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A decentralized scalable approach to voltage control of DC islanded microgrids
Michele Tucci, Stefano Riverso, Juan C. Vasquez, Josep M. Guerrero, Giancarlo Ferrari-Trecate
TL;DR
DC islanded microgrids need voltage-control methods whose stability analysis and controller synthesis scale beyond specific network configurations. The paper develops a decentralized PnP procedure using local DGU and connected-line information, and formally relates stability to the QSL model. PSCAD simulations report good voltage tracking and robustness to unknown load dynamics in radial and meshed scenarios.
Problem
DC islanded-microgrid controllers have mainly used droop control, while closed-loop stability has been analyzed only for specific microgrids.
Method
The paper uses decentralized PnP controller synthesis based only on each DGU and its connected transmission lines, with QSL line approximations and structured Lyapunov functions mapped to an LMI problem.
Results
PSCAD simulations show very good voltage tracking and robustness to unknown load dynamics, and demonstrate controller operation during plugging and unplugging in radial and meshed microgrids.
Takeaways & Limitations
Only neighboring DGUs need retune when a DGU is plugged in or out, supporting scalable decentralized control across changing microgrid topologies.
Takeaways & Limitations
The decentralized design does not generally imply stability of the interconnected closed-loop system, so controller assumptions and stability conditions remain necessary.
Abstract
from arXiv · showhide
We propose a new decentralized control scheme for DC Islanded microGrids (ImGs) composed by several Distributed Generation Units (DGUs) with a general interconnection topology. Each local controller regulates to a reference value the voltage of the Point of Common Coupling (PCC) of the corresponding DGU. Notably, off-line control design is conducted in a Plug-and-Play (PnP) fashion meaning that (i) the possibility of adding/removing a DGU without spoiling stability of the overall ImG is checked through an optimization problem; (ii) when a DGU is plugged in or out at most neighbouring DGUs have to update their controllers and (iii) the synthesis of a local controller uses only information on the corresponding DGU and lines connected to it. This guarantee total scalability of control synthesis as the ImG size grows or DGU gets replaced. Yes, under mild approximations of line dynamics, we formally guarantee stability of the overall closed-loop ImG. The performance of the proposed controllers is analyzed simulating different scenarios in PSCAD.
1 Introduction
DC islanded microgrids require voltage-stability methods that remain scalable across general interconnection topologies. The paper proposes a decentralized PnP design and evaluates it through PSCAD simulations.
- DC microgrid voltage stability is challenging because these systems cannot rely on an infinite-power source and always operate islanded.
- Existing DC islanded-microgrid stabilization controllers mainly use droop control, with stability analyzed only for specific microgrids.
- The proposed PnP procedure synthesizes each local controller using only its DGU and connected-line parameters, without information about other DGUs.
- When a DGU is plugged in or out, only physically connected DGUs retune, and optimization can deny operations that would spoil stability.
- PSCAD studies cover two radially connected DGUs and a five-DGU meshed topology, including voltage tracking, unknown-load robustness, bumpless transfer, and real-time plugging operations.
2 Model of a DC Microgrid
The model represents DGUs, loads, and transmission lines, then uses a quasi-stationary line approximation to obtain scalable microgrid dynamics. Under positive line parameters, overall stability reduces to stability of the interconnected local DGU models.
- The basic electrical model contains renewable-source voltage sources, Buck converters, LC filters, local loads, and transmission lines between DGUs.
- Unknown loads are modeled as current disturbances, allowing resistive electronic loads and negative-resistance constant-power loads.
- The two-DGU formulation defines states, inputs, disturbances, and PCC-voltage outputs for the interconnected system.
- 2.1 QSL model: The QSL approximation removes line-current states from the DGU state equations while retaining coupling through neighboring DGU states.
- 2.1 QSL model: Positive line parameters make line dynamics asymptotically stable, so stability of the overall QSL-ImG model depends on stability of the interconnected local DGUs.
- 2.2 QSL model of a microgrid composed of N DGUs: For N DGUs, each DGU is coupled to its symmetric neighbor set, yielding a generalized QSL-ImG model with stacked states, inputs, disturbances, outputs, and controlled variables.
3 Plug-and-Play decentralized voltage control
The paper develops decentralized local controllers for augmented DC microgrid models, using structured Lyapunov conditions and convex optimization to guarantee asymptotic stability while supporting plug-and-play operations.
- 3.1 Decentralized control scheme with integrators: Integral augmentation targets asymptotic tracking of constant voltage references despite constant load-current disturbances.The augmented model includes integrator states and treats load current and reference signals as exogenous inputs.
- 3.1 Decentralized control scheme with integrators: Equilibrium states and inputs exist for arbitrary constant references and disturbances because the model satisfies input-output dimensionality and invariant-zero conditions.The paper establishes these conditions using the equality of controlled-variable and input dimensions and positive electrical parameters.
- 3.2 Decentralized PnP control: Structured Lyapunov inequalities bound inter-DGU coupling so that locally designed controllers collectively guarantee asymptotic stability of the closed-loop QSL microgrid.Under Assumption 2, Proposition 3 establishes asymptotic stability of the overall closed-loop QSL-ImG.
- 3.2 Decentralized PnP control: Each local controller is synthesized from local DGU matrices and local design parameters, independently of controllers for other DGUs.The synthesis problem uses convex Linear Matrix Inequalities and yields controller gains through Ki = GiY −1.
- 3.3 Reference shaping and disturbance compensation: Reference prefilters and disturbance compensators preserve asymptotic stability when their realizability and stability conditions hold.The prefilter is open-loop, while the disturbance compensator can provide bandwidth-limited rejection when perfect compensation conditions fail.
