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Title:
STATCOM CONTROL DURING TRANSIENT OVERVOLTAGE
Document Type and Number:
WIPO Patent Application WO/2019/197023
Kind Code:
A1
Abstract:
The present disclosure relates to a method of controlling a power converter (1), the converter being connected to an AC grid (42) via a power transformer (41), wherein by means of the converter a current is injected into the grid via said transformer. The method comprises operating the converter at steady state wherein the grid has a grid voltage ugrid which is applied to the converter via the transformer which is at most 1.1 p.u. The method also comprises detecting a Transient Overvoltage (TOV) of at least 1.5 p.u. in the grid voltage. The method also comprises, in response to the detected TOV, over-modulating the converter voltage USTATCOM generated by the converter and applied to the grid via the transformer during the TOV by introducing a plurality of harmonic voltages therein.

Inventors:
MAJI, Abhishek (2-No, Ichlabad Barabenepara,P.O.-Sripally,Burdwan, West Bengal 3, 713103, IN)
MOHANAVEERAMANI, Aravind (Vindelgatan 19B, Ludvika, 77133, SE)
HASLER, Jean-Philippe (Medelpadsvägen 3, Västerås, 722 44, SE)
Application Number:
EP2018/059251
Publication Date:
October 17, 2019
Filing Date:
April 11, 2018
Export Citation:
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Assignee:
ABB SCHWEIZ AG (Brown Boveri Strasse 6, 5400 Baden, 5400, CH)
International Classes:
H02M1/32; H02M7/483
Domestic Patent References:
WO2012083963A12012-06-28
WO2015188877A12015-12-17
Foreign References:
EP3123606A12017-02-01
JP2011259538A2011-12-22
Other References:
DONG-CHOON LEE ET AL: "A Novel Overmodulation Technique for Space-Vector PWM Inverters", IEEE TRANSACTIONS ON POWER ELECTRONICS, INSTITUTE OF ELECTRICAL AND ELECTRONICS ENGINEERS, USA, vol. 13, no. 6, 1 November 1998 (1998-11-01), XP011043239, ISSN: 0885-8993
D. GRAHAME HOLMES; THOMAS A. LIPO: "Pulse Width Modulation for Power Converters - PRINCIPLES AND PRACTICE", 2003, IEEE PRESS, pages: 226 - 230
Attorney, Agent or Firm:
KRANSELL & WENNBORG KB (P.O. Box, 115 93 Stockholm, 27834, SE)
Download PDF:
Claims:
CLAIMS

1. A method of controlling a power converter (l), the converter being connected to an Alternating Current, AC, grid (42) via a power transformer (41), wherein by means of the converter a current is injected into the grid via said transformer, the method comprising: operating (Mi) the converter at steady state wherein the grid has a grid voltage (ugrid) which is applied to the converter via the transformer which is at most 1.1 per unit, p.u.; detecting (M2) a Transient Overvoltage, TOV, of at least 1.5 p.u. in the grid voltage; and in response to the detected (M2) TOV, over-modulating (M3) the converter voltage (USTATCOM) generated by the converter and applied to the grid via the transformer during the TOV by introducing a plurality of harmonic voltages therein.

2. The method of any preceding claim, wherein the TOV is within the range of from 1.5 to 2.5 p.u., such as from 1.8 to 2.1 or 2.0 p.u.

3. The method of any preceding claim, wherein the operating (Ml) at steady state comprises, introducing a third order harmonic zero sequence voltage (u3) in the converter.

4. The method of any preceding claim, wherein the plurality of harmonic voltages comprise at least one of 3rd, 5th and 7th order harmonic voltages.

5. The method of any preceding claim, wherein the power converter (1) comprises a two-level converter or a Neutral Point Clamped, NPC, converter.

6. The method of any claim 1-4, wherein the converter (1) comprises an arm (2) of a Modular Multilevel Converter, MMC, the arm having a plurality of series connected converter cells (3), each cell comprising an energy storage (5) and a plurality of semiconductor switches (S), the arm being connected to an Alternating Current, AC, grid (42) via a power transformer (41).

7. The method of claim 6, wherein the MMC (1) comprises at least two, a first and a second, arms (2), each comprising an inductor (4) in series with the converter cells (3), wherein the inductor of the first arm and the inductor of the second arm are coupled by sharing a common core.

