Patent Description:
Wind power is considered one of the cleanest, most environmentally friendly energy sources presently available, and wind turbines have gained increased attention in this regard. A modern wind turbine typically includes a tower, generator, gearbox, nacelle, and one or more rotor blades. The rotor blades capture kinetic energy of wind using known airfoil principles. For example, rotor blades typically have the cross-sectional profile of an airfoil such that, during operation, air flows over the blade producing a pressure difference between the sides. Consequently, a lift force, which is directed from a pressure side towards a suction side, acts on the blade. The lift force generates torque on the main rotor shaft, which is typically geared to a generator for producing electricity.

Wind turbines can be distinguished in two types: fixed speed and variable speed turbines. Conventionally, variable speed wind turbines are controlled as current sources connected to a power grid. In other words, the variable speed wind turbines rely on a grid frequency detected by a phase locked loop (PLL) as a reference and inject a specified amount of current into the grid. The conventional current source control of the wind turbines is based on the assumptions that the grid voltage waveforms are fundamental voltage waveforms with fixed frequency and magnitude and that the penetration of wind power into the grid is low enough so as to not cause disturbances to the grid voltage magnitude and frequency. Thus, the wind turbines simply inject the specified current into the grid based on the fundamental voltage waveforms. However, with the rapid growth of the wind power, wind power penetration into some grids has increased to the point where wind turbine generators have a significant impact on the grid voltage and frequency. When wind turbines are located in a weak grid, wind turbine power fluctuations may lead to an increase in magnitude and frequency variations in the grid voltage. These fluctuations may adversely affect the performance and stability of the PLL and wind turbine current control.

Many existing renewable generation converters, such as double-fed wind turbine generators, operate in a "grid-following" mode. Grid-following type devices utilize fast current-regulation loops to control active and reactive power exchanged with the grid. More specifically, <FIG> illustrates the basic elements of the main circuit and converter control structure for a grid-following double-fed wind turbine generator. As shown, the active power reference to the converter is developed by the energy source regulator, e.g., the turbine control portion of a wind turbine. This is conveyed as a torque reference which represents the lesser of the maximum attainable power from the energy source at that instant, or a curtailment command from a higher-level grid controller. The converter control then determines a current reference for the active component of current to achieve the desired torque. Accordingly, the double-fed wind turbine generator includes functions that manage the voltage and reactive power in a manner that results in a command for the reactive component of current. Wide-bandwidth current regulators then develop commands for voltage to be applied by the converters to the system, such that the actual currents closely track the commands.

Alternatively, grid-forming type converters provide a voltage-source characteristic, where the angle and magnitude of the voltage are controlled to achieve the regulation functions needed by the grid. With this structure, current will flow according to the demands of the grid while the converter contributes to establishing a voltage and frequency for the grid. This characteristic is comparable to conventional generators based on a turbine driving a synchronous machine. Thus, a grid-forming source must include the following basic functions: (<NUM>) support grid voltage and frequency for any current flow within the rating of the equipment, both real and reactive; (<NUM>) prevent operation beyond equipment voltage or current capability by allowing grid voltage or frequency to change rather than disconnecting equipment (disconnection is allowed only when voltage or frequency are outside of bounds established by the grid entity); (<NUM>) remain stable for any grid configuration or load characteristic, including serving an isolated load or connected with other grid-forming sources, and switching between such configurations; (<NUM>) share total load of the grid among other grid-forming sources connected to the grid; (<NUM>) ride through grid disturbances, both major and minor, and (<NUM>) meet requirements (<NUM>)-(<NUM>) without requiring fast communication with other control systems existing in the grid, or externally-created logic signals related to grid configuration changes.

The basic control structure to achieve the above grid-forming objectives was developed and field-proven for battery systems in the early <NUM>'s (see e.g., <CIT> entitled "Battery Energy Storage Power Conditioning System"). Applications to full-converter wind generators and solar generators are disclosed in <CIT> entitled "System and Method for Control of a Grid Connected Power Generating System," and <CIT> entitled "Controller for controlling a power converter. " Applications to grid-forming control for a doubly-fed wind turbine generator are disclosed in <CIT> entitled "System and Method for Providing Grid-Forming Control for a Doubly-Feb Wind Turbine Generator.

Document <CIT> discloses a wind generator providing dampening using an inverter and rotating reference frames.

