerprint for each DGS, even if they are similarly rated. The recognition of patterns in electrical waveforms after a change in the operating conditions of an MG has been reported, for example, by Díaz N. L. et al. [37], but these patterns are based on the charge/discharge characteristics of ESSs that degrade over time and can introduce uncertainty, as well as by Serban E. et al. [40], but these are based on intentional variation in the system frequency, where other phenomena that cause frequency deviations can introduce uncertainty into the information obtained, and by Baldwin, M.W. et al. [42] for detecting the natural oscillation frequency of generators and determining whether these are connected to an electric network, but the oscillation frequency is fixed, which results in similarly rated generators with a similar natural oscillation frequency. On the other hand, in this work, the oscillatory patterns depend on the controller parameters of a synchronverter algorithm that can be set to specific values, which makes it easier to discriminate among DGSs.
  • The droop controller coefficients are adjusted. This changes the slope of the droop controller of each DGS to enhance the voltage and frequency regulation and the power sharing ratio among DGSs. Adjusting coefficients has also been reported, for example, by Khayat Y. et al. [39], who propose adjusting the controller, but the focus is only on frequency regulation, whereas in this work, the voltage, frequency, and power sharing ratio are enhanced.
  • The DGSs connected to an MG can be detected. This allows the controller to be adapted to meet the requirements. Other authors have proposed adaptive controllers; for example, Belgana S. et al. [41] use an adaptive neural network droop control strategy and particle swarm optimization to generate optimal voltage references that compensate for line effects and load variations; however, the results do not consider whether a DGS is connected or disconnected from the MG, which has a great impact on voltage, frequency, and power sharing.
An additional beneficial characteristic of this work is to allow a synchronverter-based back-to-back converter to interface an MG to an electric network, which results in every DGS being aware of whether the MG is in on-line or off-line mode; this also helps to regulate the power between an EPS and an MG.
The proposed algorithm is intended for small MGs located in rural communities that can be isolated from the utility grid. These conditions also suggest that the MG should be as inexpensive as possible, hence the lack of a communication system. In these non-communicated conditions, the droop controller is the most used scheme. Although it has its challenges, as other controllers, using a non-communicated scheme is key to reducing the MG cost in terms of infrastructure and maintenance.
The rest of the paper is organized as follows: Section 2 gives a review of the conventional droop controller, along with the synchronverter; Section 3 explains the electromechanical (or virtual) oscillation phenomenon in an MG; Section 4 presents the proposed strategy for detecting the generation and load power through an analysis of electromechanical oscillations and local measurements; Section 5 verifies the advantages of the proposal through numerical simulations; Section 6 presents a discussion of challenges and future work; and finally, Section 7 gives the conclusions of the work.

2. Synchronverter Controller Based on the Droop Scheme

This section presents the basics of the droop controller along with a brief introduction of the synchronverter. Both can be used in MGs with inverter-based DGSs, SGs, or a combination and can operate with local measurements in distributed and non-communicated MGs [25,26,27]. From now on, the term DGS is used in general to refer to an SG or an inverter-based source; however, where necessary for clearness, the distinction is explicitly made.

2.1. Droop Controller

The droop controller consists of a double proportional controller that regulates the injection of active and reactive power by varying the frequency and magnitude of the output voltage of a given source; it can also be used inversely to control the frequency and magnitude of the output voltage through the injection of active and reactive power [27,28,32]. The droop control law for MGs can be deduced considering the three types of impedance that characterize a transmission link, that is, predominantly inductive, resistive, or capacitive; the controller approach varies with this impedance because the power flow is controlled differently [27,28].
Consider the MG shown in Figure 1 with k DGSs connected to a feeder node that delivers power to a load. Each DGS is represented as a voltage source U k = U k δ k with an output impedance Z k = Z k θ k in series with the impedance of the conductor Z l i k = Z l i k θ l i k that connects each DGS to the feeder node. The impedance Z l o = Z l o θ l o groups all loads and the conductors that connect them to the feeder node. The angle of the feeder node voltage U l o = U l o 0 is taken as a reference. The output impedance of each DGS and its link conductor to the feeder node can be grouped as Z t o k = Z t o k θ t o k = Z k θ k + Z l i k θ l i k . Accordingly, the current that each source sends to the feeder node is given by
I k = U k δ k U l o 0 Z t o k θ t o k = U k cos δ k U l o Z t o k θ t o k + j U k sin δ k Z t o k θ t o k .
The active and reactive power transferred from each source towards the feeder node is consequently
P k = U k U l o Z t o k cos δ k U l o 2 Z t o k cos θ t o k + U k U l o Z t o k sin δ k sin θ t o k Q k = U k U l o Z t o k cos δ k U l o 2 Z t o k sin θ t o k U k U l o Z t o k sin δ k cos θ t o k .
The common case for MGSs with SGs and/or synchronverters is the inductive approach [28,29] and can be derived considering that θ t o k 90 and that during normal operation δ k tends to be very small [20,26], which leads P k and Q k to become
P k U k U l o Z t o k δ k , Q k U k U l o U l o 2 Z t o k .
From these expressions, the droop control strategy can be formulated as
U k = U k * D Q k Q k , ω k = ω * D P k P k ,
where D Q k and D P k are the slope coefficients of the reactive and active power control loops, respectively; ω k and U k are the frequency and magnitude of the output voltage of the kth DGS, respectively, with ω * and U k * being their respective reference values.
To adjust each loop of the droop controller, the slope coefficients are given by
D P k = FCPB ω * P k * , D Q k = VCPB U k * Q k * ,
where P k * and Q k * are the reference active and reactive power for the kth DGS considering a given load, the number of connected inverters, and the power that each inverter must deliver based on its rated power. For each DGS, D Q k and D P k determine its power sharing ratio with respect to the other DGSs in an MG. Also, for an MG with multiple sources, general slope coefficients can be obtained from the individual ones; for example, to combine the kth and nth sources, one can use the expressions
D P k n = D P k D P n D P k + D P n , D Q k n = D Q k D Q n D Q k + D Q n .
According to the droop control law, the magnitude and frequency of the voltage in an MG directly depend on the amount of connected load; therefore, the general droop characteristics of an MG are used in this work to estimate the amount of active and reactive load power using local measurements at any DGS. For the frequency/active power characteristic, the level of accuracy when estimating the load is high because the frequency is a global parameter that maintains a value close to the rated one. However, in the case of the voltage magnitude/reactive power characteristic, the voltage amplitude, even though it maintains a global trend, presents variations from one measurement point to another, which are mainly caused by the line impedance and current flow throughout the network.