8. The method of any claim 6-7, wherein the MMC (1) has three arms (2) in a delta configuration.

9. The method of any claim 6-8, wherein the MMC (1) is a Voltage-Source Converter, VSC.

10. The method of any claim 6-9, wherein the MMC (1) is a Static

Synchronous Compensator, STATCOM.

11. A computer program product (12) comprising computer-executable components (13) for causing a control system (10) to perform the method of any preceding claim when the computer-executable components are run on processing circuitry (11) comprised in the control system.

12. A power converter (1) comprising a control system (10), the control system comprising: processing circuitry (11); and data storage (12) storing instructions (13) executable by said processing circuitry whereby said control system is operative to: operate the converter at steady state wherein the grid has a grid voltage (ugrid) which is applied to the converter via the transformer which is at most 1.1 per unit, p.u.; detect a Transient Overvoltage, TOV, of at least 1.5 p.u. in the grid voltage; and in response to the detected TOV, over-modulate the converter voltage (USTATCOM) generated by the converter and applied to the grid via the transformer during the TOV by introducing a plurality of harmonic voltages therein.

Description:
STATCOM CONTROL DURING TRANSIENT OVERVOLTAGE TECHNICAL FIELD

The present disclosure relates to a method and device for controlling a Modular Multilevel Converter (MMC) during a Transient Overvoltage (TOV).

BACKGROUND

A power electronic (PE) converter, e.g. a Modular Multilevel Converter (MMC), may be used in many different power application such as Static Synchronous Compensator (STATCOM), Flexible Alternating Current

Transmission Systems (FACTS) and High-Voltage Direct Current (HVDC). Each converter cell of an MMC, comprises semiconductor switches such as Insulated-Gate Bipolar Transistor (IGBT), Reverse Conducting IGBT (RC- IGBT), Bi-Mode Insulated Gate Transistor (BiGT), Integrated Gate- Commutated Thyristor (IGCT), Gate Turn-Off Thyristor (GTO) and Metal- Oxide-Semiconductor Field-Effect Transistor (MOSFET).

To meet high transient over voltage (TOV) requirement, actual STATCOM design requires additional number of converter cells per converter arm, arm inductance and cell capacitance, which has a significant impact on the total cost of the STATCOM. Increase in number of cells and arm inductance can be up to about ioo% and 200%, respectively, to meet a TOV requirement of 2 p.u.

In the literature, zero sequence harmonic reference injection has been addressed for multiple purposes, such as to reduce the size of the capacitance, to reduce the number of cells to meet high TOV requirement (see

WO 2015/188877) , to balance energies of cell capacitors during unbalanced grid conditions (see WO 2010/145706) , and to extend the range of linear modulation from unity to 1.15 p.u. (see D. Grahame Holmes and Thomas A. Lipo,“Pulse Width Modulation for Power Converters - PRINCIPLES AND PRACTICE”, IEEE PRESS, 2003, ch. 5, sec. 5.3.1, pp. 226-230). SUMMARY

According to an aspect of the present invention, there is provided a method of controlling a power converter, the converter being connected to an AC grid via a power transformer, wherein by means of the converter a current is injected into the grid via said transformer. The method comprises operating the converter at steady state wherein the grid has a grid voltage which is applied to the converter via the transformer which is at most 1.1 p.u. The method also comprises detecting a TOV of at least 1.5 p.u. in the grid voltage. The method also comprises, in response to the detected TOV, over- modulating the converter voltage generated by the converter and applied to the grid via the transformer during the TOV by introducing a plurality of harmonic voltages therein.

According to another aspect of the present invention, there is provided a computer program product comprising computer-executable components for causing a control system to perform an embodiment of the method of the present disclosure when the computer-executable components are run on processing circuitry comprised in the control system.

According to another aspect of the present invention, there is provided a power converter comprising a control system, the control system comprising processing circuitry, and data storage storing instructions executable by said processing circuitry whereby said control system is operative to operate the converter at steady state wherein the grid has a grid voltage which is applied to the converter via the transformer which is at most 1.1 per unit, p.u., detect a TOV of at least 1.5 p.u. in the grid voltage, and, in response to the detected TOV, over-modulate the converter voltage generated by the converter and applied to the grid via the transformer during the TOV by introducing a plurality of harmonic voltages therein.

By means of the over-modulation, the TOV may be handled with a lower rating of the power transformer, e.g. with fewer converter cells per MMC arm if the power converter is an MMC, thereby reducing cost thereof. It is to be noted that any feature of any of the aspects may be applied to any other aspect, wherever appropriate. Likewise, any advantage of any of the aspects may apply to any of the other aspects. Other objectives, features and advantages of the enclosed embodiments will be apparent from the following detailed disclosure, from the attached dependent claims as well as from the drawings.

Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a/an/the element, apparatus, component, means, step, etc." are to be interpreted openly as referring to at least one instance of the element, apparatus, component, means, step, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated. The use of “first”,“second” etc. for different features/components of the present disclosure are only intended to distinguish the features/components from other similar features/components and not to impart any order or hierarchy to the features/components.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will be described, by way of example, with reference to the accompanying drawings, in which:

Fig la is a schematic diagram of an embodiment of an MMC STATCOM in delta configuration, in accordance with the present invention.

Fig lb is a schematic circuit diagram of an embodiment of a full-bridge converter cell, in accordance with the present invention.

Fig 2 is an example VI diagram of a STATCOM for a 2.0 p.u. TOV

requirement, in accordance with the present invention.

Fig 3a is a schematic graph illustrating how many converter cells of an example MMC STATCOM are needed to meet the 2.0 p.u. TOV requirement at the different operating points A (solid line), B (dashed line) and C (dotted line) in the VI diagram of figure 2, in accordance with the present invention.

Fig 3b a schematic graph illustrating how many converter cells of an example MMC STATCOM are needed to meet the 2.0 p.u. TOV requirement at the different operating points A (solid line), B (dashed line) and C (dotted line) in the VI diagram of figure 2 with injection of third harmonic, in accordance with the present invention.

Fig 4 is a schematic diagram of a single-phase equivalent circuit of an example three-phase delta connected MMC STATCOM at fundamental frequency for positive or negative sequence components, in accordance with the present invention.

Fig 5 schematically illustrates fundamental phasor diagrams for the circuit of figure 4: (a) under capacitive operation; and (b) under inductive operation.

Fig 6 is a schematic diagram of a single-phase equivalent circuit of an example three-phase delta connected MMC STATCOM at third harmonic frequency, in accordance with the present invention.

Fig 7 is a schematic diagram of a single-phase equivalent circuit of an example three-phase delta connected MMC STATCOM during over modulation operation, in accordance with the present invention.

Fig 8a-b is a schematic graph for a TOV operation case of the example STATCOM, in accordance with the present invention, during over

modulation where PCC voltage (U pcc ) = 2.0 p.u., arm current (L) = 1 p.u., transformer inductcanse (Ltr) = 10%, DC link capacitance (Cdc) = 1%, and arm inductance (L r ) = 20%. Fig 8a showing: U pcc (dashed line), L (dotted line), and STATCOM output voltage (solid line). Fig 8b showing DC link capacitor voltage of the STATCOM.

Fig 9a is a schematic graph illustrating how the peak value of the arm current (Ipeak, solid line) varies with the arm inductance (Lr) during over

modulation of the example MMCSTATCOM, in accordance with the present invention. A limit for the Ipeak is set at l.i p.u. (dashed line), implying that the minimum Lr needed is 0.25 p.u..

Fig 9b is a schematic graph illustrating how many converter cells are needed depending on the arm inductance (Lr) during over modulation at the operating point A (fig 2) for the TOV requirement of 2.0 p.u.

Fig 10a is a schematic graph illustrating how many converter cells are needed depending on the arm inductance (Lr) at the operating point A (fig 2) for the TOV requirement of 2.0 p.u.: without any measures taken (solid line), with injection of third harmonics and use of inter-phase coupling of reactors (dashed line), and with over-modulation (dotted line, same as in figure 9b).

Fig 10b is a schematic graph illustrating how many converter cells are needed depending on the arm inductance (Lr) at any operating point in figure fig 2 for the TOV requirement of 2.0 p.u.: without any measures taken (solid line, cf. figure 3a where it can be seen that operation at point B requires more cells than at point A for very high inductances), with injection of third harmonics and use of inter-phase coupling of reactors (dashed line, same as in figure 10a), and with over-modulation (dotted line, same as in figures 9b and 10a).

Fig 11 is a schematic block diagram of an embodiment of a control system of an MMC, in accordance with the present invention.

Fig 12 is a schematic flow chart of an embodiment of the method of the present invention.

DETAILED DESCRIPTION

Embodiments will now be described more fully hereinafter with reference to the accompanying drawings, in which certain embodiments are shown.

However, other embodiments in many different forms are possible within the scope of the present disclosure. Rather, the following embodiments are provided by way of example so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. Like numbers refer to like elements throughout the description.

