Multi-terminal high-voltage direct current control method and system

Abstract

A method for controlling or operating a high voltage direct current (HVDC) converter within a multi-terminal HVDC system, a multi-terminal HVDC system, a controller, and computer software implementing such control. The output of the HVDC converters is controlled by providing a respective or converter-specific DC voltage reference for each HVDC converter. A feedback signal is determined for each HVDC converter, and the converter-specific feedback signal includes a modification to the DC voltage reference of the respective converter. Determining the converter-specific feedback signal includes analyzing a terminal characteristic of each converter and determining an indicator indicative of a balance loss margin, or modeling the terminal characteristic of each converter as an equivalent circuit based on or representing a response of the HVDC converter to its voltage reference modification in a given operating state. The HVDC converter terminal characteristics may include impedance, voltage droop, power, branch current, node voltage, and the like.

Description

[0001] The present invention relates to the field of power transmission, and more particularly to a method of controlling a HVDC converter in a multi-terminal HVDC system and an improvement of the multi-terminal HVDC system for achieving such control. Background Art

[0002] Large-scale deployment of offshore wind energy has been identified as a fundamental driver of the UK government’s net zero strategy for addressing climate change[1]. In the overall network design of the UK system to 2030[2], a series of multi-terminal high-voltage direct current (MT-HVDC) transmission systems are considered an efficient and economical way to deliver large amounts of offshore power to the existing onshore grid[3]. These wider direct current (DC) networks will emerge in a phased manner and coincide with the unprecedented growth in global HVDC demand and the need for transmission system operators (TSOs) to describe the phased growth and control paradigm of these DC networks. Against this backdrop, the need for multi-vendor (MV) MT-HVDC solutions is becoming increasingly likely.

[0003] In the UK, the Caithness Moray-Shetland Project (CMS)[4] was the first example of a multi-terminal voltage source converter (VSC) HVDC system outside of China, although this was delivered by a single supplier. In some pilot projects involving multiple suppliers, suppliers may need to disclose information related to the control design and / or modify their designs to make them compatible with other converters. This "open" approach is impractical in the UK and other international markets because this information is often proprietary, confidential and / or unknowable.

[0004] Therefore, there is a need for a practical and vendor-independent multi-vendor multi-terminal (MVMT) HVDC control approach that does not require disclosure or otherwise knowledge of the individual converter designs. The main challenge of MVMT control interoperability is how to ensure that HVDC converters from different vendor solutions can work together and maintain stability in a coupled DC network without sharing details of their internal designs, starting from the planning and procurement phases [5] and then supported during the detailed design testing, operation and refurbishment / retrofit phases of the MVMT-HVDC system asset lifecycle.

[0005] A challenge in all MT-HVDC control is that, unlike alternating current (AC) systems, there are no common network parameters (such as AC frequency) to inherently align behavior within the DC network. Consequently, many approaches employ single-point network control, referencing a single HVDC converter and its control of the DC system, or introduce / derive general common variables that all converters can reference. Both approaches, while feasible, require a deep understanding of the design and behavior of the HVDC converters, reference the inherent domain of the control structure, and, in practice, may create undesirable dependencies on the resilience of the control system or its communications.

[0006] By introducing constant power terminals driven dynamically by offshore wind power or onshore TSO dispatch, the MTDC system becomes a nonlinear system. In line with Lyapunov's first method [6], the stability assessment of nonlinear systems consists of two consecutive components, namely the existence of equilibrium and the adequacy of damping. Although the stability of DC systems with respect to these two aspects has been extensively studied, to date, there is no comprehensive solution that can ensure both aspects without a detailed understanding of the internal control of the participating converters. Therefore, it is currently impossible to fully support the industrial application of MVMT HVDC.

[0007] Therefore, an object of at least one aspect of the present invention is to provide vendor-independent MT-HVDC system control, which may enable widespread adoption of MVMT HVDC systems. The present invention may be embodied in a method of controlling or operating a plurality of HVDC converters, a controller for a multi-terminal HVDC system, a multi-terminal HVDC system, and a corresponding computer program product.

[0008] Further aims and objectives of the invention will become apparent from reading the following description. Summary of the Invention

[0009] According to a first aspect of the present invention, there is provided a method for controlling (or operating) a plurality of HVDC converters in a multi-terminal HVDC system, the method comprising:

[0010] controlling the output of a plurality of HVDC converters by providing a respective (or converter-specific) DC voltage reference to each HVDC converter;

[0011] determining a respective feedback signal for each of the plurality of HVDC converters, wherein the (converter-specific) feedback signal comprises a modification of a DC voltage reference of the respective converter;

[0012] Therein, determining the corresponding (converter-specific) feedback signal includes analyzing terminal characteristics of each converter and determining an indicator indicative of a balancing loss margin.

[0013] This approach may involve and imply the definition of equivalent impedances of the converter and network, as well as the control effects at the fundamental frequency and other relevant control frequencies, taking into account emergency analysis.HVDC converter terminal characteristics may include impedance, voltage droop, power, branch currents and node voltages.

[0014] Preferably, the indicator quantifies the interaction between voltage droops between a plurality of HVDC converters. Optionally, the indicator indicates a stability margin for DC power transmission.

[0015] Preferably, the modification to the DC voltage reference is determined to optimize steady-state operation (or stability) of the multi-terminal HVDC system.

[0016] Preferably, the method includes modeling the terminal characteristics of each converter as an equivalent circuit, which can be represented as a Norton equivalent circuit or a Thevenin equivalent circuit based on or representing the effect of the HVDC converter in response to a modification of its voltage reference in a given operating state. This allows the control method to be implemented without detailed information about the converter.

