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Plug-and-play voltage and frequency control of islanded microgrids with meshed topology
Stefano Riverso, Fabio Sarzo, Giancarlo Ferrari-Trecate
TL;DR
Islanded microgrids need decentralized voltage and frequency regulation that remains stable in meshed networks without real-time controller communication. The paper develops a PnP controller synthesis using local DGU and line information plus two global scalars, and simulations show effective operation under nonlinear and unbalanced loads. The design limits retuning to neighboring DGUs during plugging and unplugging, subject to stated modeling and compensation conditions.
Problem
Decentralized voltage and frequency regulation in islanded microgrids must preserve stability despite DGU interactions, particularly for meshed topologies.
Method
The paper develops decentralized PnP controllers whose synthesis uses each DGU and its connected lines, two global scalars, and measurable-disturbance compensation.
Results
Simulations show effective PnP control for meshed microgrids and robustness to nonlinear and unbalanced loads, using IEEE performance measures.
Takeaways & Limitations
Plugging in or out a DGU requires retuning only physically connected local controllers, without a global microgrid model in the design steps.
Takeaways & Limitations
Perfect disturbance compensation cannot be achieved when the stated conditions for the compensator formula do not hold, although finite-bandwidth rejection remains possible.
Abstract
from arXiv · showhide
In this paper we propose a new decentralized control scheme for Islanded microGrids (ImGs) composed by the interconnection of Distributed Generation Units (DGUs). Local controllers regulate voltage and frequency at the Point of Common Coupling (PCC) of each DGU and they are able to guarantee stability of the overall ImG. The control design procedure is decentralized, since, besides two global scalar quantities, the synthesis of a local controller uses only information on the corresponding DGU and lines connected to it. Most important, our design procedure enables Plug-and-Play (PnP) operations: when a DGU is plugged in or out, only DGUs physically connected to it have to retune their local controllers. We study the performance of the proposed controllers simulating different scenarios in MatLab/Simulink and using performance indexes proposed in IEEE standards.
1 Introduction
Islanded microgrids must regulate voltage and frequency locally, while decentralized control in meshed topologies must preserve stability without real-time communication. The paper addresses this with a PnP synthesis procedure requiring only local line information and two global scalars, validated through simulations.
- Islanded operation requires DGUs to control voltage and frequency locally, unlike grid-connected operation where the main grid sets them.
- Decentralized control becomes especially challenging when microgrids are meshed and controllers do not communicate in real time.
- Stability under decentralized control is difficult because interactions among DGUs can spoil overall stability, and meshed non-droop control remains largely unexplored.
- The proposed PnP synthesis uses each DGU's local data and connected-line parameters plus two global scalars, without requiring information about other DGUs.
- When a DGU is plugged in or out, only physically connected DGUs must retune their local controllers.
- Simulations evaluate voltage tracking, robustness to nonlinear and unbalanced loads, and real-time plugging operations in two- and ten-DGU microgrids.
2 Microgrid model
The paper models each DGU, its line interconnections, inputs, disturbances, and measured outputs, then develops a QSL-based representation for networks with N DGUs. The resulting collective model separates line dynamics structurally from the DGU states, supporting decentralized stability analysis.
- Each DGU contains a DC source, VSC, series filter, transformer-related dynamics, and a PCC shunt capacitance, while connected lines have nonzero resistance and inductance.
- The line-current expansion uses opposite directed currents, with equal line parameters and initial currents satisfying Iij,dq(0) = −Iji,dq(0).
- Load currents are treated as disturbances, and the two-DGU model defines states, control inputs, disturbances, and PCC voltage outputs explicitly.
- QSL model: The QSL approximation replaces line-current dynamics in the DGU equations with algebraic coupling terms based on neighboring DGU states.
- The line dynamics are asymptotically stable for positive line parameters, so overall stability depends on the interconnected local DGUs under the QSL model.
- QSL model of a microgrid composed of N DGUs: For N DGUs, each DGU is coupled through its neighbor set Ni, while the collective model stacks local states, inputs, disturbances, measured variables, and controlled variables.
