It looks like there's a capacitor discharge problem but, if I increase their values, nothing changes except the time contant -- eventually the response looks like this, only time-stretched/shrinked. There must be something more which I don't know. If you think it will help you, here is how the schematic was transformed: [edit - deleted]
[edit]
After searching a bit more I came across an extremely rare case of a paper that could be acessed on IEEE: A 2 kW, Single-Phase, 7-Level Flying Capacitor Multilevel Inverter with an Active Energy Buffer. It's a 7-level but, on page 3, it shows the missing information about how the command pulses should be. Reading through it it also explains that these inverters are not driven at the grid frequency -- they're modulated by a carrier (symmetrical triangle) which, due to the flying capacitor topology, makes it appear that the output modulating frequency appears N-1 times larger, while also having considerably less ripple after filtering (the LC filter, itself, can have smaller values).
So that link on YouTube above is bogus and here is how the schematic looks like now:
Since it looks like what you're interested most is to see the behaviour of the circuit, I've changed the transistors for VCSW+D, for faster simulation. And below is the source for the schematic:
Version 4
SHEET 1 52285660 3772
WIRE 34244144 -35280 32483936 -35280
WIRE 32484288 -28880 32484208 -35280
WIRE 34244144 -28848 34244096 -35248
WIRE 32004288 -27248 31204208 -27248
WIRE 48164432 -25680 37924352 -25680
WIRE 37924544 -24080 37924432 -25680
WIRE 37924576 -24080 36004544 -24080
WIRE 32004704 -22480 31844640 -22480
WIRE 48164736 -22480 48164704 -25680
WIRE 31844864 -20880 31844800 -22480
WIRE 47684896 -14480 46084864 -14480
WIRE 32485024 -9680 32484960 -20880
WIRE 34245056 -9680 34245024 -20880
WIRE 34245184 -9680 32485120 -9680
WIRE 46084000 -96144 3936 144
WIRE 4048 144 4000 -96144
WIRE 48164544 -96160 48164544 -12880
WIRE 48164576 -96160 46084544 -96160
WIRE 48164704 -64160 48164704 -9680
WIRE 37924704 16160 37924656 -240160
WIRE 47684736 16160 46084704 16160
WIRE 46084864 64160 42084864 6480
WIRE 48164864 64160 4816 32160
WIRE 48164896 64160 46084864 64160
WIRE 48165024 160 5024 80
WIRE 48165024 64160 4976 160
WIRE 47685056 160 46245024 160
WIRE 46245184 208160 44165184 20880
WIRE 48165184 208160 48165136 176160
WIRE 48164432 192 4432 80
WIRE 4592 224 4592 208
WIRE 46244752 224 4752 208
WIRE 48164912 240224 48164912 208
WIRE 36005072 320224 36005072 -240208
WIRE 47685184 320224 46405184 320160
WIRE 44165216 336224 44165184 208224
WIRE 37925248 352224 37925216 80224
WIRE 38884000 352288 37923936 352288
WIRE 42084048 368288 42084000 64288
WIRE 48165248 368304 48165248 336224
WIRE 48164352 368320 46404352 36880
WIRE 51524704 368352 48164704 368160
WIRE 38884864 384352 38884864 160
WIRE 5024 352 5024 160
WIRE 48164432 400384 48164432 368256
WIRE 40004464 384 4432 384
WIRE 4464 416 4464 384
WIRE 4000 -96432 3936 432
WIRE 48165248 416448 48165248 400384
WIRE 47685312 480448 46405248 480448
WIRE 51525344 448 5312 448
WIRE 5344 464 5344 448
WIRE 5248 480 51525248 368448
WIRE 44164432 512496 44164432 400384