[0017] Preferably, the method comprises determining the HVDC system characteristics by constructing an extended impedance matrix or an extended conductance matrix of the system.

[0018] Preferably, the method comprises determining a DC voltage droop characteristic of each HVDC converter.

[0019] Preferably, the method includes determining an initial value of the balance. Preferably, the method includes normalizing the indicator for a loss of balance. Preferably, the balance can be identified based on the complete and unexpected state of the HVDC network, such that the state may not represent an optimized position for a given operating state, but rather may represent a state optimized for safe operation in response to changes and / or unexpected events in its operation.

[0020] Preferably, the method includes determining branch currents and node voltages within the system.The branch currents and node voltages may be received at a central controller configured to implement the method.

[0021] Preferably, the control method is applicable to a range of different HVDC multi-terminal topologies, including symmetrical monopole, full bipole, and rigid bipole (without ground loop capability). Thus, the method for achieving HVDC converter characterization can be applied individually to each polar converter terminal, and further implies equivalent measurement and characterization of the neutral current terminal.

[0022] Preferably, the multi-terminal HVDC system is a multi-supplier multi-terminal HVDC system. However, this is not essential and the inventive concept may alternatively be applied to a single-supplier multi-terminal system.

[0023] A multi-terminal HVDC system may be included in an HVDC transmission system. An HVDC converter may be included in one or more interfaces between one or more HVDC power lines and one or more AC power generation systems and / or one or more AC power grids. The one or more AC power generation systems may include one or more offshore wind turbines or wind farms. The one or more AC power grids may include one or more onshore AC power grids.

[0024] According to a second aspect of the present invention, there is provided a method for controlling (or operating) a plurality of HVDC converters in a multi-terminal HVDC system, the method comprising:

[0025] controlling the output of a plurality of HVDC converters by providing a respective (or converter-specific) DC voltage reference to each HVDC converter;

[0026] determining a respective feedback signal for each of a plurality of HVDC converters, wherein the (converter-specific) feedback signal comprises a modification of a DC voltage reference of said respective converter;

[0027] Therein, determining the corresponding (converter specific) feedback signals comprises modeling the terminal characteristics of each converter as an equivalent circuit based on or representing the response of the HVDC converter to a modification of its voltage reference in a given operating state.

[0028] Optionally, determining the corresponding (converter-specific) feedback signal comprises analyzing terminal characteristics of each converter and determining an indicator indicative of a balancing loss margin.

[0029] Embodiments of the second aspect of the present invention may include features of, or features corresponding to, preferred or optional features of the first aspect of the present invention.

[0030] According to a third aspect of the present invention, there is provided a controller for a multi-terminal HVDC system, the controller being adapted or configured to perform the method of the first aspect.

[0031] Embodiments of the third aspect of the invention may include features of, or features corresponding to, preferred or optional features of the first or second aspect of the invention, and vice versa.

[0032] According to a fourth aspect of the present invention, there is provided a multi-terminal HVDC system comprising a plurality of HVDC converters and the controller according to the second aspect.

[0033] Preferably, the system comprises at least one HVDC power line, at least one HVDC converter between the at least one HVDC power line and the offshore wind farm, and at least one HVDC converter between the at least one HVDC power line and the onshore AC grid.

[0034] The multi-terminal HVDC transmission system may be a multi-supplier multi-terminal HVDC system.

[0035] The at least one HVDC converter may comprise at least one voltage source converter. Preferably, the at least one HVDC converter comprises a node-type multi-level converter.

[0036] Embodiments of the fourth aspect of the invention may include features of, or features corresponding to, preferred or optional features of the first, second or third aspect of the invention, and vice versa.

[0037] According to a fifth aspect of the present invention, there is provided a computer program comprising instructions which, when executed by a computer, cause the computer to perform the method of the first or second aspect.

[0038] According to a sixth aspect of the present invention there is provided a computer readable medium or data carrier comprising the computer program of the fifth aspect.

[0039] According to a seventh aspect of the present invention there is provided a data carrier signal carrying the computer program of the fifth aspect.

[0040] Embodiments of the fifth to seventh aspects of the present invention may include features of, or features corresponding to, preferred or optional features of any other aspect of the present invention, and vice versa. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Aspects and advantages of the present invention will become apparent upon reading the following detailed description and referring to the following drawings (like reference numerals represent like features), in which:

[0042] Figure 1 It is a schematic diagram of a multi-terminal multi-vendor offshore (MTMV) high-voltage direct current (HVDC) network;

[0043] Figure 2 It is a schematic diagram of the control architecture of the MTMV HVDC network;

[0044] FIG3 is a schematic diagram showing (a) node equivalent values ​​of each node in the MTMV HVDC network, (b) voltage-dependent control, and (c) voltage-independent control of the MTMV HVDC component model;

[0045] Figure 4 is a schematic diagram of an exemplary three-terminal bipolar HVDC network used for time domain simulation benchmark;

[0046] Figure 5 shows the Figure 4 Results of power ramp tests on the baseline system shown using (a) the initial droop factor and (b) the reduced droop factor; and

[0047] Figure 6The comparison results between pseudo-steady-state and electromagnetic transient modeling based on the power ramp test shown in Figure 5(b) are shown. DETAILED DESCRIPTION

[0048] As discussed in the background of the invention above, it is desirable to provide methods and control concepts that enable multi-terminal and multi-vendor operation of a VSC-HVDC network and systems that implement them.

[0049] Applicants have identified several factors that limit functionality and prevent widespread adoption of MTHVDC systems. These include, but are not limited to, the following (at least one of which the present invention and its embodiments seek to overcome).