To be effective, grid-forming (GFM) inverter-based resources (IBRs) must be able to maintain an internal voltage phasor that does not move quickly when there are changes in grid conditions, e.g., sudden addition/removal of loads, opening or closing of grid connections that lead to phase jumps and/or rapid change of frequency. In other words, the power from the grid-forming resource must be able to change suddenly to stabilize the grid, with a subsequent slow reset to power being commanded from a higher-level control function. In addition, the grid-forming resource must be able to rapidly enforce power limits that exist due to constraints on the power-handling portions of the device, e.g., DC voltages/currents in a battery, solar array, and/or wind generating system. Such a response is needed for severe disturbances on the grid, e.g., faults where power limits will be dynamically adjusted to coordinate with grid conditions for secure recovery from the fault. Further, the grid-forming resource should be able to rapidly follow changes in commands from higher-level controls, e.g., for damping mechanical vibrations in a wind turbine. Such requirements, however, can be difficult to achieve.

In addition, at least some known electric utility grids include one or more series-compensated transmission lines. Sub-synchronous control interactions (SSCI) is a phenomenon that occurs when power-electronic converter controls interact with such series-compensated transmission lines. These interactions can sometimes lead to control instabilities if control systems are not tuned properly or if the control margin of the power converter in properly-tuned control systems is not maintained. Moreover, series capacitors are often installed in long-distance AC transmission lines to boost the power transfer capability of the lines. The series capacitor(s) creates a resonant circuit, which may interact with the converter controls of power electronics. Dual-fed wind turbines, in particular, are susceptible to this type of interaction. If not properly damped, the oscillations can be unstable and lead to trips of the wind turbine or overall wind farm.

In view of the foregoing, an improved system and method that addresses the aforementioned issues would be welcomed in the art. Accordingly, the present disclosure is directed to systems and methods damping SSCI in GFM IBRs.

In one aspect, the present disclosure is directed to a method for damping sub-synchronous control interactions (SSCI) in a grid-forming inverter-based resource connected to an electrical grid. The method includes receiving, via a controller, a current feedback signal in a synchronous reference frame. The method also includes rotating, via the controller, the current feedback signal to a new reference frame associated with a sub-synchronous frequency range. Further, the method includes determining, via the controller, a sub-synchronous component of the current feedback signal. Moreover, the method includes rotating, via the controller, the sub-synchronous component of the current feedback signal back to the synchronous reference frame. In addition, the method includes determining, via the controller, a voltage command associated with sub-synchronous damping for the inverter-based resource as a function of the sub-synchronous component and a virtual resistance setting. Thus, the method includes controlling, via the controller, the inverter-based resource, based at least in part, on the voltage command associated with the sub-synchronous damping. It should be understood that the method may further include any of the additional features and/or steps described herein.

In another aspect, the present disclosure is directed to a converter controller for damping sub-synchronous control interactions (SSCI) in a grid-forming inverter-based resource connected to an electrical grid. The converter controller includes at least one controller having at least one processor. The processor(s) is configured to perform a plurality of operations, including but not limited to receiving a current feedback signal in a synchronous reference frame, rotating the current feedback signal to a new reference frame associated with a sub-synchronous frequency range, determining a sub-synchronous component of the current feedback signal, rotating the sub-synchronous component of the current feedback signal back to the synchronous reference frame, determining a voltage command associated with sub-synchronous damping for the inverter-based resource as a function of the sub-synchronous component and a virtual resistance setting, and controlling the inverter-based resource, based at least in part, on the voltage command associated with the sub-synchronous damping. It should be understood that the converter controller may further include any of the additional features and/or steps described herein.

Each example is provided by way of explanation of the invention.

Series capacitors are often installed in long-distance AC transmission lines to boost the power transfer capability of the lines. The series capacitor creates a resonant circuit, which may interact with the converter controls of power electronics. Type <NUM> (dual-fed) wind turbines, in particular, are susceptible to this type of interaction. If not properly damped, the oscillations can be unstable and lead to trips of the wind plant. Thus, the present disclosure is directed to a method for providing damping of the sub-synchronous resonance grid-forming control structure. In particular, the present disclosure involves adding a 'virtual resistance' in series with the voltage source produced by the grid-forming controls.