The invention is discussed herein with reference to an example MMC

Voltage-Source Converter (VSC) STATCOM in three-phase delta

configuration, which is preferred in some embodiments of the invention, but the invention may also be useful for other types of MMC in accordance with other embodiments of the invention, e.g. an MMC in wye (Y, also called star) or double-Y (double star) configuration, or for power converters in general, e.g. two-level converters and Neutral-Point Clamped (NPC) converters.

The Transient Overvoltage (TOV) requirement used herein as an example is 2.o per unit (p.u.), but embodiments of the invention may be useful also for any other TOV requirement, e.g. within the range of 1.8-2.1 p.u.

Figure ta illustrates an example three-phase, preferably High Voltage (HV), STATCOM MMC 1 in delta (D) configuration, the HV referring to the grid voltage U grid of the grid in which the MMC 1 is connected. The MMC comprises three converter arms 2, each connected between two of the three phases a, b and c. Arm and phase voltages u and currents i are indicated in the figure. Each arm 2 comprises a plurality of series connected (also called cascaded or chain-linked) converter cells 3. As indicated by the middle dashed cell 3, any number of cells 3 may be included in each arm, and it is the reduction of this number of cells needed which is conducive to reducing costs in accordance with the present disclosure. Each arm also comprises an inductor 4, typically a reactor, which creates an inductance L in the arm, in series with the converter cells 3. The inductors 4 are schematically illustrated as a single reactor but each inductor 4 may comprise an inductor

arrangement comprising any number of inductor units, in series and/or parallel, on either or both sides of the series connected cells 3 in the arm. The MMC 1 also comprises a control system 10, as schematically illustrated in figures ta. Figure lb illustrates an embodiment of a converter cell 3. The cell comprises an energy storage 5, e.g. in the form of a capacitor arrangement, comprising at least one capacitor. The cell may be a full-bridge (bi-polar, also called H- bridge) cell having four semiconductor switches S, herein conventionally named Si, S2, S3 and S4 forming a full-bridge configuration with the energy storage. Alternatively, any other configuration of the cell 3 may be used, e.g. a half-bridge (monopolar) configuration where only two semiconductor switches S are needed, but use of a bi-polar cell is preferred, especially in a full-bridge configuration. Embodiments of the present invention may be used for any type of semiconductor switches S, e.g. based on silicon (Si), silicon carbide (SiC) or gallium nitrid (GaN), or other semiconducting material. For instance, each of the switches S may comprise an Insulated-Gate Bipolar Transistor (IGBT), a Reverse Conducting IGBT (RC-IGBT), a Bi-Mode Insulated Gate Transistor (BIGT), an Integrated Gate-Commutated Thyristor (IGCT), a Gate Turn-Off Thyristor (GTO), and/or a Metal-Oxide- Semiconductor Field-Effect Transistor (MOSFET), or any other suitable switching element.

Herein, measures for reducing number of cells 3 in each arm 2 which are needed to handle relatively high TOV, e.g. 2.0 p.u., are discussed, including:

1. Injection of third harmonic voltage (e.g. of 150 Hz, for a fundamental frequency of 50 Hz).

2. Inter-phase coupling of the inductors 4 via a communal core.

3. Over-modulation.

For some STATCOM application, it is required that the STATCOM 1 shall remain connected and in operation for moderate (up to 1.4 p.u.) and high (up to 2.1 p.u.) primary Transient Over Voltages (TOV) at its Point of Common Coupling (PCC) with the with the Alternating Current (AC) grid, e.g. HV. This requirement has a significant impact on the total cost of STATCOM as it requires additional number of series connected cells 3 per arm 2, larger phase reactor 4 and bigger DC-cell capacitors 5. Use of 3 rd harmonic voltage injection with coupled reactors 4 is known for reducing the additional number of cells, see e.g. WO 2015/188877. Coupled reactors provide impedance only to zero sequence components, and thus minimizes the amplitude of the resulting 3 rd harmonic zero sequence circulating current for a particular 3 rd harmonic injection level and hence the peak value of the arm current.

For instance, a sinusoidal wave of more than 1 kV but less than 4/p kV may be achieved from a 1 kV full bridge (bi-polar) cell by adding odd frequency harmonics with specific magnitude. By over-modulation a maximum increase in the fundamental component sinusoidal wave output of 27% may be achieved.

