A grid-forming inverter (GFI) plays an important role in providing voltage and frequency support for island microgrids. This paper proposes a computationally efficient finite-set model predictive voltage control (EFS-MPVC) scheme for GFIs. To eliminate the state prediction process, a hybrid voltage-vector reference is first synthesized using the deadbeat principle, which enhances the steady-state performance and robustness to model mismatches. Then, a voltage-vector-based cost function is designed, and a fast optimal-voltage-vector (OVV) selection scheme is built to avoid multiple enumerations. Further, to reduce the additional computing efforts caused by current constraints, an offline lookup table for fast search of OVV is established. Experimental results verify that the proposed EFS-MPVC features reduced computational amount and improved control performance in comparison to conventional MPVC schemes. 10 11 inductor current and capacitor voltage are predicted using the 136 system discrete model, respectively. 137 B. DELAY COMPENSATION 138 Note that there always exists a one-step control delay when 139 the MPVC algorism is implemented in a real digital con-140 troller. The output performance would significantly deterio-141 rate if this control delay is not properly addressed. Herein, 142 a two-step forward prediction approach is used to compensate 216 tracking both capacitor voltage and inductor current is con-217 structed as 218 13)where v k+1 is the candidate voltage vectors in Table 1.
221It can be observed from (13) that the 8× predictions of 222 v p f ,k+2 in (5) are avoided, somewhat reducing the compu-223 tational cost. Nevertheless, 8 enumerations of the candidate 224 voltage vectors are still required, i.e., the cost function still 225 needs 8× evaluations to find the OVV. To further eliminate 226 these computations, a fast OVV selection scheme is con-227 ducted below. 228 C. FAST OVV SELECTION SCHEME 229 From (13), it can be seen that the selection of OVV means 230 to find a candidate voltage vector that is closest to the refer-231 ence voltage vector v ref k+1 . Based on the possible position that 232 v ref k+1 may be located and for simple comparison of the vector 233 distance, the sectors of the voltage-vector space are redivided 234 from Sector I to Sector VII by the inner center of each triangle 235 area, which is shown in Figure 2. Therein, θ is the position of 236 the hybrid reference voltage vector, which is calculated as 237 392 comparisons with +50%L f and +50%C f mismatches in 393 the controller, while Figures 11 (c) and (d) illustrates the 394 experimental comparisons under −50%L f and −50%C f mis-395 matches. It can be observed that no matter under +50%L f 396 and +50%C f or −50%L f and −50%C f model mismatches, 397 the proposed EFS-MPVC scheme has stronger robustness 398 with lower ripples and THD under a wide range of model 399 mismatches in comparison to conventional MPVC, since dual 400 objectives instead of one are employed in the proposed cost 401 function. 402 D. COMPUTATIONAL-BURD...