WO2011101027A1

WO2011101027A1 - Reactive power control for a high voltage dc link

Info

Publication number: WO2011101027A1
Application number: PCT/EP2010/051977
Authority: WO
Inventors: Jose Augusto Do Rego Menteiro; Pok Ho Michael Li; Carl David Barker; Radnya Anant Mukhedkar
Original assignee: Areva T&D Uk Ltd
Priority date: 2010-02-17
Filing date: 2010-02-17
Publication date: 2011-08-25

Abstract

A method of controlling the reactive power exchange (126) between a plurality of high voltage DC converters (118) and one or more AC networks (110), comprising the steps of calculating a single operator value based on the present DC voltages, DC voltage ranges and reactive power capabilities of the plurality of high voltage DC converters (118); and setting the target DC voltage of each high voltage DC converter (118) as a function of the single operator value such that the proportion of reactive power load of each high voltage DC converter (118) relative to its power capabilities is equal among the plurality of high voltage DC converters (118).

Description

REACTIVE POWER CONTROL FOR A HIGH VOLTAGE DC LINK

This invention relates to a method of coordinating the control of the reactive power exchange between a multiple pole high voltage direct current (HVDC) converter system and associated alternating current (AC) networks.

A HVDC converter is connected to an AC network in order to convert AC electrical power to direct current (DC) electrical power. The HVDC converter consumes reactive power during the conversion of AC power to DC power, which results in a reactive power exchange between the HVDC converter and the AC network. The amount of reactive power consumption varies with DC power load in the HVDC converter.

Figure 1 shows a schematic arrangement of the HVDC converter 118, the AC network 110 and a reactive power element 120. Conventionally the total reactive power exchange 126 between the HVDC converter 118 and the AC network 110 is controlled by adding or removing reactive power elements 120 at predefined DC power levels of the HVDC converter. Reactive power elements 120 such as filter banks and shunt capacitor banks compensate the reactive power 130 consumed by the HVDC converter 118.

A change in DC power in the HVDC converter is typically followed by a measurement of the reactive power exchange between the HVDC converter and the AC network to assess whether it is necessary to adjust the operating DC voltage and current of the HVDC converter in order to restore the reactive power exchange within a defined range. The reactive power exchange between the HVDC converter and the AC network therefore may temporarily exceed the limits of the defined range following a change in DC power until appropriate adjustment of the operating DC voltage and current of the HVDC converter takes place.

HVDC converter arrangements have multiple HVDC converters in parallel operation, each of which may have different power capabilities. Complex coordination strategies are therefore required to control the operation of different HVDC converters in order to control the overall reactive power exchange between the multiple pole HVDC converter arrangement and associated AC networks.

In addition, the reactive power loading of parallel HVDC converters is conventionally shared in a pre-defined way between the converters in which one HVDC converter acts as the master reactive power absorption means while other parallel HVDC converters provide additional reactive power absorption capability as required. This load sharing arrangement leads to high losses, and therefore poor converter efficiency.

According to an aspect of the invention, there is provided a method of controlling a reactive power exchange between a high voltage DC converter and an AC network in order to keep the reactive power exchange at a constant level or within a defined range, wherein the high voltage DC converter is connected to the AC network and a plurality of reactive power elements, and a reactive power element is added to or removed from the plurality of reactive power elements at predefined DC power levels of the high voltage DC converter; and a change in DC voltage of the high voltage DC converter is calculated, prior to the addition or removal of the reactive power element, using a linear interpolation of predefined changes in DC voltage of the high voltage DC converter for the addition or removal of a reactive power element at predefined DC voltages; and the calculated change in DC voltage is applied during the addition or removal of the reactive power element.

The above method of controlling a reactive power exchange is advantageous because it minimises or prevents any undesirable change in the reactive power exchange between the HVDC converter and the AC network by applying the calculated change in DC voltage during the addition or removal of the reactive power element to adjust the consumed reactive power to compensate for the reactive power of the added or removed reactive power element.

In other embodiments, the predefined changes in DC voltage of the high voltage DC converter and their corresponding predefined DC voltages are preferably calculated for the addition or removal of a reactive power element at minimum and maximum reactive power consumption in the high voltage DC converter.

The HVDC converter can supply different levels of reactive power consumption by adjusting its DC voltage level. Predefined values of a change in DC voltage and their corresponding predefined DC voltages of the high voltage DC converter are calculated at minimum and maximum reactive power consumption in the high voltage DC converter to cover the entire operating range of the DC voltage of the HVDC converter.

