Field of the Invention

The invention relates to the field of power converters for dc networks. Background

For high-voltage direct current (HVDC) transmission applications, it is known to provide for bidirectional single-stage dc/dc conversion using a modular structure based on the cascaded connection of half-bridge submodules, with power balance for each submodule capacitor achieved via circulating AC currents [1-2]. The use of full-bridge submodules [1-2] (or submodules that can function as full bridge submodules in certain situations [3]) is also known. Throughout this document the term "full-bridge submodules" should be understood to encompass conventional full-bridge submodules and submodules that have full bridge functionality and other enhancements.

Power-flow control in [4] (i.e. prior art) for HVDC networks, which utilizes the HVDC-DC converter in [5], inherently requires a connection to a nearby high-power ac grid or ac power supply. This connection utilizes galvanic isolation (i.e. ac transformer) and is necessary to enable the energy conversion process. Consequently, the converters deployed in [4] must be located in close proximity to a high-power ac network. Moreover, as explicitly shown in [5], the designed application of directly coupling two HVDC networks results in treating the converter strictly as a two terminal (dc input and dc output) device, with both terminals referenced to a third connection point defined as the system ground or neutral. This requires the ac transformer to have winding insulation rated to withstand potentially large voltages with respect to ground. Employing galvanic isolation rated to withstand the large differential voltage between system ground (or neutral) and the HVDC lines is thus a drawback of the power flow control topology in [4]. High voltage stresses between windings in [5] also exist due to the direct coupling between lower and higher voltage HVDC networks.

It is therefore desirable to develop a multi-port converter structure for power flow control in HVDC networks that does not require any local connection to an external high-power ac supply. Summary of the Invention

It will be evident from the foregoing, and from a review of the detailed description that follows, that the multi-port converter structures for dc networks embodied within the apparatus are of significant advantage, in that, inter alia, they: are modular and scalable

are capable of injecting either positive or negative valued dc voltages between ports

are capable of bidirectional power flow

can inject dc voltages between ports to enable power flow control of HVDC lines having similar voltage levels, with said dc voltage injections having amplitudes substantially less than the nominal operating potential of the HVDC lines

are "floating" structures where connection to the system ground or neutral, either directly or through some form of isolation, for example, galvanic isolation, is inherently not required do not necessitate any connection with a nearby high-power ac network or ac source to enable dc/dc conversion, and therefore are not constrained to be installed within close proximity of high-power ac networks

have relatively low rating of components; in particular, the ac transformer, capacitors and total installed rating of submodules are only rated for a fraction of the total dc power transfer capability of the neighbouring HVDC networks

have by design relatively low peak voltage stresses between different windings of the ac transformer

are highly flexible converter structures in that they can be directly deployed within any monopolar, bipolar and, in general, multi-terminal or "meshed-grid" based HVDC network architectures.

Forming one aspect of the invention is a method for interconnecting HVDC lines of similar voltage to obtain a defined DC power transfer therebetween, the lines including at least one controlled line and two or more uncontrolled lines, the method comprising the steps of: providing DC-to-AC converters in a number that is at least equal in number to the number of uncontrolled lines; superimposing, onto at least one of the controlled lines, a DC voltage, to achieve the defined DC power transfer; balancing power between the DC-to-AC converters via the exchange of AC power therebetween; and exchanging DC power between the DC-to-AC converters and at least one of the controlled lines to provide net power balance.

According to another aspect, at least n-1 DC-to-AC converters can be provided, wherein n is the total number of HVDC lines.

According to another aspect, the exchange of AC power between the DC-to-AC converters can be provided by linking AC terminals of said DC-to-AC converters together.

According to another aspect, two or more arms can be provided, each arm forming part of at least one closed path that includes one or more of the other arms, and the AC power is exchanged by AC currents that circulate utilizing said closed paths.

Forming another aspect of the invention is a system for interconnecting HVDC lines of similar voltage to obtain a defined DC power transfer therebetween, the lines including at least one controlled line and two or more uncontrolled lines. The system comprises: DC-to-AC converters in a number that is at least equal in number to the number of uncontrolled lines; means for superimposing, onto at least one of the controlled lines, a DC voltage, to achieve the defined DC power transfer; means for balancing power between the DC-to-AC converters via the exchange of AC power therebetween; and means for exchanging DC power between the DC-to-AC converters and at least one of the controlled lines to provide net power balance.

According to another aspect, the number of DC-to-AC converters can be n-1, wherein n is the total number of HVDC lines.

According to another aspect, the AC terminals of said DC-to-AC converters can be linked together.

According to another aspect, the DC-to-AC converters can include two or more arms, each arm forming part of at least one closed path that includes one or more of the other arms, the closed paths providing for the AC power exchange by AC currents that circulate utilizing said closed paths.

Other advantages and features associated with the multi-port converter structures will become evident upon a review of the following detailed description and the appended drawings, the latter being briefly described hereinafter.