2.2. Synchronverter Controller

A synchronverter is an inverter that mimics an SG because it combines a droop controller with the electromechanical inertial behavior of an SG [28,29,31]. Since the synchronverter is based on the behavior of a rotatory SG, its mathematical model is briefly revised; refer to Zhong Q. et al. [28,29,31] for the detailed model.
Without loss of generality, a two-pole round-rotor synchronous machine is considered, where the stator and field-rotor windings are assumed to be concentrated coils; the electrical equations are given by
e = ω r M f i f sin ˜ δ r , T e = M f i f i o , sin ˜ δ r ,
where e is the back electromotive force caused by the motion of the rotor; T e is the electromagnetic torque; M f is the mutual inductance of the field winding; i f is the field winding current; δ r and ω r are the angle and frequency of the virtual rotor, respectively; i o is the output current; sin ˜ δ r represents the variation in the mutual inductance of the system as a vector of three balanced sine functions; and · , · is the inner product of two elements. Based on these quantities, the reactive power becomes
Q = ω r M f i f i o , sin ˜ δ r .
On the other hand, the mechanical behavior is governed by the swing equation
J r ω r ˙ = T m T e D P ω r ,
where J r is the moment of inertia of the rotor due to mechanical mass; T m is the mechanical torque provided by the prime mover; and ω r ˙ is the angular acceleration.
The physical structure of the synchronverter used in this work is shown in Figure 2 and comprises a DC voltage source ( u d c ), an inverter bridge, and an output L C filter to reduce commutation harmonics. The inductance of the filter plays the role of the stator winding, and the capacitor is supposed to be a reactive power bank to improve the power factor at the point of connection [29].
Also, some sort of ESS must be included on the DC side of the synchronverter to emulate the virtual inertia. This ESS represents an electric version of the kinetic energy stored in the rotatory mass of an SG and can be accomplished using capacitors, batteries, or other types of energy storage systems [30,43]. The amount of virtual inertia that can be emulated is in direct relation to the energy storage capacity of an ESS; that is, a small-rated ESS allows for small moments of inertia, whereas a high-rated ESS allows for high moments of inertia; a synchronverter without energy storage has no inertia unless the primary DC source allows for reverse power flows [30,43]. Therefore, an ESS allows a synchronverter to emulate a range of moments of inertia that can be pre-programmed. On the other hand, the rotor mass of an SG uniquely determines the amount of kinetic energy stored and therefore the moment of inertia [30,43].
The synchronverter algorithm is shown in the block on the lower-right side of Figure 3 (Synchronverter–droop controller for a single DGS), where the current injected into the MG ( i o ) and the output voltage ( u o ) are local measurements; an amplitude detection block is used to obtain the amplitude of u o . The term A, which divides the integrator of the voltage magnitude/reactive power control loop, also plays a role in determining the time constant of this loop using the expression [28,29] τ v A ω * D Q . The coefficients D P and D Q determine the response speed, the accuracy of the power sharing ratio, and the deviation of the voltage magnitude and frequency; these are also related to the damping of electromechanical oscillations.
The voltage magnitude/reactive power control loop in the synchronverter controller in Figure 3 regulates the magnitude of the output voltage of the DGS and its reactive power to their respective references U o * and Q * . On the other hand, the frequency/active power control loop regulates the frequency of the output voltage of the DGS and its active power to their respective references ω * and P * . The active power is directly related to the mechanical torque ( T m ) of the synchronverter, which equals the electromagnetic torque ( T e ) in steady-state operation. The effects of virtual inertia appear as oscillations in, for example, the frequency, active power, or phase angle of the synchronverter, until the steady state is reached; this is in direct analogy to the electromechanical oscillations that an SG undergoes after a disturbance. A time constant that depends on the active power droop coefficient ( D P ) and the moment of inertia ( J r ) is also present and is given by [28,29] τ f = J r D P . Note that as J r decreases or D P increases, the frequency of the associated oscillation rises; the opposite behavior occurs if J r increases or D P decreases. This shows that D P plays the role of a damping oscillation coefficient, and its value must be selected considering the power sharing ratio [27,28], the damping effects [44], stability constraints [44], or a combination.
Two possible modes of operation are found in an MG: the on-line mode, where each DGS injects electric power according to a given reference, and the off-line mode, where DGSs inject electric power according to the MG load and the power sharing ratio of the DGSs. Therefore, when an MG operates in on-line mode, the power that each synchronverter must deliver is set by P * and Q * ; however, in off-line mode, these set-points become zero, and the injected power depends only on the slope coefficients and load power.
An important advantage of the synchronverter controller is that it can be combined with other droop-based controllers even if these are for SGs. For example, in an MG fed by a combination of SGs and inverters, the ICUs placed at the SGs can be conventional droop controllers, whereas the ICUs located at the inverters can be synchronverter controllers. This eliminates the need to interface all DGSs of an MG using inverters.