[0050] MT HVDC systems have no inherent operational reference, meaning that using traditional approaches requires the system to be executed by a single converter that defines the overall network behavior or requires communication and / or interaction between converters. Communication between converters brings its own challenges. Converter designs are also highly vendor-specific, so a control solution optimized for one vendor’s converter may not be compatible with another vendor’s, so methods that may be suitable for a single vendor MTHVDC system (or the “open” MVMT HVDC system implemented in China) are generally not feasible in a relatively “closed” MVMT HVDC system. Implementing these methods during online operation is also impractical. Furthermore, the computational challenge posed by complex systems is that calculating variable scenarios is time-consuming and requires a high level of engineering expertise on the part of the end user.

[0051] To this end, the applicant has developed functional models and control concepts that can be implemented in control methods and systems that facilitate interaction with HVDC converter designs and control systems in a vendor-neutral manner. As will be explained below, the inventive concepts can be applied at any stage of planning, specification, testing, and operation of an HVDC network, without requiring any knowledge of the converter's internal design (which might be proprietary, confidential, or otherwise unknowable).

[0052] In order to evaluate or help evaluate control interactions in MVMT-HVDC networks, the applicant has developed a method to quantify the interactions between converters to prevent loss of balance. The method attempts to define the effects of the converters in response to changes in terminal voltage so that conditions for stable operation can be identified and (if appropriate) guided accordingly, which can be done without knowledge of the specific converter design. This involves representing encrypted control details in a model or replica in the form of equivalent control droop in response to voltage changes under given operating conditions. Within the scope of this data provision, the method can quantify the compatibility of multiple droop coefficients while taking into account the influence of operating point and network metrics. According to the principles of Lyapunov's first method, this step will be a prerequisite and decoupled from the small signal evaluation before completing the steady-state stability assessment.

[0053] In summary, the present invention (and its embodiments) provides methods and systems in which individual converters can contribute to an overall de-risked voltage profile across a multi-terminal DC system, independent of continuous updates of control over communications that respect the control of individual converters. Based on received measurements of voltage and power flows within the DC system, combined with the DC system's current operating point and other time-evolving scheduling information for the DC network, a multi-terminal control approach is applied to adjust the individual DC voltage references of HVDC converter controllers based on impedance-based contingency and stability assessments of the DC system. The control concept focuses on characterizing the DC voltage droop characteristics of the HVDC converters and the small-signal impedance characteristics of the HVDC converters acting on the DC system at a given operating point, rather than relying on in-depth knowledge of the individual converters that contribute to these and other converter behaviors. Through this approach, multi-terminal control is able to assess the interactions between converters in the direct current (DC) network and set an overall operating state for the multi-terminal DC network that is inherently stable to current and evolving operating conditions, even without further continuous updates; this serves as a rapid correction to the overall operating state of the multi-terminal system.

[0054] In this approach, a safety margin for loss of balance can be calculated based on the converter's terminal behavior, without knowledge of the converter's internal design, which is often proprietary, confidential, or unknown or unknowable. This helps provide further protection against loss of communication during network outages or other trusted interruptions. Therefore, the operating conditions may not necessarily be optimal by other measures, but rather the most robust given the converter's power flow conditions and operating state at the time.

[0055] The mathematical foundations of control and the application of models related to this control form the basis for evaluating, testing, and defining various vendor approaches for implementation in real-world power system applications. The concepts described in this article are not specific to any particular converter or controller and can be applied to the planning, specification, testing, and operation of high-voltage DC (HVDC) networks and can actually be extended to low-voltage or medium-voltage DC systems.

[0056] As will be explained in further detail below, features of embodiments of the inventive concept may include extracting the DC component (i.e., 0° Hz) of network metrics and the terminal behavior of the converter. The converter terminal characteristics (including constant impedance, voltage droop control, constant power, and constant current) can be linearized at 0° Hz and assumed to behave as (for example) Thevenin or Norton equivalent nodes. Optionally, the switching stations can be modeled as passive terminals. System characteristics can be extracted by constructing an extended impedance matrix (which contains models of all terminals forming a DC network of n nodes). The existence of an initial value of DC network balance can be determined, and the resulting determinant value can be used as an indicator indicating the balance loss margin. The indicator can be normalized for balance losses to provide a universal index for HVDC networks of any topology and / or control structure.

[0057] In summary, advantages include simplicity of implementation, evaluation, and characterization. The proposed approach can provide autonomous functionality with low processing requirements, thereby shortening the control cycle. Providing a one-dimensional (normalized) metric allows for fair and unambiguous comparisons between similar and different / dissimilar converters, serving as a reference signal, and makes it easy for vendors to react or respond, such as responsively optimizing converter design and / or control.

[0058] Benchmark system

[0059] Figure 1 , a schematic diagram of a general multi-terminal multi-vendor (MTMV) high-voltage direct current (HVDC) network 101 is shown, which interconnects offshore wind farms 103A, 103B (representing x wind farms) and an onshore AC transmission network 105. The schematic diagram is used herein to demonstrate the inventive concepts and features of possible implementations of the control method and system contemplated herein.

[0060] Figure 1The network shown includes two types of HVDC terminals, namely offshore interface wind farm (WF) terminals 131 and onshore (OS) terminals 151. In this example, the WF terminals 131 include modular multilevel converters (MMCs) that generally control the AC voltage and frequency of the offshore network to which they are connected, while the OS terminals 151 include MMCs that regulate the DC voltage of the HVDC link provided by the intermediate HVDC transmission line grid 107. For the avoidance of doubt, these converters 131, 151 first convert the AC voltage generated by the offshore grids 103A, 103B to a DC voltage for transmission via the HVDC transmission line 107, and then further convert it to AC voltage for onshore distribution (e.g., directly or indirectly to the onshore AC grid 105). While MMC converters are the most common type of voltage source converter (VSC) in HVDC applications, it will be appreciated that any voltage source converter may be employed.

