Fully Decentralized Sliding Mode Control for Microgrid Frequency Regulation

Academic Editor: Giacomo Canciello
Received: 2 August 2025
Revised: 2 October 2025
Accepted: 16 October 2025
Published: 18 October 2025
Citation: Rosero, C.X.; Rosero, F.;
Tapia, F. Fully Decentralized Sliding
Mode Control for Frequency
Regulation and Power Sharing in
Islanded Microgrids. Energies 2025,18,
5495. https://doi.org/10.3390/
en18205495
Copyright: © 2025 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
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(https://creativecommons.org/
licenses/by/4.0/).
Article
Fully Decentralized Sliding Mode Control for Frequency
Regulation and Power Sharing in Islanded Microgrids
Carlos Xavier Rosero * , Fredy Rosero and Fausto Tapia
Faculty of Engineering in Applied Sciences, Universidad Técnica del Norte, Ibarra 100102, Ecuador;
faroser[email protected] (F.R.); [email protected] (F.T.)
*Correspondence: cxr[email protected]
Abstract
This paper proposes a local sliding mode control (SMC) strategy for frequency regulation
and active power sharing in islanded microgrids (MGs). Unlike advanced strategies,
either droop-based or droop-free, that rely on inter-inverter communication, the proposed
method operates in a fully decentralized manner, using only measurements available at
each inverter. In addition, it adopts a minimalist structure that avoids adaptive laws and
consensus mechanisms, which simplifies implementation. A discontinuous control law is
derived to enforce sliding dynamics on a frequency-based surface, ensuring robust behavior
in the face of disturbances, such as clock drifts, sudden load variations, and topological
reconfigurations. A formal Lyapunov-based analysis is conducted to establish the stability
of the closed-loop system under the proposed control law. The method guarantees that
steady-state frequency deviations remain bounded and predictable as a function of the
controller parameters. Simulation results demonstrate that the proposed controller achieves
rapid frequency convergence, equitable active power sharing, and sustained stability.
Owing to its communication-free design, the proposed strategy is particularly well-suited
for MGs operating in rural, isolated, or resource-constrained environments. A comparative
evaluation against both conventional droop and communication-based droop-free SMC
approaches further highlights the method’s strengths in terms of resilience, implementation
simplicity, and practical deployability.
Keywords: sliding surface; voltage source inverter; nonlinear control; communication-free
strategy; filippov solutions; lyapunov stability
1. Introduction
Microgrids (MGs) are self-sufficient energy systems that mainly integrate distributed
generation (DG) units, storage components, and loads. When operating in islanded mode,
MGs disconnect from the main grid. They must autonomously regulate their internal vari-
ables to ensure voltage amplitude/frequency quality, as well as balanced power sharing [1].
Voltage source inverters (VSIs), which constitute the interface layer of DG units, are central
to this operation, acting as controllable bridges between energy sources and the islanded
grid. From a cyber–physical viewpoint, MGs are regarded as multi-agent systems where
each VSI functions as an autonomous agent interacting through electrical couplings such
as voltage and frequency [2].
Traditional MG control relies on a hierarchical scheme. Primary control typically
applies droop laws to achieve proportional power sharing using only local variables,
but it inherently introduces steady-state frequency deviations [ 3 ]. Secondary control,
Energies 2025,18, 5495 https://doi.org/10.3390/en18205495