3. Electromechanical Oscillations as Information Carrying Signals

The phenomenon of electromechanical oscillations occurs in an EPS fed by an SG, and the characteristics of these oscillations are determined by the circumstances that cause them and the physical nature of the system [45,46]. Therefore, the phenomenon itself reveals valuable information that can be harnessed to adjust control actions in an MG without the need for communication and measurement networks.
When an EPS comprises only one electrical source with inertia, the oscillatory phenomenon does not occur because there is no exchange of stored inertial energy with another source [42,45,46]. In addition, the oscillations cannot be measured because there is no reference point [42,45,46], as will be discussed.
Consider the simple case of two electrical sources with inertia connected through a purely inductive transmission link ( X g ). In this case, the swing equation in Equation (9) states that the acceleration torques ( J r k ω ˙ and J r n ω ˙ ) acting on DGS k and DGS n , respectively, are zero if the electromagnetic torques ( T e k and T e n ) produced by the current flowing between the sources are equal to the mechanical torques ( T m k and T m n ) produced by the prime mover of each DGS; this condition is known as an equilibrium state and accounts for steady-state operation. The damping effects in Equation (9) are present only during transient processes that involve acceleration/deceleration behavior [46]. In the case of a synchronverter, the damping loop acts only during transient processes in which the frequency deviates from the synchronous virtual speed. Other damping effects, such as those of the resistances of the electric network, are compensated for by the DGSs and can be considered part of the load.
Any change in the current flowing between the DGSs modifies the electromagnetic torques, and the balance between T e and T m is broken, causing J r ω ˙ to experience variations. In this process, when the kinetic energy stored in the masses of each rotor is exchanged between the DGSs, the oscillatory phenomenon appears, and both DGSs oscillate against a common center of mass located within the transmission line [42]; however, the oscillations cease when a new equilibrium point is reached. The system used in this example has no damping, and this is not the case in actual networks where damping forces the amplitude of the oscillation to gradually decrease over time.
To reach the natural frequency of the oscillatory phenomenon, let us start by representing the moment of inertia of the kth DGS as
J r k = M r k A c s k ,
where A c s k is the area of the cross-section of the rotor and M r k is its mass. This indicates that the larger the rotors, the lower the oscillation frequencies and vice versa.
The moment of inertia helps determine the inertia constant given by [46]
H r k = J r k ω * 2 2 S k * ,
where ω * is the reference angular frequency of the MG and S k * is the rated apparent power of the kth DGS; since ω * and S k * remain constant, H r k mainly depends on J r k .
The natural frequency of the oscillatory phenomenon also depends on the power synchronization coefficient represented as
S P k = P m a x k cos δ r 0 k ,
where δ r 0 k is the initial value of the rotor angle, and P m a x k is the maximum power that the kth DGS can deliver [42], as given by
P m a x k = U k U n X e k ,
where U k and U n are the voltage magnitudes of the kth and nth DGSs, and X e k is the electrical distance from the kth DGS to the center of mass, expressed by
X e k = J r n J r k + J r n X g ,
where J r k and J r n are the moments of inertia of the kth and nth DGSs, and X g is the inductance of the conductor linking the kth and nth DGSs. This impedance ( X e k ) directly depends on the inertia moments of the kth and nth DGSs, affecting P m a x k and ultimately S P k , making these parameters strongly dependent on the electrical distance of the kth DGS to the center of mass.
In Equation (13), U k and U n may change, but only in a narrow band since these must be maintained close to their rated value; therefore, P m a x k mostly depends on X e k ; S P k also mostly depends on X e k since δ r 0 k is an initial value and remains constant and can be set to zero.
Finally, the natural frequency of the oscillatory phenomenon of the kth DGS with respect to the center of mass is given by [42]
f n k = 1 2 π ω * S P k 2 H r k ,
where ω * is the reference angular frequency of the electric network, which remains constant. Therefore, f n k depends on S P k and H r k , making this frequency mainly dependent on the moment of inertia ( J r k ) and the electrical distance from the kth DGS to the center of mass ( X e k ); J r k remains constant for a given cross-section and mass of a rotor, even if it is a virtual rotor, and X e k only changes if a DGS is connected or disconnected to the MG, and this is what has to be taken into account when detecting the oscillation frequency of a given DGS.
Equation (14) shows that the location of the center of mass depends on the relationship between the inertia moments of the DGSs; the center of mass is drawn to the DGS with the highest inertia. If one of the DGSs largely outweighs the other, as in the case of an infinite bus, the center of mass can be considered to be inside the biggest DGS. However, in general, DGSs oscillate against each other with a natural oscillation frequency ( f n ) that depends on the center of mass located at some point of the link that connects them. Both DGSs oscillate against the center of mass with the same frequency due to the relationship between inertia and electrical distance. The DGS with higher inertia also has a proportionally larger synchronization coefficient, whereas the one with lower inertia has a proportionally lower synchronization coefficient, making the quotient S P k / 2 H r k the same for both DGSs. Therefore, the two DGSs oscillate against each other in the counter-phase, making the oscillations visible at any point except at the center of mass, where they cancel each other out. Even though these types of oscillations occur in EPSs due to the electromechanical behavior of SGs, they are also present when synchronverters are used because these can emulate inertia.
Since this work proposes identifying the DGSs that participate in the oscillation phenomenon of an MG, it is important to establish that each oscillation frequency can be calculated using Equation (15). And because X e k , related to the configuration of the MG, is the main factor affecting the oscillation frequency, the frequency fingerprint of all possible combinations of connected/disconnected DGSs is incorporated into the proposed controller as a truth table for the algorithm to be able to determine which DGSs are connected to the MG at a given time. Baldwin, M.W. et al. [42] already showed the feasibility of detecting the natural oscillation frequency of generators to determine whether these were connected to an electric network. In addition, Chen, X. et al. [47] showed that the center of mass does not change with the load flow conditions, strengthening the idea that the impedance of an MG is the most determining factor that influences the oscillation frequency of a DGS.
In the case of an EPS composed of three or more DGSs and/or connected to other EPSs, the oscillatory phenomenon occurs in a combined way because it is composed by the oscillations produced by each pair of sources. For example, in an MG with three DGSs, the oscillating behavior combines waveforms from the pairs DGS 1 - DGS 2 , DGS 1 - DGS 3 , DGS 2 - DGS 3 , and so on. This is similar to what occurs on the surface of a water pond, where several disturbances cause different waves that overlap. The combined oscillatory phenomenon can be mathematically described by [48]
a o t = A 1 0 + A 1 e ξ 1 2 t cos ω n 1 t + A 2 0 + A 2 e ξ 2 2 t cos ω n 2 t + ,
where A 1 0 , A 1 , ξ 1 , and ω n 1 are the mean value, amplitude, damping factor, and natural frequency, respectively, of the first oscillating signal, which can be a frequency, phase angle, electric power, or another associated waveform. In addition, the amplitude of the oscillating component depends on the electrical distance between the center of mass and the measurement point. This means that when measuring at the kth DGS, the amplitude of a given oscillating signal predominates over the rest; however, the combined signal still contains all of the components [48].
The analysis of these electromechanical oscillations allows critical information to be obtained, e.g., which of the DGSs are connected to an MG [42]; this is exploited in this work to perform control actions beyond the first level, such as adjustment of the power sharing ratio among DGSs. It should be noted that when a disturbance produces a low-amplitude oscillation, the change in the operating condition of an MG is small and can be neglected due to the action of the ICU.

