RELATING TO POWER TRANSMISSION NETWORKS

Abstract

In the field of high voltage direct current (HVDC) power transmission networks, there is a need for improvements to allow a single power converter to control individual AC network voltages carried by multiple AC transmission conduits to multiple AC network elements, such as respective wind parks.

A power transmission network (10; 100) comprises a power converter (12) which has first and second DC converter terminals (14, 16) that are for connection, in use, to a DC network. The power converter (12) also includes an AC converter terminal (22) which is electrically connected to a plurality of AC transmission conduits (24.sub.1, 24.sub.2, 24.sub.n), each of which is for connection, in use, to a respective AC network element (26.sub.1, 26.sub.2, 26.sub.n) that is configured to operate at a respective individual AC network voltage. The power converter (12) further includes a primary converter controller (34) which is programmed, in use, to control the transfer of power through the power converter (12) and thereby between the DC network and the plurality of AC network elements (26.sub.1, 26.sub.2, 26.sub.n). The primary converter controller (34) is further programmed, in use, to control each individual AC network voltage by establishing a virtual voltage which is representative of the plurality of AC network voltages and altering a single AC converter voltage produced by the power converter (12) at the AC converter terminal (22) to adjust the virtual voltage and thereby adjust each individual AC network voltage.

Claims

1-13. (canceled)

14. A power transmission network comprising a power converter having first and second DC converter terminals for connection in use to a DC network and an AC converter terminal electrically connected to a plurality of AC transmission conduits each of which is for connection in use to a respective AC network element configured to operate at a respective individual AC network voltage, the power converter including a primary converter controller programmed in use to control the transfer of power through the power converter and thereby between the DC network and the plurality of AC network elements, and the primary converter controller being further programmed in use to control each individual AC network voltage by establishing a virtual voltage representative of the plurality of AC network voltages and altering a single AC converter voltage produced by the power converter at the AC converter terminal to adjust the virtual voltage and thereby adjust each individual AC network voltage.

15. The power transmission network according to claim 14, wherein the primary converter controller is programmed to establish a virtual voltage commensurate with the average of the individual AC network voltages.

16. The power transmission network according to claim 14, wherein the primary converter controller is programmed to establish the virtual voltage in a vector form having real and imaginary parts.

17. The power transmission network according to claim 14, wherein the primary converter controller is additionally programmed to compare the established virtual voltage with a predetermined virtual voltage reference and to alter the AC converter voltage produced by the power converter to reduce any difference between the established virtual voltage and the predetermined virtual voltage reference.

18. The power transmission network according to claim 14, wherein when altering the AC converter voltage produced by the power converter to reduce any difference between the established virtual voltage and the predetermined virtual voltage reference, the primary converter controller takes into account: a voltage difference across a converter reactance; and a virtual voltage difference representative of a plurality of voltage differences across a conduit reactance of each AC transmission conduit.

19. The power transmission network according to claim 14, wherein the virtual voltage difference is commensurate with the average voltage difference across the conduit reactances of the AC transmission conduits.

20. The power transmission network according to claim 14, wherein the primary converter controller is programmed to take into account cross-coupling between the real and imaginary parts of the voltage difference and the virtual voltage difference.

21. The power transmission network according to claim 14, wherein the power converter further includes a secondary converter controller programmed in use to establish the predetermined virtual voltage reference against which the primary converter controller compares the established virtual voltage.

22. The power transmission network according to claim 14, wherein the second converter controller establishes the virtual voltage reference in a manner aimed at maintaining all of the individual AC network voltages within a desired voltage range.

23. The power transmission network according to claim 14, wherein the second converter controller establishes the virtual voltage reference in a manner aimed at maintaining all of the individual AC network voltages within a desired voltage range.

24. The power transmission network according to claim 14, wherein the second converter controller establishes the virtual voltage reference in a manner aimed at maintaining all of the individual AC network voltages within a desired voltage range.

25. The power transmission network according to claim 14, wherein the secondary converter controller: considers whether any AC network voltage is below a predetermined voltage minimum and if one or more AC network voltages is below the voltage minimum modifies the virtual voltage reference to raise the or each errant AC network voltage to be equal to or above the voltage minimum; and considers whether any AC network voltage is above a predetermined voltage maximum and if one or more AC network voltages is above the voltage maximum modifies the virtual voltage reference to reduce the or each errant AC network voltage to be equal to or below the voltage maximum.