According to another aspect of the invention, there is provided a method of controlling a reactive power exchange between a high voltage DC converter and an AC network in order to keep the reactive power exchange at a constant level or within a defined range, wherein a change in DC voltage of the high voltage DC converter is calculated prior to a change in DC power in the high voltage DC converter based on a predefined change in DC voltage with DC power; and the calculated change in DC voltage is applied during the change in DC power in the high voltage DC converter.

The above method of controlling a reactive power exchange is advantageous because it minimises or prevents any undesirable change in reactive power exchange between the HVDC converter and the AC network by applying an appropriate change in DC voltage during the change in DC power.

In embodiments of the invention, the predefined change in DC voltage with DC power may be a gradient of a function describing a linear relationship between present values of DC voltage and power, and values of DC voltage and power at the point of convergence between a plurality of functions describing a change in DC voltage with DC power at minimum and maximum reactive power consumption in the high voltage DC converter when the present value of the DC voltage at the present DC power level lies within the limits defined by the plurality of functions describing a change in DC voltage with DC power at minimum and maximum reactive power consumption in the high voltage DC converter. The HVDC converter can supply different levels of reactive power consumption by adjusting its DC voltage level. The predefined change in DC voltage with DC power is therefore calculated based on the plurality of functions describing a change in DC voltage with DC power at minimum and maximum reactive power consumption to cover the entire operating range of the DC voltage of the HVDC converter.

In other embodiments, the predefined change in DC voltage with DC power in the high voltage DC converter may be equal to the gradient of the function describing minimum reactive power consumption in the high voltage DC converter when the difference between the gradient of the function describing a change in DC voltage with DC power at minimum reactive power consumption and the gradient of the function describing a change in DC voltage with DC power at maximum reactive power consumption is less than a predefined limit.

The inclusion of a predefined limit prevents a situation in which the gradient of the function describing a change in DC voltage with DC power at minimum reactive power consumption is equal to the gradient of the function describing a change in DC voltage with DC power at maximum reactive power consumption, resulting in non-convergence of the two functions and thereby making it impractical to calculate the predefined change in DC voltage with DC power.

An algorithm is preferably implemented to select a method of controlling a reactive power exchange between a high voltage DC converter and an AC network depending on a DC power level and a requested change in DC power of the high voltage DC converter.

Both of the above methods of controlling a reactive power exchange may be combined into a single method for operating a HVDC converter in which the algorithm selects the appropriate method of controlling the reactive power exchange depending on the present operating conditions of the HVDC converter.

According to a third aspect of the invention, there is provided a method of controlling the reactive power exchange between a plurality of high voltage DC converters and one or more AC networks, comprising the steps of calculating a single operator value based on the present DC voltages, DC voltage ranges and reactive power capabilities of the plurality of high voltage DC converters; and setting the target DC voltage of each high voltage DC converter as a function of the single operator value such that the proportion of reactive power load of each high voltage DC converter relative to its power capabilities is equal among the plurality of high voltage DC converters.

The proportional sharing arrangement for the reactive power load means that there is no need for a master HVDC converter which handles the majority of the reactive power load because each HVDC converter operates at the same level of reactive power loading in relation to their individual power capabilities. As a result the proportional load sharing arrangement minimises converter losses and improves converter station efficiency.

The single operator value can be calculated based on any number of HVDC converters with different power capabilities and operating modes. A reactive power control strategy based on the single operator value therefore can accommodate any different number of HVDC converters and there is therefore no requirement to design different control strategies for different numbers of HVDC converters.

In embodiments of the invention, the plurality of high voltage DC converters is operably associated with a master controller which is controllable to modify the single operator value in response to data signals; and the modified single operator value replaces the single operator value for the calculation of the target DC voltage of each high voltage DC converter.

The provision of a master controller allows the implementation of a single reactive power control strategy common to multiple HVDC converters just by modifying the single operator value instead of providing separate sets of instructions to each HVDC converter. In addition, the use of a single master controller to control the plurality of HVDC converters avoids the situation in which there is a risk of mis-coordination between multiple controllers. In other embodiments, the calculated target DC voltage of each individual high voltage DC converter may be subjected to a change in DC voltage calculated using a method of controlling a reactive power exchange between a high voltage DC converter and an AC network.