- 3.5 PnP operations: Plug-and-play operations preserve stability while restricting redesign to the plugged or unplugged DGU and its physical neighbors.The redesign does not propagate farther through the network, so unaffected local controllers remain unchanged.
4 Simulation results
PSCAD simulations evaluate PnP decentralized voltage controllers in two- and six-DGU islanded microgrids, including startup tracking, hot plugging, load changes, and reference changes. The reported responses show stable operation, strong voltage regulation, and robustness across these scenarios.
- Voltage reference tracking at startup: At startup, the controllers provide excellent PCC voltage-reference tracking in a very short time for the two-DGU scenario.Local pre-filters use desired low-pass closed-loop transfer functions with 0 dB DC gain and 100 Hz bandwidth.
- Hot plugging-in of DGUs 1 and 2: After the DGUs are interconnected at t = 2 s, updated local controllers preserve excellent voltage regulation with no significant output deviations during switching.The interconnection changes each DGU’s dynamics, requiring updated controllers and compensators; bumpless transfer handles the switch.
- Robustness to unknown load dynamics: Halving the load resistances at t = 3 s produces very good compensation of current disturbances, with only small oscillations that disappear after a short transient.The oscillations are attributed to complex conjugate poles in the coupled closed-loop transfer function, while load currents are treated as measurable disturbances.
- Voltage-reference changes: A 47.6 V reference step at PCC1 yields good tracking within a reasonable time and small interactions between the two interconnected DGUs.The small reference change is sufficient to drive appreciable current through the low-impedance line.
4.2 Scenario 2
Scenario 2 evaluates the PnP decentralized controllers on a heterogeneous, meshed ImG and tests stability and voltage tracking during DGU plug-in, load changes, and unplugging.
- Scenario setup: The second scenario uses a meshed ImG in which some DGUs have multiple neighbours, increasing disturbances and complicating voltage regulation.The scenario considers a five-DGU topology before the plug-in operation.
- Scenario setup: The simulated DGUs have non-identical electrical parameters and supply loads of 10 Ω, 6 Ω, 20 Ω, 2 Ω, and 4 Ω.The local controllers are designed while accounting for inter-DGU couplings.
- Plug-in operation: After DGU 6 is plugged in, only neighbouring DGUs are candidates for controller updates, while the new DGU receives a newly synthesized controller.For this topology, DGU 6 has neighbours 1 and 5; the optimization test succeeds and Algorithm 1 synthesizes C[6].
- Plug-in operation: The six-DGU QSL-ImG remains stable after plug-in, and the voltage controllers maintain reference tracking during the operation.The closed-loop eigenvalues and singular values are evaluated, and Figure 15 reports the hot plug-in performance at t = 2 s.
- Load robustness: Halving DGU 6's 8 Ω load at t = 3 s produces short transients that are effectively compensated, after which the PCC voltages converge to their references.The neighbouring PCC voltages show very small, short-lived variations, while DGU 6 exhibits a short transient.
5 Conclusions
The paper concludes that decentralized PnP control can guarantee voltage stability in DC islanded microgrids while limiting controller updates during DGU changes. It also identifies higher-level power-flow regulation as a future extension.
- The proposed decentralized scheme guarantees voltage stability in DC islanded microgrids.
- When a DGU is plugged in or out, only a limited number of local controllers must be updated.The conclusion frames this as the main feature of the approach.
- Local voltage controllers should be coupled with a higher control layer for power-flow regulation and mutual help among DGUs.The paper proposes studying whether secondary-control ideas can be adapted to this setting.
A Matrices appearing in microgrid models
The appendix collects the matrices used in the microgrid models.
- The appendix contains all matrices appearing in Section 2.
A.3 QSL model of microgrid composed of N DGUs
The QSL microgrid model organizes the overall system from DGU and line parameters into block matrices describing interconnection dynamics.
- The appendix identifies Rij and Lij as the resistance and inductance of the line between DGUs i and j.It also states that Bi, Ci, Mi, and Hi match matrices introduced earlier.
- The overall microgrid model is represented for a microgrid composed of N DGUs.
- The model includes block matrices Aij describing interactions among DGU subsystems.The displayed structure contains diagonal and off-diagonal blocks across the N subsystems.
- The model also includes block-structured input, output, interconnection, and parameter matrices.The listed blocks include Bi, Ci, Hi, and Mi terms.
B Bumpless control transfer
The bumpless transfer implementation maintains continuity of the control signal when PnP controller switching changes local dynamics. Switching is delayed until the old and updated control signals become sufficiently similar.
- Bumpless control transfer: The implementation addresses state consistency when a dynamic controller is plugged in or unplugged at time t̄.The updated controller may initially produce a control variable different from the previous controller output.
- Signal commutation: Block A switches between the previous control signal ũ_prec and the updated signal û at the commutation time.The controller parameters activated at t̄ are supplied to the switching implementation.
- Signal commutation: Compensator N(s) can generate an additional input ũ to account for the post-commutation system dynamics.N(s) is set to zero when compensation is not implemented.
- Bumpless control transfer: The switch waits until the two control signals become similar, avoiding jumps in the control variable.This delay accommodates a possible transient in the updated controller response.
C Electrical and simulation parameters of Scenario 1 and 2
The appendix specifies the electrical, filter, transmission-line, and common DGU parameters used for simulation Scenarios 1 and 2.
- Parameter scope: The appendix provides the electrical and simulation parameters for Scenarios 1 and 2.These scenarios are described in Sections 4.1 and 4.2, respectively.
- Electrical setup: Table 1 lists the electrical setup and line parameters.
- Component parameters: Tables 2–4 provide VSC filter, transmission-line, and common DGU parameters, including Scenario 2 line settings.Table 3 is specifically identified as covering transmission lines for Scenario 2.