26. The power transmission network according to claim 14, wherein the secondary converter controller receives in use a virtual voltage command from a higher-level controller and modifies the virtual voltage reference it establishes by determining an adjustment factor and applying the adjustment factor to the received virtual voltage command.

27. The power transmission network according to claim 14, wherein if at least one AC network voltage is below the voltage minimum and at least one AC network voltage is above the voltage maximum, the secondary converter controller is programmed to modify the virtual voltage reference in a manner that equalizes the amount the or each of the AC network voltage deviates from the corresponding voltage minimum and voltage maximum.

28. A method of controlling a power transmission network comprising a power converter having first and second DC converter terminals for connection in use to a DC network and an AC converter terminal electrically connected to a plurality of AC transmission conduits each of which is for connection in use to a respective AC network element configured to operate at a respective individual AC network voltage, the power converter including a primary converter controller programmed in use to control the transfer of power through the power converter and thereby between the DC network and the plurality of AC network elements, the method comprising: controlling each individual AC network voltage by establishing a virtual voltage representative of the plurality of AC network voltages; and altering a single AC converter voltage produced by the power converter at the AC converter terminal to adjust the virtual voltage and thereby adjust each individual AC network voltage.

Description

[0040] There now follows a brief description of preferred embodiments of the invention, by way of non-limiting example, with reference being made to the following figures in which:

[0041] FIG. 1 shows a schematic view of an idealised power transmission network according to a first embodiment of the invention;

[0042] FIG. 2 shows a schematic view of a primary converter controller for a power converter which forms a part of the power transmission network shown in FIG. 1;

[0043] FIG. 3 shows a schematic view of a secondary converter controller for the power converter which forms a part of the power transmission network shown in FIG. 1;

[0044] FIG. 4(a) shows a schematic view of an example power transmission network according to a second embodiment of the invention;

[0045] FIG. 4(b) shows the effect of adjusting a virtual voltage, in the manner shown in FIG. 4(c), on first and second AC network voltages in corresponding first and second AC transmission conduits within the power transmission network shown in FIG. 4(a); and

[0046] FIG. 4(c) shows the said adjustment of the virtual voltage.

[0047] A power transmission network according to a first embodiment of the invention is designated generally by reference numeral 10, as shown in FIG. 1.

[0048] The first power transmission network 10 includes a power converter 12, such as a voltage source converter, although other types of power converter may be included instead.

[0049] In any event, the power converter 12 has first and second DC converter terminals 14, 16 which, in use, are connected to a DC network (not shown), e.g. via respective first and second DC transmission conduits 18, 20 in the form of respective transmission lines, although other forms of interconnection are possible.

[0050] The power converter 12 also includes an AC converter terminal 22 that is electrically connected to a plurality of AC transmission conduits, i.e. first, second and nth AC transmission conduits 24.sub.1, 24.sub.2, . . . 24.sub.N.

[0051] Each AC transmission conduit 24.sub.1, 24.sub.2, 24.sub.N is, in use, connected to a respective AC network element 26.sub.1, 26.sub.2, 26.sub.N, such as corresponding first, second or nth wind park 28.sub.1, 28.sub.2, 28.sub.N (either offshore or onshore). Each such AC network element 26.sub.1, 26.sub.2, 26.sub.N, e.g. each such first, second or nth wind park 28.sub.1, 28.sub.2, 28.sub.N, is configured to operate at a respective individual AC network voltage v.sub.lw1, v.sub.lw2, v.sub.lwN.

[0052] Each AC transmission conduit 24.sub.1, 24.sub.2, 24.sub.N includes, in an idealised sense, a conduit reactance 30.sub.1, 30.sub.2, 30.sub.N, in the form of a series-connected conduit inductance L.sub.t1, Lv.sub.t2, L.sub.tN and conduit resistance R.sub.t1, RV.sub.t2, R.sub.tN.

