Half and Full-Bridge Modular Multilevel Converter Models for Simulations of Full-Scale HVDC Links and Multi-terminal DC grids

Transcription

1 Half an Full-Brige Moular Multilevel Converter Moels for Simulations of Full-Scale HVDC Links an Multi-terminal DC gris Abstract This paper presents an improve electromagnetic transient (EMT) simulation moels for the half an full-brige moular multilevel converters that can be use for full-scale simulation of multilevel high-voltage c transmission systems, with hunres of cells per arm. The presente moels employ minimum software overhea within their electromagnetic transient parts to correctly represent moular multilevel converters (MMC) behaviour uring c network faults when converter switching evices are blocke. The valiity an scalabilities of the presente moels are emonstrate using open loop simulations of the half an full-brige MMCs, an close loop simulation of a full-scale HVDC link, with 20 cells per arm that equippe with basic HVDC controllers, incluing that for suppression of the 2 n harmonic currents in the converter arms. The results obtaine from both emonstrations have shown that the presente moels are able to accurately simulate the typical behaviour of the MMC uring normal, an ac an c network faults. Key wors electromagnetic transient simulation; highvoltage c transmission system; half an full-brige moular multilevel converter; an hybri multilevel converters. I. INTRODUCTION Increase operational flexibilities of the voltage source converter base high-voltage c (VSC-HVDC) transmission system within ac power systems in the last ecae have encourage its universal acceptance by the power system utilities worlwie[-2]. Aitionally, its evolution from that buil aroun the two-level an neutral-point clampe converter topologies to that built using true multilevel converters, with low semiconuctor losses an improve ac sie waveforms quality have accelerate its aoption in many of the recent HVDC transmission systems projects[3-9]. Replacing of the traitional concept of voltage source converter that uses concentrate reservoir capacitors at the converter c input by that uses istribute capacitors such as that in moular multilevel converter has improve the resiliency of the VSC-HVDC transmission systems to ac an c network faults[20-27]. For aforementione reasons, moular multilevel converter has become the preferre technology for large-scale HVDC links an c gris that coul ensure safe an reliable operation uring ac an c network isturbances. Full-scale moelling of the VSC-HVDC links that use half or full brige cell moular converters, with hunres of cells per arm is computationally intensive task that requires machines with high computing power an large memory, an takes long time to simulate. The traitional switching moels that use power electronic builing blocks with full capabilities of mimicking conuction of the physical evices (such as IGBT G.P. Aam an B.W. Williams are with the Electronic an Electrical Engineering Department, University of Strathclye, Glasgow, UK ( grain.aam@strath.ac.uk an barry.williams@strath.ac.uk). G.P. Aam, IEEE Member, an B.W. Williams an its anti-parallel) are proven to be inefficient for full-scale moelling of the MMC base HVDC links as simulation times become prohibitively long. Despite the above shortcomings, this approach remains wiely use, where transient response of the MMC base HVDC links to ac an c network faults are stuie using reuce number of cells. This is because the switching moel is extremely useful when comes to capturing of the MMC internal ynamics in great etails uring ac an c network faults. In attempt to reuce simulation time, the authors in [28, 29] presente an average moel of the MMC base HVDC link where the ac component of the MMC upper an lower arms moulation functions are obtaine irectly from the inner current controller an appropriate c offsets are ae. These moulating functions are use as inputs to the two controlle voltage sources that mimicke the voltage evelope across MMC upper an lower arms. The main weakness of this approach is that it oes not allow natural evelopment of the arm current c component an circulating current, thus not able to naturally evelope c power as in real worl MMC. For this reason, the authors in [28, 29]inclue aitional stage that artificially injects c components into converter arms, estimate base on power balance principle, an also this stage has been use to mimic MMC converter operation uring gate blocking as require uring c network fault. Aitionally, injection of the c components into converter arm currents as in [28, 29] results in instantaneous balance between MMC ac an c powers, an this eprives the approach presente in [28, 29] from accurately reprouce the c power ynamics ue to MMC inertia an propagation elays ue to arm an c line inuctances (inuctances in the c current paths). Although, the approach in [28, 29] provies an efficient way of moelling MMC base HVDC link for general system level stuies, it cannot reprouce MMC internal ynamics at microscopic levels as require in esign stage an for protection purposes uring ac an c network faults. Reference [30] presente an efficient metho for full-scale moelling of the MMC base HVDC link that uses electromagnetic transient approach. The authors in [30] use Dommel s Norton an Thevenin equivalent circuits of the MMC cell capacitors, an two-state resistor representation of the switching evices to reuce the entire arm of the MMC to a simple Thevenin equivalent circuit, with two terminals. This approach significantly reuces computation buren that arises from solution of the power circuit, while that ue to moulation an capacitor voltage balancing is retaine as in etail switching moels. Despite above simplification, this approach is able to capture some of the MMC internal ynamics that associate with the cell capacitor voltages an arm currents, an also allow natural evelopment of the c an circulating current components of the MMC arms, hence, it is able to reprouce the ynamics of the c power. However, the electromagnetic transient approach as iscusse in reference [30] cannot reprouce ynamic interaction between ac an c sies uring c network fault. The accelerate moel of the MMC presente in [3] is evelope in similar theoretical basis as that in [30], except