Referring now to the drawings, <FIG> illustrates a perspective view of one embodiment of a wind turbine <NUM> according to the present disclosure. As shown, the wind turbine <NUM> generally includes a tower <NUM> extending from a support surface <NUM>, a nacelle <NUM> mounted on the tower <NUM>, and a rotor <NUM> coupled to the nacelle <NUM>. The rotor <NUM> includes a rotatable hub <NUM> and at least one rotor blade <NUM> coupled to and extending outwardly from the hub <NUM>. For example, in the illustrated embodiment, the rotor <NUM> includes three rotor blades <NUM>. However, in an alternative embodiment, the rotor <NUM> may include more or less than three rotor blades <NUM>. Each rotor blade <NUM> may be spaced about the hub <NUM> to facilitate rotating the rotor <NUM> to enable kinetic energy to be transferred from the wind into usable mechanical energy, and subsequently, electrical energy. For instance, the hub <NUM> may be rotatably coupled to an electric generator <NUM> (<FIG>) positioned within the nacelle <NUM> to permit electrical energy to be produced.

The wind turbine <NUM> may also include a wind turbine controller <NUM> centralized within the nacelle <NUM>. However, in other embodiments, the controller <NUM> may be located within any other component of the wind turbine <NUM> or at a location outside the wind turbine <NUM>. Further, the controller <NUM> may be communicatively coupled to any number of the components of the wind turbine <NUM> in order to control the operation of such components and/or implement a corrective or control action. As such, the controller <NUM> may include a computer or other suitable processing unit. Thus, in several embodiments, the controller <NUM> may include suitable computer-readable instructions that, when implemented, configure the controller <NUM> to perform various different functions, such as receiving, transmitting and/or executing wind turbine control signals. Accordingly, the controller <NUM> may generally be configured to control the various operating modes (e.g., start-up or shut-down sequences), de-rating or up-rating the wind turbine, and/or individual components of the wind turbine <NUM>.

Referring now to <FIG>, a simplified, internal view of one embodiment of the nacelle <NUM> of the wind turbine <NUM> shown in <FIG> is illustrated. As shown, a generator <NUM> may be disposed within the nacelle <NUM> and supported atop a bedplate <NUM>. In general, the generator <NUM> may be coupled to the rotor <NUM> for producing electrical power from the rotational energy generated by the rotor <NUM>. For example, as shown in the illustrated embodiment, the rotor <NUM> may include a rotor shaft <NUM> coupled to the hub <NUM> for rotation therewith. The rotor shaft <NUM> may, in turn, be rotatably coupled to a generator shaft <NUM> of the generator <NUM> through a gearbox <NUM>. As is generally understood, the rotor shaft <NUM> may provide a low speed, high torque input to the gearbox <NUM> in response to rotation of the rotor blades <NUM> and the hub <NUM>. The gearbox <NUM> may then be configured to convert the low speed, high torque input to a high speed, low torque output to drive the generator shaft <NUM> and, thus, the generator <NUM>.

The wind turbine <NUM> may also one or more pitch drive mechanisms <NUM> communicatively coupled to the wind turbine controller <NUM>, with each pitch adjustment mechanism(s) <NUM> being configured to rotate a pitch bearing <NUM> and thus the individual rotor blade(s) <NUM> about its respective pitch axis <NUM>. In addition, as shown, the wind turbine <NUM> may include one or more yaw drive mechanisms <NUM> configured to change the angle of the nacelle <NUM> relative to the wind (e.g., by engaging a yaw bearing <NUM> of the wind turbine <NUM> that is arranged between the nacelle <NUM> and the tower <NUM> of the wind turbine <NUM>).

In addition, the wind turbine <NUM> may also include one or more sensors <NUM>, <NUM> for monitoring various wind conditions of the wind turbine <NUM>. For example, the incoming wind direction <NUM>, wind speed, or any other suitable wind condition near of the wind turbine <NUM> may be measured, such as through use of a suitable weather sensor <NUM>. Suitable weather sensors may include, for example, Light Detection and Ranging ("LIDAR") devices, Sonic Detection and Ranging ("SODAR") devices, anemometers, wind vanes, barometers, radar devices (such as Doppler radar devices) or any other sensing device which can provide wind directional information now known or later developed in the art. Still further sensors <NUM> may be utilized to measure additional operating parameters of the wind turbine <NUM>, such as voltage, current, vibration, etc. as described herein.

Referring now to <FIG>, a schematic diagram of one embodiment of a wind turbine power system <NUM> is illustrated in accordance with aspects of the present disclosure. Although the present disclosure will generally be described herein with reference to the system <NUM> shown in <FIG>, those of ordinary skill in the art, using the disclosures provided herein, should understand that aspects of the present disclosure may also be applicable in other power generation systems, and, as mentioned above, that the invention is not limited to wind turbine systems.