[0053] In a similar sense, the power converter 12 includes a converter reactance 32 in the form of a series-connected converter inductance

[00001]$\frac{L_v}{2}$

and converter resistance

[00002]$\frac{R_v}{2}.$

[0054] In addition, the power converter 12 includes primary and secondary converter controllers 30, 32.

[0055] The primary converter controller 30 is programmed, in use, to control the transfer of power through the power converter 12 and thereby between the DC network and the plurality of AC network elements 26.sub.1, 26.sub.2, 26.sub.N.

[0056] The primary converter controller 30 is further programmed, in use, to control each individual AC network voltage v.sub.lw1, v.sub.lw2, v.sub.lwN, and does so by establishing a virtual voltage which is representative of the AC network voltages v.sub.lw1, v.sub.lw2, v.sub.lwN The primary converter controller 30 then alters a single AC converter voltage v.sub.conv, which is produced by the power converter 12 at the AC converter terminal 22, to adjust the virtual voltage and thereby adjust each individual AC network voltage v.sub.lw1, v.sub.lw2, v.sub.lwN.

[0057] More particularly, the primary converter controller 30 is programmed to establish a virtual voltage that is commensurate with the average of the individual AC network voltages v.sub.lw1, v.sub.lw2, v.sub.lwN, and to establish such a virtual voltage in a vector form that has real and imaginary parts, i.e. to establish a virtual voltage vector.

[0058] For example, if Kirchhoff s voltage law is applied across the conduit reactances 30.sub.1, 30.sub.2, 30.sub.N and the converter reactance 32, the following equation is obtained

[00003]$v_{\mathrm{conv}}-\left(\frac{1}{N}\underset{k=1}{\overset{N}{.Math.}}{v}_{\mathrm{lwk}}\right)=\frac{L_v}{2}\frac{{\mathrm{di}}_{\mathrm{vw}}}{\mathrm{dt}}+\frac{R_v}{2}{i}_{\mathrm{vw}}+\frac{1}{N}\underset{k=1}{\overset{N}{.Math.}}\left(L_{\mathrm{tk}}\frac{{\mathrm{di}}_{\mathrm{vwk}}}{\mathrm{df}}+R_{\mathrm{tk}}{i}_{\mathrm{vwk}}\right)$

where,

[00004]$\frac{1}{N}{.Math.}_{k=1}^N{v}_{lwk}$

is the average or the individual AC network voltages v.sub.lw1, v.sub.lw2, v.sub.lwN;

[00005]$\frac{L_p}{2}\frac{d{i}_{\mathrm{vw}}}{dt}+\frac{R_{\nu }}{2}{i}_{vw}$

is the voltage difference across the converter reactance 32; and

[00006]$\frac{1}{N}{.Math.}_{k=1}^N\left(L_{\mathrm{tk}}\frac{d{i}_{\nu wk}}{dt}+R_{\mathrm{tk}}{i}_{vwk}\right)$

is the average voltage difference across the conduit reactances 30.sub.1, 30.sub.2, 30.sub.N,
with

[00007]$\frac{d{i}_{\nu w}}{dt}$

being the rate or change of a converter current i.sub.vw flowing through the converter reactance 32; and

[00008]$\frac{d{i}_{\nu wk}}{dt}$

being the rate of change of a conduit current i.sub.lw1, i.sub.lw2, i.sub.lwN flowing through a respective conduit reactance 30.sub.1, 30.sub.2, 30.sub.N.

[0059] It is therefore possible to establish the following virtual voltage which is commensurate with the average of the individual AC network voltages v.sub.lw1, v.sub.lw2, v.sub.lwN, i.e.:

[00009]$\frac{1}{N}\underset{k=1}{\overset{N}{.Math.}}{v}_{lwk}$

[0060] Moreover, converting the above-mentioned, Kirchhoff derived, equation into a vector form within a rotating dq-frame, gives