Brief Description of the Drawings

Figure 1 General definition of a converter "arm" as the series-cascaded connection of n submodules with arm choke J _arm ;

Figure 2 Commonly employed submodule configurations for Figure 1, which include the half-bridge and full-bridge switching cells; Figure 3 Three-port converter structure in open-delta configuration with six arms per delta branch, where central ac link for circulating ac currents between branches is enabled via galvanic isolation;

Figure 4 Three-port converter structure in closed-delta configuration with six arms per delta branch, where central ac link for circulating ac currents between branches is enabled via galvanic isolation;

Figure 5 Three-port converter structure in radial configuration with six arms per radial branch, where central ac link for circulating ac currents between branches is enabled via galvanic isolation;

Figure 6 Three-port converter structure in closed-delta configuration with six arms per delta branch, where central ac link for circulating ac currents between branches is enabled via capacitors;

Figure 7 Three-port converter structure in open-delta configuration with six arms per delta branch, where central ac link for circulating ac currents between branches is enabled via capacitors;

Figure 8 Three-port converter structure in closed-delta configuration with four arms per delta branch, where central ac link for circulating ac currents between branches is enabled via galvanic isolation;

Figure 9 Three-port converter structure in closed-delta configuration with four arms per delta branch, where central ac link for circulating ac currents between branches is enabled via capacitors;

Figure 10 Three-port converter structure in closed-delta configuration with a single arm per delta branch, where path for circulating ac currents between branches is achieved by exploiting the inherent closed-delta structure;

Figure 11 Three-port converter structure in Figure 10 where single arm of an arbitrary delta branch is replaced with a capacitor; Three-port converter structure in closed-delta configuration with two arms per delta branch, where path for circulating ac currents between branches is achieved by exploiting the inherent closed-delta structure;

Three-port converter structure in Figure 12 where the two arms of an arbitrary delta branch are replaced with two capacitors;

Example filtering implementation for closed-delta three-port converter structure in Figure 10, where low-pass LC arrangement is employed;

Example filtering implementation for closed-delta three-port converter structure in Figure 10, where coupled inductors are employed;

Simplified model of the three-port closed-delta converter structure without central ac link in Figure 10;

Four-port converter structure in symmetric configuration with six arms per symmetric branch, where central ac link for circulating ac currents between branches is enabled via galvanic isolation;

Four-port converter structure in radial configuration with six arms per radial branch, created by enabling access to the internal dc node in Figure 5, where central ac link for circulating ac currents between branches is enabled via galvanic isolation;

Four-port converter structure in radial configuration with six arms per radial branch, created by the addition of a fourth MMC while retaining the internal dc node in Figure 5, where central ac link for circulating ac currents between branches is enabled via galvanic isolation;

Four-port converter structure in symmetric configuration with three arms per symmetric branch, where path for circulating ac currents between branches is achieved by exploiting the inherent symmetric structure; Figure 21 Example deployment of general three-port converter structure to interface three bipolar HVDC networks, where any required external filtering has been neglected for clarity of illustration;

Figure 22 Low-frequency simulation model for the two-phase implementation of Figure 3, i.e.

three-port converter structure in Figure 3 implemented using two-phase MMCs, with control logic omitted for clarity of illustration.

Figure 23(a) Example simulation result for Figure 22 where power is transferred into ports DC ₂ and

DC ₃ , and out of port DCi: dc waveforms

Figure 23(b) Example simulation result for Figure 22, where power is transferred into ports DC ₂ and

DC ₃ , and out of port DCi: MMC#1 waveforms

Figure 23(c) Example simulation result for Figure 22, where power is transferred into ports DC ₂ and

DC ₃ , and out of port DCi: MMC#2 waveforms

Figure 24(a) Example simulation result for Figure 22, where power is transferred into port DC ₃ , and out of ports DCi and DC ₂ : dc waveforms

Figure 24(b) Example simulation result for Figure 22, where power is transferred into port DC ₃ , and out of ports DCi and DC ₂ : MMC#1 waveforms

Figure 24(c) Example simulation result for Figure 22, where power is transferred into port DC ₃ , and out of ports DCi and DC ₂ : MMC#2 waveforms

Figure 25 Example simulation result for Figure 16, where power is transferred into port DCi, and out of ports DC ₂ and DC ₃ , with ac filtering implemented via low-pass LC arrangement;

Figure 26 Example simulation result for Figure 16, where power is transferred into ports DCi and

DC ₂ , and out of port DC ₃ , with ac filtering implemented via low-pass LC arrangement; Figure 27 Example simulation result for Figure 16, where power is transferred into port DCi, and out of ports DC ₂ and DC ₃ , with ac filtering implemented via coupled inductor arrangement;

Figure 28 Low-frequency simulation model for the three-phase implementation of Figure 3, with control logic omitted for clarity of illustration;

Figure 29(a) Example simulation result for Figure 28 with closed-loop regulation where the current in port DC ₃ is changed from 0.5 kA to 1 kA at 25 seconds: dc power transfer

Figure 29(b) Example simulation result for Figure 28 with closed-loop regulation where the current in port DC ₃ is changed from 0.5 kA to 1 kA at 25 seconds: dc power delivered by MMCs

Figure 29(c) Example simulation result for Figure 28 with closed-loop regulation where the current in port DC ₃ is changed from 0.5 kA to 1 kA at 25 seconds: output currents

Figure 29(d) Example simulation result for Figure 28 with closed-loop regulation where the current in port DC ₃ is changed from 0.5 kA to 1 kA at 25 seconds: node voltages

Figure 29(e) Example simulation result for Figure 28 with closed-loop regulation where the current in port DC ₃ is changed from 0.5 kA to 1 kA at 25 seconds: MMC#1 capacitor voltages

Figure 29(f) Example simulation result for Figure 28 with closed-loop regulation where the current in port DC ₃ is changed from 0.5 kA to 1 kA at 25 seconds: MMC#2 capacitor voltages

Detailed Description

The series-cascaded connection of n submodules (SMs) with arm choke J _arm is shown in Figure 1. The arm choke is employed to accommodate the switching action of the SMs. Modular multilevel converter architectures utilizing the basic building block in Figure 1 are known to provide for bidirectional dc/ac conversion, as well as bidirectional single-stage dc/dc conversion. As shown in Figure 1, the cascaded set of n SMs and arm choke should be understood to define a respective "arm". Commonly employed SM configurations include the half-bridge switching cell and full-bridge switching cell as shown in Figure 2. In general, an arm of n SMs can employ any combination of half-bridge SMs and full-bridge SMs.