The above method of controlling the reactive power exchange between a multiple pole HVDC converter arrangement and associated AC networks is advantageous because it minimises or prevents any undesirable change in the reactive power exchange between the multiple pole HVDC converter arrangement and the associated AC networks while ensuring that the reactive power load of the multiple pole HVDC converter arrangement is proportionally distributed among the plurality of HVDC converters.

Preferred embodiments of the invention will now be described, by way of non-limiting examples, with reference to the accompanying drawings in which:

Figure 1 shows a schematic arrangement of the HVDC converter, the AC network and a reactive power element;

Figure 2a and Figure 2b show the flow path of the reactive power element switching process in the HVDC converter;

Figure 3a shows the change in DC voltage for the addition of a reactive power element;

Figure 3b shows the change in DC voltage for the removal of a reactive power element;

Figure 4a shows the linear interpolation of predefined values of a change in DC voltage during the addition of a reactive power element at predefined DC voltages;

Figure 4b shows the linear interpolation of predefined values of a change in DC voltage during the removal of a reactive power element at predefined voltages;

Figure 5 shows the calculation of the next DC voltage, Ud_order, from four operating points predefined at the design stage of the HVDC converter.

Figure 1 shows a simplified example of an arrangement of the

HVDC converter, the AC network and a reactive power element. The AC network 110 is connected to a first end 113 of a short circuit impedance 114. A second end 115 of a short circuit impedance 114 is connected to an intersection 116 which is also connected to a HVDC converter 118 and a first end 119 of a reactive power element 120. A second end 121 of the reactive power element 120 can be connected to ground 122. The reactive power element 120 compensates the reactive power 130 required by the HVDC converter 118, and thereby reduces the reactive power exchange 126 between the HVDC converter 118 and the AC network 110.

The single reactive power element 120 in Figure 1 may be replaced by a plurality of parallel reactive power elements. Reactive power elements 120 may be in the form of filter banks, shunt capacitor banks, shunt reactor banks or any combination thereof which compensate the reactive power 130 consumed by the HVDC converter 118.

A method of controlling a reactive power exchange 126 between a high voltage DC converter 118 and an AC network 110 according to a first embodiment of the invention is shown in Figures 2a and 2b.

Each HVDC converter 118 can be operated using a predefined DC target voltage for each steady-state operating mode. The alpha and gamma angles at a fraction of the nominal DC power are kept within set values of the nominal values of the alpha and gamma angles at the nominal DC power in order to minimise converter losses and filtering requirements. This sets upper and lower limits 135,136 for the DC target voltage for the HVDC converter 118 for different DC power levels as shown in Figures 2a and 2b.

Switching of reactive power elements 120 in the form of an addition or removal of a reactive power element 120 from the plurality of reactive power elements can take place at predefined DC power levels in a HVDC converter 118. Each time a reactive power element 120 is added or removed, a change in DC voltage of the HVDC converter 118 is applied by changing the firing angles of the HVDC converter 1 18 to adjust the consumed reactive power 130 such that the reactive power exchange 126 between the HVDC converter 118 and the AC network 110 remains unchanged or within a predefined range. Figures 2a and 2b show the DC voltages before (at point B 132) and after (at point C 133) an addition of a reactive power element 120 and the DC voltages before (at point D 134) and after (at point A 131) a removal of a reactive power element 120.

Application of a change in DC voltage of the HVDC converter 118 takes place by decreasing the DC voltage during the addition of a reactive power element 120 (from point B 132 to point C 133) or by increasing the DC voltage during the removal of a reactive power element 120 (from point D 134 to point A 131). The required change in DC voltage of the HVDC converter 118 is calculated as follows.

The HVDC converter 118 can supply different levels of reactive power consumption by adjusting its DC voltage level. Limits of the DC voltage of the HVDC converter 118 during the addition or removal of the reactive power element 120 are therefore calculated for minimum and maximum reactive power consumption in the HVDC converter 118 to cover the entire operating range of the HVDC converter 118.

In order to compensate for the reactive power of the added or removed reactive power element 120 and thereby ensure that the reactive power exchange 126 remains unchanged or within a predefined range, the required change in reactive power consumption, AQdc, is calculated using Equations (2) and (3).

+ AQdc≡x% Qfilter (2)

- AQdc≡-x% Qfilter (3)

Where Qfilter is the reactive power of the reactive power element;

x is the percentage of the reactive power to be compensated and is related to the specified step voltage;

+AQdc is the required change in reactive power consumption during an addition of a reactive power element; and -AQdc is the required change in reactive power consumption during a removal of a reactive power element.

