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Microgrid architecture, control, and operation                     31

              a microgrid moves from autonomous mode of operation to grid-tied mode, or vice versa,
              the inner control performs the islanding detection and smooth change of mode. A desired
              microgrid inner control is one that can handle both planned and unplanned islanding of
              microgrid [13].
           2.  Management level control: A Microgrid Central Controller performs at management level
              and establishes a synchronism between microgrid and main grid. As an algorithm, vari-
              ous techniques such zero crossing method, grid voltage filtering method, or phase locked
              loop methods are used for obtaining point of synchronism. In addition to that, a decision
              regarding continuing with a load or shedding a load is also taken at management level. An
              economic operation of microgrid requires optimal generation from different microsources.
              This task is also performed at management level control [14].
           3.  Grid level control: This is the outermost control layer in hierarchical control scheme, in
              which several microgrids operating in parallel are managed and coordinated. Coordination
              between several Microgrid Central Controllers is achieved at grid-level control [15].


           5  Mathematical model of hierarchical control


           A  hierarchical  control  based  operation  of  grid-interacted  microgrid  structure  is
           often found to be very big in size. A mathematical model for such a big system
           requires mathematical tools that simplify the analysis. Normally such big systems
           are presented in linearized state space model for steady-state operation around an
           operating point. Dynamic model of a dedicated individual microgrid structure is
           presented as follows:


                d
                dt  xt()  = Ax t() + But ()                                (2.11)                                       ddtx(t)=Ax(t)+Bu(t)y(t)=Cx(t)
                yt ()  = Cx t () + Dut ()
                                                                                                                        +Du(t)

              A dynamic model of all such dedicated microgrid units is obtained separately. Size
           of the overall system consisting a number of individual microgrids becomes signifi-
           cantly large. To simplify the analysis, model-order reduction technique has been sug-
           gested in literature [22]. A linearized, reduced-order model of the complete microgrid
           system is presented as follows:


                            A 0   B 1 
                            1
                [][]
                 AB         0 A    B  
                  [][]    =   2    2                              (2.12)                                       ABCD=A 1 00A 2 B 1 B 2 C 1 C 2 D
                         
                 CD
                                D
                          [  CC 2 ][]  
                            1
           where A 1  and A 2  contain r dominant and (n − r) nondominant modes of A. As we
           know that most of the renewable energy sources are indeterministic in nature, the
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