4. Generation and Load Assessment Using Local Measurements

The inability of droop-based controllers to perform second- and third-level control actions is mainly due to the fact that there are no communication channels to exchange information among ICUs. In this section, a strategy is proposed to mitigate this drawback by using local measurements to detect the power sources available and the load power of an MG.
The MG used in this work, shown in Figure 4, is composed of three DGSs that feed a load node: two of these ( DGS 1 and DGS 2 ) are renewable energy (RE)-based sources interfaced with inverters. The third source ( DGS 3 ) is a high-speed gas turbine coupled with a power converter due to the high speed of the rotor. The MG is connected to the external EPS through a back-to-back converter. Connecting an MG with the electrical network using a back-to-back converter is a practice that serves different purposes—for example, fault isolation, power conditioning and power flow control, smooth islanding and re-synchronizing (anti-islanding) operations, or DC microgrid integration [49]. It is also useful when asynchronous MGs are connected to the power system [50] or to interlink MGs among them [51,52]. In this work, controlling the back-to-back converter with the proposed strategy has several advantages; for example, since there is no communication system between DGSs, the proposed controller can detect whether the MG is on-line or in islanded mode and provide control over the power exchanged between the electric system and the MG, actively supporting its voltage magnitude and frequency. In addition, it decouples the dynamics of the electric system and the MG, preventing the propagation of disturbances.
Although the controller is designed for the MG in Figure 4, the strategy is usable with other configurations as long as these are fed by sources linked with power converters regulated by droop-based controllers with virtual inertia or by sources with real inertia. Also, the estimation of the load through the general slope characteristics can also be applied in MGs regulated by droop-based controllers without inertia.

4.1. Detection of the DGS Through Electromechanical Oscillations

There are different methods for decomposing oscillatory signals [46]; however, since signal processing is not the aim of this work, a Fourier algorithm based on the work of Baldwin MW et al. [42] and Barocio E et al. [53] is used. The measured signal is separated by means of a filter bank, where the individual frequencies are tuned according to the natural frequencies present between pairs of DGSs; the damping effect is then compensated using the amplitude of the corresponding signal. Finally, the frequency components are identified using the fast Fourier transform and compared against the corresponding natural oscillation frequencies to determine which of the sources are connected to the MG. Each DGS has a flag that denotes its state: when S t k = 1 , the kth DGS is connected to the MG; when S t k = 0 , it is disconnected. The process is shown on the upper-right side of Figure 3 (flag detector of DGSs) and it contains k filters, each one to detect a specific DGS.
Since a Fourier-based algorithm is used to process the oscillatory signals, at least one oscillation period is required. The algorithm in the flag detector of the DGSs in Figure 3 shows that the signal processed by the Fourier algorithm is delivered by a bandpass filter which removes noise, and only the components related to the natural frequency of oscillation of a DGS are allowed to pass. The output of the FFT block in the flag detector of the DGSs in Figure 3 delivers only the natural oscillation frequency of a particular DGS. The oscillatory frequency of a DGS depends on the parameters of the synchronverter controller and especially on the moment of inertia. Different moments of inertia are selected to prevent multiple DGSs from oscillating at the same frequency and allow the proposed controller to determine which DGSs are connected to an MG.

4.2. Load Estimator

Using expression (4), the magnitude and frequency of the load voltage can be written as U l o = U l o * D Q l o Q l o and ω = ω * D P l o P l o , respectively, from which a strategy is developed to estimate the load power of an MG. These expressions consider the voltage magnitude at the load node ( U l o ) and its reference value ( U l o * ); the general slope coefficients of voltage magnitude/reactive power ( D Q l o ) and voltage frequency/active power ( D P l o ); the active ( P l o ) and reactive ( Q l o ) load power; and the frequency of the MG ( ω ) and its rated value ( ω * ). Clearing for Q ^ l o and P ^ l o , one can obtain the expressions for estimating the load power using voltage magnitude and frequency measurements, given by
P ^ l o = ω * ω D P l o , Q ^ l o = U l o * U l o D Q l o ,
where D P l o and D Q l o are general slope coefficients that combine the three DGSs (as in Expression (6)) of the MG in Figure 4. A block diagram of the load estimation strategy is shown in Figure 5a.
The variation in the magnitude of the voltage across the MG affects the performance of the load calculation strategy, and this is solved using an artificial neural network (ANN) to estimate the droop coefficients in (17) as D ^ P l o and D ^ Q l o . Since the training patterns for the ANN are obtained directly from the MG, the voltage magnitude variations are already taken into account to calculate the slope coefficients that yield the proper load values. As shown in Figure 5b, the training data for the ω -P ANN consider ω , D ^ P 1 , D ^ P 2 , D ^ P 3 , and D ^ P b b as input signals, and P ^ l o is the output; for the case of the U -Q ANN, the inputs are U o , D ^ Q 1 , D ^ Q 2 , D ^ Q 3 , and D ^ Q b b , and Q ^ l o is the output. The ANN used in this work is a two-layer feedforward neural network with four sigmoid activation functions in the hidden layer and a single neuron with a linear activation function in the output layer and is designed using the Matlab® R2018a neural fitting tool with four neurons in the hidden layer, trained using the Levenberg–Marquardt backpropagation algorithm. The input–output vectors used for the training are obtained from simulations using the MG in Figure 4 with fixed control parameters and considering different scenarios for load power and power sharing between DGSs. These training vectors contain the load power, the voltage magnitude and frequency of the load node, and the droop coefficient values.