[00010]$v_{\mathrm{convdqpn}}-\left(\frac{1}{N}\underset{k=1}{\overset{N}{.Math.}}{v}_{\mathrm{lwdqpnk}}\right)=\frac{L_v}{2}\frac{{\mathrm{di}}_{\mathrm{vwdqpn}}}{\mathrm{dt}}+\frac{R_v}{2}{i}_{\mathrm{vwdqpn}}+\frac{1}{N}\underset{k=1}{\overset{N}{.Math.}}\left(L_{\mathrm{tk}}\frac{{\mathrm{di}}_{\mathrm{vwdqpnk}}}{\mathrm{dt}}+R_{\mathrm{tk}}{i}_{\mathrm{vwdqpnk}}\right)+\left(\frac{L_v}{2}{\mathrm{Ji}}_{\mathrm{vwdqpn}}+\frac{1}{N}\underset{k=1}{\overset{N}{.Math.}}\left({\mathrm{JL}}_{\mathrm{tk}}{i}_{\mathrm{vwdqpnk}}\right)\right)$

where,

[0061] v.sub.convdqpn is an AC converter voltage vector that controls the power converter 12 to produce the required AC converter voltage v.sub.conv at the AC converter terminal 22;

[00011]$\frac{1}{N}{.Math.}_{k=1}^N{v}_{\mathrm{lwdqpnk}}$

is the virtual voltage vector that can be established by the primary converter controller 34; and

[00012]$J=\left[\begin{array}{cccc}0& \omega & 0& 0\\ -\omega & 0& 0& 0\\ 0& 0& 0& -\omega \\ 0& 0& \omega & 0\end{array}\right]$

which represents cross-coupling between the real and imaginary, i.e. real power and reactive power, parts of the converter reactance 32 and the respective conduit reactances 30.sub.1, 30.sub.2, 30.sub.N,
with,

[0062] ω being the angular frequency of the rotating dq-frame.

[0063] The primary converter controller 34 is additionally programmed to compare the established virtual voltage, i.e. the established virtual voltage vector

[00013]$\frac{1}{N}\underset{k=1}{\overset{N}{.Math.}}{v}_{\mathrm{lwdqpnk}}$

with a predetermined virtual voltage reference, i.e. with a predetermined virtual voltage reference vector v.sub.dqpn*, and to alter the AC converter voltage produced by the power converter 12, i.e. by altering the AC converter voltage vector v.sub.convdqpn that controls the power converter 12, to reduce any difference between the established virtual voltage vector and the predetermined virtual voltage reference vector v.sub.dqpn*.

[0064] In addition, when altering the AC converter voltage v.sub.conv produced by the power converter to reduce any difference between the established virtual voltage vector and the predetermined virtual voltage reference vector v.sub.dqpn*, the primary converter controller 34 is further programmed to take into account:

[0065] (i) the voltage difference across the converter reactance 32, e.g. take into account

[00014]$\frac{L_v}{2}\frac{{\mathrm{di}}_{\mathrm{vwdqpn}}}{\mathrm{dt}}+\frac{R_v}{2}{i}_{\mathrm{vwdqpn}};\mathrm{and}$$\frac{L_v}{2}{\mathrm{Ji}}_{\mathrm{vwdqpn}}$

and

[0066] (ii) a virtual voltage difference that is representative of the plurality of voltage differences across the conduit reactance 30.sub.1, 30.sub.2, 30.sub.N of each AC transmission conduit AC transmission conduit 24.sub.1, 24.sub.2, 24.sub.N, and which is commensurate with the average voltage difference across the conduit reactances 30.sub.1, 30.sub.2, 30.sub.N, e.g. take into account

[00015]$+\frac{1}{N}{.Math.}_{k=1}^N\left(L_{\mathrm{tk}}\frac{{\mathrm{di}}_{\mathrm{vwdqpnk}}}{\mathrm{dt}}+R_{\mathrm{tk}}{i}_{\mathrm{vwdqpnk}}\right);\mathrm{and}$$\frac{1}{N}{.Math.}_{k=1}^N\left({\mathrm{JL}}_{\mathrm{tk}}{i}_{\mathrm{vwdqpnk}}\right)$

[0067] Moreover, the primary converter controller 34 is still further programmed to take into account cross-coupling between the real and imaginary parts of the aforementioned voltage difference and the virtual voltage difference.

[0068] Accordingly, the primary converter controller 34 need on take into account those elements of the respective voltage difference and virtual voltage difference in which cross-coupling is represented, i.e. only take into account

[00016]$\frac{L_v}{2}{\mathrm{Ji}}_{\mathrm{vwdqpn}};\mathrm{and}\frac{1}{N}{.Math.}_{k=1}^N\left({\mathrm{JL}}_{\mathrm{tk}}{i}_{\mathrm{vwdqpnk}}\right)$

[0069] One way in which the primary converter controller 34 can be programmed to compare the established virtual voltage vector, i.e.