In the embodiment of <FIG> and as mentioned, the rotor <NUM> of the wind turbine <NUM> (<FIG>) may, optionally, be coupled to the gearbox <NUM>, which is, in turn, coupled to a generator <NUM>, which may be a doubly fed induction generator (DFIG). As shown, the DFIG <NUM> may be connected to a stator bus <NUM>. Further, as shown, a power converter <NUM> may be connected to the DFIG <NUM> via a rotor bus <NUM>, and to the stator bus <NUM> via a line side bus <NUM>. As such, the stator bus <NUM> may provide an output multiphase power (e.g., three-phase power) from a stator of the DFIG <NUM>, and the rotor bus <NUM> may provide an output multiphase power (e.g., three-phase power) from a rotor of the DFIG <NUM>. The power converter <NUM> may also include a rotor side converter (RSC) <NUM> and a line side converter (LSC) <NUM>. The DFIG <NUM> is coupled via the rotor bus <NUM> to the rotor side converter <NUM>. Additionally, the RSC <NUM> is coupled to the LSC <NUM> via a DC link <NUM> across which is a DC link capacitor <NUM>. The LSC <NUM> is, in turn, coupled to the line side bus <NUM>.

The RSC <NUM> and the LSC <NUM> may be configured for normal operating mode in a three-phase, pulse width modulation (PWM) arrangement using one or more switching devices, such as insulated gate bipolar transistor (IGBT) switching elements. In addition, the power converter <NUM> may be coupled to a converter controller <NUM> in order to control the operation of the rotor side converter <NUM> and/or the line side converter <NUM> as described herein. It should be noted that the converter controller <NUM> may be configured as an interface between the power converter <NUM> and the turbine controller <NUM> and may include any number of control devices.

In typical configurations, various line contactors and circuit breakers including, for example, a grid breaker <NUM> may also be included for isolating the various components as necessary for normal operation of the DFIG <NUM> during connection to and disconnection from a load, such as the electrical grid <NUM>. For example, a system circuit breaker <NUM> may couple a system bus <NUM> to a transformer <NUM>, which may be coupled to the electrical grid <NUM> via the grid breaker <NUM>. In alternative embodiments, fuses may replace some or all of the circuit breakers.

In operation, alternating current power generated at the DFIG <NUM> by rotating the rotor <NUM> is provided to the electrical grid <NUM> via dual paths defined by the stator bus <NUM> and the rotor bus <NUM>. On the rotor bus side <NUM>, sinusoidal multi-phase (e.g., three-phase) alternating current (AC) power is provided to the power converter <NUM>. The rotor side converter <NUM> converts the AC power provided from the rotor bus <NUM> into direct current (DC) power and provides the DC power to the DC link <NUM>. As is generally understood, switching elements (e.g., IGBTs) used in the bridge circuits of the rotor side converter <NUM> may be modulated to convert the AC power provided from the rotor bus <NUM> into DC power suitable for the DC link <NUM>.

In addition, the line side converter <NUM> converts the DC power on the DC link <NUM> into AC output power suitable for the electrical grid <NUM>. In particular, switching elements (e.g., IGBTs) used in bridge circuits of the line side converter <NUM> can be modulated to convert the DC power on the DC link <NUM> into AC power on the line side bus <NUM>. The AC power from the power converter <NUM> can be combined with the power from the stator of DFIG <NUM> to provide multi-phase power (e.g., three-phase power) having a frequency maintained substantially at the frequency of the electrical grid <NUM> (e.g., <NUM> or <NUM>).

Additionally, various circuit breakers and switches, such as grid breaker <NUM>, system breaker <NUM>, stator sync switch <NUM>, converter breaker <NUM>, and line contactor <NUM> may be included in the wind turbine power system <NUM> to connect or disconnect corresponding buses, for example, when current flow is excessive and may damage components of the wind turbine power system <NUM> or for other operational considerations. Additional protection components may also be included in the wind turbine power system <NUM>.

Moreover, the power converter <NUM> may receive control signals from, for instance, the local control system <NUM> via the converter controller <NUM>. The control signals may be based, among other things, on sensed states or operating characteristics of the wind turbine power system <NUM>. Typically, the control signals provide for control of the operation of the power converter <NUM>. For example, feedback in the form of a sensed speed of the DFIG <NUM> may be used to control the conversion of the output power from the rotor bus <NUM> to maintain a proper and balanced multi-phase (e.g., three-phase) power supply. Other feedback from other sensors may also be used by the controller(s) <NUM>, <NUM> to control the power converter <NUM>, including, for example, stator and rotor bus voltages and current feedbacks. Using the various forms of feedback information, switching control signals (e.g., gate timing commands for IGBTs), stator synchronizing control signals, and circuit breaker signals may be generated.