[0061] In principle, the more converters that participate in the DC network voltage control, the greater the flexibility of this control; but as long as there is at least one terminal providing this capability, the entire DC network can be controlled and the concept of the present invention can be implemented. However, the control of DC networks is subject to practical limitations related to the requirements of onshore and offshore AC systems.

[0062] For the offshore AC system (i.e., the corresponding MMC) providing the interface to the offshore wind farm, grid-forming control is typically required, where the HVDC converter defines the frequency and voltage of the offshore network (e.g., the connected wind farm). This, in turn, represents a fixed power flow to the DC system during steady-state operation, independent of the DC dynamics. This needs to be considered within the overall solution for the DC network, but this definition offers no further flexibility, instead operating within the available DC voltage range as a consequence of the DC voltages defined elsewhere within the system. The onshore connection interface can operate with specific expected power flows, which does not preclude the need for droop power control based on the voltage within the DC network, but again depends on the prevailing operating state of the onshore AC system. Direct control of the AC system, for example at the point of withdrawal, can be introduced, but in the above example, such direct control limits the MVMT network to a single voltage control point, making it susceptible to losses.

[0063] System control architecture

[0064] Figure 2A general control architecture 201 is shown in FIG, which includes n individual converters 231. As shown, each converter station includes an inner loop of current control or its equivalent. The low-level design characteristics of each converter are aggregated and "masked" under the assumption that these designs are proprietary, confidential, or otherwise unknown. These designs may include current loop (voltage) regulators, AC voltage control, modulation schemes, voltage balancing between submodules / arms / phases, main circuits, and other controls related to the converter operating principles and topology of AC and DC systems.

[0065] Under extreme conditions of operation of a given DC network or associated converters, the expression of control may appear non-linear. The objective of supervisory control is to ensure that these conditions do not occur in steady-state or post-steady-state operation of the network or individual converters; post-steady-state operation means the range of N-1 and other contingencies that inform the control priorities and associated control margins.

[0066] The functions of supervisory control 221 are implemented by a central control unit 223 (or controller), which will, for example, be owned and / or operated by a transmission system operator (TSO). In contrast, the individual converters 231 may be wholly owned and independently operated by one or more third parties and may be provided by a range of suppliers. As described above, the converter designs may therefore be proprietary, confidential or unknown to the TSO, and while the TSO would like to be able to control these converters directly, this may not be possible. Therefore, the control itself is delegated to the supplier (more specifically, to the converter), but the standards, feedback signals, etc. are determined by / for the TSO and provided to the individual converter controls for processing, for example by providing a DC voltage reference for each converter and updating or providing modifications 225 to this DC voltage reference as required.

[0067] Based on the feedback measurements of node voltage and branch current and the input commands of nominal voltage and power dispatch, the output of the supervisory control will update the incremental value (ΔV) of the DC voltage reference of each converter 231 through the respective communication links. ref ).

[0068] As the name implies, the purpose of supervisory control 221 is to course-correct the operation of the entire system toward a stable and robust steady-state condition. In this way, the concept does not rely on the reliability of the communication link, as operation under a given condition will remain stable under that operating condition and a set of trusted scenarios before any further updates. Actions taken by supervisory control will (slowly) modify the voltage reference response at the terminals of the relevant converters to correct and drive the DC network to a new, safer operating condition, and transitions in operating state, such as ramping up or down power flow, can be achieved by positively steering slow changes over extended periods of time.

[0069] DC network node model

[0070] To assess interoperability, the MTMV-HVDC system is modeled or otherwise represented as a circuit with shunting controllable sources at selected nodes. The nodes represent the locations of cable joints and converter terminals in the DC network.

[0071] Each branch of the circuit characterizes the aggregate impedance of the corresponding point-to-point DC cable and connected series elements (eg DC breaker, DC reactor, etc.) between the two nodes, if applicable.

[0072] As shown in Figure 3(a), each node is modeled as a Norton equivalent circuit 350. The current source 351 of the Norton equivalent circuit 350 is controllable and represents the active control of the converter. The shunt impedance 353 represents the shunt passive elements at the node, such as the aggregate capacitance of the MMC unit and inductor, dump resistors, etc. The DC node (e.g., a switching station without a converter connected) is modeled as a specific node where the order of the controllable current source is zero (i.e., there is no source). Note that in other embodiments, the converter terminal characteristics can be modeled as a Thevenin equivalent circuit, or indeed any other relevant / feasible representation.

[0073] During operation, the nodes at the converter terminals are divided into two categories, namely voltage-dependent and voltage-independent.

[0074] The voltage-dependent control model is shown in Figure 3(b). Assuming that the modulation process of the HVDC converter is linearized, the S-domain admittance of the converter control is modeled as K i and Reg i The product of , thus:

[0075]

[0076] Among them, I i 、V refi and V i represents the order of the reference voltage, terminal voltage, and output current of the active control at node i. Therefore, when it is under voltage-dependent control, the order of the controllable current source of the voltage-dependent node can be expressed as:

[0077] I i (s)| s＝0 =K i (V refi -V i ) (2)

[0078] For nodes with voltage-independent control, the control focuses on constant power because constant DC current control is rare and does not change the node shunt impedance at 0 Hz. Assume that the equivalent power order is the result of the local converter control mechanism, such as autonomous balancing of the connected AC network [9] or the operator's scheduling command. In both cases, the output power is determined by the unidirectional input of the DC system. According to the control mechanism shown in Fig. 3(c), at steady state, there is:

[0079]

[0080] Branch model of DC network

[0081] For each DC branch including the positive and negative poles between nodes i and j to provide a return path, the aggregated impedance Z ij (s) is written as:

[0082] Z ij (s)| s＝0 =R ij (4)

[0083] where R ij (i≠j) is the aggregated resistance of the branch, including the return resistance; R ii is the shunt resistance at the i-th node.