A value of 100% for x means that 100% of the reactive power of the reactive power element 120 is compensated and there is 0% change in step voltage.

Figures 3a and 3b show possible locations of the DC voltage of the HVDC converter 118 for minimum and maximum reactive power consumption before and after a reactive power 120 is added or removed.

The DC voltages after the addition (point C 133a) and before the removal (point D' 134a) of a reactive power element 120 are located along the function describing maximum reactive power consumption in order to minimise the reactive power exchange 126 between the HVDC converter 118 and the AC network 110.

Calculation of the DC voltages before the addition (point B' 132a) and after the removal (point A' 131a) of the reactive power element 120 is based on the required change in DC voltage in order to achieve the required change in reactive power consumption, AQdc, from Equations (2) and (3) respectively.

Similarly the DC voltages before the addition (point B" 132b) and after the removal (point A" 131a) of the reactive power element 120 are located along the function describing minimum reactive power consumption in order to maximise the reactive power exchange 126 between the HVDC converter 118 and the AC network 110.

Calculation of the DC voltages after the addition (point C" 133b) and before the removal (point D" 134b) of the reactive power element 120 is based on the required change in DC voltage in order to achieve the required change in reactive power consumption, AQdc, from Equations (2) and (3) respectively.

The above-calculated DC voltages before and after a switching of a reactive power element 120 for minimum and maximum reactive power consumption provide predefined values for calculating the required change in DC voltage in the HVDC converter 118 once the HVDC converter 118 reaches a predefined DC power level at which a reactive power element 120 is to be added or removed.

At the predefined DC power level the present DC voltage of the HVDC converter 118 may lie between the predefined DC voltages at points B' 132a and B" 132b prior to the addition of a reactive power element 120, and may lie between the predefined DC voltages at points D' 134a and D" 134b prior to the removal of a reactive power element 120, as shown in Figures 4a and 4b.

The required change in DC voltage of the high voltage DC converter 1 18 is calculated, prior to an addition or removal of the reactive power element 120, using a linear interpolation of predefined changes in DC voltage of the high voltage DC converter 1 18 during the addition or removal of the reactive power element 120 at predefined DC voltages 120, and the calculated change in DC voltage is applied during the addition or removal of the reactive power element 120.

As shown in Figure 4a, for an addition of a reactive power element, the required change in DC voltage, AUd_tar_get, is calculated by linearly interpolating between the predefined changes in DC voltage for the addition of the reactive power element 120 at their corresponding DC voltages for maximum reactive power consumption (point B' 132a) and for minimum reactive power consumption (point B" 132b).

As shown in Figure 4b, for a removal of a reactive power element, the required change in DC voltage, AUd_tar_get, is calculated by linearly interpolating between the predefined changes in DC voltage for the removal of the reactive power element 120 at their corresponding DC voltages for maximum reactive power consumption (point D' 134a) and for minimum reactive power consumption (point D" 134b).

The required DC voltage for the addition of a reactive power element 120 is calculated using Equation (4) while the required DC voltage for the removal of a reactive power element 120 is calculated using Equation (5).

Ud i,arg ei , (Vnew) = Ud f,arg ef , (Vold /) - AUd t,arg et , ( V4) / Ud_{tas et} (new) = Ud_{tsIg et} (old) + MJd_{tsIg et} (5)

Where Ud_tar_get (old) is the present DC voltage of the HVDC converter 118;

Udtarget (new) is the required DC voltage; and

AUdtarget is the required change in DC voltage to be applied during the addition or removal of the reactive power element.

The required change in DC voltage from Equation (4) or Equation (5) is then applied during the addition or removal of a reactive power element 120 to minimise any change in reactive power exchange 126 between the HVDC converter 1 18 and the AC network 1 10.

A method of controlling the reactive power exchange 126 between a high voltage DC converter 1 18 and an AC network 1 10 according to a second embodiment of the invention is shown in Figure 5.

Referring to Figure 1 , the reactive power exchange 126 between a HVDC converter 1 18 and an AC network 1 10 is equal to the difference between the compensated reactive power 128 of the filter 120 and the consumed reactive power 130 of the converter 1 18. The compensated reactive power 128 has a constant value that is dependent on the reactive power element 120 and the AC system voltage and frequency.

The consumed reactive power 130 has to be kept within a defined range in order to maintain the reactive power exchange 126 between the HVDC converter 1 18 and the AC network 1 10. Changing the DC voltage or power of the HVDC converter 1 18 can cause the consumed reactive power 130 to vary. The variation of the consumed reactive power 130 during a requested DC power level, P_order 166, in the HVDC converter 1 18 can be minimised or prevented by applying an appropriate DC voltage, Ud_order 170, during the change in DC power.

