Optimal sparse control of interval networks: Voltage source converter based DC grid study

Abstract

Decentralized optimal control of interval state space systems involves significant complications due to the required sparsity, robustness, and convergence rate. By adding an l1 term to the standard linear quadratic optimization, the obtained composite index, accommodating the sparsity, contains both differentiable and non-differentiable terms. Knowing that the choice of optimization techniques are problem-dependent, in this paper, several smart provisions such as "Active set", "Coordinate descent", and separately managing the differentiable part of the cost function are put together to form a relatively fast algorithm. In addition, a rule is introduced to adjust automatically the degree of sparsity and a constraint to confine the interval closed-loop system eigenvalues to the desired s plane region. As a result, a robust sparse decentralized control (RSDC) approach for interval networks is established. The RSDC method is utilized for the control of a multi-terminal VSC (Voltage Source Converter ) -based DC (Direct Current) grid with parametric uncertainty under various external random perturbations. The test results show that the proposed method with just 20 feedback links (out of available 100) performs superiorly to the alternative ones in terms of sparsity, convergence rate, and time-domain performances, verified through extensive simulations.

Robust decentralized control of interval DC linked hybrid microgrids network

“…A robust sparse design has been discussed in [24] where the H 2 feedback control for an interconnected system with polytopic uncertainties is simulated. Optimal sparse control of interval networks based on poles clustering has been elaborated in [25]. In [26], a sparse H 2 control design has been developed, where the sparsity is a function of delay communication and bandwidth.…”