[0084] Steady-state network model

[0085] By interconnecting the n-node equivalent shown in Fig. 3(a) with the branch loops between any two nodes, the Kirchhoff voltage law

[10] can be used to characterize the balance of the n-node HVDC network as:

[0086]

[0087] where G is the n×n symmetric matrix of the network conductance (i.e., the network admittance at 0°Hz). is the n-dimensional vector of the node voltages; its i-th (0 < i ≤ n) dimension V i represents the voltage measurement value of the i-th node. Similarly, is the n-dimensional vector of the node current injections from the converters. Using G ij to represent the element of G in the i-th (0 < i ≤ n) row and j-th (0 < j ≤ n) column, we get: <​​​​​​​​​​. Considering Figure 2 and the control in Figure 3, the vector of node current injection can also be expressed as:

[0090]

[0091] where K is an n×n diagonal matrix of droop gains (supervisory droop control?). The diagonal element K at its i-th row i (0 < i ≤ n) represents the voltage droop coefficient of the i-th node; if the node is not under droop control, then K ii = 0. is an n-dimensional vector of droop control reference values (coefficients?), and its i-th (0 < i ≤ n) component is V refi (the voltage of the i-th node); INV is an n×n diagonal matrix, and its diagonal element INV i (0 < i ≤ n) is is an n-dimensional vector of arbitrary power injection at all nodes, and its i-th (0 < i ≤ n) component P refi represents the expected power injection at the i-th node. P refi is determined by the scheduling signal from the supervisory control function or the embedded function of the converter at the i-th node.

[0092] Substituting (7) into (5), a function can be defined:

[0093]

[0094] Regarding the vector [[ID=3C]]as the dependent variable driven by the independent variable , then the corresponding function of the solution of is implicitly defined by the function .

[0095] If the converter node is designed to operate in a voltage-independent or voltage-dependent exclusive manner, then this assumption can be mathematically expressed as

[0096] K i P refi = 0 (9)

[0097] Assessing the existence of equilibrium

[0098] According to the definition in (9), for the actual design of the HVDC network, the function of and All elements are continuously differentiable and analytic

[11] . By applying the implicit function theorem

[12] to (9), as long as the following two conditions hold simultaneously, there must exist a unique function of in the neighborhood of (or the open set containing the operating point ): Condition (I): There indeed exists an equilibrium point at the operating point of

[0099] Condition (II): The Jacobi matrix of with respect to

[0100] is not singular at the equilibrium point. That is: with respect to is not singular at the equilibrium point. That is:

[0101]

[0102] By satisfying condition (II), the domain of the above implicit function can be extended by iteratively repeating the following steps: 1) Select a new equilibrium point on the neighborhood boundary to satisfy condition (I); 2) Then satisfy condition (II) again based on the new equilibrium point.

[0103] By iteratively expanding the domain, the operating point can be extended to the entire manifold basis that always conforms to (8) and condition (II); thus, the existence of equilibrium is ensured in the entire aggregated manifold. This process is consistent with the principle of analytic continuation

[11] . Substituting (8) into (10) gives:

[0104] |G + K - INVS| ≠ 0 (11)

[0105] where INVS is an n×n diagonal matrix, and the diagonal element INVS ii (0 < i ≤ n) on its i-th row is Define G ex as the extended conductance matrix:

[0106] G ex = G + K - INVS (12)

[0107] For an actual HVDC network, the operating point of power must be restricted. To ensure that the condition of (10) (i.e., the existence of equilibrium) always holds within the bounded space of the power vector defined by the following formula:

[0108] P = {P ref1 , P ref2 ,..., P refn |P mini ≤ P refi ≤ P maxi} (13)

[0109] Either of the following two conditions should be met only for All qualified operating points Established:

[0110] Condition 1, where G ex The determinant of is positive:

[0111] |G ex |>0 (14)

[0112] Condition 2, where G ex The determinant of is negative:

[0113] |G ex |<0 (15)

[0114] Therefore, the operating margin for balancing losses can be defined as |G ex |, the larger its value, the higher the margin.

[0115] Considering that the extended conductivity matrix is ​​real and symmetric according to its mathematical definition, condition 1 (14) can be replaced by the sufficient (enhanced) condition that the extended conductivity matrix is ​​positive definite, since it will guarantee that its leading major and minor terms of all orders (including its determinant) are positive

[13] ,

[14] , which is expressed as condition 3, where G ex is positive definite:

[0116] G ex >0 (16)

[0117] Or equivalently ensure that G ex The lowest eigenvalue of is positive [13,14]

[0118] λ min (G ex )>0 (17)

[0119] Similarly, condition 2(15) can be satisfied by extending the conductance G in the entire P space. ex The enhanced condition of uniform negative definiteness is replaced by Condition 4, where G ex is negatively definite:

[0120] G ex <0 (18)

[0121] Or equivalently ensure that G ex The highest eigenvalue of is negative:

[0122] λ max (G ex )<0 (19)

[0123] For the enhancement condition, when the extended conductance matrix G exare positive or negative timing respectively, the operating margin of the balance loss can be expressed by λ max (G ex ) or λ min (G ex )express

[0124] Initial balancing and refined assessment criteria

[0125] By iteratively complying with conditions (I) and (II) and ensuring predefined margins using (14), (15), (17), and (19), the existence of balance in the HVDC system can be guaranteed in each control cycle. As the iteration begins, the initial balance of the operating point under condition (I) must be guaranteed.

