(0) (0) (0) (0) (0) (0) (0) (0) sin cos cos sin , cos sin sin cos od oq S C od oq I I T T I I where (0) is the initial value of . Similarly, the input signal to the inverter model is the bus voltage which is expressed on the common reference frame. The bus voltage can be converted to the individual inverter reference frame using reverse transformation, given by 1 1 bdq S bDQ V v T v T where
28 (0) (0) 1 (0) (0) sin cos cos sin bD bQ V bD bQ V V T V V It is noted that in case of multiple inverters, the inverter whose dq frame is taken as the common reference frame has to provide its reference frequency change ∆ ω com to all the sub‐ modules. Also, care should be taken to apply this modification in the power controller model. A complete state‐space model of the i‐th VSC (inverter) is given below by combining the state‐ space models of the power controller, voltage controller, current controller and output LCL filter, com inv INV inv INV com i i i i bDQi i x A x B v B . INVω inv INVc i i i oDQi i C x i C where inv T i i i i dqi dqi ldqi odqi odqi x P Q i v i and 1 2 1 1 1 1 2 2 INV 1 1 1 1 2 1 1 1 1 1 2 2 3 13 13 0 0 0 0 0 0 0 Pi Pi V i Pvi V i C i V i Pvi C i Vi C i V i C i i LCL i C i V i Pvi LCLi LCL i Vi LCL i C i Vi LCL i Ci LCL i C i V i C i LCL i P i A B B C B B D C B C B D B A B D D C A B T B D C B C B D D D B C com com INV 1 2 13 2 13 1 0 0 0 , 0 0 0 P i i LCL S B B B B T 1 13 INVω 1 13 0 0 0 1 0 0 0 0 1 P i C i C i INVc 2 13 0 0 0 0 0 0 i C S C T T 5.8 State Space Representation of an Islanded Microgrid System The islanded operation is realized by opening the isolating the PCC switch (shown in Figure 26) which disconnects the microgrid from the main grid. Once the microgrid is isolated the
29 microsources feeding the system are responsible for maintaining the voltage and frequency while sharing the power. During autonomous operation it is important to avoid over‐loading of inverters and to ensure that the changes in load are taken by VSC converts in a well‐controlled manner.
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- Spring '14