The required change in DC voltage of the high voltage DC converter 1 18 is calculated prior to the change in DC power in the HVDC converter 1 18 and is determined as follows.

The HVDC converter 1 18 operates within the limits defined by the linear functions Pn 152 and Gn 150, as shown in Figure 5. The DC voltage of the HVDC converter 118 varies with power along function Pn 152 for maximum reactive power consumption, and varies with power along function Gn 150 for minimum reactive power consumption.

Each of the linear functions Pn 152 and Gn 150 can be defined by two pairs of values for DC voltage and DC power. Function Pn 152 is identified by points (xl, yl) 158 and (x3, y3) 160 while function Gn 150 is identified by points (x2, y2) 154 and (x4, y4) 156. The values of x and y respectively refer to DC voltages and DC power levels of the HVDC converter 118.

The points (xl, yl) 158, (x2, y2) 154, (x3, y3) 160 and (x4, y4)

156 are defined during the design stage of the HVDC converter 118 and are specific to a particular HVDC converter 118.

The upper, Limitup, and lower limits, Limitdw, of a DC voltage at a specific DC power level of a HVDC converter 118 are calculated using Equations (6) to (9). aLup =——— (6)

x4 - x2 aLdw = ^{y ~ yl} (7)

x3 - xl

Limitup = aLup^■ (Porder - xl) + yl (8)

Limitdw = aLdw^■ (Porder - xl) + yl (9)

Where Porder is the requested DC power level in the HVDC converter 118.

When a change in DC power of the HVDC converter 118 is requested, the corresponding change in DC voltage of the high voltage DC converter 118 is calculated prior to the change in DC power in the high voltage DC converter 118 based on a predefined change in DC voltage with DC power. The value of the predefined change in DC voltage with DC power is dependent on certain conditions being met.

In one embodiment of the invention, if the present value of the DC voltage at the present DC power level lies within Limitup and Limitdw, the predefined change in DC voltage with DC power in the HVDC converter 118 is a gradient of a function describing a linear relationship between present values of DC voltage 168 and power 164, and values of DC voltage and power at the point of convergence 162 between a plurality of functions describing a change in DC voltage with DC power at minimum, function Pn 152, and at maximum reactive power consumption, function Gn 150, in the high voltage DC converter 118.

The predefined change in DC voltage with DC power therefore may be calculated using Equation (10).

AUdc yp - Udi

(10)

APdc xp - Pdi

Where Udi 168 is the present DC voltage of the HVDC converter 118,

Pdi 164 is the present DC power of the HVDC converter 118, and xp and yp are the DC voltage and DC power at the point of convergence

162 between function Pn 150 and function Gn 152.

The values of xp and yp are calculated using Equations (11) to

(12).

yl · aLup - v2^■ aLdw - x\^■ aLup^■ aLdw + x2^■ aLup^■ aLdw .. ..

yp := - — (11)

aLup - aLdw

._ l - 2 - xl · aLdw + x2^■ aLup

aLup - aLdw

In the case of aLup = aLdw, functions Pn 152 and Gn 150 cannot meet at a point of convergence, and applying Equations (11) and (12) will generate an infinite value for both xp and yp, which is impractical for use in Equation (10) to calculate the magnitude of change in DC voltage with DC power.

In another embodiment of the invention, the above situation is avoided by setting a condition on the relationship between aLup and aLdw as follows.

aLup - aLdw < margin

Where "margin" is a limit defined during the design stage of the HVDC converter 1 18. In the event that this condition is met, the predefined magnitude of change in DC voltage with DC power in the high voltage DC converter 118 is set to be equal to the gradient of the function describing minimum reactive power consumption in the high voltage DC converter, aLup.

The predefined magnitude of change in DC voltage with DC power in the high voltage DC converter 118 is used to calculate the required change in DC voltage following a request in change in DC power of the HVDC converter 118. The calculated change in DC voltage is then applied during the change in DC power of the HVDC converter 118 to minimise any change in reactive power exchange 126 between the HVDC converter 118 and the AC network 110. .

In an embodiment of the invention, an algorithm may be implemented to choose between the first or second embodiments of a method of controlling a reactive power exchange between a high voltage DC converter 118 and an AC network 110 depending on a DC power level and a requested change in DC power of the high voltage DC converter 118.