4.3. Slope Coefficient Calculator

Once the load power and DGSs connected to an MG are known, it is possible to calculate the droop coefficients according to specific requirements to achieve a proper load sharing ratio among sources. For example, suppose that the rated power of the sources in Figure 4 is S 1 * = 1 kVA , S 2 * = 2 kVA , S 3 * = 3 kVA , and the back-to-back converter is S b b * = 6 kVA . Since DGS 1 and DGS 2 are sources based on RE, it is desirable that both provide their full capacity to harness their renewable nature [54]; this makes DGS 3 and the back-to-back converter play the role of backup sources to fully supply the load.
The objective is to develop a strategy that forces DGS 1 and DGS 2 to fully utilize their capacity. If the load still exceeds the combined generated power, the surplus must be supplied by DGS 3 and the back-to-back converter; the order in which DGS 3 and the back-to-back converter supply the load can also be established. A block diagram of the slope coefficient calculator is shown in Figure 3, which calculates the amount of load power that each DGS must inject to obtain suitable values for D P 3 and D P b b , i.e., D ^ P 3 , and D ^ P b b , to account for load changes, while D P 1 and D P 2 remain fixed. The strategy requires each DGS flag ( S t k ) and its known rated power ( P k * ), the total power demanded by the load ( P ^ l o ), and the droop coefficients for DGS 1 and DGS 2 ( D P 1 * and D P 2 * ). In the event that one of the RE-based DGSs is disconnected, the other RE-based DGS is forced to supply its full power; moreover, if both RE-based DGSs are disconnected, the load is supplied by DGS 3 and the back-to-back converter according to their rated power.
Other control actions can also be considered; for example, the connection or disconnection of each DGS can depend on the load power, or if the load power does not exceed the capacity of the RE-based DGSs, DGS 3 and the back-to-back converter can be left disconnected, and when the load power increases, the order of connection of the DGSs can also be specified.
The slope coefficient calculator in Figure 3 is presented for the ω -P droop coefficients; however, the structure can also be used for the U -Q relation.

5. Simulation Results

To demonstrate the usefulness of the proposal through numerical simulations, two test cases are presented using the Simscape Electrical tool from Matlab®/Simulink® R2018a. Both consider the MG shown in Figure 4 with the parameters in Table 1. The rated power of the sources is S 1 * = 1 kVA , S 2 * = 2 kVA , and S 3 * = 3 kVA , and that for the back-to-back converter is S b b * = 6 kVA ; these are, however, considered to be 20 % below the maximum power to avoid damage. For the test, it is assumed that RE-based DGSs, DGS 1 and DGS 2 , have their full power capacity available.
For all simulations, gray lines represent the case with fixed coefficients, whereas black lines represent the case where the coefficients are adjusted using the proposed strategy.
The objective of the test is to show that the proposed strategy is capable of setting appropriate values for the slope coefficients of each DGS controller to comply with specific generating conditions.

5.1. Full Renewable Energy Power Injection

In this test, the MG operates in isolated mode with the back-to-back converter deactivated and DGS 1 , DGS 2 , and DGS 3 supplying the load power; the two RE-based DGSs, DGS 1 and DGS 2 , must maintain their maximum generated power, and the SG-based DGS, DGS 3 , must adjust its power. Comparison against a simulation with fixed coefficients is made to assess the performance of the proposed strategy.
The output power of each DGS is set by computing the appropriate slope coefficients based on detecting the DGSs connected to the MG and the calculated load. Also, the load is set to draw only active power since the intention is to show that the full power of the RE-based DGSs can be harnessed, but the same procedure can be used to include reactive power. The load increases during the test to show the change in the slope coefficients, which has a direct impact on the load power sharing ratio among the DGSs.
The simulation starts at t = 0 s under steady-state conditions with a load power of 5 kW and a power sharing ratio for the three DGSs of P 2 = P 3 = 2 P 1 ( D P 1 * = 1 , D P 2 * = 2 , and D P 3 * = 2 ). The load increases at t = 1 s by 0.6 kW , and the proposed strategy calculates the connected load and computes new slope coefficients for the controller of each DGS. These coefficients are calculated to force the RE-based DGSs, DGS 1 and DGS 2 , to continue injecting their full available power, while DGS 3 provides the surplus. This modifies the power sharing ratio, preventing DGS 1 and DGS 2 from providing part of the increased load power and therefore exceeding their respective power limit; these changes are solely due to the increase in load power, as the configuration of the MG remains unchanged. This test shows the performance of the load power calculation strategy, as well as the one that modifies the slope coefficients considering the DGSs connected to the MG; signals that show the results are presented in Figure 6 and Figure 7.
The power delivered by each DGS is shown in Figure 6a–c, where for fixed parameters, the power delivered by each DGS increases proportionally with the load power at t = 1 s ; this increase follows the originally set power sharing ratio. As a consequence, both RE-based DGSs increase the supplied power beyond their rated value, exposing themselves to disconnection due to the proper protection schemes. On the other hand, for the case of adjusted coefficients and after a transient period, DGS 1 and DGS 2 maintain the injection of power to the value prior to the increase in power load, thus avoiding disconnection, while DGS 3 increases its injection power to account for the increase in power load. In the case of fixed slope coefficients, the power sharing ratio remains fixed; however, when the proposed procedure is used, these coefficients are updated to effectively modify the power sharing ratio. Note that in this particular case, since the objective is to maintain the power injection of DGS 1 and DGS 2 unchanged, only the slope coefficient of DGS 3 is modified; the updated value of D P 3 (Figure 6d) is based on the connected DGSs and power load and changes the load sharing ratio to P 2 = 2.5 and P 3 = 2 P 1 , while P 1 remains unchanged.
Finally, Figure 7 shows the behavior of the feeder node, where the active power of the load is obtained using u l o and i l o , as shown in Figure 7a. Figure 7b,d,f present the estimated load power obtained using the proposed strategy at each DGS using local measurements; these signals are needed to be able to change the corresponding slope coefficients without the need for communication links. As can be seen, the load power values calculated at each DGS and the one at the feeder node are very similar, confirming the validity of the proposal. Furthermore, Figure 7c,e show the magnitude and frequency of the voltage at the load node; note that as expected in an MG regulated by droop controllers, the magnitude of the voltage decreases when the load increases. Similar behavior is found with the frequency of the voltage, where it can be noticed that the frequency also falls when the load increases; however, in the case where the slope coefficients are updated, it recovers to a value closer to the rated one. This contributes to enhancing the frequency profile and highlights the importance of a suitable load sharing ratio; note that this overload is related to the virtual machine (synchronverter) parameters. It is important to mention that the active power depends on the frequency; therefore, for the case where the slope coefficients are updated and the frequency recovers, the calculated load power at each DGS (Figure 7b,d,f) closely matches the measurement of the load power at the feeder node (Figure 7a), as opposed to the case where the coefficients are fixed and the frequency deviates from its rated value. For the magnitude of the voltage, the recovery does not occur because in the synchonverter algorithm, the frequency and magnitude are decoupled; therefore, an increase in voltage frequency is not reflected as an increase in voltage magnitude, as happens in real synchronous generators.