[0126] This initial equilibrium can actually be chosen as a condition for the no-load condition. Mathematically, this condition is obtained by replacing All components of are assigned the value 0 to represent.

[0127] Therefore, the operating voltage vector The initial operating point can be solved by (8) as:

[0128]

[0129] As long as the following conditions hold

[14] :

[0130] |G+K|≠0 (21)

[0131] In HVDC systems, the probability of not satisfying (21) is practically zero. n The nominal value (>0) is assigned to the voltage reference vector Each component of the initial voltage Each component of should be kept at its nominal value, thus ensuring that the initial equilibrium satisfies condition (I). Under this initial condition, there exists

[0132]

[0133] Among them, G s is defined as the self-conductance diagonal matrix of the HVDC network, whose diagonal elements G sii Defined as the reciprocal of the shunt (self) resistance

[0134]

[0135] Substituting (6) and (23) into (22), we can obtain the mutual derivative matrix G m The elements of

[0136]

[0137] Considering the mutual derivative matrix Gm The definition in (24) is the Laplace matrix, and the positivity of all branch resistances, that is, R ij ∈(0,+∞],G m must be positive semidefinite

[15] . Therefore, for any nonzero n-dimensional real vector G m The quadratic form of should conform to [13,14]:

[0138]

[0139] Since the actual design of the droop coefficient must be greater than or equal to zero, the diagonal elements of the diagonal matrix K must be greater than or equal to zero; considering (23), it must be G s . Therefore, there exists:

[0140]

[0141] By adding inequalities (25) and (26) on both sides of the operator, we can write the following to prove that the expanded conductivity matrix G under the initial power-on condition is ex The positive semidefinite property of :

[0142]

[0143] Since the initial conditions must actually be contained in the desired manifold set of operating power P, the above conditions 2 and 4 are excluded from the actual scenario of HVDC operation because the semi-positive definite matrix G exini There can be neither negative determinants nor eigenvalues ​​

[13] ,

[14] . Therefore, the evaluation criteria for the existence of equilibrium can be simplified to conditions 1 or 3.

[0144] Normalization of evaluation margins

[0145] While conditions 1 or 3 can be used as a margin for balancing losses, the actual meaning of the value can change significantly with changes in the circuit or control structure. One consequence is that it is difficult for operators to interpret the electrical meaning of the resulting margin. This makes it difficult to establish a universal standard to specify the requirements for interoperable HVDC systems for TSOs. With this in mind, two types of normalized indices, CX-index-I (corresponding to condition 1) and CX-index-II (corresponding to condition 3), were created to universally index HVDC networks of any topology and control structure, as shown below:

[0146] CX-Index I (where G ex The determinant is positive):

[0147]

[0148] CX-Index II (where G ex is positive definite or the ex lowest eigenvalue of G is positive):

[0149]

[0150] (28) or any one of the indices in (29) can adequately indicate the operating conditions of the balance loss. A value close to 1 indicates operating conditions closer to the risk-free no-load state, while a value close to 0 indicates a higher risk of balance loss (voltage collapse).

[0151] To obtain the index of (28) or (29), the inputs are the droop coefficient K, the network metric G, the (desired or measured) power injection and the measured values of the terminal voltage . According to the requirements of interoperability, information on the internal design of the converter is not required.

[0152] Incorporate supervisory control

[0153] The extended conductance matrix G ex can be further extended by including another component matrix K s for supervisory droop control as follows:

[0154] G ex = G + K + K S - INVS(30)

[0155] where K s is an n×n matrix. Each of its elements K Sij defines the weight of the voltage measurement at the j-th node (0 < j ≤ n) for adjusting the voltage at the i-th node (0 < i ≤ n) towards the global reference value. This component is scheduled by the supervisory control function (or more than one supervisory control function) based on the node voltage feedback through the communication between the converter and the central control unit (e.g., included in the supervisory control, see Figure 2 ). The influence of the communication will be reflected by its off-diagonal elements. Since incorporating the supervisory control does not change the essence of the method, for simplicity, assume that K S is a zero matrix.

[0156] Case Studies

[0157] To verify the method, a benchmark system was developed for the case study, as Figure 4 shown, with the parameters as shown in Table 1 below:

[0158] parameter value <![CDATA[R 12 ,R 12 ]]> 10Ω, 10Ω Rated voltage 1050kV (bipolar) Valve capacitor 29μF (each pole) <![CDATA[K1, K3 (bipolar)]]> 8.258A / kV, 8.258A / kV <![CDATA[R n12 ,R n12 ]]> 10Ω, 10Ω Time step for pseudo-steady-state EMT simulation 100μs, 3.57μs MMC conduction resistance (per arm) for EMT simulation 0.56Ω

[0159] Table 1: Initial parameters for the three-terminal reference

[0160] like Figure 4 As shown, a three-terminal bipolar HVDC network 461 shows that each half-bridge multi-module converter (HB-MMC) 463 has an identical current loop at 600 Hz and a control frequency of 20 kHz. Lead-lag regulators are used for all DC regulators, with lead and lag time constants of 0.004 and 0.02 seconds, respectively. Terminal 2 (HB-MMC-2) is designated as a constant power terminal, with a proportional gain of 0.1 kV / MW and a time constant of 0.001 seconds.

[0161] Two models were used for time-domain simulation: pseudo-steady-state DC power flow and EMT. Power flow simulation was performed using MATLAB / Simulink and EMT combined with real-time digital simulation (RTDS). For pseudo-steady-state simulation, all controls and circuits were forced to be steady-state, i.e., s = 0 in the transfer function; while in the EMT model, a general average HB-MMC model

[16] was used, which includes inter-arm and inter-phase balance control. In addition, a frequency-dependent model of the DC cable

[17] was used to simulate the DC cable in the EMT simulation.