- The collective model has block-triangular structure because line states do not influence the stacked DGU state vector x.
3 Plug-and-Play decentralized voltage control
The paper augments each DGU with integrators and designs decentralized local controllers whose neutral interactions guarantee asymptotic stability. The resulting procedure supports plug-and-play operations while requiring only local information and two global parameters.
- 3.1 Decentralized control scheme with integrators: Integrators augment the microgrid model to track constant voltage and frequency references with zero steady-state error.The augmented exogenous signals include load currents and reference signals in dq coordinates.
- 3.1 Decentralized control scheme with integrators: The augmented DGU pair is controllable, allowing each local subsystem to be stabilized by state feedback.The paper establishes controllability of (Â_ii, B̂_i) and uses it to stabilize the augmented model.
- 3.2 Decentralized PnP control based on neutral interactions: Local controller synthesis uses local matrices and design parameters once the global quantities η and C_s are fixed.Each controller problem depends on the corresponding DGU, while controller computations for other DGUs remain independent.
- 3.2 Decentralized PnP control based on neutral interactions: Neutral-interaction conditions make the overall closed-loop microgrid asymptotically stable despite coupling among DGUs.The result assumes identical shunt capacitances and controller conditions that produce the required neutral interaction structure.
- 3.3 Performance enhancements: Reference prefilters preserve asymptotic stability when they are realizable and asymptotically stable, while measurable-disturbance compensation may require bandwidth-limited rejection.If the conditions for the compensator are not met, perfect compensation cannot be achieved using the stated formula.
- 3.2 Decentralized PnP control based on neutral interactions: Plug-and-play redesign is localized: after a DGU is connected or disconnected, controllers outside the affected neighborhood need not be retuned.The redesign is not propagated further through the network, provided the relevant algorithmic operations terminate successfully.
4 Simulation results
Simulations on two-DGU and larger microgrids evaluate voltage tracking, disturbance rejection, nonlinear and unbalanced-load robustness, and PnP control performance using realistic component models.
- Simulation setup: The simulations use MatLab/Simulink realistic models, first testing two DGUs and then a 10-DGU microgrid.The evaluation includes voltage-reference tracking, disturbance robustness, nonlinear and unbalanced loads, and real-time DGU plugging and unplugging.
- Voltage tracking: The two-DGU controllers stabilize the overall microgrid and track voltage-reference steps with small inter-DGU interactions.Reference tracking is achieved in less than two cycles in the reported DGU 1 test.
- Unknown load dynamics: Load-resistance changes are absorbed within a cycle, while disturbance compensators shorten transients caused by resistance variations.The compensators react to measurable load-current disturbances to reduce their effect on PCC voltages.
- Nonlinear loads: With a highly nonlinear rectifier load, average voltage THD is 4%, below the IEEE-recommended 5% maximum.The controllers maintain voltage tracking despite distorted rectifier currents.
- Unbalanced loads: Under highly unbalanced loads, the voltage imbalance ratio VN/VP remains below 0.5%, below the IEEE permissible value of 3%.The result is also observed when PCC capacitances differ from the common design value.
4.2 Scenario 2
Scenario 2 applies the PnP controllers to a meshed 10-DGU microgrid, including a loop and real-time plug-in and unplugging operations. The reported closed-loop model remains asymptotically stable and preserves the desired transfer function after both operations.
- Scenario 2: The meshed test network contains 10 DGUs, multiple-neighbour connections, and a loop that complicates voltage regulation.The paper presents this as a previously unattempted setting for loop-connected DGUs in a meshed topology.
- Initial controller design: The QSL microgrid has asymptotically stable closed-loop eigenvalues, with identical desired low-pass responses using 0 dB DC gain and 1 kHz bandwidth.The local controllers and compensators are synthesized through the decentralized design algorithm.
- Plug-in operation: After plugging in a new DGU, only its physical neighbours retune their controllers and compensators, while the new DGU receives locally synthesized control components.The algorithm permits controller replacement after the plug-in operation.