The power converter <NUM> also compensates or adjusts the frequency of the three-phase power from the rotor for changes, for example, in the wind speed at the hub <NUM> and the rotor blades <NUM>. Therefore, mechanical and electrical rotor frequencies are decoupled and the electrical stator and rotor frequency matching is facilitated substantially independently of the mechanical rotor speed.

Under some states, the bi-directional characteristics of the power converter <NUM>, and specifically, the bi-directional characteristics of the LSC <NUM> and RSC <NUM>, facilitate feeding back at least some of the generated electrical power into generator rotor. More specifically, electrical power may be transmitted from the stator bus <NUM> to the line side bus <NUM> and subsequently through the line contactor <NUM> and into the power converter <NUM>, specifically the LSC <NUM> which acts as a rectifier and rectifies the sinusoidal, three-phase AC power to DC power. The DC power is transmitted into the DC link <NUM>. The capacitor <NUM> facilitates mitigating DC link voltage amplitude variations by facilitating mitigation of a DC ripple sometimes associated with three-phase AC rectification.

The DC power is subsequently transmitted to the RSC <NUM> that converts the DC electrical power to a three-phase, sinusoidal AC electrical power by adjusting voltages, currents, and frequencies. This conversion is monitored and controlled via the converter controller <NUM>. The converted AC power is transmitted from the RSC <NUM> via the rotor bus <NUM> to the generator rotor. In this manner, generator reactive power control is facilitated by controlling rotor current and voltage.

Referring now to <FIG>, the wind turbine power system <NUM> described herein may be part of a wind farm <NUM>. As shown, the wind farm <NUM> may include a plurality of wind turbines <NUM>, including the wind turbine <NUM> described above, and an overall farm-level controller <NUM>. For example, as shown in the illustrated embodiment, the wind farm <NUM> includes twelve wind turbines, including wind turbine <NUM>. However, in other embodiments, the wind farm <NUM> may include any other number of wind turbines, such as less than twelve wind turbines or greater than twelve wind turbines. In one embodiment, the turbine controllers of the plurality of wind turbines <NUM> are communicatively coupled to the farm-level controller <NUM>, e.g., through a wired connection, such as by connecting the turbine controller <NUM> through suitable communicative links <NUM> (e.g., a suitable cable). Alternatively, the turbine controllers may be communicatively coupled to the farm-level controller <NUM> through a wireless connection, such as by using any suitable wireless communications protocol known in the art. In further embodiments, the farm-level controller <NUM> is configured to send and receive control signals to and from the various wind turbines <NUM>, such as for example, distributing real and/or reactive power demands across the wind turbines <NUM> of the wind farm <NUM>.

Referring now to <FIG>, a block diagram of one embodiment of suitable components that may be included within the controller (such as any one of the converter controller <NUM>, the turbine controller <NUM>, and/or the farm-level controller <NUM> described herein) in accordance with example aspects of the present disclosure is illustrated. As shown, the controller may include one or more processor(s) <NUM>, computer, or other suitable processing unit and associated memory device(s) <NUM> that may include suitable computer-readable instructions that, when implemented, configure the controller to perform various different functions, such as receiving, transmitting and/or executing wind turbine control signals (e.g., performing the methods, steps, calculations and the like disclosed herein).

As used herein, the term "processor" refers not only to integrated circuits referred to in the art as being included in a computer, but also refers to a controller, a microcontroller, a microcomputer, a programmable logic controller (PLC), an application specific integrated circuit, and other programmable circuits. Additionally, the memory device(s) <NUM> may generally comprise memory element(s) including, but not limited to, computer readable medium (e.g., random access memory (RAM)), computer readable non-volatile medium (e.g., a flash memory), a floppy disk, a compact disc-read only memory (CD-ROM), a magneto-optical disk (MOD), a digital versatile disc (DVD) and/or other suitable memory elements.

Such memory device(s) <NUM> may generally be configured to store suitable computer-readable instructions that, when implemented by the processor(s) <NUM>, configure the controller to perform various functions as described herein. Additionally, the controller may also include a communications interface <NUM> to facilitate communications between the controller and the various components of the wind turbine <NUM>. An interface can include one or more circuits, terminals, pins, contacts, conductors, or other components for sending and receiving control signals. Moreover, the controller may include a sensor interface <NUM> (e.g., one or more analog-to-digital converters) to permit signals transmitted from the sensors <NUM>, <NUM> to be converted into signals that can be understood and processed by the processor(s) <NUM>.