Three-Port Converter Structures Utilizing Central AC Link

Reference is now made to Figure 3, which shows a three-port modular converter structure. The three ports, labelled as "DCi" "DC ₂ " and "DC ₃ " are dc nodes serving as the connection points whereby three HVDC lines of similar voltages can be interconnected. HVDC lines of similar voltages refers to line voltages that remain within a relatively small operating band, for example, typically within +/- 10% of the nominal network voltage. To enable control of power flow between the HVDC lines, the three-port converter structure need only inject dc voltages between node pairs DCi-to-DC ₂ and DC ₃ -to-DCi having amplitudes substantially less than the nominal potential of the HVDC lines. That is, a desired power flow routing between HVDC lines can be achieved by injecting the appropriate incremental dc voltage between converter ports. The dc voltage injections can be either positive or negative valued. The three-port converter structure therefore effectively serves as a power flow controlled junction for HVDC networks. It is possible to either inject or withdraw dc power from any one of the ports, i.e. the three-port converter structure has bidirectional power flow capability.

The three-port converter structure will be seen in Figure 3 to be in an "open-delta" configuration, where each of the two "delta branches" utilizes six arms. In each delta branch the six arms are arranged as shown to form a conventional three-phase dc/ac modular multilevel converter (MMC). Series-stacking of the two MMCs around node DCi forms a bidirectional dc/dc converter structure. To accommodate the single-stage dc/dc conversion process, the ac terminals of the two MMCs are linked together via an ac transformer as shown. This central ac link provides a path for fundamental frequency ac currents to circulate, which are established by appropriate fundamental frequency ac modulation of the converter arms, and thereby allows near lossless transfer of average power between the MMCs. This ac power transfer is the primary mechanism enabling charge balance of the SM capacitors. The transformer also serves to block the dc voltage bias that exists between the ac terminals of the two MMCs. Observe that, unlike in the prior art [4], the central ac link for active power transfer between MMCs need not be connected to a nearby high-power ac source. It should be understood that although the MMC is explicitly used in Figure 3, in principle any dc-to-ac converter technology, for example, the conventional 2-level voltage-sourced-converter, can be employed. In general, the arms in Figure 3 can be comprised of any combination of half-bridge SMs and full-bridge SMs. Half-bridge SMs provide positive voltage injection (i.e. v _sm > 0) while full-bridge SMs allow both positive (i.e. v _sm > 0) and negative (i.e. v _sm < 0) voltage injection. It should also be noted that each MMC need not employ the same number of series-cascaded SMs per arm. As a simple example provided for illustration purposes only, one MMC in Figure 3 may utilize «=20 SMs per arm while the second MMC may utilize «=30 SMs per arm. In general, the chosen number of SMs per arm depends on the desired range of dc voltage injection between ports, which is an application specific design choice. It should also be noted that each arm in Figure 3 includes a choke (J _arm ) as depicted in Figure 1. However, restructuring of arm chokes in Figure 3 to eliminate individual chokes is possible, provided the basic requirement of an inductance in every voltage loop is not violated. It should also be noted that the ac modulation of the arms is not restricted to conventional 50/60 Hz. The ac currents remain internal to the converter structure, and therefore the fundamental frequency can be chosen freely. Modulating frequencies higher than 50/60 Hz can therefore be exploited to enable reduction of SM energy storage requirements (i.e. C _sm ). Moreover, ac modulation of the arms is not limited to merely sinusoidal excitation. For example, some form of square wave excitation could also be employed. This flexibility in choosing the ac operating parameters is a salient feature of the proposed three-port converter structure.

The primary application of the three-port converter structure in Figure 3 is for dc power flow control in HVDC networks of similar voltage levels. That is, the three ports DCi, DC ₂ and DC ₃ are connected to HVDC lines that have similar nominal voltages. This enables the converter structure to facilitate dc power flow control between networks, by injecting only relatively small dc voltages between port pairs DCi-to-DC ₂ and DC ₃ -to-DCi. To accommodate interconnecting HVDC lines of similar nominal voltages, the bipolar voltage injection capability (i.e. +/- v _sm ) of full-bridge SMs is seen as highly advantageous. By using full-bridge SMs, positive or negative valued dc voltages can be injected between ports as needed to accommodate the natural fluctuation of HVDC line voltages around their nominal value. However, as mentioned before, the use of half-bridge SMs are also beneficial for certain applications.

Due to the primary application of interfacing HVDC lines of similar voltage levels, the three-port converter structure in Figure 3 offers many significant benefits. Only a relatively small number of SMs need be installed for each arm to provide the required incremental dc voltage injection capability. This lowers the overall converter cost and operating losses. The ac transformer rating and the peak voltage

1 stress between transformer windings is also relatively low, when compared to the full dc power transfer capability and voltage rating of the neighbouring HVDC lines. A significant advantage is that the ac transformer in Figure 3 is not connected to any nearby high-power ac grid or ac power supply. This allows the three-port converter structure to be a "floating" device, in that accommodating isolation between the converter structure and system ground or neutral is not required. Thus, the three-port converter structure does not need to be located in close proximity to a high-power ac network. This offers significant flexibility and is a primary advantage over prior art [4].

For ease of analysis the preceding discussion has explicitly considered the "open-delta" configuration in Figure 3. However, it is possible to realize different three-port converter structures that enable additional dc power flow control capability relative to the "open-delta" configuration. Two such three-port converter structures termed the "closed-delta" and "radial" configuration will now be introduced.