2 the authors unknowingly have treate each iniviual MMC cell as a primitive circuit that share the same current injection equal to the arm current, an this assumption permits application of the generalize circuit theory by Kron [32-34]. Aitionally, this allows Kron connection matrix to be constructe using relationships between arm current an iniviual cell currents, an such connection matrix can be use to prove that valiity of the approach presente in [3]. The accelerate MMC moel in its present form has the same attributes an limitations of that presente in [30]. Nevertheless, they remain the only practical ways to simulate full-scale MMC base HVDC link, with hunres of cells per arm. The authors in [35] presente two simplifie MMC funamental average moels for slow ynamic stuies that eliberately ignore converter switching actions an ynamics of the cell capacitors, while consiering that of the ac sie in orer to enable the use of large time step an reuce simulation time. Reference [35] has shown that this approach is suitable for transient an small signal stability stuies where manipulation of the converter output active an reactive powers are useful for improving stability of the ac parts of the power systems; but it is inappropriate for use in any stuies that concern with the c sie an fast transient. Furthermore, both MMC moels propose in [35] are unable to naturally evelope c current components of the arm currents; thus, unable to prouce c power naturally. The authors in [36, 37] propose an interesting approach that uses a factitious network known as Surrogate to moel fullscale MMC base HVDC link. This approach replaces the actual MMC cells in each converter arm by their Surrogate equivalents that prouce the same computational results as the true cells. Surrogate network for each arm of the half or fullbrige MMC contains three sub-networks that represent converter blocking state, sub-moules bypass state, an positive an negative sub-moules insertion states. This approach is appeare to be promising for large-scale moelling of the multi-terminal HVDC networks where MMC internal ynamics are less important. References [36, 37] have emonstrate the suitability of Surrogate network moelling approach of the MMC for real-time simulation an harware in loop, with much smaller time step than other commercially available real-time igital simulators. However, its ability to accurately simulate c fault is yet to be seen. This paper improves the MMC moelling approach presente in [3] to be able to simulate the performance of full-scale MMC base HVDC links uring ac an c network faults, an to capture its internal ynamics to microscopic levels (cell capacitor voltages, arm currents, current stresses in switching evices, an ynamics of ac an c powers). The ability to simulate c fault is achieve by setting values of the two-state resistors that represent the MMC switching evices to mimic exactly the physical operation of gate insulate bi-polar transistors(igbt) an their anti-parallel ioes uring gate blocking, taking into account arm currents polarities. The first part of this paper presents an open loop emonstrations of the half an full-brige MMC, incluing valiation of the presente half-brige MMC moel against its switching counterpart, an scalability of the full-brige MMC moel. The secon part of this paper presents a close loop emonstration that uses a full-scale moel of the half-brige MMC base HVDC to simulate its performance uring normal operation, an ac an c network faults. The results obtaine from both emonstrations have shown that the presente MMC moel is able to reprouce the typical behaviour of MMC base HVDC links to microscopic level in all the above stuies. This qualifies the presente MMC moel to be use for etaile stuies of the MMC base HVDC links at esign stage such as fine tuning of MMC passive parameters, an valiation of the control an protection systems. II. REVIEW OF THE MODULAR MULTILEVEL CONVERTER Figure shows three-phase generic moular multilevel converter with N cells per arm. For input c link voltage V c, voltage stress across each switching evices is Vc N, provie that the voltage across each cell capacitor is maintaine at V c [38-4]. In each instant, K an N-K cell capacitors from N the upper an lower arms must be inserte in the power path in orer synthesize ifferent output voltage levels. This ensures that v a +v a2 =V c ±v; where v a an v a2 represent voltages across the upper an lower arms of phase a, an V represents ac plus c voltage rop in the internal resistance (R ) an inuctance (L ) of the arm reactors. In other wors, from 2N available cell capacitors in each phase (upper an lower arms) of the moular converter, only N cell capacitors must be switche into the power path while the N remaining cell capacitors must be bypasse. Such restriction necessitates complementary operation of the upper an lower arms of the moular converter[42]. Since moular converter synthesizes the amplifie version of the moulating signals (sinusoial output voltage) by insertion of its cell capacitors into power path sequentially, flow of funamental current through these capacitors plus voltage rop across arm reactors will cause the cell capacitor voltages to oscillate aroun fixe c component. The exact value of the cell capacitor voltages c component is influence by power flow irection, an can be etermine by (V c ±2R I )/N; where I is the arm current c component. Oscillation of the upper cell capacitor voltages against that of the lower arm, an that of iniviual phase against main c link voltage cause aitional current components to flow in the moular converter arms (inrush plus circulating currents). The inrush currents are cause by switching of the cell capacitor in an out of the power path for the purpose of maintaining capacitor voltage balancing, an oscillation of the upper arm against the lower arm. The circulating currents are cause by oscillation of iniviual phase arm voltages such as v a +v a2, v b +v b2 an v c +v c2 against the main c link voltage (V c ); where v b an v b2, an v c an v c2 are the voltage evelope across the upper an lower arm cell capacitors of the phases b an c. Unlike conventional voltage source converters, the upper an lower arms of the moular converter conuct simultaneously, an this result in each arm contributes half of the output phase current, thus, half of the ac power per phase converter exchanges with the ac sie. The power exchange between each phase an c sie is achieve through c power, which is relate to I (c component of the arm current). Flow of the three current components in the semiconuctor switches cause moular converter to have higher on-state loss when compare to traitional voltage source converters such as two-level an neutral-point clampe[43]. Since funamental an c components of the arm currents are necessary for power exchange between ac an c sies, the inrush an circulating current component of the arm current must be minimize in

3 orer to reuce moular multilevel converter on-state loss as iscusse in [44-46]. However, active suppression of the 2 n harmonic in the arm current, which is the ominant component of the circulating current as suggeste in [47-52] is associate with aitional switching losses, an also limits the maximum attainable moulation inex (hence, results in smaller converter P-Q envelope). Metho that uses passive filter to suppress arm current circulating in the moular converter is propose in [53]. This metho avois the shortcoming of the previous metho that actively suppresses arm circulating current, but its ownsie is that it requires aitional passive component, which may slightly increase converter station footprint an losses. For more etails on the moulation an cell capacitor voltage balancing aopte in this paper, refer to [4, 42, 44, 54-60]. III. Figure : Schematic iagram of generic three-phase moular multilevel converter GENERIC ELECTROMAGNETIC TRANSIENT MODELLING OF MODULAR MULTILEVEL CONVERTER A) Half-brige MMC moel Figure 2 (a) an (b) show half-brige cell version of the moular multilevel converter an its electromagnetic transient representation base on Dommel trapezoial metho. Switching evices S xi an S ai in Figure 2(a) are replace by switche resistances R xi an R ai in the electromagnetic transient simulation equivalent circuit in Figure 2(b). The cell capacitor in Figure 2(a) is replace by its trapezoial Norton equivalent circuit in Figure 2(b). When switching evices S xi or S ai are on their corresponing switche resistances are set to R on or R on2 (on-state resistances of the switches S xi an S ai ). When S xi or S ai are off their corresponing switche resistances are set to R off or R off2 (off-state resistances of the switches S xi an S ai ). Switche resistances R xi an R ai are set to mimic operation of typical switches of the moular converter when they receive gating signals from the moulator. Thus, uring normal operation, R xi an R ai are set on an off in complementary manner as in typical operation of S xi an S ai in MMC [4, 42, 6]. To mimic MMC operation uring gate signal blocking as happens uring c short circuit faults, R xi an R ai are set base on the arm current polarity an peak of line-to-line voltages. Line-to-line voltages at converter terminals are use to mimic ioe rectifier operation of the typical MMC when gate signals are inhibite. Arm currents polarities are use to mimic conuction of the anti-parallel ioes of the switching evices S xi an S ai. For example, assume arm current I mi in Figure 2 (a) an (b) is positive, when I mi <0, R ai for all cells in the upper an lower arms that expose maximum line-to-line voltage are set on, an all remaining switches must set to off-state (typical ioe rectifier operation). When I mi 0, an R xi for the entire arm must be on to mimic the gate blocking conition in typical MMC operation when the conuction path is through anti-parallel ioes of S xi an cell capacitors. In this manner, the electromagnetic transient representation of the MMC cell mimics the exact operation of the physical half-brige MMC cell operation in all operating moes. For full MMC representation, this paper aopte per arm representation of the MMC in [3] that consiers each arm of MMC comprises of N iniviual cells riven by one current source its value equal to arm current, an each cell generates voltage v mi between its terminals (x i relative to imaginary groun). The total voltage evelope across each converter arm is assume to be equal to sum of the cell voltages ( V arm N V ), where N is the number of cells per arm. mi i Assuming the imaginary groun of each cell is locate at its zero voltage level, the noal equation that escribes ynamics of each cell within each time step t can be expresse as follow: Rxi Rai R V xi xi I mi 2C V yi I () hci Rxi Rxi t Where V xi an V yi represent the noal voltages of the noe y an x in the i th cell measure relative to virtual groun of the same cell. Observe that V xi an V yi represent the i th cell output an capacitor voltages respectively. Therefore, V mi =V xi an V ci =V yi. The current of each cell is efine base on Dommel trapezoial integration metho as: 2C Ihci Ici ( t t) Vc ( t t) (2) t Instantaneous currents in the composite switches S xi an S ai (IGBT plus anti-parallel ioe) are: Vxi Vyi ISxi (3) R I V xi xi Sxi (4) Rai However, this paper oes not formulate noal equation matrix for the entire arm as in [3], instea it computes the cell output an capacitor voltages for N cells irectly from () as: 2C V ( t) V ( t) I I R xi t Rxi mi xi mi hci V ( t) V ( t) I I i R xi Rxi Rai ci yi mi hci 2C 2C Where i ; an observe that for N Rxi Rai t t Rai cells, equations (5) an (6) nee to be solve N times single (5) (6)