Figure 2 illustrates a voltage-current (VI) diagram of an example STATCOM 1, to be design for a 2.0 p.u. TOV requirement. As shown, operating points A, B, and C correspond to: A - TOV operating point (inductive), B - highest steady state capacitive operating point, and C - highest steady state inductive operating point, and these three operating points in the VI diagram are typically the most critical operating points and thus dominate for the design of the STATCOM.

As the voltage difference between operating point A and operating point B or C is significantly higher (almost double in the example considered), operating point A dominates for the design of the STATCOM. As shown in figure 3a, the STATCOM design is dominated by operating point A for the entire range of arm inductance Lr, except for extremely high arm inductances where point B dominates. Thus, the number of cells required at point A is almost always higher than the number of cells required at the other two critical operating points B and C in the VI diagram of figure 2. For this example, the increase in number of cells needed depending on arm inductance in order to meet the 2.0 p.u. TOV requirement, instead of the 1.1 p.u. steady-state continuous requirement of point C, as illustrated in figure 3a, is given in Table 1 (where the cost of added number of cells has been weighed against the cost for increased arm inductance).

requirement.

In general, a TOV is of very short duration (e.g. 0.08 s) and the harmonics generated by the STATCOM 1 are guaranteed based on average of long measurement intervals, e.g. 3 min or 10 min, or even several weeks, whatever harmonics generated by STATCOM for short duration (TOV operating point) should fade away by the average and will normally not impact the overall harmonic spectrum of the STATCOM.

In the document: D. Grahame Holmes and Thomas A. Lipo,“Pulse Width Modulation for Power Converters - PRINCIPLES AND PRACTICE”, IEEE PRESS, 2003, ch. 5, sec. 5.3.1, pp. 226-230, it is shown that the range of linear modulation can be extended by a factor of 1.15 by optimal 3 rd harmonic injection and can be extended further to a limiting value of 1.273 (4/p) by entering into the nonlinear region of over modulation. A disadvantage with operating in over modulation is that the STATCOM will generate all odd harmonic components, i.e. 3, 5, 7, 9, 11 etc. harmonics, and inject the same into the grid, which can be a serious concern to meet grid code requirement. But, as stated above it will not be a problem if operation of the STATCOM in over modulation is of very short duration corresponding with the TOV. By operating the STATCOM in square-mode operation (over-modulation), a further theoretical reduction of (1.273-1.15)71.15*100% = 10.69% in peak DC- voltage is possible as compared to 3 rd harmonic injection alone with coupled reactor.

Therefore, operating the STATCOM in over-modulation at operating point A, and (optionally) operating the STATCOM with common mode harmonic injection (3 rd harmonic zero sequence) at operating points B and C may be advantageous to reduce the number of additional cells 3 needed, and to reduce the increase in arm reactor needed, for high TOV requirements (up to 2.1 p.u.), which may be better than 3 rd harmonic injection with coupled reactor only. To meet constraint on the peak value of the arm current, arm inductance may have to be increased (15-30%) during over-modulation operation. At a higher values of arm inductance, the number of cells required at operating point B may become comparable with the number of cells required at operating point A, especially when the relative distance between operating points A and C in the VI diagram is shorter. For those designs, 3 rd harmonic injection at operating points B and C may be especially beneficial.

As shown in figure 3b, 3 rd harmonic injection may help in reducing the number of additional cells 3 and increase in arm inductance L needed to meet a TOV requirement of 2.0 p.u., but not to a great extent. Figure 3b shows the number of cells needed at the different critical operating points A (solid line),

B (dashed line) and C (dotted line) from the VI diagram (fig 2) to meet a 2.0 p.u. TOV requirement with 3 rd harmonic injection. With 3 rd harmonic injection, the increased number of cells needed may be reduced from 70% to 57% as shown in Table 2.

Table 2: Number of cells and arm inductance needed to meet a 2.0 p.u. TOV requirement when 3 rd harmonic voltage injection is used.

Thus, to meet high TOV requirements, the actual STATCOM design requires an additional number of series connected cells 3 per arm 2, increased arm inductance L and cell capacitance C, which has a significant impact on the total cost of the STATCOM l. 3 rd harmonic injection can be useful in reducing the additional number of cells needed and the increase in arm inductance to meet high TOV requirements, but not to a great extent, as shown in the Table 2. This is mostly because the voltage difference between the TOV operating point (i.e. point A) and highest steady state capacitive or inductive operating point (i.e. point B or C) is significantly higher. As a consequence, the TOV operating point A in the VI diagram dominates for the design of the STATCOM.