Referring now to <FIG> and <FIG>, a system <NUM> and method <NUM> for providing grid-forming control of a double-fed generator of a wind turbine according to the present disclosure is illustrated. <FIG> illustrates a schematic diagram of one embodiment of the system <NUM> according to the present disclosure, particularly illustrating a one-line diagram of the DFIG <NUM> with a high-level control structure for grid-forming characteristics. <FIG> illustrates a flow diagram of one embodiment of method <NUM> for providing grid-forming control of the DFIG <NUM>.

Referring particularly to <FIG>, the system <NUM> may include many of the same features of <FIG> described herein, with components having the same reference characters representing like components. Further, as shown, the system <NUM> may include a control structure for controlling the line-side converter that is similar to the control structure shown in <FIG>. More particularly, as shown, the line-side converter control structure may include a DC voltage regulator <NUM> and a line current regulator <NUM>. As such, the DC voltage regulator <NUM> is configured to generate line-side current commands (e.g., ILCmdx) for the line current regulator <NUM>. The line current regulator <NUM> then generates line-side voltage commands (e.g., VLCmdx, VLCmdy) for a modulator <NUM>. The modulator <NUM> also receives an output (e.g., a phase-locked loop angle, θPLL) from a phase-locked loop <NUM> to generate one or more gate pulses for the line-side converter <NUM>. The phase-locked loop <NUM> typically generates its output using a voltage feedback signal.

Furthermore, as shown, the system <NUM> may also include a unique control structure for controlling the rotor-side converter <NUM> using grid-forming characteristics. In particular, as shown in <FIG>, the system <NUM> may include a stator voltage regulator <NUM> for providing such grid-forming characteristics. In addition, as shown, the system <NUM> may include a grid voltage/VAR regulator <NUM>, an inertial power regulator <NUM>, a rotor current regulator <NUM>, and a modulator <NUM>. Thus, in an embodiment, as shown, the system <NUM> is configured to determine voltage command(s) (e.g., VS_MAG_Cmd, VS_ANGLE_Cmd) via the voltage/VAR regulator <NUM> and/or the inertial power regulator <NUM> using, e.g., one or more reference commands from an external controller. In such embodiment, the external controller may include, for example, the turbine controller <NUM> of the wind turbine <NUM> or the farm-level controller <NUM> of the wind farm <NUM>. Moreover, as shown, the reference command(s) may include at least one of a voltage reference (e.g., VT_Ref) or VAR reference from the farm-level controller <NUM> and/or a power reference (e.g., Power_Ref) from the turbine controller <NUM>.

Still referring to <FIG>, the stator voltage regulator <NUM> of the system <NUM> is configured to determine one or more rotor current commands (e.g., IRCmdy and IRCmdx) as a function of a magnetizing current command <NUM> and/or a stator current feedback signal <NUM> of the DFIG <NUM>. It should be understood that the stator feedback current <NUM> is a strong indicator of the characteristics of the externally connected power system, i.e., the grid. Therefore, the stator feedback current <NUM> can be used as a feedback signal to decouple the response of stator voltage to variations to the nature of the grid. Further details of the stator voltage regulator <NUM> can be better understood with respect to <FIG> and <FIG>. Thus, the output(s) (e.g., rotor current commands IRCmdy, IPCmdx) from the stator voltage regulator <NUM> can be implemented in the rotor current regulator <NUM> by generating rotor voltage commands (e.g., VRCmdx and VRCmdy) for a modulator <NUM>. The modulator <NUM> also receives the phase-locked loop angle from the phase-locked loop <NUM> and a reference angle (e.g., θFFBK) to generate one or more gate pulses for the rotor-side converter <NUM>.

Series capacitors are often installed in long-distance AC transmission lines to boost the power transfer capability of the lines. The series capacitor creates a resonant circuit, which may interact with the converter controls of power electronics. Dual-fed wind turbines, such as those illustrated in <FIG>, can be susceptible to this type of interaction. If not properly damped, the oscillations can be unstable and lead to trips of the wind farm <NUM>. Thus, systems and methods of the present disclosure are directed to providing damping of the sub-synchronous resonance grid-forming control structure, such as the structure illustrated in <FIG>.