Reference is now made to Figure 4, which shows a three-port modular converter structure in a "closed-delta" configuration. In comparison to Figure 3, a third three-phase dc/ac MMC has been inserted between ports DC ₂ and DC ₃ . The central ac link in Figure 4 now incorporates a three-winding transformer to interconnect the ac terminals of all three MMCs. This central ac link allows average power transfer between the three MMCs via flow of fundamental frequency ac currents. The fundamental operation of Figure 4 is similar to that of Figure 3.

The closed-delta three-port converter structure in Figure 4 provides additional dc power flow control capability in comparison to the open-delta configuration. Specifically, in Figure 4 is it possible to now directly control the dc voltage injection between any pair of ports, i.e. DCi-to-DC ₂ , DC ₃ -to-DCi and DC ₃ -to-DC ₂ . This configuration enables a dc current to internally circulate within the closed-delta structure, which can be regulated via suitable control action. Thus, in comparison to the open-delta structure, the power routing controllability between ports is extended. This enhanced control capability of the closed-delta structure (enabled by closed-loop path that allows dc current to internally circulate) provides greater flexibility in the power flow management of HVDC networks.

Reference is now made to Figure 5, which shows a three-port modular converter structure in a "radial" configuration. The "radial" configuration in Figure 5 is created by connecting a third three-phase dc/ac MMC to port DCi in Figure 3, where access to this port is removed to create an internal dc node. The internal dc node in Figure 5 corresponds to the common connection tying the lower dc rail of all three MMCs together. Similar to Figure 4, the radial configuration in Figure 5 utilizes a central ac link with three-winding transformer to connect the ac terminals of all three MMCs.

The radial three-port converter structure also provides additional dc power flow control capability in comparison to the open-delta configuration. Specifically, in Figure 5 it is possible to now directly control the dc voltage injection between any pair of ports, i.e. DCi-to-DC ₂ , DC ₃ -to-DCi and DC ₃ -to-DC ₂ , without imposing a dc voltage across any of the MMCs. Thus, in comparison to the open-delta structure, the power routing controllability between ports is extended. This enhanced control capability of the radial structure (enabled by internal dc node that prevents external dc lines from directly imposing dc voltage across MMCs) provides greater flexibility in the power flow management of HVDC networks.

In Figures 3 to 5 the central ac link has been realized via galvanic isolation, i.e. an ac transformer with appropriate number of windings. It is also possible to implement the central ac link by other means. Figure 6 (closed-delta configuration) and Figure 7 (open-delta configuration) illustrate the use of capacitors, as opposed to galvanic isolation, to establish the central ac link. Similar to the use of a transformer, the capacitors permit the near lossless transfer of average ac power between all three MMCs, as well as block the dc voltage bias that exists between ac terminals of the different MMCs.

The three-port converter structures in Figure 3 through Figure 7 all utilize three-phase dc/ac MMCs. The use of three-phase MMCs is not essential. More or fewer phases can be adopted. In general, any multi-phase MMC is sufficient. Reference is now made to Figure 8, which implements the closed-delta three-port converter structure in Figure 4 using two-phase dc/ac MMCs. The operation of Figure 8 and Figure 4 are fundamentally similar - the primary difference is the phase shift between fundamental frequency ac quantities of the different phases. For example, ac quantities in Figure 4 are phase-shifted 120° between phases whereas a phase-shift of 180° between phases is employed in Figure 8. The ability to utilize different number of phases for the MMCs offers additional freedom in design of the three-port converter structure. In particular, for a given type and rating of SM, adopting more phases increases the total dc power transfer capability of the three-port converter structure. Although not explicitly shown, it should be understood that, similar to the closed-delta three-port converter structures, it is possible to utilize any multi-phase MMC for the open-delta three-port converter structures and radial three-port converter structures. For example, Figure 3 and Figure 5 can alternatively be implemented using multi-phase MMC structures (i.e. not restricted to three-phase systems).

It should be understood that all topology variations previously discussed for the three-phase MMC based open-delta, closed-delta, and radial converter structures also apply to Figure 8. In particular, the central ac link in Figure 8 can be realized using a capacitive structure as shown in Figure 9.

Three-Port Converter Structures Elimination of Central AC Link

The open-delta, closed-delta, and radial three-port converter structures in Figure 3 through Figure 9 all utilize a central ac link to facilitate dc power routing. This central ac link enables average power transfer between the different delta branches, via the flow of fundamental frequency ac currents, in order to maintain charge balance of the SM capacitors (as well as the capacitive structures, for example, those shown in Figure 6 and Figure 7).

It is possible to realize an alternate converter structure for the three-port closed-delta configuration that does not rely on a central ac link for average power transfer between delta branches. Such a structure is shown in Figure 10. Here each delta branch is comprised of a single arm. In general, each of the three arms may employ a different number of cascaded SMs, and can be comprised of any combination of half-bridge SMs and full-bridge SMs. Instead of a central ac link, in Figure 10 the circulation of fundamental frequency ac current for SM capacitor power balancing is achieved by exploiting the inherent closed-loop delta structure. That is, the ac current circulates within the closed-loop delta structure itself. Power balance of each SM capacitor is achieved by transferring average ac power between delta branches as needed via the circulating ac current. The required circulating ac current is established by appropriate fundamental frequency ac modulation of each arm. This power balancing mechanism is conceptually similar to that described in [1-2].