Energies 2025,18, 5495 2 of 17
often communication-based, compensates for these deviations by coordinating invert-
ers via centralized or distributed algorithms [ 4 , 5 ]. Despite improvements in accuracy
and flexibility [ 6 , 7 ], these approaches are vulnerable to communication failures [ 8 , 9 ],
and their dependency on digital links limits their applicability in isolated, or degraded
infrastructure environments.
To overcome these limitations, some approaches have proposed sparse-communication
schemes for frequency restoration and active power sharing [ 10 ]. However, such methods
still rely on digital channels, and their performance deteriorates in the presence of link
failures. Recent advances have aimed at reducing this communication burden, for instance
through event-triggered or sampled-data protocols that minimize message exchanges
while preserving coordination [ 11 ]. Nevertheless, these methods still depend on digital
infrastructure and remain vulnerable to packet loss, synchronization errors, or cyberattacks.
As more resilient alternatives, other works have explored fully communication-free
control architectures that exploit the physical coupling of the electrical network to enable
coordination through purely local interactions [ 12 , 13 ]. In these frameworks, each inverter
adjusts its frequency based solely on internal variables, enabling plug-and-play operation
and increased robustness in environments where reliable communications cannot be guar-
anteed. Beyond control-based solutions, other studies have pursued physically grounded
strategies to enhance fault resilience without communication. For example, ref. [ 14 ] pro-
poses a fault ride-through mechanism based on current limiters that ensures continued
system operation under severe conditions, reinforcing the broader shift toward robust,
communication-independent architectures across power system domains.
Sliding mode control (SMC) is a robust nonlinear control strategy widely used for
its ability to reject matched disturbances and ensure finite-time convergence to a desired
manifold [ 15 , 16 ]. Its implementation relies on discontinuous control actions that guide
system trajectories onto a predefined sliding surface, providing resilience under model
uncertainties and parameter variations. These features make SMC particularly appealing
for MG inverter control, where robustness and simplicity are paramount [17].
Most SMC-based approaches for MGs, including [ 17 – 21 ], incorporate communication,
consensus dynamics, higher-order sliding modes, or sensor observers that rely on global
system information. Moreover, while most existing strategies focus primarily on steady-
state performance, they often neglect performance analysis under perturbations. As a
result, these methods may struggle to maintain robust operation in the presence of clock
mismatches, abrupt load changes, or network reconfigurations.
To the best of the authors’ knowledge, strictly local SMC schemes, where each inverter
uses only its own frequency and power measurements, without estimation, synchronization,
or messaging, remain largely unexplored in the literature. In response to this gap, this
paper proposes a local SMC method for frequency restoration and active power sharing in
islanded MGs, entirely free of communication dependencies. The sliding surface is defined
solely in terms of the local frequency error, eliminating the need for neighbor information
or external synchronization. The proposed control law is embedded within a droop-based
hierarchical framework, and its switching strategy operates exclusively on local variables.
This design is particularly suited for resilient MG operation in scenarios where digital
communication is impractical, unreliable, or intentionally avoided. A Lyapunov-based
analysis is provided to establish theoretical guarantees of closed-loop stability, and sim-
ulation results confirm that the system maintains synchronized frequency and balanced
power sharing even under disturbances.
Beyond performance and robustness, the communication-free nature of the controller
also offers benefits in terms of cybersecurity: avoiding digital links reduces the system’s
attack surface. While not the primary focus of this study, related concerns such as attack

Energies 2025,18, 5495 3 of 17
detection in resource-constrained environments [ 22 ] warrant further investigation. Finally,
this work openly acknowledges its limitations: the frequency regulation is bounded rather
than exact; chattering may occur due to the discontinuous nature of the control law; and
the validation is limited to a testbed without hardware-level modeling.
The remainder of this paper is structured as follows. Section 2presents the MG
modeling and Section 3, the local control framework. Section 4introduces the proposed
sliding mode control law. Section 5develops a formal Lyapunov-based stability analysis.
Section 6reports simulation results on a four-inverter MG. Section 7discusses system
performance and limitations. Finally, Section 8concludes the paper and outlines directions
for future work.
2. MG Electrical Network Model
The electrical structure of the islanded MG is modeled under the assumption of purely
local control. Unlike distributed approaches that rely on inter-node communication, the
proposed scheme operates without any communication links, and therefore, the dynamic
behavior is driven exclusively by local measurements and electrical coupling.
The MG is represented as an undirected graph GE= (N , EE) , where N={ 1, 2, . . . , n}
denotes the set of n DG units, and EE⊆ N ×N is the set of electrical connections among
them. Each edge in EE corresponds to an impedance line characterized by an admittance
yij =gij +jbij , where gij and bij denote the conductance and susceptance between each
pair of nodes (i,j), respectively.
Under the standard assumptions of power systems modeling [ 23 ], namely, uniform
voltage magnitudes and small phase angle differences, the active power injected by each
node i,pi(t), is given by
pi(t) = v2n
∑
j=1
gij +v2n
∑
j=1
bijθi(t)−θj(t), (1)
where v is the common voltage magnitude, and θi,j(t) are the voltage phases at nodes i , j .
The first term accounts for the resistive losses, while the second term represents the power
exchange due to phase differences.
Let p(t)=[p1(t) , . . . , pn(t)]⊤ be the VSI active powers and θ(t)=[θ1(t) , . . . , θn(t)]⊤ ,
the set of phase angles; the active power injection (1) can be expressed in vector form as
p(t) = v2G1n+v2Bθ(t), (2)
where G∈Rn×n contains the conductance values gij , B∈Rn×n is the susceptance Laplacian
matrix of the electrical graph, and 1n∈Rn is the all-ones vector. The Laplacian matrix is
defined as
B=
∑j̸=1b1j−b12 ··· −b1n
−b21 ∑j̸=2b2j··· −b2n
.
.
..
.
.....
.
.
−bn1−bn2··· ∑j̸=nbnj
. (3)
In this work, B is defined under the assumption of a balanced electrical network, where
the total susceptance observed at each node is symmetric. Consequently, B is a Laplacian
matrix satisfying B=B⊤ , B⪰ 0, and B·1n= 0. This structural property simplifies
the derivation of stability results. Nonetheless, practical MGs may exhibit topological
asymmetries or parameter mismatches that violate this ideal balance.