The algorithm evaluates the present status of the HVDC converter 118 in order to calculate the change in DC voltage of the HVDC converter 118 following a requested change in DC power. This algorithm is implemented by carrying out a sequence of steps to select the required action. The sequence of steps is shown as follows.

a) Is the present DC power in the HVDC converter 118 outside the limits of the DC power range for the present set of reactive power elements 120? If yes, the algorithm chooses to implement the reactive power element 120 switching process and ends the evaluation. If no, the algorithm moves to step (b).

b) Is the requested DC power level is equal to the present DC power level? If yes, the change in DC voltage for the HVDC converter 118 is zero. If no, the algorithm moves to step (c).

c) Is the requested DC power level higher than the present DC power level? If yes, the algorithm moves to step (d). If no, the algorithm moves to step (e). d) Is the present DC power level lower than the maximum DC power level for the present set of reactive power elements by a predefined margin, ΔΡ? If yes, the present DC power level is increased by the required change for the HVDC converter 118 calculated based on the predefined change in DC voltage with DC power. If no, the change in DC voltage for the HVDC converter 118 is zero.

e) Is the present DC power level higher than the minimum DC power level for the present set of reactive power elements 120 by a predefined margin, ΔΡ? If yes, the present DC power level is decreased by the required change for the HVDC converter 118 calculated based on the predefined change in DC voltage with DC power. If no, the change in DC voltage for the HVDC converter 118 is zero.

The predefined margin, ΔΡ, is the difference between the DC power level in which the reactive power element 120 is removed, and the DC power level in which the reactive power element 120 is added.

It is envisaged that a method of controlling the reactive power exchange between a plurality of high voltage DC converters 118 and one or more AC networks 110 according to a third embodiment of the invention may be provided to distribute the reactive power load proportionally among the plurality of HVDC converters 118 as follows.

The total reactive power consumption 130 of the multiple pole HVDC converter arrangement is calculated using Equation 13.

Qdc Total = Qdcl + Qdcl + ... + Qdcn (13)

Where Qdc Total is the total reactive power consumption of the plurality of HVDC converters in parallel operation;

Qdcl, Qdc2...Qdcn are the reactive power consumptions for the individual HVDC converters.

The above expression may be fulfilled for an infinite amount of combinations of values for Qdcl, Qdc2...Qdcn. The limits of reactive power consumption for each individual HVDC converter may vary depending on its power capacity and operating mode.

The distribution of the reactive power load may be optimized by adjusting the DC voltage and therefore the reactive power consumption, Qdcn, of each HVDC converter 118 so that the proportion of the reactive power loading in each individual HVDC converter 118 relative to the converter's power capabilities is equal among the plurality of high voltage DC converters 118, and the total reactive power exchange between the plurality of high voltage DC converters and a plurality of AC networks remains at a constant level or within a defined range.

Assuming n converters in operation, the total consumed reactive power 130 before and after optimization is based on Equations (13) to (15).

Qdc Total 1 = Qdclop + Qdclop + ... + Qdcnop (14)

Qdc Total 1 = Qdc Total (15)

where Qdc Total is the total instantaneous reactive power consumption before optimization;

Qdc Total 1 is the total instantaneous reactive power consumption after optimization;

Qdcl is the reactive power consumption of the 1st converter before optimization;

Qdc2 is the reactive power consumption of 2nd converter before optimization;

Qdcn is the reactive power consumption of the nth converter before optimization;

Qdclop is the reactive power consumption of the 1st converter after optimization;

Qdc2op is the reactive power consumption of the 2nd converter after optimization; and

Qdcnop is the reactive power consumption of the nth converter after optimization.

The corresponding DC voltages before distribution optimization are:

El order DC voltage at the 1st converter

E2_order DC voltage at the 2nd converter Enordei- DC voltage at the nth converter

The corresponding DC voltages after distribution optimization are:

E 1 oporder DC vo ltage at the 1 st converter

E2op_order DC vo ltage at the 2nd converter

Enoporder DC vo ltage at the nth converter

A single operator value, Ur, is calculated by selecting the values of El op, E2op and Enop in order to obtain the following identity in Equation (17). Ur i^E °P O orrddeerr ^{~ U} ^^d^^min )/ __ ( V^E^ ²^°PF oorrddeerr ~ ^U ^ ^d^ ²^ nmnmn )! _- . . . _- i V^E^ⁿ'^°P ' oorrddeerr ~ ^nnn )

AE\ ^xmx AE2 max AEn max

(17)

The calculation for the single operator value, Ur, can be rewritten as Equation (18).