4 time step, without the nee for matrix inversion, an voltage evelope across converter arm is compute as explaine above. In this manner, computation intensity of the moel is greatly reuce. Figure 2(e) an (f) show typical MMC arm an its electromagnetic transient equivalent circuit, an Figure 3 shows one phase leg of the MMC, incluing interfacing of the electromagnetic transient part into Simulink SimPower builing blocks. B) Full-brige MMC moel Figure 2 (c ) an () show typical full-brige MMC cell an its electromagnetic transient equivalent circuit. Observe that the switching evices S i through S i4 are replace by the switche resistances R i through R i4, an cell capacitor by its Norton equivalent. During normal operation, R i an R i3 are set on an off to prouce cell output voltage V mi equal to V ci, 0 an -V ci at noe x i relative to cell virtual groun, an operation of switche resistances R i2 an R i4 are complementary to that of R i an R i3 respectively. V mi =V ci is achieve by setting R i =R on an R i3 =R off ; V mi =-V ci is achieve by setting R i =R off an R i3 =R on ; an V mi =0 can be achieve either by setting R i =R on an R i3 =R on or vice versa. During gate blocking, arm current polarity is use to set the switche resistances of the equivalent cell in the entire arm simultaneously. For example, assuming I mi in Figure 2() is positive, R i =R on an R i3 =R off for I mi >0, an R i =R off an R i3 =R on for I mi <0. Observe that because as the total voltage across cell capacitors is greater than the peak of line voltage, the cell capacitors will oppose the current flow in the arm, an there is no irect path for the current to flow through the switche resistances as in halfbrige cell case. Aitionally, in case the total voltage across the cell capacitors of the all three phases happen to be smaller than the peak line voltage uring the gate blocking, the cell capacitors of the full-brige MMC will be charge for positive an negative arm currents. The noal equation that escribes the ynamics of Dommel electromagnetic transient moel of the full-brige MMC in Figure 2 () within each time step is: Ri Ri 2 Ri Ri 2 Vxi Imi 2C 2C V yi I hci Ri Ri Ri 3 t t (7) Vzi Ihci 2C 2C Ri 2 t Ri 2 Ri 4 t Where, each cell output an capacitor voltages are efine as: Vmi Vxi (8) V V V ci yi zi Currents in the switching evices of each cell can be expresse as explaine in the half-brige MMC case. The voltage evelops across each converter arm is expresse as the sum of the iniviual cell output voltage. For large number of cell as will be consiere later in this paper, matrix inversion must be avoie to reuce computation buren on the processor (intensity) by precalculation of the noe voltages as: Vxi Imi ( 2 3) Ihci i V I ( ) I yi 2 mi hci i V I ( ) I zi 3 mi hci i (9) Where: i i3 i2 i4 i2 i4 i i3 i i3 i2 i4 t( R R )( R R ) 2 R R ( R R ) C 2 R R ( R R ) C ; R t( R R ) 2 R C( R R ), 2 2 i3 i2 i4 i4 i2 i 3 3 Ri 4t( Ri 3 Ri ) 2 Ri 3C( Ri 2 Ri ) ; 22 Ri 3t( Ri Ri 2 Ri 4) 2 Ri 4C( Ri 2 Ri ) ; Ri 3Ri 4 t 2 C( Ri 2 Ri ) R t( R R R ) 2 R C( R R ) ; an tr R R R ) 2 CR R R R R R R R ). 33 i4 i i2 i3 i3 i2 i ; i i i2 i3 i4 i i3 i2 i3 i i4 i2 i4 y i 2 C I hci I ci ( t t ) V c ( t t ) t Vci () t t 2C Ici () t x i R xi Iai() t R ai V () t V mi xi I mi (a) Half-brige cell (b) Dommel electromagnetic transient representation of the halfbrige cell y i I i3 R i3 I i R i Vci () t t 2C x i I mi I i4 R i4 I i2 R i2 V mi I 2C Ici ( t t) Vc ( t t) t hci (c) Full-brige cell () Dommel s electromagnetic transient representation of the fullbrige MMC cell z i

5 Cell I hc V c I m V m Cell 2 V arm I hc2 V c2 I m2 V m2 Cell N I hcn V cn I mn V mn (e) One arm of the generic moular multilevel converter (f) Dommel electromagnetic transient representation of the generic moular multilevel converter arm Figure 2: Cell an arm of the generic moular multilevel converter an their Dommel electromagnetic transient representation Figure 3: Illustration of the interfacing of the electromagnet transient moel of the moular converter arms to SimPower System builing blocks on a singlephase

6 IV. MODEL VALIDATION This section presents a valiation of the generalize electromagnetic transient moel of the MMC iscusse in section III-A against its switching counterpart. In this valiation, both moels are built in Simulink; use the same circuit parameters shown in Table, an generalize moulator base on staircase moulation an capacitor voltage balancing; an proportional-integral controller for suppression of the arm currents 2 n harmonic. For valiation only, both moels are operate in open loa at 0.8 moulation using sinusoial references. Figure 4 isplay simulation waveforms obtaine from both moels. Figure 4 (a), (b) an (c) show prefilter phase an line-to-line voltages at converter terminal, an three-phase loa currents that obtaine from MMC EMT moel superimpose over that obtaine from the MMC switching moel, an observe that both moel agree to smallest etails as seen from the ac sie. Figure 4 () an (e) present upper an lower arms cell capacitor voltages obtaine from MMC switching an EMT moels, an observe that both results are ientical. Figure 4 (f) shows the sample of the upper an lower arm currents obtaine from both moels are ientical as they coincie to microscopic level. Despite the level of agreements shown in Figure 4 (a) to (f), sample of the common-moe current of the phase a that obtaine as i a +i a2 from the MMC switching an EMT moels shows high level of agreement, with noticeable minor ifferences between the results of the two moels. Base on these results it can be conclue that the presente EMT moel of the MMC is sufficiently accurate since it is able to match its switching counterpart in every etails to microscopic level. This valiation is carrie out when both moels are simulate in iscrete omain, with 5s time step, an cell capacitor voltage measurements for the capacitor voltage balancing are upate on regular space of 500s. Further valiations of the presente EMT moel versus its etaile switching counterpart uring ac an c faults are presente in the appenix. Table : Summary of converter parameters use for valiation Parameter Value c link voltage V c (kv) 400 cell capacitance C m (mf).4 arm inuctance L (mh) 50 Arm inuctance internal resistance R (Ω) 0. Loa resistance R L (Ω) 250 Loa inuctance L L (mh) 597 Number of cell per arm (N) 2 (a) Phase voltage measure converter terminal relative to supply mipoint (switch moel superimpose on that obtaine from EMT moel) (b) Line-to-line voltage measure at converter terminal(switch moel superimpose on that obtaine from EMT moel) (c) Three-phase currents (switch moel superimpose on that obtaine from EMT moel) () Sample of the cell capacitor voltages of the phase A that obtaine from switch moel (e) Sample of the cell capacitor voltages that obtaine from electromagnetic transient moel 3.5 (f) Sample of the upper an lower arm currents of the phase A ( switch moel superimpose on that obtaine from EMT moel)