[00017]$\frac{1}{N}\underset{k=1}{\overset{N}{.Math.}}{v}_{\mathrm{lwdqpnk}}$

with the predetermined virtual voltage reference vector v.sub.dqpn*, and to alter the AC converter voltage vector v.sub.condvqpn, to reduce any difference between the established virtual voltage vector and the predetermined virtual voltage reference vector v.sub.dqpn*, is illustrated schematically in FIG. 2.

[0070] It is noted that in the schematic programming example illustrated in FIG. 2, the primary converter controller 34 is additionally programmed to take further account of the predetermined virtual voltage reference vector v.sub.dqpn*, downstream of other considerations. This optional feature can be used to finetune, i.e. trim, the resulting AC converter voltage vector v.sub.condqpn it outputs to control the AC converter voltage v.sub.conv produced at the AC converter terminal 22, and thereby control each individual AC network voltage v.sub.lw1, v.sub.lw2, v.sub.lwN.

[0071] Meanwhile, in the embodiment shown, the secondary converter controller 36 is programmed, in use, to establish the predetermined virtual voltage reference v.sub.dqpn* that is used by the primary converter controller 34, i.e. against which the primary converter controller 34 compares the established virtual voltage vector, i.e.:

[00018]$\frac{1}{N}\underset{k=1}{\overset{N}{.Math.}}{v}_{\mathrm{lwdqpnk}}$

[0072] More particularly, the second converter controller 36 establishes the virtual voltage reference v.sub.dqpn* in a manner which is aimed at maintaining all of the individual AC network voltages v.sub.lw1, v.sub.lw2, v.sub.lwN within a desired voltage range.

[0073] In the embodiment shown, the secondary converter controller 36 is programmed to achieve this by, firstly, considering whether any AC network voltage v.sub.lw1, v.sub.lw2, v.sub.lwN, i.e. whether any instantaneous average AC network voltage V.sub.tw1.sup.rms, V.sub.tw2.sup.rms, V.sub.twN.sup.rms, is below a predetermined voltage minimum V.sub.min and, if one or more AC network voltages v.sub.lw1, v.sub.lw2, v.sub.lwN (i.e. one or more instantaneous average AC network voltages V.sub.tw1.sup.rms, V.sub.tw2.sup.rms, V.sub.twM.sup.rms) is below the voltage minimum V.sub.min, then the secondary converter controller 36 modifies the virtual voltage reference vector v.sub.dqpn* to raise the or each errant AC network voltage v.sub.lw1, v.sub.lw2, v.sub.lwN to be equal to or above the voltage minimum V.sub.min.

[0074] Then, secondly, the secondary converter controller 36 considers whether any AC network voltage v.sub.lw1, v.sub.lw2, v.sub.lwN, i.e. any instantaneous average AC network voltage V.sub.tw1.sup.rms, V.sub.tw2.sup.rms, V.sub.twN.sup.rms, is above a predetermined voltage maximum V.sub.max and if one or more AC network voltages v.sub.lw1, v.sub.lw2, v.sub.lwN (i.e. one or more instantaneous average AC network voltages V.sub.tw1.sup.rms, V.sub.tw2.sup.rms, V.sub.twN.sup.rms) is above the voltage maximum V.sub.max, then the secondary converter controller 36 modifies the virtual voltage reference vector v.sub.dqpn* to reduce the or each errant AC network voltage V.sub.tw1.sup.rms, V.sub.tw2.sup.rms, V.sub.twN.sup.rms to be equal to or below the voltage maximum V.sub.max.