5.2. Increasing the Imported Energy of an MG to Aid in Load Supply

This test is performed to demonstrate the effectiveness of the proposed strategy in identifying when a DGS is disconnected from an MG; however, the load is also calculated, and the slope coefficients are adjusted. The test is performed with DGS 3 deactivated while DGS 1 , DGS 2 , and the back-to-back converter supply a constant load of 5 kW . It is also assumed that the RE-based DGSs, DGS 1 and DGS 2 , inject their full rated power and an event causes DGS 2 to disconnect from the microgrid. The load sharing ratio is P 2 = P b b = 2 P 1 ( D P 1 * = 0.5 , D P 2 * = 1 , and D P 3 * = 1 ); nevertheless, to show the effectiveness of adjusting the coefficients to different values, the slope coefficients are half the value of those used for the first test.
The test starts in a steady state at t = 0 s with the DGSs supplying the load according to the specified load sharing ratio, and it remains in this condition until t = 1 s , where DGS 2 is disconnected. Once the absence of DGS 2 is detected, the slope coefficients are adjusted to account for the loss of injected power. The results are shown in Figure 8, Figure 9 and Figure 10.
As can be seen in Figure 8, DGS 2 delivers 2 kW and at t = 1 s stops injecting power (Figure 8b). In response, DGS 1 and the back-to-back converter tend to increase their injected power to account for the power loss (Figure 8a,c). In the case of fixed slope coefficients, both sources increase their output power according to the prespecified power sharing ratio; note that this may cause DGS 1 to disconnect due to proper protection schemes, while the back-to-back converter is subutilized. However, when the proposed strategy is used to adjust the slope coefficients, the disconnection of DGS 2 is correctly identified during the transient period (Figure 8d), and the injected power returns to 1 kW for DGS 1 (Figure 8a), while the back-to-back converter increases its power injection (Figure 8c) to account for the increase in load power.
The signals in Figure 8d account for detecting when DGS 2 is disconnected and are obtained by the controller of each DGS using local measurements. As can be seen, all signals correctly account for the loss of DGS 2 , which confirms the performance of the proposed strategy in detecting when a source is connected or disconnected. Note that since this is accomplished using distinctive electromechanical frequencies, there is a delay from the time a DGS disconnects to the time it is detected. This work uses a Fourier-based algorithm, and at least a full cycle of the oscillation is needed; however, other algorithms can be used to shorten the detection time.
Figure 9 shows the slope coefficients of DGS 2 and the back-to-back converter, where it can be observed that D P b b changes to a higher value while D P 2 changes to zero due to the disconnection of DGS 2 . Note that this modifies the load power sharing ratio to P b b = 4 P 1 , to allow the back-to-back converter to fully supply the injected power from the disconnected DGS 2 . To update these coefficients, the DGSs actually connected to the MG must be taken into account, which adds a delay corresponding to the detection process; these coefficients change when the disconnection of DGS 2 is detected (Figure 8d).
Finally, Figure 10a shows the load power of the MG measured at the load node using u l o and i l o . It is noticeable that the frequency deviates greatly from the nominal value when using the fixed coefficients; on the other hand, when using the proposed strategy it recovers to its nominal value after detecting that DGS 2 disconnects from the MG, as observed in Figure 10c, which confirms the effectiveness of the proposal. The disparity in signals between the cases with fixed and adjusted coefficients responds to the frequency recovering to the appropriate value in the case of the proposed strategy (Figure 10c); also, the magnitude of the voltage in Figure 10b shows a small variation between the two cases.

6. Discussion

This section discusses challenges and future work related to the results found in this work.