7 (g) Sample of the common moe current of the phase A (I a+i a2) Figure 4: Waveforms presente aim to valiate the MMC generalize moel base on electromagnetic transient simulation approach against switch moel that uses Simulink power electronics builing blocks from SimPowerSystems library In attempt to illustrate the scalability of the full-brige moel presente in this paper while restraining paper length, only sample results obtaine from open loop operation of a singlephase full-brige MMC with 5 an 30 cells per arm, ±320kV c link voltage, 0.8 moulation inex, an 300 an 690mH loa are presente. Figure 5 presents selecte waveforms obtaine when number of cells per arm is 5. Figure 5 (a) an (b) samples of the phase an line voltage obtaine with 5 full-brige cells per arm, an observe that the converter being stuie generates nearly pure sinusoial output with only 5 cells per arm. This clearly justifies the reuce cell approach aopte in cascae two-level converter presente in [53] that significantly reuces the complexity of the power circuit an moulation. Figure 5 (c) shows the upper an lower arm currents obtaine for phase a, an notice that with the suppression of the 2 n harmonic in the arm currents, the upper an lower arm currents (i a an i a2 )ten be ominate by the funamental plus c components, which are responsible from the power transfer between converter ac an c sies. Figure 5 () shows the voltage balance of the cell capacitor voltages of the upper an lower arms are maintaine tightly aroun V c /N (640kV/52.55kV). Figure 5 (c) to (h) samples of the currents in the switching evices of one fullbrige MMC cell (top cell of the upper arm). Observe that the switching evices of the full-brige cells MMC operate more frequently compare to that of the half-brige cells MMC as will be shown later. This is ue to exploitation of the extra reunancies offere by the bi-polar capability of the fullbrige cells that have been use to maintain cell capacitor voltage, an reuce the cell capacitance size. Aitionally, it must be notice that the switching evices S a2 an S a3 are use only to balance the capacitor voltages using reunant switch states that permit insertion of some the cell capacitor with the opposite polarities when synthesizing intermeiate voltage levels between ½V c an -½V c. This inicates that the usage of switching evices S a an S a4 are much higher than that of the S a2 an S a3, hence higher rate heat sinks may be require for S a an S a4. The results obtaine when number of cells per is increase to 30 per arm are presente in Figure 6. Figure 6 (a) an (b) show the phase voltage obtaine with 30 cells per arm is pure sinusoial, an cell capacitor voltages of the upper an lower arms are maintaine tightly aroun 2.3kV as anticipate. Figure 6 (c) shows the upper an lower arm currents are pure sinusoial plus c components. The samples of the currents in the switching evices of one full-brige MMC cell in Figure 6 () an (e) show the switching frequency per evice is not significantly reuce espite large increase in the number of cells per arm compare to the case presente in Figure 5 (e) an (g). Base on the results presente in Figure 5 an Figure 6, it can be conclue that the presente moel in III-B is able to reprouce the typical behaviour full-brige MMC in similar way of traitional switching moel. (a) Full-brige MMC output phase relative to c link mi-point (b) Output phase current (c) Current waveforms in the upper an lower arms of the full-brige MMC () Cell capacitor voltages of the upper an lower arms

8 (e) Current in switching evice (S a) (f) Current in switching evice (S a2) (g) Current in switching evice (S a3) (h) Current in switching evice (S a4) Figure 5: Waveforms obtaine from EMT moel of the full-brige MMC iscusse in section III-B, with 5 cells per arm when 2 n harmonic suppression of the arm currents controller is incorporate (cell capacitance=5mf, R =0.05 an L =50mH) (a) Full-brige MMC output phase voltage (b) Cell capacitor voltages (c) Upper an lower arm currents () Sample current waveforms in switching evices S a (e) Sample current waveforms in switching evices S a3 Figure 6: Waveforms obtaine from EMT moel of the full-brige MMC iscusse in section III-B, with 30 cells per arm an 2 n harmonic suppression of the arm currents controller is incorporate (cell capacitance=4mf, R =0.05 an L =50mH) V. CONTROL SYSTEMS DESIGN For the purpose of the control esign, consiers the simplifie representation of the gri connecte moular multilevel converter in Figure 7, where o represents the groun (c link mi-point of the symmetrical mono-polar as normally set by the stray capacitance of the c line). Consiering the upper an lower arms of the generic moular converter in Figure 7 when the total voltage evelope across the upper an lower arms are replace by their low-frequency components, the following equations are obtaine for phase a : ia V c vao Ria L va 0 (0) t ia 2 V c vao Ria 2 L va2 0 () t Converter terminal voltage v ao can be expresse in terms of output current i a an gri voltage v ga as:

