A symbolic approach to voltage stability and power sharing in time-varying DC microgrids

In this paper we address the problem of voltage stability and power sharing in DC microgrids with time-varying power demand. By exploiting the monotonicity property enjoyed by the system, and under the assumption of full observability of the bus voltages, we design a centralized, abstraction-based symbolic controller that, once refined into a controller for the original system, ensures the required specifications. Whereas load voltages cannot be measured, we propose an appropriate decomposition of the system, such that the control problem can be reformulated in terms of assume-guarantee contracts to be satisfied by the observable and unobservable components. A constructive procedure to determine suitable contracts is further investigated and the obtained results are validated with two numerical examples.

[1]  Juan C. Vasquez,et al.  DC Microgrids—Part I: A Review of Control Strategies and Stabilization Techniques , 2016, IEEE Transactions on Power Electronics.

[2]  Murat Arcak,et al.  Finite abstraction of mixed monotone systems with discrete and continuous inputs , 2017 .

[3]  Antonella Ferrara,et al.  A Robust Consensus Algorithm for Current Sharing and Voltage Regulation in DC Microgrids , 2017, IEEE Transactions on Control Systems Technology.

[4]  Gunther Reissig,et al.  Feedback Refinement Relations for the Synthesis of Symbolic Controllers , 2015, IEEE Transactions on Automatic Control.

[5]  Antoine Girard,et al.  Contract Based Design of Symbolic Controllers for Interconnected Multiperiodic Sampled-Data Systems , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[6]  Pulkit Nahata,et al.  A passivity-based approach to voltage stabilization in DC microgrids with ZIP loads , 2020, Autom..

[7]  Oded Maler,et al.  Approximating the Pareto Front of Multi-criteria Optimization Problems , 2010, TACAS.

[8]  Claudio De Persis,et al.  A power consensus algorithm for DC microgrids , 2017 .

[9]  A. Girard,et al.  Reachability analysis of linear systems using support functions , 2010 .

[10]  Calin Belta,et al.  Formal Methods for Discrete-Time Dynamical Systems , 2017 .

[11]  Juan C. Vasquez,et al.  DC Microgrids—Part II: A Review of Power Architectures, Applications, and Standardization Issues , 2016, IEEE Transactions on Power Electronics.

[12]  Antoine Girard,et al.  On the Composition of Discrete and Continuous-time Assume-Guarantee Contracts for Invariance , 2018, 2018 European Control Conference (ECC).

[13]  Giorgio Rizzoni,et al.  Robust stability analysis of DC microgrids with constant power loads , 2017, 2017 American Control Conference (ACC).

[14]  Antoine Girard,et al.  Safety control with performance guarantees of cooperative systems using compositional abstractions , 2015, ADHS.

[15]  Y. Candau,et al.  Computing reachable sets for uncertain nonlinear monotone systems , 2010 .

[16]  Florian Dörfler,et al.  Distributed control and optimization in DC microgrids , 2015, Autom..

[17]  Pranav Tendulkar,et al.  Mapping and Scheduling on Multi-core Processors using SMT Solvers. (placement et ordonnancement sur les processeurs multi-core en utilisant un solveur SMT) , 2014 .

[18]  Francesco Bullo,et al.  Electrical Networks and Algebraic Graph Theory: Models, Properties, and Applications , 2018, Proceedings of the IEEE.

[19]  Christel Baier,et al.  Principles of model checking , 2008 .

[20]  Paulo Tabuada,et al.  Verification and Control of Hybrid Systems - A Symbolic Approach , 2009 .

[21]  Florian Dörfler,et al.  A power consensus algorithm for DC microgrids , 2016, Autom..

[22]  Sanjit A. Seshia,et al.  Compositional controller synthesis for vehicular traffic networks , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[23]  Antoine Girard,et al.  Scheduling of Embedded Controllers Under Timing Contracts , 2017, HSCC.

[24]  Wei Zhang,et al.  Robust Stability Analysis of DC Microgrids With Constant Power Loads , 2018, IEEE Transactions on Power Systems.

[25]  Alexey S. Matveev,et al.  On the Existence and Long-Term Stability of Voltage Equilibria in Power Systems with Constant Power Loads , 2018, ArXiv.