Optimal Control of a Network of Power Microgrids Using the Pontryagin's Minimum Principle

Abstract

The optimal control of the power flows in a network\ud of microgrids (MGs) is presented. The problem is solved using\ud the mathematical formalization of the optimal control based on\ud the Pontryagin’s minimum principle (PMP). The objective is to\ud deliver an optimal control strategy for the minimization of the\ud power flows among MGs, and to maintain the storage system\ud operating around a given reference value. This study proposes\ud an original formulation based on the PMP that may be viewed as\ud a preliminary continuous time attempt to model and control the\ud exchange of power in a network of MGs. Its main originality\ud is the use and the exchange of information and forecast of\ud energy production and consumption on the whole set of MGs, to\ud improve the overall quality of the power management, and energy\ud storage. A method based on the PMP is developed to solve the\ud corresponding constrained optimal control problem in an almost\ud exclusively analytical way and thus, to calculate the optimal\ud control. To prove the viability of the proposed approach, an\ud example has been solved for the case of four MGs collaborating\ud in a network

Coordinated Model Predictive-Based Power Flows Control in a Cooperative Network of Smart Microgrids

“…The main drawback of the approach is again related to unbounded character of the state and control variables resulting from the optimization problem. Dagdougui et al [16] solved a similar problem using an original modeling approach based on the mathematical formalization of the Pontryagin minimum principle. Despite the inclusion of the constraints, the approach remains more on the theoretical side as it is difficult to implement it for real cases.…”

Coupling Neighboring Microgrids for Overload Management Based on Dynamic Multicriteria Decision-Making

“…From this table, it is seen that alternatives A 1 and A 3 are selected by the aggregators. Hence, a risk matrix is defined for these alternatives from (18) and (19), as given in Table XII. From this table, alternative A 3 (i.e., {MG-1, MG-2}) is selected as it demonstrates a lower risk index.…”

“…The trade of power among MGs in the system of CMGs is addressed in [18]. Optimal control of a distribution network composed of utility-connected MGs forming a CMG is also studied in [19]. Dynamic operation of DERs within CMGs is investigated in [20] and the dynamic security of the CMGs is examined in [21].…”

Development of a Self-Healing Strategy to Enhance the Overloading Resilience of Islanded Microgrids

“…Since all DERs have the same f , from (2) it can be concluded that (15) is satisfied if the UAPC of each DER of MG-1 is less than α 2 times of the maximum capacity of that DER, that is…”

“…The trade of power among MGs in CMG is addressed in [13] and [14]. Optimal control of a distribution network composed of utility-connected MGs forming a CMG is studied in [15]. The dynamic operation of DERs within CMGs is investigated in [16] and the dynamic security of the CMGs is examined in [17].…”