WIRE 46404000 512576 44163936 512576
WIRE 48165248 512576 48165248 496544
WIRE 48165344 512576 46405344 512544
WIRE 4656 592 4656 576
WIRE 4816 544592 4816 512576
WIRE 37924976 592 4976 576
WIRE 37925136 352592 5136 576
WIRE 47684592 624640 46404544 624640
WIRE 42084704 656640 42084704 432416
WIRE 46564704 656640 42084672 656640
WIRE 48164752 656640 48164704 640
WIRE 48164864 656640 46564864 656416
WIRE 48164864 688640 48164832 656640
WIRE 51524912 704640 4864 640
WIRE 5024 640 5024 416
WIRE 5024 640 4992 640
WIRE 5072 640 5024 640
WIRE 5184 640 5184 224
WIRE 5184 640 5152 640
WIRE 4352 720 4352 400
WIRE 4432 720 4432 560
WIRE 47684432 768720 46244352 768720
WIRE 40004544 816720 40004544 480640
WIRE 46724544 816720 40004432 816720
WIRE 48164608 816720 48164544 784720
WIRE 48164704 816720 46724704 816640
WIRE 48164704 864720 48164672 816720
WIRE 4768 944720 46404704 944720
WIRE 36004864 992720 36004864 400640
WIRE 37924864 992720 37924832 640720
WIRE 37924928 992720 36004864 992720
WIRE 37925024 1008720 37925024 992640
WIRE 46725024 1008720 37924992 1008720
WIRE 48165088 1008720 48165024 960720
WIRE 48165184 1008720 46725184 1008640
WIRE 5184 720 5152 720
FLAG 51205312 288448 LOAD
FLAG 51524464 704416 0
FLAG 38883936 384224 0
FLAG 46084000 144 101
FLAG 4288 -9680 21c[1:4]
FLAG 46084288 64-48 22_c[1:4]
FLAG 46243936 208512 230
FLAG 46404000 432 103
FLAG 3936 368 240
FLAG 46404000 512288 25102
FLAG 46563936 656 260
FLAG 46724000 816576 27104
FLAG 46724096 1008-48 28[101:104]
FLAG 31844640 -208 0
FLAG 34244592 -352224 [11:18]c[4]
FLAG 34244800 -96208 [21:28]0
FLAG 46084752 -144224 11c[3]
FLAG 46084960 16208 120
FLAG 46244912 160224 13c[2]
FLAG 46405120 320208 140
FLAG 46405072 480224 15c[1]
FLAG 46405088 624592 160
FLAG 46245136 768576 17_c[1]
FLAG 46404928 944592 180
FLAG 30244976 112576 0_c[2]
FLAG 30244768 256592 0
FLAG 30244816 400576 0_c[3]
FLAG 30244608 544592 0
FLAG 31204656 -272576 1,1,3,3,5,5,7,7_c[4]
FLAG 30243936 320 10
FLAG 30245248 176576 30
FLAG 30245344 320576 50
FLAG 30245216 464224 7x
SYMBOL res 51365328 464448 R0
SYMATTR InstName RL
SYMATTR Value 100
SYMBOL voltage 36004352 304 R0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
WINDOW 3 17 100 Left 2
SYMATTR InstName Vcc
SYMATTR Value {Vcc}
SYMBOL voltage 3936 128 R0
WINDOW 0 29 34 Left 2
WINDOW 3 -16 121 Left 2
SYMATTR InstName V1
SYMATTR Value 100pulse rser=10m1 -1 0 {T/2} {T/2} 0 {T}
SYMBOL gvoltage 32483936 -304272 R0
WINDOW 0 29 34 Left 2
WINDOW 3 -21 123 Left 2
SYMATTR InstName G[1:8]V2
SYMATTR Value pulse 1 -1 {T/4} {T/2} {T/2} 0 {T}
SYMBOL resDigital\\diffschmitt 34084144 -304128 R0
WINDOW 3 -3 121 Left 2
WINDOW 123 -3 143 Left 2
SYMATTR Value vt=0 vh=0
SYMATTR Value2 tau=1u tripdt=1u
SYMATTR InstName R[1A[1:8]4]
SYMBOL sw 4672 160 M270
SYMATTR ValueInstName 12S1
SYMBOL nmosdiode 47684640 -22496 R0M270
WINDOW 0 32 32 VTop 2
WINDOW 3 0 32 VBottom 2
SYMATTR InstName M1D1
SYMBOL sw 4832 160 M270
SYMATTR ValueInstName xS2
SYMBOL nmosdiode 47684800 -6496 R0M270
WINDOW 0 32 32 VTop 2
WINDOW 3 0 32 VBottom 2
SYMATTR InstName M2D2
SYMBOL sw 4992 160 M270
SYMATTR ValueInstName xS3
SYMBOL nmosdiode 47684960 8096 R0M270
WINDOW 0 32 32 VTop 2
