S S S C C C C ic ic 0 0 I V dc 2 0 dc ic s exc s s dc ic s V s C n V P V Hybrid

# S s s c c c c ic ic 0 0 i v dc 2 0 dc ic s exc s s dc

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S S S C C C C ic ic ,(0) (0) , , I V ,dc, 2 ,(0) , , dc ic s exc s s dc ic s V s C n V P V  
Hybrid AC/DC Microgrid Model AC and DC sections are combined into one system when forming the small-signal state-space model of the microgrid. We start with the AC terminal. At the AC terminal of IC s , we have: where is the incidence matrix for the IC at the AC section; in each row, the element at the column corresponding to the IC of the AC section is “1” and other elements are “0”. The corresponding small-signal model is given as: 48 ref ω s net C ω icDQ, bus,ic-ac bus, ac ac V C V T ac,out bus,ic-ac icDQ,in I C I bus,ic-ac C ref ω s C ω icDQ, bus,ic-ac bus, ac ac  V C V T ac,out bus,ic-ac icDQ,in  I C I
Hybrid AC/DC Microgrid Model Fig. 12 shows the coordinated transformation for the output voltage and current of IC. Since the operating frequency of each IC is identical to the network frequency, the angle between a dq frame and the DQ frame is constant during transients. In particular, the voltage at AC section is converted to that in the common DQ-frame as follows: 49 ω ref ω ref q s D d s q s Q V ic,s ω i ω ref q s D d s q s Q I icd,s (a) Output Voltage (b) Output Current I icq,s , , , cos sin ac ac ac ic s icD s s icQ s s V V V q q Fig. 12 Reference frame transformation for ICs
Hybrid AC/DC Microgrid Model The small-signal state-space model for the AC section voltages of all ICs in their individual dq frames as follows: where Equivalently, we have: 50 ic,ac TV,ic icDQ,ac  V C V T icDQ,ac ,1 ,1 ,2 ,2 , , ... ac ac ac ac ac ac icD icQ icD icQ icD S icQ S V V V V V V   V TV,ic,1 TV,ic,2 TV,ic TV,ic, 2 ... ... ... S S S C 0 0 0 C 0 C 0 0 C M M O M TV,ic, cos sin s s s q q   C bus,ac ic,ac TV,ic bus,ic-ac TV inv TV,ic bus,ic-ac V δ     V C C C V C C C δ
Hybrid AC/DC Microgrid Model Similarly, the inflow current is converted to the common DQ-frame: which result in the following small-signal state-space model: where 51 , , , cos sin in in in icD s icd s s icq s s I I I q q , , , sin cos in in in icQ s icd s s icq s s I I I q q icDQ,in TI,ic icdq,in   I C I T icDQ,in ,1 ,1 ,2 ,2 , , ... in in in in in in icD icQ icD icQ icD S icQ S I I I I I I   I TI,ic,1 TI,ic,2 TI,ic TI,ic, 2 2 ... ... ... S S S C 0 0 0 C 0 C 0 0 C M M O M TI,ic, cos sin sin cos s s s s s q q q q C
Hybrid AC/DC Microgrid Model Likewise, At the DC terminal of IC s , the following equations are satisfied: where is the bus incidence matrix; in each row, the element at the column corresponding to the DC-terminal-bus variables of that IC is “1 and other elements are “0”.

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