[0075] Additionally, if at least one AC network voltage v.sub.lw1, v.sub.lw2, v.sub.lwN, i.e. at least one instantaneous average AC network voltage V.sub.tw1.sup.rms, V.sub.tw2.sup.rms, V.sub.twN.sup.rms, is below the voltage minimum V.sub.min and at least one AC network voltage V.sub.lw1, V.sub.lw2, V.sub.lwN, i.e. at least one instantaneous average AC network voltage V.sub.tw1.sup.rms, V.sub.tw2.sup.rms, V.sub.twN.sup.rms, is above the voltage maximum V.sub.max, the secondary converter controller 36 is programmed to modify the virtual voltage reference vector v.sub.dqpn* in a manner that equalises the amount the or each said AC network voltage v.sub.lw1, v.sub.lw2, v.sub.lwN deviates from the corresponding voltage minimum V.sub.min and voltage maximum V.sub.max.

[0076] The secondary converter controller 36 shown receives, in use, a virtual voltage command V.sub.d* from a higher-level controller (not shown), e.g. a controller at a location remote from the power converter 12, such as a control location.

[0077] The secondary converter controller 36 modifies the virtual voltage reference it establishes, i.e. the virtual voltage reference vector v.sub.dqpn* it establishes, by determining an adjustment factor δV.sub.d* and applying the adjustment factor δV.sub.d* to the received virtual voltage command V.sub.d*.

[0078] One way in which the secondary converter controller 36 modifies the virtual voltage reference it establishes, i.e. the virtual voltage reference vector v.sub.dqpn* it establishes, by determining an adjustment factor δV.sub.d* and applying the adjustment factor δV.sub.d* to the received virtual voltage command V.sub.d*, while additionally maintaining all of the individual AC network voltages v.sub.lw1, v.sub.lw2, v.sub.lwN within a desired voltage range in the manner set out above, is illustrated schematically in FIG. 3.

[0079] As shown in FIG. 3, after comparing each AC network voltage v.sub.lw1, v.sub.lw2, v.sub.lwN, i.e. each instantaneous average AC network voltage V.sub.tw1.sup.rms, V.sub.tw2.sup.rms, V.sub.twN.sup.rms with the corresponding predetermined voltage minimum V.sub.min and voltage maximum V.sub.max, the secondary converter controller 36 implements an asymmetric proportional integral control regime 38 in order to establish the aforementioned re-centring of the AC network voltages v.sub.lw1, v.sub.lw2, v.sub.lwN within the desired voltage ranged defined by voltage minimum V.sub.min and voltage maximum V.sub.max limits.

[0080] By way of example of the invention in use, the operation of a power transmission network 100 according to a second embodiment of the invention is illustrated with reference to FIGS. 4(a) to 4(c).

[0081] The second power transmission network 100 is very similar to the first power transmission network 10 described herein above, and similarly includes a power converter 12. Other identical features, which the second power transmission network 100 shares with the first power transmission network 10 are also identified by the same reference numerals, i.e. as shown in FIG. 4(a).

[0082] However, the AC converter terminal 22 of the power converter 12 in the second power transmission network 100 is instead electrically connected to only two AC transmission conduits, i.e. only first and second AC transmission conduits 24.sub.1, 24.sub.2.

[0083] Each such AC transmission conduit 24.sub.1, 24.sub.2 is, in turn, connected to a respective first and second AC network element 26.sub.1, 26.sub.2 in the form of a respective first and second wind park 28.sub.1, 28.sub.2. Each of the first and second wind parks 28.sub.1, 28.sub.2 is configured to operate at a corresponding individual first and second AC network voltage v.sub.lw1, v.sub.lw2.

[0084] Meanwhile, each of the first and second AC transmission conduits 24.sub.1, 24.sub.2 includes a corresponding first or second transformer 102.sub.1, 102.sub.2 which takes the place of the idealised conduit reactance 30.sub.1, 30.sub.2, 30.sub.N included in the first exemplary power transmission network 10.

[0085] The predetermined voltage minimum V.sub.min is set at 0.98 pu, i.e. 2% below the nominal normal desired operating voltage, and the predetermined voltage maximum V.sub.max is set at 1.01 pu, i.e. 1% above the nominal normal desired operating voltage.

[0086] Between zero and 1 second, the power converter 12 is charging up such that, as shown in FIG. 4(b), the actual average 104 of the first and second AC network voltages v.sub.lw1, v.sub.lw2 is increasing.