The closed-delta three-port converter structure in Figure 10 utilizes one arm in each delta branch. The use of three arms to form the closed-delta structure (and thus enabling ac current circulation) is not essential. It is also possible to replace one, or, more than one, of the arms with a suitable alternate structure. Reference is now made to Figure 11, which illustrates replacement of the arm located between ports DC ₃ and DC ₂ in Figure 10 with a capacitor. The arm between ports DC ₃ and DC ₂ was selected for replacement arbitrarily _, i.e. any arm in Figure 10 could have been replaced with a capacitor. Charge balance of the capacitor located between ports DC ₃ and DC ₂ is achieved by transferring the requisite average power via the circulating ac current. The capacitor also provides the necessary dc voltage blocking between ports.

Each delta branch in Figure 10 is comprised of one arm. However, it is possible to connect additional arms in parallel. The primary benefit of utilizing multiple parallel arms for each delta branch is to increase the total dc power flow capability. Reference is now made to Figure 12, where each delta branch in Figure 10 is now comprised of two parallel arms. Each of the parallel arms within a single branch is modulated in a similar manner, i.e. the current (both dc and fundamental frequency ac components) carried by each branch would split equally between the two parallel arms. In general, each delta branch can be comprised of an arbitrary number of arms connected in parallel. It should also be understood that, similar to Figure 11, it is possible to replace any branch (or, possibly, more than one branch) of multiple paralleled arms with a suitable capacitive structure. For example, Figure 13 shows the converter structure in Figure 12 where the two arms located between ports DC ₂ and DC ₃ have been replaced with two parallel capacitors. It is also possible to install a single capacitor in place of the two parallel capacitors shown in Figure 13.

Filtering Requirements

The closed-delta three-port converter structures in Figure 10 through Figure 13 ultimately have one arm in series with any two ports, e.g. ports DCi and DC ₂ in Figure 10 and Figure 12 are physically displaced by a single arm. This is the case regardless of how many arms are connected in parallel, as parallel arms within each branch are modulated in the same manner, and therefore act as a single composite arm. Consequently, fundamental frequency ac voltage cancellation between ports in Figure 10 through Figure 13 is not achieved naturally. As a result, the converter structures in Figure 10 through Figure 13 require filtering to prevent propagation of the fundamental frequency circulating ac current to the DC lines. This is inherently different from the central ac link based structures in Figure 3 through Figure 9, which, due to use of multi-phase MMCs, are able to achieve natural ac voltage cancellation between ports. In this case, ac currents do not propagate to the DC lines. The inherent cancellation of fundamental frequency ac phase currents, a well-known characteristic of the multi-phase dc/ac MMC, is a key feature of the three-port converter structures in Figure 3 through Figure 9. The closed-delta three-port converter structures in Figure 10 through Figure 13 require augmentation of external filtering to prevent the circulating ac current from propagating to the DC lines. Reference is now made to Figure 14, which depicts an example filtering implementation for the closed-delta three-port converter structure in Figure 10. The augmented filter structure resembles a conventional low-pass LC filter. Filter inductors are connected at the converter ports, and filter capacitors are placed in shunt with each delta branch. The filter inductors and filter capacitors are sized to provide sufficient attenuation of fundamental frequency ac voltages between converter ports, i.e. the measured voltage between any combination of converter ports DCi ^fllt , DC ₂ ^fllt , and DC ₃ ^fllt is near constant dc potential. As a result, negligible fundamental frequency ac currents enter the DC lines.

AC filtering solutions incorporating magnetics can also be employed. Figure 15 illustrates an example filtering implementation for the closed-delta three-port converter structure in Figure 10, where coupled inductors are exploited. To achieve dc flux cancellation in the core of each coupled inductor, two closed-delta structures from Figure 10 are connected in a parallel manner as shown. The two closed-delta structures are operated in concert, in particular, the ac modulation of similar arms between converter structures are phase-shifted by 180°. For example, the ac voltages from DCi-to-DC ₂ and DCi -to-DC ₂ are phase-shifted 180° relative to one another. The use of coupled inductors allows a large ac impedance to be realized via the magnetizing branch, while the symmetric interposing of converter structures shown in Figure 15 ensures cancellation of dc flux within the core.

It should be understood the filter implementations in Figure 14 and Figure 15 are also applicable to all possible variants of the general closed-delta three port converter structure without central ac link. Thus, the filter implementations in Figure 14 and Figure 15 are applicable to Figure 11 through Figure 13.

A person of ordinary skill in the art should recognize the example filter structures in Figure 14 and Figure 15 are merely two possible implementations. The illustrated examples shall not be considered to be limiting. Many different filter types are possible, which may include a variety of structures employing suitable combinations of passive filter elements. Active filtering solutions that employ additional SMs to achieve ac voltage attenuation can also be employed. A key filtering requirement is to provide sufficient attenuation of the fundamental frequency ac voltages that exist between converter ports, thereby preventing propagation of ac current to the DC lines. Theory of Operation

In the following passages, the operation of the three-port closed-delta converter structure in Figure 10 is detailed. In particular, the analysis focuses on the DC and AC relationships of the converter and their constraints such that power balance of all SM capacitors is achieved. Unless otherwise indicated, the following assumptions are used: each arm employs a large number of SMs such that ideal sinusoidal ac voltages are synthesized AC voltages and currents are represented by their steady-state fundamental frequency components Any required ac filtering is assumed to be ideal, i.e. fundamental frequency ac currents do not enter the HVDC lines

Each of the three arms in Figure 10 can be viewed as a controllable ac voltage source with a variable dc component. The dc component is varied by controlling the number and polarity of SM capacitors inserted in each arm, and this dc component can be positive or negative depending on the deployment of half-bridge and/or full-bridge SMs in each arm. The ac component is synthesized through appropriate switching of the SMs. The fundamental frequency of the ac component can be freely chosen, since the ac quantities remain internal to the closed-delta structure.