- Plug-in results: After plug-in, the closed-loop eigenvalues remain stable and the closed-loop transfer function coincides with the desired one.The plug-in causes short voltage deviations that are compensated after retuning.
- Unplugging operation: After unplugging a DGU, the remaining 10-DGU microgrid remains asymptotically stable and retains the desired closed-loop transfer function.Retuning compensates short voltage deviations at the affected PCCs.
5 Conclusions
The paper presents a decentralized scheme guaranteeing voltage and frequency stability in islanded microgrids, including meshed topologies, while limiting controller retuning during plug-and-play operations.
- The proposed decentralized control scheme guarantees voltage and frequency stability in islanded microgrids.
- Plugging in or out a distributed generation unit requires updating only a limited number of local controllers.
- The design does not require a global islanded-microgrid model at any design step.
- Numerical results confirm plug-and-play control effectiveness for meshed microgrids with practical component nonlinearities.
- Over longer horizons, source dynamics and stochasticity become important because constant-voltage-source modeling is no longer valid.
A Matrices in microgrid models
The appendix provides the matrices appearing in the microgrid models.
- The appendix lists all matrices appearing in Section 2.
A.1 Master-Slave model (2)
This subsection presents a matrix entry associated with the Master-Slave model.
- The displayed matrix entry is associated with the Master-Slave model.
A.2 QSL model (5) and (6)
This subsection presents a matrix entry associated with the QSL model.
- The displayed matrix entry is associated with the QSL model.
A.3 QSL model of microgrid composed by N DGUs
The QSL model represents an N-DGU islanded microgrid through block matrices describing local DGU dynamics and inter-DGU connections.
- Overall model: The overall microgrid model is organized as an N-by-N block matrix of subsystem dynamics and interconnection terms.The supplied matrix layout lists blocks A_ij across all DGU pairs.
- Overall model: The model includes block input, output, and interconnection matrices associated with each DGU.The supplied expressions show B_i, C_i, H_i, and M_i arranged in block structures.
B Relevance of coupling in the decentralized design of regulators for the Master-Slave model
The Master-Slave analysis shows that controllers designed for decoupled DGUs can stabilize the isolated subsystems but may fail to stabilize the coupled microgrid.
- Coupled Master-Slave model: The augmented Master and Slave models include local dynamics, cross-coupling matrices, control inputs, and disturbances.The state equations contain A_12 and A_21 as well as local feedback inputs and disturbance terms.
- Decentralized regulators: LQR controllers are designed for the individual DGUs using specified state and input weighting matrices.The weights are Q_1 = diag(I_8, 10I_2), Q_2 = diag(I_6, 10I_2), and R_1 = R_2 = I_2.
- Decoupled system: The decoupled closed-loop system is asymptotically stable under the stabilizing local controllers.The eigenvalues of system (47) are shown as asymptotically stable in Figure 23.
- Open-loop system: The open-loop system is stable except for eigenvalues at the origin associated with the integrators.This behavior is shown in Figure 22.
- Coupled system: When coupling terms are included, asymptotic stability is not guaranteed because some eigenvalues of system (48) have positive real parts.Figure 23 identifies the coupled-system eigenvalues in red.
C Electrical and simulation parameters of Scenario 1 and 2
The appendixed parameters cover the electrical models, VSC filters, lines, common DGU settings, and reference steps used in the two simulation scenarios.
- Scenario 1: Scenario 1 uses a table of electrical parameters for a microgrid with two DGUs.Table 2 provides the scenario-specific electrical parameters.
- Common model parameters: The simulations specify VSC filter parameters for the modeled DGUs.These settings are listed in Table 3.
- Scenario 2: Scenario 2 includes parameters for the three-phase connection lines and common DGU settings.Tables 4 and 5 provide these electrical and DGU parameters.
- Scenario 2: Scenario 2 uses parameter sets indexed over DGUs i = {1, ..., 11}.The supplied appendix entries identify this index range for Scenario 2.
- Simulation inputs: Reference-step simulations define final V_d,ref and V_q,ref values after the step time T_step.These reference parameters are described in Table 6.