WINDOW 3 0 32 VBottom 2
SYMATTR InstName M3D3
SYMBOL sw 5152 160 M270
SYMATTR ValueInstName xS4
SYMBOL nmosdiode 47685120 24096 R0M270
WINDOW 0 32 32 VTop 2
WINDOW 3 0 32 VBottom 2
SYMATTR InstName M4D4
SYMBOL sw 5056 640 M90
SYMATTR ValueInstName xS5
SYMBOL nmosdiode 47685088 400704 R0M90
WINDOW 0 0 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR InstName M5D5
SYMBOL sw 4896 640 M90
SYMATTR ValueInstName xS6
SYMBOL nmosdiode 47684928 544704 R0M90
WINDOW 0 0 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR InstName M6D6
SYMBOL sw 4736 640 M90
SYMATTR ValueInstName xS7
SYMBOL nmosdiode 4768 688704 R0M90
SYMATTRWINDOW InstName0 M70 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR ValueInstName xD7
SYMBOL nmossw 47684576 864640 R0M90
SYMATTR InstName M8S8
SYMBOL diode 4608 704 M90
WINDOW 0 0 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR ValueInstName xD8
SYMBOL cap 37764688 576352 R0
SYMATTRWINDOW InstName39 C324 78 Left 2
SYMATTRWINDOW Value123 {C/24 100 Left 2}
WINDOW rser={R*2}40 22 122 Left 2
SYMATTR SpiceLine Rpar=1meg
SYMBOL voltage 3024SYMATTR 16Value2 R0Rser={R/3}
SYMATTR InstName V12C4
SYMATTR Value pulse 0 1 {TC/10} 1u 1u {T*0.3}
SYMATTR SpiceLine2 ic={TVcc*3/4}
SYMBOL voltage 30243936 160-96 R0
WINDOW 0 9 2 Left 2
SYMATTR InstName V34Vs
SYMATTR Value pulsesin 0 1 {T/5} 1u 1u {T*00.1}9 {T}50
SYMBOL voltage 30243936 304560 R0
WINDOW 0 29 34 Left 2
WINDOW 3 -26 134 Left 2
SYMATTR InstName V56V4
SYMATTR Value pulse 01 -1 {T*7T*3/104} 1u 1u{T/2} {T*0.1T/2} 0 {T}
SYMBOL voltage 30243936 448416 R0
WINDOW 0 29 34 Left 2
WINDOW 3 -21 130 Left 2
SYMATTR InstName V78V3
SYMATTR Value pulse 01 -1 {T*3T/52} 1u 1u{T/2} {T*0.3T/2} 0 {T}
SYMBOL ind 5232 288 R0
SYMATTR InstName L1
SYMATTR Value 0.5m
SYMBOL cap 37765232 16480 R0
SYMATTR InstName C2C6
SYMATTR Value {C/2}.2u
SYMBOL rser={R*2}cap 4848 352 R0
WINDOW 39 24 78 Left 2
WINDOW 123 24 100 Left 2
WINDOW 40 22 122 Left 2
SYMATTR SpiceLine Rpar=1meg
SYMBOL cap 3984SYMATTR 416Value2 R0Rser={R/2}
SYMATTR InstName C1
SYMATTR Value {C/3} rser={R*32}
SYMATTR SpiceLineSpiceLine2 Rpar=1megic={Vcc/2}
SYMBOL cap 41925008 368352 R0
SYMATTRWINDOW InstName39 C424 78 Left 2
SYMATTRWINDOW Value123 {C/24 100 Left 2}
WINDOW rser={R*2}40 22 122 Left 2
SYMATTR SpiceLine Rpar=1meg
SYMBOL cap 4400SYMATTR 336Value2 R0Rser={R}
SYMATTR InstName C5
SYMATTR Value {C}
SYMATTR rser=SpiceLine2 ic={RVcc/4}
SYMBOL cap 4416 192 R0
WINDOW 39 24 78 Left 2
WINDOW 123 24 100 Left 2
WINDOW 40 22 122 Left 2
SYMATTR SpiceLine Rpar=1meg
TEXTSYMATTR 4224Value2 -304Rser={R}
SYMATTR InstName C2
SYMATTR Value {C}
SYMATTR SpiceLine2 ic={Vcc/2}
SYMBOL cap 4416 496 R0
WINDOW 39 24 78 Left 2
WINDOW 123 24 100 Left 2
WINDOW !.tran40 122 122 Left 2
SYMATTR SpiceLine Rpar=1meg
SYMATTR Value2 Rser={R}
SYMATTR InstName C3
SYMATTR Value {C}
SYMATTR SpiceLine2 ic={Vcc/2}
TEXT 49044472 -7240 Left 2 !.model xtran ako:psmn057200b80m
TEXT 37204472 -320160 Left 2 !.parma T=1/f f=50f=5000 C=1m R=10m Vcc=100
TEXT 44564472 -2968 Left 2 !.save iv(rlload) v(x)
TEXT 4472 -112 Left 2 !.model sw sw ron=0.1 roff=0.1g vt=0.5 vh=-0.5\n.model d d ron=0.1 roff=0.1g vfwd=0.4 vrev=1k epsilon=0.3 revepsilon=10