A simplified representation of the three-port converter structure (without central ac link) in closed-delta configuration with a single arm per delta branch is shown in Figure 16. The nomenclature introduced for this analysis is listed in Table 1.

Table 1: Nomenclature for sim lified model in Fi ure 16

DC Relationships

For ease of analysis, the following conditions are imposed on the system

1. The circulating ac current remains internal to the three port converter structure, i.e. the ac current does not enter the external HVDC lines

2. Steady state power balance of SMs capacitors is enabled by the shuttling of average ac power between arms, which is facilitated by the common ac current

3. The net voltage of the three arms must sum to zero

A dc operating point is defined by the set {Ii, Vi, I ₂ , V ₂ , I ₃ , V ₃ }, where

{Ii, I ₂ , 1 ₃ } are the dc output currents corresponding to port DCi, DC ₂ , and DC ₃ , respectively {Vi, V ₂ , V ₃ } are the dc node voltages corresponding to port DCi, DC ₂ , and DC ₃ , respectively

In order to be realizable under the imposed conditions, the dc operating point must satisfy the following expressions: i _{1 =} v _{L =} Va

k ν _β

= _Va

Where the dc branch voltages relate to the dc node voltages as shown

Va = V ₂ - V ₁

ν _β = ν ₃ - v ₂

Vy = V ₁ - V ₃

The above expressions are derived from power balance constraints. An equivalent set of expressions from power balance constraints can also be derived: Where the output currents satisfy KirchhofP s Current Law + l ₂ + = ^Q

Thus, the voltage Vi can be expressed as

The output currents are a function of the dc node voltages, since they are related by the connecting line impedances. The dc node voltages can be expressed by the voltage Vi and the branch voltages v ₂ = v ₁ + v _a

It is straightforward to demonstrate from these expressions that one possible dc operating condition is to set the power transferred between two of the nodes, by adjusting the dc node voltage and dc output current of the third node and setting two of the three dc branch voltages. For example, an operating point (I ₂ , V ₂ , ¾, V ₃ } can be achieved by setting the quantities {Vi, Ii, V _a , V _y ). Note, in this example the current Ii is imposed by Kirchhoff s Current Law and the voltages Vi, V _a , and V _y are appropriately selected.

Observe in the above example it must be possible to control voltage Vi (node voltage at port DCi) in order to achieve the specified power transfer for ports DC ₂ and DC ₃ . As current L is imposed by Kirchhoff s Current Law, in order to set port voltage Vi it must be possible to control the voltage of the DC line that connects to port DCi. The DC line that connects to port DCi is therefore referred to as a "controlled line". In comparison, in order to achieve the specified power transfer it is not necessary to have control over the voltages of the DC lines that connect to ports DC ₂ and DC ₃ . Thus, the DC lines that connect to ports DC ₂ and DC ₃ are referred to as "uncontrolled lines".

It is possible to select any one of the three DC lines that connect to the three ports in Figure 16 to be the "controlled line". For example the DC line that connects to port DC ₂ can be the "controlled line" and the DC lines that connect to ports DCi and DC ₃ can be the "uncontrolled lines". In general, a multi-port converter structure requires connection to at least one "controlled line", i.e. connection to more than one "controlled line" is possible. Requirement on AC quantities

For every valid dc operating point there are an infinite number of theoretical ac operating points capable of achieving power balance in the branches.

An ac operating point is defined by the set {V _{a rms} , νβ, _Τ τηε· ,r s< θ _α · θβ· θγ> IAC } -. where

The ac branch voltages in the alpha, beta, and gamma branches are represented as phasors with rms voltage {V _{a ms} , ν _{β τη5} , V _{Y ms} } and phase {θ _α , θ _β , θ _γ }, respectively

The circulating ac current is represented as a phasor with rms current I _AC and is defined to have zero phase for convenience

The power balance requirement can be formulated as

'β

β, ,rms OS Θ 'β,

For convenience, the circulating ac current is defined to have zero phase. This current is driven by the sum of the ac branch voltages. In order for the ac current to have a resulting zero phase, while assuming a purely reactive net ac impedance within the closed-loop delta structure, the sum of the ac branch voltages must be purely imaginary. This condition is expressed mathematically as

V _a + V _p + Vy = jX _r I _A c

Where X _r is the net reactance of the closed-delta loop. This imposes an additional constraint on the ac branch voltages

It is clear that the ac system is under-constrained, and thus there are infinitely many theoretical ac operating points capable of achieving power balance for any given dc operating point. Practically these operating points will be limited by physical constraints in the system including, but not limited to, the deployment of half-bridge versus full-bridge SMs, the installed SM voltage and current rating of each arm, and the current carrying capacity of each branch.

Four-Port Converter Structures

The open-delta, closed-delta, and radial structures in Figure 3 through Figure 15 are all based on a three-port converter architecture. It is possible to utilize these general three-port structures as basic building blocks to form more advanced converter architectures having a greater number of ports. Figure 17, Figure 18, and Figure 19 illustrate examples of four-port converter structures with a central ac link. Observe Figure 18 is created by enabling access to the internal dc node in Figure 5, while Figure 19 is created by adding a fourth MMC in Figure 5 and retaining the internal dc node. Figure 20 illustrates an example of a four-port converter structure without central ac link. The operation of these four-port converter structures are fundamentally similar to the described operation of their three-port counterparts. The ability to realize "floating" converter structures that offer a different number of ports enables significant additional flexibility for power flow control of HDVC networks. For example, a four-port structure has the ability to interconnect up to four different HDVC lines with a single converter architecture. It is also possible to create converter structures having more than four ports.