[0162] Verification of DC power flow CX indicator

[0163] In order to verify the proposed indicators, according to Figure 4 A power ramp test was performed on the benchmark system in Table 1. The results are shown in Figure 5.

[0164] As shown in Figure 5(a), the system starts at a constant power terminal (Terminal 2), operating at 0 MW at time 0s. When a power ramp of -1000 MW / s is applied to P2, the other two terminals begin to meet this power demand in equal proportion, due to the symmetry of the droop coefficient and network metrics. As the constant power load increases, the voltage V2 at Terminal 2 decreases from its nominal value of 1050 kV. Simultaneously, the two CX indicators Ind CX 1 and Ind CX 2 drop from 1, corresponding to a no-load condition, to 0, with voltage collapse occurring at approximately 4.17 seconds. Once any CW indicator reaches 0, all quantities begin to oscillate chaotically.

[0165] For comparison, in Figure 5(b), the ramp test is repeated with the droop factor K3 at terminal 3 reduced by 10%. This is reflected in the lower power sharing at terminal 3 in accommodating the constant power demand at terminal 2. Due to the lower droop factor, resulting in lower grid strength to accommodate the constant power load, the DC power transfer limit decreases to approximately 3750 MW and collapses at 3.75 seconds, at which point both CW indicators reach zero again. As expected, this collapse occurs earlier than in the previous case.

[0166] Comparison of pseudo-steady-state and EMT simulations

[0167] In order to verify the effectiveness of the CX metric in EMT simulations that are closer to actual performance, a comparison is conducted based on a case study in Figure 5(b). Figure 6 As shown in Figure 2, the same power ramp was performed at time = 0.6 seconds. The EMT measurements of the voltage V2 at terminal 2 and the CX indicator 1 are nearly identical to the power flow results, with an error of less than 0.2%. Considering that the -1000 MW / s ramp is more adverse than in reality and that there are still unaccounted-for converter losses in the DC pseudo-steady-state simulation, the accuracy of the CX indicator is determined to be satisfactory.

[0168] in conclusion

[0169] The present invention provides an MVMT HVDC control paradigm that is independent of proprietary, confidential, or otherwise (potentially) unknowable aspects of converter control and has been validated through simulation under relatively extreme conditions. By defining and resolving DC network conditions based on the expression of converter control effects, and defining operating margins related to steady-state stability, an overall vendor-neutral solution can be achieved that is consistent with the TSO priorities for the expected operation of the DC network. This allows both MVMT HVDC control and the associated converter contributions to be described, designed, specified, tested, and deployed with clear definitions of the roles and performance of individual vendors. This vendor-neutral unified control concept enables multi-vendor interoperability in multi-terminal, multi-vendor HVDC networks.

[0170] The simulations above demonstrate that the proposed indices (i.e., CX-Index I and CX-Index II) effectively quantify the interaction between converter droop, DC network metrics, and operating point in HVDC networks. Each of these indices provides an indication of the stability margin of DC power transmission, or equivalently, the balance loss, with a scalar value between 0 and 1.

[0171] Defining control metrics for each converter offers many advantages, notably simplicity of implementation, such as the ability to be programmed as an autonomous function, and reduced computing power requirements, meaning shorter control cycles can be accommodated, leading to system-wide improvements. Converter-specific normalized metrics can be communicated to the converter as feedback signals, shifting the burden of optimizing the system to the supplier that provides and / or operates the converter, while retaining control over how the optimized system is defined (e.g., prioritizing stable operation). The TSO does not require detailed or other knowledge of more complex aspects of converter design or frequency response.

[0172] The provision of a control metric also solves a problem with existing systems (or attempts to implement existing systems) in that multi-terminal HVDC systems have no inherent or common reference and require communication between potentially incompatible resources operated by different suppliers and known systems, each with its own optimization approach, where a single common feedback signal is shared between all converter stations based on the overall voltage level in the DC transmission network.

[0173] Although this indexing approach is derived from the static behavior of the HVDC system, real-time EMT simulations show that it provides good accuracy in the online assessment of significant power ramps transitioning from one steady-state to a new steady-state operation.

[0174] Compared to prior art approaches, the present method is more inclined to quantify the "impact" of an HVDC converter on the DC system in a multi-terminal control scheme, in order to identify and indicate a stable operating point on the converter, and then provide resilience to a range of contingencies, including the subsequent loss of multi-terminal control within a given time period. This impact can be quantified without identifying sensitive areas of the inherent control structure within the converter itself, and will vary between different operating points and control priorities. In these terms, from the perspective of the DC system, the effect of the converter is either a droop control response to the DC voltage or a constant power terminal, providing connectivity to offshore wind power (for example). Within the given control tolerance provided / captured in the multi-terminal control, other behaviors on the AC system, such as grid forming control for various applications, can be represented by these two aforementioned DC-side representative behaviors. Throughout this specification, unless the context requires otherwise, the term "comprise" or "include", or variations such as "comprises" or "comprising", "includes" or "including", will be understood to imply the inclusion of a specified integer or group of integers but not the exclusion of any other integer or group of integers.

[0175] The foregoing description of the present invention has been presented for purposes of illustration and description and is not intended to be exhaustive or to limit the invention to the precise form disclosed. The embodiments described were chosen and described in order to best explain the principles of the invention and its practical application, thereby enabling others skilled in the art to best utilize the invention in various embodiments and with various modifications as suited to the particular use contemplated. Therefore, further modifications and improvements may be made without departing from the scope of the invention as defined by the appended claims.