6.1. Quality of the Voltage Magnitude and Frequency and Its Relation to Stability of the Droop Controller

It is known that when using non-communicated droop controllers, the most common problem is that voltage magnitude and frequency deviate from their rated values. However, the proposed controller is capable of detecting DGSs and the load connected to an MG modifying the droop coefficients accordingly, which improves voltage magnitude and frequency by keeping them closer to their rated values. Nevertheless, if the change in the droop coefficients is high enough, it can affect the operation of the MG; for example, varying these parameters will change the damping of the synchronverter. On the one hand, if the values of the coefficients increase, the influence of the controller also increases, improving the voltage magnitude and frequency. However, the network becomes overdamped, causing oscillations to end faster, or if the coefficients are large enough, the system could cease to oscillate. In contrast, if the values of the coefficients decrease, the influence of the controller also decreases, deteriorating the voltage magnitude and frequency. Now, the network becomes underdamped, causing the oscillations to last longer. The authors in [55,56,57] reported this behavior.

6.2. Operation Under Short Circuits

The response of a system to a short circuit will depend on its type, location, impedance, and duration, as well as the operational state of the system before, during, and after the fault. If a fault is severe enough to disconnect a DGS, the oscillations produced after clearing the fault will help the proposed controller identify the DGSs connected and change the droop constants, which can help maintain the variables of the MG close to their nominal values. If the fault does not result in a DGS disconnecting from the MG, the oscillations produced after clearing the fault will also help the proposed controller to identify the DGSs connected to the MG. There is no doubt that protection schemes are a topic of interest and will continue to be studied by the research community.

6.3. DGSs Reaching Their Power Limit

When operating at maximum load during stand-alone mode, one or more DGSs can disconnect if the load power increases. This would generate the “electromechanical” oscillation required for the proposed algorithm to detect which DGS disconnected from the MG. If the remaining DGSs can supply the load, the MG will continue to operate; otherwise, part of the load may need to be disconnected to prevent other DGSs from reaching their power limit.

6.4. Constantly Changing Load Power

The proposed algorithm performs two tasks: one is to detect whether a DGS is connected to the MG, and the other is to calculate the load power using local measurements at the terminals of each DGS. In the case of constantly changing loads, the ANN-based load power calculator operates at all times. Even if a load change produces an “electromechanical” oscillation, the proposed algorithm will detect the oscillation frequency of all DGSs and will not change the droop controller coefficients. To determine whether an oscillation frequency is present or not, and consequently whether a DGS is connected to the MG or not, in this work, a Fourier-based algorithm is used that requires at least one oscillation cycle. The algorithm for processing the oscillating signal is not a key part of the proposal, and other approaches have to be tested to reduce the processing time well below a full cycle. In this regard, if a DGS is disconnected from the MG, the proposed algorithm with the Fourier-based approach will determine which one is disconnected after a full oscillation cycle, and if a second DGS were to disconnect before detecting the first one, the proposal would not be able to determine which source actually disconnected from the MG.
On the other hand, in the case of operating at the maximum load power during stand-alone mode, in which case a DGS can disconnect if the load power increases. This would generate the “electromechanical” oscillation required for the proposed algorithm to detect which DGS disconnected from the MG and change the droop controller coefficients accordingly.

6.5. Occurrence of Subsynchronous Oscillations

The phenomenon of subsynchronous oscillations is a problem found in electric networks fed by inverter-based power sources, and it is still under study. This phenomenon has been associated with the interaction of controls and PLL synchronizers, as mentioned in [58,59]. However, the proposed algorithm does not use PLL synchronizers, which reduces the possibility of subsynchronous oscillations appearing. Nonetheless, this is an important topic that needs to be studied.

6.6. Non-Fourier-Based Algorithm for Detecting Oscillations

A full period is needed for the Fourier-based algorithm to process the oscillatory signals in this work. Moreover, in the case of weak or poorly damped oscillations, the oscillation period increases, also increasing the time required to detect whether a DGS is connected to an MG. In such cases, other phenomena may occur during the time needed to process the oscillatory signal. Therefore, it is important to maintain the detection time low, which suggests that other signal processing algorithms need to be investigated.

7. Conclusions

A strategy is proposed to enable control actions beyond the first level in droop-based controllers that incorporate virtual or real inertia. It was shown that the proposal is able to detect the connection/disconnection of DGSs in an MG and calculate the load power using local measurements at the terminals of each DGS; this is used to adjust the slope coefficients of the DGSs in an MG.
The developed tool is tested through numerical simulations to demonstrate its effectiveness in two specific cases to readjust the load sharing ratio as needed: the first case results from increasing the load demanded by the MG, and the other one from increasing the energy imported from an EPS after a DGS is disconnected from the MG. The results obtained show that the proposed strategy is able to identify the DGSs that are connected/disconnected to an MG, calculate the load power, modify the slope coefficients, and, ultimately change the load sharing ratio to comply with specific needs when using RE-based DGSs; all these actions are accomplished using only local measurements at the terminals of each DGS. The tests also deal with second-level control actions that aid in balancing the generated and load power of an MG. Moreover, the proposed algorithm can detect the back-to-back converter that connects the MG and the EPS, allowing the controller of each DGS to be aware of whether the MG is in on-line or off-line mode and changing the power sharing ratio of the DGSs and also the power exchanged with the EPS; this constitutes a third-level control action since it manages the injection of power from an EPS through the back-to-back converter.
The test cases show the potential of the proposal to solve problems within a wider scope than that presented in this work, as it can consider other operating conditions by combining some or all of the enhancements presented here; the performance of the proposal can also be improved by using other methods to extract information from the electromechanical oscillations.

Author Contributions

Conceptualization: M.G. and P.Z.; methodology: M.G. and P.Z.; software: M.G.; validation: M.G., P.Z., D.d.P.-F., F.U. and E.B.; formal analysis: M.G. and P.Z.; investigation: M.G. and P.Z.; resources: M.G.; data curation: M.G.; writing—original draft preparation: M.G. and P.Z.; writing—review and editing: M.G., P.Z., D.d.P.-F., F.U. and E.B.; visualization: M.G., P.Z., D.d.P.-F., F.U. and E.B.; supervision: M.G. and P.Z.; project administration: M.G. and P.Z.; funding acquisition: E.B. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Secretaría de Ciencia, Humanidades, Tecnología e Innovación (SECIHTI) through scholarship 307342 and project CF-2019/1311344. The APC was funded by the Program to Enhance the Productive Conditions of Researchers (PROSNII-2025) at the University of Guadalajara.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors.