Note that, as described previously for the three-port converter structures without central ac link, suitable external filtering must be augmented to the four-port converter structure in Figure 20.

It should be understood that all of the topology variants described for the three-port converter structures are also applicable to the four-port converter structures shown in Figure 17 through Figure 20. Furthermore, the structures shown in Figure 17 through Figure 20 are only examples of possible converter structures offering four unique ports. Many different realizations of a four-port converter structure are possible, as can be derived based on the three-port converter structures, and therefore the specific examples illustrated in Figure 17 through Figure 20 should not be considered to be limiting.

2 Deployment

The three-port and four-port converter structures in Figure 3 through Figure 20 can be deployed to interconnect FIDVC lines of similar voltage levels. As an example for illustration purposes only, Figure 21 shows deployment of the general (i.e. either with or without central ac link) three-port converter structure as an interface for three bipolar HVDC networks of similar voltage. As shown, the example deployment effectively creates a power flow controlled network junction, where prescribed dc power flow routing between the different FIDVC lines can be achieved. That is, by injecting the appropriate incremental dc voltages between the ports of each three-port converter structure, in a controlled manner, a desired power flow between the HVDC networks can be realized.

Observe the three-port converter structures in Figure 21 do not require connection to a nearby high-power ac network, unlike prior art [4]. The three-port converter structures can be viewed as "floating" devices in that they do not require any connection either directly or through isolation means to system ground or neutral.

It should be understood the three-port and four-port (and, in general, any derived multi-port) converter structures are not restricted to deployment in bipolar HDVC systems. They can be readily deployed within any monopolar, bipolar and, in general, multi-terminal or "meshed-grid" based HVDC network architectures. For example, one four-port converter structure could be used to interconnect four monopolar HDVC lines.

Simulation Results Three Port Open-Delta Converter Structure With Central AC Link

An averaged (low-frequency) simulation model is employed to demonstrate the steady-state operation of the three-port open-delta converter structure with central ac link. The model is derived based on established averaging techniques. The adopted simulation model, which is provided in Figure 22, corresponds to Figure 3 where the three-phase MMCs are replaced with two-phase MMCs. As highlighted previously, any multi-phase MMC can be utilized for the central ac link based three-port converter structures. The simulation model in Figure 22 enables validation of SM capacitor power balance via average ac power transfer between MMCs, while accommodating dc power transfer between the three HVDC lines. The following two operating scenarios are considered for the interconnection of three HVDC lines:

Power transferred into ports DC ₂ and DC ₃ , and out of port DCi

Power transferred into port DC ₃ , and out of ports DCi and DC ₂

Where power transferred "out of a port implies that the product of the dc port current and dc port line-to-neutral voltage is positive i.e. power is transferred "out of the structure. Positive dc port currents denote current leaving the structure as shown in Figure 22. All waveforms are generated using the software package PSCAD/EMTDC. The fundamental operating (i.e. modulating) frequency of the ac waveforms is selected as 60 Hz for both scenarios.

Power transferred into ports DC ₂ and DC ₃ , and out of port DCi

Figures 23(a), 23(b) and 23(c) show the simulation results corresponding to the first operating scenario. The operating condition is defined by:

{Vi, V ₂ , V ₃ } = {400kV, 401kV, 399kV}

{Pi, P ₂ , P ₃ } = {686MW, -332MW, -354MW}

Where

P ₁ = V _x l _x

P ₂ = V ₂ I ₂

Observe the two-phase MMCs provide ac current cancellation at all three ports, and thus negligible ac current enters the HVDC lines. Both MMCs require the use of full-bridge SMs to synthesize the bipolar ac arms voltages as shown (i.e. arms voltages must have ability to be negative valued). As shown, the ac power transfer between MMCs (via central ac link) maintains power balance of all SM capacitors. In this scenario, ports DC ₂ and DC ₃ approximately split the power transfer throughput of port DCi. Power transferred into port DC ₃ , and out of ports DCi and DC ₂

Figures 24(a), 24(b) and 24(c) show the simulation results corresponding to the second operating scenario. The operating condition is:

{Vi, V ₂ , V ₃ } = {400kV, 380kV, 399kV}

{Pi, P ₂ , P ₃ } = { 164MW, 5.7MW, -169.7MW}

In this scenario the power transferred into port DC ₃ is routed primarily to port DCi, with very little power transfer occurring at port DC ₂ . When compared to the simulation results of Figures 23(a), 23(b) and 23(c), this operational scenario demonstrates the ability of the three-port open-delta converter structure to split power transfer unequally between ports.

Simulation Results Three Port Closed-Delta Converter Structure Without Central AC Link

Idealized voltage and current waveforms are simulated to demonstrate the steady-state operation of the three-port converter structure in closed-delta configuration with a single arm per delta branch, shown in Figure 10. The corresponding simplified model is given in Figure 16.

The following two operating scenarios are considered, with ac filtering implemented via the low-pass LC arrangement in Figure 14:

Power transferred into port DCi, and out of ports DC ₂ and DC ₃

Power transferred into ports DCi and DC ₂ , and out of port DC ₃

Where power transferred "out of a port implies that the product of the dc port current and dc port line-to-neutral voltage is positive, i.e. power is transferred "out of the structure. Positive dc port currents denote current leaving the structure as shown in Figure 16.

An additional operating scenario is considered, with ac filtering implemented via coupled inductors as shown in Figure 15. This scenario is identical to the first scenario above, namely power is transferred into port DCi, and out of ports DC ₂ and DC ₃ .