One aspect of STATCOM designs, dominated by the TOV operating point A, is that since the duration of the TOV is very short, even if the designed STATCOM injects significant amounts of lower order harmonics into the grid during a transient over voltage condition, the overall harmonic spectrum of the STATCOM will not be much affected. It has thus now been realized that, in addition with 3 rd harmonic injection, it is it possible to add other harmonics in the modulation signal during TOV conditions in order to further reduce the Direct Current (DC) -link requirement at the TOV operating point A. The harmonics thus injected may, depending on how much harmonics, make the output voltage of the MMC l more and more like a square wave, rather than a sine wave, e.g. with a PCC (input) TOV of 2.0 p.u. When the STATCOM 1 can be operated in square-wave operation during high TOV condition, the number of cells needed to meet the high TOV may be reduced significantly as compared to 3 rd harmonic injection alone.

When analysing the possible STATCOM design, the STATCOM is represented by its single phase Thevenin’s equivalent i.e. an ideal voltage source at fundamental frequency with arm inductance in series. Switching frequency components of converter AC output voltage are not considered since we are interested in lower order harmonics (e.g. 3 rd , 5 th , 7 th etc.) of the sum cell De link voltage generated by the converter arm 2.

Since the converter arms 2 are connected in delta configuration, positive or negative sequence equivalent circuits of the STATCOM 1 will differ from it’s zero sequence counterpart. When positive or negative sequence currents are involved in power exchange between the STATCOM and the grid, zero sequence current remains trapped in the delta loop.

Equivalent circuits of the STATCOM at fundamental frequency (figure 4) and at 3 rd harmonic frequency (figure 6), respectively, are developed and the relationship between voltages and currents is established by applying

Kirchhoff s current law (KCL) and Kirchhoff s voltage law (KVL). In this analysis, load convention is used for instantaneous voltage and current polarity of the STATCOM. In deriving the equivalent circuit of the STATCOM, resistance of the arm inductance and winding resistance of the transformer is not considered and the transformer 41 is represented by its leakage

inductance L tr . The positive or negative sequence equivalent circuit at fundamental frequency of the STATCOM is shown in the figure 4 where the primary voltage u pr im is the voltage on the primary side of the transformer 41 and is the same as the grid voltage u gr id, and the secondary voltage u sec is the voltage on the secondary side of the transformer 41. In some embodiments, the grid voltage u g rid/u P rim is within the range of 50-250 kV, with typical values including 63, 110 and 230 kV. In some embodiments, the secondary voltage U sec is within the range of 10-50 kV, with typical values including 11, 15, 25, 33 and 36 kV. For example, the voltage u g rid/u P rim of the grid 42 may be 230 kV and a step down transformer 41 of 230/33 kV may be used to connect the MMC, e.g. STATCOM, to the grid, whereby the secondary voltage Usec is 33 kV.

When performing circuit analysis where the circuit has a transformer 41, the entire circuit must be either referred to the primary or the secondary side of the transformer. For example, reference is made to the entire circuit on the secondary side, then all the circuit components connected to the primary side of the transformer need to be transformed to their equivalent values on the secondary side and represented. The single line diagram of figure 4 may be related to the secondary side of the transformer, where u S ec and u P rim are the voltages referred on the secondary side (LV side) and primary side (HV side) of the transformer, respectively. The turns ratio of the transformer 41 is Nt = u Prim /u sec using the real primary voltage before referring it to the secondary side, implying that the new primary voltage after referring to the secondary side is llprim (new) = llprim (real)/N T .

Applying KVL in the circuit shown in the figure 4 (using the new u P rim), the following equations are obtained:

Where: ki=i represents capacitive operation, whereas ki=-i represents inductive operation, iq = iqzO (Reference phasor), (6)

For capacitive operation, k t = 1: u sec = i ·^ · 0 + w G / 1 7 t: = (iq— w! G / 1 )z 0 (ΐo)

prim = U 0 + w(ί G + L^^Z I = [iq— w( G + t / zO (12) (13)

For inductive operation, k t = -1: usec = u 0 + w! G / 1 0 = (iq + w! G / 1 )z 0 (14)

(17)

Therefore, for given voltage and current conventions, the general expression for voltage at secondary and primary side of the transformer 41 is given by:

U sec 0 kiOjL r I-^)/-0 (18)

Since, in this analysis, the STATCOM 1 is represented by an ideal voltage source (lossless), and also the resistance of the transformer 41 and arm inductor 4 are not considered, Ui,u se c and u P rim will be in same phase. i ( Vsec F kiCoL- f l-t) (20)