Acknowledgments

The contributions in this article are the result of ongoing research in the Department of Mechanical and Electrical Engineering of the Centro Universitario de Ciencias Exactas e Ingenierías (CUCEI), Universidad de Guadalajara, Jalisco, México.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
ANNArtificial Neural Network
CCUCentral Control Unit
DGSDistributed Generation Source
EPSElectric Power System
ESSEnergy Storage System
FCPBFrequency Control Proportional Band
ICUIndividual Control Unit
MGMicrogrid
RERenewable Energy
SGSynchronous Generator
VCPBVoltage Control Proportional Band

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Figure 1. A schematic diagram of a microgrid.
Figure 1. A schematic diagram of a microgrid.
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Figure 2. The physical configuration of a synchronverter.
Figure 2. The physical configuration of a synchronverter.
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Figure 3. Proposed controller.
Figure 3. Proposed controller.
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Figure 4. The microgrid for the simulation tests.
Figure 4. The microgrid for the simulation tests.
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Figure 5. Block diagrams for (a) the computed load using the droop characteristic, and (b) the estimated load using an ANN.
Figure 5. Block diagrams for (a) the computed load using the droop characteristic, and (b) the estimated load using an ANN.
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Figure 6. Results of the first test: (a) Active power of DGS 1 . (b) Active power of DGS 2 . (c) Active power of DGS 3 . (d) Droop coefficient of DGS 3 .
Figure 6. Results of the first test: (a) Active power of DGS 1 . (b) Active power of DGS 2 . (c) Active power of DGS 3 . (d) Droop coefficient of DGS 3 .
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Figure 7. Results of the first test: (a) load power at the load node. (b) Estimated load power at the DGS 1 . (c) Voltage magnitude at the load node. (d) Estimated load power at the DGS 2 . (e) Frequency of the voltage at the load node. (f) Estimated load power at the DGS 3 .
Figure 7. Results of the first test: (a) load power at the load node. (b) Estimated load power at the DGS 1 . (c) Voltage magnitude at the load node. (d) Estimated load power at the DGS 2 . (e) Frequency of the voltage at the load node. (f) Estimated load power at the DGS 3 .
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Figure 8. Results of the second test: (a) active power of DGS 1 . (b) Active power of DGS 2 . (c) Active power of the back-to-back converter. (d) State flag of DGS 2 .
Figure 8. Results of the second test: (a) active power of DGS 1 . (b) Active power of DGS 2 . (c) Active power of the back-to-back converter. (d) State flag of DGS 2 .
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Figure 9. Results of the second test: (a) droop coefficient of DGS 2 . (b) Droop coefficient of the back-to-back converter.
Figure 9. Results of the second test: (a) droop coefficient of DGS 2 . (b) Droop coefficient of the back-to-back converter.
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Figure 10. Results of the second test: (a) load power at the load node. (b) Voltage magnitude at the load node. (c) Frequency of the voltage at the load node.
Figure 10. Results of the second test: (a) load power at the load node. (b) Voltage magnitude at the load node. (c) Frequency of the voltage at the load node.
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Table 1. Test system data.
Table 1. Test system data.
ValueDescriptionAppears in
Microgrid data Z l i 1 , 2 , 3 , b b = 0.065 Ω + j 5 mH Line impedance of all sourcesFigure 4
Controller data U o * = 220 V DGS voltage referenceFigure 3
U l o * = 220 V Load node voltage referenceFigure 3
ω * = 50 Hz Microgrid frequency of referenceFigure 3
J r 1 = 0.1 kgm 2 Moment of inertia of DGS 1 Figure 3
J r 2 = 0.3 kgm 2 Moment of inertia of DGS 2 Figure 3
J r 3 = 0.5 kgm 2 Moment of inertia of DGS 3 Figure 3
J r b b = 0.7 kgm 2 Moment of inertia of back-to-backFigure 3
A 1 , 2 , 3 , b b = 555.17 Integral constant of allFigure 3
Inverter data f s = 15 kHz Switching frequencyFigure 2
R = 0.130 Ω Inductor filter resistanceFigure 2
L = 5 mH Filter inductanceFigure 2
C = 40 μ F Filter capacitanceFigure 2
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Gutierrez, M.; Zuniga, P.; del Puerto-Flores, D.; Uribe, F.; Barocio, E. Communication-Less Power Sharing Strategy for Microgrids Using Oscillations Generated by Inertia-Enabled Power Sources. Electricity 2025, 6, 59. https://doi.org/10.3390/electricity6040059

AMA Style

Gutierrez M, Zuniga P, del Puerto-Flores D, Uribe F, Barocio E. Communication-Less Power Sharing Strategy for Microgrids Using Oscillations Generated by Inertia-Enabled Power Sources. Electricity. 2025; 6(4):59. https://doi.org/10.3390/electricity6040059

Chicago/Turabian Style

Gutierrez, Marco, Pavel Zuniga, Dunstano del Puerto-Flores, Felipe Uribe, and Emilio Barocio. 2025. "Communication-Less Power Sharing Strategy for Microgrids Using Oscillations Generated by Inertia-Enabled Power Sources" Electricity 6, no. 4: 59. https://doi.org/10.3390/electricity6040059

APA Style

Gutierrez, M., Zuniga, P., del Puerto-Flores, D., Uribe, F., & Barocio, E. (2025). Communication-Less Power Sharing Strategy for Microgrids Using Oscillations Generated by Inertia-Enabled Power Sources. Electricity, 6(4), 59. https://doi.org/10.3390/electricity6040059

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