AE\^■ AQ\ AE2^■ AQ2 ₊ AEn - AQn ^ AEi - AQn

Where ΔΕ1 = (Udl_actuai - Udl_min);

ΔΕ2 = (Ud2_actuai - Ud2_min);

ΔΕ^η = (Udi uai - Udn_min);

ΔΕ 1 _max = (Ud 1 max - Ud 1 _min) ;

ΔΕ2 _max (Ud2_max^— Ud2_min) ₅

AEn max = (Udnmax - Udnmin);

Ur is the operator value;

Udriactuai is the present DC voltage of the nth converter;

Udxmax is the maximum Ud_order for a specific DC power level and operating mode;

Udxmin is the minimum Ud_order for a specific DC power level and operating mode; and AQn is the maximum converter reactive power variation capability for a specific DC power level and operating mode assuming that some tap variation might occur.

The values of AQl, AQ2...AQn are calculated based on the following expressions:

Δβ (^ ), ,_; , = fx{P_dc ), ,_; , = [Qdc{gx{P_dc ), P_dc ) - Qdc{px{P_dc ), P_dc ) J]x=l,2,...,« R - I

Udx_^ = gx{P_dc ) _=l _,

Qdc(U_d , P_dc )_R = m(U_v ,a (U_d , P_dc ), μ (U_d , P_dc ), X_c

Qdc(U_d , P_dc = m(U_v ,y(U_d , P_dc \ μ(υ„ , P_dc ), X_c

Where fx, gx and px functions defined at the design stage of the HVDC converter 118

Uv valve winding voltage

a alpha firing angle

y gamma angle

μ overlap angle

Xc commutation reactance

m function to calculate the consumed reactive power for rectification

n function to calculate the consumed reactive power for inversion

The single operator value Ur may vary from 0 to 1 wherein a value of 0 means that the HVDC converter arrangement is operating at maximum reactive power consumption while a value of 1 means that the HVDC converter arrangement is operating at minimum reactive power consumption.

The target DC voltage of each high voltage DC converter 118 is a function of the operator value Ur such that the proportion of the reactive power load of each high voltage DC converter 118 relative to its power capabilities is equal among the plurality of HVDC converters 118 in parallel operation.

The individual target DC voltages for each HVDC converter 118, Elop, E2op...Enop are calculated by the following expressions: Elop = AEl_max x Ur + Udl_min

E2op = AE2_max x Ur + Ud2mi_n

Enop = AEn_max x Ur + Udn_mi_n

If the present DC voltage of the HVDC converter 1 18 is larger than the DC voltage at minimum reactive power compensation, ΔΕη for the nth HVDC converter 1 18 is equal to AEn_max.

Udlorier > Udl_max→ ΔΕ1 = ΔΕ1 ^L m_Γ ax

Ud2_order > Ud2_max→ ΔΕ2 = ΔΕ2 -m_Ε ax

Udn_order > Udn_max→ ΔΕ3 = AEn_max

If the present DC voltage of the HVDC converter 1 18 is smaller than the DC voltage at maximum reactive power compensation, ΔΕη for the nth HVDC converter 1 18 is equal to zero.

Udl _order < Udl_mi_n - →ΔΕ1 = 0

Ud2₀rder < Ud2_min - →ΔΕ2 = 0

Udn₀rder < Udn_min - →· ΔΕη = 0

The reactive power load due to the reactive power exchange 126 between a multiple pole HVDC converter 118 arrangement and associated AC networks 110 can therefore be distributed proportionally among the plurality of HVDC converters 118 to minimise converter losses and improve converter station efficiency.

In embodiments of the invention the single operator value Ur may be fed into a master controller which controls the operation of the plurality of high voltage DC converters 118. The purpose of the master controller is to implement a common reactive power control strategy for the plurality of HVDC converters 118. The master controller may take the form of a common reactive power control dynamic/logic block which receives data signals from AC networks 110 on both sides of the multiple pole HVDC converter arrangement. A reactive power control strategy defined by the data signals is implemented by the master controller for each HVDC converter 118 by modifying the single operator value Ur before it is used to calculate the target DC voltage of each high voltage DC converter 118. This method avoids the situation in which there is a risk of mis- coordination between multiple controllers, each providing a separate set of instructions to a different HVDC converter 118.