9 ia Assuming, the -axis is aligne with the phase a of the gri vao RT ia LT vga (2) t voltage, equation (5) is transforme into -q synchronous After subtracting () from (0) an combine with (2), the reference frame as: following equation is obtaine: i va2 va R ( ia ia2) L ( ia ia2) ( L LT ) ( L LT ) iq ( R RT ) i mv 2 c sin vg t t (3) (6) i i a q 2RT ia 2LT 2vga 0 ( L LT ) ( L LT ) i ( R RT ) iq mv 2 c cos vgq t t Recall that ia ia ia 2, va V 2 c msin( t ) an For current control esign, equation (6) is re-arrange as: i ( R ( ) R ) vc vg L LT i T q va2 V 2 c msin( t ), where V c presents the mean c i (7) t ( L LT ) ( L LT ) voltage of the upper an lower arms cell capacitors, m is the i q ( R ( ) R ) vcq vgq L LT i T moulation inex, v ga is the gri voltage, an is the angle i q (8) between converter terminal v ao an gri voltage v ga. With t ( L ) ( ) LT L LT these assumptions, equation (3) can be reuce to: With the following change of variables: i u v v ( L L ) i an u v v ( L L ) i, u a c g T q q cq gq T ( L ) ( ) sin( ) LT R RT ia mv 2 c t vga (4) t * * an u q are obtaine by forcing i an i q to follow i an i q From (4), ifferential equations that escribe funamental currents for all three phases in the moular converter can be using proportional-integral controller as: * * * * euce as: u kp( i i ) ki( i i ) t an uq kp( iq iq ) ki ( iq iq ) t, ia where k ( L ) ( ) sin( ) LT R RT ia mv 2 c t v p an k i represent the proportional an integral gains. ga t After manipulations of equations (7) an (8), an efinitions i given for u b 4 ( L ) ( ) sin( ) LT R RT ib mv 2 c t v 3 gb (5) an u q, where the integral parts of u an u q are t replace by an q the following equation is obtaine: ic 2 ( L ) ( ) sin( ) LT R RT ic mv 2 c t v 3 gc t ( R RT k p) k p i ( L ) ( ) ( ) LT L LT i L LT ki ki 0 * i i t q ( R ) RT k p i * (9) q k p i q q ( L ) ( ) ( ) LT L L T q L L T 0 0 ki 0 0 k i After Laplace manipulation of (9), the initial gains of the equation (2) is written as in (22) an broken into (23) an inner current controller can be selecte using (24): 2 kp 2 n ( L ) ( ) LT R RT an ki n ( L ) LT, an ih R ( I ih) ( I ih) ( Vc 0 vh) (22) natural frequency n can be selecte assuming settling time t L L 4 I R T s an amping factor from n. However, the I V c0 (23) T t L L s ih R i h v h (24) t L L final gains must be fine tune to ensure that satisfactory performance is achieve over the entire system operating range, incluing ac an c network faults. From efinitions of the u an u q, where u an u q are the outputs of current controller in the an q channels, the block iagram for the inner current controller in Figure 8 is obtaine. For esign of the supplementary current controller that responsible for suppression of the 2 n harmonic component of the common moe current, a equations (0) an (), an the following equation is obtaine: Vc ( va va2) R ( ia ia2) L ( ia ia2) 0 (20) t Recall that the common moe current of the upper an lower arms can be efine as i com =i a +i a2, therefore equation (20) can be reuce to: i R V V i (2) t L L com c c com Since flow of the ac current components of the i a an i a2 in the arm reactors an cell capacitors cause capacitor voltages of the upper an lower arms to oscillate (thus, V c ), the common moe current i com contains c an ac components. Therefore, Observe that equation (23) escribes ynamics of the arm current c component I, which is responsible for power transfer between converter an c sie. Equation (24) escribes ynamics of the ac component of the common moe current i h, which is ominantly 2 n orer harmonic plus other harmonics, epening on the moulation strategy employe; where v h represents the cell capacitor voltage ripple. In attempt to reuce the semiconuctor losses ue to 2 n harmonic of the arm current, this paper favours the use of a simple PI controller over the proportional resonance to minimize 2 n harmonics in the MMC arm currents (or i h ). This requires i h to be passe through a ban pass filter (BPF), tune at 00Hz with high quality factor in orer to extract only the 2 n harmonic component i 2h from i h. Consiering 2 n harmonic only, equation (24) becomes: i2h R i 2h v 2h t L L (25) The voltage v 2h neee to minimize the 2 n harmonic in the MMC arm current is estimate from PI controller as:

10 * * v2h p( i2h i2h) i ( i2h i2h) t (26) which inclues all expecte HVDC basic controllers an supplementary controller for suppression of the arm currents After replacing the integral part in (26) by z 2h, an algebraic 2 n harmonic component. manipulations of (25) an (26), the following equation is obtaine: ( R p) p i2h i 2 h L L L * i2 t z h 2h z (27) 2h i 0 i After Laplace manipulations of (27), the following close loop transfer function for the 2 n harmonic suppression is obtaine: p s i i2h () s L L (28) * i2 () 2 ( p R) h s s s i L L From (28), the PI gains are : 2 L R an p n L, 2 i n where an n are amping factor an controller natural frequency in ra/s. To accommoate BPF ynamics an avoi interference with the main power flow controllers, the gains for the 2 n harmonic suppression controller must be selecte to be as slow as possible, an its output is limite to 5% of moulation inex. This inicates that inclusion of such supplementary controller reuces converter c link utilization an P-Q envelope if compare to the approach that uses passive filter for arm current 2 n harmonic suppression as emonstrate in.[53, 62, 63]. Figure 8 summarises the overall control system that has been use in the MMC an MMC 2, Figure 7: Simplifie illustration of generic moular multilevel converter connecte to gri Figure 8: Block iagram illustrates generic control systems use in both converter stations MMC an MMC 2 VI. SIMULATION OF FULL-SCALE HVDC LINK To emonstrate the effectiveness of the electromagnetic transient (EMT) moelling approach iscusse in section III when use to simulate full-scale VSC-HVDC links, an example link in Figure 9 is built in Simulink environment with converter stations MMC an MMC 2 moelle with 20 halfbrige cells per arm, with parameters liste in Table 2. MMC is configure to regulate active power exchange between AC systems an 2, an provies voltage support at PCC. MMC 2 regulates c link voltage level at 400kV (pole-to-pole), an supports ac voltage at PCC 2. Both MMC an MMC 2 employ staircase moulation, with sinusoial references. Small time step of 5s is use throughout this section to show the computational efficiency of the presente MMC when simulating HVDC links with large number of cells per converter (206 cells per converter, an 242 cells per moel).

11 Figure 9: Simulink moel of full-scale VSC-HVDC Table 2: Parameters of the full-scale MMC base HVDC link in Figure 9 Converters MMC an MMC2 interfacing transformer 200kV/400kV DC link voltage ±200kV Interfacing transformer leakage reactance 0.32pu Rate apparent power 450MVA Resistance of the interfacing transformer pu Maximum active power capability 400MW AC systems an MVA, 400kV an X/R=0 Maximum reactive power capability ±206MVAr DC line resistance (R c) 0mΩ/km Inuctance of the arm reactor (L ) 3mH DC line capacitance (C c) 0.5µF/km Resistance of the arm reactor (R ) 0.05Ω DC line inuctance (L c) 0.6mH/km Cell capacitance (Cm) 6mF DC line length 00km Number of cells per arm 20 A) Normal Operation This section presents simulation results obtaine when converter station MMC of the full-scale HVDC link in Figure 9 ramps its output power from 0 to 0.7pu (35MW) in orer to export power from ac system 2 to. At time t=0.8s, MMC reverses the power flow by graually ramping own its output power from 0.7pu to -0.7pu. Observe that the selecte waveforms in Figure 0 reprouce the typical behaviour of the MMC base HVDC link in great etail than similar works presente in [28, 30, 3]. Figure 0(a) an (b) show active an reactive power at ac sies of the MMC an MMC 2. Figure 0(c) an (), an (e) an (f) show ac current waveforms MMC an MMC 2 inject into PCC an PCC 2, an their arm currents. Notice that the shape of the arm currents in Figure 0 (e) an (f) are typical to the SIEMENS HVDC PLUS presente in [64] as the power flow irection changes. Figure 0 (g) an (h) show c link current, an converter line-to-line terminal voltage. Figure 0 (h) shows that with such large number of cells, MMC presents pure sinusoial voltage to the interfacing transformer. Figure 0(i) an (j) show the c link voltage of the MMC an MMC 2. Figure 0 (k) an (l) isplay cell capacitor voltages of both converter stations, an observe that they are balance an settle aroun.99kv as expecte. Figure 0(m) shows zoome version of the cell capacitor voltage of the MMC, phase a. Figure 0 (n) an (o) present sample of the current waveforms in the switching evices of one cell (top cell in the phase a upper arm). The results in Figure 0 have shown that the presente moelling approach is able to reprouce the typical behaviour of full-scale MMC base HVDC link in great etail, incluing access to all internal variables of the moular converters which are of great importance from system esign prospective. (a) Active an reactive power MMC exchanges with PCC (b) Active an reactive power MMC 2 exchanges with PCC 2