In particular, and referring now to <FIG>, a flow diagram of one embodiment of the method <NUM> for damping sub-synchronous control interactions (SSCI) in a grid-forming inverter-based resource connected to an electrical grid is provided. In general, the method <NUM> is described herein with reference to the wind turbine <NUM> of <FIG>. However, it should be appreciated that the disclosed method <NUM> may be implemented with wind turbines having any other suitable configurations. In addition, although <FIG> depicts steps performed in a particular order for purposes of illustration and discussion, the methods discussed herein are not limited to any particular order or arrangement. One skilled in the art, using the disclosures provided herein, will appreciate that various steps of the methods disclosed herein can be omitted, rearranged, combined, and/or adapted in various ways without deviating from the scope of the present disclosure.

As shown at (<NUM>), the method <NUM> includes receiving, via a controller, a current feedback signal in a synchronous reference frame. As shown at (<NUM>), the method <NUM> includes rotating, via the controller, the current feedback signal to a new reference frame associated with a sub-synchronous frequency range. As shown at (<NUM>), the method <NUM> includes determining, via the controller, a sub-synchronous component of the current feedback signal. As shown at (<NUM>), the method <NUM> includes rotating, via the controller, the sub-synchronous component of the current feedback signal back to the synchronous reference frame. As shown at (<NUM>), the method <NUM> includes determining, via the controller, a voltage command associated with sub-synchronous damping for the inverter-based resource as a function of the sub-synchronous component and a virtual resistance setting. As shown at (<NUM>), the method <NUM> includes controlling, via the controller, the inverter-based resource, based at least in part, on the voltage command associated with the sub-synchronous damping.

For example, referring now to <FIG>, a schematic diagram of an embodiment of a grid-forming control structure <NUM> according to the present disclosure is illustrated. In particular, as shown, the control structure <NUM> receives the current feedback signal <NUM> (e.g., IS_Fbk_xy) in a synchronous reference frame. The current feedback signal may include two components (both x and y components), with one component in phase with a local voltage reference and one component in quadrature with the local voltage reference. Further, as shown at <NUM>, the current feedback signal <NUM> may be filtered to remove one or more fundamental frequency components. In particular, as shown, the control structure may include a high-pass filter <NUM> (or any other suitable filter or combination of filters) for filtering of the current feedback signal <NUM>. Thus, as shown at <NUM>, the control structure <NUM> is further configured to rotate the filtered current feedback signal <NUM> to a new reference frame associated with a sub-synchronous frequency range. For example, as shown, the filtered current feedback signal <NUM> may be rotated by the phase-locked loop angle <NUM>.

Moreover, as shown at <NUM>, <NUM>, and <NUM>, the control structure <NUM> may further determine a sub-synchronous component <NUM> of the current feedback signal <NUM>. More specifically, as shown, the control structure <NUM> may further determine a sub-synchronous component of the current feedback signal <NUM> by applying a low-pass filter <NUM> and phase compensation <NUM>, <NUM> to the current feedback signal <NUM> to obtain the sub-synchronous component <NUM>. Thus, as shown at <NUM>, the control structure <NUM> can then rotate the sub-synchronous component <NUM> of the current feedback signal <NUM> back to the synchronous reference frame, e.g., using a negative phase-locked loop angle <NUM>.

Accordingly, the output <NUM> (e.g., IS_Dc_xy) can then be used by the control structure <NUM> to determine a voltage command <NUM> (e.g., VCmd_dc_xy) associated with sub-synchronous damping for the inverter-based resource as a function of the sub-synchronous component <NUM> and a virtual resistance setting <NUM>. In such embodiments, the virtual resistance setting <NUM> may be a fixed value that is tuned as part of the normal control design process. More particularly, in an embodiment, the virtual resistance setting <NUM> (or the phase compensation <NUM>) may be tuned to provide a positive damping effect over a certain frequency range (such as the sub-synchronous frequency range from about <NUM> to about <NUM>). Further, in an embodiment, the control structure <NUM> is configured to determine the voltage command <NUM> associated with the sub-synchronous damping by multiplying the output <NUM> by the virtual resistance setting <NUM> to obtain the voltage command <NUM>.