[0176] For example, the inventive concept is described with reference to offshore wind connections, but it should be understood that it is equally applicable to other DC grids more generally. Furthermore, as mentioned above, the inventive concept is not limited to application in high-voltage DC applications; the principles are also applicable to low- and medium-voltage DC applications. Furthermore, the inventive concept is not limited to MMC converters but can include secondary and tertiary converters, hybrid converters, and any combination of different converter types as appropriate.

[0177] References

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[0180] https: / / www.nationalgrideso.com / future-energy / the-pathway-2030-holistic-net work-design.

[0181] [3]X.Chen et al., "Integrating wind farm to the grid using hybridmultiterminal HVDC technology," IEEE Transactions on IndustryApplications, vol.47, no.2, pp.965-972, 2010.

[0182] [4]TNHCentre."Caithness-Moray HVDC Project During Delivery."TheNational HVDC Centre.https: / / www.hvdccentre.com / our-projects / caithness-moray / .

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[0186] [8]S.Dong,Y.Chi,and Y.Li,"Active voltage feedback control for hybridmultiterminal HVDC system adopting improved synchronverters,"IEEETransactions on Power Delivery,vol.31,no.2,pp.445-455,2015.

[0187] [9]D.B.Rathnayake et al.,"Grid forming inverter modeling,control,andapplications,"IEEE Access,2021.

[0188]

[10] R.L.Boylestad,Introductory circuit analysis.Pearson Education,2013.

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[0190]

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[0193]

[16] D.Guo et al.,"Detailed quantitative comparison of half-bridgemodular multilevel converter modelling methods,"The Journal ofEngineering,vol.2019,no.16,pp.1292-1298,2019.

[0194]

[17] J.Beerten,S.D'Arco,and J.A.Suul,"Frequency-dependent cablemodelling for small-signal stability analysis ofVSC-HVDC systems,"IETGeneration,Transmission&Distribution,vol.10,no.6,pp.1370-1381,2016.

Claims

1. A method for controlling a plurality of HVDC converters in a multi-terminal HVDC system, the method comprising: controlling the output of a plurality of HVDC converters by providing a corresponding DC voltage reference to each HVDC converter; determining a respective feedback signal for each of the plurality of HVDC converters, wherein the feedback signal comprises a modification of a DC voltage reference of the respective converter; Determining the corresponding feedback signal includes analyzing terminal characteristics of each converter and determining an indicator indicating a balance loss margin.

2. The method according to claim 1, wherein The indicator quantifies interactions between voltage droops between the plurality of HVDC converters.

3. The method according to claim 1 or 2, wherein: The indicator indicates the stability margin for DC power transmission.

4. A method according to any preceding claim, wherein: A modification to the voltage reference is determined to optimize steady-state operation of the multi-terminal HVDC system.

5. A method according to any preceding claim, comprising modelling the terminal characteristics of each HVDC converter as an equivalent circuit based on the effect that the HVDC converter has in response to a modification of its voltage reference in a given operating state; the equivalent circuit may be a Norton equivalent circuit or a Thevenin equivalent circuit.

6. A method according to any preceding claim, comprising determining the HVDC system characteristics by constructing an extended impedance matrix or an extended conductance matrix of the system.

7. A method according to any preceding claim, wherein: The method comprises determining a DC voltage droop characteristic of each HVDC converter.

8. A method according to any preceding claim, comprising determining an initial value of balance and normalising the indicator of loss of balance.

9. A method according to any preceding claim, wherein: The method includes determining branch currents and node voltages within the system.

10. The method according to claim 9, wherein: The branch currents and the node voltages are received at a central controller configured to implement the method.

11. A method according to any preceding claim, wherein: The multi-terminal HVDC system is a multi-supplier multi-terminal HVDC system.

12. A method according to any preceding claim, wherein: The multi-terminal HVDC system is included in an HVDC transmission system.

13. A method according to any preceding claim, wherein: The HVDC converter is comprised in one or more interfaces between one or more HVDC power lines and one or more AC power generation systems and / or one or more AC grids.

14. The method according to claim 13, wherein: The one or more AC power generation systems include one or more offshore wind turbines or wind farms, and / or the one or more AC power grids include one or more onshore AC power grids.

15. A method for operating a plurality of HVDC converters in a multi-terminal HVDC system, the method comprising: controlling the output of the plurality of HVDC converters by providing a converter-specific DC voltage reference to each HVDC converter; determining a respective feedback signal for each of the plurality of HVDC converters, wherein the converter-specific feedback signal comprises a modification of the converter-specific DC voltage reference; Therein, determining the respective converter-specific feedback signals comprises modeling the terminal characteristics of each converter as an equivalent circuit based on or representing the response of the HVDC converter to a modification of its voltage reference in a given operating state.

16. A controller for a multi-terminal HVDC system, the controller being adapted or configured to perform the method according to any one of the preceding claims.

17. A multi-terminal HVDC system comprising a plurality of HVDC converters and the controller according to claim 16.

18. The system of claim 17, comprising at least one HVDC power line, at least one HVDC converter between the at least one HVDC power line and the offshore wind farm, and at least one HVDC converter between the at least one HVDC power line and an onshore AC grid.

19. The system according to claim 17 or 18, wherein: The system is a multi-vendor multi-terminal HVDC system.

20. The system according to any one of claims 17 to 19, wherein The at least one HVDC converter comprises at least one voltage source converter.

21. The system of claim 20, wherein: The at least one HVDC converter comprises a node-type multi-level converter.

22. A computer program comprising instructions which, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 15.

23. A computer-readable medium or data carrier comprising the computer program of claim 22.

24. A data carrier signal carrying a computer program as claimed in claim 22.

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