12 (c) Current waveforms MMC injects into PCC () Current waveforms MMC 2 injects into PCC 2 (e) MMC six arm currents zoome aroun power reversal (f) MMC 2 six arm currents zoome aroun power reversal (g) DC link current (h) Sample of the line-to-line voltage MMC presents to its interfacing transformer (measure at converter terminal before interfacing transformer) (i) VSC DC link voltage (j) VSC 2 DC link voltage (k) Voltage across 402 cell capacitors of the MMC (phase A) (l) Voltage across 402 cell capacitors of the MMC 2 (phase A) (m) Zoome version of the 402 cell capacitors of the MMC (phase A) (n) Current in the swicthing evice S a (MMC )

13 (o) Current waveform in the swicthing evice S x (MMC ) Figure 0: Selecte waveforms that emonstrate the suitability of the EMT approach iscusse in section III for full-scale moelling of the MMC base VSC- HVDC link B) AC fault To examine the suitability of the presente MMC moelling approach for stuying ac network faults, the full-scale Simulink moel of the HVDC link in Figure 9 is subjecte to a three-phase ac fault at PCC, through 2Ω fault resistance at time t=0.4s an cleare after 200ms. After ac fault is etecte, MMC active output is reuce immeiately to 0 an restore when the fault is cleare. Figure isplays selecte waveforms obtaine from the full-scale Simulink moel when it is subjecte to a three-phase fault at PCC. Figure (a) an (b) show active an reactive powers MMC an MMC 2 exchange with their point of common couplings PCC an PCC 2. Observe that although the active power of the MMC is reuce to zero immeiately when ac fault is etecte, the active power at the ac sie of the MMC 2 that regulates c link voltage takes longer time to fall to zero. This is because the ynamics of the c power (or c component of the arm currents) is strongly link to the change in the cell voltages, which take several funamental cycles to ajust following power orer at MMC. The results in Figure (a) an (b) inicate that the MMC base HVDC link has relative slow ynamic response when compare with conventional VSC- HVDC links that use two-level or neutral-point clampe converters. Figure (c) an () show the voltage magnitue an ac current waveforms at PCC, an notice that although the voltage at PCC collapses to less than 30% of the rate voltage, the current contribution of the MMC to the ac fault is limite an less than the pre-fault currents. The c link voltages of the MMC an MMC 2 in Figure (e) an (f) exhibit slight increase uring brief perio of ac an c powers mismatch as a result of ac fault an suen reuction in MMC power orer; thanks to the large energy storage capacity of 206 cell capacitors per converter. Figure (g) an (h) show the cell capacitor voltages of the MMC an MMC 2 experience some isturbances uring ac fault, with the cell capacitor voltages of the MMC (near to the fault) experience larger voltage ripples than that of the MMC 2 (remote converter). These results have emonstrate the ability of the presente moel to capture the behaviour of typical MMC base HVDC link, incluing internal converter station ynamics an interactions between ac an c sies. Therefore, it can be conclue that the presente moel is qualifie to be use for ac network faults stuies, an other etaile systems stuies at esign stage, incluing esign of the link an converter protection systems. (a) Active an reactive MMC exchanges with PCC (b) Active an reactive MMC 2 exchanges with PCC 2 (c) Voltage magnitue at PCC () Current waveforms MMC injects into PCC

14 (e) MMC DC link voltage (V c) (f) MMC 2 DC link voltage (V c2) (g) Voltage across cell capacitors of phase A in the MMC (h) Voltage across cell capacitors of phase A in the MMC 2 Figure : Waveforms obtaine from full-scale Simulink moel in Figure 9 when it has been subjecte to three-phase ac fault at PCC, with 200ms fault uration C) DC fault To assess the suitability of the presente full-scale MMC base HVDC link for c faults stuies, the Simulink moel of HVDC link in Figure 9 is subjecte to a soli pole-to-pole c short circuit fault at the mile of the c line between MMC an MMC 2 at t=0.4s, with 200ms fault uration. When c fault is etecte, converter switches are blocke immeiately. In pre-fault conition, the link exports 35MW (0.7pu) from ac system 2 to. When c fault is etecte at t=0.4s, power comman to MMC is reuce immeiately to zero an its restoration to pre-fault value is elaye until t=s to allow all transients associate with the fault an converter e-blocking at t=0.6s to ie out. Figure 2 (a) an (b) show the HVDC link being stuie is able to recover with increase reactive power consumptions ue to current in-fee through anti-parallel ioes of MMC an MMC 2 as expecte in typical half-brige MMC base HVDC link. Current waveforms in Figure 2 (c) an () show large current in-fees at ac sies of the MMC an MMC uring fault perio as previously mentione. Figure 2 (e) an (f) isplay c currents at the terminals of the MMC an MMC 2. Observe that ue to the concept of istribute cell capacitors of the MMC the transient component of the c fault that associate with ischarge of c line istribute capacitors is much smaller than the steay, which is mainly ue to gri contribution through converter anti-parallel ioes. Figure 2 (g) shows the collapse of the MMC DC link voltage uring pole-to-pole DC fault at the mile of the HVDC link (as a sample). Figure 2 (h) an (i) isplay current waveforms in six arms of the MMC an MMC 2, an observe that the arm currents of both converters ten to be negative, an this confirms that the in-fee currents from the ac to c sies uring c fault are flowing through anti-parallel ioes as expecte in typical MMC link. Figure 2 (j) an (k) show the current waveforms in the switching evices S a an S x (top cell in the phase a, upper arm of the MMC ), an observe that there is no current in the switching evice S x which is in series with the cell capacitor as anticipate in typical MMC link uring c fault when converter switches are blocke. Whilst the current in the main switch S a is naturally commutate as in typical ioe rectifier, but with large overlap which is cause by present of large inuctances in the conuction path (converter transformer leakage inuctances plus arm reactors) when converter switching evices are gate off. Figure 2 (l) an (m) present the cell capacitor voltages of the MMC an MMC 2, an observe that the cell capacitor voltages of the MMC an MMC 2 become flat when they are blocke as no currents are following through the cell capacitors as previously shown in Figure 2 (k). Results presente in Figure 2 have shown that the full-scale moel of the MMC base HVDC link being simulate using converter moel iscusse in III-A) is able to reprouce the typical behaviour of the HVDC links that employ half-brige moular multilevel converters. (a) Active an reactive power MMC exchanges with PCC (b) Active an reactive power MMC 2 exchanges with PCC 2

15 (c) Current waveforms MMC injects into PCC () Current waveforms MMC 2 injects into PCC 2 (e) MMC c link current (f) MMC c link current (g) Sample of the c link voltage measure at the terminal of MMC (V c) (h) Current waveforms in the six arms of the MMC (i) Current waveforms in the six arms of the MMC 2 (j) Sample of the current waveform in the switching evice S a ( st cell in upper arm of MMC, phase a ) (k) Sample of the current waveform in the switching evice S x ( st cell in upper arm of MMC, phase a ) (l) Voltage across cell capacitor 402 cell capacitors of phase A of the MMC (m) Voltage across cell capacitor 402 cell capacitors of phase A of the MMC 2 Figure 2: Waveforms obtaine when a full-scale Simulink moel of the MMC base HVDC link in Figure 9 is subjecte to a pole-to-pole c short circuit fault