It is envisaged that the above-described methods of controlling reactive power exchange may be adapted to different operating modes simply by modifying any input data while retaining the overall structure of the methods as described in the foregoing.

The use of predefined values and functions for each HVDC converter 118 means that the control of the multiple pole HVDC converter arrangement may be based on a look-up table of the predefined values and functions of the HVDC converters 118 in parallel operation. The look-up table is particular to a specific operating mode. Adapting the multiple pole HVDC converter arrangement to another operating mode, which may include operation with different numbers of converters or converters operating in opposite directions, only means that a new look-up table of predefined values and functions is required.

It is also envisaged that the proportional sharing of the reactive power load among the plurality of HVDC converters 118 may be applicable to multiple pole HVDC converter arrangements in which the DC voltage does not vary. In this case, the firing angles instead of the DC voltages provide the input information for the single block reactive power controller to create a single firing per-unit signal which is similar to the single operator value Ur.

Claims

1. A method of controlling a reactive power exchange (126) between a high voltage DC converter (118) and an AC network (110) in order to keep the reactive power exchange at a constant level or within a defined range, wherein the high voltage DC converter (118) is connected to the AC network (110) and a plurality of reactive power elements, and a reactive power element is added to or removed from the plurality of reactive power elements at predefined DC power levels of the high voltage DC converter (118), characterized in that a change in DC voltage of the high voltage DC converter is calculated, prior to the addition or removal of the reactive power element, using a linear interpolation of predefined changes in DC voltage of the high voltage DC converter for the addition or removal of a reactive power element at predefined DC voltages; and the calculated change in DC voltage is applied during the addition or removal of the reactive power element.

2. A method according to Claim 1 wherein predefined changes in DC voltage of the high voltage DC converter and their corresponding predefined DC voltages are calculated for the addition or removal of a reactive power element at minimum and maximum reactive power consumption in the high voltage DC converter.

3. A method of controlling a reactive power exchange between a high voltage DC converter (118) and an AC network (110) in order to keep the reactive power exchange at a constant level or within a defined range, characterized in that a change in DC voltage of the high voltage DC converter is calculated, prior to a change in DC power in the high voltage DC converter, using a predefined change in DC voltage with DC power; and the calculated change in DC voltage is applied during the change in DC power in the high voltage DC converter.

4. A method according to Claim 3 wherein the predefined change in DC voltage with DC power is a gradient of a function describing a linear relationship between present values of DC voltage and power, and values of DC voltage and power at the point of convergence between a plurality of functions

5 describing a change in DC voltage with DC power at minimum and at maximum reactive power consumption in the high voltage DC converter when the present value of a DC voltage at the present DC power level lies within the limits defined by the plurality of functions describing the change in DC voltage with DC power at minimum and maximum reactive power consumption in the high voltage DC o converter.

5. A method according to Claim 3 or Claim 4 wherein the predefined change in DC voltage with DC power in the high voltage DC converter is equal to the gradient of the function describing minimum reactive power5 consumption in the high voltage DC converter when the difference between the gradient of the function describing a change in DC voltage with DC power at minimum reactive power consumption and the gradient of the function describing a change in DC voltage with DC power at maximum reactive power consumption is less than a predefined limit.

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6. A method according to any one of Claims 1 to 2 and any one of Claims 3 to 5 wherein an algorithm is implemented to select a method for calculating a change in DC voltage of the high voltage DC converter depending on a DC power level and a requested change in DC power of the high voltage DC5 converter.

7. A method according to any of Claims 1 to 6 wherein the plurality of reactive power elements include filter banks, shunt capacitor banks and/or shunt reactor banks.

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8. A method of controlling the reactive power exchange between a plurality of high voltage DC converters and one or more AC networks, comprising the steps of calculating a single operator value based on the present DC voltages, DC voltage ranges and reactive power capabilities of the plurality of high voltage DC converters; and setting the target DC voltage of each high voltage DC converter as a function of the single operator value such that the proportion of reactive power load of each high voltage DC converter relative to its power capabilities is equal among the plurality of high voltage DC converters.

9. A method according to Claim 8 wherein the plurality of high voltage DC converters are operably associated with a master controller which is controllable to modify the single operator value in response to data signals; and the modified single operator value replaces the single operator value for the calculation of the target DC voltage of each high voltage DC converter.

10. A method according to Claim 8 or Claim 9 where the calculated target DC voltage of each individual high voltage DC converter is subjected to a change in DC voltage calculated using a method according to any of Claims 1 to 7.