The primary side voltage U prim of the step-down transformer 41 is often referred to as the PCC voltage. Therefore, the STATCOM reference voltage U can be expressed as follows: (22) From equation 22, it is evident that under capacitive operation [figure 5(a)], the STATCOM 1 has to generate a higher voltage (u se c) than the PCC voltage (uprim), whereas STATCOM voltage is lower than the PCC voltage under inductive operation [figure 5(b)]. Figure 5 shows fundamental phasor diagrams: (a) under capacitive operation, and (b) under inductive operation. During capacitive operation, Ui>u S ec>u P rim, and during inductive operation,

Ui<Usec<Uprim·

The single phase zero sequence equivalent circuit at 3 rd harmonic frequency (w 3 =3 ΰ ) of the three-phase delta connected chain link STATCOM 1 is shown in figure 6. In general, this equivalent circuit holds true for zero sequence harmonic components.

Applying KVL in the circuit shown in the figure 6, the following equations are obtained:

(31)

The equivalent circuit used for the mathematical analysis of over-modulation is shown in figure 7 where the arm voltage USTATCOM=U I +U 3 +U5+U 7 +... for each of the odd harmonics, wherein: i6

The grid 42 is represented by it’s ideal Thevenin equivalent voltage source at fundamental frequency. Background harmonics and grid

impedance is ignored in this analysis to emulate the worst case scenario assuming grid impedance to be inductive at harmonic frequencies. Special attention has to be given when grid becomes capacitive, cancelling the arm reactor inductance, creating a resonance for the lower order harmonics.

If we consider the STATCOM output voltage USTATCOM to be a perfect square wave, then it can be represented as summation of all odd frequency harmonic sinusoids by Fourier series. Depending upon the frequency number, frequency harmonic components can be positive sequence, negative sequence and zero sequence (triplen harmonics). As zero sequence

harmonics are co-phasal, these will not come out from the delta

configuration, which is not considered in the time domain solution for arm current and DC-link voltage of the STATCOM.

For a given operating point (TOV operating point) and system parameters i.e. for given u P rim, L ,L tr , and Cdc and a particular value of arm inductance (L r ), it is possible to calculate the fundamental voltage reference for STATCOM as given by:

Considering ideal over modulation, i.e. stiff DC-link voltage, the required DC link voltage is given by:

In this analysis, DC-link voltage Udc ripple due to harmonic components in the arm current L is considered and corresponding waveforms for a given operating point is shown in the figures 8a and 8b, where the STATCOM output voltage USTATCOM is close to a square wave (solid line) due to over modulation, and the magnitude of the DC-link voltage Udc (figure 8b) is reduced as a result. If the STATCOM l is operated in over-modulation at operating point A, the peak current I pe ak and number of cells needed depending on the arm inductance Lr are shown in figure 9a. It can be seen that an arm inductance Lr of at least 0.25 p.u. is needed to keep the peak current I pe ak below the STATCOM over current limit of 1.1 p.u.

If the MMC has more than one arm, then the total converter voltage applied to the grid is a combination of the respective arm voltages.

Figure 9b shows the maximum number of cells 3 per arm 2 needed under over-modulation for a TOV requirement of 2.0 p.u. at operating point A. It can be seen that a maximum of only 20 cells 3 are needed when the inductance Lr is at least 0.25 p.u. (as required in accordance with figure 9a) thanks to the over-modulation used.

As is shown in figure 10a, operating the STATCOM in over-modulation (dotted line) at operating point A for a TOV requirement of 2.0 p.u. can significantly reduce the number of cells needed. As previously mentioned, the considered STATCOM design is dominated by operation point A, the TOV operating point. Thus, operating the STATCOM in over-modulation at the TOV operating point, the number of cells needed can be reduced significantly also when looking at all operating points, as shown in the Figure 10b.

It can be concluded that operating the STATCOM 1 in over-modulation may play an important role in reducing the number of cells needed if the

STATCOM design is dominated by the TOV operating point A. Thus, operating the STATCOM in over-modulation may give higher reduction of the number of cells needed compared with if only 3 rd harmonic injection is used for STATACOM designs dominated by the TOV operating point, as shown in Table 3. Also, the increase in arm inductance needed may be reduced when using over-modulation.

Table 3: Number of cells and arm inductance needed to meet a 2.0 p.u. TOV requirement.

