In fact, the FBSMs can be connected in series as shown in Figure 4(d), which means that the surge current can be changed in different situations, which is more flexible than the 1st type.
During normal operation, if the FBSMs are inserted, the current flows through IGBT1 and IGBT4 (Figure 6(b)).
Another kind of topology is the hybrid MMC, which consists of FBSMs and hBsMs.
The number of FBSMs is 90 and the number of HBSMs is 60.
For hybrid MMC (HY-MMC), as mentioned above, there are 90 HBSMs and 60 FBSMs in each arm.
Because the modulation index is one, the FBSMs can just output zero or [V.sub.c].
The loss of one arm in the hybrid MMC is shown in Figure 18, which includes 60 HBSMs and 90 FBSMs.
(d) The FBSMs can be connected in series to change surge current.
Now we take an optimal control problem as test problems which we solve by FBSM using Euler and Trapezoidal schemes and executed by MATLAB.
Similarly we use Euler trapezoidal and Rung-e-Kutta methods with FBSM for solving above system.
We use FBSM to solve bounded and unbounded control problem with payoff term.