Energies 2025,18, 5495 4 of 17
Taking the time derivative of the power injection (2) , and noting that frequency is the
time derivative of the phase, ω(t) = ˙ θ(t), the dynamic relationship is stated as
˙
p(t) = v2Bω(t), (4)
that links the frequency dynamics directly to the rate of change in active power, and serves
as the foundation for analyzing the stability of the proposed local sliding mode control law.
3. Local Control Framework
This section revisits the standard droop control paradigm for local frequency regula-
tion in islanded MGs.
3.1. Conventional Droop Control
In islanded MGs, frequency droop control is a widely adopted strategy for decen-
tralized regulation of DG units [ 3 ]. The droop method establishes a linear relationship
between the frequency deviation and the active power injection at each inverter, enabling
autonomous load sharing and frequency regulation based solely on local measurements.
The classical frequency droop control law implemented at each node i∈ N is given by
ωi(t) = ω0−mpi(t), (5)
where ωi(t) is the instantaneous frequency of inverter i , ω0 is the nominal reference fre-
quency, pi(t) is its locally measured active power injection (1) , and mi> 0 is the uniform
droop gain applied across all nodes. This scalar coefficient governs the trade-off between
dynamic response and steady-state frequency deviation. Although in practice each inverter
may have a distinct droop gain mi , this work adopts the homogeneous case mi=m for
all i∈ N to simplify the analysis. The proposed method and its theoretical properties
remain applicable to the heterogeneous scenario, which can be addressed through local
gain rescaling or adaptive extensions.
Defining the vector of VSI local frequencies ω(t)=[ω1(t) , . . . , ωn(t)]⊤ , the droop
control law (5) can be written as
ω(t) = ω01n−mp(t). (6)
3.2. Steady-State Requirements for Frequency and Power Sharing
In steady-state conditions, defined as t→∞, the system is required to satisfy
ω(t)→ω01n, (7)
p(t)→pT
n1n, (8)
where pT is the total active power demanded by the load. These asymptotic conditions
ensure frequency synchronization and balanced active power sharing under decentralized
and communication-free operation.
3.3. Local Voltage Regulation
Although the main focus of this work is on frequency and active power control, voltage
amplitude is assumed to be regulated independently at each node via a conventional
voltage droop law. In vector form, this control can be expressed as
v(t) = v01n−cq(t), (9)

Energies 2025,18, 5495 5 of 17
where v(t) = [v1(t) , . . . , vn(t)]⊤ is the vector of voltage magnitudes, q(t) = [q1(t), . . . , qn(t)]⊤
is the vector of local reactive power injections, v0 is the nominal reference voltage, and c> 0
is a proportional gain applied identically at all nodes.
4. Sliding Mode-Based Frequency Control
This section introduces an enhancement to conventional droop control through a
sliding mode term that enforces finite-time convergence to the nominal frequency.
4.1. Local SMC Law and Sliding Surface
The control objective is to synchronize all local inverter frequencies to a common
nominal value ω0 , relying solely on local measurements of frequency. To enhance the
baseline behavior defined by the conventional droop law (5) , a discontinuous sliding term
is added. As a result, the dynamic behavior of each ith node is defined by
ωi(t) = ω0−mpi(t) + ksgn(si(t)), (10)
where k> 0 is the sliding mode gain to enhance robustness, and si(t) is the sliding surface
defined as the local frequency error
si(t) = ω0−ωi(t). (11)
The sign function in (10) applies a maximal corrective action when the error is non-
zero and ceases once the system reaches the surface, satisfying si(t) = 0. This yields the
switching behavior
sgn(si(t)) = 
+1 if si(t)>0,
0 if si(t) = 0,
−1 if si(t)<0.
(12)
By aggregating all variables into vector form, the SMC law (10) becomes
ω(t) = ω01n−mp(t) + k·sgn(S(t)), (13)
where the vectorial version of the sliding surface in (11) is defined as
S(t) = ω01n−ω(t). (14)
Differentiating (14) gives the frequency error dynamics
˙
S(t) = −˙ω(t). (15)
This expression clearly shows that the frequency dynamics are directly influenced by the
discontinuous control term and do not require neighborhood information or power-sharing
calculations, as in droop-free and consensus strategies.
4.2. Sliding Mode Behavior
Once the system trajectories reach the surface S(t) = 0 , the dynamics enter the sliding
regime. By enforcing ˙ S(t) = 0, the induced motion becomes
˙ω(t) = 0⇒ω(t) = ω01n,∀t≥ts, (16)
with ts being the finite reaching time. Therefore, frequency synchronization is achieved for
all nodes.