All waveforms are generated using the software package PSCAD/EMTDC. The fundamental operating (i.e. modulating) frequency of the ac waveforms is selected as 1 kHz for all scenarios. The ac voltages for each arm are chosen such that the resulting circulating ac current achieves power balance for all delta branches, i.e. each arm produces zero average power. Power transferred into port DCi, and out of ports DC ₂ and DC ₃ , with ac filtering implemented via low-pass LC arrangement

Figure 25 shows the simulation results for this condition. The operating condition is:

{Vi, V ₂ , V ₃ } = {399.3kV, 417kV, 383kV}

{Pi, P ₂ , P ₃ } = {-640MW, 320MW, 320MW}

Where

P ₁ = V _x l _x P ₂ = V ₂ I ₂

The branch voltages drive a common circulating ac current. The common circulating ac current is evident in the plots for the branch currents.

Power transferred into ports DCi and DC ₂ , and out of port DC ₃ , with ac filtering implemented via low-pass LC arrangement

Figure 26 shows the simulation results for this condition. The operating condition is:

{Vi, V ₂ , V ₃ } = {385.62kV, 400kV, 390kV};

{Pi, P ₂ , P ₃ } = {-440MW, -200MW, 640MW}

Power transferred into port DCi, and out of ports DC ₂ and DC ₃ , with filtering implemented via coupled inductor arrangement

Figure 27 shows the simulation results for this condition. The operating condition is:

{V _{D C} ftit , V _{D C} fut, V _DC fm } = {399.3kV, 417kV, 383kV}

{P _{D C} fut , P _{D C} ftit , P _DC } = {-640MW, 320MW, 320MW} Where these quantities define the voltage of, and power transferred out of, the ports DC( ^llt , Dc ^llt , and

OC{ ^ilt in Figure 15. It can be seen from the branch voltages that the two closed-delta structures are operated in concert, and the ac modulation of similar arms between converter structures are phase-shifted by 180 ^° In this configuration the two structures equally share the output current demand, and as a result the dc branch currents are halved as compared to the dc branch currents in Figure 25.

Simulation Results Closed Loop Control of Three Port Open-Delta Converter Structure With Central AC Link

An averaged (low-frequency) simulation model is employed to demonstrate closed-loop control of the three-port open-delta converter structure with central ac link, shown in Figure 3. The adopted simulation model is given in Figure 28. The simulation model in Figure 28 enables validation of SM capacitor power balance via average ac power transfer between MMCs, while accommodating dc power transfer between the three dc lines. Closed loop control is employed to regulate the currents out of ports DC ₂ and DC ₃ while ensuring SM capacitor power balance. Regulation of the port currents enables regulation of the power delivered to each dc network.

All waveforms are generated using the software package PSCAD/EMTDC. The fundamental operating (i.e. modulating) frequency of the ac waveforms is selected as 60 Hz.

The following operating scenario is considered for the interconnection of three HVDC lines: the currents out of (i.e. leaving) port DC ₂ and port DC ₃ are both initially regulated to 0.5 kA (corresponding to 250 MW), and the capacitor voltages are regulated to 8 kV. At t=25 seconds, the command for the current out of port DC ₃ is stepped from 0.5 kA to 1 kA (corresponding to a step from 250 MW to 500 MW). Figure 29 shows the results of this operating scenario. The current out of port DC ₃ is regulated to the desired value (Figure 29(c)), and the average value of the SM capacitor voltages recover from the associated disturbance (Figure 29(e) and Figure 29(f)), validating SM capacitor power balance. It is important to stress that the MMCs need only be rated for a fraction of the nominal power rating of the adjacent dc networks. In this case study example, Figure 29(b) demonstrates that MMCi and MMC ₂ each process 2.5 MW, while Figure 29(a) shows the power transferred between the adjacent networks ranges from 250 MW to 500 MW. Variations

Whereas specific embodiments of the invention have been discussed, variations are possible. For example, the chosen ac transformer configurations used to establish the central ac link, for example the transformers in Figure 4, Figure 17 and Figure 18, are merely examples of possible implementations of galvanic isolation. Other transformer types with different winding configurations are also possible. Further, the use of capacitors to establish the central ac link, for example, as shown in Figure 6, are merely examples of possible implementations of isolation via primarily capacitive means. Other capacitor configurations or capacitive structures are also possible, which may incorporate inductors to adjust the circuit reactance. Further, the disclosed filter arrangements in Figure 14 and Figure 15 are merely examples of possible implementation, and should not be considered as limiting.

As well, whereas the benefits of the converter topology are immense in the context of FIDVC networks having similar voltage levels, this is not essential. As well, whereas specific operating conditions and parameters are disclosed as part of the simulations and others, persons of ordinary skill will understand that these are included for illustration, only, and are not intended to be limiting.

References

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[2] G.J. Kish, M. Ranjram and P.W. Lehn "A modular multilevel DC/DC converter with fault blocking capability for HVDC interconnects " IEEE Trans. Power Electron., vol. 30, no. 1, pp. 148-162, Jan.

2015.

[3] R. Marquardt "Modular multilevel converter: An universal concept for HVDC-networks and extended DC-bus-applications " in International Power Electronics Conference, Jun. 2010, pp. 502-507.

[4] HVDC-Energieubertragung: Leistungselektronische Losungen fur DC-Netze, Universitat Bayreuth Zentrum fur Energietechnik (ZET), [Online] March 22, 2014. Available: http://www.zet.uni-bayreuth.de/de/ Technologien/downloads/IB-ZET-LfM-HVDC.pdf

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