Thus, as shown and explained in more detail with reference to <FIG>, the voltage command <NUM> can be used by the stator voltage regulator <NUM> to control the inverter-based resource. In particular, as shown in <FIG>, a schematic diagram of an embodiment of example components of the stator voltage regulator <NUM> is illustrated. In the illustrated embodiment, the signals are in x and y coordinates with reference to the terminal voltage phase angle. Complex variable notation is used for clarity. Further, as shown, the stator voltage regulator <NUM> may include a predictive path <NUM> and a corrector path <NUM>. Thus, as shown at the start of the predictive path <NUM>, the stator voltage regulator <NUM> is configured to receive a higher level command (e.g., EI) for magnitude of the stator voltage and a higher level command (e.g., δIT) for angle of the stator voltage with respect to the phase-locked loop angle. Further, continuing along the predictive path <NUM>, the stator voltage regulator <NUM> can then convert the voltage command(s) to a stator voltage command <NUM> (e.g., VS_Cmd_xy) as shown at <NUM>. As shown at <NUM>, the stator voltage regulator <NUM> is configured to determine a sum <NUM> (or total voltage command) of the stator voltage command <NUM> and the voltage command <NUM> associated with the sub-synchronous damping (from <FIG>). As shown at <NUM>, the stator voltage regulator <NUM> may then determine a magnetizing current feed forward signal <NUM> (e.g., IM_FF_xy) as a function of the sum <NUM> and a magnetizing admittance <NUM> (e.g., jBmag <NUM>). In one embodiment, for example, the magnetizing admittance <NUM> may correspond to a magnetizing susceptance. As such, the magnetizing current feed forward signal <NUM> is configured to facilitate a rapid response of stator voltage to the stator voltage command.

Referring particularly to the corrective path <NUM>, the stator voltage regulator <NUM> may also receive a stator voltage feedback signal <NUM> (e.g., VS_Fbk_xy) and a stator current feedback signal <NUM> (e.g., IS_Fbk_xy). Thus, as shown at <NUM>, the stator voltage regulator <NUM> is configured to sum the stator voltage feedback signal <NUM> and the stator current feedback signal <NUM> to determine a voltage magnitude feedback signal <NUM> (e.g., VM_Fbk_xy). Moreover, as shown at <NUM>, the stator voltage regulator <NUM> is configured to determine a difference between the voltage magnitude feedback signal <NUM> and the total voltage command <NUM> from the predictive path <NUM>.

Thus, in an embodiment, as shown, the stator voltage regulator <NUM> may also determine a magnetizing current correction signal <NUM> (e.g., IM_Corr_xy) via a proportional-integral regulator <NUM>. Accordingly, as shown at <NUM> in the predictive path <NUM>, the stator voltage regulator <NUM> can then add the magnetizing current feed forward signal <NUM> to the magnetizing current correction signal <NUM> to determine the magnetizing current command <NUM> (e.g., IM_Cmd_xy). In alternative embodiments, the magnetizing current command <NUM> may be a constant value.

Furthermore, as shown at <NUM>, the stator voltage regulator <NUM> may determine the rotor current command(s) <NUM> (e.g., IR_Cmd_xy) as a function of the magnetizing current command <NUM> (e.g., IS_Fbk_xy) and the stator current feedback signal <NUM> (e.g., IS_Fbk_xy) of the DFIG <NUM>. For example, in an embodiment, the stator current feedback signal <NUM> of the DFIG <NUM> may be measured. Thus, in an embodiment, the measured stator current signal <NUM> of the DFIG <NUM> may be fed into a rotor current command of the DFIG <NUM>, as shown at <NUM>, so as to substantially decouple a stator responsive stator voltage from one or more grid characteristics. More specifically, in particular embodiments, as shown, the stator voltage regulator <NUM> may determine the rotor current command(s) <NUM> by adding the magnetizing current command <NUM> to the measured stator current feedback signal <NUM>. In addition, as shown, a limiter <NUM> may place limits to the rotor current command <NUM> as appropriate to respect equipment rating(s).

Claim 1:
A method for damping sub-synchronous control interactions, SSCI, in a grid-forming inverter-based resource connected to an electrical grid, the method comprising:
receiving, (<NUM>) via a controller, a current feedback signal in a synchronous reference frame;
rotating, (<NUM>) via the controller, the current feedback signal to a new reference frame associated with a sub-synchronous frequency range;
determining, (<NUM>) via the controller, a sub-synchronous component of the current feedback signal;
rotating, (<NUM>) via the controller, the sub-synchronous component of the current feedback signal back to the synchronous reference frame;
determining, (<NUM>) via the controller, a voltage command associated with sub-synchronous damping for the inverter-based resource as a function of the sub-synchronous component and a virtual resistance setting; and
controlling, (<NUM>) via the controller, the inverter-based resource, based at least in part, on the voltage command associated with the sub-synchronous damping.