16 VII. CONCLUSIONS This paper presente improve electromagnetic transient moels for the half an full MMC that can be use to simulate normal an transient responses of the full-scale HVDC links that employ moular multilevel converters, hunres cells per arm. Aitionally, it provies comprehensive qualitative an quantities iscussions of the half an full-brige MMCs that cover evice an system aspects, which are of great importance for correct moelling of the MMC base HVDC links. It has been shown that the presente moels can reprouce the typical behaviour of the half an full brige MMCs as that normally obtaine from the switching moel. Scalabilities of both MMC moels presente in this paper have emonstrate the suitability of this approach for moelling of full-scale HVDC links an multi-terminal c gris. Unlike the previous works which are platform epenent, this paper has shown that the presente generic MMC moel can be implemente in any platform. VIII. APPENDIX This appenix presents valiations of the EMTP moel iscusse in section III-A against its switching counterpart uring ac an c faults, consiering the test system in Figure 3. Figure 3 represents one terminal of the HVDC link which is configure to regulate active power an ac voltage at PCC. Both moels are simulate with reuce number of cells per arm (2 cells per arm), with the same control systems as epicte in Figure 8. Figure 4 isplays selecte waveforms obtaine when the test system in Figure 3 is subjecte to a temporary three-phase fault at PCC, at t=0.4s an cleare after 200ms. Figure 4 (a) shows that the three-phase currents both MMC moels inject into ac gri uring steay state an ac fault are closely matche. Figure 4(b) presents the error between the threephase currents of the two moels shown Figure 4(a), swicth EMTP calculate as i i i. Observe that the peak abc abc abc percentage errors uring steay-state an ac fault are 2A/644A 00%=0.3% an 7A/55A 00%=.27% when converter output active power is reuce to zero. Figure 4(c) an () show sample of the upper an lower arm currents (phase A ) obtaine from both moels an their corresponing error. Observe that the results of the EMTP moel agree to that of switch moel to the finest etails, with some limite errors uring fast transient initiate by the ac fault as epicte in Figure 4 (). Aitionally, notice that as the error in Figure 4 () fluctuates between positive an negative, which inicates oscillations of the EMTP currents aroun that of the switching moel. Figure 4 () inicates that the average error between the two moels is expecte to be sufficiently small. Figure 4 (e) an (f) show the common moe current I a +I a2 obtaine from both moels an their corresponing error, an notice that both moels agree to great etails uring steay state an ac fault, with small average error. Figure 4 (g) an (h) isplay sample of the cell capacitor voltages an their zoome version aroun the fault perio. Observe that the EMTP moel is able to reprouce similar results as that of the switching moel, with sufficiently small error. Base on the results in Figure 4 it can be conclue that the presente EMTP moel is able to reprouce the output of its switching counterpart, with high level of accuracy. Therefore, it qualifies for any kin of etaile stuies of the ac network faults. To further valiate the c fault performance of the presente EMTP moel against its switching equivalent, the test system in Figure 3 is subjecte to temporary soli pole-to-pole c short circuit at the mile of the c link at t=0.4, with 200ms fault uration, an results obtaine are isplaye in Figure 5. During c fault perio, the gating signals to converter switches are blocke, an active power comman is reuce immeiately to zero. Figure 5 (a) shows the snapshot of the three-phase currents converter injects into PCC, zoome aroun the fault perio. Observe that both moels prouce almost ientical results, with small relative error of less than switch EMTP Iabc Iabc 2600A 2700A 4% ( 00% 3.85% ) uring c switch I 2600A arm fault. Such level of error is conceivable as the switch moel uses relative complex moel for the switching evices (IGBT an anti-parallel ioe), while EMTP approach uses only twostate resistance to mimic on an off states of the switching evices. Figure 5(b) isplays the snapshot of the upper an lower arm currents for phase A. Observe that the presente EMTP moel is able to reprouce the output of the switching moel, with small relative error of less than 4% ( switch EMTP Iarm Iarm 5300A 5500A 00% 3.77% 200A) uring switch I 5300A arm c fault when converter switches are gate-off. This confirms the valiity of the moifications introuce in the setting of the MMC two-state resistors when gating signals are inhibite as previously iscusse in section III-A. Figure 5(c) isplays the zoome version of the cell capacitors (first three cell capacitor voltages from the upper an lower arms of the phase A ). Notice that the cell capacitor voltages obtaine from the EMTP moel are similar to that of the switching moel, with some small error of less than % uring c fault perio. Simulation waveforms presente in Figure 4 an Figure 5 have shown that the presente EMTP moel is sufficiently accurate to be use for wie range of the etaile stuies of full-scale HVDC links an multi-terminal HVDC networks, incluing ac an c faults.

17 50km 50km PCC 400kV Vc N N N 450MVA 200kV/400kV 0.32pu AC System 4000MVA 400kV X/R= N N N MMC Figure 3: One terminal of the MMC HVDC link use to valiate the present EMTP against its switching counterpart, with number of cells per arm is reuce to 2 an cell capacitance.4mf (a) Snapshot of the three-phase currents converter injects into gri zero aroun the time where the fault is initiate (switch moel superimpose on that obtaine from EMT moel) (b) Errors between the two moels in the currents converter station injects into ac gri () Errors in the arm currents between the two moels (c) Snapshot of the upper an lower arm currents zoome aroun the instant where the ac fault is initiate (phase A, switch moel superimpose on that obtaine from EMT moel) (e) Common moe currents I a+i a2 (phase A, switch moel superimpose on that obtaine from EMT moel) (f) Error in common moe current