Figure 11 schematically illustrates an embodiment of the control system 10 for or comprised in the MMC 1 of the present disclosure. The control system 10 comprises processing circuitry 11 e.g. a central processing unit (CPU). The processing circuitry 11 may comprise one or a plurality of processing units in the form of microprocessor(s). However, other suitable devices with computing capabilities could be comprised in the processing circuitry 11, e.g. an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or a complex programmable logic device (CPLD). The processing circuitry 11 is configured to run one or several computer program(s) or software (SW) 13 stored in a data storage 12 of one or several storage unit(s) e.g. a memory. The storage unit 12 is regarded as a computer readable means as discussed herein and may e.g. be in the form of a Random Access Memory (RAM), a Flash memory or other solid state memory, or a hard disk, or be a combination thereof. The processing circuitry 11 may also be configured to store data in the storage 12, as needed. The control system 10 may also comprise a communication interface for internal communication within the system and/or external communication with e.g. the other parts of the MMC, e.g. for sending firing pulses to the switches S of the converter cells 3. The control system may be centralized or distributed, or (typically) a combination thereof with a central part, e.g. located in a control room, and a local part, co-located with the MMC 1, or each phase leg 2, e.g. comprising local controllers with each of the cells 3 of the phase leg. In some embodiments, the control system 10 may be arranged to perform

embodiments of the method of the present disclosure.

Figure 12 is a flow chart illustrating some embodiments of the method of the invention. The method is for controlling a power converter 1, the converter 1 being connected to an AC grid 42 via a power transformer 41. By means of the converter 1, a current is injected into the grid 42 via said transformer 41. The method comprises operating Mi the converter at steady state wherein the grid has a grid voltage u grid which is applied to the converter 1 via the transformer 41 which is at most 1.1 per unit, p.u.. The method also comprises detecting M2 a TOV of at least 1.5 p.u. in the grid voltage. The method also comprises, in response to the detected M2 TOV, over-modulating M3 the converter voltage USTATCOM generated by the converter and applied to the grid via the transformer during the TOV by introducing a plurality of harmonic voltages therein.

In some embodiments of the present invention, the TOV is within the range of from 1.5 to 2.5 p.u., such as from 1.8 to 2.1 or 2.0 p.u.

In some embodiments of the present invention, the operating Ml at steady state comprises, introducing a third order harmonic zero sequence voltage u 3 in the converter.

In some embodiments of the present invention, the plurality of harmonic voltages comprise at least one of 3 rd , 5 th and 7 th order harmonic voltages.

In some embodiments of the present invention, the power converter 1 comprises a two-level converter or a Neutral Point Clamped, NPC, converter.

In some embodiments of the present invention, the converter 1 comprises an arm 2 of an MMC, the arm having a plurality of series connected converter cells 3, each cell comprising an energy storage 5 and a plurality of

semiconductor switches S, the arm being connected to an AC grid 42 via a power transformer 41. In some embodiments, the MMC 1 comprises at least two, a first and a second, arms 2, each comprising an inductor 4 in series with the converter cells 3, wherein the inductor of the first arm and the inductor of the second arm are coupled by sharing a common core. In some

embodiments, the MMC 1 has three arms 2 in a delta configuration. In some embodiments, the MMC 1 is a Voltage-Source Converter (VSC). In some embodiments, the MMC 1 is a STATCOM.

Embodiments of the present invention may be conveniently implemented using one or more conventional general purpose or specialized digital computer, computing device, machine, or microprocessor, including one or more processors 11, memory and/or computer readable storage media 12 programmed according to the teachings of the present disclosure.

Appropriate software 13 coding can readily be prepared by skilled

programmers based on the teachings of the present disclosure, as will be apparent to those skilled in the software art.

In some embodiments, the present invention includes a computer program product 12 which is a non-transitory storage medium or computer readable medium (media) having instructions 13 stored thereon/in, in the form of computer-executable components or SW, which can be used to program a computer to perform any of the methods/processes of the present invention. Examples of the storage medium can include, but is not limited to, any type of disk including floppy disks, optical discs, DVD, CD-ROMs, microdrive, and magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, DRAMs,

VRAMs, flash memory devices, magnetic or optical cards, nanosystems (including molecular memory ICs), or any type of media or device suitable for storing instructions and/or data.

The present disclosure has mainly been described above with reference to a few embodiments. However, as is readily appreciated by a person skilled in the art, other embodiments than the ones disclosed above are equally possible within the scope of the present disclosure, as defined by the appended claims.