[0087] From 1 second to 2 seconds, power is running through the first and second wind parks 28.sub.1, 28.sub.2, and each of the first and second AC network voltages v.sub.lw1, v.sub.lw2 (represented as corresponding first and second instantaneous average AC network voltages v.sub.tw1.sup.rms, v.sub.tw2.sup.rms in FIG. 4(b)) is increasing. The average AC network voltage 104 remains essentially constant and, as shown in FIG. 4(c), the AC converter voltage v.sub.conv produced at the AC converter terminal 22 settles down, such that the virtual voltage reference vector v.sub.dqpn* output by secondary converter controller 36, and used by the primary converter controller 34 to control the said AC converter voltage v.sub.conv, is able also to remain essentially constant.

[0088] Between 2 and 3 seconds, the first AC network voltage v.sub.lw1, i.e. the corresponding first instantaneous average AC network voltage v.sub.tw1.sup.rms, begins to increase above the predetermined voltage maximum V.sub.max, i.e. begins to deviate, and so the secondary converter controller 36 acts to reduces the virtual voltage reference vector v.sub.dqpn* which results in the primary converter controller 34 reducing the AC converter voltage vector v.sub.convdgpn which in turn reduces the AC converter voltage v.sub.conv produced by the power converter 12, and thereby reduces the average AC network voltage 104 to maintain the first AC network voltage v.sub.lw1, i.e. the corresponding first instantaneous average AC network voltage V.sub.tw1.sup.rms, below the voltage maximum V.sub.max.

[0089] Normal, safe operating of the second power transmission network 100 takes place between 3 and 4 seconds, with both the first and second AC network voltages v.sub.tw1.sup.rms, v.sub.tw2.sup.rms, i.e. the corresponding first and second instantaneous average AC network voltages vms vms remaining with the desired voltage range, i.e. between the voltage maximum V.sub.inci, and the voltage minimum V.sub.min, and the average AC network voltage 104 remaining essentially constant.

[0090] At 4 seconds, the voltage minimum V.sub.min is artificially set at 1.0 pu, and the secondary converter controller 36 reacts by increasing the virtual voltage reference vector v.sub.dqpn*, which causes the primary converter controller 34 to increase the AC converter voltage v.sub.conv produced by the power converter 12 (by increasing the AC converter voltage vector v.sub.convdqpn it outputs) which, in turn, increases the average AC network voltage 104 and thereby lifts the second AC network voltage v.sub.lw2, i.e. the corresponding second instantaneous average AC network voltage V.sub.tw2.sup.rms Z, above the temporarily revised voltage minimum V.sub.min.

[0091] Between 5 and 6 seconds, the second power transmission network 100 returns again to normal, safe operation.

[0092] At 6 seconds, a critical deviation of the first and second AC network voltages v.sub.lw1, v.sub.lw2, i.e. the corresponding first and second instantaneous average AC network voltages V.sub.tw1.sup.rms, V.sub.tw2.sup.rms, is simulated in which the first AC network voltage v.sub.lw1, i.e. the corresponding first instantaneous average AC network voltage v.sub.tw1.sup.rms, exceeds the voltage maximum V.sub.max and the second AC network voltage v.sub.lw2, i.e. the corresponding second instantaneous average AC network voltage V.sub.tw2.sup.rms, falls below the voltage minimum V.sub.min. In these circumstances the primary and second converter controllers 34, 36 again work together to alter, i.e. reduce, the AC converter voltage v.sub.conv, produced by the power converter 12, and thereby reduce the average AC network voltage 104 in an effort to maintain the first and second AC network voltages v.sub.lw1, v.sub.lw2 within the desired voltage range limits set by the voltage maximum V.sub.max and the voltage minimum V.sub.min.

[0093] Such control by the primary and second converter controllers 34, 36 is unable to maintain the first and second AC network voltages v.sub.lw1, v.sub.lw2 within the desired voltage range because the deviations are too great, but the secondary converter controller 36 does modify the virtual voltage reference vector v.sub.dqpn* in a manner that equalises the amount each of the first and second AC network voltages v.sub.lw1, v.sub.lw2, i.e. the amount each of the first and second instantaneous average AC network voltages V.sub.tw1.sup.rms, V.sub.tw2.sup.rms, deviates from the corresponding voltage minimum V.sub.min and voltage maximum V.sub.max.