18 (g) Sample of cell capacitor voltages (phase A upper an lower arms, switch moel superimpose on that obtaine from EMT moel) (h) Detaile view of the cell capacitor voltages zoome aroun the instant where the fault is initiate (three first cells from the upper an lower arms of phase A, switch moel superimpose on that obtaine from EMT moel) Figure 4: Waveforms aim to valiate the presente EMTP moel versus its switching equivalent uring three-phase ac fault at PCC (2 cells per arm, 450MVA converter with 400kV c link voltage) (a) Snapshot of the three-phase currents measure at the converter transformer high-voltage sie (400kV, gri sie), zoome aroun instant when c fault is initiate (b) Phase A upper an lower arm currents (switch moel superimpose on that obtaine from EMT moel), zoome aroun instant when c fault is initiate (c) Detaile view of the cell capacitor voltages zoome aroun the instant where the fault is initiate (three first cells from the upper an lower arms of phase A, switch moel superimpose on that obtaine from EMT moel) Figure 5: Waveforms aim to valiate the presente EMTP moel versus its switching equivalent uring soli pole-to-pole c short circuit fault at F 2(2 cells per arm, 450MVA converter with 400kV c link voltage, c cable ) IX. REFERENCES [] M. P. Bahrman an B. K. Johnson, "The ABCs of HVDC transmission technologies," Power an Energy Magazine, IEEE, vol. 5, pp , [2] S. Karugaba an O. Ojo, "A Carrier-Base PWM Moulation Technique for Balance an Unbalance Reference Voltages in Multiphase Voltage-Source Inverters," Inustry Applications, IEEE Transactions on, vol. 48, pp , 202. [3] L. Chi-Seng, C. Wai-Hei, W. Man-Chung, an H. Ying-Duo, "Aaptive DC-Link Voltage-Controlle Hybri Active Power Filters for Reactive Power Compensation," Power Electronics, IEEE Transactions on, vol. 27, pp , 202. [4] M. A. Saye an T. Takeshita, "All Noes Voltage Regulation an Line Loss Minimization in Loop Distribution Systems Using UPFC," Power Electronics, IEEE Transactions on, vol. 26, pp , 20. [5] A. Lopez, R. Diez, G. Perilla, an D. Patino, "Analysis an Comparison of Three Topologies of the Laer Multilevel DC/DC Converter," Power Electronics, IEEE Transactions on, vol. 27, pp , 202. [6] S. Wensheng, F. Xiaoyun, an K. M. Smeley, "A Carrier-Base PWM Strategy With the Offset Voltage Injection for Single-Phase Three-Level Neutral-Point-Clampe Converters," Power Electronics, IEEE Transactions on, vol. 28, pp , 203. [7] J. Pou, J. Zaragoza, S. Ceballos, M. Saeeifar, an D. Boroyevich, "A Carrier-Base PWM Strategy With Zero-Sequence Voltage Injection for a Three-Level Neutral-Point-Clampe Converter," Power Electronics, IEEE Transactions on, vol. 27, pp , 202. [8] M. Hagiwara, R. Maea, an H. Akagi, "Control an Analysis of the Moular Multilevel Cascae Converter Base on Double-Star Chopper-Cells (MMCC-DSCC)," Power Electronics, IEEE Transactions on, vol. PP, pp. -, 200. [9] M. Hagiwara, R. Maea, an H. Akagi, "Control an Analysis of the Moular Multilevel Cascae Converter Base on Double-Star Chopper-Cells (MMCC-DSCC)," Power Electronics, IEEE Transactions on, vol. 26, pp , 20. [0] H. Akagi an R. Kitaa, "Control an Design of a Moular Multilevel Cascae BTB System Using Biirectional Isolate DC/DC Converters," Power Electronics, IEEE Transactions on, vol. 26, pp , 20. [] K. R. Sekhar an S. Srinivas, "Discontinuous Decouple PWMs for Reuce Current Ripple in a Dual Two-Level Inverter Fe Open-En Wining Inuction Motor Drive," Power Electronics, IEEE Transactions on, vol. 28, pp , 203. [2] Z. Zhengming, Z. Yulin, G. Hongwei, Y. Liqiang, an L. Ting, "Hybri Selective Harmonic Elimination PWM for Common- Moe Voltage Reuction in Three-Level Neutral-Point-Clampe Inverters for Variable Spee Inuction Drives," Power Electronics, IEEE Transactions on, vol. 27, pp , 202.

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20 [53] B. Jacobson;, P. Karlsson;, G.Asplun;, L.Harnnart;, an a. T. Jonsson, "VSC-HVDC Transmission with Cascae Two-level Converters," presente at the CIGRE 200, 200. [54] D. Schmitt, Y. Wang, T. Weyh, an R. Marquart, "DC-sie fault current management in extene multiterminal-hvdcgris," in Systems, Signals an Devices (SSD), 202 9th International Multi-Conference on, 202, pp. -5. [55] R. Marquart, "Moular Multilevel Converter topologies with DC-Short circuit current limitation," in Power Electronics an ECCE Asia (ICPE & ECCE), 20 IEEE 8th International Conference on, 20, pp [56] R. Marquart, "Moular Multilevel Converter: An universal concept for HVDC-Networks an extene DC-Bus-applications," in Power Electronics Conference (IPEC), 200 International, 200, pp [57] S. Allebro, R. Hamerski, an R. Marquart, "New transformerless, scalable Moular Multilevel Converters for HVDC-transmission," in Power Electronics Specialists Conference, PESC IEEE, 2008, pp [58] S. Rohner, S. Bernet, M. Hiller, an R. Sommer, "Analysis an Simulation of a 6 kv, 6 MVA Moular Multilevel Converter," in Inustrial Electronics, IECON '09. 35th Annual Conference of IEEE, 2009, pp [59] G. P. Aam;, K. H. Ahme;, S. J. Finney;, an B. W. Williams, "H-BRIDGE MODULAR MULTILEVEL CONVERTER (M2C) FOR HIGH-VOLTAGE APPLICATIONS," presente at the 2st International Conference on Electricity Distribution (Cire), Frankfurt, 20. [60] G. P. Aam, G. O. Anaya-Lara, an G. Burt, "Statcom base on moular multilevel converter: Dynamic performance an transient response uring ac network isturbances," in Power Electronics, Machines an Drives (PEMD 202), 6th IET International Conference on, 202, pp. -5. [6] G. P. Aam, O. Anaya-Lara, G. M. Burt, D. Telfor, B. W. Williams, an J. R. McDonal, "Moular multilevel inverter: Pulse with moulation an capacitor balancing technique," Power Electronics, IET, vol. 3, pp , 200. [62] N. N. V. Surenra Babu an B. G. Fernanes, "Cascae two-level inverter-base multilevel static VAr compensator using 2-sie polygonal voltage space vector moulation," Power Electronics, IET, vol. 5, pp , 202. [63] R. L. Sellick, x030a, an M. kerberg, "Comparison of HVDC Light (VSC) an HVDC Classic (LCC) site aspects, for a 500MW 400kV HVDC transmission scheme," in AC an DC Power Transmission (ACDC 202), 0th IET International Conference on, 202, pp. -6. [64] D. Retzmann. (2008, Benefits of Power Electronics Unerstaning HVDC an FACTS. B.W. Williams receive the M.Eng.Sc. egree from the University of Aelaie, Australia, in 978, an the Ph.D. egree from Cambrige University, Cambrige, U.K., in 980. After seven years as a Lecturer at Imperial College, University of Lonon, U.K., he was appointe to a Chair of Electrical Engineering at Heriot-Watt University, Einburgh, U.K, in 986. He is currently a Professor at Strathclye University, UK. His teaching covers power electronics (in which he has a free internet text) an rive systems. His research activities inclue power semiconuctor moelling an protection, converter topologies, soft switching techniques, an application of ASICs an microprocessors X. BIOGRAPHIES G.P. Aam receive a first class BSc an MSc from Suan University for Science an Technology, Suan in 998 an 2002 respectively; an. a PhD in Power Electronics from University of Strathclye in He has been working as a research fellow with Institute of Energy an Environment, University of Strathclye in Glasgow, UK, since His research interests are fault tolerant voltage source converters for HVDC systems; control of HVDC transmission systems an multi-terminal HVDC networks; voltage source converter base FACTS evices; an gri integration issues of renewable energies. Dr Aam has authore an co-authore several technical reports, an journal an conference papers in the area of multilevel converters an HVDC systems, an gri integration of renewable power. Also, he is actively contributing to reviewing process for several IEEE an IET Transactions an Journals, an conferences.